a new light (repaired) 16 x 9 - a new light .pdf · einstein in 1905, is based on the observations...

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A New Light on the Expanding Universe

A different idea of what light consists of brings about an

altogether different view of how the Universe is put together, and how it functions.

Examining the consequences of the concept that the Universe is expanding into a fourth spatial dimension t a speed which researchers may have mistaken for the speed of light leads to an array of interesting differences from currently accepted theories of physics and cosmology.

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A New Light on the Expanding Universe Copyright 2010 All rights reserved Written and Published by Les Hardison Arinsco, Inc. 1682 Edith Esplanade Cape Coral, FL 33904

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CONTENTS Chapter 1 Introduction………………………….1 Chapter 25 The Expanding Universe…………5 The Problems with Modern Physics ...................................... 6 Hubble’s Constant and the Shape of the Universe ............. 8 The Age of the Universe ....................................................... 19 The Constancy of Hubble’s Constant ................................. 21 The Size of the Universe ....................................................... 25 Expansion into the Fourth Dimension. .............................. 27 The Conclusions Summarized .............................................. 29 The Expanding Universe as the Stage ................................. 36 Chapter 3 Special Relativity……………………37 Basis of Special Relativity Equations ................................... 39 Derivation of Equations ........................................................ 43 Special Relativity in an Expanding Universe ...................... 47 The Lorentz Reinterpreted .................................................... 49 Conclusions ............................................................................. 65 Appendix – The Lorentz Transformation .......................... 67 Chapter 4 A New Thory of Light………………75 What is really known about light .......................................... 77 Alternative Theory --- a Lightless Universe ........................ 83 Need for a Fifth Dimension ................................................. 89 Mathematical Restrictions ..................................................... 97 Wave-Particle Duality .......................................................... 100 Conclusions ........................................................................... 101 Chapter 5 Energy in an Expanding Universe..103 The Problem with Energy ................................................... 105 Special Relativity Energy Equations .................................. 109 An Alternative Theory of Mass and Energy ..................... 113 The Question of Potential Energy ..................................... 117


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Conclusions ........................................................................... 119 Chapter 6 Bohr’s Atom evisited………………121 Bohr’s Derivation ................................................................. 123 The Problems with Bohr’s Atom ....................................... 129 An Alternative to the Bohr Atom ...................................... 135 The Minimum Orbital Radius ..................................... 140 The Case for Redeced Velocities ........................................ 155 Notes on Planck’s constant ................................................. 155 Hot Hydrogen ....................................................................... 158 Outer Shells ........................................................................... 159 Heavier Atoms and Molecules ............................................ 160 The Helium Atom ................................................................ 161 Atoms Heavier than Helium ............................................. 1644 The Hydrogen Molecule ...................................................... 167 Nutshell Picture of the Hydrogen Molecule ..................... 171 Summary ................................................................................ 173 Chapter 7 General Relativity in an Expanding Universe......................................................................175 General Relativity…….………….………………….177 Gravitational Forces…………………………….…..187 Some Simple approximations ............................................. 197 Orbital Motion ...................................................................... 203 Energy Considerations ......................................................... 211 Comparison of Galactic and Local Times ........................ 215 Generalization to the three dimensional world ................ 229 Additional Energy Considerations ..................................... 233 Translation, Rotation and Orbital Motion ....................... 237 Conclusions ........................................................................... 241 Chapter 8 Planck’s Constant revisited……… .245 Conclusion ............................................................................. 253 Chapter 9 Heisenberg’s Uncertainty Principle255 Chapter 10 Schrödinger’s Wave Equation…….259

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Chapter 11 Electrostatics and ElectroDynamics……………………………267

Rotation of Electrons and Protons .................................... 269 Compensation for Swirl ....................................................... 275 Electron Orbiting Proton .................................................... 279 Electrodynamic Effects ....................................................... 285 Conclusions ........................................................................... 289 Appendix 1 Charge Deformation of the x – y Surface ... 292 Appendix 2 Vector Addition of Velocities ...................... 296 Appendix 3 “Offsetting” T Direction Vector ............................................................... 301 Chapter 12 Summary………………………….306

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CHAPTER 1

INTRODUCTION I have, for as long as I can remember, been disturbed by

the idea that light moves through empty space at “the speed of light”, or around 300,000 km per second, and that nothing can go faster. What is there, about empty space, which sets a speed limit for light? Or, if empty space doesn’t have the ability to limit the speed, what is it about light that sets its own limit? Finally, if light has this self-regulating character, what gives it the authority to limit the speed of travel of everything else, from physical bodies to the effect of gravitational attraction, to the same exact velocity?

When I retired from working as a chemical engineer some years ago, I found that I had time to think about these questions, even though they were not causing me any particular problem. But, one thing led to another, and I found myself questioning all sorts of things about the basic assumptions of current physics, at least so far as I am able to understand them.

I went back to the basics, when Michelson and Morley and others measured the speed of light in the late 1800s, and declared the measurement independent of the motion of the measuring equipment. Although their experiment has been repeated and refined, I found reason to question whether they were measuring the speed at which light passes through the vacuum of space, or rather the speed at which the Universe is expanding in a fourth dimensional direction which we can’t perceive. If it is the latter, the speed of light is really something altogether different. The concept of a Universe expanding into a dimension of which we know nothing changes everything.

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The Special Theory of Relativity, as proposed by Albert Einstein in 1905, is based on the observations of Michelson and Morley. The theory of Relativity has, of course, withstood the test of time, which means that the predictions based on the theory have been tested and found to be accurate. Again, both theories were evolved before there was clear-cut evidence that the Universe is expanding.

Special Relativity is one of the most insightful and useful ideas ever produced, and, like Newton’s concept of gravity and laws of motion, it is elegant in its simplicity and cohesiveness. However, elegance, simplicity and cohesiveness don’t necessarily mean it is the best depiction of the way the Universe behaves. Again, I would suggest some different interpretations of the conclusions of both Special and General Relativity.

It is hard for me to tell how much of my discomfort with the constancy of the speed of light, and with all of the succeeding physics based on it is due to fundamental problems with the theory, and how much is due to my lack of understanding. Never the less, I have forged ahead, and put together a picture of the Universe we live in which is compatible with the Universe expanding into a fourth dimension, in which the speed of light is in one respect infinite, and in another indefinable. It requires a completely revised definition of what light and other forms of radiation really are, and calls for changes in the picture of Bohr’s hydrogen atom, Planck’s constant, the Schrödinger wave equation, and so on.

In this book I will try to lay out the program that led me to wonder if the physicists got it right when, early in the 20th century they laid the basis for all of our marvelous technological progress. The theories of Maxwell, Einstein, Planck,, Bohr, and scores of others opened up the fairy land of relativistic h]physics, quantum mechanics, and showed us a picture of the Universe too large and complex to comprehend on one end of the scale, and too unimaginably small complex to comprehend on the other end of the scale.


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It is a beautiful picture, and one that has been useful beyond description.

On the other hand, it has also revealed some places where the pieces don’t fit together as neatly as it seems they should. I will start by describing some of these places, and the project I undertook a few years ago to try to figure out why they don’t fit, and what could be done about it.

I have made some, but not much, effort to keep the explanations simple enough that anyone interested in physics can follow them, but rigorous enough to make my case, using mathematics through differential and integral calculus. If this isn’t your cup of tea, you can skip over the equations, and assume that I have gotten most of them right anyway.

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CHAPTER 2

THE EXPANDING UNIVERSE

I have had trouble understanding some of the concepts accepted as the basis for modern physics, starting with the constancy of the speed of light. Much of modern physical theory is based on what has become axiomatic, that light moves through the vacuum of space at a constant speed, just as sound moves through a medium of constant density and elastic properties at a constant speed.

All or radiation physics, and the theories of what electromagnetic radiation is are tied to this basic “fact”. Questioning the constancy of the speed of light involves questioning much of modern physics, developed in the twentieth century, including the basic structure of the atom, relativistic physics, and quantum mechanics.

I have had some time to consider some of the problems which do not seem to be explained adequately by physical theory and have drawn several alternate conclusions. Some of the conclusions amount to heresy from the standpoint of modern physics. This rather lengthy book explains these conclusions, and how I arrived at them.

All of them have grown out of the notion that the three dimensional Universe in which we live is expanding in fourth dimensional direction. This paper is aimed at describing this expansion process, setting the stage for discussions of nature of light, the relations between time, space and radiation contained in Special Theory of Relativity, gravity and energy considerations in the General Theory of Relativity, and other subjects such as the Bohr model of the hydrogen atom, Planck’s constant, the Schrödinger wave equation, and Heisenberg’s uncertainty principle, which provide the foundation of quantum mechanics.

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THE PROBLEMS WITH MODERN PHYSICS Somr of the problems I have had are listed below.

1) If the Universe is expanding, as Edwin Hubble demonstrated, what is it expanding into?

2) Why should the speed of light in a vacuum be a constant? It is not like the speed of sound in air or water, which has a finite value (although not a constant one) based on the elastic properties and density of the medium through which it is propagated. There is no “medium” through which light is propagated in interstellar space. It doesn’t seem reasonable to me that nothingness should be able to impose a maximum velocity on light, nor does it seem that light, unlike anything else we can perceive, should choose an arbitrary speed on its own.

3) Assuming that light has, somehow chosen its own speed of transmission through empty space, what is so special about this choice that nothing can ever go faster? Presumably other things like electromagnetic and electrostatic attraction and repulsion, and even gravity are believed to be limited to the speed of light. It seems that there is some fundamental limitation at work that we do not understand.

4) If Einstein’s mass-energy equivalence relationship E=mc2 is based on the rest mass of matter, what is the matter at rest with respect to?

5) How does the curvature of space make massive bodies at rest tend to accelerate towards each other? I can see how the curvature of space around a massive star is sufficient to cause the orbit of a planet to bend around so as to give the impression that the planet is moving in a straight line, rather than an ellipse. However, it is difficult


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to understand how two bodies at rest with respect to each other can be influenced by the empty space around them in such a way as to cause them to accelerate toward each other.

6) How can elemental particles and photons change from physical bodies to waves and back again, as is suggested by various experiments with light waves and electron beams.

After considerable though, I have put together a picture of the Universe that seems to be consistent with the observations of the physicists, but which does not have the difficulties I have outlined. The picture is pretty bizarre.

Thinking about these things has led me to believe that perhaps Michelson and Morley and others after them measured something different from the speed of light when they did their experiments, and to suggest an alternative mechanism which would account for their measurements.

This leads to a completely different picture of the Universe, and the way physical things interact with each other. Michelson and Morley were not aware that the Universe is expanding, nor was Einstein at the time he advanced his Special Relativity Theory. It wasn’t until much later that Hubble advanced the evidence that the Universe is expanding, which, I think, provided the key to many of the mysteries.

My picture of the Universe, with a theory of how light is transmitted through the vacuum of outer space, and how gravity works, is quite different from Einstein’s in some basic ways, and has led me to question a great many of the accepted fundamentals of physics, such as Bohr’s concept of the structure of the Hydrogen atom, Heisenberg’s uncertainty principle, wave-particle duality, Schrödinger’s wave equation, etc.

I have tried to assemble this alternate theory of the Universe in several Chapters which involve starting with the question of how the Universe can be expanding, and proceeding to the question whether Michelson and Morley

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actually measured the speed of light in vacuo, or something else quite different.

If you are willing to accept my picture of the way the Universe is expanding, which is quite at odds with that of many cosmologists, you will have less trouble with many of the subsequent proposals.

HUBBLE’S CONSTANT AND THE SHAPE OF THE UNIVERSE

The following few paragraphs are aimed at explaining an

alternative model of the Universe, which seems to fit most of the mathematical relationships established over the past one hundred years.

The basic presumption here is that empty three dimensional space, which contains no matter has no properties of its own, but that the entire Universe containing the space does have limits and, therefore, a shape. The concept of space having no properties is not consistent with current physics, which assigns properties like permeability to empty space, and which populates volumes containing no matter with quantum mechanical events and species.

These characteristics of empty space are required to make some of the more complex theories consistent. For the most part, I have been able to maintain my position that empty space is simply empty, and has no properties other than that the direction of the flow of time differs from point to point. The behavior of matter, at least at the superficial level I have been able to master, can be explained without any reference to any other “properties” of empty space. The discovery that the Universe seems to be expanding, in that all of the galaxies are moving away from our galaxy at a speed that is proportional to their distance away from ours, was made by Edwin Hubble in 1929. It gives a significant clue as to the general shape and character of the universe. The speed of recession of the galaxies from our galaxy is proportional to


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the distance to the galaxy times a value called Hubble’s constant. This discovery gave a great deal of weight to the “Big Bang” theory of the origin of the Universe, as it suggests there was a time when all of the material in the Universe was at a single point, or at least in a very small volume..

It occurred to me that there is a possibility that both the special theory of relativity, based on the measured speed of light being constant in all directions, and the idea of an infinite speed of light, might both be correct if the Universe can be represented by a particular model which is suggested by the observation that the Universe is “expanding”.

It should be clear that the Universe cannot expand if there is nothing for it to expand into. For example, a sphere, which is a three dimensional body, has a two dimensional surface. It is possible for the two dimensional surface of the sphere, like the surface of a spherical balloon, to expand only because the sphere exists in three dimensions. There is no way the surface of the sphere could get larger if the universe in which it existed had only two dimensions. Similarly, our three dimensional Universe can only be expanding if there exists a four dimensional space for it to expand into. This fourth dimension would, of necessity, be a real, physical dimension, similar to the three ordinary spatial dimensions. The fourth dimension would be a spatial one, in which distances could be measured in conventional units, were we able to perceive it.

The configuration proposed is that our three dimensional universe behaves as though it were the three dimensional “surface” of a four dimensional hyper sphere. This is not really a departure from the commonly accepted notion of a curved space-time. In this model, the Universe has its center at the original location of the Universe at the moment of the “Big Bang”. The fourth dimension, which I have called the “T dimension” throughout this discussion, is presumed to be a real, physical dimension, which is measurable in length units, as are the three ordinary spatial

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dimensions. It is related to, but is not to be confused with, time, which will be discussed later.

This configuration is consistent with the origin of the Universe at the beginning of time as a Big Bang, with the matter moving outward from the starting point at a very high velocity through a fourth spatial, but time-like dimension. The reason for calling it “time-like” will, hopefully, become clearer as we go along. For now it is sufficient to note that with a substantially constant velocity of all of the matter in the Universe in the direction of increasing T, measurements of distance in the T direction from the time and location of the Big Bang would correspond with specific values of time.

It is extremely difficult to talk about or think about four dimensional systems, as we are limited entirely to functioning in three dimensions. We can imagine time as a fourth dimension by simply tagging on a fourth coordinate value onto the coordinates of a point in space, like this. “Barrington, Illinois, is located at 42º 6.29’ North Latitude, 88º 15.98’ West Longitude, 700 feet above sea level”, ( Three physical dimensions determine its unique position in space, relative to the earth) and to say we are talking about July 20, 2010 at 4:00 PM, with the latter as the fourth, or time coordinate.

However easy this may be in concept, it is impossible to represent graphically a point that is moving through three dimensional space and also passing through a fourth dimension. So, for most of this discussion, I am going to use an analogous universe (with a small “u”) when referring to a two dimensional analog of our three dimensional Universe (with the capital “U”.)

Figure 1 is a representation of the present universe (the version with two spatial dimensions, x and y, and a third, T dimension) where the physical Universe as we know it is represented by the surface of a sphere , which started with zero, or near-zero size at time of the Big Bang, and has expanded to its present size. As the current value of T has


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gotten larger, the values of x and y representing points on the sphere have also gotten larger.

Another way to think of this is to imagine in the x – y – T model that the x – y universe is defined as a spherical cross-section of the x – y – T universe formed by looking at all of the x – y points at a particular constant value of T.

In Figure 1, a coordinate system has been set up in the simplest possible way, with the origin at the point at which the “Big Bang” occurred, where x = y = T = 0.

The relationship between the points on the surface of

the sphere, time, t, and the T dimension can be represented by the equation:

2 2 2 ( )x y T f t . EQUATION 1

FIGURE 1

COORDINATE SYSTEM WITH ORIGIN AT THE BIG BANG

Thus, if

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)(2 tfT , EQUATION 2

then

022 yx , EQUATION 3

which represents a point at the origin at the present time, at what might be thought of as the North Pole of the sphere representing the universe.

Other values for ( )T f t give

2 2 2 ,x y r Equation 4

which represents circles equidistant from the origin on the surface of the sphere, or spheres in the real three dimensional Universe.

The real three dimensional Universe cannot be represented adequately. If it is assumed to be curved into the fourth dimension, as the two dimensional spherical surface is curved in the third dimension, we have no way of drawing a picture of it. It is, however, just as easy to represent it mathematically as it is to do the two dimensional analog, by simply adding the third spatial dimension.

)(2222 tfTzyx . Equation 5

In both of the above equations, t is a sort of galactic time,

a parameter which increases at an apparently uniform rate, and which has the same value throughout the Universe.

This absolute coordinate system can, of course, be used to identify any point in space and time explicitly by specifying two of the three variables, along with the time in Equation 1. Thus, we might currently be located at t = 13.712371836


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trillion years since the big bang. To specify the position on the surface of the sphere, in the two dimensional analog, we should have to choose an arbitrary point on the surface of the sphere as a reference point.

Although this coordinate system is a perfectly legitimate way of describing the Universe after the Big Bang, there are several problems with it. One is that it is inconvenient. It would be much simpler to describe the position of something in space relative to a coordinate system with the origin actually within conventional three dimensional space, rather than at a point like the origin in the above figure which is in a four dimensional space outside our present three dimensional Universe.

Another problem involves the differentness of the T dimension from the x, y and z dimensions. The model pictured in Figure 1 treats T the same way as the regular spatial dimensions.

When dealing with the geometry of the earth, it would be acceptable to assign a coordinate system origin at the center of the earth, and specify all locations with x, y and z dimensions relative to this origin, with the polar axis as the z direction, and two arbitrary axes in the equatorial plane as the x and y axes. There would be no difficulty from a mathematical or geometric standpoint.

However, there are some problems in that motion along the surface of the earth is relatively easy compared to motion perpendicular to the surface. Although the x, y and z dimensions are perfectly legal, it is much more practical to identify an origin on the surface of the earth, and to specify locations on the surface with two dimensions (latitude and longitude are no simpler than would be great circles in both directions) and altitude above sea level (or any other datum elevation).

For this reason, it is useful to assign a point on the surface of the Sphere representing the x and y dimensions of the Universe as the origin. The T direction is treated as the altitude above the surface of the sphere. T, like altitude above

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the earth, points outward at right angles to the surface of the sphere. Or, it might be assumed to be the direction from the original point of the Big Bang to a particular location on the surface of the sphere.

A convenient reference point is, of course, our present location. Measurements of distance, performed with a yardstick, or some other measuring device from this point, needs to have a pair of fixed coordinate axes to measure along, and these axes can be chosen at any arbitrary orientation through the present location. Thus, from the point of view of an observer at the reference point, the x and y axes stretch out to his right and left and in front and in back. The T axis points straight up from any point on the surface of the sphere. The surface of the sphere itself can be assumed to represent the region of space-time in which matter is located.

Alternately, it can be presumed to simply be the sum of all points in space (irrespective of whether there is any matter present at the points) at a distance, T, given by T2 = f(t) from the point of the Big Bang. We have yet to define the function that relates T to t.

The movement of matter through the T dimension is something that can only be determined with reference to the local direction of the T vector (which is identical with the direction of the time, or t, vector at the same point) of the observer.

At the observer’s location, the direction of the T or t vectors is the direction of his path as the time parameter increases. No observer has “access” to the direction of time at a different location. Of course, the sphere representing the real Universe is of enormous diameter and the differences in time between observers relatively close together are not easily discernable. So, we tend to think of time as being the same everywhere. This is absolutely true in the galactic sense, and the parameter t can be taken as identical for all locations in four dimensional space. However, we have no way of observing this directly.


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Because a real observer is limited to making measurements with respect to the three physical dimensions, it is reasonable to utilize a coordinate system where the x and y coordinates lie within the surface of the sphere, and the T dimension simply points outward at right angles from whatever reference point is chosen. An observer can only assess changes in time by observing changes in the position of physical objects in the three dimensional Universe which he believes to be moving at uniform speed with respect to one another.

FIGURE 2 COORDINATES THROUGH

PRESENT TIME AT OBSERVER'S LOCATION

The spatial coordinate origin and the axes can be

oriented in any direction from the observer. There is no reason to choose one orientation over another.

Using this coordinate system, x and y represent distances within the spherical surface to a point in question, and the T axis is always at right angles to the surface of the sphere

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representing the present galactic time1 at every point. The passage of time involves moving along the T axis, whereas relative motion of any point or body away from the observer at the origin represents the motion through three dimensional space, as this space, in turn, expands through the time-like T dimension.

The spherical shape is consistent with the assumption that Hubble’s constant is truly a constant with respect to spatial variables, and it does not matter which direction we are looking .when we determine the speed at which other galaxies are retreating from our galaxy.

From our point of view, at an arbitrary origin on the surface of the two dimensional sphere, we see the x and y dimensions stretching out away from the origin, but the T direction is incomprehensible to us, much as an ant crawling on the surface of a plain has no concept of the vertical dimensions above it. This picture is not altogether correct, but we will have to refine the model of the Universe somewhat before a clearer picture emerges.

This picture is consistent with the observation that the Universe is expanding, with each point in it appearing to be the center of expansion. Successive positions of the surface of the spherical Universe represent different successive galactic times. Movement outward along a radius at right angles to the x and y dimensions at the surface of the sphere (the “outward”, or T direction) always indicates the passage of time. The local “outward” direction, along the T axis, has the characteristics of a local time1 scale.

The transformation from the absolute coordinate system, with the origin at the location in space and time of the Big Bang, to a local coordinate system with the origin at an

1 The distinction between local time, observed which we

“experience” and galactic time, which is independent of the observer’s location, velocity, etc. is very important. For this reason I will use these terms in a special way, and italicize them to emphasize that they are my special terms.


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arbitrary point in time (such as right now) and location on the surface of the two-dimensional spherical analog of the real 3-D Universe (for example, at our present location) is somewhat complicated mathematically.

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THE AGE OF THE UNIVERSE The age of the Universe can be estimated from

measurements of Hubble’s constant, the rate at which astronomical bodies are receding from each other. Hubble’s constant was calculated by Astronomer Wendy Freeman recently as being between 67 and 78 km/sec per mega parsec. A parsec is 3.09*1013 km, so the value of Hubble’s constant is about:

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191043.2

1009.3

sec/75 xkmx

km km/mm-sec EQUATION 6

using Freeman’s value. Other calculations are only in rough agreement. According to Hubble's constant on the Internet. H is between 15 and 30 km/sec per 1,000,000 light years. A light year is 9.18 x 10+12 km. This calculates to .5 to .9x10-18 km/km/sec. NASA gives a somewhat larger figure of 50 km/sec/mega parsec, or about 1.6 x 10-18 km/km/sec. The website at

hhtp://imagine.gsfc.nasa.gov/docs/ask_astro/answers/971124x.html gives additional references.

Figure 3 shows a cross-section of the two dimensional x – y universe with the T direction taken as “up”. It shows the relationships involved in the definition and the measurement of Hubble’s constant.

If the radius of the sphere is taken as r, and the distance between our present position and a distant galaxy which is receding from us at a rate given by Hubble’s constant, the following relationships hold.

tHt

t

r

r

l

l

EQUATION 7

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This is basically the definition of Hubble’s constant (assuming for the moment that Hubble’s constant is invariant over space at any given time, but allowing that it may change with time.

When ∆t = 1 second, l = c, the apparent speed of light in appropriate units, such as 299,792.458 km/second, the official definition of a meter, and the value of Hubble’s constant, H, which is somewhere around 2.4x10-18 km/sec/km, the age if the Universe is given by:

HtHtt

t

1 EQUATION 8

Ht

1 18

1810*25.4

10*4.2

1

Seconds

EQUATION 9

FIGURE 3 GEOMETRY OF HUBBLE'S CONSTANT


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or about 13.5 billion years. The smaller values of H yield greater ages for the Universe, with the highest values on the order of 30 billion years old.

THE CONSTANCY OF HUBBLE’S CONSTANT The diameter of the Universe involves some

assumptions about how the expansion of the universe has proceeded since the Big Bang at the beginning of time. The most important one of these is the “constancy” of Hubble’s constant.

If one presumes Hubble’s constant is constant with respect to both space and time, the following conclusions result.

Equation 7 could be written:

lHt

l*

, EQUATION 10

or, in differential form:

lHdt

dl*

EQUATION 11

or,

dtHl

dl* . EQUATION 12

This can be integrated between time t = t0, the present, and t = t0 + Δt, or simply integrated using the open integral

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Hdtl

dl, EQUATION 13

Yielding

KHtl ln EQUATION 14

or

Ht Kl e . EQUATION 15

At

00, t l l , Equation 16

SO 0

01HtelK EQUATION 17

where: 0t present time, seconds

0l measured distance light traveled” in one second

and 0 0( )

1 0 0*Ht Ht Ht H t tl K e l e e l e EQUATION 18

or

)(

0

0ttHel

l 00 t

t

r

r EQUATION 19

This suggests that if Hubble’s constant were, in fact, a

constant (i. e., invariant with time) then the Universe must be expanding at an exponential rate.

This, in turn, suggests an anomalous situation, in which all the galaxies in the universe are receding from each other at velocities that are proportional to the distances between them, (which seems reasonable), but also at rates that are increasing with time. This does not seem reasonable, as it


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would require energy to accelerate them relative to one another, and there is no apparent energy source. Alternatively, we could give up the conservation of energy theory, when applied to the Universe as a whole, which doesn’t seem reasonable either.

What does seem more acceptable is that the galaxies are moving apart with a velocity proportional to their separation, but at a velocity which is not changing with time. That is, that Hubble’s constant is decreasing with time, and the rate of expansion of the Universe is actually slowing down in inverse proportion to the passage of time. This would be represented by the following equations.

Assume that Hubble’s constant, H is given by:

t

HH 0 . EQUATION 20

Equation 11 becomes

lt

H

dt

dl 0 , EQUATION 21

Or

t

dtH

l

dl0 EQUATION 22

And

KtHl lnln 0 EQUATION 23

0

000

H

t

t

r

r

l

l

EQUATION 24

If the age of the Universe is one over H, then H0 =1.

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After all of this rather round about calculation, it seems fair to conclude that if the Universe is expanding through a time-like fourth dimension with a constant velocity, Hubble’s “Constant” is, in fact the reciprocal of absolute time, and is a direct measure of the age of the Universe.

This makes sense. The galaxies, and in fact, all matter in the Universe, is moving apart, but at a velocity that is constant with time, simply because there is no force acting on all of the matter in the Universe to change the velocities in the T direction. Gravity (which shall be dealt with in detail later) does not counteract the expansion in the T direction, because gravity acts to draw massive objects toward each other in the three ordinary spatial directions, and each massive body on the surface of the x – y – T spherical universe is pulled equally in all spatial directions, but not at all in the direction of expansion of the Universe, the T direction. Gravity acting in the T direction does not have much effect, as the massive bodies involved are separated from each other by the diameter of the Universe.

If we presume that H is equal to 1/t, then the current value t is simply 1/H. This also implies that there is an absolute measure of time (“galactic time”), which is not dependent on the location or velocity of the observer. This is not consistent with Einstein’s concept of time, which will be dealt with in a later Chapter.


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THE SIZE OF THE UNIVERSE Because the apparent speed of light, c, is the distance light

appears to travel during the time the Universe expands in the T direction for one second, the geometry of Figure 4 indicates that if

l r

H tl r

, EQUATION 25

and

tclr , EQUATION 26

then

c tH t

r

, EQUATION 27

or

Hr

c . EQUATION 28

As

Ht

1 , EQUATION 29

ctr , EQUATION 30

and

H

ctfr )( . EQUATION 31

Numerically, this is

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kmr 2318

5

10*23.110*4.2

10*3 , EQUATION 32

which is on the order of 13,400,000,000 light years. The diameter would, of course, be on the order of 27 billion light years.

It is apparent that there are parts of the Universe that are unknowable to us, because they are so far away that, in Einsteinian terms, the speed of light is not as great as the rate at which the region is receding from us, so the light would never get here. A more straightforward argument is presented for this same point further on in this book.


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EXPANSION INTO THE FOURTH DIMENSION. From the foregoing relationships,

t

t

r

r

, EQUATION 33

it is possible to determine the velocity of matter in the Universe in the fourth dimensional, or T direction

c

H

H

c

t

r

t

rv

1

EQUATION 34

or, simply,

ctTr EQUATION 35 The radius r, is, of course, measured from the center of

the hyper-sphere outward, in the T direction. This is the basis for setting T = ct. This suggests that the three dimensional physical Universe is expanding through time with the velocity that is equal to the apparent velocity of light. This means that each and every atom of matter in the physical Universe has essentially this same very high velocity into the fourth dimension, which is a real, physical dimension, although not accessible to us.

An observer at the origin of our coordinate system on the surface of the two dimensional spherical surface is moving straight up in the T direction at velocity c. He has a velocity vector c in the T direction. An observer at any other point would disagree about the direction of the T axis if he could, in fact, see the overall picture, because the T direction would be “outward” from the central point of the big bang through a point on the spherical surface other than the origin. Of necessity, each physical particle or body in the Universe

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has its own unique direction of motion through the “time-like” T dimension.

Note that any point taken as the origin has a T direction that points straight up, regardless of whether this point is assumed to be moving with respect to any other point or object in the Universe. There is some question about the relationship between a particular point is space, and any matter that may be occupying the space.

For the present, it is convenient to presume that the space has no properties at all, other than the time direction assigned to it and its direction from the Big Bang origin (which is its x – y –z coordinates in our three dimensional Universe), unless some reason is found to assign other properties.

Thus the “velocity in the T direction” is presumed to the velocity of matter in the T direction. If there is no matter present, the T direction of a point in space will be assumed to be a vector in the T direction which is the same as the direction of time at that point, with a magnitude c.

This velocity in the T direction suggests that the “rest energy” of a physical body of mass, m, is

g

mc

g

mvE

22

22

0 EQUATION 36

This is at odds with the derivation by Einstein and others

of the classic E=mc2. The “g” term in my equation is so that the mass can be expressed in kilograms, the preferred unit of mass for engineers, rather than in Newtons, a unit more properly applied to weight. Weight is a force, and I will have more to say on this subject (with some difficulty) in the Chapters on General Relativity and on Electrostatics and Electrodynamics. Also, the factor of two in Equation 36 is not present in Einstein’s classic equation. This mismatch is handled during the discussion of electrostatic attraction and


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repulsion, in Chapter 11 and is believed to relate to the energy of the particles due to spin.

E=mc2 is the energy imparted to all matter by the Big Bang. There is nothing to slow it down, because “Gravitational Forces” (We shall get into why gravity is described as a “Force” later on, under General Relativity) all act in the three-dimensional Universe, and are at right angles to the outward velocity, so they have no effect on it. Also, the matter directly “behind” the outward vector is 2 x 13.4 x 109

light years away, on the opposite side of the physical Universe, so it doesn’t have much effect either.

So, the Universe is still chugging along, expanding outward time-wise, at pretty much the same velocity we got at the time of the Big Bang. There may be some slight slowing taking place, as the result of agglomeration of masses that originally had slightly different directions to their velocity vectors, in which the component of velocity towards each other was lost, resulting in a very slightly lower velocity.

My picture of the Universe is consistent with Hubble’s observation that the Universe is expanding, It is essentially the three dimensional “surface” of a four dimensional hyper-sphere which is growing in radius at a uniform velocity. Thus all points in space, and all matter in the Universe has an inherent velocity in the fourth dimensional direction which is numerically equal to c, the apparent speed of light.

THE CONCLUSIONS SUMMARIZED Here are the main conclusions I have drawn from this

model. Some of them have been explained in this Chapter, but others will remain to be dealt with in later Chapters.

1) The velocity of light is essentially infinite. It doesn’t

take any “time” to get from one place to another. There is no speed limit. Nothing can go faster than “the speed of light” because it would have to travel at infinite velocity to do so, which would require an infinite amount of energy.

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2) The perceptible universe is the three dimensional

“surface” of a four dimensional “hyper sphere”. It is expanding in the fourth dimensional direction at a rate equal to the “apparent speed of light”. It is this speed of expansion of the universe which is measured by experiments aimed at measuring the speed of light.

3) The expansion rate is essentially unchanged from the time of the Big Bang, at which time the Universe occupied a small space. The rate is not affected by gravitational forces between the stars and planets because the direction of the expansion is at right angles to the three perceived spatial dimensions. There may be some slowing of the expansion rate, but it is trivial at most.

4) Hubble’s constant is a measure of the rate of expansion of the Universe. It is numerically equal to the reciprocal of the age of the Universe, and is decreasing linearly with the reciprocal of the age of the Universe. Hubble’s constant is not constant with time, but the rate of change is very small relative to the present value.

5) The three dimensional Universe is many times larger

than the volume which is observable. The inability to observe all of it is not due to the “speed of light” limitation, but rather to the curvature of space through the fourth, time-like, dimension.

6) All matter in the Universe has a substantially constant,

uniform velocity, c, equal to the apparent speed of light, or about 300,000 Km/sec) in the direction of the fourth dimension. The “equivalency of energy and matter” is simply accounted for by the high inherent


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energy associated with the motion of all matter through the fourth dimension, E = mc2.

7) The fourth dimension is a real, physical dimension. It

is not time. Movement in this dimension is in some ways a measure of the passage of time, because the velocity in this direction is constant. The real, three-dimensional universe we experience is simply a cross-section view of the four-dimensional world, with the position of the cross-section defined as the present time. In this four dimensional space, time is a vector (more properly a tensor) which can be assigned an arbitrary unit length, but at any point in our three dimensional space, and at any position of our three dimensional hyper sphere, it has a direction.

8) Gravity is the result of slight differences in the

distance matter has traveled from the time of the big bang until the present time. Space containing no matter is farther, in the fourth dimensional direction, from the starting point than is space which contains a massive body. The result is a three-dimensional universe which looks flat to us, but which has depressions in the fourth dimensional direction which are proportional to the mass of the objects within the depressions. The depressions are basically shaped like hyperbolas. Because distance in the fourth dimension is at right angles to each of the ordinary three dimensions, the outward velocity vector, c, possessed by each mass, is tipped inward, because the time vectors are tipped inward, at right angles to all three normal spatial dimensions. The bodies tend to accelerate toward each other because the tipping becomes more pronounced as the distance between the bodies decreases. The relative accelerations of the massive bodies in three dimensional space obey Newton’s laws.

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This picture, although somewhat bizarre, is simpler than Einstein’s four dimensional tensor field equations and Minkowsky’s four dimensional space-time, with time having imaginary coordinates. The “gravitational field” assigned by General Relativity as a property of empty space is, in reality just a description of the direction of the time vector at each point in space. It is determined by the presence of matter in the space, and, in turns, controls the movement of matter through space.

9) Electrostatic and Electromagnetic attraction are

similar but more complex deformations of the three dimensional Universe in the direction of the fourth dimension. However, rather than being simple depressions in the fourth dimensional direction, they involve a twisting of the space around the direction of the time vectors in the fourth dimensional direction. This allows integration of the electrostatic and electromagnetic forces into the same pattern as gravitation, which General Relativity has failed to do. The electrostatic and magnetic fields, as well as the dielectric and diamagnetic properties of empty space are replaced by the pattern of time vectors, and no other properties need be assigned to empty space.

10) Light, and electromagnetic radiation in general, is neither waves nor particles (photons), but is actually the effects of direct transfer of kinetic energy over spatial distance and time by physical contact of the source and receptor atoms. Electromagnetic radiation is something of an illusion, created to account for the transfer of kinetic energy between atoms which are often far removed from one another in space and time. It is a very convincing illusion, which fooled Michelson and Morley and Einstein.


33

This direct contact requires us to consider the four dimensional universe wrapped up in a fifth dimensional direction, analogous to the layers of a four dimensional onion. This is hard to visualize, but makes a consistent story.

It explains many of the peculiarities of light, such as the wave-particle duality, and how electrons can behave as though they are waves under some circumstances. The dual slit experiment with either electrons or light rays can be explained in terms of the probabilities of contact of atoms on opposite sides of the slit, at slightly different times. The transfer of a quantity of energy from one atom to another requires that a number of conditions be met, which make the time of the transfer subject to statistical probability. Many of the complex optical phenomena such as interference patterns and refraction can be readily explained in terms of the statistical nature of the transfer between emitters and receptors which are proper aligned.

11) There are some problems with quantum mechanics.

Like relativity, quantum mechanics produces highly accurate and precise prediction of many physical quantities. However, it provides no explanation whatever as to what determines when an excited atom will “emit a photon” or a specific radioactive atom will decay. The best explanation consistent with quantum mechanical theory is that the basic elements of the Universe are probabilistic, and have no single value for position and energy at a given time, but rather a probability field, or wave function. The actual transfer of energy does not require a proximate cause. This kind of assumption is not required for the atom based on the properties of the Universe postulated here.

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12) Nils Bohr’s concept of the atom, and the more recent “electron cloud” models are not good representations of atomic structure. An alternative which is simpler and consistent with the above assumptions is presented. Bohr’s atom does not, for example, offer an explanation for what keeps an electron which is shared by several atomic nuclei in a crystal, and therefore can have no orbital velocity around a particular nucleus, from falling into the nucleus. A consistent picture of atomic structure which permits electrons in fixed orbits with essentially no velocity relative to the nucleus is presented. The model is applicable to heavier atoms than hydrogen and helium.

13) Planck’s constant is a measure of the radius of a five dimensional hyper spherical “kernel” around which the four dimensional universe is wrapped. A better basic constant would be H=hf2, where f is the frequency of rotation of an orbital electron, and H is a measure of the kinetic energy of the electron due to its orbital velocity. In my picture of the Universe, there is no form of energy other than kinetic energy associated with bodies having mass.

14) Schrödinger’s wave equation is not a description of the “Wave Function” relating to the likelihood of an electron or other particle existing as a pseudo-wave at a given spatial coordinate, but rather of the probability of an emitter atom and a receptor atom being properly aligned in space and time to permit the transfer of “radiant energy” from one to the other.

Some of these conclusions are a little far out, but they all fit together very nicely. On the other hand, the currently accepted physics based on the work of Einstein, Planck,


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Bohr, Heisenberg, Schrödinger and all the others, has had a tremendous amount of success in explaining physical phenomena, and I have not looked at a very large fraction of the positive results derived from their work. In those cases I have considered, my concept of the Universe seems to either produce the same answers as conventional physics, or answers that are more satisfying, but not, in my limited experience, any more useful.

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THE EXPANDING UNIVERSE AS THE STAGE The picture of the Expanding Universe describe here

sets the stage for the reconsideration of the basic physical assumptions that have gone into the measurement of the speed of light, Special and General Theories of Relativity, the development of Bohr’s model of the hydrogen atom, Planck’s constant and the basics of Quantum Mechanics.

I have tried to deal with each of these subjects in a separate Chapter.


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CHAPTER 3

SPECIAL RELATIVITY Albert Einstein wrote his paper on The Special Theory

of Relativity2 in 1905, when the world was concerned about the experiments of Michelson and Morley, in which they determined that the speed of light was essentially the same when measured in the direction of the earth’s rotation or at right angles to it. This seemingly inexplicable finding did not fit with the theory of propagation of light waves through "ether" using Euclidian geometry, wherein the measurements of distance and time were independent of the motion of the reference system. It seemed that the velocity of the observer should be subtracted from or added to the velocity at which light was moving through the “ether”, which was presumed to permeate empty space, and act as the medium for transmission of light waves.

There was no evidence that the Universe was expanding into a fourth dimensional void at that time, and no reason to suspect that the measurements of velocity could be anything different in kind from the measurement of the motions of physical bodies. This left a huge question as to why light could behave differently than Euclidian geometry and the presumption that light was conducted through a medium (like all other known waves) predicted it should behave.

Einstein found that the equations developed by H. A. Lorentz could be fitted to the results obtained by Michelson and Morley to account for a situation where the speed of light would be measured as an identical speed by observers moving relative to one another. However it required a new concept of

2 Zur Elektrodynamik bewegter Körper, published in the Annalen der Physik in German in 1905.

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time, wherein each observer had a special, separate time, different from that of each other observer that had a velocity relative to his own.

Also, it required a new definition of the word “simultaneous”, one in which events were “simultaneous” if light from those events reached the observer at the same time. In other words, time had something to do with the transmission of light from one place to another, and the velocity of light was a fundamental concept in defining what “time” meant. He went on to draw some conclusions about the relationship of matter and energy which proposed that they are, in a sense, interchangeable, and suggest that mass is a form of energy, or vice versa.

The conclusions derived from the Special Theory of Relativity were so astounding that little attention was paid to why things should fit together in the Special Relativity way. Nor were some of the puzzling aspects of Special Relativity questioned, particularly those relating time, space, matter and energy all bundled together.

I propose that the basic input information Einstein used --- the measured speed of light ---was not what it seemed to be at the time (and is still considered to be by most physicists). So, some of his conclusions are, likewise, not what they ought to be. In spite of this, the conclusions drawn from the Special Theory of Relativity have been well documented,, accepted as bedrock facts, and essentially all of modern physical science is built upon them.

I am aware that I am speaking heresies when I challenge some of the conclusions although most of them fit my framework as well as they fit into Einstein's. The exceptions have to do with energy and mass, which were are counted as the most significant aspects of the theory. Rather, I believe his remarkable insight was the introduction of the concept that time measured in one's own spatial reference system does not hold for other reference systems moving relative to one's own. With regard to the relationship between energy and


39

matter, I think he was on the right track, but took the wrong train.

BASIS OF SPECIAL RELATIVITY EQUATIONS The basic premises of the Einstein’s theory of special relativity are:

Light is very special, in that it moves at a constant high velocity, c, of approximately 300,000 km/sec, independent of the motion of the reference system for the measurements.

Any reference system, regardless of its velocity relative to any other reference system, should be as good as any other one, so far as measurements of physical characteristics of a system are concerned, as long as it is not accelerating.

From these premises, several conclusions were drawn: The measurement of the passage of time

made by two observers in moving relative to one another will differ depending on the relative velocity of the two. This is only important for observers who are moving at speeds which are significant when compared with the measure speed of light, so the effect is not noticeable in everyday life.

The velocity of an object measured by observers with reference systems moving relative to one another will differ in a predictable way.

The dimensions of an object decrease as its velocity increases toward the speed of light as determined by a “stationary” observer.

The mass of an object increases as its velocity increases toward the speed of light, as determined by a “stationary” observer

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There is an equivalency between energy and mass, which is the basis for nuclear energy.

The first three of these conclusions are accepted, pretty much without question, for, although the premise of the constancy of the speed of light at a finite value is not correct (in my opinion), the results come out mathematically correct anyway. Only the interpretation of the meaning of the equations is questioned.

The fourth and fifth conclusions are not, in my opinion, correct, and should be revised. This does not detract from the extraordinary insight shown by Einstein when he put them forward, any more than his theories denigrated the genius of Sir Isaac Newton.

Einstein’s basic equations did not lead directly to his most widely known conclusion; that the energy of a moving object is not simply:

2E mc , EQUATION 37

where E = Kinetic Energy

m = mass v = velocity but is rather:

2

2

2

1cv

mcE

EQUATION 38

where: c = velocity of light. This is the result of applying the law of conservation of

energy to a body which moved relative to the observer with a velocity v, and having a residual rest energy of E0. This leads directly to:


41

20 mcE , EQUATION 39

where: E0 = rest energy,

for a body at rest with respect to whatever reference system is chosen to make the measurements, and the value E is the measure of this same energy in a system moving with a velocity v, relative to the reference system.

The equivalency between mass and energy results from defining the energy required to accelerate a body from rest to a velocity v, relative to a fixed coordinate system, and accepting that the mass of the moving body increases with velocity. This is a straightforward derivation, once you have accepted the premises on which the theory was based, and the conclusions relating to the constancy of the velocity of light, c 300,000 km/second in a vacuum.

In Chapter, I put forward the notion that the speed of light is not the value usually assigned to it, but is, instead (in my opinion), infinite. What the experimenters who have measured "the speed of light" were, instead, measuring was the speed at which our three dimensional Universe and all the matter in it, is expanding into a fourth spatial dimension. I have used the letter T, for "time-like" to represent this dimension, or direction, as shown in Figure 4.

My proposition is that light does not take any time at all to move from one place to another, and that the radiant energy is transferred from one atom to another without passing through the space between the emitter and the receptor. The emission and the absorption of the energy are "simultaneous events" so the speed of light is essentially infinite. That is why nothing, not even gravity, can act faster.

If one accepts this notion, and that the matter in the universe is moving in the T direction (at right angles to all three of our x, y and z dimensions at the velocity c , then it is obvious that 2

0 mcE , or possibly 20 / 2.E mc

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I would like to proceed with this discussion by first going through the explanation of the equations derived by Einstein in the Special Theory of Relativity, presuming that his input information was correct. I will repeat the derivation using my alternative hypothesis, to show that most of equations are the same as derived via the Special Relativity route. Then I would like to point out the differences in the interpretation of the underlying meaning of the equations if my interpretation of the input data, rather than that used by Einstein, is the correct one.

FIGURE 4 TWO DIMENSIONAL ANALOG OF

THE EXPANDING 3D UNIVERSE

In some ways, I believe my interpretations might be

more to Dr. Einstein's liking than his own, in that they lead one to believer that there is an underlying reality to the physical Universe that is more straightforward and deterministic than that which the quantum mechanics advocates envision.


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DERIVATION OF EQUATIONS Before getting into the meat of this presentation, it is

best to review the equations which are the critical centerpiece of Einstein’s position, which was based on the Lorentz Transformation. I have had, since heaven knows when, but probably since my college days, a copy of the book by Albert Einstein titled Relativity.3 I based most of my representations of what Einstein said about things on his book, rather than on the original publications.

The Lorentz transformation is the basis for all of the Einsteinian relationships comprising Special Relativity. The derivation of the Lorentz transformation is reproduced here, pretty much as Einstein wrote it up in the appendix to Relativity. The derivation is carried out using the apparent velocity of light, c, as though light passes entirely through the three dimensional space continuum as a sound wave passes through air or water, and is consistent with the findings of Michelson and Morley and the assumptions made by Einstein.

This is represented by the sketch in Figure 5. Here, t represents time, and there is no representation that there is any physical analog of the graphical representation.

Consider the coordinate system with x (distance) positive to the right, and t (time) positive upward. The origin is at x=0, t=0, and the coordinate system is considered stationary. The basic premise of relativity is that the velocity of light must be constant whether observed relative to this coordinate system or any other arbitrarily chosen coordinate system moving at a constant velocity relative to the stationary one. This is what the Michelson – Morley experiments seemed to prove.

3 Einstein, Albert, Relativity, 1931 translation by Robert D. Lawson, University of Sheffield, of the original “Relativity”, 1916, Crown Publishing, New York, NY.

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Assume an alternate coordinate system with the origin initially at x = 0, but moving to the right at a velocity v relative to the stationary system. The location of any point x on the original coordinate system will have a corresponding location, x’ relative to the moving system.

FIGURE 5 EINSTEIN'S VERSION OF THE

LORENTZ TRANSFORMATION

The distance traveled by light in the x direction is presumed to be the same constant value when measured relative to either of these two systems. This is a fundamental assumption upon which the entire theory of relativity rests.

That is:

ctx EQUATION 40

for all values of x and t, and

'' ctx , EQUATION 41

for all values of x’ and t’.


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I am going to skip over the details of the development of the Lorenz Transformation, which can be found in the Appendix to this Chapter, and simply point out that Einstein was able to reconcile the observations of velocities of bodies from coordinate systems which were moving relative to each other, and the fact that the measurement of the velocity of light within any of the systems gives the same result as though the system were considered stationary, only by presuming that the two observers moving relative to each other would experience the passage of time differently from each other.

That is, each observer would consider himself stationary relative to his own coordinate system, and the observer moving along with the other coordinate system to be the one in motion. Each would think the clock held by the other fellow would be running slower than his own clock. In short, time slows down in systems that are moving relative to the observer.

How much time shrinks depends on the velocity of the other system relative to ours, and to a lesser extent on how far away the other system is:

2

2

2

'

1

vt x

ctvc

. EQUATION 42

This shrinkage in time is dependent only on the relative

velocity of the system when the distances are small, compared to the apparent velocity of light, so

2

2

'

1

tt

vc

EQUATION 43

is a good approximation for less than interstellar distances. The effect of defining time differently in coordinate systems

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moving relative to ours also causes distances to be distorted relative to what we would measure,

2

2

'

1

x vtx

vc

,

EQUATION 44

and also causes velocities of objects we observe to be moving relative to us to be lower that would be the case if the observation were made from the moving system.

2

2

'

1

vv

vc

.

EQUATION 45

Einstein asserted that, based on the above equations, and "energy considerations", the mass of objects moving relative to our reference system had to increase as their velocity increased, according to

0

2

21

mm

vc

.

EQUATION 46

This led to the equation for the total energy of the body.

2

2

21

mcE

vc

.

EQUATION 47

You can see from these equations why he considered it

impossible for any physical body to reach the velocity of light, c. In all of these expressions, if v=c, the denominator becomes zero, so the body would become infinitely heavy. It would appear to have an energy level approaching infinite, and time would appear to stand still as measured by a clock moving with it.


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To some extent, it was necessary to believe that these were actual physical changes which take place on objects which are moving at high speed relative to us, because they all seem necessary if one accepts the constancy of the speed of light and the shrinkage of time in systems moving rapidly with respect to our own.

This is inconsistent with the notion that any coordinate system could be used with equally valid results. So, if we imagine we are, ourselves, piloting the space ship which is moving rapidly relative to an observer on earth, we would find that we were not the ones becoming enormously heavy (not if we weren't accelerating at the moment, but that is covered in the General Relativity section) and our clock would appear to be working perfectly normally, clocks on earth would seem to us to be running slowly and things getting heavy.

SPECIAL RELATIVITY IN AN EXPANDING UNIVERSE

The remarkable thing about the Special Theory of

Relativity is that it produced such useful and precise results, even though the fundamental premise, the uniformity of the speed of light regardless of the reference system chosen to measure it, was a misinterpretation of the experimental data (my opinion, of course).

It is possible to repeat the development of the equations of Special Relativity without making either of the assumptions Einstein used:

1) Light is very special, in that it moves at a constant high velocity, c, of approximately 300,000 km/sec, independent of the motion of the reference system for the measurements.

2) Any reference system, regardless of its velocity relative to any other reference system, should be as good as any other one, so far as measurements of physical characteristics of a system are concerned.

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I will attempt to do this, but you should be forewarned that the equations relating space and time come out exactly the same. They are essentially the equations developed by Lorentz, and they apply equally well to the Universe I have depicted in which:

1) The velocity of light is infinite. That is, it is emitted and absorbed simultaneously.

2) )The Universe is moving in the T direction at the velocity, c, which is measured as the apparent speed of light.

FIGURE 6 THE PAST AND FUTURE IN AN

EXPANDING UNIVERSE

In Figure 6, the horizontal line in the center of the

picture represents the surface of the two dimensional sphere which serves as an analog for our three dimensional Universe. The vertical axis represents the T direction, so the universe is moving upward at velocity c.


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All the matter in the Universe shares this same velocity component.

The picture is drawn with all of the units measured as distances, such as km or miles, or alternately, all are measured in time units, where the T axis is measured in seconds and the x distances are in x'=x/c units such as light -years.

THE LORENTZ REINTERPRETED

The model of the Universe proposed involves two premises that are quite different from those used by Einstein. These are:

The speed of light is essentially infinite, in that the emission and absorption of light are substantially simultaneous, regardless of the separation of these events in space and time.

The matter in the Universe is all moving in a fourth dimensional direction at the velocity c, which is the apparent speed of light.

These premises, used with what is essentially the Lorenz transformation, lead to similar results, but with a completely different understanding of the meaning of the equations. The methodology is quite different.

One must revaluate what an observer "sees" as he looks at the world around him, from the origin of his own reference system, moving with him at the apparent speed of light in the fourth dimensional direction. Picture such an observer at the origin in the two dimensional analog of the three dimensional Universe in which we live, looking out into the world to his left and right.

When the observer at the origin of our two dimensional analog universe looks about him, he does not see objects arrayed along the x axis in either direction at the time depicted. Rather, his view is limited to objects located along the 45 degree lines at the boundary between the light gray

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Local Future, and the dark gray Local Past. This is his Local Present. Everything in his Local Past is out of sight, and will always remain so, as this area gets larger as the observer and the x axis move upward in the T direction. The objects in the light gray area will come into his view at later times. This includes all of the objects along the x axis, in either direction. His present will consist of the objects which lie along the lines A-C and A-B in the picture, which would be along the surface of a cone if both the x and y dimensions were depicted. In the three dimensional Universe, the cone, which may be thought of a as a collection of concentric circles of ever expanding diameter, would be replaced by a series of concentric spheres, each with its center at point A, and each representing a portion of the past from the Galactic standpoint, but comprising the observable present for the observer at A. This is the world we see and deal with every day.

Figure 7 is a repeat of the coordinate system with the observer at point A and a stationary object at point C, but an object at point B which is moving relative to the observer at A, and his coordinate system.

In Figure 7, an observer at point A would see a stationary object at point C, and have no difficulty establishing the distance by optical means (the object at point C can radiate in any direction, and the relative size of the object and intensity of the radiation will decease with increasing distance from A). At subsequent times relative to the moment shown, the relative position of C to A will not change.

However, presume that an object at point B is also visible at point A, but the object is moving relative to A with a velocity v. In this example, v is apparently less than ½ c, the velocity of all points in the T direction. What is the observer at point A witnessing when he sees the motion of point B? How will the observer at A measure the velocity of point B?

Because we have postulated that all matter in the real Universe is moving in the fourth dimensional, T, Direction


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with the velocity c, there are two interpretations which may be made.

1) The total velocity of each object, whether atom, planet of star, is c

, a vector quantity. The c

vectors

may be considered to be simply the scalar quantity, c, times the unit time vector, t

, at the point in

question. The c

vectors are not necessarily parallel with a central T axis. Any physical object may be chosen as the “stationary” reference, and the direction of the T axis through this point taken as the direction of expansion of the Universe. This object will have no component of the velocity c which appears as a velocity in the x – y – z space.

FIGURE 7 RELATIVE MOTION DEPICTION

Other bodies which have the velocity c which in not parallel to the reference T axis will appear to have a

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component of velocity in the three dimensional world we live in. However, it will appear to an observer that the velocity in the T direction is c, rather than a smaller component of c

. This implies that the orientation of

the Universe relative to the T direction must be different at points which have different velocities, and that the velocity, v

observed in the x – y – z Universe

is a component of the c vector. This would imply that

the total energy of a body is 2

2

mcE for all matter,

and that the energy associated with the velocity in the x, y, z Universe is a part of this total energy.

2) The velocity of an object, v

, which is observable in the x – y – z Universe is a vector which may be added to the vector velocity c of matter moving in the T direction, giving a total velocity which is greater than c

. This is consistent with the

conclusions of Einstein and the Special Theory of Relativity. The T directions of nearby objects would all be essentially parallel, but it should be recalled that where large distances are considered, the direction of all of the T arrows are perpendicular to the surface of the hyper sphere, as shown in and all point radially outward from the center of the Big Bang, in four dimensional space.

For reasons that may become clearer as the story develops, the first of these two options is the one which fits my prejudices best and is, in my opinion the most likely to be correct. It answers some of the questions I have always had relating to the differences between potential energy and kinetic energy, how anything can be considered to have a "rest mass", etc.

The question of how the observer at point A determines the velocity of a body at point B which is moving relative to his position requires some analysis. We have to define how


53

he can tell whether the object is moving, and what its velocity is.

Here are some of the factors in his observations. In his judgment (the observer at point A), he has no

velocity. He and his coordinate system are moving at the same rate through four dimensional space at the velocity c, which he cannot perceive because his reference system is moving along with him.

The passage of time can only be measured (or perceived) by the change in relative position of two or more bodies which can be "seen" at successive local times, t1, t2, t3, etc..

His view of the Universe away from his point of origin is not of the Universe as it exists "now" in galactic time, but rather as it existed in the galactic past, at times varying from a nanosecond ago for close by objects, to years in the past for objects located light years away.

Anything on the horizontal line (or portion of the great circle) representing the galactic present, lies at some point in his local future. He will not be able to "see" it until his local present has advanced to the point where he is connected to that location by a 45 degree line.

What he will see, when he advances far enough into the future to "see" an object which is not in his galactic present, will not be the object itself, but the image of the object as it was in the past by an amount equal to the distance in space divided by the apparent speed of light, c.

His perception of distance, measured perhaps by the brightness of light emitted from a known source (like a star) is accurate, but his measurement of time is dependent on the observation of changes in position of things not at the origin, and therefore not in the galactic time present, but instead in his local present, observed from point T4 on the T axis through the origin.

His perception of the velocity of movement of a distant object relative to his position will be different from that which would be determined by an omniscient observer, operating on galactic time, rather than local time, and also

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different from that of an observer with a different local time with a velocity relative to that of the primary observer.

It is of critical importance to his measurement of time that he know how much differently he sees the passage of time than would an observer moving with the object, or with any other reference system moving with respect to his own.

The observer must recognize that an observer moving with respect to his coordinate system has his whole view of the Universe influenced by the tipping of the T axis. He sees the passage of time paralleling his path in his own private, T' direction, and his x – y – z coordinate system tilted along with it. The moving observer's local present is tipped, in this case around the y axis, so his past, present and future all differ from those of an observer stationary with respect to the coordinate system

To an observer at the origin, at point T3 he observes the object m2 to be at a distance x1. If m2 is not moving relative to the origin, at time T4, the distance is still observed to be x1, and the velocity is calculated to be zero. The time interval between T4 and T3 is taken as

4 2( ) /T T T c EQUATION 48

In Figure 7, consideration is given to the differences

between the observation of time and velocity from a point at the arbitrary origin, and one some distance away, moving at a finite velocity of v with respect to the origin.

Assume that values without primes refer to the "stationary" origin as a reference and that the primes reference the same values but as observed for the moving object.

Point 2' is closer to point A than the original position, but it is not as much closer as it seems it should be. The observer reaching A's position T4 would not see m2 at this position, but rather would have seen it earlier, when he was only 2/3 of the way from T3 to T4.


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FIGURE 8 THE LOCAL PRESENT FOR A MOVING OBJECT

The measurement problem here is that, from the point

of view of an observer at point B, he is moving with the velocity c in the T direction, and is stationary with respect to his coordinate system, just as the observer at point A is. So, while he sees himself progressing in the T direction, it is his

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own T direction, not that of the observer at point A. Thus, he does not move the distance c Δt in A's T direction. Instead he moves only to point 2'.

.

FIGURE 9 MOTION FROM A TO B

Figure 10 shows the same area as Figure 8, but with the path of m2 traced through several incremental increases in time as its location changes from point 1 to point 2' and finally to point 3', where point B is moving closer to Point A.

Now, if m2 is moving toward the origin, the position of m2 at T3 is still observed to be x1, but at T4 the position has moved to point 3'. The distance moved is greater than the top leg of the lower gray triangle in Figure 10, which is

.x v t , EQUATION 49


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using for t the time scale appropriate to Point A, the "stationary" reference point, and keeping in mind that an observer moving along with point B would have an altogether different time scale. He would view this same time interval as

't . Point B would move, instead to point 2' in the time interval 't .

Point 2' can be "seen" from a point on the T axis, but not at T4, where point 2 is "seen". Rather, it would appear to be at an earlier local time. The location of point 3', where m2 will have to be before it can be seen from Point A at T4, can be found by constructing an infinite number of additional triangles, all similar to the lower one shaded in gray. This is illustrated more clearly in Figure 10, which shows a close-up of the area around point 3'.

FIGURE 10 DETAIL OF LOCATION OF A

MOVING BODY

In order to get the dimensions of the smaller triangles, it is necessary to note that the larger, gray-shaded triangles in

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Figure 9 are equilateral, and that the largest of these has c t as both the altitude and base.

The smaller shaded triangles can be used to determine that each is smaller than the preceding one by the ratio v/c, again using the time scale (for v) appropriate to point A's reference system, but not to point B's.

The next such triangle adds the incremental distance in the x direction which is in the ratio of the top side of the lower triangle to the right side. This ratio is

v

ratioc

EQUATION 50

The third triangle adds an increment equal to the second

one, again multiplied by v/c, and so on ad infinitum, yielding the infinite series

2 3

1 ...v v v

x v tc c c

. EQUATION 51

This series is easily recognizable as

2 311 ...

1a a a

a

. EQUATION 52

with

va

c , EQUATION 53

so,

1'

1x v t

v

c

, EQUATION 54


59

where 't is the time interval appropriate to the moving reference that has B at its origin. The moving observer sees his trajectory from point 1 to point 2' to be 'c t , and the distance from point 1 to point 2 as simply the component of

velocity in this arbitrary direction, which is 2 2c v . So,

2 2 'c v t c t , EQUATION 55

and

2 2 2

2

1

'1

t c

t c v vc

, EQUATION 56

which is the same result as obtained using the Lorentz transformation and assuming that the speed of light in a vacuum is constant, independent of the motion of the observer.

The velocity determined by an observer at point A is, by definition, v, so the velocity is simply the distance from point 3 to point 3' in the x direction, divided by the time interval the observer at B measures, which is the change in position T4-T3/c.

The observer at point B, with his coordinate system moving along with him, would have judged that he did not move at all, as his only motion was the velocity c, in what he judged to be the T direction.

Were the motion of B away from A, at the arbitrary stationary origin, the location at which m2 could be seen from A when it reached point T4 is as shown in Figure 11, the x = ct line connecting T4 to point 3', a position at which m2 can be seen , is again derived by adding the incremental triangles, as depicted in Figure 10

However, in this case, the successive approximations, represented by the shaded triangles in Figure 11 produce a series with terms which are alternatively positive and negative:

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FIGURE 11 OBSERVED MOTION AWAY

FROM THE REFERENCE

2 3

1 ...v v v

x v tc c c

.

This

series, similar to that of Equation 51, is easily recognized as


61

FIGURE 12CLOSE-UP OF SUCCESSIVE

TRIANGLES

EQUATION 57

Again, with

v

ac

EQUATION 58

1'

1x v t

vc

. EQUATION 59

This is exactly the same result that would be obtained

had we simply used the negative value of v in Equation 51. It should be unambiguously pointed out that the observation of velocities from a "stationary" reference system is never the same as the velocity which would be measured by an

2 311 ...

1a a a

a

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omnipotent observer using galactic time rather than the local time which must be used by any observer.

This indicates that from the standpoint of the observer moving with m2, time passes at a normal rate, while a stationary observer at point 1 would think his time progressed more slowly.

Were the object at point B, a measuring stick, one meter long, the location of the two ends would offer no problem were the measuring stick stationary with respect to the observer at A. He would "see" the two ends of the stick simultaneously, at his present time, and would see them each at a distance one meter apart. However, it is apparent that, if the measuring stick is moving relative to the stationary observer, the length of the stick would lie along the baseline for the moving system, which is tipped relative to the stationary system at an angle whose tangent given by

2 2 2

2

arctan arctan

1

vv c

c v vc

.

EQUATION 60 Thus the measuring stick would appear, to the stationary

observer, to be not one meter long, but rather

2 2 2

2' cos 1

c v vL L L L

c c

EQUATION 61

This foreshortening is also exactly the amount derived in

the Lorentz transformation. What remains to be dealt with in comparing the system

proposed here with Einstein's Special Relativity Theory are


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his conclusions about mass and energy. These seem much simpler in the crude system I have depicted.

In my view, all particles in the entire Universe, without exception, have a translational energy level

2

.2

mcE EQUATION 62

This is due entirely to the velocity of matter moving in the fourth dimensional direction as the Universe expands.

Bodies that are at rest with respect to our reference coordinates have this same amount of energy, and so do bodies which are in motion. The only difference is that bodies which are in motion relative to our own position have their direction of motion rotated slightly, so that a portion of their velocity in the T direction appears to us to be a component of velocity in the three dimensional world in which we can see it. It doesn't change their total energy at all.

In order to be in motion relative to us in our three dimensional Universe, an observer attached to the moving body would see the Universe tipped so that it is his T axis that is pointed straight up (at right angles to the normal x, y and z coordinate system we use), and that everything is perfectly normal to him. His clock runs at the normal rate, his lunch pail does not gain weight because his coordinate system is moving rapidly with respect to the star Proxima Centauri.

The whole concept of "rest mass" being the mass of a body which is "not in motion" is absurd when you think about it. It can't be a property of matter, because it depends on how you choose your reference system. I could demote everyone on earth to a much lower energy level by using a coordinate system centered on the sun, which would increase their kinetic energy enormously, but it certainly wouldn't change their total energy, so they would automatically lose weight!

Einstein went on to assert that as a body is accelerated, it increases in mass, according to:

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0

2

21

mm

vc

. EQUATION 63

Based on the assumption that Equation 63 represents the

true state of affairs, Einstein posited that the energy of a body is

2 22

2

2

21

mc mvE mc

v

c

. EQUATION 64

Of course, I don't believe this either. Again, is the mass

of my lunch pail based on my velocity with respect to the chair I am sitting on, or the velocity of my chair spinning through a 8,000 mile diameter circle every day, or the velocity of the earth around the sun?

I think he was wrong, and based his conclusions on c being a "magic number" which had no reason to have the value c, rather than something else. Of course, my c value, representing the speed of the Universe expanding into the fourth dimension, also has a little of the flavor of a magic number.

Then there is the matter of kinetic energy and potential energy, but I will deal with that inn a separate Chapter.


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CONCLUSIONS The equations of Special Relativity, which work quite

well, are for the most part, compatible with the hypotheses that:

1) The speed of light is essentially instantaneous, in that the emission and absorption are simultaneous events for any given observer.

2) The apparent speed of light is simply the measurement of the speed of the Universe through the fourth dimension, into which it is expanding.

The relativistic concepts based on the Lorentz Transformation, and having to do with the apparent differences in the passage of time in relationship to coordinate systems which are moving relative to each other, are no different for the universe in which light is not a wave nor a particle traveling through space, but simply a transfer of energy through an extra dimensional space.

The concept of "rest mass" and the energy associated with mass having something to do with the velocity of the mass relative to anything else at all is incorrect. There is no such thing as rest mass, and the total energy of a body is

given not by Einstein's 2

2

21

mcE

vc

, but by the much

simpler equation, 2E mc . The total energy is independent of the velocity, v.

The hypothesis that the mass of objects moving at very high speeds increases is entirely incorrect. In my view, they doen’t even appear to be more massive that objects stationary with respect to our coordinate system.

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The notion that the direction of motion into the T dimension is different between objects that are moving relative to one another, suggests that the orientation of normal 3D space is warped in such a way that the fourth dimension appears to be perpendicular to both moving objects, and in directions that are not parallel. This will be dealt with in more detail in the Chapter on General Relativity.


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APPENDIX – THE LORENTZ TRANSFORMATION

Consider the coordinate system with x (distance) positive

to the right, and t (time) positive upward. The origin is at 0, 0, and the coordinate system is considered stationary. The basic premise of relativity is that the velocity of light must be constant whether observed relative to this coordinate system or any other arbitrarily chosen coordinate system moving at a constant velocity relative to the stationary one. This is what the Michelson – Morley experiments seemed to prove.

FIGURE 13 EINSTEIN'S VERSION OF THE

LORENTZ TRANSFORMATION

Assume such a coordinate system with the origin initially

at x = 0, but moving to the right at a velocity v relative to the stationary system. The location of any point x on the original coordinate system will have a corresponding location, x’ relative to the moving system.

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The distance traveled by light in the x direction is presumed to be the same constant value when measured relative to either of these two systems. This is a fundamental assumption upon which the entire theory of relativity rests.

That is:

ctx EQUATION 65

for all values of x and t, and

'' ctx . EQUATION 66

This can be expressed as

( ) ( ' ') 0x ct x ct . EQUATION 67

Similarly, ( ' ') ( )x ct x ct EQUATION 68 and

)()''( ctxctx EQUATION 69

This is a little tricky, but it derives from assuming that if

x-ct = 0, then k(x-ct) = 0, and so on. Now, let

2

a EQUATION 70

and

2

b . EQUATION 71

Solving Equations 68 and 69,


69

bctaxx ' EQUATION 72

bxactct ' EQUATION 73

ta

bcx EQUATION 74

a

bcv . EQUATION 75

If the relative velocity of the two systems is v, and the

two systems are interchangeable (that is, if a measurement, K on one system appears as K’ on the other, the converse is also true.

At = 0,

'x ax bct , EQUATION 76

which reduces to :

axx ' . EQUATION 77

Two points which are one unit of distance apart on the

moving system of reference must be

)(1'' 1212 xxaxx EQUATION 78

or

ax

1 . EQUATION 79

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The same can be done with a unit distance on the stationary coordinate system. At 0't ,

'ct act bx EQUATION 80

reduces to

bxact , EQUATION 81

or

ac

bxt . EQUATION 82

Substituting this in Equation 76 to eliminate t gives

x

ca

cbax

ac

bxbcaxx

22

22

'

EQUATION 83

or

2

2

1'c

vaxx EQUATION 84

and

2

2' 1

vx a x

c

. EQUATION 85

2

2

11

c

v

a EQUATION 86

so,


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2

2

'

1

x vtx

v

c

EQUATION 87

2

2

2

1

'

cv

xcv

tt

. EQUATION 88

According to either reference system, light is propagated

according to

ctzyx 222 , EQUATION 89

or

022222 tczyx . EQUATION 90

Finally, the piece de resistance, the well-known

matter/energy equivalence equation

2E mc , EQUATION 91

which is the degenerate form of the complete equation

2

2

2

.

1

mcE

vc

EQUATION 92

Although Einstein was meticulous in describing his

derivations up to this point, he does not offer a derivation Equation 91, but rather states it as fact.

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This squares with the more common form of the equation which is usually written:

2

2 00 2

m vE m c .

EQUATION 93

This is derived from the expansion of Equation 92 via

2 31 1 1 3 1 3 5 1 3 5 7

1 ....2 2 4 2 4 6 2 4 6 81

a a aa

EQUATION 94

with

2

2

va

c . EQUATION 95

This reduces to 2

2

2

mvE mc ,

EQUATION 96

Equation 94 contains an infinite number of very small terms involving v/c to the fourth or higher power, which are neglected to yield Equation 96. This, of course, limits the generality of the approximate equation to conditions where the velocity v is significantly lower than c.

The whole point of the exercise was to demonstrate that the mass increased without limit as the value of v approached the apparent speed of light, so eliminating high velocities of v from consideration demonstrates the absurdity of the equation in the first place.

One can also approach the problem of

,F ma EQUATION 97


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with the relativistic increase in mass with relative velocity (this mass increase is not a necessary element in the relativism of my proposed cosmos),

0

2

21

mm

vc

EQUATION 98

where it is necessary to presume that this is the perceived increase in mass by an observer who determines the velocity v relative to his own "stationary" coordinate system, and assumes that light is, in fact moving at velocity c, so he has to presume that the mass is really increased over the rest mass of the body, although he has no way of determining this other than by his visual sightings of the body, using his own private clock to measure accelerations, etc.

The energy required to accelerate a body to velocity v (as determined by the observer) is found by integrating the force applied times the distance. Again, he has no way to measure the force other than by observing the acceleration of the mass, and no way to measure the mass other than by observing the acceleration.

2 2 2 20 0 0 0

2 2

1

1 1

x x v vdv v vE Fdx m dx m dv mc dv

dtv v c vc c

EQUATION 99

This integral is well known in the following terms

2 2

2 2

xdxa x

a x

, EQUATION 100

and the definite integral can be evaluated with a c and x v as

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2 2 20E m c c v c EQUATION 101

2

2 2 2

2

111

1

c cE mc mcc v v

c

EQUATION 102

Because c is a large number compared to 1, the first term in the numerator of Equation 102 can be neglected.

E= 2 2

2 2

2 2

11 1

1 1

cmc mcv vc c

This is the same as Equation 92, and suggests that if you

have assumed that mass must increase to prevent velocities from exceeding the apparent speed of light, you can use this assumption to demonstrate that it is a good assumption.


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CHAPTER 4

A NEW THORY OF LIGHT

The previous Chapter put forth the theory that the speed of light is not the constant 300,000 kilometers per second in a vacuum it is commonly accepted, but is, instead, infinite, and that experiments. which were conducted in the past to

FIGURE 14 LOCAL AND GALACTIC TIME FRAMES

determine the speed of light instead determined the rate of expansion of our three dimensional universe into a fourth spatial dimension

Each observer thinks of himself as viewing objects in a sort of universal, or galactic time frame, where all the objects in

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the three dimensional hyper sphere that share a common time. This is far from the truth of the matter, in that each individual observer has his own spatial coordinate system and "local universe" which consists of the things he can see simultaneously at any given moment. These things are all in the "galactic past" in that any visible body at a distance from him will only be visible at its present position at some slightly later time. For very distant bodies like stars, the light reaching the observer at his "present time" originated at the star years earlier according to galactic time. That is, far in the galactic past. However, the observer sees the star as it was in the galactic past as part of his local present time. He can see many bodies simultaneously, but all of them are at different distances from him, and all of them are in the galactic past, but in his local present time, as shown in Figure 14..

The bodies that make up an observer's local present time are all arranged such that there is no apparent time difference between them, even though they may be far apart in space and in galactic time. Everything he can see comprises a "simultaneous event", using Albert Einstein's definition of simultaneity Einstein describes simultaneous events as those which are seen by an observer at the same time. The mechanism of instantaneous transfer of light from a source to a receptor requires a different concept of light than that currently used by physicists. I would like to present such a concept, and the reasoning behind it. First, I will review the things that are known about light (and all other forms of electromagnetic radiation, such as radio waves, X-rays, etc.) The concept I am proposing seems to fit all of the characteristics in my list.


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WHAT IS REALLY KNOWN ABOUT LIGHT Light is a phenomenon which involves moving energy

from one place to another. We always think of light as moving from one place (a source) to another (a receptor, like the human eye or a photocell), and never of light as a stationary object or process.

The amount of energy associated with a beam of light depends on the intensity of the light, but the intensity is in turn, determined by how many “quanta” or “photons” are emitted. The quanta are all the same size for light of a given color (frequency), and the energy in each quantum is given by Planck’s constant,

hvE , EQUATION 103

where: E = energy in Joules h = Planck’s constant

ν = frequency in cycles per second. The value of h can be thought of as the amount of

energy transmitted per cycle of radiation, regardless of the frequency. I will have more to say about Planck's constant as the discussion progresses.

Light always has a frequency. In the visible light range of frequencies, this is the color of the light. The frequency is associated with a wave length, which is taken as

c

v . EQUATION 104

where: frequency, cycles/second wave length, meters

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This is, of course, presuming that light travels at “the speed of light”, around 300,000 km/second. In my approach, the speed of light is infinite, and the frequency is not associated with a real wave length, but may be assigned a wave length by dividing the apparent speed of light, c, by the frequency, as in the above equation. However, it is the frequency that is the important characteristic, and the wave length is simply assigned.

All forms of radiant energy transfer are presumed to follow the same rules as apply to visible light. All forms of radiant energy are presumed to use little packets of energy/matter, photons, to carry the radiant energy from the emitter to the absorber.

Light has polarity. This property is associated with waves, where the polarity indicates the way in which the waves are oriented about an axis in the direction of the light path. Polarity makes no sense at all if light is taken as discrete particles, or photons. Apparently, each individual quantum of light has its own individual polarity, but light can be filtered to block out all but a relatively narrow group of orientations, yielding “polarized” light. This adds a good deal of weight to the argument that light consists of waves, and the waves are transverse. Longitudinal waves do not have polarity. Transverse waves usually involve the medium of transmission moving back and forth at right angles to the direction of transmission, but, of course, for light there need be no such medium.

Light is always associated with atoms. There is every indication that light originates only by the movement of an electron in an atomic shell to a lower energy state, and that light is “received” only by the reverse process, or, for electrons already in a high energy shell, by dislodging the electron from the atom altogether (the photo-electric effect). This idea is strongly supported by the association of the emission spectra of stars with the emission frequency bands for hydrogen and helium.


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Apparently, the quanta of light involve exactly the same amount of energy for each cycle, regardless of the color or intensity of the light, and this energy is entirely independent of the nature of the source. This sets it far apart from sound or water waves, in which the amplitude of the wave covers a continuous spectrum and is essentially unlimited. Also, for sound waves, the wave is “coherent” in that all the energy in the sound wave is present in a single resonant pulsation of the medium through which it is passing.

Light has a phase angle. The “initiation time” or phase identity of light waves is ordinarily chaotic when many quanta are emitted by a source, in that the individual quanta, emitted by individual atoms, come out at random times. Lasers are able to emit coherent light, with the phase angles of all the quanta in synchronism. Again, the phase angle property tends to be very confusing when the light is thought of as a stream of photons.

Light is directional. The direction of emission of a particular quantum is also likely to be a random thing. However, when it is emitted, it always moves in a single direction. A piece of sodium heated in a flame emits light of a characteristic frequency, but emits it in all directions. Each quantum of light, though, moves in a single direction.

Light can be emitted from crystals in “coherent” form, where the waves comprised of individual quanta are all lined up with identical initiation times, identical wave lengths, and identical or nearly identical directions.

Light does not require a medium of transmission as light passes freely through a vacuum. Although light is transmitted through many transparent substances, such substances are not required. It seems to simply appear at a receptor without having had to be passed along from one point to another in the intervening space.

In this respect light is most unusual. It is also remarkable that a quantum of light arriving from a distant star seems to contain exactly as much energy as would a quantum of light from a nearby source. There has been no attenuation or loss

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of energy to the medium, unless one counts the red shift in the light reaching us from very distant stars. With most other wave forms, the medium of transmission absorbs some of the energy being transmitted, and results in relatively large attenuation for transmissions over long distances.

While the inverse square law holds for the total light reaching a receptor from a single source, this is accounted for by the photons having to be spread out over a larger receptor area when the receptor is far away. Each individual photon arrives at the receptor substantially un-attenuated.

Light is refracted when it passes into a medium other than a vacuum, and from one medium to a different one. The refraction is directly proportional to the difference in the “speed of light” in the two media. The light always bends toward the normal to the surface with the slower speed.

When a light beam consists of two or more colors (frequencies), the shorter wave length (higher frequency) is bent more than the longer wave length. This is the reason prisms separate colors in a beam of white light. The speed of light in dense matter must, therefore, be different for different wave lengths of light. This is quite revealing. First of all, because a vacuum has absolutely no effect on the speed of light related to color, and secondly, because the process of refraction, which must involve absorption of light in atoms of the refracting medium, and then reemission in the direction of propagation of the light, must be frequency dependent, somehow.

The index of refraction is equal to the speed of light in the first medium divided by the speed of light in the second medium. The speed of light in the medium is equal to the reciprocal of the square root of the product of the permeability and the permittivity. Thus, a vacuum must have a permeability and permittivity to be consistent with Maxwell’s equations, even though there is nothing there to have any properties. Quantum physicists have overcome this problem of empty space needing to have properties by


81

populating empty space with “quantum energy” which has the needed properties.

The direction of the light travel is random except under unusual circumstances. However, the direction has some way of preserving itself when light is conducted through a dense medium, for example. Also, the polarity, or angle the light makes with respect to the path of motion, is random unless there is something to cause it to be aligned one way or another, like passing through polarized glass, where only the properly aligned light waves are transmitted, and those at other angles are absorbed.

Light beams form interference patterns when their frequencies are close to each other. This is one of the strong arguments for the light consisting of waves.

When decreasing intensities of light approaching one quantum per unit time have the opportunity to pass through two slits in a screen, they will be obstructed completely, or go through one slit or the other, as would an electron beam. This is a strong argument for light consisting of photons, or particle-like entities.

The photo-electric effect, where a light beam shining on a photo-electric material causes emission of electrons when the frequency of the impinging light exceeds a threshold is another argument for light consisting of photons, rather than waves.

There may be other properties of characteristics of light which I have omitted, but these are all that I could think of. I do not believe I am in error in stating that there has never been a satisfactory description of light that makes sense of all of these diverse characteristics. Particularly for the wave/particle duality of light.

So, I will attempt to provide one.

Les Hardison

82


83

ALTERNATIVE THEORY --- A LIGHTLESS UNIVERSE

I will propose a theory as to the basic nature of light that

will account for all of the diverse properties described, including the apparent conflicting properties associated with waves and particles. I believe the reason light seems to have such a perplexing combination of properties, such as sometimes behaving like a particle and sometimes like a wave, is that light is simply an illusion created by our senses to account for the transfer of energy.

Figure 15 shows two electrons in the in the x – y – T analog universe, separated in distance in both the x – y plane and in the T direction, which indicates a separation in time.

FIGURE 15 TRANSMISSION OF RADIANT ENERGY

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The electron at Point 1 has a higher energy level (associated with higher orbital velocity) than the electron at Point 2.

Could it be that the electron with energy in excess of the base state at point 1 physically exchanges it with the second electron at point 2 by something akin to direct physical contact?

If this were the case, there would be no “light” transmission. No “radiation” would pass between the emitting electron and the absorbing electron except the kinetic energy itself. An exchange of orbital velocities of the electrons in the emitting and the receiving atoms would be accomplished without any radiation at all.

The emitter would be unable to get rid of its excess energy unless there were an absorbing electron with a lower energy level in exactly the right time and place (i.e., somewhere along the line 1 - 2, and at an integral number of distance units, which will be defined later). This would account for the problem that has puzzled physicists for many years regarding what determines when an excited electron will emit a photon, or when an atomic nucleus will decay.

The thing that determines when this will happen is simply when there is a suitable receiver for the energy at one of the infinite combinations of appropriate time and place so that the exchange can take place.

The transmission of energy from an atom containing an electron in an excited state to one which is in a lower state of excitation might occur in several ways. The very simplest of these is that the emitting electron does not actually collide with, or come into proximity with the receptor electron at all, but rather that the atom which has an electron in an excited state simply donates that electron to the atom which is in a lower state of excitation, and receives the less excited electron in exchange, keeping the electrical balance neutral, and avoiding any requirement that the two electrons ever have to approach each other, in spite of their extremely strong


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electrostatic repulsion. The energies and momenta of the electrons involved would be unchanged.

The quantum nature of “light” would have to do with the fact that the electron kinetic energy levels are limited, and the energy could only be emitted in quanta sufficient to account for the change in kinetic energy from one permitted state of the orbiting electrons to another permitted state. The wave properties would have to do solely with the characteristic rotation of the electron around the nucleus, which has polarity, frequency, phase angle and specific energy content.

The notion of a limited number of permitted orbits of electrons around the nucleus in an atom was introduced by Nils Bohr, who developed a very elegant theory of the atomic structure of the hydrogen atom.

He theorized that there were only certain orbital radii for the electrons in an atom, and that each established a unique velocity, and therefore energy level for the electron. I will deal with this subject in considerable detail in a later Chapter. However, for now it is sufficient to say that the discrete energy levels the electrons can have accounts for the discrete quantities of energy involved in the transfer of radiant energy from one atom to another.

All of the statistical measures assigned by Quantum Electrodynamics would be involved with the probability of the transfer of energy taking place between two atoms at a more or less statistically random time, when they happen to line up. The great puzzle of QED has been, “How does the atom know when to give up the photon after it has become excited?”

The theory predicts the probability of it happening within a given time frame, but can find no proximate cause for the emission when it actually occurs. There seems to be nothing special about the time when it happens. The physicists involved with Quantum Mechanics have, as far as I can tell, given up worrying about the proximate cause of emissions, and simply accept that there is none. It is

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completely random. They even go so far as to say that if no one observes it, it may not happen.

The same situation occurs in the radioactive decay of a nucleus of a Uranium atom. The half-life is well known, and it can be predicted with a high degree of precision that exactly half of the atoms in any given large sample will decay within the half-life. Yet for any one atom, it may remain stable for a thousand years, or only a second.

The reason for the apparently random transfers of energy is simply that they occur when an emitting atom and a receiving atom are lined up exactly right in space-time to permit “radiation” to occur. This means that they must both lie on the “x = ct” line, have an integral number of distance units from each other, and have the proper alignment and orbital frequency of the electron pair. These conditions are easily achieved for the simple transmission of ordinary light energy, and difficult for the high energies involved in nuclear decay.

The transmission of light in a complex way, such as, for instance, sunlight shining through a prism, and separating into many colors, which are reflected off of a white screen and received by receptors in our eyes, suggests an incredibly complex set of circumstances coming into play. On the other hand, all of the things we (I am using this in the royal sense. What I really mean is “I”) understand to be true of light are consistent with this interpretation.

It seems to me that the paradox of the double slit refraction of light, wherein individual “photons” seem to go through either of two slits, and not both at the same time, yet when there are many photons, they form interference patterns, can be explained by the probability of having receptors lined up just right on the receiving end, which is different when there are two slits available instead of one. This experiment has been one of the strong points in arguing that electrons exhibit wave-like characteristics, yet the phenomenon can be better explained by probability distributions, than by the electrons turning into waves.


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How can the emitter and receptor atoms which define the ends of a “ray of light” be defined to line up just right? They would have to lie on the 45 degree line on the T - x diagram representation used for a two dimensional analogue of the three dimensional Universe, expanding through into a fourth spatial dimension, T.

With x , y and T dimensions all using the same units,, the path of light from a source would be a cone with a 45 degree angle, composed of circles with the radius equal to x at a distance ct from the origin. There is an additional condition relating to the specific distance between the source and receptor. The source and receptor must be at even multiples of a distance that relates to Planck's constant, that will be defined when we talk about the basic configuration of the hydrogen atom and other atoms.

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NEED FOR A FIFTH DIMENSION The transfer of energy by direct contact between a more

energetic atom and a less energetic atom located at a substantial distance in space, and at a substantially different time, requires that the points in space must somehow overlap each other. This can be accomplished by the space being bent around, through an extra-spatial dimension.

The time-like dimension T, is such an extra spatial dimension, and it is not inconceivable that somehow the three normal spatial dimensions x, y and z, are, along with T, wrapped up in such a way that various sets of x, y and T points are in direct contact with other points at different times. However, it is clear that in order for the four dimensions discussed so far to be bent or warped or rolled up, there must be at least one more dimension besides the four we have been working with.

If this model is to have any significance, it must be configured such that points which line up properly can act as emitters and receptors of the energy transfer we recognize as light. Such points may be far separated in time and distance, but if they lie on top of one another in a closely wound cylinder, the windings of which have no ‘thickness” at all, they can behave as though they are in essentially the same place at the same time, so far as the x, y, z and T dimensions are concerned.

They can transfer energy directly without having to rely on the existence of a medium between them. The model would have to be configured in such a way that the properties of light described in the previous section will all be accounted for without paradoxes more serious than those involved with the wave-particle/duality encountered in quantum mechanics.

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F

IGURE 16 WAVELESS TRANSFER OF RADIANT

ENERGY

FIGURE 17 ROLLING UP THE X –T PLANE


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circle around the center of the cylinder. It is apparent that these points can overlap on a cylindrical piece of paper formed by rolling the paper up starting from the upper right hand corner, and rolling it up as though around a cylindrical core with a circumference equal to the spacing of the time interval lines as shown in Figure 17. It is apparent that the rolling up process requires bending the x - T plane in a direction at right angles to the plane and therefore at right angles to the x and T directions. The direction is definitely not the y or z direction. This apparently requires the presence of a fifth spatial dimension, at right angles to the x, y, z, and T axes.

In Figure 16, light originating at x0 at t = t0 would appear to traverse a distance c∆t in the time ∆t, arriving at x0 after the time interval ∆t, even though the energy transfer from point x0 to x1’ was essentially instantaneous, or rather involving no time at all, as the two points lie on adjacent turns of the cylinder. Thus the points x0, x1’, x2’, x3’, x4’ and x5

can be considered to be the same point, in both time and space. The only way in which they differ is that they maintain their sequence.

The energy is transferred from x0 to the closest point of the xn series which is capable of receiving it. It seems axiomatic that light energy always passes from the past to the future, and never the other direction. This is, perhaps, an alternative way of defining the direction of time, or suggests that time is, in fact, a vector quantity. It may be assigned an arbitrary unit, such as a second or a year, but in addition, it has a direction, and the direction is not the same for points in space moving relative to one another.

Several things are remarkable about this configuration. As long as the picture is confined to a single x spatial dimension and the time-like T dimension, the cylindrical wrapping of the universe around a cylindrical spindle works well. Not only does it provide that all points on the light path emanating from x0 lie directly over one another, but also all of the possible light paths from other emission points along the

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x axis also line up with each other, so the analog would work perfectly for the emission of light from any point along the x axis, and for any time in the past, present or future.

FIGURE 18 ROLLING UP THE X - T PLANE

COMPLETED

The cylinder would, of course, have to have a staggering number of turns to encompass the known life of the Universe, from the time of the Big Bang to some far distant future, as yet undefined.

In addition, to be consistent with the picture of the Universe as a hyper sphere expanding in the T direction, the x axis has to circle the entire diameter of the Universe as a great circle, and close back on itself. The length of the cylinder would have to correspond to the length of a great circle around the “spherical” x – y – T surface which does not even hint at the magnitude of the length or number of turns comprising the cylinder.

Because the plane is “rolled up” along a centerline that is 45 degrees to both the T axis and the x axis, both of these axes come out as lines which spiral around the cylinder. In the configuration shown in Figure 19. The x axis spirals around with the positive direction to the right, and the T axis,


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at right angles to it, spirals around with the positive direction to the left.

While point x traversed a distance equal to c∆t, represented by a short distance along one “turn” of the winding, the light went from x0 to x1’, in no time at all, but appeared to get there in ∆t . What is more important, the fact that all of the points on the path of light were in adjacent windings means that they were in physical juxtaposition, and could exchange energy, and perhaps even electrons, directly without the need for any intervening photons, or light rays or any electromagnetic radiation whatever.

FIGURE 19 THE X - T PLANE ROLLED UP

Figure 20 shows how the x – T universe could be rolled up in both directions at the same time, so that both the x=ct and x=-ct light paths would be wound around a single sphere, on which the points representing potential light receptor points would lie on circles, now around a sphere, rather than a cylinder but there must be a fifth spatial dimension available. Obviously, if the x and T axes are in a plane which has curvature in a direction at right angles to both of them, the direction in which the plane is bent must be the y or z directions, or a fifth, as yet un-named direction.

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Because it is necessary to account for light moving through space-time with reference to both the y and z dimensions, as well as x, it seems to require rolling up in two directions.

FIGURE 20 ROLLING UP THE CYLINDER

It takes a big stretch of the imagination to picture this same process being employed to roll up a three dimensional solid (the model of the universe with x – y and T coordinates) the same way. It would not be difficult physically if the T dimension were considered to be a real dimension, because what we are rolling up is really mostly space, which doesn't get stretched, wrinkled of squished when deformed. It is just very difficult to visualize.

Taking this one step further, imagine a model of the four dimensional Universe where the three normal spatial dimensions and the time-like T dimension are all wound


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around a relatively small hyper sphere with all the regular dimensions on the "surface" if the fifth dimensional kernel.

FIGURE 21 THE X – T PLANE WRAPPED AROUND THE X – T – U KERNEL

The important thing about this bizarre construct is that all of the lines representing possible lines of sight are superimposed on the hyper sphere as straight radial lines, pointing outward from the center of the hyper sphere. They are all positioned in such a way that direct energy transfer can take place from the orbiting electron in one atom to the orbiting electron in another atom far away in both time in space, but at a position that is "simultaneous" with all other positions along the line. This is shown in Figure 21 for the x – T plane wrapped around the fifth dimensional "kernel". Wrapping more dimensions around the kernel can't be depicted, but can be imagined.

In Figure 21, the electron and proton in a hydrogen ion are shown at essentially the same position on the x – t kernel. This was done purposely, but in order to understand better how the transfer of energy from one atom to another can take place, it will be necessary to consider the possible

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construction of simple atoms, using the approach applied by Nils Bohr, but with some modifications. This will be done in a subsequent paper.


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MATHEMATICAL RESTRICTIONS To look at the picture in a more mathematical way, one

could write the equations relating the positions of points in the x – y –z Universe with the T dimension and points on the fifth dimensional kernel like this:

22 2 2 2 2 2r x y z T N r ,

EQUATION 105

where r0 is the radius of the kernel. This makes the points line up when

22 2 2 2x y z N r

EQUATION 106

and

0T , EQUATION 107

or conversely, when

2 2 2

1 0x y z N r

EQUATION 108

and

2 0T N r EQUATION 109

Where: N, N1, N2 = 0, 1, 2, 3...

0 Orbital radius of H atomr

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All of the points in space which satisfy either or both of these two conditions represent the locus of simultaneous events when viewed from the origin at x = y = z = T = 0.

Points which do not satisfy these conditions are "out of sight". That is, they are, according to the observer's local time, either in the past, or the future, or in the present, but in the spaces between those points which are visible. There will be more to be said about such "invisible places" later.

Because we cannot picture the five dimensional space, and are stuck with setting y and z equal to zero to squeeze in the T axis on the surface of the sphere, we get a situation where points along the line of sight down in the x direction only line up when

0* 2x xx N r N r EQUATION 110

or

0* 2T TT N r N r EQUATION 111

which is to say, when

0 0x T Nr ct Nr EQUATION 112.

If N = 0, this gives the diagonals along which light seems to pass in Figure 16 viewed at the present moment in local time. Other values on N represent light paths in the local past or future. Thus, it is apparent that each point on the surface of the kernel represents a point in our three dimensional space at a particular time, and the remainder of the entire universe which can be seen at this point and this time.

For now it is sufficient to propose as a model of the Universe a three dimensional hyper sphere, expanding at the apparent speed of light through a fourth spatial dimension,


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with all four of these spatial dimensions wrapped around a kernel in yet a fifth dimension.

This model puts all of the points which are properly related to each other by space and time to appear at one single location on the surface of the hyper sphere, where the orbital energy of the electrons (or possibly the electrons themselves) can be exchanged between the emitting and absorbing atoms without any intervening electromagnetic waves or photons. These things have simply been defined to account for the results which we see continually, and for which we have no other completely rational explanation.

The energy might be considered to be passing, not through the intervening three dimensional space between the emitting electron and the absorbing electron, but rather through the fifth dimension short-cut.

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WAVE-PARTICLE DUALITY The apparent wave/particle duality has been an enigma

since it was discovered that radiant energy transfer is limited to discrete amounts of energy. It suggested that there was a packet, or particle, called a photon, involved. Experiments often emphasize this duality, such as the double slit experiment which shows that a single "photon" must go through either one or the other of the two slits like a particle, but that when there are many photons, they make interference patterns, which the light to consist of waves. This is easily accounted for in terms of the requirement that there be an alignment of emitter and receptor and that the statistical probabilities of these alignments happening will produce the "interference patterns” when there are two slits and many possible emitters and receptors.

The emission of energy from an atom is not a random, statistical thing which has no proximate cause, as the quantum physicists teach, but is, simply a process which requires the proper positioning and alignment of an atom with an electron at a high energy level with one at a lower energy level with regard to both space and time. This is the proximal cause of the emission of a "photon" of radiation, or a gamma ray from a radioactive atom.


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CONCLUSIONS Light, as we perceive it, consists neither of waves nor of

streams of particles (photons) but is, instead the result of the direct transfer of orbital velocity of an electron in one atom to another atom located at a distance in both space and time from the first. Out perception of light as “passing through space at a fixed speed” is simply based on the analogy with physical bodies, which do not move from place to place without crossing the intervening distance.

It is not possible to tell if the electrons involved in the transfer of “radiant energy” simply exchange their velocities, or if the electrons themselves switch places. Because all electrons appear to be identical in properties, it does not make any difference which mechanism is involved in the transfer of energy.

The process of transmission of energy by radiation requires a fifth, extra-spatial, dimension, which permits atoms at different places in the ordinary x, y, z Universe, and at different times (T coordinates in the fourth, time-like spatial dimension) to come into direct contact with one another.

The transmission of energy in this way accounts for all of the properties observed for light, such as frequency, polarity, discreteness of the quantities of energy transmitted, etc. It also accounts for the mechanism of transmission of light at essentially infinite speed (that is, allowing the emission and reception of the energy to be simultaneous), which provides a logical reason why nothing can go faster than the speed of light.

The transmission of radiant energy by this mechanism is entirely consistent with the modifications to the Theory of Special Relativity which presumed that the “speed of light” in a vacuum was infinite, in that the emission and absorption of radiant energy are “simultaneous” events when measured in

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an observer’s local time system. This will be discussed in greater detail in a subsequence Chapter1.

The apparent wave/particle duality enigma has a simple explanation. Radiant energy transfer does not involve either waves or particles (photons). It is a process wherein the electrons orbiting the emitting atom and those orbiting the absorbing atom exchange energy by direct contact. The energy levels which can be attained by the electrons orbiting the nuclei of hydrogen and heavier atoms in the innermost shell are limited to discrete levels, and it is this limitation which accounts for the discrete energy levels associated with the transfer of energy by “radiation”.

There is no such thing as a photon. This suggests that perhaps some of the other particles physicists have invented without being able to “find” them, such as gravitons, are similarly mythical.

The emission of energy from an atom is not a random, statistical thing which has no proximate cause, but occurs when an atom with an orbiting electron at a high energy level becomes properly aligned with one of a lower energy level. This can only occur if both the positions in space and in local time are exactly right. It appears to happen at random because have insufficient knowledge of the positions of the emitter and possible receptors atoms.

The quantum energy values associated with the emission of radiation are restricted by limitations on the orbital velocities of the electrons, which was not dealt with in this Chapter, but will be discussed in The Bohr Atom Revisited.

Schrodinger's Wave Equation isn't a wave equation at all, but a probability function, and will be discussed in detail in a separate Chapter

The whole of quantum mechanics is a misinterpretation of physical observations, just as the "measured speed of light" was.


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CHAPTER 5

ENERGY IN AN EXPANDING UNIVERSE

The Special Theory of Relativity, as proposed by Albert Einstein in 1905 has been accepted as the bedrock of modern science. It introduced the concept of space-time, where the Universe is described as four dimensional, rather than three dimensional, and proposed relationships between space, bodies occupying space, and light, which is used to determine the positions and velocities of objects relative to each other. Over the past 100 years it has proven an invaluable tool, and is accepted as literally true.

Despite its usefulness, I have some concerns about the way the world works as described by Special Relativity These have led me to propose a somewhat different way of looking at these relationships. Mainly, the differences involve the contention, on my part, that light is not the wave/particle phenomenon described alternately as wave-like fluctuations in the field properties of empty space, and as discrete photons, which are tiny particles of something like matter, but with no detectable mass, which transport definite quantities of energy .

I have considered the problems with the nature of light, and why I think it involves neither waves nor particles, and is not limited to the apparent speed of light in a vacuum. Also, I have proposed a somewhat altered meaning of the equations of Special Relativity when this basis is used.

For the most part, the equations derived by Einstein based on light having a finite, limited velocity, and yet yielding the same speed relative to various moving reference

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systems are useful and consistent, although representative of a somewhat different reality than I perceive.

On the other hand, those aspects of Special Relativity which deal with the relationship between mass, velocity and energy, do not seem to me to have followed in a straightforward fashion from the space, time and velocity relationships. Also, they have raised some significant questions concerning energy in general. This Chapter is aimed at defining these problems, and proposing an alternative to the energy-related equations of Special Relativity which answers these questions.


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THE PROBLEM WITH ENERGY Energy is usually considered to be of three principle

kinds. Kinetic energy is associated with the velocity of objects which have mass, and Potential energy is associated with the work done on a massive object to move it away from an different object exerting a force, such as gravity or electromagnetic force, on it. Radiant energy is considered a third type of energy.

However, radiant energy is, it is, in my view, simply the transfer of kinetic energy from the orbiting electrons of one atom to those of another, so it is a form of kinetic energy, just as is thermal energy, the kinetic energy of the atoms and molecules which make up an object.

The Special Theory of Relativity does not deal with potential energy, but is left for the later General Relativity, which introduces a theory of gravitation.

I will deal first with the problems of kinetic energy as I see them, and then try to explain the paradox associated with classical kinetic energy theory. First, let us examine the energy relationships which were derived in Special Relativity.

Einstein started with the Newtonian definition of the energy of a body, which consists of the sum of its kinetic energy and potential energy.

K PE E E EQUATION 113

Where the kinetic energy term, EK is given by classical mechanics as

2

2K

mvE . EQUATION 114

The kinetic energy of a body is also equal to the work done on by a force that moves the body through a distance,

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while bringing about a change in velocity. This is, in Newtonian mechanics

KW E Fx , EQUATION 115

or, if the force is not constant,

2

0 0 0 0 2

x x x v

k

dv mvE Fdx madx m dx vdv

dt

EQUATION 116 Now, Einstein had demonstrated that nothing could

move faster than the apparent speed of light, so it is obvious that applying a constant force to a body for an infinitely long time should not be able to accelerate it to an infinite velocity, but would, instead, approach the upper limit of

2

KE mc EQUATION 117 So, as the body approached the speed of light, it was

apparent that the velocity could not be increasing, but if not, where was the additional energy going?

Einstein got around the apparent paradox that the energy simply disappeared on the one hand, and that it could not be destroyed on the other hand, but introducing an another relativistic correction. Not only did time, and distance contract when accelerated to high velocities, but mass muss increase, to account for the additional energy absorbed.

2

2

'

1

mm

vc

EQUATION 118


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In my simplified book on Special Relativity4, written by Einstein in 1931, he goes into elaborate detail as in the development of the Lorentz equation based contractions of time and space, and the errors involved in velocity measurement when the object in question is moving at a significant velocity when compared with the speed of light.

However, when he introduces the relativistic correction for the mass of the object, he simply states that it is based on "energy considerations." There is good reason for this omission, because the expression cannot be derived directly from the basic assumptions on which the theory was based.

Rather, it is necessary to use this expression in the development of the final, blockbuster equation of Special Relativity,

2

2

21

mcE

vc

EQUATION 119

from which he derived the equation

2E mc , EQUATION 120

which is probably the most widely equation known of all time. It is derived by setting the velocity, v, equal to zero in equation 119.

This states that the Total energy of a body which is not in motion with respect to the reference system in which its mass was measured, is equal to the mass times the square of the apparent speed of light. This is a truly enormous amount of energy per unit of mass. So far, only tiny fractions of the energy inherent in the mass of a few substances has been converted to energy by bringing about atomic fission, where

4 Einstein, Albert, Relativity, 1931 translation by Robert D. Lawson, University of Sheffield, of the original “Relativity”, 1916, Crown Publishing, New York, NY.

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the reaction products are slightly lower in mass than the parent elements, or by hydrogen fusion, where the resulting helium weighs slightly less than the parent hydrogen atoms.

Very few people question any of the assumptions or the results of Special Relativity, particularly the mass-energy equivalency demonstrated by Equation 120. In order to illustrate the roundabout nature of the calculations required to move from the simple energy equations to the relativistic mass correction, I have included the derivation in the Appendix to this Chapter, for those of you who want to spend a few hours exploring the subject.

There are, some interesting conundrums built into this acceptance. I will try to explain all the areas in which I have trouble fitting the parts of this energy picture together, and then propose an alternative which does not raise these questions. I also have problems with the concept of potential energy, as used in Newtonian mechanics, which fits into this discussion nicely, I will include them here also.


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SPECIAL RELATIVITY ENERGY EQUATIONS Einstein's method of accounting for the work done on

an object as it is accelerated toward the speed of light as an ultimate limit gives on an uncomfortable feeling that the mass of an object is not a real thing, but a property which fluctuates with its velocity relative to the coordinate system being used. It is not simply a property which, when observed by a stationary observer, seems to be getting larger as the object speeds up; it is really getting larger. Thus, my lunch pail which weighted a kilogram, when taken aboard my space ship, gets heavier as the space ship accelerates, and grows very heavy if my velocity relative to the earth, where the mass was determined, approaches the apparent speed of light. I can understand it seeming to have a high mass while the space ship was accelerating, and the lunch pail was being pressed down against the table (my space ship is going straight up relative to my table top) but now that I am coasting, with no acceleration, it still has a mass equal to a ton.

Surely, this would not seem to be the case, because if I now chose to use a coordinate system commensurate with the space ship table top, it would still have a mass of 1 kg, although presumably it would be weightless because of the distance from earth. My rules would apply, just as well as earth's rules, and I would find myself able to move the lunch pail easily enough. Still, Einstein would say that in order to accelerate my space ship any more, I would have to treat it as though the lunch pail weighed a ton. I would argue that I will accelerate it according to my coordinate system. Why not? It is equally applicable.

While Einstein was justified in reaching his conclusions based on the assumption that light actually moves through 3D space at a constant 300,000 km/sec. I don't think his conclusion was right. I do not think there is any change in the

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mass of an object with velocity, None. Mass is not one of the things that takes well to correction by relativistic calculations.

Problem Number Two has to do with the definition of the equivalence between the "rest mass" of an object, and its intrinsic energy. The problem is defining "rest" in using the rest mass. What is the object at rest with respect to? All velocities are relative, Einstein said, and I believed, that one reference system is as good as another, and that the laws of nature ought to apply equally well in any of them.5

So, am I to presume that the mass of an object would be different if it were measured at the surface of the moon, rather than at the surface of the earth? Certainly the weight would be difference but the mass seems to be a completely independent property of the matter in the object, and it would not matter if I determined on the surface of the moon. When brought to earth, and subjected to the earth's velocity through space rather than that of the moon, I would expect the mass to be precisely the same, whether I had measured it on the moon. If the moon is not moving fast enough for you, let us repeat the though experiment using a planet moving around a distant star.

Again, I do not think equation, E=mc2, as written, is the whole story, atomic energy notwithstanding.

Finally, there is, in my list of discomforts the energy area a dislike for "Potential energy", the EP in Equation 113. Potential energy was simple enough to understand when it was viewed as the work which had to be added to an object to raise it a certain distance above the ground, and there was no conceivable way to get the weight far enough away from the earth that gravitation wouldn't have any significant effect.

5 By Reference System, I mean an inertial reference system. That

is, one which is moving at a constant velocity. The velocity of a system cannot be independently determined by considering the system without reference to anything else. However, a system which is accelerating can be defined and its rate of acceleration determined without reference to any other system, provided there are no gravity or electrical or magnetic forces involved.


111

So, when one threw ones baseball into the air, he imparted to it a certain amount of kinetic energy, and as it rose into the air, it slowed down and the energy was converted from kinetic energy to potential energy. There was nowhere else for the energy to go.

This made perfect sense, and you can use the initial potential energy to calculate how high the ball will go (neglecting air friction) and exactly what its velocity will be at any second it is in the air. So, it is a useful concept.

My problem with potential energy arises when one looks at an object, say and electron, that is far enough away from an unpaired proton that there is essentially no effect of the proton on the electron. In this case, the potential energy is customarily taken as zero with respect to the distant proton, which seems fair, as there essentially no effect of the proton on the electron, and might as well not be there.

However, with an infinitesimal nudge in the direction of the proton, it will feel some slight attraction and start to "fall" toward it, gaining speed as it does, until it is moving quite rapidly and takes up an orbit around the proton, spinning at perhaps 0.0035 times the apparent speed of light; a very high velocity for such a tiny thing. So, where did the energy come from that now constitutes its relatively high energy level?

Obviously, it came from the “potential energy” it had relative to the proton, which it didn't even know was there. So, the physicists usually assign the proton zero potential energy when it begins its journey and the large amount of kinetic energy it acquires come out of nowhere. Rather than violate the conservation of energy law, the physicists say that, in its orbit around the proton, it now has a negative potential energy, exactly equal in absolute value to the kinetic energy.

Negative Energy? This is like saying I have 5 negative children. There is no physical concept that matches negative energy. It is not energy that is subtracted from something. If I had seven children and five of them left home, I would not have gained 5 negative children, as the concept is absurd. The

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5 children, which are real things and can only be counted with positive integers, left home.

I tweak my nose at negative potential energy. Like many concepts in physics, it is a made up entity, which exists solely to account for something that would, otherwise, be unaccountable.


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AN ALTERNATIVE THEORY OF MASS AND ENERGY

I am proposing an alternative picture of the way the

Universe works, which takes into account most of the useful parts of Special Relativity, and manages to solve all my problems with the energy questions raised in Special Relativity. It also handles the problem of potential energy rather well, by banishing the concept. I will be a bit repetitive, and go over some of the points already made, to be sure they are properly related to the solution of the energy problems I have described.

In my theory of the Universe, we in three dimensional space occupy an Universe which is expanding in a fourth dimensional direction, which I have called the T dimension, suggesting that it has some connection with the passage of time. This is in contrast to Einstein’s time dimension, which is defined by the equation

2 2 2 2 2x y z c t , EQUATION 121

in which time is considered an imaginary quantity, so that

2 2 2 2 2 0x y z c t EQUATION 122 makes sense.

In Einstein's picture of the Universe, the x, y and z coordinates define the spreading of light waves from the origin at

0x y z EQUATION 123

outward through space at the velocity c.

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In my picture of the Universe, there is a fourth spatial dimension, T, which is similar to ordinary space, except this is the direction in which the three dimensional Universe is expanding at the apparent speed of light, according to the measurements of Hubble's constant. The governing equation is

2 2 2 2 2 2x y z T c t . EQUATION 124

It is difficult to picture this adequately in three dimensional space, so where possible, I have used a two dimensional universe with only x and y spatial coordinates, expanding in the T direction.

The speed represented by the letter c in this equation is the speed of expansion of the Universe, not the speed of light. In an earlier Chapter, I made the case that it appears to me that light can be transferred from one emitting atom to another by events which are simultaneous (using Einstein’s definition of simultaneous), even though separated in both space and time.

In this circumstance, the measurement of the apparent speed of light by Michelson and Morley and others would mistakenly assign the value c to the speed of light. At the time they were doing the experimentation, there was no indication that the Universe was expanding rapidly and therefore no incentive to question how fast it was moving in this fourth dimensional direction.

This model suggests that all matter, every atom and every star, has a velocity c in the T direction. There are two apparent possibilities here:

Alternate 1 takes the velocity in the T direction as c, but there is, in addition, a velocity at right angles to it, v, which is additive to the c component as a vector. This means that the total velocity of the object is

2 2

Tv v c EQUATION 125


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and the total energy

22

2

mvE mc . EQUATION 126

FIGURE 22 A TWO DIMENSIONAL

UNIVERSE, EXPANDING AT THE RATE R = CT

In Alternate 2, the velocity c is the total velocity of the object, and it has, so far as an observer moving with the object is concerned, no other components of velocity. In this case, the object has, by its own reference system, a fixed, invariant mass, m, which is moving at velocity c, and the total energy is:

2E mc . EQUATION 127

Neither the mass nor the total energy varies with the velocity. “Velocity” as we see it in the three dimensional Universe, is simply a component of the velocity c

, which we

are able to see because the motion of the body is nor parallel with the our different direction for c

.

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Equation 126, (Alternative 1) agrees with the results of the Theory of Special Relativity.

For a number of reasons, I believe Alternative 2 is more descriptive of the way things work, and it suggests an alternative theory of energy.

I have for the time being, neglected to account for the factor of 2 ratio of Einstein’s mc2 and my mc2/2. This will be dealt with in the Chapter on Electrostatics and Electrodynamics.


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THE QUESTION OF POTENTIAL ENERGY In the Universe I described, what we see as “velocity” is

simply a tilting of the T axis through any body moving at a significant velocity with respect to the apparent velocity of light, c. The energy of the body is always


and not

2

2

2

mvE mc , EQUATION 129

when measured with reference to a coordinate system which is tipped such that the tangent of the angle is v/c. Bodies do not really have any "potential energy", but rather possess a total energy which is invariant, but which may appear as velocity when the three dimensional space in which they are located is "tipped" relative to the reference system T axis so that part of the c velocity corresponds with the x – y – z space of the observer. In the example given in the first part of the Chapter, an electron located at a great distance from an unpaired proton, the electron and proton, if both were at rest with respect to each other, had parallel T directions. There is no relative velocity, so there is no kinetic energy. There is no potential energy either. Only the total energy, mc2 for each of the two bodies, both of which are too far apart to be influenced by the gravitational effect of the other body. Given a nudge in the direction of the more massive body, the is experiences s slight tipping of its T axis toward the central mass, caused by the effect the greater mass on the

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direction of time around it. The T Axis tipping slightly toward the central requires that the x – y plane at the location of the satellite also tilt, to remain at right angles to the T axis, and this tilt, not being experienced by the central mass, causes the satellite to move in the direction of the main mass with an ever increasing velocity. The total energy of the satellite stays exactly the same, while a larger fraction of the velocity becomes visible in the x – y plane.

Viewed from the reference system of the central mass, the satellite develops increasing velocity, but without changing the total energy level at all. Orbiting the central mass, it continues to have the same E=mc2 total energy level, with that part of the energy observed as orbital velocity simply a component of the total.

From the central mass, it appears that the satellite has both the velocity c in the T direction and the velocity v in the orbital direction. Viewed from the satellite, it has only the velocity c, and no velocity relative to its coordinate system.

The concept of potential energy is still useful in ordinary Newtonian mechanics, just as many concepts in Physics and Engineering are useful while not fundamentally correct.

Examples are centrifugal force, which is, of course, not a force at all, but simply the tendency of matter moving in a circle to leave the circle and move straight along a tangent if not constrained in some way. Coriolis forces are another example.


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CONCLUSIONS The fundamental equation of Special Relativity equating

matter and energy is incorrect. The total energy of matter, regardless of its velocity relative to any coordinate system is

2E mc . EQUATION 130

The velocity of a body observed relative to a coordinate

system of velocity v, relative to the body is a portion of the fundamental energy of the body. However, from the point of view of the observer, the energy of the body appears to be

22

2

mvE mc .

EQUATION 131

The difference between these two points of view is accounted for by the difference in the time systems of the observer at his “fixed” reference and that of which is observed relative to coordinating system moving with the body. This difference causes the observer at the fixed origin to believe that the first term in equation 131 is accurate, but when the relativistic time correction is applied, the equation becomes

2 2 2 2( )

2 2 2

m c v v mcE

, EQUATION 132

where the factor of 2 in the total energy is due to the rotational velocity of the electrons and protons, which had not been dealt with yet.

Matter and energy are not interchangeable. Adding energy to a body does not make it heavier, and the bulk of the energy associated with matter, related to the velocity, c, in the T direction cannot be converted to energy.

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The space, time, velocity relationships derived as part of Special Relativity are fundamentally correct, except that the value c is the speed of the expansion of the Universe into the fourth dimension, and not the velocity of light, which is substantially infinite for points with only vacuum between them.

Potential Energy does not represent any real physical reality. It is useful in making engineering calculations, but bodies do not "acquire" potential energy when moved away from a body exerting a gravitational attraction, or an electrical attraction or repulsion or an electrostatic or electrodynamic attraction or repulsion.


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CHAPTER 6

BOHR’S ATOM REVISITED

Electrons and protons come in approximately equal

numbers, as there does not seem to be a net positive or negative charge on anything within our sphere of observation. There is some suggestion that this is because they were created as pairs. They are certainly separable, on a non-technological basis by rubbing a glass rod with a silk cloth, or running a comb through dry hair, or by use of electron emitting cathodes in Cathode Ray Tubes (CRTs).

More of the electrons and protons in the Universe appear to be in Hydrogen atoms than in any other form, although all gross matter is formed of combinations of electrons, protons and neutrons. The configurations of all of the elements are pretty well understood, and chemistry is basically the science of how these elements interact with each other, principally by means of sharing or donating electrons from one atom to another atom or group of atoms to form compounds.

In 1905, Einstein’s Special Relativity provided a link between the properties of light and characteristics of matter. Max Planck provided another when he introduced the cornerstone of quantum mechanics when he postulated that radiant energy could only be transferred in finite packages, the energy of which was related to the frequency of the radiation by

hfE , EQUATION 133

where: E = total energy, ergs

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h = Planck’s constant = 6.62E- 27 erg seconds/cycle f = frequency of radiation, cycles per second.

This states, in effect, that the amount of electromagnetic energy transmissions is exactly the same for each cycle of perceived radiation, regardless of the nature of the radiation. There are many implications about the nature of electromagnetic “waves” implied by this simple equation, and I will spend a lot of time with Planck’s constant in subsequent pages.

A basic structure for the hydrogen atom was proposed by Nils Bohr, which included what was then known about electrostatic field theory, embodied in Maxwell’s equations, Planck’s law, and Newtonian mechanics. The derivation he published is beautiful in its cohesiveness, and won immediate acceptance because of its ability to provide a basis for the measured emission spectra of hydrogen.

While modern Quantum Electrodynamics provides a somewhat different picture of the atom than Bohr’s, it is still the picture generally accepted as fundamentally descriptive of the hydrogen atom.

In order to arrive at a theory of how radiant energy is transmitted, it is necessary to have a model for the structure of the atom as a starting point. I have problems with a number of basic premises of Bohr’s description of the hydrogen atom, and with the conclusions he drew from them. However, it provides a good place to start, so I will go through Bohr’s development, and the proceed to repeat the process using premises more in keeping with my ideas of the nature of light, Planck’s constant, and the meaning and causes of electrostatic and electromagnetic attraction and repulsion.


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BOHR’S DERIVATION Nils Bohr introduced his concept of the hydrogen atom

in 19136. It embodied theory of light emission in discreet energy packages called quanta by Einstein, and Max Planck’s relationship indicating that all light has the same energy content per cycle, regardless of wavelength.

Bohr calculated the allowable orbital shells for electrons in the hydrogen atom by setting the electrostatic attraction between the electron and the proton equal to the centrifugal force due to the rotation of the electron about the nucleus.

The potential energy of the electron relative to the associated proton was assumed to be zero when the electron is far removed from the proton, and decreases to a negative value as the electron approaches the proton.7 The field strength at a distance r from the proton is given by: Coulomb’s Law.

2

2

r

ZeFe , EQUATION 134

where: F = force on the electron, Newtons

Z Coulombs Law Constant =8.99E09 Newton meters2/Coulomb2 e = electron charge, 10.633E-19 Coulomb r = atomic radius, meters..

6 "On the Constitution of Atoms and Molecules", Philosophical

Magazine, Series 6, vol. 26, July 1913, pages 1-25. 7 This is simply a convention used by physicists. Elsewhere, it

will be argued that the total energy possessed by the electron is constant, regardless of its location and the proximity to other charged particles, or lack of proximity, just as the energy of masses is constant, and not dependent on the velocity of the particle or proximity to other gravitational masses. However, for this derivation, the conventional approach and terminology will be used.

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The centrifugal force tending to increase the radius of

the orbit around the proton is

r

vFc

2 , EQUATION 135

Where: μ = electron mass

= 9.1095E-31kg v = electron velocity, meters/second.

Setting the electrostatic force acting on the electron just

equal to the centrifugal force acting in the opposite direction,

r

v

r

Ze 2

2

2 . EQUATION 136

From this,

2

2

v

Zer

. EQUATION 137

This relationship allows for an infinite number of

combinations of electron orbital radius and electron velocity. Bohr postulated that the electron angular momentum

was restricted to specific values so as to account for the emission of radiant energy only in specific wave lengths. By using

nhvr , EQUATION 138

where: n = the quantum number (an integer) associated with the electron h = Planck’s constant =6.62 E-34 Joule seconds.


125

By inserting the velocity from equation 138, the radius of each electron orbit for the hydrogen atom is

2

22

Ze

nhr

EQUATION 139

and the velocity is

nh

Ze

r

nhv

2

. EQUATION 140

For n = 1, this calculates to be about r = 0.53 x10-10

meters. The quantum number, n, is 1 for the innermost orbital radius. For larger quantum numbers, the radius size increases with the square of the quantum number, and the velocity is inversely proportional to the quantum number.

The total energy of an electron, in Bohr’s concept of the atom, is the sum of the Kinetic Energy and the Potential Energy. The Potential Energy is given by:

22

422

nh

eZ

r

ZeEP

, EQUATION 141

which relates to the energy which would be released by an electron allowed to fall from a distance, r, to the center of the proton. This is usually considered to be a negative value, because the energy of the electron at a great distance from a proton is taken as zero. The positive kinetic energy is calculated as:

22

4232

22 hn

eZvEK

, EQUATION 142

which is a component of the total energy. The total energy of the electron with quantum number n, is

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22

422

2 nh

eZEEE KP

. EQUATION 143

When an electron loses energy by dropping to a lower

energy level, as indicated by a decrease in the quantum number from n = 2 to n = 1, the amount of energy lost is given by

2

22

12

422 11

2 nnh

eZE

EQUATION 144

This makes an intriguing and elegant picture of the

atomic structure of a hydrogen atom. The single electron orbits the nucleus at a radius r0, which represents its minimum energy level.

The “wave length” assigned to the electron, assuming that it has the properties of both a wave and a particle, is, according to de Broglie, exactly the circumference of the circular orbit for n=1. When the hydrogen atom is excited (it is not proper to say that the electron is excited, as its energy is measured relative to the nucleus) it pops out of the minimum radius orbit to one which is four times as large, and its velocity drops to half what it was while in the innermost orbit.

The longer path length and the lower velocity represent a lower kinetic energy level, but the presumption here is that the potential energy represented by the removal of the electron to farther away from the proton is increased considerably, thus resulting in a higher energy level for the electron in an orbit of greater radius.

Bohr maintained that the electron has wavelike properties which required it to fit an even number of the wave lengths corresponding to the electron mass and velocity into the orbital path of the electron. With an integral number of waves, the electron “resonated” with itself, whereas if the


127

path length were other than an integral number of wave lengths, the waves would “interfere” with each other, and could not exist over a significant period of time. At four times the radius, the electron velocity is half that of the basic, innermost orbit. The longer path length and the lower velocity allow the orbit to accommodate eight “waves” at the new, lower frequency of the electron, calculated from

h

cmvf

1

EQUATION 145

which is de Broglie’s equation for the frequency of the “wave” associated with any mass in motion. From de Broglie’s equation, it is possible to calculate the “frequency” or “wave length” of a bowling ball rolling down an alley.

The innermost possible orbit of the electron corresponds to the radius where the wave length is exactly equal to the circumference of the path, so only one wave fits. The electron cannot fall closer to the nucleus of the atom, because the path would be less than one wave length, and it would be “unstable”. It knows this, and does not try.

The proof of the pudding, for physicists, was that the model of the atom proposed by Bohr accounted for the frequencies of light actually emitted by hydrogen gas, called the Balmer and Lyman spectra, and was in reasonable agreement with the then-current estimates of the size of the hydrogen atom.

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THE PROBLEMS WITH BOHR’S ATOM Although the Bohr atom provides an elegant picture of

the hydrogen atom, it has some aspects that are unsatisfying, and must be sorted out in trying to reach an understanding of how electromagnetic radiation originates within the atom, and how energy is transferred from and excited atom to another atom.

Bohr’s elegant derivation accounts for a number of properties of a simple Hydrogen free radical (the combination of a single proton orbited by a single electron) and is a reasonable starting point for building an alternative model which does not have the shortcomings of the Bohr model. Some of these shortcomings are:

High radiant energies being associated with slow moving electrons and vice versa

Electrons changing orbital radii by a factor of

36 or more when excited

Electrons switching back and forth between particles and waves

Electrons keeping their distance, rather than

falling into the nucleus.

HIGH ENERGY, LOW VELOCITY Most puzzling is the notion that the n = 1 state of the

electron in the hydrogen atom is the lowest energy state. It has the highest velocity for the electron, and the kinetic energy of the electron has nothing to do with the radius of its orbit. It is simply

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2

2

mvE , EQUATION 146

relative to the nucleus. There is, in my concept of the Universe, no potential energy at all, and potential energy cannot be transferred from one electron to another. All matter, including electrons, have momentum if they are moving in three dimensional space relative to the coordinate system. Each electron has a momentum v where is the mass

of the electron and v

is the component of the total velocity c

in the three dimensional space, where v

is a velocity vector with both magnitude and direction. The magnitude of v

is always c

, the apparent speed of light, but the direction of the velocity varies. Momentum can be transferred from one electron to another, where:

` MOMENTUM TRANSFER BETWEEN ELECTRONS


131

1 1,1 2 2,1 1 1,2 21 2,2v v v v

EQUATION 147

Because the mass of all electrons appears to be identical,.

1 2 , EQUATION 148

This momentum exchange is as illustrated by Figure 23.

It seems most likely that the energy that is transmitted from one atom to another by “radiation” would relate to the kinetic energy of the electrons, which can be transmitted by mechanical means (collisions), whereas the potential energy, related to the distance the electron is from the proton, is not readily “transmittable”, and does not, in my estimation, have any physical counterpart at all. Thus it seems quite unlikely that the inner shell, where the electron is moving the fastest, would represent the lowest energy state of the electron in relationship to energy transmission.

In Figure 23, it seems equally likely that the momentum transfer can be accomplished by the emitting and the receiving electron (in this case, it is electron 2 which appears to have a high kinetic energy, and electron 1 which has none, relative to the coordinate system chosen), with each electron retaining its identity, but changing velocity (i.e., changing the

direction of the vector, v

, associated with it, or by the electrons each retaining their original velocity and simply trading places in the four dimensional continuum.

Because individual electrons cannot be identified, it is impossible to tell which takes place, and, more importantly, it makes no difference which scenario is enacted.

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EXPANDABILITY

The second puzzling thing about the Bohr atom is that it

is so expandable. There are at least six levels of excitation of the electron in a hydrogen atom indicated by the emission spectra, requiring that the radius of the electron orbit varies from approximately .053 nanometers to a value 36 times as great when highly excited. This makes it difficult to imagine a hydrogen molecule in a gas which acts like a little billiard ball, and obeys the gas laws rather exactly. It seems more like a fluffy pillow than a billiard ball.

For atoms more complex than hydrogen, the inner electrons could not easily be constrained within their inner orbits if the addition of radiant energy to the electrons would cause the orbit to expand by a factor of 36. It is not at all clear how this expandability of the orbits would work for larger atoms where a second orbital shell required .

ELECTRONS KEEPING THEIR ORBITAL DISTANCE

Also, there is the problem of what really keeps the

electron from "falling" into the proton. In the Bohr model of the atom, it is the centrifugal force, and only one unique velocity can prevent the electron from either flying out of orbit if it moves faster, or falling into the nucleus of the atom if it moves slower. This concept does not pose a problem for hydrogen in the gaseous state. However, atoms heavier than Helium form compounds with share electrons, and share them in such a way that they cannot be orbiting the nucleus of all of the atoms which share them. For solids, it seems that there much be electrons which have no orbital velocity at all, yet they exist without the atoms collapsing.


133

Additionally, there is the difficulty understanding how raising the temperature of the gas would cause the electrons in orbit around the nucleus to slow down and move farther away from the nucleus as they became more excited. It seems far more likely that increasingly vigorous collisions with neighboring atoms would cause the electrons to acquire additional kinetic energy, and to speed up. This may be simply a mechanical engineer’s aversion to neglecting mechanical effects.

Overall, it seems that a more fundamental way of keeping the electrons spaced at a minimum distance, or at several minimum distances from the nucleus must be presented in order to account for the fact that the electrons seem to be able to orbit at lower velocities than the synchronous velocity without “falling” into the nucleus. Such a mechanism will be presented, and described in detail.

ELECTRONS MAINTAINING THEIR IDENTITY

Finally, the particle/wave duality of the electron is

disturbing. The assumption that electrons have characteristics of both particles and waves seems to solve a lot of problems, but it doesn’t help one gain any fundamental understanding of what an electron is.

In part, this is because the feeling we have about what a particle “is”. It is a relatively concrete one, whereas a wave defies definition if we don’t have a medium such as air or water which is oscillating in wave-like motion. It would be considerably more satisfying if there were a theory of matter that did not require the transmogrification of particles into waves and back into particles again in order to explain all of the observed phenomena.

These problems suggest that one suspend judgment of the accepted model of the atom and rethink the whole

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proposition. Is there direct experimental evidence for the radius of the electron orbit increasing in size as the atom radiates energy? I am not aware of any beyond the presumption that the centrifugal force due to the electron’s orbit around the nucleus must not exceed the Coulomb force due to the opposing charges of the electron and the proton. In rethinking the basic configuration of the atom, one may also rethink the particle/wave duality.


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AN ALTERNATIVE TO THE BOHR ATOM In a previous Chapter, the gravitational attraction of the

electron to the proton was explained. The bending of the T axes along which the electron and proton are moving at the velocity c, produces the appearance of gravitational attraction between the particles.

Similarly, the velocity of the electron in orbit must be interpreted as a tilt of the T axis in the direction of rotation. Although the magnitude of the total velocity does not change (presuming the electron to be in a circular orbit), the direction of the motion changes, which has to be interpreted as an acceleration of the electron in the direction from the electron to the proton.

Because there is no velocity in the radial direction, the x – y surface at the electron must be horizontal (that is, in line with the general position of the x – y plane.) A diagram of this simple hydrogen free radical is shown in Figure 24.

FIGURE 23 DIAGRAM OF A SIMPLE HYDROGEN FREE RADICAL

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The slightest tendency for the paths of the proton and

electron to tilt toward each other would be cause the particles to move toward each other, and be interpreted as a velocity in the three dimensional space which we can observe. Any change in the degree of tilt would be interpreted as “electrostatic force” acting upon them. Because the T directions are, by definition, perpendicular to the “surface” of the analogous two dimensional sphere at the point where the matter exists, the irregularities in the shape of the surface is, ultimately, the essence of the observed velocity of the mass, and the “force” bringing about changes in the velocity. The force increases with the inverse square of the distance, so the closer they come together the more strongly they are “attracted” to each other. The force of gravity acts on both electrons and protons, but the electrostatic forces between them and between like particles, is much, much greater.

The electrostatic and electromagnetic forces must be due to the same sort of bending of the T axes through the particles relative to each other, but there are two the complicating factors. First, these forces only apply to charged particles, and not to neutral particles. Secondly, there is a velocity change taking place in the radial direction, toward the proton (because there is a change in the vector velocity along the orbital path) but there is no movement of the electron closer to the proton.

My picture of the hydrogen free radical is simpler than Bohr’s, in that it consists of a particle (not a wave) which orbits the proton at a fixed distance, r0 from the nucleus. The velocity of the electron is, at most, the synchronous velocity given by Equation 140.

For a moment, let us discount the “electrostatic force of attraction”, just as we discounted gravity as “force” acting between massive bodies. Assume for now that the inner shell electron orbital radius of the Hydrogen atom, r0 is fixed, and


137

that the various energy levels are achieved by simply speeding up or slowing down the electron in orbit around the nucleus.

The questions associated with the failure of a slow moving electron to “fall” toward the proton after reaching the radius of the inner-most orbit of the hydrogen atom will be dealt with in detail somewhat later on. The velocity of the electron is

02 fv EQUATION

149

where: f0 = Orbital rotation frequency, revolutions/sec

r = radius, m

The energy of the electron due to its velocity is

2220

0

(2 )

2 2

m rfmvE Kf

g g

EQUATION 150

where f0 is the highest frequency, which is essentially the frequency when the electron makes one circuit around the path per unit of time. At half the velocity, the electron would make half a circuit around the nucleus in the same length of time, and would have half the frequency of rotation. At one third of the velocity it would make 1/3 of a circuit in this same length of time, t .

If the quantum number is the number which is the multiplier of the wave length, or divisor of the frequency

0f f n , EQUATION 151

and

0n , EQUATION 152

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where 0 = distance traveled by the electron in t .

202n

fE K

n . EQUATION 153

If one takes the difference in the energy levels of two

states, n1 and n2, one gest the Balmer, Lyman and other series:

2 21 2

1 1'RE R

n n

EQUATION 154

Where: ER = radiant energy emitted at a specific frequency R’ = Rydberg Constant, the energy associated with radiation8 n1, n2 are integers greater than zero, denoting the energy level of an electron in orbit.

This makes a little more sense, as the higher energy state

is the n = 1 state, and the lower energy state the second term with the higher value of n. It is easier to see how heating the gas causes the electron to gain velocity, and the atom loses its fluffy, expandable quality.

Also, the problem of dealing with the helium atom, with two electrons, which are likely to be at opposite sides of the same orbit, where moving one electron to a higher orbit and leaving the other in the original orbit, would produce an ugly, unbalanced molecule.

Bohr’s derivation and mine give an approximation to the Rydberg Constant based on the assumption that the mass of


139

the electron is insignificant compare to the mass of the proton. This is not important in this rather general discussion.

The shapes of the surfaces of the x – y plane around the proton or electron are more complex than those around neutral masses, as dealt with in the sections on General Relativity and on Electrostatics and Electrodynamics..

The simple depression of the x – y plane (or the x – y – z Universe) in the -T direction derived on the basis of the mass of the electron or proton, is, of course, applicable. However, such a depression can only account for the properties relating to the mass of the electron or proton, and not the electrostatic and electromagnetic attraction and repulsion associated with electrical charge.

These require an additional distortion of space, in the form of a twisting about the local T axis through a charged particle, in one direction for positively charged particles, and in the opposite direction for negatively charged ones. These matters are dealt with in detail in the Chapter on Electrostatics and Electrodynamics.

For now it is sufficient to say that there is a twisting of the space around a proton or an electron centered on the T axis, and proportional to the velocity of the charged particle through four dimensional space. As the velocity of all matter (when viewed relative to the coordinate system affixed to the matter) is in the T direction, with no components in the x – y – z space, the twist will be entirely in the x – y – z space.

However, when viewed with respect to a coordinate system moving with relative to the matter, the twist will be around the apparent direction of motion through the four dimensional space. That is to say, if there is a twisting around the T axis, and the T axis of the particle is tilted with respect to the T axis of the coordinate system, there will be an apparent twisting of three dimensional space around the apparent direction of motion in the three dimensional space.

Just as the velocity of the particle is a vector, the twisting of the space around it is also a vector quantity.

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This is exactly the case when the proton is assumed to be a stationary body with the electron rotating around it. It is apparent that the electron will appear to have a twist around the T axis parallel to the proton’s T axis, and in addition, a twisting around the velocity vector observable from the proton to be in the direction of motion of the orbiting electron.

The twisting around the T axis parallel to that of the proton is responsible for the electrostatic attraction or repulsion between unlike and like charged particles, and the twisting around the direction of motion in the three observable spatial dimensions is what we interpret as a magnetic field.

The quantification of these distortions of space, and the relation between them and the “forces” we interpret to be acting on the particles will be left to the separate Chapter on Electrostatics and Electrodynamics. Suffice it to say here that they do, of course, match the observed behavior of charged particles, and that the particles do, in fact, follow Maxwell’s Equations.

I should add parenthetically, that Maxwell’s equations, which were very useful to Einstein in formulating Special Relativity, are every bit as elegant and cohesive as was Bohr’s theory of the atom, but, unlike Bohr‘s atom, I can find no basic fault with them, other than that they presume the existence of electromagnetic radiation, and must therefore assign both electrical and magnetic properties to empty space.

The Minimum Orbital Radius So, if there is an distortion of space around an electron

orbiting the proton in a simple hydrogen free radical, why does in not accelerate toward the nucleus and fall into it, at any time the velocity is slowed (presumably by radiation to an atom with an even slower orbital velocity) below the synchronous velocity? Bohr postulated that is does not


141

because the electron has wave properties, and that the wave length corresponds exactly to the circumference of the orbital path. As long as the single wave fit into the orbit, the electron would tend to reinforce itself, whereas if it moved at a slower velocity it would not, and would therefore go out of existence. If I deny the existence of wave-like properties for the electron, this explanation no longer holds water.

Instead, I propose that there is a simple explanation which is consistent with that explained in the Chapter on A New Theory of Light. This proposes that radiant energy is transferred between the orbiting electrons of two atoms which may be far apart in both space and time, by direct contact between the atoms.

It is difficult to illustrate this because of the problem of only being able to show three spatial dimensions in a picture. The simplest way to illustrate the points being made is to set one of the three spatial coordinates equal to zero, and draw a picture involving the remaining two spatial dimensions, along with the time-like dimension, T as the third dimensions.

Figure 25 illustrates this procedure, where the x and y dimensions are chosen to incorporate the circular orbit, and the T dimension is perpendicular to the plane of the paper.

This can be accomplished only if there exists a fifth spatial dimension, around which the four spatial dimensions are wound into a ball of very small diameter. In fact, the ball is smaller than a single hydrogen atom, in that the circumference of the hyper spherical ball is equal to the radius of the hydrogen atom’s electron orbit.

In this picture, the proton and the electron occupy exactly the same position on the surface of the five dimensional hyper sphere. Because there are five dimensions,

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FIGURE 24 ELECTRON ORBIT IN TWO

SPATIAL DIMENSIONS

and we can only picture three, the y and z coordinates are presumed to be zero, and the x axis stretches to completely around the curved surface of the x – y – T sphere in the three dimensional model of four dimensional space.

FIGURE 25 THE HYDROGEN ATOM ON THE SURFACE OF THE UNIVERSAL KERNEL

The T dimension, representing the direction the Universe is moving as time progresses, is also wound around the kernel,


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but there is no indication of whether this dimension is also looped back on itself as are the three spatial dimensions, or simply continues outward without limit.

Because all of the possible lines of sight in the three dimensional Universe are wound around this kernel, and the present moment is represented on all of them by the same point, at which the electron and proton are located, the entire observable universe, from the point of view of an observer located at the proton, is located at this exact point.

Further, only atoms which have the nucleus at a distance of nr0 from the proton, and are at a distance Nr0 along the T axis (where the time must be Nr0/c), where both n and N are integers, can exchange energy. Thus, any electron which in not located an even multiple of the minimum radius are not in a position to exchange energy with other atoms, and for all practical purposes, do not exist.

FIGURE 26 DEPICTION OF THE LOCAL TIME UNIVERSE FOR A PARTICLE AT THE ORIGIN

One might question the possibility that an electron would fall all the way into the nucleus, and thus come to a position where n=0. If one presumed that Coulombs law of

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electrostatic attraction applied at sub atomic distances (which is probably impossible to determine), then the velocity gained by accelerating from zero velocity would be sufficient to take the electron only half way to the nucleus before it reached a synchronous speed, and would try to establish a stable orbit. At this location, as pointed out, it would be unable to exchange energy with any other atoms which occupy “our world”, and would simply no longer exist.

The relationship also holds for n=0, but in this case the positions of the proton and electron would coincide, and the electrostatic properties (the twists in opposite directions around the T axis) would cancel each other, and the particle would be recognizable as a neutron, a particle with the mass of a proton plus that of an electron, but with no electrical charge.

In my concept of the hydrogen atom, the orbital radius is, therefore, the same as that calculated by Bohr, and the size of the hydrogen atom reported in the literature9. This was later modified by Dirac to take into account the effects of relativistic time dilation. However, the synchronous orbital velocity is no longer the only velocity permitted to the electron in this orbit, but simply the greatest velocity permitted. Instead, any inverse integer multiple of the synchronous speed is acceptable, down to zero orbital velocity, which would be experienced at a temperature of absolute zero, when the hydrogen atom has no kinetic energy at all.

These yield the same results for the Balmer and Lyman series obtained by emission spectrographs for hydrogen, but limits the energy content of the orbiting electron to kinetic energy alone, with no reference to potential energy.

9 About 5 x 10E-8 mm

http://web.jjay.cuny.edu/~acarpi/NSC/3-atoms.htm).


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It is my contention that the total energy of the electron is constant at 2E c , where is the effective mass of the electron and c is the apparent speed of light.

What we observe in the three dimensional world is a part of the velocity, c, which is apparent to us because the velocity is following a slightly different time path in four dimensional space than the proton around which it is orbiting, and the apparent linear velocity is the component of the vector v ct

which we can see in three dimensional space. As the

velocity of the electron in orbit decreases (due to losses of energy by radiation or by mechanical collision with other atoms) the total energy remains E, but the velocity vector, v

,

becomes more nearly aligned with that of the proton. The stationary electron appears to be “attracted” toward

the proton because all of the Time axes in the vicinity of the proton are tipped toward the proton, so that anything close to it will, if not acted on by outside forces, tend to follow the time arrow as it moves into the future. The time arrows all get closer to the proton and the closer the electron comes, the more steeply they are tilted in the direction of the proton so the higher will be the acceleration in this direction. This acceleration, divided by the electron mass, is usually taken as the electrostatic “force”.

It is reasonable to picture the magnetic field generated by the electron and proton in a hydrogen atom into account and try to understand how it affects the behavior of the atom, but there are some difficulties. First of all, two dimensions are required to draw a picture of an electron orbiting a proton. The circular orbit in the simplest case defines a plane. If the “magnetic field” is produced at right angles to this plane, it is necessary to use a third spatial dimension to picture it. This leaves no room for the fourth, T dimension.

The magnetic field consists, essentially, of the twist imposed on space around the axis of motion of the charged particle through four dimensional space. For the proton, assuming it to be “stationary” with respect to the three

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ordinary space dimensions, and moving at the apparent speed of light, c, in the T direction, the twisting takes the form of a series of vectors pointing in the direction tangent to circles drawn around the proton, along with an equal vector in the T direction, so the resultant is a series of vectors pointing upward at 45 degrees.

It is apparent that a collection of all of the locations represented by the totality of values of n and N (assuming that both can be any positive or negative integer, including zero) represents the outline of the universe which can be experienced with the location of the proton as the coordinate system origin.

THE CASE FOR REDUCED VELOCITIES The description of the hydrogen free radical proposed

requires that the orbital velocities of the electron consist of a family of velocities,

0 0vn v n EQUATION 155

where 0v =Synchronous velocity for radius r0 n=1, 2, 3, 4……. In equation 155, n is the equivalent of the quantum number.

The question which must be answered is, “Why are these velocities favored, and all other velocities precluded?” The answer is relatively simple, when the mechanisms for transfer of radiant energy proposed is examined.

The radial lines in Figure 27 depict x - y coordinates where the electron may exist with r = nr0, and the circles spaced downward from the origin represent locations where T = -Nr0. An electron which exists at the intersection of any of these lines "overlaps" the proton and electron at the origin, and is in a position where a physical interchange of energy, or even possibly an interchange of the electrons, could take


147

place. Electrons at other points are simply unable to undergo energy transfers. Because these energy transfers include the kind of energy we call radiation, it means that if there are electrons in these interstitial points, we cannot see them, and they have no way of obtaining or releasing energy.

Were there an electron at such a point, unless it were, by chance to have zero velocity relative to the proton, or other coordinate origin of our choosing, it would at seemingly random times happen to cross one of the points at which it would be observable. Our experience does not seem to include the sudden appearance of electrons out of nowhere, and their disappearance, which suggests that there are no "interstitial" electrons. That is, all of the electrons and protons in the Universe are positioned at locations where n and N are integers, and they do not wander off base.

There are some interesting relationships between the energy of an electron orbiting a proton in a hydrogen atom, and the energy which it would have if it simply “fell” from an infinite distance toward the proton, apparently losing potential energy as it acquired kinetic energy (velocity). The total energy of an electron at rest, but at a substantially infinite distance away from a proton is given by

2E mc EQUATION 156

As it falls toward the proton because of the warping of

the x - y plane so it is tipped in the direction of the proton, and also twisted around the proton, the electron acquires a velocity component in the x - y plane which is given by

2Ze

vr

, EQUATION 157

and it is accelerating according to

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2

2

Zea

r EQUATION 158

By virtue of the twisting of the x - y space around the proton and electron, the electron tends to move into a circular orbit where this velocity is appropriate. That is, which is not too high that it escapes because the acceleration away from the proton, given by

2

'mv

ar

. EQUATION 159

In a stable orbit, these accelerations are equal in

magnitude, and opposite in direction, and cancel each other out:

'a a , EQUATION 160

so,

2 2

2

Ze mv

r r EQUATION 161

and

2

2 Zev

r . EQUATION 162

or

2

0 20

Ze

vr

EQUATION 163


149

FIGURE 27 SYNCHRONOUS POSITIONS OF THE ELECTRON

In equation 163, we can use r0 for the inner orbital

radius, and v0 for the synchronous velocity which just permits a stable orbit.

At a higher velocity, the electron would fly out of orbit losing velocity in the x - y – z space until if found a distance from the proton at which it could maintain a stable orbit. At the synchronous velocity, it is apparent that the electron would return to its original position on the orbital path only if the synchronous velocity times the path length 02 r , and

0r

N c

EQUATION 164

where N is the number of time periods, each equal to r0/c required to complete one orbit. , in this case, is not the wave length but simply the circumference of the orbit.

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Because the original position was one for which n=1 and N=Successively increasing integer values, the electron would appear repeatedly at a position amenable to transfer of radiant energy, and would, for practical purposes, exist in the real world.

FIGURE 28 ENERGY TRANSFER IN THE LOCAL TIME UNIVERSE

In Figure 28, eight positions were chosen to represent the possible positions of the electron moving at synchronous orbital velocity around the hydrogen atom nucleus. Eight positions is sufficient to account for all of the lines in the absorption spectrum of hydrogen, but it is likely that the number is considerably larger than eight, because all of the heavier atoms will have higher synchronous velocities of the inner electrons which are proportional to the mass of the nucleus.

The same thing would be true if the velocity were exactly one half v0. In this case, the electron would make one half orbit in the same time interval, but it would appear regularly at the halfway point, t4, and the original point, t0 = t8.


151

The same reasoning holds for velocities that are integer fractions of v0. One third the synchronous velocity would produce a return to the original position in three time intervals, but again, this would occur less frequently than for the full synchronous velocity or one half the synchronous velocity.

Fractions with higher integers in the denominator would all produce such repetitive locations, with decreasing fractions of the time at the location, and hence lower chances of interaction with other electrons, as the integer increases

Non integer fractions of the synchronous velocity would never produce a repetitive position of the electron at an integer value of the time.

For the electron to complete an orbit in one of the minimum acceptable time intervals, the velocity would, of course, have to be

0 0

0

2 22

r rv c

rc tc

. EQUATION 165

This is a velocity equal to the apparent speed of light, and one unattainable in a universe where all matter has a total velocity of c, and nothing moves faster when observed with respect to universal time. When the local time of any observer is considered, the velocity of light appears to be infinite, and the time of transfer is essentially zero.

So, it is apparent that there are many more steps in the inner orbit, each spaced at t or r0/c

In order to get a numerical value for r0, and for v0, it is convenient to use the values derived by Bohr, based on the conventional Planck’s constant. The values I calculate are:

2 2

0

3.14159... 8.99E 09 (1.60E 19)

6.62E 34

Zev

h

meters/second EQUATION 166

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or,

0 0.00365v

c . EQUATION 167

The corresponding minimum radius is

2 2

0 2 20

8.99E 13 (1.60E 19)

9.10E 31 (1.50 10)

Zer

v E

meters

= 5.29E-11 meters EQUATION 168

I have no reason to question these values, even though I

think the basis for using Planck’s constant is faulty. For now, we can presume that synchronous velocity for

the hydrogen atom is some fraction of the apparent speed of light, and that

0 1v

c N

EQUATION 169

so,

2

02

0

v Ze

c N cr . EQUATION 170

The values for all of the constants on the right hand side of the equation can be obtained by measurement except that of r0. It will be recalled that r0 the radius of the innermost orbit, is also the circumference of the Universal Kernel, around which the entire Universe is wound.

In Equation 170, there is no reason to assume limitations on the values of N other than that it is a positive, real number. However, it will be demonstrated that N is probably an integer. The particular integer suggested by equations 169 and 170 is a multiple of 274 (1/0.0035).

The mechanism for transfer of radiant energy from an emitting electron to a receptor electron is described with reference to Figure 27. In Figure 29, a proton, p1, is at the


153

apex of the cone representing the entire universe (in the two dimensional analog of the real 3D Universe) at a particular instant in time. For purposes of this discussion, it will be presumed that the cone representing the local time for both p1 and e1, the electron orbiting the proton and forming a hydrogen atom, is moving in the T direction at the velocity c, with the configuration in Figure 29 as the starting point.

In this picture, as second hydrogen is shown with its proton, p2, one more r0 interval away from p1, and along the same “line of sight” defined by the linear element of the surface of the cone. The cone contains all of the matter in the universe that can be “seen” from p1, and the element contains all of the matter in the universe which can be seen from p1 looking in the direction toward the original position of e1.

If we presume that e1 is orbiting p1, and e2 is orbiting p2, the electrons will move around their circular orbits at their individual velocities, v1 and v2.

It can be seen that, on the Universal kernel, as shown in Figure 26, the locations of e1 and e2 coincide on the surface of the kernel at a the instant depicted. This is true whether p1 and p2 are separated by only two of the r0 intervals of T or hundreds or millions of intervals. Presumably, they can either exchange energy levels, or possibly even exchange places. As the electrons seem to be identical in all respects except for the velocity component in the x – y space, it does not make any difference which occurs.

Because the synchronous speed, which represents the highest velocity the electron in the hydrogen free radical can have, there must be at least 6 or possibly 8 or more acceptable velocities which are integer fractions of v0, which means that there must be 6 or more acceptable electron positions within the first subdivision of the 274 positions the electron must occupy as it progresses around the orbit. Therefore, there must be a minimum of 6 x 274 , or 1642 or 8 x 274 = 2192.

It can be easily seen that the time to traverse the orbit is considerably longer than

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0vt

c , EQUATION 171

So there will be many intermediate positions around the orbit representing successive time intervals, t , of progress of the whole system in the T direction. If one presumes that the velocity cannot be greater than v0 for either e1 or e2, there will be several (say 274 for taking purposes) positions of e1 spaced around the orbital path. At any integer multiple of the time increment, t . The electron 2e must be at one of these incremental distances in order to interact with other electrons.

During this same time, the electron, e2, will proceed along its orbital path also. If it has the same, synchronous velocity, v0, it will also return to its original position after 274 time periods have passed. Thus the two electrons will be in positions of correspondence once every 274 time periods. However, because both have the same velocity, there will be no energy exchange between the two. Or, if there is, the two energy levels are identical, so there would be no observable change indicating a transfer of velocity.

On the other hand, were the velocity of e1 to be less than v0, it is apparent that e1 could receive energy from e2 by mechanical contact, wherein e2’s velocity would be transferred to e1, and vice versa. This energy transfer could only take place if e1 and e2 were in positions that coincide with one another. Although e1 remains at the same location on the universal kernel as it moves around its orbital path, e2 does not. After electron e2 moves away from the position shown in Figure 7, it can no longer exchange energy with e1 until it has completed its orbit and returned to the same position shown. In the time it is progressing around its orbit, it is no longer in the local present of e1, it is inside the cone and in the local past of e1. The likelihood of the transfer taking place would be proportional to the fraction of the time that the two electrons occupied positions on the same element of the local time cone for e1 (which would also coincide, at least


155

in part, with the local time cone for e2.) However, if the two electrons are orbiting at other than the synchronous velocity, it is apparent that they will both lie on the same element if each moves at an inverse integral factor of the synchronous velocity. That it, they will be in position to line up occasionally, if, and only if, the two velocities are

01

1

vv

n

EQUATION 172

and

02

2

vv

n . EQUATION 173

It is apparent that the position of e2 will never line up with that of e1 except in the event that both are back on the same line of sight element they started on, for they will never, under any circumstances, share any other element.

Thus is safe to say that the energy transferred from e2 to e1 can always be represented by the equation:

20

2 21 2

1 1,

2

vE

n n

EQUATION 174

which is the form of the Lyman series representing the energy content of the various lines of the spectrum of the hydrogen atom

This is somewhat simpler than the result of the Bohr derivation.

NOTES ON PLANCK’S CONSTANT I would prefer to believe that the basic energy

relationship should be given in a slightly different form. Returning to the value of Energy given in Equation

174,

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3 2 4

2 2 21 2

1 1

2

Z eE

h n n

EQUATION 175

I have argued that Planck’s constant should be written in

terms of the frequency squared, to bring it into conformity with other cyclic processes where the energy content of the system is proportional to the square rather than the first power of the frequency:

2E Hf EQUATION 176

for reasons that are explained in detail in a separate paper on Planck’s constant. In this case,

220 0

02 2

v vH

r

, EQUATION 177

which is satisfied for an value of v0, and yields a measure of the minimum orbital radius.

0

222

Hr

, EQUATION 178

or 2 2

02H r . EQUATION 179

This simply says that Planck's constant (or at least my

version of it) is the product of the mass of the electron times the circumference of the five dimensional kernel, r0, squared, and is independent of the velocity of the electron, or anything else.

Or, using my preferred version which eliminates Planck’s constant altogether, and uses instead the value of r0, the circumference of the Universal Kernel, as the primary constant,


157

2

2 20 1 2

1 1

2

ZeE

r n n

. EQUATION 180

Thus, the discrete emissions of energy in finite “lumps”

is simply explained by showing that this is the only circumstance in which electrons can exchange energy when at a distance and when apparently separated in time, by direct physical contact, and it is consistent with the New Theory of Light in an Expanding Universe. It will also be shown that the description of the electrons in energy transfer between the inner shell of the hydrogen atom is consistent with the structure of heavier atoms and compounds, whereas the Bohr atom is not.

Because there seems to be some parity between the number of electrons in the Universe and the number of protons, it is not unreasonable to assume that the natural, or original, state of matter was with paired protons and electrons forming free hydrogen radicals, and that there is still a preponderance of hydrogen free radicals in the universe over most other forms of matter.

Heavier elements grew out of high energy collisions between electrons or protons with the nucleus of a hydrogen atom to form helium in the first instance, and atoms with a neutron in the nucleus in the latter. It is unlikely that the average hydrogen free radical near the time of the Big Bang had a velocity exceeding that of the escape velocity from the hydrogen nucleus, because this condition would be, in a sense, self-sustaining.

The only way a free electron can get rid of velocity in the x – y – z space is by collision with another electron, in which case, it is likely that the two electrons would simply exchange velocities in a perfectly loss-free transaction, which would leave one electron going at the very high speed, and it would be indistinguishable from the original high velocity electron.

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HOT HYDROGEN Now, energy can be transferred to or from the orbiting

electron in two (and only two) ways that I can see. The first is straightforward, in terms of energy transferred, is radiant energy, in which atoms which are present in the same local time and place, as shown in Figures 27 and 30, line up properly, and the electrons exchange velocities. The momentum of the two electrons must remain constant, and the simplest way for this to happen is that the velocity is simply exchanged by the two atoms. Other outcomes are possible, but only if the electrons are not moving in exactly the same direction when the transfer takes place and this seems unlikely.

The second method involves collision between the atoms, or between compounds, which have a high velocity relative to one another, and which we would ordinarily characterize as “heat” for a collection of many atoms. It is obvious that a gas which is heated to a high temperature by compression increases in temperature, and that at high temperatures, the gas loses heat by radiation. This is the principle mechanism for transfer of heat from the sun to the earth.

But, in order for the heat to be radiated, kinetic energy of the atoms and molecules moving relative to one another must be converted, in part, to velocity of the orbiting electrons. This mechanism must be similar to the process which occurs when a glass marble is placed in a glass fruit jar, and the jar is shaken vigorously. When the oscillatory motion of the jar is right, the marble will spin around inside the jar, and relatively small movements of the jar can result in very high speeds of the “orbiting” marble.

When such a process takes place with the hydrogen atom in a cloud of hydrogen at high temperature and pressure, in


159

the Sun, for example, the electron can only be accelerated to the escape velocity, v0, before it will either leave the atom as a free electron (ionization of the hydrogen) or it will radiate energy to a second hydrogen atom which is at a lower energy level (and is, therefore, quite likely to be a long way from the sun).

Because the highly excited hydrogen atom can only radiate to an atom with a lower energy level, and because the two can transfer energy only if the velocities of the two are inverse integer fractions of the synchronous velocity, v0, the energy levels at which one hydrogen atom can “see” another are limited to those described in Equations 155 and 164.

Some other types of energy exchange are possible, such as that involving the photoelectric effect, but these will require atoms of higher atomic weight than hydrogen, so as to have higher synchronous velocities for the inner orbit electrons. These will be discussed later.

OUTER SHELLS The Bohr model of the hydrogen atom, and my model,

both allow for orbits outside the innermost orbit which has been described. In the Bohr model, it is necessary to assume that any electron moving at a lower velocity than the synchronous velocity for the innermost orbit will occupy an larger orbit farther out, at a distance r2 = 4r0, r3=9r0, r4=16r0,… and the synchronous (and only possible) velocity in these orbits would be v2=v0/2, v3=v0/3, v4=v0/4,….

It seems to me that, while this is possible, it is very unlikely to be the best description of the hydrogen atom with higher states of excitation than that that for the electron orbiting in the innermost orbit. Not only would this require a hydrogen atom of enormously expandable size for the higher excitation states, but it would make the model very cumbersome for elements heavier than Helium, which are known to have outer shells.

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In my estimation, the hydrogen atom can have one or more outer shells, but it is unlikely that these are stable. Any loss of energy would not send the electron outward to a more distant shell, but inward, where it would fall into orbit around the proton. In order to make this transition, the electron would have to lose a good deal of energy by radiation or it would arrive at the innermost orbital shell moving too fast to stay there. In fact, any electron that “falls” from the first outer shell or any point beyond would arrive at the innermost orbital radius with far too much velocity to be captured in orbit.

Rather, I think the levels at distances 2r0, 3r0, 4r0, etc. are likely to be occupied by the outer shells of the heavier atoms, and not by the inner shell electrons of the hydrogen atom or free radical which have become “energized”.

HEAVIER ATOMS AND MOLECULES It is also possible that a high energy electron will interact

with one of lower energy level, which I likely to have such a high velocity in the x – y – z space as to be able to pass through the inner orbit without slowing down enough to be captured, and continue on to impact with the nucleus. It is probably that this would require a speed near the apparent speed of light. These would lead to the formation of heavier atoms than hydrogen, and to isotopes with varying numbers of neutrons in the nucleus of the atom.

The number of protons in the atom determines the number of orbiting electrons which will be required to maintain electrical neutrality, and the sequence is pretty well known to consist of shells that have a maximum of :

Inner shell 2 electrons Second shell 8 electrons Third shell 8 electrons Fourth shell 32 electrons


161

While the outer shells may or may not contain electrons

with a substantial orbital velocity when the atoms are isolated, it is difficult to see how they can maintain an orbital velocity when they are shared between several nuclei.

THE HELIUM ATOM The helium atom is similar to the hydrogen atom in

structure, but has two protons in the nucleus and two electrons sharing a common orbit around it. There are two new characteristics at play here. One is the heavier nucleus, which suggests that the balance of centrifugal force on each electron with the attraction to the protons will be different, because of the doubled positive charge on the nucleus.

The force balance from Equation 161 for the hydrogen atom can be restated for the helium atom as follows:

r

v

r

Ze 2

2

22 , EQUATION 181

or,

222

vr

Ze . EQUATION 182

where

0r r , EQUATION 183

and r0 is understood to be the radius of the inner orbit of the electron in the Hydrogen atom.

202v v , EQUATION 184

2

00

22

Zev v

r , EQUATION 185

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which is an irrational velocity. Because the velocity must be an inverse integer fraction of the apparent speed of light, it is apparent that were the helium atom to utilize the inner hydrogen orbit for its two electrons they would have irrational velocities which would prevent them from ever occupying positions which would put them “in play” with respect to radiant energy transfer.

A more tenable alternative is to assume that the orbital radius of the helium atom corresponds to the second permissible orbit of the hydrogen atom. This case deserves to be looked at in more detail. Here the synchronous orbit and velocity are determined by the force balance just as was done for the hydrogen free radical.

FIGURE 29 TWO DIMENSIONAL DIAGRAM

OF THE HELIUM ATOM

2

22

Ze

hr

. EQUATION 186

and the velocity at this radius is:


163

h

Zev

2

, EQUATION 187

which is the same as for the hydrogen atom. Thus the picture of the helium atom on a flat x – y plane is shown in Figure 31.

The picture of the helium atom mapped on the x – y – U kernel shows the two protons at the origin, just as in the hydrogen atom, except that the two protons are both in substantially the same place. Both of them are at the origin in this case, rather than in two overlapping layers of the kernel. Also, the two electrons appear at the origin when mapped onto the kernel, but they are one layer farther away from the origin.

The picture of the Helium atom is, however, exactly the same as for the hydrogen atom in Figure 26.

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ATOMS HEAVIER THAN HELIUM The geometric construction of atoms heavier than the

helium molecule requires electrons inhabiting the second “synchronous” spherical orbit out from the nucleus, which can be populated by up to eight electrons. The geometry of the heavier atoms is simple enough when visualized in three dimensions. Here the four electrons in the second orbital shell are shown at the corners of a square overlaying a circle in the flat x – y plane, and would be at the corners of a cube overlying a sphere in the x – y – z – plane. When wrapped around the x – y – z – T – U kernel, with the nucleus at the origin, all eight electrons would overlie the origin, just as do the two electrons in the inner orbit.

.

FIGURE 30 OUTER SHELL ELECTRONS


165

The picture is a little more complex in the case of, say, oxygen, with an atomic number of 8. The six electrons in the outer shell will, of course, try to distribute themselves so as to maintain the greatest possible distance from each other, forming a polygon with six vertices

It is an interesting geometric problem to determine how 2, 3… 6, 7 and 8 electrons would distribute themselves uniformly around the surface of the second spherical shell, so as to always maintain the maximum possible distance from each other. There are, however simple distributions for each number of electrons. They are summarized below.

Two

electrons Opposite each other in a

single plane Three

electrons Spaced 120 degrees apart

in a single plane (the three electrons determine the plane.

Four electrons

At the corners of a square in a single plane

Five electrons

Two planes at right angles, each with three

electrons at 120 degrees apart. One of the electrons is common to both planes

Six electrons Two intersecting planes at right angles with four

electrons at the corners of a square in each plane. Two

electrons are In both squares Seven

electrons Three intersecting planes, each containing three

electrons at 120 degrees. Two of the electrons are in Two of

the planes Eight

electrons At the corners of a cube.

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166


167

THE HYDROGEN MOLECULE The bothersome questions raised by Bohr’s description

of the atom get even more troublesome if one looks at the hydrogen molecule.

In the hydrogen molecule, it is pretty apparent that the components are held together by the mutual attraction of the two protons for the pair of electrons, which repel each other to keep as far apart as they can, while holding on to the two electrons. The “attraction” of the charges is, in my opinion, the influence of each of them on the direction of time associated with the space around each of them, but it is simpler to refer to the phenomenon in the familiar terms, rather than via the roundabout mechanism proposed in this paper.

The natural configuration to assume is that of the two protons at opposite ends of an axis, about which the electrons revolve, in a planar orbit with the plane midway between the protons and at right angles to the line connecting them, as shown in Figure 32.

FIGURE 31 THE HYDROGEN MOLECULE

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Molecular hydrogen consists of two protons and two

electrons. The accepted configuration, barring the general disclaimers that the position of the electrons are, in effect, distributed according to the Uncertainty Principle, is that the two electrons circulate about a point midway between the two protons, in a plane perpendicular to the line connecting them. This appears to be the most likely configuration.

The radius of the orbit about the protons may be considered to be to be the same value as the fundamental radius established above, but the radius of the circuit about the centerline, which is no longer centered on the proton, is smaller in diameter.

In Figure 33, an analog of Bohr’s calculation can be used by taking the forces acting on the two protons and two electrons as follows.

On the Proton, the mutual attraction with the two electrons is

20

2

r

ZeFep , EQUATION 188

and the repulsive force from the other proton is

2

2

d

ZeFpp . EQUATION 189

A force balance around one of the protons yields

cos2 eppp FF , EQUATION 190

and

02

0

2

20

2

2

2

22cos2

r

d

r

Ze

r

Ze

d

Ze . EQUATION 191

Rearranging,


169

30

2

3

2

r

Ze

d

Ze , EQUATION 192

or

0rd . EQUATION 193 This indicates that the distance between the two protons

is equal to the distance between each proton and either of the electrons. In order to solve for these values, a third equation involving the three variables is required. This comes from the simple geometry

21

22

0 2r

dr

EQUATION 194

4

3

22

20

2

020

22

02

1

rrr

drr

EQUATION 195

01 2

3rr . EUATION 196

These calculations are consistent with the assumption that this configuration does not depend on the velocity of the electrons in the orbit. As the distance of the electron from each of the protons is the same as was the case for the hydrogen atom, it is reasonable to assume that the maximum orbital velocity of the electron in the hydrogen atom is the same as it was in the hydrogen ion, and that other

synchronous velocities are given by 2Ze

vnh

, where N is any

integer, and 2 2

0 2

n hr

Ze , just as it was for the hydrogen atom.

However, the circular path of the electrons now appears to have a smaller diameter orbit than was the case for the

hydrogen atom, and has a radius half or r1, or2

22

2

3

Ze

hN

. This

would, indeed be the case, were the electrons considered to

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be rotating around a point in space other than the protons. However, when either proton is taken as the orbit, the two electrons are, obviously, orbiting around it at the radius r0, but the orbit is no longer in a flat plane that contains both the electron and the proton.

A force balance around one of the electrons gives

21

2

4r

ZeFee EQUATION 197

20

2

r

ZeFep EQUATION 198

02

0

2

20

2

21

2

1

2

22cos2

)2( r

d

r

Ze

r

Ze

r

Ze

r

v

.

EQUATION 199

Setting the velocity of the electron equal to that in the

orbit around the single hydrogen atom,

21

2

1

2

r

Ze

r

v

EQUATION 200

02

0

2

21

2

21

2

22

4 r

d

r

Ze

r

Ze

r

Ze . EQUATION 201

Substituting

21

21

21 3

4

3

11

rrr , EQUATION 202

which checks.


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NUTSHELL PICTURE OF THE HYDROGEN MOLECULE

The hydrogen atom can be depicted in the T – x - y

space as shown in Figures 26 and 27. However, it is not possible to picture the hydrogen molecule in the same way, because, while the hydrogen atom may exist essentially in a single plane, the hydrogen molecule requires three spatial dimensions. the same point on the surface of the kernel although they are each located one orbital radius away from both protons, and in the y – z orbital plane which is not shown in the figure at all.

Relative to the surface of the kernel, all four particles appear to be stationary.

FIGURE 32 THE HYDROGEN MOLECULE

IN A NUTSHELL

Because the two electrons must occupy the same orbit,

and must move at the same orbital velocity, it is apparent that

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the transfer of energy from an ordinary hydrogen molecule must involve the loss of energy from both electrons simultaneously. This can only be accomplished by the alignment of this molecule with another hydrogen molecule, which must lie at the same point on the surface of the kernel. This is another way of saying that the second, or receptor, hydrogen molecule must exist at the same local time, at the same place.

Because the two molecules may be separated by as little as one orbital radius, or by as much as one eighth the circumference of the entire Universe, the galactic time difference between the two molecules can be as small as r0/c, or as large as c/H.


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SUMMARY The picture of the hydrogen atom derived by Nils Bohr

does not fit into my picture of the Universe, in which light and other forms of electromagnetic radiation are transfers of energy from one atom to another simultaneously, and in which there is no intermediate wave action. A similar derivation, arriving at a somewhat different picture the atom avoids this problem, and also answers some questions about the Bohr atom which are troubling.

The principle differences between the two models are: 1. The orbiting electron in Bohr’s atom occupies

one of six or more orbits with the highest energy level occupying the outermost orbit. In my model, the electrons, regardless of energy level are likely to occupy the innermost orbit.

2. The highest energy levels of the orbiting electrons in Bohr’s modes are due mainly to potential energy, and the kinetic energy is a relatively minor factor. In my model, there is no potential energy associated with these electrons. All of the energy is kinetic. There is no other kind of energy.

Bohr posits that the electron in the innermost orbit does not fall into the nucleus if it loses energy by radiation because it has wave properties, and the wave length matches the length of the inner orbit. It cannot get closer to the nucleus because the wave forms would no longer reinforce themselves.

In my picture, there is no wave-particle duality. The electron is always an electron, never a wave.

It is maintained at the minimum orbital distance by its position on a universal kernel around which the entire physical universe is wound. Electrons can only exchange energy or position between locations on the surface of this

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kernel. It cannot traverse the distance to the nucleus without acquiring a velocity equal to the apparent speed of light.

The velocity of electrons can decrease below the synchronous speed in any orbit without collapse of the atom. This is necessary for electrons which are shared by more than one atom, and is not explained by the Bohr model.


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CHAPTER 7

GENERAL RELATIVITY IN AN EXPANDING UNIVERSE

Unlike Special Relativity, General Relativity is not a simple matter of geometry and algebra. Instead, abstruse vector and tensor analysis is used to characterize the way space and matter interact, and rigorously detailed properties are assigned to empty space in the form of gravitational and electromagnetic fields. The amateur mathematician is at grave risk when he sets out on a voyage of exploration in the sea of General Relativity.

My main quarrel with General Relativity has been a difficulty of accepting that gravity is a property of space. It is easy to follow the popular illustration of the “gravity well” around a star acting like the depression in a rubber sheet, representing space. The motion of a planet circling a star is like the motion of a marble rolling around the inside of the conical depression created by a bowling ball. Instead of running off in a straight line, the marble follows a path that is circular, but “looks like” a straight line to the marble. Two bowling balls in proximity to each other, would tend to roll together.

However, it is difficult to understand how two massive bodies, essentially at rest with respect to one another, are acted upon by the empty space surrounding them in such a way as to cause them to accelerate towards each other. The space is, after all, empty, and whatever force acts on one of the two massive bodies is not countered by an equal and opposite force acting in the empty space around it, but rather

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by an equal and opposite force on the other body. The space, with no substance or mass, doesn’t seem like it is capable of exerting the force.

And, the rubber sheet illustration falls short of explaining gravity because the bowling ball pressing downward on the sheet and making an indentation into which the marbles roll naturally, depends on the force of --- gravity!

Rather surprisingly, the concept of gravity as a natural, relatively simple function of the relation between space and time seems more straightforward in a Universe that is expanding at the velocity c, in a fourth dimensional direction, and where the velocity of light is unlimited.

It is not hard to visualize. While it has some similarities with the rubber membrane supporting a bowling ball and some marbles, it does not depend on the force of gravity to explain the force of gravity.


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GENERAL RELATIVITY Special Relativity deals only with the properties of

systems which are at rest or are moving at constant velocity with respect to one another. Further, Special Relativity deals with the properties of matter only in a somewhat superficial way. General Relativity addresses systems which are accelerating or rotating (a special form of acceleration) relative to one another or which have gravitational effects. General Relativity proposes that all systems which are moving relative to one another, including accelerations and rotations, are equivalent as points of reference; that gravitational mass and inertial mass are numerically equal because they are different aspects of the same property of matter, and that gravitational effects are indistinguishable from accelerations.

One of Einstein’s main points is that time must be regarded mathematically as an imaginary quantity to be treated as a fourth coordinate in so-called Minkowski Space-Time. I do not see the need to treat time as imaginary, or to try to integrate it into a four dimensional coordinate system other than the one I used in the Special Relativity discussion. A fourth spatial dimension is clearly necessary to allow an expanding three dimensional Universe to expand into it. Time doesn’t quite fit this requirement. However, if the Universe is expanding in a fourth direction, the rate of expansion is clearly related to the passage of time.

Also, I do not see the need to try to generalize that all systems are equivalent. Einstein’s basis for these assumptions is the need to explain gravity fields as the equivalent of acceleration fields. I think they can be explained more rationally in terms of the mechanics of expansion of the Universe through the fourth dimension.

Previously, a fifth dimension was introduced to account for some of the properties of light and other electromagnetic radiation. However, for now, four dimensions are enough,

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and will continue to be enough until it is necessary to bring electrostatic and magnetic effects into the same picture as gravitational attraction.

To begin with, suppose that three-dimensional space simply stretches between the stars and planets, as well as electrons and protons and such, and is defined only by the relationship between our three ordinary spatial dimensions and the fourth spatial dimension, which is at right angles to the other three. The progress of the expansion of the Universe is measured in this fourth dimensional direction, which I have called the T direction, and is the constant velocity we know as the apparent speed of light. c. Conversely, time may be defined by the progress the universe has made in the expansion outward along the local T direction from the point in time and space where the Big Bang origin of the Universe took place. However, the location of the three dimensional Universe with regard to displacement in the fourth dimensional direction, T, defines what I have called the galactic time. That is, the time which is the same for all points in the three dimensional Universe. Galactic time, while simple in concept, cannot be used for practical measurements of time, because simultaneous events (that is, events which appear to occur at the same galactic time,) do not appear to be simultaneous because of the delays in observation due to the apparent speed of light being less than instantaneous.

Rather, it is necessary to presume that each observer has his own reference system, with himself at the origin, and his own local time, comprising all of the things he can see simultaneously (occurring at the same local time).

An observer at the origin in our three dimensional analog universe will always perceive himself to be in the midst of a flat, horizontal, x – y plane, with the T direction(which he cannot perceive) at right angles to the plane, or pointed straight up. He will measure the passage of time by the observation of changes in the relative positions of material objects as his observation point moves along the T axis at the


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apparent speed of light, c, away from the location of the Big Bang.

FIGURE 33 THREE DIMENSIONAL ANALOG OF A FOUR DIMENSIONAL UNIVERSE

As the three dimensional Universe moves outward, away from the Big Bang, there are also small differences in the direction of expansion.

An observer at any arbitrary point in the expanding three dimensional Universe, and using his own coordinate system with himself at the origin, will see himself as having no velocity relative to his system. But he “sees” most matter in three dimensional space as having some velocity relative to his own, apparently stationary, position. This means that, in addition to the lack of parallelism associated with the T directions due to the sphericity of the universe, most bodies will appear to have a tilt in their T direction due to their velocity relative to his own.

and space where the Big Bang origin of the Universe took place. However, the location of the three dimensional

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Universe with regard to displacement in the fourth dimensional direction, T, defines what I have called the galactic time. That is, the time which is the same for all points in the three dimensional Universe. Galactic time, while simple in concept, cannot be used for practical measurements of time, because simultaneous events (that is, events which appear to occur at the same galactic time,) do not appear to be simultaneous because of the delays in observation due to the apparent speed of light being less than instantaneous.

Rather, it is necessary to presume that each observer has his own reference system, with himself at the origin, and his own local time, comprising all of the things he can see simultaneously (occurring at the same local time).

An observer at the origin in our three dimensional analog universe will always perceive himself to be in the midst of a flat, horizontal, x – y plane, with the T direction(which he cannot perceive) at right angles to the plane, or pointed straight up. He will measure the passage of time by the observation of changes in the relative positions of material objects as his observation point moves along the T axis at the apparent speed of light, c, away from the location of the Big Bang.

Figure 35 shows a sketch of such a coordinate system around a mass, m1, at the arbitrarily chosen origin.

Where a single particle, such as a proton is considered, it is reasonable to assume that the position of the particle at galactic time, t, defines the position of the Universe at the spatial coordinates of the particle at time, t. Likewise, a second particle, with a velocity, v, relative to the first, will also define the position of the Universe at time t at its spatial coordinates. However, the direction of the T axis, at the position of the second particle will not be identical to that of the first, stationary particle. Although both have the velocity c it the T direction, the second particle will have a T direction that is tipped toward the mass m1 if m2 has a velocity component toward m1. Because T is always perpendicular to the x – y plane (by definition of what a fourth dimension


181

consists of), this means that the x – y plane through the second particle is tipped relative to the "flat plane" around m1.

The observer at the origin will see the particle m2 as moving toward it, because as his position moves in the T direction (time passes) he will see m2 getting closer and closer. An observer at the second particle's location, m2, would perceive himself stationary, with the expansion of the Universe proceeding along his T axis, perpendicular to his position on the x – y plane, and it would appear that it is the particle m1 which is moving toward him.

The m1 observer cannot observe the velocity of m2 through four dimensional space, but only the part that is measurable in three dimensional space. Thus the velocity vector c at m1 has the component velocity, v, in the x – y space and another component

2 2

Tv c v , EQUATION 203

in the direction parallel to the T axis through m1. Gravity, as it is observed to function, results in particles with mass

FIGURE 34 SHAPE OF SPACE AROUND A

MASSIVE BODY

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tending to move toward each other at linearly accelerating rates, such that they will eventually collide if not prevented from doing so. The velocities bodies naturally assume as a small mass, m2 falls toward a larger mass, m1, are as pictured in Figure 34.

Because the relative angle between the paths of the two particles becomes sharper as the distance between them decreases, it suggests that the T arrows (the normal movement of the particles with increasing time) are tipped increasingly toward each other as depicted In Figure 35. The curvature of the path of the particle is the rate of change of the angle, and represents acceleration of the second particle relative to the first.

It is presumed that the passage of time is measured by the change in the T dimension in the reference system chosen, so if the mass, m1 is used as the origin of the "stationary" reference system, then the direction of T will be straight up perpendicular to the broad x - y surface. The position of the x – y plane as subsequent times (values of t) are defined by t=T/c. However, one must remember that this time is associated only with this coordinate system. If one were to change the coordinate system to a body, m2, moving with respect to m1, the time references would also necessarily change, and would now be based on a new T direction T', at an angle to the T associated with m1.

That is, the local time system is skewed in such a way that at the center of the massive body, the T axis points straight up (regardless of whether or not the body has a velocity with respect to any other body), but that the nearby T values are skewed slightly toward the central T axis, as shown in Figure 35. The skewing becomes more pronounced as the distance to the more massive body decreases.


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FIGURE 35 EMPTY SPACE IN THE X - Y

PLANE

Let us look for a moment at the change that occurs in a region of empty space if a massive body in inserted into it.

The T direction arrows all point in the “up” or “outward” direction, and the surface in a small local area appears to be a flat plane as shown in Figure 36.

FIGURE 36 INSERTION OF MASS INTO

EMPTY X - Y SPACE

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The direction of the T arrow through the material body is still directly along the T axis, perpendicular to the x – y plane, and the directions of local time arrows at a distance are likewise substantially parallel to this T axis. However, in the immediate vicinity of the matter, the time lines should make some sort of continuous pattern, as shown in Figure 38. Although empty space has, in my opinion, no other properties but each point in space has position, relative to all other points, and velocity, c, in its unique T direction. These characteristics, taken together, suggest that the passage of time, itself, has a direction which coincides with the direction of the T arrows, and this direction alone constitutes all of the properties possessed by empty space.

The effect is exactly as if the x – y plane were “dimpled”, with the T arrows for all the points in the vicinity tilted inward, with the tilt inversely proportional to the distance from the center of the dimple. Of course, any mass would be accompanied by such a “dimple” with the depth proportional to the magnitude of the mass. Two bodies mutually attracted to each other by gravitational force would, of necessity, each have its own dimple, and the attraction of the two masses would be attributable to the tilting of the two T axes toward

FIGURE 37 SHAPE OF SPACE AND TIME AROUND THE MASS


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each other. There would be nothing to suggest the use of the position of one of the bodies as the reference point over that of the other.

The direction motion of the point through four dimensional space is set by the T direction at the point, and the only way to measure the passage of time is by noting the change in position of massive objects relative to the coordinate system which is moving in the local T direction.

In Figure 39, the value of y is presumed to be zero to simplify the picture, and the values of x in the –x to +x direction represents the x – y surface, which consists of all of the points at galactic time t, which form a continuous surface perpendicular to the T axis through each

However, the direction of the passage of time, represented by the T arrows through all the points, is of real concern, because it influences the behavior of any matter present in the space.

It should also be kept in mind that the direction of the T vectors is indicative of the direction in which galactic time is progressing in the vicinity of any matter that is present. For now, it is sufficient to say that all of our observations of the real world are based on our local time, which differs from place to place, and for observers moving relative to one another. The relationship between galactic time and local time is illustrated in Figure 39.

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FIGURE 38 LOCAL TIME AND GALACTIC TIME


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GRAVITATIONAL FORCES The behavior of an isolated object which is accelerating

relative to a fixed reference point must be identical to that of an object in a gravitational field at the same fixed reference point. That is, its local time axis is tilted relative to the general time axis by an increasing amount. This is exactly equivalent to being on the downward slope of the gravitational hill around a massive body.

In the following pages, I have reviewed the way in which the expansion of the Universe and the implications that light is a different sort of process than radiation of waves through space, impact much of the remainder of physics, including gravity, electrostatic and magnetic forces, and even the concept of force itself.

The only assumptions required here are: 1. All of the mass in the Universe has essentially the

same, original velocity, which is c, the apparent velocity of light. The direction of the velocity vector varies from one mass to another, but the general direction is outward from the point in space and time at which the Big Bang origin of the Universe occurred.

2. The space around massive bodies is dimpled inward (in the negative T direction) by a very slight time (or distance ct in the negative T direction), which is possibly caused by some loss of energy as elemental particles combine to form a more massive particle.

The cross-section of the x – y – z – T four-dimensional hyper sphere which we perceive as the three dimensional universe at the present galactic time is “dimpled” in the direction opposite the direction of expansion of the universe, and as a result the direction of time at nearby points

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progresses in a direction skewed toward the T axis through the massive body.

The perception of the passage of time differs for observers with velocities relative to one another. That is, an observer located at a mass, m2, will perceive his own velocity as zero (he is not moving relative to himself), while an observer at m1 will see him as having a velocity v in the x – y plane. The observer at m1 will ascribe this velocity as being in addition to the velocity c in the direction of the T axis through m1, and will, therefore take the total velocity of m2 to be

2 2'v c v . EQUATION 204

The perceived velocities of m2 as observed relative to

reference systems moving with respect to m2 are the relativistic corrections dealt with in Special Relativity.

The shape of the depression of the x – y surface (representing the 3-D Universe by analogy) around a massive body can be determined by using the measurements of the Universal Gravitational Constant.

We can start with a look at Newton’s “Law of Gravity”.

221

r

GmmF , EQUATION 205

where “r”, in this case is the distance between the bodies, not the radius of the Universe. This says the “force” acting on one of two bodies with masses m1 and m2 is equal to the product of the masses, a Gravitational Constant, G, and inversely proportional to the square of the distance between the two bodies. In our two dimensional analog universe, with both bodies located along the x axis, one at the origin and the other to the right of it, the distance r is simply the value of x at the second object. Built into this assumption is that Newton's laws of motion are very nearly correct, at least when there are no


189

relative velocities significant as compared with the apparent velocity of light.

A force of equal magnitude and opposite direction acts on the other body. (“Force” is used as a convenient term here, although we shall argue later that all “forces” are reflections of the acceleration of matter brought about by the alterations in the direction of time, and that there is no observable physical entity representing “force” at all.)

This can be thought of as each of the two bodies having a “field” around it, which is inversely proportional to the distance away from the body, and the mass of the body. The field is another concept which appears to be invented to provide a cause for changes in the velocity of one body with respect to another.

r

Gm

r

GmFFF 21

21 * . EQUATION 206

As it is apparent that the component of the “force”, F2,

is produced by the mass m1, one can write

r

GmF 2

1 . EQUATION 207

And, similarly,

r

GmF 1

2 .. EQUATION 208

These forces could be assumed to constitute a “Force

Field” around m2 and m1 respectively. However, the concept of force is, for reasons which should become clear later on, not one that is fundamental, and it will be better to use acceleration as the measure of the effect of gravity on bodies.

The direct effect of gravity on a pair of bodies in proximity to each other is acceleration of each toward the other:

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1 1F m a , EQUATION 209

and 2 2F m a EQUATION 210

or

22

11 r

Gm

m

Fa EQUATION 211

and

12 2

2

m GFa

m r

EQUATION 212

The accelerations of each body produced by the other can be taken to be due to acceleration “Fields” surrounding the bodies in question, the strength of which is proportional to the mass of the body, and inversely proportional to the distance away from the body. The acceleration, unlike the force, can be measured, essentially with a ruler and a stopwatch. The force must be calculated based on the acceleration and the mass.

FIGURE 39 CHANGES IN TIME AROUND AMASSIVE BODY


191

The local picture, around a mass, m1 at the origin and y = 0, to reduce the picture to two dimensions, is shown in Figure 40.

The massive object m1 causes the time-like coordinate T, to be slightly behind galactic time, ct, in the immediate vicinity of the mass. The magnitude of the time lag is proportional to the mass of m1. Any smaller object m2, located at a distance x from m1 tends to accelerate toward m1 in three dimensional space at a rate predicted by the universal gravitational constant, G, which is measured as 6.672 * 10-11 Newton-m2-kg-2.

A Newton is 100,000 dynes, or the amount of force required to accelerate one kg of mass one meter per second per second. In fundamental units, G has the dimensions m3/kg-sec.

The smaller mass, m1, would, of course, also produce deformation of the x – y plane in proportion to its mass. However for the time being, the mass will be assumed to be small enough that this effect can be neglected. The object of this exercise is to determine the shape of the x – y surface in the area around the mass m1.

The vector, v, representing the perpendicular to the x – y surface at m2, is tipped to the left.

As depicted, the mass m2 has a velocity v relative to m1 and appears to have the velocity c in the direction of m1's T axis. Were the observer located at m2 and using a coordinate system which kept m2 at its origin, he would see vt as c, and vx as zero. He would attribute the relative velocity to the motion of m1 toward him. This is completely consistent with Special Relativity.

This acceleration of m2 in the direction of m1 is what we describe as the acceleration due to gravity, G, It is the result of tipping of the T axis toward m1 at an angle which increases as m2 approaches m1. The velocity, vT, is perpendicular to the x – y surface and constitutes the general direction of time, as it would be experienced by the m2 mass. It would be presumed by an observer at m2 to be the direction in which

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time is progressing, and the direction the expanding Universe is moving in the T direction.

The vector vT, representing the “Time Arrow” in red in the Figure 43, pointing outward from the surface at m1, and at right angles to it, has a slope relative to the coordinate system through m1 given by:

xvSlope

c EQUATION 213

where: vx = x-direction velocity component

c=T-direction velocity component

Because the total velocity vector vT is perpendicular to the x – y surface, the slope of the surface is given by:

xvdT

dx c EQUATION

214 We should be able to use this relationship to establish

the shape of the x – y surface in the x – y – T space. This is relatively easily done by using the velocity calculated by Newton’s second law if the mass m2 "falls" unimpeded from a great distance toward m1. Its velocity at each point gives the slope of the surface of the x – y plane at that point, and the acceleration is simply the rate of change of the slope. It can also be taken as the velocity a body with essentially no mass will have if located at any point along the x axis.

The details of this mathematical derivation are spelled out in the appendix. The solution which comes out of is simply:

1

2

0

c

mG

c xTe

T

, EQUATION 215

where:


193

T0 = position of the x – y plane without distortion by m1 (i. e., the distance the surface is from the Big Bag point.)

or

A plot of the x – y surface obtained from this equation, using instead of x, the radial distance, r, where r is measured in distance units of c2/m1G is shown in Figure 41.

12

0 0 1m G

c xT T T T e

EQUATION 216

FIGURE 40 THE X – Y SURFACE NEAR A

SUBSTANTIAL MASS

The central mass, m1, is shown at x = 0, and the smaller

mass is shown at 7 units in the positive direction along the x axis. This is done by simply adding the exponents representing the two masses and using x -7 for the denominator in the second term for the smaller mass.

The value of T/T0 approaches 1.0 and the slope of the curve of the x – y surface produced by

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approaches zero as values of x become large.

Close to the mass, m1, the slope becomes steeper. The slope is given by

12 2

.m GTdT

dx c x

EQUATION 217

Of particular interest is the point at which the slope

becomes 1.0, which corresponds to a velocity equal to c, the apparent velocity of light. We have argued that the maximum velocity any body can have is c, the velocity imparted to all matter at the time of the Big

FIGURE 41 APPROXIMATION TO SLOPE

NEAR M1

Bang. It is unlikely that the "law of gravitation" applies at

distances smaller than the critical distance at which the calculated slope is 1.0 or greater. The value of x, below which the apparent velocity of light would be exceeded, is determined as follows.

Setting the rate of change of x with respect to T, which is dx v

dT c

equal to 1.0 in equation 217 yields


195

2 1

2

m G Tx

c

. EQUATION 218

The x and T values at this critical point are:

2 12

cc

m G Tx

c

. EQUATION 219

One pair of values satisfies this relationship

12c c

m Gx T

c . EQUATION 220

These values give some clue as to the depth of the

depression in the x – y plane around the mass, m1, but do not define it exactly.

The Newtonian gravitational relationship does not seem to apply for distances closer that xc, and in order to complete the definition of the shape of the plane it is convenient to simply assume that the velocities of matter could not increase beyond the value of c, so the slope of the plane within the

range 1c

m Gx x

c remains at 1.0.

This is depicted in Figure 42. It is useful to remember that x represents the distance from the central mass, m1, rather than an algebraic number, so the plot in Figure 45 is symmetrical about the T axis.

It is reasonable to rewrite Equation 215 as

120

0 0 0

1 1m G

c xT TT T

eT T T

. EQUATION 221

Because

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1

2

0

1 c

m G

c xcTe

T

, EQUATION 222

12

1

0

1

m Gc eT

. EQUATION 223

or

1 10 2

2

1.5821... 1.5821...1

1c

m G m GT T

cce

EQUATION 224

we can simplify the equations by writing

0

1cx

xT

eT

EQUATION 225

for 12c

m Gx x

c

and

0

2 cc

T xx

T x

EQUATION 226

for -xc<x<xc - In each of the above equations the x values should be

regarded as distances from the central mass, rather than as algebraic values. The distances can only have positive values.

That is, where there seems to be a deviation from Newton's second law for very short ranges, we have taken the easy way out, and simply limited the velocity to a slope of 1.0, equivalent to a velocity equal to the apparent speed of light when


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viewed in galactic time, or infinite velocity when view in ordinary, local time

SOME SIMPLE APPROXIMATIONS Because it is difficult to work with absolute values of T

(as we only know approximately the age of the Universe, etc.), calculations based on deviations of the value of T from some arbitrarily chosen T0 are easier to work with.

Beginning with the ratio in Equation 215, we can

manipulate the formulas to make a more useful expression as follows:

12

0

c

mG

c xTe a

T

EQUATION 227

0

1 1T

aT

EQUATION 228

0

0 0

1T T T

aT T

EQUATION 229

11c c

T aT a

EQUATION 230

So, from Equation 227 and Equation 230,

2

2

1 1

11

m G

c xc

m G

c x

c c

T a e

T ae

, EQUATION 231

where the exponents are easy to deal with if the appropriate units for x where each unit is equal to (m1G/c2) are used.

Some very other useful approximations to the exponential form o the gravity equation can be made by

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noting that the exponential can be written as an infinite series similar to ;

2 3

1 ...2! 3!

p p pe p EQUATION 232

or by the approximation

2

1 12 2

0

11 1 ... .

2!

m G m GT

T c x c x

EQUATION 233

Because the terms involving c4 in the denominator are likely to be very small for all but sub atomic values of x, 282 can be simplified to:

12

0

m GT

T c x

EQUATION 234

Again, at x values lower than xc, it is necessary to use

Equations 225 and 226 to avoid imputing greater than infinite velocities to regions of space very close to massive body.

Figure 46 is a plot T as a function of the distance x, using units of x each equal to 2/mG c .

12

12

c

c

c

m GxT c x

m GT xc x

, EQUATION 235

where,

12c c

m GT x

c

EQUATION 236


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FIGURE 42 COMPARISON OF APPROXIMATE AND CALCULATED CURVATURE

OF THE X – Y PLANE

Earlier, it was pointed out that both the exponential form of the gravity well equation and the approximation produce velocities approaching, in the case of the exponential curve, and exceeding, in the case of the approximation, the apparent speed of light at small distances from the center of the mass in question

There is no particular problem with this, in that ordinarily we are interested in mechanics only at much greater distances. However, a simple approximation which avoids this difficulty would be useful and can be easily substituted in most calculations.

Instead of substituting

12

0

m GT

T c x

, EQUATION 237

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one might use: 2 3

1 1 12 2 2

102

11 ......

1

m G m G m GTm GT c x c x c xc x

EQUATION 238

Equation 238 represents the exact, exponential equation

much more closely than does the Newtonian approximation for all values of x.

FIGURE 43 PROPOSED APPROXIMATION

TO THE CURVATURE OF THE X – Y PLANE

Figure 44 is a repeat of Figure 43, but with this curve

added in yellow. It is apparent that for values of 2/ 3mG c , there is no perceptible difference, and the slope of the curve approaches 45 degrees (equivalent to v=c ) at x = xc.


201

The table below compares the two approximations, and clearly shows that the proposed approximation represents a much closer match than the Newtonian Approximation.

The proposed approximation leads to the relationship;

2

2 1 12 2

11 1

1c

m G m GTp p

T p c x c x

Equation 239

Algorithm Name

Formula Series

Exponential (exact solution)

p

c

Te

T

2 3

1 ...2! 3!

p p pe p

Newtonian Approximation

1 .c

Tp

T

1 1 .p p

Proposed Approximation

1

1c

T

T p

2 311 .

1p p p

p

From this it can be seen that cT T

where 2/x mG c , and the slope of the x = y plane is 1 at this point, indicating a velocity of any matter at this point as c, the apparent speed of light, relative to the stationary mass, m1.

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203

ORBITAL MOTION The simple dimpling of the s x – y space around a

massive body seems to represent the way matter changes the relationship between space and time around it. It may be concluded that each body "sees" the space surrounding it in galactic time as being bent in such a way that the T vectors are perpendicular to it locally, but appear to be at an angle to the surface with a different reference point moving with respect to the arbitrarily chosen “stationary” reference. This situation is illustrated by Figure 45, where space seems to be bent in the direction perpendicular to the direction of relative motion of the two reference systems.

It is immaterial whether Space is bent by the relative velocity of the two masses, or rather that the curvature of space is responsible for the appearance of relative velocity of the two masses. This just seems to be the way space, time and velocity are related.

Although this is true so far as translator motion of bodies relative to one another is concerned, it does not seem to describe the relationship when one mass is orbiting another, or when two masses are moving relative to each other along a line perpendicular to the a line connecting them. In this case, there is obviously a difference in the angles of the two T axes through the bodies, but they are pointed in opposite directions. This can only be accounted for by a skewing or twisting of the x – y surface about the line connecting the two bodies, as shown in Figure 46.

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FIGURE 44 BENDING OF SPACE PRODUCES RELATIVE TRANSLATION

FIGURE 45 TRANSVERSE MOTION REQUIRES A TWIST IN SPACE

When one body is orbiting another (a special case of transition, where the relative motion of two bodies is at right angles to the line connecting their centers) this skewing or twisting has to be changing continuously as the orbital


205

motion takes place. Thus there must be a more complex pattern that those shown in Figures 45 and 46.

A body in a circular orbit around another has a velocity only in the tangential direction, and this means that the slope of the x – y surface around the in the orbital in the plane of the orbit must be that which is assumed by any orbiting body at that orbital radius. That is, it must be the velocity at which the "centrifugal force" (another of the "forces" which really has no physical counterpart, but which is convenient for calculations) is just equal to the gravitational force. That is,

2

1 2 22

TC G

m m G m vF F

r r . EQUATION 240

From Equation 162, the orbital velocity, as a function of

the radius, is

2 1T

m Gv

r , Equation 241

or,

1T

m Gv

r . Equation 242

The condition necessary for a small body approaching a

larger one to go into orbit around the larger body is that it must have a transverse velocity as the approach begins. Otherwise, the smaller body would accelerate straight toward the center of the larger one, and ultimately impact it. If, however, there is a component of velocity perpendicular to the line connecting the centers of the two bodies, the approach path will be curved and the result will be an elliptical orbit, which is, in its simplest form, circular.

In the case of a small body located at a great distance from a more massive one, the transverse velocity component

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is associated with (caused by or causing) a twist in the space around a line connecting the two bodies. Just as the gravity well around the particle appears to be of constant, unvarying shape when viewed from a coordinate system moving with the body, an observer moving with a velocity relative to the body would see not only the gravity well "tipped" in the direction of apparent motion but he would also see the space surrounding the body tipped in this same direction. Because the body is in motion relative to the stationary observer, the observer "sees" that the gravity well tipped in the direction of motion, at an angle given by

arctanv

c

EQUATION 243

When the motion of the smaller body is in the radial

direction from the larger, the motion is simple and linear, as described

in FIGURE 46 TIPPED GRAVITY WELL AROUND A "MOVING" BODY

Newton's equations, with the velocity observable from

any coordinate system limited to the velocity c, simply


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because the observable velocity is a component of the velocity through four dimensional space, c, essentially constant since the Big Bang

When the velocity of one body relative to another is tangential, or, in a sense, orbital, the velocities of the "moving" body cannot be ascribed to the effect of the heavier body on the shape of the space around it, as that effect is only capable of producing radial velocity toward the heavier body. Therefore, it must be attributed to some third, unseen body, which had the effect of producing a twist is the x - y - T space around the lighter body.

The tangential velocity of the less massive body relative to the heavier one produces an imperceptible twist in the x – y plane when the two bodies are very far apart, but the twist becomes more pronounced as the less massive body approaches the heavier one. When the velocities are such that it is "captured" and orbits the heavier body, the twist is both pronounced and periodic, moving around the massive body with the motion of the satellite.

FIGURE 47 TWIST IN SPACE WITH AN ORBITING SATELLITE

The degree of tipping of the velocity vector for the orbiting mass is simply that which is created by the downward curvature of the x – y plane in the direction of the larger mass, but the direction has been changed by the

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twisting of the plane. Now the velocity is neither toward nor away from the central mass, but rather completely tangential to it.

The direction of the absolute motion is x – y – T space is now entirely tangential, and the velocity, measured from a reference system moving along with the orbiting body is still c. However, measured using a reference system affixed to the stationary central body, the tangential velocity vT appears to be added to the velocity c parallel to the T direction through the central mass, thus

12 2

sin Tv m GtdT

dr c c r

EQUATION 244

Here we have used the distance from the body being

orbited, r, in place of the x used when we were talking only about transitional motion.

So, it can be seen that, when there is an initial velocity transverse to the line connecting the falling object and the large mass, the falling object will traverse a curved path leading to an orbit where all of the kinetic energy associated with the velocity gained as it falls is now directed along the tangential path of the orbital ellipse or circle, and none of the velocity remains in the radial direction.

In the previous case, the x dimension was taken to be the distance of the smaller mass from the larger one. However, in the more general case, r, the distance between the two masses, regardless of direction, should be substituted, and the velocity is now considered to bet the velocity in the tangential direction, which procures acceleration in the negative radial direction. Thus, the slope on the "depression" in the x – y plane must be considered to have a twist in the tangential direction which increases as the distance from the central orbital point deceases.

This is exactly the same slope in the circumferential direction as exists in the radial direction. So, the x – y plane


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may be considered to be twisted such that there is no twist at an infinite distance from the mass, and a twist that reaches 45 degrees when

1c c

m Gr r T

c

EQUATION 245

The usual equations governing the motion of the planets, etc. are exactly the same in this situation as derived from Newtonian mechanics with relativistic corrections. The differences from General Relativity are more in the line of why the deformations is space create the universal gravitational force, and there is little different in the equations which describe the effects of this spatial distortion.

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211

ENERGY CONSIDERATIONS There are a couple of significant differences in concept.

One is that, rather than the Einsteinian concept that the rest energy of a mass, m, is


To which is added the kinetic energy of the body in

motion (one must ask, in motion with respect to what?) so the total energy of the mass is

2

2

2

vE mc m . EQUATION 247

Instead, I believe the total energy of the mass is simply

mc2 , and the kinetic energy is simply that part of the total energy which appears to an observer moving with respect to the body, to be in the x – y – z space rather than in the T direction in which the Universe is expanding. Equation 49 led Einstein to the conclusion that the mass of bodies moving with respect to the coordinate system under consideration increases according to:

0

2

21

mm

v

c

. EQUATION 248

A more detailed derivation of Equation 248 is given in Appendix 2 following this Chapter.

Einstein and, I believe, most physicists since, believed that the mass of moving objects actually increases relative to objects at rest, and that the mass increase is necessary to avoid violations of the "law of conservation of energy". In my view, the mass is simply m. It does not change with

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changes in velocity, which is really only that part of the total velocity we can see because the direction of motion of the matter being observed is not parallel to our own through four dimensional space. The total velocity stays constant at c, the apparent speed of light. The mass is constant at m, and the energy is constant at mc2.

The apparent increase in energy with changes in velocity relative to our coordinate system are the result of a portion of the total velocity appearing as components in the x - y - z spatial directions. Because the observer stationary with respect to the "fixed coordinate system" cannot see the component of velocity in the T direction, he presumes this to be the velocity c, and presumes that the total energy is given by Equation 271.

Einstein was wrong on several counts. First, Special Relativity dealt only with the relation

between space, time and constant relative velocities. Acceleration, which is the necessary result of the application of “Force”, was not dealt with. So there was no valid basis for the postulation of a force which could act over a very long period of time at this point in his development.

Secondly, the assumption that no mass could have a velocity exceeding the apparent speed of light, c, was faulty, as the apparent speed of light was taken to be an actual velocity of movement of light through space, whereas light does not (in my view) actually move through the space between an emitter and receptor of radiant energy, but rather is transfer of energy between two atoms which occurs simultaneously, making the speed of light infinite.

Finally, equation 271 is untenable on the face of it. While Equation 272 appears to show increases in mass as

the velocity of the mass becomes significant with respect to the apparent velocity of light, c, The equation leads to some untenable conclusions.

If we substitute the mass of equation 272 into equation 271 we obtain


213

2 22 0 0

0 2

2

21

m v m cE m c

vc

. EQUATION 249

The right hand terms of Equation 273 fits the format of

( ) ( )kf x a x EQUATION 250

Where: 1a

2

2

vx

c

1

2k .

Equation 274 can be expanded as an infinite series

2 3( 1) ( 1)( 2)(1 ) 1 ...

2! 3!n n n n n n

x xn x x

EQUATION 251

Substituting the values from Equation 273 yields

2 2 4 620

0 2 4 62

2

3 151 .. .

2 4 2! 8 3!1

m c v v vm c

c c cvc

EQUATION 252

It is apparent that when the values of v are very small compared to c, the equation can be approximated by

2 2220 0

0 022

2

1 .22

1

m c m vvm c m c

cv

c

Equation 253

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However, it is equally obvious that at values of v large enough to be of significance in a relativistic sense, for example at

0.01v

c EQUATION 254

The two sides of equation 252 are no longer an equality.

One side or the other must be incorrect. It is my position that the whole basis for writing equation 248 was a mistaken premise on the basis of Einstein that the apparent speed of light could not be exceeded, so energy additions to matter which would cause it to exceed the apparent speed of light were impossible. Therefore the mass of the matter had to increase to account for the energy.

Viewed more logically, the total energy of a mass is always equal to mc2, and the observable “energy” of the body is that part of this total which appears, by virtue of relative motion with the observer, to be in the x – y – z space.

By the same reasoning, the concept of potential energy is greatly simplified if one presumes that all masses have the same inherent velocity, created at the time of the Big Bang.

The concept of potential energy was created to account for the kinetic energy which seems to appear by magic when a body "falls" toward the earth, or toward another body of considerable mass. What is actually happening is that the bending of our 3D space in the fourth, T, dimensional direction around the large mass is causing a greater part of the velocity c to appear to be in the three dimensional directions, rather than the T direction. This is an important point, and I have devoted a separate chapter to it.


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COMPARISON OF GALACTIC AND LOCAL TIMES

As was mentioned previously, and observer cannot see

things that are happening in his galactic time, but is limited to making observations in his local time. All that he sees or can experience is limited to the matter which exists, and the events which occur, in his local time. All of his local time is in the “past” from the standpoint of galactic time.

Because the galactic time, t, and the corresponding value of T = ct were used in the derivation of the shape of the x – T surface, it is useful to look at how these values relate to the local time, t', which an observer at the location of the mass in question, experiences, and to demonstrate that the conclusions will be the same, if based on local time-based observations. The only difference is that the path to the conclusions is considerably more difficult than when one assumes omnipotence, and observes on a galactic scale.

Recall that the observer at the arbitrary origin of the coordinate system cannot "see" objects located at his galactic time. Rather, all objects at the same galactic time as the observer will be in his "future". Instead, he will be able to see only objects which fall on the chevron (viewed on an x – T plot), or the cone, viewed on a three dimensional scale with x , y and T directions, representing his "present". In our three dimensional Universe, the cone will consist of a three dimensional sphere, which is what we experience when we look out on the real world. It is not apparent that objects which are distant from us are, in fact, associated with a different galactic time than we are. It is not much different for nearby objects, and something we don't notice, ordinarily.

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FIGURE 48 PATH OF A FALLING OBJECT IN LOCAL TIME

The path of a mass, m2, falling from a great distance toward a larger mass, m1, can be traced through both space and time, and illustrates the relationship between our observations of the object, and the four dimensional path which we have been working with.

In Figure 49, the observer at x = 0 at T1 observes m2 at a great distance to his right, but at his same local time, t1’.

As time passes, his position moves upward, in the T direction at velocity c, and passes through t'2, t'3 etc. At each successive time, the velocity of m2, represented by the arrow, bends from the vertical, representing zero velocity in the x – y plane, or an object at rest with respect to the observer at the origin, to the substantially 45 degree angle at t'8, representing substantially the velocity of light in the x direction, viewed from a galactic time viewpoint, or an infinite velocity when viewed in reference to an observer's local time.


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FIGURE 49 LOCAL PRESENT FOR A MOVING OBJECT

At each value of t or t', the x – y plane is warped in the

–T direction around the mass m1, such that the velocity of m2 remains perpendicular to the x – y plane. The shape of the x – y depression remains the same for all of the T1 through T8 positions, and is essentially that given by Equation 237.

The question of how the observer at point A determines the velocity of a body at point B which is moving relative to his position, requires some analysis. We have to define how he can tell whether the object is moving, and what its velocity is.

Here are some of the factors in his observations. In his judgment (i. e., that of the observer at point A), he has no velocity because his reference system is moving along with him. He and his coordinate system are moving at the same

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rate through four dimensional space at the velocity c, which he cannot perceive.

Anything on the horizontal line (or portion of the great circle) representing the galactic present, lies at some point in his local future. He will not be able to "see" it until his local present has advanced to the point where he is connected to that location by a 45 degree line.

What he will see, when he advances far enough into the future to "see" an object which is not in his galactic present, will not be the object itself, but the image of the object as it was in the past by an amount equal to the distance in space divided by the apparent speed of light, c.

His perception of distance, measured perhaps by the brightness of light emitted from a known source (like a star) is accurate, but his measurement of time is dependent on the observation of changes in position of things not at the origin, and therefore not in the galactic time present, but instead in his local present.

His perception of the velocity of movement of a distant object relative to his position will be different from that which would be determined by an omniscient observer, operating on galactic time, rather than local time, and also different from that of an observer with a different local time with a velocity relative to that of the primary observer.

It is of critical importance to his measurement of time that he know how much differently he sees the passage of time than would an observer moving with the object, or with any other reference system moving with respect to his own. The observer must recognize that an observer moving with respect to his coordinate system has his whole view of the Universe influenced by the tipping of the T axis. He sees the passage of time paralleling his path in his own private, T' direction, and his x – y – z coordinate system tilted along with it. The moving observer's local present is tipped, in this case around the y axis, so his past, present and future all differ from those of an observer stationary with respect to the coordinate system.


219

In Figure 51, consideration is given to the differences between the observation of time and velocity from a point at the arbitrary origin, and one some distance away, moving at a finite velocity of v with respect to the origin.

Assume that values without primes refer to the "stationary" origin as a reference and that the primes reference the same values but as observed for the moving object.

To an observer at the origin, at point T3 he observes the object m2 to be at a distance x1. If m2 is not moving relative to the origin, at time T4, the distance is still observed to be x1, and the velocity is calculated to be zero. The time interval between T4 and T3 is taken as

4 3( ) /T T T c EQUATION 255

The measurement problem here is that, from the point

of view of an observer at point B, he is moving with the velocity c in the T direction, and is stationary with respect to

FIGURE 50 LOCAL PERCEPTION OF VELOCITY OF A DISTANT OBJECT

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his coordinate system, just as the observer at point A is. So, while he sees himself progressing in the T direction, it is his own T direction, not that of the observer at point A. Thus, he does not move the distance c Δt in A's T direction. Instead he moves only to point 2'.

Figure 51 shows the relationship between the position of an object, m1 at Point A moving with respect to the stationary observer at point A., but with the path of m2 traced through several incremental increases in time as its location changes from point 1 to point 2' and finally to point 3', where Point B is observed from point T4 on the T axis through the origin. Point 2' is closer to point A than the original position, but it is not as much closer as it seems it should be. The observer reaching A's position T4 would not see m2 at this position, but rather would have seen it earlier, when he was only 2/3 of the way from T3 to T4.

Now, if m2 is moving toward the origin, the position of m2 at T3 is still observed to be x1, but at T4 the position has moved to point 3'. The distance moved is greater than the top leg of the lower gray triangle in Figure 50, which is

.x v t Equation 256

using for t the time scale appropriate to Point A, the "stationary" reference point, and keeping in mind that an observer moving along with point B would have an altogether different time scale, and would view this same time interval as

't . Point B would move, instead to point 2' in the time interval 't .

Point 2' can be "seen" from a point on the T axis, but not at T4, where point 2 is "seen". Rather, it would appear to be at an earlier local time. The location of point 3', where m2 will have to be before it can be seen from Point A at T4, can be found by constructing an infinite number of additional triangles, all similar to the lower one shaded in gray. This is


221

illustrated more clearly in 525 which shows a close-up of the area around point 3'.

In order to get the dimensions of the smaller triangles, it is necessary to note that the larger, pink-shaded triangles are equilateral, and that the largest of these has c t as both the altitude and base. The smaller pink shaded triangles can be used to determine that each is smaller than the preceding one by the ratio v/c, again using the time scale (for v) appropriate to point A's reference system, but not to point B's.

FIGURE 51 DETAIL OF LOCATION OF A MOVING BODY

The next such triangle adds the incremental distance in

the x direction which is in the ratio of the top side of the lower triangle to the right side. This ratio is

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vratio

c EQUATION 257

The third triangle adds an increment equal to the second

one, again multiplied by v/c, and so on ad infinitum, yielding the infinite series

2 3

1 ... .v v v

x v tc c c

EQUATION 258

This series is easily recognizable as

2 311 ...

1a a a

a

. EQUATION 259

with

va

c

. EQUATION 260

so,

1'

1x v t

v

c

, EQUATION 261

where 't is the time interval appropriate to the moving reference that has B at its origin. The moving observer sees his trajectory from point 1 to point 2' to be 'c t , and the distance from point 1 to point 2 as simply the component of

velocity in this arbitrary direction, which is 2 2c v . So,

2 2 'c v t c t , EQUATION 262


223

and

2 2 2

2

1

'1

t c

t c v v

c

, EQUATION 263

which is the same result as obtained using the Lorentz transformation and assuming that the speed of light in a vacuum is constant, independent of the motion of the observer.

The velocity determined by an observer at point A is, by definition, v, so the velocity is simply the distance from point 3 to point 3' in the x direction, divided by the time interval the observer at B measures, which is the distance between change in position (T4-T3)/c.

The observer at point B, with his coordinate system moving along with him, would have judged that he did not move at all, as his only motion was the velocity c, in what he judged to be the T direction.

Were the motion of B away from A, at the arbitrary stationary origin, the location at which m2 could be seen from A when it reached point T4 is as shown in Figure 52, the x = ct line connecting T4 to point 3', a position at which m2 can be seen, is again derived by adding the incremental triangles, as depicted in Figure 54.

However, in this case, the successive approximations, represented by the shaded triangles in Figure 52 produce a series with terms which are alternatively positive and negative:

2 3

1 ...v v v

x v tc c c

EQUATION 264

This series, similar to that of Equation 258, and is easily

recognized as

2 311 ...

1a a a

a

EQUATION 265

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Again, with

1'

1x v t

v

c

. EQUATION 266

va

c EQUATION 267

FIGURE 52 OBSERVED MOTION AWAY FROM THE REFERENCE

This is exactly the same result that would be obtained

had we simply used the negative value of v in v

ac

.

should be unambiguously pointed out that the observation of velocities from a "stationary" reference system is never the same as the velocity which would be measured by an


225

omnipotent observer using galactic time rather than the local time which must of necessity be used by any observer

FIGURE 53 CLOSE-UP OF SUCCESSIVE TRIANGLES

.This indicates that from the standpoint of the observer moving with m2, time passes at a normal rate, while a stationary observer at point 1 would think his time progressed more slowly.

Were the object at point B, rather than a point, a measuring stick, one meter long, the location of the two ends would offer no problem were the measuring stick stationary with respect to the observer at A. He would "see" the two ends of the stick simultaneously, at his present time, and would see them each at a distance one meter apart. However, it is apparent that, if the measuring stick is moving relative to the stationary observer, the length of the stick would lie along the baseline for the moving system, which is tipped relative to the stationary system at an angle whose tangent given by

2 2arctan

v

c v

EQUATION 268

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2

2

arctan

1

vc

vc

. EQUATION 269

Thus the measuring stick would appear, to the stationary observer, to be not one meter long, but rather

2

2' cos 1

vL L L

c . EQUATION 270

This foreshortening is also exactly the amount derived in

the Lorentz transformation. While the equations derived here are in general

agreement with those of Special Relativity, the differ considerably in the area covered by General Relativity, particularly in regards to the definition of the energy possessed by masses (and why they inherently possess energy). The conclusions I have drawn suggest that E= mc2, not because matter and energy are equivalent, but because all matter possesses a high level of kinetic energy of which we are ordinarily unaware. Only part of this kinetic energy manifests itself as velocity in the universe in which we live.

In my view, all particles in the entire Universe, without exception, have a total energy level

2

.2

mcE EQUATION 271

Bodies that are at rest with respect to our reference coordinates have this same amount of energy, and so do bodies which are in motion. The only difference is that bodies which are in motion relative to our own position have their direction of motion in four dimensional space rotated


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slightly, so that a portion of their velocity in the T direction appears to us to be a component of velocity in the three dimensional world in which we can see it. It doesn't change their total energy at all.

In order to be in motion relative to us in our three dimensional Universe, an observer attached to the moving body would see the Universe tipped so that it is his T axis that is pointed straight up (at right angles to the normal x, y and z coordinate system we use), and that everything is perfectly normal to him. His clock runs at the normal rate, his lunch pail does not gain weight because his coordinate system is moving rapidly with respect to the star Proxima Centauri.

The whole concept of "rest mass" being the mass of a body which is "not in motion" is absurd when you think about it. It can't be a property of matter, because it depends on how you choose your reference system. I could demote everyone on earth to a much lower energy level by using a coordinate system centered on the sun, which would increase their kinetic energy enormously, but it certainly wouldn't change their total energy, so they would automatically lose weight!

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229

GENERALIZATION TO THE THREE DIMENSIONAL WORLD

For simplicity in the derivation, the generalized point of reference was taken on the x axis, such that x represents the distance between m1 and m2. . However, if a point anywhere on the x – y plane were considered, and the distance, r, of the mass m2 from m1 were substituted for x, there would be no loss of validity. The same thing holds for the real three dimensional Universe, where :

2 2 2r x y z

. EQUATION 272

This immediately leads to the approximate shape of the

x – y - z surface in the three spatial dimensions, x, y, z and T.

12

1 11 c cT rm G

r rc r

c

Te e e

T

EQUATION 273

where 0T T T , and 0T represents the upper horizontal line (the x – y plane in the analog universe in Figure 43), or the x -y – z space in the real Universe.

So the foregoing material which was all developed using

a simplified two dimensional universe, should apply equally well for the three dimensional Universe where

2 2 2r x y z ,

EQUATION 274

so long as the value of 12

m gr

c

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While this gives the shape of the “surface” around a massive body in terms of local time, the shape of the sphere representing the entire Universe in terms of galactic time, can be written as

22 2 2 2 2 ,

Tx y z T c t

r

EQUATION 275

or, expanding the last squared term,

2 2 2 2 2 2 12

1m g

x y z T c tc r

. EQUATION 276

Again, the last term on the right, involving c2 in the

denominator along with 1/r, is likely to be very small compared to the previous terms, and can be neglected for values of r not very close to 0, where the equation does not apply anyway. This yields a simplified equation for the area around a mass, m1, which is approximately

22 2 2 2 2 10 0 0 0 0 2

( ) ( ) ( ) ( ) 1m g

x x y y z z T T c t tc r

. EQUATION 277 Were there to be two massive bodies, m1 located at x = 0

and m2 located at x = x2, the equation would become 2

2 2 2 2 2 1 22 2

2( )

m G m Gx y z T c t

c r c r r

.

EQUATION 278

It is apparent that the shape of the curve representing the x - y surface, viewed at y = 0, is a hyperbola, which is asymptotic to the T0 plane at large values of r, and to the r = 0 line ( T axis) at very small values of r, but at the small do not accurately represent the shape.


231

There are some philosophical conclusions which can be drawn from the form of this equation. It shows the effect of gravity on time is proportional to the mass of the object in question. It also makes clear that the shape of the Universe (formed by a surface at right angles to the local time axes) is really quite a smooth sphere, with only the faintest dimples in it, which are apparent only under close magnification. It is smoother than a highly polished Christmas tree ornament.

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ADDITIONAL ENERGY CONSIDERATIONS Here are some interesting aspects of shape of the

dimples around gravitational masses. First, it is apparent that the depth of the depression is a

measure of the distance the mass lags behind the rest of the Universe in its expansion in the T direction, and the depth of this depression is directly proportional to the mass. It might actually be the mass, as it is only by means of the depression in the surface that its effect on other bodies can be seen.

The depression is not very large in terms of the diameter of the Universe, or in terms of the physical dimensions of the solar system, for example.

The question of why there should be a retardation of time in the vicinity of massive bodies does not have a clear-cut answer other than the possibility that mass is simply the property we assign to these depression singularities in space. It is possible that, when a massive body was formed by the aggregation of smaller bodies, each had to have some loss of the energy it possessed from the Big Bang, and the aggregate, therefore, was moving very slightly slower after the amalgamation than the smaller bodies were before. This makes sense, because each massive body has to have a different location in the Universe, and each unique location has its own unique “Arrow of Time”, which points outward from the Galactic Origin, through the particular point. Therefore, no two bodies ought to have exactly the same outward velocity before aggregation.

It seems apparent that, by virtue of 3D space being “dimpled” in the direction opposite the direction of expansion of the Universe in the T direction around a mass, m1, the mass somehow represents a lower energy level than would be the case were the dimpling not there. That is, by lagging behind the surrounding matter as it passes through space in the T direction, it has lost some of the energy it had

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at the moment of the Big Bang. It is not moving more slowly than less massive bodies; it is simply lagging behind by the distance

2 2 .T c t EQUATION 279

The kinetic energy of the mass m2, after it has fallen from

a distance to x is given by

22

2x

k

m vE EQUATION 280

where vx is the component of the total velocity c, which appears as a velocity in the ordinary Universe when viewed from a remote reference system. The energy of the mass is, of course, mc 2, a small portion of which appears as kinetic energy because the T axis of m2 is tipped relative to the reference system.

This potential energy observed from the reference system attached to m1 is entirely due to the presence of m1 at the origin, therefore it can be assigned to the difference in the value T0-T at point x, or

10 0 2

m GT T T T

c x EQUATION 281

In this view of the Universe, there is really no such thing

as potential energy, but the kinetic energy of m2 can be interpreted as the quantity which appears as the slope of the x – y plane increases, or as the quantity delta T increases. So, we may write

22

2x

p k

m vE E . EQUATION 282


235

Both of the energy expressions have units of mass-length2/time2, whereas the depression in the x – y plane is a simple measure of distance, albeit in the fourth dimensional direction. The proportionality factor is

2

( )( )

( )kE mass length

T time

EQUATION 283

This corresponds to the units of the gravitational

constant. G. So,

( )kElength

G

EQUATION 284

Is it possible to associate an energy value with the time

lag experienced by the space in which m1 is located? The ratio of the energy of the mass, m1 to the depression

in the x – y surface is

2 41 1

102

E m c cm GT Gc

, EQUATION 285

or,

4c

E TG

. EQUATION 286

This demonstrates the linear relationship between the

mass and the depression, which is independent of the absolute value of the mass. This is important, because it is necessary for mass and energy to be conserved.

If one considers that, in the case of m2 actually colliding with m1, as in the case of a meteorite falling to earth, the energy associated with the mass of m2 will simply be added to that of m1, and the depression will be increased in proportion to the increase in mass at m1.

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The kinetic energy of the particle at m2, if it has fallen freely from a great distance, is

20 2

.m G

Tc

EQUATION 287

And this energy seems to disappear. It is, of course,

converted to thermal energy, which indicates the conversion of the organized energy of all of the atoms comprising m2 moving together in the –x direction as they fall toward m1, into disorganized velocities of the individual atoms moving in random directions. But this is getting a bit ahead of the story.

It is also interesting to note that black holes, where the mass is concentrated into a relatively tiny volume, exist wherever a mass m1 is contained within a sphere with a radius given by

11 2

,Gm

rc

EQUATION 288

letting x = r in 2 2 2r x y z .

.

12

1 ,Gm

xc EQUATION 289

In other words, the Schwarzschild radius for a black hole

is the radius r1 within which the mass m1 is contained.


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TRANSLATION, ROTATION AND ORBITAL MOTION

The case of rotary, and particularly orbital, velocity of

one body relative to another is more complex than the simple translation velocity which has been dealt with in previous discussions. When two bodies are moving directly toward or away from each other, it is simple enough to presume that the x – y plane in which they are located is curled up along the centerline connecting the two bodies. When they are involved in translational motion, the x – y plane must be twisted around the line in 3D space connecting the two bodies.

The relative motion of any two bodies can always be resolved into a combination of translation in a direction directly toward or away from each other, plus a component that is at right angles to a line connecting the two.

In these figures, the slope of the surface at any point can be presumed to be the velocity that would be assumed by a particle with no significant mass, which would, from the point of view of a reference system moving along with it, always be at right angles to the surface, and would always have the velocity c.

Bodies with mass or charge, on the other hand, do not follow the general surface configuration exactly, but instead, modify it. In the case of the mass of the body, the modification is a depression or deformation in the –T direction that is proportional to the mass, and which diminishes with distance according to:

2

0

1mG

c xTe

T

EQUATION 290

When a body with mass is moving with respect to

another considered stationary at the origin, the x – y surface

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is warped but the gravitational displacement of the x – y surface, and the shape of the depression around the body is also by the tilted by the velocity. The gravitational displacement of a stationary mass is shown in Figure 55, and the displacement of a moving mass is shown in Figure56.

Here the mass affects the x – y plane orientation in the immediate vicinity of the mass, but the effect is diminished with distance away from the mass.

FIGURE 54 A MASS WITH NO VELOCITY

RELATIVE TO THE COORDINATE SYSTEM

A complicating factor is the fact that there is a cusp, or discontinuity of the surface at the point at which the mass is located. So, if the particle is stationary with respect to the reference system, the time vector is straight up, and the conical depression is symmetrical around the mass. However, if the mass is moving with respect to the coordinate system, the time vector will be tilted in the direction of motion, and the conical depression will be similarly tilted in the direction of motion, as shown in Figure 56.

In Figure 56, the mass has a velocity along the x axis away from the stationary reference origin. The effect of the mass it to tip the depressed cone, and the whole x – y plane in the direction of motion, but again, the effect diminishes with distance from the mass. This local tilting of the x – y plane relative to the T direction of the assumed stationary


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origin is most important in the consideration of transverse motion of particles (transverse with respect to the stationary origin), and in particularly with reference to masses, and charges, orbiting the stationary origin. The particular case of circular orbits involves particles which have no translation velocity at all.

In the case of either translation or transverse motion of one mass with respect to another, it is quite appropriate to use the two dimensional analog of the three dimensional Universe for simplicity, as long as it is kept in mind that any plane which contains the “stationary” central mass and the orbiting less significant mass, could be used to represent normal three dimensional space, simply by choosing to define the third coordinate as having a zero value. It is true that both the masses will orbit a point at the center of gravity of the pair or, with the greater mass closer to the center of rotation. However, for this superficial discussion, the central mass is presumed to be infinitely greater than that of the orbiting mass, so it can remain stationary at the origin.

FIGURE 55 A MASS WHICH IS MOVING

FROM LEFT TO RIGHT RELATIVE TO THE COORDINATE SYSTEM

Figure 57 is a drawing of the warping of the x -y plane

around a massive body, where the warping would appear to be a circular conical depression, symmetrical around the

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FFIGURE 56 SATELLITE ORBITING A MASS

central mass. An orbiting minor mass also produces a depression in the x – y plane, which is moving with respect to the central mass, so its depression appears to be skewed or tilted in the direction tangential to the orbit. The angle of tilt is arc tan v0/c. where v0 is the orbital synchronous velocity and c the apparent speed of light. The skewing of the depression around the minor orbiting mass twists the x – y plane around the y Axis in Figure 60, but the twisting is local to the minor mass., so both the gravitational depression in the x – y plane due to the mass of the object, but also the twist in space because of the presence of the minor mass, and also the tipping of the x – y plane.

This tipping around the orbiting mass is likely to be limited to the according the equation:

0 1vv

c c r , EQUATION 291

where r= distance from the minor mass.


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CONCLUSIONS

The velocity observed for a body relative to a "stationary" frame of reference is, in fact, the component of the velocity vector c, which is the velocity of all matter in the Universe. While the magnitude of the vector is the same for all matter, the direction differs for masses which appear to be moving relative to one another in the three dimensional world in which we live.

The velocity vectors are always pointed in the direction T, which is perpendicular to the three x – y – z dimensions we are familiar with. Thus we always observe ourselves as “stationary”--- that is, as having no velocity in the x – y – z directions, but see other bodies as having velocities because they moving perpendicular to other areas of the x – y – z surface not parallel with our own.

Because the velocity vector c is always perpendicular to the x – y – z spatial coordinates, it means that space is, itself warped in the T direction, by an amount that is proportional to the mass of the matter occupying it. For those masses which are at rest with respect to our coordinate system, the depression around the mass is symmetrical to it. However, if the mass is moving relative to our coordinate system the depression appears to be about the T axis of the moving particle.

The only properties which need to be associated with space involve locating each point in terms of where it is relative to other points in space in the direction of the expansion of the Universe.

The warping of the three dimensional universe in the fourth dimensional direction is not apparent to three dimensional observers. However, all matter occupying the space that is so warped will have an observable velocity in the

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direction of the matter responsible for the deformation. This is ordinarily called the acceleration due to gravitational forces.

The depression of the surface representing our three dimensional universe in the two dimensional analog used here is proportional to the mass of the matter occupying the space at any point. The rate of change of the slope of the surface, or the curvature of space in the fourth dimensional direction, is proportional to the acceleration of matter located therein. It is also proportional to the "Force" of gravity exerted by the nearby masses, and might be called the gravitational field around the mass.

When two or more masses are present in a region of space, the each creates a deflection in the three dimensional Universe in which we live, in the fourth, or time-related dimension. These deflections, added to the all the other masses in the Universe, and determine the shape of the space in the vicinity of the masses at the present galactic time.

The shape of the Universe in galactic time is not observable, as we can only perceive events or objects in our individual local time. This suggests that "reality" consisting of those things we can perceive, is totally in the galactic past, and that the configurations of the Universe, viewed from a galactic time standpoint, continue to be real so long as there is anyone capable of observing them.

The "shape of space" is synonymous with the direction of time at every point in space. Time, for any observer, passes as the point in space he occupies moves in the fourth dimensional direction, and can only be determined to be passing by observations of the change in position of other bodies in reference to the observer's.

Space has no other properties besides the distance it lies from the moment of the Big Bang, relative to other points in space, and the direction of time at the point.

The "Force of Gravity" is simply a measure of the acceleration of bodies relative to each other, caused by the deformity in the shape of space around them. Masses do not "attract" each other, but rather bend three dimensional space


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in a way that makes the component of velocity of other masses which they can see increase relative to them.

All matter in the Universe has the total energy content given by E=mc2, all of which is kinetic energy. The observable kinetic energy is simply that due to the component of the velocity which observable in three dimensional space. Kinetic Energy of a body is always zero relative to an observer moving along with the body, and greater than zero for observers who are not moving in unison with it.

Potential energy is a useful, but basically imaginary concept. A body does not acquire potential energy when it is lifted off the earth and flung into outer space. Rather, the total energy of the body remains a constant E=mc2, and the relative direction of the body through four dimensional space determines the fraction of the energy which can be 'seen" by an observer affixed to the earth, and which changes in according to the familiar rules.

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CHAPTER 8

PLANCK’S CONSTANT REVISITED

There is a glaring difference between my picture of the

hydrogen atom developed previously, and Bohr’s. This becomes apparent if any orbital value with a quantum number other than n=1 is taken for calculating the value of Planck’s constant.

There is an incompatibility between Planck’s constant

E hf EQUATION 292

and the energy of an electron in orbit at radius r.

22 22

1

2

1rfmmvE , EQUATION 293

where E would be proportional to the frequency squared, except for the case where

r

kv , Equation 294

which is the case assumed for the development of the Bohr atom, and which leads to some inconsistencies when heavier atoms are considered.

Possibly, Planck’s constant ought to be defined by

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2E Hf . EQUATION 295

I think this is where Planck and, consequently, Bohr,

went wrong. E = hf looks like a bad assumption. The energy in any kind of mechanical wave is proportional to the square of the frequency, not to the frequency.

Planck was likening the electromagnetic radiation he was studying to other types of waves, and trying to make sense out of the radiation assumed to be transmitted from black bodies. He was able to solve the problem that the energy of the radiation increased with the frequency seemingly without limit, by presuming that the energy could only be transmitted in packets, later called quanta by Einstein and others.

That energy is available in packets is pretty reasonable, but it should be proportional to the frequency squared.

The energy involved in generating a mechanical wave, which is substantially the same for any kind of oscillatory motion, is pretty much like it is for a weight on a spring set to oscillating. The equation of motion of the weight is

tAx sin . EQUATION 296

FIGURE 57 WEIGHTS ON A SPRING MAKING WAVES


247

The kinetic energy of the weight is given by the velocity, which is

tfAwtAdt

dx cos2*cos EQUATION 297

The energy associated with the wave consists of the

kinetic energy which reaches a maximum as the weight passes through the zero deflection point in the cycle, and the potential energy, which is zero at the zero deflection point and reaches a maximum at the extremes of motion, where the kinetic energy is zero.

2 2

2( 2 cos 2 ) ( 2 cos 2 ).2K

v mfE m m A f ft A ft

g g

EQUATION 298

The energy, Ek, is proportional to the square of the frequency. Likewise the total energy is proportional to the square of the frequency.

Planck’s constant was evolved in order to make sense of the emission of radiation from a black body, which, according to earlier concepts of radiation would require the radiation energy from any black body to increase with increased frequency without any upper limit, and would, in theory, require infinite radiation from all black bodies.

In order to make the observed radiation fit a theoretical framework, Planck proposed that the emission was limited to packets of energy which are proportional in amount to the frequency of the radiation, and the radiation at each frequency is given by Planck’s equation,

1

2)/(

3

2

KThff e

f

c

hB . EQUATION 299

This matches the experimental data for black body

radiation..

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How would this equation look if, instead of h, we used H as defined below?

2

EH

f EQUATION 300

2 Ef

H EQUATION 301

2Hf E hf EQUATION 302

h

Hf

EQUATION 303

h Hf EQUATION 304

Substituting in Equation 310,

3

2 /

2

1f E KT

Hf fB

c e

EQUATION 305

2

4

2 '

2

1

f h f

KT

H fB

ce

. EQUATION 306

This seems to make just as much sense as Planck’s

original equation, and, of course, produces numerically equal results.

While Planck’s constant or my proposed alternative work equally well in the black body radiation equation, Planck’s constant does not properly represent the ratio of energy to frequency in the orbits of electrons, other than the inner orbit, as derived by Bohr.

For an electron in a minimum radius orbit, r0,


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frv 00 2 EQUATION 307

2

20

0

vE EQUATION 308

0

00 2 r

vf

. EQUATION 309

Planck’s constant is

0

0

0

0

20

2

2

2r

v

r

v

v

f

Eh

. EQUATION 310

However, at other values of v and r provided by Bohr’s derivation

200

02 3 3

0 0 0

0

12 2 2

2

vvvE hnh

vf r n r n nr

.

EQUATION 311

Obviously, Equation 322 is not correct for values of n

other than 1. This seems to be a serious limitation on the generality of the definition of Planck’s constant. On the other hand, the proposed alternative definition,

20

2 202 2

0

0

2 2

2

vE

H rf v

r

EQUATION 312

is satisfactory for all values of n .

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2

0

2 2022

0

0

2 2

2

v

nE

H rf v

nr

EQUATION 313

This says that the energy in a wave is proportional to the square of the frequency. The energy per cycle goes up as the frequency goes up. This makes more sense than saying that the energy in all electromagnetic radiation is the same for each cycle. The black body radiation formula continues to work if you use “Hardison’s Constant”, H, instead of Planck’s Constant, h.

Now, how does Bohr’s atom come out, if you use Hardison’s Constant? We can return to Bohr’s derivation of the electron orbits at equation 191.

r

v

r

Ze 2

2

2 . EQUATION 314

From this,

2

2

v

Zer

. EQUATION 315

This relationship allows for an infinite number of

combinations of electron orbital radius and electron velocity. Bohr postulated that the electron angular momentum was restricted to specific values so as to account for the emission of radiant energy only in specific wave lengths. By using

2E Hf , EQUATION 316


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22

2 2

v vH

r

, EQUATION 317

where the v terms cancel out, leaving

222

Hr

, EQUATION 318

which is independent of velocity, and

2

2

2

vE Hf

, EQUATION 319

for

0vv

n , EQUATION 320

where n = 1, 2, 3, 4,…. which is necessary to place the electron back at the origin periodically, in the kernel view of the rolled up Universe , and is independent of the orbital radius.

For the innermost orbit, with the maximum velocity possible,

2 4

20 2

0

4Zev

r H

, EQUATION 321

which gives the maximum velocity the electron can have and still stay within the minimum orbital radius. If the electron velocity increases, it will escape the orbit altogether. However, it can have lower velocities given by equation 320.

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CONCLUSION It appears that the use of the constant H (which I

modestly called “Hardison’s Constant) defined by the equation

2E Hf EQUATION 322

instead of Planck’s constant, defined by E hf EQUATION 323

eliminates some of the inconsistencies in the model of the hydrogen atom presented by Nils Bohr, and modified to fit my picture of the structure of hydrogen and other atoms.

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CHAPTER 9

HEISENBERG’S UNCERTAINTY PRINCIPLE

The preceding discussions of the basic relationships of

mass, charge, velocity and energy leads me to conclude that the Heisenberg Uncertainty Principle, the Schrödinger Equation (and Dirac’s Equation derived from it, incorporating relativistic effects) and De Broglie’s assignment of wave properties to particulate matter, are all based on the concept that the position and velocity of an electron cannot both be established with great precision. This is because the “momentum” of light quanta alters the course of the emitting and receiving atoms. Thus a statistical approach to the definition of physical laws on the atomic levels is required.

It is my contention that the uncertainty principle is a simple reflection of the fact that ”radiation” is an exchange of energy levels between two atoms which have to have electrons in very exact positions and velocities to make the exchange possible. Consider the moments just before the simultaneous exchange of energy with a second atom takes place.

The energy of the electron in a hydrogen atom before and after the transfer of energy can be calculated from the emission spectrum (assuming a spectrum analyzer of sufficient sensitivity were available to measure the emission from a single atom)

2

11

Zev

n h EQUATION 324

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and the momentum is

2

1 11

Zep v

n h

. EQUATION 325

After the transfer of energy, the velocity is

2

22

Zev

n h , EQUATION 326

and the momentum is

2

2 22

Zep v

n h

. EQUATION 327

The exact angle of the line of sight is determined by the direction from the proton at the origin to the distant emitting atom. The distance of the emitting atom is entirely irrelevant, as the energy transfer takes place without loss or elapsed time, regardless of distance, as illustrated in Figure 30. So, it appears that all the parameters to determine the exact location of the electron, and its velocity at the moment of just prior to the radiant energy transfer, and immediately after the transfer has taken place, requiring only that the measuring apparatus were sensitive enough to detect the transfer of radiation from a single excited hydrogen atom to a less excited one, with our measuring apparatus co-located with the proton.

Of course, the problem here is that the measuring apparatus is not small enough, or sensitive enough to determine the properties of the energy transfer involving a single pair of atoms. What we see, with a spectrograph, is light from many emissions from many atoms, over a time period that is relatively long in comparison to the orbital period of the electron. So, we are unable to establish which


257

particular atoms were involved in the transmission. However, the energy level before and after the transfer allows us to establish the velocities before and after precisely, assuming that the orbital radius is, as I have postulated, fixed at r0 regardless of the velocity of the electron. What cannot be pinned down with great accuracy is where the receptor was located that gave us the spectrum. Certainly, the location cannot be localized to the volume within the orbit of the electron in the receptor atom. So, the imprecision in the measurement is likely to be on the order of the atomis radius, r0.

The uncertainty of the location is at least the radius of the hydrogen atom, where n is presumed to be 1 for all velocities is

2

0 2

hr r

Ze . EQUATION 328

The product of these two is

2 2 2

22 1

Ze Ze hp r

n h n h Ze

. EQUATION 329

2 1

hp r

n n

EQUATION 330

Thus the maximum error would be that obtained for

n1=1 and n2=2, so I would write the uncertainty principle as

p r h EQUATION 331

Thus it looks like the Uncertainty Principle is simply the

statement that the position of the electron in the atom and the momentum associated with the synchronous velocity at is on the order of Planck’s constant which is a measure of

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radius of the kernel around which the four dimensional universe I have postulated is wound.

I would prefer to see Equation 331 written as:

v r H EQUATION 332

where

2E Hf . EQUATION 333


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CHAPTER 10

SCHRÖDINGER’S WAVE EQUATION

The culmination of the development of the basic

quantum theory of Heisenberg, Schrödinger, de Broglie, Bohr, etc., was the formulation of Schrödinger’s Wave Equation. Solutions to this equation are reputed to describe the hydrogen atom in great and accurate detail, and to provide support for all of the pieces and parts of quantum theory. Included in this array of accepted physical theories is the Uncertainty Principle, the idea that the position and momentum of the electron, or any other particle, can only be established statistically at any given time.

Schrödinger’s Wave Equation as it applies to the hydrogen atom is often written like this:

)(2

22

xFh

ti EQUATION 334

where: tx, ”The amplitude of the wave

function at x and t.”

2h

Planck’s constant

22

2

2

22

zyx

mass of the electron

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F = the strength of the magnetic or electric field acting on the electron, which is e2Z/x2.

Both the terms on the right side of the equation in brackets are forces; the “centrifugal force” on the electron due to its velocity, and the electrostatic force due to the presence of the proton.

The terms are relatively simple except for the

22

2

2

22

zyx

business. This is an “operator”, in

that when placed in front of another expression, has you perform the operations indicated on the expression. This particular one is called the “Del” operator when it has no exponent, and “Del squared” when it appears as it does here with the exponent 2. This crops up all the time in vector analysis, because it has a very straight forward physical

meaning. Dell squared ψ, or tx,2 , says “take the sum of the second derivative of ψ(x,t) with respect to x while holding y, z and t constant, plus the second derivative with respect to y while holding , x and z constant, plus the second derivative with respect to z while holding t, x and y constant.”

The meaning of this expression is a little easier to see in two dimensions rather than three, where the first derivative of a function )(xfy , taken at a given time, t, would give the slope of the curve. The second derivative of the function gives the rate of change of the slope.

The slope of the curve is called the “gradient” and the rate of change of the slope is the “divergence”.

A solution to Schrödinger’s equation for a wave traveling in the x direction is:

)(, tkxietx EQUATION 335

where:


261

1i

k= The wave number2

,

λ= the wave length ν= The frequency of the wave. Because

)22

()(

tx

itkxi ee

EQUATION 336

and

1)2sin()2cos(2 ie i EQUATION 337

t

x

tkxi eetx

)(2, . EQUATION 338

This can be interpreted as either a complex function

which has sine waves in both the real and imaginary directions, or as an oscillating function which grows smaller as the distance from the origin becomes larger.

I have always been uncomfortable with the concept of imaginary number when they are applied to real things, like, in this case, waves in a real, physical medium. It is somewhat comforting to note that whenever imaginary numbers are appropriate to the solution of a problem, the imaginary part of the complex number can always be considered to represent a variable that is outside the plane of the rest of the problem. In the case of the sin wave in Equation 337, it represents the oscillation in the x – z plane which accompanies a “real” sine wave in the x – y plane, caused by the oscillatory motion of an electron in the y – z plane. If one were limited to looking at actions within the x – y plane, it would appear that the wave motions at right angles to it were “imaginary”.

Now, what, exactly, is Schrödinger’s Wave Function? Mechanical waves, like waves in a violin string, or sound

waves, or waves in water, have a relatively straight forward physical basis. They are governed by the physics of water

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molecules bouncing into one another and conveying energy by physical contact. All mechanical waves have properties that can be represented by the General Wave Equation,

2

2

2

2

2

1

x

y

t

y

v

Equation 339

where:

y = physical displacement at right angles to the direction of propagation of the wave, for simple transverse waves, such as in a violin string v = velocity of the wave through the medium, such as along the violin string.

The physical basis for this equation is very simple. The

left hand side gives the transverse acceleration of a point along the string, and the right hand side the “divergence” or rate of change of the slope of the string.

It can be derived by simply taking

dt

dxv EQUATION 340

and substituting it in Equation 339,

2

2

2

2

2

1

x

y

t

y

dt

dx

EQUATION 341

or

2

22

2

2

x

y

dt

dx

t

y

EQUATION 342


263

This is a partial differential equation, which can be

solved by integration.

dxdxy

ydtdt

t

y

2

2

2

2

, EQUATION 343

which yields

yy . EQUATION 344

A solution to this differential equation is

)sin( vtkxAy , EQUATION 345

which is very similar to the solution to the Schrödinger Wave Equation. The difference is that the general wave equation has some physical basis, and the displacement of the violin string is a clearly defined, measurable physical property of the string.

Equation 345 can also be written:

y = the imaginary part of ( )

xi t

e

Equation 346 Now how does one square the use of an equation that

accurately represents a physical wave to describe the behavior of a particle in a statistical way, particularly when that behavior is couched in terms of imaginary numbers?

One way of looking at this is to show that there is a great similarity between the normal probability distribution curve and the sine wave. When the frequency of occurrence of an event is measured against some yardstick, the frequency often plots as a “normal distribution” with respect to the yardstick.

For example, if one were to plot the frequency of occurrence of a given length of banana in a sample (such as a

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stalk of bananas) against the number of bananas measured, the frequency would likely be fall into a pattern represented by the equation

2

2

2

)(

2

1

mx

ey

EQUATION 347

where: y = length of banana

x = number of measurements the banana length which have a length less than y. σ = standard deviation of the samples about the mean m = mean length of all the bananas in the sample.

The probability of finding a banana with a length

between y1 and y2 is given by

2

2

2

1

2

)(

2

1

mxy

yeP

. EQUATION 348

Of course, the normal distribution curve for the bananas

in the sample used in this illustration is not expected to be changing with time. However, if the sampling process were going on continuously, this would be a more appropriate comparison.

For example, if new samples were taken every month for a particular plantation (assuming that there were bananas growing on a year-round basis with two crops per year), one would expect to see the mean banana size fluctuate from 0 to some maximum near harvest time, and recede afterward. While the variations with time might not follow a normal distribution curve, the example comes closer to the determination of the probability of locating a moving target


265

like an electron at a given place and time. To take the assumed sinusoidal variation of the banana sizes with time, we would multiply the sizes found in Equation 367 by a normal function varying with time, using the time divided by the period, T, or multiplied by the frequency for the multiplier.

tety )( EQUATION 349

22

2

2

2

2

2 222

2

1),(

tvxx

t Aeeetxy

.

EQUATION 350

This looks a lot like Schrödinger’s Wave Equation, where

A=1 and 2σ2 = λ2. The only real difference is that the x and t terms in the exponents are squared. This makes sense, in that the wave function is usually taken as the square root of probability of the particle existing at a specific place.

So, I think they should call it Schrödinger’s Probability Function, and drop the reference to waves. Then the probability of an electron being in a given position, or a radiant energy transfer taking place could be used in the equation, rather than the “wave function”.

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267

CHAPTER 11

ELECTROSTATICS AND ELECTRODYNAMICS

This Chapter is aimed at describing a mechanism of

electrostatic a and electrodynamic effects consistent with the assumptions that the speed of light is infinite, the speed of expansion of the universe in a fourth dimensional direction is equal to c, the apparent speed of light, and that all matter in the Universe has a constant velocity, c, in the fourth dimensional direction, as measured by a time standard unique to that body.

Also, a somewhat different model of the hydrogen atom than that proposed by Nils Bohr is suggested in previous Chapters, as are a number of deviations from commonly accepted physical concepts.

While gravity is easily explained by the model presented, electrostatic attraction and repulsion, and magnetic attraction and repulsion are harder to fit into the picture because of the differences between the observed motions of particles under the influence of gravity and those associate with electrical charges:

The effect of the electrostatic charges of the proton and the electron on the space around them must be limited so as not to lead to any relative motion of uncharged particles other than the motions due to gravitational effects.

This implies that the of motion of the 3D Universe into the fourth, or T dimension, must be such that uncharged particles are not affected by the presence of charged particles, so they must react as though the analog x – y plane is flat around isolated charged particles. .

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The effect of the of two or more charged particles on the x – y surface shape, which is always perpendicular to the direction of expansion into the T dimension, is such that particles of like charge are tilted away from each other, while particles of unlike charge are tilted toward each other, and neutral particles are not affected.

The question, then, is what kind of deformation of space around the electron and proton will lead to the effects observed as electrostatic attraction and repulsion and to electrodynamic accelerations of charged particles moving in the vicinity of charged particles.


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ROTATION OF ELECTRONS AND PROTONS It seem apparent that he effect of the electric charge on

the particles has to be in the nature of a rotational effect, where the particle creates a region around it where the space is twisted in one direction for the proton and in the opposite direction for the electron. This must occur in such a way that charged particles will interact by virtue of their charges, whereas an uncharged particle or physical body with no net charge will not interact.

A deformation of space around charged particles that has both a rotary component and a translation component in the T direction satisfies these requirements.

However, when a charged particle is observed with reference to any system in which it appears to be moving ---for example, when the orbiting electron is observed relative to a coordinate system with the proton at its origin --- the electron appears to have a velocity component in the direction tangential to the orbit, and also has an apparent velocity in the T direction parallel to that of the proton. Thus the electron, which sees itself as having only the single velocity, c, appears to move the length of only ct’ as shown in Figure 59.

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FIGURE 58 TWO POINTS OF VIEW OF

VELOCITIES

This velocity vector, when viewed from a coordinate

system attached to the electron, is simply the velocity c, and the two values are reconciled by the relative time distortion when one observes moving bodies. The time passing from the electron’s point of view in traversing the distance of one time unit is ct whereas the time observed from the electron’s coordinate reference system is c’t.

2 2 2 2 2 2'c t c t v t EQUATION 351

Such that the time on appears to pass more slowly from

the standpoint of the moving body according to

2

2

'1

t v

t c . EQUATION 352

The Einsteinian time contraction for bodies moving with

respect to our own is, in essence a difference in the point of view. From the Universal viewpoint, bodies which are moving with respect to our coordinate system (presumed to be “stationary”) seem to be moving through three


271

dimensional space with a velocity which is in addition to the velocity they must have in “our” T direction due to the expansion of the Universe. The difference is in our perception of how time is proceeding, and in fact, a difference in the direction time is proceeding through four dimensional space.

In an earlier Chapter, it was shown that when r, the distance between two masses in 3D space, is substituted for x in the two- dimensional analog, this equation can be approximated closely by

1

0

11 11

rT r

eT r

r

’ EQUATION 353

when r is measured in units equal to 12

m G

c. This same

equation can represent the depression around a charged

particle when 2

2

Ze

cis the unit of measuremtnt/

Or, the depression in the x – y surfaces T can be represented by:

1

0

0 0 0

11 1

1 1r

TT T re

T T T r r

. EQUATION 354

Where:

2 2r x y The attractive action might be dealt with simply by

presuming that both electrons and protons effect the deformation of the x – y analog surface (representing the 3D Universe in the two dimensional analog model) the same way mass does, only to a much greater degree, and in opposite directions for the electron and proton. However, this would cause the much stronger effect of electrostatic forces to

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completely blot out all effect of gravity. For the model to make sense, the proton and electron both must warp the x – y plane in the negative T direction, each according to its mass, but must produce some other type of warping that causes like particles to appear to repel each other, and unlike particles to attract each other, while having no effect whatever on neutral particles.

Now, the interaction between two unlike charges brings about a positive attraction between them, which requires a tipping of the T axes toward each other, and interaction between two like particles require a tipping of the two T axes away from each other. However, when an uncharged particle is present in the neighborhood of a charged particle, there is no interaction whatever, save the slight effect of the gravitational masses of the two particles.

It is clear that the combination of two or more charged particles must cause a deformation of the surface that is not apparent when there is only one particle involved. Further, the presence of two or more particles of like charge must lead to an additive effect, where as a mixture of unlike particles must permit the canceling out of the charges on equal numbers of unlike pairs.

The proposed solution to this apparent problem involves the proposal that the electron and proton each warp the space in the immediate vicinity of the particles in a way which amounts to a rotation of the space rather than a simple displacement in the third, or T direction.

I propose that the proton, for example, creates a rotational field around itself wherein there is a twist to the time vectors which are nominally perpendicular to the x – y surface. This amounts to creating a “velocity” of the x – y space around the proton (assumed to be at the origin) which is perpendicular to any radius drawn from the proton in the x – y surface outward, and which has a magnitude equal that is given by some arbitrarily (for the moment) chosen velocity V, and the obeys the vector relationship


273

0 0 0

1

1

v t T

v t T r

. EQUATION 355

Here the v

vector is understood to be at right angles to the radius vector, r, from the origin to any given point I the x – y plane, and to lie wholly within the x – y plane. Thus the plan view of the plane containing the charged particle would look somewhat like a pinwheel, with the arrows denoting rotation of the space around the particle decreasing in length as the radius increased, as shown in Figure 1. The values of r, are, of course, scalar distances, rather than vectors, and are, therefore limited to positive values. It is proposed that the rotation is clockwise for protons and counterclockwise for electrons. This is purely arbitrary, and the opposite assignments would not make any significant difference.

Whereas the appearance of a velocity in the 3D Universe represented by the x – y plane in the analog universe used here would ordinarily require a dimpling of the surface in the negative T direction, according to

2 2 2 2 2c t v t T , EQUATION 356

and would produce an x – y surface depressed in the –T direction because of the necessary shortening of the t (time vector) which accompanies velocity in any of the x – y – z directions, so that the surface would look like that shown in Figure 63..

It is apparent that, were this the configuration of the x – y surface, any matter within several of the distance units of the charged particle would be influence to move toward the charged particle, because of the tipping of the x – y surface toward the particle. This is clearly not in accord with the observations of charged and neutral particles, which indicate that charged particles are influenced while neutral particles are not influenced at all. These statements ignore, for the time being, the very small effect of gravitational mass of the particles involved, which may generally be neglected when

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compared with the electrostatic and electromagnetic forces equal in magnitude to the swirl vector.

FIGURE 59 SWIRL PATTERN AROUND AN

ISOLATED PROTON

That is, the presence of a charged particle, a proton for example, not only modifies the space nearby by imparting a twisting motion to it, but it also modifies the space in the positive T direction just enough to offset the depression created by the twist.


275

COMPENSATION FOR SWIRL So, there is some additional factor at work which

contributes to the motion of charged particles and counteracts any force that might be exerted on uncharged particles. I believe that this factor is a further modification of the space around the charged particle, in such a way that it counteracts the depression completely, while allowing

FIGURE 60 DEPRESSION OF THE X – Y

SURFACE IN THE -T DIRECTION

the rotary effect on the space to remain. The distortion takes the form of a displacement in the positive T direction as shown in Figure 62.

This counteracting, or compensating, distortion of space is a distortion in the T direction that is exactly equal in magnitude to the swirl vector. This is done by providing an increase in the T value in the immediate vicinity of the charged particle which is exactly the opposite of the depressions shown in Figure 61. This is shown in Figure 63, and the combined effect is shown in Figure 64.

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FIGURE 61 THE COMPENSATING VECTOR

IN THE T DIRECTION

FIGURE 62 “OFFSETTING” WARPAGE OF THE X – Y PLANE

Figure 64 presents, to neutral matter, a clean slate, more or less, with no tendency for a neutral particle to accelerate toward or away from the proton.


277

FIGURE 63 THE “OFFSETTING” T VECTOR

However, the swirl vectors are still clearly imprinted on

the surrounding space, so that if another charged particle is in the vicinity, the swirl effects will add, in the same sense as vectors add together to produce a resultant vector which may be of greater magnitude or lesser than either of the two parent vectors.

Now, were an electron located at a large distance from the proton, it would produce exactly the same bland picture, except that its rotary warping of space would be in the opposite direction as that of the proton. If we assumed for the moment that all protons tend to bring about clockwise warping of space around the location of the proton, and electrons warp space in a counterclockwise direction, there would be a complex interaction of the two sets of effects.

For particles of opposite charge, the “offsetting” warpage is in the T direction for both the electron and proton, and add together to produce twice the offset at every point along the line midway between the two particles in the x – y plane. Thus the offsetting warpage for a proton located at the origin and an electron located at coordinates x = 0, y = 3 would be as shown in Figure 63.

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FIGURE 64 SIMPLIFIED PLOT OF PROTON AND ELECTRON DISTORTION OF X – Y PLANE

(NO COMPENSATION

The compensating displacement in the T direction does not have much physical significance, until it is added to the displacement due to the swirling, where displacement caused by the proton and the electron are in opposite directions.

Appendix 1 gives a detailed procedure for the addition of the swirl vectors in the x – y plane, and illustrates how the existence of an uncompensated swirl vector produces a deformation of the x – y lane in the negative T direction, no matter which rotational direction constituted the swirl.

Appendix 2 describes the procedure for calculating the sum of the swirl and displacement vectors produced in the space around two charged particles. The method is exactly the same in both cases, but the vectors are added to each other in the case of like particles, and subtracted for unlike particles.


279

ELECTRON ORBITING PROTON A much simplified picture is presented if one assumes

that the swirl vectors in the x- y plane result in a depression in the case of the proton, and an elevation in the plane in the case of the electron. These, like the swirl vectors, are additive in the case of like particles, and one subtracts from the other in the case of unlike particles. Thus, for like particles they counteract each other along the line bisecting the line connecting the centers of the two particles, and result in a zero change in elevation. However, for unlike particles, they are additive, and result in a depression twice as deep as either particle alone would produce. This situation depicted by

2

2

1 0

1 1

1Ze

c x

T Tr

e

EQUATION 357

Where T0 is taken as 1,

2 2r x y ,

and x is measured in units equal to 2

2

Ze

c for

the particle at the origin, and

2

2

2 0

1 1

1Ze

c x

T Ts

e

Equation 358

where

2 20s x x y

for the particle at x0, y.

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280

Equations 357 and 358 can be added to produce Equation 379, as all three represent deflections of the x – y plane in the T direction.

1 1

1 1T

r s

, EQUATION 359

where the plus sign applies for like particles and the minus sign for unlike particles.

Figure 65 is a plot of the x – y surface described by Equation 359.

Because a simple deflection of the x – y surface in the T direction would affect not only charged particles, but uncharged ones as well, there must be a compensating factor which limits the effect of isolated charged particles on the deformation of the surface surrounding an isolated particle, and limits the distortion of the surface to the space between charged particles when there is more than one in a given area. As was previously explained, this may consist of a compensating vector in the T direction which is equal in magnitude to the swirl vector within the plane, but which, unlike the swirl vectors, is always in the positive T direction.

A simplified picture of the compensating effect produced when there is no other charged particle in the vicinity is obtained by the expedient of multiplying the deflection produced by the reciprocal of the distance between the two charged particles.

10

1 1

1T

r x

EQUATION 360

and

20

1 1

1T

s x

. EQUATION 361


281

Equations 360 and 361 can be added to produce

0 0 0

1 1 1 1 1 1 1

1 1 1 1T

r x s x x r s

. Equation 362

The picture of an electron in close proximity to a proton (actually, at the minimum orbital radius), but with no velocity relative to the proton is shown in Figure 66, with this proximity correction taken into account.

Figure 67 shows the x – y plane with the electron at a substantial distance (20 units) to the off-stage right position relative to the proton. Once again, it can be seen that there is substantially no distortion of the x – y plane produced by the presence of the proton, and this is also true of the unseen electron.

FIGURE 65 PROTON AND ELECTRON IN AT ORBITAL DISTANCE WITH COMPENSATION

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FIGURE 66 PROTON REMOTE FROM ELECTRON OR OTHER CHARGED PARTICLES

HAS NO EFFECT ON X – Y PLANE

Were several electrons and protons near each other, the mutual attractive and repulsive forces would be apparent, but they would have little effect on uncharged matter in the vicinity. This would possibly account for the observation that uncharged matter tends to become charged electrostatically when brought into a strong electric field.

Actually, either particle could be presumed to be the reference point, or any other point chosen arbitrarily could be selected in the simple derivation included here.

A similar picture could be produced for the case of a distant proton approaching a second proton. The only difference would be that the “trough” would be replaced by a hill, of essentially identical shape. The hill would not exist until the second proton came close to the reference proton. The result of the hill between the two particles would be that the T axes through the two particles would tip away from each other, and there would be the appearance that the two particles were being accelerated away from each other by a “force” of repulsion.


283

Once again, it is emphasized that the energy level of the two particles remains unchanged as they approach each other, and there is no conversion of potential energy into kinetic energy. All that happens is that the direction of motion of the particles relative to each other changes in such a way that, while it appears to an observer moving with the particle that nothing has changed at all, an observer at the origin would observe an increasing velocity in the radial direction as the electron is “drawn” toward the proton.

There is another inescapable conclusion which must be drawn from the consideration of the swirling effect produced in the space around the electrons and protons. Whereas, when the charged particle is “stationary” with respect to the coordinate system chosen, it produces a swirling electric field that lies wholly within the x – y plane in the two-dimensional analog, and within ordinary space in the three dimensional universe, when the particle is moving relative to the coordinate system chosen, it appears to have two components to the velocity vector. One of these lies in the T direction relative to the “stationary” coordinate system, and the other in the x – y plane in the model, or in any of the three dimensional directions in the real world.

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285

ELECTRODYNAMIC EFFECTS Because we demonstrated the existence of a rotational

field around the T axis for the “stationary” charged particles, or at least the probability of such a field, it follows that the appearance of a velocity component in the observable spatial dimensions will be accompanied by a swirling field around the observable velocity vector. This will have all of the ordinary characteristics of a vector field, and will comprise a collection of rotational vectors in the plane perpendicular to the direction of motion.

This is illustrated pictorially in Figure 68. These vector fields are subject to the usual rules of

vector addition, in the case of fields that are due to two or more charged particles, such that the fields attributable to electrons and protons are essentially non-existent when charged particles are isolated, and become apparent only when two or more charged particles are relatively close to one another, so that they have no effect on neutral matter, just as the electrostatic force was negligible in the vicinity of a single isolated charge.

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FIGURE 67 APPEARANCE OF A VECTOR FIELD AROUND A MOVING CHARGED

PARTICLE

Like the electrostatic effect of fields on charged particles,

they are subject to vector addition effect, when for example, a stationary particles of similar charge is nearby. When a charged particle is present in a vector field attributable to many charged particles, it reacts the sum of the charges.

The charged particles follow Coulomb’s law,

1 21 2

Ze em a

r EQUATION 363


287

Where: m1=mass of the particle under consideration e1=charge of the particle under consideration

22

e

r= Strength of the electric field at

the location of m1

The acceleration is a vector quantity, as is the electric

field in the vicinity of the particle. For clarity, this type of vector field will be referred to as a magnetic field in the following paragraphs.

When the rotational vector (magnetic field) accompanying the movement of a charged particle relative to the coordinate system chosen, it interacts with the electrostatic field surrounding all charged particles due to their movement in the T direction (their static electric fields) and also with other rotational vectors within the three spatial dimensions due to their movement.

When any charged particle is considered to be in motion relative to another charged particle, their fields interact normally. That is, if there are a number of charged particles moving in the same direction in the three dimensional space (which also means they are moving parallel to each other in four dimensional space as well), their magnetic l fields are additive. When they interact with electrostatic fields, which are, by definition perpendicular to the three spatial dimensions, the resultant acceleration tendency is determined by the vector cross product of the two fields. That is, by the vector cross product of the strength of the field (represented by the vector in the T direction sum of the charge/distance values for all of the charged particles close enough to be significant), times the product of the charge and the velocity of motion of the charge.

The well-known Lorenz Force Equation is:

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11 1 ( )F m a e E v B

EQUATION 364

Where: F = Force on particle m1=mass of particle e1=charge on particle, culombs E= Electric Field, and

3

ZerE

r

EQUATION 365

and

2 22 3

2

Ze rB v

r

EQUATION 366

The proposition that the electric field consists of the

rotational vector field around the T axis of a proton or electron as it moves at the apparent speed of light in the T direction, and that the magnetic field is simply a component of this same vector field which can lies in the three dimensional Universe when the proton or electron is in motion relative to the coordinate system chosen is completely consistent with the view of the organization of the Universe presented in this book.


289

CONCLUSIONS The electrostatic and magnetic forces observed are

always measured by the acceleration of bodies with some mass. The “forces” appear to be simply the result of the enormous velocity of matter in the Universe, directed outward from the origin of the Big Bang, but having slightly different directions.

The directional difference are partly caused by the presence of matter, which tends to make the three dimensional universe warp in the direction opposite the direction of expansion, while electrostatic and electrodynamic “forces” relate to rotational warping in the three dimensions , around the fourth dimensional direction of motion.

In this paper, a model of the deformation of the three dimensional universe in a more complex, swirling deformation pattern around charged particles which results, indirectly, in the same sort of deformation of the three dimensional universe as is created by objects with mass. The effect of charges on electrons and protons were shown to be essentially non-existent when there is a single charged particle in isolation. However, when two or more charged particles are present the space between then and very close by is warped sufficiently to account for electrostatic attraction and repulsion.

This mechanism is consistent with Coulomb’s law and with the Lorenz equation. In using this approach, it is not necessary to assign properties to empty space, such as dielectric constant, magnetic permeability, etc. Instead, r0 and v0, the synchronous orbital radius and velocity of the hydrogen atom are used as fundamental constants and the direction of the passage of time is the only property that need be assigned to each point in space..

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Electromagnetic effects depend on the fact that all matter has the same velocity, c, the apparent speed of light, which I maintain is actually the speed of all matter in the Universe in the fourth dimensional direction, and the velocity of an object observed in our ordinary three dimensional world is simply a small component of the total velocity. We, see the object as moving in the three dimensional world because its overall trajectory through the four dimensional space is not parallel to our own direction of travel, and the difference between the four dimensional velocity vectors is the velocity we perceive.

As the velocity of a charged particle appears as a component of the total velocity of the particle, c, there is a component of the rotary velocity around the fourth dimensional path of the particle that also appears as a rotational velocity in the ordinary three dimensions. This component is what we ordinarily consider the magnetic field associated with a moving charged particle.

This field is consistent with the observed magnetics effects, and conforms to the Maxwell equations which describe the properties of both electric and magnetic fields. Once again, the “Force” acting between charged particles in motion and magnetic fields is attributable to the accelerations of the particles observed when they move through fields. It is precisely the same “force” which is recognized as gravity when observations of neutral masses are in proximity to each other, and electrostatic attraction or repulsion when the particles under observation are charged.

In the case of both electrostatic and electrodynamic phenomenon, the necessity of assigning properties such as dielectric constant, magnetic permeability or permittivity can be avoided by substituting r0 and v0, the synchronous orbital radius and velocity of the hydrogen atom as fundamental constants.

Just as there is essentially no meaning to the term “potential” energy when applied to a particle subjected to a gravitational attraction (as all of the energy of the particle is the result of its velocity in the T direction) there is not really a


291

“magnetic field” around the charged particle at all. If the observer uses a coordinate system which is stationary with respect to the particle, there will be no magnetic field in his view. If he chooses a reference system attached to, say, a proton around which the electron is orbiting, he will see the normal magnetic field which is expected to exist for any hydrogen free ion or hydrogen molecule.

It must be kept firmly in mind that in this view of the construction of the Universe, the total energy of a particle does not change at all, no matter what its orientation or velocity with respect to other matter in the Universe. Part of the total energy that is always there is recognized as kinetic energy because a part of the total velocity through four dimensional space is in the three dimensions we can observe, and appears to have come from nowhere, as we cannot observe the vast amount of energy associated with its motion in the fourth dimensional direction. Gravity is one manifestation of changes in the direction the space around masses is modified by their presence, and electrostatic charge is another. Electromagnetism is simply the interaction charged particles due to the deformations in space which are associated with the relative motion of charges.

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APPENDIX 1

CHARGE DEFORMATION OF THE X – Y SURFACE

The following material constitutes the derivation of the

curvature of the x – y surface of a two dimensional analog of the three dimensional Universe surrounding an isolated charged particle presuming that the electrostatic forces follow Coulomb’s law.

The velocity, vx, is that which would be achieved by a body of mass m2 falling from a large distance toward a body of mass m1, under the influence of the electrostatic force

F a Equation 367 Where:

2

2

ZeF

x , EQUATION 368

Or F

a

. EQUATION 369

We will consider for the time being that the x – y plane is depressed in the –T direction, and that , in the cross section view, T = f(x). Rather than considering each point in the x – y plane to have a slightly different value of t associated with it because of the Depression in the T direction, we can consider that each value of T has a particular value of x and y associated with it.

If we substitute

xv at

EQUATION 370

or


293

2

2x

Ze tv at

x . EQUATION 371

The x – y surface is perpendicular to the velocity vector,

and has a slope that is the negative reciprocal of the slope of the total velocity vector vT.

In Equation 371, the value of x should be regarded as the distance between the proton and the electron, and thus having a positive value. It does not make any difference in equation 371, but in the subsequent equations serious errors will result from using negative values for x.

2

2xvdT Ze t

dx c cx

EQUATION 372

The value of T, the fourth dimensional coordinate, has

been presumed to be given by T ct , EQUATION 373

yielding

2

2 2xvdT Ze T

dx c c x , EQUATION 374

and in turn:

1

2 2

dT Zedx

T c x

. EQUATION 375

Integrating gives

2

2ln

ZeT C

c x . EQUATION 376

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This integration can be done using the definite integral,

with an initial value of x taken at a fairly great distance to the right along the x axis, such that the difference between T and T0 are essentially zero. It does not matter exactly where this value is, so long as it is large enough that that T0 – T is substantially zero. Equation 376 can then be written:

2 2

2 2ln lni

i

Ze ZeT T

c x c x

.

EQUATION 377

Because the initial value of Ti was taken so as to be

essentially equal to T0 at the initial starting point, xi, we can let:

0T T T . EQUATION 378

By definition,

2

0 2ln ln

ZeT T

c x , EQATION 379

which reduces to

2

20

lnT Ze

T c x

, EQUATION 380

or,

2

2

0

Ze

c xTe

T

. EQUATION 381

If one uses for the measure of x


295

2

2

Zeunit

c ,

EQUATION 382

then

1

0

xTe

T

EQUATION 383

Throughout this derivation, the electron and proton have been presumed to lie along the x axis, with values of y and z equal to zero. However, any coordinate system would work equally well, and the distance r substituted for x. It must be remembered that r is a distance, and the absolute value of r must be used in evaluating the depression of the x – y surface

.

1

0

11 11

rT r

eT r

r

. EQUATION 384

Also,

1

0

0 0 0

11 1

1 1r

TT T re

T T T r r

EQUATION 385

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APPENDIX 2

VECTOR ADDITION OF VELOCITIES When the electrostatic field around an isolated charged

particle is considered to consist of as swirl vector around the T axis of the particle, which reaches a peak magnitude at the particle, the swirl vectors can be quantified and relatively straight forward rules set up for adding and subtracting the vectors produced by two different particles in proximity to each other. In particular, it is necessary that the model produce on field at all in the case where there is a single, isolated charged particle, as any such field would affect the behavior of uncharged particles as well as charged ones.

There are presumed to be an electron and a proton, with the proton located at the origin of the coordinate system. The distance to the proton from any point x, y is r1.

EQUATION 386

The electron located at x0, y0 produces a similar field, but

the direction of spin is opposite that of the proton. The distance from the electron to the point x, y is r2.

2 2

2 0 0( ) ( )r x x y y EQUATION 387

The x – y surface is presumed to be tilted in such a way

that the space located at a distance r1 from the proton and r2 from the electron has a swirl magnitude indicated by

11

1

1v

r

EQUATION 388


297

and

22

1

1v

r

, EQUATION 389

The geometry of this arrangement is shown in Figure

which depicts the radius vector to an arbitrary point in the x – y plane near a proton, and the swirl vector at that point. The magnitude of the vector is given by equation 387, and the x and y coordinates of the point, relative to the proton, give the direction of the radius vector, and therefore, of the swirl vector. The direction of swirl is presumed to be clockwise for the proton and counterclockwise for the electron, and in all cases perpendicular to the radius from the respective particle.

FIGURE 68 GEOMETRY OF THE SWIRL VECTOR

The components of this velocity vector in the x and y

direction are defined by the geometry of the situation to be

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1 1 21 1 1

x

y yv v

r r r

EQUATION 390

and

1 1 21 1 1

y

x xv v

r r r

. EQUATION 391

Similarly, for the electron, positioned at x0, y0,

0 02 2 2

2 2 2x

y y y yv v

r r r

, EQUATION 392

and

0 02 2

2 2 2y

x x x xv v

r r r

. EQUATION 393

Adding the x and y component of these two vectors give the components of the resultant vector at the point in question as follows: ,

01 2 2 2

1 1 2 2y y y

x xxv v v

r r r r

. EQUATION 394

The sum of the components yields the total vector in

the x – y plane, 2 2 2t tx tyv v v EQUATION 395

The direction of the swirl vector is given by the relative magnitudes of the y component and the x component,

arctan ty

tx

v

v EQUATION 396

The effect would be to depress the x = y surface by an amount, ∆T, given by

2 2 2 2

tT c t c t v t

EQUATION 397


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At this point, it might be apparent that the velocities imputed to the space around both the electron and proton which are in the x – y plane of necessity are components of the total velocity of the particles in the T direction normal to the x – y plane. This means that the plane must be tipped in the direction of the velocity, and that this tipping, which is due solely to the charges on the particles, would affect not only charged particles, but neutral ones as well.

For this reason, it is necessary to presume that there is an offsetting velocity, ∆T, in the T direction, which, in effect, erases the tipping effect when a single charged particle exists in a region free of other charged particles, but has an effect when other charged particles are present.

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APPENDIX 3 “OFFSETTING”

T DIRECTION VECTOR The requirement that the warping of the x – y surface in

the analog x – y – T universe effect accelerations only of charged particles requires that the effect of the charged particles on the shape of space must have a second component. Whereas the swirl velocities imparted cannot warp the x – y surface in the T direction when there is an isolated particle requires that the second component be capable of completely offsetting the depression due to the swirl velocity for the isolated charge, but still permit charged particles in proximity to each other produce an effect between them.

This offsetting component can be thought of as an incremental velocity in the T direction, at each point in space, which will offset the shrinkage of the component of the velocity perpendicular to the x – y surface without the influence of the charged particle. Correction is defined as ∆T, which is a function of location relative to the particle.

The magnitude of this “velocity” in the positive T direction, Tv , is given by

220

1 2 2 21 1 2 2

x x x

y yyv v v

r r r r

.EQUATION 398

22

0

1 2 2 21 1 2 2

y y y

x xxv v v

r r r r

. EQUATION 399


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In equation 398 and subsequent equations, the square root of the square of a variable is taken for variables that represent distances, and cannot have negative values.

It can be seen that the addition of the squares of the

xv and yv yields the square of the “compensating velocity

vector”, Tv , which can be simplified as follows:

2 2

11 2 2 22 2

11 11 1 1 1

1

1

ry xv

rr rr r r r

EQUATION 400

and

2 2

0) 0 22 2 2 22 2

22 22 2 2 2

( ( ) 1

1

y y x x rv

rr rr r r r

.

EQUATION 401

The offsetting velocity for each particle, is simply equal

to the magnitude of the velocity vector in the x – y plane, derived above. However, these magnitudes are always positive, whereas the velocity vectors in the x – y plane can be either positive or negative. So, when the velocity vectors cancel out, the correction in the positive T direction does not, and results in an outward bulge in the x – y plane for like particles, and a depression in the x – y plane for particles with unlike charges.

It can be easily seen that if a single charged particle is present in a region of x – y space free of the effect of other charged particles, there will be no deformation of the x – y plane whatever, whether this particle is a single proton or a single electron. Thus, the lone charged particle will have no effect on an uncharged particle, except for the slight gravitational attraction.

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FIGURE 69 AN ISOLATED PROTON AT THE ORIGIN

On the other hand, if a second or third or more charged

particles are present in the region, the compensating ∆T values, all of which are in the same, positive T direction, will be additive, whereas the x and y components of the velocity in the x – y plane will add vector wise. Thus the swirl effect ∆T and the compensating ∆T will not offset each other for a proton and electron located relatively close together, but will, instead result in deformations in the x – y plane. In Figure 25, a slight depression in the x – y surface can be seen forming between the proton and electron when they are separated by a distance of three units. The size of these units has not, as yet, been discussed, and will have to be quantified later.

The deformations will result in a tipping of the axes through the proton and electron toward each other and those through like charged particles will tip away from each other. This deformation o the x – y surface an tipping of the axes between the charged particles becomes more pronounced as the distance separating the charged particles decreases, as illustrated in Figures 77 and 78, which depict a proton


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FIGURE 70 ELECTRON APPROACHING A PROTON AT 3 UNITS DISTANCE

In Figure 77, a small depression can be seen to be forming between the proton at the origin and the electron at a distance of 3 units from the origin. In the previous figure, the distance separating the proton and electron was 6 units, and there is no visible depression.

FIGURE 71 ELECTRON APPROACHING A PROTON AT 1.5 UNITS DISTANCE

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When the distance is decreased further, as in Figure 78 where the electron is shown as only 1.5 units away from the origin, the depression has become quite marked, and it appears that both the proton and the electron are perched on the brink of a hill.

The calculations for these figures were carried out using Wolfram Mathmatica.

FIGURE 72 TWO PROTONS SEPARATED BY

A DISTANCE OF 1.5 UNITS

In Figure 79, two protons are shown in close proximity,

and it is apparent that, rather than forming a valley in the x – y plane which would bring about a tipping of the T axes for the two particles toward each other, as was the case for particles of unlike charges, a hill has formed in the plane, and each of the protons is at the foot of the hill, with the axes tipped away from each other. Any motion which would bring the two protons closer to each other would result in the tipping of the axes away from each other, indicating an increasing tendency for the particles to move away from each other.


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The proposed mechanism results in the formation of a valley between unlike particles in close proximity with each other, and a hill when like particles, positive or negative, are close together.

When there are many charged particles in an area, the deformations of the x – y plane will be additive just as for a pair of particles.

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CHAPTER 12

SUMMARY I don’t expect many readers to have gotten this far. The subject matter is likely to be boring and of little interest to people who are not physicists, or don’t see much relevance to the more esoteric physical concepts to our daily lives. Nor do I expect many people who are vitally interested in physics, the academic physicists and researchers who know far more about what I have been writing about than I do, to be very interested. I have, after all, questioned some of their most fundamental concepts, and have done so without any authority at all. Total disbelief is the expected reaction, and reading the details of why I think the way I do would be a waste of time. However, for those few of you who have gotten this far, here is my story. I have done my best to present a picture of the Universe in which we live that is consistent with the notion that light does not consist of waves or streams of photons which travel through space like sound passes through air or water. It is, instead, a process where energy is transferred from one atom to another without anything at all passing through the space between them. Rather, the atoms come into direct physical contact because the space and time in which they are located is curled up on a tiny five-dimensional kernel. Our three dimensional Universe is expanding into a fourth dimensional space at an essentially constant velocity of about 300,000 kilometers per second, and this velocity is what has been measured by experiments intending to measure the speed of light through space.


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In this model, the velocity of light is essential infinite, because the “emission” and “absorption” of the energy in radiant energy transfer is simultaneous. This is the way it appears when we observe events in the universe, because we are limited to observations which occur in our “local present”. In order to explain how energy can be transferred in this way, I have had to evolve and entirely new concept of the phenomenon of radiation. In this picture, radiant energy transfer takes place when the inner orbital electrons of an atom transfer some of their energy to the inner orbital electrons of a distant atom. Neither space nor time differences interfere with this process, if the atoms are lined up properly in space and time. The concept explains some of the paradoxes associated with light and optics, including the elimination of the wave/particle duality of light. If light is regarded as a wave which is transmitted through the vacuum of outer space like sound is transmitted through the air, it is reasonable to expect that the speed can be measured by sending out a light wave, bouncing it off a distant mirror and timing how long it takes to bounce back, just like sound waves echo off a distant cliff face. But light (radiation in general) is not like sound waves, or any other kind of wave within our experience. Because Einstein used the “fact” that the speed of light through space was 300,000 kilometers per second regardless of the motion of the observer, he created a picture of the relationship between spatial geometry and time which works, but which is not the best description of the Universe. Also, he concluded that the mass of objects increases as their velocity increases, which I believe is completely incorrect. More importantly, he concluded that energy and mass are interchangeable, which led to the production of nuclear power. Again, I think he was wrong in principle, although the results have had great benefits. In the physical model I have presented, gravity and electrostatic and electromagnetic forces are all manifestations

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of the same, relatively simple distortion of the three dimensional Universe, in a fourth dimensional direction into which the Universe is expanding. In this picture of the Universe, there is no need for “dark matter” or “dark energy” to prevent the Universe from expanding without limit. In fact, it appears to be expanding without limit, at a constant rate. There is a sort of universal or galactic time, which is common to all matter in the universe, represents the position of the universe in its motion into the fourth spatial dimension, but we are unable to perceive anything taking place at the present moment in this time, all of the Universe except the point we presently occupy lies in our local future. The constancy of the speed of light forms a basis for so much of the accepted basics physics that challenging this concept requires reevaluation of many of the bedrocks of modern physics. For example, I have proposed the Hubble’s constant is, in fact, not constant, but is decreasing linearly with the passage of time; That Planck’s constant doesn’t fit the facts properly and should be replaced; Schrodinger’s wave equation does not relate to waves (because the waves it relates to done exist) at all, but is, instead, a probability function; and finally, that Heisenberg’s uncertainty principle, basically the foundation of quantum mechanics, is simply a statement that we cannot tell what the state of an atom is at present without “looking at it”, which requires the transfer of energy away from the atom, so we only see it as it was, before we changed it. The Universe is not constructed of probabilistic matter, in which atoms emit photons at times which have no proximate cause, but simply at statistically random times. Instead, it is entirely deterministic, based on the occurrence of the proper alignment between emitting atoms and absorbing atoms. In my model, there is no incompatibility between Einstein’s Relativity and Quantum Mechanics. The same physics which describes the movements of the stars and


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galaxies also describes the movement of electrons, protons and neutrons. While all this leads me to be suspicious of much of modern physics which I do not understand in depth, like quantum mechanics and string theories involving eleven or more spatial dimensions. My picture of the Universe does appear to have similarities to a four dimensional construct where all matter, made of elementary particles like protons, electrons and neutrons, are very small in diameter in our three dimensions, but have a fourth dimensional physical direction which extends for light years. Our three dimensional universe is simply the cross-section of the four dimensional world where we see things a “solids” which move about as the cross section moves through tangle of strings through the fourth dimensional direction . That suggests that the future exists concurrent with the present and the past, and makes a case for a deterministic universe. But, not one in which we can see the future, nor travel into the past even though electrons may be doing it all the time. While all of this makes me feel a little better about the way the Universe fits together and how the laws of nature should be formulated, nothing I have done seems be more useful than the conventional science, which I viewed a flawed. For the most part, conventional physics works, and produces useful results in spite of the few inconsistencies.

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About the Author:

Les Hardison is an eighty one year old retired engineer. He graduated from Illinois Institute of Technology in 1950 with a degree in Mechanical Engineering. During his working years, he was a Petroleum Process Design Engineer for UOP, Inc., and later Technical Director of UOP Air Correction Division.

During the last twenty-five years of his working career he was President of ARI Technologies, Inc. a small air pollution control company which developed, among other things, the LO-CAT® Hydrogen Sulfide Oxidation Process.

He has never had any special training in Physics or Cosmology and recognizes that if he knew more about them, he would probably not have written this book. Fools rush in where angels fear to tread.

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