rado, steven - aethro-kinematics - the reinstatement of common sense - an alternate solution to the...

“Miserable mind, you get your information from your senses, and do you try to overthrow them ?

The overthrow will be your downfall." -- Democritus: Atomism. Sixth century B.C.

PROLOGUE

This work attempts to outline a complete descrip-tion of the physical universe founded and executedon the laws, concepts and ideas of The Kinetic Theoryof Gases and on the overriding assumption that allnatural phenomena can be derived from, analyzed,described and humanly understood through the com-paratively simple kinematics of an all-pervadingideal gas.

This idea is not at all new. In different times, dif-ferent forms and levels of natural philosophy and sci-ence, the idea and search for a fundamental sub-stance as the cause for all natural phenomena hasintertwined the whole body of knowledge.

This universal kinematic theory could be present-ed through the description of an unnamed prototypeof an ideal gas without even mentioning the discard-

ed, re-established, ridiculed and re-incarnated, andfinally totally distorted classical concept of Ether.But with due respect to the hundreds of geniuseswho spent their lives on this concept, from Epicurusand Euclid to Newton, Descartes, Bernoulli, Huy-gens, Faraday, Maxwell, Lorentz and hundreds ofothers, this worn out hypothesis will be finally andirrevocably clarified and authenticated in this work.Accordingly, the fundamental, single assumption ofAETHRO-KINEMATICS reinstates the existence ofan all-pervading medium in the form of the ideal gasof Aether.

The spelling of the word, A-e-t-h-e-r, indicates aredefining of this medium by starting over from theera of Descartes' mechanicism, with the firm convic-tion that the human mind, which has evolved by thesensations of the mechanical world, can only compre-hend nature through mechanical pictures, or cannotcomprehend it at all! In this realm of mechanicism,action at a distance is unthinkable and the only con-ceivable transmission of force from one body toanother is by actual bodily contact through collision.

Motion can only be caused by motion, and canonly produce motion in turn.

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Aethro-kinematics

The task this theory takes upon itself is that ofDescartes'; to weed out all action at a distance forcesfrom physics and replace them with the kinematicunderstanding of the construction of each force out ofthe capabilities of an ideal gas. - KINEMATICS isdistinct from kinetics, mechanics and dynamicswhich were founded on Newton's conceptually imper-ceptible mathematical proportionalities amongForce, Mass and Acceleration.

Kinematics is a branch of physics which dealsonly with the abstract motion of geometrical pointswithout any regard to forces or inertia.

For some further clarification, it might be added,that one of the characteristics of geometrical pointsis that in order to distinguish one from the other,they cannot overlap each other in space; that is, theyare impenetrable to one another, just like the atoms ofan ideal gas. It will be attempted to show below thatall Newtonian concepts of earthly and celestialmechanics, Gravity, Inertia, Force and Acceleration,including Kepler's Laws of Planetary Motion can besimulated and explained through the simple laws ofkinematics applied through the general characteris-tics of an isotropic, homogeneous ideal gas.

In AETHRO-KINEMATICS, Aether is taken asan all-pervading ideal gas on the ultra-microscopicorder of magnitude. The constituents of this medi-um, named Aethrons, are conceptually equivalent tothe atoms of an ideal gas; geometrical points, impene-trable to one another. – On the average, Aethrons rep-resent the ultimate units of mass, equal to oneanother and on the average they move with thespeed of light. Therefore, Aethrons are the funda-mental definitive units of mass and motion.

Aether is a system of equal masses, in which theNewtonian concepts of inertia and the law of the con-servation of momentum are naturally reduced to thesimple concept of motion and its eternal nature. Thecollisions among the Aethrons are perfectly elasticand the transfer of motion is instantaneous. Fordescribing the various kinematical phenomena ofnature, Aethrons do not need to exert any action at adistance forces on one another and therefore they donot need to possess any internal structure that needbe the subject of further speculations.

AETHRO-KINEMATICS is founded on the exis-tence of a supermundane, all-pervading ideal gas ofAether. Nevertheless, there are some more or less

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Aethro-kinematics PROLOGUE

important, and allegedly uncontestable argumentsagainst this ideal-gas-model. Some essential ones aredescribed below in order to avoid the impression thatthis study is oblivious to those objections :

The hypothesis of the Transverse nature of light-waves, which claims that ether must be an elasticsolid to sustain restoring forces required to explainthe phenomena of polarization and double refraction.

The Theory of the Expanding Universe, based onHubble's galactic red shift, which is a confusing issueregarding to Universal Rotation.

The Aberration of starlight, which is supposed toprove that the earth is quietly swimming relative tothe motionless ocean of ether.

The Michelson null result, the foundation of thearguments of Special Relativity, which postulates a'way out' of the hopeless choice that either the Earthis not moving, or there is no ether at all.

Some of these arguments will naturally dissolvein the course of the kinematic solution of the majorperplexities of modern physics, some others will bedealt with at a later stage when the new theory hasgained some credibility through the alternatedescription of the fundamental natural phenomena.

PART I.Chapter One renders a condensed and simpli-

fied history of the physical thoughts embodied inClassical Physics, most importantly to emphasize thetheoretical duality in its development, which haslead to some seemingly irreconcilable differencesbetween the results and predictions of Newton'sMechanics and those of the classical Electromag-netic Theory.

Chapter Two reviews one of the most importantrevolutionary breakaways from classical methods bythe Theories of Relativity based on the unmitigatedacceptance of the duality of the classical theories. Forthe sake of impartiality some notes are disclosed onthe existing doubts and critiques of the present stateof Modern Physics by prominent physicists of thelater part of the century.

Chapter Three deals with the other main revo-lutionary concept of Modern Physics; the QuantumTheory and its long term developments, which arealso founded on the primary conviction, that the the-oretical duality in Classical Physics cannot berelieved conceptually, but only by mathematical sup-plements.

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Chapter Four reviews the general opinion andoutlook of modern scientists about the revolution inscientific approach, epistemology and philosophybrought by the twentieth century.

PART II.The Foreword is firstly an appeal against the

neo-prejudicism of the relativistic philosophy againstAether. Secondly it is a declaration of the non-argu-mentative nature of this study which is rather anattempt to render an alternate explanation for theunrelieved perplexities of both classical and modernphysics.

Chapter Five introduces universal rotation anduniversal gravitation as the most general phenome-na of both micro- and macrocosmos and discusses theclassical approach of finding their origin and charac-teristics, culminating in Isaac Newton's laws ofMechanics and his theory of Universal Gravitation.

Chapter Six describes Kepler's three laws ofplanetary motion especially his astronomical formu-la, initially tailored for the solar system, and laterfound to be valid for all rotational phenomena bothin the micro- and macrocosmos. Follows the re-estab-

lishment of the known, but not sufficiently publicizedimportant fact that Kepler's Formula is the realfoundation, from which Newton derived the mathe-matics of Universal Gravitation and not the otherway around.

Chapter Seven introduces the kinematic phe-nomenon of the sink vortex as a natural tendency ofan isotropic homogeneous ideal gas and shows amathematical and mechanical equivalence withthose of the phenomenon of gravitation.

Chapter Eight contains the kinematic descrip-tion of Newton's Mechanics and establishes the con-ceptual content of Newtonian mathematics bydescribing the underlying kinematics of the conceptsof inertia, force and acceleration.

Chapter Nine – having all the above available,– takes a detour back to Kepler's mythical formulaand uncovers its mathematical origin from the sinkvortex of an ideal gas. The kinematics of inertiatogether with the sink vortex is shown to be theplausible concept to explain the elliptical orbits ofthe planets, satellites and all sub-units of all rotatinggravitational systems.

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Chapter Ten finally replaces the hypotheticalideal gas with Aether, as a real, fundamental and allpervading substance with all the characteristics ofan ideal gas. It establishes the already existing andthe potentially acquirable knowledge about its orderof magnitude, and the size, the average speed, andthe density of the Aethrons. Also suggest anapproach to realize the fundamental role of the inter-nal kinetic energy of the Aether.

Chapter Eleven – To establish the naturalcause for the formation of a Sink-vortex, some ideasand designs are offered for describing theKinematical Evolution of Matter. Since the electro-magnetically organized state of Aether, called matter,takes up less space than its random state, the evolu-tion is accompanied by the continuous and progres-sive consumption of the free Aether, which thereforerepresents the initial kinematic cause for the originof the Sink-vortex and Rotational Gravitation. Theresulting natural condensation of the Aether's kinet-ic energy in matter, finally fills the famous formulaE=mc2 with kinematically conceivable content.

The theory suggests an evolutionary arrowpointing in the opposite direction to that of Entropy.

Chapter Twelve re-establishes Faraday's andMaxwell's initial aether concepts of lines, tubes andfields of forces in the ideal gas model of the Aetherand introduces a kinematical understanding of elec-tricity and magnetism without the action at a dis-tance attraction and repulsion between elementarycharges.

Chapter Thirteen describes the kinematiccausality of the Lorentz Transformation and that ofthe Fitzgerald ratio, as the natural resistance againstthe motion of a foreign object within the ideal gas ofthe Aether. It is shown that there is a perfect mathe-matical analogy between the aerodynamic theory ofresistance, expressed by the Mach number, and thekinematical resistance of the Aether, represented bythe Lorentz-Fitzgerald formula. While the air-resis-tance increases as the speed of the foreign bodyapproaches the speed of sound, the Aether-resistanceincreases as the speed of a particle approaches thevelocity of light.

Thus, this hypothesis clears up all the confusingphilosophical speculations about relative motionsbetween light, matter and observer, and the myth ofthe relativistic mass-increase.

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Evidently, by these ideas, the Special Theory ofRelativity and its philosophical postulates are ren-dered to be superfluous.

Chapter Fourteen uncovers the fundamentalhidden ambiguity of the classical mechanical wavetheory, which ultimately led to the theory of theuniquely transverse nature of electromagnetic waves.This condition of the transverse oscillation wasimposed on the undulatory theory of light by theallegedly otherwise unexplainable phenomenon ofpolarization. In turn, the restoring force required forthe transverse oscillation of light made all feasiblemechanical model, including the ideal gas model ofthe Aether, physically impossible. After uncoveringthe misconceptions of the over-simplified mechanicsof the transverse waves on a string that affected allsubsequent wave theories, a new kinematical theoryof wave-motion is presented. Based purely on thekinetic theory of periodical compression pulses, thishypothesis offers a kinematical solution for all opti-cal phenomena, including double refraction andpolarization without the imposed assumption of theuniquely transverse nature of electromagnetic radia-tion. With this, the seemingly impenetrable theoreti-

cal barrier, that has blocked the ideal gas model ofthe Aether for two centuries, has been removed.

Chapter Fifteen represents an alternate kine-matic description of the production of electromagnet-ic radiation. With the acceptance of the ideal gasmodel of the Aether and the kinematic theory of theAetherial compression pulses, this theory describesthe origin of radiation based on the previously estab-lished explanation of the electron current. That is, atheory, purely founded on the circulatory flow of theAether through the terminals of the battery and theresulting cylindrical vortex around and within theconductors. Moreover. this approach creates a plausi-ble picture for the electromagnetic oscillators, whereall forces and potential differences are explained bythe circulations and local pressure fluctuations of theAether and in the gas of free electrons locked into thebulk matter of the conductors.

Chapter Sixteen discusses the two main groupsof classically unresolved quantum problems:

1) Blackbody radiation, Photo-electric Effect andCompton Effect, where radiation manifests particlenature, justifies the concepts of quanta and photons.In general, the origin of the wave-particle duality,

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2) The diffraction phenomenon of electrons andother elementary particles, which demonstrates thewave nature of matter, which initiates the DeBroglie's hypothesis of matter-waves. In general theorigin of the particle-wave duality.

A declaration of insolvability of each of theseproblems formed the justification of the mathemati-cally equivalent, but conceptually divergent Quan-tum Physics, Wave Mechanics, Matrix Mechanics,and Quantum Mechanics.

For every one of these perplexities an alternatekinematic solution is offered in the pursuit of therehabilitation of conceptual theoretical physics in thereach of human comprehension and common sense.

Chapter Seventeen consists of three parts:1. A condensed reiteration of the conceptual

development of quantum theory from 1900-1930with the resulting acceptance of the ambiguousCopenhagen interpretation of quantum mechanics.

2. The philosophical and metaphysical argumen-tation of the last six decades about the obvious suc-cess of the mathematical formalism and the obviousincomprehensibility of that success.

3. The Aethro-kinematical analysis and re-inter-pretation of the meaning and of the limitations ofquantum mechanics based on the fundamental idealgas properties of the all-pervading Aether.

Chapter Eighteen suggests an alternate solu-tion for Hubble's cosmological red-shift, replacing theDoppler effect interpretation with the Aethro-kine-matic explanation of dispersion, which re-establishesthe validity of the long forgotten Tired Light Theory.This solution, founded on observational facts, finallyunites Physics, Cosmology and Cosmogony andrelieves the Rotating Universe of AETHRO-KINE-MATICS from the potential attacks based on theartificial authenticity of the theories of the Expan-ding Universes, and that of the Big Bang.

The following AETHRO-KINEMATIC descriptionof the physical world is clearly conceptual and wellwithin the reach of common-sense logic. The minimaluse of simple mathematics serves one purpose only,to prove the mathematical identity of the alternativekinematic explanation of the given phenomena withthe conceptually unreachable mathematical postu-lates of modern physics.

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PART I.

THE DUALITY OF THEORETICAL PHYSICS

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Aethro-kinematics

CHAPTER ONE

CLASSICAL PHYSICS

In Aristotelian philosophy, 'rest' was generallyregarded as the natural state of matter, meaningthat anything not continually pushed or pulled insome way must sooner or later return to its naturalstate of rest. Galileo Galilei’s greatest contribution tophysics was to be able to break away from this phi-losophy, ruling for two thousand years, and to estab-lish a new concept of motion in empty space; nowcalled the principle of inertia.

The inert property of all material bodies is theresistance against any change in the state of theirmotion. The phenomenon that moving bodies on theEarth tend to slow down and eventually stop comes

from the fact that there are always some externalforces in action, that slow down and stop the motion.In an imaginary experiment, however, where allexternal forces were removed, a body would moveindefinitely with uniform speed on a straight line.

In Isaac Newton’s mechanics, Galileo’s inertiabecame the fundamental concept of the laws ofmotion, from which he derives the concepts of accel-eration and force. In turn, from these concepts withthe aid of Johannes Kepler’s three empirical laws ofplanetary motion, Newton formulates the Law ofUniversal Gravitation and establishes a completeand successful theory of celestial mechanics.

Both Galileo's Principle of Inertia and Newton'sLaws of Motion demand that space must be mecha-nically neutral in which no resistance is offered tothe motion of material bodies. The Classical Principleof Relativity only works in space that has no mecha-nical effect on the Laws of Motion. From this, it fol-lows that Newton's force of gravitation, the force ofmutual attraction which produces the acceleration ofdistant bodies must be an action at a distance with-out any mechanical transmission of that force fromone point of space to the other.

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Aethro-kinematics CHAPTER ONE Classical Physics

Some other philosophers of the seventeenth cen-tury, however, like Rene Descartes and ChristianHuygens, had entirely different ideas about mechan-ics and space. Descartes’ fundamental postulate ofmechanics was that the only thinkable and conceiv-able interactions between material bodies are theactual bodily collisions among them and refused alltheories that assumed action at a distance betweenmaterial bodies. His Universe was filled with an all-pervading Aether, a supermundane mechanicalmedium, in which the heavenly bodies were caughtand carried along. The planets, for example, wherecarried on their orbits by the Aether particles of agiant vortex with the Sun in its center. while thesatellites were carried by the vortices of the planets.

Huygens also filled the Universe with Aether asthe transmitting medium for the propagation of hissound-like mechanical waves of light and attemptedto explain gravity as an effect of the grand scalemotion of this same mechanical medium. Both ofthem and other contemporaries strongly criticizedNewton’s theory of gravitation declaring that theadmittance of an inherent mutual attractionbetween bodies, a force that produces motion at a dis-

tance without mechanical mediation is an unaccept-able regression to occult qualities.In defense of hisearthly and celestial mechanics, Newton showed thatDescartes’ vortex scheme is contradicted by theobservable facts stated in Kepler’s Third Law of plan-etary motion. Against Huygens’ wave theory of light,Newton introduced his corpuscular theory of lightwhich does not require a transmitting medium.Withthese arguments Newton temporarily saved the per-fect void of the universe for the sake of the concept ofinertia, his celestial mechanics, and the theory ofuniversal gravitation, all based on empty space.

“Newton claimed nothing more for his discoverythan that it provided the necessary instrument formathematical prediction, and he pointed out that itdid not touch on the question of the mechanism ofgravity.”

However he also said: “To suppose that one bodymay act upon another at a distance through vacuum,without the mediation of anything else,...is to me sogreat an absurdity, that I believe no man, who has inphilosophical matters a competent faculty for think-ing, can ever fall into.’ ” (Whittaker: Aether andElectricity, 1919-1962).

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Nevertheless, Newton’s laws of mechanics anduniversal gravitation, together with his mathemati-cal innovation of the differential calculus, have beenworking with great success and opened up a newdirection in scientific research; Mathematicalphysics, which is a way of getting results throughmathematical predictions without the necessity of aconceptual understanding of the given phenomena.

Clearly, whether the mechanics of gravity, inertiaand force are understood or not, Newton’s mathemat-ics was most powerful in analyzing and predictingboth earthly and celestial phenomena of motions.

It took almost a century after Newton’s death forthe aether to regain some of its territory in theoreti-cal physics. This happened in the beginning of thenineteenth century, when Thomas Young andAugustin Fresnel with their theories of interferenceand diffraction gave the final blow to Newton’s cor-puscular theory of light. With this victory of the wavetheory, the luminiferous Aether filled up space onceagain to serve as the transmitting medium for thewaves of light all through the Universe.

Parallel to this, Michael Faraday and JamesClerk Maxwell achieved a complete conceptual and

mathematical theory for electric and magnetic phe-nomena, also based on the various dynamic proper-ties of the mechanical aether. Finally, all these theo-ries had been consolidated into one great scientificachievement by the prediction and experimentalproof, that light itself is also an electromagnetic wavehaving the same speed of propagation as the electricand magnetic forces.

James Clerk Maxwell wrote in the EncyclopediaBritannica: “The evidence for the existence of theLuminiferous Aether has accumulated as additionalphenomena of light and other radiations have beendiscovered. And the properties of this medium, asdeduced from the phenomena of light, have beenfound to be precisely those required to explain elec-tromagnetic phenomena. Whatever difficulties wemay have in forming a consistent idea of the consti-tution of the aether, there can be no doubt that theinterplanetary and interstellar spaces are not emptybut are occupied by a material substance or body,which is certainly the largest, and probably the mostuniform body of which we have any knowledge.”

In general, physicists and philosophers of thenineteenth century saw classical physics as the com-

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pletion of the world-picture, culminating in Newton’smechanics, the discovery of the first and second lawsof thermodynamics, the growth of electromagnetismand the development of statistical mechanics basedon the classical conceptions of causality and deter-minism. They were confident that the difficultieswere merely passing pains of growth, the solutions ofthe detail problems were within the scope of themechanical world-picture and with a satisfactorymodel of the aether, the final correlation of the twomajor departments of physics, mechanics and elec-tromagnetism, would be achieved in the near future.

Nevertheless, in the first three decades of thetwentieth century, certain unresolvable problems ledto a profound modification of the whole of physicalthoughts. This historical period also marks the begin-ning of Modern Physics.

As the number of unsuccessful attempts to solvethe detail problems grew, it gradually became evermore evident that a fundamental contradiction andduality existed in classical theoretical physics. Thetwo major physical theories, Newton’s mechanics andthe Electromagnetic Theory, each successfullyexplained a multitude of various physical phenome-

na, were based on two entirely contradictory con-cepts of space.

On the one hand Earthly and Celestial Mecha-nics was founded and explained on the assumptionthat space is perfectly void.

On the other hand, in its development the elec-tromagnetic theory was wholly dependent and per-fectly understandable through the mechanical trans-mission of forces and energy by the hypotheticalaether, pervading all of space.

Emerging from this duality, there were two majorproblems that could no way be fitted into the smooth-ly functioning mechanical Universe.

One of the perplexing puzzles appeared in theunexpected experimental results in the measure-ments of the speed of light.

The other puzzle showed itself at about the sametime in the uncovering of a theoretical and mathe-matical inadequacy of the electromagnetic theory toexplain the facts of the interaction between matterand radiation. To give a proper quantitative descrip-tion for these phenomena, two entirely new theoreti-cal systems had to be developed:

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1. The theories of relativity, dealing with the con-stancy of the speed of light, re-evaluates the conceptsof space and time and finally geometrizes Newton’smysterious force of gravitation.

2. The somewhat simpler system of quantum the-ory revolutionizes the classical conception of continu-ity of energy and radiation and empirically establish-es the fundamental quantum of interchange of ener-gy between radiation and matter.

Both systems are now accepted pillars of modernphysics. Both describe the phenomena in their fieldsquantitatively, in terms of consistent mathematicalrelationships, but offer no conceptual understandingfor their effectiveness. They do not answer theNewtonian ‘how’ anymore than Newton’s lawsanswered the Aristotelian ‘why.’

Hence, in accepting a purely mathematicaldescription of nature, physicists have been forced toabandon both the ordinary world of sense perceptionand the validity of common sense derived from that.

THE SPEED OF LIGHT-WAVESOne of the questions which arose from the duali-

ty of classical physics was about the model of the all-pervading aether.

In order to transmit light-waves with the speed of300.000 km/ sec, the aether was supposed to bedenser than the heaviest metal. However, at thesame time, it must be able to pass heavenly bodieswithout the slightest measurable resistance: Couldtheory correlate these two totally contradictoryrequirements? – All attempts have failed to design amechanical model for such a medium, and towardthe end of the nineteenth century a special experi-ment was designed to answer this dilemma one wayor another. Initially James Clerk Maxwell suggestedthe experiment in the same article, quoted above: “Ifit were possible to determine the velocity of light byobserving the time it takes to travel between one sta-tion and another on the Earth’s surface, we might, bycomparing the observed Velocity of Light in the oppo-site directions, determine the velocity of the aetherwith respect to these terrestrial stations.”

If light-waves are propagated in the motionlesssea of Aether and the Earth is orbiting around theSun submerged in this same medium, then becauseof the Earth’s motion relative to the aether, our mea-surement of the speed of light-waves should be differ-ent in different directions.

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Aethro-kinematics CHAPTER ONE The Speed of Light Waves

No doubt, the measured speed of the sound-waveswill be different when it is taken in different direc-tions on the top of a railroad car which moves rela-tive to the motionless air. In case when the trainmoves toward the source, its speed will be added tothe normal speed of sound, and if it moves away fromthe source, its speed will reduce the measured speedof sound. The differences in these measurements willbe equal to the speed of the train relative to the air.The speed of sound is always the same if it is mea-sured relative to the air.

Analogous to this, the famous Michelson-Morleyexperiment was designed to discover a difference inthe measurements of the speed of light due to theEarth’s motion relative to the motionless aether.

The orbital velocity of the Earth is 30 km/sec,hence if the Earth moves toward the light source, thespeed of light and the speed of Earth should beadded and measure a total of 300.030 km/sec. If thelight propagated in the same direction as the Earthmoves in the motionless Aether, the speed of lightshould measure 299.970 km/sec. The actual experi-ment was more complicated, but the basic idea wasthe same. The measuring methods were more than

sufficient to sense the expected difference, but allattempts through 60 some years failed to show any-thing other than a definite null result.

It follows that at least one of the assumptions ofthe experiment is faulty; either the Earth is not inmotion relative to the aether, or light is somethingdifferent than waves of the aether, or somethingmust be wrong with our method of measurements.

After the shocking null result of the Michelson-Morley experiment, there were a number of inge-nious efforts to escape from this scientific and philo-sophical stalemate. The most successful was theContraction Theory of G.F. Fitzgerald (1893) whichproposed that all objects must suffer a contraction inthe direction of its motion because of the resistanceof the aether. If all solid bodies contract in the direc-tion of their motion, then the measuring of distanceswill also be affected by the motion of the devices andthe null result can be explained. The theory alsoassumed that the extent of this contraction should beproportional to both the speed of motion of the objectand the speed of light. The ratio, β (Beta) betweenthe length of an object at rest, to its length in motionis expressed by the formula:

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____________ β = √ 1 − V 2 /C 2

Where C is the velocity of light and V is the veloc-ity of the body, both measured relative to the motion-less aether. This contraction is extremely small atordinary velocities. With the Earth’s orbital speed of30 km/sec, the contraction would be merely 62.5meter in the earth’s 12.000 kilometer diameter.

The next steps in this theory were made byDutch physicist, H.A. Lorentz, who showed that,based on the electromagnetic structure of matter,the resistance of aether would indeed produce a con-traction in the same ratio as Fitzgerald proposed. Hewent on to show that if the contraction is applied tosubatomic particles in rapid motion, their mass mustincrease in the same proportion as their lengthdecreases.

This prediction was exactly verified before theturn of the century by experiments conducted in thefirst particle accelerators and brought up the idea,that if the motion relative to the aether produces ameasurable increase in the mass of the moving parti-cle, then this might reveal Absolute Motion.

Thus, experiments were designed to find if thismass increase maybe different in different directions,but like all others, they gave null results.

If two particles move in opposite directions in anearthly laboratory, they must show different extentsof mass increase and the same time reveal theEarth’s motion relative to the Aether.

Unfortunately, this method also failed to showthe expected difference in exactly the same way asthe Michelson-Morley experiment. There was nomass-increase difference in the opposite directions,and all efforts to detect and measure the Earth’sabsolute motion relative to the motionless Aether hadto be discarded. With this, at the beginning of thetwentieth century, the duality of theoretical physicswas in its full-blown perplexity and the two majortheories of classical physics stubbornly refused allattempts at consolidation.

Hence, either one or the other, or the approach oftrying to consolidate them must be wrong.

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CHAPTER TWO

RELATIVITY

THE SPECIAL THEORY OF RELATIVITYThe motion of something can only be described

relative to something else. Since Descartes, it is cus-tomary in physics to use rectangular coordinateswith the x,y,z axes as a frame of reference to describethe motions of a particle. Newton’s basic laws ofmechanics can describe the positions, motions andmomenta of bodies in terms of the x,y,z,t coordinates,where t marks the time.

With the same method, the forces acting on thebodies can also be described by the x,y,z components

of the force vector. An inertial frame is a frame of ref-erence which is either at rest or moving with uniformspeed on a straight line, in which a body not underthe influence of forces, and initially at rest, willremain at rest.

From the nature of inertia, follows the classicalprinciple of relativity, which states that no mechani-cal experiments can distinguish between the state ofrest and the state of uniform motion on a straightline. Galileo’s illustration for this principle was thecannon-ball drop from the top of the mast of a ship(the ship itself is an inertial frame of reference). Theball hits the deck right at the bottom of the mastregardless whether the ship is at rest or in uniformmotion on a straight line. On a train, riding smoothlyon a straight track, the balls on a billiard table obeyexactly the same laws of mechanics as in the poolhall on the ground. According to the classical princi-ple of relativity no mechanical experiment can revealthe difference between the two systems.

Sometimes it is necessary to compare the posi-tions, motions or the velocities of a body, observedfrom two different coordinate systems, which aremoving relative to each other. The method of calcu-

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Aethro-kinematics The Special Theory of Relativity

lating the speed of motion from one inertial systemto the other, is simply based on the addition of dis-tances or velocities.

Galileo’s example: If a man walks on the deck of aship with the speed of 1 mph. The ship moves withthe same speed in the same direction relative to theshore. Then the man’s total speed relative to theshore is 2 mph. If the man walks with the samespeed in the opposite direction, then he will be atrest relative to the shore. This method is called theGalilean. or Classical Transformation.

Sound spreads in still air through spherical com-pression waves. The speed of propagation of sound is330 meter/sec. This speed comes from the elasticproperties of the air and therefore it must always bemeasured relative to the motionless air.

(Unless otherwise specified, the following quota-tions are taken from Einstein’s work of The Evo-lution of Physics, written with Leopold Infeld, pub-lished in 1938.)“We are sitting in a closed room so isolated that no

air can enter or escape. Experiment has shown thatthe velocity of sound in air is the same in all direc-tions, if there is no wind and the air is at rest in the

chosen coordinate system. Let us now imagine thatour room moves uniformly through space. A man out-side sees, through the glass walls of the movingroom, everything which is going on inside. The wholeroom is in motion relative to the coordinate system ofthe outside observer.“Here again is the old, much discussed problem ofdetermining the velocity in one coordinate system ifit is already known in the other.

“The observer in the room claims: The velocity ofsound is, for me, the same in all directions.

The outside observer claims: The velocity ofsound spreading in the moving room and determinedin my coordinate system is not the same in all direc-tions. It is greater than the standard velocity ofsound in the direction of the motion of the room andsmaller in the opposite direction.”

THE ALL-PERVADING ETHER“There is now an important question: Could we

repeat what has just been said of sound waves in thecase of a light waves? Does the Galilean transforma-tion apply to mechanical, as well as optical and elec-trical phenomena?

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Aethro-kinematics CHAPTER TWO The All-pervading Ether

"In the case of the sound waves in the room, movinguniformly, relative to the outside observer, the follow-ing intermediate steps are essential for our conclu-sion: (A) The moving room carries the air in whichthe sound wave is propagated. (B) The velocitiesobserved in two coordinate systems moving uniform-ly relative to each other, are connected by the classi-cal transformation.

“The corresponding problem for light must be for-mulated a little differently. Let us assume, that thelight waves move through ether as sound wavesmoved through air. Is the ether carried with theroom as the air was?

"Since we have no mechanical picture of ether it isextremely difficult to answer this question. If theroom is closed, the air is forced to move with it. Thereis obviously no sense in thinking of the ether thisway, since all matter is immersed in it and it pene-trates everywhere. No doors are closed to ether. Ifthat is true, then no analogy with sound wave is pos-sible and the conclusions drawn in the case of sounddo not hold for a light wave.”

Actually it is quite simple to create an analogybetween sound and light in this respect. Imagine a

cage moving through the motionless air with aninside and outside observer, and the air would freelyflow through the cage. If the cage moves 30 m/sec rel-ative to the air, the inside observer will measure thespeed of sound 330 m/sec + 30 m/sec = 360 m/sec inone direction and 330-30=300 m/sec in the otherdirection, while the outside observer, being at restrelative to the air, will measure 330 m/sec in everydirection and also measure 30 m/sec speed for themoving cage. In fact, the Michelson-Morley experi-ment, was based on exactly the same analogy wherethe Earth was moving through the motionless ether,and this was the expected difference in the measure-ment of the speed of light they were looking for. Thiswas the difference that has never been found and thenull result became the starting point of the SpecialTheory of Relativity.

As Einstein summarizes:“All our attempts to make ether real failed. It

revealed neither its mechanical construction, norabsolute motion* (Earth’s motion relative to theether). Nothing remained of all the properties of theether except that for which it was invented, i.e., itsability to transmit electromagnetic waves.

19


"Our attempts to discover the properties of theether led to difficulties and contradictions. After suchbad experiences, this is the moment to forget theether completely and to try never mention its name.Our only way out seems to be to take for granted thefact that space has the physical property of transmit-ting electromagnetic waves, and not to bother toomuch about the meaning of this statement. We maystill use the word Ether, but only to express somephysical properties of space!

“Let us now write down the facts which have beensufficiently confirmed by experiment without bother-ing any more about the 'e - - - r' problem.

“1. The velocity of light in empty space always hasits standard value, independent of the motion of thesource or receiver of light.” (Here it is establishedthat light is a wave phenomenon. In the corpusculartheory the speed of light would be affected by themotion of the source, like the speed of a bulletdepends on the speed of the gun. )“2. In two coordinate systems moving uniformly rel-

ative to each other, all laws of nature are exactlyidentical and there is no way of distinguishingabsolute uniform motion.

"3. Positions and velocities are transformed fromone inertial system to another according to the clas-sical transformation. The contradiction is then evi-dent. We cannot combine (1), (2), and (3).

"It is not at once obvious why the 3 points cannotcombine. In (2) “all laws” of physics is mentioned,that includes the laws of mechanics and electromag-netics, and according to the latter, the speed of propa-gation of electromagnetic waves is always the samerelative to the motionless ether."Therefore, the speed of light should be different for

observers who are moving relative to each other andrelative to the ether. But (2) states that it should bethe same, and if we apply the simple classical trans-formation laws (3), the contradiction between (1) and(2) becomes evident.“The classical transformation seems too obvious and

simple for any attempt to change it."We have already tried to change (1) and (2) and

came to disagreement with experiment. All theoriesconcerning the motion of ‘e - - - r’ required an alter-ation of (1) and (2)."This was no good. Once more we realize the serious

character of our difficulties. A new clue is needed and20


it is supplied by accepting the fundamental assump-tions (1) and (2), and strange enough though itseems, giving up (3), the classical transformation.”

The result is the two fundamental postulate ofThe Special Theory of Relativity:

“1. The velocity of light in vacuum is the same forall coordinate systems moving uniformly, relative toeach other.

“2. All laws of nature are the same in all coordinatesystems moving uniformly relative to each other. It isessential here, as always in science, to rid ourselvesof deep-rooted, often uncritically repeated, preju-dices. Since we have seen that changes in (1) and (2)lead to contradiction with experiment, we must havethe courage to state their validity clearly and attackthe one possibly weak point, the way in which posi-tions and velocities are transformed from one coordi-nate system to another.”

THE LORENTZ TRANSFORMATION“Once more, the example of the moving room with

the outside and inside observers will be used. Againa light signal is emitted from the center of the roomand again we ask the two men what they expect to

observe, assuming only our two principles and forget-ting what was previously said concerning the medi-um through which the light travels.“The inside observer: The light signal traveling from

the center of the room will reach the walls simulta-neously, since all the walls are equally distant fromthe light source and the velocity of light is the samein all directions.

“The outside observer: What I see is a light signaltraveling with standard speed, the same in all direc-tions. One of the walls (of the moving room) is tryingto escape from, and the opposite wall is approachingthe light signal. Therefore, the escaping wall will bemet by the signal a little later than the approachingone.“Comparing the predictions of our two observers we

find the most astonishing result, which flatly contra-dicts the apparently well-founded concepts of classi-cal physics. Two events which are simultaneous inone coordinate system may not be simultaneous inanother coordinate system. Two events, i. e. the twolight beams reaching the two walls, are simultaneousfor the observer on the inside, but not for the observ-er on the outside.

21

Aethro-kinematics CHAPTER TWO The Lorentz Transformation

“In classical physics, we had one clock, one timeflow for all observers in all coordinate systems. Twoevents happening at the same time in one coordinatesystem, happened necessarily simultaneously in allothers. Assumptions (1)and (2), the relativity theoryforces us to give up this view.

“We remember: The velocity of light is the same inall inertial coordinate systems. It is impossible to rec-oncile this fact with the classical transformation. Thecircle must be broken somewhere. Can it not be donejust here? “Can we not assume such changes in the rhythm of

a moving clock and in the length of the moving rodthat the constancy of the velocity of light will followdirectly from this assumptions? Our argument canbe reversed: If the velocity of light is the same in allcoordinate systems, then moving rods must changetheir length, moving clocks must change theirrhythm and the laws governing these changes arerigorously determined.

“We have to substitute new laws and deduce themfrom the fundamental assumptions of the specialtheory of relativity. Let us not bother about themathematical expression for this new transforma-

tion law, and be satisfied that it is different from theclassical. We shall call it briefly the Lorentz transfor-mation.”

As it was mentioned before; When Fitzgerald rec-ommended his contraction hypothesis, Lorentzderived his transformation laws from the electro-magnetic structure of matter and worked out themathematics of a complete theory of transformation.

One of the consequences of his theory, the pre-dicted mass-increase of high speed particles, hadbeen verified by experiments before1905.

“It can be shown that Maxwell’s equations, that is,the laws of the electromagnetic field are invariantwith respect to the Lorentz transformation, just asthe laws of mechanics are invariant with respect tothe Classical transformation. – In all inertial coordi-nate systems the same laws are valid and the transi-tion from one coordinate systems to another is givenby the Lorentz Transformation.”

Here are Asimov’s notes on the subject:“What is the difference between starting with the

assumption of the Lorentz-Fitzgerald contractionand deducing from it the constancy of the velocity oflight, or starting from the assumption of the mea-

22

Aethro-kinematics CHAPTER TWO The Lorentz Transformation

sured constancy of the velocity of light and deducingfrom it the Lorentz-Fitzgerald contraction?!

"If that were all, there would be no significant dif-ference, indeed. However Einstein combined hisassumption concerning the measured constancy ofthe velocity of light with his first assumption, that allmotion is relative.

"This meant that foreshortening or mass-gain wasnot a ‘real’ phenomenon but only a change in mea-surement. While Lorentz who was still clinging on toether, stated that they are real electromagneticeffects.

“Einstein deduced a further conclusion from hisassumption and went beyond the Lorentz-Fitzgeralddealings of length and mass, to take up the questionof time as well. Again the Fitzgerald ratio isinvolved." (Understanding Physics, 1966).

Moving clocks are slowing down in the same ratioas moving rods are contracting. And of course the dif-ferent rhythm of moving clocks is just as unreal asthe relativistic foreshortening or mass-gain.

All in the eye of the measuring observer ! "The Lorentz transformation is the basic set of equa-tions for special relativity. H.A. Lorentz introduced

the transformation one year before relativity wasproposed by Einstein, though this was then unknownto Einstein. Many years later, in 1932, an experimentby Kennedy and Thorndike disproved the Lorentzviewpoint, which was based on the existence of theether. By then, it had already become clear manyyears before that Einstein had pointed out the realsignificance of the transformation. Though Lorentzhad introduced the transformation from considera-tions based on the existence of the ether, Einsteinobtained the same transformation in a derivationrejecting the ether but assuming the constant valueof c for all Galilean observers.” (A.Shadowitz, Specialrelativity, [69])

THE LIGHT-CLOCK AND SIMULTANEITYEinstein continues :

“Let us first answer a simple question. What is aclock?” Any physical phenomenon may be used as aclock, provided it can be exactly repeated as manytimes as desired. – How can we make sure that dis-tant clocks always show exactly the same time? Icould stand near one of the clocks and look at a tele-vised picture of the other. but this would not be a

23

Aethro-kinematics CHAPTER TWO The Light-clock and Simultaneity

good proof. The televised picture is transmittedthrough electromagnetic waves and thus travels withthe speed of light. Through the television I see a pic-ture which was sent some very short time before,whereas on the real clock I see what is taking placeat the present moment.“This difficulty can easily be avoided. I must taketelevision pictures of the two clocks at a point equal-ly distant from each of them and observe them fromthis center point. Then if the signals are sent outsimultaneously, they will all reach me at the sameinstant.“For the definition of simultaneous events, the clocksare synchronized by the help of signals. It is essentialin our arrangement that these signals travel withthe velocity of light, the velocity which plays such afundamental role in the Special Theory of Relativity.”

For some undisclosed reasons, in this work pub-lished in 1966, Einstein stays away from his famous‘train-experiment’ which proves that simultaneity isrelative and here he simply assumes that it is.Nevertheless it can be seen that the prescribedmethod of synchronizing by light signals togetherwith the postulate of the constant velocity of light

directly lead to the same conclusion.“According to the classical principle of relativity, no

mechanical experiment can distinguish between thestate of rest of a system or its uniform motion on astraight line. In this respect, when two observers arein motion relative to one another, each of them canrightfully assume that he is at rest and the other isin motion. Also, as the postulate of the special theoryguaranties, both observers measure the same valuefor the speed of light.

It follows that as they pass by and observe thesynchronized clocks of one another, both of them willarrive to the following conclusion:

“I am at rest at the center of my system, thereforethe signals emitted from my two clocks with thespeed of light reach me simultaneously. The otherobserver, however, is in motion and as the signals areemitted by the clocks, he is moving toward the signalcoming from the front and away from the one emit-ted at the rear.“Since the speed of light has the same value for him

regardless of his motion, the two signals cannotreach him simultaneously.”

24


If both observers record the same event in space,they will expect that the other marks a differenttime for the event than themselves. Consequently,the two observers must mutually arrive to the con-clusion that simultaneity is relative.“What happens when two sets of clocks are moving

uniformly, relative to each other? The classical physi-cist would answer; 'nothing, they still have the samerhythm...'. But this is not the only possible answer.We can equally well imagine a moving clock havingdifferent rhythm from one at rest. Let us now discussthis possibility. What is meant by the statement thata moving clock changes its rhythm?”

To answer this question, the following procedureis recommended by Atkins, Physics, 1976 [480]:

“We shall try to avoid making any assumptionsabout time and space. Instead we shall always con-sider an experimental procedure whereby an observ-er can measure a time interval or a distance andcompare his measurements with another observermoving relative to him. However, in the interpreta-tion of these measurements we shall assume withoutquestions the validity of the modern principle of rela-tivity.

“Imagine two physicists A and B, each in his ownspace ship equipped with a laboratory, travelingthrough empty space with different constant veloci-ties. A convenient clock for our present purpose canbe constructed as follows:

Figure 2-1,“Two parallel mirrors are placed exactly 1 meter

apart. A pulse of light is continually reflected back-ward and forward between these mirrors. Every timethe pulse reaches the lower mirror, it operates alight-sensitive device and a pen makes a mark on thepaper moving past it.

25


M I R R O R

M I R R O R

1 meter

LIGHT PULSE

LIGHT SENSITIVESURFACE

'Ticks ofclock

“Each mark on the paper can be regarded as a ‘tick’of the clock. In term of our present units, we can saythat in between ticks, the light travels 200 cm withthe speed of light, 3X1010 cm/sec. The number ofticks per second is 150,000, 000. The two space physi-cists must, of course, use the same value for thevelocity of light.“It might be argued that, by designing a clock based

upon the properties of light, we have prejudiced thesituation by making our measurements necessarilysensitive to any peculiarities in the behavior of light.

Figure 2-2.

“What will happen when two physicists make obser-vations on one another’s clocks? To make a start onthis problem, we assume, that the two clocks are heldso that the line joining the to mirrors of each clock isperpendicular to the direction of the relative velocity(Figure 2-2).“Now let us consider A’s point of view on the behav-

ior of B’s clock as compared with his own. As far ashis own clock is concerned, he sees that the lightbetween the mirrors travels vertically up and downon the same line. Since B is passing by him, A doesnot see the pulse of light traveling up and downbetween the mirrors along the same path as it doesin his own clock.

“While B’s light pulse is traveling from one mirrorto the other, the mirrors themselves are moving rela-tive to A, therefore he sees B’s light pulse travel in adiagonal path between the two mirrors; from P to Qand from Q to R, along the line of PQR.

“Applying Pythagoras’ theorem to the right angledtriangle PQS, simple mathematics shows that Amust conclude that B’s clock is slower than his ownin the same ratio as that of the Lorentz-Fitzgeraldcontraction.

26


1 meter

MIRROR

LIGHTPULSE

(a)

(b)

MIRROR P

Q

S

MOVING CLOCK

1 meter

LIGHT PULSE

1/2 Vt

1/2

ct

R

“It is not permissible, however, to say that B’s clockis slow compared with A’s. This would introduce abasic difference between the two observers which iscontrary to the principle of relativity. The correctstatement is that, according to A’s observations, B’sclock is slow. The same goes for B’s observationsabout A’s clock. The total observational phenomenonis called the slowing down of clocks, or time dilation.”

“Yet another example. Take a yardstick; this meansthat a stick is a yard in length as long as it is at restin a coordinate system. Now it moves uniformly. Willits length still appear to be one yard? How are we tomeasure this stick in motion? At a given moment twoobservers simultaneously take snapshots, one of theorigin of the stick and the other of the end.

“Since the photographs had to be taken simultane-ously, which is, as we already know, a relative con-cept depending on the coordinate system, it seemsquite possible that the result of this measurementwill be different in different coordinate systems mov-ing relative to each other. – We can well imagine thatnot only does the moving clock change its rhythm,but also that a moving stick changes its length, so

long as the laws of the changes are the same for allinertial coordinate systems. – An assumption shouldnot be regarded as unreasonable simply because itdiffers from that of classical physics. We can wellimagine that a moving clock changes its rhythm, solong as the law of this change is the same for all iner-tial coordinate systems.”

Thus, with the aid of these and other similarthought experiments based on his fundamental pos-tulate of the absolute speed of light, Einstein suc-ceeded to derive the identical formula, that Lorentzderived from the electromagnetic nature of matterand on the assumption of a resistance of the aetheragainst the motion of matter. From here on, theLorentz Transformation became the mathematicalexpression of the postulates of special relativity.

RELATIVISTIC MECHANICS “The velocity of light is the same in all coordinate

systems. It is impossible to reconcile this fact withthe classical transformation. We must accept the con-cept of relative time and relative length in everycoordinate system, because it is the best way out ofour difficulties.

27

Aethro-kinematics CHAPTER TWO Relativistic Mechanics

“In classical physics we had transformation laws forspace but not for time, Time was the same in all co-ordinate systems. However, in the relativity theory, itis different. We have transformation laws differentfrom the classical for space, time, and velocity.”

Thus, in relativity four variable coordinates areneeded to describe an event. Three for the threedimensions of space and one for the dimension oftime. In short, this representation is called a fourdimensional space-time continuum, where continu-um simply means that the units of measurementsboth in space and in time are infinitely divisible andcan be taken as continuous.

“But the relativity theory claims that all laws ofnature must be invariant with respect to the Lorentztransformation and not to the classical transforma-tion. Or in other words classical mechanics cannot bevalid if the velocities approach that of light.“It was simple to change classical mechanics in such

a way that contradicted neither the relativity theorynor the wealth of material obtained by observationand explained by classical mechanics. The oldmechanics is valid for small velocities and forms thelimiting case of the new one.”

As Asimov explains:“To put it briefly, it is possible to deduce from

Einstein’s assumption of the constancy of the mea-sured velocity of light that the velocity of any movingbody will always be measured as less than the veloci-ty of light. This can be achieved by applying theLorentz-Fitzgerald ratio to the classical addition ofvelocities.”

Thus when someone throws a ball ahead from amoving car, classical physics simply adds the twovelocities, the velocity of the car relative to theground and the velocity of the ball relative to the car.The sum of these two equals the velocity of the ballrelative to the ground. The relativistic addition ofvelocities is again based on the Fitzgerald ratio,which governs, how much less than the ball’s velocityrelative to the car has to be added to the car’s veloci-ty in order that the two could never exceed the speedof light. This difference, of course, is immeasurablewhen the velocities involved are very small. In thosecases the relativistic and classical addition of veloci-ties are identical.

The last important consequence of relativisticphysics, is the equivalence of mass and energy.

28


Einstein explains :“A body at rest has a definite mass, called the rest

mass. We know from mechanics that every bodyresists a change in its motion (inertia); the greaterthe mass, the stronger the resistance, and the small-er the mass, the weaker the resistance.

"But in relativity theory we have something more.Not only does a body resist a change more strongly ifthe rest mass is greater, but also if its velocity isgreater.... In classical mechanics the resistance of agiven body was something unchangeable, character-ized by its mass alone. In relativity theory it dependson both rest mass and velocity. The resistancebecomes infinitely great as the velocity approachesthat of light.

“According to the theory of relativity, there is noessential distinction between mass and energy.Energy has mass and mass represents energy.Instead of two conservation laws we have only one,that of mass-energy, E=mc2.

“The old energy-substance is the second victim ofthe Theory of Relativity. The first was the mediumthrough which light waves were propagated.

“The influence of the theory of relativity goes farbeyond the problem from which it arose. It removesthe difficulties and contradictions of the field theory;it formulates more general mechanical laws; itreplaces two conservation laws by one; it changes ourclassical concept of absolute time. Its validity is notrestricted to one domain of physics; it forms a gener-al framework embracing all phenomena of nature.”

From the work of Robert Martin Eisberg aboutthe experimental verification of the theory :“The Theory of Relativity was designed to agree

with the experimental fact that the velocity of lightis observed to be the same in frames of referencewhich are in uniform translation with respect to eachother.

“However, in addition to achieving this, the theorypredicts a number of new phenomena, such as lengthcontraction, time dilation, relativistic increase inmass, and a relation between mass and energy. Thesepredictions of the theory of relativity have been con-firmed in every point and there is now universalagreement on its validity.” (Fundamentals of ModernPhysics, 1964).

29


THE GENERAL THEORY OF RELATIVITY One of the basic assumptions in the special theo-

ry was that it is impossible to measure absolutemotion; that any observer had the privilege of consid-ering himself at rest, or moving uniformly on astraight line. However when considering non-uni-form motion, the possibility arises that this is not so.Galileo and Newton were convinced that acceleratedmotion, and rotation are absolute, which can bedetected, not related to anything else.

The smoothly running train with the billiardtable is a good example. While the train is movinguniformly on a straight line, line, the classical rela-tivity principle is valid, but any change in the stateof motion of the train, either in the speed or in thedirection would show up in the movements of theballs on the table and from the directions and accel-erations of them the change in the train's motion canbe calculated, without the necessity to relate it toanything outside of the train. For the case of rota-tion, there is Newton's famous bucket experiment:when a bucket of water is rotated, the surface of thewater shapes itself into a parabola, forming a con-cave surface in the bucket.

If the bucket is placed into a closed coordinatesystem which is in rotation, the observer, who alsorotates, cannot see the rotation of the water, but fromthe concave surface of it, he can detect that the wholesystem is in rotation. Is this proof of absolute motionin absolute space? Are there special frames of refer-ence that can reveal absolute space and motion?

Atkins addresses these in his book, 'Physics' :"There would appear to be one such frame, that of

the fixed stars. Leon Foucault showed its existencewith his pendulum in 1851. By a weight suspendedso as to be free to swing in any direction, he showedthat the pendulum's direction was not affected by therotation of the earth, but in fact it keeps its plane ofmotion, while the Earth makes a complete rotationunder it once every twenty-four hours. Careful obser-vations has shown that the plane of motion of thependulum was fixed relative to the fixed stars. Dothe fixed stars represent absolute space and the rota-tion of the Earth's rotation, absolute motion?

"In Newton's mechanics the answer was a definite'yes'. These phenomena were contributed to the basicproperty of all matter, called inertia, which however,is merely a name for something unexplained.

30

Aethro-kinematics CHAPTER TWO The General Theory of Relativity

"The questions still remain: What causes inertia?Why does mass resist acceleration? Why does cen-trifugal force appear when a body rotates?

"The Austrian philosopher, Ernst Mach suggestedthat there is a hitherto unrecognized interactionbetween a moving body and all the other matter inthe Universe.

“This interaction depends on the acceleration of thebody relative to the distant matter. Can we adopt theunderlying philosophy of relativity and describe thesituation from the point of view of an observer sittingon the body and moving with it? "If a spaceship begins to accelerate in a forward

direction the crew-men feel an inertial pressureimpelling them to the rear. But they might insist onbeing at rest and interpret their observations accord-ing to Mach, that all the stars and galaxies are mov-ing backward and this acceleration of the other mat-ter of the Universe drags them backward. The sameapplies to rotation of the Earth, by assuming that theearth stands still, while the whole Universe rotatesaround it. The point is, that inertial effects cannot beused to prove absolute motion."

In classical physics, while motionless ether filledall space, there was a hope that a special frame ofreference could be detected; the ether frame thatwould explain absolute motion, and maybe even iner-tia. But this idea, together with the whole hypothesisof e---r was discarded by the conclusions of theSpecial Theory of Relativity.

SOME MORE THOUGHT EXPERIMENTS "Einstein, in his general theory of relativity, worked

out what properties the Universe must possess toprevent the determination of absolute motion in thecase of non-uniform motion." (Asimov: Understand-ing Physics)

Here is Einstein's basic approach to the problemof absolute and relative frames of reference:"Could we build a real relativistic physics valid in

all coordinate systems? A physics in which therewould be no place for absolute, but only relativemotion. ..this is the program for the general theory ofrelativity. But in sketching the way in which it wasaccomplished, we must be even vaguer then we havebeen so far. New difficulties arising in the develop-ment of science, force our theory to become more andmore abstract.

31

Aethro-kinematics CHAPTER TWO Some More Thought Experiments

"To embrace an ever wider region of facts, we mustmake the chain longer and longer. The simpler andmore fundamental our assumptions become, themore intricate is our mathematical tool of reasoning.Although it sounds paradoxical, we could say: mod-ern physics is simpler than the old physics andseems, therefore, more difficult and intricate."

The essential characteristic feature of gravitationwas discovered by Galileo, namely that all bodies fall(i.e.accelerate) equally fast at a given place in a grav-itational field. Since then this phenomena has beentested with very high precision. Einstein in his gen-eral theory of relativity raised this discovery to therank of a basic principle, called The Principle ofEquivalence and claiming that:"In a homogeneous gravitational field all motions

take place in the same way as in the absence of agravitational field in relation to a uniformly acceler-ated coordinate system."

This principle is the foundation of the GeneralTheory of Relativity. The rest of this chapter willconcern itself with presenting and explainingEinstein's theories and will be quoting extensivelyfrom his works.

It should be noted here first, that there are threedifferent concepts of mass, which are distinguishedby the method of measuring them : a) Inertial Mass,which is measured by the acceleration produced by aknown force. b) Passive Gravitational Mass, mea-sured by its weight, (the property of matter that isacted on by a gravitational field), and c) ActiveGravitational Mass which produces a field, measuredby the orbit of a body, i.e. the centripetal accelerationcaused by the field.

From Einstein's notes:"The law of inertia was gained by the contemplation

of an idealized experiment. From that example andlater from many others, we recognized the impor-tance of the idealized experiment, created bythought. Here again idealized experiments will bediscussed. There are four of them to demonstrate thetrain of thoughts of the general theory of relativity toachieve the above described program: physics with-out absolute motion." FREE FALL – ACCELERATED FRAME..."Imagine a great elevator at the top of a skyscraper,

much higher than any real one. Suddenly the cable

32

Aethro-kinematics CHAPTER TWO Free Fall - Accelerated Frame

supporting the elevator breaks, and the elevator fallsfreely towards the ground. An observer takes a hand-kerchief and a watch from his pocket and dropsthem. What happens to these two bodies? For theoutside observer, who is looking through the windowof the elevator, both handkerchief and watch falltoward the ground in exactly the same way, with thesame acceleration."We remember that the acceleration of a falling

body is quite independent of its mass (or density)and that it was this fact which revealed the equalityof gravitational and inertial mass."For the inside observer the handkerchief and the

watch remains were he let them go. He finds that noforces act upon the two bodies, and so they are atrest, just as they were in an inertial coordinate sys-tem. All bodies (in the elevator) behave in the wayexpected by the law of inertia. (The classical princi-ple of relativity* is valid). Our new coordinate systemrigidly connected to the falling elevator differs froman inertial system in only one respect. The inertialcharacter of this coordinate system is limited inspace and time. This local character of the coordinatesystem is quite essential.

"The inertial character of this coordinate system islimited in space and time. This local character of thecoordinate system is quite essential."If our imaginary elevator were to reach from theNorth Pole to the Equator, with the handkerchiefplaced over the north pole and the watch over theequator, then, for the outside observer, the two bodieswould not have the same acceleration...(they wouldboth fall towards the center of the earth on exactlyperpendicular and not parallel paths)...and for theinside observer they would not be at rest relative toeach other, (but accelerating toward each other.) andour whole argument would fail.

"The dimensions of the elevator must be limited sothat the equality of acceleration of all bodies relativeto the outside observer maybe assumed."

It is equally important to save the assumption ofthe inside observer that he is in an inertial systemand not in a gravitational field, which would be obvi-ous if the elevator was large enough to detect thatthe bodies are not at rest but moving towards eachother while gravitating towards the center point ofthe gravitational mass.

33

Aethro-kinematics CHAPTER TWO Free Fall - Accelerated Frame

"With this restriction, however, at least we can indi-cate a coordinate system in which all the physicallaws are valid, even though it is limited in time andspace. If we imagine an other elevator moving uni-formly relative to the one falling freely, then boththese coordinate systems will be locally inertial."All laws are exactly the same in both. The transi-

tion from one to the other is given by the LorentzTransformation. Accelerated motion of the elevatorin the gravitational field exist for the outside observ-er rest and absence of the gravitational field exist forthe inside observer. We see from this example that aconsistent description of physical phenomena in twodifferent coordinate systems is possible, even if theyare not moving uniformly, relative to each other."This example shows that it is possible to change

non-uniform motion produced by a gravitational fieldinto uniform motion merely by looking at it from adifferent coordinate system. The frame of free fall.The conclusion is that gravitational acceleration can-not be accepted as absolute motion. But for suchdescription we must take into account gravitation,building so to speak, the bridge which effects a tran-sition from one coordinate system to the other."

THE PRINCIPLE OF EQUIVALENCE For the next subject Einstein introduces a differ-

ent idealized experiment where the elevator uni-formly accelerates upward."This represents an inertial coordinate system, in

which the law of inertia (classical principle of relativ-ity) is valid. Someone outside has fastened a rope tothe elevator and is pulling, with a constant force. It isimmaterial how this is done. Again we shall listen tothe explanation of the phenomena going on in theelevator and given by both the outside and insideobservers."The outside observer: 'My coordinate system is an

inertial one. The observers inside the elevator are inabsolute motion. They do not find that bodies onwhich no forces are acting, are at rest. If a body is leftfree, it soon collides with the floor of the elevator.‘The observer inside must always be on the floor

because as soon as he jumps, the floor will reach himagain.' "The inside observer: 'I do not see any reason for

believing that my elevator is in absolute motion. Mywatch, my handkerchief and all the bodies are falling

34

Aethro-kinematics CHAPTER TWO The Principle of Equivalence

because the whole elevator is in a gravitational field.' "There are two different conclusions; either nonuni-

form motion and the absence of a gravitational fieldfor the outside observer, or rest and the presence of agravitational field for the inside observer. The out-side observer might also assume that the elevator isin absolute nonuniform motion. But motion which iswiped out by the assumption of an acting gravita-tional field cannot be regarded as absolute motion."

This is the conclusion mentioned before.However, it should be noted, that the same re-

striction has to be applied to this example as to theprevious one. This accelerated motion of the elevatorwill not produce exactly the same motions as the cen-tripetal force of gravity, which, of course, can bedetected if the size of the elevator is not restrictedproperly.

THE BENDING OF LIGHT At this juncture Einstein brings the phenomena

of light into his argument, and goes on with histhought experiment;"Now imagine that a light ray enters into the (accel-

erated) elevator horizontally through a side window

and reaches the opposite wall after a very short time.Again let us see how the path of the light would bepredicted by the two observers. The outside observer:'The light ray enters the window and moves horizon-tally, along a straight line and with constant velocitytowards the opposite wall. But the elevator movesupward (accelerating) and changes its position. Thusthe ray will meet a point not exactly opposite itspoint of entrance, but a little below.'

"The inside observer, who believes in the gravita-tional field acting on all objects in his elevator, wouldsay, 'a beam of light is weightless and therefore willnot be affected by the gravitational field. If sent in ahorizontal direction, it will meet the wall at a pointexactly opposite to that at which it entered.' "If there is nothing illogical in either of the explana-

tions just quoted, then our whole previous argumentis destroyed, and we cannot describe all phenomenain two consistent ways, with and without a gravita-tional field. But there is fortunately, a grave fault inthe reasoning of the inside observer, which saves ourprevious conclusion. A beam of light carries energyand energy has mass (special theory.) But every iner-tial mass is attracted by the gravitational field as

35

Aethro-kinematics CHAPTER TWO The Bending of Light

inertial and gravitational masses are equivalent. Abeam of light, therefore, will bend in a gravitationalfield exactly as a body would, if thrown horizontallywith the velocity equal to that of light."

ROTATION This time imagine that the room of the inside

observer is rotating relative to the inertial coordinatesystem of the outside observer. What will be the con-clusions of the two observers? “The outside observer: 'Your coordinate system is in

rotation and therefore it is in absolute motion. Theclassical principle of relativity is not valid in yourcoordinate system, because all bodies in it have thetendency to move away from the center of the room,eventually all hitting the walls. From this phenome-non you can conclude that your system is in absoluterotation. On the other hand my system is inertialand I am at rest.'

"The inside observer: 'I do not want to hear any-thing about absolute motion. My coordinate systemis just as good as yours. What I noticed was yourrotation relative to my room. No one can forbid me torelate all motions to my room. As for the tendency ofthe bodies to move towards the walls, I hold a

strange gravitational field acting in my room respon-sible for it.' "

Note that this strange gravitational field requi-res an even greater restriction, since it replaces cen-tripetal acceleration, which is directed radiallyinward, with a centrifugal acceleration, which isdirected radially outward. – Einstein still concludes:

"It follows from these examples that there is a well-founded hope of formulating a relativistic physics.But for this we must first tackle the problem of grav-itation.

"We saw from the examples of the elevator the con-sistency of the two description. (With or withoutgravitational field). Non-uniform motion may or maynot be assumed.

“We can eliminate absolute motion from our exam-ples by a gravitational field. But then there is noth-ing absolute in non-uniform motion. (Rememberexample 1, where in free fall an inertial system couldbe reinstated). The gravitational field is able to wipeit out completely....

"...But absolute motion is made possible only by theidea of an inertial system, for which the classicalprinciple of relativity is valid. Therefore ...the ghost

36

Aethro-kinematics CHAPTER TWO Rotation

of absolute motion and (with it the concept of) iner-tial coordinate system can be expelled from physicsand a new relativistic physics built."

THE SPECIAL THEORY AND NEWTON "The general theory of relativity attempts to formu-

late physical laws for all coordinate systems. Thefundamental problem of the theory is gravitation.The theory makes the first serious effort, sinceNewton's time to reformulate the law of gravitation.But is this really necessary?

"In Newton's law of gravitation, the force betweentwo masses depends upon their distance from eachother. The connection between force and distance, aswe know, invariant with respect to the classicaltransformation, which law does not fit the frame ofspecial relativity. On the other hand, distance is notinvariant to the Lorentz Transformation.

“We tried to generalize Newton's gravitational law,but it opposed obstinately all our efforts to simplifyand fit into the scheme of the special theory of rela-tivity. Even if we succeeded in this, a further stepwould still be necessary: the step from the inertialcoordinate systems of special relativity to the arbi-

trary coordinate systems of the general relativitytheory.

“On the other hand, the idealized experimentsabout the falling elevator show clearly that there isno chance of formulating the general relativity theo-ry without solving the problem of gravitation.

"From our argument we see why the solution of thegravitational problem will differ in classical physicsand general relativity.

"1. The gravitational equations of the general rela-tivity can be applied to any coordinate system.Theoretically all coordinate systems (uniform andnon-uniform) are permissible. By ignoring the gravi-tation, we automatically come back to the inertialsystem of the special relativity theory.

"2. Newton's gravitational law connects the motionof a body with the action of another body at the sametime in the far distance. In Maxwell's field-equationswe realized a new pattern for the laws of nature.They connect events, with other events which hap-pen a little later in the immediate vicinity. The sameway, our new gravitational field-equations are de-scribing the changes of the gravitational field.

37

Aethro-kinematics CHAPTER TWO The Special Theory and Newton

"3. Our world is not Euclidean. The geometricalnature of the world is shaped by masses and theirvelocities. The gravitational equations of the generalrelativity theory try to disclose the geometrical prop-erties of our world."

THE GEOMETRY OF SPACE Einstein goes on to explain his statement in 3.

above, with another thought-experiment."What is meant by the statement that our three-

dimensional space has a Euclidean character? Itmeans that all logically proven statements of Eucli-dian geometry can also be confirmed by actual exper-iment. We can construct objects corresponding to theidealized objects of Euclidean geometry. The edge of aruler or a light-ray corresponds to the 'straight-line;'the sum of the angles of a triangle built of rigid rodsis measured 180 degrees; The ratio between theradius and the circumference of all circles are alwaysthe same."But we can imagine that some discrepancies could

be discovered, and if we should not succeed in com-bining Euclidean geometry and physics into a simpleconsistent picture, we should have to give up the idea

of our space being Euclidean and seek more generalassumptions about the geometrical character of ourspace." "Let us consider another experiment with rotation.

This time there are two disks, one above the other ona mutual axis. Both disks have a very small and avery great circle on them and the upper disk is inrapid rotation. The lower disk is at rest."The observer on the upper, rotating disk begins

measuring the radius and the circumference of thesmall circle. The disk near the center has very smallvelocity. This means that the measuring rod will notbe different for the upper and lower observer, and theresults of these two measurements will be the samefor both. Now he places the measuring rod on theradius of the great circle. The rod is moving relativeto the lower observer, however a rod moving perpen-dicular relative to an observer, does not contract."Therefore the measurements of the radii of the

great circles will also be the same for both observers.But it is not so with the fourth measurement! Therod placed on the circumference of the great circle inthe direction of motion now will appear contracted tothe lower observer, compared to his resting one.

38

Aethro-kinematics CHAPTER TWO The Geometry of Space

“If, therefore, we apply the results of the special rel-ativity theory, the ratio of the two radii cannot beequal to the ratio of the two circumferences for theupper observer, as it is for the lower one. This meansthat the observer on the rapidly rotating disk cannotconfirm the validity of the Euclidian geometry in hiscoordinate system. The breakdown of the Euclideangeometry is due to absolute rotation."

Similar result follows the curving of the light-rayin the accelerated elevator. Example 3."If we wish to reject absolute motion and to keep up

the idea of the General Theory of Relativity, thenphysics must be built on the basis of a geometrymore general than the Euclidean."The changes brought about by the general relativi-

ty theory cannot be confined to space alone. Suppose,the inside observer takes two clocks and places oneon the smaller inner circle and the other on the larg-er outer circle. The clock on the inner circle has verysmall velocity, therefore we can conclude that itsrhythm will be the same as that of the lower observ-er's inside clock."But the clock on the large circle has considerable

velocity, changing its rhythm compared to the out-

side clock of the lower observer and therefore com-pared to the clock placed on the small circle."Thus the two rotating clock will have different

rhythms and applying the results of the special rela-tivity theory, we again see that in our rotating coordi-nate system we can make no arrangements similarto those in an inertial coordinate systems. (To holdthe principle of relativity valid.) "In order to make all coordinate systems permissi-

ble, the existence of an appropriate gravitationalfield must be assumed, with its influence upon rigidrods and clocks. The gravitational field, non-Eucli-dean geometry and clocks with different rhythms areall closely connected."

At this point, touching the most complex andleast understood terrain of the General Theory, itseems to be helpful to quote several different descrip-tions of the relativistic connection between Eucli-dean and non-Euclidean geometry, and the phenome-non of gravitation, so the reader can choose the onethat gives the most clarity.

a) Calder, – Einstein's Universe, 1979 , [60] "Albert Einstein abolished the 'force of gravity' and

said that the planets and moons were falling freely39


and travelling as straight as they could go throughcurved space. The massive body distorts time andspace around it and those distortions guide themovements of other objects in its vicinity. The curva-ture (of space) is sufficient to cause an object that istravelling at the right speed to go right around themassive body back to its starting point...."With no expenditure of energy and no force acting

on it, the object follows a curved track. The require-ment for an orbit is that you should be moving side-ways to start with at the appropriate speed. Go tooslowly and you will drop down and collide with thesource of gravity; go to fast and you will fly away intospace. Amazingly, Einstein started from a completelydifferent view of gravity and arrived at the same lawwith which Johannes Kepler and Isaac Newton con-jured about the relationship between the speed ofmotion required for an orbit at a given distance fromthe massive body."

b) Rothman, – The Laws of Physics, 1963, [140] "Gravitation produces exactly the same acceleration

of all bodies. Einstein decided that it must reflect abasic property of the gravitational field. To explainthis he worked out a new method of describing the

gravitational field which did not use the word 'force'at all. Instead he said the space around a massivebody (star or planet) is 'curved' so that the objecttravels along a path dictated by the curvature. Thisidea is the core of Einstein's general theory of relativ-ity."

c) Richtmyer, – Introduction to Modern Physics1955, [74] "The Principle of Equivalence implies that we per-

ceive a gravitational field on earth only because weare using the wrong frame of reference. We ought touse a frame relative to which the earth is acceleratedupward at the rate of 'g' (Gravitational acceleration);"Then we would find that the apparent gravitation-

al field had completely disappeared. From this stand-point gravitational influence consist merely in deter-mining what class of frames it is relative to whichthere is no apparent field, and relative to which freebodies move in straight lines."It does not follow, however, that the gravitational

influence of one piece of matter on another is entirelyillusory. For only a uniform gravitational field can betransformed away in its entirety by the proper frameof reference. Any field can be transformed away in

40


the neighborhood of a single point but, in general thechoice of frame that does this varies from point topoint."There remains the problem as to the law according

to which gravitating matter determines whichframes have the inertial property. Einstein surmisedthat the law could probably be stated most simply interms of a formulation that would permit not only ofany frame of reference in the ordinary sense, but ofany sort of generalized coordinates."With the aid of the mathematician Grossmann, he

found out how to write physical laws in a form that isvalid for any choice of space-time coordinates what-ever. The method involves the use of general tensoranalysis. Einstein found that among all possibleguesses as to the correct law of gravitation this stoodout in contrast to all others as the simplest in mathe-matical form. He adopted this law as a tentativehypothesis then proceeded to look for predictionsbased on it which could be tested by experiment."

d) Taylor, – The New Physics, 1972, [218] "Einstein realized that in order to satisfy the Prin-

ciple of Equivalence, gravity must be described bysome geometrical property of space-time. The ability

to write down the laws of physics in a fashion inde-pendent of the reference frame, in other words, ofcoordinates used to take measurements of positions,times and velocities, is called general covariance."Since a gravitational field could not really be repla-

ced by an accelerating frame of reference, Einsteinrequired that the theory of gravitation satisfy theprinciple of general covariance. Evidently, if distortedframes of reference are to be used in which to formu-late the laws of physics, we are effectively working incurved space-time. Possibly we are living in a curvedspace-time, in a similar fashion to the curvature ex-perienced on the surface of a balloon."In a geometrical theory, particles should move

along paths that are intrinsic to the curvature ofspace-time and independent of the coordinate frameused to make detailed measurements. Such paths incurved space, called geodesics; these paths are theshortest length between any two points. Using thiscondition that particles move along geodesics in thewarped space-time, whose curvature is due to thedistribution of matter. Einstein showed that New-ton's equations of motion were valid, provided thecurvature caused in space-time was not too great."

41


e) Atkins, – Physics, 1974, [533] "A good practical definition of a straight line, which

might have been accepted without question beforethe general theory, is that it is the path followed by abeam of light in vacuum. But as it has been shownthat light is bent in a gravitational field and nolonger travels along a straight line. There is a gen-uine problem."Suppose we could draw a triangle around the sun

out of light-beams connecting the three corners.Because of the bending of light in the sun's gravita-tional field, we can be sure that the sum of the threeangles formed by the curved light-beams will begreater than 180 degrees, and this result is in fla-grant contradiction to the precepts of Euclideangeometry. Physicist must therefore seriously askwhether it is not possible to use another, more gener-al system than Euclidean geometry."This course was the one followed by Einstein. The

general theory assumes that the four dimensions ofspace and time show the same sort of peculiar behav-ior. Space-time is curved! This curvature is producedby the gravitational effect of nearby matter. The cur-vature increases as the mass of the nearby matter is

increased, and also increases if the matter is broughtnearer."

f) Barnett, – The Universe and Dr. Einstein, 1957,[95] "So far as the surface of the Earth is concerned,

Euclid's geometry is not valid. A giant triangle,drawn on the Earth's surface from two points on theequator to the north pole, would not satisfy Euclid'stheorem that the sum of the interior angles of a tri-angle is always equal to two right angles or 180degrees."And if someone should draw a giant circle on the

Earth's surface, he would find that the ratio betweenits diameter and its circumference is less then theclassic value 'Pi'. These departures from Euclid aredue to the curvature of the Earth, and man did notdiscover this fact by getting off the Earth and lookingat it."The curvature of the Earth can be computed very

comfortably by a proper mathematical interpretationof easily observable facts. In the same way, by syn-thesis of astronomical facts and deduction, Einsteinconcluded that the Universe is neither finite norEuclidean.

42


"It has already been shown that Euclidean geome-try does not hold true in a gravitational field. Light-rays does not travel in straight lines when passingthrough a gravitational field. For each concentrationof matter in the Universe, there is a correspondingdistortion of the space-time continuum."Each celestial body, each galaxy creates local irreg-

ularities in space-time, like eddies around islands inthe sea. The greater the concentration of matter, thegreater the resulting curvature of space-time and thetotal effect is an over-all curvature of the whole spacetime continuum. The combined distortions producedby all the incalculable masses of matter in theUniverse cause the continuum to bend back on itselfin a great cosmic curve."

g) Einstein: – 'Notes on the origin of The GeneralTheory of Relativity,' Centenary volume, 1934, [307] "When by the Special Theory of Relativity I had

arrived at the equivalence of all so-called inertialsystems for the formulation of natural laws, (1905)the question whether there was not a further equiva-lence of coordinate systems followed naturally."If only a relative meaning can be attached to the

concept of velocity, ought we nevertheless to perse-

vere in treating acceleration as an absolute concept ?From the purely kinematic point of view there wasno doubt about the relativity of all motions whatever;but, physically speaking, the inertial system seemedto occupy a privileged position."I was of course acquainted with Mach's view,

according to which it appeared conceivable that whatinertial resistance counteracts is not acceleration assuch but acceleration with respect to the masses ofthe other bodies existing in the world. But this pro-vided no workable basis for a new theory."Within the framework of the special theory of rela-

tivity, I tried to frame a field-law for gravitation,since – owing to the abolition of the notion of ab-solute simultaneity, – it was no longer possible tointroduce direct action at a distance....But in the the-ory the acceleration of a falling body was not inde-pendent of its horizontal velocity or the internalenergy of the system (relativistic mass increase).This did not fit with the old experimental fact thatall bodies have the same acceleration in a gravita-tional field... I now abandoned as inadequate theattempt to treat the problem of gravitation, withinthe framework of the Special Theory of Relativity....

43


"The principle of the equality of inertial and gravi-tational mass now could be formulated quite clearlyas follows: In a homogeneous gravitational field, allmotions take place the same way as in the absence ofgravitational field in relation to a uniformly acceler-ated coordinate system. For the moment the oneimportant thing was the discovery that a reasonabletheory of gravitation could only be hoped for from anextension of the principle of relativity."Galileo's formulation of the principle of inertia

amounts to this: a material point, which is acted onby no force, will be represented in four dimensionalspace by a straight line, that is to say, by the shortestline, or more correctly an extremal line. This conceptpresupposes that of the length of a line element, thatis to say, a metric."The timelike extremal lines of this metric furnish

the law of motion of a material point, which is actedon by no force. The coefficients of this metric at thesame time describe the gravitational field with refer-ence to the coordinate system selected. Therefore aphysical significance attaches not to the differentialsof the coordinates but only to the Riemannian metriccorresponding to them.

"A workable basis had now been found for theGeneral Theory of Relativity.

EXPERIMENTAL VERIFICATION Asimov, – Understanding Physics , [121] :"The consequences of the Special Theory of Rela-

tivity – mass increase with motion and the equiva-lence of mass and energy, for instance – were easilydemonstrated. The validity of the General Theorywas much more difficult to prove. Einstein's pictureof gravitation produces results so nearly like those ofNewton's picture, that it is tempting to consider thetwo equivalent and then accept the one that is sim-pler and more 'common sense,' and that of course, isthe Newtonian picture.

"However, there remained some areas – at leastthree important ones – where the consequences ofthe Einsteinian picture were indeed somewhat dif-ferent from those of Newton's:

1) The advance of the perihelion of Mercury.2) The bending of light in a strong gravitational

field.3) The change of the wavelength of light in a

strong gravitational field.44

Aethro-kinematics CHAPTER TWO Experimental Verification

"1) The closest point of an elliptical orbit of a planetis called the 'perihelion'. It was known before relativ-ity that the planet Mercury does not repeat itsmotion exactly as it is orbiting around the Sun, butits perihelion is slowly advancing."Part of this discrepancy was explained in Newton's

picture by the gravitational effects of the planets, butthere was still a part unexplained. It was greater by43.03 seconds than it ought to have been. This meantthat the advance of the Mercury's perihelion is sup-posed to make a complete extra turn in every3,000,000 Earth years."In 1915 Einstein showed that the General Theory

of Relativity altered the view of gravity by justenough to introduce an additional factor that wouldaccount for the unexplained portion of the motion ofthe Mercury's perihelion.

"2) The effect of the predicted bending of light in agravitational field is very small. Even if the lightcoming from a star just grazed the Sun's enormousmass, the shift in the star's position would be only1.75 seconds of arc. Nevertheless in 1919 an elabo-rate expedition was sent to the Island of Principle,West Africa to test the predictions of relativity. The

experiment was conducted twice, six months apart,to have the sun at the two opposite end of the sky,and the results in both cases confirmed the validityof the General Theory.

"3) Finally Einstein predicted that light would loseenergy if it rose against gravity and would gain ener-gy if it 'fell'. The loss of energy would show a verysmall decline in the frequency and an increase in thewavelength."In 1925 the spectrum of a white dwarf, (thousands

of times heavier than ordinary stars) the companionof the star Sirius confirmed the prediction. Later, bya 1958 experiment, called 'The Mossbauer effect, thesame prediction was confirmed in a laboratorydemonstration."

Einstein's own summation :"The problem of testing the General Theory of

Relativity by observation is an intricate one and byno means definitely settled. As we are concernedwith principal ideas, we do not intend to go deeperinto this matter, and only state that the verdict ofexperiment seems, so far, to confirm the conclusionsdrawn from the General Relativity Theory."

45

Aethro-kinematics CHAPTER TWO Experimental Verification

SOME RETROACTIVE NEGATIVES 1. ABSOLUTE MOTION.

Nigel Calder, – Einstein's Universe, 1979, [115] :"Having sung the praises of Einstein's theory, I

must now prepare the philosophically minded readerfor a nasty shock: special relativity is not after all,strictly correct ! What is false is nothing less thanone of Einstein's fundamental assumptions: That itis impossible for an astronaut moving at steadyspeed to tell whether he is moving or the outsideworld is moving. In fact it turns out that he can.Recent discoveries do, though, give us back some-thing not unlike the absolute frame of space thatEinstein thought he had abolished. To cut a longstory short: empty space is filled with energy corre-sponding to a temperature of about three degrees(3K) above absolute cold. The quantity of radiation isimmense. For every atom of hydrogen in the Univer-se there are about a hundred million particles of 3Kradio energy, and their total mass-energy is aboutone thousandth of the mass of the galaxies.... Also itis remarkably uniform in every direction.... For one,traveling at high speed in space, the microwaveenergy will appear, by the Doppler-effect, more

intense in the direction in which he is moving andweaker in his wake.... The 3K radio-energy pervad-ing space provides the means of measuring a steadyspeed in relation to the universe at large." In a spaceship you could adjust your motion until

you see the 3K radio-energy to be exactly the same inall directions; then you are at rest (relative to theUniverse)."

Based on this phenomenon... "experimentersfrom the Lawrence Berkeley Laboratory made a cos-mic speedometer for the Earth. They found that theintensity of the 3K radio energy was strongest in thedirection of the constellation Leo. Considering themotion of the Earth around the Sun, and of the Sunin the Milky Way, it turns out that the Milky Way iscruising through the Universe at 1/500 of the speedof light (400 miles a second) in that direction."

Thus, absolute motion is about rehabilitated!

2. EXTENSION OF THE PRINCIPLE OF RELATIVITY."The basic postulates of special relativity state that,

the velocity of light in vacuo is the same for all coor-dinate systems moving uniformly relative to eachother, and that all laws of nature are the same in all

46

Aethro-kinematics CHAPTER TWO Some Retroactive Negatives

coordinate systems moving uniformly relative toeach other.""To Einstein, who held that space is emptiness and

motion is relative, the apparently unique characterof non-uniform motion was profoundly disturbing. Inthe Special Theory of Relativity he had taken as hispremise the simple assertion that the laws of natureare the same for all systems moving uniformly rela-tive to one another. And as a steadfast believer in theuniversal harmony of nature, he refused to believethat any system in a state of non-uniform motionmust be a uniquely distinguished system in whichthe laws of Nature are different. Hence as a basicpremise of his General Theory of Relativity, he stat-ed: The laws of nature are the same for all systemsregardless of their state of motion."

Einstein, – Die Grundlage der Allgemeinen Rela-tivitats theory, 1916, (Anthology, [493])

"The need for an extension of the postulate of rela-tivity; In classical physics and no less in the SpecialTheory of Relativity, there is an inherent epistemo-logical defect.... We will elucidate it with the follow-ing example: Two fluid bodies of the same size andnature hover freely in space.... Let either mass as

judged by an observer at rest relatively to the othermass, rotate about the line joining the masses. Thisis a verifiable relative motion of the two bodies. Nowlet us imagine that each of the bodies has been sur-veyed by means of measuring instruments at restrelatively to itself, and let one surface prove to be asphere and the other an ellipsoid of revolution. Whatis the reason for this difference in the two bodies?"Newton's mechanics does not really satisfy therequirement of causality, since it makes a fictitiouscause (inertia) responsible for the observable differ-ence.

"The only possible answer must be that the physi-cal system consisting of the two bodies, reveals noimaginable cause to which the differing behavior canbe referred. The cause must therefore lie outside ofthe system and be caused by distant masses whichwe have not included in the system." (Mach's theoryof inertia)

"These distant masses take over of the fictitiouscause. It follows that of all imaginable spaces, in anykind of motion relative to one another, there is nonewhich we may look upon as privileged a priori with-out reviving the above mentioned epistemological

47


objection. The laws of physics must be of such anature that they apply to systems of reference in anykind of motion. Along this road we arrive at anextension of the postulate of relativity."

3. CONSTANCY OF THE VELOCITY OF LIGHT .Remember that the 'laws of physics' include the

laws of the Electromagnetic Theory too, and as it hasbeen established by the Special Theory for uniformmotion, one would expect that somehow the constan-cy of the measured velocity of light should also holdfor systems in nonuniform motion. Acceleratedmotion, from the standpoint of velocity can be takenas a sequence of uniform motions with increasingvelocities.

If in uniform motion the measured constancy ofthe velocity of light is secured by the contraction ofrulers and the slowing down of clocks, then accelera-tion should result in continuous contractions ofrulers and in continuous decreases in the rhythm ofthe clocks, thereby assuring the measured constancy.

However this is not really the case...Einstein, – The Foundation of the General Theory

of Relativity (Anthology, [489]) :

"It will be seen from these reflections that in pur-suing the General Theory of Relativity we shall beled to a theory of gravitation, since we are able to'produce' a gravitational field merely by changing thesystem of coordinates. It will also be obvious that theprinciple of the constancy of the velocity of light invacuo must be modified, since we easily recognizethat the path of a ray of light with respect to K'(accelerated system) must in general be curvilinear,if with respect to K (uniformly moving system) lightis propagated in a straight line with a definite con-stant velocity."

Discussing the subject within the frame work ofgeneral relativity, Calder writes:

"An atomic clock on the ceiling of an acceleratingspaceship will be seen to run slightly faster than aclock mounted on the floor. Look up and the accelera-tion carries you towards the clock, so that you see theclock registering its next second sooner than youwould if the spaceship were travelling at a steadyspeed; look down, and the indications of the otherclock are delayed, so it is running slow.... If you areaccelerating towards a source of light, its speedseems greater. If you are accelerating away from it,

48


its speed seems diminished.... A cardinal rule of rela-tivity, that light always seem to travel at the samespeed, applies only to systems that are moving at asteady rate, or else falling freely under gravity."

4. THE PRINCIPLE OF EQUIVALENCE .The extension of the basic postulate of relativity

seems to fail even more seriously. The very funda-mental idea of the General Theory, 'the sword that inEinstein's hand slayed the dragon of absolute mo-tion', that a gravitational field can be replaced by asimilarly accelerated system, has been proven to beunacceptable.

Calder, – Einstein's Universe, [78] :"The equivalence of acceleration and the experi-

ence of gravity is the cosmic principle of Einsteinianphysics. There are two versions of it. The 'weak' prin-ciple says, as Galileo did, that all objects fall at thesame rate under gravity. The strong equivalenceprinciple declares, as Einstein did, that the laws ofphysics are the same everywhere and at all timesthroughout the observable universe, despite anyeffects of motion or gravity. The latter is what Ein-stein craved for during his years of mental struggle."

Herman Bondi, – The relativity theory andgravitation, 1979. (Centenary, [114])

"Gravitation as a universal force (Newton) mustbe measurable everywhere, and our position on thesurface of a massive body, the Earth, is highly atypi-cal of the Universe, most of which is empty. How doesone observe gravitation in empty space? Sinceeverything falls the same way, nothing measurableseems to be left. Are we thus talking about a pseudo-force, one which can be observed if one has a solidground under one's feet but not in space?"A closer analysis shows this pessimism to be mis-

placed."Though all bodies fall equally fast, this common

acceleration varies with position. Consider a space-craft in orbit near the Earth and remember that it isof finite size, small though it is compared to the scaleof its orbit."The acceleration of free fall at the point of the

spacecraft closest to the Earth is higher than at itsmiddle, which is, in turn higher than at the point ofthe spacecraft furthest from the Earth. Specks ofdust near the part of the spacecraft furthest from theearth will tend to drift further that way, for they will

49


fall with the local acceleration which will be margin-ally less than the 'compromise' acceleration adoptedby the spacecraft as a whole. Similarly, dust near thepart of the spacecraft closest to the Earth will fall alittle faster than the spacecraft."Thus the astronaut will observe dust settling in

the two portions of the (freely falling) spacecraft, fur-thest from and nearest to the Earth. From this facthe will be able to infer that he is in a gravitationalfield."

"Indeed, this effect has been used to engineer a'gravity gradient' stabilization for certain space-crafts. Hence we arrive at the following conclusion:since in physics we always define quantities by howwe measure them, a gravitational field is a relativeacceleration of neighboring particles. The concept of'uniform gravitational field,' i.e., one where the accel-eration is the same throughout the field, according tothis analysis would be described as a zero gravita-tional field.

"It is curious that Einstein, who in other areas ofphysics (notably Special Relativity) criticized any-thing that transcended actual experience, should inthe case of gravitation have insisted instead on the

physical equivalence of accelerated frames. Suchequivalence does not in fact hold! But Einstein pro-ceeded from the Principle of Equivalence to his gen-eral relativistic theory of coordinate transformation,and ignored the fact that gravitation cannot be com-pletely transformed away by a general accelerationof an extended region, however small.

"The magnitude of Einstein's achievement in creat-ing a theory of gravitation is of course not lessenedby such consideration.

"Hence the extension of the principle of relativityfailed, but in the procedure physics became richerwith the geometrization of gravity."

50


CHAPTER THREE

FROM QUANTUM THEORY TO PROBABILITY WAVES

In spite of the spectacular revolution of Einstein'stheories of relativity, which equally effected physics,epistemology and philosophy, the real water-shed in thehistory of science proved to be Max Planck's seeminglymore modest quantum theory of action, published inthe year of 1901.

This hypothesis turned out to be the starting pointfor a comprehensive theory which, far more than rela-tivity, overthrew a centuries old world-picture. All phys-ical theory that did not take quanta into account, but

assumed energy to be continuous, is now lumpedtogether as classical physics, where as physical theoriesthat do take quanta into effect is now modern physicswith the convenient dividing point of the year 1900.

In the course of an attempt to resolve some discrep-ancies between the observed energy spectrum of ther-mal radiation and the predictions of the classical theo-ry, Planck was led to the idea that a system executingsimple harmonic oscillations can only have energieswhich are integral multiples of a certain finite amountof energy.

A closely related idea was later applied by Einsteinin explaining the photoelectric effect, and by Bohr in atheory of the complex features of the atomic spectra.Subsequent development in the same direction by deBroglie, Schrodinger and Heisenberg constitutes whatis known in modern physics as the quantum theory.

THE SPECTRUM In 1666 Isaac Newton made the first crucial

advance in the study of light and colors. He allowed abeam of white sunlight, coming through a small holeinto a dark room, to fall on a prism. The beam of

51

Aethro-kinematics The Spectrum

refracted light then struck a white surface, producingan extended band of colors in the same order as they doin the rainbow; red, orange, yellow, green, blue, violet.This phenomenon was named dispersion and theimage of the range of colors, spectrum.

Since the spectrum was produced from white sun-light going through a colorless glass, Newton concluded,that white light must be composed of a vast assemblageof different varieties of colors, each with its own charac-teristic way of being refracted.

Newton's spectrum seemed to be continuous, asthough all the infinite possible refractivities were pre-sent in sunlight. Before the turn of the nineteenth cen-tury, however, William Hyde Wollaston discovered a fewdark lines in the sun's spectra. Shortly after Joseph vonFraunhofer, working with finer prisms, noticed hun-dreds of such dark lines and carefully mapped the rela-tive positions of the most prominent ones. These spec-tral lines, called Fraunhofer-lines , are always found atthe same place of the color spectrum.

One generation later Gustav Robert Kirchhoffstarted to use prisms and the spectra for analyzingchemical elements, founding the science of spectroscopy.It was already known that the vapors of different ele-

ments, heated to incandescence, produce light of differ-ent individual colors. Kirchhoff passed such lightthrough a spectroscope and found that each elementproduced only a few refractive varieties which spreadwidely apart.

The exact position of each line was measuredagainst a finely calibrated background and it was foundthat each element always and uniquely produces linesof the same color at the same specific place of the spec-trum. Therefore, this so called emission spectrum cameinto use as the chemical finger-print for each element.

By allowing white light to go through cooled sodiumvapor, Kirchhoff also found that the gas absorbs pre-cisely the same varieties of the white light that it emitswhen heated. This method produces dark absorptionlines at the same places where the emission lines fallwhen the sodium vapor is heated. The resulting imageis called an absorption spectrum, which gives us awealth of information about the elements contained inthe sun and the stars.

Thus, in general, Kirchhoff discovered that the sub-stance which absorbs certain frequencies of light, alsoemits the same frequencies when it is heated. It followsthen, that if a body appears to be perfectly black, its

52

Aethro-kinematics CHAPTER THREE The Spectrum

substance is capable of absorbing all white light and ifsuch a black body is heated to incandescence, its emis-sion should be as complete as its absorption. As a resultof Kirchhoff's work at the end of the nineteenth centu-ry, physicists became interested in the quantitativeaspects of radiation and in the manner in which suchradiation varied with temperature.

Usually the electromagnetic radiation of a heatedbody is characteristic of the chemical composition of itshot surface. However, it has been found possible to sim-ulate an idealized heated solid, by constructing a cavityin a metal block with a small hole, a so-called cavityradiator, equivalent to a black body. Consequently, thisdevice emits radiation which depends only on the tem-perature of the heated solid, independent of its chemi-cal composition.

The distribution of the radiant energy at variouswavelengths is also the same for all cavity radiators. Byreasoning based on thermodynamics, if the tempera-ture of such cavity radiator is constant, the quantity ofthe radiant energy absorbed and emitted by the inter-nal walls per second is equal. Such isothermal enclosureis in the state of thermal equilibrium.

Figure 3-1 illustrates the experimental facts plot-ted by wavelengths (l) against the quantity of radiat-ed energy at different absolute temperatures. Thetotal energy radiated at a given temperature is rep-resented by the area under the curve.

In 1879 Joseph Stefan, Austrian physicist estab-lished his empirical law, stating that the total energy

53


8

6

4

2

0 2 3 4 5

10

61(in units of 10 cm)λ -5

( )

(ar

bitr

ary

units

)T

λI

2000T = Ko

T = Ko1750

T = Ko1500

T = Ko1250

T = Ko1000

Figure 3-1.

radiated by a black body increases as the fourth powerof the absolute temperature.

As it is shown by the energy curves, at any giventemperature, a greater amount of energy is radiatedin the shorter than in the longer wavelengths. It canalso be stated, that more energy is radiated in higherthan lower frequencies. At each temperature, howev-er, there is a certain frequency at which the maxi-mum energy is radiated, called the peak frequency.Above that the radiated energy per frequency gradu-ally decreases.

In the next decade German physicist, WilhelmWien, experimentally determined the distribution ofradiation among various wavelengths at differenttemperatures. He also found empirically, that thewavelength of the maximum energy radiation multi-plied by the absolute temperature is a constant. Thestatement of this relationship between temperatureand maximum energy wavelength, is called, Wien'sdisplacement law. – At this stage four branches ofClassical Physics were involved in the analysis of theproblem of black body radiation; The Theory ofElectromagnetic Waves, Thermodynamics, The KineticTheory of Gases, and Statistical Mechanics.

Based on the atomic theory of matter, and on theanalogy of sound waves, water waves, and the waves ona string classical Electro- magnetic theory suggested,that radiation is produced by the simple harmonic oscil-lation of the atoms, the amplitude of which is propor-tional to the temperature of the heated body.

The oscillating atoms produce oscillating electricand magnetic fields which propagate in the space of thecavity, and are eventually absorbed and re-emitted bythe walls. Based on Wien's empirical law of displace-ment, the task of theoretical physics was to derive amathematical formula from the above theories, whichwould result in the same distribution curves as thoseplotted from the experimental facts.

Although the displacement law merely representeda simple inverse proportionality between temperatureand the maximum energy wavelength, there was nosensible conceptual explanation for such distribution ofradiation and all attempts of deriving the right formulafrom classical physics failed.

One of the two most important attempts to producethe proper mathematics was Wien's proposal derivedfrom special assumption concerning the process ofemission and absorption of radiation.

54


The other attempt was proposed by Raleigh andJeans founded upon a general consideration of theprobabilities of the energy distribution, and on the clas-sical mechanical law of the equipartition theorem.

Wien's formula contained two unexplained con-stants to be found experimentally, but with them itcould be made to fit the experimental curve at thewavelengths shorter than the maximum energy wave-length. However, his curve was considerably off atlonger wavelengths.

The Raleigh-Jeans probability formula was freefrom all unknown constants, however, at wavelengthsnear or beyond the maximum energy radiation it gaveenormously wrong values. In fact, their solutionassigned no maximum at all. This prediction, of course,was not supported by the experimental facts andreceived the somewhat sarcastic name: The UltravioletCatastrophe. – By the end of the century, the intensivetheoretical and mathematical research on the blackbody radiation produced three different energy curvesillustrated by Figure 3-2:

1) A plotting of the experimental facts. 2) The curvegiven by Raleigh's equation, a fair approximation inlower frequencies but totally wrong in the higher ones.

3) The theoretical curve plotted by Wien's Law, whichwas close to the experimental curve at higher frequen-cies, but not justified in the lower ones.

Thus, based on the classical theories, there was nosensible conceptual and mathematical explanation ofwhy the amount of radiating energy should be distrib-uted among the frequencies in the manner observedthrough the experiments.

55


8

6

4

2

0 2 3 4 5

10

61

Raleigh's prediction

Experimental curve

Wien's law

( )

(ar

bitr

ary

units

)T

λI

(in units of 10 cm)λ -5 Figure 3-2.

PLANCK'S CONSTANT At this stalemate, in 1899 Max Planck, a German

scientist, began to consider the problem. From a purelymathematical point of view he found that by a verysimple addition of a '–1' term Wien's equation can pro-duce a curve that perfectly matches the experimentalfacts. This formula, although a very important mathe-matical achievement, was still totally empirical andgave no clue to a conceptual understanding of the phe-nomenon.

Planck sought such an understanding in terms of amodel of the atomic processes taking place at the cavitywalls. He assumed that each atomic oscillator emitselectromagnetic energy at a characteristic frequencyinto the cavity and absorbs the same from it. Hence, itshould be possible to deduce the characteristics of thecavity radiation from those of the oscillators with whichit is in equilibrium.

He asked the following question: What if all fre-quencies were not radiated with equal probability, asRaleigh assumed, but besides the plain probability,there was some other factor that decreases the chancesof radiation in the higher frequencies? With such a fac-tor there would be two opposite tendencies to govern

the distribution of the energy of the black-body radia-tion. Raleigh's random probability would be domi-nant at low frequencies, but in the distribution of theenergy at higher frequencies this new factor wouldtake over and reduce Raleigh's extreme probabili-ties to match with Wien's predictions.

But is there any conceptual explanation to accountfor such artificial mathematical tendency?

In an article in 1913, (quoted by Sambursky's'Physical Thoughts, Anthology', [482]), Max Planckattempts to give a conceptual explanation for his quan-tum theory of radiation as follows:"Let us imagine a sheet of water in which strong

winds have produced high waves. Even after the totalcessation of the wind, the waves will be maintained forsome times and will pass from one shore to the other.But there will be a certain characteristic change inthem.

“During their impact on the shores, the energy ofmotion of the longer and coarser waves is converted toan ever greater extent into the energy of motion ofshorter and slighter waves; and this process will contin-ue until at last the waves have become so small andtheir motion so slight that they are quite lost to view.

56

Aethro-kinematics CHAPTER THREE Planck’s Constant

"That is the familiar transmutation of visible motioninto heat, of molar into molecular, of ordered into disor-dered motion (entropy); for in ordered motion manyneighboring molecules have a common velocity, whilstin disordered motion every molecule has its separateand separately directed velocity."But now let us take another and quite analogous

process, not dealing with water waves but with wavesof light and heat.“Let us assume that rays emitted by a brightly glow-

ing body are collected by suitable mirrors into a com-pletely enclosed hollow space. Here also there will be agradual transmutation of the energy of radiation fromlonger waves to shorter waves, from ordered radiationto disordered radiation. The longer and coarser wavescorrespond to the infra-red rays, and the shorter andslighter waves correspond to the ultra-violet rays of thespectrum."Hence according to the Classical Theory we must

expect the total energy of radiation to concentrate itselfupon the ultra-violet portion of the spectrum; or inother words, we must expect the infra-red and the visi-ble rays to disappear gradually and convert themselvesultimately into invisible ultra-violet or chemical rays.

"But of such a phenomenon no trace can be discoveredin Nature. The conversion sooner or later attains a per-fectly definite and assignable limit, and after that, theradiation-conditions remain stable in every respect. Inthe case of the water waves, the disintegration of theenergy of motion is limited by the fact that the atomshold the energy together. In a way, each atom repre-senting a certain finite material quantum which canonly move as a whole."In the same sort of way certain processes must be at

work in the case of light and heat rays, although theyare quite an immaterial nature, which shall holdtogether the energy of radiation in definite finite quan-ta, and shall unite it the more strongly the shorter thewaves and the quicker therefore the frequency of theoscillations."

Thus, Planck made the bold assumption that ener-gy does not flow continuously, but it is given off in dis-crete quantities and that a radiating body could onlygive off one quantum of energy or two or any integernumber, but never a half or a quarter or any part of awhole unit. Furthermore, Planck went on to suppose,that the amount of energy of such quanta is propor-tional to the frequency, of light in which it is radiated.

57

Aethro-kinematics CHAPTER THREE Planck’s Constant

If the energy content, E of one quantum of radia-tion is proportional to the frequency of that radiation,then E = h×ν , where ν is the frequency and h is a con-stant of proportionality, commonly called Planck's con-stant. Solving this equation for h, we find, that h = E/ν.Since both the energy and the frequency are measur-able quantities, the value of h can be found empirically.In order to correlate Raleigh's probability equation withWien's empirical results, Planck derived his own equa-tion, containing h, as the value of a counter tendency ofRaleigh's probability. If h is the right value, then h×νshould describe the distribution of black body radiation,as actually observed over the entire range of frequen-cies.

It has been found that the best working value of h = 6.6256×10-27 or h = 0.0000000000000000000000000066256 erg/ sec.

Notice, how fine the scale is. For the visible, orangelight of wave-length 6000 Å with a frequency5×1010/sec. The energy content in a quantum is, 5×1010

x 6.625×10-27= 3.33×10-10ergs.In order to acquire a kinetic energy of this magni-

tude, a grain of sand would have to fall a height of only

3×10-10 cm, which is much less than the diameter of asingle atom.

Hence the quantum theory offers the followingexplanation: Violet light, with twice the frequency ofred light, would have to radiate in quanta twice the sizeof those of red light. In each frequency only a full quan-tum of energy can be radiated, therefore the probabilityof the accumulation of a full quanta in violet light isonly half of the probability to accumulate a quanta inred light.

The higher the frequency of light, the smaller is theprobability that enough energy would accumulate toform a complete quantum without bleeding off to forma quanta of lesser energy content in the lower frequen-cies. It also follows, that with increasing temperature,the probability of forming larger quanta would increaseand the radiation peak would advance into higher fre-quencies.

REVIVAL OF THE CORPUSCULAR THEORY – THE PHOTON.

Planck's hypothesis was introduced mainly in orderto explain the distribution of black-body radiation andscience was not ready at that time to accept such radi-

58

Aethro-kinematics CHAPTER THREE Revival of the Corpuscular Theory - the Photon

cal change of view, just for that one victory. Even Planckhimself tried to draw his quantum theory as close aspossible to classical notions by supposing that only theenergy of the oscillators were quantized, but the radia-tion was still propagated in the continuous manner ofelectromagnetic waves.

Meanwhile in a different department of physics, inthe last two decades of the century, physicist werebeginning to understand that electricity was associatedwith the movements of subatomic particles called elec-trons, and developed methods to detect them and mea-sure their velocities. During the experimentation it hasbeen found that certain frequencies of light produce theejection of these electrons from metallic surfaces.

This new phenomenon, named, photoelectric effect,introduced another prime puzzle into the subject of theinteraction between radiation and matter. Germanphysicist, Philip Leonard, in 1902 found that for eachmetal surface, that showed photoelectric effect, there isa threshold frequency, only above which, the ejection ofelectrons can happen.

Higher frequency light falling on the metal, liber-ates electrons with proportionally greater velocities.Leonard also found that increasing the intensity of

light only increases the number of electrons ejected,and does not effect their individual velocities. Somehow,therefore, the kinetic energy of the photo-electrons isuniquely connected to the frequency, but independentfrom the intensity of the radiation which liberatesthem from the metal. – There was no classical hypothe-sis to account for this phenomenon until in 1905Einstein proposed a bold innovation that made use ofPlanck's quantum theory of radiation.

"There is an essential formal difference betweenthe theoretical pictures physicists have drawn ofgases and other ponderable bodies and Maxwell'stheory of electromagnetic processes in so-calledempty space. Whereas we assume the state of a bodyto be completely determined by the positions andvelocities of an, albeit very large, still finite numberof atoms and electrons, we use for the determinationof the electromagnetic state in space continuous spe-cial functions, so that a finite number of variablescannot be considered to be sufficient to fix complete-ly the electromagnetic state in space."The energy of a ponderable body cannot be split

into arbitrarily many small parts, while the energyof a light ray, emitted by a point source of light is,

59


according to Maxwell's theory of light, distributedcontinuously over an ever increasing volume."The wave theory of light which operates with con-

tinuous functions has been excellently justified forthe representation of purely optical phenomena andit is unlikely ever to be replaced by another theory.One should, however, bear in mind that optical ob-servations refer to time averages and not to instan-taneous values and notwithstanding the completeexperimental verification of the theory of diffraction,reflection, refraction, dispersion and so on, it is quiteconceivable that the theory of light will lead to con-tradictions with experience, if it is applied to thephenomena of the creation and conversion of light."In fact, it seems to me that the observations on

black-body radiation, photo-luminescence, the pro-duction of cathode rays by ultraviolet light and otherphenomena involving the emission or conversion oflight can be better understood on the assumptionthat the energy of light is distributed discontinuous-ly in space."According to the assumption considered here,

when a light ray starting from a point is propagated,the energy is not continuously distributed over an

increasing volume, but it consists a finite number ofenergy quanta, localized in space, which move with-out being divided and which can be absorbed oremitted only as a whole." (Einstein; About the cre-ation and conversion of light; Sambursky, AnAnthology of Physical Thought, [499].)

Here is Einstein's popular explanation from hiswork (Einstein, Infeld,The Evolution of Physics, [260]):"Homogeneous light, such as violet light, which is, as

we know, light of a definite wave-length and frequency,extracts electrons from a metal surface. The electronsare torn from the metal and a shower of them speedsalong with a certain velocity. From the point of view ofthe energy principle we can say: the energy of light ispartially transformed into the kinetic energy ofexpelled electrons. The observed electrons all have thesame speed, the same energy, which does not changewhen the intensity of the light is increased."Obviously, we cannot deduce from the wave theory

the independence of the energy of electrons from theintensity of light. We shall, therefore, try another theo-ry. We remember that Newton's corpuscular theory oflight, explaining many of the observed phenomena oflight, failed to account for the bending of light (refrac-

60


tion, diffraction and interference), which we are nowdeliberately disregarding."In Newton's time the concept of energy did not exist.

Later, when the concept was created and it was recog-nized that light carries energy, no one thought of apply-ing these concepts to the corpuscular theory. Newton'stheory was dead and, until our own century, its revivalwas not taken seriously."To keep the principal idea of Newton's theory, we

must assume that homogeneous light is composed ofenergy-grains and replace the old light corpuscles bylight quanta, which we shall call photons, small por-tions of energy, travelling through empty space with thevelocity of light. The revival of Newton's theory in thisform leads to the quantum theory of light."It is at once evident that this quantum theory of light

explains the photo-electric effect.A shower of photons isfalling on a metal plate. The action between radiationand matter consists here of very many single processesin which a photon impinges on the atom and tears outan electron. These single processes are all alike and theextracted electron will have the same energy in everycase. We also understand that increasing the intensityof light means, in our new language, increasing the

number of falling photons. In this case, a greater num-ber of electrons would be thrown out of the metal plate,but the energy of any single one would not change."What will happen if a beam of homogeneous light of

different color, say, red instead of violet, falls on themetal surface? As it turns out to be, the photons belong-ing to the color red have half the energy of thosebelonging to the color violet. Or, more rigorously: theenergy of light quantum belonging to a homogeneouscolor decreases proportionally as the wavelengthincreases.""We can detect individual photons and measure their

energies only when they knock electrons out of theatoms. In order to effect the state of motion of the elec-trons, the photons must possess momentum, whichshould be, like that of any other particle, its mass multi-plied by its velocity."Thus, in our new picture, light is a shower of photons,

and the photon is an elementary quantum of light ener-gy. If, however, the wave theory is discarded, the con-cept of wave-length (and frequency) disappears. Whatnew concept takes its place? The energy of light-quan-ta! Homogeneous light contains photons of a definiteenergy. The energy of the photon for the red end of the

61


spectrum is half that of the violet end. But what is lightreally? Is it a wave or a shower of photons? "There seems no likelihood of forming a consistent

description of the phenomena of light by a choice of onlyone of the two possible languages. We have two contra-dictory pictures of reality; separately neither of themfully explains the phenomena of light, but together theydo! How can we understand these two utterly differentaspects of light?"

In 1922 a more clear-cut example of the particle-like properties of light was advanced by Arthur HollyCompton, American physicist. He demonstrated thathigh-frequency X-rays not only exerted pressure on theelectrons but themselves were deflected in the collisionswhile the electrons recoiled in such direction as toaccount for the deflection of the radiation.

Based on Einstein's mathematical derivation of themomentum of the photon and applying the law of theconservation of momentum, the energy transfer of theCompton effect between radiation and matter wasfound to be in quantitative agreement with the resultsof a mechanical collision between two billiard balls. Thex-ray photon clearly showed the behavior of a momen-tum carrying particle.

This, however, was not yet the full scope of the prob-lem with the duality of radiation. Before any solutionwould emerge on the horizon for the general dilemma,the use of Planck's Theory spread over to the otherdepartments of physics and brought up more questionsthan answers.

THE QUANTIZED ATOM With the acceptance of the quantum theory, matter

was supposed to emit and absorb radiation in a discon-tinuous manner. This supposition brought up the ques-tion of whether this nature of energy exchange wouldserve as an explanation for the behavior of the elec-trons within the atom? At the beginning of the centurythe most acceptable model of the atom was based onErnest Rutherford's experimental conclusion, that vir-tually all the mass of the atom is concentrated in a tinynucleus, the volume of which is less than one trillionthof that of the atom as a whole.

Even the lightest nucleus of the hydrogen atom(called proton) is 1836 times the mass of an electron,while the nuclei of heavier elements are half a milliontimes more massive. Normally the atoms are electroni-cally neutral, having the same number of positivelycharged protons as electrons with negative charges.

62

Aethro-kinematics CHAPTER THREE The Quantized Atom

Based on these conclusions, Hantaro Nagaoka, aJapanese physicist, suggested the so-called solar modelof the atom, in which the electrons are circling aroundthe massive, positively charged nucleus on theirKeplerian orbits just as the planets are orbiting aroundthe sun. According to this theory, as the electronsrevolve about the nucleus, they act like oscillatingcharges and radiate energy of specific frequencies, cor-responding to the size of their orbits. If an electronmade five hundred trillion revolution per second, itwould move with a very possible speed of 150 km/secand produce a radiation of frequency within the rangeof the visible light.

There are, however, some fundamental difficultieswith all atomic models that involve revolving electrons.One problem is with the basic assumption of Maxwell'stheory, that accelerating charges constantly radiateelectromagnetic waves.

Since orbiting electrons have constant centripetalacceleration, they must radiate energy and they mustloose kinetic energy too.

Thus orbiting electrons must eventually spiral intothe nucleus, and if this would be the case, all atomswould collapse. Obviously, this does not happen.

Another short-coming of Nagaoka's model was thatit could not explain the facts of spectroscopy, that eventhe simplest atom, the hydrogen, which consists of oneproton and one electron, radiates and absorbs light ofseveral frequencies, giving a well-defined discontinuousspectrum. Thus, in Nagaoka's model the Hydrogen elec-tron should have several unique, but not all the possi-ble orbits. – It has been found, that the spectrums of allelements consist of more than one, but a finite numberof lines in specific distances from each other. When thewavelengths of these lines were plotted in scale, somedefinite mathematical regularities were found .

As spectroscopy improved, several series of lineswere discovered throughout the whole spectrum, whichalways occurred at the same positions. Thus, if thesolar-model of the atom were to be improved, it mustaccount for the fact that the electrons do not fall intothe nucleus, and also explain that their radiation is notcontinuous but appear only at certain characteristic fre-quencies. This later phenomenon applied to the solar-model could mean that electrons can occupy only specif-ic orbits in the atom.

The necessary improvement on Nagaoka's solarmodel was initiated in 1913 by Danish scientist, Niels

63


Bohr, who incorporated Planck's quantum, as the deter-mining factor in the selection of possible electron orbitsin the Hydrogen atom.

Bohr suggested that, contrary to classical electrody-namics, electrons do not emit radiation while movingwith uniform speed on a permanent orbit, but only whenthey pass from one stationary orbit to another. If thequantum theory is accepted, then electrons ought toradiate only in whole quanta when converting theirkinetic energy into radiation.

If a quantum of visible light is radiated by the elec-tron, a sizable fraction of its kinetic energy has beenconverted all at once and it would suddenly take on anew orbit closer to the nucleus. By the absorption of awhole quantum of a given frequency, an electron couldgain enough energy to jump into another orbit fartherfrom the center. Bohr also suggested that the electronhad a certain minimum orbit, which he called theground state, outside of which are the excited stateswhere the electron could be lifted by the absorption ofan appropriate quantum of energy. With this theory theatom is said to be quantized and the origin of the specif-ic characteristics of the spectral lines were successfullyexplained. For the simpler series of the spectral lines

the Bohr model of the hydrogen atom rendered a rea-sonably satisfactory description.

Nevertheless, as the spectral analysis was furtherrefined, it was discovered that each line of the seriesconsisted of several distinct lines lying close together.As though an electron could take, not only one, but sev-eral closely spaced orbits.

To save the Bohr atom and the basic assumptionsof the quantum theory, Arnold Sommerfeld, Germanphysicist, suggested that besides the circular orbit, thatBohr assumed, the electron might have elliptical orbitswith different eccentricities and each of them wouldproduce radiation with slightly different frequencies.Hence, from here on there were two quantum numbersfor describing the position of the electrons; the principaland the orbital quantum numbers. But the spectrallines turned out to be even more complicated. Thenewly discovered lines that seemed to be single, spliteven further in a magnetic field and to account for this,a third concept, the magnetic quantum number had tobe introduced. Finally, a fourth number had to be initi-ated, called the spin quantum number, to account forthe spin of the electron about its axis. Thus, to describeall available orbits in a given shell of space, science had

64


to introduce orbital quantum families, (circular, ellipti-cal and tilted) described by the principal quantumnumbers and three others.

The next question was, how many electrons can bein one shell?

Austrian physicist, Wolfgang Pauli, found at thisstage that in order to account for the various spectrallines of the different elements through the quantumtheory, one must assume that no two electrons can haveall four quantum numbers identical. This hypothesiswas called Pauli's Exclusion Principle.

The concept of shells and sub-shells of the electronsaround the nucleus were successful in rationalizing theperiodic table, but the attempt to produce a literal pic-ture of the solar atom got more and more complicated,and finally collapsed.

Later it became more common to discuss the prob-lems through the concept of energy levels instead oforbits or shells. Thus, electrons moved from one energylevel to the other and the difference between them wasdetermined by the energy quantum, proportional to thefrequency of the radiation, both emitted and absorbed.

In 1925 the German physicist, Werner Heisenberg,worked out a system whereby the energy levels of the

atoms could be written out as a set of numbers,arranged in arrays, called matrices. When these num-bers were applied to atomic data, by the proper manip-ulation, called matrix algebra, all spectral lines of thedifferent series could be predicted. With this approach,no actual picture of any sort was rendered or requiredfor the atom or for radiation. The conceptual content ofthe atomic system had faded away completely into amere collection of numbers. This stage of the theoreticalevolution of the quantum theory is called matrixmechanics.

Hence, Planck's simple concept of the quantum ofdiscontinuous energy, initially introduced to establishthe analogy between radiation and the waves of ordi-nary discontinuous fluids, turned out to be but a com-plex, physically meaningless, mathematical operationwithin the multitudes of families of quantum numbers.

Still, this was only one side of the whole puzzle. Themore perplexing other side of the problem was discov-ered during the same decade: Not only did light-wavessometimes display particle behavior, but in certainimportant experiments, material particles, like elec-trons and protons, demonstrated unmistakable wave-like characteristics.

65


THE WAVES OF MATTER If the Compton-effect represents a convincing evi-

dence of the particle character of radiation, then theeffects of interference, refraction and diffraction shouldjust as clearly indicate the wave characteristics of thesame phenomenon.

In 1924 Louis de Broglie made the bold suggestionthat if radiation sometimes could behave as particles,maybe at special circumstances material particles couldbe observed to behave like waves. Making use of themathematical relationships developed for treating pho-tons as particles, he recommended a general expressionto relate wave characteristics to material particles. Heproposed that the wavelength of a so-called matter-wave should be equal to Planck's constant, divided bythe momentum of the particle: λ = h/mv.

Theoretically, this equation should apply to anymoving body; electron, atom, baseball, or planet. Theformula shows, that the greater the mass and the speedof the particle, the shorter is its related wavelength.Consequently, the wave character of ordinary macro-scopic bodies is immeasurable but in case of the smallmass of the electron, the equation predicts a wave-length, which is comparable to the range of the X-rays.

A few years later Davisson and Germer in the U.S.,demonstrated the existence of such matter-waves byproducing interference phenomena through double-slitexperiments using electron beams instead of light.

Not long afterwards the wave properties of moremassive particles, like protons, neutrons, atoms andmolecules were detected. In following research DeBroglie's equation proved to be a good approximation ofthe experimental results and there is no reasonabledoubt now that the wave-particle and particle-waveduality is a fundamental phenomenon of nature. Withthe experimental proof of electron interference deBroglie's matter-waves became part of physical realityand similar questions arose as those Ein- stein askedhimself regarding the nature of his photons:

What is an electron? Is it really a particle or really a wave? What hap-

pens with the fundamental concepts of wave-motionwhen they are applied to material particles? How canwe understand these two utterly different aspects of aparticle? Here again, we have two contradictory pic-tures of reality; separately neither of them fullyexplains the phenomena, but together they do ?!

66

Aethro-kinematics CHAPTER THREE The Waves of Matter

THE RECONCILIATION OF DUALITY In order to appreciate the extreme conceptual diffi-

culties of a possible resolution for this perplexing duali-ty of light and matter, one should recall the very originof the concepts of wavelength, frequency, amplitude,phase and others, and their mathematical justification,that led in the 19th century to the unanimous accep-tance of Young’s wave theory of light over Newton'smechanical corpuscular theory .

Turning into that century, the proponents of thewave theory were assuming that light is also a mechan-ical phenomena, just like the waves of water or those ofsound, consisting of alternating compression and rar-efaction layers, but they are generated and propagatedin the supermundane isotropic medium of the luminif-erous aether.

With this, all mechanical concepts of sound waves, –like wavelength, frequency, phase, etc. – were trans-ferred unchanged to the phenomenon of light waves.

Hence, in the century-long argument withNewton's corpuscular theory, the task was to demon-strate a specific light phenomenon, which could only beexplained by the known concepts, mechanism andmathematics of wave-motion.

(a) Figure 3-3. (b) In 1801 Thomas Young achieved exactly this goal.

First he clarified the phenomenon of interference of thewater-waves in a ripple tank. Figure 3-3 (a) is an actualphotograph of the interference pattern of the water-waves. Figure 3-3 (b) illustrates a simplified diagram,showing how the generated plane waves produce inde-pendent circular ripples as they pass through the gaps,and the way they interfere with one another. When twocrests coincide they augment one another and producea combined crest twice as high as the original.

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Aethro-kinematics CHAPTER THREE The Reconciliation of Duality

G E N E R A T O R

P L A N EW A V E S

- -

When troughs coincide they produce double depthon the surface of the water. When a crest superimposedon a trough, they cancel one another and the water isneither raised nor lowered.

As the two circular ripples are continually crossingone another, the total result is the appearance of alter-nate high-wave and no-wave beams radiating outwardfrom the center point between the gaps. Certain sec-tions of the back wall always receive high waves, oth-ers in between receive no waves at all. This is the pat-tern of interference.

Next, Young succeeded in producing the same phe-nomenon with the waves of light. Figure 3-4 (a) showsthe diagram of his famous double slit interferenceexperiment. From a lamp, light is passed through a fil-ter that transmits only one of the colors of the whitelight with a definite frequency and wavelength. Thesemonochromatic light-waves then pass through a colli-mator lens, which produces plane waves. Thus, fromhere monochromatic plane waves are propagatingtoward the next screen which contains two parallel nar-row slits.

The two narrow slits act like independent sources,producing two separate spherical waves again, which

are oscillating in unison, and interfering just like thetwo water waves in the ripple-tank.

(a) Figure 3-4 (b) The light and dark bands on the projection screen

prove that light waves manifest the same interferencephenomenon as the ordinary mechanical waves ofwater. They reinforce or cancel one another, dependingon their phases, just like the compression and rarefac-tion layers of water or sound.

Figure 3-4 (b) illustrates the mathematical proofof the wave theory of light. Wherever the rays of lightfrom the two sources reinforce each other on the pro-

68


P L A N EW A V E S

__

D

r1

θ

P

r2

S1

S2

O

y

d

λ

D E T E C T O R S C R E E N

θba

jecting screen they must be in phase with one another.This can only be the case, if the difference between thedistances of each slit from the point of meeting on thescreen is an exact multiple of the wave-length of thelight used. By this method Young was able to calculatethe length of a single wave. Using different color lightshe found that the wavelength of red light is about twicethe length of the violet light.This result agrees with therequirements of the wave theory when it is applied tothe facts of refraction, dispersion and to those of spec-troscopy.

Young's double-slit interference experiment and itscomplete mathematical justification put an end to allarguments for the corpuscular theory of light and theconcepts of wave, amplitude, wavelength, frequency andspeed of propagation became inseparable from the phe-nomenon of light.

These fundamental concepts were incorporated intothe theories of electricity and magnetism and led toMaxwell's theoretical discovery and prediction thatlight is an electromagnetic wave propagated throughthe light-conveying, luminiferous, allpervading aether.

Nevertheless, at the turn of this century new exper-imental facts appeared in the form of the photoelectric

effect which, according to Einstein, could not beexplained by the electromagnetic wave-theory, butclearly required the concentration of light energy in aparticle-like manner, so that the whole energy could beabsorbed by the individual photoelectrons through colli-sion-like interactions.

But if light was made up of photon particles, andsent through a narrow slit, they should be expected toact like machine-gun bullets, moving on a straight linethrough the slit and reproduce the exact image of theslit on the screen between sharp shadows. Instead, pho-tons emerge from the slits in uniquely divergingbeams, just like waves, forming bright and dark dif-fraction fringes on the screen. Thus, photons canexplain the photoelectric effects but not the phenom-enon of diffraction.

Modern Physics attempts a reconciliation of thiscontroversy by the following mathematical procedure.

According to the electromagnetic theory the intensi-ty of illumination of the bands is given by the totalenergy of the oscillating electric vectors at the givenpoint of the screen as they destructively or construc-tively interfere with one another. The intensity of lightis given by the amount of energy crossing a unit area

69


per unit time at the screen. In the diffraction or inter-ference experiments the total energy projected at anypoint of the screen depends on the wavelengths, phasesand amplitudes of the interfering waves and can onlybe predicted through the mathematics of the wave the-ory. In order to make this method applicable to the pho-ton interpretation the amplitude at each unit area firstmust be calculated by the wave theory, and then rede-fined as the density of photons, i.e., the number of pho-tons crossing per unit area per unit time.

In other words there are two separate procedure inthe calculation. First the energy passing through a unitarea per unit time is calculated by the classical methodof the electromagnetic theory, based on wavelength,amplitude, phase, etc.

Next, based on the photon hypothesis, this result istranslated into the new language of the corpusculartheory, taking the concept of photon density to beequivalent with the established energy distribution inthe interfering electromagnetic waves.

The mathematical transformation was achieved bya new formula representing the equivalence of theintensity of electromagnetic waves with the density ofphotons. Eventually, this mathematical resolution

between wave energy and particle density was linkedtogether with de Broglie's matter-waves and by the useof a so-called wave function, the theory was successfullyapplied to the diffraction and interference phenomena,not only for the photons of light, but for electrons andother elementary particles.

By this approach of modern physics, if a beam ofelectrons of suitable de Broglie wavelength emergefrom a slit, the density of the electrons at the surfaceof the photographic plate can be calculated by thewave-function and translated to electron density.

Nonetheless, even this new method did not coverthe full scope of the problem. For the same way as thewave-character cannot be totally discarded in the phe-nomenon of light, the individuality and concentration ofmaterial particles is just as undeniable. Thus, the ques-tion rightfully presents itself: What if a single electronpasses through the slit on its own? Would the particlespread itself over the whole diffraction pattern, aswaves do, or would it strike a definite single point onthe plate? Nature's direct answer to these questions ismost surprising.

It is an experimental fact, that interfering electronbeams produce the characteristic diffraction pattern on

70


the photographic plate. If the plate is replaced by a rowof counters, by which the arrival of each individual elec-tron can be recorded, the experimental result is thateach electron strikes a single counter only, but it istotally unpredictable which one of them.

Surprisingly, however, after a million electrons arerecorded, the distribution of electrons on the differentcounters turns out to be the same, whether they werepassing through the slit individually or by the thou-sands and they do so in accordance with the diffractionpattern predicted by the de Broglie matter wavehypothesis.

Evidently, the path of an individual particle is notpredictable, but the total diffraction pattern of a greatnumber of particles is predicted by the wave-function.Even more surprising was the similar results of theinterference produced by the electron-matter-waveseven in Young's original double slit experiment.Whether it was executed by single electrons or thou-sands of them at a time, they have produced the sameinterference pattern on the screen, analogous to light,as de Broglie's wave-function predicts.

Evidently, the first slit diffracts the electron, whichthen must go through either one or the other slit of the

second screen, and certainly, it can not go through bothof them. Still, between those slits and the projectionscreen (or counters) something must interfere withsomething, which augment or weaken one another,because, even arriving individually they produce theunique pattern of Young's interference. Thus, it mustbe assumed, that each individual electron mustinterfere with itself.

According to de Broglie's summation of these ideas,called by him 'the theory of double solution': there is acontinuous wave function with a solution of statisticalsignificance, and a singularity solution constituting thephysical particles under discussion."Particles would then be clearly localized in space, as

in the classical picture, but they would be incorporatedin an extended wave phenomenon. For this reason themotion of a particle would not obey the laws of ClassicalMechanics, according to which the particle is subjectonly to the action of forces exerted on it, without experi-encing any effect from the existence of obstacles thatmaybe situated at some distance outside of the trajecto-ry. On the contrary, the motion of the singularity was tobe dependent on all obstacles that hindered the freepropagation of the waves surrounding it and there

71


would be a reaction of the wave phenomenon on the par-ticle. And this way the appearance of interference anddiffraction would be explained."(M. Jammer, The Con-ceptual Development of Quantum Mechanics, [309])

WAVE MECHANICS Eventually, the matter-wave hypothesis spread over

to the theory of quantized atom when de Broglie suc-ceeded in deriving Bohr's quantum conditions based onthe angular momentum of the orbiting electron byapplying proper boundary conditions to his electron-matter-waves in the hydrogen atom.

Figure 3-5 (a) illustrates a vibrating string clampedat both ends to rigid supports. This represents a bound-ary condition, which determines the spacing (nodes)and wavelength of the possible standing-waves on thestring. Figure (b) shows De Broglie's approach to useBohr's radius and angular momentum in conjunctionwith his matter-waves to quantize the electron orbits inHydrogen atom. Since Bohr's radius determines theKeplerian orbit and the angular momentum, andbecause the matter wave of the electron is proportionalto its momentum, it is assumed that an electron canonly exist on certain orbits where its wavelength fitsaround the circumference an integral number of times.

Following this idea theAustrian, Erwin Schro-dinger, interpreted theatomic structure interms of the particle-waves, picturing theelectron itself as astanding wave circlingabout the nucleus.

Schrodinger alsoassumed, that if theelectron gains someenergy, its wavelengthdecreases and no longerfits that orbit, and thesame is true if it losesenergy.

Thus, the electron must radiate or absorb energy incertain quantities that would correspond to the circum-ference of the next orbit where its new wavelengthagain must fit the requirements of a de Broglie stand-ing wave. This smallest possible difference in the ener-gy, fitting into two consecutive orbits was assumed to bequantitatively equal to Planck's quantum.

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Aethro-kinematics CHAPTER THREE Wave Mechanics

R

(a)

(b)

Figure 3-5.

As for the electrons themselves, Schrodinger com-bined his electrodynamic interpretation of the wavefunction with the idea that the particles of corpuscularphysics are essentially only wave groups composedfrom infinitely many wave functions. As he expressedhis opinion:

"There seems to be no doubt that we can assumethat similar wave packets can be constructed whichorbit along higher quantum number Kepler ellipses andare the wave-mechanical representation of the hydrogenatom." (M. Jammer, The conceptual Development ofQuantum Mechanics, 1989. [300])

Such analysis of the atomic behavior on the basis ofthe Schrodinger wave equation is termed Wavemechanics.

It should be noted that the mathematical predic-tions of Wave mechanics was in total agreement withthe results of Matrix mechanics, and when applied tothe simple Hydrogen atom both of them agreed withthe predictions based on Bohr's solar model.

In principle, it would seem that wave mechanicsoffers a complete description of the atom, and howeverhard to grasp, it is still conceptually superior toHeisenberg's pictureless mathematical matrices.

Nevertheless in general, a complete analysis of theatom, based on wave-mechanics, turned out to beimpractical even with modern computer techniques,because of the sheer difficulties of its extremely com-plex mathematics.

THE UNCERTAINTY PRINCIPLEFurther attempts to resolve the wave-particle duali-

ty of light and the particle-wave duality of matter led toeven more revolutionary new conceptions about thenature of the physical universe.

Pondering these perplexities Werner Heisenberg,the author of matrix mechanics, tried to resolve theproblem of dualities by analyzing what exactly the con-cept of particle means. He decided that the essentialcharacteristics of a particle are, that at a fixed instantof time it must have a definite location at a definitepoint in space and must have a well-defined velocity.He then asked, how it might be possible to determineexperimentally these two definite quantities and cameto the startling conclusion, that only either one or theother can be determined precisely. This statement isHeisenberg's Uncertainty Principle and the physicalreason for it can be illustrated by his thought experi-ment on electron diffraction.

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Aethro-kinematics CHAPTER THREE The Uncertainty Principle

As Figure 3-6 illustrates, that in order to fix theexact position of a particle one must find its Cartesiancoordinates; x, y, z. Consider the following attempt todetermine precisely the x coordinate of the position ofan electron in a diffraction experiment If the particlepasses through the narrow slit of a given width, at thatinstant the x-coordinate of its position must be on apoint within the distance between x1 and x2.

This point can be determined more exactly by mak-ing the slit narrower and there is no limit to the accura-cy in this respect. However, as it has been found with

light, sound or water-wave experiments, when the slit ismade narrower the diffraction pattern spreads propor-tionally wider.

Therefore, as the electron emerges from a narrowerslit, it is diffracted in a more unpredictable directionand consequently acquires a more indeterminate x-component in its velocity.

Hence, the process of determining the position of theelectron with more accuracy inevitably introduces anindeterminate component in its velocity and momen-tum. Conversely, the uncertainty in the velocity can bereduced by making the slit wider but there is then anincreased uncertainty in the position of the electron.

Recall now, that in de Broglie's matter-wave equa-tion the wavelength (λ) associated with a particleequals Planck's constant divided by the momentum ofthe particle (λ = h/p).

Thus, Heisenberg's uncertainty relations must alsobe proportional to those quantities. If the uncertainty inthe position is dx and the uncertainty in the momen-tum is dp, then Heisenberg's uncertainty relations canbe expressed as dxdp = + − h, again Planck's quantum(where '=+ −' means not very different from).

74


w

L

x x21

(a)

λLw

M

N D1

p

p

y

x

p

(b) (c)

w

w

Figure 3-6.

Since this conclusion is drawn from de Broglie'smatter-wave formula, it is applicable to all particles,including macroscopic bodies, with the difference thatthe uncertainty factor becomes proportionally more andmore negligible as the mass and the momentum of theobject increase. De Broglie's wave-function also assignsa given wavelength and some kind of oscillation to allbodies, but the greater the object the shorter is thewavelength and consequently greater the frequency ofthe oscillation. Thus, the straight line path of a bullet ora golf-ball appears to be straight merely because of theirgreat mass and extremely short wave-length.

This is analogous to the apparent rectilinear propa-gation of light, due to its small wave-length and highfrequency. It follows from all these, that the generalizedconsequence of the uncertainty principle is, that noth-ing in nature can be totally at rest.

In classical physics a solid at absolute zero temper-ature was visualized as an array of atoms at rest on thepoints of a periodically repeating lattice. This is clearlyinconsistent with the uncertainty principle because ifthe atoms are located exactly on the lattice points thereis no uncertainty in their positions and it would makethe velocity or momentum of the atom infinitely uncer-

tain. This would mean that it might have any velocitybetween zero and C in any possible direction.

Conversely, to require that an atom shall be at totalrest with a velocity exactly zero, would cause its posi-tion to be infinitely uncertain, meaning that the atommight be located anywhere in the whole universe. Inorder not to violate the inviolable uncertainty principle,theorists were forced to assume that, even at absolutezero temperature, the atoms are not permanently locat-ed at the lattice points, but roam around within aregion of a given diameter which would represent theextent of the uncertainty in its position.

This would secure the validity of the uncertaintyprinciple, but the question is how can this be correlatedwith the foundation of thermodynamics-dynamics andthe kinetic theory of heat according to which absolutezero temperature is defined and calculated by theassumed zero kinetic energy of the atoms?!

The contemporary answer is, that when a gas coolsdown in a container of fixed volume, it either liquifies orsolidifies before it reaches absolute zero. To prevent itfrom doing so the volume of the container must be pro-portionally increased as the temperature is lowered.Approaching absolute zero, without the condensation of

75


the gas, it is necessary to make the volume of the con-tainer infinitely large. Under these circumstances it ispossible for the gas atom to be at rest with zero velocity,because its position can be anywhere in the infinitelylarge container and Heisenberg's uncertainty principlecan retain its validity.

As a further illustration of this principle, consideran attempt to fix the position of an electron by shininglight on it, and observe the reflected rays through amicroscope.

The difficulty with this method is that the size ofthe electron is very small compared to the wavelengthof visible light and the inevitable result is a strong dif-fraction effect and a blurred image.Thus the electron isnot seen at an exact point with precise coordinates butits image spreads out in diffraction rings over a regionwhich is approximately the magnitude of the wave-length of the light. Furthermore, the center of the dif-fraction pattern cannot be taken as the exact location ofthe electron. This becomes evident when the illuminat-ing light is taken as a stream of photons. Their scatter-ing by the electrons involves Compton-effect collisions.

When photons are scattered by an electron, in eachcollision, some of momentum of each individual photon

is transferred to the electron. This means that the veryact of using photons to determine the position, is auto-matically changing the initial velocity and the momen-tum of the electron by an unknown and indeterminablequantity. It follows, that no subsequent observation ofthe path of the electron can possibly uncover what wasits velocity and momentum before the first observation.

Evidently, in the micro-world of atom physics themeans of observation, and the observed object are of thesame order of magnitude and the disturbing factors orthe magnitude of uncertainty can never be reducedbelow a quantity, which is comparable with Planck'squantum of action.

In the combined evaluation by any conceivableexperiment there is always an uncertainty in the mea-sured value of the position and velocity, or both. This isnot due to imperfections in the design or construction ofthe experimental apparatus. Even with the best ofthose, the uncertainty would still be present. It is anunavoidable consequence of the way in which naturebehaves. Moreover, this is not believed to be a conse-quence of unknown factors that we have not yet discov-ered, but rather that the future behavior of a particle isnot completely determined by its past history.

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THE WAVES OF PROBABILITYThrough a quarter of a century of development, the

final establishment of quantum theory, called quantummechanics resulted from the penetrating discussionsamong the leading scientist.These began by de Broglie'sNobel lecture, with the question, whether Schrodinger'swave function of wave mechanics had to be taken liter-ally or statistically. In other words, did this mathemati-cal expression indicate that an electron in the field of anucleus is a physical reality, which is 'smeared out' as amatter wave, or were these waves to be interpreted asmere probability waves, which allowed only for a statis-tical evaluation of the probability of finding the electronparticle in a given place?

The overwhelming majority of scientist acceptedthe radical probability interpretation, which amountedto a complete break with the concepts of classicalphysics. One important result to emerge from this epis-temological revolution was the inclusion of the obser-ver in the description of a physical phenomenon.

By this, the dual nature of light or matter wasexplained as a consequence of different, mutually exclu-sive experimental arrangements used for the observationand for the description of the same phenomenon.

The so-called Copenhagen interpretation of quan-tum mechanics prevails today despite many attemptsto refute it. The theory was crystallized in Bohr's lec-ture, given in the presence of the leading physicists atthe fifth Solvay Congress in 1927, as it is freely quotedfrom Allen and Unwin, Physics and Philosophy, (1958):

"This interpretation starts with a paradox: The lan-guage of classical physics is merely a refined form ofthe language of daily life and that is the only languagewe have. Any experiment in physics, whether it refersto the phenomena of daily life or to atomic events, is tobe described in the terms of classical physics. The care-fully defined concepts of kinematics, dynamics and elec-tromagnetism form the language of science by whichwe describe all arrangements of our experiments andstate all results."Consequently we cannot and should not replace these

concepts by any others. Nevertheless, we have learnedthat the application of these classical concepts indescribing the structure of the atoms or that of radia-tion creates unresolvable contradictions. We have foundthat the language which was so successful for threecenturies of science, reached its conceptual limits whendescribing the duality of radiation and matter, and we

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Aethro-kinematics CHAPTER THREE The Waves of Probability

must keep this in mind while using it. We cannot andshould not try to improve these concepts, but extendthe description of an event where it is needed by thelanguage of the quantum theory, with its uncertaintyrelations and probability functions as described by mat-ter-waves. Therefore, the theoretical interpretation ofan experiment requires four distinct steps:"1. The description of the theory and the method of an

initial measurement of the phenomenon in the lan-guage of classical physics,"2. the translation of this experimental situation into

the probability function of the quantum theory,"3. the following up of this function in the course of

time,"4. the statement of a new measurement to be made

at the new time, and a statement of that result, whichcan then be calculated from the probability functionand expressed again in the initial language of classicalphysics."With this method the duality of waves and particles

becomes a problem of mathematical transformation.The formalism is written to resemble classical mechan-ics, with equations of motion for the coordinates and

the momenta of the particles. By a simple transforma-tion it can then be rewritten to resemble the wave-equa-tion for an ordinary three-dimensional mechanicalwave, where this wave-function gives the amplitude ofthe waves resulting from diffraction or interference atany point of space. For matter-waves the same formulacan be interpreted as a function which gives the diffract-ed electron's probability to be at any point of space. Thatis why, in this interpretation, matter waves are calledprobability waves."Thus the classical conceptual possibility of playing

with different complementary pictures of waves andparticles, has its parallel in the transformation of themathematical expressions from one into the other. Toillustrate this method, consider the following simple,ideal experiment:"(1) The Bohr-model of the atom consists of a nucleus

and one or more orbiting electrons. If this description ofthe atom is accepted, then at least in principle, it shouldbe possible to observe the electron on its orbit through amicroscope of ideally high resolving power. In order toachieve accuracy in this measurement, the microscopeshould use gamma-rays with wave-length smaller thanthe size of the atom.

78


“The electron's initial position is determined when itscatters the illuminating gamma-rays into the objectivelens, through which it reaches the observers retina orthe photographic plate. To determine what happens tothe electron when it scatters the gamma-rays, the pho-ton concept of radiation and the correspondingCompton collision should be considered.

"(2) From this point on the language of the quantumtheory has to be applied. The electron is taken as amatter-wave, the probability function is set up and theclassical equations of motion is transformed into thewave-equation of probabilities."(3) Following up the probability function in the course

of time is a mathematical procedure and the result is acombination of statements about possibilities or ten-dencies in the position and momentum of the electron,together with statements about the uncertainty rela-tions, which represent our potential knowledge of thefacts. It is also statistical in nature, since the wave func-tion only predicts the probabilities of the electron to bein a certain place at a given time."(4) Based on the prediction of the probability func-

tion a second gamma-ray experiment has to be set

up to determine the actual position of the electronwhich, will again involve the uncertainty principle."Since the energy of the first gamma-ray photon was

more than enough to knock the electron out of theatom, the second determination could only show theelectron on its path receding from the atom and we cannever observe more than one point of the orbit, there-fore, there is no electronic orbit in the ordinary sense.Further more, quite generally, quantum mechanics can-not describe a trajectory in its classical sense, becausethere is no way of describing what happens betweenany two consecutive observations in the atomic order ofmagnitude."

This is then the present stage in the history ofhuman knowledge.

According to 20th Century physics and philosophy,the potential understanding of the works of Naturethrough the improving rational comprehension of phys-ical phenomena and the ever-widening logically consis-tent description of reality, finally and unavoidablyreached its ultimate evolutionary limitations.

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CHAPTER FOUR

THE EPISTEMOLOGICAL REVOLUTION

Looking at the history of science as of part of thehistory of ideas means seeing it primarily as a continu-ous attempt by men to arrive at a rational comprehen-sion of natural phenomena, and to construct a logicallyconsistent picture of nature.

The expansion and rapid growth of knowledge fromthe seventeenth century onwards, which establishedscience as an autonomous field of human thought,occurred mainly in the field of mechanics and astrono-my. There are several reasons why these two branches

of physical science were developed first, out-pacing allother branches of physics. One is that the starting pointof mechanics is kinematics, the study of motion, andmotion is the simplest and most universal phenomenonof both earthly and celestial observations. The direct,everyday experience with macroscopic objects and theregular motions of astronomical bodies naturally creat-ed the concepts of distance, time and velocity and sug-gested a differentiation and categorization of allmotions by those concepts.

The observation of 'push and pull' by muscularforces, impacts in collisions between bodies and in gen-eral every direct contact that alter the motions of mate-rial bodies suggest a most intuitively obvious and sim-ple means of explanation for all kinds of physical occur-rences. In other words, mechanical models lend them-selves more readily than any others to analogies for thedemonstration and clarification of how events are relat-ed in Nature.

The mechanistic mode of thought has been presentin physical explanations since antiquity. From the timeof Gallileo, Descartes, and Huygens the trend towardsuch a way of thinking expanded into an all-embracingmechanical view of the world.

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Aethro-kinematics

The innovations of algebraic and geometric meth-ods for calculating speed and acceleration, and theappearance of the three dimensional Cartesian coordi-nate system created the stage for the scientific short-hand of mathematics, symbolizing the intuitive physicalconcepts and rendering the ability for a precise descrip-tion of their empirically established quantitative ratiosand proportionalities.

With Descartes' and Huygens' introduction of theluminiferous aether, an all-pervading hypotheticalmedium, the conclusions and theories of terrestrialmechanical experiences was extended into the wholespace of the Cosmos.

The phenomenon of light received its mechanicalinterpretation based on a direct analogy with the wavesof sound as the compression waves in the aether andattempts were made to explain the regularity of themotions of heavenly bodies based on the assumedhydrodynamic characteristics of the same medium. Thesystematic motion of the planets were not guided by theGods anymore, but they were quietly carried by theDescartian aether in the cosmic vortex of the Sun, simi-lar to the circulating fallen leaves in the eddies of a run-ning spring.

Mechanicism has profoundly influenced philosophi-cal and epistemological thoughts by restricting scientif-ic modes of explanation of natural phenomena to purelycausal considerations through mechanistic analogiesand gradually discarding all theological speculationsfrom the description of the physical world. The full pro-gram of mechanicism was to replace the concept ofaction at a distance all together by tracing back thecause of all natural forces to the simplest mechanism ofcollision and impulse between material particles.

Nevertheless, this ambitious program of mechanis-tic philosophy proved to be an impossible task at thelevel of experimental science at that time.

Instead, toward the end of the seventeenth centuryNewton's 'Principia' appeared on the stage and ren-dered the first serious attempt to construct a theory ofmechanics through a systematic scientific method start-ing from definitions and axioms, followed by theoremsand conclusions of a general nature, based on the wholebody of theoretical and experimental knowledge avail-able. Implicit in his work was an analysis of the meta-physical foundation of mechanics by clerly defining thebasic concepts needed for the description of physicalreality: time and space.

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Aethro-kinematics CHAPTER FOUR The Epistemological Revolution

"I. Absolute true and mathematical time, of itself,and from its own nature, flows equably without rela-tion to anything external.II. Absolute space, in its own nature, without rela-

tion to anything external, remains always similarand immovable." (Principia)

Newton's work furnished most of the basic tools forthe systematic dynamical approach to the physicalworld. The concept of inertial mass, the laws of inertia,force, acceleration, action and reaction, and that of uni-versal gravitation implicitly contained all the essentialsfor the subsequent development of physics, not only inthe description of earthly and celestial mechanics, butin the most general manner in all departments of nat-ural sciences.

Nevertheless, this simple axiomatic system ofmathematical ratios and proportionalities was set upbetween the conceptually unclear and mechanicallyinconceivable notions, such as the inertial mass, and theaction at a distance force of gravity, and therefore it rep-resented a total desertion of the reigning philosophy ofmechanicism. Boyle, Huygens, Leibnitz and othermechanistic philosophers characterized the notions ofNewton's Principia as a relapse into medieval concep-

tions, a kind of treason against the doctrines ofmechanicism which already emancipated scientistsfrom the animistic explanatory principles of scholasticphysics based on the powers possessed by inanimateobjects, like that of the inertial tendencies of Newtonianmass.

The reason for this severe apprehension was for thepossible retrograde metaphysical influence on the fur-ther development of theoretical physics. Indeed,through the development of classical and modernphysics the word 'force' all too frequently performed afunction which did not differ essentially from thescholastic concepts of qualities and powers. The samephysicist, who scoffed at the description based on ani-mistic explanatory principles, felt perfectly satisfied bythe statement that a 'force' was being exerted on a bodyin spite of the complete blank in his mind about themode of this exertion. And the effect has not yet ceasedto work even today, for it can be observed too often, thatthe pronunciation of the magic word of 'force', or its var-ious modern substitutions, still creates some seeminglysatisfactory imitation of conceptual understanding.

To avoid any false impressions, it should be clarifiedhere, that Newton never believed or stated that the ulti-

82


mate causes of his forces are essentially unknowable.On the contrary, his statement of not attempting tohypothesize about the origin and mechanism of theforce of gravity, or the fictitious force of inertia, in nosense meant a final abandonment of the problem, or theultimate description of the causes of the phenomena inquestion. He stated, that the absolute quantity of a cen-tral force, the strength of a centre of force, is merely amathematical concept. When it is said a centre attracts,this is not intended to indicate the true character of theoperation of the force or to describe its physical cause.

Describing the physical phenomenon of the force ofgravity, one is only justified in stating, that two particlesin each others presence have accelerations in oppositedirections along the line joining them and vary inverse-ly as certain invariable coefficients to be assigned to theparticles, namely their masses. Acceleration is a purelykinematic magnitude and mass is a quantity deter-mined empirically for a given material body. Therefore,the physical concept of force is merely an abbreviationof the interaction described above.

Newton declares the following points as cardinalimportance in his scientific method; "firstly the reduc-tion of all phenomena to the operation of a small num-

ber of active principles of motion, of which gravitationforms an instance, and secondly the hope or expectationthat ultimately the causes of these principles too willnot remain hidden." For him the existence of gravita-tion is no hypothesis, but an empirically establishedfact, and he looks upon it as only a matter of time beforethe cause and transmission of this force will be discov-ered. Although Newton discarded Descartes' aether-vor-tex hypothesis, until the end of his long life, he neverquit speculating about the mechanics of "a most subtlespirit which pervades and lies hid in all gross bodies, bythe force and action of which the particles of bodiesattract one another."

Describing the grounds, methods, limitations andthe conceptual validity of his theories, it can be stat-ed that Newton took a stand with respect to the phi-losophy of knowledge laying down the foundation forthe epistemological rules of classical physics.

Through the subsequent evolution of scientificthoughts, these tendencies has never been revoked orrevised by Newton or by anybody else who took anactive part in the construction of human knowledge.The problem of the action at a distance forcesremained a temporarily accepted mystery, but the

83


search for a mechanistic solution for this phenome-non has never left the agenda of theoretical physics.

In its philosophical implications, this mechanisticview of the world led directly to causality and determin-ism. If the world is a machine, that once had been putinto motion by its creator then, no matter how complexit is, in principle, every effect is the result of a cause,and itself becomes the cause of the next effect.

It is only a matter of finding the general design andlaws of the machine and forming a complete under-standing of the present state of the system, from whichboth the future and the past can be calculated for anyinstant of time.The following quote is taken from Sambursky, An

Anthology of Physical Thought [19])"The conflicting epistemological tenets of empiricism

and rationalism were brought to a practical synthesisin the course of the development of exact sciences dur-ing the last three hundred years. A survey of the historyof physics since the age of Galileo and Newton shows inparticular that the formation of scientific theoriesbegins with the putting forward of hypotheses, after aminimum of emperical data has been accumulated.

Then the consequences of the hypotheses are deduced,and put forward as factual assertions to be comparedwith, and checked against, the experimental results.

"Thus theory and experiment constantly interact withand mutually support each other. What actually hap-pened in the course of a long process of merging 'factual'and 'conceptual' elements into a higher unity was thatthe former gradually came to be seen less as 'purefacts', immediately dependent on sense perception, andmore as 'higher order facts', the understanding of whichtacitly presupposed the knowledge of simpler facts aswell as an increasing theoretical element.

"The conceptual components, on the other hand,became more and more remote from the elementaryabstractions of the world of commonly accepted con-cepts and changed into scientific constructs which com-bined the results of purely theoretical considerationswith the knowledge of facts of a higher order. In brief:the synthesis of the factual and conceptual componentsof scientific knowledge emerged as the result of a longand gradual evolution, during which each of these com-ponents itself turned out to be the product of a synthe-sis of factual and theoretical elements.

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"The gradual emergence of a physical picture of theworld, including the scientific constructs which arealready regarded as elements of physical reality in noless degree than observed facts, became more obviousfrom the early nineteenth century onwards when scien-tific observations and theoretical deductions began tosupport and confirm one another in fields other thanpure mechanics."The physicist of this era succeeded in putting the phe-

nomena of light, electricity, magnetism and heat on aconsistent and systematic basis. Further, it graduallybecame clear that several of these partial domains ofreality were interconnected, as in the linking ofmechanics to heat, the fusion of electricity and magnet-ism, and the explanation of the essential features oflight within the framework of electromagnetism. Thissuccessive fusion of previously partial pictures into onepicture of increasingly universal validity appeared initself as a confirmation of the synthetic method of phys-ical sciences and as a kind of verification of the episte-mological principles on which these sciences werefounded."Thus it became increasingly unlikely that one of the

major laws of physics could be falsified without affect-

ing the rest. Indeed, modern science is like an edificewhich could easily collapse if one of its essential build-ing stones were removed."The most typical and demonstrative example of the

power of abstraction based on mechanical analogieswas the initiation and development of a theory of elec-tricity and magnetism based on Huygens' supermun-dane light-conveying aether. The theory of electromag-netism was conceived through Faraday's tireless con-ceptual effort to draw a mechanically conceivable sys-tematic analogy between hydrodynamic and electric-magnetic phenomena by the designs of lines, tubes andfields of forces, originating from the stresses and strainsin the supermundane aether medium. This most com-plex model of various electromagnetic phenomena wascompleted by Maxwell's ingenious mechanical detailsand their expression and incorporation into a completemathematical system, which finally embraced lightwaves themselves as a small fraction of the multitudeof so-called electromagnetic radiation.

Maxwell's electromagnetic equations became thecomplete description of the supermundane dynamics ofelectricity, magnetism and their various intertwinedphenomena, including most everything that was

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invented in the past, and exists in the wealth of today'selectronics.

Through this era of unprecedented expansion ofhuman knowledge and deepening understanding ofphysical reality the mechanical approach to explainnatural phenomena became so deeply rooted in scientif-ic thinking that toward the end of the nineteenth centu-ry the majority of physicists believed in the epistemo-logical rule that a scientific theory had not been proveduntil its validity had been demonstrated in terms ofmechanical analogies. Ironically, this very tendency cre-ated the seemingly unavoidable stumbling block in theprogress of classical physics.

Faraday's giant leap of abstraction over two ordersof magnitude, from macroscopic matter to ultramicro-scopic aether, had never been completed. The hypothe-sis of the electromagnetic medium came to its finalchallenge; the requirement of producing a mechanicalmodel for the aether itself.This mechanical model of theaether, which pervades macro- and micro-cosmos, hadto comply with all all known natural phenomena, in allorders of magnitude.

The medium that conveys light waves through allspace of the universe must also allow the unaffected

eternal motions of the stars and planets within.Furthermore, since the speed of propagation of lightwaves is finite, as other wave-phenomena, it should bemeasurable relative to the conveying medium itself. Itfollows, that the state of rest or the state of motion ofthe medium to the measuring device should also be ameasurable quantity. In other words, the state of restor motion of the aether relative to a laboratory sub-merged in it should be found in the variation of thespeed of light when measured in different directions.

If the aether exists, this experiment would furnishan universal aether frame of reference , which would bethen the mechanical proof of Newton's metaphysicalconcepts of absolute space and absolute motion.

Maxwell proposed a possible testing of the existenceof such absolute frame of reference by proving theearth's orbital motion relative to the motionless aetherthrough the measurements of the velocity of light in anearthly laboratory in different directions.

This test has been executed by Michelson in 1887and has been repeated with ever increasing sensitivity,but proving no more than an unexpected and illogicalnull result. There was no trace of relative motionbetween the earth and the light-conveying medium.

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Maxwell's followers, Fitzgerald, Lorentz and oth-ers set their goal to explain the phenomenon by theelectromagnetic theory and based on the electromag-netic structure of matter.

Their basic hypothesis was, that matter is com-pressible and when moving relative to the aether it con-tracts in the ratio between the velocity of this relativemotion and the velocity of light (β=√1−v2/c2). Thishypothesis also explained another discovery of the1880's, that the force needed to accelerate an elemen-tary particle not only depends on the mass of the parti-cle, as Newton predicted, but also on its velocity, andagain in the same ratio as above. Based on the electro-magnetic construction of matter, Michelson's null resultand Fitzgerald contraction ratio, Lorentz derived amathematical system to describe and explain most ofthe problems of this new group of phenomena. TheLorentz-Fitzgerald contraction hypothesis was the lastattempt to preserve the central position of mechanicsand that of the aether in theoretical physics and with itthe conceptual coherency of scientific thoughts and themethods of classical epistemology. The mathematicalsystem of this theory was later adopted by relativityunder the name of Lorentz Transformation.

No doubt, this was the exact turning point not onlyin the evolution of physical sciences, but more generallyin the evolution of human knowledge, philosophy andepistemology.

For a historical background, it should be noted here,that the upheaval of revolutionary advances were notrestricted to the field of scientific thoughts. By the turnof the century the accelerating growth of knowledge inall fields of science resulted in an explosive industrialrevolution and in the wake of the great success ofmechanicism came a general philosophical and sociolog-ical unrest. As metaphysics lost ground in the descrip-tion of Nature, the religious controlling power of thechurches alarmingly dissipated, and in its place com-mon sense, causality, determinism and materialismgained strength in the social ideologies. Meanwhile,World-war I. was in the making, and international com-munism spread through the world keeping steps withtechnology and industrialism.

One might ponder upon what parallel could befound between this stormy background and the simul-taneous epistemological revolution?! For whatever rea-son, after three centuries of continuous and systematicdevelopment of an ever more comprehensive mechani-

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cal description of the physical world, within a couple ofdecades of the twentieth century the majority of thewestern scientific establishment was not only ready toconsider that something is basically wrong with themechanistic and deterministic views of classicalphysics, but was also willing to accept fundamentalchanges in theory of knowledge totally at variance tothe epistomological principles that guaranteed the suc-cessful evolution of classical experimental physics fromthe times of Galileo and Newton.

Where did this sudden revolution of physicalthoughts lead and what had modern physics to offeras a substitution for mechanical understanding?

Consider the following excerpts from S. Sambursky:An Anthology of Physical Thought, [Introduction]:"Nineteenth century physicists clung to the idea of

aether tenaciously because the wave theory of light andof electromagnetism strongly suggested the aether as amedium of propagation of these phenomena. Einstein'sinterpretation of the failure to detect the aether(Michelson's null result) was revolutionary in manyrespect; by discarding the aether he implied that therewas a limit to the value of mechanical models andanalogies.

"Einstein's principle of relativity deeply effected philo-sophical and, in particular, epistomological thoughts inthat it abolished Newton's fundamental metaphysicalconcepts of absolute space and time, which were super-seded by that of the absolute magnitude of the velocityof light. Intervals of length and time became relativemagnitudes, depending on the state of relative motionof observer and the observed body."Space itself and time itself were reduced to mere

shadows and only the space-time interval between twoevent in the four-dimensional world was held as aninvariant. The obvious philosophical conclusion wasthat reality was of a more abstract nature than theworld of 'common sense' made familiar through dailyexperience."The theories of pre-quantum physics, including rela-

tivity theory, were deterministic in the sense that fromthe state of a system at a given moment they derivedmathematically its state at any other moment. The ini-tial state of a system was determined if two indepen-dent sets of data, the positions and velocities of the bod-ies were known. In classical epistemology it was tacitlyassumed that there were no limits to the exactness ofthis knowledge. Things are different, however, in the

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micro-region where the means of observation and theobserved object are of the same order of magnitude. Theepistomological consequence of quantum mechanics isthe revision of the concept of a phenomenon. Anobserved phenomenon cannot be completely divorcedfrom the experimental arrangement."The events connected with the observation will

always force the scientist to make an arbitrary divisionbetween observer and the observed object. The well-known duality of corpuscle and wave, or rather that ofthe discontinuous particle aspect and the continuousfield aspect of light and matter, represents the experi-mental confirmation of the idea that the observer ispart and parcel of the phenomenon.“Thus, the centuries-old argument whether light con-

sists 'in reality' of waves or of particles has thus becomemeaningless."There is, however, an interesting parallel between the

operational aspects of the conceptual revolutionscaused by relativity and by quantum mechanics. If thespeed of transmission of the signal assumed to be infi-nite, not finite, the classical picture of absolute spaceand time, and the discarded concept of simultaneity ofevents is restored; if Planck's quantum of action is

assumed to be zero, but not small and finite, the classi-cal picture of determinism and a continuous sequenceof physical events is likewise restored."The most prominent feature of this newest venture

was the fact that science itself took the lead from philos-ophy when physicists, on the advent of relativity andquantum mechanics, had to look at the foundation oftheir subject and were forced to revise their epistemolo-gy of science. In the light of the scientific world-picturewhich has emerged from these efforts, nobody woulddeny any longer the metaphysical nature of those foun-dations.""The new concept of a phenomenon, denying as it does

the existence of an 'objective' reality independent fromthe observer, has shed new light on the relationbetween physical thought and other fields of humanknowledge. Niels Bohr, by coining the notion of comple-mentarity, has drawn attention to the universal signifi-cance of the new attitude to the problem of man versusthe outside world. His interpretation of Heisenberg'suncertainty principle , the mathematical expressions ofthe indeterminacy of a physical state, centered roundthe notion of a pair of complementary opposites (wave-particle), the two sets of data characterizing that state.

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“(...) Bohr's contention is that this physical comple-mentarity represents a logical extension of the classicalnotion of causality, and that it is to be regarded as aspecial case of a universal phenomenon pertaining tothe world of human experience. He pointed at severalpairs of complementary opposite concepts, such asthinking and feeling,... and referred to examples takenfrom ethics, aesthetics, epistemology and sociology, suchas the problem of the freedom of the will, or that of jus-tice and love....In the forty years of the last great theo-retical breakthrough, an enormous wealth of newexperimental data has accumulated in elementary par-ticle physics, astrophysics and cosmology.“However, theory has been lamentably lagging behind

experiment in recent decades. Many eminent physicistsof the last generation, notably Bohr and Pauli, haveexpressed the opinion that quantum mechanics maywell be the first of many more steps, which will leadphysics away from the familiar classical concepts. Amajor theoretical advance from here could possibly beachieved only through ideas involving further radicalrenunciations of some notions to which physicistsbecome accustomed in the age of determinism, whichwas also the age of mechanical conceptions."

For an even less optimistic point of view, considerthe following:"Today the outer limits of man's knowledge are

defined by Relativity, the inner limits by the QuantumTheory. Relativity has shaped all our concepts of space,time, gravitation and the realities that are too remote tobe perceived."The quantum theory has shaped our concepts of the

atom, the basic units of matter and energy, and the real-ities that are too elusive and too small to be perceived.Yet these two great scientific systems rest on entirely dif-ferent and unrelated foundations. They do not, as itwere, speak the same language."Believing in the harmony and uniformity of nature,

Einstein looked for a single edifice of physical laws toencompass both the phenomena of the atom and thephenomena of outer space. The purpose of his UnifiedField Theory was to construct a bridge between them.Its obvious minimum achievement was supposed to be,to unite the laws of gravitation, and the laws of electro-magnetism within one basic superstructure of universallaw."'The idea that there are two structures of space inde-

pendent of each other, the metric-gravitational and the90


electromagnetic,' -- Einstein observed, -- 'is intolerableto the theoretical spirit.' A complete Unified FieldTheory touches the 'grand aim of all science to cover thegreatest number of empirical facts by logical deductionfrom the smallest possible number of hypotheses oraxioms.'(...) Yet despite all his efforts in the last twenty five

years of his life he could not incorporate electromagnet-ic laws into general relativity."But the irony of man's quest for reality is that as

nature is stripped of its disguises, as order emergesfrom chaos, as concepts merge and fundamental lawsassume increasingly simpler form, the evolving picturebecomes ever more remote from experience. For there isno likeness between the image of a tree transcribed byour senses and that propounded by wave mechanics, orbetween a glimpse of the starry sky and the four-dimen-sional space-time continuum that has replaced our per-ceptual Euclidian space. In trying to distinguishappearance from reality and lay bare the fundamentalstructure of the Universe, science has had to transcendthe 'rabble of the senses'. 'But its highest edifices,(Einstein has pointed out) have been purchased at aprice of emptiness of content.'

"A theoretical concept is emptied of content to the verydegree that it is divorced from sensory experience. Forthe only world man can truly know is the world createdfor him by his senses. If he expunges all the impres-sions which they translate and the memory stores,there is nothing left. And what today's scientists andphilosophers call the world of reality, the colorless,soundless, impalpable cosmos which lies like an icebergbeneath the plane of man's perceptions, is a skeletonstructure of mathematical symbols. (Barnett's TheUniverse and Dr. Einstein, 1957, [109] )

PROFIT AND LOSSSince there is no coherent theory about the meta-

physical foundation, methods and validity of modernknowledge, modern epistemology, the expected result ofthis revolution exists mainly in the sporadic personalfoot-notes of the eminent scientists. Most probably dueto the fact that the two major theoretical breakthroughsrest on entirely different foundations, executed by dif-ferent methods, and described in different languages,modern epistemology cannot give an unified direction tobe followed by future science.

Now, at the ending of this century of revolutions, inthe absence of a unifying description of the fundamen-

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Aethro-kinematics CHAPTER FOUR Profit and Loss

tal aspects of modern physics, one might attempt togain a general evaluation by simply drawing the bot-tom line of the profit and loss statement of humanknowledge for this past century. However, before gettinginto the details of this scientific balance sheet, somevery noticeable but so far practically unmentioned gen-eral aspects of modern scientific methods should bepointed out.

There was an unwritten, though universallyrespected epistemological method in the evolution ofscientific thoughts up until the twentieth century thatcan be described in short as follows:

When a highly successful and widespread physicaltheory was opposed by some accumulated experimentalevidence about a newly discovered group of phenomenain a particular field, the tendency has been first of all totry to save the theory by all means. In case of persistentdisagreement with the facts of this specific field, for thesake of preserving the validity of the theory for the rest,serious attempts had to be made to re-evaluate eachdetail constituents of the theory that might cause thiscontradiction.

Sometimes the theory had to be disassembled tothe faulty point, from which it could be rebuilt again

explaining all facts of its whole territory in the samelanguage and with the inclusion of an explanation forthe newest empirical facts. This relentless investigativeapproach was a must for the successful growth of threecenturies of classical physics.

Examining one by one of the crucial problems, thattriggered the epistemological revolution by modern the-oretical physics, it can be found that at least five impor-tant deviations had to be committed with respect to theabove described method before the first fundamentalpostulate of the new theories could be declared.

First, after some accumulation of opposing data in acomparatively narrow field of classical physics, comes acategorical negation of the ability of the present theoryto explain the problematic phenomenon. This includesthe conviction that no details of classical physics can berevised without affecting its validity as a whole.

Second; the categorical negation then extended tothe general conclusion that the tools, concepts, laws,logic and language of classical physics are insufficientto describe the problematic phenomena.

Third; since there is no solution to this problem, butthe classical principles must be saved for the rest oftheir territory, this new group of phenomena must be

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isolated from the body of physics and to be described bydifferent concepts, language and logic, which are beyondthe critical boundaries of common sense.

Fourth; since the predictions of the otherwise uni-versally successful classical theory was proven to bewrong for this isolated group of phenomena, a mathe-matical formula should be found to express the exactratio for the difference between the classical predictionsand the experimental facts. This formula, incorporatedwith classical mathematics will then render a methodof transformation, which in each individual calculationwill give the mathematically adjusted right predictions.

Fifth; because there is no humanly conceivable rea-son for this mathematical transformation, except to fitthe new experimental facts, it must be raised to thelevel of a fundamental metaphysical assumption, whichtranslated into the language of classical physics,becomes the first postulate of the modern theory.

Consider the two major examples: Both the specialtheory of relativity and the quantum-photon theory fol-lows these exact steps. The results were, the metaphysi-cal postulate of relativity in the form of the absolutespeed of light, which was derived from the Michelsonnull result and mathematically expressed by the

Lorentz Transformation. Similarly, metaphysical quan-tum postulate of the discontinuity of radiation energywas based on Planck's quantum, established empirical-ly and derived through the mathematical interpolationof two erroneously predicting classical equations.

There is also a sixth very important step in thismodern method:

The final and general acceptance of the new hypoth-esis is based on the total reversal of the true procedurevia the so-called correspondence principle, which statesthat the modern theories represent the most generalform of scientific knowledge, out of which the laws ofclassical physics merely represent the special cases,when the velocity of motion is much less than that oflight, or when the matter-wavelengths of macroscopicbodies are very small relative to Planck's Quantum.The same method can be found in all aspects of modernphysics, from the major breakthroughs down to thevery details of the individually designed experimentaltheories, all through the astonishing modern achieve-ments of the twentieth century.

As far as the profit and loss statement goes:The fundamental theoretical duality which has

shown itself in the nineteenth century as a mechanical93


problem between Newton's cosmic void and Maxwell'sallpervading aether, now transformed into the admittedmodern controversies between waves and photons, par-ticles and matter-waves, continuity and discontinuity,determinism and probability.

But while originally it was a duality within the ter-ritories of classical physics, and described by the samelanguage, now the duality spread into the two separatedepartments of modern theoretical physics, which how-ever, do not communicate with one another. Thus, theold-fashion duality now is quadrupled.

Nevertheless, finally, in the conceptual labyrinth ofquantum mechanics, and that of Bohr's notion of 'com-plementarity' which justifies the transformationbetween conceptually empty and mathematically mutu-ally exclusive statements, the problem of dualityallegedly dissolved into a mathematical formalism andhence declared to be all together meaningless. By thistime, however, it is quite difficult to distinguish betweenmeaningless' and 'meaningful', since even meaning hasdifferent meanings in each theory.

Hence, within these few revolutionary decades wehave successfully expelled from physics the 'three

frightening ghosts'; absolute time, absolute space andabsolute motion. But we have gained an absolute veloci-ty for light, which is, however, mechanically measurableand varies with the densities of different media.

We got rid of the covariance of electromagnetismand the invariance of the accelerated coordinate sys-tem, though we had to invent contracting yardsticksand ill-rhythmed clocks, shrinking and ticking by theguidance of the different illusions of different observers.

We have ingeniously escaped from the primitivenotions of the mysterious inertia and acceleration bysimply rotating the whole universe around Newton'sbucket.

In order to free physics from the perplexing notionsof light and the action at a distance force of gravity, wehad to learn about the basic capability of empty spaceto transmit waves of nothing through nothing, and thesophisticated non-euclidian capability of the samenothing to react to the presence of matter by bendingitself into different curvatures which for some unknownreasons quantitatively still depend on the mysteriousgravitational mass, still proportional to Newton'sinverse square-law and astonishingly enough still cre-ates orbits according to Kepler's heavenly harmony.

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We have left Descartes' mechanicism, Newton'smathematical forces, Faraday's stress and strain fields,and Maxwell's clumsy mechanical scaffolding, we havediscarded logic and common-sense, left behind the out-dated conceptual perception of reality, and finally in asweeping epistemological revolution we have trashedthe very hope that we can ever understand anythingaround us. – Nonetheless, we have achieved the ulti-mate skill of fabricating, abstract mathematical super-structures to fit any experimental curve for the sake ofpredicting the otherwise unpredictable, though unfortu-nately this final description of modern reality is foreverburied in the humanly unscramblable language ofempty symbols.

Only through these inevitable, bold, astonishing,modern innovations and sacrifices did we finallyachieve Einstein's religiously humble goal of demolish-ing the infantile mechanical notion of the allpervading,luminiferous, unmentionable e - - - r.

...Or did we...?!

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PART II.

THE KINEMATICAL SOLUTION

96

Aethro-kinematics

FOREWORD

POSTULATES VERSUS COMMON SENSE "Of all the branches of physics, only thermodynam-

ics attracts more cranks than special relativity. Is itreally scientific to just dismiss them ? Should we notexamine each case on its scientific merit, lest ourconservatism lead us to miss out on the next scientif-ic revolution ? No, not at all."The reason we can give such a flat answer is that

most critics of special relativity are concerned withits inconsistency, not with the experiments that veri-fy it. All such claims of inconsistency can be ignored,because the logical consistency of special relativitycan be demonstrated. Although a physical theory is acorrespondence between things in the physical worldand structures in mathematics, the question of con-sistency is a question about the mathematical model;and, like many mathematical questions, it can beanswered decisively." (W.L.Burke: Spacetime,Geometry, Cosmology [55])

It is only fortunate that classical physicists weremore open minded, or less preconditioned by theirown successful theories than their relativistic suc-cessors, otherwise the patent clerk from Bern wouldremain forever unknown, there would be no EinsteinCentenarium, and professor Burke would not havethe chance to write those wise words. As for the firstpart of the quotation, we must call Doctor Einsteinto our defense, who said:

"Theoretical physics is best done by a plumber,who is not constantly pressured to justify his exis-tence by producing scientific research, but insteadcan consider the most important problems." (Taylor,New Physics, 1972, [92])

The main reason, however, for including Burke'sthoughts is, that the point, from which we meant tostart this study is exactly what he refers to; the rela-tionship between the theory of relativity, its mathe-matical model, and its experimental verification.

Here it should be clarified again that the abovementioned mathematical model was developed byLorentz in 1888, seventeen years before the actualbirth of special relativity. The hypothesis was anextension of Maxwell's Electromagnetic Theory and

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Aethro-kinematics Postulates versus Common Sense

based on the existence of the aether. The fundamen-tal set of equations of Relativity is still called: TheLorentz Transformation.

In 1905 Einstein declared his basic philosophicalpostulates and re-derived from them exactly thesame equations. Nevertheless, even within the framework of the Special Theory, the mathematical modelkept Lorentz's name and the best that relativity canclaim is that the mathematics derived fromEinstein's postulates are equivalent to that ofLorentz's. - An objective way to find the general opin-ion of physicists about the subject is, to read about itfrom several authors.

Here are a few informative quotes :a) Silvio Bergia, Einstein Cent. - 1979, [86]

"A really experimental decision between the theoryof Lorentz and the theory of relativity is indeed notto be gained; and that the former, in spite of this, hasreceded into the background, is chiefly due to thefact that, close as it comes to the Theory of Relativity,it still lacks the great simple universal principle, thepossession of which lends the Theory of Relativityfrom the start an imposing appearance." The differ-ence in the two theories is that: "for Lorentz they are

equations of transformations which make the equa-tions of the electromagnetic theory covariant, forEinstein, expressions of the general properties ofspace and time."

b) Lincoln Barnett, Dr. Einstein..., 1957, [51] "Einstein concluded that a new transformation rule

must be found to enable the scientist to describe therelations between moving systems in such a waythat the results satisfy the known facts about light."(Michelson's null-result)."Einstein found what he wanted in a series of equa-

tions developed by the great dutch physicist, H.A.Lorentz, in connection with a specific theory of hisown. Although its original application is of interestnow chiefly to scientific historians, the Lorentztransformation lives on as part of the mathematicalframework of relativity."

c) Lincoln Barnett, Dr. Einstein..., 1957, ,[129] "From his two postulates Einstein deduced a num-

ber of surprising results. The most basic one is a newset of transformation equations which allow us towrite down what an observer sees when he looks atanother moving coordinate system and 'vice versa'.These equations are known as the Lorentz Transfor-

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Aethro-kinematics FOREWORD Postulates versus Common Sense

mation, because it was Lorentz who first found thatthey could explain how it was that the speed of lightwas constant, though he still clung to the idea of the'ether'. Einstein did away with the ether andobtained the same transformation in a much simplerand more basic manner."

d) Bertrand Russell, ABC of Relativity, 1969, [52] "Indeed one of the main motives of this whole theo-

ry (special relativity) is to secure that the velocity oflight shall be the same for all observers, howeverthey may be moving. This fact, established by experi-ment (Michelson-Morley), was incompatible with theold theories, and made absolutely necessary to admitsomething startling."The quantitative laws of electromagnetic phenom-

ena are expressed in Maxwell's equations and theseequations are found to be true for any observer, how-ever he may be moving. It is a straight forwardmathematical problem to find out what differencesthere must be between the measures applied by oneobserver and the measures applied by another, if inspite of their relative motion, there are to find thesame equations verified. The answer is contained inthe Lorentz transformation, found as a formula by

Lorentz, but interpreted and made intelligible byEinstein."

e) Taylor, The New Physics, 1972, [88] "Lorentz who put forward relations between the

distances and the times as observed by persons mov-ing relatively to each other, still believed in the exis-tence of the ether. Even fifteen years later Lorentzstill attached some value to the idea of absolutespace."The lengths of moving objects, which appear short-

ened according to special relativity is identical to thecontraction of lengths that was suggested by Lorentzand Fitzgerald to explain the null result of theexperiment of Michelson and Morley. The agreementbetween this earlier suggestion and the results ofEinstein's Special Theory of Relativity is certainly tobe expected, since they both concern the fact that thevelocity of light is independent of how it is mea-sured.

“However, we must remember that Einstein tookthis result as a postulate and deduced that objectswould appear to contract on moving, while Lorentztook the contraction as basic and tried to explain theconstancy of the velocity of light."

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f) Atkins, Physics, 1976, [464] "A most ingenious suggestion to explain the Mich-

elson-Morley experiment was made by Fitzgeraldand elaborated by Lorentz. They suggested that,when a body moves through the ether, its length iscontracted in the direction of motion."The atoms of a body are held together by electro-

magnetic forces. If the ether is the medium throughwhich these forces are transmitted, motion throughether might modify the forces in such a way as tomake the atoms move closer together in the directionof motion.“However this possibility was excluded by an exper-

iment performed by Kennedy and Thorndike, whichwas designed to counteract the predicted contrac-tion, and still produced a null result. A possible mis-understanding of the significance of the Kennedy-Thorndike experiment should be avoided.

The point to be made is that the Theory of Rela-tivity predicts the Fitzgerald-Lorentz contractionplus other effects (slowing clocks), whereas theKennedy experiment proves that the Fitzgerald-Lorentz contraction alone is not adequate.

(To avoid the faulty impression, that Lorentz'stheory was disproved before relativity was accepted,it should be noted that the Kennedy experiment wasexecuted only decades later, in 1932.)"Lorentz solved the mathematical problem of how

the laws of electromagnetism could be made the samein all inertial frames, but it was Einstein who firstfully understood the physical significance of theprinciple and who worked out its startling conse-quences."

Our point is, that if more than one philosophicalinterpretation can fit the same mathematical model,then the experimental verification, as such, cannotsingle out one of the several interpretations as apreference over the others.

The very basis of the model; the so-called Fitz-gerald Ratio was constructed to fit the null-result ofthe Michelson-Morley experiment in general. It is aratio between the velocity of light and the velocity ofthe observer which serves as a scale for the propor-tional difference between what is expected by theclassical transformation and what is actually mea-sured as the speed of light in the experiments. Thesquare root one in the formula is merely an operator

100


which guarantees that while the velocity of theobserver is small, the difference is unmeasurable,but as it approaches the velocity of light, the result-ing difference approaches infinity. Fitzgerald usedhis formula as a factor of contraction of the measur-ing device in motion, to explain why there is a null-result instead of what was expected by the classicaladdition of velocities.

This mathematical model can be further strip-ped from the concepts of the velocity of light andobserver, and just plainly described as a formulawhich assures that when quantity x increased to thequantity of y, the resulting proportion z increasesfrom zero to infinity. This is the essential mathemati-cal model that was filled with the different conceptu-al contents; the Fitgerald's Contraction, Lorentz'selectromagnetic theory, and Einstein's apparent con-traction of rulers and slowing down of clocks. As longas any theory based on this formula merely searchesfor the expected but undiscoverable difference in themeasurements of the speed of light, they are all logi-cally consistent with the Lorentz Transformation.

Evidently, as for the experimental verification,nothing else has been proven but the validity of the

Fitzgerald ratio itself, which of course is totallymeaningless, since it was constructed to agree withthe experimental facts. Hence the experimental veri-fication of the mathematical model represents nohelp whatsoever in the decision about the validity ofany one of the existing theories or any others thatcan still be invented. Professor Burke is indeed verywrong to dismiss all arguments about the inconsis-tencies of The Special Theory of Relativity, basedmerely on the experimental verification of the math-ematical model.

Nevertheless, an argument about the inconsis-tencies in the Special Theory would surely be futile,since discarding common-sense, Relativity left nopossibility for logical disapproval.

The goal of this study is to introduce an alter-nate conceptual content for the same experimentallyverified mathematical model. An attempt to uncoverthe physical meaning of the Lorentz Transfor-mation, its relation to the other departments ofPhysics and to explain the classically unpredictableMichelson Null Result.

In the course of what follows, the Special Rela-tivity, as a conceptual solution of the problem will

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prove to be superfluous, in as much as, through theview here to be developed, the modern principle ofrelativity will neither be required for explaining theMichelson Null Result nor for the sake of unifyingTheoretical Physics. Admittedly, there are some wellaccepted theories of certain phenomena, which sup-port the relativistic conviction, that the only way outof the dilemma is through Einstein's postulates.Naturally, these theories will be in direct contradic-tion to any alternate scenario. In order to createsome hesitation, in taking them as the indisputabletruth, consider the following excerpts from the antol-ogy; ‘The Origin of the Solar System’:

“THE CREATION MYTHS Speculation about the origin of the Earth and the

celestial bodies is probably as old as human think-ing. During the millennia which is covered by thehistory of science, philosophy and religion we candistinguish three types of approach to this problem."The first one is the theocratic-myth approach,

according to which the evolution of the world wasgoverned by gods, who created it by bringing orderinto a pre-existing chaos. The world was ungenerat-ed and indestructible - as Aristotle puts it - and the

gods were part of this world and also eternal. Therise of the monotheistic religions changed this view.When one of the gods got higher status than others,he continued to increase in prestige and power untilhe became the Supreme Lord, the undisputed rulerof the whole world. Then it was not enough that hecreated the world in the sense of organizing a pre-existing chaos, he had created it all from nothing ('exnihilio') by his will power.

“THE MATHEMATICAL MYTHS "With the rise of philosophy and early science, the

gods became less despotic and increasingly philo-sophically and scientifically minded. The creation ofthe world and its evolution were parts of a masterplan, and it was not unreasonable anymore that manshould be able to understand this plan. The break-through in this thinking came with the Pythagoreanphilosophy."The Pythagoreans had discovered how beautiful

and powerful mathematics was. They had found thatmusical harmonies could be explained as ratiosbetween integers, and they demonstrated that therewere five, and only five regular polyhedra.

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Aethro-kinematics FOREWORD The Creation Myths - The Mathematical Myths

"With such achievements it was quite natural thatthe Pythagoreans applied the same method to themacroscopic structure of the world. They tried toexplain this in terms of simple numerical relationsand in terms of logically and mathematically beauti-ful concepts - just like musical harmonies and geo-metrical figures."It was the task of philosophers and scientists to

find what this cosmological mathematical principlewas. They believed, they needed only one formula inorder to understand the whole world. This approachmay be called the mathematical myth, developedduring the centuries into the Ptolemaic cosmology,which is impressive by its logical reasoning andmathematical beauty."However a comparison between this cosmology

and observation led to a number of discrepanciesand it was necessary to introduce a series of epicy-cles etc. which made the system increasingly compli-cated."

EMPIRICAL APPROACH "In the sixteenth and seventeenth century the

Ptolemaic system broke down, and a new celestialmechanics was introduced. This represents the third

type of approach, the empirical approach. This wasbased especially on the investigations of falling bod-ies by Galileo and the very accurate astronomicalobservations by Tycho Brahe. With this break-through the scientific age started. The old myths,both the theocratic myths and the mathematicalmyths are dead forever. We live in the scientific age,the age of reason. But is this really true ?"

THE COSMOLOGICAL FORMULA "What about the modern mathematical myths ?

Does the scientific community still subscribe to thePythagorean belief that the structure of the universecould be solved by one simple mathematical formula? I am afraid that the answer is yes."Eddington, no doubt one of the leading

astronomers of his time, claimed that the number137 contained the solution of the cosmological prob-lem. In his fascinating book The Philosophy ofPhysical Science, he claims that sitting in his arm-chair he had counted the number of protons in theuniverse and found it to be 1.57477x1079 or moreexactly 136x2256 = 15.747,724,136,275,002,5778,605,653,961,181,555,468,044,717,914,527,116,709,366,231,425,076,185,631, 031,296.

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Aethro-kinematics FOREWORD Empirical Approach - The Cosmological Formula

"Considered as a myth this is beautiful, but consid-ered as science, it is a nonsense, and is nowadaysgenerally recognized to be so. However, the collapseof Eddington's cosmology has not discredited themodern mathematical myths in general. On the con-trary it seems rather to have acted as a fertilizer fora rich flora of mathematical myths of which some nodoubt are attracted from an aesthetic point of viewbut none from a scientific point of view.

"One of them, the Big Bang cosmology (based onthe Theory of the Expanding Universe) is at presentgenerally accepted by the scientific community. Theobservational support for it, which he and othersclaimed, is totally obliterated, but the less there is ofscientific support, the more fanatical is the belief init. This cosmology is utterly absurd - it claims thatthe whole universe was created at a certain instantas an exploding atomic bomb much smaller than thehead of a pin. It seems that in the present intellectu-al climate it is a great asset of the Big Bang cosmolo-gy that it offends common sense: credo quia absur-dum... (I believe, because it is impossible!)".

The above quote originates from one of the mostreputable anthologies on this subject, 'The Origin of

the Solar System' edited by S.F. Dermott, first pub-lished in 1976. The anthology contains the works ofseveral eminent cosmologists and astrophysicistswho had attended the meeting on the subject, spon-sored by the NATO Advanced Study Institutes of theSchool of Physics. The specific article, that is quotedwas written by H. Alfven, Department of AppliedPhysics and Information Science, University ofCalifornia at San Diego.

The contents and atmosphere of these remarkssurely relieve one from the obligation to disprove thepresently accepted cosmological theories beforeintroducing an alternative description of the phe-nomena. What remains is the common sense require-ment and ultimate goal of Natural Sciences andPhilosophy: Obtaining an unified and universal theo-ry of the micro- and macro-cosmos, based on theleast number of fundamental assumptions, and bothconceptually and mathematically capable of explain-ing and predicting the experimental results of thewidest variety of natural phenomena.

Nothing less is the ultimate goal of the writingswhich follow...

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Aethro-kinematics FOREWORD The Cosmological Formula

CHAPTER FIVE

UNIVERSAL ROTATION -UNIVERSAL GRAVITATION

Rotation plays a pervasive role in the Universeon both the small and the large scales. On the smallscale many of the fundamental particles, in particu-lar electrons, protons and neutrons are found to bespinning like tops. Moreover the angular momentumof this spin is not arbitrary, but has a fixed valuerelated to the fundamental constant of quantummechanics, Planck's constant h.

An electron, a proton or a neutron always spinwith precisely one-half a unit of angular momentum.Other particles such as the particle of light, the pho-

ton, spin with exactly one whole unit of angularmomentum. When an electron is inside an atom, itrevolves around the nucleus and in addition to itsintrinsic spin of one half a unit, its orbital motion hasan angular momentum which is always an exactintegral number of basic units. When atoms cometogether to form a molecule, the molecule as a wholerotates with an angular momentum which is againan exact integral number of basic units. On an astro-nomical scale the Earth is well known to be rotatingabout its north-south axis once a day, producing avelocity at the equator of about 900 mph. The Earthalso revolves around the sun with an orbital velocityof about 70,000 mph (30 km/sec).

The Sun itself is spinning at a rate which varieswith latitude on the Sun but corresponds to aboutone revolution per month. There is evidence thatmost stars are rotating in a similar way. Many starsjoin together in pairs with the two members of thepair rotating around one another.

Together with the Earth, nine planets, theirsatellites and some asteroid belts are revolvingaround the Sun and each body rotates on its axis inthe disk-shape formation, called the Solar System.

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Aethro-kinematics CHAPTER FIVE Universal Rotation - Universal Gravitation

Our Sun is a member of a group of some hundredbillion stars, called the Galaxy which is also a disk-shaped rotating system. Although it takes two hun-dred million years for the sun to complete a revolu-tion about the galactic center, this requires an enor-mous tangential velocity of about one half a millionmiles per hour (250 km/sec).

The observable universe contains billions of suchgroups of stars, and there is good evidence that theyare all in rotation. Observations reveals pairs ofgalaxies revolving about one another just like binarystars. There are also rotating clusters of galaxies, invarious sizes, from a few members up to thousands .One of these is the so-called 'local group', which con-tains 17 galaxies, including our own Milky Way. All ofthese show the signs of rotation. It is now knownthat the normal state of a galaxy is to belong to clus-ters of different sizes. − The next and last in theorder of magnitude within the observable universe isthe cluster of clusters, called 'super-cluster' which isa conglomerate of the clusters of galaxies. It is quitesafe to assume that these units are also in rotationaround their centers of mass. The orders of magni-tude in the above description of rotating units rang-

ing from the size of the electron, 0.0000000000001cm to the size of a super-cluster, millions of light-years in diameter, which if we would attempt towrite down in centimeters, the zeros after the firstdigit would fill up a whole book. Nevertheless thereis one common characteristics to all of them ; Eachrotating unit, regardless of its order of magnitude orthat of its constituents, sustains some kind of auton-omy with respect to the rest of the Universe. Theforces from the immense external space only actupon a whole unit and only in very special cases dothey effect the internal structure of one another.

If there is any epistemological validity in creatingcosmological and cosmogonical theories at this stageof human knowledge, than the totally universalnature of the phenomenon of rotating systems allthrough space and time should outweigh all othersingle phenomenon with regards to serving as a fun-damental assumption for such theories.

What has been described above, is not merely abunch of unrelated discoveries from different branch-es of natural sciences, but seems to show a funda-mental structural characteristic of the cosmos, whichshould be analyzed and treated as such.

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It seems to us that our own order of magnitude,the solar system, falls roughly midway between thesize of the elementary particles and that of the galac-tic superclusters. It is obviously not the first timewhen an optical or other anthropomorphic illusionhas placed us into the very center of the Universe.

Whether the Universe is taken as finite or infi-nite, our center-position obviously originates fromthe contemporary level of the observational technolo-gy, which gives us an even penetration in all direc-tions into the micro- and the macro-cosmos. There isthan, the possibility for an infinite chain of smallerrotating units that make up the smallest we canobserve, and the largest known units could be merelythe constituents of the units of higher and higherorder of magnitudes.

Since we know neither the internal structure ofthe electron, nor the hyperstructure that could existbeyond the superclusters, the possibility is not at allabsurd that the rotating unit of a certain higherorder of magnitude forms the internal structure of asuper-electron, or that our electron's internal struc-ture consists of galactic super-clusters of a lowerorder of magnitude.

Hence, the old inconceivable phrase, infinity, ishere again; not only for space and time, but as theorders of magnitude structure of the Cosmos itself.

Nevertheless, no matter where we draw the bor-der in this infinite chain, within that border, we arefacing an autonomous Rotating Universe. The mag-nitude of this specific territory is quite indifferent Itcan be assumed that either our laws of physics andastronomy are not affected by the external forces ofthe higher or lower orders of magnitude, or that theyare all the same as we have established them in ourlimited but autonomous Rotating Universe.

In general, it can hardly be accepted that theserepetitious formations of individual rotating systemswere formed entirely on their own, and by pure acci-dent. More likely, either smaller units have theinherent tendency to conglomerate into a higherorder, or the internal mechanism of the larger onesbore the chance to form the smaller units. It couldalso be the inert character of matter, that createsrotating systems, or, the other way around, the uni-versal mechanism of rotation is responsible for thecreation of matter. Whichever is the case, one conclu-sion can surely be drawn from this universal phe-

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nomenon: The very plausible correlation between themicro- and macro-cosmic units suggests that no theo-ry about the Laws of Nature can be complete withoutdescribing the origin and maintenance of this univer-sal phenomenon and the method of its propagationthroughout the cosmos.

MECHANISTIC ASTRONOMYWhat do we know about the origin, the mecha-

nism, or the possible correlation between these rotat-ing systems? In general, human speculations aboutrotating system are as old as philosophy itself.

Around the year of 400 B.C., 2400 years ago, thegreek Exodus of Cnidus proposed a system of astron-omy, representing the motions of the celestial bodiesby a combination of rotating spheres. By giving eachsphere an appropriate rate of rotation and just theproper inclination of axis, he was able to reproduceapproximately the complicated motions of the Sunand the planets as they revolved around the Earth.

About 140 A.D. Claudius Ptolemy worked out ageometrical representation of the solar system, thatpredicted the motions of the planets with consider-able accuracy. He, of course, also believed in a

Geocentric Universe and it is a tribute to his geniusas a mathematician, that he was able to conceive asystem to successfully account for the observationalfacts. Ptolemy's immensely complicated hypothesis,describing how everything rotates around the Earth,was accepted as absolute authority throughout themiddle ages.

Next, Nicolas Copernicus in the fifteenth centuryintroduced his much simpler theory of theHeliocentric Universe.

This approach did not prove that the Earth wasmoving around the sun, but showed that the hypoth-esis of a moving Earth involved fewer ad hocassumptions than the system with an orbiting Sun.Copernicus also placed the six (known) planets intheir right positions in the solar system, puttingMercury nearest to, and Saturn farthest from theSun. He also deduced the fact, that the nearer aplanet to the Sun, the greater its orbital velocity.

The next great achievement in the investigationof the rotating Solar-system came through JohannesKepler's Three Laws of Planetary Motion.

Living in the sixteenth century, Kepler's charac-ter was a mixture of a dark age mystic, and an incor-

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Aethro-kinematics CHAPTER FIVE Mechanistic Astronomy

ruptible modern scientist. His tireless effort in dis-covering the most basic rules of planetary motionsand his theories about the mechanistic nature of thesolar system makes his work the turning point in thehistory of natural philosophy from the Aristotelianschool, toward modern science.

Not having, however, Galileo's clear concept ofinertia, Kepler had not succeeded in ridding himselfof the erroneous idea of Aristotle that even uniformmotion requires the action of a constant force.

According to the concepts already known byKepler from the theories of Grosseteste and Baconabout light-transmitting immaterial species, heassumed that the rotation of the sun imparts arotary motion to these species and they represent theforce that carries the planets along their orbits.

Under the influence of William Gilbert's workabout magnets, Kepler outlined a magnetic theoryfor the celestial systems, where he assumes that allheavenly bodies are like magnets attract each otherthrough their magnetic filaments which are concen-trated in circles along the plane of the ecliptic.

These ideas already contained the seeds of bothDescartes' Aether-vortex theory and Newton's funda-

mental idea of universal gravitation. Nevertheless,Kepler's most important contribution to the investi-gation of rotating systems came from the mysticalside of his character. The religious faith in a divineharmony of Nature, expressible by mathematics,drove him on a tireless search for some kind of heav-enly system, to be found in the motions of the Sun,planets and satellites. Through the examination ofan immense amount of observational data and by themethod of pure trial and error, he finally found thethree simplest and most universal laws for the rota-tion of the Solar-system.

I. THE LAW OF ORBITS: All planets move inelliptical orbits having the sun as one focus.

II. THE LAW OF AREAS: A line joining any plan-et to the sun sweeps out equal areas in equal times.

III. THE LAW OF PERIODS: The square of thePeriod of revolution of any planet about the sun isproportional to the cube of the planet's mean dis-tance from the sun.

Evidently these laws were purely empirical, theysimply described the observed similarities in themotions of the planets. Kepler himself neither couldconnect these mathematical discoveries with his

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mechanical ideas nor could he derive them fromother known laws of astronomy or physics."Kepler's teaching provided the chief inspiration of

Renee Descartes, French philosopher. His philosophyimplied that bodies can act on each other only whenthey are contiguous; in other words, he denied actionat a distance. This had the further consequence thatif there is a force acting between the earth and moon,or between any bodies in space, then space could notbe void. It is occupied partly by ordinary materialthings - air and tangible bodies; but the intersticesbetween the particles and the whole of the rest ofspace, must be filled by particles of a much more sub-tle kind, which everywhere press upon or collidewith, each other: they are the contrivance introducedin order to account for physical happenings."Space is, thus in Descartes' view a plenum, being

occupied by a medium which,though imperceptible tothe senses, is capable of transmitting force, andexerting effects on material bodies immersed in it, -the Aether, as he called." (Sir Edmund Whittaker,Aether and Electricity, [5])

Descartes' theory about the rotation of the solarsystem was also based on Aether. In his interpreta-

tion, a giant mechanical vortex formed in this medi-um around the sun, which caught and carried theplanets with it, thus initiating a coherent rotatingsystem with general dynamical laws of vortexmotion, which governs all of the revolving units.Similarly, planets create their own subvortices, whichcarried their satellites.

Descartes was the founder of the strictly mechan-ical view of the Universe. His philosophy accepts noother explanatory principles for natural phenomena,but matter and motion. It followed from this princi-ple that there can be no transfer of motion or forcebetween material bodies, except through actual con-tact in bodily collision.

The mechanistic science of the seventeenth cen-tury reached its culmination in the work of ChristianHuygens as described by the quotes below from E.J.Dijksterhuis, The Mechanization of the WorldPicture, [462]):

"Like Gassend and Descartes, he thinks, that in thephysical world, motion can only be caused by motionand can only produce motion in turn. He resolutelyrejects all thoughts of qualities or forces that may beimmanent in matter, capable to cause action at a dis-

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tance; gravity calls for a mechanistic explanation justas much as sound, heat, light, magnetism, and elec-tricity, and he considers it his task to furnish thisexplanation." "Huygens was the first to propose a geometrically

and mathematically detailed wave-theory of light,based on the mechanical properties of theLuminiferous Aether."The idea that light is the vibration of a mechanical

medium served later as the conceptual foundation ofFaraday's and Maxwell's work, which led to the com-plete theory of electromagnetism. Huygens initiatedthe method of investigation of the phenomena oflight-waves, magnetism and electricity throughmechanical and hydrodynamic analogies. He alsoproposed a mechanical theory for gravitation."The explanation which Huygens gives for gravity

is based on the idea introduced by Descartes' Aether-vortex, whirling around the earth. If among theserapidly moving particles of subtle fluid matter thereare some coarser particles, which cannot follow theirmotion, the stronger centrifugal tendency of the for-mer will propel them towards the centre of the earth.Huygens illustrated his theory by means of the fol-

lowing experiment: On a revolving table he placed acylindrical vessel filled with water and in it smallfragments of sealing wax, whose specific gravity wasslightly greater than that of water. When the tablewas set rotating, these fragments moved to the sidesof the vessel. When the water had attained the sameangular velocity as the table, the latter was broughtto a standstill."It is now found that the bits of wax collect near the

centre. As the water carries the bits of wax along,they move in spiral paths toward the axis, but whenthey are prevented by horizontally stretched threadsfrom being carried along, a bit of wax confinedbetween such threads moves radially towards theaxis."

Thus, Huygens was already aware of Galileo'sconcept of inertia, but in connection to rotation, hecalled it centrifugal force. His next step was to find,what kind of centripetal force is needed to overcomethe inertial tendency of the bodies to fly off tangen-tially from the rotating system of the vortex.

Taking the earthly example of a stone whirlingon a string, Huygens showed through simple geome-try that the centripetal acceleration of a body is

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directly proportional to the square of its tangentialvelocity and inversely proportional to the radius ofthe circle on which it is moving. But not having aclear idea of mass and force, he could not incorporatethis result with his mechanical theory of gravitation.

Gassend, Leibnitz, Descartes, Huygens and oth-ers of that era contributed a great deal of clarity tonatural philosophy and mathematics, but the princi-ple that force cannot be communicated except bypressure or impact compelled them to provide anexplicit mechanism for each of the known forces ofNature.

This task was evidently impossible for that eraand still, even presently, it is much more difficultthan the principal willingness to admit action at adistance as an ultimate property of matter or replac-ing the concept of force with the extraordinary prop-erties of empty space.

Whittaker remarks in a footnote of 'Aether andElectricity [9] :

"It is curious to speculate on the impression whichwould have been produced had the spectacular spiralgalaxies been discovered, before the overthrow ofDescartes' vortex-theory of the Solar-system."

Nevertheless within a few decades, Isaac New-ton appeared on the philosophical scene and simplycut the conceptual Gordian Knot by altogether disre-garding the restrictions of mechanicism and pre-senting a purely mathematical theory of earthly andcelestial 'mechanics'.

In his Three Laws of Motion Newton re-definedand finalized Galileo's concept of inertia correlatingit with the concept of force and acceleration, clarifiedtheir conceptual relations and established the math-ematical proportionalities among them. He postu-lates the fundamental assumption, that all materialbodies exert an attractive force on one another andwith the aids of Huygens' equation of centripetalacceleration and Kepler's laws of planetary motion,formulates the Law of Universal Gravitation.

Newton laid the foundations of classical physicsand astronomy by rendering the complete theories ofterrestrial and celestial mechanics, but before,proposing his own theory of Universal Gravitation,he refuted the Kepler-Descartes-Huygens Solar-vor-tex theory, based on the following argument:"The hypothesis of vortices is pressed with many

difficulties. That every planet by a radius drawn to112


the sun may describe areas proportional to the timesof description, the periodic times of the several partsof the vortices should observe the square of their dis-tances from the sun; but that the periodic times ofthe planets may obtain the 3/2th power of their dis-tances from the sun, the periodic times of the parts ofthe vortex ought to be as the 3/2th power of their dis-tances."That the smaller vortices may maintain their less-

er revolutions about Saturn, Jupiter, and other plan-ets, and swim quietly and undisturbed in the greatervortex of the sun, the periodic times of the parts ofthe sun's vortex should be equal; but the rotation ofthe sun and the planets about their axes, whichought to correspond with the motions of their vor-tices, recede far from all these proportion."The motions of the comets are exceedingly regular,

are governed by the same laws with the motions ofthe planets, and can by no means be accounted for bythe hypothesis of vortices.""...Still it was significant that Newton himself dur-

ing his long life looked for such a mechanical expla-nation and tried to construct a model of an Aetherwhose density gradients could explain gravitation as

well as certain optical phenomena."(Sambursky :Physical Thoughts., Anthology, [305-17])

Obviously, Descartes' Solar-vortex hypothesis wasfar from being a scientific theory by modern stan-dards. The theory was neither based on strict obser-vational facts nor was it derived from some otheralready established laws of physics. However, fromthe standpoint of searching for the origin and mecha-nism of rotation, Descartes approached the phenome-na of planetary motions as the problems of a rotatingsystem, with a potentially coherent mechanicalstructure. From the same point of view, it is animportant question, what alternative was offered byNewton's Theory of Gravitation to replace the cen-tral, mechanical role of the Solar-vortex?"Newton claimed nothing more for his discovery

than that it provided the necessary instrument formathematical prediction and he pointed out that itdid not touch on the question of the mechanism ofgravity. However he still felt obligated to make thestatement:'...To suppose that one body may act upon another

at a distance through vacuum, without the mediationof anything else...is to me so great an absurdity, that

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I believe no man, who has in philosophical matters acompetent faculty for thinking can ever fall into'..."(Sir E. Whittaker ; Aether and Electricity, 1962 [68])

THE TANGENTIAL COMPONENT It was originally Galileo's discovery, that the tra-

jectory of a falling body can be separated into two ormore entirely independent components of motion,caused by separate and independent forces.

Figure 5-1(a) illustrates this idea by the trajecto-ry of two balls, dropped from the same height. Onestarts from rest, the other has an initial horizontalvelocity. The two balls reach the ground in differentplaces but at the same time, which shows that thehorizontal and vertical components of motion aretotally independent from one another. The same isvalid for the forces that create the trajectory.

The force of gravity produces exactly the samevertical acceleration on both balls, regardless of theirdifferent initial horizontal motion. Similarly, the hor-izontal velocity would take the ball exactly to thesame distance during the same time, regardlesswhether the ball is falling under the influence ofgravity or rolling freely on a horizontal plane.

(a) Figure 5-1. (b)

Figure 5-1.(b) is Newton's original illustration,extending the same idea to the flight of a cannonball.It explains how the increase of the initial horizontalcomponent of motion can create a longer and longertrajectory for the cannonball.

Finally, it illustrates, that by the further increaseof the force, producing sufficiently great horizontalmomentum, the cannon ball can be sent into a per-manent orbit around the Earth.

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Aethro-kinematics CHAPTER FIVE The Tangential Component

X

Y

v

g

a

b

c

vb vc

va

The ball will continually fall toward the center ofthe earth because of the radial force of gravity, but itwould never reach the ground, because of the hori-zontal, or tangential component of its momentumproduced by the force of the gun-powder.

Newton wondered whether the force of attrac-tion of the earth on the objects near its surface mightextend as far as to the moon and produce the cen-tripetal acceleration required to keep the moon in itsorbit around the Earth.

This hypothesis was proven by the inversesquare law of gravitation, which predicts the neces-sary centripetal acceleration and right magnitude ofthe radial component of motion for the moon to stayin orbit about the earth.

But how about the very tangential components inall these cases? They are not without significance.

Take the case of an apple, dropped from the topof a two story building. During the first second itfalls radially toward the center of the earth 9.8meters. The same time the ground of the rotatingearth moves some 400 meters in west-east direction.Hence, in order to hit the ground radially under thepoint of release, the apple must have a tangential

component, 40 times greater than its gravitational,radial fall. For the apple the origin of the tangentialcomponent is naturally contemplated by terrestrialmechanics. Even before release, the apple wasalready rotating with the earth surface and sharedits 400 meter/sec tangential velocity.

The cannonball had the same initial velocity asthe apple, plus in order to maintain an orbit over thesurface of the earth, it needed an additional tangen-tial velocity of 8000 meter/sec

The moon is a different case altogether. Neitheris there an acceptable theory to explain why themoon should share the angular momentum of theearth, like the apple or the cannon ball, nor is thereany imaginable parallel for the force of the gunpow-der. Nevertheless, the radial component of the moon'sorbit is merely a fraction of a centimeter, while thetangential component is more than a kilometer/sec,100,000 times greater. The same goes for the planets,greater the orbit greater difference between the twocomponents. Where is the tangential componentcoming from?

Newton himself in his 'Principia' gave a negativeanswer to this question;

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"...above the Earth's atmosphere all bodies willmove with the greatest freedom; and planets andcomets will constantly pursue their revolutions inorbits already given in kind and position, accordingto the laws above explained; but though these bodiesmay, indeed continue in their orbits by the mere lawsof gravity, yet they could by no means have at firstderived the regular positions of the orbits them-selves, from those laws."

This problem has never been seriously reopenedor discussed by Newton's followers. Astronomy soonbecame the testing ground of the mathematical theo-ry and immense amounts of experiments have beenexecuted, proving beyond any doubt, the validity ofthe Law of Universal Gravitation.

In the turmoil of this amazing success, there wasno time or reason to ponder about the origin of thetangential component of planetary motion or evenabout the general mystery of the gravitational force.

Newton's fundamental assumption of mutualattraction took care of the origin of the radial compo-nent and if it was needed, the tangential velocities ofthe planets or satellites could easily be obtained byactual measurement or by Kepler's Third Law, with-

out the necessity of investigating their origin. Even-tually, scientists learned not to ask questions aboutthe perplexing concepts of the 'action at a distance'and not to wonder about other conceptual problems ifthey were not essential for the mathematical predic-tion of the phenomena.

Einstein's Theory of General Relativity alsoleaves this subject untouched. Replacing the actionat a distance force of gravity, relativity introduces theconcept of a special gravitational field in which masseffects the geometry of space around it.

In the case of the Solar system the mass of thesun causes the curvatures in space, which in turn,bend the initial, straight line motion of the planetsinto circular or elliptical orbits. Again, no cluesabout the question as to why the planets are moving,in the first place, and where the perfect tangentialvelocities are coming from to suit the distances andcurvatures so well ?! This complete lack of inquiryabout the origin of the tangential momentum of theplanets, suggests that in general, the presently exist-ing theories of gravitation can have no part in theinvestigation of the origin or the possible mechanismof the rotating systems.

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The problem, however, cannot be settled by neg-lecting it, since in general, wherever there is gravita-tion, there is also rotation and vice versa. These twoseemingly very independent, universal phenomenastubbornly refuse to separate.

Consider the following, quote: (Owen Gingerich,Introduction, Cosmology+1, 1977) "Given the concept of Universal Gravitation, the

obvious question was; Why didn't all the stars drawthemselves together into one grand fiery ball? Thesolution to this puzzle proved so elusive that cosmol-ogy simply went into hibernation for two centuries."Today, the idea of gravitational attraction leading

to gravitational collapse plays a key role in ourunderstanding of many astronomical phenomena.The sun, for example, was once an extended, rotatinggaseous sphere as large as the present solar system.Warming as it shrank, it finally achieved sufficientlyhigh temperatures, and rotational momentum, whichhave temporarily balanced the powerful gravitation-al pull."Our Milky Way galaxy, too, shows signs of gravita-

tional collapse. Initially its mass was spreadthroughout a giant sphere. Most of the original gas,

dust,and stars has now been pulled into a rotatingpinwheel about 100,000 light-years across."As in the formation of the solar system, rotational

momentum prevented the stars from falling directlyinto the center of the galaxy. That is the only knownreason why the stars remain distributed in a greatflat plane rather than in a small central conglomera-tion. But what about the universe as a whole? Will itnot also collapse under the inexorable gravitationaltug? Newton's question has been revived to becomethe leading problem of cosmology today."

The obvious answer to this last cosmologicalquestion should be the same as it is already acceptedfor the solar system or the galaxies. The mere factthat the universe is spread throughout space, insteadof existing in a fiery ball, calls for the only observedand known solution: rotational momentum, or ratherthe tangential component of the momentum keepsthe Universe from its gravitational collapse.

The acceptance of this alternative, however,would give the central role in cosmology to universalrotation, whose origin and mechanism lies complete-ly out of the scope of the major gravitational theories.Hence, modern cosmology rather turns toward the

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mystical and adventurous Expanding Universe ideaand to the all-exciting Big Bang Theory, where uni-versal gravitation is not confused by universal rota-tion. Indeed, even in cases like the origin of the solarsystem or that of the galaxies, where Cosmology can-not neglect the phenomenon of rotation, the specula-tion simply starts from already rotating gas clouds.

Even so, Cosmology still runs into one of its mostperplexing problems; Somehow, all heavenly bodies,satellites, planets, stars and Galaxies position them-selves exactly on Keplerian orbits around the centerof their system and mysteriously all of them movewith the right tangential velocities, at the right dis-tances. How and why?

Should one then simply acquiesce to the possibili-ty that the origin of these rotating systems is purecoincidence; the result of some kind of a hit or miss,capturing procedure? That at one time, satellites,planets and stars were moving in totally randomchaos, and through some cosmic natural selection,eventually most of them, were captured by a greatermass when they happened to hit the right orbit withthe right speed from the right direction?! Not really."It is interesting to note that if two objects app-

roach each other from a distance in space, they cannever capture each other into circular or ellipticalorbits. Their mutual attraction will speed them up sothat they pass each other with a relative speedgreater than their mutual velocity of escape, andthey will swing away from each other again." (GeorgeAbell: Exploration of the Universe, [61])

The first step toward clarifying this situation isto find the point in the development of the Theory ofUniversal Gravitation, where it lost sight of the fact,that the sun and its planets are a system and not anaccidental gathering of heavenly bodies.

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CHAPTER SIX

CELESTIAL MECHANICS

CONCEPTS AND MATHEMATICS In its final form the Law of Universal Gravitation

states that the force between any two particles havingmasses m1 and m2 separated by a distance R is a mutu-al attraction acting along the line joining the particles.The magnitude of this force F, is directly proportionalto the product of the masses and inversely proportionalto the square of the distance between them.

m1 m2F = G −−−−−−−−− (6.1),

R2

where G is the Gravitational Constant, whose valuedepends on the units of mass, distance, and force used,and has to be determined by laboratory measurementsof the attractive force between two material bodies ofknown masses.

It has been established, that if metric units areused, G has the numerical value 6.67 x 10-8 =0.0000000667 gr × cm/sec/sec. Once this value is estab-lished, it can be used to determine the gravitationalforces between any pair of particles.

This simple equation expresses the whole concept ofNewton's Theory of Universal Gravitation and due tothe ratio between force and distance, it is commonlycalled, The Inverse Square Law.

Most contemporary physics or astronomy studiesemphasize the conceptual triumph and a mathematicalapproval of the Theory of Universal Gravitation forderiving Kepler's mystical and purely empirical lawsfrom its fundamental assumptions. Since Kepler'slaws clearly reflect the observational facts, their mathe-matical derivation is equivalent to observationalapproval. It is also suggested by these texts, thatKepler's mystical approach finally gained conceptualunderstanding in its Newtonian interpretation.

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Aethro-kinematics Concepts and Mathematics

Nevertheless, such description of the situation, nei-ther complies with the historical facts, nor with the logi-cal sequence of deductions, that lead to the final form ofNewton's fundamental equation.

As Fred Hoyle, one of the inventors of the famousSteady State Universe of modern cosmology remarks inhis book,The Frontiers of Astronomy [27]:

"Usually in astronomical texts, the inverse squareform of the law of gravitational force is stated as anaxiom. Then reversing the original procedure, Kepler'sthird law is deduced from it. This, however, is not theway the pioneers of astronomy proceeded. In fact it hashappened exactly the other way around. They startedwith Kepler's laws of planetary motions and derived theinformation for the gravitational force from that."

As it will be seen, the clarification of this fallacy isquite significant for the investigations of the origin andmechanism of rotating systems. It is not a matter ofwho gets the credit for being more fundamental, butsomething much more important. The problem with thepresent approach is, that once the mystery of Kepler'sLaws were explained away by Newton's more funda-mental theory, they were placed on the shelves of thehistorical archives of knowledge as a closed file, which

very likely, never will be opened up again for furtherdiscussion.

However, if Hoyle's statement was true, thenKepler's Laws were the more fundamental statementsand, although they are still mysterious, potentiallythose laws could be the ones that contain more funda-mental information about the origin and mechanism ofthe solar system, or even for those of universal rotationin general.

In order to evaluate Hoyle's statement, consider thefollowing chronological description of the derivation ofthe fundamental concepts and mathematics of theTheory of Universal Gravitation. The philosophicalstage has been set for Universal Gravitation in theknowledge accumulated through centuries, but themain ingredients for the derivation of Equation 6.1came from three major sources.

a) Kepler third law of planetary motion states thefact, that there is a definite and simple correlationbetween the orbital velocities and distances of all plan-ets in the Solar system.

The square of the period, P divided by the cube of theradius, r, is a constant for all planets.

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Aethro-kinematics CHAPTER SIX Concepts and Mathematics

P−−− = K or P 2 = Kr 3 (6.2),r 3

where K is a constant of proportionality whose valuedepends only on the units used to measure time anddistance. Once K has been found through one example(say, Earth's Period and its distance from the sun, oneknown quantity and K, it will render the other for anybody revolving in the solar-system.

If the Earth's distance from the sun is taken as theastronomical unit of length and its period of revolution,the year, as the astronomical unit of time, than Kequals to one, and therefore

P 2K = −−−−−− = 1 or P 2 = r 3 (6.3).

r 3

Measured in astronomical units, the square of theperiod for each orbiting body equals the cube of its dis-tance from the sun.

b) The conceptual foundation of Newton'sTerrestrial Mechanics originates from Galileo's funda-mental concept of inertia. In their final form, inNewton's 'Principia' inertia, force , mass, acceleration

and their mathematical relations are stated in theThree Laws of Motion.

I. Every body continues in its state of rest, or of uni-form motion in a straight line, unless it is compelled tochange that state by forces impressed upon it.

II. The change of motion is proportional to themotive force impressed, and is made in the same direc-tion of the right line in which the force is impressed.

Newton defines force, F as an agent, capable ofcausing acceleration, A, in face of the opposition of iner-tia, which occurs in the direction of the force, directlyproportional to the magnitude of the force and inverselyproportional to the amount of the inertial mass, mi, themagnitude of the inertial resistance of the body:

F A = −−−−−−, or F = mi A (6.4).

mi

III. To every action there is always opposed an equalreaction; or , the mutual action of two bodies upon eachother are always equal and directed to contrary parts.

c) In connection with his mechanistic theory of grav-itation, Huygens was the first who attempted todescribe the centripetal force that must be exerted on aplanet in order to keep it on a circular orbit.

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Analyzing the earthly example of a stone, whirledaround on a string, he found that the measurable quan-tities in this case are the velocity of the stone and thelength of the string, which is the Radius of the circle.

In Huygens' work the concept of velocity, v alreadyrepresents both the speed and the direction of motion ofa body. All changes in the velocity of a body is calledacceleration, A.

(a) Figure 6-1. (b)If the string would break at any time, the stone

would fly off on a straight line, tangential to the cir-cle, in the direction DE. After a brief interval of time,however, by the force of the string, the stone was

kept on a circular path and it is now at a certain dis-tance along the arc of the circle at G, having a direc-tion of GH.

If this interval of time, ∆ t is considered to be veryshort then the arc can be taken as approximately equalto the length of the cord between D and G, Since dis-tance equals velocity times time, the length of the cordequals v∆t . Although the speed of the stone still equalsto v, its direction changed toward GH, thus the stonehas accelerated; for it did not continue to move alongthe direction DE, on a straight line.

When the acceleration is only a change in the direc-tion of the motion, it can be represented in a vector-dia-gram, as in Figure 6-1 (b). The initial velocity had amagnitude, v and a direction OA, the new velocity hasthe same magnitude, but its direction has changed toOB. The vector representing v has turned through anangle, α (alpha) at O.

Thus the magnitude of the directional accelerationis represented by the angle, α, or the direction andlength of the resultant vector AB. It can be seen thattriangle ODG (Fig.6.1a) and triangle OAB (Fig.6.1b)are exactly similar and the angle, α is the same in both.

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α

D

r

G

O

E

H

vt∆

v1

v2

v1

v2v∆

The acceleration of the stone is its change of velocity ∆vper second ∆t , therefore there is a simple proportionbetween ∆v/v (from triangle OAB) and v∆t/r (from tri-angle ODG).

∆v ∆v −−−−−− = −−−−−− (6.5a)

∆t v From this it follows, that the centripetal accelera-

tion can be expressed by v∆t v 2

Ac = −−−−−− = −−−−−− (6.5b)r r

Hence, Huygens concluded that the directionalacceleration of the stone or any other body on a circularpath is in direct proportion to the square of its tangen-tial velocity and in inverse proportion to its distancefrom the center. Beyond this geometric argument, how-ever, another factor also takes part in the experiment;the weight of the stone.

It is evident from everyday experience that a heav-ier object swung around, requires more strength to holdfrom flying off the circular path than a lighter one.Thus, Huygens further concluded that the magnitude ofthe central force needed to keep the stone in the circle

(the tension on the string) must also be directly propor-tional to the mass, m of the stone.Therefore

v 2FC = m −−−−−−− (6.5c).

r

In the case of the whirling stone, the centripetalforce, FC is directly proportional to the weight of thestone times the square of its velocity and inversely pro-portional to the radius of the circle.

It should be noted here, that Huygens' simple con-cept of weight became more sophisticated in Newton'sterrestrial mechanics. It is the a result of the mutualattraction between the earth and a body that producesweighing differences. The earth exerts the same forceon all bodies, but a larger stone weighs more than asmaller one because it exerts a proportionally greaterforce on the earth.

These were the basic historical ingredients, readyfor Newton to create his system of celestial mechanics.

Applying these laws and concepts to the motions ofthe celestial bodies, Newton arrived at the followingconclusions: According to the law of inertia, in theabsence of the action of external forces all material bod-

123


ies continue to move with uniform speed in a straightline. If the planets are moving on a circular orbit, theymust suffer a constant acceleration under the influenceof a constant force.

Since all planets revolve about the sun, it must bethe one that exerts a constant force on them.

Starting with Huygens' result, the following is atypical mathematical description of the development ofEquation 6.1. (Abell, Exploration of the Universe [55]).

mv 2FC = −−−−−−− (6.5d).

r

"Using the result of the last section, we find that thecentripetal force that the sun must exert upon a planetof mass mp moving with speed v in a circular orbit ofradius, r is

mpv 2" force = −−−−−−− (6.6).

r

" Now, the period, P of the planet, that is the timerequired for the planet to go completely around thesun, is the circumference of its orbit, 2Πr divided byits speed, or

2π rP = -------- (6.7a)

v

"Solving the above equation for v, we find

2prv = -------- (6.7b).

P

"On the other hand, from Kepler's third law, weknow that the square of the period of a planet is inproportion to the cube of its distance from the sun.Because the sun is observed to be almost at the cen-ter of the planet's orbit, that distance is very nearlythe radius of the orbit, r and we have

P 2 = Kr 3,

Combining the last two equations, we find

4π 2r 2 4π 2r 2 4π 2 1v2 = −−−−−−= −−−−−−= −−−− or v 2 ≈ −−− (6.7c),

P 2 Kr 3 Kr rwhere the symbol '≈' means 'proportional to'."If we substitute the above formula for v2 into the

one expressing the sun's centripetal force on the planet, we obtain

124


mpforce ≈ −−−−− (6.7d).

r 2

"The centripetal force exerted on the planet by thesun must therefore be in proportion to the planet'smass and in inverse proportion to the square of theplanet's distance from the sun."

Evidently, Hoyle's statement is clearly justified.The inverse square law of the centripetal force has

been derived from the equations of Huygens and Keplereven before Newton's mutual attraction of the gravita-tional force was introduced. In fact, it can be seen thateven the insertion of the mass of the planet is not neces-sary at this point, since the same result would bereached from merging only the equations of Huygensand Kepler.

Huygens' Equation 6.4b is based on the definition ofvelocity and acceleration and states in purely kinemati-cal terms, that any point moving on a circular path per-forms centripetal acceleration, which is directly propor-tional to the square of the velocity of the point andinversely proportional to the radius of the circle. Thisstatement is entirely independent from the dynamicconcept of mass.

Kepler's Third Law, Equation 6.3, brings into thederivation the characteristic period-distance relation,which exists in the solar system. This proportionalitybetween the tangential velocities of the planets andtheir distances from the sun is also entirely indepen-dent from the concept of mass.

Therefore, based on the two purely geometricalstatements of Huygens and Kepler, the centripetalacceleration of a point can be expressed without themass of the planet. Hence, the most general form of theinverse square law, is a mathematical statement aboutthe specific centripetal acceleration of all revolving bod-ies in the solar system, and regardless of their masses:

1AC ≈ −−−−−−− (6.7e ).

R 2

If the centripetal acceleration is physically pro-duced in face of the opposition of the inertial mass of abody, say that of a planet, then the concept of inertialmass and the concept of centripetal force should enterinto the equation.

Only at this stage of the derivation, aside from thealready established geometrical inverse square relationof Equation 6.7e, the centripetal force must also be

125


directly proportional to the magnitude of the mass ofthe planet,

Mpforce ≈ −−−−−− (6.8a).

r 2

From here on the derivation can introduceNewton's dynamic assumption of mutual attraction.

Using of the sun's mass and repeating the previ-ous procedure, based again on Kepler's formula thederivation this time establishes the acceleration ofthe sun around the planet:"According to Newton's third law, however, the plan-

et must exert an equal and opposite attractive forceon the sun:

msforce ~ −−−−− (6.8b),

r 2where ms is the mass of the sun"(...)"therefore theattractive force between the two has the mathematicalform:

ms mpforce ~ −−−−−−− (6.8c).

r 2

"For Newton's hypothesis of universal gravitation to

be correct, there must be an attractive force between allpairs of objects everywhere, whose value is given by thesame mathematical formula as that above between thesun and a planet."Thus the force, F between any two bodies of masses

m1 and m2 and separated by a distance d, ism1 m2

F = G −−−−−−−− (6.1)”d2

This is the final form of Universal Gravitation,which, -- as Hoyle stated, -- has been obviously derivedfrom the equations of Huygens and Kepler.

Nevertheless, the derivation proceeds to re-stateKepler's third law including Nerwton's addition ofmutual attraction. With the aid of the concept of thecenter of mass and with some mathematical operationsa new form of Kepler's third law is presented:

" (ms + me ) P 2 = R 3 (6.9a)"Newton's version of Kepler's third law differs from

the original in that it contains a term involving thesum of the masses of the two revolving bodies." "However (....) the sun has a mass of about 300,000

times that of the earth. Thus the combined mass of126


the sun and the earth, or that of any other planet isfor all intents and purposes, is no different than themass of the sun itself. Then in the combined system,m1+m2 = m1."Thus if we apply the equation Newton derived to the

mutual revolution of the sun and a planet and chooseastronomical units for the units of time and distance,and the solar mass for the unit of mass, then Newton'sequation reduces to

ms = 1; (ms+ me) = 1; (ms+ me)P2= P2; P2 = R3 (6.9a)in agreement with Kepler's formulation of the law."

KEPLER’S FORMULA Let us now reconstruct, what happened with the

terrestrial mechanical concepts of mass and forceand the fundamental assumption of mutual attrac-tion in the course of the derivation.

First the planet's mass has been inserted in order toestablish the magnitude of the centripetal force neededto keep it on its orbit. A few steps later, however, themass of the planet was declared to be insignificant andtherefore the centripetal force could either not be in pro-portion to that mass or it must have been zero. Thus,the equation expressed nothing more than the

Huygens-Kepler centripetal acceleration and thedynamic concepts of mass and force were meaninglessat that stage.

In the next step, introducing Newton's mutualattraction, the mass of the sun was inserted, this timein the role of the secondary body in order to find its owncentripetal acceleration about the planet and the forceexerted on it. But the magnitude of the sun's accelera-tion was also declared to be insignificant, since it wascaused by an insignificant force exerted on it by aninsignificant mass.

Evidently, the end result of m1+m2 = m1 is, that thetotal mass belongs to the dominant body, the sun andthe total acceleration belongs to the secondary body, theplanet.

Hence, the derivation is back where it started from,replacing Kepler's original mathematical constant bythe mechanical constant of the mass of the sun, deter-mining the magnitude of the non-mechanical force thatproduces the centripetal acceleration of the planets.

It is evident that from the beginning till the end ofthis procedure nothing else was known and nothingelse was learned about the relationship between sunand planets, but the facts embodied in Kepler's three

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Aethro-kinematics CHAPTER SIX Kepler’s Formula

laws of planetary motions and the mathematics derivedfrom them together with Huygens' concept of cen-tripetal acceleration.

No doubt, that Universal Gravitation works inevery two-body problem in the universe. It alsoworks in cases of the perturbations of the planetswhen their orbits do not exactly fit the predictions ofKepler's Laws. – Seemingly, Universal Gravitationexplains away the Keplerian mysticism and concep-tually simplifies the phenomenon by unifying earthlyand celestial mechanics. In fact, however, in each andevery case, in all two body problems, universal gravi-tation reverts back to the Huygens-Kepler accelera-tion formula to establish the magnitude of thedynamical quantities of the mass of the dominantbody and from that the magnitude of force exerted onthe secondary one.

"Our only means of measuring the masses of ast-ronomical bodies is to study the way they react gra-vitationally with other bodies. Newton's derivation ofKepler's third law, which includes a term involvingthe sum of the masses of the revolving bodies is mostuseful for this purpose." (Abell, Exploration of theuniverse [66]).

It is obvious that Kepler's mystical harmony hasnot been replaced by some truly conceivable explana-tion, but by a mechanical mystery of the action at adistance force, which is for some unknown reasonproportional to a factually unmeasurable quantity ofthe mass of the dominant body.

The choice of analogies offered, to help graspthese ideas are not too sensible either: there are theprimitive concept of muscular effort of push and pull,the whirling stone on a string or rather on a rubberband, the more scientific approach of the gravitation-al field, which is only perceptible when a materialbody accelerates in it, and the most modern hypothe-sis of the inherent capability of matter to producenon-Euclidian geometry in empty space...

Is any one of these concepts less mystical andmore conceivable than Kepler's Harmony ?

But beyond the obvious confusion, there is a definitenegative effect of this method on future advances. Inthe course of the dynamical metamorphosis, a totallyunrecognized value of Kepler's Third Law was alsoexplained away; The only factual knowledge everobtained about the correlation between universal gravi-tation and universal rotation is expressed in this law.

128


The simple proportionality between the tangentialvelocities of the orbiting bodies and their distances fromthe center of the rotating system. This is the essence ofKepler's third law, which has been melted into themathematics of Universal Gravitation without trans-ferring its conceptual content.

As far as it is known today, our solar system con-sists of nine planets, thirty one satellites, some aster-oid belts and an unknown number of comets, all ofwhich revolve around the sun like clockwork, onKeplerian orbits. Imagine now a different solar sys-tem, with a million asteroids revolving around theirsun, resulting in a great non-solid rotating disk, withall its members orbiting around in different dis-tances with different tangential velocities. Some ofthem even revolving around one another.

Chaos ? Not at all.Once a single example is established; the Period

of revolution of one member and its distance fromthe sun were measured, Kepler's Formula renders adynamic map of the the whole system:

P 2−−−−−− = K or P 2 = Kr 3 (6.2),

r 3

The square of the Period divided by the cube ofthe radius is a constant for each member of the wholerotating system. − Since P = 2πr/ v

4π 2r 2P2 = −−−−−− and then 4π 2r 2 / v 2 = Kr 3 (6.10a),

v 2

multiplying both sides by v 2 gives 4π 2 r 2 = Kr 3 anddividing both sides by Kr 3 gives 4π 2/ Kr = v 2,therefore

−−−−−−− 2πv = √ 4π2 / Kr = −−−−−− (6.10b)

−−−√ Kr

If time and distance are measured in astronomi-cal units (both the period and the distance of theexample = 1), then the constant of proportionality, K= 1, hence

1 v ≈ −−−−− (6.11)

−−−√ r

The tangential velocity of any orbiting body inthis rotating system is inversely proportional to thesquare-root of the radius of the orbit.

129


Hence the full recognition of Kepler's third law cre-ates a new concept in celestial mechanics: RotationalGravitation,.

Because of the masses of all secondary bodies areinsignificant, all orbits are taken as perfect circles.Therefore, the force responsible for the dynamic natureof the system has two components; a) the tangentialcomponent, which is represented by a vector, directed ata right angle to the radius and its instantaneous veloci-ty is inversely proportional to the square-root of theradius; b) the radial component is represented by theconstant centripetal acceleration of the same vector,(Huygens-Newton) which is inversely proportional tothe square of the radius.

As controversial as this statement sounds, these arethe conditions that a complete theory of RotationalGravitation must fulfill.

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CHAPTER SEVEN

ROTATIONAL GRAVITATION

THE CONCEPT OF A FIELD"A basic fact of gravitation is that two masses exert

forces on one another. We think of this as a directinteraction between two particles, if we wish. Thispoint of view is called action at a distance; the parti-cles are interacting even though they are not in con-tact (Newton's choice)."Another point of view is the field concept which

regards a mass particle as modifying the spacearound it in some way and setting up a gravitational

field. The field, therefore, plays an intermediate rolein our thinking about the forces between two massparticles."According to this view, we have two separate parts

to our problem. First we must determine the fieldestablished by a given distribution of mass particles;and secondly we must calculate the force that thisfield exerts on an other mass particle placed in it.

Figure 7-1

131

Aethro-kinematics CHAPTER SEVEN The Concept of Field

"For example, consider the earth as an isolatedmass. If a body is now brought in the vicinity of theearth, a force is exerted on it. This force has a defi-nite direction and magnitude at each point in space.The direction is radially inward to the center of theearth and the magnitude is mg. We can therefore,associate with each point near the earth a vector gwhich is the acceleration that a body would experi-ence if it were released at the point in question."The field concept is particularly useful, in fact,

indispensible, for understanding electromagneticforces between moving electric charges. It has dis-tinct advantages, both conceptually and in practice,over the action at a distance concept. The field con-cept was not used in Newton's days. It was developedmuch later by Faraday for electromagnetism andonly then applied to gravitation."Subsequently this point of view was adopted for

gravitation in the general theory of relativity."(Resnick-Halliday: Physics, 1978 [339]) "Imagine a rapidly flowing trout stream containing

several whirlpools that dimple its surface."A complete description of the flow could be

obtained by giving the velocities of the water at each

point in the stream. The velocity of a small sample ofwater located at P could be given as three vectors ina Cartesian coordinate system: Vx, Vy and Vz. Theresulting description of the flow might be referred toas a velocity field.

Figure 7-2"A pictorial representation of this velocity field is

obtained from the stream-lines. Each stream-linerepresents the path of a small sample of water as itflows down the stream. In the vicinity of eachwhirlpool the water is moving in circles. Each

132


whirlpool produces a dimple on the surface of thewater. This dimple is a highly localized entity, whichcan move over the surface of the stream in the sameway as an elementary particle moves through space.However, there is no material body located at thedimple. It is merely a point at which the stream-linesbehave in a peculiar manner."This suggest to us an extreme swing of the pendu-

lum in our attitude toward describing the universe.Now the emphasis is placed on assigning propertiesto all points in space so that it is filled with variousfields, whose action is independent from the factwhether there is anything to move or not. On theother hand an elementary particle could be merely apoint in space at which a field behaves in a peculiarway. In the case of a whirlpool the stream-lines goround in circles permanently. Another possible situa-tion, which is perhaps more akin to an elementaryparticle, occurs when the stream-lines all convergeon a point."Suppose that a dam is built across the stream and

the flow is taken under the dam by a narrow tunnelbelow the bed of the stream, starting at point A,some distance upstream of the dam and emerging at

a point B, some distance downstream of the dam.The stream-lines all converge upon A and thendiverge from B. The behavior of the stream-lines atthe vicinity of A and B is similar to the behavior of agravitational or electric field in the vicinity of an ele-mentary particle." K. R. Atkins, Physics, 1976 [263]

Figure 7-3

Part (a) of Figure 7-3 illustrates the field of flowof a linear source. All stream-lines are directed radi-

133


(a)

(b) (c)(c)

ally outward. The field of flow around a linear sink,(b) is the same as the source except for the directionof the flow, which is directed radially inward to thesink. For a linear source and a linear sink, with thesame strength and slightly separated, there is a com-bined field, called linear dipole flow, (c).

THE IDEAL GAS The observational facts, expressed in Kepler's

first and second empirical laws require the action ofa force in the solar system whose magnitude is pro-portional to the inverse square of the distance fromits origin. Only such force can oppose the fictitiousforce of inertia, guarantee the permanence of ellipti-cal orbits, and the acceleration and deceleration ofthe planets in agreement with the law of areas. Thenthe formula of Kepler's third law sets the angularvelocities also proportional to the distances from thecenter of the rotating system . This is the formulathat describes the general clockwork, not only for thesolar system but for the phenomenon of universalrotation in all orders of magnitude.

So far neither classical and modern physics norastronomy and cosmology made any serious attemptto fill these laws with some conceivable conceptual

content. Instead, it has been loosely assumed to bejustified by their derivation from the law of universalgravitation which, as Newton himself declared, wasmerely a mathematical theory with no conceivableexplanation.

Moreover, there are good reasons to believe, thatthis conceptual vacuum in the very foundation of ourdescription of nature is one of the main sources ofthe present mathematical perplexities lingering overall departments of modern physics.

In the following an alternate hypothesis will bepresented combining Newton's universal gravitationand the fully recognized third law of Kepler's plane-tary motion; a first draft of a kinematic description ofthe phenomenon of Rotational Gravitation;

This discussion involves the re-evaluation of mostof the laws and concepts discussed above and thebuilding of a new conceptual understanding from thebottom up. Consider carefully and step by step thefollowing train of thoughts:

In order to explain the empirical laws of Thermo-dynamics through the concepts and mathematics ofNewton's mechanics, physicists worked out an atom-ic and kinetic theory of gases. Taking the simplest

134

Aethro-kinematics CHAPTER SEVEN The Ideal Gas

approach to describe the molecular mechanics ofmacroscopic phenomena like temperature, diffusion,pressure and wave-propagation, they introduced ahypothetical medium of an ideal gas with some sim-plified characteristics.

The gas is monatomic, its molecules are singleatoms of a pure element. All of its constituents areequal in mass and size and they are in ceaseless ran-dom motion. As a distinction from real gases, in anideal gas there are no dynamic interactions betweenthe atoms. No gravitational, electromagnetic or otheraction at a distance forces are in effect between theatoms and therefore all changes in the perfectly ran-dom isotropy of the gas come from external kinemat-ic impulses. These local disturbances are propagatedthroughout the medium by no other means butthrough the impacts between the atoms in their col-lisions.

Hence, an ideal monatomic gas can be visualizedas a collection of submicroscopic spheres, impenetra-ble to one another and separated by distances muchlarger than their diameters. The atoms of this gasare in rapid motion on straight lines, with uniformvelocity until they rebound from the wall of the con-

tainer or collide with one another. They are in com-plete random motion; meaning, that on the averageat any given time the same number of atoms aregoing in one direction as in any other direction.

Although the distance between the atoms arealso completely random, there is an average colli-sion-free path between interactions, which is deter-mined by the macroscopic density of the gas and theaverage velocity of the atoms. Since no forces are act-ing between the atoms and the collisions are perfect-ly elastic, there is no internal friction and the onlyform of energy of the gas is the kinetic energy ofmotion. Consequently, in an ideal gas, all statementsof the kinetic theory and the laws of Newton'smechanics are valid.

THE INVERSE SQUARE LAW OF GEOMETRYIn accordance with the above, imagine a great

room filled with an ideal gas, which is homogeneous,isotropic and globally motionless. The basic macro-scopic characteristics of the gas is that the pressureit exerts on objects submerged in it, and the propaga-tion of local disturbances from point to point, are uni-form all through space. The changes in this isolatedsystem is suitable for comparatively simple mathe-

135

Aethro-kinematics CHAPTER SEVEN The Inverse Square Law of Geometry

matical description and mechanically conceivable bythe pure and sensible concepts of motion, impact andcollision. It is also assumed, that the dimensions ofthe room are great enough, so that it can be taken asinfinite, therefore the reflections of the disturbancesfrom the walls can be neglected.

Consider now, that at the middle of the greatroom there is a small balloon which suddenlyexpands and creates a short pulse of compression inits vicinity. Depending on the extent and speed of theexpansion, there will be a layer of certain thicknessin the gas next to the balloon with a greater thanaverage density and consequently, a greater thanaverage pressure. Within this layer of compressionthe average collision free path of the atoms will beshorter and the number of collisions per unit volumewill increase. As a result the layer will exert a pres-sure on the next layer and in turn the next and thenext. As the gas is compressed, work is done, and isstored as potential energy in the medium. As the dis-turbance propagates, this energy is transmittedthrough space.

The pulse, like all disturbances in an isotropicmedium, will travel outward from the source in the

form of a growing spherical shell. The intensity ofsuch disturbance, just like that of sound, is measuredby the amount of energy passing through a unit areaper unit time.

Figure 7-4.As the illustration shows, that the intensity of

the pulse at different distances from the source isdetermined by the fact, that the surface of a sphereis increasing in direct proportion to the square of theradius and as the pulse travels outward, the initialenergy dissipates over greater and greater areas.

The surface area of the sphere is 4πR2.If E is the initial energy of the disturbance at the

source, and the intensities at two different distances

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SOURCE

1

2

3

are I1 and I2 and the radii of the different spheresare R1 and R2 , then

Ii E/4πR22 E

−−−− ≈ −−−−−−−−− or I ≈ −−−− (7.1).I2 E/4πR1

2 R2

Hence, the intensity of the pulse is directly pro-portional to the initial energy and inversely propor-tional to the square of the distance from the source.

This inverse square law is valid for the intensityof sound-waves and light waves or other electromag-netic radiations and for any other kind of distur-bances, propagating in an isotropic homogeneousmedium. Whether these disturbances are defined bythe concepts of the kinetic theory, or those ofNewton's mechanics, or described by the field con-cepts of the electromagnetic theory, they all obey thesame inverse square law which simply originatesfrom the spherical propagation of the local densitydisturbances.

All these are resulting from the isotropy of themedium and from the geometrical fact that the sur-face area of a sphere is directly proportional to thesquare of its radius.

Next, consider the reciprocal; a pulse of rarefac-tion, created by a sudden decrease in the volume ofthe balloon.

As this happens, depending on the extent and thespeed of the contraction of the balloon, there will be alayer of certain thickness of rarefaction, representinga smaller than average density and a smaller thanaverage pressure.

This layer of rarefaction represent a deficiency ofdensity or negative pressure in the vicinity of theballoon into which a number of atoms from the nextlayer can emigrate without opposition. This in turncreates a decrease in the density in that layer, andthat in the next to it. Consequently, like any otherdisturbance, this pulse will also propagate outwardfrom the source in an expanding spherical shell ofrarefaction, a negative pressure, the intensity ofwhich is also decreases according to the inversesquare law.

Now, instead of the contracting balloon, let usintroduce a small pipe erected into the middle ofspace, with an opening, covered by a small sphere ofporous substance. The pipe is connected to a vacuumpump.

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At first consider a sudden and short switch onand off the pump. The result is the same as that ofthe sudden decrease of the balloon. A rarefactionpulse propagates outward from the sphere and itsnegative pressure decreases with distance accordingto the inverse square law.

The periodical repetition of the switching, pro-duces a train of pulses in which rarefaction layersand initial density layers alternate in expandingspherical shells. Each rarefaction shell represents anegative pressure, the magnitude of which dependson the shell' s distance from the center.

Next the cycle of the switching can be graduallyshortened approaching an infinite frequency of puls-es, or a continuous train of pulses. This is equivalentto a constant production of rarefaction around theporous sphere, which in turn is analogous to the con-cept of fluid-dynamics, called a linear sink.

It follows, that the continuous operation of thissink creates a density deficiency in the mediumwhose magnitude is directly proportional to thecapacity of the sink and inversely proportional to thesquare of the distance from the sink.

Figure 7-5.

From a macroscopic point of view, there is also athree dimensional radial flow of the gas toward thecenter of the room to replace the volume of gas, thatis continuously withdrawn by the sink. This could bevisualized as some kind of radial wind blowing fromall directions, whose speed is directly proportional to

138


CE

the extent of rarefaction in the medium and there-fore also inversely proportional to the square of thedistance from the sink.

This kinematical description of the operation of athree dimensional sink bears undeniable analogieswith the kinematical results of the operation of theaction at a distance force of gravity.

In the first place, since there is an increase in theinstantaneous velocity of the radial winds as theyapproach the sink, each small portion of the mediummust undergo constant acceleration, just like a testparticle would do as it fell freely from a great dis-tance under the influence of the increasing magni-tudes of gravitational attraction of a massive body.This analogy reflects the whole of space influencedby the force of gravity and the Newtonian mathemat-ics of the inverse square law.

In the second place, the analogy is also perfectlyextendible to the modern concept of the gravitationalfield of a given region. Assume the existence of a for-eign particle comparable in size and mass with theparticles of the ideal gas and movable by the pres-sure of the radial winds.

If this particle now brought to the vicinity of thesink, a force is exerted on it. This force has a definitedirection and magnitude at each point in space. Thedirection is radially inward to the center of the sinkand the magnitude is inversely proportional to thesquare of the distance.

We can associate with each point near the sink avector s, which is the acceleration, that the particlewould experience if it were released at the point inquestion ... the emphasis is placed on assigning prop-erties to all points in space representing a field,whose action is independent from the fact wetherthere is anything there to move or not.

Hence, an operating sink submerged in ideal gasis both conceptually and mathematically equivalentto a solid body surrounded by a gravitational field.The important difference is, that while the gravita-tional field is a mere mathematical convenience, theideal gas can be physical reality.

THE CONSTANT FORCE OF GRAVITY It is an experimental fact, that a body released

from rest in the vicinity of the Earth, gains the samespeed in each second of free fall, 9.80 m/sec. Its total

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Aethro-kinematics CHAPTER SEVEN The Constant Force of Gravity

speed at the end of the second second is 19.60 m/sec,at the end of the third second is 29.40 m/sec, and soon. Such gaining of speed represents a uniform accel-eration, and according to the second law of motion,this requires the action of a constant force.

Newton declared in the 'Principia' that his theo-ry is merely a mathematical system and does notspeculate about the possible mechanics of the force ofgravity, or that of the constancy of such force. At thetime, this was quite a turn against the reigningmechanistic philosophy, but because of the great suc-cess of his mathematics, Newton's approach waseventually unanimously adopted by the scientificcommunity.

Today, after three centuries of practice of not ask-ing questions, nor of expecting comprehension ofnature, the uniform acceleration under the influenceof the constant force of gravity seems to be just asself-explanatory as the impulsive force between twobilliard balls in the collision.

Nevertheless, in the mechanicism of sixteenthcentury, philosophers were neither satisfied with themystery of the origin of gravity nor with its mechani-cally inconceivable constancy. Before the complete

acceptance of Newton's purely mathematical theory,prominent philosophers made several valuableattempts in designing mechanical models for apotential comprehension of the constant force ofgravity.

Isaac Beeckman, Dutch physicist in collabora-tion with Descartes, in the 16th century discoveredfirst that the distance travelled by a falling body isproportional to the square of the time intervals.Hence, before Galileo and Newton, Beeckman wasalready aware of the uniform acceleration of thefreely falling bodies and was also the first to assumethat gravity is a constant attractive force.

In order to tie these concepts together with themechanistic philosophy, he formulated his theorybased on the following ideas : The speed of themotion of a body, once it has been generated, contin-ues unchanged as long as no external force destroysor reinforces it. This assumption was the first formu-lation of the concept of inertia, which was later com-pleted by Galileo and Newton.

As for uniform acceleration, Beeckman furtherassumed, that gravity acts in such a way that at cer-tain intervals of time it gives, as it were a jerk of pull

140


on the falling body. If the same strength of pull, isrepeated at regular intervals, the same amount ofnew velocity is being accumulated in the motion ofthe body. Assuming a great but not infinite frequen-cy, as the time interval between each pull approacheszero, the force of gravity, or that of the periodicaljerky pulls approaches the concept of a continuousaction; a constant force, which in turn produces uni-form acceleration.

With the help of this model, Beeckman indeedarrived to the right mathematical result, giving aclose to final description of free fall. He alsodescribed inertia, and gave a potential explanation ofhow a high frequency periodical impulsive force cangive the illusion of the constancy of gravity and theresulting uniform acceleration.

Nevertheless, Beeckman's theory was refused bythe era, because the jerky pulls of attraction still rep-resented a kind of non-mechanical action at a dis-tance force, which therefore could not be accepted bymechanicism.

Around the middle of the same century, whenGalileo's principle of inertia had already been recog-nized, Giovanni Alfonso Borelli, Italian physicist and

astronomer, made an attempt to replace Beeckman'saction at a distance force with something more tangi-ble. He agreed with the assumption that gravity ismade up of periodical, impulsive forces, whose fre-quency approaches infinity. But instead ofBeeckman's jerky pulls, he compares gravity to theimpulsive actions of quickly tapping small hammers,which continuously accompany the falling body.

Each individual tapping adds the same amountof impulse and speed to the motion of the body andthis accumulative process results in uniform acceler-ation.

Both Borelli and Beeckman adopted the idea of agreat, but not infinite frequency for their periodicalforce instead of the mechanically inconceivable con-stancy, and assumed the accumulative process of agreat number of individual impulses in action.Borelli's other new point of view was that the colli-sion-like impulsive force of the tapping of the littlehammers were acting from the opposite directionthan Beekman's attractive force, producing the samecentripetal acceleration, but by pushing from the out-side instead of pulling from the direction of the cen-ter of the massive body. With this, he relieved the

141


theory from the non-mechanical concept of theattraction from a distance.

Nevertheless, the hypothesis presents some otherproblems. Borelli's little hammers are to accompanythe falling object regardless of its constantly increas-ing speed. If each tapping imparts the same units ofextra speed to the body, the hammers must acceler-ate with it, or have a much greater initial velocitythan the body and in the same direction, which theytransfer in each tapping. They must also be verysmall compared to any material particle, otherwisethey would soon accelerate them on their own speed.They must also fill all space around the body, whichsuggests the existence of an all-pervading medium.

Considering all the above, it can be seen, thatBorelli's theory not only brings up all the mechanicalproblems involved in the concept of the simplesounding constant force of gravity, but also offers apossible solution to all of them, including an earlysuggestion of the Kinetic Theory of Gases, which wasto be formulated only two centuries later.

There is indeed a kinematic solution for Borelli'stheory, if the assumption is admitted that the ham-mers are the constituents of a medium, being every-

where in space, moving with great, but not infinite,radial velocity toward the center of the massive body.These supermundane particles of the flowing medi-um constantly tapping and accelerating everythingthat gets in their way. How else can all the perplexi-ties of this universal phenomenon be brought withinhuman comprehension, if not by the assumption,that gravitation is a flow of a medium toward thecenter of the mass, and carries all objects with it.

This mechanical process of the acceleration ofmacroscopic bodies is, indeed an every day experi-ence wherever a fluid in flow carries a foreign objectsubmerged in it. Think of a river, that accelerates aheavy log unto its own velocity by the periodic,impulsive force of the immense number of water mol-ecules colliding with the slow moving solid body, likelittle hammers tapping on it with immense frequen-cy.

Should this simple phenomenon be judged as theact of a mysterious constant force or merely as theinsufficiency of our senses to record the frequencyand recognize the periodicity?!

Borelli's hammers truly exist as the atoms of thekinetic theory of all fluids as they are hammering

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the wall of a container or any solid body submergedwithin. If this hammering is random and isotropicfrom all directions, it creates the macroscopic effectof kinetic pressure. If the fluid itself is in globalmotion, superimposed on their random motion, allhammers possess an excess kinetic energy in thatspecific direction and by their immense number, theyuniformly accelerate and carry all foreign bodies intheir way. Thus, in order to solve the perplexingmechanism of the constant force of gravity, Borelligave a close to perfect description of a seemingly con-stant, but actually a high frequency, periodic, impul-sive force. The same force, that has been simulated inour analogy through the effect of a sink, operating inthe isotropic ideal gas.

Let us now assume, that somewhere in the spaceof the great room a small soap bubble is produced. Itsexistence is determined by the balance between theinternal and external pressure of the gas, and thecohesional forces acting in the soap film. Assume fur-ther, that as it suddenly appears at a point in space,it should be at rest relative to the non-operatingsink. In a motionless, isotropic medium the pressureexerted on an object is also isotropic. Pressure is a

vector quantity which is always normal to the sur-face of the object. Therefore, the force exerted on thesphere of the bubble from every direction is exactlycounteracted by a pressure directed against theopposite point of the sphere. Thus, in a motionlessgas, the net force exerted on the soap bubble is zeroand it can be considered at rest relative to theisotropy of the medium.

Once the sink starts operating and the first rar-efaction pulse reaches the bubble the isotropy of thepressure on its wall ceases to exist. Due to the nega-tive effect of the pulse, there is a smaller pressureexerted on the bubble from the direction of the sink,than from the opposite direction. This directionalpressure difference represents a net force; a tendencyto move the bubble toward the sink, that is, to pro-duce acceleration.

This is the net centripetal force that can be repre-sented by the vector s, which has the same magni-tude at any point of the surface of a sphere of a givenradius and directed from every point radially inwardto the sink. It is evident, that this description ismathematically equivalent to Newton's concept ofgravitational attraction. If the capacity of the sink is

143


measured by the number of atoms, n, withdrawnfrom the medium per unit time and the mass of eachatom is m, then the capacity of the sink, S is, S =mn/sec. It follows, that the two equations describingthe centripetal force, Fc , in the two different phenom-ena are identical.

m SFc = G −−−−− or K −−−−

R2 R2

where G and K are constants of proportionality,depending on the unit of time and length used. Themagnitude of gravitational mass is comparable to thecapacity of the sink, the centripetal force is directlyproportional to either and inversely proportional tothe square of the distance from the center.

It should be emphasized here, that the inversesquare law, expressing the effect of the sink, has notbeen derived from empirical facts, as Newton hadachieved his Law of Universal Gravitation fromKepler's empirical formula. This law is constructedconceptually from the isotropy of the propagation ofdisturbances in an isotropic ideal gas together withthe geometrical axiom, that the surface area of thesphere is proportional to the square of its radius.

It can be expected, that, if Newton was able toderive his inverse square law from Huygens' cen-tripetal acceleration and Kepler's formula, the recip-rocal procedure should also be possible. From thegeometrical inverse square law of the sink, with theaid of Huygens' equation, one should be able toderive the formula of Kepler's third law of planetarymotion?!

At this stage of the analogy, however, the cen-tripetal force of the net negative pressure, just likeNewton's force of gravitation, only renders the verti-cal component of planetary motion and Kepler's for-mula still means nothing more than before; anincomprehensible mathematical wonder.

Nevertheless, in the following extensions of theanalogy, it will be shown, that there are well knownand well understood phenomena in Nature whichcan conceptually tie together the kinematics of thesink and the mathematics of Kepler's formula.

THE VORTEX In analyzing an orbit or the trajectory of a body

in free fall, Newton's theory of universal gravitationcompletely separates the forces responsible for thevertical and horizontal components of the motion.

144

Aethro-kinematics CHAPTER SEVEN The Vortex

He only discusses the force of gravity as thecause of the radial acceleration and leaves the initialtangential component of the orbits to be an effect ofunknown causes. The modern concept of the gravita-tional field inherited this one dimensional view.Figure 7-1, the illustration of the earth's gravitation-al field is a typical example, where the lines of forceare straight lines, directed radially toward the centerof the earth, with the complete negligence of theearth rotation.

This method of description can be taken either asthe result of an optical illusion, coming from disre-garding the rotation of the frames of reference of theearth or that of the sun, in which the phenomenon isdescribed, or the deliberate dismissal of this part ofthe problem, as indifferent from the stand-point ofthe mathematical analysis.

For the sake of simple analogy, the sameapproach has been taken in the above ideal-gasthought-experiment, which lead to the description ofa straight line radial flow toward a sink from alldirections. In this picture the kinematical tendencyof the acceleration of the soap bubble had been foundmathematically equivalent to the effect of the accel-

eration caused by a gravitational field around a mas-sive body.

The analogy was based on the Newtonian simpli-fication; neglecting the tangential component of forceand motion. The fact, however, is, that there is nosuch thing as a permanent three-dimensional radialflow into a sink, but it is always accompanied byrotation just like gravitation itself.

Consider two common earthly examples of rota-tional systems; the great storms, like the cyclonesand tornados, and the miniature rotating system ofthe draining water in the kitchen sink.

In the case of the storms, it has been found byobservations, that whenever a great mass of airheats up over a suitable terrain on the earth's sur-face, it rises and leaves a low pressure area behind.Next the surrounding colder air starts drifting radi-ally towards this area and winds come into existence,blowing from all directions toward the low pressurecenter. Naturally, the momentum of these winds can-not dissipate when they finally reach the center. Thefirst result of this radial rush of air from all directionis, that in the central area the low pressure changesover to high pressure and a core of dense air forms,

145


which bounces back the still oncoming winds. Butbehind the first layers of the winds there are greatmasses of air still moving toward the center andpush the rebounding air sideways. No doubt, the onlypossible kinematic balance in this situation is rota-tion, where the linear momentum of the inward flowis transformed into angular momentum.

(a) Figure7-6, (b)

The question of the direction of rotation could beleft coincidental, but in certain cases, maybe in morethan presently known, the decisive factor in thedirection of rotation has been found to be the influ-

ence of an already existing rotation in a higher orderof magnitude.. In case of the great storms, this high-er order is represented by the earth's rotation, andthe result is called the Coriolis effect.

Any object moving freely over the surface of therotating earth appears to be deflected to the right inthe northern hemisphere and to the left in the south-ern hemisphere. Figure 7-6. (a) shows the path of aprojectile, which is fired directly to the north fromthe equator and therefore shares the earth's angularvelocity of 410 meter/sec eastward.

As the projectile proceeds north, the circumfer-ence of the globe gets smaller under it, and has alower velocity than at the equator. The result is, thatthe projectile moves in a curved path relative to theground, veering off toward the east. Because of thesame effect, the winds of a cyclone also tend to veeroff to the side, but in this case, at the same time themass of air is continuously attracted by the low pres-sure area (b).

Thus, instead of blowing radially into the center,the winds begin to circle around the area, producingthe circular motion of a great mass of air. This hap-pens in the clockwise direction in the northern and

146


counter clockwise direction in the southern hemi-spheres (c). Once this pattern is formed, it has a ten-dency to grow. The core begins to flatten out to a ring,which rotates like a solid body. It transfers its angu-lar momentum by friction at the edges and producesgreater and greater rings, concentric to the 'eye of thestorm.' The system gradually gains angular momen-tum and perpetuates its own existence. Tropicalcyclones can attain diameters of 100 to 500 miles,with wind velocities up to 300 mph, and their lifetimes are often measured in several days.

Theoretical hydrodynamics, initiated in the 18thcentury, named this phenomenon a circular vortexand established some of the basic rules about its ori-gin, nature and mechanism.

In general, a vortex is defined as a mass of fluidin which the flow is circulatory. A thorough analysisof fluid flow, attributed to Hermann Helmholtz hasproduced the following laws governing vortex flow:

1. The strength of a vortex is constant along thefilament.

2. The identity of the fluid in a vortex does notalter during the life of the vortex.

3. Filaments have no ending, they are eitherclosed paths, or their ends extend to infinity."From the above rules, it follows that the filaments

in a circular vortex must form closed rings, in whichalways the same particles are present. It is clearfrom this symmetry that the speed of the particles atevery point of a circle is the same, and their velocityis tangential to that circle, which is exactly counter-acted by the static pressure of the outside layers."This must be the case, since any radial component

of the velocity would entail a net flux across therings, which would make the center of rotation eithera source or a sink."Hence, in a circular vortex, the induced velocities

at the extremities of oppositely directed radii are ofthe same magnitude but in the opposite sense, sothat the mean velocity of the fluid within the vortexis zero. Thus, if a circular vortex of small radius isplaced in a motionless fluid, it will stay at rest rela-tive to the isotropy of the medium, and when placedin a field of flow, it will 'swim with the stream' like amaterial substance, carrying its vorticity with it."More over the vortex cannot disappear, for it has

been proved that rotational motion is permanent.147


"It follows, that when in the actual cases the vortexrings do dissipate, the internal friction of the fluidmust be the cause. In a non-viscous fluid a circularvortex, once formed, remains in existence indefinite-ly." (L.M. Milne - Thompson, Theoretical Hydro-dynamics [79]) "In the Theory of Aerodynamic Circulation a mass

of air in rotary motion is said to be in circulatoryflow, if its velocities at various radii from the centerare of the proper magnitude to induce radial equilib-rium of the circulating mass. Considerations of therequirements for equilibrium consists in balancingcentrifugal forces against static pressures, derivedfrom Daniel Bernoulli's theorem and results in thespecification that the velocity of a particle must beinversely proportional to its radius from the center ofrotation (1 / R).“Air in this condition is described as a free vortex."

(Van Nostrand's Encyclopedia, 1976 [49]).The example of the kitchen sink represents an

entirely different kind of circulatory flow. In this casethe vortex develops around a sink, which consumesthe water and there are some important differencesbetween the two types of vortices.

On the one hand, it was established above, thatthe circular vortex is made up of closed rings whoseparticle content does not change in time. This means,that no radial flux exists inward or outward throughthe circular vortex. Each small portion of the medi-um, therefore stays on the same orbit and moveswith constant tangential velocity.

This radial equilibrium is maintained by the bal-ance between the centrifugal force of the rotationand the centripetal force of the static pressure of theexternal isotropic medium. In the case of a cyclonethe in-blowing winds represent the centripetal pres-sure and when they cease to operate, the circularvortex gradually dissipates, simply because of theunbalanced centrifugal tendencies.

On the other hand, there exists a different kind ofcirculatory flow. Two examples of that are the vortexin the kitchen sink and the vortex described by thethought experiment in the ideal gas. These are circu-latory flows developing around a sink as it continu-ously withdraws a certain volume of fluid. Theresulting density difference produces a constant radi-al flux of the medium toward the sink across thewhole vortex.

148


Figure 7-7 It follows, that no closed vortex-rings could devel-

op in this type, but the paths of the particles in thefluid are circles of continuously diminishing radii.Thus, each small portion of the medium moves on aseparate spiral channel with increasing tangentialvelocity as it approaches the center. Eventually, allthe particles caught in such vortex will be consumedby the sink.

Theoretically the territory of the vortex is infi-nite, but its effectiveness to accelerate particles endsat a distance in space where the centripetal effect ofthe sink combined with the isotropic pressure of theexternal medium are less than the force needed forthe centripetal acceleration of the spiraling orbits ofthe atoms. In fluid-dynamics such a rotating systemis called a spiral vortex. In this analogy it is moreclarifying to use the name, sink vortex.

The schematics of Figure 7-7 show a sink (a), acircular vortex (b) and the combination of the two; asink vortex (c).

Of course, the number of spiral stream-lines inFigure 7-7 (c) is merely a convenient choice of theartist. In a fully developed spiral vortex, like thewater vortex in the sink, there are an immense num-ber of spiral stream lines, winding gradually inwardto the drain.

Each layer of the water, practically each row ofthe atoms can be visualized as a continuous stream-line forming the same shape of spiral from the edgeof the vortex all the way into its center, as it is illus-trated by Figure 7-8.

149


(a)

(b) (c)

It should be recalled here, that the effect of thesink is first of all a localized disturbance in theisotropic medium. The resulting constant rarificationis propagated through the fluid according to theinverse square law. It follows, that the extent of rar-efaction in each individual spiral channel also obeysthe same law. It is evident, that both conceptuallyand mathematically the sink vortex is distinctly dif-ferent from the circular vortex.

Since the theoretical development of hydrody-namics only started around the beginning of the 18thcentury, it is not clear, what kind of vortex Descarteshad in mind two centuries earlier for his solar-vortextheory.

However, Newton explicitly states in the 'Prin-cipia', that his refutal of Descartes theory was basedon the mathematics of the circular vortex:"(a) The speed of an ether particle in the vortex

varies inversely as its distance from the sun (1/R).− (b) The period of revolution of such a particlevaries directly as the square of its distance from thesun (P = (1/R2). (c) This result contradicts Kepler'sthird law (P2 = KR3)."

As it will be shown in details in Appendix I. themathematical analysis of the inverse square law ofthe propagation of disturbances in a rotating medi-um reveals, that the orbital velocity of a mass-parti-cle in the Aetherial sink-vortex is inversely propor-tional to the square root of the radius, 1 / √R; inagreement with Kepler's formula. The understandingof Appendix I., however, requires the reading up tothe end of Chapter Eleven.

150


r

r1 2

Figure 7-8

This result suggests the inherent kinematic func-tion of the sink vortex, which combines both the cen-tripetal force of universal gravitation by the radialcomponent of the flow and the unknown force repre-sented by Kepler's third law as the tangential compo-nent of the spiral. Hence, combining the laws of uni-versal gravitation and universal rotation, the law ofthe sink-vortex gives the law of RotationalGravitation.

Another important facet of the analogy is, thatthe Coriolis Effect is also assumed to be responsiblefor the direction of rotation of the vortex formed inthe kitchen sink. This miniature rotating system alsoturns clockwise in the northern, and counter-clock-wise in the southern hemisphere of the globe.

To recognize the improbability of a permanent,straight-line radial flow toward a sink, note theinfinitesimal magnitude of the Coriolis Effect in thiscase, since it originates from the different angularvelocities of the surface of the earth between the alti-tudes of the northern, and southern borders of thekitchen sink.

Considering all the above, it is not only reason-able but rather compelling to conclude, that rotation

is an inescapable kinematic consequence of the opera-tion of a sink in an isotropic medium.

An idea should be inserted at this stage:The torque that creates the vortex in the kitchen

sink and in the atmosphere originates from a largerorder of magnitude, through the Coriolis Effect of therotation of the earth. In the case of the origin of oursolar system, the Coriolis Effect could be produced bythe rotation of the galaxy and the ultimate cause ofany rotation could be the differential rotation of theUniverse!?

Figure 7-9. NGC 3031 (M81), face-on view of a spiral galaxy.

151


As a visual aid for all of the above, it should beworth while to ponder a bit over the following pic-tures, illustrating the various vortices of differentphenomena.

To Sir Edmund Whittaker's pondering on thedirection of science if the spirality of nebulae wouldhave been discovered before the overthrow of Des-cartes' vortex theory, we might add, what impulsewould have been created by the image of a modernsatellite picture of a hurricane. .

Figure 7-10.A satellite picture of Hurricane Elena, 1985.

a) A satellite view of a double hurricane.b) A double whirlpool galaxy.

a) NGC4622, face-on view of a spiral galaxy.b) A synthetic optical photograph of the Milky-way.

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Figure 7-11.

Figure 7-12.

Figure 7-13.M51 whirlpool galaxy with its companion.

It is, indeed, difficult to accept, that some of thesephenomena can not be imagined without the accep-tance of the kinematic of rotation of a real medium,while some others are simply believed to be a mani-festation of the accidental gathering of variouschunks of matter under the mysterious influence oftheir mutual attraction, acting at infinite distancesthrough the mathematical abstraction of gravitation-al fields in totally absolutely empty space.

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CHAPTER EIGHT

THE KINEMATICS OF THE THREE LAWS OF MOTION

Up to this point, with the aid of the ideal gasanalogy, the following ideas have been developed:

In the isotropic medium of an ideal gas all locallyinduced disturbances, periodical or continuous, arepropagated outward in expanding spheres with aspeed, related to the density of the medium and theaverage speed of its constituent units. A sink operat-ing in this medium, can be taken as the generator ofa continuously reproduced disturbance, having a

negative effect on the average density of the medi-um. This in turn results in a net force of pressuretoward the sink, which is directly proportional to thecapacity of the sink and inversely proportional to thesquare of the distance from it. The local withdrawalof a constant volume of the gas results in a radialflow toward the sink from all directions. The velocityof this flow is greatest close to the sink and falls offwith distance according to the inverse square law.

The space around the sink simulates the gravita-tional field surrounding a massive body, as it is gen-erally described within the rotating frame of refer-ence of that body.

In this analogy the constant centripetal force ofgravity is simulated by the net pressure directedtoward the sink and transferred through the periodicimpulsive force of the individual particles of the gen-eral flow. It follows, that any foreign particle, compa-rable in mass to the atoms of the gas, is carried bythe medium and accelerated toward the sink. For allintents and purposes, this directional force, exertedon a foreign body by the atoms with immense but notinfinite frequency, should be taken as being a con-stant force, just like the force of pressure.

154

Aethro-kinematics The Kinematics of the Three Laws of Motion

There is also an inevitable kinematic procedureacting through the head-on collisions of the radialflows, eventually creating a circulatory flow aroundthe sink. The linear momentum of the radial flowstransform into the angular momentum of rotation.

The circulatory flow, generated around the sink,is called a sink-vortex, and its kinematics can bederived mathematically from the geometric inversesquare law of propagation of disturbances, togetherwith Huygens equation of centripetal acceleration.Consequently, it is mathematically equivalent toKepler's third law of planetary motion and thereforeagrees with the observational facts. Within the sink-vortex the individual atoms, or any particles movableby them, are carried on a spiral path toward the sinkwith instantaneous tangential velocities inverselyproportional to the square root of the distance fromthe center. (See App. I. for mathematical derivation.)

Such a description of the gravitational phenome-non requires a break from the Newtonian rotatingframe of reference, in which only the radial compo-nent is realized. For example, the Earth's gravita-tional field should be observed in the frame of refer-ence of the Sun or that of the Galaxy or from the

isotropic space of the Universe. Then it becomes evi-dent that the radial and transversal components ofgravitation are inseparable.

A sink, operating in an isotropic medium with aresulting flow-pattern of a sink-vortex can be takenas a plausible kinematic simulation of the commonorigin for both the tangential components of univer-sal rotation and the radial components of universalgravitation. These two, together, result in the univer-sal phenomenon, which shall be called RotationalGravitation.

The two counter parts of the analogy, gravity andsink-vortex, originate from two separate depart-ments of physics and from entirely different concep-tions, however, they are mathematically clearlyequivalent.

Nevertheless, this simplified kinematical simula-tion of the constant force of Rotational Gravitationmerely represents the capability of a flow pattern tocarry comparable bodies in a manner similar to agravitational field. The extension of this analogy toinclude the simulation of the uniform gravitationalacceleration will involve Newton's grand scheme ofcorrelating terrestrial and celestial mechanics.

155

Aethro-kinematics CHAPTER EIGHT The Kinematics of the Three Laws of Motion

In order to simulate uniform acceleration as aresult of the constant force of the sink-vortex, all con-cepts and mathematics of the Three Laws of Motionmust be simulated in the ideal gas, within the lawsand concepts of the Kinetic Theory of Gases.

FREE EXPANSION Systematizing the vast variety of the possible

motions of bodies, Newton constructed the followingthree laws of mechanics:

(1) Inertia is the inert property of all bodies tomove on a straight line with uniform speed, unlessan external force acts upon them.

(2) Acceleration produced by a force is proportion-al to the strength of the force and takes place in thedirection of the force.

(3) Action and Reaction are a pair of equal andopposite forces, that always exist together.

The quantitative relationships between thesefundamental concepts are as follows:

FORCE = inertial mass × acceleration ACCELERATION = force / inertial mass INERTIAL MASS = force / acceleration

The extent of our weak comprehension of theseconcepts is clearly expressed by the following quotefrom Van Nostrand's Scientific Encyclopedia, 1976;Laws of Dynamics, [1612] :

"The first Law states, that bodies of matter do notalter their motion in any way except as a result offorces applied to them. It is quite conceivable thatNewton's interpretation of 'force' was the primitiveconcept which we all have, based on the musculareffort, and he regarded this statement as the expres-sion of a natural law connecting force with motion."On the other hand, he may have recognized in this

first law, as we now do, an objective definition offorce, namely, that which is capable of altering bodilymotions in the face of the opposition called inertiawhose nature is even now not fully understood."

Nevertheless, as the above equations show, thesebasic concepts of mechanics are inseparably inter-related, and a successful kinematic simulation ofthem must deal, not only with the individual con-cepts, but with their specific relationships as well.

Newton describes the force of gravity as an inert,unexplainable property of matter, acting throughimmense distances without contact or conceivable

156

Aethro-kinematics CHAPTER EIGHT Free Expansion

means of transmission. Similarly, Newtonian inertiais another inert property of all bodies of matter; astill not fully understood inanimate resistanceagainst any change in the state of their motion.

In the foregoing, by the thought-experiment inthe great room it was shown, that an operating sink-vortex in an ideal gas can successfully simulate theeffects of the inert properties of gravitational massand that of the force of gravity. Now, we may inquire,if there is any way to simulate on the microcosmicscale of an ideal gas the so-called fictitious force ofinertial resistance ?!

First, however, a possible confusion involving themechanical role of the vacuum pump in the simula-tion should be clarified.

In order to realize that the pump does not repre-sent an external mechanical force, which in any wayaccelerates the atoms of the ideal gas, let us replaceit with the existence of another room filled with a gasof much lower density than the room of the experi-ment. This set-up, through the known thermodynam-ic phenomenon of free expansion, will produce thesame results as a pump without any involvementregarding the concept of force.

"A process of much theoretical interest is that of'free expansion'. This is an adiabatic process in whichno work is performed on or by the system. Somethinglike this can be achieved by connecting one vesselwhich contains gas to another evacuated vessel witha stopcock connection. When the stopcock is opened,the gas rushes into the vacuum and expands freely.That is, the initial and final internal energies of thesystem is equal in free expansion." (Halliday-Resnick: Physics, [490])

Hence, instead of the vacuum pump, there is nowan extended isolated system of two rooms; A and B,initially filled with different densities of gases andconnected by a small pipe with the porous sphere,reaching into the middle of the space of room A, as itwas described before. When the sink opens the gasescapes through the pipe, from the room of higherpressure A , to room B. The volume of gas per unittime escaping from A depends on the cross sectionarea of the pipe (the capacity of the sink), and thedensity difference between the two compartments.Since the process is adiabatic, there is no change inthe temperature of the gas or in the average velocityof the atoms.

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"Gases expand indefinitely when released, notbecause of repulsion between the molecules, as for-merly supposed, but because the molecules are inrapid motion and do not stop unless they collide withsomething. Air is not forced out through a tire punc-ture; only those air molecules pass out which in theiraimless wanderings, happen to encounter the open-ing. Molecules also pass in from the outside; butsince there are several times as many per unit vol-ume inside as outside, many more pass out than in.The rapidity with which this takes place only empha-sizes the speed of the molecules and the relativeinsignificance of the internal friction opposing it."(Van Nostrand: Sci.Enc. - Kinetic Theory, [1428])

Figure 8-1

Putting all these pieces together, it turns out thatin the sink analogy of gravitation, there is no suchthing as a force in action in terms of Newton'smechanics. Since there is no change in the total ener-gy of the isolated system of the two rooms, there canbe no external or internal force in action in theprocess of free expansion.

But the Kinetic Theory of gases was constructedto work by the laws of Newton's mechanics and ifthere is no force in action in an isolated system,there is no cause for acceleration either.

Indeed, a closer analysis of the motion of the indi-vidual atoms reveals, that in fact, there is no changein their uniform velocity through the whole process offree expansion. The macroscopic phenomenon of theaccelerated flow toward the sink is merely an opticalillusion, which can be explained by considering thekinematic events taking place between the tworooms filled with gases of different densities.

For the sake of simplicity, let us assume that thesink is simply a round hole in the wall between thetwo rooms, operating with a fast moving shutter.Starting with the closed position, gases A and B arecompletely separated, they are both isotropic, homo-

158


geneous and in equilibrium. The atoms are movingwith the same average velocity in both side in com-plete randomness, but they have different densitiesand therefore different total kinetic energies. Say,that gas A is 10 times denser than gas B, it also has10 times greater kinetic energy both per unit andtotal volumes. The density difference can also beexpressed by stating that the atoms of gas B have anaverage collision-free path 10 times longer than thatof gas A.

This difference also means that at any giventime, 10 times more A atoms go in any given direc-tion, than B atoms, and therefore 10 times more colli-sion happens on the surface of the shutter facingroom A than that in room B. Now, recall the case ofthe punctured tire and realize, that upon the suddenopening of the shutter, on the average, only one ofeach 10 A atom will collide with a B atom andrebound, back into room A, the other nine will beable to continue to move freely into the space of roomB. It is evident from this picture, that none of theatoms accelerate or decelerate, but simply gainspace, being able to move further in the same direc-tion with the same uniform velocity. In other words

going into room B the collision free path of the Aatoms are lengthening, while in room A, next to thesink the B atoms rebound much sooner than before,thus their collision-free paths are shortening.

This process then affects both media layer bylayer and, as it was described before, it represents acontinuous disturbance, propagating spherically intoboth rooms; in the form of rarefaction in A and con-densation in B.

THE CENTER OF OSCILLATION In order to fully comprehend this non-accelerat-

ing process, based on the fundamental assumptionsof the Kinetic Theory, consider first the simplerNewtonian field with the purely radial flow of themedium and some further generalizations.

The assumed existence of an average collision-free path can be extended by combining it withanother general concept of randomness, namely, thatin an isotropic medium at any given instant thesame number of atoms are moving in every possibledirection. Hence, within a given interval of time, eachatom moves an equal collision-free distance in everydirection. In three dimensions this can be represent-

159

Aethro-kinematics CHAPTER EIGHT The Center of Oscillation

ed by a collision-free sphere for each atom, the radiusof which equals the collision-free path. On the aver-age means here, that the frequency of the randomoscillation is so immense, that within any crude,macroscopic time interval the atoms not only movein all possible directions, but even this full cycle isrepeated great number of times.

Hence, when an atom collides within or beyondthe border of its sphere or when some wander awayfrom its initial position, it averages out by the greatnumbers and becomes negligible, compared to thetotal statistical isotropy of the medium. The collision-free sphere can be described by the three rectangularCartesian coordinate axes (x,y,z); in this case theyrepresent six vectors of equal magnitude, the sixcomponents of all possible directions of the motionsof an atom. Within this sphere each atom moves on astraight line with uniform velocity, until it collideswith another atom, on the border of their neighbor-ing spheres, where they both rebound into their ownterritory.

Thus the motion of each atom can be consideredas an omni-directional oscillation, whose center-pointcan be called, the center of oscillation. The diameter

of the sphere represents the amplitude of the oscilla-tion and the velocity of the atoms divided by thelength of the diameter, gives the frequency of theoscillation. These hypothetical collision-free spheresdo not change their positions or their shapes, as longas the density and the pressure around each atom isisotropic, that is; as long as the medium, as a whole,is motionless.

(a) Figure 8-2. (b)

Figure 8-2 (a) shows six vectors, enclosed in a col-lision-free sphere, representing the random oscilla-tion of a particle in an isotropic, motionless medium.

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V = d

V = 0d

In the case of an operating sink, however, thelocal disturbance of the withdrawal of the atomseventually destroys the isotropy of the whole medi-um. The atoms in the immediate vicinity of the sinkare able to move radially further toward the sink,than in any other direction. The initially isotropicoscillations of these atoms become lopsided. Theircenters of oscillation begin to drift and the collision-free spheres become elongated into spheroids withtheir major axes, x pointing toward the sink, (b).

Evidently, the atoms in the next layer of themedium experience a similar freedom in theirmotions toward the sink, but to a smaller extent,since the extra space left by the first layer is dividedamong the greater number of atoms of the secondlayer.

Similar is the case for each consecutive layer.The result is a drift of the center of oscillation of

each individual atom toward the sink. This driftvelocity, Vd of the atoms (b) is increasing as theatoms and their spheres of oscillation approach thesink. In this respect there is a global acceleration ofthe gas, but obviously without any change in the uni-form velocity of the atoms. The drift, which is super-

imposed on the initial random motion of the atoms, isproportional to the extent of the rarification of themedium, thus again, directly proportional to thecapacity of the sink and inversely proportional to thesquare of the distance from it.

For future references, one more step of general-ization is needed. From the theory of FreeExpansion, where the total kinetic energy of the sys-tem is constant, together with the concept of isotropy,it follows, that the total kinetic energy of each indi-vidual atom also remains the same even in the caseof a drift, superimposed on randomness.

Consequently, as the oscillation of a drifting atomtakes up more space in the direction of the majoraxis of the spheroid, the minor axes are shortening inthe same proportion. In other words, when the colli-sion-free-sphere is elongated into spheroids of vari-ous eccentricity the volume contained in the differentshapes remains constant. This concept will be usefullater in connection with Bernoulli's constancy of thecombined kinetic and dynamic pressure of an idealfluid.

It has been stated in the first part of the simula-tion, that the rarification of the medium due to the

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sink is inversely proportional to the square of thedistance and therefore it produces a radially acceler-ated flow toward the sink. However it is now clearthat this acceleration of the flow is a macroscopicillusion, simply mistaken for the lopsided oscillationsof the atoms and the consequent drifting of the cen-ters of oscillation with a uniformly increasing con-tiguous radial flow.

All this of the above had been described inNewton's rotating frame of reference, where the tan-gential component of the rotating gravitational fieldis neglected. Leaving now this frame and recognizingthe rotation of the flow-field, we can conclude that allthe above is valid for the motions of the atoms in thesink-vortex, except the velocity vector of their drift isnot radial, but always tangential to the spiralstream-lines of the vortex.

According to the analogy, in a gravitational field acertain magnitude of potential energy can beassigned to every point. When a body of matter isreleased from rest at that point it experiences uni-form acceleration, and according to Newton's secondlaw, this uniform acceleration requires the continu-ous action of a force, that is, a constant force.

In the flow-field of the sink-vortex it has beenfound that the atoms of the gas do not change theirvelocities in free expansion toward the sink, The neg-ative potential energy of any layer of the medium isrepresented by a deficiency of pressure from thedirection of the center of the vortex, which in turnresults in a net force of pressure toward the sink.Kinematically speaking, this unbalanced pressure atany point in the field of the vortex only means thatmore atoms are moving with their average uniformvelocity toward the sink, than in any other direction.

A successful simulation of the uniform gravita-tional acceleration in the ideal gas, this net pressure,without the acceleration of the atoms, must be foundkinematically capable of acting in the face of theopposition of the inertial resistance of mass as a con-stant impulsive force with great but not infinite fre-quency.

MOMENTUM = KILOGRAM × METER / SECHaving an approximately clear kinematical simu-

lation of the constant force of gravitation, the nextstep should be to simulate the product of this force;the uniform acceleration, which is produced against

162

Aethro-kinematics CHAPTER EIGHT Momentum = Kilogram x Meter / Second

the resistance of the inertial mass of a test-particlewhen released from rest in a gravitational field.

Nevertheless, gravitational acceleration in free-fall is not the clearest process to familiarize the con-cept of inertia because of the problematic subject ofthe equivalence of inertial and gravitational mass,which results in the same acceleration of all bodiesregardless of their different inertial masses.Therefore, it is more practical to follow the historicalroute and the general educational approach todescribe the concepts of mechanics.

Inertia is defined by Galileo and Newton as theinert property of all material bodies, to resist anychange in their state of motion. In the absence of theaction of an external force a body moves with uni-form velocity on a straight line.

The state of rest is taken as a special state ofmotion, where the velocity of the body is zero.

Acceleration is any change in the state of motionof a body, whether it is only an increase or decreasein speed, or only a change in direction.

The magnitude of the change in the state ofmotion, that is, the acceleration, is directly propor-tional to the magnitude of the force and inversely pro-

portional to the inertial mass of the body. A greaterinertial mass needs a greater force for the sameacceleration than a smaller mass. Also, if two bodiesare moving with the same velocity, the one with thegreater inertial mass requires a greater oppositeforce to stop it. The same is true for the case whentwo bodies have equal masses but one has a greatervelocity than the other.

In classical mechanics, from Descartes on, theserelations were described by the concept of theamount of motion, which arises from the velocity andthe quantity of mass conjointly.

In the modern language of mechanics the'amount of motion' is called momentum. It is a vec-tor quantity produced by the multiplication of thevector quantity of the velocity, v by the scalar quanti-ty of mass, m. The symbol p is used to represent themomentum vector; p = mv. In the 'Principia' the sec-ond law of motion is expressed in terms of the rate ofchange of momentum of a body, which is proportionalto the resultant force acting on the body and it is inthe direction of that force.

The principle of the conservation of momentumstates, that regardless of the interactions between

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bodies of different masses, moving with variousvelocities, the total momentum of an isolated systemdoes not change in time. That is; the total quantity ofmasses multiplied by the total velocities of all bodies,is a constant.

Figure 8-3.Consider the simple elastic collision between two

solid spheres of equal inertial masses. (Figure 8-3).They are positioned on same line going throughtheir centers. Before collision body mA is moving fromleft to right with a velocity, VA = 10 m/sec.

Body mB, is at rest, its velocity,VB = 0. In the colli-sion between equal masses, the bodies simply

exchange their velocities. While mA stops dead, mB

moves away with the total initial velocity, 10 m/sec.If their velocities after collision are UA and UB , then

VA + VB = UA + UB since after collision UA = VB

and UB = VA.In this special case of an isolated system of equal

masses, the total velocity is also conserved:Before collision : VA + VB = 10 m/secAfter collision : UA + UB = 10 m/sec

The essence of Newton's second law and the con-servation of momentum is, that the acceleration ofthe bodies are not only directly proportional to theforce, but also inversely proportional to the magni-tude of their inertial masses.

Therefore, as Figure 8-3 (b) shows, if mA is 20kgand mB is 10kg, the total velocities after the collisionwill not be conserved, but differ from the initialvelocities. The 20kg of mA will not be completelystopped by the 10kg mass of mB, but it will only loosehalf of its velocity and continue to move in the samedirection with 5 m/sec. The same time mB will moveaway from the collision with the total initial speed ofmA , 10 m/sec.

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Before collision After collision

m

(a) Equal masses

(b) Unequal masses

A mB

mA

mB

mB

mA mB

mA

VB UBVA UA

VA VB UA UB

The principle of the conservation of momentumstates, that the product of each mass times its veloci-ty, that is, the total momentum of the systemremains the same after collision.

(mA×VA) + (mB×VB) = (mA×UA) + (mB×UB) (8.1).

By knowing the initial velocities and the finalvelocity of one of the bodies, this principle makes itpossible to calculate the final velocity of the otherbody. If A's velocity decreases in the collision to 5m/sec, the magnitude of the final velocity, UB can befound as follows:

mA(VA − UA) (20kg) (10 m/s − 5 m/s)UB = −−−−−−−−−−− = −−−−−−−−−−−−−−−−−−−−

mB 10kg

20kg× (5 m/s) 100kg⋅ m/sUB = −−−−−−−−−−−−− = −−−−−−−−−− = 10 m/s

10kg 10kg

Total velocity before:(VA + VB) = (10 m/s + 0 m/s) = 10 m/s

Total velocity after :(UA + UB) = (5 m/s + 10 m/s) = 15 m/s

Momentum before:(20kg×10 m/s) + (10kg×0 m/s) = 200kg-m/s

Momentum after:(20kg×5 m/s) + (10kg×10 m/s) = 200kg-m/s

Obviously the total velocity of the isolated systemhas changed in the collision, but the total momentumhas been conserved. − This is one of the most funda-mental laws of physics and has been experimentallyverified beyond any doubt.

A NON-INERTIAL SYSTEM Descartes believed that the total amount of

motion in the universe is conserved. Now, in classicaland modern physics it is believed that the totalmomentum is the eternal quantity.

Nevertheless, since the concepts of inertia andforce are still not clearly understood, it is alsounclear, what the concept of momentum could repre-sent in physical reality.

Adding apples and oranges together can makesome sense, calling the resulting sum fruits, butwhat could be the meaning of the product by multi-plying them with one another ?!

165

Aethro-kinematics CHAPTER EIGHT A Non-inertial System

What can be this 'amount of motion' that wantsto preserve itself, and how can inanimate chunks ofmasses resist a forced change in their momentum ?!

As we have seen in the analysis of the gravita-tional force, the nature of kinematic simulation issuch, that the Newtonian concept first must be disas-sembled to a point where it means nothing morethan the clearly kinematic concept of motion. Then,based on the underlying kinematic process, it has tobe rebuilt to its full meaning.

Let us first recognize, that the concept of inertia,force, acceleration and momentum, or theirNewtonian relation to one another is completelyunnecessary and useless in a system of bodies, whereall constituents have equal masses. Whether the bod-ies are atoms of the same element, or ball bearings,or uniform bowling balls, as long as they interactonly through the impulsive forces of one-to-one colli-sions, and exert no other actions on one another, theonly necessary concepts are; motion, direction andspeed, that is, velocity. In an isolated system of suffi-ciently great number of equal masses, there is nocause for a change in the total motion of the bodiesduring collisions. On the average they are all moving,

going into, and coming out of the collisions with thesame speed in totally random directions.

The total velocity of the system is evenly distrib-uted among its members; each one represents oneunit of motion and on the average at any instant inany considerable volume, the same number of unitsmoving in every directions. Evidently, such a systemis non-inertial, there is no reason to create theanthropomorphic assumption that material bodiesresist the change in their state of motion, or to inventa force which acts in the face of the opposition of thefictitious force of inertia.

In this system a moving body represents a unit ofmotion, nothing more, nothing less.

Since all units of the system are of equal masses,the concept of momentum is superfluous and whenthe bodies interact, via collision, they merely ex-change or mix velocities.

Here the Newtonian concept of force means themere transference of motion. Since the internalstructure of the members of the system, do not affecttheir interactions, the transference of motion is total-ly elastic and instantaneous, thus the concept ofacceleration is also foreign to the system.

166


Consequently, both the concepts of force and accel-eration revert back to the pure concept of motion.

In a non-inertial system like an ideal gas, themost general conservation law is the conservation ofmotion. Thus, this system can be fully described bythe concepts of length and time and the third funda-mental Newtonian dimension of the inertial mass,becomes unnecessary.

In the following a kinematic simulation of theNewtonian concepts of inertia, force, momentum andacceleration will be attempted, showing the origin ofthese concepts, their conceptual relationships andthe unavoidable necessity for inventing them.

Consider then an isolated, system of uniform ballbearings in weightlessness, somewhere in space, act-ing in every respect as an ideal monatomic gas.Assume that the all over size of this cloud of ball-bearing-gas is much greater than the experimentalvolume thus its peripheral expansion is negligible.Also assume that the members of the system aremoving with an average velocity of 10cm/sec, in total-ly random directions. As long as they only interactwith one another, and only through collisions, thesystem is non-inertial, meaning that during all inter-

actions the total initial velocity in the system is con-served. In this non-inertial system, inertia, force andacceleration means nothing more than motion, andthe transference of motion.

Imagine now, that in this non-inertial ideal gas ofball bearings, two units are somehow bound togetherinto a double-ball. This joining of the two units canbe illustrated by an imaginary axis Q, which goesthrough the centers of both balls which are sliding onit without friction. The length of this Q-axis is threetimes the diameter of a ball and has a stopper oneach end by which the motion could be transferredfrom the front to the end of the group, and vice verse.

Figure 8-4.

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b.

c.

a.

Q - axis

d.

e.

f.

This device of the Q-axis is assumed to have totalrigidity and negligible mass. In the followingthought-experiment the Q-axis should simulate theconcept of an elastic force, binding two or more ballsloosely together. In more general terms, the Q-axissimulates cohesion, the tendency of keeping the con-nected parts of matter within a limited distance.

For the sake of comparison, a larger group of fiveballs should also be assembled with a Q-axis whoselength is six times the diameter of a ball.

Let us call a single ball A, and the double ballGroup/B, and the five connected balls, Group/C.

Since it would be impossibly complex to followthe motion of these groups among the totally randommotions of all the other balls, consider a greatly sim-plified situation in one dimension.

It is a common example of elastic collisions, thata moving ball collides with one of equal mass, at rest.Upon impact the moving one stops and transfers itstotal velocity to the other. This can be taken as thebasic example of all collisions, since the frame of ref-erence of the observer can always move such a way,that one of the bodies is in a state of rest relative tothe observer.

Another well known simple example of elasticcollisions is when two equal masses move with thesame velocities in opposite directions on a mutualaxis. In a head-on collision, they simply exchangedirections and move away in the opposite directionswith exchanged speeds. Restricting the system tothese simplified events only, the Q-axis and allmotions are one dimensional, and the direction ofmotions coincides with the line going through thecenters of the balls.

Figure 8-5 illustrates the consecutive snapshotsof the horizontal movements of three isolated groups:the single ball A, Group/B and Group/C.

On snapshot (a) ball A and both groups are con-sidered to be at rest touching the vertical line, 0 rep-resenting zero centimeter at the time -0.1 second.With the three additional black balls, X, Y and Z ,already moving from left to right (⇒ ), each group onits own dotted line represents an isolated systemwith one unit in motion and 10cm/sec initial velocity.

Snapshot (b) shows the situation one tenth of asecond later, at time=0. The moving black balls X, Yand Z, each collide with their own groups. X hits thesingle ball A, transfers its total velocity and stops.

168


Figure 8-5.

The single ball, A moves away with a uniformvelocity of 10 cm/sec to the right.

Evidently, without cause, there is no change, inthe state of motion of the single ball A, thus, fromhere on it moves undisturbed along a straight linewith uniform velocity to the right, while X is at restat the point where it was stopped by the collision. Inthis case, before and after the interaction, the totalvelocity of the system remains the same; 10 cm/sec.

On the second dotted line Y hits the first memberof Group/B and on the third line Z hits the firstmember of Group/C. Since the balls in both groupsare touching one another, upon the collisions with Yand Z, the velocity is instantaneously transferredover to the last ball of the group to the right, which isfree to move. In both groups, this last ball inheritsthe initial velocities of Y and Z, while those arestopped at the point of the collision.

Counting from left to right, in Group/B, B2 ismoving and in Group/C, C5 is moving. Both of themare sliding freely on their Q-axes with 10 cm/sec, rep-resenting the total velocity of their systems at thisinstance. In snapshot (c), however, at the end of thefirst tenth of a second, they both hit the right end

169


a.

0 1 2 3 4 5 6 7 8 9 10 cmTime interval (0.1 sec)

-0.1

b.

0.0

c.

0.1

d.

0.2

e.

0.3

f.

0.4

①

③

②Group/B

A

Group/C

X

YZ

X1

stopper of their Q-axes. In the case of Group/B, B1 ishit from the back by the left-end stopper and throughthat it inherits the total velocity of B2. while B2 isstopped by the impact. The same happens inGroup/C where C5 stopped by the Q-axis and trans-fers the motion to C1 which instantaneously trans-mits the motion through C2 and C3 to C4 which is freeto move toward the right with the total velocity ofthe system. And so on and on... The rest is self-explanatory, as Figure 8-6 shows, the snapshots from(g) to (l), taken in one tenth of a second intervals.

If the length of the field is 10 cm and the initialvelocity is 10 cm/sec, the single ball, A with its con-tinuous motion reaches the end of the line in one sec-ond. At line 10 A collides with X1 at rest, transfers itstotal velocity to that unit, and itself stops. During theinteractions the total velocity of this isolated one unitsystem was conserved.

However, as it can be seen, during the same timeinterval Group/B only moved half of the distance, 5cm, and therefore it will take two seconds for thissystem to reach the end of the field. Group/C movedonly one fifth of the whole distance, 2 cm, so it willreach the end in five seconds. Figure 8-6.

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g.


0.5

h.

0.6

i.

0.7

j.

0.8

k.

0.9

l.

1.0

①

③

②

X

YZ

X1

A X1

It is evident that in all systems at every instantthe total velocity was always 10 cm/sec. All membersof the groups, when they moved, carried the total ini-tial velocity. One of them was always in motion, butthat did not change the position of the group, as such,in space. − The group itself was at rest part of thetime. Namely Group/B was at rest half of the totaltime and Group/C was at rest four-fifth of the totaltime. This means that Group/B had only 5 cm/sectotal velocity and Group/C had only 2 cm/sec velocity.If there was a Group/D, consisting 20 balls, it wouldonly move in one twentieth of the total time, at theend of every two seconds, and it would take 20 sec-onds to reach the end of the field, thus its groupvelocity would be 0.5 cm/sec.

From this scenario it is evident, that there is adefinite relationship between the initial velocity Vi,,the number of balls, N in the group, and the group-velocity Vg: The group-velocity is directly proportion-al to the initial velocity and inversely proportional tothe number of balls in the group.

Vi Vg = −−−−− (8.2).

N

Now, we have two different ways to look at thesame situation : On the one hand, we can measurethe velocity of each moving ball separately in eachsystem and conclude, that in all isolated non-inertialsystems, at any instance during the interactions, thetotal velocity is conserved. On the other hand, we canmeasure the velocities of the groups, and then itbecomes evident that the initial velocity is immea-surably buried in the velocity of the group, and thelaw of the conservation of velocities is not valid any-more. In order to uncover the initial velocity, thatwas imparted to the group, we must multiply thegroup-velocity by the number of balls in the group:

Vi = N × Vg (8.3)But if each ball represents one unit of mass, then

the total number of balls N represents the total massof the group and this total mass multiplied by thevelocity of the group is equivalent to the Newtonianconcept of momentum. − Thus Vi, the initial velocityof one unit of motion in this case, represents the ini-tial momentum of the group, which has been con-served through the interactions. This, then is theactual kinematical reason, why Newton's multiplica-tion of mass with velocity works.

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Let us assume that each ball bearing is 1 gram.The single ball A represents one unit of mass,Group/B combines 2 units and Group/C 5 units ofmass. X,Y and Z each represents 1 gram mass inmotion. In each isolated system, at the beginningonly 1 ball was in motion, having a velocity of 10cm/sec. Hence the total initial momentum of eachsystem was 1gr×10cm/sec = 10gr× cm/sec. A carriedthe total momentum of X all the way through and atthe end of the field put X1 into motion bearing thesame momentum. The initial momentum of Y, how-ever, was dispersed among the members of Group/Band resulted in the momentum of 2gr×5cm/sec, alsoequal to 10gr×cm/sec. The initial momentum of Zwas dispersed in Group/C, resulting in 5gr×2cm/sec,also equal to 10gr×cm/sec. The total momentum ofeach system was 10gr×cm/sec in every instance dur-ing the interactions, thus the momentum of each iso-lated system was conserved.

We can also conclude, that in the above examples,the initial ‘one unit of motion', like that of X, Y or Z,produced different group-velocities, which were pro-portional to the number of units in the groups, thusN is equivalent with the Newtonian concept of iner-

tial mass, representing a kind of resistance to motionwhich is directly proportional to the magnitude of N.The same time Vi, the initial velocity of the unit ofmotion, imparted to the group can be taken as oneunit of Newtonian force (gr × cm/sec).

So far only one unit of force was transferred toeach system and therefore Newton's concept of accel-eration did not enter into the simulation. However,just as a unit force can be dispersed among a groupof units, momentum can also be accumulated fromthe repetition of the impulses of individual unitforces, periodically imparted on the same group.

This will result in different group velocities andmomenta, proportional to the number of impulsesper unit time, that is, the frequency of the impulses, f=gr×cm/sec/sec.

Through the concept of the Q-axis the snapshotsof Figure 8-7 shows how Group/C can accumulatemore than one unit of velocity under the influence ofan impulsive, periodical, constant force..

In Newton's mathematics, acceleration equals therate of change of velocity; cm/sec/sec :

FORCE = mass × acceleration; gr×cm/sec/sec.

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At time -0.1 all members of Group/C are at rest,while a row of units of force are moving from left toright on the horizontal axis of of the group.

Figure 8-7

Each unit of force is 1 gr. mass, moves 10 cm/secand they follow one another in three ball diameterdistance, which means, that at any vertical line, oneunit passes through in each 0.33 second time inter-vals (3.33gr ×10cm/sec/sec). Hence, the frequency ofof the periodical impulsive force is 3.33 cycle/sec.

The first unit of force, F1 hits C1 of Group/C atzero second. As before, this one unit of motion isinstantaneously transferred through C2, C3 and C4 toC5, which is free to move. The unit transferring thefirst impulse stops in the impact. At the end of 0.1second C5 hits the right end stopper of the Q-axiswhich transfers the impulse through C1, C2 and C3 toC4. If nothing else happened, Group/C would move,as before, with a uniform group-velocity of (Vg=Vi/N)2 cm/sec. Meanwhile, however, the second unit offorce, F2 moved closer and by the end of 0.2 second itputs the first force unit back into motion, which hitsC1 again. Hence, with this impulse, already two unitsof Group/C is moving simultaneously. This in turnmeans that at this rate the group velocity should be(20gr×cm/sec)/5 = 4cm/sec. − And so on...

As the consecutive snapshots show, at every 0.3second interval Group/C accumulates another unit

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0.0

0.1

0.2

0.3

0.4

-0.1

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

F3

F4

F5

F1F2 Group/C

of motion and by the end of 1.2 seconds all five mem-bers are in uniform motion, thus the whole group hasbeen accelerated to the magnitude of the initialvelocity of 10 cm/sec.

From this experiment, several conceptual paral-lels can be drawn between the workings of thesegroups and Newton's concepts of mechanics :

a) The last example clearly shows, how theNewtonian force changes the state of motion of abody and produces the acceleration in the direction ofthe force. The acceleration is directly proportional tothe magnitude of the force; that is, the velocity of theunit of force, and the number of units colliding withthe body per unit time, gr×cm/sec/sec. The force isconstant and the acceleration is uniform if the forceis periodical, that is, if the same number of forceunits hit the body per second. The acceleration isinversely proportional to the amount of inertial massof the body; that is, the number of units in a groupconnected elastically by the Q-axis.

b) Based on the above, other experiments can bedesigned. For instance, let us say that Group/C ismoving with constant velocity of 10 cm/sec, meaningthat all units are moving simultaneously. At the

right end of the field, on the same line of motion fiveindividual units (x1 to x5) are placed at rest, at equaldistances from each other. This situation is the recip-rocal of the procedure in Figure 8-7. The single unitsat rest represent units of a retarding force, or a resis-tance. They are included in the isolated system,whose total initial momentum is the momentum ofGroup/C, 5gr×10cm/sec = 50gr×cm/sec. After the firstimpact between Group/C and x1 single unit, C1 stopsand X1 is set into motion with 10 cm/sec. At this stageGroup/C gave up 10gr−cm/sec momentum andretained 40gr×cm/sec momentum, its group-velocitytherefore decreased to (40gr×cm/sec)/5gr = 8cm/sec.However, the total momentum of the system remainsthe same: (40gr×cm/sec) + (10gr×cm/sec). As X1 movesto the right, it collides with X2 and stops. NextGroup/C catches up with X1 and looses another unitof momentum.

It follows, that during five consecutive collisionswith the singles, Group/C is gradually decelerated tozero velocity by the constant resistance of the singlebodies. Meanwhile, the total momentum of the iso-lated system, 50gr×cm/sec, was imparted to five sin-gle units, each inheriting 10gr×cm/sec momentum,

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thus the total momentum of the isolated system wasconserved.

c) Suppose now, that two groups are positioned onthe same axis of motion. Group/C, as before, moveswith a group-velocity of 10cm/sec, Group/B standsstill at the right edge of the field. The initial totalmomentum of the isolated system is equal to themomentum of Group/C, 50gr×cm/sec. From the pre-vious examples all consecutive collisions can betraced and a final result can be deduced. After twocollisions between the groups, both units of Group/Bwill be in motion representing 20gr×cm/sec momen-tum and 10cm/sec group-velocity. At the same timeGroup/C decelerates, two of its units stop in theimpacts, and therefore move with (30gr×cm/sec)/5gr= 6cm/sec group velocity. As it can be seen, the totalmomentum of the isolated system has been con-served; (20gr×cm/sec)+(30gr−cm/sec) = 50gr×cm/sec.but the total initial group-velocity increased from10cm/sec to 16cm/sec. Where did this excess motioncome from?

Not knowing the internal workings of the Q-axes,there would be no other answer than; this is one ofthose mysteries of inertia.

d) So far, all examples were collisions betweenresting and moving masses and in one dimension,but the same idea can be extended to singles orgroups moving in opposite directions with equal ordifferent speeds colliding head on or off-center.

Since momentum is a vector quantity, by some-what more elaborate examples, it can be shown, thatin the one-to-one interactions of an isolated system,where momentum remains the same, not only theproduct a mass times speed, but mass times direc-tion is also conserved.

In other words, the basic rule of the kinetic theo-ry, that at any given time the same number of ballsare going in any one direction in a non-inertial sys-tem also has its parallel in an inertial system.

It follows that, in principle, the groups of the Q-axes can be extended into three dimensions and intounlimited sizes, the kinematic nature of inertia, forceand acceleration, and all derived Newtonian mathe-matical concepts remain the same in three dimen-sions and they can still be explained through theone-to-one collisions of classical mechanicism.

At this point we may recall Maxwell’s favoriterepresentation of three-dimensional electromagnetic

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cohesional forces through ball-bearings connected toone another by spiral springs to picture the elasticityof the fields. We would call them the Q-springs.

No doubt, all ingredients are now available forthe simulation of the constant force of gravity, and itsresulting phenomenon of uniform acceleration infree fall.

Next, let us attempt to incorporate these kine-matic simulations for the sake of a better descriptionof the complex kinematics of Kepler's formula andwith it, the complete kinematics of RotationalGravitation.

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CHAPTER NINE

THE LAWS OF PLANETARY MOTION

In the discussion of the sink-vortex, we have suc-ceeded in deriving Kepler's formula from the inversesquare law of the propagation of disturbances in anisotropic medium. From this, followed the equationfor the instantaneous tangential velocities of the por-tions of the spiraling medium in the sink-vortex;

1V ∝ −−−−−− (9.1)

−−− √ R

This equation can be derived from Newton's Lawof Universal Gravitation with the simplification of

assuming circular orbits, and it agrees with the for-mula of Kepler's third law; K = P2/R3.

However, Kepler's first and second laws do notallow this simplification. In agreement with theobservational facts, these laws state that the planetsare moving on elliptical orbits with the Sun at one ofthe focuses and accelerating and decelerating in sucha way that a line drawn from the Sun to the planetsweeps out equal areas in equal times.

The following quote from a contemporary astrono-my text represents a typical description of the deriva-tion of Kepler's first law from Newton's UniversalGravitation :"Kepler's laws of planetary motion are empirical laws,

that is they describe the way the planets are observedto behave. Kepler himself did not succeed in findingmore fundamental laws or relationships from which histhree laws of planetary motion would follow. On theother hand, Newton's three laws of motion were pro-posed by him as the basis of all mechanics. Thus itshould be possible to derive Kepler's laws from them.Newton did, in fact, show that the motions of the plan-ets, as described by Kepler, followed from his fundamen-tal postulates.

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Aethro-kinematics

"Consider a planet of mass Mp at a distance R from thesun moving with a speed V in a direction at right anglesto the line from the planet to the sun. The centripetalforce needed to keep the planet in a circular orbit is :

Fc = MpV2/R."Now suppose the gravitational force between the

planet and the sun happens to be greater than the forcegiven by the above equation. (This can only happen ifthe planet moves slower than it should on its orbit.Why?) Then the planet will receive more accelerationthan is necessary to keep it in a circular orbit and it willmove somewhat closer to the sun. As it does so, becauseof its increased speed and its decreased distance fromthe sun, a greater centripetal force is required to keep itat a constant distance from the sun."Eventually a point will be reached at which the gravi-

tational force is insufficient to produce enough cen-tripetal acceleration to keep the planet from moving outaway from the sun. Thus the planet will move outwardas it rounds the sun until it has reached its originalposition, where the gravitational force is again greaterthan it is needed for the circular centripetal accelera-tion, and the process is repeated. Thus we see qualita-tively, how a planet may follow an elliptical orbit."

(Abell, Exploration of the Universe, [60])Evidently, this 'derivation' of Kepler's first law is

not only an example of the total neglect of the originof the tangential components of the planetarymotions, but it also uses this ignorance to make theinsufficient tangential components responsible forthe elliptical orbits of all planets.

Nevertheless, now with the aid of the kinematicaldescriptions of the Newtonian concepts of constantforce, inertia and acceleration, it seems possible torender a sensible simulation for Kepler's empiricallaws of planetary motion.

Thus, by some stretching of our imagination, letus picture the following: Somewhere in space, in totalweightlessness there is a great cloud of isotropic,ideal gas of ball bearings stripped from all action-at-a-distance forces among them. In completely randommotion, they interact only through one-to-one colli-sions. Each ball represents one unit of velocity andone unit of mass, thus in this non-inertial, isolatedsystem all rules and assumptions of the KineticTheory, and its extensions executed earlier, are valid.

Deep in the cloud there exist an empty Sphere,say, a hundred times larger in diameter than the size

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Aethro-kinematics CHAPTER NINE The Laws of Planetary Motion

of the individual balls, but having such a thin wall,that its inertial mass is exactly equal to the mass ofone unit. Hence, the collisions between the sphereand the balls are exactly equivalent to the one-to-onecollisions between the balls. Let us call this conceptthe Q-sphere.

(a) Figure 9-1 (b)

Since time is infinitely divisible, it can be assum-ed that no two collisions in the system happen simul-taneously. Therefore, in each collision a single balltransfers its total motion to the sphere, which thenmoves in the direction of the impulse with uniformvelocity on a straight line until it receives a new

impulse from another ball. Evidently, under the con-stant bombardment of the surrounding gas, the Q-sphere performs a distinct omni-directional oscilla-tion, whose amplitude and frequency is determinedby the density of the gas, the surface area of the Q-sphere and the velocity of the balls.

Considering that, in the absence of an externaldisturbance the gas of ball bearings is isotropic, thecenter of oscillation of the Q-sphere is in the state ofrest relative to this isotropy.

Now, let us introduce a sink somewhere in thecloud, through which a given volume of the gas isbeing withdrawn from the medium per unit time. Asa result, the familiar radial winds come into exis-tence, blowing toward the sink from all directions.

At this stage, no matter where the Q-sphere islocated, it receives an unbalanced pressure onaccount of the rarefying effect of the sink and by theresulting drift of the centers of oscillation of the balls.The excess pressure of the gas in the direction of thesink represents a net centripetal force, actingthrough one-to-one collisions between the individualballs and the surface of the Q-sphere.

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It follows, that each impulse toward the sink,unbalanced by one from the opposite direction, cre-ates a lopsidedness in the initially isotropic oscilla-tion of the Q-sphere, and the center of oscillation ofits own also begins to drift toward the sink.

Considering the comparatively great surface areaof the Q-sphere, it engages in a much greater num-ber of collisions than any individual ball. Therefore,in proportion to its size, the frequency of its oscilla-tion is higher and its collision-free path is shorterthan those of the unit balls. Being, however, merelyone unit of mass, the smaller amplitude and greaterfrequency evens out, and the Q-sphere simply driftswith a velocity characteristic to its distance from thesink and equivalent with the drift-velocity of theneighboring individual balls.

It should be remembered, as it was establishedearlier, that in the macroscopic accelerating flow ofthe ideal gas, actually none of the atoms are acceler-ating, but simply on account of the rarefication andthe lengthening of the collision-free path, they areable to move for a longer period of time toward thesink than in any other direction. In such system, theonly continuous motion and velocity is the motion

and velocity of the individual atoms. Everything elseis merely a drift of the center of the oscillation of theatoms or in this case, that of the sphere.

Next, let us fill up the Q-sphere with the rightnumber of ballbearings, say 100, and assume thatthis will make an internal gas of the same density asthe external one. The balls inside are moving in com-plete randomness, with the same speed, and interact-ing with the inside wall of the sphere through per-fectly elastic collisions.

In general, the Q-sphere with the enclosed gas,represents the same restrictions on the motions ofthe group of internal balls as the Q-axis produced inGroup/C; a kind of elastic force, binding a number ofballs loosely together within a fixed volume of space.

Taking the external gas away for a moment, itcan be seen, that the internal gas also generates anomni-directional oscillation of the Q-sphere on itsown account. In the absence of an external distur-bance, this internal gas and its effect on the insidewall is also isotropic, therefore it tends to keep thecenter of oscillation of the sphere in the state of restrelative to the internal isotropy. Figure 9-1. (b).

180


Putting the whole picture back together, it followsfirst of all, that the frequency of the oscillation of theQ-sphere is doubled from the external and internalcollisions.

On the average, under the equal external andinternal pressures the Sphere would still be in thestate of rest relative to the isotropy of the gases.However, the net centripetal force of the sink and theresulting unbalanced excess external collision fromone direction tends to off-set the equilibrium.

But the Q-sphere is not free to move anymorewith the external flow as a single unit. Each unbal-anced external collision is absorbed by one of theinternal balls and then, through the averaging effectof the randomness, it is dispersed throughout thewhole internal gas, just as in the dispersion ofmotion in the examples of the Q-axis. In the case ofGroup/C one unit of net force was dispersed amongthe five balls and the resulting drift-velocity wasequal to the initial velocity of the ball divided by thenumber of units in the group. Since the unbalancedcollisions do not represent a change in the speed, butstrictly in the direction, the net force on the Q-spherealso acts in one dimension only.

Hence, aside from the very details, the same endresult can be expected here as in the case of the Q-axis. The constant net centripetal force is equal to thesum of the periodical unbalanced external collisionsin the direction of the sink per unit time.

The inertial resistance of the Q-sphere againstthe change in its state of motion arises from the con-stant dispersion of the units of directional forcethroughout the internal gas. The acceleration of theQ-sphere is directly proportional to the constant peri-odical impulsive force, and inversely proportional tothe number of units of the internal gas, within whichthe impulsive force disperses.

Each ball inherits an increasing share of theexternal drift, which in turn, affects the oscillation ofthe sphere. Thus the total drift-velocity of the centerof oscillation of the Q-sphere toward the sink gradu-ally increases. In other words, under the influence ofthe constant net force, in the face of the opposition ofinertia, the Q-sphere is uniformly accelerating.

There is, however, an important difference bet-ween the kinematics of the Q-axis and the Q-sphere.On the one hand, the collisions in the Q-axis-experi-ment were arranged in such a way, that the transfer-

181


ence of motion was instantaneous through the ballstouching one another; the impulse of an external ballon Group/C was transmitted through four balls in arow and put the fifth one into motion at the verysame instant.

On the other hand, in the internal gas of the Q-sphere the balls are in random motion with an aver-age collision-free distance between them, thus thetransference of motion from each unit to the othertakes a distinct time interval, which depends on thedensity of the gas and the velocity of the units.Consequently, the dispersion of the net force-vectorthroughout the internal gas is a function of time andtherefore the drift-velocity of the Q-sphere is alwayslagging behind the drift-velocity of the neighboringgas, that tends to accelerate it.

It follows, that the transmission of any change inthe drift-velocities between the external and internalgas, both in speed and direction, is also a function oftime. It should be noted here, that in Newton's sec-ond law, force is expressed as the rate of change ofmomentum and in this simulation, while the Q-sphere undergoes uniform acceleration, it also accu-mulates momentum.

Recall now the decelerating process of Group/C.Similarly, if the drift of the medium would suddenlyslow down, speed up, or change direction, the drift ofthe Q-sphere would tend to continue with its initialspeed and direction until its own momentum will begradually dispersed in the external medium. Again,the process of dispersing the momentum throughone-to-one collisions is also a function of time.

For a macroscopic analogy consider the following:You are standing on a low bridge above a river

holding a balloon filled with water. When you let itgo, it has zero horizontal velocity, while the riverflows with considerable speed. As the balloon sub-merge into the river it will not instantaneouslyinherit the flow, but accelerate only gradually fromzero up, and finally at a given time will it reach thespeed of the river.

Imagine now, that you could look at this proce-dure with such a powerful microscope that showseach molecule of the river water, and the balloon andalso those of the internal water. Based on the Q-sphere concept, you can conclude, that all river-watermolecules have a drift velocity superimposed on theirisotropic random motion. The process of acceleration

182


is the transmission of this excess momentum by one-to-one collision with the molecules of the balloon skinand through them to those of the internal water. Thewater-filled balloon will flow with the river onlywhen each one and all of the molecules of this systeminherited a unit of drift velocity from one of the mole-cules of the river. This is the kinematics and timedependency of acceleration produced by a constantforce.

Going back to the Q-sphere and the sink, consid-er now, that the existence of the radial winds ismerely a temporary effect of the sink. Ultimately, thekinematics of any gravitational system evolves intothe rotation of a sink-vortex, where both the radialand tangential components of motion are set by theinverse square law of the propagation of distur-bances.

Let us now assume that the Q-sphere is posi-tioned in the state of rest at a distance from the sinkwhere the gradual expansion of the vortex motionjust begin to effect the isotropy of the medium. Asbefore, the center of oscillation of the Q-sphere startsto drift, however in this case not only radially, in thedirection of the sink, but also almost perpendicularly

to that, in a direction tangential to every point of thespiral channels of the vortex.

(a) Figure 9-2 (b)

Figure 9-2 shows a schematic comparisonbetween the vector components of the theory of uni-versal gravitation and those of the force of the sink-vortex. a). In Newton's theory the planets are movedby two independent forces, acting perpendicularly toeach other; the initial tangential momentum of thebody (horizontal vector) and the radial, centripetalforce of gravity. In the case of the sink-vortex themedium is twisted into an immense number of spiralpaths through which, from the very edge of the vor-

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RadialComponent

Tangent ia lComponent

Kepler 'sCurve

Orbi ta lMot ion

Force ofSink-vortex = Centripetal Force Rotation+

tex, each unit of the medium is moving toward thesink with gradually increasing drift-velocity and onan orbit of diminishing radial distance, that is, on aspiral.

From these points it follows, that unlike New-ton's centripetal force, which points directly towardthe center and requires a independent tangentialmomentum in order to form a circular orbit, the forceof the sink-vortex acts in the direction of an in-wind-ing spiral, and is represented by a single force vectorwhich combines both the tangential and centripetalcomponents of the spiraling motion. Evidently, boththe speed and the direction of this vector are con-stantly changing.

These factors lead to the conclusion that the spi-rals of the sink vortex ought to create a greater cen-tripetal acceleration, than what Huygens' equationprescribes as necessary for a circular orbit. If therewas no other factor involved in the kinematics of theorbits, then all planets and every body, including theQ-sphere of our experiment would follow a spiralpath and eventually unavoidably be pulled into thesink. As we have seen, however, the acceleration of abody, in the face of the opposition of its inertia, is a

function of time, and therefore it always lags behindthe magnitude and the direction of the force.

With this in mind, it becomes clear, that thedirectional acceleration of the Q-sphere carried in thespiral path of the sink-vortex cannot keep up withthe constantly changing speed and direction of therotating medium..

In other words, just like the speed of a body infree-fall lags behind the speed of the gravitationalstream, there is a similar time-lag in the directionalacceleration of the Q-sphere, relative to the direction-al acceleration of the spiraling medium.

This 'lagging behind' simply means, as Figure 9-3illustrates that the Q-sphere, accelerated by the con-stantly changing force-vector of the sink-vortex,gradually derails from the in-winding spiral streamof the medium and overshoots toward the less steepand slower moving outer threads of the vortex.

But from the logic of the kinematical situation itfollows, that the Q-sphere is affected two differentways while crossing over the spiral paths. The outerthreads of the spiral, being slower, decelerate the Q-sphere but the same time still force it to turn moretoward the sink.

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Hence the Q-sphere decelerates in speed andaccelerates in direction simultaneously. As a result,eventually it again fits into the curvature and thespeed of one of the outer spiral paths, swimmingwith it temporarily, until the whole process starts allover again.

From the spiral nature of the sink-vortex, it fol-lows, that no orbit around the sink can have a centerin the simple way as circular vortex does. Thus, thetwo radii leading to two opposite points of the spiralare always different in length. This geometrical char-acter of the vortex combined with the abovedescribed inertial overshooting of the Q-sphereinevitably results in an elliptical orbit around the eyeof the sink. Further more, it can be also be seen,that due to the constant acceleration and decelera-tion of the Q-sphere and for the different speeds ofthe spiral paths at different distances from the sink,the radius of this forced elliptical orbit of the Q-sphere, or an analogous inertial unit, like a planet,sweeps out equal areas in equal times.

Hence, in the environment of the hypotheticalideal gas, by the fundamental rules of the KineticTheory, a definite conceptual understanding has

been presented for the concepts of Newton's Mech-anics and for the empirical fact stated in Kepler'sThree Laws of planetary motions.

Figure 9-3The task remaining in this subject is to establish

the plausibility of a universal medium to replace thehypothetical ideal gas and then uncover the causali-ty and the kinematical plausibility in that mediumfor the formation, evolution and maintenance of agravitational sink-vortex.

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CHAPTER TEN

THE ALL-PERVADING AETHER

Introducing his Special Theory of Relativity in 1905,Einstein declares his conclusion:"All our attempts to make ether real, failed. Our

attempts to discover the properties of the ether led todifficulties and contradictions. After such bad experi-ences, this is the moment to forget the ether completelyand to try never mention its name.“We shall say: our space has the physical property of

transmitting waves, and so omit the use of the word wehave decided to avoid.

"Our only way out seems to be to take for granted thefact that space has the physical property of transmit-ting electromagnetic waves, and not to bother too muchabout the meaning of this statement."The next position which it was possible to take up in

face of this state of things appeared to be the following;the ether does not exist at all." (Einstein-Infeld: TheEvolution of Physics. [176])

Twenty years later, in the introduction of GeneralTheory of Relativity, Einstein recalls and corrects hislast conclusion, now declaring quite the opposite:"More careful reflection teaches us, however, that the

Special Theory of Relativity does not compel us to denyether. The electromagnetic fields appear as ultimate,irreducible realities, and at first it seems superfluous topostulate a homogeneous, isotropic ether-medium, andto envisage electromagnetic fields as states of this medi-um. But on the other hand there is a weighty argumentto be adduced in favor of the ether hypothesis. To denythe ether is ultimately to assume that empty space hasno physical qualities whatever. The fundamental factsof mechanics however do not harmonize with this view."In order to be able to look upon the rotation of a sys-

tem, at least formally, as something real, Newton objec-186

Aethro-kinematics

tivizes space. Since he classes his absolute space togeth-er with real things, for him rotation relative to anabsolute space is also something real. Newton might noless well have called his absolute space ether. What isessential is merely that besides observable objects,another thing which is not perceptible, must be lookedupon as real, to enable acceleration and rotation to belooked upon as something real."It is true that Mach tried to avoid having to accept as

real something which is not observable by endeavoringto substitute in mechanics a mean acceleration withreference to the totality of the masses in the Universein place of an acceleration with reference to absolutespace. But inertial resistance opposed to relative accel-eration of distant masses presupposes 'action at a dis-tance'; and as the modern physicist does not believe inaction at a distance, he comes back once more to theether, which has to serve as medium for the effects ofinertia."But this conception of ether, to which we are led by

Mach's way of thinking differs essentially from theether as conceived by Newton, Fresnel and by Lorentz.Mach's ether not only conditions the behavior of inertmasses, but is also conditioned in its state by them.

"Mach's idea finds its full development in the ether ofthe General Theory of Relativity. According to this theo-ry, the recognition of the fact that 'empty space' in itsphysical relation is neither homogeneous nor isotropic,compelling us to describe its state by ten functions has,(the gravitational potentials of General Relativity) Ithink finally disposed of the view that space is physical-ly empty."Recapitulating, we may say that according to the

General Theory of Relativity space is endowed withphysical qualities; in this sense, therefore, there existsan ether."According to the General Theory of Relativity space

without ether is unthinkable; for in such space therenot only would be no propagation of light, but also nopossibility of existence for standards of space and time(measuring rods and clocks), nor therefore any space-time intervals in the physical sense."But this ether may not be thought of as endowed with

the quality characteristic of ponderable media, as con-sisting of parts which may be tracked through time.Theidea of motion may not be applied to it." (AlbertEinstein: Aether and Reletivitatstheorie (1920). ShmuelSambursky, Physical Thought - Anthology [496])

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Aethro-kinematics CHAPTER TEN The All-pervading Aether

Hence, ether has been reinstated to full force by itsarch-enemy, Einstein, except the very last remark,inserted obviously to save the already accepted postu-lates of the Special Theory.

This theory presented here is based rigidly and rig-orously on the existence of the all pervading ether andthe concepts and ideas of the kinetic theory of matter.Accordingly, the name of the theory is AETHRO-KINE-MATICS, where the spelling, A-E-T-H-E-R marks thetendency to redefine the universal medium by startingover from the era of Descartes, Gassend, Huygens,Leibnitz, Lorentz and others.

From the age of firm conviction that the humanmind, which has evolved in a mechanical world, canonly comprehend nature through mechanical pictures,or cannot comprehend it at all! In this realm ofmechanicism the action at a distance is unthinkableand the only conceivable transmission of motion fromone body to another is through collision, by actual con-tact; motion can only be caused by motion, and can onlyproduce motion in turn.

KINEMATICS stands as a distinction from kinetics,mechanics and dynamics which were founded onNewton's conceptually imperceptible mathematical pro-

portionalities. Kinematics is a branch of physics whichdeals only with the abstract motion of geometrical pointswithout any regard to forces or inertia. For some clarity,we might add that one of the characteristics of geomet-rical points is that in order to distinguish one from theother, they cannot overlap each other; that is, they areimpenetrable to one another, just like the atoms of anideal gas. Dealing with abstract motion is dealing withcontinuous displacement in space in a given frame ofreference. As we have found through our previously dis-cussed thought-experiments in the non-inertial systemof the ideal gas, the only continuous displacement is therandom motion of the individual atoms, moving on astraight line, with uniform velocity. This motion, howev-er, is indeed abstract, since it is only detectible and mea-surable through the random averaging process of themacroscopic state of motion of the medium and nospeed or direction can be assigned to any one individualunit at a given time.

Through the same process, in the motionless idealgas, the collision-free path assumed to be equal in alldirections, forming collision-free spheres for each atomand therefore their motion can be taken as an isotropicomnidirectional oscillation, the center of which is in the

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state of rest, relative to the global isotropy of the medi-um. The result of any local disturbance is a layer-by-layer deformation and restoration of the collision-freespheres whose effects are propagated outward from theorigin in the form of concentric, expanding spheres withthe average speed of the atoms. The global movementsof the medium results from a continuous local distur-bance, like a sink or source, which steadily deforms thecollision-free spheres.

A macroscopic flow of the medium is executedthrough the drifting of the centers of oscillation of theindividual atoms. The drift-velocity of these globalmovements toward the source of disturbance (or awayfrom it) is proportional to the extent of the local distur-bance and to the inverse square of the distance from itsorigin.

As we have shown in the foregoing, all Newtonianconcepts of earthly and celestial mechanics and similar-ly the mysterious mathematics of Kepler's Laws can besimulated and explained through the kinematics of anisotropic, homogeneous ideal medium.

In AETHRO-KINEMATICS, Aether is taken as anall-pervading ideal gas in the ultra-microscopic order ofmagnitude and we call its constituents, the Aethrons,

which are conceptually equivalent to the atoms of anideal gas; geometrical points of impenetrability to oneanother. Aethrons are the ultimate units of motion andfor describing the various phenomena of nature, they donot need to exert any action-at-a-distance forces on oneanother and therefore they don't need to possess anyinternal structure that could be the subject of furtherspeculation.

Hence, if Aether is accepted as an ideal gas, alldetails, concepts, results and conclusions of the forego-ing experiments in the ideal gas are directly transpos-able to this universal medium and expandable to thewhole of space which it pervades.

Being nothing more, or less than an ideal gas, justas much information can be found about Aether asabout any other gas. It can be studied and calculatedfrom the phenomena associated with it, just like thecharacteristics of air or water or any other fluids can beinvestigated through the quantitative analysis of thephenomena discussed by Fluid-dynamics and by therules and assumptions of the Kinetic Theory.

With regards to the comparison in the conceivabili-ty and available knowledge about real gases and theAether, consider the following:

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There is a known upper limit for the highest fre-quency of sound-waves in ordinary matter. The wave-length of sound cannot be shorter than the distancebetween the atoms of the medium because there isnothing in there to oscillate.

In one of its forms, the basic equation of wave-motion states, that

Wave-velocity Wavelength = −−−−−−−−−−−−− .

Frequency which makes it clear that the higher the frequency theshorter is the wavelength and both of them depend onthe velocity of the propagation of the waves. Accordingto our best estimation, the speed of propagation ofsound in steel is 106 cm/sec. The highest known fre-quency propagated in steel is 1014 cycle/sec, thereforethe calculated average distance between the atoms ofsteel is 10–6 cm/sec / 1014 = 10–8, (0.00000001) cm.

Based on the same train of thought, – as the mini-mum waves of sound informs us about moleculardimensions, – the quantitative analysis of the electro-magnetic waves can supply the same information aboutthe basic characteristics of the Aether.

The highest known frequency of electromagneticwaves presents itself in the form of gamma rays, rang-ing from 1018 to 5×1024 /sec, (5,000.000.000.000.000.000.000.000 cycles/second). The correspondingwavelength is approximately 6×10-15 (0.000000000000006) cm. If the shortest possible wavelength ofsound was determined by the shortest possible averagedistance of the vibrating atoms of steel, than theapproximate average distance between the Aethrons inthe Aether should be 6×10-15 cm, (0.00000000 0000006).

It is assumed that the size of the Aethrons are neg-ligible compared to their distances apart and thereforethe above quantity also sets the density of the Aether. Itturns out that the Aethrons are 6,000,000 times closerto one another than the atoms of steel, thus as a medi-um,Aether is six million times denser than steel.

This is certainly quite inconceivable and makes itfully understandable why classical scientist could notimagine the frictionless translatory motion of the plan-ets through this medium. However, as it has beenshown above, the planets and other heavenly bodies donot perform translatory motions relative to the Aether,but they are rather carried by the medium in their eter-nal journey.

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Another fact also should be noted here. The limitsof human comprehension of the smallness or greatnessin the measurements of atoms and space and time, hasbeen by passed long time ago. Nobody can really con-ceive the speed of light, being equivalent with some-thing that flies around the globe eight times within asingle second, or the tremendous distance of a lightyear; 9.4×108 (9,460.800.000 km), or that a row ofatoms placed side by side to make up one centimetertakes about one hundred million of them.

Regardless of how great or small the subject ofmeasurement is, in our modern age they are simplyexpressed by the powers of ten. Although we have noidea what we are talking about, we can still counttheir magnitude on our fingers. For example, thedensity of steel is 6×1024 and that of the Aether is3×1037. Thus, the difference is merely 13 units ofsomething.

Our modern knowledge about the cosmos is accu-mulated indirectly through theories and mathematicalderivations based on abstractions beyond our sensescreated by analogies with the sensory experiences of thereal world. Hearing sound or touching matter does notsupply any more information about the molecules of the

air or the atomic structure of a piece of steel, than thesensation of starlight or the heat of the Sun or the pullof a magnet tells us about the Aether, bur the abstractKinetic Theory of Gases does for both. If electromagnet-ic waves are 9×107 times finer than the waves of sound,it only means that our eyes are 6×107 times more sensi-tive than our ears, and nothing else. If Aether is ninemillion times denser then air, it does not mean that itsconstituents the Aethrons are nine million times lessconceivable than the atoms of the air.

In comparing the available information aboutAether to those of other media, it becomes evident, thatthrough the theories of optics, electricity and magnet-ism, things were not only learned about the Aetherthrough hydrodynamic analogies, but it also worked theother way around. New discoveries about the behaviorof the Aether in electromagnetism have been success-fully applied later to the dynamics of real fluids, andthings have been learned about them, that had previ-ously not been known.

As it was mentioned before, the concepts of the linesand fields of force were invented for the pictorial analy-sis of electric and magnetic phenomena conveyedthrough the Aether. The concept of field was successful-

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ly extended later to describe fluid flows, aero-dynamicsand for the field of gravitational force.

There is indeed an all-pervading Aether, not only inspace, but all through our knowledge about physicalreality. The fundamental assumption of the theory ofAETHRO-KINEMATICS is that Aether is a real idealgas which pervades all space. A Universal Ocean, with-in which exist the Cosmos, including Galaxy, solar sys-tem, Earth, steel, air, water and us, and within thecoarse interstitches of all matter, there exist the all-per-vading Aether.

The internal kinetic energy of the Aether, in oneform or another, is the source of all energies and forcesof nature, some of which produce more or less perma-nent motion-patterns, and the conglomerates of those,through our macroscopic perception, we call: matter.

Like the above description of Newton's mechanicalconcepts, inertia, force, acceleration, momentum, theforce of gravity, and that of Kepler's Laws, eventually allknown phenomena of Nature can be kinematicallydescribed, conceptually understood and mathematicallyexpressed through the Ideal Gas of Aether.

The understanding of Nature depends on the devel-opment of suitable kinematical designs for the various

local disturbances, permanent localized circulatory pat-terns and the global motions of an ideal gas in the rightorder of magnitude. Thus AETHRO-KINEMATICS asa Natural Philosophy is the single fundamentalassumption required to correlate all phenomena of thewhole of Nature.

NOTICE OF AWARENESSThere are some, more or less important general

arguments against the existence of an all pervadingAether. Most of those objections came with the SpecialTheory of Relativity and based on the Michelson NullResult. Many of the detail arguments of relativity hasbeen already resolved through the procedure of thekinematic description of some major phenomena ofNature, while others will be better understood in thefollowing chapters and thereby better clarified for theirultimate kinematical analysis.

There is, however, another kind of objection, origi-nates from classical physics, which is not against theAether in general, but represent a century long futileargumentation about the possible models of the all-per-vading medium.

In this respect the classical wave theory of light, towhich one must revert when the special theory is dis-

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Aethro-kinematics CHAPTER TEN Notice of Awareness

carded, is directly in opposition to the ideal-gas-modelof the Aether; by the hypothesis about the transversenature of the oscillation of light-waves.

This assumption has been accepted as the only pos-sible explanation for the phenomenon of the polariza-tion of light and leads ultimately to the conclusion, thatif the Aether is capable to support transverse oscillationat the immense frequencies and speed of propagation oflight, it must be an elastic solid with extreme restoringforces and extreme density, much greater than those ofsteel.

This problem must be addressed here to avoid theimpression of being oblivious to a very strong andimportant argument. Nevertheless, there are two com-pelling reasons for the postponement of the considera-tion of this obstruction.

a) At this stage, the Theory of RotationalGravitation, which has been developed in the previouschapters, required the introduction of the ideal gasmodel of the Aether for the sake of the following discus-sion about the origin of the sink-vortex and its mainte-nance by the Evolution of Matter. The same was alsonecessary for the following chapter on the LorentzTransformation, which is the completion of the kine-

matical description of Newtonian Mechanics andElectromagnetism.

b) It has been found, however, that the problemwith the theory of the transverse nature of light wavescannot be resolved singularly without the completerevision of the classical wave theory, which is also nec-essary for the resolution of the presently accepted dualnature light. Through this discussion, besides polariza-tion, several other major optical phenomena must berevisited and clarified and the length and complexity ofthe analysis would astray the train of thought of thepresent subject.

The hidden misconceptions of the classical wavetheory, both mechanical and electromagnetic and theresulting duality of the theory of light in ModernPhysics will be discussed and kinematically resolved inChapter Fourteen.

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Aethro-kinematics CHAPTER TEN Notice of Awareness

CHAPTER ELEVEN

THE SINK OF MATTER

DONUT VORTEXFor the generation, which has been educated in

the 20th century's anti-mechanic and anti-common-sense atmosphere, the following reminder seems tobe necessary:

In the eighteenth century, during the develop-ment of the electromagnetic theory based onFaraday's concepts of lines, tubes and fields of forces,for each and everyone of the active geniuses ofphysics, the Aether medium was a totally acceptedpart of the physical reality. Just as it was known thatthe kinetic energy of the molecules of the air creates

physical sensations, like wind and sound, it was alsoknown that the kinetic energy of the Aether commu-nicates with our senses through the phenomena oflight, heat, electricity and magnetism. Aether hadbeen accepted as a frictionless gas at a supermun-dane order of magnitude.

During the evolution of scientific theories themechanical analogies for some complex phenomenaalways served as simplified conceptual models, fromwhich the final mathematical expressions could bederived. One of the greatest achievement of thismethod was the electromagnetic theory.

To make this method sufficiently clear, a typicalexample of the scientific procedure is quoted below :"It was therefore natural to identify the density of

the medium (Aether) at any place with the magneticpermeability, and the circumferencial velocity of thevortices with the magnetic force."But the objection to the proposed analogy now pre-

sents itself. Since two neighboring vortices rotate inthe same direction, the particles in the circumferenceof one vortex must be moving in the opposite direc-tion to the particles contiguous to them in the cir-cumference of the other vortex; and it seems there-

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Aethro-kinematics

fore, as if the motion would be discontinuous.Maxwell escaped from this difficulty by imitating awell-known mechanical arrangement.

"When it is desired that two wheels should revolvein the same sense, an idle wheel is inserted betweenthem so as to be in gear with both. The model of theelectromagnetic field to which Maxwell arrived bythe introduction of this device greatly resembles thatproposed by Bernoulli in 1736. He supposed a layerof particles, acting as idle wheels, to be interposedbetween each vortex and the next, and to roll withoutsliding on the vortices; so that each vortex tends tomake the neighboring vortices revolve in the samedirection as itself. The particles were supposed to benot otherwise constrained, so that the velocity of thecenter of any particle would be the mean of the cir-cumferencial velocities of the vortices between whichit is placed.“On comparing the mathematical expression of this

system to that which represents Oersted's discovery,(the attraction between current carrying wires), it isseen that the flux of the movable particles interposedbetween neighboring vortices is the analog of theelectric current.

"It should be noticed that in Maxwell's model therelation between electric current and magnetic forceis secured by a connection which is not of a dynami-cal, but of purely kinematical character." (Whittaker:Aether and Electricity, 1951 [247])

...and so on...until the whole wonder of the math-ematical reflections of the internal kinetic energy ofAether and Maxwell's electromagnetic equationswere perfected to their final form, giving us our pre-sent electronic technology.

Since Aether has been reincarnated by its archenemy, Einstein, the kinematics of the electromag-netic field, a characteristic behavior of the Aethermedium, should also be reinstated to its originalform, as it had been discovered and worked out indetails by Faraday and Maxwell. If, for the GeneralTheory of Relativity 'space without ether is unthink-able' on both of the scales of gravitation and thepropagation of light-waves, then the 'nonsense of theaction at a distance' must be abandoned in thedescription of electromagnetism too. It follows, thatthe binding nuclear forces, the attraction and repul-sion of elementary particles, the cohesional forces ofthe molecules and the structural binders of the crys-

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Aethro-kinematics CHAPTER ELEVEN The Donut Vortex

talline lattice in solid matter, all microcosmic linesand fields of forces should be admittedly conveyedthrough the all-pervading Aether medium.

Similarly, if Aether is rehabilitated, particlephysics should no longer be restricted to sterilemathematical speculations in the unimaginable cos-mic void. From this stand point of the existingAether, all our modern particle accelerators and par-ticle smashers, with today's modern experimentersresemble to the kids in the bath tub, poking thewater surface and recognizing an infinite variety ofpatterns in the flow of the white soap layer. Somepatterns are swimming surprisingly far, almost likepermanent designs, some others dissipates slowly,some others disappear as soon as they formed in thewake of their fingers. According to their different lifespans, these flow-patterns can be recorded, named,grouped and filed into an infinite list of entities, how-ever, due to the internal friction of the water andsoap, none of them could really be permanent.Nevertheless, – since the individual Aethrons haveno internal structure and exert no forces on oneanother, – one of the fundamental properties of theideal fluid of Aether is being totally frictionless.

As an introduction to the investigation for thecausality, origin and maintenance of the gravitation-al sink-vortex, consider first the possibility, as wehave learned about vortices in hydrodynamics, that asimilar pattern, once it's formed in the Aether, has noreason to dissipate into randomness again, unless itsdynamic structure is destroyed by another dynamicstructure.

It must be emphasized here again, that none ofthe foregoing or following rough or detailed ideas areclaimed to be final solutions. Rather, they are merelyheuristic and introductory attempts to express analternative point of view. Even if they do make senseas they are, the complexity of the phenomena isimmense, and it could require decades of research bymany, before AETHRO-KINEMATICS will be able toproduce the right answers in all details.

With this in mind, consider the illustrations ofFigure 11-1, showing a kinematically natural chainof events, triggered by the least possible local distur-bance in the isotropy of the medium which eventual-ly could evolve into a locally organized, permanentand autonomous circulatory system of a three-dimen-sional donut-vortex.

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(a) As Figure 11-1(a) shows, any relative motionbetween two layers of an isotropic medium can gen-erate local turbulence. The different speeds of thelayers shown at the left are equivalent with theopposing relative velocities shown at the right side.

(b) Under suitable circumstances this relativemotion can act as a torque and induce rotationalmotion. This form of disturbance is called vorticityand it is quite common in moving fluids, especiallywithin the fluid of a large scale vortex, where, due toits differential rotation, each layer of the mediumrepresents a different angular velocity.

(c) While the torque of the relative motion of thelayers acts continuously, a centrifugal tendency ofrotation comes into existence. This is simply thenature of motion, that each particle tends to move ona straight path and therefore tends to get out of a cir-cular one. This centrifugal tendency opens up thecenter of the beginning vortex and creates a localrarefaction in the middle, which then graduallydevelops into a sink. It follows, that both from the topand bottom of the plane of the vortex, the fluid startsdrifting toward the rarefied area of the sink. Let usnow assume, that by chance, the flow from the top

has a slight advantage and the two drifts of oppositedirections collide somewhat below the plane of thevortex. As a result, the top flow pushes the bottomsideways and a vertical flow of the medium developsthrough the vortex ring.

Figure 11-1 (a),(b),(c).197


=

(a)

(b)

(c)

The result is a rarefaction at the top and a com-pression on the bottom, which now represents asource. But since in an isotropic medium all distur-bances are propagated in expanding spheres, therarefaction and compression will eventually curvetoward each other. As the sink pulls in and thesource pushes out the medium, the drifting Aethronsform a multitude of streams through the center ofthe vortex, which ultimately re-enter into themselvesinto an endless loop in the surrounding space.

(d) Figure 11-1 (d) shows the resulting threedimensional donut-shape, rotating and spinning vor-tex, surrounded and penetrated by endless loops ofdrifting fluid. In this donut-vortex a certain volumeof Aether, an immense number of individualAethrons, are organized into a complex circulatorysystem, which, upon reaching the kinematic balancewith the isotropic external pressure of the medium,gains permanency both in shape and in substance.Being self-sustaining and autonomous, it also repre-sents a fixed quantity of aggregated kinetic energy.

The Earth's magnetic field shows that the flowpattern of the Donut vortex is not totally unfamiliar.

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Figure 11-2.

Figure 11-1 (d).

Illustration 11-3 depicts the potential dynamiccoupling between two donut-vortices, oriented insuch way that their flow-patterns form an interact-ing, permanent connection. The new flow pattern ofthis couple is equivalent to a linear dipole flow.

It is now easy to imagine that all kinds of furthercouplings are possible. For instance, a larger kine-matic organism might be formed out of a whole rowof such donuts and by the connection of the right sideof the last member to the left side of the first in a

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Figure 11-3.

permanent ring. By a more complex inter-lockingflow-pattern in three dimensions, horizontally orient-ed donuts can be inserted between vertical ones. Inall cases, eventually a kinematic equilibrium isreached between the sinks and sources, the externalstatic pressure and the internal elastic cushion of themedium. The size of the loops stabilizes and by thatmaintains a constant distance between the donut-vortices. Evidently, the continuous re-generation ofthe same flow-patterns in the frictionless environ-ment of the Aether, the conservation of the shape andsubstance of the systems and their inherent abilityto connect with one another implies that the donut-vortex could represent a potential kinematicaldescription of a permanent elementary buildingblock of matter.

Once again it is emphasized, that none of theseideas claim finality, but rather planned to be thegerms of a complete description, which will probablybe achieved through elaborate sculpturing. Forinstance, an electron can be a single donut-vortex orsimilar circulatory pattern, but it can also be a con-glomerate of many of them, depending on therequirement of the complex characteristics of an ele-

mentary negatively charged particle. The big poten-tial of the donut-vortices is in their connectabilityand that each unit has its own intake and output.

Organized communities of these vortices can bedesigned, connected in such ways, that the totalintake of the system is received from one definitedirection, while the output is dispersed in manydirections isotropically. Or vice verse; the intake isisotropic and the output is directional. Or bothintake and output are directional or both isotropic

There might be ways in this line of designing toachieve the characteristics of negative, positive andneutral elementary particles. Most likely, this will beachieved by computer simulation based on the kine-matical algorithm of an ideal gas.

The same concept also renders an elementarykinematic pattern for electromagnetic interactionsand illustrates the basic kinematic characters of bothelectric and magnetic force fields; unlike the one-directional drift of the gravitational field toward asingle sink (monopole); electric and magnetic fieldsalways result from a sink and source couple, calleddipole, which are surrounded by a complex circulato-ry system contained in endless elastic loops.

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It can be seen now, that with sufficient brain-power and research time, especially with the aid oftoday's computer generated design, this conceptmight be extended to simulate all the various electro-magnetic forces, giving a conceivable kinematicaldescription of the origin and maintenance of the ele-mentary particles and those of the macrocosmic con-glomerates of ponderable matter.

BERNOULLI'S PRINCIPLE Daniel Bernoulli, Swiss mathematician in the eigh-

teenth century, proposed that for a horizontal channel,carrying an ideal fluid, the sum of the forces of the stat-ic pressure, due to the random motion of the atoms plusthe dynamic pressure, due to the motion of the fluid, isa constant.

P + 1/2 ρV2 = K (11.1),where P represents the static pressure applied to thefluid, the term 1/2 ρV2 is the kinetic pressure developedin the fluid, ρ (Greek; Rho) is the mass-density of thefluid and V is its velocity. This expression is essentiallya statement of the principle of the conservation of ener-gy, applied to fluids in motion and the conclusion is thatas the velocity of a fluid increases, its static pressure

decreases and vice versa. The total of the energy compo-nents in a moving fluid remains constant.

As an experimental example, imagine an arrange-ment of a section of metal tubing, provided with smallholes at regular intervals along its length.The diameterof the pipe is not constant, but it is constricted in themid-section. Letting gas into the tube through the inlet,the jets can be ignited.

As it is illustrated in Figure 11-4 (a), with the outletclosed, the flames all reach the same height, whichmeans that the pressure of the gas at each jet is thesame, including that of the mid-section.

Figure 11-4

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Aethro-kinematics CHAPTER ELEVEN Bernoulli’s Principle

However, when the outlet is open (b), the gas in thetube is no longer motionless, but flows to the right. Inthis case the middle jet, over the constricted section ofthe pipe, shows a significant decrease in pressure. As itis expressed by the equation of continuity, since the vol-ume of intake and discharge must always be the same,the gas in the constricted part ought to flow faster thanin the full size pipe.

From this experiment Bernoulli concluded, that thestatic pressure is inversely proportional to the speed ofthe flow of the gas. The kinematical understanding ofthis empirical law follows from the concept of the centerof oscillation of the atoms, which is at rest in a motion-less isotropic fluid and drifts when the fluid performs amacroscopic flow. As it was established earlier, the driftof the atoms is merely superimposed on their initialrandom motion and the velocity of the individual atomsdo not change in a flowing fluid. They simply move withunchanging uniform speed of their random motion, butfor a longer period of time toward the outlet than in anyother directions. Since the velocity of the atoms is con-stant, their kinetic energy also remains constant.Consequently on the average, the space within whichthey oscillate, should also remain a constant volume.

As it was shown before, whenever the collision-freepath of the atom lengthens in a given direction, it mustbe shortened in all other directions. The collision-freesphere becomes elongated in the direction of the freepath and the resulting ellipsoid has a major axis direct-ly, and a minor axis inversely proportional to the veloci-ty of the drift. In other words, the volume of the colli-sion-free sphere or ellipsoid is a constant.

In general, this is how the oscillation of the atomstransverse to the flow and their contribution to theaverage static pressure decreases in proportion to theirdrift-velocity.

The extreme case in this respect would be, when anatom reaches vacuum and moves in a given directionwithout collision indefinitely. In this case the major axisof the ellipsoid becomes infinitely long and the minoraxis equals to zero. This atom does not drift or oscillateanymore but moves continuously on a straight line withuniform speed.

Proving that Bernoulli's theory is not only true foran enclosed medium, like the gas in the pipe, but alsovalid for the open and contiguous isotropic medium,physicists devised an other experiment, as illustrated inFigure 11-5.

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(a) Figure 11-5 (b) Two ping pong balls hang close together in the

motionless air when a jet of air from a straw is injectedbetween the balls (a). Contrary to expectation, the ballsmove closer, as if they were attracted to one another.The candle flames proves the same (b).

The reason for this is the same as in the case of themoving gas in the pipe. The increase in the velocity ofthe air-jet in the narrow space between the ballsreduces the static pressure, transverse to the jet, andtherefore, the unreduced external pressure of the air

from the outsides of the balls pushes them together.It is evident, that whether the balls are present or

not, the air-jet injected anywhere into the isotropicmedium decreases the local static pressure rectangularto the direction of the jet, and therefore, the surround-ing higher pressure air tends to expand into that area.

Let us now recall the kinematics of the sink-vortexand consider the potential role of Bernoulli's effect dur-ing the development of such motion-pattern. As it hasbeen established, the initial macroscopic radial flow is aresult of the lengthening of the collision-free paths andthe drifting of the center of oscillation of the atomstoward the sink.

The collision-free spheres of the atoms are elongat-ed in the direction of the radial drift, but as rotationdevelops, the ellipsoids of the oscillation turn with theirmajor axes into the direction tangential to the spirals ofthe vortex.

Thus, as Bernoulli's theorem predicts, each rotatinglayer of the drifting atoms should represent a lesser sta-tic pressure rectangular to the spiral, than that of theisotropic external medium. Hence, as its atoms join tothe rotating vortex, each layer of the medium is con-densed into a smaller volume of space than it would fill

203


with its initial, average static pressure. Since the staticpressure is inversely proportional to the velocity of thedrift, and the angular velocity of the vortex depends onthe radius, it follows, that the average density of themedium in the sink-vortex also varies with the distancefrom the sink.

When Bernoulli's theorem and other kinematicalcharacteristics of an ideal gas are transposed into thefrictionless medium of the Aether, a fundamental ten-dency of nature presents itself:

Consider, an imaginary sphere floating in theisotropic, motionless Aether, marking the boundary of agiven volume of space. The Aether has the same densityinside and outside.

The total kinetic energy enclosed in the sphere isequal to that of any other part of the Aether containedin the same volume of space and therefore the imagi-nary sphere experiences an equal static pressure onboth its internal and external surfaces.

Let us now assume, that by some cause, rotation isinduced at the center of the marked space. Recall andapply the evolution of the donut-vortex to this situa-tion, as it has been described before and illustrated inthree steps on Figure 11-6.

After the initial vortex has been formed, the driftingmotion of the Aethrons are superimposed on their ran-dom oscillations. As it was established before, the drift-ing of the Aethrons toward the sink or the formation ofthe loops involve no acceleration, but merely means theability of some to move in a given direction for a longerperiod of time.

Hence, Bernoulli's distinction of dynamic energyand kinetic energy is merely a differentiation betweenAethrons of the isotropic medium oscillating in com-plete randomness and the Aethrons whose centers ofoscillation are drifting in an organized manner in agiven direction. Evidently, the total kinetic energy of the

204


Figure 11-6

system and therefore the sum of these two shouldremain the same throughout the evolution of the donut-vortex.

Nevertheless, an important difference between thisand the two previous examples should be noted. In bothof the former experiments, the gas pipe and the balls,the dynamic energy of the linear drift enters and leavesthe space within which Bernoulli's theorem is valid.Thelighting gas flows in and out of the pipe and the air-jetenters and leaves the space between the balls. Unlikethese, in the present example the dynamic energies ofthe drifts turn into themselves in the rotation of thedonut. The continuous circulation of each endless loopforms a permanent unit of dynamic energy. Thus, by theassumption that the imaginary sphere is impenetrable,the donut-vortex together with the locked-in, randommedium can be accepted as an isolated system.

Although Bernoulli's theorem of the conservation ofkinetic and dynamic energy is still applicable, here anew factor must be considered. The initially completelyrandom medium is now separated into two parts; thepart that has been organized into the flow patterns ofthe donut-vortex, and the part that did not take part inthis organization, but stayed in its initial random state.

On the one hand, the kinematics of the donut-vor-tex shows that eventually a balance must be reachedbetween the sink and source, the external pressure andthe internal cushion of the random Aether, that is, thedynamic and kinetic pressure should reach equilibrium.But in the light of Bernoulli's theory this means, that asthe rotating and revolving Aether gains drift-velocity ordynamic energy, at the same time, the static pressure ofeach drifting layer decreases. It follows, that during theformation of the donut-vortex, each layer is condensedinto a decreasing volume by the dominating static pres-sure of the surrounding random medium.

On the other hand, as the number of Aethronsinvolved in the circulations are taking up less space, therest of the Aethrons, still in random motion, must fill upmore space than before the formation of the donut andtherefore the random Aether within the spherebecomes rarefied in proportion.

Indeed, the total kinetic and dynamic energieswere conserved within the isolated system of thesphere, but the content of the donut-vortex takes upless space than before, thus the medium in the rest ofthe sphere must be rarer than the average density ofthe external medium.

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At the boundary of the isolated system, the internalwall of the imaginary sphere experiences lesser staticpressure than the average isotropic pressure exerted bythe external Aether on the outside surface of thesphere.

From these two important kinematical tendenciesthe following can be established:

1) If the wall of the sphere would suddenly disap-pear, the denser external medium would rush into thesphere to re-establish the isotropic density. But this alsomeans that if the sphere were open from the beginningof the formation of the donut, then the external mediumwould continuously re-adjust the average isotropic pres-sure by an influx of Aethrons from the whole of themedium. In this case the donut-vortex is compelled toform under greater pressure into a smaller volume ofspace.

This influx from the surrounding medium simplymeans that anywhere in space the formation of adonut-vortex is equivalent to the kinematical concept ofa sink

2) Taking another count on the contents of the vol-ume of space initially marked by the imaginary sphereit is now found that there are a greater number of

Aethrons and an excess amount of kinetic energy withinthan in any other equivalent volume of space in the freeAether.

This is then the AETHRO-KINEMATIC descrip-tion of a natural tendency of the all-pervading Aether:The condensation of its kinetic energy into the dynamicforms of elementary particles, binding forces, electro-magnetic fields, atoms, molecules, crystalline struc-tures, etc.; A natural, evolutionary condensation ofkinetic energy into ponderable matter...

THE EVOLUTION OF MATTERNext, consider another group of general ideas:With respect to the origin and history of matter, the

two most widely accepted cosmogonical ideas; the BigBang and the Steady State Theories present extremeopposite views in their accounting for the origin andabundance of the different elements in the universe.According to laboratory experiments and astronomicalobservations 99.999% of all matter in the observableuniverse is made up between the two simplest ele-ments, Hydrogen and Helium.

The total abundance of all the other 101 knownheavier elements make up the remaining 0.001%. Onthe one hand, according to the Big Bang Theory as

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Aethro-kinematics CHAPTER ELEVEN The Evolution of Matter

George Gamov renown expert puts it, all elements, asthey are in existence today, were produced in the firsthalf hour of the life of the universe in the primordialatomic pressure-cooker. On the other hand, Bondi, Goldand Hoyle's Steady State Theory declares, that all ele-ments of matter are in continuous creation everywherein the universe. Hydrogen is created in inter-stellarspace at the rate of one atom per gallon in every 250million years.The heavier elements are being created inthe extreme internal heat of stars and spread throughthe whole of space mostly by supernova explosions.

Both theories were invented to synchronize withthe Theory of the Expanding Universe and with theempirically found abundance of the various elements.

The Big Bang Theory leads to an ever thinning uni-verse as the initially created amount of matter expandsinto greater volumes of space. In the Steady StateTheory, the assumed rate of the creation of hydrogen iscarefully adjusted to keep up with the expansion andthereby achieve a constant density of matter in the uni-verse.

Needless to say, that at the present state of cos-mogony and astrophysics, there is no observational,experimental, mathematical or logical verification or

disapproval for either of these extreme speculations.Their validity merely comes from their synchronizationwith the expanding universe hypothesis which itselfsuffers the same uncertainty. Therefore, the same freecredit should be allowed for any newly invented hypoth-esis which may lie in between the two extremes, or evenif it is not adjusted to the requirements of the expand-ing universe.

With this in mind, let us first consider the fate ofsolid matter, say a piece of rock, when it is heated tohigher and higher temperatures. Rocks are made upof the crystalline lattices of molecules, composed bythe atoms of different chemical elements. At low tem-perature (under 1000° Celsius) the crystalline latticeof the rock is a rigid system and the thermal vibra-tion of the molecules are controlled by the cohesiveelectromagnetic forces. From the stand point of thekinetic theory of matter, the added heat transformsinto kinetic energy in the form of the increasingamplitude of vibrations of the molecules. Over themelting point (1063° C), the molecules still remainstrongly attracted to each other, though the thermalagitation is strong enough to dislocate them from thefixed positions in the crystalline lattice, and the rock

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liquifies. At still higher temperature (2600° C) the lique-fied rock reaches its boiling point, the cohesive forcesare not able to hold the molecules together anymore,they fly apart in all direction and the rock reaches itsgaseous state.

In general, over a few thousand degrees not eventhe molecules can stay together, but they separate intotheir constituents; the atoms of pure chemical elements.The violence of thermal collisions at such high tempera-tures also damages the atoms by chipping off theirouter electrons. This thermal ionization becomes moreand more pronounced when the temperature rises tohundreds of thousand of degrees and reaches comple-tion at a few million degrees, which is quite common inthe interiors of stars. Inside the sun it is about 20 mil-lion degrees and the atoms, as such, cease to exist. Allelectronic shells are completely stripped off, and matterbecomes a gaseous mixture of bare nuclei and free elec-trons, called Plasma.

At temperatures above 10 billion degrees the ther-mal agitation of the protons and neutrons is greatenough to overrule the strong force that keeps themtogether and the nuclei begin to vaporize. Temperaturesof this magnitude may well occur for short periods of

time during supernova explosions. At this point, howev-er, the speculation must stop since neither can we imag-ine higher temperature, nor do we have any plausibleidea of the internal structure of the elementary parti-cles. This procedure is called the thermal dissociation ofmatter and agrees with the assumption of thermody-namics, that the kinetic energy of the elementary parti-cles is proportional to the absolute temperature in allstates of matter.

In order to come back to the present state of theuniverse, the whole procedure can be projected back-ward, creating a reciprocal sequence, which may becalled thermal association.

Starting from the slow cooling of the billion degreeshot proton- neutron- electron-gas, as the individual ele-mentary particles slow down, nuclei and electrons canform. Later, at a given level of the temperature, by thecapture of free electrons, atoms can come into existence.As the thermal kinetic energy further decreases, theforce-fields of the atoms succeed in creating molecularties and by the induction of cohesional forces, liquifica-tion becomes possible. Finally, in the total domination ofthe nuclear, atomic and molecular forces, matter solidi-fies in crystalline-lattices.

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Observation proves that this thermal associationdoes happen everywhere in the universe at all times atdifferent temperatures and in various circumstances,parallel to the evolution of the Earth, planets, suns,stars and galaxies.

But the thermal effects on the kinetic energy of theparticles is not the only cause for the changes in thestates of matter. Besides the rapid and large scale disso-ciation and association due to heating and cooling, thereare other subtle transformations on nuclear and atomiclevels, which effect only a small percentage of an ele-ments at a time, proceeding slowly and independentlyof temperature. − Radioactive decay of certain elementsis a special case of dissociation which happens indepen-dently from thermal agitation. The radioactivity of dif-ferent elements manifests different types of radiation inthe forms of the continuous emission of a specific parti-cle. It has been found that in the process of disintegra-tion, the expulsion of a particle leaves behind a new sys-tem, which is lighter than before and possesses physicaland chemical properties quite different from those ofthe parent element. The number of atoms that disinte-grate during a given time interval is in a definite pro-portion to the atoms initially present.

This proportion is a characteristic constant of thebody. For example, one half of a given number ofUranium atoms will decay into something else in fourand a half million years. This period of time is called thecharacteristic Half-life of Uranium and since it decayson its own power, it has been classified as an unstableelement. It is evident, however, that the concept of half-life is purely quantitative, expressing a given rate ofradioactive dissociation of an element, it merelydepends on the sensitivity of our devices and an arbi-trarily chosen time-scale whether an element is classi-fied as stable or unstable.

If four and a half million years of half-life repre-sents un-stable, what should then be the higher limit ofstability; forty million, four hundred million, or fourand a half billion years?! The concept of half-life demon-strates that radioactivity is a random and accidentalprocedure and could only be measured on statisticalbasis. If one hundred uranium atoms could be separat-ed and their radioactivity measured, the predictionwould be the same; in four and a half million years 50out of the 100 will disintegrate into something else, butthere is no way to foresee which 50 will change andwhen. In order to even discover radioactivity in a group

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of 100 atoms, the experimenter should be able to detectthe triggering of his counter by an emission, on theaverage, once in every 90,000 years, but there is still anon-zero probability for two emissions within a tril-lionth of a second. When it comes to atomic particles, itis impossible to predict how single individuals willbehave. All that can be done is to foretell the averagebehavior of an immense number of particles in a groupaccording to the rules of probability.

Theoretically nothing is infinitely improbable andthere is no known reason to assume, that a similarlyaccidental procedure cannot occur in the opposite direc-tion. After all, how does matter solidify from the plasmaall the way to the crystalline structure of matter if notby accidental association of the elementary particles.

Until most recently, the general belief was that theorigin of the heavier elements requires immense heatand must happen in a biblical type creation under veryextreme circumstances, like in the primeval atom or inSupernova explosions.

The main reason for this belief was the large forceof repulsion that exists between protons, which must beovercome in collisions with tremendous velocities inorder to get them close enough together for the short

range nuclear force of attraction to take charge. In thelast few decades, however, research shows more andmore results that contradict this belief. The latest dis-coveries of cold nuclear fusion established the fact, thatcertain electron-like particles, called muons can cat-alyze nuclear associations which circumvents the needof high temperatures or extreme velocities entirely. It isexperimentally proven that muon-catalyzed cold fusioncan take place rapidly at room temperature or evenclose to absolute zero.

Muons are particles with a negative charge equal tothat of the electron but about 207 times more massive.When they are introduced into a chamber containingisotopes of Hydrogen, Deuterium and Tritium, somemuons form unusually tight associations between thenuclei of two Hydrogen atoms. These nuclei then bondtogether into one Helium nucleus which ejects themuon, capture some free electrons and become aHelium atom.

The muon in turn goes on to catalyze other fusionreactions. Obviously there is Helium association in thechamber with a reciprocal half-life, which is proportion-al to the initial number of Hydrogen atoms and thenumber of muons in a unit volume of space. The pre-

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sent theory about the procedure of muon-catalysis isbased on the explanation of molecular cohesion. Whenatoms collide in a gas, their electrons come close enoughthat they are captured by the other nucleus and theycontinue to orbit around both nuclei. The result is anattraction between the two atoms and the formation ofa molecule. In the cold fusion muons take over the roleof the electrons, but they are much heavier and slowerand they can pull the two nuclei close enough togetherthat eventually fusion occurs.

The discovery of muon-catalysis might revitalize atheory proposed by William Prout in 1815. According tohis hypothesis, the hydrogen atom, (one proton and oneelectron) is the basic unit of 'matter' out of which allother elements were compounded.This idea was strong-ly supported by the repetitious chemical properties ofthe elements in the periodic table and by the fact thatthe weights of elements were nearly all multiples of theweight of the hydrogen atom.

Later, however, atoms were discovered that did notfit Prout's hypothesis. For instance, the weight of a chlo-rine atom has been found thirty-five and one-half timesthat of the hydrogen atom. Because of this and otherdiscrepancies and since the way out of this difficulty

was not known to Prout, his theory was abandoned andnever reinstated. However, after the discovery of thethird elementary particle of the atom, the neutron, hav-ing nearly equal mass with the proton, Prout's contro-versy were effectively resolved.

It has been found that the chemical properties of anelement are determined purely in terms of the numberof electrons and protons in the atom, but the number ofneutrons in the nucleus, can take a range of differentvalues. In the crucial case of chlorine, with seventeenprotons, there can be between sixteen and twenty-twoneutrons in the nucleus. Out of these isotopes, only twochlorine atoms with eighteen and twenty neutronsoccur to any extent in Nature and there is about threetimes as many lighter ones in the common mixture ofchlorine as heavier ones. This results in exactly theright proportion for Prout's theory, giving an averageweight for the chlorine atom; thirty-five and a halftimes that of the Hydrogen atom.

There is no doubt today that the basic buildingblock of matter is the proton-electron pair but the roleof the neutron in the stability of a nucleus is still notknown. It has been found however, that under certainconditions, a neutron can disintegrate in the nuclei,

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changing over to a proton and ejecting an electron. Thesame happens to a free neutron with a half-life oftwelve minutes.

In any case, based on present knowledge, it canhardly be declared that the probability of cold fusion issurely limited to the case of Helium creation or thatthere is no chance for the accidental association ofhydrogen atoms, a cold procedure of building matter todifferent levels of complexity, similar to Prout's specula-tion.

In an other department of experimental physicsUranium atoms are bombarded by accelerated neu-trons with the result of nuclear fission.

A certain isotope of Uranium, having 92 protonsand 143 neutrons (235) by absorbing one of the neu-trons, becomes a new isotope with 236 nucleons andsplits up in to two equal parts, producing a radioactiveisotope of Barium. Since the bombarding is completelyrandom, why does the Uranium atom split in halfinstead of into different other fractions? According topresent theories, the binding energy of medium heavyelements is the strongest, therefore lighter nuclei gainstability by fusion and heavier ones when they breakup in fission.

Is there zero probability for a procedure throughwhich two Barium nuclei could fuse into a Uranium235 atom and eject a neutron, say, with a half-life of 16million or 160 million years?

It might be useful to assume, that the accidentalfusion of matter at any level of complexity is merely aquestion of the lapse of time and the coincidental effectof a suitable catalyzer, or maybe several of themsequentially or simultaneously.

There is a great inventory of particles with differentcharges and various masses to take the role of catalyz-ers and most certainly there is time enough in the life ofthe Universe. If there was an evolutionary theory ofmatter based on some thermal or catalytic or someother presently unknown procedure, it would be found-ed on the probability of an accidental, step by step asso-ciation of the elements with gradually decreasingchances as matter grows more and more complex. Thefinal equation and the predicted half-life for the evolu-tion of matter through the different elements would becarefully adjusted to synchronize with the empiricallyfound quantities of the natural abundance of the ele-ments and with the presently believed age of theUniverse.

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This will be then a kind of mutational evolution ofmatter from the random state of kinetic energy of theAether toward the organized and condensed forms ofelementary particles, atoms, molecules and conglomer-ates of them; a procedure in the opposition to the arrowof entropy; an accidental evolutionary tendency exposedto a natural selection through the radioactive dissocia-tion of the unstable elements; a Darwinistic cos-mogony?!

Correlating the kinematic theory of RotationalGravitation with the three groups of ideas, suggestedabove, consider the following hypothesis:

The elements of matter are permanent circulatorypatterns in the frictionless ideal gas of the all-pervadingAether triggered by the universally existing torque ofdifferential rotation. The concept of the donut-vortexshows the possible existence of such patterns with theirpotential to form interlocking complexes of differentconstructions and various sizes.

Predictably, similar designs can be achieved for thekinematics of the internal structure of elementary par-ticles and thereby an explanation for their differentfields in the medium and through that, the forces exert-ed on one another. Having a rarefying effect on the

medium within their space of origin, a tendency is cre-ated for random cloud formations and their rotationalseparation.

Atoms, molecules, crystals and their conglomeratesare organized from elementary particles and sustainedby electromagnetic activity. The lines and tubes andfields of electromagnetic forces, as it was already estab-lished in the nineteenth century, are also circulatorypatterns in the Aether, produced by the sink-sourceaction of the elements and their elementary particles.

It is assumed that the formation of ponderablematter begins with the Hydrogen atom, the nucleus ofwhich is a single proton, holding a single electron inorbit. Through a step by step evolutionary process, morecomplex nuclei are formed out of protons and neutrons,which capture free electrons equal in numbers withthose of the protons.

Atoms are bound into molecules in gases by theirinterlocking force fields. The molecular cohesional forcestie together immense numbers of atoms, producing flu-ids and solids on all levels of complexity. Each minutechange in this evolution requires a re-arrangement inthe construction of the bond between these elements ofmatter and calls for a more complex network of electro-

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magnetic force-fields to sustain the equilibrium of thenew state.

The formation of particles, nuclei, atoms etc. andthe complex network of the electromagnetic structure;that is, the formation of all circulatory drifts of theAethrons in various shapes and sizes proceeds underthe constant pressure of the random, isotropic medium.Consequently, in agreement with Bernoulli's theorem,as the Aethrons are being organized into these dynamicconstructions of matter and accumulating drift-veloci-ties, their static pressure, rectangular to the driftsdecreases in proportion. Thus, under the unchangedstatic pressure of the external medium, the Aethronsinvolved, are gradually condensed into a smaller andsmaller volume of space compared to what the samenumber of Aethrons have occupied by their initiallyrandom oscillation.

As a result, there are two evident kinematical con-sequences of the formation and evolution of matter:

a) When some part of the Aether is condensed into asmaller volume of space, the local procedure produces aproportional rarefaction around and within the 'matter',which is constantly re-adjusted by an in-flow of the sur-rounding isotropic medium. As it was discussed earlier

in connection with the ideal gas, this radial drift towardthe sink, the state of motion of a test-particle can bedescribed in Newton's concepts in a way that its radialcomponent is a result of the constant, centripetal forceof gravity and its tangential component is determinedby Kepler's Laws.

Thus, whenever and wherever matter is formingand evolving it can be considered as the center of an in-flow, which consumes Aethrons at a steady rate fromthe surrounding medium and therefore equivalent witha sink of matter.

This phenomenon appears everywhere in theobservable Universe in various sizes and capacities, atall ages at concomitant levels of evolution and seeming-ly in an infinite chain of orders of magnitude. In mod-ern terminology these evolutionary stages of matter arecalled rotating gas-clouds, proto-stars, proto-planets,planets, suns, red giants, white dwarfs, quasars, black-holes and in the higher orders of magnitude, galaxies,galactic clusters, super clusters, etc.

The two most common characteristics of these sinksof matter are Rotational Gravitation and the gradualcondensation of kinetic energy into the various states ofmatter.

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The evolution starts with the formation of elemen-tary particles, nuclei and the atoms of Hydrogen.Eventually and by chance, these formations gather intorare gas-clouds, form a core in their densest part and,due to the differential rotation of the one stage higherorder of magnitude, the cloud start rotating.

From here on Rotational Gravitation and theimmensity of chaotic chances drives the evolution allthe way up to the super heavy solids with mean densi-ties exceeding that of water by a factor of 500,000.

To point out the plausibility of this hypothesis, itshould be noted, that the volume of space taken up bythe orbit of the most inner electron of an atom is tenthousand times greater than the volume of the nucleus.Therefore, the electromagnetic tie between nucleus andorbiting electron reaches through distances comparablein proportion to the vast space in the solar system.

From the stand-point of Aethro-kinematics, thisvast, allegedly empty space, is filled with vorticity andthe interlocking electromagnetic force-patterns of theall-pervading Aether, forming and re-forming, adjustingand re-adjusting to each minute mutation of matterthrough unthinkable distances in all orders of magni-tude of the Cosmos.

On the one hand, there is a slow, step by step evolu-tion of the elements on all levels of complexity, but themost minute changes in the microcosmic structure ofmatter involves the consumption of comparatively greatquantities of Aethrons.

On the other hand, the small extent of this con-sumption and the magnitude of the proportional gravi-tational Aether-drift can be judged from the experimen-tal fact, that the strength of the force of gravity is 1036

(trillion×trillion) weaker than that of the electromag-netic forces. Recall, how a tiny horseshoe magnet picksup a nail from the floor when it gets in its vicinity, doingit with ease against the colossal gravitational mass ofthe whole Earth.

Consequently, the rate of the evolutionary process ofmatter, the capacity of the resulting sink, and that ofthe consumption of Aether can be comparatively slowand small.

The consumption of the number of Aethrons per unittime is equivalent to Newton's qualitative concept ofgravitational mass. The kinematical effects of the spiralvortex are equivalent to Huygens' centripetal accelera-tion and Kepler's formula for the angular velocities ofthe planets on their elliptical orbits.

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Hence, in a rough sketch, the kinematical descrip-tion of Newton's earthly and celestial mechanics andthe conceptual simulation of their origin and mainte-nance in the ideal, isotropic, all-pervading Aether iscompleted.

b) There is a tendency parallel with the evolution ofmatter from the initially random motion of theAethrons toward the organized dynamic stream-lines ofthe particles and binding forces among them, which isequivalent to the general tendency of condensation ofkinetic energy into ponderable matter.

The quantity of matter is proportional to the num-ber of Aethrons involved in the dynamic motion-pat-terns or drifts organized into particles and force fields.If in some way the condensed state of these organizedpatterns were broken up and the Aethrons were forcedout of their permanent flows, and they would regaintheir state of random motion, they would expand intothe surrounding space with their average velocity, equalto that of light.

This immense kinetic energy, freed by the de-con-densation of matter, can be expressed by the famousmathematical equation: E = mc2.

PHILOSOPHICAL NOTES Before closing this chapter and discussing its conse-

quences, (while it is fresh in the mind,) let us note someof the unique philosophical aspects that emerge from allof the aforementioned.

1. As it has been discussed before, one of the char-acteristics of the universally observed phenomenon ofrotation is, that the units of rotation, in all orders ofmagnitude are autonomous and isolated systems. Inthe global result, this is true, but in the case of the kine-matical units of sink-vortices, there exists an exchangeof dynamic and kinetic energies between the rotatingand the surrounding medium. Since the capacity of thesink is proportional to the average atomic density of thematerial body, that produces it, so is the size of the spi-ral vortex, that delivers the Aether to the sink.

Parallel to the evolution of the material substancefrom gas to solid, from light to heavy, the capacity of thesink is constantly increasing. As it was discussed before,between the vortex and the isotropic medium, at agiven distance from the center, there exists a boundaryof equilibrium, where the centripetal effect of the sinktogether with the isotropic pressure of the surroundingmedium are in balance with the inertial centrifugal ten-

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Aethro-kinematics CHAPTER ELEVEN Philosophical Notes

dencies of the Aethrons. The diameter of this boundaryis also a function of the density and size of the body.Thus, the state of matter and sink and vortex are alltaking their parts in the process of evolution.

Nevertheless, these evolutionary effects are ex-tremely slow and small and, because of the vast dis-tances between the rotating units, with regards to theautonomy and independence they are totally negligible.For all observational and theoretical purposes, withinhumanly measurable time interval the boundary of asink vortex can be taken as constant and beyond that,the sink does not affect the isotropy of the externalmedium. Vice versa, the extremely slow thinning of theall-pervading Aether (on account of the evolution ofmatter) does not affect the internal structure of therotating units.

If the external medium is involved in the rotation ofa higher order of magnitude, it carries the vortex with itas an autonomous, immutable unit.

Since it is generally assumed that the fundamentallaws of physics are the same throughout the observableUniverse, it can also be assumed that the laws are thesame in all orders of magnitude. Although there seemsto be an endless chain of orders of magnitude, because

of the autonomy of each system, the theory ofAETHRO-KINEMATICS is not involved with the prob-lem of infinity. The laws of physics can be discoveredand established in any one of the orders of magnitudeand extended to higher orders, as they enter into thescope of human observation.

As for the lower orders of magnitudes; the basicassumption of the theory is, that all phenomena ofNature can be explained based purely on the kinemat-ics of the Aethrons and therefore their internal struc-ture, if there is any, is non-essential for the descriptionof the laws of physics. Thus the concept of RotatingUniverse is an open ended assumption, which merelydescribes the presently imaginable highest order ofmagnitude, within which the laws of AETHRO-KINE-MATICS are valid.

2. Another fundamental character of the sink-vor-tices is their differential rotation. As it has been shownthrough the origination of the donut-vortex, any rela-tive motion between adjacent layers of a medium hasthe potential to produce vorticity, which eventuallycould generate some kind of permanent kinematic pat-terns, like a sink-source dipole and its resulting perma-nent force-fields.

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The dependence of angular velocity on the distancefrom the center, that is, the differential rotation of theAether in the sink vortex represents a relative motionbetween adjacent layers and such constant torque-likeeffect has been shown to be the only requirement forthe origination of the elements of ponderable matter.Thus, universal rotation is not only concomitant withuniversal gravitation, but with the universal evolutionof matter, as well.

3. With the concept of the center of oscillation andits drift, it has been established, that truly continuousmotion only exist in Nature in the order of magnitude ofthe Aethrons and therefore the only true speed, thatmeasures continuous motion against time and space isthe average speed of the Aethrons, which is equivalentto our measurement of the speed of light.

It can be seen through the analyzes of the gravita-tional drift, that the formation of matter, and the transi-tion of directional drift-velocities through one-to-one col-lisions, create the illusion of the Newtonian inertia, andthat the intuitive human concept of motion is also anoptical illusion, similar to that of motion pictures.

Under the constant bombardment of the Aethronsof the isotropic static pressure, everything that exist in

Nature is oscillating with the speed of light and with animmense frequency, proportional to the number ofAethrons in the conglomerate of the body. This oscilla-tion, however, is unrecordable on the human time scale.

What is recorded by our senses as changes in posi-tion in space is merely the drift of the center of the oscil-lation of the bodies in a given direction. Our senses arefooled, recording continuous motion, when 24 frames ofstill-pictures jumps into view per second, and likewise,we are deceived by the 60 mph speed of our automobile.

In kinematical reality the car is oscillating with afrequency of trillions times trillions per second with thespeed of light in every possible direction. Superimposedon this random oscillation, under the constant impulsesof the crankshaft, the machine is forced to oscillate for-ward an infinitesimal time-interval longer than back-ward or in any other direction. It is this drift velocity ofthe huge mass of the car, that we measure 60 mphsmooth riding.

Keeping all this in mind, we can now attempt torehabilitate the kinematical details of electricity andmagnetism, most of which has been already done by thegeniuses of the nineteenth century and were discredit-ed and ridiculed by those of the twentieth.

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CHAPTER TWELVE

ELECTROMAGNETISM IN THE IDEAL GAS

THE PICTURES OF EMPTY SPACE The hypothesis of the all-pervading light trans-

mitting medium of Aether, had been an essentialpart of natural philosophy from the Greeks on.According to the theories of Descartes, Huygens,Leibnitz, Euler and others, Aether was the conveyerof light-waves as well as the rotational and gravita-tional forces, and even Newton believed in its exis-tence.

Further more, in the nineteenth century Faraday,Oersted, Gauss, Maxwell, Lorentz and othersassumed that electricity and magnetism would alsofind their final analysis and explanation through thecharacteristic behavior of the Aether medium.

The two thousand years of research on magnet-ism and electricity culminated in Maxwell's electro-magnetic equations, which were the mathematicalcompletion of a step by step conceptual investigationof the kinematical and fluid-dynamical properties ofAether as the foundation of all electromagnetic phe-nomena.

The composite result, Maxwell's great mathemat-ical memoir; A Dynamical Theory of the Electromag-netic Field, was read to the Royal Society in 1864.

With the modern tendency to justify the non-con-ceptual solutions of twentieth century physics and todepreciate the value of the old conceptual classicaltheory, contemporary teaching presents Maxwell'smemoir as his final turn away from the simplemechanical analogies, and in general, from the use ofthe hypothetical Aether. While new physics acceptsMaxwell's complete mathematical system, his stepby step conceptual investigation had been declared

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Aethro-kinematics

mere temporary scaffolding with little scientificvalue, which should be discarded to avoid confusion.

The historical fact, however is, that Maxwell nei-ther had the intention of giving up the hypotheticalAether, nor to turn away from the clarification ofphysical concepts by mechanical and kinematicalanalogies. Among other important later writings, in1871 he published his Treatise on Electricity andMagnetism, a thorough comprehension of everybranch of electromagnetism from the point of view ofFaraday, which was clearly based on Hydrodynamicanalogies applied to the Aether medium.

Nevertheless, when it comes to electromagnet-ism, modern educators try to keep young scientificminds away from the historical importance ofmechanic and hydrodynamic analogies and withalmost fanatic desperation try to describe the phe-nomena in the aetherless, characterless void ofempty space.

In the totally inter-related nature of the complexsystem of electric and magnetic phenomena, it ispractically indifferent where one starts the descrip-tion of the subject. Both the sciences of electricityand magnetism were originated by the Greeks and

developed separately until 1820, when Hans Chris-tian Oersted observed that an electric current has amagnetic effect in the space surrounding the conduc-tor. From there on, the concepts of electricity andmagnetism became entirely interdependent. No mag-netic phenomenon could be explained without theuse of the concepts of electricity and vice versa. It fol-lowed, that a simple, step by step separate descrip-tion of either one of the two phenomenon becameimpossible. A condensed version of the contemporaryapproach of explaining the subject is given here.

The introduction of the theory of electricity com-monly starts with some simple experiments on pro-ducing static electricity and forming the concepts ofnegative and positive charges, carried by the elemen-tary particles of matter, the electrons and protons.The basic character of these electric charges is, thatlike charges repel and unlike charges attract oneanother.

Thus the forces of static electricity are described,just like gravity, as action at a distance forcesthrough empty space. These two entirely differentforces, gravity and electricity are also equivalentmathematically. The inverse square law of the elec-

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Aethro-kinematics CHAPTER TWELVE The Pictures of Empty Space

trical attraction and repulsion was establishedempirically by Augustin de Coulomb in 1785.

M1 M2 q1 q2Fg = G −−−−−−−− Fe = −−−−−−−,

R2 R2

where Fg is the force of gravity, M1 and M2 are themasses involved, Fe is the electric force between thecharges q1 and q2 .

(a) Figure 12-1 (b)

The essential difference is that while gravity isan exclusively attractive force, electric charges pro-

duce both attraction and repulsion. Figure 12-1shows the schematics of the electric fields in emptyspace in the vicinity of two unlike charges attracting(a), and two like charges (b), repulsing one another.Next, as it follows historically, the theories of batter-ies and electric currents are presented, which arebased on the attractive forces between the unlikecharges of protons and electrons.

By certain chemical processes between lead, lead-dioxide and sulfuric acid an electric potential differ-ence is created between the two poles of the battery;that is, a surplus in electrons at the negative poleand deficiency of them, or rather an excess of protonsat the positive pole.

In copper and other conductors, some of the elec-trons on the outside of the atoms are held loosely andeasily escape."These valence electrons move in a random manner

within the body of the wire like an 'ideal gas'. Whenthe circuit is closed, or 'on', under the influence of theattractive force of the protons, the free electrons startdrifting towards the positive terminal. To keep thecurrent continuous, however, after arriving to the

221


positive terminal, the electrons must somehowreturn to the negative terminal. The transfer of elec-trons through the sulfuric acid back to the negativeterminal against the repulsion of the negativecharges is a consequence of certain complicatedchemical processes." (Atkins, Physics [293])

Figure 12-2

Discussing the parallel between gravity and forceof electricity Figure 12-2 illustrates a storage bat-tery by the picturesque analogy of the gravitationalpotential energy of a ski-lift where the skiers are rep-resenting the drifting electrons.

According to the theory of static electricity, thesedrifting electrons supposed to constantly acceleratetoward the positive terminal, however, they constant-ly collide with the atoms of the metal, transfer theirkinetic energy, and have to start accelerating again.This transfer of the kinetic energy of drifting elec-trons is an electromotive force, which converts intothe electromagnetic radiation of heat and light.

(a) Figure 12-3 (b)

Next, magnetism is represented by the phenome-non of a bar magnet. Figure 12-3 (a) shows the mag-netic field of a permanent bar magnet traced by ironfilings. (b) illustrates Faraday's concept of the lines of

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force around the same bar. The three dimensionaleffect of these lines of force in the neighboring spaceof the magnet is called the Magnetic Field. Faradayhimself was firmly convinced that these lines offorce, surrounding the magnet are actually flow pat-terns or stresses in the aether, and they exist evenwhen no iron filings were present to trace them.

Faraday found that the lines of force act as if theywere stretched fibers in space which are continuallytrying to contract and thus pulling on the poles attheir ends. They also act as if they were pushing oneanother sideways as they contract. Their strengthdepend on the distance from the magnet and on themedium they pass through. Lord Kelvin called theease with which lines of force may be established in amedium, the permeability of the medium comparedwith vacuum."There is no insulator for magnetic lines of force,

just like there is none for gravity, but soft iron, withits supreme permeability attracts them and guidesthem, and it is frequently used as a magneticscreen." (Newton H.Black, College Physics, [321]).

The Earth also seems to be a magnet. Compassneedles point toward the Earth's magnetic north pole

because they are under the influence of the Earth'sMagnetic Field. The same needles brought near a barmagnet align themselves in definite directions rela-tive to the poles of the magnet. – A detailed descrip-tion and kinematic explanation of the bar magnetcan be found in Appendix II.

The next step is the introduction of the discoveryof Christian Oersted; the magnetic effects of a cur-rent carrying conductor on compass needles. Theexperimental fact of this discovery is, that a currentcarrying wire deflects the compass needle from it'snormal position of pointing toward the north pole.

Figure 12-4 (a) shows, that if a wire is held overthe needle and the current flows from south to north,the needle is deflected toward the west. When thecurrent flows the other direction, the needle isdeflected toward the east. When compass needles areplaced in a plane perpendicular to the wire, they allline up tangential to the circle, centered on the wire,(b). If the current is reversed, all needles align them-selves end to end in the opposite direction.

The photograph of Figure 12-4 (c) was obtainedby sprinkling iron filings on a sheet of paper, whichwas held in a plane perpendicular to the current car-

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rying wire. The filings of soft iron are long and thinand align themselves in the magnetic direction likeminiature compass needles. They evidently trace outcircles centered on the wire.

Figure 12-4 The schematic drawing (d) illustrates the vector

representation of these circles. The circular vectorsand the distances between them represent the direc-tion of the force on the needles and the inversesquare relation in the magnitude of the force withthe different distances. These vectors represent thesame circular vortex which has been discussed inconnection with the great storms and Newton's refu-tal of Descartes solar vortex.

It is assumed that a Magnetic Field exists wher-ever a compass needle takes a definite alignment inspace. Obviously one of these cases is the currentcarrying wire with the resulting circular alignmentof the compass needles or that of the iron filingsaround it. However, the field around the conductorseems to have no resemblance to the field around amagnet and for distinction, it is called a CircularMagnetic Field, where there is no south or northpoles to which the needles would be attracted. Thelines of force appear to form circles centered on thewire, but neither starting nor ending on it. While thelines of force of a magnet are endless loops and theirdirections always point from its South to its Northpole, the force of the Circular Magnetic Field isalways tangential to a circle about the wire, and itsdirection depends on the direction of the current.

The magnitude of the magneto-motive force isdirectly proportional to the strength of the currentand inversely proportional to the square of the dis-tance from the wire. If the current stops, the CircularMagnetic Field ceases to exist.

Coordinating these findings with the assumptionthat the electric currents are made up of drifting

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a)

b)

d)

c)

electrons, scientists concluded that moving electronsproduce a magnetic field in the plane perpendicularto their motion. − Some further characteristics of theCircular Magnetic Field is demonstrated by AndreM. Ampere's experiments on the magnetic forcesbetween two conductors.

(a) Figure 12-5 (b) Figure 12-5 illustrates Ampere's equipment. The

vertical wires are freely hinged at the top and theirlower ends dip into mercury pools, which also con-duct electricity. This way the wires can freely swingwithout breaking the circuit. When the currents gen-erated by the two batteries flow in the same direc-tion (a), the vertical wires attract one another andwhen the currents flow in opposite directions (b),

they repel each other. If either one of the currentceases, no force exist between the wires.

Since the conductors always contain as manyprotons as electrons, the forces between them cannotbe the result of static electricity and therefore it isassumed that this phenomenon is a further conse-quence of the Circular Magnetic Fields around theconductors, produced by the moving electrons.

When this assumption is accepted, the followingconclusions can be established:

"A charge moving with constant velocity produces aCircular Magnetic Field in the plane rectangular toits motion. In turn, this magnetic field effects themotion of the other charges. Aside from the electro-motive attraction and repulsion, when two chargedparticles are both in motion, they exert on one anoth-er a new kind of force that depends on their speedsand directions. This force is zero, if the velocity ofeither one of the charges is zero. A charge producesno magnetic field unless it is in motion." (Atkins,Physics, [311] ) .

Note, that these statements are not purely empir-ical descriptions of the facts, but rather speculativepostulates, tailored to fit the phenomena.

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Seemingly these conclusions are somewhat con-tradictory to the statement of the theory of staticelectricity, namely, that like charges repel one anoth-er. Ampere's experiments shows, that conductors,carrying currents in the same direction, attract oneanother. It should follow from this, that parallel mov-ing electrons would exert two forces on each other atthe same time; an electric force of repulsion, as likecharges of static electricity, and a magnetic force ofattraction, because they move in the same direction.Moving in the opposite direction they would doublyrepel each other.

Figure 12-6

This contradiction supposed to be eliminated bythe intermediate role of the circular magnetic fieldsand the phenomenon was explained by Faraday'slines of force, as illustrated."We may understand the effect of two parallel con-

ductors by studying the magnetic fields traced byiron filings about the two wires. Figure 12-6 (a)shows the magnetic field about the two wires inwhich electric currents flowing in the same direction."Here we would expect the wires to attract each

other because of the tension in the lines of magneticforce. Picture (b) shows the magnetic field about twowires carrying currents flowing in opposite direc-tions. Here we have repulsion between the wires dueto the sideways push between the magnetic lines offorce." (Newton Henry Black, College physics [400]).

Faraday also proved experimentally that the cir-cular magnetic fields are also in rotation about theconductors. Figure 12-7 shows Faraday's rotator cupsfilled with mercury through which the electric cur-rent can pass from the overhead support to the con-ductor: The north pole of a magnet rotates aroundthe current-carrying rod, (a). The current carryingrod rotates around the north pole of the magnet, (b).

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Figure 12-7The next link in the introduction is illustrated by

Figure 12-8: If a circular loop is formed out of a cur-rent carrying wire it produces a magnetic field verysimilar to that of a bar magnet.

A compass needle brought to the vicinity of anypart of this loop, acts as if it was close to a magnet.The magnetic field of the loop has a north and asouth pole, which are reversible by changing thedirection of the current. With some three-dimension-al imagination it can be pictured, how the rotatingCircular Magnetic Field everywhere around the

curved wire is creating the overall flow-patternthrough the ring. The endless loops of the lines offorce, emerge from the north pole of the ring and re-entering at the south pole.

Figure 12-8By changing the direction of the current, the

poles can be reversed. It follows, that two circularloops of conductors with unlike current must attract,and with like must repel one another. When a helicalcoil is formed by winding a number of such loops, the

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magnetic effect is greatly strengthened because thefields of the individual loops reinforce each other.

Figure 12-9A coil of this type, called solenoid, is shown on

Figure 12-9. When an iron rod is placed within adensely wound solenoid, it intensifies the strength ofthe magnetic field hundreds of times and the twotogether form a powerful electro-magnet.

Soft iron loses its magnetic properties as soon asthe current ceases to flow through the solenoid.However, permanent artificial magnets can be pro-duced from other ferromagnetic materials by placingthem into the magnetic field of a solenoid. Next, the

magnetic properties of a material are explained interms of microscopic electric currents due to thebehavior of the electrons. An electron can produce amagnetic field in two ways.

"An electron moving around the nucleus of an atomin a circular orbit is equivalent to a circular loop ofcurrent and produces a similar magnetic field,Figure 12-10 (a). In addition, an electron may bevisualized as a small spherical cloud of negativecharge which is spinning about its axis. Any smallportion of the electron describes a circular pathwhich is equivalent to a current in a circular loop ofwire, producing a magnetic field, (b).

(a) Figure 12-10 (b) "Most materials show no magnetic effect because of

the orientation of the orbiting and spinning of the

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electrons are random and cancel out the magneticfields of one another. The important exceptions arethe ferromagnetic materials in which there is anexcess of electrons spinning about axes pointing inthe same direction and adding together they producea large combined magnetic field." (Atkins, Physics)

In a normal size bar magnet there are about 1024

spinning electrons. In soft iron, such as a nail, theelectron spin is random, but very easily turned aboutin any direction by an external magnetic field. Figure12-11 illustrates how the spin of the electrons of abar magnet are lined up, which then aligns the elec-trons of the nail, and draw it to one of its poles.

(a) Figure 12-11 (b)

With this, the conceptual circle has been com-pleted; electricity explains magnetism and magnet-ism explains electricity. The description of these phe-nomena resembles to that of Newtonian mechanics,where one concept is defined by the other and noneof them, on their own, are really understood.

Just like the concept of force cannot be explainedby the concept of inertia, the mystery of magnetismcan hardly be explained away by the mystery of elec-tricity. The assumption, that a magnet has its proper-ties because it is made of tiny magnets, says nothingabout the nature of magnetism. Theorizing that anorbiting electron is equivalent to the electric currentin a circular wire and it creates its own magneticfield, is merely a transference of the mystery into alower order of magnitude.

Hence, after the final removal of the so-calledscaffolding, Maxwell's ingenious mathematical sys-tem of electromagnetism has been left in a completeconceptual vacuum.But if the conceptual descriptionof electromagnetism is impossible, then where shouldwe file the pictures that scientists drew for us on thecanvas of empty space. Are they mere ghosts of ourimagination? Can it be a mere coincidence that these

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pictures makes mathematical and conceptual sense?Or maybe Einstein hit it right in the second timearound, and perhaps empty space is not really andcompletely empty?!

The AETHRO-KINEMATIC description of New-ton's mechanics showed that the complexity of thephenomena, recorded by our senses, evolves from thechaotic simplicity of the ideal gas. Thus, the mysteryof the action at a distance force and that of the unex-plainable Kepler's Formula has been reduced to thecomparatively simple kinematics of the sink-vortex.Let us now see if there is any possibility for a similarkinematical simulation of the action at a distancemysteries of electromagnetism.

MAGNETISM AND KINEMATICS Oersted's and Ampere's discoveries about the

Circular Mag- netic Field, an interaction betweenelectricity and magnetism, seem to involve all funda-mental ingredients of electromagnetism, and for nowit is assumed that the kinematic understanding ofthese experiments and the Circular Magnetic Fieldwill serve as a key to explain all other phenomena.To simulate these experiments, it is necessary to

describe the kinematics of the following phenomena:a magnet, a battery, a conductor, an electric current,and a circular magnetic field.

Thus, the first thought-experiment, will be a sim-ulation of a bar magnet in the familiar great roomfilled with the isotropic and homogeneous ideal gas.

Suppose somewhere in space a small cylindricaldrum is suspended, and that initially both the cylin-der and the gas are motionless. Next, a fan-propelleris introduced inside the cylinder, at its mid-section.When the blades start to rotate the fan draws thegas from behind, pushes it forward, and creates acurrent flowing from left to right through the drum.Evidently, there will be a movement of the gas insidethe drum, and some random turbulences in the medi-um because of the compression in the front and therarefaction at the end.

Now, suppose that the wall of the cylinder is notsolid, but it is perforated in such a way that the ran-dom kinetic energy, or the flow patterns between theexternal and internal gas can be freely exchanged.Figure 12-12 (a) illustrates a magnified portion of theperforated wall which is an essential part of the thisand following simulations. As the external gas is

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Aethro-kinematics CHAPTER TWELVE Magnetism and Kinematics

sucked in behind the propeller, each individual holeof the perforated walls becomes a sink and wherethe internal gas pushes out in front of the propeller,each hole becomes a source. With this, the evolutionof a complex circulating system begins.

Figure 12-12

The rarefaction produced by each hole behind thefan and the condensation in front of it are both localdisturbances in the isotropy of the external medium.These disturbances with opposite density differencesare propagated outward from the holes in sphericalshells. Pulses of compression and rarefaction.

Some of these shells, generated by neighboringsinks and sources, in the vicinity of the propeller, willmeet each other outside the cylinder. Eventually twoshells with opposite pressures will interconnect overthe wall and form a circular stream; a loop of gas cir-culating in and out through the perforated wall.

As a consequence of this circular stream, the sta-tic pressure around the new loop decreases, which inturn, helps in the formation of a larger loop, bridgingover sinks and sources further apart. Beyond thoseeven larger ones, and so on and on...

Eventually, a whole three dimensional system ofloops evolves in a complex pattern of circulation,entering at one end leaving at the other end of thecylinder, then turning back in space and reenteringagain. The schematics of this pattern is identicalwith the magnet illustrated above on Figure 12-3.

Further more, as it has been shown in the kine-matics of gravity, no steady radial flow toward a sinkcan exist without triggering rotation. The same isexpectable in each case of a source which is pushingagainst the isotropic medium or that of a sink, suck-ing in fluid. The final flow pattern around andthrough the cylinder is a system of endless elliptical

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(a)

(b)

circulating filaments, which greatly resemble the pic-ture of Faraday's lines, or tubes of force, as they weretraced by the iron filings around a magnet.

It follows from above, that the core of the system,the cylinder itself become a sink at one end, wherethe greatest loops enter and drags the free gas withthem, which is ejected at the other end, creating asource. These are the two poles of the 'magnet'.

When two such cylinders are placed nearby infree suspension, they will eventually turn towardeach other and seek out their opposite poles; thesource finds the sink and vice versa. The kinematicreason is illustrated on Figure 13, where two fan-magnets are shown parallel but offset to each other.The white dotted lines represent the initial circula-tion of the medium around the bars. The emphasis ison the envelope currents (black) evolves around thetwo separate circulatory systems which connects theopposite poles of the two units.

Figure 14, (next page) shows how the whole sys-tem evolves, under the constant isotropic pressure ofthe medium, representing a tendency for condensa-tion and symmetry that force the two units to turn toa mutual axis and connect their opposite poles.

Hence, Faraday's rubber-band-like lines of forceis not needed to pull the magnets together, it israther the isotropic pressure on the two circulatorysystems, which turns and pushes them into the mostcondensed symmetry, which is a new combined unit,again possessing only one North and one South pole.

Figure 12-13

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ENVELOPECURRENT

MAXWELL'SIDLE WHEELS

Figure 12-14

Now, it follows naturally, that there will be arepulsion between like poles because the circulationsof the two systems are in opposite directions whichdrives the poles away from one another. (See App.II.)

The collisions between the two opposite currentsbrake up the loops and turbulence is created. Thetemporary increase in the static pressure betweenthe two systems overpowers the external pressure.The results is a repulsion between the two like poles.

Next, recall the classical electron theory of mag-netism. Figure 12-15 and 16 (next page) illustratesan analogous hypothesis.

Consider a great, perforated, cylinder, withinwhich, instead of one big fan at the center, there exista great number of miniaturized fan-magnets, justlike the unit described above.

These tiny units are freely suspended in a waythat each can turn in any possible direction, however,their centers are fixed in space in an organized sym-metry relative to the great cylinder, and to oneanother. In the initial state of the system, (Figure 12-15) all the small fan units are active, but they areoriented in completely random.

This means, that the same number of fans arepointing in every direction and therefore the densitydisturbances they produce with their individual cir-culation cancel out each other. As a result, there is nonet flux or flow pattern within the great cylinder,

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N

S

and the internal and external densities and pres-sures of the gas are in equilibrium.

Figure 12-15Let us now introduce a mild external vertical

draft in the medium, a current, which passesthrough the location of the main cylinder, analogous

to a uniform magnetic field (dotted white lines).Since the main cylinder is also freely suspended atits center, the draft will eventually turn it to thedirection of least resistance, lining up its axis withthe draft, (Figure 12-16).

Figure 12-16

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>

>

> > >> >

> > >

Consequently the draft will enter and leavethrough the open ends of the cylinder and since atthis stage the draft is the same inside and outside, ifnothing else happened, there would be no kinematicreason for the formation of any circulatory patterns.

However, the draft inside the cylinder, will gradu-ally turn all freely suspended, active fan units intothe same direction, parallel to the axis of the maincylinder. Without the draft, the individual currents ofthe fans were cancelled by their random orientation,but now they lined up, and the strength of their com-bined currents are adding to the draft. As more andmore fan units turn into the direction of the draft,they produce an overall flow of the internal gas of thebig cylinder far greater than the strength of the ini-tial mild external draft.

The flow pattern through and around the bigcylinder is now developing by the draft combinedwith internal drives of the aligned fan units. Due tothe greater internal flow, and the resulting smallerinternal static pressure, and because of the interven-ing perforated wall, the final product is the samesink and source circulatory system as that evolvedaround the original small fan units. Hence, the same

kinematic phenomenon is recreated in a higher orderof magnitude.

If the general draft ceased to exist, the smallunits gradually loose their mutual orientation andthe system returns to its initial random state. This isthen the hydrodynamic analogy of the temporarymagnetization of a soft iron bar.

Consider now, that the suspension of the fanunits might not be completely free, but they aresemi-fixed in random directions and their re-orienta-tion would cause some resistance. In this case, a cer-tain minimum strength of a draft is required toestablish their re-alignment. A sufficient strength ofdraft which overpowers the resistance, can producethe uniform orientation of the units and then the cir-culation through the cylinder will remain perma-nent, even when the draft ceases to exist.

Substituting now the ideal gas with the all-per-vading Aether, the miniaturized fan units can bereplaced by the kinematically equivalent donut-vor-tices. The perforated wall is a representation of kine-matic communication between the internal andexternal Aether through the spaces and interstitchesof the crystalline structure of ponderable matter.

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This solution allows the development of the tem-porary or permanent circulatory systems throughthe body between the internal and external Aether.

The non-free suspension of these units representsthe electromagnetic construction of matter, that is,the complex internal flow-patterns, connecting thedonut-vortices by the force of cohesion that keepsatoms, molecules and crystalline structures rigidly orelastically together.

The draft, affecting the cylinder and the fan unitsinside, can be taken as the effect of a solenoid or thatof the Earth's magnetic field or, in general, the capa-bility of a uniform magnetic field to produce magnetsout of certain metals.

Hence, the natural magnet, Faraday's fields offorce, the kinematics of the action at a distanceforces of magnetic attraction and repulsion has beensimulated in the environment of the all-pervadingideal gas of Aether.

THE ELECTROMAGNETIC FLUIDThere remains the task of describing the kine-

matical origin and maintenance of the complex phe-nomena of an electric current and the circular mag-

netic field around a current carrying conductor.These phenomena includes the magnetic effects oncompass-needles and on another current carryingconductor.

As it was mentioned before, there is very littleresemblance between the magnetic field of a magnetand that of a current carrying wire. In fact, the onlysimilarity between the two is, that they both move acompass needle out of its initial orientation by anaction at a distance force, although even the changein the direction of the needle, relative to the source ofthe field, is entirely different in the two cases.


236

Aethro-kinematics CHAPTER TWELVE The Electromagnetic Fluid

N

S

N

S

N

S

NSN SN

S

N

S N SNS

N

SN

S

NS

N

S

N

S N

S

N S

NS

N

S

NS

N

S

N

S

On the one hand, as Figure 12-17 (a) illustrates,all lines of force in the vicinity of a magnet are end-less elliptical loops surrounding end penetrating thematerial body. The torque exerted on the compassneedles turns their axes tangentially to the ellipticallines of force, which at the center of the external fieldis parallel to the axis of the magnet. Closer to eitherends, the directions of the needles first turns perpen-dicular to the bar, then directly toward the poles.

On the other hand (b), the lines of force aroundthe conductor do not have any contact with the mate-rial body of the wire. They seem to be exactly circu-lar, centered on the wire and in the planes rectangu-lar to the axis of the wire. As a result, the torqueexerted on the needles at any point of this field isalways exactly rectangular to both the wire and tothe radius of the circle. Hence, from a kinematicpoint of view, the circular patterns of the magneticfield surrounding a current carrying conductor andthe elliptical endless loops passing through a regularbar magnet must be entirely different in their originand maintenance.

Nevertheless, there is one similarity betweenthese fields, that the strength of both forces are

inversely proportional to the distance. The force ofthe circular magnetic field is, F ∝ 1/R, the same for-mula that describes the circular vortex.

As it stands at present, this part of the theory ofelectricity and magnetism is quite ambiguous evenin Maxwell's and Lorentz's versions. The fundamen-tal assumption that moving charges, like electrons,are producing magnetic fields is itself an enigma.There isn't even an approximate theory of how thiscould work nor is there any parallel to this phenome-non in Nature. According to the presently acceptedhypothesis, an electron moving in a conductor cre-ates a circular force-field perpendicular to the direc-tion of its motion. The force vector is also perpendicu-lar to the radius in the plane of the circle.

Reversing the direction of the motion of the elec-tron also reverses the direction of the force. If thereare two conductors and electrons moving in both,there is an attraction or repulsion between the wires,dependent on whether the directions of currents arethe same or the opposite.

This differentiation, is not simply the result ofthe relative motions of the electrons, because theforce does not exist at all, when the charges are at

237


rest in one of the wires. This empirical fact, howeverbrings up the question; At rest relative to what?!

Remember, that a frame of reference can alwaysbe chosen to be at rest relative to one of the electrondrift. Not even relativity attempted to answer ques-tions like this. But there are other sensitive ques-tions as well. – Even the hypothesis of the motion ofelectrons in a current is unclear, since it is based onthe concept borrowed from static electricity; on theaction at a distance force of attraction between theopposite charges of protons end electrons.

Figure 12-18

It is assumed that certain chemical processes inthe battery creates an excess positive charge at oneterminal and an excess negative charge at the other.Since the positive protons are firmly fixed in theatoms of the metal, under the influence of the mutu-al attraction the free electrons are the ones thatmust migrate toward the positive pole.

One problem with this idea is, that the forcebetween charges decreases by the square of the dis-tance and it can hardly be assumed that the positivepole would attract all electrons evenly at unspecifieddistances through the whole length of a conductor. Toremedy this ambiguity, it is hypothesized, that freeelectrons in the body of the wire act like the random-ly moving particles of an ideal gas which expand intothe rarefied space from which the electrons werepulled into the positive terminal.

But even if this overly speculative theory isaccepted, another question arises; In order to keepthe current going contiguously, after arriving to thepositive terminal, the electrons must escape again,drift through the fluid, back to the negative poleagainst the increasing repulsion of the negative ter-minal. How ?

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E L E C T R O N C U R R E N T

The answer is another unclear assumption: "thisis the consequence of certain complicated chemicalprocesses".

There are also great complications with the cre-ation of the circular magnetic field by the movingcharges. To visualize the complexity of this circularfield, consider Figure 12-18, illustrating the threedimensional schematics of the magnetic lines of forcearound a straight portion of a current-carrying con-ductor. − Recall the experiment with the iron filingson the sheet of paper, held in the plane rectangularto the conductor, Figure 12-4.

It is evident that the circular pattern will remainthe same if the sheet was moved up or down parallelto itself. Meaning, that the circular magnetic fieldexists in each infinitesimal plane, continuously andsimultaneously in the whole length of the wire. Theresulting description is not only a circular, but rathera cylindrical magnetic field, which surrounds thebody of the conductor and follows its direction fromone terminal to the other.

Now, try to imagine the contribution of each indi-vidual electron to the creation of the cylindrical fieldwhile it is in random oscillation in the electron gas,

drifting toward the positive terminal, colliding withthe atoms, loosing its drift, and re-accelerated againby the static electric attraction toward the protons.In- deed, the only possible conceptual simplificationhere is to assume that the cylindrical magnetic fieldis an effect of the drift of the free-electron gas, as akind of electromagnetic fluid.

Still, there are more perplexities in the presentlyaccepted theory. A single current-carrying conductormoves the magnetic compass needle, but does notmove a nail or another conductor that carries no cur-rent. As it is hinted by the pattern of the iron filings,(Figure 12-5) the attraction or repulsion between thewires are most likely the results of the interactionbetween the two magnetic fields generated separate-ly. For any interaction at a distance between twomaterial bodies, there must be a magnetic fieldaround both; either two current-carrying wires orone of those and an active magnet.

Insisting on keeping these forces as 'actions at adistance', one must end up with Einstein's gravita-tional curvatures of empty space. In this case, how-ever, the geometry of these curvatures is much morecomplex, and the interaction is not between field and

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Aethro-kinematics CHAPTER TWELVE The Hydrodynamic Battery

matter, as it is with gravity, but between field andfield, or let's say, between two sets of the curvatures ofempty space?!

Adding to this the comparatively primitive rela-tivistic excuse that gravitational mass simply dis-torts the texture of space, but complicating the prob-lem with the negative charge and the moving massof the electron-fluid, it is not surprising that the lastquarter century of Einstein's life did not produce asuccessful unified field solution to the phenomena.

A HYDRODYNAMIC BATTERYIn the previous discussions, the magnetic field

around magnets were simulated in the ideal gas andtransposed to a kinematically conceivable flow-pat-tern of the Aether through and around the materialcore of the magnet. Continuing with the same tech-nique, the following thought experiment is anattempt to describe the AETHRO-KINEMATIC ori-gin and maintenance of the battery, the electric cur-rent and the resulting Cylindrical Magnetic Fieldaround a current carrying conductor.

Let us start with the popular way to explain theoperation of a battery by hydrodynamic analogies:

"The action of an electric cell (battery) may be com-pared with that of a pump for circulating waterthrough a system of pipes. A battery cell may bethought of as a machine for pumping electricity. Therate at which a current of water flows through a pipemay be expressed as a certain number of gallons persecond. In the same way, the rate of a current of elec-tricity may be expressed as a certain quantity of elec-tricity flowing per second past a certain point.

"Suppose two tanks, Aand B in Figure 12-19,are placed so that Astands on a higher levelthan B. A pipe with apump P leads from thebottom of B to the bottomof A. If the tanks arepartly full of water andthe pump is started,water will be drawn fromtank B to tank A, which

raises the water level in the latter. If an overflowpipe is carried from tank A to tank B, the overflowwill run back to the depleted tank and the water will

Figure 12-19

simply be circulated by the pump in a current flow-ing through the system of pipes and the two tanks.This is somewhat like the electric cell (battery) whenthe external circuit is closed."Now, if the overflow pipe is closed by a valve V, the

pump will soon empty the tank B; after this it maycontinue to run, but it cannot pump the water, andno current of water will flow through the pipes. Thisis similar to the condition in an electric cell whichdoes not have its terminals connected by a wire. Theplates are maintained at a difference of electricpotential, but no current flows." (N. Black, CollegePhysics, [363])."The flow of charge through a conductor is often

compared with the flow of water through a pipe,which occurs because there is a difference in pres-sure between the ends of the pipe, established per-haps by a pump. This pressure difference can be com-pared with the potential difference between the endsof a resistor established by a battery. The flow ofwater (liters/second, say) is compared with the cur-rent (amperes/second). The rate of flow of the waterfor a given pressure difference is determined by thenature of the pipe. Is it long or short?

'Is it narrow or wide? Is it empty or filled, perhapswith gravel? These characteristics of the pipe areanalogous to the resistance of a conductor."(Halliday-Resnick, 1964 Physics, [679])

The flow of water is a close analogy to electriccurrent for another reason. The electrons, as theydrift through the conductor, suffer the same viscousresistance by the collisions with the atoms of themetal as the water molecules suffer by their frictionwith the wall of the pipe or by their collisions withthe gravel or any other obstructing filler in the pipe.Viscosity is one of the mutual characteristics of bothwater and electric currents.

Going this far with hydrodynamic analogies, wecontinue the following thought experiment in water,adding the assumption that it is an ideal frictionlessfluid and the system is described in weightlessness.In order to extend these analogies to the phenome-non of the Circular Magnetic Field, some adjust-ments should be introduced on the initial design ofthe water-battery.

Suppose, we use only one container to representthe battery and a rounded-square shaped pipe as aconductor which leads from one side of the tank to

241


the other. As Figure 12-20 illustrates, at the left endof the pipe a pump is installed, which pulls the waterfrom the pipe and driving it into the tank, creates asource. The same time, the other end of the pipe pullsthe water from the tank, creates suction, which rep-resents a sink.

Figure 12-20

In the assumed weightlessness, this setup givesthe same result as the double tank, that is, it createsa steady current of water, which continuously circu-lates through the whole system. Regarding to thedirection of an electric current relative to the positive

and negative labels attached to the terminals, thefollowing quote shows that this is also a somewhatconfusing issue in the electromagnetic theory."...When a battery is connected in an electric circuit,

it sets the free electrons in motion in a definite direc-tion. This stream of electrons, moving through theconductor is an electric current, but it should be care-fully noted that its direction in the external circuit(conductor or pipe) is from the negative to the positiveterminal. This is just the opposite direction fromthat in which convention has so long assumed."The source of the confusion is an old hypothesis,

according to which the electric current flows frompositive to negative. By the time of the electron theo-ry was established, so much has already been writ-ten based on this idea, that scientist decided to leavethe old convention as the direction of a hypotheticalpositive current. This fallacy is still in use. (Black,College Physics, [360]).

Evidently, in the water-current analogy, there isno such problem. With regards to the average pres-sure in the container the pump-end or source-endshould be the positive and the sink-end should be thenegative terminal.

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P U M P

W A T E R C U R R E N T

B A T T E R Y

While the pump works, there is a complete circu-lation of the water, from negative to positive throughthe external circuit (pipe), and from positive to nega-tive in the internal circuit (within the space of thetank). From sink to source outside and from source tosink inside. − When very small pieces of wax are sus-pended in the whole body of water, they are carriedby the current through the pipe from the negative tothe positive terminal. Then the source dispersesthem into the tank, from where they are recollectedby the sink at the negative terminal. This is equiva-lent to the direction of the current of electrons in elec-tricity, which is, in this case, obviously equivalentwith the current of the water. Note, that the onlyforce acting here is the pump and the drifting of thewax particles or the circulation of the water are notproduced or hindered by any action at a distanceforces, like attraction and repulsion.

In order to simulate the cylindrical magnetic fieldproduced by a current carrying conductor, the nextstep is to submerge this water-battery in a great con-tainer, also filled with water, which exerts an isotrop-ic pressure on the system, normal to the surface atall points. At this stage, the external and internal

media are completely separated by the solid walls ofthe battery-device.

However, as we have found in the earlier simula-tion, in order to generate a continuous flow-fieldaround and through the fan magnet, it was necessaryto establish an isotropic communication between theinternal and external medium. This was done by theperforation of the walls of the cylinder.

Before the introduction of the concept of the per-forated pipe-conductor in the hydrodynamic batterysimulation, a special character of a suction pipeshould be discussed.

THE CYLINDRICAL SINK-VORTEXIt is a common method to replace a suction-pump

by a simple device inserted into a garden hose whichhas a hole on its wall transverse to the flow of water.As Figure 12-21 (a) shows, when the hose is sub-merged, and water flows through the device, it sucksin and carries away the neighboring external water.

This is again based on Bernoulli's theorem. Theflowing water in the tube has a smaller static pres-sure than the external water, therefore, the latterpushes through the holes into the hose.

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Aethro-kinematics CHAPTER TWELVE The Cylindrical Sink-vortex

(a) Figure 12-21 (b) Consequently, a perforated pipe submerged in

water and itself carrying a flow will act as a multi-tude of sinks, which will initiate a radial flow towardthe pipe around its whole length.

Recall now the kinematic conclusion from thegravity simulation, that a general radial flow to asink must trigger rotation. As it is illustrated on (b),the same kinematic necessity will not only result in asink-vortex around each individual hole, but anentire rotational system will develop perpendicularto the pipe; a cylindrical sink-vortex, surrounding thesubmerged pipe through its whole length.

Next, let us submerge this whole device into agreat container, also filled with water, which exertsan isotropic pressure on the walls of the battery, nor-mal to the surface at all points. At this stage, thepipe, representing the conductor, is isotropically per-forated between the terminals.

Figure 12-22Based on the behavior of an ideal fluid, from the

illustration of Figure 12-22 several plausible kine-

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V O R T E X F L O WR A D I A L F L O W

matic effects can be contrived which are closely anal-ogous to the concepts of electromagnetic phenomena.

(a) While the pump is idle, the pressure and thedensity is isotropic and the medium is motionless allthrough the outer and inner spaces of the device.However, once the pump starts working and drawingthe water from the pipe into the container, the staticpressure inside the pipe falls below the externalisotropic pressure. Thus, the kinematic result is acylindrical spiral vortex surrounding the perforatedpipe-conductor between the terminals. Evidently thisresult is closely analogous to the phenomena calledthe Circular Magnetic Field.

(b) When a fan-magnet, described above, placedin the vicinity of the perforated pipe, it will line uptangentially to the vortex, and in a plane rectangularto the pipe. When the direction of the current isreversed, the device will rotate its poles, in the oppo-site direction, analogous to the behavior of a compassneedle.

(c) The question now presents itself; What hap-pens with the excess water, which is sucked inthrough the perforated pipe from the external medi-um and continuously pushed into the internal space

of the battery? Evidently, it cannot disappearthrough the sink and dispersed through the perfora-tions of the pipe, because this would stop the circula-tion of the system. Nevertheless, as the illustrationshows, the natural solution to this problem is toassume that the battery wall is not totally impene-trable either. Thus, through the perforation of thesewalls the excess water and the excess pressure canbe dispersed omni-directionally and isotropically intothe external medium without disturbing the generalcharacter of the circulation.

(d) Since the rotation of a sink vortex extends farinto the surrounding space, it follows from the differ-ent directions of the rotation of the cylindrical vortex,that there will be a global flow of water through thewhole ring, the direction of which will depend on thedirection of the current in the pipe. This is againidentical to the lines of force or the flux, or theinduced magnetic field through and around a ring-shaped conductor, (Figure 12-7).

(e) It also follows, that when the current carryingperforated pipe is bent into a continuous coil, theexternal medium will be driven through the internalspace of the so-called 'solenoid' of the spiral pipe,

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exactly as it is illustrated on Figure 12-19.(f) A common analogy for the electric resistor is a

local constriction of the flow of water by the installa-tion of a narrower pipe into the circuit. According tothe equation of continuity the local speed of flow ofthe fluid and the carried wax particles should in-crease in the narrow pipe and the resulting greaterfriction among them will actually generate heat.

(g) As for the attractive and repulsive magneticforces between two freely suspended conductor, con-sider the following analogy in the ideal fluid.

A pair of operating perforated pipes are sub-merged and freely suspended in the water parallel toeach other, and currents flow through them in thesame direction. The combined effect of the two result-ing vortices, spinning in the same direction, will dragthe external medium all around in the same direc-tion forming layers of circulating envelopes aroundthem. As the kinematics of this drag has beendescribed around the two magnets, these envelopes,in turn, move the pipes toward each other because ofthe isotropic pressure of the surrounding medium.

When the currents are flowing in opposite direc-tions, the cylindrical vortices are spinning in opposite

directions. In this case, due to the increasing turbu-lence and the static pressure between them, the twopipes are pushed apart. Recall the flow-patternmarked by the iron filings in Figure 12-4 (a) and itsreciprocal in (b), which represent the top view of twocircular magnetic fields.

It can be seen from the above that all known elec-tric and magnetic phenomena can be simulated in anideal gas or fluid. It seems to be merely a matter ofimaginative designing to simulate the effects of thewhole of electromagnetism, including static electrici-ty, electric and magnetic induction, and any otherrelated phenomena.

SINKS AND SOURCES In the ideal gas of Aether the perforation of the

water-pipes, as before, represents the gaps betweenthe atoms in the crystalline structure of the metalconductor. The Aether-current, that replaces the flowof water is, of course, much more responsive and per-sistent, having no friction among its constituents.From the above analogies it is evident, that thestream lines in the Circular Magnetic Field are notclosed circles centered on the conductor, as it isbelieved, but are spiral filaments of a cylindrical sink

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Aethro-kinematics CHAPTER TWELVE Sinks and Sources

vortex. This could probably be made visible by slowmotion photography of the patterns of the iron filingswhile the glass plate is gently vibrated and movedperpendicularly up or down on the current carryingconductor.

The pieces of wax, carried by the water, can betaken as analogous to the free electrons, or donut-vortices, drifting with the Aether circulation betweenthe negative and positive terminals.

In the water analogy, it is evident, that themotion of the wax particles have nothing to do withsome mysterious action at a distance attraction bythe positive terminal, or to the creation of the cur-rent or that of the cylindrical vortex around the pipe.Instead, the circulating water, is responsible for theacceleration of the wax particles in the pipe from thenegative to the positive terminal and for the driftingthrough the internal space of the battery in the oppo-site direction. The same current through the perfora-tions of the pipe sucks in the external medium andtherefore it also originates the cylindrical vortex.

It follows, that in the AETHRO-KINEMATICdescription of the electric current, the action at a dis-tance forces of attraction or repulsion is not needed to

create the drift of electrons toward the positive ter-minal, consequently, there is no repulsion eitheragainst their internal drift back to the negative ter-minal. Similarly, the mysterious connection betweenthe motion of the charges and the surrounding mag-netic field is also explained away by the AETHRO-KINEMATICS of the cylindrical sink vortex.

Obviously, the cause and effect is totally reversed.The magnetic field is not produced by the movingcharges, but the constant circulation of the Aether,which is also the carrier of the electrons through thecircuit and the internal space of the battery.

There remains the fundamental question;What is the original cause of the circulation of

the Aether, or in the analogy, what is the initiatingforce, that circulates the Aether and replaces thepump of the water battery?

Recall that the initial cause for the gravitationalsink-vortex has been found to be the evolution ofmatter. In other words, the decrease in the densityand pressure of the Aether in the vicinity of theevolving matter is a result of the ongoing organiza-tion and reorganization of the medium into the moreand more condensed electromagnetic force-fields,

247


particles, nucleons, atoms, molecules and crystallinestructures. This evolution is assumed to be driven bythe random kinetic energy of the Aether and depen-dent on the incidental local disturbances, which gainpermanency in rotation and create fusions amongthe force-fields of the elementary constituents ofmatter. This procedure is a localized condensation ofthe Aether, producing the phenomenon, which hasbeen called, the sink of matter.

In a miniature scale a similar procedure is initi-ated chemically in the electric battery. That is, in agiven chemical procedure, matter is being organizedand thereby the Aether is being rarified at the posi-tive terminal, which therefore becomes a sink.

Seemingly, the molecular characteristics (perme-ability) of a metal conductor provides the fastestroute toward achieving equilibrium. Very likely, inthe rigid crystalline structure, the parallel position-ing of the atoms of a good conductor leaves continu-ous open channels for the Aether flow, unlike non-conductors or dielectrics, where either the unparallelstructure, or the random motion of the atoms, moreor less blocks the free flow of the Aether. This differ-ence in permeability could account for the preference

of pulling the Aether from the conductor rather thanfrom the internal structure of the battery.

Similar to the magnetization of iron by an initialdraft, once the circulation of the Aether has beenestablished in the external and internal circuits, asmall and steady re-creation of pressure differencebetween the terminals can perpetuate the circula-tion. The magnitude of the flow and with that thenumber of electrons carried and accelerated by themedium is proportional to the pressure, or the so-called electric potential difference between the termi-nals, and therefore proportional to the strength ofthe chemical procedure.

The same is the case of the Circular MagneticField, where the force, exerted on the compass needleis directly proportional to the magnitude of the cur-rent, and inversely proportional to the square of thedistance from the conductor.

An intriguing thought occurs here.It seems quite clear now, that the long lasting

mechanical mystery of gravitation and electromag-netism has been originated and maintained by thesame over-sights, happened three centuries apart;Newton's refutal of Descartes solar-vortex, and the

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electromagnetic theory of the circular magnetic field,both has been based on the mechanics and mathe-matics of the 'wrong' circular vortex instead of theconcepts, mechanics and mathematics of the mediumconsuming spherical and cylindrical sink-vortex.

THE RULE OF THUMB Finally, the relation between the direction of the

current and the direction of the rotation of the cylin-drical sink vortex should be discussed.

The discoveries of Oersted and Ampere and theexperiments of their followers established the factthat the direction of rotation of the Circular Magne-tic Field is dependent on the direction of the currentin the conductor. In this respect a most practical rulehas been found; the 'rule of thumb' or 'right handrule' which gives a pictorial description of this rela-tionship.

When a conductor is grabbed by one's right handand the extended right thumb points in the directionof the conventional current, the direction of rotationof the field will follow the curling of the fingers as itis illustrated an Figure 12-23.

Nevertheless, one who looks for the relation bet-

ween the real electron current and the direction ofrotation, should reverse both rules and end up with aleft-hand rule, exactly the opposite of the illustration.The origin of this rule is strictly empirical and nei-ther classical nor modern theoretical physics madeany attempt to reason with the phenomenon.

Recall that we have met this very same problemin a higher order of magnitude, discussing the kine-matic necessity of rotation around a gravitationalsink. Obviously the head-on collision of the initial

radial momentum musttransform into angularmomentum, and the ques-tion was, what is thedetermining factor for thedirection of rotation of theresulting sink-vortex.Recalling the Corioliseffect and the role of thedifferential rotation of thesurface of the Earth indetermining the directionof cyclonic vortices or the

differential rotation of the galaxy as a factor of the

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Aethro-kinematics CHAPTER TWELVE The Rule of Thumb

Figure 12-23

rotational direction of gravitational vortices, itseems, that the all-pervading Aether itself has a dif-ferential rotation, which preconditions space at anypoint of the Universe for the rule of thumb. At least,this seems to be the case in our local order of magni-tude of the observable universe.

Consider, in this respect, the common nature ofthe galaxy, the Cyclone, the kitchen sink and thedirection of the spiral in the growth of human hair.The right or left handedness, conventional or real,seems to be a general character of the Universe.

Nevertheless, as we can notice in the kitchen sinkand in the special events of galactic disasters, or inthe man made confusion created in the particle accel-erators, there are exceptions even to this generalrule. For at some exclusive times and places, inuncommon circumstances, the universal Aetherialpreconditioning of handedness can be locally over-powered and a rotation can be triggered in the'wrong' direction.

In particle physics this phenomenon is calledmatter and antimatter, particle and antiparticle, pro-ton and antiproton, all of which, of course, due to

their oppositely rotating vortices, annihilate oneanother on contact.

It is maybe needless to emphasize the awarenessof the greatly simplified nature of the above de-scribed analogical simulation.

Nonetheless, a distinction should be pointed outbetween the concepts of perplexity and complexity. Itis assumed here, that AETHRO-KINEMATICS isindeed able to dissolve the old perplexities of theaction at a distance forces of both classical and mod-ern theories, but the same time it opens up the prob-lems of the immense kinematical complexity ofNature's mechanism.

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Aethro-kinematics CHAPTER TWELVE The Rule of Thumb

CHAPTER THIRTEEN

KINEMATICS AND THE LORENTZ TRANSFORMATION

THE NULL RESULTAs it was originally suggested by Clerk Maxwell,

the theory of the Michelson-Morley experiment wasfounded on four fundamental assumptions:

1) It was assumed that all space is filled with thesuper-mundane, isotropic medium of Aether, which iseternally motionless.

2) From Huygens to Lorentz, through three cen-turies, a basic assumption has evolved that light is

propagated in the form of waves through the Aetherwith a velocity of 300,000 km/sec relative to theisotropy of the motionless medium.

3) The observational facts of astronomy, inter-preted through the scheme of Copernicus, andNewton's Celestial mechanics lead to the assumptionthat the Earth revolves around the Sun with approx-imately a 30 km/sec orbital velocity.

4) It was assumed, that the Galilean Transfor-mation, or the Law of the Addition of Velocities isuniversally valid for all relative motions.

From the Galilean Transformation and the otherthree fundamental assumptions, scientists conclud-ed, that since the Earth is in motion relative to themotionless Aether, the velocity of light-waves mea-sured in different directions on Earth should revealits orbital velocity."This situation has been picturesquely described in

terms of an 'Aether Wind' (30 km/s) blowing throughthe earthly laboratory, giving resultant light veloci-ties between a minimum of C−V and a maximum ofC+V, V being the velocity of the wind." (Centenaryvolume, Silvio Bergia [73])

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Aethro-kinematics

If all assumptions are right, according to the the-ory of the Michelson experiment, the measured veloc-ity of light should be 300,000−30 = 299,970 km/sec inthe first case, and 300,000+30 = 300,030 km/sec inthe second case.

Starting with Michelson's first experiment, per-formed in 1881, several similar experiments weredesigned by him and others to prove the Earth'smotion relative to the motionless Aether by measur-ing the speed of light in different directions and dif-ferent times during the Earth's yearly revolution.

Various other electromagnetic phenomena weresimilarly measured with devices much more sensi-tive than needed to find the small difference.But forfour decades of experimentation without exception,each produced an undeniable 'null result'. Theseexperimental facts clearly manifest that at least oneof the fundamental assumptions of the theory of theMichelson experiments must be wrong.

But which one? The abandonment of the Aether alone would not

solve the problem of the null results, because, even iflight was propagated in empty space, its finite speed

should still show a difference in the measurements ofmoving observers.

The Earth's motion cannot be given up withoutthe collapse of the whole Celestial Mechanics andmodern astronomy.

Interestingly, discarding the wave theory for acorpuscular theory of light would have solved thisproblem of the null result, but scientist rejected theidea because it would cancel the scientific under-standing of most of Optics and that of various elec-tromagnetic phenomena.

To escape the dilemma without discarding anyfundamental principles, George Francis Fitzgeraldproposed in 1882, that the fourth basic assumption,Galileo's addition of velocities is the one that doesnot work in the special case of the speed of light.

According to this hypothesis, the expected differ-ence cannot be found because all material bodies,including the measuring devices, are contracting inthe direction of motion relative to the Aether. In orderto agree with the null result, this effect should beproportional to the ratio between the velocity of lightand the velocity of the moving observer.

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Aethro-kinematics CHAPTER THIRTEEN The Null Result

Thus, based on the mathematics of the Michelsonexperiment, Fitzgerald concluded that, if the velocityof the Earth is V, and the velocity of light is c, andthe factor of the undetectable difference is represent-ed by the Greek letter Beta, β then :

−−−−−−−−−β = 1 / √ 1 - V2 / c2 (13.1).

For explaining the Michelson null result by hiscontraction theory, FitzGerald recommends that thelength of the moving measuring devices must con-tract according to the above ratio.

Hendrik A. Lorentz, one of the great followers ofMaxwell and the author of the first consistent elec-tron theory of electricity, proposed a scientific expla-nation for Fitzgerald's ad hoc hypothesis. Based onthe electromagnetic construction of matter, this theo-ry lead to the same mathematical conclusion:

1 LoL = −−−−−−−−−−− or L = −−−−−−−−−−−− (13.2),

−−−−−−−−− −−−−−−−−−−√ 1 − V2 / c √ 1 − V2 / c2

where L is the length of a body in motion and Lo isLorentz's distinction for the proper length of thebody at rest relative to the Aether.

This is the reason why in the case of the velocity oflight the Galilean Transformation does not work.

Our measuring devices are foreshortened in thedirection of motion in the ratio that guarantees thenull result in all cases. It has to be realized, that thissuggested foreshortening is very minute. For ins-tance, in the case of the earth's orbital velocity of 30km/sec, its diameter of 28,000 miles would only con-tract 2.5 inches in the direction of motion."Lorentz went on to show that when the FitzGerald

contraction is applied to subatomic particles, onecould deduce that the mass of the body must increasewith motion in just the same proportion as its lengthdecreases. In short, if its rest mass is mo and itsmass while moving is m then :

mom = −−−−−−−−−−−− (13.3).

−−−−−−−−−−√ 1 - V2 / c2

"The mass of such particles can be obtained by mea-suring their inertia, that is, the force required toimpose a given acceleration upon them." (Asimov:Understanding Physics [99])

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The issue was all the more important, because inthe last decade of the nineteenth century, experi-ments with fast moving electrons already showedsome unexpected increase in their resistance againstacceleration. This could be interpreted as an increasein mass, which depends on Fitzgerald's contractionratio between the velocity of light and the velocity ofthe particle relative to the Aether. The experimentalresults showed that the mass-increase, or the excessforce needed to accelerate the particles agreed withthe predictions of the Lorentz Transformation.

These phenomena opened up new possibilities :"If the gain in mass of a speeding particle is the

result of its motion relative to the Aether, then a newmethod of measuring 'Absolute Motion' might offeritself. Suppose some particles measured as they spedalong in one direction, others as they sped in anotherdirection, and so on. If all directions are taken intoaccount, some particles are bound to be moving withthe Aether Wind while others are moving against it.Those moving against the Aether will have a morerapid motion relative to the Aether than will thosemoving with it. By the changes in gain of mass in dif-ferent directions, the Absolute Motion of the Earth

can be determined." (Isaac Asimov, UnderstandingPhysics [101])

This seemed to be a winning proposition, since,contrary to the undetectable foreshortening andtime-dilation, the mass increase is certainly measur-able by the magnitude of the excess force requiredfor the same acceleration on a higher speed.Nevertheless, this idea also failed, like all the preced-ing ones. The gain in mass proved to be the same inall directions and the experiment ended with anothernull result.

About the same time, a new experiment was con-ducted by Kennedy and Thorndyke, which wasspecifically designed to exclude the effects of contrac-tion in the measurements. Like all others, this exper-iment also produced a null result, thus totally refut-ing the Lorentz-Fitzgerald contraction hypothesis.

With all these failures to prove the Earth'smotion relative to the Aether, in spite of its success-ful mathematics, the Lorentz- Fitzgerald theory,based on the Aether and the electromagnetic con-struction of matter, collapsed. The scientific societywas stunned, frustrated and well prepared to admitthat there is no imaginable solution to this riddle.

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Indeed, in the famous article, published in 1905,Einstein declared the whole problem physicallyinsoluble by postulating the pure and unarguableconclusions and consequences of the Michelson nullresults:

The velocity of light is always measured the sameregardless of the motion of the observer or that of thesource.

Using the Constant Speed of Light as the ulti-mate transmission signal, both the concepts of lengthand time become relative and with that, simultaneityalso turned out to be dependent on the subjectivemeasurements of the moving observers. It also fol-lows from the postulates of relativity, that the hypo-thesis of an all-pervading Aether is useless and need-less, and that it is physically impossible to detectAbsolute Motion.

The relativistic conclusion was that the LorentzTransformation is mathematically correct, but it isconceptually false. The same mathematics can bederived from the basic philosophical postulates of rel-ativity, which have nothing to do with any physicalcontraction, time-dilation and mass-increase, or theelectromagnetic construction of matter. Nevertheless,

out of the respectable loyalty of the scientific commu-nity, the mathematics of relativity retained the nameof its original author and still called: The LorentzTransformation.

In the theory of AETHRO-KINEMATICS animportant distinction must be made between thenull results of all Michelson-type experiments andthe latest ones concerned with the mass-increase ofthe speeding sub-atomic particles.

On the one hand, the goal of all Michelson-typeexperiments were to prove the existence of a relativemotion between the Earth and the Aether. However,as it follows from the theory of the solar sink-vortexof matter and Universal Rotational Gravitation,according to AETHRO-KINEMATICS the planets arecarried by the solar vortex and therefore no relativemotion exists between the rotating Aether and therevolving Earth.

Consequently, the Michelson-type experimentscan show nothing but null results and since there isno relative motion, there is neither any physical rea-son for the Lorentz-FitzGerald theory of real contrac-tion nor Einstein's illusorical contraction and timedilation. It follows, from the acceptance of Rotational

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Gravitation that both the significance of the Michel-son-Morley null results and the philosophical andepistomological conclusions based on those experi-ments and postulated by Einstein in the theory ofspecial relativity are needless and useless from thestandpoint of theoretical physics.

On the other hand, in the mass-increase experi-ments the particles are indeed speeding relative tothe laboratory, therefore also moving relative to thelocally motionless Aether. It is also important topoint out, that these particles perform translationalmotion like bullets and are not propagated in theAether like the waves of light or other electromag-netic disturbances. These experiments do producepositive results individual, by the measurements ofdefinite quantities of 'mass-increase'. This, in turn,proves that there is a real and measurable physicalinteraction between Aether and moving particles,and exactly in the proportion as the Lorentz Trans-formation formulae had predicted.

The fact that these mass-increases measure thesame quantity in all directions, which has been con-sidered to be another negative result, only provesagain, that there is no Aether-wind, but that indeed

the Earth and the earthly laboratories all carriedalong by the Aetherial vortex stream.

Nevertheless, if the mass-increase is not the illu-sion of the observers, as it has been lumped togetherwith the contraction and time-dilation in relativity,then it is a real physical phenomenon, which musthave an explanation within this theory.

MASS-INCREASE AND MACH-NUMBER The following is a three centuries old foreword to

this subject; Descartes words from his PrincipiaPhilosophiae (1644):"...We think that the sky, as well as the sun and the

fixed stars, is made from liquid matter. This view isnow commonly accepted by all astronomers...But itseems to me that several are mistaken, for, instead ofattributing to the sky the properties of liquid, theythink of it as a completely empty void, not only offer-ing no resistance to the movement of other bodies,but also having no power to move them and carrythem with it. For apart of the fact, that such void inNature is impossible, all liquids have this in com-mon: that the reason why they offer no resistance tothe movements of other bodies is not that they consist

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Aethro-kinematics CHAPTER THIRTEEN Mass-increase and Mach-number

of less material substance, but they are equally ormore disturbed, and that their small parts can easilybe made to move in all directions; and in cases whenthey are caused to move all together in one direction,this means, they are forced to carry with them anybodies which they contain and surround all sides."

Indeed, the elasticity and resistance not onlydepend on the density of the fluids, but also on theaverage speed of their constituents. The speed ofsound in air is a direct consequence of the averagespeed of the randomly moving air molecules, whichalso determines the speed of the dissipation of thelocal pressure differences caused by a moving body.

This time, the AETHRO-KINEMATIC simulationof the phenomenon of mass-increase requires neitherthe great room of ideal gas, nor the innovation ofthought-experiments. The kinematics of the 'mass-increase' has been already established theoretically,experimentally and mathematically in the field ofAerodynamics by the theory of the Mach-number."The incompressible fluid theory of classical hydro-

dynamics has proved useful for the estimation ofaerodynamic parameters, and when applied to prob-lems of low-speed flight has yielded sufficiently accu-

rate results. Newton's law of hydrodynamic resis-tance states, that the force opposing the steadymotion of a solid body through a fluid medium is pro-portional to the square of the velocity of the body, itscross-sectional area, and the density of the fluid."It has been found, however, that the flow pattern

about a body moving through air at high speeds isaffected to a large degree by changes in density re-sulting from compression or expansion of the fluid.An understanding of compressible flows is, therefore,of the utmost importance to the designer of highspeed aircraft. (The simplification of incompressibili-ty is not allowable,) "A consideration of the theory of elasticity as

applied to fluids, indicates, that the effects of smallpressure changes in a real fluid are transmittedthroughout the fluid in the form of waves which trav-el at the speed of sound. It may be seen then, thatthe effects of a pressure change which occurs behindthe critical point at which the speed of sound hasbeen reached, cannot influence the flow field aheadof the point."Since at the critical point the forward motion of the

pressure waves are completely arrested by an air257


stream velocity equal to the velocity of wave propa-gation, a wave front is formed, that constitutes asharp discontinuity in the flow, associated with largeincreases in pressure, density and temperature and adecrease in the velocity of the moving body."The speed of sound is taken as a reference velocity,

because it is a function of fluid elasticity. As appliedto compressible flows, this means that the amount ofpressure necessary to cause a given change in densityin any given fluid is proportional to the speed ofsound in the fluid.""Since the pressure is proportional to the square of

the velocity, the velocity which a body may attainbefore appreciable density changes occur, is also pro-portional to the velocity of sound in the fluid."It is apparent, therefore, that the flow pattern

about a body will be altered by density changes to adegree dependent upon the ratio of the velocity of thebody to the velocity of the sound in the fluid. Thisratio is known as the Mach-number and is taken asan index of the effects of compressibility on the flowpattern." (V. Nostrand, Scientific Encyclopedia [48])

If the velocity of sound is S, and the velocity ofthe body is V, then the Mach number, M = V/ S. When

V is very much smaller than S then the Mach-num-ber is much smaller than one. Up to about M=0.3 thefluid can be taken as incompressible and Newton'slaw of hydrodynamic resistance is valid. However, asthe velocity of the body increases and graduallyapproaches the velocity of sound, the Mach-numberapproaches one and the medium suffers an increas-ing incapability to dissipate the disturbances.

As a result, the fluid becomes compressed in frontof the body, which creates an increasing density andresistance against its motion. Consequently, to accel-erate an airplane to a speed approaching the speed ofsound requires a greater amount of force than it ispredicted by Newton’s hydrodynamic law of resis-tance based on incompressibility. Since theNewtonian resistance of the fluid is proportional tothe square of the velocity of the body, the factor of theextra resistance, β can be expressed as

1 1 β = −−−−−−−−−− i.e., −−−−−−−−−−− (13.4).

−−−−−−−−− −−−−−−−−−√ 1 − M2 √ 1 − V2 / S2

Thus, depending on the ratio between the speedof a body and the speed of sound, Aerodynamics uses

258


two different theories to explain and calculate theresistance of the air against the motion of a body:

a) At low speeds, based on incompressibility,Newton's law is valid and the resistance of the fluidis proportional to the square of the velocity.

b) As the velocity increases and gradually app-roaches the speed of sound, the resistance increasesbeyond Newtonian proportion and the theory of thecompressible flow, and the Mach-number must beapplied. If the Newtonian resistance is Ro and thecombined total resistance is R, then its magnitudecan be expressed in the following equation:

Ro R = −−−−−−−−−−−− (13.5).

−−−−−−−−−−−√ 1 − V2 / S2

where Ro is the Newtonian resistance, V is the speedof the body and S is the speed of sound.

At the other side of the analogy, the situation isthe same:

Depending on the ratio between the speed of aparticle and the speed of light, there are two differ-ent theories to explain and calculate the magnitudeof inertial resistance of a body against acceleration:

a) According to Newton's Second Law of motion,mi = F /A the classical inertial mass is constant andit requires the same magnitude of force for each unitof acceleration regardless to the initial uniform veloc-ity of the particle.

b) However, at higher velocities, approaching thatof light, it has been found, that beyond Newton's law,there exist an increase in the requirement of forceneeded to achieve the same unit of acceleration. Thisshould mean an increase in the inertial resistance ofthe body, which in turn, has been interpreted as arelativistic increase in its inertial mass.

If the total inertial resistance, is expressed bycombining the Newtonian initial inertial mass, mo

and the relativistic mass-increase, due to high speed,represented by m, then the total magnitude of theinertial mass can be calculated by the equation of theLorentz Transformation:

mom = −−−−−−−−−−−− (13.6),

−−−−−−−−−−√ 1 − V2 / c2

where mo is the classical inertial mass, V is the veloc-ity of the body and c is the velocity of light.

259


This obvious equivalence of Equ.13,5 and 6, rep-resenting the two sides of the analogy, can hardly bea pure mathematical coincidence without some con-ceptual resemblance.

Since the fundamental assumption of AETHRO-KINEMATICS is, that all space is filled with theideal gas of Aether, the Relativistic Transformation isaccepted by this theory for what it was originallydesigned by Lorentz; a mathematical system todescribe the effects of real motion of electromagneticmatter relative to the isotropic Aether, and viceversa. As such, Lorentz's mass-increase is a physicalphenomenon, which requires and suggests a kine-matically understandable explanation.

AETHRO-KINEMATICS describes inertia, forceand acceleration as the different forms of the one-to-one, accumulative transmission of the drift velocitiesbetween the Aethrons of the isotopically randommedium and those, which have been organized intoelectromagnetic matter.

It follows, that inertia is simply a time-consum-ing transmission of the directional kinetic energyfrom one part or form of the Aether to its other part

or form. Once the drifting of a body, or rather, thedrifting of its center of oscillation has been created bya constant force, the motion of a body in the all-sur-rounding isotropic medium gives rise to the samekinematic action; a one-to-one transference of thedirectional kinetic energy of its drifting to the ran-domly moving individual particles of the medium.

In other words, the motion of electromagneticmatter produces a directional disturbance in theisotropic Aether, which is dissipated in all directionsin the form of waves with the average speed of theAethrons, e,i,. the speed of light. It is exactly thesame procedure as it is in air and indexed by theMach number of the speed of sound.

Once this part of the analogy is established, it isquite evident that instead of the inconceivable con-cept of mass-increase, the Lorentz Transformationmust be interpreted the same as the Mach-numberin Aerodynamics:

An mathematical description of the compressionof the fluid, − in this case the Aether, − and itsextreme density changes due to the motion of theparticle when approaching the speed of dissipation oflocally caused disturbances.

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Figure 13-1Evidently, the mathematical formula of both the

Mach number and the Lorentz Transformation sim-ply describe the ratio of the fluid-resistance, set bythe reference velocity of sound in air and the refer-ence velocity of light in the Aether.

This is then the point where the fundamentalduality of theoretical physics and the incurable con-tradiction between the total void of Galilean andNewtonian space and the all-pervading motionless

Aether of the Maxwellian electromagnetic theory canbe clarified and resolved.

The original goal of the theory of the Michelsonexperiment was to unify Newton's celestial mechan-ics with the electromagnetic wave theory of light,that is, to correlate the Galilean total void with theexistence of the hypothetical medium of Descartesand Huygens; the luminiferous, all-pervading Aether.

Nevertheless, it finally becomes evident, that thefundamental duality between the two major depart-ments of theoretical physics was originated by thetwo faulty assumptions.

It follows from all above, that neither Galileo'seternal uniform motion in empty space norMaxwell's eternally motionless Aether have ever real-ly existed.

On the contrary.It is quite clear now, that, measurable or not, the

resistance of fluids does not come into existence onlywhen the speed of motion approaches the limitingspeed of the dissipation of disturbances in the media.It is already there in the form of an isotropic pres-sure exerted on a body even at rest, and turns into a

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0

Increasedmass,

Velocity,

m

Rest mass, mo

v c

mm = v 1 - c√

o

2

2

m

mo

LORENTZ'S FORMULA FOR MASS INCREASE

0

Mach's increasedresistance,

Velocity,

R

Newtonianresistance, Ro

v S

RR = v 1 - S √

o

2

2

R

Ro

MACH'S FORMULA FOR AIR RESISTANCE

= Speed of soundS= Speed of lightc

directional density and pressure difference; a retard-ing force, acting against all motions with any velocitygreater than zero.

Consequently, instead of Galileo's resistancelesseternal uniform motions in empty space, all displace-ments of material bodies relative to the ideal gas ofAether is opposed by a definite force of resistance,the magnitude of which is expressed by the Electro-magnetic Mach-number; the Lorentz Transformation.

It is also quite evident, that Maxwell's electro-magnetic Aether is not at all motionless, but exists inan all-pervading turbulence through the infinitechain of orders of magnitude, from micro-cosmos tosuper-cosmos.

Nevertheless, it can also be seen, that there is asole exemption to this turbulence in our subjectivehuman observation, finding Aether at rest whenmeasuring the phenomena of electricity and magnet-ism and the speed of light in the frame of reference ofour earthly laboratories which, of course, are rotatingand orbiting together with the Earth around its axisand being carried about its yearly revolution aboutand within the turbulent vortex of the Sun.

This is the physical cause of the illusionary 'NullResult', measuring the propagation speed of electro-magnetic phenomena on Earth, which was discov-ered by Michelson, and misinterpreted by Einstein.

DESCARTES ONCE MOREThus, both perplexing enigmas of the Newtonian

inertial resistance of matter against acceleration andthat of the mysterious relativistic mass-increase dueto high velocities, can be described by the simplecommon-sensible, kinematical concepts of the Aether.How come then, that the natural fluid-resistance ofthe Aether remained hidden from science for so long?

The velocity of sound in air is 330 meter/sec, thevelocity of light in the Aether is 300,000.000 m/sec. Iflight would follow the surface of the Earth, it wouldcircle the globe more than seven times in a singlesecond. Although Aether is some ten million timesdenser than air, the dissipation of disturbances inthis medium is one million times faster than thesame in air. It follows, that the effects of normalresistance and the extra retardation, due to theincreasing density in front of the speeding body, areone million times smaller in Aether than in the air.

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Aethro-kinematics CHAPTER THIRTEEN Descartes Once More

There are good reasons to assume that Newton'sapproximate law of hydrodynamic resistance is alsovalid for the motion of matter in Aether: The retard-ing force is proportional to the density of the medi-um, to the amount of matter (inertial mass), and tothe square of its velocity. In addition, there is theinfinitesimal addition, due to changing density infront of the body, at high speeds, expressed by theLorentz Transformation.

One very important aspect of Descartes hypothe-sis is, that the Aether not only offers a resistanceagainst the relative motion of material bodies, but bythe same factor it is also capable of moving them.

The Lorentz Transformation serves as an indexnot only for the deceleration of the bodies movingfaster than the local motion of Aether, but also forthe acceleration of those, moving relatively slower. Inboth cases, the tendency of the effect in the mediumis, just like that of the frictional forces of fluiddynamics; to reduce and eventually eliminate theexisting relative motion.

In the earlier discussion about gravitation, thiseffect has been made responsible for the accelerationdue to gravity. Thus, an inquiry is justifiable, if all

the kinematical ingredients would be available forcalculating the local velocity of the inflow of theEarth’s Rotational Gravitation.

Within the scope of this discussion it can be men-tioned here, that an attempt to achieve this shouldstart from the empirical quantitative knowledge ofthe acceleration due to gravity at a given point overthe surface of the Earth. This will represent the radi-al (Newtonian) component of the fall of the body,while the velocity of the rotation of the surface of theEarth will represent the tangential (Keplerian) com-ponent of the fall.

Newton's hydrodynamic law of resistance and theLorentz ratio for higher speeds can render the quan-titative interaction between the flowing Aether medi-um and the accelerating matter, giving the requiredflow-velocity at that point. Once this has been achie-ved, a mathematical possibility can be seen for calcu-lating the speed of the tangential and radial compo-nents of the spiraling Aether-flow at any point in agravitational sink-vortex.

In connection with the same subject, it shouldalso be mentioned, that Michelson's results were notexactly and always explicitly zero.

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Aethro-kinematics CHAPTER THIRTEEN Descartes Once More

There were some experiments made for the peri-od of a whole year, at opposite points of the orbitwhich showed some very minute but systematic devi-ations from the null result. As it was shown in thedescription of the gravitational vortex, at the cross-ings of the threads of the spiral current, on the ellip-tical orbit of a planet, there were occasional relativemotions, inertial accelerations and decelerations ofthe planets, manipulated by the Aether.

It might just be the case, that through these twoseemingly unrelated phenomena; the minute devia-tions from Michelson's Null Results may finallyagree with Kepler's second law of planetary motion.

This is then the kinematic essence of Descartes'message from the past about the swiftly movingAether particles and the existing but extremelysmall resistance of the liquid matter of the sky,which also creates the power to move and carry theheavenly bodies in the solar and planetary vortices.

As a memento, note here, that these ingeniousideas of Descartes were on the shelves of the libraryof discarded human thoughts for three centuries,untouched and unreviewed, because of their quiterudimentary refutation by Newton's authority.

SPECIAL RELATIVITY REVISITEDGoing somewhat further, however, there is a need

for the clarification of some philosophical remnants,which belong to the same subject.

An AETHRO-KINEMATIC statement has beenmade that, since no relative motion exists betweenthe Earth and the Aether in the sun's gravitationalvortex, the Null Result of the Michelson experimentshad nothing to do with the Lorentz-Fitzgerald Con-traction. The same conclusion should be natural withrespect to the relativistic slowing down of clocks.

The question now arises, however, whether ornot, there exists a real contraction and time-dilationin the case of a true relative motion between matterand Aether?

Evidently, according to Lorentz original theorybased on the Aetherial construction of electromag-netic matter, the answer should be positive in bothcases. According to this theory, any elastic unit innature, whether it is a solid piece of macroscopicmatter like a billiard ball, or a soap-bubble, a livingcell, a crystal, or an elementary particle, when anexternal directional force exerted upon it, it must

264

Aethro-kinematics CHAPTER THIRTEEN Special Relativity Revisited

undergo some distortion of its original undisturbedshape even before any translational displacement ofthe body occurs. Taking a simple analogy in air: theshape of a soap-bubble is perfectly spherical whilethe internal and external pressure of the air is equaland isotropic. The inside volume of the air is constantas long as the soap-film is intact and the bubble is inexistence.

Consider now, that a directional force exerted onthe bubble by a mild jet of air. Since there is a resis-tance of the medium in the opposite direction, thesphere must become distorted between the two oppo-site forces and take the shape of an ellipsoid of someeccentricity. As long as the soap-film is intact theinternal volume of the bubble remains constant. Thismeans, that the contraction of the sphere in thedirection of motion must be accompanied by a pro-portional expansion in the direction transverse to thedirection of the motion.

If the force is constant, this procedure should becontinuous while the bubble gradually accelerates. Inextreme cases, when the external force is too great ortoo sudden and overpowers the cohesional strengthof the soap-film, the bubble bursts and dissipates.

This example can be extended into a rod made upof a row of soap-bubbles, or a conglomerate of bub-bles forming a three dimensional foam object, andthe basic kinematics remains the same. The acceler-ating body retains the original volume of air within,but it is constantly forced into a state of contractionin one direction and that of expansion in the other.

Although this phenomenon proceeds in the airand the air resistance is expressed by the Mach-index, it is evident that the permanency of the bub-ble or rod or foam only depends on the cohesivestrength of the soap-film and its burst and dissipa-tion will happen independently from the velocity ofsound and most likely long before reaching thatvelocity.

From all the above, it is justified to assume, thatthe constituents of electromagnetic matter wouldbehave similarly, when being at rest or in motion rel-ative to the isotropy of the Aether. The kinetic anddynamic pressure is in equilibrium in all the circularor spherical flow-patterns of the rotatory units whenthey are at rest relative to the Aether. But when aconstant force compels them to accelerate against theresistance of the isotropic Aether, they must also

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become distorted into some kind of ellipsoids withminor axis pointing in the direction of motion andthe major axis pointing transversally to that, evi-dently proportional to the magnitude of the force.

The same is valid to the macroscopic conglomer-ates of such units. It can be seen from the analogy,that the volume of Aether organized into a materialbody does not change as long as the inert balance ofthe flow-patterns of electromagnetic forces are ableto keep the body intact. Consequently, the contrac-tion in one direction must be accompanied by a pro-portional expansion in the other.

Consider now these effects of contraction andexpansion on the Michelson equipment, while it is inmotion and measuring the speed of light in rectangu-lar directions.

Einstein takes care of this ambiguity by convinc-ing himself in his empty space with the thought-ex-periment of moving yardsticks and paint brushes.From the stand point of common sense, however, thevery least it should be agreed here, that the phenom-enon is somewhat more complicated than it appearsin its relativistic description.

The same applies to the conclusion that mattershould shrink to nothing, when it reaches the veloci-ty of light. It follows from above, that the kinematicstability of matter depends only on the strength ofthe permanency of the delicate flow-patterns of theelementary units, and those of the electromagneticcohesive forces, which keep the units together.

A particle or a chunk of matter will burst verylikely long before it reaches the limiting velocity oflight. Thus again, simply note, that the final dissipa-tion of matter is in a much more complex relation tothe speed of light than it is suggested in the funda-mental postulates of relativity.

It should be also emphasized here, that the mea-sured velocities of the particles driven by electromag-netic accelerators are not authentic to evaluate theeffects of distortion of the particles in relative mo-tion, since in the particle accelerators the Aetheritself is being accelerated by the magnetic fields andthe particle, just like a soap-bubble in the wind, iscarried imbedded, with the streaming medium.

Consequently, the difficulty here is not to acceler-ate a particle to the speed of light, but to accelerate

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the bulk drift of the Aether to that velocity. The parti-cle carried within the stream is not contracted, mass-increased or time-dilated by its speed, but only dis-torted by its inertial adjustment to the gradual accel-eration of the Aether flow.

With regards to the philosophical postulate thatno material body can move faster than the limitingspeed of light, there is an agreeing kinematical rea-son for it. As it has been shown, the global accelera-tion or flow of the Aether is nothing else, but thedrifting of the center of oscillation of the individualAethrons. It follows, that to produce a global flow inthe medium higher than the speed of light is simplyimpossible. Even if all transverse oscillation is damp-ened, the drift velocities of the individual Aethrons ina given direction cannot exceed their overall averagerandom speed, which is also the very source, of thepropagation velocity of electromagnetic waves.

For science-fiction interest the analogy can beextended by comparing the Mach number and soundbarrier with the Lorentz-Fitzgerald ratio and thelight barrier. As the first was thought wrongly to beunbreakable for a time, one may speculate about thepotential of breaking the latter. Part of the answer

has been given by the average speed of the Aethronsas the limiting drift velocity of the center of oscilla-tion of any material body in Nature.

The other part of the answer is, that the possibili-ty of breaking the sound barrier was based on theinertia and momentum of jet propulsion. Neglectingthe existence of Aether, in Newtonian mechanics thisforce, the momentum of mass, was supposed to createa thrust purely depending on inertial properties ofmatter in the totally empty space.

Nevertheless, as it was shown above, the complexkinematics of inertia is created through the interac-tions between Aether and matter and therefore thephenomenon cannot be isolated from the surround-ing isotropic medium. Hence, breaking the soundbarrier by the fictitious force of inertia is essentiallyleaning on the random but isotropic kinetic energy ofthe Aether and not on the complete void. It follows,that to break the light barrier, one would need someother form of energy to lean on, even more funda-mental and powerful than that of the Aether.

With regards to the Special Theory of Relativity,the fundamental point here is, that if real motion rel-ative to the Aether does cause real contraction and

267


mass increase, their proportionality to the speed oflight cannot justify the relativistic postulates or theepistomological limitations.

On the contrary, all these phenomena are kine-matically explainable and calculable as the results ofinteractions between Aether and electromagneticmatter. Once these phenomena are accepted to bereal, they prove the explicitly opposite concepts. Anyreal effect of the motion of matter relative to theAether is a proof of the existence of an absoluteframe of reference; the 'Aether-frame'.

Although on the astronomical scale the turbu-lent motion of Aether itself is immensely complex,the local motion relative to this all-pervading fluidcan still be taken as a superimposed 'Absolutemotion'. It directly follows from these, that in case oftrue relative motion, the constancy of the 'measured'speed of light can be challenged by the detectableresistance of the medium, presently called, ‘relativis-tic mass-increase’. The same is valid for the illusion-ary measurements of light-speed on the famous trainof the Einsteinian thought-experiment, which there-fore cannot support the refutation of the general con-cept of simultaneity.

With these, all major aspects of the LorentzTransformation have been AETHRO-KINEMATI-SIZED and the relativistic epistemology could bereplaced by purely kinematical concepts, calculatedby Lorentz's original mathematical transformation.

It follows, that the philosophical postulates of themodern principles of relativity and that of the ab-solute constancy of the velocity of light, and all con-clusion drawn from the misinterpreted MichelsonNull Results are rendered needless and superfluous.

EXPERIMENTAL JUSTIFICATIONBased on all the above, and on a lengthy analyti-

cal discussion with my best physics friend, Dr. BertMcInnis, (theoretical physicist of Ottawa, Canada),we have arrived to the conclusion that a simple in-controvertible experiment can be designed withexisting scientific equipment to discriminate bet-ween the contradictory predictions of Relativity andAETHRO-KINEMATICS and in case of a very plau-sible positive result the problem will be reopenedand solved, Thus, the all-pervading ideal gas of theAether medium will be irrevocably and permanentlyreinstated.

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Aethro-kinematics CHAPTER THIRTEEN Experimental Justification

First some general clarifications:From the foregoing it becomes obvious that the

two relativistic postulates declaring the constancy ofthe speed of light, based on the Michelson null-result,and being the limiting velocity of Nature, based onthe relativistic mass-increase experiments, - have notheoretical relation with one another.

On the one hand, Michelson’s null-results havebeen rendered natural and expectable by the Aethro-kinematic gravitational theory of the aethereal sink-vortex which, by carrying the planets in its stream,assures no relative motion between the Earth andthe light-conveying medium, which predicts exactly anull result of all Michelson-type experiments. (Withsome sophisticated mathematics, the same mecha-nism can render the argument of the aberration oflight superfluous.)

Since there is no ‘ether wind’ in the laboratory,because, together with the whole Earth, it is carriedquietly within the medium, the Michelson-Morley,and similar type experiments do not represent mea-surements relative to the motionless Aether.

On the other hand, the postulate of the absoluteand limiting light-velocity based on the experimen-

tally established ‘relativistic mass-increase’ refers toa real relative motion between the particle and theAether. This phenomenon is explained by AETHRO-KINEMATICS as a result of the hydrodynamic resis-tance of the medium which is expressed calculablyby the electromagnetic Mach-formula, called LorentzTransformation.

Thus let us, for the time being, forget about Mi-chelson’s zero and also suspend, till the followingchapters, the major arguments against the ideal gasmodel of the Aether, rendered by the allegedly neces-sary transverse nature of light, invented for the solepurpose of explaining the still perplexing phenome-non of polarization.

According to AETHRO-KINEMATICS all space,cosmic, macrocosmic, and microcosmic are pervadedby an ideal mechanical gas, of a supermundane orderof magnitude. Its constituents, the Aethrons are thefundamental units of mass, motion, velocity andmomentum, therefore not only can kinematicallyexplain Newton’s mysterious mathematical conceptsof inertia, force and gravitation, but as an idealmechanical medium, it also obeys the laws ofNewtonian mechanics and hydrodynamics.

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Thus, as it has been justified in details above,this theory suggests that in all particle-accelerationexperiments the counter-intuitive and counter-New-tonian concept of mass increase should be replacedwith the simple hydrodynamic concept of Aether-resistance, which by the mathematical formula of theLorentz Transformation becomes totally analogous toair-resistance described by the identical mathemati-cal Mach-formula of Aerodynamics.

So, following this line of thought in the discussionwith Dr. McInnis, we’ve realized that there is a possi-ble fundamental classical distinction between thepredictions of Special Relativity and Aethro-kinemat-ics and it concerns Galileo’s Invariance Principle.

Relativity is still based on Galileo’s empty, resis-tanceless space, just like Newton’s mechanics, butAethro-kinematics states, that Galileo’s Principle isonly approximately true, and only for macroscopicobjects moving with macroscopic velocities. Thishypothesis is clearly expressed in the Lorentz Trans-formation by the Lorentz-Fitzgerald ratio related tothe speed of the object with the speed of light.

−−−−−−−−−β = 1 / √ 1 - V2 / C2 (13.1).

Where β represents the ratio of the increase ofthe hydrodynamic resistance of Aether as the veloci-ty of the object, V relative to the medium varies and cis the velocity of the speed of light, which also repre-sents the dissipation velocity of local density distur-bances due to the motion relative to the medium.

This same formula is also the template for therelativistic mass-increase,

mom = −−−−−−−−−−−− (13.3).

−−−−−−−−−−√ 1 - V2 / C2

Experimentally speaking, the above formula sim-ply states, that greater the speed of the particle,greater the force that is needed to produce a unit offurther acceleration.

Einstein states that space is empty and the onlypossible explanation for the requirement of an excessforce is that the inertial mass of the particle mustincrease as its speed approaches the speed of light.

Why in that particular ratio? - No one knows.Thus, it must be postulated as an axiom.

Aethro-kinematics suggests that space is filledwith Aether which, like any other mechanical gas,

270


exerts a resistant force against the motion of anyobjects submerged in it. − Why in the above ratio?Everybody knows Mach’s Theory about the limitingcompressibility of the air, which produces an increas-ing magnitude of air-resistance related to the ratiobetween speed of the airplane to the speed of sound.Lorentz gave us the identical formula for an objectmoving in the Aether and the limiting compressibili-ty of this medium, related to the speed of light.

RoR = −−−−−−−−−−−− (13.3).

−−−−−−−−−−√ 1 - V2 / C2

Where Ro the initial hydrodynamic resistance ofthe Aether at its regular isotropic density and R isthe total, increased resistance, due to the increasingdensity of the Aether in front of the particle which isaccumulating in the ratio between the speed of theparticle and that of the dissipation of the excess den-sity with the velocity of light.

The analogy with the Aerodynamic Mach-numberis so perfect that if relativity would have been app-lied to the near to supersonic flights, we would becompelled to conclude that the extra trust for accel-

erating the plane is needed because the mass of theplane increases and even the passengers are gettingheavier with the increasing speed. Or, which is evenworse, we could find the reason for the requirementof higher trust by postulating that some observersare watching the plane and find it getting contractedand all clocks on the plane are slowing down.

In any case, this situation renders a crucial dis-tinction between the predictions of Special Relativityand the predictions of AETHRO-KINEMATICS:

Thus, here we are raising the never-asked-ques-tion; what ever happens with the relativisticallyincreased mass when a particle does not collide withanything, but continues to move uniformly forever inempty space with its latest accelerated velocity?

Is there now that much more mass existing per-manently in the universe?

− But of course, this is no problem for relativity,since the mysterious mass-increase is merely anobservational illusion.

Well, it is not an illusion of some relatively mov-ing observers for AETHRO-KINEMATICS. It is asimple hydrodynamics calculation, based on New-

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ton’s third law of the action and reaction between thekinetic energies of the particle and the opposingresistance of the Aether, which is explicitly expressedby the above Lorentz formula.

In this picture Newton’s mass never looses itsconstancy and conservation, it remains as constantas in classical physics. However, there is the physi-cally real increase in the hydrodynamic resistance ofthe Aether which is in a strict mathematical propor-tion with the speed of the particle and the speed ofdissipation of the disturbance in the medium.

Now, we ask the same question from AETHRO-KINEMATICS; what happens with the particle if itdoes not collide with anything but continues to movein the Aether with its last accelerated velocity?

Evidently, the relativistic particle would move tilleternity with its last uniform speed carrying itsincreased mass forever. The Aethro-kinematic parti-cle, however, due to the real resistance of the Aetherwould gradually decelerate in proportion to its everdecreasing speed, which can also be explicitly pre-dicted by the Lorentz Transformation.

Therefore, a crucial and decisive experiment canbe executed by existing equipment as follows:

Accelerate a compact group of electrons in a syn-chrotron type accelerator where the particles arekept revolving on a circular orbit of a fixed radiusbetween the poles of a great magnet. Cyclic RFsources are located on the orbit providing incrementsof energy on each revolution. When the designedvelocity is attained, the magnetic field is turned offat the right instant and the particles are extractedfrom the orbit into a straight, evacuated flight cham-ber which lead them to a target sight. Normally, atthat location the collisions and the results can beobserved and measured.

The aethro-kinematic suggestion only differs inthe last phase of the experiment. Instead of having atarget practice on the end of the straight channel, werecommend a time of linear flight measurementbetween the beginning and the end of the straightpath. This simple experiment will unequivocally dis-criminate between the contradictory predictions ofrelativity and those of AETHRO-KINEMATICS andthe same time irrevocably establish the existence ofthe all-pervading Aether.

Evidently, on the one hand, with the empty spaceof relativity and based on the Galilean Principle of

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Inertia the accelerated particles simply preservetheir lastly attained velocity and continue to movewith this uniform velocity (and with their increasedmass) regardless of the length of the linear flight.

On the other hand, also evidently, in the all-per-vading Aether which produces a kinematical resis-tance force, in proportion to the ratio between thespeed of the particle and the velocity of light, the par-ticles must gradually decelerate in proportion to thelength of the chamber.

Therefore, in the Equ.13.3 of the Lorentz Trans-formation, interpreted for the resistance of the idealgas of Aether, gives an explicit prediction of a cru-cially different time of arrival for the deceleratingparticles depending on the length of the flight.

Since both the relativistic mass-increase and theGalilean uniform motion is supposedly eternal, theonly Aethro-kinematical requirement is to make thelinear chamber long enough to take care of the nat-ural fuzziness in the time and length measurements,and for the quantitative revelation of the decelerat-ing force of the kinematical resistance of the Aether.

As Dr. McInnis has remarked at the end of thediscussion: − I believe, this experiment could give us

a perfectly decisive empirical result. It is a simpletime of flight experiment. − How much more basiccan you get to be able to discriminate between twocontradictory theories?! − In my experience, time offlight experiments were always the simplest to com-prehend. If such an experiment agreed with the pre-dictions of Aethro-kinematics, it would represent themost incontrovertible proof of the existence of theAether and the validity of its ideal gas model.

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CHAPTER FOURTEEN

THE AETHRO-KINEMATIC THEORYOF WAVE-MOTION

The fundamental duality of physics initiated inthe sixteenth century between Newton's absoluteand empty space and Huygens' all-pervading lumi-niferous aether, finally culminated without possiblesynthesis at the turn of the twentieth century.

The weight of the tremendous success of the twomajor departments of physics, mechanics and elec-tromagnetism ultimately and hopelessly clashed inthe Null Result of the Michelson experiment. The

laws of both sectors were as valid as can be in experi-mental science, but the contradiction among themseemed to be just as unavoidably valid as the lawsthemselves.

Modeling an ether for the requirements of elec-tromagnetic phenomena has been rendered impossi-ble by the opposing laws of mechanics. Absolute andempty space, required by earthly and celestial me-chanics was unthinkable for the nature of electricand magnetic phenomena.

Science took the only route that seemed concep-tually possible at that stage: By Einstein's recom-mendation the stalemate and the lack of solutionwithin the existing laws has been postulated and thecontradiction, which had been incubating for overthree centuries, finally gave birth to an epistemologi-cal compromise; the official acceptance of the DualNature of Light.

To undo the resulting conceptual labyrinth andreturn to a single language theory of light, some mis-conceptions in the classical mechanical and electro-magnetic wave theories will be pointed out, and thesame time an alternate choice of description, theKinematic Theory of Wave-motion will be introduced.

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Aethro-kinematics

The presently accepted explanation of some wellknown phenomena should be re-examined and theinadequacies of the classical theory and the descrip-tion of an alternate kinematical solution should bepresented together in the sequence of the develop-ment of the classical theories.

THE EVOLUTION OF THE WAVE THEORY OF LIGHT

On contemporary college level, the waves in elas-tic media, is generally discussed in the followingmanner (freely quoted from D. Halliday, R. Resnick,Physics, [404]):"Wave motion appears in almost every branch of

physics. First of all we distinguish between mechani-cal and electromagnetic waves. The wave-motions ofvarious ponderable matter, for which familiar exam-ples are water-waves, waves on elastic strings andsprings and sound-waves in gases, liquids and solids.Since Newton's laws are applicable to the waves inelastic, deformable matter, they are called mechani-cal waves. Light-waves, radio-waves, micro-wavesand radiating heat, which are propagated in vacuum,or rather in empty space and therefore no ponder-

able matter is needed for their transmission, areelectromagnetic waves."Mechanical waves originate in the displacement of

some portion of an elastic, deformable medium fromits normal position, causing it to oscillate about anequilibrium position. Because of the elastic proper-ties of the medium, any local disturbance is trans-mitted from one layer to the next, and thereforepropagates through the medium."Mechanical waves are characterized by the trans-

port of energy through matter by the motion of a dis-turbance without any corresponding bulk motion ofthe matter itself. The properties of the medium, thatdetermine the speed of a wave are its inertia and itselasticity. It is the elasticity that gives rise to therestoring force on any part of the medium displacedfrom its equilibrium position; it is the inertia thattells us how this displaced portion of the mediumwill respond to the action of the restoring force. Wecan distinguish different kinds of mechanical wavesby considering how the motions of the particles ofmatter are related to the direction of propagation ofthe waves themselves. If the oscillation of the matter-particles, conveying the wave, is perpendicular to the

275

Aethro-kinematics CHAPTER FOURTEEN The Evolution of the Wave Theory of Light

direction of propagation of the wave itself, we thenhave a transverse wave. For example, when a verti-cal spring stretched by a weight is set oscillatingsideways at one end, transverse waves travel downthe string; the disturbance moves along the stringbut each particle oscillates transversely to the direc-tion of propagation of the waves." (See Figure 14-1-2)

Figure 14-1.

"In a longitudinal wave, when a horizontally stret-ched coil-spring moves back and forth, on the axis ofthe spiral, the particles of the medium oscillate inthe same direction in which the wave itself propa-gates (b). Sound waves in air are longitudinal com-pression waves. The disturbance in this case is apressure change that propagates outward from the

Figure 14-2.

276


(d)

(e)

(a)

(b)

(c) (f)

source in spherical shells. The molecules of the medi-um move back and forth in the direction in which thewaves themselves move (c).

"Some waves are neither purely longitudinal norpurely transverse. For example in waves on the sur-face of the ocean the particles of water move both upand down and back and forth, tracing out ellipticalpaths as the water waves pass by (d). Waves can alsobe classified as one, two, and three-dimensionalwaves. Waves moving along a string or a spring areone-dimensional. Surface waves or ripples on water,caused by dropping a pebble into a quiet pond, aretwo-dimensional. Sound waves and light waveswhich emanate radially from a small source arethree-dimensional."

With this conceptual description comes a mathe-matical analysis of wave-motion using the two-dimensional transverse waves on a string, as the sim-plified general representation of all fundamentalproperties of wave-motion in an elastic medium.

Consider a long string stretched in the x-directionalong which a transverse wave is traveling, Figure14-1 (a). At some instant, say t=0, the shape of thestring can be represented by

y = f(x) t = 0 (14.1),

where y is the transverse displacement of the stringat the position x, and f is a function which describesthe particular shape of the wave.

Illustration Figure 14-1 (b) shows a single wave-form, or a pulse on the string at t=0. As time goeson, such a pulse travels along the string withoutchanging its shape. At some time, t later the wavehas travelled a distance vt, where v is the magnitudeof the wave velocity. The equation of the curve at thetime t is therefore

y = f (x - vt) (14.2),

where y is the transverse displacement of the stringat position x. This is the general equation for a waveof any shape traveling on a string. To describe a par-ticular shape only the function, f has to be specified.The equation defines the actual shape of the stringand how the transverse position of each point of thestring changes with time.

By Hooke's law, a string provides a restoringforce, which is proportional to the displacement ofthe string from its equilibrium position. The greaterthe displacement, the greater the force that tends to

277


restore the equilibrium. Thus, the resulting motion ofeach particle is equivalent to a simple harmonicoscillation.

The restoring force is also directly proportional tothe tension on the string. When the end of a string ismoved up and down repeatedly and the motion isperiodic, it produces a periodic train of waves, (a)which are called simple harmonic waves. The parti-cles of the string are in transverse simple harmonicoscillation and the form of the wave is sinusoidal, (c).

The maximum vertical displacement y is theamplitude of the sine curve, which itself is producedby the periodic repetition of the value of the trans-verse displacement. Each point on the curve repre-sents a phase of the wave. The distance between twoidentical phases of the wave is the wavelength, λ ofone wave.

The time required for a wave to travel a distanceof one wavelength is called the period, T. The numberof waves that travel through one point in space persecond, is the frequency, ν of the wave. The speed ofpropagation of the wave is its wavelength times itsfrequency; c = λυ. The same concepts and mathemat-ical expressions hold for longitudinal compression

waves, in different media, like waves on a coil-spring(c), or sound-waves Figure 14-2 (d). The analogouslongitudinal example for the transverse wave on astring is a long tube filled with gas. In this case thepulse is a single pressure change or change of densityin a certain volume of the air, which travels in thetube along the x axis. The sound is produced by theoscillation of a loud-speaker which is attached to along tube. The repetitious back and forth motion ofthe membrane produces a wave-train in which alter-nate compression and rarefaction layers are movingthrough the medium along the tube.

For compression waves, like sound, in a similarequation as Equ. (14.2), y gives either the back andforth (longitudinal) displacement of the particles or,by a different concept, the magnitude of the pressurevariations in the medium as the wave progressesthrough the medium at a given point in the pipe.

Analogous to the waves of sound in a pipe it ispossible to send electromagnetic waves through ahollow metal pipe with a rectangular cross section,called a waveguide (e). The quantity, y which meantparticle displacement in the transverse waving of thestring and pressure fluctuation in the longitudinal

278


waves of sound, in this case, it measures the ampli-tude of the electromagnetic vectors. Figure 14-2 (f)illustrates the transversally oscillating electric andmagnetic vectors of radio waves.

POLARIZATION AND WAVE THEORY In the year 1669, a Dutch physicist, Erasmus

Bartholinus, discovered that if a crystal of Icelandspar was placed on a picture, it produced a doubleimage. For instance, when placed on a black dot, twodots were seen. Apparently, light passing through thecrystal, split up into two rays that were refracted bydifferent amounts. This phenomenon was nameddouble refraction.

Both Huygens in his wave theory and Newton inhis corpuscular theory considered the phenomenon,but neither of them could come to a clear conclusion.

Newton made some vague speculations to theeffect that light corpuscles might have two differentpolarities like the 'poles' of a magnet, but did not getany further into the problem. More than a centurylater, in 1808, Etienne Louis Malus experimentingwith Iceland spars, discovered that if light wasreflected from a window at a certain angle, there was

no longer a double image through the iceland sparcrystal. Based on Newton's concept of possible polari-ty, he decided that the window reflected only one ofthe poles of the light.

Thus, Malus called the reflected beam polarizedand the effect, polarization. By experimentation ithas been also found, that a thin tourmaline crystal,cut parallel to its optic axis, only transmits lightwhich is polarized in a certain direction. If this lightgoes through a second crystal, the final intensity oflight depends on the relative orientation of the twocrystals. When their axes are parallel, considerableamount of light is transmitted, but when one of themis rotated, the intensity gradually decreases andwhen the optic axes reach right angles, the transmit-ted light is practically zero.

At that time and until the end of the nineteenthcentury, scientists believed that, analogous to soundwaves in air, light is a longitudinal compression wavein the all-pervading luminiferous aether.

The discovery of double refraction and polariza-tion brought up some serious questions for whichthere were no easy answers based on the compres-sion wave theory of light.

279

Aethro-kinematics CHAPTER FOURTEEN Polarization and Wave Theory

Around 1820 Thomas Young, in his letter to Fran-cois Arago, proposed an addition to the wave theoryof light as follows:"I have been reflecting on the possibility of giving

an imperfect explanation of the affection of lightwhich constitutes polarization, without departingfrom the genuine doctrine of undulations. It is a prin-ciple in this theory that all undulations are simplypropagated through homogeneous mediums in con-centric spherical surfaces like undulations of sound,consisting simply in the direct and retrogrademotions of the particles in the direction of the radiuswith their concomitant condensations and rarefac-tions (that is, longitudinal waves). And yet, it is pos-sible to explain in this theory a transverse vibration,propagated also in the direction of the radius, andwith equal velocity, the motions of the particles beingin a certain direction with respect to that radius, andthis is a polarization."

Unfortunately, Young has never explained hisidea in more details and his successors have chosenthe simplest possible interpretation of this assump-tion, that light waves are analogous to the transversewaves on a string. In order to visualize the possible

mechanism of polarization, scientist created an anal-ogy, based on the motion of transverse waves on ataut string. This simple mechanical parallel is illus-trated on Figure 14-3.

Figure 14-3 When a string is oscillating up and down, we may

erect two grids with vertical slots without interferingwith the transverse displacements of the string, (a).However, turning the second grid at right angles tothe first, as illustrated in (b), the transverse wavescannot pass through it. The grids represent the twotourmaline crystals. P on the first grid stands forpolarizer, and A on the second grid stands for analyz-er, as they are called in the experimental polariscope.

280


From here on, in order to explain the phenome-non of polarization, theorist assumed that light andelectromagnetic waves are uniquely transverse oscil-lations. But what could the mechanics of the waveson a string possibly mean in the case of the trans-verse oscillation of electric and magnetic fields?

According to modern theories, electric and mag-netic fields induce one-another and alternately oscil-late in transverse directions to the direction of thepropagation of the waves themselves. In this case, inthe analogous mathematical expression, taken fromthe waves on a string, y represents the amplitude ofthe transversally oscillating electric and magneticvectors related to a given point on the x-axis.

"Common sources of visible light differ from radioand microwave sources in that the elementary radia-tors, that is, the atoms and molecules acts indepen-dently. The light propagated in a given direction con-sists of independent wave-trains whose transverseplanes of vibration are randomly oriented about thedirection of propagation. Such light is unpolarized.

Figure 14-4 "shows unpolarized light falling on asheet of commercial polarizing material. There existin the sheet a certain characteristic polarizing direc-

tion shown by the parallel lines. This direction isestablished during the manufacturing process byembedding certain long-chain molecules in a flexibleplastic sheet and then stretching the sheet so, thatthe molecules aligned parallel to each other. Thesheet will only transmit those wave train compo-nents whose electric vectors vibrate parallel to thisdirection and will absorb those that vibrate at rightangles. The emerging light will be plane-polarized.

Figure 14-4281


Polarizer 1.

Analyzer

Polarizer 2.

(c)

-- Natural light --

Analyzer

Polarizer

(b)E o

xE

yE

(a)

- Plane polarized light

No light

"Let us place a second polarizer sheet, called ana-lyzer in place as shown. If it is rotated about thedirection of propagation, there are two positions 180degree apart, at which the transmitted light intensi-ty is almost zero. These are the positions when thepolarizing directions of the two sheets are at rightangles. Longitudinal waves could not possibly showsuch effects." (D. Halliday, Resnick, Physics. [1072])

The illustration above shows the basic idea ofthe present theory: (a) illustrates that an electric vec-tor, Eo, in any oblique direction can be resolved intotwo components related to the rectangular coordi-nates as Ex and Ey.

Part (b) shows, that when the Polarizer and theAnalyzer set in a rectangular angle with their trans-mitting axes, no light can be detected beyond theanalyzer. Part (c), however, shows, that whenPolarizer 2. is inserted in between, and in an obliqueangle, some light reappears again.

To clarify and explain this last experimental fact,a more popular style description has been presentedin the 1990 video-tape edition of the college course:The Annenberg / CPB project: 'The MechanicalUniverse and Beyond'.

Dr. Robert L. Goodstein professor first explainspolarization similarly as above, in the language ofthe classical electromagnetic wave theory. He thendemonstrates that when the analyzer is at 45° anglewith the polarizer, the light intensity decreases byapproximately 50%. According to Dr. Goodstein, thisresult is not entirely obvious if it was assumed thatthe first plate let exclusively the vertically oscillatinglight through, or if the light emerges is uniquelyplain polarized. But then explains, that each vertical-ly oscillating vector has some oblique components,which could still pass when the analyzer is in theoblique angle."This is very easy to understand" - he says, - "so

long as we believe that light is a wave, but rememberthat light is also a particle and there must be a parti-cle explanation of how this occurs as well. So let metell you how that works. The problem here is, that Ican't say that part of the light gets through the sec-ond filter when it is oblique, because a particle eithergets through or it doesn't get through. So, here is theway it works."The light particles, or photons, come along to the

first filter, which says: Listen guys, every one of you282


is either polarized up and down or sideways. Nothingelse is permitted. But you are polarized up and downor sideways with some probability; half of you are upand down and half of you are sideways. Then thelight gets through the first filter, the one that is upand down, and all the sideways photons got stopped.""Now, between the two filter, there are only photons

that are polarized up and down. The second filter, aslong as it is in the sideways direction, says: You guysare all up and down, and I only permit sideways pho-tons through, so nothing gets through. If the secondfilter is up and down, it says; You guys are all up anddown and I let up and down photons through. Sothey all get through and you can see the light on thescreen.

"The tricky part happens when the second filteris turned left in the oblique (45°) direction, becausethen it says: listen guys, you thought that you are allup and down, but it is not true. Everybody has got tobe oblique either to the left or oblique to the right(315°) with some probability and you thought thatyou are up and down only because half of you areoblique to the left and half of you are oblique to theright and now the filter lets through the ones that

are polarized oblique left direction. And that is theparticle explanation of polarization.""Now, I would like to do one more experiment for

you. I will turn the analyzer in the sideways direc-tion, so nothing gets through. Then I set a thirdpolaroid in the oblique left direction and insert itbetween the other two. What will happen now is thefollowing: only up and down photons get through thefirst filter, they get to the oblique one in the middleand he says, no, you are not up and down, but youhave a fifty percent probability of being oblique tothe left and getting through, and fifty percent proba-bility of being oblique to the right and not gettingthrough.“So, the ones oblique to the left get through and

then they get to the last filter, which is set sideways.It says: you guys all thought that your are polarizedoblique to the left, but you are not. Each one of youhas a fifty percent probability to be horizontal andgetting through and each one has a fifty percentprobability of being vertical and not getting through.So, the horizontal ones gets through, and that meansthat the beam of light will reappear on the screen.And there it is.

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"And this is the essence of how the new physicsworks!"

There could be some objection about quoting thissimplistically popular lecture. However, although themathematics get more complex, the conceptual con-tent even at the highest theoretical level offers noth-ing better in explanatory value.

On the contrary.For example, George Gamov, inventor of the

famous Big Bang Theory has a more sophisticatedview of the wave-particle duality of electromagneticradiation. (Matter, Earth, Sky. [173])"Instead of considering electric and magnetic fields

as stresses in a certain universal substratum, wenow ascribe to them a definite physical reality, infact, about as much reality as we ascribe to ordinarymaterial bodies. Probably the most important inno-vation brought by Einstein to our views concerningelectromagnetic and optical phenomena is that wemust ascribe a certain mass to electromagnetic ener-gy as well as to any other form of energy (176). (...)Thus, the field around an electrically charged con-ductor or a magnet should be considered as a jelly-like material surrounding them in the form of a local

cloud rather than as local deformations in a jelly likemedium which fills up all space (120). Similarly,while classical physics considered light waves aspropagation of elastic deformations through the'world ether' filling the entire space, we considerthem now as vibrations taking place within thelumps of a certain physical entity, (i.e., electromag-netic field), flying freely through the empty space."(176)

Figure 14-5 is Gamov's original illustration andhis explanation of this most modern concept of lightwaves.

Figure 14-5

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(a) A wave propagating through a stationary elastic ribbon,(b) a moving wave-shaped rigid ribbon."

"In other words, the propagation of an electromag-netic wave is more similar to the wave-like motion ofa snake crawling through the grass and carryingalong its body as well as its form than it is to thewaves on the surface of water, where only the form ofmotion but not the material itself is moving for-ward."

This is then the latest phase of the conceptualand mathematical evolution of the transverse natureof light-waves. Evidently, a painstaking effort, toexplain the phenomenon of polarization by a visuallycomparable crude analogy of the waves on a string.

Nevertheless, this simple method turned out tobe very costly in the evolution of science. The pio-neers of the field concept, Faraday, Maxwell, Lorentzand others, until the turn of the century, thought ofelectrical and magnetic fields as real physical quanti-ties, and manifestations of the stresses and strains inthe all pervading electromagnetic aether.Unfortunately, the construction of a mechanicallyfeasible model of this medium was never achievedbecause of the unavoidable stumbling block of thetheory of polarization. The explanation, based on thewaves- on a string, required the uniquely transverse

nature of the waves of light, which, in turn, called foran extremely dense solid medium with immenserestoring forces capable of transmitting the great fre-quencies and extreme speed of light-waves.

As a result, the turn of the century brought anamazing revolution with a complete metamorphosisof the theories of light, electricity and magnetism.The transversally oscillating waves of light excludedall possibilities of designing a transmitting mediumbased on the principles of physics, and became atransversally waving emptiness, or in another dia-lect; a jelly-like cloud of alternating electric and mag-netic fields, or still another language; a frozen snake,or a rigid, ribbon-like arrow, whizzing through thevoid with an absolute speed relative to all movingobservers.

It should be a real challenge to visualize whatwould really happen to this creature when it meetsthe polarizer and analyzer and the one in between ?!Attempting this task, one may justifiably arrive tothe modest conclusion, that the description of polar-ization, in spite of the acceptance of various lan-guages of modern physics, is still not sufficientlycomplete for that task.

285


This is the exact point that AETHRO-KINEMAT-ICS intends to emphasize. The explanation of polar-ization, based on the transverse nature of light is notunambiguous enough to justify the impossible condi-tions it forces on the model of a light transmittingmedium, and by that on all departments of physics.

In other words, because of the above explanationof polarization, and only because of that, Aether wasrequired to be an extremely dense solid with restor-ing forces beyond that of steel. Consequently it hasbeen discarded as an absurd abstraction.

ABOUT MECHANICAL TRANSVERSE WAVESLet us now attempt a new view of things, take a

couple of steps back into classical physics, and recon-sider Young's 'imperfect' proposition of the trans-verse nature of light-waves, as seriously, as he proba-bly meant it:

'...without departing from the genuine doctrine ofundulation, it is possible to explain this theory oftransverse vibration, propagated also in the directionof the radius and with equal velocity' .

Obviously, Young merely proposed an addition tothe longitudinal oscillation, and not a uniquely trans-verse one. It should be a component of the sound-like

compression waves in the same isotropic, gaseousaether, on which he had originally founded his undu-latory theory. Nevertheless, it seems quite plausiblethat there were no serious attempts to correlate thetheory of longitudinal waves with their potentialtransverse components.

Let us now attempt a closer analysis on themechanics of the examples of uniquely transversewave-motions on which the transverse nature of elec-tromagnetic waves were founded."Water waves are very unsuitable for a detailed dis-

cussion because they are more complicated thanother waves. We shall discuss instead the case of atransverse wave on a long spring, which is moreclosely analogous to the electromagnetic waves thatwill eventually be our main interest.“Imagine a long horizontal spring with one end

attached to the wall, the other end held in the handand pulled taut. By moving the hand up and downrapidly two or three times, a wave can be made totravel in horizontal direction along the spring.

Meanwhile each point of the spring oscillates upand down in a vertical direction. Their motion is sim-ple harmonic. (Figure 14-6)

286

Aethro-kinematics CHAPTER FOURTEEN About Mechanical Transverse Waves

"A wave is called transverse wave if the oscillatorymotion of any part of the system is at right angles tothe direction in which the wave is traveling. Theshape of the spring at a fixed instant of time is a sinewave function." (Atkins, Physics, [397])

There are some obvious oversimplifications in theabove description: A coil-spring is tempered to holdits form, which is usually a straight spiral of equidis-tant coils. This form of the spring represents its equi-librium state, and the external forces that tend todeform this shape meet an equal and opposite re-storing force in order to re-establish the initial stateof equilibrium. As it is shown on Figure 14-1 (c) thespring can be compressed or stretched longitudinallyalong its x axis by fixing one end and pushing orpulling the other in a plane parallel to the coils. Inthis case the spring can be taken as an homogeneousmedium and the top and the bottom points of thecoils can symbolically represent the displacement ofthe particles of the medium. The propagation of theanalogous disturbances must evidently be restrictedto one dimension only, along the x axis.

If the pushing and pulling is done periodically,longitudinal compression waves can be produced,

which travel along the original axis of the spring andtransfer the energy of the initial force. In this casethe compression and rarefaction pulses are repre-sented by the changing distances between the coils.As the simplified view of modern text books defines,it is a back and forth, longitudinal oscillation of theparticles in the spring. − From this definition it fol-lows that the undisturbed initial state of the mediumis explicitly the straight, unbent, unstretched andunsqueezed, one dimensional form of the coil-spring,into which the wire was originally tempered.

Consequently the propagation of any disturbancein this homogeneous, isotropic medium must alwaysbe longitudinal in one dimension and parallel to thex axis of equilibrium of the spring.

The classical definition states, that 'mechanicalwaves are characterized by the transport of energythrough the propagation of a disturbance without anycorresponding bulk motion of the medium itself'.

Evidently, no forceful bending of the spring out ofits initial one dimensional equilibrium can be takenas a normal disturbance, but it should be defined asthe bulk motion of medium as a whole, including thedeformation of its axis of equilibrium.

287


Figure 14-6

The above illustrated jerking of the spring isequivalent to produce transverse waves on a pond byshaking the entire water, like a blanket, instead ofdropping a stone unto its surface.

Nevertheless, it is possible to produce wave-motions on a long spring by jerking it rectangular toits axis alternately and periodically. In such wavesthe symbolized particles of the spring oscillate trans-versely to the direction of propagation and with somestretching of the symbolism, the phenomenon can becalled transverse wave-motion.

However, this classification is a total misinterpre-tation of the mechanical nature of the spring.

Figure 14-7The best way to understand the true mechanics

of this kind of deformation is to consider the relativepositions of the coils in different situations. Figure14-7 (a) illustrates the stretched, relaxed and con-densed state of the spring. (b) shows the relative ori-entation of the coils when the spring is forced into acircle. It is evident that by bending the spring, we

288


X

X

X

X

X

o

o

d

d

d

Normal

( c )

(b )(a )

have bent the whole one dimensional medium and itsaxis into two dimensions. The coils of the spring inthe circle are forced into both compression and ex-pansion at the same time; the internal parts of thecoils are compressed, the external parts of the samecoils are spaced apart.

Clearly, the restoring force acting toward the ini-tial equilibrium is the tendency to re-establish theinitial density of the whole medium; that is, restorethe spring into its straight shape.

Evidently this force must act longitudinallyalong its distorted axis, Xd against both the internalcondensation and external expansion of the coils inthe circle.

With regards to the transversal sine waves,Figure 14-7 (c) illustrates a section of the wave onthe spring. The sine curve can be taken as two oppo-site halves of a circle connected with a gradual tran-sition between them. The mechanics of the deforma-tion here is the same as in the case of the circle; It isan artificial distortion of the one dimensional medi-um, in which there are simultaneous longitudinalcompressions and expansions of the coils at the oppo-site sides of the spring.

By the original symbolism, plotting the density ofthe particles at the top and bottom of the spring, it isfound, that there are two sets of longitudinal com-pression and expansion waves existing at exactly inthe opposite phases. The straight doted lines, erectedfrom the center of the circles, show the different den-sities of the internal and external part of the coils. Inthis case, the arrows show the directions of the re-storing forces.

The top part of the sine wave starts with expan-sion, goes through a straight, normal density portionand ends up condensed. The bottom part starts withcondensation and follows the same all the way withexactly opposite density changes.

The visual appearance of the phenomenon, theshape of the spring, on which the whole concept ofthe transverse displacement wave is based, is merelythe effect of the bulk distortion of the medium itself,due to the artificially directed initial forces whichjerk the spring and its axis out of its straight, onedimensional equilibrium. It is obvious, that both thedensity differences and the restoring forces act strict-ly longitudinally to reestablish the equilibrium of thedistorted axis of the spring.

289


It is now easy to see, that the waves on a tautstring demonstrates the same mechanics in its mole-cular construction. The same out-of-phase longitudi-nal compression wave-pair produce the macroscopicchanges in the shape of the string. Hence, the restor-ing forces in the so called transverse waves on astring, merely act toward the initial longitudinalisotropic density of the molecules both inside andoutside of the curves, which is inherent in the origi-nal straight shape of the string.

Therefore, the statement that the particles of themedium oscillate transversally to the direction ofpropagation, is a total misconception, based merelyon a macroscopic optical illusion. The same conclu-sion is valid for all other types of transverse wavesand vibrations in elastic media, including the waveson the surface of water.

As it is shown by Guy Murphie's ingenious illus-tration, (Music of the Spheres, [368]), the transversewaves on the water surface is merely a manifestationof the three dimensional longitudinal compressionwaves, as the compressed layers bulge into theisotropic atmospheric pressure of the air.

From the above, it can be concluded, that there isno mechanical wave motion, which can be describedby the oscillation of the particles transverse to thepropagation of the waves in an isotropic elastic fluidmedium. Therefore the theory of transverse waves ofany kind is also based on misconception.

ABOUT LONGITUDINAL WAVES Consider now the following description of the

uniquely longitudinal waves of sound:

290

Aethro-kinematics CHAPTER FOURTEEN About Longitudinal Waves

Figure 14-8

"Sound waves are longitudinal mechanical waves.The material particles transmitting such a waveoscillate in the direction of the wave itself. Sound, ifunimpeded, spreads out in all directions from asource. It is simpler to deal with one-dimensionalpropagation, than three-dimensional propagation, sothat we consider first the transmission of longitudi-nal waves in a tube.

Figure 14-9

"Figure 14-9 (a) shows an oscillating piston at oneend of a long tube filled with a compressible medium.The vertical lines divide the fluid medium into thinslices, each of which contains the same mass of fluid.Where the vertical lines are relatively close together

the fluid pressure and density is greater then theyare in the normal undisturbed fluid, and conversely."We shall treat the fluid as a continuous medium

and ignore for the time being that it is made up ofmolecules that are in continual random motion. If wepush the piston forward, the fluid in front of it iscompressed, which moves forward, compressing thefluid layers next to it, and a compression pulse trav-els down the tube. If we then withdraw the piston,the fluid in front of it expands, its pressure and den-sity falls below the normal undisturbed values; apulse of rarefaction travels down the tube."These pulses are similar to the transverse pulses

travelling along a string, except that the oscillatingfluid elements are displaced along the direction ofpropagation (longitudinal) instead of at right anglesto this direction (transverse). If the piston oscillatesback and forth, a continuous train of compressionand rarefaction will travel along the tube."As the wave advances along the tube, each small

volume of the element of the fluid oscillates about itsequilibrium position. For convenience, let us repre-sent the displacement of any such fluid element fromits equilibrium position at x by the letter y.

291


"It is to be understood, that the displacement of theparticles is along the direction of propagation for alongitudinal wave, whereas for a transverse wave thedisplacement, y is at right angles to the direction ofpropagation."It is usually more convenient to deal with pressure

variations in a sound wave than with the actual dis-placement of the particles conveying the wave, Fig.14-9 (b). Let us therefore write the equations of thewave in terms of pressure variation, rather than interms of displacement. Just as we let y represent thedisplacement from the equilibrium position, so wenow let p represent the change from the undisturbedpressure. If the particle displacement is simple har-monic, then the pressure variation at each position xis also simple harmonic. The maximum change inpressure is called the pressure amplitude." (Halliday-Resnick, Physics, 1978, [434]).

With this, the conceptual and mathematical equi-valence between the transverse waves on the stringand the longitudinal compression waves of sound ina tube has been established.

So, some of the allegedly negligible aspects of thephenomenon, which was temporarily suspended for

the sake of simplification, now may be reinstated.Thus, let us first re-establish the deliberately by-passed facts, that sound is not one, but three dimen-sional, and that air is not a continuous medium, butmade up of molecules, which are in constant rapidrandom motion.

According to the kinetic theory of gases, this ran-dom motion of the molecules is responsible for theisotropic three dimensional pressure exerted by thegas on the walls of a container.

In the hypothetical example of the sound wavesin a long tube, we were discussing only the longitudi-nal component of the pressure variations of the gas,and for the sake of simplicity, nothing was mentionedabout the effects of the other components of the pres-sure directed toward the wall of the tube. A compres-sion pulse contains an excess density and thereforean excess pressure, which travels from layer to layerand effects the average density of the medium.

Each of the 'thin slices' of the medium should betaken as a given volume of gas of higher densityenclosed by the surrounding medium and the ran-domly moving molecules exert an equal force on thewalls of its imaginary container in all directions.

292


Figure 14-10 illus-trates that accord-ing to the kinetictheory, in a cubicalcontainer only 1/6of the total pres-sure effects eachwall. If the thoughtexperiment withsound was perfor-med in a rectangu-lar tube, it wouldbe found evidentthat only 2/6 of the

total pressure difference of the compressed layer hasbeen accounted for in the longitudinal directions, but4/6 of the force which should effect the four side wallsof the tube, was omitted from the analysis for thesake of simplification.

Since the force of pressure always acts at a nor-mal angle to all walls, in this case only two of thenormal angles represent longitudinal directions, thenormal angles to the remaining four walls are trans-verse to the direction of propagation of the wave.

Evidently, it is a clear case of oversimplificationthat the particles in a longitudinal wave only oscil-late back and forth and only in the direction of prop-agation. If they do oscillate longitudinally, they mustalso oscillate transversally. Thus, the excess pressureof the compression pulse of sound must exert a forcein all directions, regardless whether there is a wall ornot. In fact, nothing else but these transversal com-ponents are responsible for the spherical expansionof the longitudinal compression waves in the freeisotropic elastic medium.

It follows, that the distinctive classification oflongitudinal waves is just as superficial and falla-cious as its transversal counterpart.

It must be assumed then, that the compressionwaves created in an isotropic medium possess bothlongitudinal and transversal components of theexcess pressure and the individual particles do notperform specific oscillations in any preferred direc-tion. Figure 14-11 is a schematic representation ofthe radial and transversal vectors acting mutually inthe propagation of longitudinal compression waves.

This illustration is the clearest argument againstthe artificial restriction in dimensions or the bodily

293


1/6

1/6

1/6

1/6

1/6

1/6

Figure 14-10

distortion of a medium for the sake of the conceptualsimplification. It clearly shows the role of the longi-tudinal and transversal components in the mechan-ics of compression waves, which always exist togeth-er, whether there is a restriction or distortion of themedia, or not.

Figure 14-11

Thus, there is no reason for classifying wavesseparately as longitudinal and transverse, and theo-rize about the different oscillations of the particles,proven by different artificially simplified examples.AETHRO-KINEMATICS not only refuses the trans-verse wave theory of light but, based on the above,denies the existence of uniquely transverse wavesaltogether.

A kinematical extension of the classical mechani-cal wave-theory contemplates the transverse andlongitudinal components of the compression wavesas mutually active ingredients of a three dimension-al transference of momentum through an isotropical-ly free fluid. With this conclusion the forced condi-tions of an exclusively transverse wave theory of lightare lifted.

With the admittance of the ideal gas model ofAether a new approach has opened for the explana-tion of polarization. In agreement with Young's origi-nal suggestion, a kinematic explanation must bebased on the co-existence of transverse and longitudi-nal components of compression waves propagatedwith equal velocity through an isotropic and homoge-neous medium.

294


Z

X

Y

S O U R C E

Almost all of the phenomena of wave optics hasbeen simulated by the mechanical experiments withwaves of water or those of sound. If light waves weremechanical, then double refraction and polarizationshould be also reproducible experimentally in realgases and liquids. Indeed, in Classical Physics doublerefraction has been explained by the different speedsof light in different directions of the transparentmatter, due to the asymmetry of the crystalline lat-tice. Thomas Young proposed a dynamical hypothesisto explain the different speeds of light by assumingthat the transparent matter is more easily compress-ible in one direction than in another.

This theory has been confirmed by Brewster in1815, showing that by simple mechanical compres-sion an isotropic transparent solid becomes doublyrefracting. These facts should be kept in mind for thefurther discussion.

In the same decade M. Chladny found that themere obliquity of the fibers of a Scotch fir rod chan-ges the velocity of sound in different directions in theproportion of four to five. This proves, that with suffi-cient precision, sound could be found doubly refract-ed in asymmetric materials. Nevertheless, so far no

experiment was recorded trying to achieve the polar-ization of sound. (Maybe it is merely a matter of theproportionality between the size of the grids and thewavelength of sound.)

SIMPLE HARMONIC OSCILLATORSAlong with the artificial classification of mechani-

cal waves as longitudinal and transversal in nature,comes another simple generalization, that the oscil-lations of the particles in all basic sinusoidal wavemotions are simple harmonic in nature, mathemati-cally analogous to the oscillations of a weight on aspring, or those of the swings of a pendulum. Again,based on the example of the transverse waves on astring, the concept of simple harmonic waves was for-mulated, and its mathematical formalism wasapplied to all other waves, including the compressionwaves of sound and the electromagnetic waves oflight. Mimicking the hypothetical transverse dis-placements of the particles in a string, the propaga-tion of the waves of sound is explained by the simpleharmonic back and forth oscillations of the particlesof the air.

Accordingly, the simple harmonic oscillator of thesource produces simple harmonic oscillations of the

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Aethro-kinematics CHAPTER FOURTEEN Simple Harmonic Oscillators

air-particles, which propagate in the isotropic medi-um and directly produces the simple harmonic oscil-lation of the receiver.

Although the Mechanical Theory of Waves and itsmathematics seems to work in most cases, there isan obvious kinematical ambiguity in this simpletransition of the concepts and mathematics from thetwo dimensional transverse waves on a string to thethree dimensional longitudinal pressure waves ofsound, and from the behavior of solid string to thebehavior of gases.

On the one hand, as it is described by the abovemethod, in a gaseous medium the kinetic energy ofan oscillator is supposed to be transmitted in threedimensional longitudinal waves by the simple har-monic back and forth oscillation of the particles ofthe medium. According to the classical wave theory,the only difference between longitudinal and trans-verse waves is in the direction of the oscillation ofthe particles of the medium relative to the directionof propagation of the waves themselves. These for-ward or sideways oscillations of the particles, initiat-ed by the oscillator at the source propagate through-out the medium in simple harmonic oscillation and

directly produce the resonance of the oscillator at thereceiver.

On the other hand, in a different department ofphysics, most of the characteristics of gaseous sub-stances, like flow patterns, resistance, pressure, etc.are successfully explained by the Kinetic Theory ofGases, through the fundamental concept of the idealgas. According to this model the kinetic energy inthis medium is transmitted solely through the colli-sions between the randomly moving particles. Allother forces between the particles of the gas, like elec-tromagnetic and gravitational forces are taken to benegligible and therefore non-existent.

It directly follows, that the kinematics of wavemotion in gases cannot be based on any kind ofrestoring forces, acting among the atoms, and there-fore no simple harmonic oscillation can be producedor assumed to exist in such medium.

Hence, the motion of the particles in longitudinalwaves in a gaseous media could not directly mimicthe waves on a solid string or mimic the motion ofthe oscillator of a source, or simply transmit kineticenergy to the receiver by their own simple harmonicoscillations.

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Aethro-kinematics CHAPTER FOURTEEN Simple Harmonic Oscillators

The method of the transmission of sound energymust be determined and described by the kinematicsof the dissipation of local disturbances through anisotropic gaseous medium.

Interestingly enough, this ambiguity has beenstrongly emphasized and made quite clear in thevehement scientific arguments against the gaseousmodels of Aether by the denial of its capability totransmit the transverse oscillation of light, becauseof the absence of restoring forces among the gas par-ticles. − This argument, however, has never beenapplied against the hypothesis of the longitudinalsimple harmonic oscillation of the particles of air inthe mechanical description of sound.

HARMONIC WAVES OR PERIODICAL PULSES

For a visual clarification of this alternate Kine-matic Theory of Compression Waves, consider the fol-lowing thought experiment in the ideal gas:

Let us go back into the great room, consideringthat a small spherical balloon is set in mid air, thevolume of which can be changed by pumping more orless air into it through a thin pipe.

While the balloon is at rest in its initial size, thegas atoms simply rebound from its surface andrebound again from the atoms of the next surround-ing layer. Thus, it can be assumed, that the density ofthe gas is the same around the balloon as anywhereelse in the medium.

Calculations show that in the air at 0° C and atstandard atmospheric pressure there are about3×1019 (3 followed by 19 zeros) atoms per cubic cen-timeter, within which some 5 billion collisions takeplace per second. The length of the average collisionfree path is of the order of a few millionths of a cen-timeter and the average speed of the atoms is about5-7 km/sec. Let us suppose that the volume of theballoon is only one cubic centimeter.

Even if the expansion is only one percent of theinitial volume of the balloon, it would produce a dis-turbance in the random motion of billions of atoms.This seems to be an extremely complex kinematicprocedure, but as it was shown earlier, it is permissi-ble to simplify the situation.

As long as the balloon is at rest and the random-ness is completely isotropic, on the average, theCenter of Oscillation of the atoms can be assumed as

297

Aethro-kinematics CHAPTER FOURTEEN Harmonic Waves or Periodical Pulses

fixed in space and that each atom is at rest at thatpoint. In this simplified picture, all stands still untila sudden expansion of the balloon puts the neighbor-ing atoms into motion. These atoms move with thevelocity of the expansion and collide with the otheratoms at rest in the next spherical layer. Taking thesimplest head-on collisions between equal masses,each moving atom stops and transfers its momentumto one at rest sending it into the next layer. There, inturn, those atoms will stop and send others into thelayer next to that.

As the pulse proceeds in the medium in an ex-panding spherical shell, each group of atomsmigrates into the space of the next layer and trans-mits its excess forward momentum to that group ofatoms.

Superimposing now the initially existing isotrop-ic random motion of the atoms, the fundamentalkinematics of the compression pulse does not change.Evidently, the excess momentum, originating fromthe movement of the balloon, spreads through themedium in the form of an excess radial and transver-sal pressure represented by the migration of theatoms from each spherical layer into the next. The

intensity of the pulse is directly proportional to theinitial magnitude and velocity of the expansion of theballoon. Because of the initial forward momentumdisperses into an expanding spherical shell, theintensity of the pulse, or the density of momentumper unit area is also proportional to the inversesquare of the distance from the origin.

Now, consider the opposite of the compressionpulse; a single rarefaction pulse.

Starting with the motionless mid-position of theballoon, as before, the density of the medium isisotropic and all atoms can be taken as being at restin the position of their average Center of Oscillation.

When the balloon suddenly contracts, it leaves acertain volume of empty space around it. Obviously,in this simplified picture nothing else happens.Since the contraction of the balloon exerts no force onany of the atoms, they all remain at rest.

Thus, by superimposing the initial isotropic ran-dom motion, there can be no transference of excessmomentum to the atoms in the backward direction,but the empty space, created by the contraction, ismerely filled up by the atoms which happen to betravelling in that direction in their random motion.

298


This procedure is equivalent to a free expansion,which was discussed earlier in connection with thekinematics of the gravitational sink.

From this obvious difference between compres-sion and rarefaction pulses, it follows, that withoutany restoring forces or some kind of backwardmomentum, the randomly moving particles of agaseous medium do not, and cannot perform simpleharmonic, or any other kind of oscillation.

According to the Kinetic Theory of Gases every-where in the ideal gas, all six inside walls of an imag-inary cube receive the same isotropic pressure by theaverage random collisions of the atoms. It can beseen, however, that the superimposed excess pressureof a passing compression pulse only effects the oneforward and four side walls of the cube. No excesspressure is exerted on the back wall, opposite to thedirection of propagation. In fact, this absence of thebackward momentum and the resulting net forwardand transverse forces are responsible for the abilityof the waves to propagate at all. Evidently, a wavetheory based on the Kinetic Theory of Gases leads todifferent results than a theory derived from themechanics of the transverse waves on a string.

For a strict distinction, it should be stated, thatthe kinematics of the transmission of sound-energythrough a gaseous medium must be described by atrain of periodical individual compression pulses,possessing both the longitudinal forward and all thetransverse components of the initial momentum.

Consequently, the mechanical theory, stating thatsound propagates through the longitudinal back andforth, harmonic oscillation of the atoms of the air isbased on total misconception.

This distinction could be all the more important,because the uncovered ambiguity of the MechanicalTheory might be the very sprout of the later misin-terpretation of the facts, which led science into thelabyrinth of the duality of light.

Indeed, this argument can be strengthened byuncovering another hidden contradiction within themechanical theory. Both classical and modernphysics imply that the mechanical theory of waves ina gaseous medium can readily explain the resonantoscillation of the receiver, simply because the parti-cles of the medium are directly conveying the oscil-lating energy of the source, by themselves movingback and forth in harmonic oscillation.

299


This assumption, however, leads to ambiguitieswith respect to the pressure of waves, or their abilityto produce translational acceleration of freely float-ing particles in the direction of propagation. For ifthe atoms of the gas performed harmonic back andforth oscillations, they would have equal momentumin opposite directions and therefore the total netforce exerted by the passing waves at any point ofspace would be zero.

Hence, on the one hand, the mechanical theory,takes it as self explanatory, that harmonic wavesdirectly transmit the kinetic energy of an oscillatingsource to the receiver, but it fails to explain the otherpossible interactions between matter and waves.

On the other hand, the net forward momentum ofthe kinematic theory can readily explain the pres-sure of waves and the translatory acceleration of freeparticles by the momentum of the periodical pulses,but it must come up with an alternative explanation,how this momentum can produce the exact resonantsimple harmonic oscillation at the receiver.

The kinematic explanation for the conveyance ofthe oscillatory energy between source and receivermust be achieved without assuming the harmonic

oscillation of the particles, and based solely on theforward momentum of the periodical individual com-pression pulses. Taking sound, produced by the sim-ple harmonic oscillation of a tuning fork, the ques-tion is, how can the net forward force of a train ofcompression pulses reproduce the same exact simpleharmonic oscillation of the eardrum without the sim-ilar oscillation of the particles of the conveying medi-um ?

Consider then the following:The elastic eardrum is completely submerged in

the gaseous medium of air and in silence the mem-brane stands still in its equilibrium position, receiv-ing isotropic atmospheric pressure.

When the first compression pulse arrives, themomenta of the migrating atoms push the mem-brane inward, in the direction of propagation. As it isdisplaced from the equilibrium position, the distortedelastic membrane tends to restore its initial state.

As the compression pulse is partially reflectedfrom the drum, it receives again normal pressure.Meanwhile, the restoring force of the elastic mem-brane not only moves it back to the equilibrium posi-tion, but because of its inertial mass and elasticity, it

300


over-shoots in the opposite direction beyond its ini-tial position into the oncoming rarefied layer with anequal displacement.

The next layer is again normal density and themembrane swings back toward the center. Since therestoring force is proportional to the extent of thedisplacement, and the period of oscillation is inde-pendent of the amplitude, the motion of the mem-brane should be synchronous with the on-comingperiodic pulses. Consequently, the next compressionpulse arrives exactly at the time when the mem-brane reaches its original mid-position. The pulseexerts the same inward force as before, but at thistime the membrane already has a momentum in thesame direction, consequently the same net force pro-duces a greater displacement than before in the di-rection of propagation.

From here on, this whole procedure repeats itselfperiodically. The result is a gradual increase in thedisplacement of the membrane in both directionsuntil the net forward force of the compression pulseis equalized by the restoring force of the membrane.At this point both the initial amplitude and frequen-cy of the oscillation of the source are reproduced in

the simple harmonic oscillation of the receiver.Hence, the simple harmonic motion of the oscillatorof the source is reproduced in the resonance of thereceiver by a periodical net forward force, withoutthe necessity of assuming that the particles of themedium perform simple harmonic oscillation.

Thus, the kinematic theory of periodical pulses,based exclusively on the net forward momentum ofthe compression layers render a simple explanationfor both the reproduction of the harmonic oscillationin the receiver and the capability to exert pressureon matter or produce translational acceleration ofmaterial particles floating freely in the transmittingmedium.

The difference between these two phenomenasimply originates from the different specific state ofthe bulks of matter, affected by the compression puls-es. Both the small free particle and the massive oscil-lator accumulate their velocities from the periodicalforward momentum of the pulses, but while the freeparticle is able to continue to accelerate in the samedirection of the propagation, the massive receiver iscompelled to oscillate under the influence of its ownelastic restoring force.

301


HUYGENS' PRINCIPLE −KINEMATIC INTERFERENCE

The methods of the Kinetic Theory can clarifysome other unresolved problems of the classical wavetheory of light, which originates from the ambiguous-ly assumed simple harmonic oscillation of the parti-cles of the conveying medium.

Opposing Newton's corpuscular theory, in 1678Christian Huygens, Dutch physicist, proposed thewave theory of light, which simply suggested thatlight is a periodic disturbance in the all-pervadingsupermundane, gaseous medium of the aether, justas sound is such disturbance in the air or other fluidmedia.

The central idea of this theory was the so-calledHuygens Principle, which hypothesized, that eachinfinitesimal part of a spherical compression wavefront acts as a new point-source, producing secondarywavelets, which propagate outward with equal speedin all directions.

As a result of this assumption, by the simple geo-metrical construction of an envelope, projected at thesurface tangency of these secondary wavelets it

became possible to predict where a given wave-frontwill be at any time in the future if its present posi-tion was known.

One of the decisive factor in choosing betweenNewton's corpuscular theory and Huygens' wave the-ory was answering the question whether the speedof propagation of light should be lower or higher as itenters into a denser media. According to Newton thelight corpuscles should speed up in the denser medi-um, while Descartes assumed that the waves shouldslow down. The choice was forced by Jean BernardFoucault's experiment in 1850 when he proved con-clusively that light is propagated more slowly inwater than in air.

As an example, Figure 14-12 shows the HuygensConstruction, representing the spherical propagation(a) and the phenomenon of refraction of light (b)based on the assumption that the speed of propaga-tion of light is smaller in glass than in air. When abeam of light enters into the denser medium, eachsecondary wavelet slows down, their consecutive tan-gential envelopes shows a deviation toward the nor-mal from its original direction, and a decrease of theinitial wavelength.

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Aethro-kinematics CHAPTER FOURTEEN Huygens’ Principle − Kinematic Interference


The arrows erected as the radii of Huygens' sphe-rical waves and those representing plane waves ingreat distances from the source became the funda-mental concept of geometrical optics, called the ray oflight. Young's famous double-slit experiment of inter-ference and his mathematical derivation of the posi-tion of the interference fringes and that of the actualwavelengths of light, was also based on Huygens'geometrical construction.

After Young's success in explaining interferenceof two light beams by Huygens' wave theory of light,

his contemporary, Augustine Fresnel applied thesame theoretical and mathematical approach to thephenomenon of diffraction.

According to Fresnel, diffraction, which is thebending of the light beam into the geometric shadowof a opaque object, is a form of interference amongHuygens' secondary wavelets. These elementary ra-diators are at different distances from a given pointon the screen and therefore the secondary waveletsarrive to the same point in different phases. Thisresults in constructive or destructive interferenceamong the wavelets and produce light and dark dif-fraction bands within the geometrical shadow on thescreen. It follows, that Young's mathematical analy-sis of interference is also applicable to the phenome-non of diffraction.

Hence, Huygens' simple principle was capable toexplain not only the propagation of light, but its vari-ous interactions with transparent matter and there-fore became the fundamental tool of theoretical, geo-metrical and mathematical optics.

Nevertheless, there was no clear understandingof the physical reasons why this hypothesis shouldwork. In fact, there is still an unresolved contradic-

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Aethro-kinematics CHAPTER FOURTEEN Huygens’ Principle − Kinematic Interference

v1

v2

N

N

SOURCE

C

tion, generated by the assumption of the mechanicalwave theory, that longitudinal waves are propagatedthrough the back and forth oscillation of the particlesof the medium. Based on this assumption, and con-trary to observation, it may be expected that the sec-ondary wavelets of Huygens should radiate back-ward as well as forward from each point of the sec-ondary sources.

This problem has never been resolved but merelysuspended by the acceptance of Huygens' secondintuitive assumption, that the intensity of the sec-ondary wavelets are not uniform in all directions butvary gradually from a maximum in the forward di-rection to zero in the backward direction.

THE MOMENTUM AMPLITUDEBased on the above kinematic theory of periodic

compression pulses, a simple thought-experimentand its mathematical analysis can prove thatHuygens' ad-hoc hypothesis is in agreement with thefundamentals of the Kinetic Theory of Gases.

As it has been found before, in the totally ran-dom motion of the particles in an undisturbed,isotropic ideal gas, the position of each individual

particle can be taken as the center of its oscillationwithin its own collision-free sphere. Thus, on theaverage, each particle can be assumed to be at restrelative to the isotropy of the medium. Superimposedon this symmetrical arrangement of rest any locallyintroduced disturbance must result in an excessmomentum of some particles in a specific direction. Itfollows that the transfer of this excess momentumcan be described as the simplest kind of collision;namely, between pairs of particles of equal masses,one moving, and one at rest.

When a collision occurs in one dimension, the lineof motion of the moving particle leads through thecenter of the target particle. In case of a perfectlyelastic collision the particles simply exchange veloci-ties. The projectile particle stops and the target parti-cle takes off with the total initial momentum of thefirst. As it is illustrated on Figure 14-13 (a-b-c) in twodimensional collisions, the direction of motion of theprojectile, O2, can always be related as a parallel lineto the direction of the line going through the centerof the target particle, O1. The distance between thetwo parallel lines is called the impact parameter, b.In one dimensional, head-on collisions b = 0.

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Aethro-kinematics CHAPTER FOURTEEN The Momentum Amplitude

When b > 2R, twice the radius of the particles,there is a complete miss. When b > 0 and b < 2Rthen, through the collision, certain components of theinitial momentum are inherited by each particle

Figure 14-13Since all particles have equal masses, based on

Newton's third law and on the law of conservation ofmomentum, the speeds and directions, that is, thefinal momenta of the two particles after collision canbe calculated from the initial momentum and themagnitude of the collision parameter, b. As for themathematical analysis of the probabilities of the

momenta of the particles after collision, consider thefollowing initial assumptions:

a) All particles of an ideal gas are taken as equalmasses, therefore m represents the unit mass.

b) The spatial dimensions of the particles are thesame; perfect spheres with equal radii, R.

c) The collisions are perfectly elastic and friction-less.

d) In the simplest type of collision particle O1 isinitially at rest, thus its momentum, mV1 = 0. Par-ticle, O2 is in motion with a given velocity, its mo-mentum is mV2.. The total momentum of the system,before collision is: mV1 + mV2 = mV2

e) The collision parameter, b is the distancebetween the two parallel lines going through the cen-ters of the particles in the direction of the initialmomentum, mV2.

f) When b = 0, then the two parallel lines coin-cide. It is then a head-on collision and the particles,O1 and O2 simply exchange velocities. Thus, aftercollision mU1 = mV2 and mU2 = mV1.

g) In the example of Figure 14-14, b > 0. In illus-tration (b) O1O2 is the line connecting the centers ofthe two particles at the instant of collision.

305


b

O1

O2

b

O1

O2

b

O1

O2

(a) (b) (c)

The length of this line is 2R, and it also containsthe point of contact, C .

h) Through the impact point O2 exerts a force onO1 which acts along the line O1O2. According toNewton's Third Law O1 also exerts a force on O2. andthe two forces are equal in magnitude and oppositein directions.

(a) Figure 14-14 (b) It follows from all above, that through the colli-

sion O2 transfers the component of its momentum toO1 in the direction O1O2 and moves away with the

remaining component of the initial momentumwhich is rectangular to that, transferred to O1.

From the Law of the Conservation of Momentum,it follows, that the total resulting momentum of thesystem after collision is: mU1 + mU2 = mV2.

From trigonometrical considerations, it can beseen, that

mU1 mU2

−−−−− = sin θ and −−−−− = cos θ (14.4) mV2 mV2

thus,mU1 = (mV2 ) sin θ (14.5),

andmU2 = (mV2 ) cos θ (14.6)

As it has been stated before, the various resul-tant momenta of the particles after similar collisionsdepend on the magnitude of the collision parameter,b, which determines the angle between the directionof O1O2 , and that of the initial momentum, mV2.

As it can be seen, the triangle A,O1,O2 is exactlysimilar with the one before, and therefore the angle,θ is the same.

306


O1

b

O2

= 0

R

R O1

b O2

θ

θA

C

1VmU1m

2Um

2Vm

Therefore, in terms of b it can be found, that b b

cos θ = −−−−−−− = −−−−−−−, (14.7)O1O2 2R

and θ = arccos ( b/2R ), (14.8),

where θ is the angle of the velocity, mU1 of O1 aftercollision.

Further more,−−−−−−−− −−−−−−−−−−

sin θ = √ 1 − cos2 θ = √ 1 − b2/4R2 (14.9).

Substituting (14,9) into (14,6) gives−−−−−−−−−−

mU1 = mV2 sin θ = mV2 √ 1 − b2/4R2 (14.10),

where mU1 is the momentum of O1 after collision.The momentum of O2 after collision is the remainingcomponent of the initial momentum, mV2, and incase of equal masses its direction is always perpen-dicular to that of mU1 . Consequently,

mU2 = (mV2 ) cos θ = mV2 (b/2R) (14.11).

Figure 14-15 (a) illustrates the mathematicallyplotted probabilities of the velocity vectors of the tar-get particle O1, after collision, resulting from the dif-

ferent values of the collision parameter, b. This pat-tern is also valid for the resulting momentum of theprojectile, O2, which is the remainder of the initialtotal momentum, always directed perpendicular tothe direction of the target particle, O1.

(a) Figure 14-15 (b)Consider now an immense number of collisions in

three dimensions with all probable impact parame-ters between pairs of particles, due to a directionallocal disturbance, that is, the forward motion of anoscillator in an isotropic, gaseous medium.

307


Y

θ

Z

X

θX

θ

Z

On the average, the result of the transfer ofspeeds and directions should be a three-dimensionalformation of the probability plot of velocity vectors; asemi-hemisphere with its axis coinciding with thedirection of the initial forward disturbance.

Figure 14-15 (b) is a three dimensional renderingof such probability pattern, (X,Y,Z) which can betaken as a general representation of the momentumamplitude produced by a great number of randomlymoving particles colliding with one another, due to alocal directional disturbance in an isotropic medium.

It should be noted here that in the sense of theconservation law, once the directional disturbance isimprinted in the medium, this pattern of the momen-tum amplitude is transferred from one point of spaceto the other and in the course of the isotropic dissipa-tion it merely changes in magnitude but not in itsinitial directions.

Accordingly, the relative magnitude of the trans-ferred momenta remains the maximum in the longi-tudinal direction, or in the forward axis of the hemi-sphere, gradually decreases in the trans verse com-ponents, and reaches zero in the backward direction.

This description, which is based on the funda-mentals of the Kinetic Theory of Gases, is conceptu-ally equivalent with the Huygens Principle and notonly explains the total absence of backward waves,but also suggests the origin and proportionality ofthe commonly neglected transverse components ofmomentum in the longitudinal compression waves.

Thus, the transverse components of longitudinalcompression pulses and the general phenomenon ofkinematical interference serve as some new ingredi-ents for re-interpreting Young's ‘imperfect explana-tion of polarization without departing from the gen-uine doctrine of undulation’.

Since this periodical transverse momentum re-quires no transverse oscillation of the particles in themedium, the ideal-gas-model of Aether can be re-admitted, and the hypothesis of transversally oscil-lating electric vectors, together with the mysteriousabilities of empty space, can be replaced by thehumanly conceivable theory of AETHRO-KINEMAT-ICS. – Nevertheless, it should also be shown, thatthe kinematical procedure applied to polarization,leads to the same mathematical results as the theo-ry, based on the oscillating electric vectors.

308


POLARIZATION BY ABSORPTIONThere is an empirical law applying to the intensi-

ty of polarized light as affected by the polarizingapparatus. If a beam of light is plane-polarized by apolarizer and passed through the analyzer, the inten-sity (flux density) of the emergent beam falls off asthe analyzer is rotated. The intensity is the maxi-mum when the direction of transmission of the ana-lyzer coincides with that of the polarizer and it iszero when the analyzer is at right angles to thatdirection. Experiments showed, that the final inten-sity, I, is proportional to the square of the initialamplitude of the electric vector, Eo and varies as thesquare of the cosine of the angle, ψ, through whichthe analyzer was rotated.

I = Io cos2 ψ (14.12), This equation represents Malus Cosine-squared

Law, justified by the experimental facts.From all of the above it can be conjectured that

compression pulses are produced by simple harmonicoscillators and propagated in an isotropic compress-ible medium through the kinematic interference ofHuygens distribution. It is the initial forward mo-mentum of the oscillator that acts as a local distur-

bance and dissipated in the isotropic randomness ofthe fluid.

The momentum of the oscillator is kinematicallydispersed into its various components in differentdirections and amplitudes, the pattern of which isreproducing itself through the secondary waveletsand in their expanding spherical envelopes.

Thus, when it comes to the transverse theory oflight and polarization, there is no more compellingreason to assume an exclusively transverse oscillato-ry motion of the particles of a transmitting mediumand it is also needless to hypothesize about transver-sally oscillating electric fields in empty space.

The new concept of the three dimensional mo-mentum amplitude of the longitudinal compressionpulse, propagated in a real isotropic fluid can substi-tute the amplitude of the oscillating electromagneticvector in its role of explaining the characteristic pro-pagation of radiation in empty space. Nevertheless,although the two different concepts are mathemati-cally equivalent, in some respects they predict differ-ent results.

The conceptual distinction between the two theo-ries is indifferent as long as light is propagated in

309

Aethro-kinematics CHAPTER FOURTEEN Polarization by Absorption

the isotropy of Aether, or that of the nothingness ofempty space. When the secondary wavelets merelyinterfere with one another, the resulting envelope ofthe longitudinal and transversal components of theinitial momentum and its dissipation is in isotropicbalance with the general randomness of the medium.This kinetic state of the periodical compression puls-es in the Aether is equivalent with the random orien-tation of the electric and magnetic vectors in the so-called unpolarized light. The different theories, how-ever, lead to different explanatory results, when theywere applied to the interactions between radiationand matter, where the general isotropy of the kine-matical propagation is affected by the presence of theatomic structure of a transparent medium. One ofthese cases is the phenomenon of polarization.

Let us now recall the illustration of Figure 14-15(a), the two dimensional plotting of the probabilityenvelope of the momentum amplitudes resultingfrom the possible simple collisions between two equalmasses. In an isotropic fluid the forward momentumof a disturbance is distributed symmetrically in threedimensions and superimposed on the initial randommotions of the particles.

It is important to realize, that this pattern doesnot represent the momentum amplitude of a wavefront on a macroscopic level, but only that of an infin-itesimal volume of the medium at the order of mag-nitude of Huygens' secondary wavelets. The total in-terference result of these wavelets is the next tan-gential envelope of the pulse, which then reproducesthe same pattern of momentum amplitude in thenew secondary wavelets.

Figure 14-16.

310


Polarizer 1.

Analyzer

Polarizer 2.

(c)

Polarizer 1.

Analyzer

Polarizer 2.

(b)

Plane polarized light No light

Momentum Amplitude

x

y

(a)

Regenerated light

Unpolarized light

Illustration Figure 14-16 (a) shows in two dimen-sions the symmetrical pattern of the transverse mo-mentum amplitude of the secondary wavelets of acompression pulse, equivalent to unpolarized light.Illustration (b) depicts the result of an experimentwith natural, unpolarized light, that passes througha polariscope.

The transmission axes of both Polarizer 1 and 2set in the vertical direction and let only those compo-nents pass.

Evidently, the strictly horizontal component ofthe momentum has been absorbed. The Analyzer isset in the horizontal direction, therefore the angle ψis 90° and it absorbs the remaining vertical compo-nents; therefore no transversal momentum survivesand propagates beyond the Analyzer. However, it canalso be seen from the pattern of the momentumamplitude right before the Analyzer, that if the angleψ is smaller than 90°, the Analyzer would pass partof the transversal components.

Thus, there are two angles involved in the de-scription of the phenomenon with different mean-ings. Figure 14-17 shows the roles of the angles θand ψ in the explanation of polarization.

(a) (b) (c) Figure 14-17

Both angles are measured in the x, y coordinatesystem, were the direction of y equals 0°. and thedirection of x equals 90°. (a) shows that θ measuresthe magnitude and direction of the momentum amp-litude. (b) illustrates the angle between the transmis-sion angles of the Polarizer and Analyzer. (c) showsthe relation between the two angles, from which itfollows, thatθ + ψ = 90° and sin θ = sin (90° − ψ) = cos ψ.

Substituting sin θ with cos ψ in Equ. (14.9), wehave

mU1 = mV2 cos ψ (14.13)311


X

Y

θ

Y

X

ϖ

θ

Y

X

ϖ Polarizer

Analyzer

Considering that the amplitude of the electricfield, Eo transmitted by the polarizer is equivalent tothe momentum amplitude, Po, and considering alsothat the final momentum amplitude, Pf beyond theAnalyzer is

Pf = Po cos ψ (14.14). Since the intensity of light is proportional to the

square of the amplitude of Eo, it is also proportionalto the square of Po , thus,

Io = Po2 and I ≅ Pf

2 thus, I = Io cos2 ψ.With this, Malus' empirical law of polarization

has been derived from the kinematic principles ofcollisions among equal masses; in other words, it isexplained by the characteristics of the dissipation oflocal disturbances in an ideal gas.

This approach not only gives equal mathematicalresults, but better conceptual understanding of thephenomenon in those cases, where the hypothesis ofthe transversally oscillating electric vectors has nosatisfactory answers.

Recall the struggle of Dr.Goodstein and othermodern educators in explaining the partially de-creasing intensity in the case of the oblique angle of

the analyzer, and the even more problematic case,when the second obliquely inserted Polarizer 2.regenerates some of the already absorbed compo-nents of light.

The source of this inconvenience is the contradic-tory statement that the polarizer absorbs all electricoscillation of un-polarized light which are not paral-lel to its transmission axis, but when the analyzer isset at an oblique angle, it passes some light becausethe survived electric vectors, parallel to the polarizerstill have some components in the direction of thetransmission axis of the analyzer.

The misconception comes from the erroneous useof the concept of vector components. Theoretically avector, placed into a cartesian coordinate system, inan oblique angle to both the x and y axes, can beexpressed in its rectangular component along thoselines. However, in the above described explanation ofpolarization in the first part of the statement a spe-cific coordinate system has been set relative to thetransmission axis of the polarizer for describing thecomponent vectors for both the omnidirectional nat-ural light before passing, and those for the unidirec-tional plane polarized light after passing.

312


In this coordinate system, all component vectorswere supposed to be absorbed except those, parallelto the y axis.

Evidently, there is no logical or in any way right-ful reason to rotate the coordinate system from itsoriginal direction, and thereby revising the initialvector components. Evidently, it is done just for thesake of the justification of some partially survivingcomponents in the transmission axis of the analyzer.

The contradiction in the regenerated light, by theinsertion of a second polarizer, springs from the samemisuse of the theory of vector components. If boththe polarizers and the analyzer were rotated in thesame initial coordinate system, as they should be, thepresent hypothesis of polarization could hardly ex-plain the partial decrease of intensity and even lessthe regeneration of light by the insertion of the sec-ond polarizer.

Recall illustration Figure 14-16 (c) showing thatthe kinematic theory neither uses oscillating vectorsnor the total absorption of all un-parallel componentsof the initial momentum. It rather shows, in agree-ment with the Huygens Principle, that beyond thepolarizer part of the absorbed components of the

momentum was recreated by the kinematic interfer-ence between the Aether particles at different ampli-tudes in different directions, and only the exactlyhorizontal component is zero. This is an entirely dif-ferent conceptual result, which allows the explana-tion of both the phenomena of the partial decreaseand the regeneration of the lost intensity.

And most importantly, in the kinematical de-scription of polarization by absorption all these pro-cedures happen, and being explained unambiguouslyin the one and the same coordinate system, that isinitially introduced .

POLARIZATION BY REFLECTION It is evident, that this study cannot and does not

get involved with all the details of a given physicalphenomenon and their presently accepted explana-tion, but only those aspects, whose clarification isneeded or useful for the general reinterpretation ofthe phenomenon by AETHRO-KINEMATICS.

The phenomenon of polarization by reflection ismerely another form of that by absorption and it isfully covered by the above conceptual and mathemat-ical argument. Still, it is worthwhile to analyze kine-

313

Aethro-kinematics CHAPTER FOURTEEN Polarization by Reflection

matically, for it brings up a different aspect of thenature of interactions between light and transparentmatter. Also, for the sake of the plausibility of theideal-gas-model of the Aether, it is important to findthe exact logical conclusion, which lead to the trans-verse wave theory of light. The following text, whichdescribes this logical procedure is quoted from M.Ference: Analytical Experimental Physics,1956 [539]"Suppose we take a plain piece of ordinary glass, ①

having a refractive index µ = 1.55, and use it as amirror to reflect light from a candle flame or lampbulb, S. We will furthermore make a special selec-tion of the angle of incidence measured from the nor-mal of the glass, 57.2°. (Figure14-18 (a))


"We next take another piece of glass, ➁ and arrangeit parallel to the first, but placing it in a way that thereflected beam from the first glass is incident on thesecond again at 57.2°. "Looking at the light source reflected from both mir-

rors, nothing unexpected can be found: the reflectionsare entirely clear, bright, and distinct."Next we rotate the second mirror through 90° with

the ray between the two mirrors as an axis (Figure14-18 (b)). If we had been precise in making theangles as indicated, no trace of the light source re-mains ! One cannot form a virtual image of a virtualimage with two mirrors in these positions."Our choice of 57.2° for the angle of incidence on the

glass ① of index µ = 1.55 resulted in the refractedrays taking a direction at right angles to the reflectedray. This results in some sort of modification of thereflected light beam, so that it cannot be reflectedwhen at the next reflection it encounters the mirror➁, where the PLANE OF INCIDENCE is at rightangles to that of the first reflected ray from mirror ①."To understand how this can be, we have but to

assume that the light contains no longitudinal com-

314


θ θ

N

N

θ θ

θ = 57.2 Ο θ = 57.2 Ο

θ θ

N NS S➁ ➁

① ①

ponents, i.e., that its vibrations are exclusively trans-verse."Natural light has vibrations in all directions per-

pendicular to that of its propagation. Since any ofthese directions can be resolved into its componentsalong any arbitrary rectangular axes, we can repre-sent natural light as consisting of only two vibrationsat right angles (Figure 14-19 (a)).

Figure 14-19 "On encountering the glass of mirror, ① on illustra-

tion (b), the direction of the reflected ray is such as to

be identical with that of one of the two components ofthe vibration of the light as it becomes refracted atthe surface."If this vibration were transmitted, it would be lon-

gitudinal in character, i.e., have the direction of thewave's propagation. If it were not transmitted, thereflected ray would contain vibrations at right anglesto the plane of the figure only, i.e., would be planepolarized."Upon the second reflection, (c) with the plane of

incidence now 90° from its previous position (b), theresidual beam now encounters the mirror ➁ so that,if it is reflected its only remaining vibration directionlies in the direction of the reflected ray. Light thusreflected would consist exclusively of a longitudinalcomponent. The complete absence of any light in thisdirection clearly establishes the complete inability fortransmission of any LONGITUDINAL components inradiation."Thus the experiment establishes the transverse cha-

racter of light.If the angle of incidence, i, of Figure14-19 is such that the reflected and refracted raysare at right angles to each other, then it follows fromthe geometry of the figure that

315


(a)

N

N

(b)

90o

(c)

No light

①

②

i

i

µ = tan i. (14.15)"This equation is known as Brewster's law, which

states that the angle of incidence for complete polar-ization is that critical angle whose tangent is equalto the index of refraction of the reflecting material."

Note some of the conceptual ambiguity in thisdescription:

a) The foundation of the above conclusion is, thatthe transverse components of light can be resolved inany two dimensional rectangular coordinate system.This assumption already omits any longitudinalcomponent, which would be in the third dimension.This is, of course, false, since it is accepted by bothclassical and modern physics, that light delivers lin-ear momentum, which is called light-pressure.

b) The final conclusion is based on the secondreflection, where it is expected, that the remainingtransverse components should continue in the direc-tion of reflection, which would also be in the directionof propagation; that is, it would be a longitudinalcomponent. This is equal to the expectation that oneof the two-dimensional components should enter intothe third dimension. Thus, the conclusion is based onan absurd expectation.

The empirical facts merely show, that at Brew-ster's angle one of the transverse components of nat-ural light which is parallel to the plane of incidence,is totally refracted. Therefore, the emerging reflectedbeam from the first mirror contains none of thoserefracted components. This fact does not exclude thepossibility of a longitudinal component, which waspartially refracted and partially reflected, changingdirections differently. Since the second mirror isrotated relative to the beam, it totally refracts theremaining transverse component and propagates inthe glass by the remaining longitudinal component.Obviously, no light could be detected in the directionof reflection.

Attempting a kinematic analysis of the problemfrom this point of view, the first inquiry should beabout a plausible explanation of the phenomenon ofrefraction.

In classical physics most optical phenomena, likereflection, refraction, diffraction and dispersion aresimply analyzed and predicted by the Huygens prin-ciple and its geometrical construction. Two of these,refraction and dispersion are closely related andtheir analysis require the special assumption, that

316


the speed of propagation of light is lower in a trans-parent medium than in vacuum. This retardation inthe speed of propagation of light is not only propor-tional to the density of the medium, but also propor-tional to the frequency of the light.

Comparing to the speed of light in vacuum theretardation of the propagation is directly proportion-al to the density of the transparent medium and themagnitude of the frequency. These are the empiricalfacts, which were accepted by both classical and mod-ern physics as simply the nature of light. Neither ofthe languages that describes the phenomena at-tempts to explain the cause, or mechanism of thisselective retardation based on frequency.

In fact, the same phenomena also exist in simplemechanical waves, like water-waves or sound andused as explanatory analogies for the refraction anddiffraction of light but without giving a mechanicalexplanation for themselves. (Figure 14-20.)

Consider the following quote from Joseph &Leahy, Programmed Physics, 1966 (Optics 174):"The speed with which waves travel through water

depends on the depth of the water. When waves are

generated at C in a ripple tank, they travel from C toA and from A to B at different speeds."

Figure 14-20."When waves travel at different speeds in the same

substance (such as water), we say that they are trav-elling in different media. When water waves travelfrom water at one depth into water of greater or lessdepth, we say that they are moving in differentmedia." (The speed is lower in shallow water.)"Waves generated at the bottom of the Figure (14-

21, next page) are moving through a ripple tank intowhich a rectangular plate of glass has been placed.The water above the plate glass represents a secondmedium. The incident waves strike it obliquely andbend away from their original direction.

317


A B C

GLASS PLATE

Figure 14-21The incident waves are bent when they pass over

the glass plate because water waves travel at differ-ent speeds in water of different depths. This is analo-gous to the refraction of light rays as they pass ob-liquely from one medium to another."

The diffraction of water waves in a ripple tank,another analogy, seems to be a phenomenon of en-tirely different character. Consider Figure 14-22,illustrating the diffraction of plane water waves of

same wavelengths, passing through gaps of differentwidths.

The empirical factis, that the extent ofthe diffraction, that is,the spreading of thewaves into the geo-metrical shadow of thebarrier depends onboth the width of thegap and on the wave-length of the waves.When the size of thegap is several timesthat of the wave-length, there is only asmall bleeding into thegeometrical shadowbeyond the barrier.

As the width of thegap is decreased, thediffraction phenomenon increases and the emergingwater-waves show proportionally more spreadingand curving into the geometrical shadow. When the

318


(a)

(b)

(c)

Figure 14-22

width of the gap is compatible with the wavelength ofthe waves, the diffraction effect is maximum, and thegap becomes a point source. In this case the wavespropagate in half circles, covering the whole spacebeyond the barrier.

Augustine Fresnel showed experimentally thatthe result is exactly analogous when a train of planeelectro-magnetic waves pass through a slit, which iscomparable with their wavelength. − The scientificknowledge of these phenomena is purely empiricaland there are no real attempts in classical physics toexplain its mechanical origin. It has been simplyaccepted as the nature of the waves. Nevertheless, adetailed analysis of this phenomenon brings up somereasonable questions and possible answers.

First, note that the width of the gap is transverseto the direction of propagation, and the fact that thesize of the gap can alter the extent of diffraction sug-gests that there is an interaction between the solidbarrier and the transverse components of pressurecarried by the longitudinal compression pulses.

Also recall the kinematical analysis of the mo-mentum amplitude of Huygens wavelets whichshows that just by the random probability of the col-

lision parameters, each point source ought to producesome transverse pressure within the longitudinalcompression pulse.

Searching for some mutual characteristics bet-ween the refraction and diffraction experiments withwater waves, it can be found that in this case of re-fraction, the depth of the water acts as a vertical gap,and determines the extent of the diffraction, just likethe width of the horizontal gap did it before.

In both cases the deciding factor is the transverserestriction of the volume of the medium, throughwhich the longitudinal compression pulse must pass.Evidently, this restriction has a major effect on theformation of the continuing waves.

For a general simplification of the problems, hyd-rodynamics assumes that water is incompressiblewhich, in this case, cannot be allowed, since the veryexistence of the wave phenomenon is a result of com-pressibility. All fluids are compressible, and theslightest change in their local density increases theinternal and external pressure of the volume invol-ved. It is therefore plausible to assume that the re-tardation of the propagation of the waves in the shal-low water and the flaring out of the waves by the

319


smaller gaps in the barrier, are both caused by theextra density produced within the restricted volumeof fluid by the transverse components of pressure,carried in the compression pulses and reflected bythe obstacles.

When a train of plane pulses reach a solid barrierat a normal angle, they are simply reflected andpropagated backward in the opposite direction. TheHuygens Construction guarantees that all compo-nents of the momentum amplitude are reproduced bythe elementary point sources in the opposite direc-tion. This guarantee should also work when there isan opening in the barrier, where parts of the pulsesare reflected, while other parts can pass beyond.What happens in this case of the transverse compo-nents of momentum?

The flaring out of the pulses beyond the barriersuggests that their restriction by the gaps exagger-ate the transverse pressure which is inversely pro-portional to the ratio between the size of the gap andthe wavelength of the pulses.

The reflections from the edges rapidly dissipatein the medium, and therefore when the gap is great,the transverse reflections only effect the behavior of

the passing pulses in the vicinity of the edges. But,when the width of the gap is comparable with thewavelength, the reflections of the transverse compo-nents fill up the medium from both sides of the gap.The resulting density fluctuation within the gap pro-duces local variation in the index of refraction of themedium and causes the diffraction of the passingcompression pulses.

Quite certainly, some of the transverse compo-nents will be reflected parallel to the barrier and ifthe gap is small enough, they will be trapped in themedium within. The wavelength dependence of themagnitude of both refraction and diffraction effectssuggests that there is a possible formation of stand-ing waves within the gap by the transverse reflectionof the pulses.

In this respect, not only the restricted volume ofthe medium is a factor, but also the transverse prop-agation of the standing waves which, being a func-tion of time, must be dependent on the frequency ofthe periodical arrival of the compression pulses.

According to AETHRO-KINEMATICS light is atrain of periodical compression pulses, carrying bothlongitudinal and transverse momenta, transmitted

320


by the isotropic ideal gas of Aether, through all space,including that, within the interstitches of the atomicstructure of macroscopic matter.Thus, applying theabove analogies to the refraction and diffraction oflight, in transparent media, the only necessary as-sociation is to realize, that for the compression pulsesof light the atomic and crystalline structure of mac-roscopic matter is a mash of gaps and channels, filledwith the ideal and compressible gas of Aether.

Figure 14-23

Figure 14-23 illustrates the optical phenomena ofreflection and refraction, as the compression pulsesof light enters obliquely from air to glass and back toair. All space is filled with Aether of different densi-ties, including the space of air and the space of theatomic structure of the glass. The small white arrowsbetween the atoms represent the transverse reflec-tion of the pulses, the resulting excess local densityof the medium, and the consequent retardation of thepropagation of the pulses.

The denser the transparent medium is, and themore pressure is forced through the crystalline chan-nels, the greater the retardation in the speed of prop-agation. It simply follows, that the excess pressuredelivered per unit time is also a factor and conse-quently the higher frequency light is retarded moreand deviated more than the lower ones. This is thenthe kinematics of the phenomenon of dispersion. (InApp.IV there is a detailed discussion of this topic andits cosmological importance.)

The general hypothesis can be strengthen by therecollection of the AETHRO-KINEMATIC interpre-tation of the Lorentz Formula, that the resistanceagainst the motion of a body through Aether is pro-

321


NORMAL

incidence = 45

Angle of

°

portional to the speed of the body and the speed ofdissipation of the disturbances in the medium.

The kinematic reason for these effects has beenestablished by the theory of the Mach-number ofAero-dynamics. When the speed of a body approachesthe speed of dissipation of the disturbances, themedium can no longer carry away the excess densityand its resistance increases by the ratio between thetwo velocities. In this case the speed of dissipation inAether is the speed of light and the moving body isthe excess momentum carried by the compressionpulses, which also propagates with the speed of light.The result is an excess density and a local retardationin the speed of propagation of the pulses and conse-quently a change in the local index of refraction.

Finally, getting back to the kinematics of polar-ization by reflection, some further assumptions mustbe considered. – From all sources the general scien-tific description shows, that compared to their owndimensions, the atoms are at immense distancesfrom each other even in the most dense chunks ofmacroscopic matter. The volume occupied by theatoms compared to the total volume of the matterthey form, is negligible.

Nevertheless, atoms are kept together in mole-cules and those in crystals by electromagnetic forces,acting over relatively great distances. According toAETHRO-KINEMATICS these forces are communi-cated by organized and interconnected dynamic pat-terns within the otherwise isotropic Aether medi-um.When this picture is rendered for the variousinteractions between radiation and matter, some pos-sibilities emerge for plausible, though extremely sim-plified, kinematic explanations.

It has been described above how the compressionpulses, when entering into the mash of crystallinestructure, create some excess pressure within thegaps and by retarding their own propagation in themedium. Similar should be the case with the phe-nomenon of reflection. A beam of light cannot bereflected by the minimal bodies of the atoms, but atmost merely scattered by them. Thus, reflection mustbe done by something else.

Based on all above, it is plausible to assume, thatlight is reflected from matter by a boundary layer,which separates the internal and external medium.This layer acts similarly as the surface tension layerbetween air and water. Again, the compression puls-

322


es themselves deliver the momentum to this layer,which bounces back the oncoming pulses accordingto the kinematics of the Huygens distribution. Thus,visualizing a simplified version of both refraction andreflection and the momentum amplitude of compres-sion pulses, an attempt can be made to explain polar-ization by reflection through the changing effects ofthe various angles of incidence of light on its ownpropagation within the gaps and grids and channelsof the structure of macroscopic matter.

Figure 14-24 (a) illustrates the three-dimensionalversion of the momentum amplitude, characteristicof the propagation of locally induced disturbances iniso- tropic fluid media. All the transverse componentsof momentum are resolved in the two rectangularplanes of ZX and ZY.Illustrations (b), (c), (d) areseparated into two parts, showing the side view andthe top view of a single atomic layer, or a single crys-talline plate of the transparent material.

On illustration (b) the angle of incidence, q = 0,which is normal to the surface. The top view, fromthe direction of the source shows that the width ofthe channels between the atoms are equal in boththe X and the Y directions. Figure 14-24 (a)-(b)-(c)-(d)

323


Side view

Top view

°Angle of incidence = 0

θNORMAL

θ θ

Y

X

X

Y

(a)

(b)

NORMAL

Side view

Top view

NORMAL

(c)

NORMAL

θ

Side view

Top view

NORMAL

NORMAL

θ

(d)

°Angle of incidence = 30

°of polarization = 57.2Brewster's angle

Z

(c) illustrates that, keeping the source in thesame position, when the plate is tilted to θ = 30°,there is a considerable decrease in the width of thecrystalline channels in the Y direction, while thegaps in the X direction remain the same.

At θ = 57.2°, on Figure 14-24 (d), the Y channelsare practically closed. The X channels are still un-changed. Thus, the X components of the momentawere mostly refracted, while the Y components weremostly reflected. – All the above suggest, that de-pending on the density of the transparent mediumand on the specific angle of incidence, there exists atotal refraction of the transverse component, whichis parallel to the plane of incidence and leaving thereflected beam with the Y component only.

This light is called, plane polarized. As for thelongitudinal components of momentum in the Z axis,the actual forward momentum which drives thepulse in its propagation, it has been shown by thethree dimensional plotting of the momentum ampli-tude, that the genuine Z component is a very smallpercentage of the total. However, without exemption,all vectors in both the Z-X and Z-Y planes are com-posed from much greater longitudinal than trans-

verse components of the total initial momentum. Inthe free Aether these compositions of the longitudi-nal and transverse momentum produce the sphericalexpansion of the compression pulses.

When light enters into the internal Aether, thatpervades the gaps and channels of transparent mat-ter, the resulting excess density of the boundarylayer separates the total momentum according to theoblique angles of the components.

One part produces Huygens secondary waveletswithin the glass, where they are retarded and conse-quently the beam is refracted. The other part of thecomponents rebound from the compressed boundaryand the Huygens wavelets reproduce the pulses inthe proper angle of reflection.

Thus, the kinematics of Malus' polarization byreflection can be described as follows:

Both mirrors are tilted to an angle with the di-rection of propagation of the beam in such a way thatthe channels of the crystalline structure are onlyopen for the transverse components which are paral-lel to the plane of incidence. This part of the beamenters into the body of the glass to be refracted. Therest of the beam continues in the reflection. In the

324


example, at the first glass all X components wererefracted and only the Y components were reflected.By tilting the second mirror into the same angle, butrotating rectangular to the initial plane of incidence,the channels were only open for the Y components,and they were refracted in total. Since in the beam,at that stage there were no surviving X components,there was nothing to be reflected. The light wastotally polarized.

As it has been established earlier, in the case ofpolarization by polaroid sheets (or crystals) the theo-ry of the kinematical distribution of the transverseand longitudinal components of the momentum givesequivalent mathematical results with those of thepresently accepted theory. The same is valid forMalus' polarization by reflection, or rather, that ofpolarization by refraction. The difference is the con-ceptual understanding gained by the derivation ofthem from kinematic or dynamic principles.

This heuristic hypothesis of polarization, right orwrong, is presented with the intention to make onemajor point:

The presently accepted explanation of polariza-tion is ambiguous and blocking all plausible models

of the Aether, as a transmitting medium for electro-magnetic waves. The ruling hypothesis paralyzes thesearch for alternative explanations of the more gen-eral and major physical phenomena, like gravitation,inertia, electricity, magnetism, and also those of thepostulated and accepted relativistic mysteries, likeabsolute speed of light, space curvature and massincrease, etc.

At the very least, the presently accepted solutionof polarization should be suspended until a reason-able doubt about all other possible alternatives hasbeen established. The polarization file of wave-opticsshould not be left closed and forgotten, as so manyothers, but kept wide open for the inquiry of open sci-entific minds to search alternative solutions for thecrucial ambiguities of modern physics. − Prejudiceis the same retarding force, whether it has been for-med centuries ago or a day before yesterday.

325


CHAPTER FIFTEEN

THE UNDULATION OF LIGHT

ELECTROMAGNETIC OSCILLATIONLet us assume, that the foregoing chapters have

established the admissibility of the isotropic, all-per-vading, ideal-gas-model of the Aether as the conveyerof light and, in general, all electro-magnetic radia-tion. Thus, based on the above presented kinematictheory of wave-motion, and in strict analogy withsound, AETHRO-KINEMATICS suggests that radia-tion is a train of locally induced periodical density

disturbances, or compression pulses, which kinemati-cally dissipates in the all-pervading isotropic gaseousmedium of Aether.

Thus, the task of this chapter is to describe thekinematical equivalent of electromagnetic oscillation,its role in producing the local compression fluctua-tions, and to uncover the kinematics of the resultingresonant oscillation at the receiving end.

In the following, an heuristic theoretical attemptis offered to describe the origin of the compressionpulses of radiation based on the earlier suggestedkinematic theory of wave-motion, together with thelogically connected circulatory patterns of the Aether,derived through the kinematic description of electricand magnetic phenomena, presented in ChapterTwelve.

Since Maxwell and Hertz, light is taken as a cer-tain range of electromagnetic waves and its origina-tion is usually introduced by the description of elec-tromagnetic oscillations.

Two spherical metal conductor separated by aspace that does not conduct electricity represent adevice, which can store opposite electrical chargesand called a capacitor.

326

Aethro-kinematics

A most modern and somewhat mysterious de-scription of this phenomenon is found in Gamov's,Matter, Earth and Sky (121):

Figure 15-1.

"If we take two spherical electric conductors andgive their surfaces opposite electrical charges, wewill have to do work in some way to pull electrons offthe surface we charge positively and to force excesselectrons onto the surface we charge negatively. If welook to see where this work has gone, we will findthat it is stored in the electric field which now existsbetween the two conductors. Suppose we connectthese conductors by a piece of wire (Fig. 15-1 (a))."The opposite charges on the spheres will begin to

be neutralized by the flow of electric current fromone to the other, and as the charge on each spherebecomes less, the electric field between them willalso decrease."We may ask now, what happens to the energy

stored in the electric field as the field becomes weak-er? The answer is that we can find this missing ener-gy stored in a magnetic field that has been createdby the current in the connecting wire (b). In (c) wesee the situation when the charges have been com-pletely neutralized; the electric field vanished and allof its energy is now in the magnetic field. There is nodifference in charge to keep the current flowing, andif this were all, the current would stop.

327

Aethro-kinematics CHAPTER FIFTEEN Electromagnetic Oscillation

a

b

c

d

e

“But Le Chatelier's principle now goes to work tomaintain the status quo, i.e., to prevent the currentfrom stopping."Hence, the magnetic field delivers its stored energy

back into the wire to keep the current flowing, (d),and the charge begins to build up on our spheres inthe opposite direction. Finally, when the magneticfield has been reduced to zero, the current stops, andwe have the same situation, (e) we had in the begin-ning, except that the sign of the charges has beenreversed."Now, of course, the whole cycle will repeat itself in

the reverse direction, and again, and again, and soon."Part of the energy of our oscillating electric circuit

will go into creating 'electromagnetic waves' radiat-ing into space. From the point of view described inthe previous section, we can say that the 'lumps' ofjelly-like electromagnetic field material vibrating inthe space surrounding the two spheres are torn awayand travel freely in the space beyond."Here again, a propagating electromagnetic wave

should be visualized as a vibrating lump of electro-magnetic field material flying through empty space

rather than as the propagation of an elastic deforma-tion in some all-penetrating medium."

Before getting into the details of an alternatekinematical description of the phenomenon, some ofthe already established AETHRO-KINEMATICALconcepts should be recapitulated.

One of the general conclusions has been formu-lated through the kinematical descriptions of thebattery, the electric current, and the magnetic fieldaround a current carrying conductor. The generalclassical assumption of the existence of the action-at-a-distance forces of attraction and repulsion betweenopposite electric charges was shown not to be neces-sary for the kinematic explanation of the electroncurrent. Once the circulation of the Aether in the con-ducting circuit and the battery was conceptually jus-tified by the chemically induced sink and source sys-tem, both the continuous circulatory drift of the freeelectrons, and the magnetic field around the conduc-tor was fully explained.

In fact, this kinematical description resolves sev-eral confusing contradictions of the old theory, in-cluding the mysterious migration of the electronsthrough the liquid back to the negative terminal in

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spite of the alleged attraction by the protons of thepositive terminal and in spite of the increasing repul-sion of the excess electron density at the negativeterminal.

From these conjectures it follows, that the as-sumption of the classical electro-magnetic theory,that the attraction between opposite charges movesthe electrons, and in turn, the motion of the electronscreates the magnetic field around the conductor, wasmistakenly based on a reverse order of cause andeffect,,

The kinematic theory arrives to the conclusionthat both the electromotive force, that moves the elec-trons, and the magnetomotive force, that effects thecompass needles originate from one and the samecause; the sink and source system created by thelocally induced density differences of the Aether andthe resulting cylindrical sink-vortex, within andaround the battery and its current and rotation with-in and around the external conductive circuit.

Consequently, the following description of electro-magnetic oscillator should also be based on the sinkand source system of a dipole and understood by theresulting circulation of Aether.

Figure 15-2 shows the fundamental AETHRO-KINEMATICAL concept; the Donut-vortex (a), thesimplest evolutionary form of a permanent circulato-ry pattern, originated and maintained by the inter-nal kinetic energy of the Aether. This kinematicalunit is, in all aspects, equivalent with the most mod-ern scientific visualization of the elementary particle,called electron , (b).

(a) Figure 15-2 (b)The Donut-vortex represents a directional circu-

lation, which is equivalent to a dipole moment, thusit is inter connectable and capable to form higherorder systems. The same sink and source circulation

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can evolve in different orders of magnitude on atomicand molecular level. Similar circulatory patterns canexplain the electromagnetic kohesional forces ofmacroscopic matter.

Hence, it can be assumed, that any macroscopicchunk of matter should be surrounded by some kindof circulatory boundary layer to equilibrate betweenthe dynamic energies of the circulatory fields of theperipheral atoms and the random kinetic energy ofthe isotropic static pressure of the external medium.

Figure 15-3

Figure 15-3 is a schematic illustration of thestarting state of a capacitor with the two unchargedmetal spheres submerged in Aether and filled withelectron gases of equal density.

Neglecting the complex atomic structure, five dif-ferent states of the Aether can be defined in the sys-tem of a capacitor.

1. The external isotropic Aether of fundamentaldensity.

2. The medium that fills the space within themetal spheres, which is slightly rarefied by the effectof sharing the space with the atomic lattice and theisotropic gas of conduction electrons, (donut-vortex)schematically represented by the coarser dots.

3. The circulatory boundary layers, which equili-brates between the external and internal medium,represent a third density and act somewhat similarto the surface tension of a liquid.

4. The dynamic circulatory units of the individualelectrons, the donut vortices.

5. The global behavior of the free electrons, whichare in constant random motion (drift), and togetherhave the characteristics of a compressible, ideal gas.

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..... ... ... ..... ... ...... .. .......... ... ..... ........ ..... .... .. ... .... ..... ... ..... .... ......... .... ..... ..........

This medium is locked into the the spheres by thedynamics of the boundary layers.

In the next step the two spherical conductor isbeing oppositely charged by temporarily connectingthe left sphere to the negative, and the right sphereto the positive terminals of a battery by a conductor.

Figure 15-4

Figure 15-4 illustrates the five different states ofthe Aether while the spheres are being charged. Theconnection of the spheres with the battery creates atemporary current, that is, the sink and source sys-

tem of the battery produces a cylindrical sink-vortexin the Aether within and around the capacitor.

This circulation of the Aether through the con-ductors and in spite of the gap between the spheres(Maxwell's concept of displacement current) forcesadditional electrons on the left sphere and removesthe same amount of electrons from the right sphere.The result is a density difference between the elec-tron-gases of the two spheres; equivalent to an elec-tric potential difference.

Part of the cylindrical vortex represents a mag-netic field around the system, which rotates in agiven direction (white arrow). The temporary circula-tory pattern in the capacitor points from the negativeto the positive terminal of the battery and throughthe external circuit. The circulation of the Aetherexerts a directional pressure on the electron gasestrapped within the boundary layers, which ceaseswhen the circuit is broken.

Figure 15-5 represents the situation after discon-nection. The left sphere is filled with excess electrondensity which also creates an increased density ofthe Aether and plausibly an expansion of the bound-ary layer.

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+--

. ....

.....

. ........

......... ...

.... ........ .... .. ...... .. ........... ..... .. ..... ...... . ...... .........

... ...................

... ......................

... ....................... ..

Figure 15-5The state of the right sphere is exactly the oppo-

site. This reciprocal pressure in the two spheresserves as the fundamental kinematics of the electricpotential difference between the plates of the capaci-tors. The periodical release of these pressure differ-ences through the 'elastic' boundary layers is thekinematical equivalent of a static electric field.

Figure 15-6, A-B-C-D illustrate four phases of theoscillation of the electric and magnetic fields of thecapacitor after connecting the two spheres by a metal

conductor. These phases are repeating at high fre-quency, and because of the loss of the excess pressurethrough the radiation of compression pulses, thepotential energy of the system soon dissipates.

(A) illustrates the capacitor when the two oppo-sitely charged spheres are connected with a conduc-tor. Through the wire the released electron gas tendsto fill the whole available space. This tendency cre-ates a rarefaction in the Aether of the left spherewhich becomes a sink. The cylindrical vortex aroundthe conductor establishes a circulatory patternthrough the right sphere which becomes a source.

(B) shows that, the dipole moment of the Aethercirculation exerts a directional pressure on the elec-tron-gas, condensing it in the right sphere. Fromhere on the density of the electron gas graduallydecreases and eventually blocks the Aether flow atthe right end. At this stage, within the boundaries,the remaining circulation condenses the Aetheritself, until the excess pressure finally overcomes thestrength of the boundary layer and escapes into theexternal medium in the form of an Aetherial com-pression pulse.

332


.

....

... ..... ....... .. ....... .......... ..... .. ..... ...... . .................

....... ........ ...

........ .. .............

....

...

. ..

.... ........ ...... ... ........... ... ..

..... ...... .... ...

333


( A )

+--

...

. ..... ... ... ... . .. ..... . ........ . ... ..... ...... ............................. ............. ..

.. ...... .... ...... .... .

( B )

. ................

..................................................

.......

.

...

......

( C )

+

--

.

.... .. ... .... ... ... ....... ........ .... ..... ..... ............................ .. .... .... ....

.......... ..... .... .....

. .

( D )

.......

.. ..... .... ........ ............. ...............

............ ...........

......

.. .

Figure 15-6

(C) shows the reciprocal tendency of (A). Thistime the condensed electron gas is released by theceasing of the circulation and by the energy radiatedaway via the compression pulse. The free expansionof the electron-gas creates a sink at the right sphere,which in turn starts up the Aether circulation in theopposite direction and creates a source at the leftend. The spheres changed signs in the procedure; theright sphere became positive, the left spherenegative. Both the electron current and the rotationof the magnetic field have changed directions.

(D) illustrates the reciprocal state of (B) as thereversely directed Aether flow creates a new com-pression pulse. Evidently (A) is the direct continua-tion of (D) and the whole procedure starts all overagain. The oscillation has been established.

The compression pulses are propagated in theisotropic Aether through space as a train of periodi-cal disturbances, the frequency and wavelength ofwhich depends on the dimensions and the resultingperiodicity of the capacitor.

As Hertz discovered, a resonant oscillation can beproduced through space in another capacitor, provid-ed that it has exactly the same dimensions as the

oscillator. The requirement of dimensional equality isan important clue in that respect, that electromag-netic oscillators and receivers just like tuning forks,are only resonant to their own frequencies. This alsomeans, that their oscillation is determined only bytheir own restoring forces and not on the oscillationof the particles of the medium.

It is again a justification of the conclusion, hadbeen reached before, that like in the case of sound inair, the harmonic back and forth or transverse oscil-lations of the particles of the Aether is not requiredfor the transmission and reception of harmonic oscil-lation. A train of the periodical forward force of com-pression pulses, produced in a harmonic oscillator isadequate to create resonant harmonic oscillation in adimensionally equal receiving system. The elasticrestoring forces of an electromagnetic oscillator andreceiver is rendered by the compressibility and inter-nal kinetic energies of both the electron-gas, and thatof the Aether contained within the boundaries of theconductors.

The classical theory of light is given in two de-partment of physics. Geometrical optics is based onHuygens' intuitive principle and the hypothetical

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concept of the light rays and secondary wavelets. Thephysical character of light and radiation, describedby Faraday's and Maxwell's electromagnetic theory,was initially based on the physical reality of a trans-mitting medium, however, due to the relativistic in-fluence, it acquired the fundamental obscurity of allother physical theories; the acceptance of the actionat a distance through empty space.

The above presented AETHRO-KINEMATICradiation theory is an attempt to extend and corre-late the classical methods of geometrical and physi-cal theories of light and radiation. The KinematicalTheory of Wave-motion renders a conceptionalunderstanding for Huygens' intuitive geometricalconstruction and with the admission of the Aethermedium as an ideal gas, it dismisses all related mys-teries of the action at a distance.

Nevertheless, some radiation phenomena havebeen discovered toward the end of the last century,which stubbornly refused to fit in all previous theo-ries of classical physics. The modern solutions forthese problems are contained in Quantum Physics.The analysis and explanation of these new myster-ies, profoundly changed our world picture, forced an

epistemological revolution and the acceptance of thetheoretical duality of light and that of matter. Theseare the topics of the next chapter.

This topic, as the kinematic description of thephenomenon of electrostatics, will be discussed inAETHRO-KINEMATICS III.

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CHAPTER SIXTEEN

QUANTUM AND KINEMATICS

As it has been described in Chapter Three, in thecourse of resolving the discrepancies between theobserved energy spectrum of black body radiationand the predictions of the classical theories, MaxPlanck was led to the hypothesis that a system exe-cuting simple harmonic oscillations only can haveenergies which are integral multiples of a certainfinite amount of energy (1901). A closely related ideawas later applied by Einstein in explaining the pho-toelectric effect (1905), backed up by Compton's colli-sion hypothesis. In 1913 Bohr published his theorybased on the new concept of the quantum, which pre-

dicted with great accuracy many of the complex fea-tures of atomic spectra . The work of these physicists,and the subsequent developments by de Broglie,Schrodinger and Heisenberg (1920−30), constitutewhat is known in general as the Quantum Theory.Today's highest level of theoretical physics, which ismostly complex mathematics of probability, is calledQuantum Mechanics.

While the theories of relativity originated fromthe inability of classical physics to explain the empir-ical facts of the absolute speed of light (Michelson'snull result), the quantum theory originates from theincapability of classical principles to explain thetransition of energy between radiation and ponder-able matter, which is closely related to the structureof the atoms and their spectra, and the peculiarbehavior of elementary particles.

There are eight major innovations, throughwhich the modern Quantum Theory has affected theconceptual foundations of classical physics and phi-losophy. Each of the revolutionary ideas is tied to thename of the innovator and to a group of phenomena,which have been found unexplainable by classicaltheories:

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Aethro-kinematics

1. Planck's Quantum Theory of black-body radia-tion.

2. Einstein's Photon Theory of the photo-electriceffect.

3. Bohr's quantized Theory of the Hydrogen atom,and spectra.

4. The collision hypothesis of the Compton effect.5. DeBroglie's theory of the existence of matter-

waves.6. Heisenberg's discovery of the Uncertainty

Principle.7. Schrodinger's equation of quantized waves of

probability.8. The discovery of matter and antimatter by

Dirac.This chapter is a continuing attempt to give

alternative explanations for the insolvable problemsof classical physics within the reach of human per-ception, and by the original and intelligible, singlelanguage of classical science and epistemology.

Instead of re-iterating the classical problems andtheir quantum solutions in full details, if necessary,the reader may refer back to Chapter Three.

PLANCK'S FORMULAIn his striving to produce a mathematical formu-

la of radiation that fits the experimental curve,Planck was forced to the following deviations fromthe standard procedures of classical physics:

a) At a given stage of the derivation of the aver-age energy of an oscillator, according to the classicalrules the increment of the integration must approachzero. This method had been used by Raleigh and pre-dicted the probability of the ultraviolet catastrophe.Planck noticed that by keeping this increment as anextremely small, but non-zero quantity, Raleigh'sfaulty end-result can be eliminated. This constraintcreated the constant h, which in turn, resulted in theconcept of discontinuity of the average energy levelsof the atomic oscillators.

b) The universal constant, h achieved the granu-larity of electromagnetic energy, but in order to corre-late this constant with Wien's empirically provenDisplacement Law, Planck had to assume that thefinite quantity of energy exchange between radiationand matter is proportional to the frequency,ν of theemitted or absorbed radiation; i.e., a quantum ofenergy, ε = hν.

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Aethro-kinematics CHAPTER SIXTEEN Planck’s Formula

Accordingly Planck's semi-classical conceptualinterpretation of his final formula assumed that thedistribution of energy among electromagnetic har-monic oscillators in thermal equilibrium cannot varycontinuously, but must always be an integral multi-ple of a certain quantity and therefore take on one ofthe discrete set of quanta; E = 1hν, 2hν,.....nhν,,where n is an integer, h is a universal constant, and νis the frequency of radiation. It follows, that an oscil-lator must have a discrete set of energy levels, and theemission and absorption of radiation must also beassociated with the discontinuous transitions, orjumps between levels, which always happens by theloss or gain of a whole quantum of radiant energy ofmagnitude, hν.

c) Finally, to eliminate the initial deviations ofWien's curve from the experimental facts, Planck haselected to modify Boltzmann's method of countingthe probabilities of the energy distribution amongthe different frequencies. He also attempted to give aconceptual explanation for this modification by rea-soning that it takes more time for an oscillator toaccumulate a quantum of the higher frequencies,than that of the lower ones and consequently, the

probability of accumulating lower frequencies isgreater than higher ones.

Undoubtedly, the resulting mathematical formulagave a perfect match to the experimental curve forthe distribution of radiant energy at all tempera-tures. Nevertheless, Planck's retroactive attempt toconstruct a conceptual theory of the physical mean-ing of the formula was not that successful.

In the 'Introduction to Modern Physics' Richt-meyer [128] presents a condensed summary of thesituation at this critical stage in the evolution of thequantum theory:"The problem of the absorption and emission of

radiation, in fact, presented serious difficulties forthe new theory. If the energy of an oscillator can varyonly discontinuously, the absorption and emission ofradiation must likewise be discontinuous processes.As long as the oscillator remains in one of its quan-tum states, it cannot emit or absorb radiation accord-ing to the laws of classical physics, for the classicaltheory absolutely requires an isolated, acceleratedelectric charge to radiate energy."According to Planck's new theory, emission of radi-

ation occurs only when the oscillator jumps from one338


energy level to another (lower one) ... the energy, hνthat it loses, is emitted in the form of a short pulse ofradiation. Absorption was also assumed at first to bediscontinuous.“An oscillator can absorb a quantum hν of energy,

and jump instantaneously (or nearly so) up to itsnext-higher energy level. This assumption met withspecial difficulties, however. For the quantum of radi-ant energy emitted, according to the classical wavetheory, would spread out over an ever expandingwave front, and it is hard to see how another oscilla-tor could ever gather this energy together again so asto absorb and thereby acquire the energy for anupward quantum jump. To avoid this difficulty,Planck later modified his theory so as to allow theoscillator to absorb in a continuous manner, and onlythe process of emission being discontinuous. Thiscame to be known as the second form of Planck'squantum theory."Having read thus far, the student may perhaps

have reached a state of confusion as to what were theessential assumptions of Planck's quantum theory!This confusion can not be worse than that whichexisted in the minds of most physicists in the year,

say 1911. The situation was made still more puzzlingby the success of Einstein's theory of the photoelec-tric effect; for Einstein assumed not only that radia-tion came in quantized spurts but that each spurtwas closely concentrated in space, contrary to theclassical wave theory."

This is then the exact stage in the evolution ofthe quantum theory, where it breaks away not onlyfrom the principles of classical physics, but also fromthe fundamental epistemological requirement of theconceptual coherency of a physical theory.

Einstein's method to solve the problem of thephotoelectric effect was the same as in the case of theperplexing problem with Michelson's null result. Inboth cases, he simply and boldly postulated the insol-ubility of the problem based on classical principles.To explain the photo-electric effect, he reinstatedNewton's corpuscular theory of light and declaredthe unavoidable necessity for a dual language todescribe the dual nature of light; one for the casewhen light is manifesting wave nature, and one forthose when is behaves like it was a particle.

No doubt, if there exists a way to rehabilitate thevalidity of common sense and the fundamental faith

339


of science in humanly conceivable physical lawsthen, besides the theories of relativity, this issue isthe other major cross-road, where science, and epis-temology must attempt to find an alternate solution.

From the standpoint of AETHRO-KINEMATICS,in the most general sense, the fundamental concep-tual problem with the continuity of the classical elec-tromagnetic energy is eliminated by the acceptanceof the ideal gas model of the Aether. In spite of the dif-ficulty to imagine the supermundane order of magni-tude of this medium, it is still materialistically gran-ular. The discontinuity of Aether is represented bythe fundamental units of the size, mass, velocity andthe momentum of the Aethron, all of which are relat-ed to the velocity of the propagation of disturbances inAether, which is that of light and radiation; c.

As it was discussed earlier, there exists a non-zero collision free path among the Aethrons, and justlike in the case of sound- or water-waves, there exista minimum possible wavelength, and therefore amaximum frequency, for any periodical disturbancethat is kinematically producible in this medium.

Planck's intuitive analogy between radiation andwater waves and the role of the water molecule, or

the atom of a monatomic gas as the limiting factor inthe dispersion of the kinetic energy, is also valid inthe ideal gas of Aether. Thus, the Huygens-Max- wellundulatory theory of radiation, based on Aether, doesnot demand an infinite range of frequencies and con-sequently it is free from the danger of Raleigh'sultra-violet catastrophe.

Nevertheless, Planck's analogy was not entirelycorrect. As the shortest possible water- or sound-waves are not represented by the kinetic energy of asingle atom, similarly the energy of the shortestwavelength of radiation cannot be represented by thekinetic energy of a single Aethron. The granularity ofthe energy is not equivalent to that of the medium.

The foregoing kinematical thought-experimentabout the periodical compression pulses of sound ledto the conclusion that both the frequency and ampli-tude of the simple harmonic oscillator of a soundsource are reproducible in the resonant oscillation ofthe ear-drum without requiring that the particles ofthe medium also perform simple harmonic oscilla-tion. The following quote is presented to clarify thevalidity of the exclusively forward momentum in thekinematical wave-theory:

340


"...with regards to the momentum carried by waves,you would conclude prematurely that since themomentum of the mass oscillates and thus whoseaverage value is zero, the sinusoidal wave cannotcarry net momentum.“This, however, is a wrong argument. As a mass

moving with constant velocity has both kinetic ener-gy and momentum. Thus any waves, (mechanicaland electromagnetic) should carry both energy andmomentum. If we stretch a spring, the mass densitydecreases, if we compress it, the mass densityincreases. The quantity we have to watch carefully isthe variation in the mass density. Thus, in the pres-ence of a wave at any point in the medium themomentum density (the momentum per unit length)is also varies."After defining a 'density wave' we find the impor-

tant conclusion, that the average energy density

Momentum density = −−−−−−−−−−−−−−−−−−−−−− .wave velocity

"Note that the momentum transfer rate is equiva-lent to a force. Thus, electromagnetic waves canindeed carry momentum and the force exerted by

them is called radiation pressure." (Akira Hirose,Introduction to Wave Phenomena [66])

Hence, the propagation of the individual, periodi-cal compression pulses forming all wave-motions rep-resents a discontinuous delivery of a force in theform of a periodical forward momentum transmittedthrough the medium. This discrete amount of period-ical force might as well serve as Planck's concept ofdiscontinuity. – For the clarification of this sugges-tion, consider the detailed mechanics of the produc-tion and reception of compression pulses by a simpleharmonic oscillator in an isotropic gaseous medium.

First examine the structure and mechanics of theideal simple harmonic oscillator of a frictionless pis-ton of given mass, oscillating in empty space underthe influence of the restoring force of the coil springswith a given force constant.

The distance between the center of oscillationand one of the points of extreme displacement repre-sents the amplitude. The time it takes to complete afull cycle, which also includes the return of the oscil-lator to its initial point of displacement, is the period.The restoring force of the springs is directly propor-tional to the displacement and therefore with greater

341


displacement the piston is forced to move and accel-erate faster. Consequently the period of oscillation isindependent from the amplitude. It follows, that thefrequency of the oscillator depends exclusively on thestructure of the oscillator. In this ideal examplethere are two determining factors; the mass of thepiston and the force constant, i.e. the restoring abilityof the spring. The ratio between the mass and theforce constant clearly determines the natural fre-quency of the oscillator.

Thus, in order to produce different frequencyoscillations one of these mechanical factors must bealtered. Decreasing the mass of the piston or increas-ing the restoring force of the springs result in higherfrequencies, and increasing the mass or decreasingthe restoring force results in lower frequencies.

Figure 16-1, (Fr.-0) illustrates the isolated systemof an oscillator, which is initially at rest. The smallsphere that is approaching the piston from the rightrepresents an external force in the form of a projec-tile of a mass, say 1/10 that of the piston.

This projectile moves to the left with a givenvelocity. After collision at mid-point (Frame-1), theprojectile transfers part of its momentum and

rebound while the oscillator moves in the initialdirection with velocities in accordance with the law

of the conservation ofmomentum.Due to theincreasing restoringforce of the springs thepiston gradually decel-erates to zero, thenchanges direction, andaccelerates toward themid-point where itreaches its maximuminitial velocity.

However, due to itsinertial properties, itovershoots to the right.From here on, if noth-ing else happens withthe system, there willbe a steady oscillationat the given naturalfrequency of the oscilla-tor, which depends onthe ratio between the

342


Figure 16-1.

7.

3.

1.

5.

2.

4.

6.

8.

0.

0

mass of the piston and the force constant of thesprings.

The amplitude of the oscillation, i.e., the maxi-mum displacement from the center, depends on theinitial momentum of the projectile. In each cycle, thepiston passes through the original position, at mid-point, with its highest velocity. − This example canbe extended with the repetitions of the external forceby sending identical projectiles into the system withsuch frequency, that each collision happens while thepiston moves to the left and at mid-point. From eachof the periodical impacts the piston will gain thesame increment of momentum, which will take it to alarger maximum displacement, producing a greateramplitude in its natural frequency.

In general, one can conclude, that the oscillatorabsorbs energy in a discontinuous manner by dis-crete increments (momentum of projectile) and thatthe amplitude of oscillation, or the energy level of thesystem is also altered by 'jumps' of finite quantities.

Next consider the case when this oscillating sys-tem produces compression pulses in an isotropiccompressible medium. The illustration of Figure 16-2deliberately starts with the extreme left position of

the piston at zero velocity, because the cycles of theproduction of periodical compression pulses start and

end at the extreme dis-placement points of theoscillator. The reasonfor this follows fromthe consideration thatthe compression of themedium starts whenthe velocity of the pis-ton becomes greaterthan zero.

In this two dimen-sional oscillating sys-tem, two separate com-pression pulses areproduced in oppositedirections during eachcomplete cycle startingat one of the extremedisplacement points.Thus, the motion of thepiston produces period-ical compression puls-

343


Figure 16-2.

0

1.

2.

3.

4.

5.

6.

7.

8.

0

es, propagating in opposite directions with the speedof the dissipation of disturbances in the medium.This produces a frequency determined by the struc-ture of the oscillator.

There is also a discrete amount of forward mo-mentum in each pulse, characterized by the mechan-ical structure (mass and spring) of the simple har-monic oscillator.

It follows from all above, that the momentumdensity of a single compression pulse is proportionalto one half of the energy of a single total cycle of theoscillator, and therefore the 'emission' of the energy,or the transference of the forward momentum frompiston to medium must also be represented by dis-crete quantities.

Finally, the reciprocal of the above example canbe conjectured. When an oscillator at rest receivesindividual compression pulses, carrying discretequantities of forward momentum, it moves out fromits equilibrium position in proportion to the force andbegins to perform simple harmonic oscillation. If thefrequency of the pulses matches the natural frequen-cy of the oscillator and synchronized with it in phase,each pulse will increase the displacement, of the pis-

ton, i.e., the amplitude, or energy level of the oscilla-tor by a discrete increments of energy.

The final limit of the accumulation of energy isreached at the extreme displacement when the re-storing force of the spring is equal to the momentumcarried by the pulse.

By direct analogy, the same mechanism is applic-able to the radiating energies transmitted by theAether to the simple harmonic electromagnetic oscil-lators. The acceptance of an all-pervading granularmedium, and that of the kinematic theory of periodi-cal compression pulses and its correlation with themomentum density of classical electromagnetic theo-ry create a kinematical explanation for the disconti-nuity of the electromagnetic fields.

Further more, it opens up a variety of plausibletheoretical schemes to fill the conceptual vacuum ofPlanck's mathematics. With this the kinematical roleof the quantum, hν, as it will be discussed later, maybecome humanly conceivable.

Nevertheless, historically, before anything en-lightening has been given for Planck's conceptuallyunclear discovery, a new problem, and with it, a newsource of confusion occurred.

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THE CORPUSCULAR WAVES OF RADIATIONIn 1887, while conducting experiments on electro-

magnetic waves, the German physicist HeinrichHertz happened to observe that a metal surface canemit electric charges when ultraviolet light shines onit. The phenomenon has been named, the photoelec-tric effect. The later discovery of the electron suggest-ed the hypothesis that the photoelectric effect is dueto the ability of radiating energy to liberate free elec-trons from the metal.

In 1902 Philipp Leonard, Hertz's assistant pub-lished a detailed account of his experimental study ofthe effects of radiation on metal surfaces. Figure 16-3illustrates the schematic of Leonard's device forobserving photoelectric effects.

Leonard allowed light of different frequencies tofall on a clean metal surface in a vacuum tube. Theelectrons liberated from the surface of the positivelycharged cathode were accelerated toward the nega-tively charged anode. Some passed through the open-ing and reached the plate and the electrometer (1),by which the photoelectric current was measured.Their velocities could be measured by adjusting theelectric potential, and attracting the electrons to the

Meter 2, via electric and magnetic fields.After the thorough examination of the experi-

mental facts the following conclusions were reached:1. The ejection of the photoelectrons occurs only

when the frequency of radiation exceeds a certain

minimum value. This is called the threshold frequen-cy, which is characteristic of the emitting metal. Thethreshold energy is independent from the intensity ofthe radiation.

2. The effect is a surface phenomenon and thethreshold frequency varies considerably with thestate of the surface. Highly polished surfaces de-crease the threshold frequency of emission.

345

Aethro-kinematics CHAPTER SIXTEEN The Corpuscular Waves of Radiation

± CathodeAnode

Ground Meter 2

Meter 1

SourcePump

Quartz

Magnetic Field

Figure 16-3.

3. Electrons, liberated from the chatode, move inall directions with various velocities. The emission ofthe electrons are distributed randomly in time. Theaverage rate of emission, or the kinetic energy of thetotal number of ejected electrons per unit time isproportional to the intensity of the radiation.

4. When negative potential applied to the cathode,which repels the electrons, the photoelectric currentincreases up to a limit. Above 'about 15 or 20 voltsnegative' there is no more increase in the current.This is called the saturation value.

5. A positive, retarding potential decreases thephotoelectric current, but upon reversal it does notimmediately drop to zero. This proves that the elec-trons are emitted from the cathode with a finite, non-negligible kinetic energy.

6. By the gradual increase of a retarding poten-tial to the exact point where the current stops, Voe,the value of the maximum energy electrons can befound. The magnitude of the stopping potential, orthe velocity of the maximum energy electrons is inde-pendent from the intensity, but directly proportionalto the frequency of the radiation.

7. A variation in the intensity of the radiation is

proportional only to the number of electrons emittedfrom the photocathode.

8. The time delay between the incidence of radia-tion and the ejection of the first electrons does notexceed 10-9 sec and independent of both the frequen-cy and the intensity of the radiation.

Most of the above listed empirical facts and con-clusions are completely at variance with the classicalelectromagnetic theory and the efforts to find amechanism for the photoelectric effect encounteredgreat difficulties.

It was early assumed that conducting metals con-tain a great number of free electrons which are inrandom motion within the crystalline structure, sim-ilarly to the atoms of an ideal gas. Electric currentsare due to the drift of these free electrons throughthe conductor under the influence of the electricfield. It was also assumed that, when electromagnet-ic waves incident on the surface of a metal, the oscil-lating electromagnetic field exerts a force on the freeelectrons, which thereby set into oscillation withsteadily increasing amplitude.

Eventually, some electrons would acquire enoughkinetic energy to overcome the attractive force of the

346


metal and succeed in breaking through the surfacewith considerable velocity.

There are some contradictions between this me-chanism and the empirical facts. For example; theamplitude of the oscillating electric field is propor-tional to the square-root of the intensity of radiation.Therefore the energy accumulated by the electronsshould be dependent on the intensity. However, thisis not the case.

Another problem with the gradual accumulationof energy by the electron is that, based on thespread-out energy of the waves and on the size of theelectron, it would take a long time to absorb therequired kinetic energy. Experiments shows, howev-er, that the time interval between the incidence ofradiation and the ejection of the first photoelectronsis exceedingly small. Finally, based on the classicaltheory, radiation far below the threshold frequencyshould still be capable to eject electrons, provided itis given enough time to build up the necessaryamplitude in the oscillation of the electron to escape.This, however, does not occur.

Such unavoidable contradictions led to anotherclassical hypothesis, namely, that the ejected photo-

electrons are not the free electrons, but coming frominside the atoms, and their release is of the nature ofa resonance mechanism.

Thus, the light of a given frequency might func-tion merely as a trigger releasing the electrons tunedto the same frequency, which thereby already possessproportional kinetic energy. However, this alternativewas also refuted, based on the unlikely pre-requisitethat atoms must contain resonating systems of allfrequencies for which photoelectric emission wasobserved.

Experimental facts thus seem to demand the con-clusion that the photoelectric energy must comedirectly from the energy of the incident electromagnet-ic radiation.

In Chapter Three it has been quoted in Einstein'sown words, how he established the philosophicalinsolubility of the problems of the photoelectriceffect, and what train of thoughts led him to theseemingly only possible solution; the unavoidableacceptance of two incompatible languages for de-scribing the dual nature of light, being waves in cer-tain phenomena and photon-particles in others.

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In the following, Einstein's mathematically justi-fied explanation of Leonard's empirical conclusionswill be given:

Planck's quantum hypothesis assumed, that elec-tromagnetic oscillators can only emit or absorb ener-gy discontinuously in discrete quanta, hν, but thepropagation of this energy still happens according tothe wave theory. Einstein extended Planck's quan-tum concept to the mechanism of electromagneticradiation itself. He boldly postulated that the burstof energy, which is initially localized in a small vol-ume of space when emitted by the quantized oscilla-tor, remains localized and moves through space like aparticle instead of spreading out its energy in aspherical form like moving waves do.

a) The energy content ε, of such burst, or photon,is related to Planck's constant h, and to the frequen-cy ν, (rho) of the oscillator by the equation ε = hν. Inthe photoelectric process one whole concentratedphoton of the incident light beam is completelyabsorbed by a single free electron. In other words,the total energy of the photon is transformed into thekinetic energy, Ek of a free electron in a collision-likeevent. Thus, Ek = 1/2 mve

2 = hν.

Figure 16-4b) The intensity of a beam of monochromatic light

is equivalent of the flux, or the number of photonspassing through per unit area per unit time. Since allphotons have the same energy hν, and one photoncan only strike one electron, the intensity, or the pho-ton density, of the beam only affects the number ofejected photoelectrons but not their kinetic energies.

c) In order to explain why the ejected electronsshow a whole spectrum of kinetic energies in spite ofthe uniform energy of the absorbed photons, it wasassumed that the absorption of the photons happens

hν

3σ = 0

hν

2σ

hν

1σ

En

ergy

V e

or

/ m

vo

2 m2

1

Frequency, o νν

ωo ωo ωo

E = h - ( + )σ ων - o

348

at different depths in the metal and therefore theelectrons might lose various amounts of energy byinternal collisions with the atoms before they reachthe surface.

On Figure 16-4 (a) this variable loss of energy isrepresented by the symbol, (sigma) σ1−σ3.

d) A photo-electron, which absorbed the photon-energy just at the surface, does not lose energythrough collisions, (σ3=0 and omitted). The electronstill has to spend part of the photon's energy to over-come the attraction of the metal, and therefore itsenergy after escape will be the energy of a photon, hνless the work function, ωo.

Therefore Einstein's photoelectric equation forthe final energy of the maximum energy electrons is:

Emax = hν − ωo (16.1),where ωo is a constant for all frequencies, and variesonly with the chemical composition of the metal ofthe photocathode.

Based on experimental facts, a simple linear rela-tion has been found to exist between the maximumenergy photoelectrons and the frequency of light thatcauses the emission.

As was shown by Millikan in 1916, Figure 16-4(b), if the curve is plotted for the maximum kineticenergy, 1/2 mvm

2 and frequency, ν, the result is astraight line which shows an intercept, νo on the fre-quency axis. The physical meaning of this is thatlight of frequency less than νo (the threshold fre-quency) cannot cause electron emission. The equa-tion of the curve may be written

1/2 mvm2 = h(ν − νo) = hν − ωo (16.2),

where h is a constant and ωo is the work-function, orthe energy spent on liberating the electron from agiven metal. Thus, it can be stated that the energy ofthe maximum energy electrons is directly proportion-al to the frequency of the light.

Since h = (1/2 mvm2 + ωo )/ν, if the kinetic energy

is expressed in ergs and the frequency in cycles/sec,as found by Millikan, h = 6.56×10−27 erg sec, which isin good agreement with the magnitude of Planck'sconstant explaining black-body radiation.

(For future references, it should be bared in mind,that Millikan's calculation was based on the assump-tion that the maximum energy electrons absorbedthe total energy of a photon.)

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Thus, Leonard's experimental facts and the con-clusions drawn from them have been fully explainedby Einstein's bold photon hypothesis and its mathe-matical description.

Nevertheless, as it is described by Ritchmyer andco-authors, 'Introduction to Modern Physics' in 1954[99], the scientific situation was not entirely clearand simple:"The difficulties with such a radical theory of light,

however, are many. For one thing, if we regard lightas a shower of photons, what can possibly be themeaning of frequency? There is nothing periodicabout a falling raindrop, for example.“As a matter of fact, in order to find the frequency of

a beam of light (a shower of photons), we must mea-sure the velocity c of the light and its wavelength λ onthe assumption that light consists of waves, and thanwe compute the frequency as ν = c/λ. Thus, we have torely on the wave theory of light to give us the energyvalue hν of the photon."The situation thus created was perhaps the most

puzzling one that has ever arisen in the whole histo-ry of physics."

And the puzzle only deepened at a later stagewhen Compton, (1923) announced that photons alsopossess momentum. Then it became clear thatEinstein's initial idea, that photoelectrons were freeelectrons liberated by radiation, is quite impossible.

For if a single free electron would absorb theentire energy of a photon, it would have, at least tem-porarily, − still within the boundary, − a kinetic ener-gy hν and also a momentum equal to hν/c.

If, however, 1/2 mvmax2 = hν and also mv = hν/c,

then v, being the velocity imparted to the electron,would be 2c, double the velocity of light, which isimpossible, of course, on account of the postulate ofthe special theory of relativity.

The remedy to this problem came in the form ofthe revision of the initial assumption about the ori-gin of the photoelectrons. For if the electron is notfree in the metal, but attached to one or more atoms,part of the photon's momentum could be absorbed bythe atoms and by that the velocity of the extractedelectron would not have to exceed the speed of light.

Nevertheless, there are serious problems withthis hypothesis, too. It contains still another unknow-able factor, that is, the ratio between the energies

350


absorbed by the atom and by the electron. This oughtto cause an uncertainty in the evaluation of the finalenergy of the maximum energy electrons, therebycausing some unavoidable doubts about the credibili-ty of Millikan's derivation of Planck's constant fromthe photon theory. − Further developments in thetheory of free electrons in metals brought up evenmore contradictions, due to problems originated inconnection with specific heats.

According to the classical theory free electronshave the usual Maxwellian distribution of velocities,proper to a gas of electrons at a given temperature ofthe metal.

Thus, because of their light mass, free electronswould have much higher velocities than the atomsdue to thermal agitation. Several lines of evidencealso indicated that the number of free electronsshould be of the order of magnitude as the number ofatoms; according to the principle of equipartition, afree electron should have the same average kineticenergy as an atom.

This theory had some success in accounting forthe electrical and thermal conductivities of metals. Aserious difficulty was encountered, however, in con-

nection with specific heats, where the total thermalenergy was fully accounted for by the energy of theatoms only.

Therefore, it was necessary to suppose that theheat energy of the free electrons must either be verysmall, or even totally independent of temperature.

This difficulty was eventually resolved by wave-mechanics, a simplified form of which was proposedby Sommerfeld (1928), reproducing the most impor-tant features and conclusions so far as they concernphotoelectric and thermionic emission. Sommerfeldretained the concept that free electrons form a gas inthe metal, but because of the light mass and highdensity of the electrons, he assumed that it is adegenerate gas, which should be treated by theFermi-Dirac distribution of energies. This formulaattributes a much greater average kinetic energy tothe free electrons than the Maxwellian theory, butalso states that the rate of increase of the electronicenergy with temperature is much less than it is pre-dicted by the classical theory.

In view of all these difficulties and new develop-ments, modern physics had to introduce a somewhatdifferent explanation of the photoelectric effect and a

351


revised mechanism for the emission of photoelectrons,which requires some correlation with the closelyrelated phenomenon of the thermal emission of elec-trons.

It has been long known that metals emit freeelectrons in a chatode-ray tube filled with gas due tothe bombardment of the surface of the cathode by theenergetic ions and atoms.

Emission of electrons can also be produced by theincrease of the internal thermal energy of a chatode.The process is called thermionic emission, and theemitted electrons are called thermions. A thermioniccurrent can be produced and the kinetic energy ofthe thermions can be measured.

Through such experimentation it has been foundthat the energy of the thermions at constant temper-ature varies with the chemical composition of theemitter, which shows that thermions, like photoelec-trons, must spend part of their energy on the attrac-tion of the metal and escape through the surfaceboundary. At a given temperature, T, and internalthermionic energy, ET , with the adjustment of aretarding potential, the kinetic energy of the maxi-mum energy thermions can be found;

1/2 mvm2 = Voe = Eth-max = ET − Φ (16.3),

where Eth-max is the energy of the maximum energythermions and Φ is the thermionic work function ofescaping.

It was early assumed that thermions and photo-electrons come from the same source inside themetal, the two types of emission differing chiefly inthe mechanism by which an electron acquires suffi-cient energy; in the first case by thermal agitation, inthe second by the absorption of radiant energy. Onthis view, the work-function Φ in the thermionicequation ought to be at least approximately the sameas the quantity ωo in Einstein's photoelectric equa-tion. It has been also found that the thermionic max-imum energy at room temperature is not much dif-ferent from that of the maximum energy of the pho-toelectrons.

Because of the increase of thermionic kineticenergy, predicted by the Fermi-Dirac distribution ofthermal energy, it follows that the already existinginitial thermal energy of the free electrons cannot beneglected in the derivation of the photoelectric ener-gy. The question thus arises, where is this internal

352


thermionic energy of ET in the photoelectric equa-tion?! This is discussed and illustrated (Figure 16-5)by Ritchmyer's Introduction to Modern Physics [103]:"If a free electron in the surface of a metal already

has thermal kinetic energy Ei and absorbs a quan-tum hν, it will have a total kinetic energy hν + Ei . If

this energy exceeds the work Ω that must be done byany electron against attractive forces in escapingfrom the surface of the metal, the electron willemerge as a photoelectron with kinetic energy

1/2 mv2 = Ei + hν − Ω."Since Ei cannot much exceed the limit of the maxi-

mum energy thermions, Em the photoelectric ener-gies will thus have a fairly definite maximum valuegiven by the equation

1/2 mvm2 = hν + Em − Ω. (16.4)

"Comparison with Eq. (16.11) the constant ωo inEinstein's photoelectric equation must have theapproximate value

ωo = Ω − Em."There are, however, some ambiguity in this repre-

sentation.a) It is quite evident from the above that the

newly introduced work-function, Ω, has little ornothing to do with experimental facts, but is merelyan invention to preserve Einstein's equation from theeffect of the uncalculated thermionic energy.

b) But even with Ω, looking for the maximumenergy photoelectrons, there is no reason to add thequantum, hν to the average energy Ei but rather, itshould be added to the maximum thermal energyelectrons Em at variance with the above schematicillustration.

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En

ergy

of

an E

lect

ron

22

1 / mvE =ph

Em

Ei Ei

hν

Φ = ωο

Ω

Figure 16-5.

If in spite of these, the new work-function, Ω is stillsufficient to preserve the original photoelectric equa-tion then, merely due to the lack of factual argu-ments, it must be simply adjustable.

Adding the impossibility of finding the ratio ofthe absorption of the total energy of a photon bet-ween the electron and one or more of the atoms, itseems quite clear that the quantitative derivation ofPlanck's constant by Millikan from Einstein's origi-nally simple photoelectric equation has been foundedon too many unmeasurable, and therefore easilyadjustable factors.

Hence, it is hard to accept that the theories ofPlanck and Einstein can justify one another, or thattogether they do establish the universality of one ofthe same single constant.

THE PHOTO-THERMIONSNow, in the fashionable style of modern theories

it is hereby boldly stated that the presently acceptedphoton theory of photoelectric effect not only totallyincompatible with the rest of physical knowledge andstill in its quantitative operation must revert to theclassical concepts of the electromagnetic wave theory,

but that there are also irreconcilable ambiguitieswithin itself.

Further more, contrary to its modern presenta-tion, the ambiguous derivation of Planck's radiationconstant, h justifies neither one of the two theories.Hence, there is an obvious need for an alternatedescription of the effect, preferably in a better corrob-oration with the principles of the rest of physics.

Accepting the basic assumption of AETHRO-KINEMATICS that all space filled by the ideal gas ofAether, and applying the kinematic revision of themechanical wave theory, consider an alternativeheuristic hypothesis:

First, let us deliberately disregard all complica-tions and con- fusions generated by the concentrated,localized and instantaneously transmitted photonenergy. Instead, we revert back to the simple andsensible idea, that the kinetic energy of the gas offree-electron in the cathode originates solely fromthermal agitation. Also assume that the essential dif-ference between thermions and photoelectrons ismerely in the different mechanisms of their libera-tion from the body of the metal.

354

Aethro-kinematics CHAPTER SIXTEEN The Photo-thermions

The following quote is given for re-iterating thisassumption:"It was early assumed that thermions and photo-

electrons come from the same source inside themetal, the two type of emission differing chiefly inthe mechanism by which the electron acquires suffi-cient energy to enable it to escape from the emitteragainst the action of attractive forces of some sort.

“The agreement between the values of the work-functions determined photoelectrically and ther-mionically seems good enough to warrant the hypo-thesis that the photoelectrons and thermionic elec-trons have a common origin.” (Richtmyer-Kennard,Introduction to Modern Physics [95])Thus, three different mechanism can cause electron

emission:1. In the gas-filled cathode-tube by the bombard-

ment of the surface of the metal by the atoms of thegas. 2. In a vacuum-tube, by increasing the tempera-ture of the cathode, thereby increasing the thermalkinetic energy of the electrons. 3. In the thermionicequilibrium of a vacuum-tube, by high frequencyelectromagnetic radiation, which liberates photo-electrons .

Consider then the following:As it was presented in Chapter Fifteen, by the

description of the capacitors, any macroscopic chunkof matter is surrounded by a special circulatory layerof the Aether, which equilibrates between the uncom-pensated dynamic flow-patterns of the force fields ofthe peripheral atoms, and the random kinetic energyof the isotropic pressure of the external medium.

This boundary layer represents a buffer betweenthe geometrically periodical circulatory flow-patternswithin the crystalline structure, and the randomnessof the external medium. As such, the flow-patterns ofthis boundary layer must be in a plane parallel tothe surface of the metal between the internal andexternal pressures, assimilating to the geometry ofthe crystalline structure both in its kinematics andits local density fluctuation.

Here, it is assumed that instead of 'attractiveforces of some sort', this kinematical barrier isresponsible for the internal reflection of the free elec-trons in the transverse directions to the plane of thesurface, thereby trapping them within the bound-aries of the metal. Thus, the possibility of escapedepends on two factors: the velocity of the electron,

355


and the opposing strength of the kinematical barrier,called the work-function.

In scientific descriptions of thermionic emission,the mechanism of this barrier are often comparedwith the surface tension at the boundary between liq-uids and gases, and the escape of the electrons withthe evaporation of the molecules of the liquid."Thermionic emission is a term used to describe the

emission of electrons (and/or ions) from a solid whenit is heated in vacuum. Thermionic emission can beviewed as an evaporation process,.....depending ontemperature.....and the related work-function, can beinterpreted as an electron latent heat of vaporiza-tion." (Lerner-Trigg, Encyclopedia of Physics, [1251])

The analogy between evaporation and electronemission may seem to be far fetched by present theo-ries. However, but once the existence of a kinematicmedium is accepted as a general conveyer of energybetween micro- and macro-cosmos, a definite mecha-nical resemblance is found between the effects of sur-face tension and those at the boundary between twodifferent media.

Thus, the analogy justifies the attempts for fur-ther correlation.

Consider, therefore, that a metal of certain chem-ical composition at a given temperature, To showszero thermionic emission, but by a very small in-crease in the temperature some thermionic currentis detected.

Thus, at To the system is in thermionic equilibri-um, meaning that the internal kinetic energy of theelectrons ETo is equal to and not greater than thestrength of the barrier, which is represented by thework-function, Φ, thus

ETo = Φ,where To can be taken as the thermionic thresholdtemperature and ETo as the thermionic thresholdenergy.

In this state of thermal equilibrium, thermionicemission can be produced by external forces, like thebombardment of the chatode's surface by the ener-getic gas atoms. This suggests that the thermionicemission is not resulting from the increase of thekinetic energy of the internal electrons, but ratherfrom the decreasing strength of the boundary barrier.

Let us recall Murphie's artistic rendering (Fig.14-6), but this time as an analogy with an electromag-

356


netic boundary layer between the atomic construc-tion of metal and the external isotropic pressure ofthe Aether (a). Instead of a stone falling into a pond,atoms plunge through the this special medium, eachproducing spherical compression waves which inter-fere with one another.

Figure 16-6

Because of the resulting random pattern in theblocking strength of the boundary, some thermionsthat were trapped before now are capable of escapingthrough the weakened points of the layer and beingemitted into the external medium.

At a constant temperature of the system, thetotal energy of the emitted thermions, Eth is propor-tional to the density of the gas in the tube, that is,the number of atoms hitting the surface per unitarea. Therefore, the work-function is not a constantanymore, but rather clearly, it is inversely related tothe kinetic energy and the density of the bombardinggas atoms.

It follows that, as the work-function decreases,the electrons spend less energy on escaping, thus thethermions emerge with increasing external kineticenergy; Eth = ET − (φ − β), where β represents thenegative effect of the gas atoms on the strength ofthe barrier, or that of the magnitude of the work-function.

Going back to the thermionic equilibrium, butthis time in a vacuum tube, consider the productionof thermionic emission by the increase of the internalthermal energy of the electrons.

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Recall the two quotes relating to the ratio bet-ween the thermal kinetic energies of the electronsand the atoms.

On the one hand:"The thermionic current from agiven emitter is found to increase very rapidly withincreasing temperature."

On the other hand, however, according to theFermi-Dirac theory, "The total energy of the free elec-trons changes very little with the rise of the tempera-ture". Ritchmyer, Introduction to Modern Physics[96-102]

There seems to be a contradiction between thetwo statements if the thermionic emission is thoughtto be a result of the increasing internal thermalkinetic energy of the free electrons.

This contradiction can be relieved by assumingthat this is also a case where the value of the work-function is not a constant but, this time, the strengthof the barrier is negatively affected by the internalthermal excitation of the peripheral atoms. The resultis again a decrease in the thermionic work-function.

Both classical and modern theories are based onthe assumption that the thermionic work-function, Φ

is a constant, and the increasing thermionic emissionresults solely from the increase of the internal ther-mal kinetic energy of the electrons. This idea of theconstancy of the work-function and the role of theincreasing kinetic energy of the electrons was natu-rally inherited by Einstein's description of the photo-electric effect.

In the application of the photon theory of theemission of photoelectrons, Einstein's work-function,ωo also became a constant, determined only by thechemistry of the metal. The emission and the energyof the photoelectrons, Eph or Eph-max was thought to bedependent solely on the kinetic energy absorbed bythe electrons from the incident photons of given fre-quencies.

Totally at variance to this view, the alternativehypothesis of AETHRO-KINEMATICS is based onsome well known phenomena of ultrasonics.Following the established direction of the alternatehypothesis of thermionic emission, consider the anal-ogy between the present subject and the macro-cos-mic phenomena, discussed in the following quotes(Benson Carlin, Ultrasonics; The physical effects ofultrasound. [239-244]).

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"Among the most outstanding effects of ultrasoundare cavitation, local heating, local pressure, and pro-duction of fog. At present cavitation is a generic termapplied to a number of ultrasonic effects character-ized by the formation and collapse of bubbles in a liq-uid. These bubbles may be empty or filled with gas orvapor. Among the factors which govern the onset ofcavitation are....intermolecular bond, frequency, sys-tem pressure, etc. Cavitation usually forms at thepoint of greatest intensity, .......in standing waves sys-tems the bubbles are trapped in the nodes."Fog production happens when intense waves hit

the interface between a liquid and air, a jet of liquidis thrown up, and a fine mist or fog is produced. Theintensity of the fog is a function of the surface tensionand the power of focusing, etc. Mist has been pro-duced with water, molten metals and other liquids.The size of the particles seems to be a function of fre-quency."The term degassing is applied to the expulsion of

gases from liquids or solids. Ultrasonic waves canbring a degassing action. However, the application isinfluenced by frequency and operates better at lowerfrequencies (about 200 kc). The degassing appears to

be caused by the collection of the gas at the nodes ofthe waves and by cavitation."

Based on all the above and on the existence of theideal gas of Aether, consider the following heuristicpostulates:

1. The only source of kinetic energy for all theemitted electrons is the thermal energy accumulatedby the electron-gas within the boundary of the heatedmetal. If the maximum thermal energy of some elec-trons exceeds the thermionic work-function, φ, thenthermions are ejected. If the thermal energy of eventhe most energetic electrons is under the value of thework-function, Φ there is no thermionic emission.

However, when in this thermionic equilibrium(ETo = Φ), sufficiently high frequency radiation is inci-dent on the surface of the metal, it decreases thestrength of the boundary barrier and the maximumenergy electrons can escape by their initial thermalenergy. In modern theories these electrons are called'photo-electrons', but according to this hypothesis, dueto the origin of the electrons and the mechanism oftheir emission, the name 'photo-thermions' would bemore fitting and clarifying.

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2. It is kinematically plausible that between thegeometrical periodicity of the internal surface of theboundary layer and the pressure fluctuations exertedon its external surface by the incident periodical com-pression pulses of radiation, a related 'standing wavesystem' is generated in the plane of the barrier. Thestanding waves create nodes and antinodes, compres-sions and rarefactions, by which it decreases thestrength of the barrier and decreases the magnitudeof the thermionic work-function. Evidently, the stand-ing-wave-effect should be in proportion to the frequen-cy of the incident radiation.

3. It follows, that the resulting external kineticenergy of the emitted maximum energy photo-ther-mions is:

1/2 mvph-th-max2 = Eph-th-max = Em − ( Φο − βν) (16.5),

where Em is the energy of the maximum thermal ener-gy electrons in a given metal at a given temperature,and Φο is the original constant thermionic work-function. β is a new constant, and ν is the frequency ofthe incident radiation. The expression (Φο − βν) rep-resents the photo-thermionic variable work-function,where Φο, ιs the initial strength of the retarding force

of the boundary which is reduced by the negativeeffect of the incident radiation (− βν).

Equation (16.15) can also be expressed asEph-th-max = (Em − Φο) + βν = Em + βν − Φο (16.6),

which is exactly equivalent to the relations stated byEinstein's equation, hν − ωo (16.12), except a meredifference in the notation, where

Φο = ωο and β = h.Hence, the energy of the maximum energy photo-

thermions is exactly in the same linear relation withthe frequency of radiation, as it was demonstrated byMillikan's plotting. (Fig. 16-5.b)

4. The variation in the intensity of the radiationshould not affect the geometrical periodicity of thestanding wave system which is responsible for theattenuation of the barrier. Based on the analogy withsupersonic effects, it is feasible that the strength of thebarrier only depends on the density of the nodes, thatis, the wavelength of the standing waves.

Higher intensity merely creates higher amplitudeand proportionally greater cavitations at the nodes,through which a greater number of photo-thermions,possessing maximum energy, are capable to escape.

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5. The artificial assumption that all electronsabsorb the exact total quantum of energy of a photon,but they lose more or less of that by colliding with theatoms at different depths of the metal, is not needed,since in the electron-gas the thermal energies are dis-tributed randomly through the whole spectrum.

6. Naturally, there is no 'time-lag' either betweenthe incidence of radiation and the emission of thephoto-thermions, since the formation of the standingwaves proceeds with the velocity of light, and thekinetic energy of the emerging photo-thermions is nota matter of time-consuming accumulation, since itwas already in existence within the electron-gas.

7. The Fermi-Dirac-Sommerfeld distribution ofthe thermal energies between atoms and electronsexplains the experimental facts showing that the pho-toelectric energy is independent from the temperature.

The value of the new constant, β can only befound experimentally by establishing the fluctuationof the value of the work-function at constant temper-ature at various frequencies. Since this constant rep-resents the energy content of a single compressionpulse of the radiation, which creates and maintainsthe standing wave system in the barrier, its quantita-

tive value may resemble to Planck's black-body radi-ation constant, h.

Hence, by the derivation of the same mathemati-cal relations from the above postulates, based on thesimple kinematics of the wave theory, Einstein's pho-ton theory and the accompanying dual nature oflight, at least, as being the only possible solution forthe photoelectric effect, has been found superfluousand therefore avoidable.

At about this stage of the conceptual develop-ment of the quantum theory, (1913) Niels Bohrattempted to explain the inner structure of the hyd-rogen atom and its discontinuous spectrum based onPlanck's quantum and Einstein's photon theories.For purposes of conceptual continuity, this develop-ment will be discussed after the description of analternate explanation of a closely related subject;Compton's electron-photon collision theory.

THE COLLISION OF LANGUAGESIf Einstein's photons are rightfully described as

bold and astonishing, then some new superlativeadjectives must be designed for describing theunique theories of the Compton-effect.

361

Aethro-kinematics CHAPTER SIXTEEN The Collision of Languages

The actual experiments on the subject startedout as research on the phenomenon of X-ray scatter-ing. Eventually they were designed, executed andinterpreted as proving not merely the existence ofEinstein's light corpuscles, but even to demonstratethat, in suitable circumstances, a collision can bearranged between a photon-corpuscle and an elec-tron which is like that, between two billiard balls ona pool table. That is, in both events the Laws of theConservation of Energy and Momentum are upheld.By the year 1927, this goal had been achieved byexpertly juggling between two or more totally incom-patible languages.

Instead of pointing out where one language endsand the other starts in every paragraph or evenwithin each sentence, the reader should be madeaware of the following. Whenever the words or theunderlying concepts of mass, inertia, momentum, col-lision, etc. appear in the text, the language is basedon the thousands of pages of scientific description ofthe concept of a material particle, or a conglomerateof them. Whenever the words or concepts of wave-length, frequency, phase, speed of propagation and thephenomenological concepts of refraction, diffraction,

dispersion, interference, Doppler shift, appear thelanguage in use is based on the thousands of pages ofscientific description of the phenomenon of wave-motion.

Modern physics, especially quantum mechanics,were founded on the alternate use of these two lan-guages, which was legitimized by Niels Bohr'sPrinciple of Complementarity.

"This principle states, that for the description ofNature both languages are necessary, but the waveaspect and the particle aspect of a given phenomenoncan never be observed at one of the same time. If thewave theory provides an explanation then the parti-cle theory will not, and vice verse. The wave theoryand the particle theory thus complement each otherin the interpretation of natural phenomena. (Feren-ce-Lemon-Stephenson, Analytical ExperimentalPhysics, [563]).

Nevertheless, in practice complementarity is notexactly justified. Even the switching between the twolanguages is different in each phase of the modernquantum theories; Planck's quantum of action is dif-ferent from Einstein's photon, which is different fromCompton's billiard balls, which is different from

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Bohr's, and that from DeBroglie's, Heisenberg's, Som-merfeld's. Depending on what sub-language is need-ed to achieve some conceptual compliance with themathematical formula that fits the experimentalfacts. An astonishing example of this method is thequantum interpretation of the experimental facts ofthe Compton effect:

Figure 16-7When fairly high voltage of the order of 20,000

volts is applied to a gas-discharge tube, the heatedfilament of the cathode produces high velocity elec-trons which accelerate toward the positively charged

anode. When the electrons hit the metal block of theanode, X-rays are produced.

Until 1912 scientists believed that X-rays consistof energetic particles, but Laue showed that theycould be diffracted and polarized, just like light. Hethus established the wave nature of this radiation.Measurements on the diffraction patterns showedthat the wavelength of X-rays are in the order of 10-5,about 10.000 times shorter than the wavelength ofultraviolet light.

Figure 16-7. schematically illustrates the experi-mental device by which in 1923 Compton allowed abeam of mono-chromatic X-rays, of well definedwavelength, to fall on a block of carbon and, by acrystal spectro-meter, measured the intensity of thedifferent wavelengths of the scattered X-rays in alldirections.

As illustrated by Figure 16-8 Compton found thatfor any scattering angle two predominant wave-lengths were present: the unmodified wave, whichhad the same wavelength, λ as the incident beam,and the modified wave, which was observed alwaysto be a longer wavelength, λ' and to increase with theincreasing angle of scattering.

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X-raysource

Wavelengths

Incidentradiation θ

Scatteringangle

λ'

λ

Carbon target

Scatteredradiation

SpectrometerCompton shift, ∆λ = λ′ − λ

Figure 16-8Thus, ∆λ =λ'− λ . At θ = 90°, ∆λ= 0.0243 × 10−8 cm

(Angstrom). The wavelength shift is the maximumwhen the scattering is measured in the oppositedirection of the incident beam, i.e., at θ = 180°, ∆λ=0.049 × 10−8 cm. Expressed by the general Comptonequation,

∆λ = 0.0243 (1 − cos θ ) (16.7),which states that independently from the material ofthe scatterer, the wavelength of the scattered radia-tion is greater than the incident radiation by thequantity of 0.0243 (1− cos θ ) A. For a given angle θ,

this quantity is a constant and independent of thewavelength of the incident radiation. This constant iscalled the Compton shift.

Seemingly, the scattering, demonstrated by Com-pton, does not have an evident explanation based onclassical principles."According to the classical theory, when a mono-

chromatic electromagnetic wave interacts with acharged particle, it will be acted upon principally bythe sinusoidally varying electric field of the wave.Under the influence of this changing electric forcethe particle will oscillate in simple harmonic motionat the same frequency as that of the incident radia-tion, and since it is accelerated continuously, it willradiate electromagnetic radiation of the same fre-quency in all directions. The charged particle neithergains or loses energy, since it re-radiates at the samerate as it absorbs. The classical scattering theoryagrees with experiment for all visible or longer wave-length of radiation."A simple example of the unchanged frequency of

coherent scattered radiation is this: light reflectedfrom a mirror (a collection of scatterers) undergoesno apparent change in frequency." (X.Y.Z, Particle

364


Incident radiation

Scattering angles

Carbon target

Scatteredradiations

45°

90°135°

180°

λ λ

'λ

∆

unmodified wave λmodified wave 'λ

Aspects of Electromagnetic Radiation, [134])Thus, there was no clue in the classical approach

which would suggest that higher frequency X-rayscould produce a shifted scattering, and Compton wasforced to look for a solution different than the classi-cal scattering theory of electromagnetism."At first he attempted to account for this observed

softening of the secondary radiation within theframework of classical conceptions and thus tookrecourse to the Doppler effect, (one of the most typicalundulatory phenomena in optics)."He found, however, that in order to account for the

observed shift, all of the electrons in the scattererwould have to be moving in the direction of the inci-dent radiation with a velocity of about half that oflight. Since such an assumption was obviously unac-ceptable, Compton concluded that the classical theorywas irreconcilable with experience.""Since neither Thompson's theory of scattering nor

the Doppler effect could explain the experimentalfacts, Compton decided to examine 'what would hap-pen if each quantum of X-ray energy were concentrat-ed in a single particle and would act as a unit on asingle electron?! Thus, finally he boldly applied the

extreme quantum picture of the radiant energy.'"(Max Jammer, Conceptual Development of QuantumMechanics, [168])"Planck introduced the idea that radiation must be

emitted by bundles of energy, although he believedthat once emitted, the energy spread in waves.Einstein extended Planck's idea to the absorption ofradiation and added the assumption that once thequantum of energy was radiated, it preserved itsidentity as a photon until it was finally absorbed. Inthe special theory of relativity it was shown thatmass and energy are identical. Since photons haveenergy, they must have mass. This gradually devel-oping concept that the photons are true particlesthroughout their life comes to its climax in Comp-ton's assumption that the photons had the very 'me-chanical' property of momentum, and solved theproblem of impact of a photon and a material particleby means of relativistic mechanics." (X-rays [204])

Hence, from here on, Compton's theoretical goalwas to make his description of X-ray scattering byelectrons as analogous as possible with the collisionsbetween billiard balls. First, in order to justify theapplication of the conservation laws, both 'particles';

365


the electron and the photon must have qualitativelycompatible energies and momenta. This can be achie-ved as follows:"In a collision between a photon and an electron,

the electron assumed to be initially at rest and essen-tially free, that is, not bound to the atoms of the scat-terer. Let us apply the law of conservation of energyto this collision. Since the recoil electrons may have aspeed, v that is comparable to the speed of light, wemust use the relativistic expression for the kineticenergy of the electron." (Halliday, Physics [1101]

(Bear in mind that the Doppler effect interpreta-tion was dismissed, based on the unacceptablerequirement of electron velocities up to about halfthat of light.)

Based on Einstein's fundamental equation, E =mc2, the relativistic kinetic energy of a particle, K =mc2−moc2. The initial energy of a photon is hν, whichis also the total energy of the system before collision.Therefore, after collision we may write

hν = hν ' + ( m − mo )c2. (16.8),in which hν' is the energy of the scattered photonafter collision and the second term on the right is the

relativistic expression for the kinetic energy of therecoiling electron, m being the relativistic mass andmo the rest mass of the electron."Substituting c/λ for ν (and c/λ' for ν'), and elimi-

nating the relativistic mass m, leads us to−−−−−−−

hc/λ = hc/λ' + moc2 (1/√ 1 − (v/c)2) − 1. (16.9)"Now let us apply the (vector) law of conservation of

linear momentum to the collision of Figure 16-9.

Figure 16-9"We first need an expression for the momentum of

the photon. Earlier we saw that if an object complete-

366


λPhoton Electron

v = 0

x

y

x

y

λ'Photon

Before After

Electron

ψ

θ

ly absorbs an energy U from a parallel light beamthat falls on it, the light beam, according to the wavetheory of light, will simultaneously transfer to theobject a linear momentum given by U/c."

(Note, that this electromagnetic transfer of wavemomentum, or light pressure is measured per unitarea per unit time.)"On the photon picture, we imagine this momentum

to be carried along by the individual photons, eachphoton transporting (its concentrated) linear mo-mentum in the amount p = hν/c, where hν is thephoton energy. Thus, if we substitute λ for c/ν, wecan write the momentum, p of the photon as

E hν hp = −−− = −−−− = −−−. (16.10)

c c λ"For the electron the relativistic expression for the

linear momentum is given by−−−−−−−−−−

p = mo v /(√ 1 − (v/c) 2). (16.11)"Our immediate aim is to find ∆λ ( = λ' − λ )", the

wavelength shift of the scattered photons. Carryingout the necessary algebraic steps leads to this simpleresult:

∆λ = h/mo c (1− cos ψ . (16.12)"Thus the Compton shift, ∆λ depends only on the

scattering angle ψ and not on the initial wavelengthλ. Compton's experiment did not involve observa-tions of the recoil electron in the scattering block.""Note from the equation that ∆λ varies from zero

(for ψ = 0, corresponding to a 'grazing' collision whenthe incident photon being scarcely deflected) to2h/moc (for ψ = 180°, corresponding to a 'head-on'collision, the incident photon being reversed in direc-tion). " (Halliday, Physics [1102]Further more:"Because the incident and scattered photons have

different frequencies, the latter is not to be thoughtas merely the incident photon moving in differentdirection; rather the incident photon is annihilatedand the scattered photon is created." (Particle as-pects of electromagnetic radiation [137])

To make the conceptual content of these conclu-sions perfectly clear, consider the following quotefrom Kompaneyets, Basic Concepts in Quantum Me-chanics [136]:

367


"The relationship between the frequency and theangle of scattering may be obtained immediately ifthe laws governing the collision of two elastic spheresare applied. One 'sphere' is the particle and the otheris the photon. ...The greater the angle of scattering ofthe photon, the more energy it imparts to the elec-tron. Thus, the energy of the photon reduced: i.e., itsfrequency is lowered.""Classically, the wavelengths of the incident and

scattered radiations are essentially equal; hence,Compton scattering agrees with classical scatteringin the region of ∆λ /λ << 1. We see here an exampleof the correspondence principle as applied to quan-tum effects." (J. Patrick, Particle Aspects of Electro-magnetic Radiation, [139])"The presence of the unmodified line may be ac-

counted for as follows. In setting up our equations, itwas assumed that the electron with which the pho-ton collides is free. It is possible, however, that anoth-er kind of collision may occur in which the electronremains bound to the atom. Such a collision may beregarded as taking place between the photon and theatom as a whole. If the mass of the atom is substitut-ed for m, the computed change of wavelength is

found so small as to be beyond the possibility ofdetection. It may well be that, in the scattering ofphotons, the electron sometimes behaves as if itbound to the atom and sometimes as if free." (Ritch-myer, Introduction to Modern Physics [389] "Compton's experiment confirmed that X-rays can

scatter from electrons as particles. However, there isa remarkable ambiguity in the experiment, whichCompton himself points out:'The crystal spectrometer measured a wavelike pro-

perty, the wavelength, and measured it by means of acharacteristically wavelike phenomenon, interfer-ence. But the effect of the graphite scatterer on thevalue of that wavelike property could be understoodonly in terms of a particlelike behavior. Thus X-raysbehaved as both particles and waves in the same ex-periment." (M. L.Warren, Introduct. Physics, [511])

Figure 16-10 is recalling Fig. 14-12 from the kine-matic analysis of the probable momentum amplitudedue to various collisions between two elastic, spheri-cal, equal masses. This illustration is a visual state-ment about the total absurdity of Compton's collisionhypothesis. It shows what his casual assumptionabout the collision between spherical 'billiard balls',

368


one being the electron and the other being the pho-ton, must mean conceptually.

Figure 16-10As it has been presented in Chapter Fourteen,

the concepts of 'grazing' and 'head-on' or 'in-between'collisions there is an infinite variety of impacts,which explicitly depend on the collision parameter, b,that is, on the distance between the centers of thetwo spheres and there is absolutely no substitution inour minds for these concepts.

Further more, it is an unavoidable mathematicalrequirement, that the conservation laws must con-

sider the quantity of both rest masses, or both linearmomenta involved to determine the after collisionangles of the particles. Adding to this, that theunthinkable 'spherical zero mass' cannot even existin mathematics, one may try to fathom, not the pic-ture, not the concept, not the languages, but merelythe incompatible words put together incoherently inthis description: a massless spherical X-ray wave con-centrates itself in time and space, into a spherical zeromass, called a photon. Collides grazingly or head-onwith the greater spherical mass of the electron andelastically rebounds in the proper angle, as a perfectsphere should, or is annihilated and re-created, butwith a lower than its initial frequency. The resultingenergy shift can then be measured by interferencewhen the X-ray photons spread out again in spaceand time, back into their original form of sphericalelectromagnetic waves."In other words, a hypothesis, supported by uncon-

testable experimental evidence, became physicallysignificant only by the use of its own negation."(Jammer, Conceptual Devmnt. of Quantum...[173])

What then is the use of the words, if the only pos-sible comprehension gained by them is that when

369


O1

b

O2

= 0

R

R O1

b O2

θ

θA

C

1VmU1m

2Um

2Vm

certain mathematical symbols perform certain alge-braic operations, they result to some quantitativeapproximation of certain experimental facts?!

THE DOPPLER EFFECT REVISITEDThus, Planck's semi-classical quantum concept,

which survived the photoelectric effect as the energycontent of a single compression pulse in the Aether,in the Compton effect became a physical body ofspherical extension, and the elasticity of solids.

As it has been quoted above, at first Comptonattempted to account for the observed softening ofthe scattered X-rays by means of the most typicalundulatory phenomenon, the Doppler effect. How-ever, later he discarded the idea based on two basicarguments; a) In order to comply with the experi-mental facts, based on the classical Doppler effecttheory, the scattering electrons would have to bereceding from the X-ray source with a velocity ofabout one half that of light. b) For the same reason,all electrons would have to be moving in the samedirection as that of the incident radiation.

As it has happened in a later stage in the devel-opment of the photon-collision hypothesis, for the

need of establishing the mass and momentum of thewave-particle, Compton was forced to justify the useof relativistic treatment by proposing that the recoil-velocity of the electrons could approach that of light.With this assumption, however, he negated one of hisbasic reasons, a) for discarding the Doppler interpre-tation of the experimental facts.

It should also be noted here that the real require-ment for the Doppler recession velocity of the elec-trons is less than one quarter of the velocity of light.

Figure 16-11

370

Aethro-kinematics CHAPTER SIXTEEN The Doppler Effect Revisited

SO

λ

λ

V =0o

V =0s

V =0s /V =0o

λ 'S

(a)

(b)

0 o

45 o

90 o

135 o

180 o

Ψ

Compton's second argument b), will be defeatedat a later stage in the description of the Comptonscattering by the alternate theory of AETHRO-KINEMATICS.

Figure 16-11 illustrates the well-known mecha-nism and the simple explanation of the typical undu-latory phenomenon of the Doppler effect.

Part (a) shows a source, being at rest in the medi-um and produces periodical compression pulseswhich are propagated in the form of expandingspheres in the isotropic medium with a given veloci-ty. Since the pulses are generated at equal time in-tervals, the distance between them, or the wave-length, λ of the pulse train, is all the same. Becauseof the spherical propagation, the wavelength, obser-ved by any stationary observer is the same in alldirections.

Part (b) illustrates the special case, when thesource is in motion relative to the medium. It can beseen from the exaggerated diagram that, due to themotion of the source, the wavelength is found to bedifferent by stationary observers observing from dif-ferent directions. The magnitude of the so-calledDoppler shift depends on the ratio between the speed

of the source and the speed of propagation, and onthe angle between the line of sight of the observerand the direction of motion of the source.

Commonly, in the mathematical treatment of themechanical waves of sound, the conveying medium isthe idealized gas of air. In AETHRO-KINEMATICSthe waves, or the periodical compression pulses oflight, are conveyed by the ideal gas of the Aether.

In the following Doppler interpretation of theCompton scattering, the only effect involved is therecession of a source from an observer (spectrograph)at rest relative to the isotropy of the medium. Thesimple mathematical expression for this effect is

λ' = λ (1 + (Vs /c)) (16.13),where λ' is the increased, observed wavelength, c isthe velocity of light and Vs is the velocity of thesource.

It is also evident from the diagram, that thechanges are proportional to the various angles, ψbetween the line of sight of the observer and the di-rection of motion of the source.

By to the rules of elementary trigonometry,λ' = λ (1+ (Vs cos ψ/c) (16.14).

371


Thus, in the case of a receding source, the Dopp-ler shift, ∆λ between the initial, and the observedwavelength is

∆λ = (λ'− λ) = λ (1 + (Vs cos ψ /c) − λ)= ((λVs )/c) cos ψ (16.15).

As quoted above, one of the reasons given for theincapability of classical physics to explain theCompton scattering of radiation was that, accordingto the electromagnetic theory of light, a mirror (aperfect scatterer) must reflect or re-radiate the lightwaves with exactly the same wavelength. The idealexample of this is a mirror, a collection of scatterers,which reflects light with no change in the frequencyof the incident light. Consequently, the classical theo-ry of scattering of light cannot account for the shiftin the wavelength or frequency decrease of the scat-tered radiation demonstrated by the Compton effect.

Nonetheless, using the same analogy, it will beshown that the reflected radiation produced by areceding mirror results in a Doppler shift, or thelengthening of the incident wavelength, which ismathematically equivalent with that derived fromthe Compton collision hypothesis.

Consider first, the well-known nature of thereflection of light. When one stands at one meterfrom a mirror with a camera, the focus must be setfor two meters to achieve a sharp picture. The mir-ror-image is the same distance behind the surface ofthe mirror as the real object is in the front of it.

Figure 16-12Figure 16-12 (a) illustrates that when an observ-

er is looking at a source in the mirror in an angle, theimage appears at the same distance behind the mir-ror, as the source does before it. As illustrated by (b),if the mirror recedes from the source with a velocityVm = 1 m/sec, then the velocity of the image relative

372


d

ObserverMirror

d

O

Image

I

Source

S

S

S

Image

I

Source

Moving mirror

I'

mV iV

iV = 2 mV

(a) (b)

0T

1T

to the source will be Vi = 2Vm . Thus, looking at theimage from the direction of the source one will ob-serve that it recedes with a velocity of 2m/sec.

Applying the Doppler effect to this case, we canconclude that the shift in the wavelength of the re-ceived light from a receding mirror is greater thanthat produced by a receding source.

If the recession of the mirror is in the line ofsight, the shift is twice as great as in the case of areceding source.

Figure 16-13 shows a diagram for deriving thegeneral formula of the Doppler shifting of radiationwhen a scatterer is in motion relative to the trans-mitting medium and receding from a stationarysource and observer. In the illustration, a mirror isreceding from a stationary source. It is turned at anyrandom angle relative to the direction of the propa-gation of light and its own motion. The mirror isreceding with uniform velocity, Vm .

In one second, the mirror moves from the positionO to the position O'. During the same interval oftime, the image of the source moves from I to I'. Asthe diagram shows, the vector drawn between C andI' represents the velocity of the image, Vi. In order tofind out the length I'C, first the other side IC, of theright triangle I'IC must be found. It can be seen thatin the right triangle OBO' α = 180° − ψ.

OB = OO' sin α = Vi sin (180° − ψ) = Vi sin ψ.Since IC = OB,

IC = Vi sin ψ (16.16).Furthermore, it can be seen that β = 1/2 ψ, and

because the triangle O'I'D is similar to I'IC, so γ =β = 1/2 ψ.

373


Source

Image Mirror

α

C

I

I'

S

β

γ

O

O'

Observingscreen

A

Normal

D

ψ

A'B

mV

Vi

Figure 16-13

In the right triangle I'IC I'C = IC tan γ = IC tan ψ /2 (16.17).

Substituting Eq.(25) into (26), we haveI'C = Vi sin ψ (tan ψ/2)

= Vi (2sin ψ/2cos ψ/2) [(sin ψ/2/(cos ψ/2)]

= 2 Vi sin2 ψ/2= Vi (1 − cos ψ ) (16.18).

Using the Doppler formula Eq. (16-22) for asource receding from a stationary observer,

λ' = λ (1 + Vs /c) since, in this case, the image is equivalent with thesource, after substitution we have;

λ' = λ (1 + Vi ( 1 − cos ψ ) /c)

λ Vi = λ + −−−− ( 1 − cos ψ )

c

λ Vi ∆ λ = λ' − λ = −−−− ( 1 − cos ψ ) (16.19),c

where ∆λ is the Doppler shift produced by the imageof a source, receding from a stationary observer withthe velocity Vi .

At a given recession velocity, this result totallyagrees with the experimental facts for all angles ofscattering, for a given wavelength or frequency ofradiation. In comparison with Eq. (16-21), Compton'sfinal result derived from the laws of conservation ofenergy and momentum,

h ∆λ = λ' − λ = −−−− (1 − cos ψ ), (16.20),

mo c it is evident that the two equations are very similarand the only difference seems to be that, while in theCompton expression (h/moc) all members are con-stants, in the respective expression in the Dopplerinterpretation (λVi /c), the two factors, λ and Vi areseemingly independent variables. Nevertheless, asfar as the mathematical derivation is concerned, it iseasy to prove otherwise. In Newtonian mechanics,momentum is expressed by the equation p = mV.According to Maxwell, the momentum carried byelectromagnetic radiation is p = E/c. Since in thequantum theory, E=hν, the momentum carried bythe radiation is p = hν/c. But ν = c/λ, therefore

hc/λ hp = −−−−− = −−− ,

c λ374


Thus the quantum theoretical expression for thevelocity of the electron, we get

p hV = −−−− = −−−− ,

m λmsubstituting the quantum form of the velocity intothe expression of the Doppler interpretation,

λ V λ (h/λm) h−−−− = −−−−−−−− = −−−−− .

c c mc This purely mathematical result shows that the

general equation derived from the Doppler interpre-tation is exactly equivalent to that of Compton's, andthat the expression (λV/c) is also a constant, justlike Compton's (h/mc). However, while the indepen-dence of the shift from the frequency was conceptual-ly 'surprising' for the collision theory, here it is a logi-cal consequence of the basic concept that the recedingvelocity of the scattering electron is a result of themomentum of the incident radiation and thereforedirectly proportional to its frequency: V ∝ ν.

Consequently, the Doppler shift, ∆λ, measured atany given angle is a constant for all frequencies.

For the conceptual description of the Dopplerinterpretation of the Compton scattering based on

the fundamental assumptions of AETHRO-KINE-MATICS, consider the following:

1) From the stand point of this theory, the physi-cal meaning of Planck's universal constant h is sim-ply the forward momentum carried by a single elec-tromagnetic pulse. Its multiplication by the frequen-cy simply gives the total energy delivered through aunit area in space by the number of pulses per unittime.

2) Consequently, AETHRO-KINEMATICS agreeswith the expression E = hν. This also agrees with theconcept of the free electrons as scatterers, except ac-celerated not by individual collisions with wave-par-ticle photons, but rather by the forward momentumof the electromagnetic compression pulses producedby the Planckian radiators, and kinematically trans-ferred by the Aether. In this hypothesis, too, the lawsof the conservation of energy and momentum arestill applicable.

3) Hence, the Doppler interpretation of X-rayscattering does agree with the assumption that thescatterers are free electrons, but takes them as themembers of an randomly isotropic ideal gas, con-tained within the boundaries of the scattering block.

375


(This electron-gas acts very similarly to the atomic ormolecular gases, where the random velocities of theradiating units and the resulting Doppler shiftsaffect the sharpness of the spectral lines and causethe well-known phenomenon, called the Dopplerbroadening.)

Figure 16-14.As Figure 16-14 illustrates, in the ideal electron-

gas there is a constant and isotropic random motion,where at any instant the same number of particlesmoving in any direction in any part of the gas. The

acceleration of an individual electron due to thetransfer of the forward momentum of the pulses ofradiation becomes a superimposed component on itsinitial, random velocity. The result is a general tem-porary drift-velocity of the gas in the direction of theincident X-ray pulses.

This superimposed drift is temporary, becausethe electrons soon lose their individual extra compo-nent of velocity in the course of the frequent colli-sions with the atoms. Nevertheless, they soon aftergain some back again from the new pulses. Thus, thecomponent is a constant.

It is, therefore, plausible that the statistical be-havior of the electron-gas, relative to its initial iso-tropic randomness, shows a general recession in thedirection of propagation of the X-rays, which is,therefore, also proportional to the frequency of theradiation. This is the answer to Compton's argumentfor the impossibility of the motion of all electrons inthe same direction.

In the initial analogy a mirror was used as thescatterer. Now, it can be replaced by a gas of perfectlyelastic, spherical particles, the electrons, one of whichis illustrated on Figure 16-15.

376


λ

X-ray pulses

Initialrandomvelocity

Componenttransmitted byX-ray pulses

Finalrandomvelocity

Figure 16-15.As an aid for accepting this assumption, it should

be noted, that, in all sections of science involved withthe electron, it is assumed to be a spherical particle.This shape is also the only choice for statisticalmechanics in the analysis of any ideal gas. It can beshown that the behavior of a great number of ran-domly moving and colliding particles is independentfrom their shape, whether spherical, cubical, or thatof a donut-vortex.

The character of elasticity is similarly statisticaland therefore the only special assumption requiredto complete the analogy is that each infinitesimalarea of the spherical surface of the electron acts likea section of a plain mirror. Thus it is a perfect scat-terer in all directions, as illustrated in Figure 16-15.

The illustration also makes it clear why, in thescattering phenomenon, there exist a Doppler shifteven at 90° and beyond.

As for the existence of the unmodified line, Comp-ton's assumption is satisfactory; i.e., that the fixedatoms of the crystalline structure, or the bound elec-trons, do not share the recession drift and do not pro-duce a Doppler shift in the reflected X-rays.

The electron-gas contained in the boundaries of ascattering block, under the pressure of the incidentX-ray pulses and with the resulting superimposedrecession-drift, is justifiably taken as a receding mir-ror. Thus, by the simple wave-phenomenon, theDoppler shifting of the wavelength of the reflectedimage, this alternative interpretation becomes thenatural explanation of the phenomenon, in agree-ment with the classical principles .

377


Electron

λ

X-ray pulses

Ve

It should also be considered that measuring andanalyzing the velocity of the recoil electrons werenot included in Compton's experiments. Calculatingthe conservation laws, Compton exclusively concen-trated on the energy loss of the radiation (∆λ), andfor that goal he needed to consider only the mass ofthe electron. In the latter experiments of Bothe,Geiger and Bless, the post- collision velocity of therecoil electrons has been stated to be in agreementwith the terms of the theory. However, the complica-tions of such approval can only be realized when thepre-requisites of the experiments were considered indetail.

On the one hand, the intensity of the Comptonshift in a given angle is measured through the dif-fraction and dispersion of the reflected radiation. InCompton's language, this happens by the spectralanalysis through the interactions among an im-mense number of photons.

On the other hand, the velocity of the recoilingelectrons can only be found by their individual mo-tion traced through the cloud chamber under theinfluence of a magnetic field. Hence, for every smallchange in the observed angle, there is a different

shift produced by the diffracted stream of photons.Therefore, for each resulting recoil-angle, thereshould be a single electron traced in a fractionallydifferent direction with a fractionally different speed.Imagine the task of establishing the simultaneityand the identity of the photon-electron pair beforeand after the collision in order to match the resultingquantities.

It should be added that the collisions occur with-in the boundary of the scatterer. Hence, for a truerecoil-velocity, the electron must not have any othercollisions afterwards, and it should somehow alsoescape the work-function of the metal, which wassuch a determining factor in the photoelectric effect.

THE SOLAR SYSTEM OF THE MICRO-COSMOS

Planck's derivation of the experimental curve ofblack-body radiation by quantizing the electromag-netic oscillators, and Einstein's photon-quantizationof radiation itself triggered a general scientificinquiry, as to whether the same concepts and mathe-matics could be applied to the mechanism and struc-ture of the atom as a natural harmonic radiator.

378

Aethro-kinematics CHAPTER SIXTEEN The Solar System of the Micro-cosmos

In 1909, Rutherford gave conclusive experimentalverification of the so-called nuclear atom, consistingof a very small nucleus surrounded by a number oforbiting electrons."At first glance it appears that we can simply allow

the electrons to circulate about the nucleus in orbitssimilar to the orbits of the planets circulating aboutthe sun. Such a system can be stable mechanicallybecause the centrifugal force can be made to balancethe Coulomb attraction just as it balances the gravi-tational attraction in the planetary system. But a dif-ficulty arises in trying to carry over this idea fromthe planetary system to the atomic system."The problem is that the charged electrons would be

constantly accelerating (centripetal) in their motionaround the nucleus, and, according to the classicalelectromagnetic theory, accelerating charged bodiesmust radiate energy in the form of electromagneticradiation.

“The energy would be emitted at the expense of themechanical energy (tangential velocity) of the elec-tron, and it would spiral into the nucleus. Further-more, the continuous spectrum of the radiation,which would be emitted is not in agreement with the

discrete line-spectrum that is known to be emitted bythe atoms."The difficult problem of the stability of atoms actu-

ally led to a simple theory of atomic structure, pro-posed by Niels Bohr in 1913." (Eisberg: Fundamen-tals of Modern Physics. [108])"On the assumption that the hydrogen atom con-

sists of an electron revolving around a nucleus (a sin-gle proton) whose charge is equal and opposite tothat of the electron and whose mass is very large incomparison with the mass m of the electron, Bohrfirst investigated how far classical mechanics couldbe employed. From Kepler's first law he knew thatthe orbit of the electron is an ellipse with the nucleusin one of its foci. Calling the major axis of the orbit2a and the energy which has to be added to the sys-tem in order to remove the electron to an infinite dis-tance from the nucleus W, the charge of the electrone, and that of the nucleus e', Bohr could easily showthat on the basis of classical principles

−−−− −− ω = √ 2/π (W3/2 /e2 √ m) and 2a = e2/W (16.21),

which indicates that the frequency of revolution, ωand the major axis of the orbit depend only on the

379


value of W and are independent of the eccentricity ofthe orbit. Bohr now saw that by varying W, all possi-ble values of ω and 2a could be obtained. The exis-tence of sharp spectral lines, however, shows that thelatter quantities have to assume definite values,characteristic for the system." (Jammer: ConceptualDevelopment of Quantum ....[77])

In contrast to the continuous spectrum of electro-magnetic radiation emitted from the surface ofsolids, the radiation emitted by the atoms of thehydrogen gas is concentrated at a limited number ofwavelengths at which the lines of the relatively sim-ple spectrum of the hydrogen atom are found.

As Figure 16-16 illustrates, there is an obviousregularity in the spacing of the spectral lines of thediscontinuous spectrum of hydrogen.

Figure 16-16.

At the end of the last century, several scientistwas tempted to look for an empirical formula thatwould express this regularity. Such a formula wasindeed discovered by Balmer in 1885.

The simple relation of the distances between thelines of the Hydrogen spectrum made it evident thatthe electron can only orbit at certain specific dis-tances from the nucleus, and therefore having onlycertain discrete mechanical frequencies. It also sug-gested to Bohr that there is no classical mechanicalreasoning to explain these facts. Convinced of theinability of the classical approach, Bohr felt com-pelled to turn to Planck's quantum hypothesis for asolution. Indeed, eventually he was able to identifythe exact relationship that made it possible to incor-porate Balmer's Formula, Planck's quantum andRutherford nuclear model with the Newton-Keplercelestial mechanics.

How, indeed, Balmer's empirical formula suggest-ed a way to Bohr of corroborating classical mechanicswith the quantum conceptions, usually described asfollows:

According to Balmer's formula, as the distancebetween the lines decreases toward the shorter wa-

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33 30 27 24 21 18 15 12 9 6 3 0

Frequency (10 Hz)14

Lyman series Balmer seriesPaschen series

Brackett series

velengths of visible radiation, they reach a serieslimit, at which no more distinction is possible. If thewavelength of radiation is in Ångstroms (10-8 cm),this limit is λ = 3646 Å, and Balmer's simple formu-la can be written as: λ = 3646× n2/(n2−4) Å, wheren is an integer.

A few years later, Rydberg found that Balmer'sformula and its immediate generalization can mostconveniently expressed in terms of frequency, ν as:

1 1 ν = RH c (−−−− − −−−− ) (16.22),

n22 n1

2

where ν is the frequency, RH is the Rydberg constantfor hydrogen, n1 and n2 are integers, and c is thevelocity of light.

Consequently, Bohr's explicit task was to designan atomic structure for hydrogen in which, based onthe above mechanical principles, the possible orbitalfrequencies of the electron were somehow restrictedto certain discrete values, related to Planck's con-stant and in agreement with Einstein's photon con-cept, which in turn should lead to the mathematicalderivation of Balmer's formula.

Realizing that there was no other conceptuallycoherent approach to explain the stability of theatom and the discontinuity of the hydrogen spec-trum, Bohr, in direct contradiction with Newton'smechanics and Maxwell's electrodynamics, boldlypostulated the following assumptions :

"1. An electron in an atom moves in a circularorbit about the nucleus under the influence of theCoulomb attraction between the electron and the pro-ton, and obeying the laws of classical mechanics.

"2. But, instead of the infinity of orbits whichwould be possible in classical mechanics, it is onlypossible for an electron to move in an orbit for whichits orbital angular momentum L, is an integral multi-ple of the Planck constant h, divided by 2π.

"3. Despite the fact that it is constantly accelerat-ing, (centripetal acceleration), an electron moving onsuch orbit does not radiate electromagnetic energy.Thus its total energy, E, remains constant.

"4. Electromagnetic radiation is emitted if an elec-tron, initially moving in an orbit of total energy, Ei,discontinuously changes its motion so that it moves inan orbit of total energy, Ef.

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The frequency of the emitted radiation, ν (nu) isequal to the quantity (Ei −Ef) divided by Planck's con-stant, h."These postulates do a thorough job of mixing clas-

sical and non-classical physics. The electron movingon a circular orbit is assumed to obey classicalmechanics, and yet the non-classical idea of quanti-zation of orbital angular momentum is included. Theelectron is assumed to obey one feature of classicalelectromagnetic theory (Coulomb's law), and yet notto obey another feature, the imperative emission ofradiation by an accelerating charged body." (Eisberg:Fundamentals of Modern Physics [114])

So, Bohr derived the Balmer's formula as follows:Assuming a circular orbit of an electron about a

stationary nucleus (proton), the total energy of thesystem, E, is given by

E = mv2 − ee'/r (16.23),where m is the electron's mass, v is its orbital speed,e and e' are the opposite charges of the proton andthe electron representing the Coulomb force ofattraction between them, and r is the radius of theorbit. Hence, the stability of the atom based on clas-

sical principles can be expressed by the equality ofcentripetal acceleration and centripetal force:

mv2/r = e2/r2 (16.24).Combining Eqs. (2) and (3) we obtain

E = 1/2 (e2/r ) (16.25).If the frequency of the orbital motion is f, then

the orbital velocity, v = 2πrf, and from the precedingrelations, the orbital or mechanical frequency of theelectron is

−−−− −− f = √ 2/π (− E3/2/e2 √ m ) (16.26).

With this, the description of the proton-electronsystem, based on classical mechanics and electrody-namics, reaches its limitations and suggests no re-strictions in the selection of possible orbits. Depen-ding only on the angular velocity and on the radius,all orbits, and therefore all orbital frequencies, arepossible.

At this stage of his theory, with some revisionsBohr implied Planck's assumption that electromag-netic oscillators can only emit energy in discretequantities of hν, where h is a constant and ν is the

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frequency of the radiation. According to Planck, thetotal energy of a particle, such as an electron, execut-ing simple harmonic motion under the influence of aharmonic restoring force is: E = nhν, n = 0,1,2,...where n may be any integer value.

Bohr applied the quantization to the orbital an-gular momentum, L of an atomic electron movingunder the influence of the inverse square force ofCoulomb's attraction:

L = nh/2π, n = 1,2,3,...(16.27).This reveals the essence of quantization; that, for

some unknown reason, no other quantities areallowed. The next question is, how can these fixedsizes of the quantized orbits and the resulting me-chanical frequencies be related to the specific fre-quencies of the radiated energy?

(To keep the notations consistent, it should bepointed out that in Bohr differentiation between thetwo kinds of frequencies, the mechanical or orbitalfrequency of the electron is f, and the frequency ofthe radiation emitted by the electron is ν.)

At this point in the theory of the solar atom Bohrhad to make the transition from mechanics to quan-

tum theory. As he states in the fourth postulate, forthe sake of the mechanical stability of the atom, theelectron cannot radiate continuously on a permanentorbit, only at the instant when it jumps from a high-er to a lower energy level.

Mechanically, each allowed orbit or angularmomentum must represent a distinct frequency ofrevolution, but the radiation frequency is separatedfrom the orbital frequency by the assumption thatthe energy is radiated discontinuously during thejump of the electron. Thus, a further assumption isneeded, namely, that the frequency of the radiationemitted by the electron should be the averagebetween the mechanical frequencies of the initialand final orbits.

For the calculation of this average, Bohr suggest-ed that at the instant of the jump the electron shouldbe taken as unbound (free) and its orbital frequencyshould be taken as zero. After the jump, on its finalorbit, the electron is bound, and therefore its orbitalfrequency is f. Hence, the average mechanical fre-quency between the two orbits is f/2− 0, or f/2.Therefore, the relation between the mechanical fre-quency and the radiated frequency is ν = f/2, and the

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energy emitted during the jump is E = nhν = nhf/2 (16.28).

Combining Eqs (7) and (5) Bohr obtained thequantized mechanical frequency

f = 4π2me4/n3h3 (16.29).Finally, since the radiated energy by Einstein's

formula is En2 − En1 = hν (16.30),

the quantized frequency of the radiation is given by

2π2me4 1 1ν = (−−−−−−−− ) ( −−−−− − −−−−− ) (16.31).

h3 n22 n1

2

When selecting the value n2 = 2, it gives the radi-ated frequencies of the hydrogen atom in exact ag-reement with the Balmer's series of the spectrallines. The first part of the right side of the formula isequivalent to Rydberg's constant.

During experimental verification of the theory,the discovered fine structure of the spectral linesmade it necessary to account for the fact that thenuclear mass is actually finite. Based on this distinc-tion, Bohr refined the formula, which then turned

out to agree with the detailed spectroscopic data towithin 3 parts in 100,000!

Nevertheless, in spite of its great success, the the-ory was not fully accepted as is freely quoted fromRitchmyer's 'Introduction to Modern Physics':

..."a hybrid theory of this sort was widely felt to beunsatisfactory. Bohr solved the old problem of thestability of the atom merely by stating that it did notexist so long as the electron remained in one of itsallowed stationary orbits. But the problem of stabili-ty was solved at the expense of throwing away theonly picture we had of the mechanism by which theatom could emit spectral lines. For Bohr's postulatesprovide no picture of the sequence of events duringtransitions between orbits."...Wave-mechanics, that ultimately replaced Bohr's

solar model, leads very nearly to the same quantumstates, but suggests a quite different picture of thebehavior of the electron while in a quantum state. Itis only half true that the electron is in motion in theatom, at least, it cannot be said to follow a definiteorbit. Because of the abstractness of this new theory,the original simple Bohr picture is commonly felt toretain something more than mere historical interest."

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Nevertheless, Bohr's 'hybrid' model of atomicstructure was temporarily accepted and, as for itsdeep rooted conceptual confusion, the excuse ofModern Physics was simple and superficial:..."we should not be surprised if the laws of classical

physics, which are based on our experience withmacroscopic systems, are not completely valid whendealing with microscopic systems such as the atom."(Eisberg; Fund. of Modern Physics [115])

Because of the comparatively simple mathemati-cal derivation and its explicit dependence on classicalmechanics, Bohr's theory represents one of the mosttransparent examples of modern epistemology; themethod of step-by-step sacrifice of conceptual andlogical consistency for the sake of the ultimate goal,at any cost; an experimentally verified mathematicalformula.

For the sake of a possible alternative hypotheses,it should be noted here that Bohr's solar model of thehydrogen atom has never been disapproved or super-seded by later developments of more sophisticatedquantum theories. Since, according to the correspon-dence principle, relativistic mechanics must reduceto Newtonian mechanics in cases of velocities much

smaller than that of light, the most abstract predic-tions of the latest version of quantum-mechanics stillmust agree with Bohr's predictions when it dealswith the simple case of a one-electron-atom.

Though a confusing mixture of classical and mod-ern concepts, the solar model is, nevertheless, thelast humanly perceptible and experimentally justifi-able mechanism; a conceptual link between themacro-cosmic and micro-cosmic structure of matter.It is also questionable how much of the original sim-ple Bohr picture has been retained as the conceptualfoundation, during the metamorphosis of the theorythrough matrix- wave- and quantum-mechanics. Nomatter what tremendous advance modern mathe-matical theories have made into the conceptual vacu-um of modern physics, it can hardly be denied thatbehind all sophisticated trickery of prediction, thesubject still is the solar atom and its orbiting elec-trons. In fact, at least two explicit points in the mostmodern level of quantum-mechanics, which are stillin firm contact with classical physics.

The most fundamental quantum mathematicalequation, the Schrodinger wave-function, has beenderived from the ancient formula of the waves on a

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taut string, expressing simple harmonic oscillation,which has been found applicable to all wave phenom-ena and oscillation, including the periodic orbitaloscillation of the electrons in the atom.

Buried under the incomprehensibility of the 'pro-bability waves', one can find Newton's whole celestialmechanics when one takes Bohr's solar model analo-gy somewhat further. It is evident that a consider-ably more complex macro-cosmic solar-system thanours, with a great number of planets and comets, anda complex nucleus sustained by the interactionsbetween several major solar bodies (nucleons), wouldalso call for a replacement of the simple laws ofNewton and Kepler, and would require some highlysophisticated, purely mathematical predictions, morelikely based on complex perturbational probabilities.Indeed,"...the origin and development of the mathe-

matical apparatus (matrix-mechanics) under consid-eration were intimately connected with the tech-niques of computing planetary motions in astronomy.In fact, just like the mathematics of the older quan-tum theory and, in particular, the mathematics of itstheory of perturbations, the mathematics of matrixmechanics can be traced back to the study of plane-

tary orbits and of the orbits of planetary satellites.Ironically, matrix mechanics, the outcome of Heisen-berg's categorical rejection of electron orbits, had toeventually resort to the mathematics of orbitalmotions....The extension to infinite systems of linearequations with infinitely many variables, which pro-ved to be of extreme importance for the later devel-opment of matrix mechanics and quantum mechan-ics in general, had its origin again, in astronomicalcomputations of orbital motions." (Jammer, Concep-tual Development. [225])

Thus, it should be recognized that incomprehen-sibility and complexity are two different concepts.Comprehending a system requires the whole concep-tual ability of the brain, while its complexity is mere-ly a difficulty in the mathematical department.

This distinction might justify an attempt torevise Bohr's hybrid solar-atom, thereby rendering akinematically conceivable foundation for the alreadydeveloped complex mathematics.

A MATTER OF THE ORDER OF MAGNITUDEChapter Seven, Eight and Nine described the

kinematics of Newton's gravitational force and Kep-

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Aethro-kinematics CHAPTER SIXTEEN The Matter of Order of Magnitude

ler's laws of planetary motion through the concept ofthe Sink-vortex together with the evolutionary theo-ry of ponderable matter. In Chapter Eleven, a hypo-thetical description of the purely kinematical originof a donut-vortex was given as a possible formationof an elementary particle, with its inter-connectivityto form a variety of permanent dynamic formationswith different intake and output.

No doubt, it would take a great effort of carefuldesign, correlated with mathematical and experi-mental research, to create a conceptually and mathe-matically justifiable solar-atom based on the aboveconcepts of AETHRO-KINEMATICS and analogousto the macroscopic solar-system. Nevertheless, thefact is that the only scientific hypothesis available isthe Rutherford-Bohr solar-atom structure, based onthe Coulomb law of attraction, which is a directmathematical parallel to the Newton-Kepler celestialmechanics. After all, Bohr's simple conceptual foun-dation is the last contact with the humanly compre-hensible classical world picture and according to hiscorrespondence principle, it is also the only choice ofa conceptual foundation no matter how extreme isthe complexity of quantum mathematics.

It follows that, for the time being, a heuristicassumption can be justified, and that the differencebetween the kinematics of the solar system and thekinematics of the internal structure of the hydrogenatom is merely a matter of the order of magnitude.By extending this analogy to its kinematic alterna-tive, some contradictions between Bohr's hypothesisand the principles of classical and electromagnetictheories might be resolved

The imperative demand of classical electromag-netism is that an accelerating, charged particle mustradiate energy. For the sake of the stability of theatom, Bohr elected to oppose this principle and pos-tulated that the energy of the orbiting electron isconstant; that is, it does not radiate due to its cen-tripetal acceleration on a permanent orbit. Bohr fur-ther postulated that the electron does radiate whendiscontinuously changing orbits, by jumping from ahigher stationary energy level to a lower one.

Offering no physical reason, he assumed thisemitted energy to be proportional to half the differ-ence between the kinetic energies of the electron onits initial and final orbits.

387


As discussed earlier, by this assumption not onlydoes the electron jump between two orbits, but thewhole theory leaps over from the well-defined princi-ples of classical mechanics and electromagnetism tothe physically undefined conceptions of the quantumhypothesis. There is absolutely no conceptual feasi-bility of why and how the mechanical transitionbetween the two allowed orbits, the energy exchangebetween the orbital, mechanical frequencies, and theemitted radiation frequencies can happen in physicalreality.

Bohr's explanation of the discontinuous spectrumof the hydrogen gas was achieved by the quantiza-tion of the electronic orbits; that is, by the simplemathematical statement that the angular momen-tum of the electron cannot be any other quantitythan an integral multiple of Planck's quantum ofaction.

Thus, the fact that, Bohr was able to replicateBalmer's empirical formula from all these incompati-ble physical and metaphysical concepts and theirmathematical symbolism, tells much more about theuncertain values of mathematical derivation, thanabout the justification of the conceptual theory.

Nevertheless, since even the most advance theo-ries, through all the metamorphosis of the conceptsand mathematics, still must revert back to Bohr'ssimplified quantization of the orbits and their predic-tion by perturbation mathematics, it seems worth-while to consider an attempt to revise Bohr's ideasby an alternate, conceptually more consistenthypothesis.

In the AETHRO-KINEMATIC description of thesolar-sink-vortex, the average angular momentum ofa planet is constant, and its orbit is permanent.According to this hypothesis, the planet is carried bythe spiral vortical flow of the sink and therefore, theorbital velocity of the planet does not represent a rel-ative motion between the planet and the rotatingAether.

Similarly, in the micro-cosmic solar model of theatom, the orbital revolution of the electron, while it isbeing carried by the atomic sink-vortex, does not rep-resent motion relative to the medium. Hence, themotion of the electron causes no Aether resistanceand, therefore, its angular momentum is a constant.

According to the kinematic theory of electromag-netic radiation, compression pulses are produced by

388


ponderable oscillators when they accelerate relativeto the isotropy of the Aether. The electron can besuch oscillator on its orbit if, in spite of its constantenergy, it can still perform such acceleration.

As shown it is shown above, by superimposing ofan elliptical orbit on the spiraling vortex, for bothplanetary and electronic permanent orbits, theremust be a periodical de-railing from and on-railing tothe spiral channels of the vortexing medium.

During these events, the planets and the elec-trons perform periodical accelerations and decelera-tions relative to the Aether, according to Kepler'slaw of equal areas. These accelerations toward theperihelion and deceleration toward the aphelion rep-resent motion of the electron relative to the generalflow pattern of the vortex, therefore causing periodi-cal density variations, or compression pulses in themedium. Superimposed on the vorticity, these distur-bances are transmitted to the external isotropicAether and propagated away with the speed of light.

There is a natural kinematic reason for this de-railing of the planet or the particle from the spiralchannels of the vortex during its elliptical orbits.Another empirical discovery which was not explainedby celestial mechanics. Newton's description for thecause of the elliptical orbits was based on the ad hochypothesis of a slight accidental mismatch betweenthe initial tangential velocity of the planet and thecentripetal force of the solar mass. (Chapter Six).

The theory of the gravitational sink-vortex in-cludes a kinematic necessity for elliptical orbits andthe consequential periodical variations of the orbitalvelocity of the planet, as follows:

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Aphelion

Perihelion

Figure 16-17

Any individual Aethron, which is caught in theperipheral vortical flow of a sink will acquire anorbital drift-velocity of ever increasing speed and con-stantly changing direction. In any one of the number-less spiral channels of the vortex, the drift-velocityand centripetal acceleration of the individualAethron will constantly increase, and eventually itwill be swallowed by the central mass which, by itsevolution, creates the sink.

However, any conglomerates of Aethrons, orga-nized into the dynamic pattern of a ponderable parti-cle, represents an inertial mass, equivalent to thetendency to preserve its uniform speed on a straightline as a unit. This inertial resistance also representsa centrifugal force which is proportional to the quan-tity of the organized Aethrons in the particle.

Consequently, a particle having inertial mass,that is caught in the vortex, cannot follow the con-stantly changing direction of the spiral channels. Assuggested in Chapter Five, the change of momentumof a conglomerate of Aethrons through one on one col-lisions is a function of time. The obvious result is thatthe particle cannot keep up with the constantlyaccelerating flow of the individual Aethrons, and

eventually must derail outward from the in-windingspiral channels.

This derailing, however, also represents a motionrelative to the general rotation of the vortex. Thus,the particle experiences an Aether resistance which,in turn, causes its deceleration. It is, therefore, ex-pectable that the decelerating particle will eventual-ly reach a zone of the spiral where its speed anddirection are equalized with those of the local chan-nels. From this stage on the procedure of accelera-tion starts all over again.

Although it is an extremely complex procedure, itis intuitively feasible that equilibrium can existbetween the inertial motions of the mass of the parti-cle and the flow of the vortex, where the total time-lag of the accelerations and decelerations of the massis just equal to the period of the full orbit of the spe-cific Keplerian differential rotation zone of the vortexthus the particle can start the whole procedure allover from the same position at the Aphelion.

Applying this hypothesis to the hydrogen atom, itcan be seen that all contradictions between Bohr'stheory and the principles of classical electrodynamicsare eliminated.

390


The most important problem, the stability of theatom, is explained because, in general, the electron isbeing carried by the vortex and only radiates when itaccelerates relative to the medium. Thus, the radia-tion does not come from the electron's own energy,but supplied and withdrawn and supplied again bythe angular momentum of the whole of the atomicsink-vortex.

This hypothesis also covers the problem of thepermanent elliptical orbit of the electron and its roleas a simple harmonic oscillator. It also makes Bohr'sdistinction between mechanical, or orbital frequencyand the frequency of the emitted radiation unneces-sary. Furthermore it relieves the solar model fromBohr's discontinuous jumps between orbits, and theunwarrantable bursts of emissions, which were intro-duced to artificially relieve the problem of atomicstability.

There is, however, a more abstract but intuitivelymore feasible conjecture to be derived from the abovedescription.

It was generally assumed that Kepler's laws andNewton's universal gravitation allow an infinitenumber of permanent orbits, provided that the plan-

et has the right tangential velocity at the right dis-tance from the sun.

Now it may be seen that the criterion for a per-manent elliptical orbit is not only determined by themasses of the particles, and their distances and tan-gential velocities relative to one another, but also bythe delicate exchange of energy between the orbitingparticle and the vortexing medium.

It follows that there is an altogether different cri-terion; for the permanent orbits in the solar model ofthe atom, the ratio between the underlying Kepler-ian differential rotation of the vortex and the inertialacceleration time-lag in the superimposed ellipticalorbit of the electron. Evidently, these conceptual fac-tors should render a somewhat better understandingof the physical selection of specific permanent orbits,than does Bohr's ad hoc mathematical quantization.

The earlier conclusion, that Planck's constantrepresents the momentum density carried by a sin-gle electromagnetic pulse, should also be considered.Thus, when an electron, accelerated by external radi-ation, that passes through the atom, revolves on oneof its kinematically allowed orbits, it will gain kineticenergy until its angular momentum matches the

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requirement of the next allowed orbit. The differencebetween the two energies will be proportional to themomentum density, h, of the pulses of the incidentradiation.

As for the correlation of this hypothesis withSchrodinger's quantum mechanical wave-function, itcan be seen from Bohr's example that mathemati-cians are ingenious in their methods of deriving theexact result they want to reach.

A SHIP OF WAVES ORTHE WAVES OF A SHIP

Last but not least, it is time to deal with the mostrecent, astonishingly bold and consequently, most farreaching innovation of modern physics: the matterwaves.

As a condensed demonstration of the total con-ceptual obscurity of this important pillar of wavemechanics let us quote some attempts at clarifica-tion from modern educational works:

As described in Halliday's 'Physics' [1117],"In 1924 Louis de Broglie of France reasoned, that

(a) nature is strikingly symmetrical in many ways;(b) our observable universe is composed entirely of

light and matter; (c) if light has a dual, wave/particlenature, perhaps matter has also. Since matter wasthen regarded as being composed of particles, deBroglie's reasoning suggested that one should searchfor a wavelike behavior for matter."De Broglie's suggestion might not have received

serious attention had he not predicted what theexpected wavelength of the so-called matter waveswould be."De Broglie assumed that the wavelength of the

predicted matter waves was given by the same rela-tionship that held for light,

hλ = −−−− (16.32)

pwhich connects the wavelength, λ, of the light waveswith the momentum, p, of the associated photons."Eisberg, 'Fundamentals of Modern Physics[139]:"In classical physics electromagnetic radiation had

been considered to be purely a wave propagationphenomenon. However, the work of Einstein andCompton has demonstrated that under certain cir-cumstances it displays properties characteristic ofparticles (quanta). This being the case, could it also

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Aethro-kinematics CHAPTER SIXTEEN A Ship of Waves or The Waves of a Ship

be true that physical entities which we normallythink of particles (electrons, alpha particles, billiardballs, etc.) will under certain circumstances displayproperties characteristic of waves?"It is immaterial whether the situation is described

by saying that electromagnetic radiation actuallyconsists of waves which upon interacting with mat-ter, are able to manifest particle-like behavior, or bysaying that it actually consists of particles whosemotion is governed by the wave propagation proper-ties of certain associated waves. In fact, it is some-what naive even to imply that there is a choice to bemade. However, by adopting the latter statement, deBroglie was led to investigate (and postulate) theidea that the motion of a particle is governed by thewave propagation properties of certain pilot waves (touse his terminology) which are associated with theparticle."

As it has been presented in Chapter Three, therewere two immediate major consequences of deBroglie's hypothesis:

1) The conceptual explanation of Bohr's quantiza-tion of the electron orbits by the hypothesis that thede Broglie waves of form standing waves on the

atomic orbit. Thus, quantization means, that onlythose orbits are allowed whose circumference are anintegral multiple of the de Broglie wavelength.

2) The other inescapable result of deBroglie'sstanding wave description of an electron is that theposition of the electron and the orientation of thevector indicating its linear momentum cannot beexactly specified at a given instant of time. This un-certainty in the position and the momentum of theelectron is the general feature of Heisenberg's Uncer-tainty Principle, which results from the descriptionof the motion of the particle in terms of the propaga-tion of its associated pilot waves.

Figure 16-18.

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λ L

p

yp

x

p

w

Lw

y

x

This illustration is a replica of Figure 3-6 (b), giv-ing a schematic explanation of the electron diffrac-tion experiment, the simplest proof of the inesca-pable uncertainty principle.

As shown, the extent of the diffraction dependson the ratio between the width of the gap and the deBroglie matter-wavelength. The deviation from astraight trajectory increases with the decrease in thewidth of the gap.

While the smallness of the gap is instrumental inestablishing the instantaneous position of the elec-tron within the gap, the same is true for the probablechanges in the direction of momentum beyond thegap. It follows that a minimum uncertainty in themeasurement of the position will produce a maxi-mum uncertainty in the direction of the resultingmomentum and vice versa.

Mathematically speaking, if the position of theelectron on the y axis is y, and the y-component of themomentum of emergence is py then from the deBroglie relation of the momentum and the matterwavelength, p = h/λ, it can be shown that

∆ py ∆ y ≅ h (16.33).

Another angle of the electron matter-waves isdescribed by the author Mashuri L. Warren, in Intro-ductory Physics [541]:"In quantum physics there is much discussion of

hypothetical experiments. – In principle, these'thought' experiments, or gedanken experiments,could be performed, but in practice they present realtechnical difficulties."Such gedanken experiments are at the heart of

philosophical discussions directed toward clarifyingthe foundations of quantum theory and revealinghidden contradictions in it. One such gedankenexperiment is the double slit (Young's) experiment,where a beam of electrons passes first through a sin-gle slit to form a coherent beam, and through a dou-ble slit. The intensity of the electron or photon distri-bution is then observed on a screen."If light illuminates the slits, the outcome of the ex-

periment is clear. Because of its wave character, lightpassing through each slit spreads out and forms asingle diffraction pattern. Light from the two slitsinterferes, giving rise to a double-slit interferencepattern superimposed on the single-slit diffractionpattern. This interference pattern is essentially the

394


same whether we are treating water waves, soundwaves, light waves, or quantum waves. The pattern isdetermined by the slit width, a, the slit spacing d,and the wavelength λ.

Figure 16-19.Figure 16-19 shows the "gedanken illustration" of

the electron double slit gedanken experiment. Thethin, white straight and curved lines represent thewave character, and the heavy black arrows repre-sent the particle character of the phenomenon."If we look at the double slit (gedanken) experiment

with reference to particles, we get different results.

Suppose the electrons are small particles analogousto bullets. We can allow for the bullet scattering a bitfrom the edges of the slits, but we cannot allow thebullet to break into pieces. There is no interferenceeffects with bullets; either the bullet arrives at a spotor it does not. How can one bullet cancel another?"When the photon or the electron passes through

the slits, it acts as a wave to produce an interferencepattern. But when we detect the electron, we alwaysobserve a whole electron, never 1/2or 3/4 electron."The probability of observing these particles is dis-

tributed like the intensity of a wave. Thus we havethe wave-particle duality. Is it a wave or a particle?The answer is neither and both. This is a paradox ofthe quantum theory."

After some 20 pages of description of the hypoth-esis of the de Broglie matter waves and its justifica-tion by real- and thoughtexperiments, Berkeley'sPhysics Course III; Quantum Physics (1965), rendersthe concluding clarification of the concept:"Let us tighten up our language a bit. When we dis-

cussed the discovery of the de Broglie waves wetalked about 'waves associated with a particle'.

395


"This is bad language because it sounds as wewould have a classical corpuscle traveling togetherwith a wave in some fashion. Some people like to callthe de Broglie waves 'guide waves' or 'pilot waves',but this terminology is also bad. The de Broglie wa-ves are not waves traveling together with, and 'guid-ing' a classical corpuscle. The de Broglie wave andthe particle are the same thing; there is nothing else."The real particle, found in nature, has wave prop-

erties and that is a fact. If we want to emphasize thisfact we might talk about the de Broglie wave of anelectron, but this term is really a synonym for 'elec-tron'. Our excuse for our previous bad language isthat our discussion was at first tentative, as well ashistorical, and the cautious term 'wave associatedwith a particle was therefore defensible. The timehas now come for us to be more precise and definite,and we should reject a terminology which might leadour thinking astray."Consider again, the two-slit (gedanken) experi-

ment of electron interference. There is nothing inthis experiment which suggests to us that theremight be a classical corpuscle passing through one ofthe slits, 'guided' by a wave which passes through

both slits. Better stated: Our description of whattakes place, in no way improves if we try to introducethis idea! It is quite enough to discuss the wavesonly, with the quantum mechanical interpretation(Schrodinger's wave function) of intensities and prob-abilities."Any talk about the 'hidden' corpuscle is meta-

physics, unless the assumption that the corpuscleexists has some definite experimental consequenceswhich cannot be predicted on the basis of the quan-tum mechanical wave theory alone."

From Eisberg, Fundamentals of Modern Physics,[170] :"The wave function, Ψ (x,t) is an inherently complex

function."We did not know this when we developed some of

the qualitative properties of the free particle wavefunction. However, each of those arguments could bestated again, always replacing the phrase, 'wavefunction' by, for example, the phrase 'real part of thewave function'."Recall also that in the discussion of the difference

between group and phase velocities, we described thewave function of various coordinates x at a certain

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instant to. This was done simply to provide somethingconcrete to think about. If we were to repeat that dis-cussion, we would now have sufficient acquaintancewith the idea of wave function to render such an arti-fice unnecessary. We would also realize that the hy-pothetical instruments for measuring the value of thewave function cannot possibly be exact, since thevalue of an inherently complex quantity cannot bemeasured with an actual physical instrument."The fact that wave functions are complex func-

tions, should not be considered a weak point of thequantum mechanical theory. Actually it is a desirablefeature because it makes it immediately obvious thatwe should not even attempt to attribute to wave func-tions a physical existence in the same sense thatwater waves have physical existence."That is, we should not try to answer, or even pose,

the questions: Exactly what is waving, and what is itwaving in? The reader will recall that considerationof just such questions concerning the nature of elec-tromagnetic waves led nineteenth century physiciststo the fallacious concept of the ether. As the wave func-tions are complex, there is no temptation to make thesame mistake again."

God forbid !This article was published in 1965. One would

expect, that obeying Einstein's order not to mentionits name for six decades, the 'you know what' shouldnot be a threatening ghost anymore. But the abovequote could also be raised to the rank of a modernepistemological principle; a manifestation of how themathematical machinery, which once merely symbol-ized the conceptuals, now gained power to outlaw theuse of open mind.

For the AETHRO-KINEMATIC alternative of thede Broglie–Heisenberg matter–wave–uncertaintyprinciple, consider the following fictitious "gedanken-experimental diary":

− I am Captain Smith, commanding officer of theamerican air-ship squadron, positioned in France(1943). Our primary duty is to fly beyond the frontline, investigate the heavy machinery and weaponconcentrations of the enemy and give constant infor-mation to our air-force. This is not an official militarylog, but my personal diary, which has nothing to dowith the war, but is an attempt to record a kind ofscientific discovery.

397


− The top-secret headquarter and hangars of thesurveillance squadron (13 air-ships, maybe calledblimps) were built on a foresty mountain plateau,well camouflaged from enemy eyes. As Figure 16-20illustrates, the 13 hangars were placed in a archaround the sliding gate entrance, built into the greatoutside wall. A long channel, leading to the gate, wascleared out of the forest for the landing and take offof the blimps.

Figure 16-20.

− For additional security, because of the nearbysmall village, the landing procedure was quite deli-cate. The blimps only landed at night and had to gaina certain momentum over the forest, then shot themotor shut off and decline into the forest-channelwith the right speed and direction. The pilot thenhad to guide his ship through the main gate into hisown hangar in the arch. In each hangar there was anelastic net to decelerate the blimp.

− One night, I was landing my ship according tooperational directives. I achieved the right speed anddirection, declined into the channel and moved onthe inertia of the blimp in a straight line toward thegate. My hangar was R4, the forth place to the rightfrom the center (C). At some distance from the gate Iwanted to make an adjustment in the direction, butnoticed that the steering cable broke and I'd totallylost control. There was no reason to panic, since Iexpected to drift straight into C, and had enoughtime to communicate the swap with the other pilots.

− However, just before the blimp reached the gateits nose was slowly deflected to the left, and she gra-dually swayed into a new direction. Finally, withoutsteering, she slipped into hangar L3.

398


CRL

123

45

6

1 2 34

5

6

F O R E S T

− Later, when I examined the situation I gotdeeply puzzled, because the steering wing was totallyfree, so it was not responsible for the turn, and I hadnot the faintest idea what possible forces made theship changing its direction.

− Weeks passed and the puzzle begin to fade inmy mind when I have received my monthly edition ofPopular Science Digest, and my eyes got caught on asmall article about the 'de Broglie pilot waves' thatwere supposed to explain the diffraction of the elec-tron which it was associated with.

− Needless to say, I got really excited. I remem-bered, from my aerodynamic studies in pilot school,that the motion of an object creates small densitychanges in air, which are propagated away by themedium in the form of compression waves with thespeed of sound.

− What would explain my puzzle any better thanthese pilot waves, produced by the motion of the ship,which was sent ahead in the air and reflected backfrom the wall against the ship? At once it becameclear that the continuous back and forth reflection ofthe waves builds up pressure fluctuations betweenthe wall and the ship, and the smallest sideways

deviation from the center of the gate must producean uneven transverse force that will push the nose ofthe ship in an angle proportional to the width of thegate and the size and the velocity of the ship.

− Fortunately, the German army was fallingapart, and during the following weeks I could man-age to do various experiments with different veloci-ties and deviations, with different size ships, andadjusting the width of the sliding gate. All shipslanded purely on their inertial motion with theirsteerings left alone.

− The analysis of the records convinced me thatthere is a definite trace of a diffraction pattern in theaccidental docking of the blimps with maximum andminimum probabilities for each hangar. The mostfrequently reached hangars were L2, L1, C, R1,R2.Somewhat less frequent were L3 and R3, and almostnone reached L4 and R4, obviously the first mini-mum. But L5 and R5 again showed some probabili-ties for a second maximum.

− This strange regularity, however, represented anew puzzle which caused me lots of sleepless nights,until it dawned on me that the pressure fluctuations,created by the moving ship, are not only effective

399


between the ship and the wall. Those produced bythe transverse reflections and interference of thewaves within the gap of the gate, and even beyond,inside the space of the arch, could also be a force or adensity factor which could guide the ships in anyparticular direction. Consider that the actual massand momentum of a gas-filled blimp is not that greatrelative to the mass of air around it.

− I was so sure that I got it all right, that immedi-ately wrote a letter to the Popular Science Digestabout my discovery. After a few weeks of great anxi-ety I received a very polite and patient letter fromthe editor. He assured me that my theoretical effortis greatly appreciated by the scientific communityand my hypothesis is more than interesting. How-ever, there is one minor problem with the theory,namely that the electron diffraction is neither hap-pening in air, nor in any other media. This is anunambiguous fact since Einstein postulated the non-existence of the e - - - r. Furthermore, this astonish-ing postulate was reinforced by the fact that Schro-dinger's wave-function is an inherently complexfunction, which immediately disallows human mindsto attempt to fill space by the 'you know what'.

− A small booklet was also attached, whichdescribed the evolution of quantum mathematicsfrom the simple harmonic equation of the waves on ataut string, all the way up to Schrodinger's inherentcomplexity. I felt really hopeless, because 90 percentof the text was mathematical hieroglyphy. Neverthe-less, in the Epilogue I found a sentence that soundedhumanly conceivable; 'Quantum mechanics is gener-ally accepted as a complete description of the micro-world. However some scientists still strongly deniedprobability waves and indeterminism, among themwere Schrodinger himself, and Albert Einstein...'

− Thus, I am not in the worst company when Icannot believe in the dual nature of my blimps, orthe idea that the waves are not created by the ship,but the ship is made out of waves.

BACK TO AETHER AGAIN...AND AGAIN...Aether is an ideal gas with great internal kinetic

energy, represented by the constant random motionof its constituents, the Aethrons. As long as the Aeth-rons move in total isotropic randomness, the momen-tum density at any unit volume in any specific direc-tion is zero.

400

Aethro-kinematics CHAPTER SIXTEEN Back to Aether Again...and Again...

Matter is made up of units of dynamic circulatorypatterns of the Aethrons and the conglomeration ofthose units. Once a circulatory pattern has evolved, itbecomes permanent under non-extreme circumstan-ces. The circulatory unit (like the donut-vortex), asestablished by Bernoulli's theorem, contains a grea-ter number of Aethrons per volume and thus repre-sents a greater inertial mass than that of the isotrop-ic Aether per unit volume.

All interactions between such medium and mat-ter is due to their relative motions. When, for somereason, a mass of Aether drifts in a given direction, itaccelerates matter that is caught in the flow. Whenmatter moves in the isotropic Aether, the same con-sideration for the elasticity of real fluids is valid,which 'indicates that the effects of small pressurechanges are transmitted throughout the fluid in theform of waves, which travel with the speed of sound',(Van Nostrand's Encyclopedia, [48]) in Aether, thespeed of light.

Hence, a moving particle creates periodic com-pression pulses in the Aether, therefore it is equiva-lent to a moving point source. It can also be assumedthat, as it has been found in all quantum experi-

ments, the energy density carried by a single pulse isrepresented by Planck's constant, h.

As for the wavelength of these motion-producedperiodical pulses, it stands to reason to assume thatthe volume of the affected Aether should be propor-tional to the mass of the moving body, and the mag-nitude of this effect is proportional to its velocity.Thus, the frequency of the periodical disturbanceshould be proportional to both the momentum of theparticle and h, in agreement with the Compton-DeBroglie formula, λ = h/p.

Temporarily, these conclusions are taken withoutany inquiry of their underlying kinematics, whichwill be discussed later.

Electrons are accelerated by an electric potentialdifference which has been described earlier as thecirculation of the Aether in the conductors andthrough the battery (cylindrical vortex).

An electron experimental device is constructedin such a way that the circulating Aether picks upthe electrons from the cathode and accelerates themtoward the anode (Recall Figure16-3). As the Aetherflow curves into the body of the anode-conductor, theelectrons, under the influence of their inertial ten-

401


dencies, continue to move with uniform speed on astraight line toward the screen through the isotropicgas of the Aether. In the diffraction experiment, thisprocedure represents the preparation of the coherentbeam of electrons, which moves with uniform velocitytoward the gap and through that to the screen.

The description of the AETHRO-KINEMATICalternatives for De Broglie's matter wave, Heisen-berg's uncertainty principle and their consequences,require a procedure of several steps.

Figure 16-21.

Figure 16-21 gives a long-shot, artistic visualiza-tion of the probable wave-formations when a singleelectron (point source) moves with uniform velocityand affects the isotropic density of the Aether infront, within, and beyond the gap.

The illustrated snap-shot shows the instant whenthe compression pulses (white curves), produced bythe motion of the electron, are already propagated inthe medium and reflected back from the wall towardthe electron. It is evident that this reflected pressurecould decrease the speed of the electron, and if itstrajectory is not exactly identical with the center lineof the gap, the resulting uneven transverse pressureon the electron could also affect the initial directionof its motion.

Within the space of the gap, in the excess pres-sure due to the transverse reflection of the waves,new Huygens wavelets are being produced, and theirenvelopes propagate forward. The resulting interfer-ence creates Fresnel diffraction patterns in the medi-um beyond the gap and on the projection screen.

Of course, this is not the diffraction phenomenonof the electrons, but merely the manifestation of theinfinitesimal and most likely undetectable pressure

402


fluctuations formed in the Aether between the gapand the screen. Nevertheless, as the electron moves,the interference of its waves creates some constantlychanging, pressure-variant channels which can mostplausibly influence the direction of motion of thelight-weight electron through that whole space.

This is the artistic rendering of a general kine-matic picture which could replace De Borglie's hy-pothesis of pilot-matter-waves in empty space. How-ever, for a closer conceptual and mathematical analy-sis, a much simpler approach is necessary.

Figure 16-22.

Figure 16-22 below is a simplified schematic rep-resentation of a probable wave formation. The elec-tron moves toward the gap with uniform velocity, v.Its compression waves are propagated away fromand reflected back to the barrier with the velocity oflight, c. The width of the gap in the direction of the yaxis is a.

For simplicity, let us consider first, that the wa-ves are only reflected back by the two corners of thegap, A and B. Also let us concentrate only on a singlepulse created by the electron, which has a total ener-gy density, h. It follows that the momentum density,p, at any point in the front of the electron is: p = h/2πr, where 2π r is the circumference of the wave-ring.

Since the light pressure is P = E/c, which isequivalent with the momentum density, it followsthat the pressures, PA and PB, reflected back to theelectron from the two corners, are also equal to theenergy density: pA = h/2π r1 and pB = h/2π r2.

Next, as shown in the illustration, let us establishthe position of the electron at the coordinates (x, y).The origin, O is at the center of the gap. The corners,A and B are at (O − a/2) and (O + a/2), at one half ofthe gap.

403


x

y

r 1

r2

PA

PB

O

A

B

a

P

PY

X

A

A

c

v

The distances of the electron from each cornerare expressed as r1 and r2 . Thus, we can write

________________ _______________r1 = √ x2 + (y− a/2)2 r2 = √ x2 + (y+ a/2)2 .

Thus the pressures on the electron, coming from Aand B are

_______________ ________________PA = hυ/ 2π √ x2 + (y− a/2)2 PB = hυ/ 2π √ x2 + (y+ a/2)2,where ν is the frequency, that is, the number of com-pression pulses per second, produced by the electronand reflected back by the wall.

It can be seen that the x-components of PA and PB

represent retarding forces on the electrons motion.These forces not only tend to slow down the electron,but, as shown, the y-component of PA will tend topush the electron downward (-y) and that of PB willtend to push it upward (+y). Thus, both y-componentsof these forces will tend to change the initial direc-tion of the momentum.

Evidently, both pressure forces are constantlyincreasing as the electron approaches the gap.However, it is also evident that the proportion bet-ween the x- and y-components of the forces is con-stantly changing too. While the electron is at a great

distance from the gap, r1 and r2 are close to paralleland therefore the y-component is negligible. Butwhen the electron reaches the gap, and the x-compo-nents approach zero, the transversal y-componentsbecome the only forces on the particle.

It also follows that, as long as the electron movesexactly on the center line (x-axis) of the gap, the y-components of PA and PB are equal and opposite indirection. Thus, PBY − PAY = 0. Consequently, they donot affect the direction or the final y-component ofthe momentum of the electron beyond the gap.

Before analyzing the cases when the electron'strajectory is off- center and the transverse pressuresbecome unequal, consider intuitively the magnitudeof these forces.

As has been established earlier, the interactionbetween Aether and moving matter can be most gen-erally expressed by the Lorentz formula of Aetherresistance: β = 1 /√ 1− (v/c)2.

From a macroscopic point of view, the magnitudeof this force of resistance only becomes measurablewhen the velocity of the particle approaches thevelocity of light. The same is valid in the reciprocal

404


case, when an Aether flow affects the state of motionof a particle by the same force (Cyclotron). At normalmacroscopic masses and velocities the resistance isnegligible.However, in case of the electron diffractionexperiment, at least two kinds of magnification ofthis force should be considered:

1) Between the moving electron and each corner,the disturbances are locked into a constant back andforth reflection and re-reflection. Since the distancefor these reflections is constantly decreasing, thereflected waves are always out of phase, resulting acomplex interference and beat pattern, causing somedensity fluctuations, which changes and therefore,also propagates in proportion with the speed of mo-tion of the electron.

2) Within the space of the gap itself, as Figure 16-21 shows, the waves, transversally reflected from thetwo corners, cause similar complex density fluctua-tions. The result is the formation of standing wavepatterns which change relatively slowly, again in pro-portion to the momentum of the electron. These den-sity fluctuations could greatly magnify the trans-verse component of the forces on the electron whilepassing through the gap. They are also the bed of the

formation of special Huygens wavelets, the wavetrains which fill the whole space beyond the gap. Theresulting constantly changing diffraction densitychannels could also be a factor in the guidance of theelectrons.

Getting back to the details of the simplified ana-lysis; at the instant when the electron reaches thehorizontal center, the x-component of the pressureforce on the electron is exactly zero. Thus, the forcesacting on its momentum are exclusively in the trans-verse directions, or in the y-axis.

Since the primary interest here is in the changeswhich might occur in the direction of the electronwhile it moves through the gap, let us now concen-trate only on the y-components of the pressure forcescoming from the two corners, and the possible differ-ences between them, ∆PY = PBY − PAY . Since the pres-sures of the reflected waves are equivalent with theforce F, that acts on the passing electron, we canwrite; FY = FBY − FAY , or

hν hνFY = −−−−−−−−−−−− − −−−−−−−−−−−− (16.34).

2π y + a/2 2π y − a/2

405


The change of momentum, according to Newton'ssecond law, is ∆ p = F∆ t, where ∆ t is the time inter-val during which the force acts on the particle. Thisis again inversely proportional to the momentum ofthe electron. Consequently, the force is also directlyproportional to the wavelength of the initial wavethat the electron produces by its motion. That is, ∆ t∝ λ. Therefore,

hν ∆ t hν ∆ t ∆ py = −−−−−−−−−−−− − −−−−−−−−−−−−

2π y + a/2 2π y − a/22y ∆ t

= hν −−−−−−−−−−−−−−− (16.35)2π (a 2 /4 − y2)

Let us express the position on the y-axis throughwhich the electrons pass the gap as y = f (a/2), wheref is the fractional factor, the absolute value of whichis smaller than one ( f≤ 1). Substitute this intoEquation 16.35:

2 f (a/2) ∆ t ∆ py = hν −−−−−−−−−−−−−−−−−−

2π (a2 /4) − (a2/4)f 2) 2 hν f ∆ t

= hν −−−−−−−−−−− (16.36)π a

Since the frequency of the electron-wave is direct-ly proportional to the momentum, ν ∝ p, and ∆ t ∝ λ,thus Eq. 16.36 becomes

2 h f λ p ∆ py ∝ −−−−−−−−−

π aλ

∝ −−− p (16.37).a

Thus, the predicted change in the y-component ofthe momentum, based on this hypothesis, is in agree-ment with the empirical facts of the single slit elec-tron-diffraction experiment, and with the particle-wave mathematics of de Broglie. Assuming that a co-herent, steady stream of electrons is passing throughthe gap with uniform velocity and uniform density,the y-component of momentum of each individualelectron will be affected, depending on its exact posi-tion in the gap on the y-axis while passing. It followsthat the beam will spread out in the space beyondthe gap, and therefore the intensity recorded on thescreen, or the number of electrons hitting the photo-graphic plate per unit area, will be represented bythe probability predicted by the above relation. Theplotting of these probabilities produces a curve equi-

406


valent to the Gaussian ‘normal’ distribution curvewhich is very similar to the intensity curve of diffrac-tion, showing the maximum and the first minima.

It should be noted here, that the same curvewould be produced, whether a whole beam of elec-trons were passing through and being diffracted, orone at a time. Also note that this curve does not showa second maxima, which will be discussed later.

As can be seen, ultimately both theories arereduced to the predictions of probabilities. Neverthe-less, there is an important conceptual difference bet-ween them.

On the one hand de Broglie's ad hoc hypothesiscomes from the philosophical assumption of the sym-metry of nature based on the analogy with the phys-ical assumption of the particle nature of light. Thewavelength of de Broglie's particle-wave has beenmade artificially proportional to the momentum ofthe particle, taken to be analogous to the particlebehavior of light, by the total acceptance of theabsurd concept of the massless momentum of thephoton. In this theory of modern physics the role ofthe wavelength in the calculations of superpositionsis exactly the same as it is in Young's constructive

and destructive interference theory. This nature ofthe waves gives Young a continuous distribution ofthe intensities. However, in the matter-wave hypoth-esis it is strictly incompatible with the discontinuityand indivisibility of the physical particle. This is theessential necessity for the flipping back and forthbetween the languages with the excuse of comple-mentarity, and finally for the mathematical transfor-mation of de Broglie's pilot-wave concept into theprobability-wave interpretation of the Schrodingermatter-wave-function of wave-mechanics and quan-tum-mechanics.

On the other hand, in the AETHRO-KINEMAT-IC alternative, the explanation of the phenomenon isbased merely on the kinematically logical reaction ofthe isotropic medium to the local disturbance causedby the motion of a moving particle. Thus, it followsfrom the established density difference between theisotropic medium and the dynamically organizedparticle structure, that a greater mass, and/or a grea-ter speed of motion, will produce a greater distur-bance in the medium.

Recalling the Huygens Principle of the propaga-tion of periodical pulses and their momentum distri-

407


bution, (Ch-13) it can also be seen that, due to thetransverse pressure of the Huygens Wavelets, even adisturbance, caused by uniform motion, must sepa-rate from the moving body upon reaching a certainenergy density. (App.III) This limit is represented byh, thus the frequency of separation and the produc-tion of periodical pulses are naturally directly pro-portional to the momentum of the particle.

So far, this theory does not render an explanationfor the existence and calculation of the second maxi-ma and minima and the corresponding curve whichis usually shown in text books describing the thoughtexperiments of single slit electron diffraction theory.Thus, looking back from the present stage of science,without an in depth research, it is quite impossible toseparate the real experimental facts from the merespeculations, based only on thought experiments.

In the case of the photon diffraction theory, it isobvious, that the existence of the second maximacannot be based on the particle characteristics andmust be calculated by Young's constructive and de-structive wave-interference method. Still, modernphysics is forcing the absurd argument of the doubleslit interference gedanken-experiment, even with in-

dividual photons, and claims that by a small mathe-matical switch the experimental curves can be pre-dicted from Young's the wave-interference.

The present alternative hypothesis leaves thequestion of the second maxima of electron diffractionopen, with the hint that if it is really needed, then, asshown on Figure 16-21, the theory of the diffractionchannels, produced by the real pilot waves in theAether can be further developed.

THE ULTIMATE UNIVERSAL CONSTANTSo far quantum-aethro-kinematics presented a

humanly perceivable concept to fill Planck's empiri-cally forced constant of discontinuity, h in the form ofthe minimum quantity of excess energy density of asingle pulse of electromagnetic radiation.

The same concept seems to be valid in the alter-native AETHRO-KINEMATIC solutions of Einstein'stheory of the photoelectric effect, and of the Dopplerinterpretation of Compton's collision-scattering ef-fect. With these, the bi-linguistic photon theory hasbeen rendered superfluous.

Seemingly, all kinetic energy exchange betweenradiation and matter are executed through the mul-tiples of the quantity h, and the total energy density

408

Aethro-kinematics CHAPTER SIXTEEN The Ultimate Universal Constant

delivered by a train of radiation pulses is Ed = hν /V,where ν is the frequency of radiation.

It will be shown below that an even more generalmeaning can be attached to Planck's constant as theexpression of one of the fundamental characteristicsof the ideal gas of Aether. Dimensional analysisshows that h = energy × time.

Et = kg × m/s2 × m × skg × m/s2 × m3 × s

= −−−−−−−−−−−−−−−−−−−.m2

Since 1/s is the dimension of frequency,

hν = kg × m/s2 × m × s × 1/s= kg × m/s2 × m

kg × m/s2 × m3

= −−−−−−−−−−−−−−− (16.38).m2

Now, according to Hook's law, the change in thevolume of an elastic medium is proportional to thepressure applied to it, meaning that stress/strain =constant. This ratio is called, in Young's term, theModulus of Elasticity, or simply the Bulk Modulus.

Stress = F/A, where F stands for force and A forunit area, which equals to the force of pressure, P.Strain = −∆V/V, where ∆V represents the resultingchange in the initial volume, V.

Thus, the Bulk Modulus, K can be expressed by∆P ∆PV

K = −−−−−−−−−− = −−−−−−−−− ,− ∆V/V ∆V

where the minus sign indicates that the volumedecreases upon application of a given stress.

Dimensionally, − ∆V/V represents no units,thus K= ∆P has the dimensions of pressure (F/A).

ThereforeF Newton kg × m/s2

K = −−−−− = −−−−−−−− = −−−−−−−−− (16.39).A m2 m2

Now, compare K in Eq. 16.39 with Eq. 16.38 andsee that

hν = Km3 = KV,

where m3 is the dimension of volume, and kg⋅m/s2 is energy. Thus, the Bulk Modulus, K has thedimension of energy density.

409

Aethro-kinematics CHAPTER SIXTEEN The Ultimate Universal Constant

hνK = −−−−−− (16.40).

VHere ν is the frequency and V is the volume.Taking the unit of time as the time interval of

the formation of a single pulse, and taking the unitof volume as the volume filled by the excess energydensity of one pulse, then

h = K (16.41).Consequently, Planck's universal constant repre-

sents nothing less than the Modulus of Elasticity ofthe all-pervading Aether.

ENERGY AND ANTI-ENERGYOUT OF NOTHING ?!

In the second half of the century there was agradual change in the attitude of theorists in theattempts to incorporate the classical continuum withquantum discreteness. A tendency appeared toaccept that quantum mechanics represents a wholenew intellectual structure, within which some kind of'understanding' exists how these two incompatibleconceptual systems could cohere. Based on this con-viction Planck's quantum, the principles of comple-

mentarity, correspondence and uncertainty and prob-ability wave-function invaded all microscopic depart-ments of science. A searching for elementarity devel-oped particle physics, and through the Big Bandhypothesis, the quantum expanded into astro-physics, cosmology and cosmogony. In fact, high-pow-ered scientific circles advocate a firm conviction, thatquantum mechanics is on the verge of developing the'Theory of Everything', or the 'World Equation', akind of a 'Super Unified Field Theory' that will uniteall laws of Nature into a single statement thatreveals the inevitability of everything that was, isand is to come in the physical world.

Evidently, this subject is way out of the scope ofthis study, however, the general direction of the ma-thematical evolution and its conceptual reverbera-tion in the minds of physicists create an interestinglast note for this chapter.

Consider then the following quote from the val-ued work of Peter Covency & Roger Highfield: TheArrow of Time, 1990 [140]."Schrodinger himself had realized from the start

the limitations of his own equation (wave-function) -it did not satisfy the requirements of Einstein's spe-

410

Aethro-kinematics CHAPTER SIXTEEN Energy and Anti-energy Out of Nothing

cial relativity (specifically, it was not Lorentz invari-ant) and as a result it could not account for the finerdetails of atomic spectra."Dr. Maurice Dirac attacked this shortcoming and

in 1928 had written down a relativistic equation...themathematical properties of which lead him to pro-pose the existence of the positron, a unit of 'antimat-ter'. The positron has the same mass as an electronbut is of opposite electric charge; (and spins) a colli-sion between the two results in their mutual annihi-lation, together with the production of a burst ofradiation. An experiment by Carl Anderson in 1932confirmed the existence of the positron and thereforethe reality of antimatter, a discovery that radicallyaltered the conceptual foundations of elementaryparticle physics. From then on, it was recognized thatmatter is not immutable but could be created anddestroyed at will."On the basis of the mathematical description pro-

vided by Dirac, the positron has been interpreted asits antiparticle - an electron - moving backwards intime."An intricate relationship exists between matter,

antimatter, spatial symmetry and the two direction

of time. It appears in the remarkable CTP theorem,which is a consequence of the mathematical form ofthe microscopic laws of physics. Its name arisesbecause symmetry is tested by the combined se-quence of three abstract operations:"C = charge conjugation, by means of which matter

is converted into antimatter. (Opposite sign)"P = parity inversion, which converts spatial coordi-nates into their mirror images."T = time reversal, which reverses the direction of

time."The CTP contends that the laws of physics predict

equal but opposite events in a kind of 'generalizedmirror image' world. Thus, symmetry in the guise ofthe CPT theorem can be used to make deductionsabout physics. (For different reasons most of thesetheories were found inadequate and later reappearedin a more sophisticated approach as string, super-string, super-symmetry, super-parity and super-grav-ity theories.)"Heisenberg's uncertainty principle has consequen-

ces for the measurement of time. There is a limita-tion to the accuracy with which we can measureenergy within a given interval of time.

411


“A precise measurement of an atom's energy in aparticular quantum state can only be performed atthe expense of considerable uncertainty over thetime it spends in that state. In classical physics,energy was neither created nor destroyed but rigor-ously conserved, merely being converted from oneform to another. However, over short time intervalsthe conservation of energy is undermined by Heisen-berg's uncertainty principle. The link between energyand time in Heisenberg's principle says that theshorter the interval of time considered, the moreuncertainty there will be in the energy. This allowsthe law of energy conservation to be suspended oververy short time intervals; owing to random quantumfluctuations, energy may be 'borrowed' at no costfrom nowhere at all. Such event occur even in vacu-um in which, classically speaking, there is simply'nothing' present. Quantum theory thus gives us aquite different view of what a vacuum is. Because ofthe uncertainty principle, it is in fact seething withactivity."Dirac is largely responsible this modern picture of

a vacuum. He recognized that Maxwell's electromag-netic field must be described in quantum terms if it

is to explain correctly the way matter absorbs andemits photons. In his extension of Maxwell's mathe-matical model, he pictured the electromagnetic fieldas a collection of a vast number of oscillators, each ofwhose energy levels was quantized, just like theenergy levels of an electron in the atom. But now, byvirtue of the uncertainty principle, each oscillatorcan never have less than a fixed minimum energy -the zero point energy - with the result that even avacuum is always seething with virtual activity: -there are endless fluctuations in energy of the fieldat all points within space. Fluctuations of sufficientenergy enable matter-antimatter pairs of particles,such as electrons and positrons, to be momentarilyformed - the more energy borrowed, the more tran-sient the particle pairs will be. These vacuum quan-tum field fluctuations have considerable physical sig-nificance. For example, the constant creation andannihilation of photons provides the trigger wherebyatoms swollen with energy can spontaneously emitradiation as light. In fact the vacuum fluctuation alsoresurrect in a certain sense the nebulous aether whichEinstein eliminated as excess baggage in 1905."

....Or did he ?!

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CHAPTER SEVENTEEN

THE LAST SIX DECADES

CONCEPTUAL DEVELOPMENTIN A NUTSHELL

The previous chapter was mainly involved withthe introduction of an alternative explanation for theorigin of Planck's fundamental quantum discontinu-ity as the minimum measurable kinetic energy den-sity in the ideal gas of the Aether. It has been

attempted to discuss all involved physical conceptswithin a minimum interference of the underlyingcomplex philosophical foundations of quantummechanics. For the sake of concentration and clarity,the discussion also tended to minimize the involve-ment with the unceasing dissatisfaction of scientificminds during the last six decades with the orthodoxCopenhagen interpretation of the final mathematicalformalism of quantum mechanics. To attempt to dealwith the conceptual development of quantummechanics during the years between 1930 and 1990,a highly condensed history of the conceptualdevelopment of the quantum theory is needed:

1. Planck's solution of the discrepancies ofclassical predictions for the energy distribution ofblack-body radiation is that radiation energy isproduced by electromagnetic oscillators in a dis-continuous manner; each giving off a minimumvalue of energy, called quantum, (h). With this,electromagnetic oscillators are quantized.

2. Einstein, - in order to explain the high ve-locities of energetic photo-electrons, - extendsPlanck's quantization of the oscillators, to radia-tion itself by hypothesizing that the quantized

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Aethro-kinematics

energy electromagnetic waves in some cases canbe concentrated at a single point in space, behav-ing as a particle and its total kinetic energy canbe transferred to a mass particle, like an elec-tron. The energy of the photon equals the fre-quency of the electromagnetic wave times thePlanck's constant, that is, E=hυ.

3. Compton's effect experimentally proves theparticle-like properties of Einstein's photon byshowing classical type collisions of them withelectrons according to the laws of conservation ofenergy and momentum. Thus, the wave-particleduality of light is scientifically established.

4. Bohr initiates the solar model of the hydro-gen atom in which a single electron revolvesabout the single proton nucleus on different pos-sible orbits. By applying the Planck's quantum tothe angular momentum of the orbiting electron,Bohr finds the explanation for the empiricallyfound regularities, like the Balmer-Lyman-Pa-schen series in the spectrum of the hydrogenatom. In order to save the stability of the atom,in contradiction with the electromagnetic theory,he assumes that the electron only radiates ener-

gy when it jumps from one quantum level ofenergy to another.

5. De Broglie, just by symmetrical reasoning,stipulates that, if light can have wave and parti-cle attributes, then particles may have similarduality, having wave attributes. Taking fromCompton's collision hypothesis and his momen-tum and wavelength relation of the photons, deBroglie suggests a theory of pilot waves whichare associated with all particles. He assumes,that the wavelength of these pilot waves is equalto Planck's constant divided by the momentum ofthe particle. Further more, de Broglie extendsthis theory to the solar model of Bohr's hydrogenatom by assuming that the waves associatedwith the electrons can replace Bohr's quantumjumps by forming standing wave orbits which areonly stable if the circumference of the orbit isexactly divisible by the electron's wavelength.

6. Davisson and Germer experimentally pro-ves the existence of the wave nature of mass-par-ticles by producing wave-like diffraction effects ofelectrons in quantitative agreement with the deBroglie prediction.

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Aethro-kinematics CHAPTER SEVENTEEN Conceptual Development in a Nutshell

7. Schrodinger follows the direction of deBroglie's model and develops Wave-mechanics.Taking the well known classical equation of wavemotion, correlating it with Young`s mathematicsfor light-interference and substituting the parti-cle's momentum by de Broglie's relation of mat-ter wavelength, he discovers the quantum wave-function. This formalism applied to the new theo-ry of the hydrogen atom, explains a great deal ofthe quantized structure of the atom and mathe-matically predicts the electron diffraction phe-nomenon. Initially Schrodinger interprets thewave-function as the representation of a vibra-tion in an electromagnetic field and believes thatthe underlying physical reality is strictly of un-dulatory nature. He viewed an atomic electronnot as a particle but as a collection of wave dis-turbances in an electromagnetic field with thewave-functions representing the evolution of theinterference amplitudes of the waves.

8. Heisenberg, unlike Schrodinger, does notsearch for an underlying physical reality, butmerely looks for a mathematical algorithmthrough which connections can be made between

physical quantities that would fit the knownexperimental facts. This tendency of his investi-gation leads to Matrix Mechanics.

9. Pauli shows that matrix mechanics canalso predict the hydrogen atom's emission spec-trum. Schrodinger demonstrates that wave-me-chanics and matrix-mechanics are mathematical-ly equivalent. The question at this point is whichformalism is philosophically superior.

10. According to Max Born neither of themare acceptable. Matrix-mechanics is merely amathematical machine without conceptual con-tent. Wave mechanics is unable to explain how awave-like electron can be removed from its atom-ic orbit and produce a discrete trajectory in anionization chamber. Thus, Born concludes thatthe square of the amplitude of Schrodinger'swave-function merely represents the probabilitydensity of finding a given quantum particle in agiven region. According to this interpretation, theevolution of the wave-functions represents noth-ing physical but merely the evolution of our stateof knowledge about the classical attributes of agiven quantum system.

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11. Pondering the particle-wave duality inthe electron-diffraction experiment, Heisenbergfinds that the directional change in the velocityof the particle is inversely related to the size ofthe slit through which it passes. The smaller theslit, the greater the deviation in the trajectoryfrom Newtonian mechanics. Applying de Brog-lie's wavelength-momentum formula he discoversthat the more precise the measurement of theposition of the electron (that is, as the size of theslit approaches zero), the more uncertain thedirection of its motion becomes. Thus, a precisemeasurement of the position and the momentumof a classical particle cannot be established si-multaneously. Similarly, the more sharply we canmeasure the time of the passage of a quantumparticle through the slit, the more uncertain willbe its energy, and vice versa. This statement iscalled the uncertainty principle which is againrelated to Planck's constant.

12. Heisenberg and Bohr disagree on the fun-damental philosophical character of quantum-mechanics. Heisenberg believes that the theorymerely provides a mathematical scheme that

predicts everything that can be observed andtells the limitations on what is measurable.According to Bohr the fundamental problem oftheoretical physics is the wave-particle dualityand all the rest, − including the uncertainty prin-ciple, − are mere mathematical consequences ofthe attempt of using two diametrically opposedclassical concepts to describe something that isfundamentally non-classical. Thus, quantum the-ory limits not what is measurable but what isknowable.

13. It takes Pauli's intervention, to find mutu-al ground for the different views of Heisenbergand Bohr. The cooperation of these three theo-rists finally results in the so-called CopenhagenInterpretation of quantum-mechanics, which co-ordinates Bohr's complementarity solution forthe wave-particle duality with Heisenberg's un-certainty principle, and Born's probabilisticinterpretation of Schrodinger's wave-function.The Copenhagen interpretation provides the fun-damental postulates of quantum mechanics andits mathematical structure and formalism thatresults from them.

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14. The most controversial constituent ofthis interpretation is Bohr's concept of Comple-mentarity. According to Bohr the paradox ofquantum mechanics is that it attempts to de-scribe quantum phenomena in terms of idealizedclassical concepts, like those of waves and parti-cles. Complementarity requires the acceptancethat we can never 'know' quantum concepts. Aquantum particle is neither a wave nor a parti-cle. They are simply beyond human experienceand merely elements of empirical reality. Hence,a quantum system is but a substitution of theappropriate classical concepts, the empirical real-ity of which depends on what attribute of thequantum phenomena is observed by the specifi-cally designed instruments. For Bohr, althoughthe wave picture and the particle picture are mu-tually exclusive, quantum mechanics is a suc-cessful interpolation of the controversial classicaldescriptions in a single all-encompassing mathe-matical formalism.

Thus, the resulting description gives eitherthe wave or the particle attributes of the quan-tum system but never both of them simultane-

ously. Thus, the successful predictions prove thatthe classical concepts of waves and particles arenot contradictory but complementary to eachother. Similarly, as Heisenberg's uncertaintyprinciple states, the measurement of differentparticle attributes, like those of position andmomentum are also exclusionary. To determinethese quantities requires two different kinds ofapparatus, thus, although they cannot be mea-sured simultaneously, nevertheless, they are alsocomplementary.

15. The Copenhagen interpretation essential-ly states that quantum mechanics renders a com-plete description of empirical reality, but withthat we have reached the limit of what we canknow about Nature. Any attempt to introduce anew mechanical concept to describe an underly-ing physical reality, independent of our measur-ing, inevitably returns to the idealized classicalconcepts that summarize the fullest extent of ourknowledge: waves and particles.

16. By Bohr's Correspondence Principle thisinterpretation also sets the boundary betweenclassical and quantum physics. It is assumed

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that a theory of quantum mechanics, based on deBroglie's matter-wave formula includes ordinaryparticle mechanics as a limiting case. Just as rel-ativistic mechanics contains Newtonian mechan-ics in the limit of velocities compared to whichthe velocity of light may be regarded as infinitelylarge; c → ∞, quantum mechanics is reduced toclassical mechanics when the de Broglie wave-length of the particle approaches zero; λ → 0.

17. Extended by Dirac's theory of electronspin and Pauli's exclusion principle the mathe-matical formalism of quantum mechanics pro-vides a reliable method of computation of atomicspectral frequencies and intensities, of cross-sec-tions for scattering of electrons by atomic sys-tems, of chemical bonds and many other micro-scopic properties of solids.

18. Nevertheless, Bohr's complementarity, asa solution for the fundamental problem of thewave-particle duality creates serious dilemmasand disturbing vagueness in theoretical physics.Right from the inception, there exists a philo-sophical controversy between classical epistemo-logical principles and those of quantum mechan-

ics about physical reality. The Copenhagen pos-tulates lead to the denial of causality, determin-ism and even that of physical reality itself. In thepurely mathematical switching between particleand wave attributes both classically clear con-cepts of particle and wave become elusive andthe problem of their physical relation invokesmetaphysical speculations instead of mechanicalconsiderations. Thus, scientists who contributedmuch to the conceptual and mathematical devel-opment of quantum mechanics, like Einstein,Schrodinger and others, have launched persis-tent attacks against the alleged consistency andcompleteness of the Copenhagen interpretation.

19. Einstein believes in causality and deter-minism. He directly challenges Bohr's positivistphilosophy which only accepts empirical realityand insists on not attempting to understand thephysical world as independent from our observa-tions. Einstein's opinion is that the success ofquantum mechanics lies in its statistical natureand the squares of the wave functions merelyrepresent the statistical probabilities obtained byaveraging over a great number of real particles.

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The obvious analogy is with Boltzman's sta-tistical mechanics which predicts macroscopicphysical quantities such as gas pressure andthermodynamic functions, using microscopic,molecular and atomic statistics. The probabilitiespredicted here are derived from the behavior ofan ensemble of real particles which exist in pre-determined states and obey the laws of determin-istic classical mechanics. − Einstein designs a ge-danken experiment to show in principle an alterna-tive description of the wave-like interference behav-

ior of electrons in a double slit experiment. The Co-penhagen complementarity principle states that wecan either demonstrate the particle or the wavebehavior of a quantum object but never both simulta-neously. Einstein argues as follows: suppose that thetransfer of momentum between the particle and thefirst screen is carefully measured and observed(Figure 17-1/a). A particle hitting the screen will bedeflected and its trajectory beyond the screen will bedetermined by the conservation of momentum.

From this and from the final position of the parti-cle on the detector screen we can infer which one ofthe two slits the particle passed through the middlescreen. Hence, it is possible to determine the wholetrajectory of the particle through the apparatus.When, however, we record a large number of parti-cles on the detector screen, one after the other, due totheir random collisions with the slits, we will find thetotal double-slit interference pattern. Thus, Einsteinconcludes, that it is possible to demonstrate both theparticle-like trajectory and the wave-like interfer-ence of a quantum object simultaneously and by thesame apparatus. Hence, the principle of complemen-tarity is proven to be wrong.

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Figure 17-1.

20. Bohr's simply refuses this argument byshowing that Einstein's assumption of controllingthe transfer of momentum between the particle andthe screen must imply a factor of uncertainty. If wemeasure the change in the momentum of the screenwith arbitrary precision, then an infinite uncertaintyin the position of the screen must result. Why? -According to Bohr, in order to observe the change inthe position of the screen, it should be sufficientlyilluminated and the scattering of the photons fromthe screen represents an uncontrollable momentumtransfer. Thus, Einstein's hypothesis is in contradic-tion with the uncertainty principle and with theexperimental facts.

21. Einstein, Podolsky and Rosen (EPR) thenattack the alleged completeness of quantummechanics by the following argument: Imaginethat two particles interact and separate fromeach other but some of their physical attributes,like their momenta and positions, remain corre-lated. With the aid of the laws of conservation ofenergy and momentum any later measurementof the position or momentum of one of the pairwill render the knowledge of the same attribute

of the other particle. Suppose, that these arequantum particles, going through a diffractionexperiment, and quantum mechanics applies.

According to the uncertainty principle themeasurement of the position or the momentum ofthe particles requires two different devices whichcannot be used simultaneously. However, whenone of the particle is measured by striking on thescreen, the wavefunction collapses and bothquantum particles, A and B must regain theirlocal physical reality.

It follows that measuring, say, the position ofA, means that the position of B also becomes alocal physical reality. Hence, EPR argue that,while the particles are in flight, we can still havea choice between the two devices. Waiting till thevery last moment with this decision it becomesobvious that there must be an instantaneouscommunication between the two particles for Bto regain the local reality of the same attributeas that of A's. − EPR do not believe this is possi-ble nor that it is necessary. They insist that theclassical attributes of position and momentumexist continuously and separately all along the

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path of the real particles and should be definedcontinuously and independently. Since, there isnothing in the wave function that describes theevolution of these quantities, quantum mechanicsmust be incomplete.

22. Bohr's answer to these EPR paradoxes isessentially a repetition of the philosophical argu-ment of complementarity and its application tothose special cases. He states that due to themathematical structure of quantum mechanics,the wavefunction cannot be separated for the twoquantum particles because it describes theirprobability density by the square of the ampli-tude of the interference between their superposi-tions. The concept of separation in this case istotally meaningless and in mathematical lan-guage it is expressed by the non-factorability ofthe wavefunction.

23. Schrodinger offends quantum mechanicsfrom another direction and strikes right to theheart of the measurement problem, invoked bythe Copenhagen interpretation. His famousargument is called the 'Cat Paradox', a complexscheme of events through which the classical and

quantum mechanical worlds interact. -- A live catis placed inside a chamber together with a Geigertube containing some radio-active substance ofknown half life. If an atom disintegrates, theGeiger counter triggers a switch that releases alethal gas which kills the cat. Within an hourthere is a probability of 1/2 that an atom woulddisintegrate. The purpose of this scheme is toshow the vagueness of quantum mechanics whenit comes to the definition of the boundary bet-ween classical and quantum worlds.

According to quantum mechanics, prior toactual measurement the atoms of the substanceare in the superposition of being intact, or disin-tegrated. They stay in this suspended realityuntil one atom disintegrate and measured by thecounter. At this instant the atomic wavefunctioncollapses. The probability of disintegration col-lapse to unity for that atom and zero for all oth-ers. For predicting any further event, a newwavefunction must be established. -- But whatabout the Geiger counter, or the switch, or thegas, or the cat itself? -- Schrodinger brings up thefact that classical entities, inanimate or living,

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are also made of quantum systems which canonly be described by the quantum mechanicalwavefunction and therefore all the constituentsof the measuring apparatus should be in super-position between their two probabilities of yes orno. Uncovering this ambiguity indefinitely wi-dens the boundary between the two worlds andgives no hint where and when should be the finalcollapse of the wavefunction. If it happens at theGeiger counter then a new wave function mustbe applied to the electronic switch that releasesthe gas, and so on all the way through the quan-tum systems of the brain cells of the cat. No mat-ter how many wave functions collapse, there willalways be another superposition that requires anew wavefunction. Thus Schrodinger's paradoxdemonstrates that the Copenhagen interpretationleads quantum mechanical measurements into ahopeless infinite regression.

24. In essence the Copenhagenian answer tothis argument is that since we have no othermeans of predicting the behavior of the quantumworld but through the probability density de-scribed by the wave function, we must resist the

temptation to ask ourselves what possible physi-cal state a particle or a cat actually is prior to ameasurement. Such a question leads nowhere,thus it is totally meaningless.

25. Under the title of "Wigner's friend" thescheme develops even further in the same direc-tion by adding a human observer to the list ofconstituents of the measuring apparatus. Thisextension of the Copenhagen superposition overthe human consciousness results in wild specula-tions about the relation between the observerand the observed.

26. As obvious as the success of the mathemati-cal formalism is, most physicist who care to under-stand what they are doing, cannot accept that theCopenhagen interpretation is liable for that success.Among other reasons, the dissatisfaction comes fromthe fact that, through the development of quantummechanics Schrodinger's well-defined, classicallyfounded deterministic wave function is re-interpret-ed as some unrealistic statistical probability wave,with no better justification than the ignorant rhetori-cal question: What else could it mean?! − Thus,beneath the Copenhagen power structure a hesitant

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search begins for an alternative humanly conceivableinterpretation.

27. It is characteristic to the dominantly mathe-matical thinking of the century that this search,which is supposed to uncover some, so far unknownpart of physical reality, is named as the search for"hidden variables". -- Accordingly, the search con-sists of mainly mathematical exercises to derive inprinciple whether or not, such hidden variablesadded to the wave function could somehow reinstateclassical causality and local reality, while still repro-duce exactly the quantum mathematical predictions.

28. Soon, Von Neumann's so-called "impossibilityproof" appears, in the form of a sophisticated mathe-matical derivation, proving that, if there were suchvariables added to the quantum mechanical formal-ism, they would allow us to measure simultaneouslythe position and momentum of a quantum particle,which conflicts with the uncertainty principle andthe experimental facts. Thus, for the next two de-cades scientists take this proof as a victorious rein-forcement of the Copenhagen dogma.

29. In spite of the paralyzed state of theoreticalphysics, due to von Neumann's authority, in 1951

David Bohm reopens the EPR debate. -- Most proba-bly, as an attempt to relieve the argument from theclinch of the uncertainty principle, instead of theposition-momentum correlation, Bohm considers thecorrelation of the spin orientations of two atoms dis-associated from of a hydrogen molecule. If the totalelectron spin angular momentum in the moleculewas initially zero then the atoms will move away inopposite directions with opposite spin orientations(say up and down). Hence, the correlated atoms andtheir spin orientations (1/2) are elements of indepen-dent local physical realities and measurable withoutinvoking the uncertainty principle.

Figure 17-2. (a) shows how in Bohm's thought-experiment the conservation of the angular momen-tum of a hydrogen molecule leads to the oppositespin orientation of the disassociated atoms. Part (b)shows a setup of two parallel oriented Stern-Gerlachmagnet that separates the oppositely spinning atomsinto up or down positions on the detector screens atboth sides. The source, at the center produces pairs ofrandomly oriented atoms, but if one of the pair pointsup the other invariably points down. In quantummechanics the pair of correlated atoms must be

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described by a single (or singlet) wavefunction andtheir spin orientations are in non-separable super-position until the moment of measurement, whenboth orientations become empirical reality.

Figure 17-2.Before that it is meaningless to speculate the

states of the atoms. However, EPRB (Bohm) arguethat by measuring the spin orientation of A (up)along the laboratory z axis by the left magnet makesthe orientation of B (down) at the right magnetimmediately predictable. Bohm extends the argu-

ment by asking, what if we choose to measure anoth-er component of the spin of A, say, along the x axis?!

Classical physics demands that all component ofthe opposite spins are pre-determined and correlat-ed, thus a measurement on A would also make the xcomponent of B become local reality. But the quan-tum mechanical wavefunction can only specify onespin component for each atom. Thus, either the wave-function is incomplete or the EPR definition of physi-cal reality is wrong.

30. After several discussions with Einstein,Bohm comes to the conclusion that both Bohr andvon Neumann were wrong. In 1952 he publishes acompletely developed alternative to the Copenhageninterpretation of quantum mechanics based on a hid-den variable theory, very similar to de Broglie's pilotwave theory which was rejected by the Copenha-genists and eventually even de Broglie, himself aban-doned it 25 years earlier. As Bohm states in thiswork, he was not aware of de Broglie's theory, never-theless, he states that in his version all past objec-tions are answered by developing the initial idea toits logical conclusions. Bohm calls his work; The theo-ry of quantum potentials.

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A B

(b)

(a)

A B

SOURCE

A

B A

B

MAGNET MAGNET

SCREEN SCREEN

31. Bohm's courageous work seems to awakenthe conscience of the scientific community, revitalizesthe EPRB debate and triggers a re-evaluation of vonNeumann's theory. -- John S. Bell in 1964 indeedfinds a definite inconsistency in the mathematics ofthe "impossibility proof", which at least legitimatizesBohm's reopening of the hidden variable question.But Bell also shows, that classical statistical proba-bilities, based on local reality, cannot reproduceexactly the quantum mechanical probabilities andpredictions. Bell's theorem of inequality states thatno locally real hidden variable interpretation of theexperimental facts can fully replace the Copenhageninterpretation.

32. Jumping ahead some, here are a few freequotes from books and articles written and publishedfour decades later:

Paradigms Lost by John L. Casti, 1989 [463]."Bohm began to develop de Broglie's earlier idea

into a mathematically consistent interpretationof quantum theory involving only ordinary ob-jects. Originally, de Broglie's pilot wave theorywas rejected by the Copenhagenists in view ofthe associated insurmountable mathematical dif-

ficulties. However, Bohm showed how to over-come the alleged difficulties. He regards a quan-tum object as a particle with an associated pilotwave that in effect tells it how to move. In thispicture, every quantum object is a real particlepossessing definite attributes at all times. Associ-ated with each such real particle there exists apilot-wave-field which is also real but unde-tectable other than through its effects on the par-ticle. This wave-field in Bohm's theory is termedas quantum potentials, and serves the function of'reading' the environment and reporting back tothe particle. The particle then acts in accordancewith the provided information. As a result, aquantum object is not composed of a single"thing", either particle or wave, but both a realparticle and a real wave-field. Thus, objectivereality and local causality is restored, as there isno longer the ongoing schizophrenia (complemen-tarity) between the mutually exclusive wave andparticle attributes. At all times the quantumobject possesses both attributes and at all timesthe particle side has all the usual classic attrib-utes. (position, momentum). Bohm's genius was

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to show how this scheme works mathematicallyby an extension of Schrodinger's wave function,containing not only the evolution of the pilot-wave-potentials but also the continuous evolu-tion of the position coordinates of the associatedclassical particles."

From an article by David Z. Albert, published inthe May 1994 issue of Scientific American:"Although Bohm's new interpretation of quantum

mechanics has existed in the scientific literature formore then forty years, it has until quite recentlybeen mostly ignored.Throughout that period the thinking about such

matters has been dominated by the standard dogma,usually referred to as the Copenhagen interpreta-tion. But it is now emerging that those conclusionwere settled somewhat hastily. As a matter of fact,Bohm's interpretation is a radically different, fullyworked-out theory that accounts for all known be-haviors of subatomic particles. In this theory, chanceplays no role at all, and every material object invari-ably does occupy some given space at all times.Moreover, this theory takes the form of a single set ofbasic physical laws that apply in exactly the same

way to every physical object that exists. Bohm's theo-ry accounts for all the unfathomable looking behav-iors of quantum particles as well as the standardmathematical formalism of quantum mechanicsdoes, but it is free of any of the metaphysical perplex-ities associated with the Copenhagen interpretationof superposition and measurement.""In 1982 Bell recasts Bohm's original theory into a

both mathematically and conceptually very simpleand compelling form. With this Bohm's theory in itsentirety consists of three basic elements. The first isa deterministic law, the Schrodinger's wave equation,that describes how the wave functions, or the quan-tum potentials of physical systems, evolve over time.The second element is a deterministic law of theresulting motions of the particles, represented by theactual coordinate values of the components of motionincluding the effects of the standard quantum-mechanical probability current. The third element isa statistical rule analogous to one used in classicalstatistical mechanics. It stipulates precisely how onegoes about 'averaging over' ones inevitable ignoranceof the detailed exact states of a physical system. As aresult, during the evolution of the wavefunction, at

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any time, the probabilities of the positions can be cal-culated. As this information about the positionbecomes available during a measurement, it is usedto "update" the probabilities through a mathematicalprocedure, called straightforward conditionalizationwhich renders the orthodox collapse of the wavefunc-tion. unnecessary. This is all there is to Bohm's theo-ry. Everything else derives strictly from these threebasic elements." "Bohm's theory is the only serious proposal in com-

petition with the Copenhagen interpretation. It rein-states causality and determinism, does not requirethe concept of superposition of quantum particles,not even on the microscopic level and avoids the infi-nite regress of the entangled quantum measure-ments and other perplexities of the standard dogma."

33. Nevertheless, Bohm's theory is not totallyfree from transgressions. There are three major prob-lems with the theory from the stand point of commonphysical sense.

a) In order to restore classical objective realitythe theory assumes the existence of a wave phenom-enon which is physically unobservable other than itseffects on the classical mechanics of microscopic par-

ticles. To most working physicists and experimental-ists unobservability equals to non-existence.

b) To reproduce exactly the quantum mechanicalpredictions, this theory must approach the EPRproblem of correlation through the exact mathemati-cal formalism of quantum mechanics, by a singletwavefunction, which is non-factorable. Therefore, it isin contradiction with Einstein's requirement of sepa-rability. Hence, like standard quantum mechanics,Bohm's theory is also explicitly non-local. Thismeans that it has to face the existence of an instan-taneous or superluminal communication betweencorrelated particles measured at distant places.

c) Being simple and clear, Bohm runs into prob-lems that the vague philosophy of the Copenhageninterpretation never had to face. If Bohm's quantumpotentials successfully restore objective reality, thenit also invokes the physical reality of an informationtransmission faster than light. With this and withthe unobservable pilot wave phenomena the theorynot only finalizes the unavoidable separationbetween the classical and quantum worlds, but italso reinforces the mutual exclusion between theworlds of special relativity and quantum theory.

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36. Bohm's theory has a built in explanation forthis problem. "The reason why no contradiction withrelativity arise in spite of the instantaneous trans-mission of momentum between particles is that nosignal can be carried in this way. For such a trans-mission of momentum could constitute a signal onlyif there were some practical means of determiningprecisely what the second particle would have done ifthe first particle had not been observed; and as wehave seen, this information cannot be obtained aslong as the present form of the quantum theory isvalid." (Bohm: Suggested interpretation of the quan-tum theory in terms of "hidden" variables. − PhysicalReview, 85, 1952 [166]).

34. In the wake of this novel theoretical result,the half a century old EPR debate now takes a 180°turn. For the still reigning Copenhagen administra-tion Bohm's dilemma suggests that if non-local quan-tum mechanical correlation can someway be provenexperimentally, it would not only cancel Bohm's newreality but the logical inconsistency of the whole EPRargument would forever justify the postulates of theCopenhagen interpretation.

Hence, it becomes the interest of the orthodoxgroup to show that there is not only a correlationbetween quantum particles in the EPR style, buteven beyond that, in terms of Bohm's non-localitywhich require some "spooky" superluminal communi-cation. For this reason, an ambitious search developsto find experimental proofs of the necessity of ananti-relativistic superluminal signal which discardsthe whole EPRB argument.

35. The main stream of the resulting experi-ments conveniently extends Bohm's spin-correlationidea to the elementary light particles of photons.Quantum mechanics assigns two possible compo-nents of spin to an individual photon which is as-sumed to be equivalent of the left or right circularpolarization of light waves. The spin property of thephoton is essentially a mathematical convenienceand comes with the warning that it is not to be prim-itively interpreted as if a little shiny sphere was lit-erally spinning on its axis. It is also stated, that thelaw of the conservation of angular momentum isvalid in the case of spinning photons. When a doublyexcited calcium atom, with zero angular momentum,returns to its ground state it emits two oppositely

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spinning photons, also representing zero angularmomentum. Very low intensity emission makes itpossible that a pair of single photons emitted inopposite directions in a cascade of rapid succession.Pairs of such photons are oppositely correlated, beingleft and right circularly polarized.

The most famous of correlated photon-spin exper-iment is designed and executed by Alain Aspect andassociates. Figure 17-3 illustrates the basic theoryand construction of all Aspect-type experiments. Twooppositely polarized photons are emitted from a gas

of calcium atoms excited by high-powered lasers ofdifferent wavelengths. The resulting emission of pho-ton pairs in opposite directions are passing throughmonochromatic filters which isolate the green pho-tons on the left (A) and the blue photons on the right(B). The calcite analyzer cubes in each side (PA1 andPA2) are placed 13 m apart. They transmit verticallypolarized photons and reflect horizontally polarizedones. As a result, there are four separated beams ofphotons, two on each side, emerging independentlyand enter into four photomultipliers which then sendelectronic impulses to the four-fold coincidence coun-ters at the bottom center.

The detection of a transmitted photon gives a '+'result and that of a reflected photon gives a '−' result.Each calcite-cube analyzer with the related photo-multipliers are mounted on independent axes onwhich they can be rotated, thereby altering their rel-ative orientations. By this set up the polarizationangle of one individual photon of the pair can be sep-arately altered. Further more, the coincidencecounter is set to look for the arrival of photons A andB within a 20 nanosecond time window. Hence, anysignal 'informing' B about the fate of A must travel

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Figure 17-3.

13 meter in 20 nano second which requires a greaterspeed than that of light.

36. It is always noted in the descriptions of theseexperiments that they are far from ideal and in prac-tice there are a number of physical limitations thatreduce the conclusiveness of the coincidence count-ing. To mention some; real polarization analyzers donot transmit and reflect all the photons they supposeto, but they often leak both ways. Also this leakagemay depends on their different orientation relative tothe laboratory frame. Photomultipliers are quite inef-ficient in producing signals from only the small num-ber of photons that is actually generated, thus mak-ing it hard to realize single photon measurements.Further more, because of the limited size of all thesedevices, they cannot 'gather' all the arriving photonsand, of course, with different results for the twosides, which could break up the sequence of thepairs. These and other inefficiencies limit the successof the coincidence detection of the photon pairs andsome can even be detected incorrectly. The experi-menters' way out of this impasse is through mathe-matical generalization and averaging over the differ-ent inefficiencies, Also to account for this dampening

effect on the correlation, physicists derived a slightlymodified form of the quantum mechanical prediction,taking into account that not all photons are caughtby the detection system.

Nevertheless, this quite esoteric experiment, in-volving sophisticated apparatus and complicated sta-tistical analysis with a chain of basic and auxiliaryassumptions, the total results seem to show that thecorrected quantum mechanical predictions are over-whelmingly justified by the experimental data.

37. Some stubborn proponents of local reality,causality and determinism still try to find loopholesin the theory of the Aspect experiments. − They ar-gue that, since the change in the relative orientationof the polarizers are set before the photon pairs areemitted, they believe, there is a possibility that thephotons were somehow informed about the way theapparatus was set up while they were produced. Ifso, it is possible that the photons were created andcorrelated with just the right "local hidden variables"by which they can reproduce even the adjusted newquantum mechanical predictions.

To close this loophole, Aspect and colleagues ex-tend the original apparatus with two acousto-optical

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switching device, one on each side. These switchesoperate randomly on the photons in flight alternat-ing their paths through analyzers with different ori-entations. It follows that there is no way for any pho-ton to "know" in advance and communicate its physi-cal attribute to its twin before the instant of the col-lapse of the wavefunction.

This addition, of course, also contributes some-what in the inefficiency of the apparatus, but againthe experimenters mathematically overcome the dif-ficulties and the final statistical experimental dataconvince them, that quantum mechanical predictionsof non-local correlation still prevail. If EPRB insiston local reality and causality, it must face the un-avoidable necessity of superluminal communicationbetween distant particles.

38. According to the orthodox Copenhagenists,the Aspect experiments are merely a roundaboutdemonstration of Bohr's Complementarity Principle.The problem still is the limitation of what is know-able through the classical duality of waves and parti-cles. These concepts are only applicable to quantumentities when specifically designed devices used tomeasure either one or the other characteristics, but

never both together. Thus, EPRB either give upunderlying reality, as the Copenhagen interpretationdoes, or live with the counter-intuitive, anti-causal"spooky action at a distance" involving anti-relativis-tic superluminal communication.

39. In 1979 in his Einstein Centennial AddressJ.A.Wheeler suggests an important further extensionof Aspect's experiments. After Einstein's death, therewas no hope that some kind of ingenious UnifiedField Theory will relieve theoretical physics from thevagueness of the Bohr Copenhagenism. Neverthe-less, Wheeler believes that during the half a centurythat passed since the inception of the EPR debate,science and technology finally reached the levelwhere the metaphysics of quantum mechanics can beproven experimentally right or wrong.

Wheeler proposes a simple method for the experi-mental verification of Bohr's principles of wave-parti-cle duality and complementarity. The same experi-ment can also lead to a conclusion whether or notnon-locality and super-luminal communication is anunavoidable constituent of empirical reality. The ideais to construct a single apparatus (Fig. 17-4) that canmanifest both the particle and the wave attributes of

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a quantum entity and able to switch between themin a time frame which guaranties that the predictedquantum mechanical correlation cannot be achievedany other way but by super-luminal communication.

Figure 17-4.

As it can be found in J. A. Wheeler's QuantumTheory and Measurement. III.13. Wickes [457]:"In a traditional optical double slit interference

experiment, photons from a distant source are inci-dent upon a screen containing two small apertures.With a lens behind the screen an image of the source

is formed on, for example, a photographic plate situ-ated in the focal plane of the lens. The size and shapeof the image depend upon the apertures, but theimage will be crossed by interference fringes of angu-lar frequency λ/D, where D is the separation of theapertures and λ is the wavelength of the light. Suchan experiment isolates the wave character of theincident radiation: the interference fringes can bebest understood by describing the energy containedin the radiation as passing through both apertures,even if the intensity is reduced so that usually onlyone photon at a time enters the system.""If the photographic plate is replaced by a pair of

photomultipliers situated so that each one receiveslight from only one of the apertures, then the experi-ment emphasizes the particle nature of light. Wemight imagine that the photographic plate is hingedto swing rapidly into and out of the photon paths: ifthe plate intercepts the beams, an interference pat-terns is recorded, one grain at a time; if the plate isswung out, photons passing through and individualapertures detected. If for example, one of the aper-tures is covered, there is no effect on the count rateobserved with the photomultiplier associated with

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I = 50 %

P1

P2

FROM SOURCE

DOUBLE SLIT SCREEN

LENSE

HINGED PLATE

PHOTOMULTIPLIERS

the other aperture. This effect implies that each pho-ton passes through one aperture or the other, neverboth."

"This reasoning suggests that the configuration ofthe apparatus, and hence, the choice of an experi-menter, determines whether the photons exhibit par-ticle-like or wave-like behavior. Acceptance of thisapparent paradox is central to the Copenha- geninterpretation of quantum mechanics. Bohr moreoverasserts that the outcome of a double-slit experimentwill not change even if the apparatus is changedafter the photon is already in flight."

Of course, this was still a gedanken experimentand its simplicity, like the flipping in and out of thephotographic plate with the speed of light, was notfeasible technologically.

40. A group of scientist Wickes, Alley and Jacu-bowitz (WAJ) set out to design an apparatus basedon Wheeler's theory using the most modern electron-ic devices. They call the proposed apparatus, the"Delayed Choice Interferometer". In general, thedevice creates a phenomenon which is exactly analo-gous with Young's double slit experiment, but capa-ble to demonstrate both the interference phenome-

non of light waves and the localized particle position-recording of individual photons.

Figure 17-5 (a) illustrates the schematics of theDelayed Choice Interferometer. For clarity, let usview the theory and the construction of the devicefirst solely in terms of the electromagnetic wave the-ory of light.

Figure 17-5.

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A

B

90°

I= 0 %

I=100 %

I = 50 %

I = 50 %

φ =

0°φ =

(b)

P1

P2

(b)

(a)

A pulse (short wave-train) of linearly polarizedlight-waves, generated by a laser, which splits on ahalf-silvered mirror and proceeds on two separatepaths of propagation, A and B. Three fully reflectingmirrors bring the separated beams back into coinci-dence inside of a triangular Koster Prism. Neglectingall other details for now, consider the fact that if therejoining half-intensity waves were exactly in phase,then the resulting constructive interference (peakcoincides with peak) reproduces the total initialintensity. Waves arriving at 180° out of phase (peakcoincides with trough), produce destructive interfer-ence and records zero intensity.

Next consider, a phase-shifter (PS), inserted onthe upper path, shifts beam A 90° out of phase com-pared to beam B. The triangular prism itself alsoacts as a beam-splitter, passing and reflecting eachhalf of the rejoined beams and lead them into thetwo photomultipliers, (1) and (2). Further more, theprism is also a phase-shifter and adds another 90°out of phase to the reflected half of both beams. It isimportant to consult with the details of illustration(b) and clarify that the reflected and therefore phase-shifted part of beam A (solid line) is united with the

transmitted part of beam B (broken line) and togeth-er enter into photomultiplier (1), . Since A is shiftedtwice, it is 180° out of phase relative to B, thus theydestructively interfere and record zero intensity. Onthe other hand, the Koster prism transmits the ini-tially phase-shifted A beam and reflects and phase-shifts the B beam and reunites them in photomulti-plier (2). Since both beams are 90° shifted their inter-ference is constructive, thus record the total initialintensity. Thus, final result produced by the waveattributes of the quantum particle is that only photo-multiplier (2) shows the arrival of light.

The next addition to the apparatus is the so-called Pockels Cell which is capable of rotating a ver-tically polarized light into a horizontally polarizedone. Another device is the calcite crystal which trans-mits the vertically and reflects the horizontallypolarized light. Pockels Cells are inserted in bothpath conjointly with calcite crystals. Thus, if one isturned on it rotates the polarization angle and thecrystal reflects the beam out of the path into the pho-tomultipliers (A) or (B).With this setup, each beam, Aand B can be individually deflected out of their ini-tial paths.

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Still considering strictly light-waves, it follows,that with both Pockels Cells off, the original interfer-ence result is unchanged. Either one of the PockelsCells turned on would cause the deflection of eitherA or B and let only the other beam go to through theKoster Prism. This beam will be split and guided intophotomultiplier (1) or (2), measuring 1/4 each of theinitial intensity.

Evidently, there is no mystery about the resultsof this part of the experiment based strictly on theclassical wave theory. The only requirement for theconsistent interference results is that the distance ofthe two paths must be exactly equal, or differing byan integral multiple of the wavelength, so the twobeams arrive to the point of interference at exactlythe same phases. All results of this part of the experi-ment, including the wave phenomenon of polariza-tion agrees with the classical wave-theory andMaxwell's equations.

Consider now the second part of the descriptionof the delayed choice apparatus which is concernedwith the production, guidance and recording of thestrictly particle attributes of a single photon within aspecific time frame. In this respect there are some

basic theoretical differences between the initialAspect-type experiments and this latest one. As theoriginal report of WAJ, (Wheeler [457-8]) explains:"The delayed-choice experiment looks at the behav-

ior of single photons with a choice of trajectories to asingle recombination in space-time (non-relativistic)rather than at pairs of photons at distant points. Anyinterpretation of the results of this experiment willdepend, of course, on whether it is sensible to speakof the position of individual photons, especially asregards to the extrapolation backwards in time fromthe detection of photomultiplier pulses."

In the delayed choiceexperiment both theposition and spatialextension of the pho-ton, as a particle, areimportant thus, thequantum concept ofa so-called wave-packet comes intoplay. Figure 17-6. isthe usual illustra-tion of this concept.

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Figure 17-6.

As WAJ describes: "a laser light source emitspulses with a time duration of 100 ps correspondingto a wave packet with spatial extension of 3 cm."

(Divided by a wavelength, say, 500 Å (0.00000001cm) seems to be a rather lengthy train of peak-and-troughs, an and immense number of phases, ratherthan an infinitesimal point particle.)"In the proposed system, the detection of 'particles'

and 'waves' is accomplished by photomultipliers inwhich detection events can be localized in time."

Considering now the strictly particle attributes ofthe quantum entity, let's follow the description of thedelayed choice experiment in accordance with theabove mentioned novelties:

Recall, that the polarized light-waves were splitby the first beam-splitter and then the two beamsfollow paths A and B. What happen to the indivisiblephoton at the beam-splitter? Will it go one way, orthe other, or both? Will it go through at all?

As Baggott in 'The meaning of Quantum Theory'(Photons have it both ways) describes:"Performing the experiment with the laser light

intensity reduced, so that only one photon passed

through the apparatus at a time, resulted in theexpected detection of the photons only by photomulti-plier (2). In this arrangement, the photon behavedas though it had passed along both paths simultane-ously, interfering with itself inside the prism, inexact analogy with the double slit experiment."(Constructive or destructive interference)."Thus with only one photon in the apparatus

switching on either Pockels cells was equivalent toasking which path through the apparatus the photonhad taken. This is analogous to asking which slit thephoton goes through in the double slit experiment.The choice between measuring a single photon's'wave-like' properties (passing along both paths) or'particle-like' properties (passing along one pathonly) was therefore made by switching on one of thePockels cells." "The great advantage of this arrangement was that

this switching could be done within about 9 nano sec-onds (one billionth). The lengths of the paths A an Bwere each about 4.3 m, which a photon moving withthe speed of light can cover in about 14.5 ns. Thus,the choice of measuring device could be made afterthe photon had interacted with the beam-splitter."

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"Of course, according to the Copenhagen interpreta-tion, the wavefunction of the photon develops alongboth paths. If one of the Pockels cells is switched on,the detection of the photon directed out of eitherpath collapses the wavefunction instantaneously, andwe infer that the photon was localized in one or theother of the two paths."

Hence, − based on the assumptions that the limit-ing intensity and an ideally short (3 cm) pulse oflight-wave-packet corresponds to the quantum parti-cle attributes of a single photon, and that the use ofthe photomultiplier, recording both the positions ofthe self-interfering photon particle and the construc-tively interfering light waves -- WAJ concludes: “theconfiguration of the apparatus, and hence, the choiceof the experimenter determines whether the photonsexhibit particle-like or wave-like behavior”.”Acceptance of this paradox is central to the Copen-

hagen interpretation of quantum mechanics.”Thus, a further metaphysical conclusion follows,

that even empirical reality depends on whether ornot an observer watching the path of the photon. Ifwatched, it manifests the position of a particle, if notit shows the interference phenomenon of waves.

According to the Copenhagen debaters the posi-tive results of the delayed choice experiments createinsuperable difficulties for the followers of Einsteineven nowadays.

But of course, the ‘hidden variable’-ists vehe-mently refuse this claim. They are rather willing todispose the central quantum mechanical concept ofEinstein’s photon altogether and return to the classi-cal and locally real electromagnetic wave-fields, sup-plemented by the random fluctuations in the socal-led zero-point field, or those in the so-called seethingvacuum. (Look up T.W. Marshall, Foundations ofPhysics, [22, 363] 1992)

Meanwhile, generation after generation are stillbeing educated in the spirit of the ‘standard’ Copen-hagen interpretation and learn very little else.

With this lack of competition, the search for theexperimental verification of the reigning ideologygoes on and so does the philosophical lamentationbetween positivists and realists. - Having just a fewmore years to go to complete a whole century of thismodern physics, one can ask the not very impatientrhetorical question: Are we really going anywhere?!

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AN AETHRO-KINEMATIC INTERPRETATIONThe ultimate goal of this study is to render a

coarse sketch of kinematical understanding for allknown natural phenomena, based on the ideal gasmodel of the Aether. This also means the completeunification of classical, relativistic, and quantummechanical physics, from Galilean inertia to Copen-hagenian superluminality. Stating it in an other way;this theory suggests that -- as gas-pressure and othermacroscopic phenomena can be explained by atomicand molecular statistical mechanics -- all events thatwe can predict, but are unable to comprehendthrough classical and modern physics, we should beable to contrive and explain from the conceptualview of a presently not yet existing STATISTICALAETHRO-KINEMATICS.

The foregoing sixteen chapters were written withthis general intention and the last one (with Appen-dix III) attempted to uncover the general kinematicorigin of the quantum phenomenon of discontinuanceof radiation energy. -- Hopefully, it has been donewith some initial success of opening sacred doors forfurther research. Now, besides generality, -- just toput a foot in some of those doors - it must be shown

here that the last six decades of scientific evolutionhas been totally ship-wrecked on a dangerously stub-born dogmatism. This dogma is reigning by vaguemetaphysical lamentations and ultra-sophisticatedmathematical argumentations over the results oftheoretically complex and technologically extremeexperimental jugglery.

Moreover, all this is happening in spite of thefact, that most of the real perplexities of the dogmat-ic Copenhagen interpretation of quantum mechani-cal formalism has already been solved and explainedaway more than four decades ago by the continuous-ly neglected de Broglie-Bohm theory. We have quotedsome very convincing recent expert analyzes aboutthe justification and criticism of this theory. Never-theless, there are some remaining uncleared prob-lems in the Bohm re-interpretation of quantummechanics which serve as excuses for the orthodoxschool to postpone any serious reflection.

The fundamental problem with any re-interpre-tation of the quantum facts lies in the undeniablesuccess of the mathematical formalism of quantummechanics in predicting the probabilities of experi-mental results.

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Aethro-kinematics CHAPTER SEVENTEEN An Aethro-kinematic Interpretation

Thus, the basic condition of any conceptual re-interpretation is, not to affect the quantum mathe-matical structure to any extent that would disturbthe already proven power of prediction.

The greatest merit of Bohm’s work is the success-ful combination of the de Broglie pilot-wave conceptwith the deterministic Schrodinger wave-equationand with the classical trajectory concept, withoutaffecting the general formalism of the quantummechanical mathematics. However, by reproducingexactly the quantum mechanical predictions, Bohm’stheory inherited one of its fundamental problemswhich is called non-locality, or the specific predictionthat correlated particles are not Einstein-separable.

Mathematically this means no less than that twocorrelated quantum particles must be described by asingle (singlet) wave-function which, in turn, guar-anties that they remain correlated and in communi-cation until one of them is measured.

It further follows, that the correlation betweenthe two particles at any arbitrary distance apartrequires an instantaneous and therefore superlumi-nal communication at the instant of measurement.This conclusion is totally at variance not only with

common sense but with the postulates of the theoryof special relativity as well.

According to the Copenhagen school anotherproblem with Bohm's theory is that the de Broglie'spilot waves are based on an ad hoc hypothesis whichoffers no experimental verification.

Originally, Bohm’s interpretation reinstated localreality, determinism and causality by reintroducingthe real and continuous existence of classical parti-cles and their trajectories by assuming that theirnon-Newtonian mechanical behavior results from themechanical effects of a real de Broglie wave-field,similar to those of the classical electromagnetic field.However, because of the superluminal communica-tion requirement, the mathematical formalism forcedBohm to face the choice between opposing relativityor giving up the realism of the wave-field.

As Bell addresses these problems in his collectionof lectures: 'Speakable and Unspeakable in QuantumMechanics', 1987.“Could it be that this strange non-locality is a pecu-

liarity of the de Broglie-Bohm construction, andcould be removed by a more clever construction? Ithink not. It now seems that the non-locality is

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deeply rooted in quantum mechanics itself and willpersist in any completion. Could it be that in the con-text of relativistic quantum theory, c would be thelimiting velocity and the strange long-range effectswould propagate only subluminally? Not so! Theaspects of quantum mechanics demanding non-local-ity also remain in relativistic quantum mechanics.”

More from Bell, On the EPR Paradox, Physics. I.[195-200] :

“Then for at least one quantum mechanical state,the ‘singlet’ state in the combined subspaces, the sta-tistical predictions of quantum mechanics are incom-patible with separable predetermination. -- In a theo-ry in which parameters are added to quantum me-chanics to determine the results of individual mea-surements, without changing the statistical predic-tions, there must be a mechanism whereby the set-ting of the measuring device can influence the read-ing of another instrument, however remote.“Moreover, the signal involved must propagate

instantaneously, so that such theory could not beLorentz invariant.”

Back to Aether:

The missing link in these logical argumentationsof Einstein, Bohr and de Broglie, Bohm, Bell, and ingeneral, modern theoretical physics, is representedby the complete absence of a medium within whichmicroscopic reality exists and which may render thekinematical causality and reasoning which is cer-tainly not derivable from the totally characterlessempty space.

The following section of AETHRO-KINEMATICSis an attempt to find some kinematical guidance outof this philosophical labyrinth. Thus, the first step isto re-iterate the general kinematic characteristics ofthe supermundane isotropic, homogeneous medium.

The all-pervading Aether, like the hypotheticalideal gas itself, exists in eight fundamental kinemat-ic states:

1. Free Aether. The state of total isotropic random-ness, where the motion of the individual Aethronsobey Newton’s mechanics and described in details inthe atomic kinetic theory of gases.

2. Aether flow. The state of global translationalmotion, where because of some local density fluctua-tion, each Aethron of a given volume of Aether is ableto move a greater distance in a given direction than

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in any other direction. This results in the continuousdrifting of the Aethrons in the same direction, super-imposed on their initial random oscillations. Suchmass translation, or fluid flow of the Aether toward alow pressure area ceases when the average isotropicdensity is re-established.

3. Vortex. A state of circulation, or rotationaltranslational motion which can develop around apersisting low density locality, like a sink, or becauseof a torque produced at the boundary between twolinear flows of different speeds. The later tendency oflocal rotations is called fluid-dynamic vorticity.

4. Turbulence. A state of motion in which severalof the above states are mixed together.

5. The Donut-vortex. As illustrated in Figure 11-1, this state is a complex three-dimensional flow pat-tern of drifting Aethrons which evolves from specificcircumstances under the constant isotropic pressureof the free Aether. It is kinematically plausible that,under non-extreme conditions, this flow patterncould be permanently bounded by the isotropic pres-sure and that its internal density is greater (Ber-noulli’s theorem) than that of the surrounding freeAether. This unit of mass can have its own transla-

tional motion relative to the isotropy of the Aetherand therefore possess its own inertia and momen-tum. A donut-vortex also has an intake and an out-put of Aether and therefore their interconnectabilitycan represent the natural evolution of complex sys-tems, or conglomerates of elementary mass particles,which we call macroscopic matter.

6. Force-fields. Various complex flow-patterns ofthe drifting Aethrons, produced by the dynamic con-nections between sinks and sources within andaround the interacting and conglomerated particlesof matter.

7. Wave-motion. A tendency of re-establishing theequilibrium of the isotropic density of the medium.Any locally produced density fluctuation in theisotropic free Aether dissipates in an expandingspherical shell. When the nature of the local distur-bance is periodical, the dissipation is also discontinu-ous. This is the kinematics of periodical dissipation ofexcess density in the form of compression or rarefac-tion pulses, called wave-trains or wave-motion. It isimportant to differentiate between the concept oftranslational motion of a given mass of Aether andthat of wave-motion where only local density fluctua-

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tions are conveyed through the body of the motion-less medium. The waves of density variations arepropagated through the motionless medium by theconstant speed, c which reflects the specific elasticcharacter of the Aether and proportional to the aver-age speed and collision free path of the Aethrons.

8. A subdivision of wave-motion should be noted;depending on the method of producing the local den-sity fluctuations, there are two fundamental type ofwaves in Aether :

Figure 17-7.a) As it has been described in Chapter Sixteen

and detailed in Appendix III, due to the Aether’s

resistance (Lorentz formula), a certain density fluc-tuation is generated by the simple, uniform motion ofa particle relative to the medium. This is called aparticle-wave with the clear understanding that it isa wave made by a uniformly moving particle in theAether. A macroscopic analogy is the bow-wave pro-duced by a ship. (Figure 17-7.a)

b) Electromagnetic radiation is produced bymicroscopic oscillation of elementary particles or bythe oscillation of the electromagnetic field. Oscil-lators represent accelerating and deceleratingmotions, thus the impulse exerted by them on themedium varies with time. According to the kinematicanalysis of the origin of the particle-waves (bow-waves), – as presented in App.III. – the time intervalbetween the accumulation of two individual pulses isproportional to the relative speed of motion of thebody and the separation of the pulse happens whenthe medium suffers a certain extent of compression.

From these it follows, that during the forwardmotion of the oscillator a group of sub-pulses are pro-duced with decreasing distances from each otherwhile the oscillator accelerates, and increasing dis-tances when it decelerates (Figure 17-7.b).

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a)

b)

Thus, a group of sub-pulses are created by thevarying forward velocity of the oscillator until itcomes to a stop and starts moving backwards.During this backward period the group propagatesaway from the oscillator with the speed of light. Thedistance, that the group reaches before the oscillatorturns in the forward direction again, is the wave-length of radiation. The total picture of this complexradiation pulse is similar, but not identical to thecommon illustration of a wave-packet.

It is important to note here that the abovedescription of the eight characteristic states of mo-tion of the Aether should neither be considered asprecise nor as complete, but rather as a rough sketchwhich should be refined and completed through animmense research of the detailed kinematics of theideal gas. Nevertheless, it still represents a lot morethan the total kinematic ignorance that is admittedby assuming that space is void.

With regards to the general problems of theCopenhagen interpretation of the quantum facts andthe mathematical requirement of a superluminalcommunication, there are three main groups of argu-ments, represented by three different experimental

methods to prove or disprove the orthodox theory.I. The EPR Gedanken experiment-argument is

based on the interaction and separation of elementa-ry particles to simulate the behavior of electrons in adiffraction or a double-slit experiment. The non-dis-persive correlation between these particles is basedon the law of conservation of linear momentum.

II, The EPRB version created by Bohm, is basedon the spin orientation correlation of atoms, that is,on the law of conservation of angular momentum.The predicted final position measurement, or thedetection of the spin-orientation is produced by theStern-Gerlach magnet.

III. In all Aspect-type and other Delayed Choiceexperiments the spin-orientation correlation is ex-tended to the photons. The conservation of angularmomentum in this case is represented by the preser-vation of the polarization transmission angle of thequantum particle. The predicted final position mea-surements are produced by the calcite crystal whichtransmits vertically polarized photons and deflectshorizontally polarized photons.

According to this present interpretation Aetherpervades all space. Elementary particles are perma-

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nent flow-systems formed under the isotropic pres-sure of the medium. When these ‘mass particles’ aremade to move relative to the Aether, they experiencefluid resistance, to which they react and producecompression ‘particle-waves’. Thus, the kinetic behav-ior of the particles during these experiments more orless depends on the interactions between the parti-cles and the medium.

The above described eight basic kinematicalstates of the Aether offers the following guidelinesfor those interactions:

In the special case when a single particle some-how gained momentum in the past and now movesuniformly relative to the free Aether, it suffers noother effects but a linear deceleration in the directionof motion. Its own particle-waves continually dissi-pate with the speed of light and therefore they do notalter the direction of the particle’s motion. The resis-tance of the medium is proportional to the ratiobetween the speed of motion and the speed of propa-gation of light (Lorentz Transformation).

When two or more particles move in the samedirection, initially on Newtonian trajectories in thefree Aether, they only suffer a feeble dispersion effect

due to the transverse pressure produced by theirown particle waves and their reflections from oneanother. This force is proportional to their momentaand inversely proportional to the square of distancebetween them.

Figure 17-8.There is a case when one or more small mass-

particles move relative to the Aether which is en-closed in a solid macroscopic environment, that is,capable of reflecting the waves produced by the parti-cles. Figure 17-8 illustrates the experimental setupwhich describes the electron diffraction theory and insome sophisticated way it is also used for the deriva-

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tion of Heisenberg position-momentum uncertaintyprinciple. A more complicated version of this basicidea is the electron double-slit experiment.

Now, as it has been described in details by Ap-pendix III, when one or more small mass-particlesmove along relative to the Aether in an environmentwhich reflects the particle-waves, there will be a gen-eral alteration of the initial Newtonian trajectoriesby the wave-field. For this reason the final positionmeasurements of the particles will display statisticalwave-phenomenal patterns.

If the particle-source and the reflecting environ-ment are in an exactly symmetrical setting, then theprobability of the final position measurements can bepredicted by the quantum mechanical wave-functionbased on the de Broglie wave-length of the particle.The symmetry is needed because, for the sake of pre-diction the Newtonian trajectories must be alteredevenly throughout the whole experimental field.

A clarifying note is due here about the frequentlymentioned predictive power of the quantum mechan-ical mathematics, that generates so much of the com-promise with the unbearable metaphysics of theCopenhagen interpretation.

The fact is, however, that the total success of thisformalism is weighed by lumping together atomicspectral analysis with that of the predictions of parti-cle diffraction and interference phenomena. This pro-duces a slanted picture.

The major part of the predictive power is createdby the de Broglie-Schrodinger wave-mechanics ofatomic and molecular structure. The substitution ofBohr’s quantum-jump orbits by Schrodinger’s theoryof selective standing-wave orbits, based on de Brog-lie’s electron wavelength, was the one that scoredsuccess after success. Where it failed, ‘subtle butmathematically logical modification made it evenmore powerful’ (Ch-16). This typical evolution ofmathematical formalism has been lumped togetherwith Bohr’s Principle of Complementarity and for-med quantum mechanics. Thus, Bell’s considerationof the power of the quantum mechanical singletwavefunction is not at all justifiable.

(I.) In the Aethro-kinematic interpretation, the deBroglie pilot-waves are real particle-waves (bow-waves) in the Aether and this phenomenon does notrequire any other detection, as part of physical reali-ty, but the experimental fact of the electron diffrac-

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tion itself, which proves that the reflections of thewaves from the environment can and does alter theNewtonian trajectories.

After all, the acceptance of all action at a distanceforces, as part of physical reality, is always based onthe detectible alterations they cause in the trajecto-ries predicted by the Newtonian laws of motion.Think about gravity, magnetism, or electricity.

It also follows, that the EPR thought experiment,that assumes a non-dispersive correlation betweentwo interactive and separated elementary particles, isan absurd proposition.

Consider, that after interaction and separation,both particles continuously create their own waveswhich are propagated in the enclosed Aether and arereflected back by the environment and from oneanother. Both particles and their Newtonian trajecto-ries are under the continuous influence of the chang-ing transverse and reflected pressures of their owninterfering waves. The complex kinematics of this sit-uation totally out-rules the classical conservation oflinear momentum of the individual particles and cer-tainly cancels the possibility of non-dispersive EPRcorrelation and Einstein separability.

As for the quantum mechanical singlet wavefunc-tion requirement of non-locality, note here, thataccording to this interpretation, at any instant, allwaves that fill the Aether in the experimental envi-ronment and all changes in their interference pat-terns are propagated with the speed of light inadvance of the particle’s motion and therefore locallyand instantaneously affect the trajectories of the par-ticles, wherever they are. The evolution of the trajec-tories remains correlated by the symmetrical wave-fields at all times and at the instant of mea-surement the positions of the particles are deter-mined by their history (Bohm) that is, the continuouschain of local realities of their interactions with themedium at each point. -- Hence, although the quan-tum mechanical predictions and their non-localityare totally reproduced, -- aside of the natural light-speed propagation of the particle-waves -- superlumi-nal communication between the particles or betweendistant devices are not at all necessary

But Bell states that this strange non-locality andsuperluminality are deeply rooted even in the rela-tivistic version of quantum mechanics. So, where arethey coming from ?

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As they remark in most contemporary text books,it is ironic that Einstein spent the second half of hislife fighting against the counter intuitive vaguenessof the quantum theory which was initiated by hisown photon hypothesis.

Somewhat less obvious is how much he strength-ened the positivist school by replacing the classicalreality of the electromagnetic Aether-frame with theanti-common-sense philosophical postulates of spe-cial relativity. Also it is quite evident that Einstein’svague Relativistic Correspondence Principle; c → ∞ ,(§16) has paved the way for the acceptance of itsexact conceptual and mathematical copy: the Quan-tum Mechanical Correspondence Principle, stating; λ→ 0, that is, classical mechanics is a special case ofquantum mechanics and applicable only when the deBroglie wavelength of the particle approaches zero.

Obviously, one of the problems here is that thede Broglie wavelength of the electron does approachzero, but is also definitely not zero.

Although it possesses classical mass and momen-tum, the electron is still small enough to be sensitiveto the feeble quantum effects of the Bohm-de Broglie-Aether-particle-waves and therefore becomes disper-

sive with regards to the classical conservation of itsmomentum.

It follows, that the Quantum CorrespondencePrinciple is neither conceptually nor mathematicallyadequate to map out the boundary and the border-line details between classical mechanics and quan-tum mechanics.

(II.) Bohm’s version of the EPR gedanken experi-ment shows a different shortcoming of the QuantumCorrespondence Principle. In this case Einstein’s lin-ear momentum correlation is replaced by the conser-vation of angular momentum. Bohm’s correlatedatoms are produced with opposite spin orientationswhich are detectable by a Stern-Gerlach magnet.This instrument is specifically designed, based onthe classical theory of magnetism and on the quanti-zation rules of particle spin. The strong gradient inthe magnetic field of the magnet separates the atomsof opposite spin-orientations into two sharply definedgroups on the detector screen. This result is theninterpreted as the position measurement of quantumparticles, which therefore justifies the application ofthe quantum mechanical formalism of the singletwavefunction.

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As Bell remarks: “...many measurements reduceto measurement of position. For example, to measurethe spin component, σ, the particle is allowed to passthrough a Stern-Gerlach magnet and we see whetherit is deflected up or down, i.e., we observe position insubsequent time. − The result of a ‘spin measure-ment’ for example, depends in a very complicatedway on the initial position of the particle, λ and onthe strength and geometry of the magnetic field. Theresult of the measurement does not actually tell usabout some property previously possessed by the sys-tem, but about something which has come into beingin the combination of system and apparatus.”

Now, from the point of view of the electromagnet-ic theory of magnetism, and its application to thismacroscopic measuring device, it can be seen thatthe analogy between the EPR correlation of linearmomentum and the EPRB correlation of angularmomentum, is far from being justifiable. While theelectron diffraction was produced in an environmenttotally free from macroscopic forces and the alter-ations of the trajectories were solely due to the feeblede Broglie wave-phenomenon, the detections of thespin-orientation of EPRB clearly depend on the

strength and geometry of the Stern-Gerlach magneticforce field.

Hence, if nothing else is wrong with the analogy,it certainly neglects the great difference between themagnitudes of the two allegedly ‘analogous’ forces.This misconception, however, brings up the questionsof whether or not the de Broglie particle wavesshould still be a guiding factor in EPRB beyond andabove the much stronger macroscopic magnetic field.Moreover, in general, whether or not it is still justifi-able to apply the quantum mechanical singlet wave-function to this experiment?

From the above described kinematical character-istics of the Aether, it can be seen, that there is awhole order of magnitude difference between theforce of the magnetic flow-pattern, which actually car-ries the atoms through the Stern-Gerlach magnet,and the feeble, microcosmic force of the de Brogliecompression waves produced by the moving particles.Obviously, the magnetic force is the macrocosmiccause of the alteration of the Newtonian trajectoriesand the resulting position measurements.

Hence, the conditions should be described exclu-sively by the classical electromagnetic theory and not

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by the microscopic probability densities of the quan-tum mechanical wavefunction.

Therefore, it may be suggested, that the Quan-tum Correspondence Principle should be furtherrefined by a definite restriction of the applicability ofquantum mechanical formalism only to the specificcases where there are no stronger forces acting butthose of the de Broglie-Bohm-Aether particle-waves.

(III.) Finally, consider the presently leading edgeof the experimental development: the WAJ ‘DelayedChoice Experiment’.

As experts believe, this version -- more than thesimilar tendencies of the Aspect-type experiments, -strikes directly into the heart of the matter, one ofthe foundation stones of the Copenhagen Interpre-tation: the fundamental problem of wave-particleduality. This version of EPRB promises an experi-mental display of Bohr’s Principle of Complementa-rity, that is: Wave or particle, but never both !

Moreover, this version also promises to providethe experimental justification for the inevitablenecessity of a superluminal communication betweenthe distant photons or the measuring devices. In thisexperiment Bohr’s wave-particle duality is demon-

strated by the spin-orientation-correlation of thephotons, as it has been described by §40 in the lan-guage and logic of the Copenhagen interpretation ofquantum mechanics.

(Before challenging the conclusions drawn fromthis experiment, let us recall that Chapter Sixteenintroduces an alternate explanation for the problemsof the photo-electric effect. This alternative renders asolution to the kinetic energy problems of the ejectedphoto-electrons without invoking the corpusculartheory of light and the ambiguous concept of the pho-ton. Thus it also avoids all the headaches of the lastsix decades caused by the wave-particle duality andBohr’s complementarity. Never- theless, with regardsto the uncovering of the hidden ambiguities of theDelayed Choice Interferometer, the use of the Aethro-kinematic rejection of the photon hypothesis isunnecessary.)

The Aethro-kinematic challenge of the theory andconclusions of the Delayed Choice Interferometer issimple and straight forward. As it has been pointedout earlier, without applying quantum mechanics,each and every phase of this experiment is clearlyand unambiguously explainable by the electromag-

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netic theory and predictable by Maxwell’s equations,as different facets of the typically classical wave-phe-nomenon. This includes not only the wave-like attrib-utes, but the allegedly particle-like attributes aswell. Thus, the necessity of the application of quan-tum mechanical formalism and the singlet wavefunc-tion to predict the probabilities of position measure-ments are based on artificially complicated andinternally inconsistent assumptions and thereforetotally unjustified.

For substantiating the above statement, considerthe following arguments:

In a very general way the theory of the DelayedChoice Interferometer introduces a shift in the basicconcepts of the wave-particle duality of the Comp-lementarity Principle. Here, the waves and particlesare no longer Bohr’s ‘two diametrically opposed clas-sical concepts’ but rather inherent parts of a quan-tum entity, something that is ‘fundamentally non-classical and therefore un-knowable.’ -- According toWAJ group the experiment produces single photons,possessing both wave-like and particle-like attribut-es, which can be detected and measured by differentspecifically designed measuring devices.

In Wheeler’s initial suggestion, the special devicefor measuring wave-like attributes, or interferencefringes, was a photographic plate placed in the focalpoint where the paths of two individual photonscrossed. The particle attributes were measured byhinging out the plate and let the photons continueinto two photo-multipliers, recording the photon'sfinal positions.

Incorporating the theory of this experiment withBohr’s Complementarity and with Bell’s latest analy-sis of the quantum mechanical position measure-ments, WAJ declare to achieve the same result witha single photon in the apparatus, where its wave-likeor particle-like attributes are produced by differentdevices, placed along separate routes and detected ormeasured by four independent identical photomulti-pliers.

Recalling the detailed description of the differentdevices along the different paths of the photon, it canbe seen that the manifestation of the particle-likeattributes of the photon is achieved explicitly by thePockels cells which “upon application of a high volt-age, produce a 90° rotation of the plane polarizationof the photon’ (WAJ).

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This means, that the Newtonian conservation ofthe angular momentum, that is, the spin-orientationof the photon was altered by a macroscopic electricforce. This rotation is the cause for the deflection ofthe polarized photon from its original path, a resultof which it ends up in the side-track photomultipliers(A) or (B) where its final position is recorded.

Evidently, this case is exactly analogous to theinteraction of Bohm’s atoms with the macroscopicStern Gerlach magnet. In other words, the major rollof the Pockels cells in the WAJ is identical to the rollof the Stern-Gerlach magnets in EPRB.

Hence, the conclusion for the particle-like attrib-utes of the WAJ experiment is the same as for theEPRB argument: The Quantum CorrespondencePrinciple must include a definite restriction of theapplicability of quantum mechanical formalismexclusively to those cases where there are no strongerforces in action but that of the de Broglie-Bohm parti-cle-waves of the Aether .

It should also be noted here, that photomultipli-ers are based on the photon theory of the photo-elec-tric effect. As a result, there is a general scientificimpression that the ejection of the initial single elec-

tron produced by the transmission of the kineticenergy of a single photon particle. Then the ejectedsingle electron is amplified by photomultiplier, thusit must records exclusively particle-like attributes. --This misconception, however, must have been clearedaway in the Delayed Choice experiment, since it usesidentical photomultipliers to record the wave-likeattributes of photon interference as well.

The rest of the scenario is utterly simple. Thewave-like attributes of the individual photon, andthe resulting interference phenomenon is certainlybeyond classical logic since the photon is, by defini-tion, indivisible and consequently not re-unitablewith itself. Admittedly it is not even explainable byquantum logic.

It is just one of those things that are not catego-rizable as ‘knowable’ by Bohr’s philosophical postu-lates. Hence, right from the first step of the photon,as it is entering the beam-splitter, Bohr’s rigid denialof reality must be applied, so nobody should dare toinquire what is happening and where, until the con-structive and destructive interference measurementsare already executed by the multi-talented photo-multipliers (1) and (2).

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This conceptual cascade is described by differentphrases:

Some theoreticians use the enlightening wordsthat the ‘photon behaved as though it had passedalong both paths simultaneously, interfering withitself in the Koster prism’. − These authors totallyneglect the further complication, that the Kosterprism contains a second beam-splitter, which then issupposed to chop up each of the already chopped upindivisible photon into four parts and one pair mustinterfere destructively, the other constructively inorder to produce the wave-like behavior predicted byquantum mechanics.

Some others are bothered even less with thesewavy details. They simply and literally covered thewhole experimental ground by the singlet wavefunc-tion, stating that whichever route the single photontakes, the wavefunction simultaneously developsthrough the other, ’empty’ path and then reuniteswith the photon in the prism in quantum interfer-ence. Nevertheless, - beside its Bohrian perplexity, -there is another problem with this ‘explanation’. Ifthe particle-like attributes do not justify the applica-tion of the singlet wavefunction, then nothing else

remains to explain interference but the classicalwave theory, which can be most easily reinstated. Wesimply admit that even a short laser pulse is still 3cm long, consisting of an immense number of phasesthat makes it indistinguishable from a wave trainthat is, of course, divisible and re-unitable in inter-ference.

For the very low intensity which allegedly sepa-rates the nature of waves from that of photons, recallthat the photon hypothesis also established, that theintensity of the light does not alter the kinetic energyof the ejected photo-electron. Thus, the photo-multi-plier would still work by a short, low intensity wave-train.

Moreover, not only is every phase of the wave-likeattribute of the quantum entity explainable by theclassical wave theory, but it is also easily under-standable why the quantum mechanical formalismproduces the same results, as the classical electro-magnetic theory.

Remember, that the de Broglie pilot-wave wave-length of the elementary particles was derived fromthe relativistic mass-energy formula and that themomentum of the massless photon was taken as

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merely kinetic energy. From this it follows, that thede Broglie wavelength of the photon particle is equiv-alent with the wavelength of the initial classicallight-waves. Thus replacing the electromagneticwaves by photons and then applying de Broglie'swavelength formula to this quantum particle, we endup exactly where we started from; with the originalwavelength or frequency of the electromagneticwaves. Thus, in the case of the photon, or light-parti-cle, the application of the quantum mathematical for-malism, that is, Schrodinger's singlet wavefunctionand Young's theorem, is simply a total reversal ofthe starting procedure; this time going backwardsfrom the quantum photon hypothesis to the electro-magnetic wave theory of light.

But with one obscured addition, − which is reallythe essence of the whole procedure, − the implantedsinglet wavefunction, which then mathematicallyenforces an unavoidable correlation between theinteractive and separated particles and consequentlyenforces the requirement of the inconceivable super-luminal communication. This is where the hopelessconceptual confusion of the Copenhagen interpreta-tions comes from.

These, and a number of previously discussed con-clusions demand another restriction of Bohr'sCorrespondence Principle:

The application of the quantum mechanicalmathematical formalism, especially the 'singlet wave-function' should only be allowed to a physical state ifthere was no classically proven theory which can pre-dict the same final experimental results.

This restriction achieves two most important ad-justments:

By a simple change of the roles, Quantum Mecha-nics becomes the limiting case of the more generalClassical Mechanics and the monstrous singlet wave-function is finally caged in, where it belongs, exclu-sively applicable to the diffraction and interferencephenomena of elementary particles, when moving inthe Aether, which is enclosed in a reflecting environ-ment. More importantly, with this restriction, theinfamous superluminality problem will quit haunt-ing common sense and be filed away into the scrap-heap of the other modern metaphysical speculations.

Through somewhat deeper analysis it can befound that the inadequacy of both CorrespondencePrinciples originate from the initial mathematical

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over-simplification of the meaning of the LorentzTransformation. The fundamental misconception isthat the effect of the 'relativistic mass-increase' onlycomes into existence when the velocity of a materialparticle approaches the speed of light. According tothe Aethro-kinematical interpretation both phenom-ena of the relativistic mass-increase and the quan-tum mechanical de Broglie matter-waves are merelyphysically detected demonstrations of the existenceof the all-pervading ideal gas medium and its kine-matical resistance against any motion of any materi-al particle relative to the absolute frame of referenceof the Aether.

This is the real and humanly comprehensiblemeaning of the re-interpretation of quantum mecha-nics and more generally the re-interpretation of theLorentz Transformation for all physics, which there-by renders a complete unification of the three sepa-rately discovered classical-mechanics, relativisticmechanics and quantum-mechanics into the whole ofAETHRO-KINEMATICS.

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CHAPTER EIGHTEEN

THE BIG BANG ANDTHE KINEMATICS OF DISPERSION

The theory of AETHRO-KINEMATICS and itsconceptual content, described in the foregoing seven-teen chapters, totally determines the only acceptablecosmological hypothesis: The Rotating Universe.

From the limited earthly point of view, our Uni-verse seems to be an unceasing chain of rotationalgravitational systems of materialized units floatingin Aetherial vortices, each of which is enclosed in one

of a larger order of magnitude. Each and all of themexist in the long term equilibrium of UniversalGravitation, balanced by Universal Rotation.

As far as observations can reach out in space ortime, we can only 'see' systems quite autonomous ofeach other. The only feeble thread of causalitybetween the smallest and largest observable is thekinematical inheritance of Kepler's differential rota-tion, the fundamental characteristic of all gravita-tional rotational systems. This all-pervading kinema-tical tendency of creation of matter exists throughoutspace and time, at any imaginable number of order ofmagnitudes, from the infra-microcosmic rotation ofthe elementary donut-vortex to the ultra-macrocos-mic whirling of the meta-galactic super-clusters ofsuper-clusters of clusters of galaxies.

The question of whether this inheritance startsor stops somewhere in space or time is out of thereach of human inquiry, since it is equally impossibleto imagine both a finite or an infinite Universe or abeginning or an end of time. But a Rotating Universebeing in equilibrium and in kinematical contact withall its parts, does not require an answer to thesemetaphysical problems.

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Aethro-kinematics

Nevertheless, like in all other departments, mod-ern science also managed to create a bold innovationin Cosmology with its astonishing theory of the BigBang Universe, which is completely at variance withAETHRO-KINEMATICS, thus, it must be addressedand re-interpreted as will follow.

The main pattern in the evolution of Cosmologyis a step by step degradation of the Earth's positionand importance relative to the Universe as a whole.

Within the last three centuries, the Earth's posi-tion has been devaluated from being the very centerof the World to being an insignificant planet of aninsignificant average star, called Sun, which is wan-dering on an insignificant orbit in an insignificantgalaxy. The position of the Milky Way, as we call ourGalaxy, cannot even be described, due to the billionsof such systems scattered isotropically in space with-in our observational limits.

To point out a particular grain of sand among allthe beaches of all the continents would be a compara-tively easy task compared to finding the Earth with-in the observable Universe.

Thus, it is understandable that, after believingand burning one another for the childish fantasies of

Geocentric, Heliocentric and Galactocentric univers-es, cosmologists finally took the oath, that never everagain would they fall for a similar fairy tale.

This full pledge of modern times is embodied inthe 'Perfect' Cosmological Principle, which statesthat; anywhere in Space and Time all galactic ob-servers must view the same kind of grand scale pic-ture, regardless to their particular position in theUniverse.

In other words, from here on no hypothesis willbe acceptable, which assigns any special significanceto the position of the Earth, the Sun, the Milky Way,or any other particular point or system in space, any-where in the Universe, or at any time.

To detect any motion outside of our solar system,astronomers must patiently watch even the neareststars for decades and the recording of any motion ofeven the closest galaxies is totally beyond the humantime-scale. Our direct observation of the skies is basi-cally two dimensional and non-stereoscopic. Beyondthe motion of the Planets and the Sun and themotions of a small number of nearby stars relative tothe background of fixed stars, our direct methods arecompletely useless.

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Aethro-kinematics CHAPTER EIGHTEEN The Big Bang and the Kinematics of Dispersion

Consider a typical neighborhood example of cos-mic Time and Space: The Sun is orbiting about thecenter of the Milky Way with the tremendous veloci-ty of 150 kilometers per second. Still it takes 200 mil-lion years to complete a single revolution in theGalaxy. While the Earth lived through some four bil-lion orbits, the same time, the Sun became merely20 galactic years old.

The same general picture of isotropy, combinedwith the accepted Newtonian concept of the infiniteuniverse, presented some serious contradictions bet-ween the laws of physics and the observational factsof Astronomy. In the early eighteenth century, H.Olbers discovered a cosmic paradox, which has beenpuzzling scientists ever since. It starts with the inno-cent question: Why is the sky dark at night?

The common answer, that the Sun shines on theother hemisphere of the Earth, is not satisfactory,because there are myriads of stars, greater than theSun, and shining on us from every direction of thenight sky. Maybe they are simply too far from us andtheir lights are too dim?!

No, their distances turned out to be totally indif-ferent. Olbers' paradox presented an undeniable con-

tradiction between the laws of Physics and the obser-vations of Astronomy.

Physics states that the amount of light energyfalls on a unit area of a surface per second is dimin-ishing inversely proportional to the square of the dis-tance from the source. By the same geometric logic,however, another fact of astronomy, the isotropic dis-tribution of galaxies, means that each consecutivespherical shell of space contains more and moregalaxies, which increase is directly proportional tothe square of the distance from the observer. If theUniverse is infinite, as it should be to agree with thetheory of gravitation, then at every point of the skythere should be a star no matter how far it is. Thus,mathematics shows that what is lost in energythrough the distance is exactly gained back in thedensity of the sources.

It follows, that in the case of an infinite isotropicUniverse, every point of the sky should glow with theintensity of the sun and any observer at any point ofthe cosmos would be surrounded by a sphere ofsources radiating 5000°C of heat from all direction.Obviously, these predictions do not agree with theexisting observations.

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If the Universe was finite, either in space or intime, Olbers' paradox would be solved, but Newton'sgravitation would have pulled all matter of the cos-mos into the center of mass. Another problem withthe finite Universe is, that observations reveal acomplete isotropy of the sky and show no trace ofdensity difference in any direction, that would sug-gest a center or a border.

Nevertheless, in the twentieth century, the ambi-tious human mind succeeded in producing the mostexciting cosmological theory; the Expanding Uni-verse, which, among other problems, also solved theparadox of Olbers. The most popular version of thishypothesis even attempts to explain the origin, theage and the mechanism of the Universe by the The-ory of the Big Bang.

As it will be seen, however, in spite of the promiseof the perfect cosmological oath, the new scenariostill managed to salvage some special privileges forthe human species in the Cosmos. This complex storyevolved from three basic ingredients of indirectastronomical measurements:

a) Through spectroscopic analysis of the light ofastronomical objects, scientists came to the conclu-

sion that, the chemical composition of matter is thesame everywhere in the Universe.

b) Based on this uniformity and on the rule thatthe apparent luminosity of a star is inversely propor-tional to the square of its distance, astronomersfound an indirect measuring method for great dis-tances. If the distance of a recognizable type of starin our neighborhood is established, and its intrinsicluminosity is measured, then from the apparentluminosity of the same type of star, its distance canbe calculated anywhere in the Universe.

c) Part of the general uniformity of the chemicalspectra of cosmic sources is, that the spectrum ofwhite light is not totally continuous but certain col-ors are missing at specific wavelengths. This gives auniversally recognizable pattern in the spectra of thelight received from all parts of the universe.

Based on these characteristics astronomers havefound that compared to the spectrum of a laboratorysource, the light of most stars were shifted towardeither the blue or the red end.

This phenomenon has been satisfactorily ex-plained as the result of the well known Doppler effectof light, a strictly wave-phenomenon, which was dis-

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cussed in details in Chapter Fourteen and illustratedon Figure 14-11.

Figure 18-1 illustrates the character of the Dopp-ler phenomenon when an astronomical source movesin different directions relative to the earthly observ-er. In our two dimensional view of the Universe,there is no way to tell in which direction a star reallymoves. The only information the Doppler effect cangive us is the direct, line of sight component of thevelocity of the star.

The technical possibility to measure these effectsis given by Spectroscopy which is based on somefundamental wave-characteristics of light; namelythe optical phenomena of refraction and dispersion.

It is an empirical fact that the speed of propaga-tion of light decreases in proportion with the densityof the transparent medium. Light is retarded whenpassing from air to glass. When the angle of inci-dence of a light beam is oblique to the boundarybetween the two media, its direction changes. Thisdeviation from the rectilinear propagation is the phe-nomenon of refraction.

It is also the nature of light waves, that while allcolors propagate with the same speed in vacuum, thespeed of propagation of different colors or the differ-ent frequencies of light, is different in the sametransparent medium. Higher the frequency, greaterthe retardation, that is, lower the speed and greaterthe deviation from the straight line. Since the extentof refraction depends on the speed of propagation,blue light is refracted more than the lower frequencyred light. The deviation of the different colors bet-ween these two extremes are proportional to eachfrequency. Thus, as shown below, a beam of white

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Redshift

Redshift

Redshift

Blueshift

Blueshift

Line of Sight Relative Velocity

Line of Sight Component,Doppler ShiftFigure 18-1.

light is dispersed into its components when passingthrough a prism.

Figure 18-2In case of the Doppler effects of star-light, it has

been established that each frequency of an approach-ing light source shifts a given percentage toward thehigher frequency blue, and that of a receding sourceshifts toward the lower frequency red. These shiftswere measured by comparison with the un-shiftedpositions of the two most recognizable absorptionlines in the spectrum of a laboratory source.

From the magnitude of the shift, scientists wereable to calculate the line-of-sight velocity of a movingstar. This interpretation of the spectral shift gave thefirst indirect indication of the motions and velocitiesof astronomical objects. The new possibility caused agreat upheaval in cosmological research and in thefirst decades of the century a major part of observa-tional time was spent on the measurements ofDoppler velocities.

Through these measurements, it has been foundthat the spectrum of the great majority of stars areshifted one way or another, showing their randomvelocities relative to the earth.

In 1925, during this already routine research,V.M.Slipher made a discovery, which led to anastounding extension of the size of the Physical Uni-verse toward inconceivable measures. He found fromthe line of sight velocities of certain 'nebulae', thenthought to be within our own galaxy, that they arereceding from us at phenomenal velocities up to1,800 km/sec.

Soon it was discovered, that these nebulae andthe great majority of the naked-eye-stars were, infact, distant galaxies, galactic clusters and galactic

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REDORANGEYELLOWGREENBLUEVIOLET

WHITELIGHT

NORMAL NORMAL

INCIDENT RAY

super-clusters. It was also established, that the ob-servable universe contains star systems, like ourMilky Way by the billions, spreading in randomisotropy in all directions, without indication of a den-sity difference in any direction showing a center, or aboundary of the Cosmos.

In 1929 Edwin P. Hubble reported his discoverythat the spectrum of the light of the great majority ofgalaxies are shifted toward the red end. As he wrote:

"Galactic spectra are peculiar in that the linesare not in the usual places, as found in nearby lightsources. The displacements, called Redshifts increaseon the average with the apparent faintness of theGalaxy. Since the apparent faintness measures dis-tances, it follows, that redshifts increase with dis-tance.

"Detailed investigation shows that the relation islinear. Small microscopic shifts either to the red or tothe blue have long been known in the spectra ofastronomical bodies. These displacement are confi-dently interpreted as a result of motion in the line ofsight radial velocities of recession or approach. Thesame interpretation applied to the redshift in galac-tic spectra led to the term, velocity distance relation

between redshift and apparent faintness. On thisassumption the galaxies are supposed to be rushingaway from our region of space with velocities thatincrease directly with distance. A completely satisfac-tory interpretation of the redshift is a question ofgreat importance, for the velocity-distance relation isa property of the observable region as a whole. Theonly other property that is known is the uniform dis-tribution of the galaxies.

"Now, the observable region is our sample of theUniverse. If the sample is fair, its observed character-istics will determine the physical nature of the Uni-verse as a whole. The conclusion, in a sense, summa-rizes the results of empirical investigations andoffers a promising point of departure for the realm ofspeculation." (E.Hubble, A Relation Between Distan-ce and Radial Velocity, Proc.Nat.Ac.Sci, #15, 1929)

Indeed, the modest words of this report proved tobe the seed for a gigantic plant of speculation. TheDoppler Interpretation of the galactic redshift, whichis expressed in the law of velocity-distance relation,became the catalyst that turned the apparent eternalfixity of the world into a violently dynamic picture ofthe so-called Expanding Universe.

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Hence, the contemporary scenery of Modern Cos-mology is, that everything is rushing away from usand the further they are the faster their recession.This picture is also isotropic, that is, the same inevery direction.

The direct and sensible conclusion from all thesewould be, that we are again in the very center of thisexplosion. But according to the CosmologicalPrinciple any other observer at any point of the Uni-verse must see the same general picture. Therefore,only one possible conclusion left, that everything isrushing away from every other thing.

How could this be possible?Someone came up with an ingenious analogy: If

the whole Universe was a raisin-bread baking in theowen, the raisins were the galaxies and we were sit-ting on any one of them, then due to the expansion ofthe dough all raisins would seem to recede from usand from one another with velocities proportional totheir distances. So, if we could only see a part of thebread, we would stare into an expanding system withno particular center.

In the routine calculation, based on any spectralshift of ∆λ, of any particular wavelength λ, the veloci-

ty, v was to be found by the relation of c(∆ λ /λ) = v,where c is the velocity of light. Eventually thismethod led to recession velocities of 76,000 km/sec.Hubble's law of redshift established the velocity-dis-tance relation, v = Hr, where r represented the dis-tance of the source and H was the so-called Hubbleconstant.

This empirical formula showed that according tothe Doppler Interpretation of the Redshift, for everymillion light year distance, the galaxies are dashingaway from each other with an additional 55 km/sec.(Figure 18-3.)

Beyond a certain distance the apparent luminosi-ty becomes clearly unmeasurable, however the red-shift measurements were still reliable. Thus, in theevolution of this interpretation, the Law of Redshiftitself has become the unique yardstick and thespeedometer in the immense space of the amazingExpanding Universe.

As a result, and with the appearance of the radiotelescopes in the 1950's, near to the observationallimit, the recession velocities of the galaxies wereestablished at the astonishing rate of over 100,000km/sec; more than one third of the speed of light.

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It is a natural consequence of this general pictureof expansion in every direction, that once upon atime all the individual systems of the materialUniverse must have been close together. It followed,that from the reciprocal of Hubble's Constant scien-tist were able to calculate, that some eight to twentybillion years ago the distance between the galaxiesmust have been zero.

Hence, the fast rewind of this hypothetical cosmicvideo tape reveals a picture of a fiery ball of all mat-ter of the Universe in an extremely condensed state,a kind of Primeval Atomic Egg, which either byfusion or fission, or by some unknown triggeringmechanism, has exploded into our present Universeindeed with an astonishing Big Bang.

It should be noted here, that the lower time limitof this retroactive prediction has been carefullyadjusted to fit between the Hubble velocity constantand the astrophysical and geological findings aboutthe approximate age of the sun and planets. Evi-dently, the Universe cannot be younger than the goodold Earth. Setting a safe upper age limit for the Uni-verse was even more delicate. Looking into space isalso looking into the past and as we penetrate

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Figure 18-3

immense distances, we should find a younger andyounger Universe, but so far, in the distance of fivebillion light years, no trace of a beginning has beenfound. The dozen, or so, billion years of tolerancecomes from the understandable uncertainties, due tothe indirect measurements of the tremendous dis-tances and velocities.

Hence, although the Earth and even our MilkyWay has lost their central positions by Copernicusand by the Cosmological Principle, with the theory ofthe Big Bang, we have still regained some of ourUniversal Importance, that is, being in the luckyposition on the cosmological scale to be able to dis-cover the time of the birth and maybe even the deathof our Universe. If not in space, at least, we have anenviable position in the flow time.

As for Olbers' paradox, the theories of the Ex-panding Universe claims a double solution:"As E.R. Harrison has emphasized, in conventional

(Euclidian) cosmologies, there are logically two inde-pendent ways out of this dilemma; the expansion ofthe universe and a finite age of the universe. In BigBang theories cosmological expansion and a finiteage go hand in hand. Expansion helps, because the

cosmological redshift prevents distant stars frommaking the simple Euclidian contribution to thenight-sky brightness. A finite age of the universe alsohelps, because the light from very distant stars sim-ply does not have time to get here even if we were toignore the redshift." (F.H. Shu, The PhysicalUniverse [384]To avoid all the delicately detailed arguments

among rival Big Bang theories about the plausiblestate of the Universe in the first twenty seconds ofcreation or the last couple of billion years at theother end of time, and to escape the decision makingwhether the Cosmos is expanding forever or it is acyclic one, oscillating between explosion and implo-sion, it is preferable to push the fast forward on thecosmological VCR and stop at the quote from theEncyclopedia Britannica of 1979:"Although the fact of an Expanding Universe is now

accepted by the majority of scientists associated withthis class of problems (Cosmology), there are a fewwho prefer to believe in a stationary universe andconsider the observed redshift not as a result ofrecession of the galaxies, but rather as a consequenceof some unknown property of light quanta to lose a

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part of their energy in traveling over long distances.However, none of the proponents of this point of viewwere able to formulate any reasonable and consistenttheory for such energy depletion of light quantabeyond an anthropomorphic analogy of getting tiredafter a long voyage."

Consider also the quote presented below fromWilliam Bonnor, The Mystery of the Expanding Uni-verse, 1964 [54]:"One reason for believing that the red shift is a

Doppler Effect is the negative one that nobody hasever proposed a convincing alternative explanation.It has been suggested, that the reddening might bedue to scattering of light by intergalactic dust.

"However, this explanation will not work, becausethe scattering would blur the images of the distantgalaxies to such an extent that we should not seethem as points of light.

"Other suggestions, for example that light changesits wavelength in some mysterious way on its jour-ney through intergalactic space, do not count asexplanations since they have no theoretical basis,and lead to no predictions which could be used toverify them.

"The fact is that the Doppler effect is the only possi-ble scientific explanation of the red shift at present.The Doppler law states that a given recession veloci-ty causes a fixed percentage change of the wave-length, and the same for all wavelengths. This meansthat if the velocity (of the source) is one-tenth of thespeed of light, then a wavelength of 1,000 Å in-creased by 10 percent, that is by 100 Å, one of 2,000Å is increased by 200 Å, and so on. Thus the shift isnot a bodily one -- the whole spectrum is not shiftedto red by the same amount of, say 100 Å. Nor doesthe shift affect only certain wavelengths -- it affectsthe whole spectrum of electromagnetic waves. Thered shift of the galaxies follows precisely the percent-age Doppler law. "

In fact, chronologically the Doppler effect inter-pretation of the local redshifts and blueshifts camefirst and the discovery of the distant extra galacticnebulae came later. Since it was the only means ofmeasuring any motion of distant astronomical ob-jects, it became common practice to assume that allDoppler shifts represent radial velocities. The aston-ishment came from Slipher's and Hubble's observa-tions that there is a galactic redshifts in every direc-

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tion and that in general the calculated magnitude ofthe receding velocities are in linear relation with thedistances.

Consider now the following quote from RichardBerendzen (and co-authors), Man Discovers the Ga-laxies, [206],1976:"Hubble, himself, felt that the Doppler interpreta-

tion of redshift was not completely obvious andinsisted on using the wording 'apparent velocities' toindicate this. 'The term apparent velocity may beused in carefully considered statements and theadjective always implied where it is omitted in gen-eral usage. Because the telescopic resources are notyet exhausted, judgement may be suspended until itis known from observations whether or not redshiftsdo actually represent motion'

"The arguments about the real nature of the obser-ved redshifts, however, have never been settled. Norhave the arguments been quieted over which of thenewer cosmological models (if any) is an accurate pic-ture of the universe."

Nevertheless, this initial scientific cautiousnessdid not stop the grand scale cosmological specula-tions which has flourished for over five decades.

Scientist, writer, Eric J. Lerner gives an essentialsummation for the evolution of the mainstreamtwentieth century cosmology in his book; The BigBang Never Happened (published by Random Housein 1992) :"The Big Bang arose initially as an explanation for

the Hubble expansion -- the relation of the redshiftsand distances of the galaxies. The observations of thepast several years have put that theory into gravedoubt, contradicting all its predictions as well as itsbasic assumptions. One would think that these deve-lopments would reopen a debate over the correct ex-planation of the Hubble expansion. However...For adecade now the accumulating contradictions havemet not with a reexamination of basic assumptionsbut by boilerplate hypotheses. Just as the medievalastronomers added epicycle after epicycle to Pto-lemy's spheres in order to match his geocentric theo-ries with observed planetary movement, so today cos-mologists add dark matter to cosmic strings to infla-tion, papering over the yawning crevices in their the-ory." [53-54]"The test of a scientific theory is the correspondence

of predictions and observation and the Big Bang has

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flunked. It predicts that there should be no objects inthe universe older than twenty billion years andlarger than 150 million light-years across. There are.It predicts that the universe on such a large scaleshould be smooth and homogeneous. The universeisn't. The theory predicts that, to produce the galax-ies we see around us from the tiny fluctuations evi-dent in the microwave background, there must be ahundred times as much dark matter as visible mat-ter. There's no evidence that there's any dark matterat all. And if there is no dark matter, the theory pre-dicts, no galaxies will form. Yet, there they are, scat-tered across the sky. We live in one." [39-40]

REDSHIFT IN THE PRISMAETHRO-KINEMATICS takes the common sen-

se approach for an alternate interpretation, startingfrom the acceptable observational facts used by the‘Tired Light Theory’ of the Red-shift.

The simple statement of this simple theory isbased on the direct application of the inverse squarelaw, derived from the geometrical principles and fromthe empirical facts of the distribution and depletionof light energy.

Astronomical distances are measured by thecomparison between intrinsic and apparent lumino-sities of the sources. By applying the inverse squarelaw of the distribution energy, from the differencebetween these two magnitudes, the distance of thesource can be calculated. In other words, the energyarrives to the earthly observer from a cosmic sourceis inversely proportional to the square of its distance.It has been also established in physics, that the ener-gy carried by wave-motion is proportional to thesquare of the amplitude of the waves. It follows, thatthe amplitude of light must be in linear relation withthe distance of the source. And so is the redshift.

Founded on these physical principles, based onobservational facts, the Tired Light Theory suggeststhat the galactic redshift maybe connected with thedepletion of the amplitude of light traveling throughimmense cosmical distances. Nevertheless, no hintwas given about the nature of this connection.

Aside of its undeniable logical simplicity, thishypothesis would also readily explain both Olbers'Paradox and our apparent center position in theUniverse, based on the simple fact, that wherever weare, that point is certainly the center of our own limit-

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Aethro-kinematics CHAPTER EIGHTEEN Redshift in the Prism

ed observational territory. − If one stands on the high-est peak and observes that, due to the hazy air, thecolor of the surrounding mountain ranges are fadingin proportion with their distances, one will find thatthe effect is equal in all direction, that is, centered ononeself. For Olbers' sake, one will also find that be-yond a certain distance, the color of the ranges fadestotally into the color of the haze.

According to the proponents of the Big Bang,however, the Tired Light Hypothesis was lacking thetheoretical and physical proof, that the loss of theenergy of the galactic light is physically responsiblefor the percentage decrease in each individual fre-quency, as it is accounted for by the Doppler Inter-pretation.

In the following an attempt will be made to showthat the galactic redshift is neither produced by thescattering of the light, nor by some mysterious chan-ges in the wavelengths or frequencies through thegreat distances, but neither was it produced by theDoppler expansion of the Universe. The shifting ofthe spectrum toward the red is simply happens atthe very end of the long journey, in the prism of thespectrograph as a result of the quantitative change

in the kinematics of refraction during its interactionbetween the depleted light energy and the refractivepower of the transparent matter.

The key to this alternative explanation of Hubb-le's redshift is to achieve a better understandingabout the kinematic nature of of the phenomena ofrefraction and dispersion.

As it has been described in Chapter Fourteen andillustrated on Figure 18-4 (reproduced 14-21), thephenomena of refraction and dispersion are neitherthe sole property of the refractive power of the me-dia, nor that of the frequency of the compressionpulses of light, but it is due to the interaction bet-ween the two, that is, between the pressure deliveredby the pulses and the density of the crystalline chan-nels of the transparent medium.

The denser the transparent medium and themore pressure is forced through the crystalline chan-nels, the greater the retardation in the speed of prop-agation. It follows, that the total excess pressuredelivered per unit time, that is, the frequency of theperiodical pulses, is also a factor in the resultingretardation of the light. Consequently, the higher fre-quency light is retarded more, deviated more, and

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have a higher index of refraction than the lower fre-quency light. This is then the kinematic explanationof the phenomena of refraction and dispersion.

Figure 18-4The importance of this theory of dispersion in the

alternate explanation of the cosmological redshifts

calls for a reinforcement of the idea by the wellknown theorem of hydrodynamics.

First let us point out again that, according to thekinematic theory of wave-motion, the excess pres-sure, or momentum density carried by the periodicalcompression pulses only acts in the forward andtransverse directions. (momentum amplitude, Fig.14-11/13). There is no excess backward pressure inthe direction of the source. Considering this, a beamof light, propagated in the isotropic Aether from asource to a receiver is delivering a given amount offorward momentum per unit area per unit time.

With respect to the pressure exerted on the re-ceiver, the beam can be taken as equivalent with thedynamic pressure of a fluid in motion, exerting forceon a plane perpendicular to the direction of the flow.The periodicity of the pulses can be neglected sincethe frequency is an expression for the delivery of mo-mentum per unit time, i.e., momentum density.

When this point is accepted, two fundamentaltheorems of hydrodynamics become applicable. TheEquation of Continuity is valid in this case, statingthat as a light beam 'flows' through a transparentmedium, the excess momentum that enters the inter-

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NORMAL

Θ incidence = 45

Angle of

°

nal Aether must be the same that leaves. Thus, inpassing through form air to glass and to air again,the total momentum of the pulses per unit time isconserved both in speed and direction.

More importantly, Bernoulli's Theorem of therelationship between the static pressure and thedynamic (flow) pressure developed in an ideal fluidin motion can also be applied to this case:

p + 1/2 r v2 = constant (17.1),where p denotes the static pressure, r is the

mass density and v is the velocity of the fluid.Essentially, this expression is also a statement of theprinciple of conservation of energy, applied to fluidsin motion, and derivable from Newton's mechanics.

Recall the experiment with a gas-burner descri-bed and illustrated in Chapter Eleven, Figure 11-4.where the constriction of the pipe demonstrates thatas the flow velocity of the fluid (dynamic pressure)increases, the static pressure decreases.

In the case of the refraction of a light beam a rec-iprocal situation arises. The law is that the sum ofthe static and dynamic pressures is a constant. Asthe compression pulses enter in the crystalline chan-

nels of the glass and due to the transverse compo-nents the internal static pressure of the Aetherincreases, the dynamic pressure, that is, the velocityof the propagation, must be reduced.

Since the delivered pressure is proportional tothe frequency, the beam of higher frequencies mustbe retarded and deviated more than that of the lowerfrequencies. This is the hydrodynamics of the refrac-tion and dispersion of light.

Recall now, that the concept of the 'wave ampli-tude' originates from the maximum displacement ofthe particles in the mechanical wave-motion on ataut string. By the derivation of the wave-equation,the same concept has been applied to the longitudi-nal waves of sound, where the concept of the ampli-tude expresses the peak of the pressure amplitude ofthe compression layers. Similarly, the wave equationhas been found applicable in the theory of the elec-tromagnetic waves of light, where the amplitudeexpresses the maximum transverse magnitude of thevectors of the electric and magnetic fields.

Consequently, it can be stated that in all wavepropagations the concept of amplitude marks themagnitude of the peak energy density created by a

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single oscillator and/or carried away by a singlepulse. The concept of intensity, on the other hand,marks the total energy created by a great number ofoscillators and superimposed on one another in themedium.

Mathematically, the intensity is proportional tothe square of the amplitude, and since the intensityis inversely proportional to the square of the dis-tance, the amplitude of the energy density of theindividual pulses must be in linear relation with thedistance of the source.

To put it into the form of a postulate:Refraction and dispersion are results of the inter-

action between the energy of light and the crystallinestructure of the transparent media. The magnitude ofthe deviation from the normal is proportional to thedensity of matter, to the frequency of light, and to theenergy amplitude delivered by the pulses.

Thus, the astronomical redshift, which is thedecrease in the deviation of light in the prism, is aresult of the global decrease in the specific index ofrefraction for all frequencies, proportional to thedepletion of the amplitude of light, and consequentlyin linear relation with the distance of the source.

At this point, several questions should be askedand answered.

Does this theory predicts a percentage shift for thedifferent wavelengths or frequencies, as the Dopplerinterpretation predicts in agreement with the experi-mental facts ?

Definitely. On the one hand, the Doppler percent-age law states that the magnitude of the shift of anywavelength, relative to its original position in thelaboratory spectrum, is proportional to a percentagecalculated by the division of the speed of source bythe speed of light.

On the other hand, the specific index of refractionof any wavelength in a given transparent medium isfound by the division of the speed of light in air (orvacuum) by the speed of light of the given frequencyin the given transparent medium. Since the speed oflight in the medium is inversely proportional to theenergy of light (pulse×frequency, or h×ν), so is theresulting deviation.

It then follows, that the division of the index bythe speed of light also gives a percentage deviationfor each frequency relative to its laboratory positionin the spectrum.

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In principle, if a prism of given index of refractionis replaced by one 5% less dense glass (smallerindex), it would result a shift toward the red end, apercentage shift in the position of all wavelengthsrelative to their positions given by the first prism.Based on the above hypothesis, it can be seen, that aproportional depletion in the amplitude of the energydensity of light in the same prism will demonstratean identical percentage law, being indistinguishablefrom that of the Doppler redshift.

How was this simple solution obscured throughmore than a half of a century ?

There are several psychological and scientific rea-sons for the historical rejection of the Tired LightTheory. The most general one lies in the nature andmethods of the human brain, which almost withoutexemption first directs thinking toward the mostcomplex solution and from there struggles towardsimplicity. This goes together with the instinctiveattraction of the human mind toward the most mys-terious, global and final solutions.

Remember, that the concept of the galactic red-shift and the velocity-distance relation was initiatedby Astronomy. The discovery of the galactic universe

came in the midst of the most exciting novel possibil-ity of Astronomy to measure the velocities of thestars by the Doppler Effect. Thus, the first naturalquestion was not about the origin of the redshift, but:how can they all move so fast away from us? Beforeany cautious astronomer, like Hubble, or philosopher-physicist, like Einstein would seriously search for anexplanation based on physical principles, the fron-tiers of cosmological innovators were ready to specu-late on a variety of the most exciting scenarios.

Just as all other ‘bold leaps’ of modern physics,these cosmological speculations enforced the alreadyestablished direction of modern science toward thedenial of common sense and their pessimistic sensa-tionalism was favored by the anti-materialistic ideol-ogy of the troubled ruling classes.

So the sensible, simple and boring idea of theTired Light, without any serious analysis, was sweptunder the abstract rugs of modern science togetherwith all other tired attempts to save classical com-mon sense.

An important mathematical factor that helpedobscuring the obvious is the scientific convention,used in optical theory, that "the amplitude of light

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waves is always to be regarded as infinitesimal."(C.G. Darwin, Nature [17], − which creates no ambi-guity in the short distances of laboratory experiment.The same is not true, however, when light travelsmillions of years.

The astronomical obscurity came from the phe-nomenon of the Doppler shift. Because of the variousline of sight components of the motions of nearbystars and galaxies, most astronomical spectra haveshown either blue or red shifts. Therefore, even ifthere was a deliberate search for a measurable signof amplitude depletion, it would have been impossi-ble to distinguish the amplitude-redshift among theoverwhelming positive and negative Doppler effects.However, since the relative local motions of the ga-laxies become less significant with greater distances,the amplitude redshift in the spectra of the sourcesmillions of light-years away, finally became a majorfactor in the measurements. Nevertheless, by thetime the amplitude depletion finally showed up inthe cosmic redshifts, Einstein's boldly postulatedphoton theory, as a quantitative explanation for thephotoelectric effect, was unanimously accepted andextended confusion through the whole of science.

Now, the wave-particle-photon is described as awave phenomenon during its creation by the oscilla-tor and again when it produces the refraction andspectrum. However, during its propagation throughempty space, became a full pledged particle, carryingthe total inherited energy concentrated in time endspace, in the Galilean sense of inertia, undiminishedtill eternity and infinity. The intensity of light trans-lates to photon density which diminishes with thesquare of the distance.

What about the amplitude? No wonder, by the time of the inception of the

Tired Light hypothesis, nobody dared to think thatthe linearly diminishing amplitude (??of the pho-ton??) could have anything to do with anything. Thispossibility was already deeply buried under the bilin-gual labyrinth of the duality of light.

Another deep conceptual maze has been formedthrough the method of analyzing the spectral shift ofextremely distant sources by exposures extended togreat number of hours and days. This technic of accu-mulating and multiplying the energy of faint sourceshas also created the illusion that the redshift is inde-pendent from the energy of the light.

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Nevertheless, the essential difference is that,while the photographic plate can chemically accumu-late the apparent intensity of an unobservably faintcluster during long exposures, the process of retarda-tion and deviation of the same light in the prism isdetermined by the instantaneous pressure amplitudeof the compression pulses.

How about the possible correlation of the presenttheory with the conclusions derived from QuantumKinematics?

In Chapter Sixteen, discussing Black-body radia-tion, Photo-electric and Compton effects, it has beenassumed that the kinematical equivalent of thePlanck's constant, h might express the magnitude ofa limiting energy density, produced by an electro-magnetic oscillator and carried by the individualcompression pulses in the elastic Aether. In later dis-cussions this assumption has evolved into the moreuniversal concept of h, being not only the naturallimit of compressed energy, but an expression for thebulk modulus of the all-pervading medium.

Now, after the present discussion, a distinctionshould be made between the two seemingly equiva-lent concepts of the maximum energy density of a

pulse, and that of the bulk modulus of elasticity.While the two seemed to be identical in quality andquantity in the laboratory experiments, their neces-sary differentiation became clear in astronomicalphenomena.

Planck's constant of discontinuity, h does repre-sent both concepts in the laboratory, because thecompressed energy of a single pulse is quantitativelyequivalent with both of the stress caused by themotion of the oscillator and the strain produced bythat in the elastic medium.

Hence, in these cases the ratio of stress andstrain, or the bulk modulus is unity. The energy car-ried away by the pulse equals the energy given off bythe oscillator. The amplitude of the pulse is propor-tional to the amplitude of the oscillator. Evidentlyhowever, this equality becomes invalid at any signifi-cant distance from the source, since in propagationthe amplitude of the pulse energy is depleting in lin-ear proportion with the distance.

Thus, if h represents the universal cosmic con-stant of the bulk modulus of the Aether, some othersign must be assigned for the diminishing energyamplitude of an electromagnetic pulse.

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It is evident from all of the above, that AETHRO-KINEMATICS has no need for the theories of theExpanding Universe, or the Big Bang hypothesis todescribe the physical cause of the observational factsof Hubble's cosmic redshifts.

In the Cosmology of the all-pervading ideal gasmodel, Rotational Gravitation of AETHRO-KINE-MATICS takes care of the threat of the gravitationalcollapse of the Universe, -- finite or infinite.

In the seemingly endless chain of rotating ordersof magnitude, as it has been established in Kepler'sharmonious formula of the sink-vortex, the single, allpervading thread of causality is that of the universaldifferential rotation of the next higher order. The cen-tripetal force of gravitation and the centrifugal forceof inertia are parallel aspects of the eternal equilibri-um created by the continuous evolution of Aethertoward the ever increasing complexities and conden-sation of Energy, Matter and Life.

In this hierarchy the question of infinity is purelymetaphysical in nature and indifferent from thestand points of Epistemology and Science. Hence, inany single link of this endless chain the unified lawsof physics and cosmology, they our mind is able to

conceive, are valid, and all other human endeavorcan exist in complete harmony with Nature.

This unique link, our observationally limitedUniverse, − at least at the present level of science, −can be assumed to be independent and non-contin-gent on any others.

Thus, AETHRO-KINEMATIC cosmology is liber-ated from the metaphysical perplexities of infinitetime and space and that of the initial cause.

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"Miserable mind, you get your information fromyour senses, and do you try to overthrow them ?

The overthrow will be your downfall."— Democritus: Atomism. Sixth century B.C.

EPILOGUE

THE ‘UNDERSTANDING’ OFNATURE

COMMON SENSEThe primary intention of this study was not to

criticize or try to disprove the theories of ModernPhysics, but to offer alternative explanations forthose perplexing problems of Classical Physics,which lead to the seemingly inevitable acceptance ofthe modern anti-common-sense and counter-intuitivemathematical theories.

Since modern mathematical theories are basedon the manufacturing of formulas and formalisms tomatch and predict the observational facts and exper-imental curves, any alternative conceptual descrip-tion and explanation of an experimental fact mustreproduce the same data as predicted by the present-ly used mathematical formulas and formalisms.Thus, the possible acceptance of any alternative con-ceptual theory must reproduce the results predictedby the reigning mathematical theories.

The ‘alternate explanation’ is merely a phrase ofextreme politeness, because for the perplexing phe-nomena of modern physics, humanly conceivable con-ceptual explanations. simply do not exist.

As much as it was possible, I have stuck to thisnon-argumentative approach all the way through,mainly because I believe that once common senseand classical logic were invalidated, no more tools ormethods remained to challenge the validity of anybizarre hypotheses. In fact, once we turned to sculp-turing mathematical formalism to fit the experimen-tal curve and boldly and simply discarded logic andcommon sense then even the weirdest interpreta-tions of the ‘facts’ became unchallengeable.

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Aethro-kinematics

My firm conviction is, that only one kind of logicor reasoning or intuitive feeling of reality and causal-ity exists; the one that we have inherited all throughthe billions of years of the evolution of living things.

Once a single fundamental assumption or postu-late has been accepted contradictory to these natu-rally evolved selectors of real and unreal, – scientif-ic reasoning has been traded for metaphysics, or –which is even worse – for mathematical dogmatism.

Nonetheless, there are grave inherent weakness-es in any kind of argumentation against these mod-ern mathematical theories and their verbal transla-tion into metaphysical postulates.

Both Relativity and Quantum Mechanics have si-lently but explicitly postulated that certain experi-mental facts, like the Michelson Null-result or thediscontinuity of Planck’s Black-body radiation, andwith them a whole new world of physical phenome-na, could not be and would not ever be explainedthrough common sense or by the laws and logic ofclassical physics.

Note, that without the unconditional surrender tothis assumption as a scientific fact, none of the mod-ern postulates could even be stated or accepted.

Thus – by restricting the validity of classical phy-sics to a certain part of reality, the macroscopic orderof magnitude, – relativity and quantum theory notonly slammed the door on the history of classicalphysics, but also froze it from any further evolutionor any retroactive correction of its existing theories.

Of course, as all modern innovators agree, whenit comes to the measurement of an experimental fact,physics must resort to the classical language. Forwhat else can we measure but the classical quanti-ties of mass, distance, velocity and time, etc.,...Butthe rest of classical physics; theories, methods, com-mon sense, logic and causality are gone forever. Wedon’t want them and we don’t need them!

This is the real first postulate of modern physics.

Unfortunately, without a valid alternative expla-nation of the experimental facts based on commonsense and classical logic, modern mathematical phi-losophers can postulate whatever they want to andbe as inconsistent as they are.

The sad fact is that those incomprehensible me-taphysical postulates of relativity and quantum me-chanics are the only existing ‘conceptual’ linkages

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Aethro-kinematics EPILOGUE Common Sense

between the experimental facts and the undeniablysuccessful modern mathematical formalisms.

One asks innocently: How could the mathematicswork if the philosophy that created it is so faulty?

Someone can state that it happened the otherway around; the mathematics came first by chiselingequations to fit the experimental facts. The philo-sophical postulates are merely retroactive attemptsto fit or unfit the old common sense concepts to theartificial, deconceptualized mathematical formalism.

But Relativist and Copenhagenist philosopherswonder what are these mysteriously unclear con-cepts of common sense and the understanding ofnature? And what is so sacred about them ? Accor-ding to some, they are mere fashionable prejudicesagainst new, revolutionary ideas.

Just a few centuries ago common sense told usthat the earth was flat. Now it tells us that theMichelson result should not be Null and Planck’sradiation should not be discontinuous, – Now we‘know’ that the earth is round! Common sense?!

Well, – here, at the end of this sketchy descrip-tion of the ideal gas model of a universal Aethermedium that might help to understand Nature, – I

am offering an attempt to clarify these concepts ofcommon-sense and understanding and what is sosacred about them for the regular, open minded,intelligent, – though mathematically seriously un-derdeveloped humans – who are interested in theworkings of the world and in the meaning of reality.

I’m trying to make a very long story very short:Some three and a half billion years ago in a pond,

somewhere on the surface of the sizzling Earth, akind of complicated atomic conglomerate, proteinand amino acid molecules or something like that, gotaccidentally encapsulated by a film of clay molecules.

This accident created a temporary boundary bet-ween the inside world and the outside world, justlike a soap film creates a boundary between the airmolecules inside and those outside of a soap bubble.

Like accidents that have happened a few quad-rillion times in millions of ponds for hundreds of mil-lions of years and some of these bubbles accidentallyhit the evolutionary jackpot, having just the rightthickness of the clay film to reach a feeble equilibri-um between internal and external pressure. Thesebubbles became the encapsulated units of life.

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A billion or so years later this life-unit-bubblereached the complex organism of an Amoeba whichachieved the miraculous method of self-locomotion byinternally changing the shape of its own bubble. Byadjusting the internal pressure locally, it createdbumps and lumps on its ‘body’ in different directions.With this it managed to move relative to the externalworld and soon found the sensitive position anddepth in the pond where shadow and light and heatgave just the optimum mixture of energy for its sur-vival. Thus, it had to, and became able to, ‘paddle’itself up and down, back and forth and sideways asits constantly changing environment dictated.

In my mind, this microscopic ‘blob’ of life hadalready recognized a wealth of information about theexternal world and reality.

One might oppose the usage of the concept of‘recognition’ but it can hardly be denied that theAmoeba must have reacted to the facts of life thatboth itself and its environment were existing in threedimensional space with ups and downs and side-ways. Also, it must have sensed the received mix-ture of heat and light as a changing effect which issomehow connected to its own locomotion. With this

it also reacted to the flow of time, that is, to the factthat events at a given place are happening in somekind of definite sequence. Thus, the Amoeba lives,acts, reacts and survives in a reality of three dimen-sional space, one directional sequence of time andsome definite causality between its motion and thetemperature; one is the cause, the other is the effect.

These ‘recognitions’ were the fundamental pre-conditions of its survival and therefore the Amoebialphilosophy has never ever changed in the course ofevolution but was constantly reinforced through theincreasing complexity of the conglomerations andspecializations of the interacting life-bubbles.

A couple of billions of years later, – few millionsbefore us, – somewhere in the Rain-forrest, a monkeyof some kind, in its daily food-collecting routine, tooka leisurely jump from one tree to the other. The dis-tance between the selected branches was thirty twoand a quarter feet, the elevation difference betweenthem was roughly eleven and half feet down. Themonkey weighed 220.3 kilograms, pulling toward theground and there was also a 44.7 km wind, blowingthrough the forrest in a direction 72.55° angle withthe anticipated trajectory of the jump.

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Well, – this particular monkey has missed thatparticular branch by an inch-and-an-eight and grab-bed the next lower one to the left. Nevertheless,somewhere in it’s awesome data bank the whole ex-perimental environment with initial and final condi-tions, the experimental result and a matching conclu-sion with all its immense complexity has been record-ed for future references.

“Maybe, the left big toe should have applied anextra repulsive force on the starting branch, some-thing like 2.12 kg.m/sec at 5.052° in the North-east-ward direction against the wind, maybe some of itupward, against gravity. – Hm!...Nobody is perfect.”

The reasons, why the experimental result andthe conclusion were not recorded in this manner,were that this life unit had not yet learned to thinkwith words or conceptualize its experiences, did notknow vector addition and had neither a compass nora pocket calculator on hand.

Nevertheless, in any other respects this monkeymust have been aware of most everything that New-ton axiomatically organized in his Three Laws ofMotion some hundred millions of years later.

Evidently, the procedure of life is nearly equiva-lent to practicing experimental physics and accumu-lating conclusions constantly correcting the theoriesof anticipation of experimental results. All this on aninstinctive level. This is the immensely deep source,origin, evolution and meaning of common sense.

If instinct is the storage of un-conceptualizedphysical experiments with the attached results andconclusions drawn from them, then common senseis the conceptualized and verbalized translation ofthe three billion years of evolutionary practice oflife.. – Can we have any more sacred inheritance?!

Now, just a few seconds of evolution ago, Newtonsucceeded in simplifying, generalizing and axioma-tizing the essence of the physical behavior of all ani-mate and inanimate objects in the three dimensionalimmovable space and in the absolute flow of time.This wonder became possible through the evolutionof the nervous system during the last fifty thousandyears, between the invention of the first axe andGalileo’s innovation of the first telescope.

Newton of course, possessed the whole data bank,everything that had happened and had been accu-

480


mulated from the Amoeba on. Plus whatever elsewas added to that during this latest evolution of thenervous system of the life-bubble.

Newton used all available innovations; words,concepts, language, intuition, abstraction...you nameit...! He used the whole accumulated written knowl-edge of several civilizations about geometry, algebraand mathematics and jacked it up to his own level.

He Used measuring devices of space and time,Cartesian coordinate systems, all astronomical data.He mastered all products of the sophisticated com-plexity of the brain at that stage of the homo sapiens.

But above all, with his concepts of push and pulltaken from the living muscle forces of locomotion, hedrew a line straight through the three and a half bil-lion years of evolution of common sense in the exactdirection tangential to the progression from theamoeba to the monkey to the human philosopher:

Length, time, motion, mass, force, acceleration –measurable quantities and their mathematically ex-pressible relations. – Obviously, classical physics andclassical logic was founded on this kind of commonsense, thus it is humanly comprehensible.

UNDERSTANDINGAt this point, however, we must make a distinc-

tion between the meaning of common sense and theconcept of Understanding Nature. For this is the his-torical point where these concepts are getting muddyand confusing, creating the stronghold of modernanti-common-sense, anti-reality argumentations.

For Newton proceeded further. He introduced anabstraction based on those simplest common senseconcepts of push and pull and hypothesized anattractive force between all masses in nature, similarto the force between two human pulled by an elasticrope toward each other. – He called it Universal Gra-vitation and showed that this hypothesis can tie to-gether earthly and celestial mechanics of the fallingapple and the revolving moon.

There is nothing in this generalized abstractionof muscle force that would oppose common sense.The jumping monkey does not have to know that notonly the Earth attracts him but he attracts the Earthtoo. He only had to anticipate the total force and hiscommon sense did that. Not knowing the rest of thestory doesn’t make his common sense wrong. It ismerely the case of insufficient information.

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Aethro-kinematics EPILOGUE Understanding

Think now for a second about the ignorance ofthe ‘Flat Earth’ argument.

But how about the force of gravitation? For thelast four centuries nobody could understand what itis and how it works. – Maybe the act of abstraction isthe one that separates common sense from under-standing?! But if that ‘abstraction’ is the cause ofconfusion, being something uniquely and totally dif-ferent than the rest of the biological evolution, thenjust think about the kitten who pretends that thecotton ball that he slaps around is a lively mousewhich desperately tries to escape from his claws. Orthink of the monkey who recognizes that the othermonkey behind the impenetrable shiny plate is re-peatedly making the same movements as he does,therefore it must be a ‘mirror image’ of himself. –These abstractions maybe ranked equal or higher incomplexity than that about the gravitational force.

Nevertheless, this is the point where commonsense and understanding separate from each other.For gravitation is based on the common sense of theAmoeba, the Monkey and the Homo Sapiens, but westill cannot say that we understand what it is andhow it works. Why?

Because, in all the three billion years of daily lifesensory perception only recorded the basic rule ofmechanistic reality that motion can only be causedby the motion of something else. Newton’s action at adistance force that creates motion without bodilytouch or some kind of transmitting medium, had noresonance in our data bank. Think about the rollingrock transferring its motion to another, or of theinvisible wind that moves everything in its way;monkeys, branches, falling leaves and dust.

Although his contemporary mechanistic philoso-phers severely criticized him for not giving an under-standable model of how his gravitational force works,it was no real problem for Newton. For he was con-vinced that there must be some kind of medium,maybe Huygens’ Aether, that conveys this force. Stillhe also recognized the fact that there was insufficientinformation about this substance for speculatingabout its mechanics that might explain gravity.

Newton clearly and explicitly declared his convic-tion that ‘no man who has a competent faculty forthinking can believe in the action at a distance forceof gravity through vacuum without the mediation ofsomething else.’ – Although he refused to hypothe-

482


size and claimed that the theory of gravitation mere-ly provides an instrument for mathematical predic-tion, till the end of his life, never relinquished thehope that the dynamics of the Aether or somethingsimilar will explain away the mystery of gravity.

This is the right place to note, that three hundredsome years later Einstein was just as clear andexplicit, but in the opposite direction. He declaredthat the problems with the measurements of thespeed of light will never be solved by classical com-mon sense, therefore the Aether, together with New-ton’s absolute space and time must be discarded.

According to Einstein, the mechanical models, –that helped classical physics to understand the ab-stractions into the worlds beyond sensory perception,– were merely temporary scaffolding to build the the-ory and must be removed, after the mathematicaldescription was found, for avoiding confusion. Thisattack was aimed against the Faraday-Maxwell elec-tromagnetic theory which was invented, designedand mathematically described, explicitly based onthe existence of the luminiferous Aether medium.

Newton kept an open mind ! Einstein succeededin closing everybody’s mind ! – It is just this simple.

If common sense is the conceptualized instinctthat was condensed into the brain through the wholeof evolution, then understanding is the correlationand corroboration between those necessary abstrac-tions beyond the sensory experiences and our awe-some data bank of common sense.

The comprehension of abstract hypotheses aboutphenomena beyond the range of sensory perceptionis an act of dismantling the complexity of the eventto its smallest separable constituent events whichwere already experienced and familiar within oursensory perception and thus some simple mechanicalprinciples and concepts are applicable. Or from theother end, understanding of an abstract hypothesis isa procedure of building a conceptual bridge betweenabstraction and common sense. As classical physicshas practiced for three centuries by building com-mon-sensible, understandable mechanical models.

Think about the atomistic kinetic theory of gaseswhich was based on the childish ‘scaffolding’ of thebilliard-ball-atom and brought to us the understand-ing of gas pressure, temperature and entropy, etc. bythe simplest possible common sensory experiences ofthe motion and collision of the childhood marbles.

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PREDICTIVITYThis concept and word must have been invented

to represent the major, maybe even the only merit ofmodern mathematical physics. The necessity of thisinnovation will become clear when considering theproduct of the last few nano-seconds of evolution:

A member of the latest stage of the homo sapiensevolved within the last couple of thousand years, amere evolutionary baby, called the mathematician,can exhibit the following procedure:

He can set up a scientific observation station on abeach where the ocean and the land meet. He canequip the station with a meter-rod, a clock, a calen-dar and a couple of thousand rolls of graph-paperand he can start meticulously recording the exacttime of the periodic rise and fall of the see-level rela-tive to the shore.

Pursuing this for some years, he can set up a twodimensional Cartesian coordinate system – usingrectangular lines, with the x coordinate on the hori-zontal line, representing time and the y coordinateon the vertical line, representing the position of thewaterline. – By this method he will be able to orga-nize the accumulated data and plotting them in the

form of a graph. Thereby he produced an experimen-tal curve which represents a pictorial informationabout the periodic rise and fall of the water-line.

Some meticulous study of this graph brings himto the discovery that the observational curve isapproximately periodical on a daily basis.

The next step brings out his real forte’.An experimental curve represents a complex re-

lationship between two quantities where one is thefunction of the other. If the position of the water onthe shore is y and it is changing with time x, then yis the function of x. Thus the relation between thesetwo quantities represented by the observational cur-ve can be described by a mathematical equation.

The simplest example of this is the case when thewater level is uniformly rising with the flow of time.Let’s say, one meter rise during one hour, thus thequantities of y and x increase evenly. In this case theplotting points will be the same distance from bothrectangular axes and the connecting line-graph willbe a straight 45° diagonal between the lines.

There are an infinite number of other possiblerelations between the two quantities, resulting ininfinitely complex curves, but if there is any kind of

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Aethro-kinematics EPILOGUE Predictivity

repetition in their relation, there is a good chancethat it can be expressed by mathematical equations.

Aside from the obvious daily periods of rise andfall he found the first total repetition of the curveconnected to the year, but on a closer analysis he dis-covered that the daily movement of the water levelwas not the same in every twenty four hours but itsmaximums and minimums slowly changed andrepeated itself in every 28 days. There were alsosome changes in the curve which were somehowrelated to the different seasons, ...and so on...

Fortunately, these periodical changes of the chan-ges themselves can also be plotted producing an-other graph with another curve which can also beexpressed in a mathematical equation. In case of uni-form changes we can insert a constant into the equa-tion. If the changes are non-uniform, we simply ad asub-equation. Thus, it is merely a matter of mathe-matical ingenuity and perseverance to produce acomplex equation which, when it’s plotted, repro-duces the original observational curve. – Once thiswondrous mathematical formula is chiselled to per-fection it will describe a phenomenon of Nature, theOcean Tides, without the slightest knowledge about

the roundness or the rotation of the Earth, or theexistence of the Sun, or the orbiting moon, or New-ton’s Universal Gravitation, or utilizing anythingthat the former evolution accumulated. Furthermore, it requires neither common sense nor under-standing. This is the wonder of predictivity.

Now comes the mathematician philosopher whonot only comprehends the sophisticated and elegantmathematical formalism but is also able to explain inthe laymen’s classical language, why these wondrousinterpolation of curves and equations should work.

Of course, an infinite number of different stories,can be constructed to fit between the observationalfacts and human imagination. Let us pick only three:

One could be the mythical Monster hypothesisaccording to which an extraterrestrial invisible rela-tive of the Loch-Ness monster is living in the Oceanand is breathing in and out trillions of liters of airwhile it is swimming through a complicated yearlyroute between the continents. It has a menstrualperiod of 28 days which heavily effects its breathing.This hypothesis has slight contradictions which how-ever can be worked out by introducing a few familymembers of different sizes and various habits.

485


The next interpretation can be the classical onementioned above. The story of the solar system witha Sun and an orbiting Earth which mutually pull oneanother and then a Moon with its 28 days period oforbits around the earth which pulls both the Sun andthe Earth and all three of them pull the ocean...etc.

The most modern version, a mathematical theoryis way beyond the comprehension of an average life-bubble. Nevertheless, the philosopher proponents ofthis explanation come to help with a humanly con-ceivable interpretation of the quantum mechanicalformalism which aims directly to the point:

Light has a dual nature; sometimes waves, some-times particles. Matter also has a dual nature; some-times particles, sometimes waves. The extra intrigueof this quadruplety of wave-particles and particle-waves is that no two of these quantum entities canever be measured at the same time. Now, this maybea paradox but not a contradiction and easily relievedby the simple concept of complementarity which canbe expressed by Schrodinger’s wavefunction togetherwith Heisenberg uncertainty principle. Nevertheless,since we do not know whether we measure a wave-particle or a particle-wave until we measure it and

they cannot be both at the same time, we must denythat they existed before the actual measurement. Infact, for this reason, we might as well deny all ofreality outside of the instance of measurement.Incidentally, there is a slight problem with the mea-surements too, because according to predicted proba-bility waves, two quantum entities are able to com-municate with each other by superluminal signalswhich is an absolute no-no for both relativity andquantum mechanics. – Hm!...Nobody is perfect!

So, which one makes more sense? – What sense ? In the very last fraction of the very last nano-sec-

ond of evolution came the development of the mightypower of predictivity and the crunching monsters ofsuper-computers. – Now, foretelling the future proba-bilities for a great variety of different things andtheir mysterious relationships – mathematiciansbegin to believe that it is only a matter of time whenthey will possess the ultimate equation, ‘The Theoryof Everything’ predicting the next, and every nextsecond of the whole Universe. – Then they mightbecome the high priests of the religion of Predictivity– foretelling everything and understanding nothing.

This is where evolution stands right now.486


THE ‘UNDERSTANDING’ OF NATURErequires the un-contradictory correlation of every bitof talent with which we are blessed by evolution: in-stinct, intuition, common sense, anticipation, logic,abstraction, understanding and yes, the powerfulshorthand methods of mathematical predictivity.

The human mind is an evolutionary product ofthe sensory perception of macroscopic physical reali-ty. The fundamental question is whether or not theworld of different orders of magnitude above andbelow us could be understood by this mind? – Thehistory of human philosophy and science itself is aphenomenon that shows at least an unrelinquishingfaith in a positive answer to this question.

By assuming the possibility for the understand-ing of Nature, we also create a world of reality in allorders of magnitudes that is not dissimilar to ourown macroscopic one.

It follows – as we have assumed and seeminglyfound – that matter is the same all through the Cos-mos and our macroscopically found physics, chem-istry and the conservation laws of matter and energyare valid at least within the observable Universe.

Doesn’t it clearly follow from the macroscopic ori-gin of this mind of ours, that the perplexing problemsarising in the progress of this investigation must besolved within the capabilities of our understanding?!

We invented celestial mechanics to associate theorbit of the moon to the trajectory of a falling apple,tying a higher order of magnitude together with ourlaws of earthly mechanics. We did the same goinglower in the orders, inventing billiard-ball-atoms toexplain the macroscopic behavior of gases and mech-anize the sensation of sound. We invented sub-atomicbilliard-ball-electrons, and billiard-ball protons andneutrons forming billiard-ball nuclei. One more stepdown in the sub-atomic-particle order we are search-ing for billiard-ball gluons and quarks.

We might as well realize that we must live in abilliard ball universe to understand nature, becausethat is exactly the simplest and most basic mechani-cal format comprehensible to our mind.

That is, mass, motion and collision.Nothing wrong with this. If we are to understand

physical reality it must be made up of billiard ballsof different orders of magnitude. Thus, we must findthat fundamental order of magnitude from which,

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Aethro-kinematics EPILOGUE The ‘Understanding’ of Nature

based on Newton’s simple laws of motion, we can de-sign and build an all-pervading reality.

Exactly this was the original idea of the super-mundane, luminiferous Aether which supports andtransmits the waves of light through immense dis-tances of space, just like sound is transmitted by thebilliard-ball-atoms and molecules through the airfrom your mouth to my ear.

It was also believed that Aether transmits Fa-raday’s and Maxwell’s imperceptible electric andmagnetic forces. Their lines and field of forces founddirectly analogous to the humanly already conceiv-able hydrodynamic phenomena of the relentless butsometimes correlated flows and circulations of themyriads of billiard-ball atoms of macroscopic fluids.

And the Aether was the one which also preser-ved Newton’s hope that some day his macroscopicconcepts of inertia and gravity will be no more mys-tery to our billiard-ball minds.

Through re-inventing the ideal gas model of theall-pervading Aether, AETHRO-KINEMATICS isthe embryo of an emerging possibility that one day,by strenuous work and through immense growing

pains, we might succeed in unifying the natural phi-losophy of particle-physics, atom-physics, mechanics,electromagnetism, thermodynamics, quantum-mechanics, astronomy, cosmology....etc...under the sim-ple common sense concepts and mathematics of thelaws of Newton’s mechanics.

Another day could come when, – as atoms pro-ved to be non-ultimate, – we might find phenomenawhich will force us to conclude that Aethrons are stillnot the ultimate ones, but must have internal struc-ture and made up from sub-Aethronal billiard balls.

Nevertheless, let us just deal with one order ofmagnitude at a time and see whether or not this the-ory of AETHRO-KINEMATICS gives us a betterunderstanding of Nature.

Take it...or.... leave it for the next generation.

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Aethro-kinematics EPILOGUE The ‘Understanding’ of Nature

APPENDIX I.

THE MATHEMATICS OFTHE SINK-VORTEX

Kepler's third law renders a dynamic map for allrotational systems under the influence of a centri-petal force which operates by the inverse square law.The law states, that

P2

−−−−−− = K or P2 = KR3 (1) R3

The square of the Period divided by the cube ofthe radius is a constant for each member of the wholerotating system.

The period, P of the planet, that is the time re-quired for the planet to go completely around thesun, is the circumference of its orbit, 2πr divided byits velocity V,

2πR 2πR P = −−−−−− or V = −−−−−−

V PCombining equations (1) and (2

4π2R2 4π2R2 4π2 1V2 = −−−−−− = −−−−−− = −−−−−− or V2 ∝ −−−− ,

P2 KR3 KR R

therefore according to Kepler's empirical formula:1

V ∝ −−−−− (2).−−−

√ RThe tangential velocity of any orbiting body in a

gravitational system is inversely proportional to thesquare-root of the radius of the orbit.

In the following we intend to prove the plausibili-ty that the same result can be derived from the kine-matics of the Aetherial sink-vortex.

In Chapter Seven it has been proposed that asink-vortex produces a radial centripetal force, equi-

489

Aethro-kinematics

valent with Newton's gravitational force. Based onthe Theory of the Evolution of Matter, introduced inChapter Eleven, it was further proposed, that therate of consumption of Aether, due to the evolution ofmatter, is proportional to Newton's gravitationalmass. Thus, the identity between gravitation and thesink-vortex can be expressed by

M QFgravity = G −−−−− or Fsink = K' −−−−− (3),

R2 R2

where G is the gravitational constant, K' is the sink-vortex constant and Q is the rate of consumption ofmass, or the total number of Aethrons, (nm ) con-sumed by the sink, per unit time.

Nevertheless, Newton's theory of gravitationleaves the original cause of the tangential componentof the planet's motion totally unknowable. AETHRO-KINEMATICS attempts to render a mathematicalderivation of both the tangential and radial compo-nents of the forces acting in Rotational Gravitation.

Recall Figure 7-7 which shows (a) a circular vor-tex, (b) a linear sink, and (c) the combination of thetwo; a sink vortex.

It will be shown below, that the motion of a mass-

particle, placed into any point of the field of a sink-vortex (with zero velocity) will be affected by threedirectional pressure differences, i.e., fluid dynamicalforces of different origin.

1. The external pressure of the isotropic medium,FP that exerts a force all-through the evolution of acircular vortex, keeping the rotating fluid-particles,within a constant circular orbit. Hence, it is equiva-lent with Huygens' centripetal force.

2. The tangential pressure, difference, FT of thecirculating fluid in the direction of rotation willaccelerate any mass-particle, placed in the flow withzero velocity. This force will act until the particlereaches the velocity of the orbiting fluid. Then themass-particle will merely float and carried by thefluid and the pressure difference will cease to exist.

3. The pressure of the radial flux, FR of the linearsink which is directly proportional to the rate of con-sumption of the sink and represents another radial orcentripetal force which would accelerate a test-parti-cle linearly toward the sink.

For the sake of mathematical clarity, the threecomponents of the total force of the sink-vortexshould be analyzed separately.

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Aethro-kinematics APPENDIX I. The Mathematics of the Sink-vortex

1. Consider first the origin and kinematics of theregular circular vortex of a great storm which is, the-oretically (assuming a frictionless ideal gas), a per-manent system in constant equilibrium under theisotropic pressure of the external medium. In a circu-lar vortex the medium is rotating in closed rings, andeach layer preserves its own matter. There is no ex-change of mass between the surrounding mediumand the rotating system. There is no mass or energyflux across the body of the vortex.

Two different factors should be recognized here:a) In the theory of Aerodynamics a mass of air in

rotary motion is said to be in a permanent circulatoryflow if its velocities at various radii are of propermagnitude to induce radial equilibrium of the circu-lating mass. The requirements for this radial equilib-rium consist in balancing centrifugal forces againststatic pressures as derived from Bernoulli's theorem:

PS + 1/2 ρV2 = Constant (4),where PS is the static pressure, ρ is the fluid's mass-density.

Differentiating Equ.(4) dPS + ρVC dVC = 0,

where VC is the circular velocity of the fluid particle.If VC = 0 then the external pressure, PE is a con-stant. Therefore

PE = PS + 1/2 ρVC2 (5).

The force is equal with the pressure differencethat is exerted by the medium at any two neighbor-ing points along the radius:

dPS ρVC dVCFP = −−−−−− = − −−−−−−−−− (6).

dR dRThis is the force that keeps the fluid particles on

the circular orbit, therefore it is equal to Huygens'centripetal force. Thus,

ρVC dVC VC2

− −−−−−−−− = ρ −−−−− (7).dR R

Cancel ρ and V on both sides of Equ.(7):dVC dR

− −−−−− + −−−−− = 0 (8).VC R

Now, integral Equ. (8) lnVC + ln R = lnVC R = C (a constant).

and VC R = C' (another constant).491


It follows, thatC'

VC = −−−− (9),R

and substituting Equ.(9) into the pressure force; FP =ρVC

2/R, we have(C'/R)2 ρ C'2 1

FP = ρ −−−−−−−− = −−−−−− ∝ −−−−− (10).R R3 R3

This is the relation that results in the specifica-tion required by bernoulli's radial equilibrium, andalso leads to the proportionality, VC ∝ 1/R; theNewtonian formula for the velocities of the fluid par-ticles in the circular vortex, based on which he dis-carded Descartes' solar-vortex theory.

b) If air is in circulation, based on Equ.(4), thevelocity of the rotation at the center reaches a theo-retical value of infinity. Since this is impossible, thecenter of the circulatory flow must be occupied by asmall core which is, under the isotropic pressure ofthe radial winds, compressed to its limits and simplyrotates as a solid object. The immediately surround-ing layers are rotating with exceptionally high butnot infinite velocities.

Figure AI-1It follows, that the kinematic evolution of a circu-

lar vortex (Figure AI-1.a) starts at the center by thescattering of the linear radial streams into a tem-

492


a) b)

c) d)

RADIAL TURBULENT

UNSTABLE CIRCULAR

CORIOLISFORCE

CORE

porarily turbulent flow. This unstable state of themedium near the center (b-c), being under constantisotropic pressure, will eventually be forced to takeup the least volume of space, which can only beachieved by rotation.

Once the rotation is established around the core,the radial streams bend around the already rotatinglayer (d) and under the constant isotropic pressuretheir linear momentum smoothly converts into theangular momentum of the circulation. This proce-dure repeats itself from layer to layer by kinematicfriction and as the vortex grows, the rotational veloci-ty decreases in agreement with bernoulli's formula.

The gradually changing ratio between the dy-namic and static pressures establishes the radialequilibrium of the system. It follows, that both themass and the energy density of the fluid in therotating system, is greater than that of the averagedensity of the external random medium. In otherwords, the evolution of a circular vortex also repre-sents a local condensation of mass and kinetic energy.

The spatial extension of the vortex is limited byan outermost layer, representing a close to zerodynamic pressure (rotation) and a static pressure

equal to the pressure of the external medium. At theboundary of the vortex the rotating system and theisotropic medium reaches a permanent static anddynamic equilibrium.

Consider now, that the orbit of any fluid particlein a circular vortex is a permanent circle, thereforeHuygens' law of centripetal acceleration, a =mVc

2/R, is applicable. Thus, the external pressureforce, FP that keeps each fluid particle on a constantcircular orbit equals to Huygens' centripetal force:

mV2 V2

FP = −−−−−− or for a unit mass FP = −−−−− .R R

2. It follows from the above, that the circulationof the fluid particles also represents a pressure dif-ference, or a force in the direction of rotation. Thus,when a mass-particle, say a donut-vortex (CH.−9)with a greater density, is placed into the fluid at anypoint of the vortex field with zero velocity, it willexperience an accelerating force acting tangential tothe rotation. This force will be directly proportionalto the square of the circular velocity of the fluid andinversely proportional to the square of the radius ofthe orbit. Thus, a tangential force; FT ∝ 1 /R2.

493


This is then the kinematic origin of the unknow-able force, that is responsible for the unexplained ini-tial tangential velocities of the planets or satellites orany secondary mass-particle revolving about a cen-tral mass in its Aetherial sink-vortex.

It should be noted, however, that the rotationalpressure difference on the object ceases to exist, oncethe mass-particle moves with the same velocity asthe fluid.

Nevertheless, considering the Aether medium,due to the higher density of the mass particle, thanthat of the fluid, the external pressure force, thatkeeps the fluid particle on a circular orbit is not suf-ficient enough to counteract the centrifugal tenden-cies of the multi-unit mass-particle that moves withthe circular velocity of the fluid. Hence, in addition tothe external pressure of the isotropic medium, a per-manent orbit for the mass-particle requires a grea-ter force than the one acts in the circular vortex.

3.This extra force is produced by a linear sink.A linear sink in a fluid creates a local fluctuation

in the isotropic density of the medium. From the lawof propagation of local density disturbances in anelastic medium, it follows that at any point in the

plane, perpendicular to the plane of the sink, therewill be a difference in the pressure toward and awayfrom the center, the magnitude of which will be di-rectly proportional to the consumption rate, Q/secand inversely proportional to the cube of the radiusfrom the sink; dP ∝ 1/R3.

In the two dimensional diagram of Figure AI-2,the area, S of the outer most ring equals to S= 2π R×dR. The mass, contained within this area will even-tually be consumed by the sink.

Evidently, to reinstate the pressure and densityequilibrium of the medium, there will be a radialdrift, VR of the fluid particles toward the sink.

494


Pressure Radial velocity∝

dR

R

Figure AI-2

Therefore, the total mass, or the total number offluid particles, consumed by the sink per unit time is

2π Rρ dR = Qdt (11).Hence, the radial velocity of a fluid particle

toward the sink is:dR Q 1

VR = −−−−−− −−−−−− ∝ −−−− (12),dt 2π ρR R

According to Bernoulli's Equ. (6) the radial pres-sure difference, PR and therefore the radial force, FR

toward the sink, at any two neighboring point alongthe radius is

dPS ρVR dVRFR = −−−−−− = − −−−−−−−− (13).

dR dR

Substituting VR of Equ. (12) into above, we getdPS Q Q

FR = −−−−−− = − ρ× −−−−−− × (− −−−−−− −) (14).dR 2π ρR 2π ρR2

therefore the radial force of the linear sink isQ 2 1

FR = −−−−−−−− thus ∝ −−−−− (15).4π2 ρ 2R3 R3

This kinematic system of the linear sink, alsooriginates and evolves from the center outward, andbernoulli's hydraulic requirements apply. As the fluidparticles start drifting toward the sink from all direc-tions, the dynamic pressure of the streamlines in-creases and their static pressure decreases. Hence,this system also tends to condense the medium, butin this case along the radii. As Figure AI-2. illus-trates, it leads to an inevitable conversion of the lin-ear flow into rotation and condensation.

Consequently, the superposition of the two sys-tems must be understood as the combined and simul-taneous evolution of a sink and a vortex under themutual influence of the two forces; the positive exter-nal pressure and the negative internal suction, thesum of which represents the total centripetal force:

FP + FR = FC (16).Thus, when finally the two flow patterns; the

rotational and radial flows are superimposed, form-ing a sink-vortex, all characteristics of both kinemat-ic systems will reinforce each other. resulting in adenser and relatively faster rotating system. In otherwords, by bernoulli's concepts, due to the superposi-tion, there will be a further decrease in the static

495


pressure, causing more condensation under theisotropic external pressure and an increase in thedynamic pressure of rotation, producing higher circu-lar velocities, related to the radius.

Vector wise it can be seen on Figure AI-3 that thecombination of a circular vortex and a linear sinkproduces special composite streamlines, called

equiangular spirals representing both the radial andthe circular components of forces. The illustrationalso shows that the total forces act differently on thefluid-particles (spiral flow) and on the mass-particles(circular orbit).

With this the kinematics of the sink vortex pre-sents a plausible conclusion, that there should behigher orbital velocities, VS of a mass-particle, or aplanet, in the spiraling stream of a sink-vortex, thanthat in the circular vortex. Thus, VS >VC ∝ 1/R.

It has been found, that, the two forces, FP and FR

are both inversely proportional to the cube of theradius, but, evidently their combined effect cannot befound by adding their proportionalities together.

Nevertheless, based on all the above, it is reason-able to assume that in the simultaneous, compositeevolution of the circular vortex and the sink, duringthe procedure of the conversion of linear to rotationalmomentum, the radial equilibrium requires the twocomponent forces to be equal. Thus, the magnitudesof the external pressure and that of the internal suc-tion, may be assumed to have the simple relation:

FP = FR (17).

496


Fluid-particle Mass-particle

Figure AI-3

Recalling, that the sum of the two forces, (Equ.16) equal to Huygens' centripetal force, we can write

dVC dVR V2

− ρVC −−−−−− − ρVR −−−−−− = ρ −−−−− (18),dR dR R

hence, based on the equality of the forces and relatedvelocities, we can write

dV V2

− 2 ρ V −−−−− = ρ −−−− dR R

dV V− 2 −−−−− = −−−−

dR R

dV dR− 2 −−−−− = −−−−

V RIntegral the above, we have

2 lnV + ln R = Constant 1lnV + 1/2 ln R = Constant 2

−−−lnV + ln√ R = C

−−−V √ R = C'.

−−−Therefore, V = C' /√ R and

1V ∝ −−−−− (2),

−−−√ R

in accordance with Kepler's original formula.

From this result one can make a derivation back-wards, as Newton did, and from Kepler's throughHuygens' find, that the combination of the externalpressure and the internal negative pressure of thesink, or the resulting total centripetal component ofthe force of the sink-vortex is inversely proportional tothe square of the radius, as it is stated in the Law ofNewton's Universal Gravitation and in the equiva-lent AETHRO-KINEMATIC Rotational Gravitation,expressed in Equation (3).

There is another method of derivation whichleads from the sink vortex to Kepler, involving of theratio of the mass density difference between the freeAether and its organized, condensed form in matter.This ratio can be applied to the different magnitudesof inertial tendencies of the two different states ofthe Aether and through that, determines the ratio

497


between the specific Huygens forces, that are neces-sary for their differing centripetal accelerations.

Another possible clue could occur from the abovedensity ratio for a possible analysis of the kinemati-cal origin of the elliptical shape of the orbits, as ithas been hinted in Chapter Nine. Also the same ratiomight render a kinematic reason for the existence ofBode's Law; i.e., the proportional distances betweenplanets, and also for the great difference in size andmass between the inner and outer planets of thesolar system. These problems, however, requires bothconceptual and mathematical complexities which arebeyond the scope of this study. With more sophisti-cated mathematics a further consideration should bepossible: The interaction between two or more sink-vortices, those of the sun's and the planets'.

SYNTROPYIn the mathematical treatment of thermodynam-

ic processes there occurs very often a quantity, nowassociated with the probability of a given distribu-tion of momentum among molecules and expressingthe degree in which the energy of a system ceased tobe available energy.

Application of the second law of thermodynamicsleads to the conclusion that if any physical system isleft alone to itself and allowed to distribute its ener-gy in its own way it always does so in a manner suchthat this quantity, called 'entropy' increases; while atthe same time the available energy of the systemdiminishes. It also represent that part of the entropyof a substance, that is due to a disordered arrange-ment of the particles, as opposed to a similar butordered arrangement.

This law applies to the universe as a whole,hence leads to the proposition that the entropy, thetotal disorganization and dissipation of the energy inthe universe increases as time goes on.

'Syntropy', a concept, the exact opposite of ent-ropy, is based on the existence of the Aether and theevolution of matter. The arrow of Syntropy is directedtoward a dynamic organization and a condensationof kinetic energy out of the chaotic isotropy of theideal gas of Aether.

In agreement with the law of the conservation ofmomentum any local fluctuation in the density of themedium produces radial drifts which by scatteringconverts into rotation.

498

Aethro-kinematics APPENDIX I. Syntropy

The resulting organized and condensed patternsof matter and its continuous evolution consumesmore Aether and produces a global local densitydecrease and a rotational system of a higher order ofmagnitude. Rotational gravitation causes furthercondensation, increases elementary interactions andre-creates the random oscillation of Aether on a par-ticle level. Through the resulting radiation of heatand other electromagnetic energies, matter continu-ously disperses its condensed kinetic energy.

Thus, syntropy, the organization out of chaos isthe primary tendency from which entropy can follow.

As far as the universe as a whole is concerned,these tendencies exist simultaneously in oppositedirections and their combined net result may notlead to a steady state universe. − There may exist anobservable phenomenon of these opposite tendencies;leading to the gradual evolution of Aether itself; fromthe initial isotropic aethron-randomness toward adiscontinuous quantum-randomness, due to the cha-otic interference patterns of radiations from all direc-tions at all frequencies, filling the allpervadingAether. This may be the source of the isotropic, cos-mic back-ground radiation?!

499

Aethro-kinematics APPENDIX I. Syntropy

ISOTROPIC

RADIAL

CIRCULAR

P = 0R total

P = 0C total

P = 0I total

The conservative conversion of momentum : ISOTROPIC RADIAL CIRCULAR

E

N

T

R

O

P

Y

S

Y

N

T

R

O

P

Y

Figure AI-4

APPENDIX II.

THE CYLINDRICAL SINK-VORTEXChapter Twelve proposes that the phenomena of

the electron current in a battery-circuit system andthe circular magnetic field around the current carry-ing conductor are both the effects of the circulation ofAether. According to this hypothesis the circulationof the Aether is produced by the chemical decomposi-tion of matter at one of the poles of the battery andthe chemical composition of more complex chemicalsat the other pole and by the resulting pressure differ-ence between sink and source, or -- as it is calledpresently, -- the potential difference between the two

poles or terminals of the battery. The tendency toequilibrate this pressure difference creates the circu-lation of the Aether through the external circuit.

In order to save time in explaining somethingthat has been already established, consider a quoteform Milne-Thompson, Theoretical Hydrodyn. [574]:"19-24. Electrical Analogy. - There is an exact corre-

spondence between the formulae concerning vortexmotion and those concerning certain electromagneticphenomena. In this analogy a vortex filament corre-sponds to an electric circuit, the strength of the vor-tex to the electric current, and the fluid velocity tothe magnetic force. Thus the formula for inducedvelocity corresponds exactly to the formula of Biotand Savart for the magnetic effect of a current."

Newton refuted Descartes' vortex theory and leftthe tangential component of the force, that must acton the orbiting planets, unknowable. Ironically, threehundred years later the Faraday-Maxwell electro-magnetic theory emphasized only the tangentialcomponent of the circular magnetic field and totallyneglected the radial flux toward the conductor. Bothfundamental hypotheses were based on the dynam-ics of the circular vortex and overlooked the potential

500

Aethro-kinematics

existence of the sink-vortex, which would be able toproduce both tangential and radial components.

Due to this oversight the available hydrodynamicanalogies were insufficient to physically connect the cir-cular magnetic field to the motion of the electrons in theconductor. Instead, the theory had to accept the meta-physical and unexplainable 'action at a distance' effectsof the charged particles in motion.

There exists, however, the conceptually simplehydrodynamic analogy of the water-battery (Ch-12),with its perforated pipe-circuit which, through the kine-matical concept of the cylindrical sink-vortex, may ren-der a physically conceivable explanation for the com-bined phenomenon of electricity and magnetism.

Appendix I. gives a conceptual description of thekinematical origin and maintenance of the gravitation-al sink-vortex, the mathematical derivation of Kepler'sLaws of planetary motion, and through that, Newton'sinverse square law of gravitation.

Appendix II. attempts to do the same for the cylin-drical sink-vortex, which forms within and around abattery and the current-carrying conductor. Never-theless, before presenting the actual mathematicalderivation, some similarities and dissimilarities bet-

ween the roles of the two different sink-vortices shouldbe pointed out.

As for the similarities; under the constant pressureof the Aether, the kinematical origin of the two kind ofvortices are conceptually and mathematically identical.In both cases the initial cause is the local density fluctu-ation and the consequential radial flow toward the lowpressure center, which unavoidably leads to rotation.Both vortices build up layer by layer from the centeroutward.

The difference in this respect is that, on the onehand, gravity is a result of the very slow evolutionarycomposure of matter within a great amount of mass,the center of which is the center of the sink. On theother hand, the forced and fast chemical procedure inthe battery produces both the composition and decom-position of matter at the two poles and thereby produc-ing a rapid Aether circulation in the conductor. This, inturn, results in the consumption of the external Aetherthrough a cylindrical sink-vortex around the wire. Inother words, gravity is a monopole of potential differ-ence, while the battery creates the circulation through adipole. While gravity is represented by a constant con-sumption of the Aether, the electromagnetic sink-vortex

501

Aethro-kinematics APPENDIX II. The Cylindrical Sink-vortex

only exists around the conductor when the circuit isclosed and collapses upon disconnection.

In both cases the rotating Aether exerts a tangen-tial and a radial components of a force on a mass-parti-cle placed in the vortex field. The force is directly pro-portional to the chemical potential difference betweenthe poles. The vortex, centered on the wire, is the kine-matical cause of the circular magnetic field, and theAether circulation through the conductor-battery sys-tem is the driving force that carries the electron current.

Figure AII.-1

Keeping these in mind, the mathematical deriva-tion of some of Maxwell's Equations, like Ohm's, Biot-Savart's, Faraday's and Ampere's Law from the kine-matics of the cylindrical sink-vortex can be rendered asfollows:

Let us consider the kinematics of the cylindricalsink-vortex. The sink consumes a given amount offluid at a rate of Q/sec. A layer of fluid, dr, as shownabove, will be totally consumed during the timeinterval dt. The volume of this fluid is the area timesthe density, ρ of the fluid. In agreement withBernoulli's theorem the flow of the fluid toward thesink can be expressed by the equation:

ρ 2π r dr = Qdt ,thus, the radial velocity of the fluid particle towardthe sink is

dr Q VR = −−−− = −−−−−− ( 1),

dt 2π ρ r

where ρ is the average density of the Aether.From bernoulli's equation it follows that, the

pressure difference toward the center, dP = −ρ VR dVR

which also equals to Huygens' centripetal force

502


dr

r

CURRENT

FLUX

dP ρV dVF = −−−−− = − −−−−−−−

dr drsubstituting for VR from Equ.(1), we have

Q Q 1F = − ρ −−−−−− × −−−−−− (− −−− )

2π ρr 2π ρ r 2

and by simplifyingQ 2

F = −−−−−−−−− 4π 2 ρ r 3

From Huygens' law, it also follows, that the circu-lar velocity, VC required for this centripetal force is

VC2 Q 2

−−−−− = −−−−−−−−r 4π 2 ρ r 3

therefore Q

VC = −−−−−−−− ( 2).−−

√ ρ 2π r Let's consider now the layer of the circular sink-

vortex again.The circular momentum density is

Po = ρ × VC = ρ r ω,

where ρ is the density of the fluid and ω is theangular velocity. The total circular momentum of thelayer is

∫ Podl = ∫ ρ rωdl = rω ∫ ρdl = VC × 2π ρ r.Substituting V from (2) :

Q −−∫ Po dl = −−−−−−−− × 2π ρr = Q √ ρ ( 3).

−−√ ρ 2π r

For the sake of conceptual clarity of the furthermathematical derivation, the magnetic flux around thecurrent-carrying conductor can be compared to thehydrodynamic behavior of the vortex flow of waterwhen it forms a whirl-pool as it discharges through ahole in the bottom of a shallow tank. See Figure AII-2.

503


Figure AII.-2

x

∧

ρ ,U

Unlike the forced vortex which is caused by thetransfer of mechanical energy to the fluid from anexternal force (rotating bucket), in the case of anirrotational vortex, no outside energy is imparted tothe fluid and it rotates from some internal action.Since no torque is applied to the flow, the total staticand dynamic pressure energy should be constant. Toanalyze this type of flow the principle of angularmomentum may be used."In the case of an irrotational vortex, no outside

energy is imparted to the fluid and it rotates fromsome internal action. Since no torque is applied tothe flow, the total static and dynamic pressure ener-gy should be a constant. To analyze this type of flow,the principle of angular momentum may be used."The fact that the water surface itself lowers as it

nears the hole shows the increase of circular velocitytoward the centre. As the surface approaches the cen-tre, its elevation will fall rapidly and a funnel-shapedcore will be formed, drawing air at the centre. This mayalso be verified from Bernoulli's equation." (M.Ma-honar,P.Krishnamachar, Fluid Mechanics,1982. [127]).

We have assumed, that there is a circulation ofthe Aether inside the conductor and through the bat-

tery. Consider a section of the wire and for deriving thecirculation, use the following symbols :

∆P, pressure differencej, Aether flow intensity

inside the conductorρ, average density of

the Aether in spaceρ', density of Aether

inside the conductoru, circulation velocityS, cross area of wireL, the length of the

whole conductorI, the intensity of the

electric currentThen the following equation can be written :

j = ρ u × S (4),Thus, the drift velocity has a direct proportionali-

ty relation with the pressure difference per unitlength. Let k be the constant of proportionality. Then

∆Pu = k −−−−−−

L 504


u

S

ρ

ρFigure AII-3

′ρ

Substituting u into (1) , we have∆P

j = ρ u × S = ρ k −−−− × SL

∆P= −−−−−−−−−−

L /ρ k × S Since the pressure difference is equivalent to the

electric potential difference (Volt), V, thenV

j = −−−−−−−− (5).L /ρ k S

Compare (2) with Ohm's Law; where the electriccurrent, I inside the conductor directly proportionalto the potential difference, V and inversely propor-tional to the resistance, R:

V L I = −−−− where R = γ −−−−− ,

R S

and γ is a constant; the rate of the resistance of themetal.

It follows, thatV

I = −−−−−− (6).γ L/S

Comparing Equ. (5) with Ohm's Law, Equ, (6)shows that

1j ∝ I and γ ∝ −−−

ρ kwhere the constant, k represents the Aether circula-tion velocity under a unit pressure difference.Expressing the electric current intensity, I in termsof the drift velocity, u' of the free electrons in theconductor, we can write

I = enu'S ,e is the electron charge, n is the number density, u'is the drift velocity of the electrons. S is the cross-section area of the wire.

Since j ∝ I, it can be seen that the drift velocityof the electron current is directly proportional to theAether flow intensity (circulation velocity) and therate of resistance, γ is inversely proportional to thedensity of the Aether, ρ' in the conductor.

From the kinematics of the cylindrical sink vor-tex it is evident, that the flow intensity of the Aetherin the conductor is directly proportional to the rate ofconsumption, therefore

j ∝ Q or Q = k'j.505


Substitute this result into Equ. (3). then we have−−− −−−

∫ Podl = Q √ ρ = k'j√ ρ .

We already know that I is proportional to j, there-fore they can be made equal by a new constant as; I= k" j. Thus,

k' −−− ∫ Podl = −−−−− √ ρ I (7).

k"

By comparing with Ampere's Law,

∫ Bdl = µ ο I (8)

it can be seen, that Equ. (7) is identical to Equ. (8),therefore the circular momentum density of theAether in the sink-vortex is equivalent to the mag-netic flux, described by Ampere :

Po ∝ B .Thus, the hypothesis of Aether circulation in the

battery-conductor-system renders a consistent kine-matical theory, giving a conceptual foundation for themathematical derivation of Ampere's law in agree-ment with the related Maxwell's equation.

Another law of the electromagnetic theory that isincluded in Maxwell's fundamental equations isGauss' Law of the electric field intensity:

q∫ E . dS = −−−−− (9),

ε o

where E is the electric field intensity, S is the area, qis the charge and ε o is the permitivity constant.

Gauss' law is a different form of Coulomb's law ofthe electric fields around charged particles and ap-plicable to any closed surfaces. The most general caseof Gauss' law its application to the closed surface; asphere around a negative or a positive charge.

Both laws, borrowed from fluid-dynamics, areusing the concept of flux, as the property of a vectorfield, or as a uniform flow of a fluid with constantvelocity, v through a given point or area.

When the flux is originated by a source v is radi-ally outward, while if it is produced by a sink, v isradially inward. The electromagnetic parallel to thisis a positive or a negative charge respectively.

Thus, when Gauss' law is applied to the closedsurface of a sphere around a negative charge, it istaken as equivalent with a sink in an isotropic fluid,

506


producing a radially inward uniform flow, or flux,with a constant, uniform velocity, v .

As Figure AII-4illustrates, q is anegative charge, Eis the electric fluxflows through theunit area S, and ris the radius of thesphere.Since the area ofthe sphere, dSequals 4πr2, anequation can bewritten;

ε oE ( 4πr2 = qor 1 q

E = −−−− × −−− (10),4πεo r2

Now, we have seen that the rate of suction of asink is expressed by the equation:

2π r2 ρ dr = Q dt ,consequently

Q v = −−−−−−− ,

2π ρ r2

According to the fluid-dynamic analogy the flowvector, v is proportional to the electric flux intensity,E, therefore we can express the latter as the radialmomentum density of the fluid :

E = ρ v = Pand Q

∫ E dS = ρ v× 4π r2 = −−−−− × 4π r2 = 2 Q 2π r2

which is a constant and equivalent with q/εo .Compare this result with Gauss' law, Equ.(9). It

can be seen, that the two equations are equivalent.Hence, Maxwell.s first equation can also be derivedfrom purely kinematical concepts. This derivationproves that the electric field intensity is physicallyequivalent with the momentum density of the radialcomponent of the Aether flow toward a sink.

In general Maxwell's electromagnetic theory andits mathematical expression condensed into his fourfundamental equations are accepted by both classicaland modern physics as a coherent and logically con-

507


-q

dS

r

v E

Figure AII.-4

sistent description of all known electric and magneticphenomena. Nevertheless, there is an accepted ex-emption to this; a group of phenomena, called byMaxwell, the displacement current, which requires aspecific assumption which seems to be in direct con-tradiction with one of the fundamental principles ofthe electromagnetic theory.

As Van Nostrand's Scientific Encyclopedia [465]describes:"Consider a capacitor hidden in a 'black box' with

two terminals. Charging or discharging the capacitorrequires a charge flow, or current, in the externalconnections. Viewed externally, let a current of posi-tive charges flow into one terminal; the equal currentof negative charges into the second terminal appearsto be a positive current out of the second terminal. Itis logically awkward to think of a current into oneterminal and out of the other, that doesn't go throughthe box. Hence, to maintain continuity of current, a'displacement' current is postulated; in the capacitor,equal to the 'conduction' current in the external con-nections."This concept of displacement current was invented

by Max- well to simplify the mathematical equations

of electromagnetism; it led to the prediction of elec-tromagnetic waves."The displacement current is more than a conve-

nient fiction, as is indicated by the fact that the Biot-Savart law (of induced magnetic field) hold when thecircuit surrounds a displacement current as well aswhen it surrounds a conduction current."Part of the displacement current can be accounted

for as the movement of bound charges within thedielectric, i.e., the creation or reorientation of dipoles.The balance, which is exhibited even in vacuum, maybe better understood as quantum electrodynamics isfurther developed."

There is a well definable contradiction betweenthis idea of 'action at a distance' and one of the mostfundamental assumptions of the theory, that themagnetic field is induced by the motion of chargedparticles. This hypothesis originated from the empir-ical fact that the motion of the free electrons in a con-ductor always produce a circular magnetic fieldaround the wire. Based on this connection betweenthe electron current and the magnetic field, the ideahas been generalized as a causal relation betweenthe motion of the individual electron and the circular

508


magnetic field perpendicular to its motion. Thisindeed works in the case of the conduction currents,but cannot be applied to the situation within the''black box', where no charges are in motion.

Chapter Fifteen suggested an alternative de-scription of the electromagnetic capacitor and anAETHRO-KINEMATIC theory for the origin of elec-tromagnetic waves, but did not emphasized the roleof the cylindrical-sink-vortex in the explanation ofthe ambiguous concept of the displacement current.

Nevertheless, the above mathematical deriva-tions, based on the specific circulation of the Aetherin the differing electromagnetic systems, render anunambiguous kinematical explanation for all thevarious phenomena, including that of the displace-ment current. It shows the identical origin of the con-duction currents, the displacement currents, and theinduced magnetic fields around the conductor as thecombined electric and magnetic effects of the circu-lating Aether in the cylindrical-sink-vortex, which, ofcourse, also exists in vacuum.

Thus, through the mathematical derivation of theAETHRO-KINEMATIC theory of the correlativephenomena of electricity and magnetism there is no

need for the ambiguous hypothesis of an 'action at adistance' displacement current.

Consequently, through some more sophisticatedmathematics, − which is beyond the scope of thisstudy, − it may be shown that in the kinematicalinterpretation of Maxwell's Fourth equation; the lawof Ampere does not require its ambiguous extensionby the term of the displacement current:

Id = εο dΦE/dt ...

509


APPENDIX III.

DISCONTINUITY OUT OF CONTINUITY

In Chapter Sixteen under the heading of the Ulti-mate Universal Constant, it has been proposed thatelectromagnetic radiation is equivalent to a train ofcompression pulses created and propagated in theideal gas of Aether. Relative to the average isotropicenergy density of the medium, each individual pulserepresents a certain amount of excess momentumdensity in the direction of propagation which is aconstant for all frequencies and equivalent withPlanck's quantum of action, h.

This constant excess momentum density, carriedby a radiation pulse, originates from the characteris-tic compressibility of the Aether medium and its fun-damental value is the minimum sensible and mea-surable change in momentum density, or directional

action, superimposed on the isotropic energy densityof the free Aether. Thus, the origin of the quantum, h,and the problem of continuity and discontinuity is aproblem of Fluid Kinematics.

Appendix III. is an attempt to prove this hypothe-sis in greater details both conceptually and mathe-matically.

Because of the immense diversity of Natural phe-nomena, experimental physics must work with iso-lated systems and derive the rules and laws ofNature by simplification and generalization. In clas-sical Aero-dynamics one of such general simplifica-tions is that in the analysis of the fluid resistanceagainst the motion of a solid body, the fluid can betaken as incompressible. According to this simplifica-tion the fluid density and the resulting resistanceforce against the motion of a body can be taken as aconstant. The small density changes of the fluid, thatactually occur in front of the body are quickly dissi-pated with the speed of sound and therefore they arenegligible. It follows, however, that the simplifyingassumption of incompressibility can only be allowedin cases where the relative velocity is much lowerthan that of the speed of sound.

510

Aethro-kinematics

For example, the air resistance against the sub-sonic motions of airplanes can be calculated byNewton's law of hydrodynamic resistance, based onthe assumption of incompressibility. How- ever, closeto sonic or supersonic velocities produce resistance toa much larger degree due to the change in the densi-ty of the fluid in front of the airplane. In theseextreme cases the theory of compressible flows, i.e.,the theories of shock-waves, must be applied to calcu-late the resistance, using the ratio of the velocity ofthe body to the velocity of sound, and the theoreticalformula is called the Mach-number.

It has been established in Chapter Thirteen, thatthere is a straight forward analogy between the aero-dynamic Mach-number and the AETHRO-KINE-MATIC Lorentz Formula, both based on the ratio ofthe velocity of the propagation of disturbances andthat of the motion of a solid body relative to themedium. The increase in the resistance depends onthe ratio between the speed of the body and thespeed of sound in air, and the speed of light in theall-pervading Aether. When the relative velocity ofthe body approaches the propagation velocity of dis-turbances, it produces great changes in the density of

the media in front of the body and the retardingforces become extreme in both cases.

As a general result of this simplification, classicalphysics separates the analysis of fluid resistance intotwo groups; subsonic and supersonic phenomena andapplies two different conceptual and mathematicaltheories to explain and calculate them. In fact, it iscustomary to state that the division between the twomethods is at the 0.3 value of the Mach-number.Under that, air can be taken as incompressible, overthat, compressibility must be considered and the the-ories of shock-waves to be applied.

In the Aetherless electromagnetic theory of mod-ern physics this simplification, or the problem itselfare not even recognized. The familiar conception ofresistance has been unfamiliarized by the relativis-tic innovation of mass-increase. In special relativy'sempty space resistance has been described by thetwo equally mysterious and totally contradictory the-ories; Newton's constant inertial mass, and Ein-stein's variable mass-increase. Nevertheless, withregards to the extreme resistance against motionapproaching the speed of light, something similar tothe 0.3 Mach-ratio was established, stating that at

511

Aethro-kinematics APPENDIX III. Discontinuity out of Continuity

velocities under one third of the speed of light, therelativistic mass-increase is unmeasurable and atthat level the relativistic mass corresponds with theclassical inertial mass.

This ambiguous division of the two part of onephenomenon created a confusion even about the nor-mal resistance against the slow moving objects, sincetheoretically the factually existing effects of com-pressibility of fluids were to be neglected.

In the following this misconception will be elimi-nated and an alternative description of the phenome-non will be attempted;

The theoretical separation and the empiricalfacts are described by the following quote from VanNostrand's Scientific Encyclopedia [48] and by theschematic illustration of Figure AIII.-1.

"The flow pattern in a perfect incompressiblefluid is instantaneously influenced at all points bypressure changes occurring at any point in the flowfield. A consideration of the theory of elasticity asapplied to fluids, however, indicates, that the effectsof small pressure changes in a real fluid are trans-mitted throughout the fluid in the form of waveswhich travel at the speed of sound."

From all above, it seems that this phenomenoncannot be explained by either of the existing simpli-fied theories, since the slow speed of motion wouldcall for the incompressible flow theory, but the result-ing compression pulse clearly shows the compress-ibility of the fluid.

Thus, seemingly there is no explanation for theempirical fact that the uniform, continuous motion ofa body produces periodical compression pulses in anisotropic medium, which propagate away from thebody with the characteristic dissipation speed of thatmedium. Nevertheless, there exists a mathematicaltheory discovered by Riemann and elaborated byRankine and Hugoniot in the 1860-s, dealing withthe 'Origin of discontinuity in an Ideal Fluid' whichhas been initially formulated to describe the basicproperties of shock waves, but the final mathematicalconclusion shows that the theory is equally applica-ble to the origin of regular waves."Under certain conditions the nonlinear effects

result in the appearance of surfaces at which theflow variables, such as, the velocity, density, pressureetc., become discontinuous, even if the initial distur-bance of the medium was sufficiently smooth.

512


"The statistical inequilibrium takes on a particular,sharply expressed character near these discontinuitysurfaces and determines the complex structure ofshock waves." X.Y.'s 'Experimental Study of Shock-wave Structure' [3].

Describing the fluid-dynamical formation of aone-dimensional shock-wave generated by accelerat-ing a piston in small increments from zero velocity tosome final constant velocity, an article from Lerner-Trigg, Encyclopedia of Physics [1121] states :"The first infinitesimal compression of the piston

face results in the propagation of a sound wave.However, subsequent compressions at the piston facetake place with the material (medium) at higher den-sities and result in higher local sound speeds. Thisproduces a train of waves in which the first is at thespeed of sound in the undisturbed material and thelast, closest to the piston face, is supersonic. Becausethe last wave can catch but not pass the first, allwaves eventually coalesce into a single steep wave-front across which exists a sharp discontinuity inpressure, density and temperature. The width of thediscontinuity is generally a few molecular mean-free-path lengths."

From all above it may be conjectured, that thecharacteristic compressibility of a fluid and the re-sulting density changes even in cases of slowly anduniformly moving bodies cannot be simplified awaywithout loosing the values of these minute effects inexplaining some very fundamental phenomena.

Let us repeat the question again; what can be thekinematical reason for the empirical fact, that theeffects of small density increases or pressure changesin a fluid, caused by a uniformly moving body aretransmitted throughout the fluid in the form of wa--ves or periodical compression pulses instead of akind of continuous dissipation ?

As Figure AIII.-1 below schematically illustrates,an empirical fact. A blunt object, like a ball, movingslowly and uniformly in an isotropic fluid, due to theelasticity of the medium, produces periodical com-pression pulses which are propagated away from theobject with the speed of sound. Why?

For the sake of simpler mathematical analysis weshould concentrate only on a small section of the pic-ture; a one-dimensional planar portion of the movingbody and the medium. Thus, we might as well con-sider a piston moving in an air-filled tube with a uni-

513


form velocity, V from left to right and the small den-sity changes, produced in front of the piston are prop-agated away with the speed of sound, U, which isgreater than V.

Figure AIII.-1Let us assume that the piston moves from A to B

in the time interval t. Thus the distance AB that thepiston moved in time t equals AB = Vt. During thesame period of time the initial disturbance, or com-pression, propagates in the air with the finite velocityU. Therefore, the disturbance front will be at C and

the distance travelled by the compression will beequal to AC = Ut.

As Figure AIII-2.illustrates, it followsthat there will be alayer of air between Band C within whichthe density will behigher than the aver-age isotropic densityof the medium.

Thus, the distancein which the densityof air is effected is :

BC = Ut − Vt= (U − V)t.

Suppose now that the original air density is ρothen the total mass of the air between A and C is ρo ×Ut . But because of the motion of the piston thistotal mass of air is now compressed within BC andtherefore its new density, ρa is:

ρo × Ut = ρa × BC514


Figure AIII.-2

V

U

A B C

U

V

V

Vt Ut

ρa

ρo

ρo

2

1

= ρa × (U − V)t.

or ρo Ut ρa = −−−−−−−−

(U − V)t

ρo U= −−−−−−−

U − Vor ρo

ρa = −−−−−−−− (1)1− V/U

Note, that since both velocities are constant, thedensity increase does not depend on time.

In order to find out the density distributionbetween the piston and the front of disturbances(BC), let us examine two consecutive disturbance,created by an infinitely small further motion of thepiston. Let us call the first disturbance a, where theaverage density between the piston and the distur-bance front is

ρoρa = −−−−−−−−−

1 − V/Ua

where ρa represents the first infinitesimal density

change in the medium propagated with the velocityof sound, Ua.

It is evident from above that ρa > ρo .Considering the next infinitesimal move of the

piston, it can be seen that it is already moving in adenser layer, A and creates a further compression inthe layer, B. Therefore,

ρaρb = −−−−−−−−− .

1 − V/Ub

Substituting ρa into above from Equ.(2), we haveρo

ρb = −−−−−−−−−−−−−−−−−−−−−.(1− V/Ua ) × (1− V/Ub )

Since (1− V/Ub ) < 1, it follows that ρb > ρa >ρo .Thus, the distribution of the density-increase in

front of the piston is such, that the density of themedium is the greatest closest to the piston. Sincethe propagation velocity is proportional to the densi-ty of the medium, it also follows that from layer B on,the propagation velocity is supersonic; Ub > Ua.

As it is illustrated on Figure AIII-3 each subse-quent infinitesimal movement of the piston will pro-

515


duce a similar disturbance and because of the samereasoning, as above, the result will be that ρd > ρc > ρb

> ρa > ρo and Ud > Uc > Ub > Ua .

Figure AIII-3.Hence, there exists a progressive increase of den-

sity in front of the piston which gradually dissipatestowards the front of the initial disturbance. FigureAIII-4 illustrates a graph, drawn on the density, ρ asthe abscissa and the distance, x from the piston asthe ordinate values.

Since the propagation velocity is a function of thedensity, the same curve represents both the increasesof ρ and U.

From the equationof motion of anideal fluid and therelated equation ofcontinuity the fol-lowing conclusioncan be reached.We know that thefirst infinitesimalcompression at theface of the piston

is propagated away with the speed of sound.However, subsequent compressions happens in

fluids of gradually higher densities and consequentlythese compressions are propagated with higher andhigher supersonic velocities.

Evidently, each infinitesimal subsequent com-pression layer propagated faster than the one in thefront of it, thus it catches up with it but for the samereason looses its excess density and speed and there-fore can never pass it.

Thus, the two combined layers now catch upwith the next in front, and so on and on....

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ABC

V

D

ρo

ρb ρa

UaUbUcUd

ρcρd

x

∧

∧

ρ ,U

Figure AIII-4.

Analyzing compression pulses it is convenientand customary to choose a reference frame in whichthe pulse itself remain stationary while the fluidmove through it with the speed of propagation. Thetwo different methods are totally equivalent.

In our case, where the piston moves against thestationary medium. it is more purposeful to choose areference frame in which the piston and observer arestationary and the fluid moves toward the pistonwith a given velocity.

On Figure AIII-5. as the fluid moves to the leftwith uniform velocity, V, there will be a densityincrease in the fluid when it reflects at the wall of

the piston. This disturbance will be propagated awayagainst the flow of the fluid with the characteristicpropagation speed of the medium, U. From otherexperiments, the observer knows the value of U, andhe is also capable of measuring the flow of the fluidtoward the piston. Thus, he expects to measure thespeed of the compression pulse, as it propagatesaway from the piston and against the flow of thefluid as Ua = U − V.

From the facts that both velocities are uniformand finite, − as it has been shown on Figure AIII-2.− there will be a constant accumulation of excessdensity in front of the piston. However, Figure AIII-3.has also shown, that the propagation velocity in-creases in proportion with the increase of the densityof the fluid.

Let us call the infinitesimal increase in the prop-agation velocity in each consecutive density layer,∆U. Since the density is continuously increasing,within a certain time interval ∆U will reach the mag-nitude of V. At this instant, the observer will find

Ua = U − V + ∆U = U,therefore in his reference frame the flow of the fluid

517


(U V)

V

ρoρb ρaρcρd

ρo

- ∆U+

Figure AIII-5.

will gradually slow down and finally seem to stop,relative to the propagation of the of disturbances.Since the piston is in the same frame of reference, −for an infinitesimal time interval, − there will be noaccumulation of density in front of it, and all excessdensity propagates away from it by U. In otherwords, the last infinitesimal layer finally acquired adensity and a propagation velocity high enough toseparate it from the piston wall, taking all the accu-mulated excess density with it.

Figure AIII-6.The final result is, that, due to the increasing

propagation speeds of the consecutive layers, the

total compression caused by the motion of the pistonwill coalesce into a narrow pulse within a certainperiod of time and at some distance in front of thepiston. See the approximation of the schematiccurves of this evolution on Figure AIII-6.

It follows from the above argument that at thetime of separation, due to the forward transmissionof the highest density by U, for an instant the layerbehind becomes normal density and the whole proce-dure starts all over again. The piston starts collect-ing new compressions which, by the same evolution,eventually becomes another pulse.

This is then the kinematic birth of the discontin-uous excess momentum density that propagatesthrough space, superimposed on the average isotrop-ic energy density of the medium. It exists in air asthe periodical pulses of sound, we hear as a tennisball whizzes by, and it exists in the Aether, as thelimiting measurable action; a constant quanta ofexcess momentum density, carried by an electromag-netic compression pulses of light.

As it will be shown later these periodical pulses,created by the uniform motion of a particle in theAether, is equivalent with DeBroglie's pilot waves.

518


x

∧

∧

ρ ,U

THE BULK MODULUS OF THE AETHERThere are further consequences of the above

hypothesis. Once the density increases were all coa-lesced into a single compression zone and propagatedin the medium as a unit excess energy density, or apulse, Newton's laws can be applied to the mechanicsof the phenomenon.

In this case it is customary to choose a frame ofreference in which the compression zone remain sta-tionary and the medium flows through it with thenormal speed of propagation of disturbances, U.

Figure AIII-7. illustrates this view where the ver-tical lines represent a division of the fluid to equal'slices'. each of which contains the same mass. It alsomarks the distance each element moves in the undis-turbed medium with the velocity, U.

Figure AIII-7

A fluid element as it enters into the compressionzone will encounter a difference of pressure, ∆ pbetween its leading and trailing edges. So it will bedecelerated to a lower speed, U−∆U as it enters andaccelerated back to U, as it leaves the compressedzone. The resultant force acting on the element at theentry points, directed to the right has the magnitude

F = (p + ∆ p)A − pA = ∆ pAin which A is the cross-sectional area of a rectangu-lar tube.

The length of the element outside of the compres-sion zone is, U ∆t, where ∆t, is the time required forthe element to move past any given point. The vol-ume of the element is thus VA ∆ t and its mass is ρoUA ∆ t, where ρo is the average density of the fluid.The deceleration, a experienced by the element, as itenters the zone, is −∆ U/Ut. Thus, Newton's secondlaw, F = ma yields that the force

−∆ U∆ pA = (ρo UA ∆ t) −−−−−

∆ twhich may be written as

−∆ pρo U2 = −−−−−−

∆ v/v519

Aethro-kinematics APPENDIX III. The Bulk Modulus of the Aether

po popo ∆+ p

∆tv∆ tv

Compression pulse

v ∆t∆+ v( )

UU ∆-U U

Thus, the fluid that would initially occupy a vol-ume V = AU∆ t, now is compressed by an amountA(∆ U)∆ t = ∆V. Hence,

∆V A ∆U ∆ t ∆ U −−−− = −−−−−−−− = −−−−

V AU ∆ t Uand we obtain

−∆ pρo U2 = −−−−−−

∆V/VThis ratio of the change in pressure on a body, to

the fractional change in volume is called the bulkmodulus of elasticity, B. That is

B = − V ∆ p /∆V = ρo U2

Returning to the original analogy with the uni-form motion of a particle in the medium (Figure AIII-1.) it can be seen that the particle, just like the pis-ton, must move through a given distance in order tocompress a certain volume of the medium enough tocause a separation. Let us call this distance, s. If theparticle moves with velocity v, then the time interval,t between the formation of two pulses will be:

st = −−−−− .

v

Since s depends on the the average density of themedium, which is a constant, s itself is also a con-stant. Since t is the period of the cycle, it follows, thatan increase in the velocity of the particle will de-crease the cycle and the pulses will be produced at ahigher frequency, ν = 1/t. Therefore, the frequencyof pulse-formation for sound in air is

1 U ν = −−− = −−− ,

t λ and for the pulse-formation of electromagnetic radia-tion in Aether, with the propagation velocity, c, thefrequency is

1 cν = −−− = −−− ,

t λ where λ is the wavelength. Now, the velocity of theparticle is :

sv = −−−−− (2).

t In order to find the momentum of the particle, p

let us multiply its mass, m into Equ.(2)ms

p = mv = −−−−− (3),t

520


or in the Aethermsc

p = −−−−−−− (4) ,λ

The following should be noted before further dis-cussion:

Up to this point the mass of the piston was as-sumed to be infinite and the description was restrict-ed to the pressure exerted on the medium by themoving piston. It can be seen, however, that all theabove can be applied to a small particle, with finitemass, moving in an isotropic medium. In this case,however, the pressure of the medium on the particlerepresents a retarding force, equal in magnitude andopposite in direction to the force that the particleexerts on the medium.

From this point on, with respect to the force ofresistance, the analogy between the two media, airand Aether, cease to work.

The mechanism of air-resistance is understoodthrough the kinetic theory of gases and the mutuallyexerted pressure between the mass particle and thegas is based on the collisions between a solid objectand the solid atoms and molecules of the air.

The same interactions are assumed to be bet-ween a mass particle and the free Aethrons, as it hasbeen proposed in Chapter Eight and Thirteen.

However, the classical concept of solid mass is notadequate for the description of the interactionsbetween the electromagnetic mass and the ideal gasof Aether. In this respect an object, of even the dens-est and heaviest element, is merely acts like a meshwhen it moves through the Aether, because at thesame time, the Aether moves through it. Thus, thepressure and the resulting resistance force alsodepends on the density of the mesh. (Think of theresistance of a three dimensional steel mesh of vari-ous densities moving through water).

Hence, the resistance of the Aether against amoving mass particle and the resulting disturbanceproduced in the medium by the particle must bedescribed by the Lorentz Transformation as dis-cussed in Chapter Thirteen.

Recalling Equ.(13.6):Ro

R = −−−−−−−−−−− (13.5).−−−−−−−−

√ 1 − v2 / c2

521


where Ro is the Newtonian inertial resistance, R isthe total resistance including the fractional extra,produced by the increasing density of the Aether infront due to the velocity, V of the body, and c is thevelocity of light.

If R is the total resistance and Ro represents theinertial resistance of the mass then R − Ro = ∆R isthe fractional resistance of the Aether, caused by theinability of the finite propagation velocity to dissi-pate the density changes and therefore it is propor-tional to the ratio between the square of the velocityof the particle and that of the propagation. In everyrespect the Aether resistance is directly proportionalto the total mass of the material object in motion.

Accordingly, the greater the mass, and thegreater its velocity, the greater the compression itproduces in the medium. It also follows from this,that the accumulation of a compression pulse by alarger mass and/or higher speed requires less timeand shorter distance.

From the structure of Equ.(13.5) it follows thatall related quantities, like s, t, ∆p, ∆ρ, are effected bythe ratio of the ___________

Lorentz Formula : √ 1 - v2 / c2.

It can be seen from the above, that the momen-tum of the moving particle can be related to the fre-quency and wavelength of the train of periodicalcompression pulses that produced by the particlemoving in the Aether.

Therefore, if the momentum of the particle is pand the propagation speed in Aether is c, then thewavelength, λ can be expressed as

λ = λo√ 1 − v2 / c2 (5).

Recall Equ.(4). The momentum of a particle canbe written as

mscp = −−−−−− (4).

λtherefore

msc __________ msc __________λ = −−−−−− √ 1 − v2 / c2 = −−−−− √ 1 − v2 / c2

p mo v

Note, that the distance s, in Equ.(4) is inverselyproportional to m, which means that the product msis a constant, so is msc and that it has the samedimensions as Planck's constant, h.

522


h = energy × time= momentum × velocity × time= momentum × distance

msc = mass × distance × velocity= momentum × distance

Hence, msc can be taken as equivalent withPlanck's constant, h and writing the equation for thewavelength of a train of periodical compression puls-es, produced by the uniform motion of a mass parti-cle in Aether, in the relativistic formalism, we have

h h __________λ = −−−−− = −−−−− √ 1 − v2 / c2

mv mov

an identical equation to DeBroglie's relativistic equa-tion as he first proposed the theory of matter-waves,which was later abandoned by Schrodinger becauseof the difficulties to correlate relativity with thequantum theory.

One more derivation:a) The distance, s or Ut, that the pulse-front

moves in Figure AIII-2. also represents the total vol-ume, V of the affected medium.

b) We have found that the pressure difference, ∆ pthat is created in this volume of the medium isdirectly proportional to the mass of the particle.Thus, ∆ p ∝ m.

c) ∆V is the reduced volume of the medium in thecompression zone, which is inversely proportional tothe propagation velocity (U or c), because that repre-sents the ability of the medium to dissipate the localdisturbances. Thus, ∆V ∝ 1 / c.

Putting all these relations together, we have

∆ p msc = h = −−−−− = the Bulk Modulus of the Aether.

∆V

523


ABOUT THE AUTHOR

Steven Rado was born in 1920 in Budapest, Hun-gary. Within a year after graduating from 'ZrinyiMiklos real-gymnasium, in 1939, he and his brother,Laszlo were drafted by the Hungarian army. In thesame year, forced by Nazi Germany, Hungary de-clared war on the United States and transferred alljewish and half jewish soldiers into army-controlledlabor camps.

In 1941 Laszlo was shipped to the Russian frontwith the Hungarian troops to assist the Germaninvasion, and was never to return. Steven Radoescaped from his camp and as a half-jewish armydeserter, went underground, joining the Hungarianliberation movement. His graphic, mechanical, andliterary capabilities enabled him to strengthen themovement. Among other activities, through the cre-ation of a complete laboratory of document forging,he helped hundreds of Jewish and non-jewish re-fugees and deserters to stay alive and fight.

Surviving World War II. against all odds, in 1945he had found himself in a democratic Hungary, gotmarried and worked as a journalist, play-write andcommercial artist. His political and philosophicalessays appeared in leading newspapers and maga-zines. His play, The ‘Duel' was awarded by theHungarian National Drama Society.

In 1948, backed by the Russian army, a Com-munist dictatorship took over the government. Hisrefusal to join the party cost him his livelihood in alldirections. Black listed as a writer, he took up hand-weaving and subsequently became a power-loommechanic. He continued to write a secret journal; thistime an essay on 'The inherent contradictions in thetheories of Marxism and Communism'. Somehow, theCommunist Police had been informed about it, andonly the last minute burning of the manuscriptsaved him. Without proof he only had to survive fourmonths in the Communist jail.

In subsequent years he worked in a home-laborassociation making special textile products for stateexport, and once again joined the new undergroundliberation movement, this time against the Russianoccupation.

524

Aethro-kinematics

In 1956, during the days of the victorious Hun-garian Revolution, he wrote, designed, printed andorganized the distribution of the 'Liberation Daily' inthe form of thousands of silk-screened posters. Thiswas the only source of information for the freedomfighters of Budapest about the state of the revolutio-nary war against the Russian army and which coun-tered the lies of the Communist radio-broadcasts.

The revolution won, the Russian occupationalarmy surrendered and for two whole weeks Hungarywas again a democracy, eagerly preparing for elec-tion. Nevertheless, because of the lack of the pro-mised Western intervention, on November 4th, 1956,thousands of Russian tanks flooded the country andkilled the revolution and the revolutionaries.

On the 14th of that month, under his leadership,two truckloads of Hungarian Freedom Fighters ar-rived to a small border town, as ‘well documented’communists functionaries, presenting strict instruc-tions to the local officials to assist them in securingthe new Russian occupation.

On the 15th, at 4.15 A M. after 25 miles of walk-ing and crawling through the border among the Rus-sian tanks, 35 men, women and children kissed the

free land of Austria. Thus, miraculously, StevenRado, his wife, Lenke and his seven years old son,Adam arrived at Camp Kilmer, New Jersey on De-cember 11, 1956. He became a U.S. citizens in 1962.

From early studies of history, philosophy andpolitical science, he became ever more convinced thatthe gradual moral liberation of the people is a directfunction of the evolution of technology and thereforeindirectly depends on the level of understanding ofphysics. Hence, most of the free moments of his adultlife were spent on pursuing the accumulation ofknowledge and understanding of physics, and partic-ularly its modern perplexities, postulated by relativi-ty and quantum mechanics.

At the beginning of his American life, the lan-guage barrier, his age, and the financial burden ofstarting from scratch obstructed him from gainingan official college education. Later on the financialease of making a living rewarded him with plenty offree time to be self-taught, to think, to search andfinally to write an alternate solution to the conceptu-ally unresolved problems of physics in the form ofthe theory of AETHRO-KINEMATICS.

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Aethro-kinematics About the Author

rado, steven - aethro-kinematics - the reinstatement of common sense - an alternate solution to the...

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