1 INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

THE UNIVERSE IS COMPOSED OF PARTICLESSir Isaac Newton proposed that light consists of particle likecorpuscles. Arthur Compton measured the angle of rebound-ing X-rays and discovered that they bounce like particles.This result confirmed Newton’s hypothesis. In the late nine-teenth century, it was discovered that the spectrum of ablack body contains much less ultraviolet radiation thanclassical wave theory predicted. Max Planck came up with asolution to this problem. His solution employed particles oflight. These particles are called photons. The energy of thesephotons varies directly with their frequency. Planck’s parti-cle construct solved the ultraviolet problem by showing thatthe higher frequency ultraviolet photons are not energeti-cally accessible. Albert Einstein applied Planck’s constant tothe photo-electric effect and showed that the maximumenergy of an ejected electron equals the energy of theabsorbed photon. These observations demonstrate that lightis composed of particle-like things.

The ancient Greek philosopher Democritus proposed thatmatter is constructed of particles. These particles are thesmallest unit of the substance that still retains the propertiesof the substance. Chemist John Dalton offered some of thefirst theoretical proof of Democritus’ proposition. His exper-iments revealed that particles (elements) combine in wholenumber ratios to form compounds. Ludwig EdwardBoltzmann extended this idea and showed that a gas consistsof a collection of particles. Boltzmann discovered that theproperties of a gas are established through a statistical inter-action of its particles. Robert Millikan experimented withelectrically charged droplets. His experiments revealed a firstsub-atomic particle, the electron. Ernest Rutherford’s particlescattering experiments detected a few alpha particles thatbounced directly back. This result disclosed a second sub-atomic particle, the nucleus. In the twentieth century, thetracks of a host of sub-atomic particles were directlyobserved in a bubble chamber. These observations demon-strate that matter is composed of particle-like things.

THE UNIVERSE IS COMPOSED OF WAVESChristian Huygens proposed that light is a wave. He sug-gested that the amplitude of the wave determines its inten-sity and that the frequency of the wave determines its color.The diffraction of light by a prism seemed to support thishypothesis. The dispersion of light which passes through apinhole also indicates that light is a wave. Thomas Youngoffered some of the first theoretical proof of Huygens’ propo-sition. Young passed light through two closely spaced slits.An interference pattern was produced as the light was pro-jected on a screen. This interference pattern revealed thewave-like nature of light. Radio technology was developed inthe twentieth century. This technology directly displays theamplitude and frequency of a radio wave (a form of light) onan oscilloscope. These observations demonstrate that light iscomposed of wave-like stuff.

Louis de Broglie proposed that matter is a wave. In 1927,Clinton Davisson and Lester Germer of Bell Labs conductedan experiment in which an electron was passed though fine-ly divided slits.1 An interference pattern was produced. Itwas discovered that the electron exhibits wave-like proper-ties. These observations demonstrate that matter is com-posed of wave-like stuff.

It appears that the substance of the universe simultane-ously exists as both particles and waves. The property thatemerges depends upon the bias of the observer. This dualityhas been a fundamental mystery.

PROPOSED RESOLUTIONSNiels Bohr produced an atomic model that contained a par-ticle-like nucleus. Particle-like electrons orbited around thisnucleus. These electrons carried an amount of angularmomentum that is an integer multiple of Planck’s constant.Angular momentum is the product of length, velocity andmass. These terms did not emerge from a fundamentalanalysis and are empirical. Bohr’s model described the radiiof the atomic orbits and the frequency of the emitted pho-

THE DUALITY OF MATTER AND WAVES

Frank Znidarsic*

ABSTRACTA quantum measurement may detect a particle or a wave. The bias of the observer appears to influence the outcome

of the experiment. Newton’s laws of motion are not dependent upon the bias of an observer. The nature of the influence that the observer imparts upon the observed is mysterious. I contend that observations progress through the action of the quantum transition. Both matter and waves consist of undulating fields. The local fields of matter are pinned into the structure of matter at elastic discontinuities. Vibration at a specific frequency shakes the fields

free from the grip of the discontinuity. The process of vibration is that of the quantum transition. The radiated fields of light are not attached to a discontinuity. They propagate at the luminal velocity.

JULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY 2

ton. The model did not disclose the mechanism that bindsthe electron to a state, determine the probability of transi-tion, or explain the intensity of the atomic spectra.

Werner Heisenberg extended Bohr’s particle-like analysisand developed a mathematical technique that producedintensity of the spectral lines. His technique employedmatrix mechanics and the mathematical function known asthe Hamiltonian.2 The Hamiltonian describes particle inter-actions as a function of their energy. The correspondenceprinciple was invoked. It states that the energy drop in aquantum system is equivalent to the amplitude of a classicalsystem. The position of the particle was obscured within theHamiltonian and the amplitude of the particle’s vibrationwas brushed aside with the help of the correspondence prin-ciple. The question of the fundamental nature of a substancewas avoided.

Erwin Schrödinger proposed that matter is a wave. Hissolution was slightly better than Heisenberg’s in that it incor-porated de Broglie’s electron waves. The use of the de Brogliewave presented a conceptual problem. The de Broglie waveconsists of a packet of waves that travel together at the groupvelocity V. The length of the packet decreases as its velocityincreases. It is a curious mathematical construct with noclassical analog. It has become accepted because it producesresults. Schrödinger encountered a second conceptual prob-lem. How do the discrete properties of matter naturallyemerge from a continuous wave? He proposed that thesuperposition of an infinite number of waves localized thewave function.3 Wave patterns repeat at intervals. The solu-tion suggests that the particle appears at intervals in remotelocations. Matter’s particle nature did not spontaneouslyemerge from the analysis and Planck’s empirical constant,and had to be injected ad hoc into the solution.

Max Born offered a solution, known as the Copenhageninterpretation. It proposes that matter’s de Broglie wave isnot real. It is a subjective construct that exists only in con-figuration space. The amplitude of this wave represents theprobability that a particle of matter will reside at certainlocations. A particle emerges, from the probability wave,upon the immediate collapse of the wave function. The solu-tion attempted to extract a particle out of a wave and resolvethe problem of wave particle duality. The interpretation didnot provide for a mechanism to bind the electron to a state,disclose the whereabouts of configuration space, or explainhow a continuous wave collapses at velocities greater thanlight speed. Schrödinger and Einstein never accepted thisinterpretation. The nature of the substance of the universeremained a mystery. The duality of nature remained irrecon-cilable.4

ZNIDARSIC’S INTERPRETATIONMy model reveals the mechanism that bundles a wave witha particle. The binding mechanism is classical. Classical sys-tems are constructed by fastening components together.Fasteners are mechanical discontinuities. The same bindingmechanism can attach a field. The electromagnetic field is,for example, pinned into the structure of a superconductorby introduced defects (discontinuities). This interpretationstates that the natural force fields are pinned into the struc-ture of matter at elastic discontinuities. Discontinuities nat-urally emerge when the intensity of a field exceeds the abil-ity of space to support that field. The discontinuity acts as a

pilot and replaces Heisenberg’s and Schrödinger’s superposi-tion of waves construct. The use of a single binding mecha-nism is a simplification, in accordance with the principle ofOccam’s razor.

Charles Coulomb studied the force between electricalcharges. He qualified the energy E contained by the interac-tion of two electrical charges Q. Coulomb’s formulation(Equation 1) did not disclose the mechanism that binds anelectron to a state.

The energy contained by a classical spring is proportion-ate to the product of the spring constant K and the square ofthe displacement x (Equation 2). This formula is usuallyemployed with a fixed spring constant K and a variable dis-placement x.

I regrouped the constants in Equation 1 into the form thatexpresses the elastic energy of a spring. This formulation,Equation 3, expresses both wave-like and particle-like prop-erties. It describes electrical energy in terms of the move-ment of the fixed (particle-like) displacement 2rp within thevariable elastic medium K-e.

The displacement 2rp is twice that of the maximum extentof the proton. It equals the classical radius of the electron.Mass and kinetic energy are pinned into the structure ofmatter at this discontinuity. The phase velocity of distur-bances within the pinned fields is luminal. The group veloc-ity V of the packet is that of the discontinuity. The conditionresembles that of stuck light. de Broglie suggested that thematter wave naturally emerges from the superposition of theCompton wave and its Doppler shifted reflection, under thiscondition.5 The properties of special relativity also emerge asa condition of stuck light.6,7

The variable elastic constant K-e (Equation 4) also emergedas a result of the regrouping of the electrical constants. Iemployed this elastic constant and produced the atomicenergy levels and the intensity of the spectral emission.8This analysis showed that the wave-like properties of matteremerge from its mass and elasticity. This harmonic is real; noconfiguration space is required.

The product of the harmonic frequency and the particle’sdisplacement is the velocity Vt. This velocity, as expressed byEquation 5, was extracted from the results of cold fusionexperiments. The first term in Equation 5 equals the diame-ter of the active nuclear environment. The second term rep-resents the natural frequency of an active environment.

I presented my theorem at a conference of the AmericanNuclear Society in 2000.9 It describes the action of Vt: “Theconstants of the motion tend toward the electromagnetic ina Bose condensate that is stimulated at a dimension fre-

E = (1/r) (1)2Q2

4πeo

E = Kx2 (2)12

E = K-e(2rp)2 (3)12

K-e = (4)Fmax

r

Vt = (2πnrp)(fc/n) (5)

3 INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

quency of Vt.” The convergence of the motion constants isan effect of an equalization in the strength of the magneticcomponent of the electrical, gravitational and nuclearforces. The equalization in the strength of the forces match-es the impedance of the interacting states and allows thefields to slip into a new configuration. Energy flows, thewavefunction collapses and the quantum transition pro-ceeds. The constant Vt, like Planck’s, has produced the atom-ic energy levels and the intensity of spectral emission. Theconvergence of the motion constants provides a clue as tothe origin of Vt. It is a condition where the velocity of lightwithin the electronic structure of the atom equals the veloc-ity of sound within the nuclear structure of the atom. In thecase of cold fusion, the velocity of sound within the nuclearstructure is determined by the vibration of the opticalphonons within the mass of the dissolved deuterium. In thenucleus this velocity appears, as shown in Equation 6, as theproduct of the harmonic motion of the nucleons and thespacing of the nucleons rn within the nucleus.

The equalization of the velocity of light and sound with-in the transitional atomic state is the effect that pulls themotion constants together. Vt is an emergent classical prop-erty and, as such, it is fundamental to Planck’s constant.

THE PARTICLE OF A LIGHT WAVEThis paper extended the prior analysis and produced theenergy of the photon. It was accomplished through the useof a fundamental analysis that did not require an ad hocinjection of Planck’s constant. The geometry a photon expe-riences during emission is approximately that of a flat platecapacitor. The capacitance C of a flat plate capacitor of areaA and spacing D is given in Equation 7.

The area A was set equal to the displacement of the photonsquared. The displacement between the peaks in the ampli-tudes, D, equals one half wavelength. The capacitance expe-rienced by a cycle of light is given in Equation 8.

The reduction of Equation 8 produced Equation 9.

Equation 9 describes the capacitance of the captured pho-ton. The capacitance of the “in flight” photon is indetermi-nate. Its energy is strictly a function of its momentum and,as such, it is independent of the photon’s displacement. Thelack of restriction allows the displacement λ to vary. Thegeometry of the traveling photon is that of a boundlesswave. This variability may produce, as Einstein called it, “aspooky interaction at a distance.”10 Its state is, as Feynmancalled it, the sum of every possible history.11 This is the stateof the light that simultaneously passed through the two slitsin Young’s experiment.

The Heisenberg Uncertainty Principle associates the pre-cise velocity of Vt with a boundless wave.12 This uncertaintyin position couples the quantum transitions to a change in

the state of the universe. The velocity of quantum transition,Vt, is qualified in Equation 10.

The strength and range of the natural forces converge asthe quantum transition proceeds. The wavefunction’s nega-tive gravitational potential increases to the point where itequals its positive mass energy. The zero energy wavefunc-tion then collapses without restriction. Deterministic classi-cal reality emerges, from probabilistic quantum waves, atthis instant. One half of the quantum information is lost inthe crash. Equation 10 was solved for length. This is therange at which the natural force fields strongly interact.

The amplitude of light, as expressed by its capacitance,was given in Equation 9. The action of the transitional quan-tum state (Equation 11) fixes the geometry of the light. Thesimultaneous solution of Equations 9 and 11 producedEquation 12. It expresses the relationship between the capac-itance and the frequency of the photon.

The potential energy E of an electrical charge is a function ofcapacitance C. This relationship is expressed in Equation 13.

The great scientists described the energy of a photon interms of its frequency. The energy of a classical wave is afunction of its amplitude, not its frequency. This discrepan-cy has been a long-standing mystery. The principle of quan-tum correspondence was invented in an attempt to circum-vent this problem. It proposes, with some slight of hand,that the frequency of a quantum system appears as an ampli-tude in a classical system. I have rejected this propositionand shown that the energy of light is an effect of the light’sdisplacement. The energy, of the captured photon was qual-ified through the simultaneous solution of Equations 12 and13. The result (Equation 14) expresses the relationshipbetween the energy and frequency of the photon. Equations12 and 13 reveal that the energy of captured light is a func-tion of charge and capacitance. The voltage produced by anelectrical charge increases as its capacitance decreases. Theenergy of a photon is proportionate to the amplitude of itsvoltage. The action of this voltage replaces the principle ofquantum correspondence. This is the state of the light thatproduces Einstein’s photoelectric effect.

Planck’s constant emerged from the terms within thebrackets [ ]. Planck’s constant was substituted for the quanti-ty within the brackets. Einstein’s famous photoelectric rela-tionship was produced.

The intensity of a light wave is a classical function of itstransverse amplitude. The voltage of a light wave is a classi-

Vt = 1/2π x 2nrn√ Z(Fmax/2nrn)/nMn (6)

C = (7)eoAD

λ = (11)Vtf

C = (12)2eoVt

f

E = (13)Q2

2C

E = [ ] f (14)Q2

4eoVt

E = hf (15)

C = (8)eoλ2

.5λ

C = 2eoλ (9)

Vt = fλ (10)

JULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY 4

3. Fourier, J.-B.-J. 1827. “Les Temperatures du Globe Terrestreet des Espaces Planetaires,” Mémoires de l’Académie Royale desSciences de l’Institut de France VII, 570-604.4. Einstein, A., Podolsky, B., and Rosen, N. 1935. “CanQuantum-Mechanical Description of Physical Reality BeConsidered Complete?” Phys. Rev., 47, 777-780.5. de Broglie, L.D. 1924. Ph.D. Thesis, “Recherhce sur laTheorie des Quanta,” U. of Paris.6. Einstein, A. 1905. “Does the Inertia of a Body Dependupon Its Energy-Content?” Annalen der Physik, 18, 639-641.7. Znidarsic, F. 2005. “A Reconciliation of Quantum Physicsand Special Relativity,” The General Journal of Physics,December, http://www.wbabin.net/science/znidarsic.pdf.8. Znidarsic, F. 2009. “The Control of the Natural Forces,”Infinite Energy, 15, 87, 30-33, September/October.9. Znidarsic, F. 2000. “The Constants of the Motion,”Transactions of the American Nuclear Society, 83, November 12.10. Bell, J.S. 1987. Speakable and Unspeakable in QuantumMechanics, Cambridge University Press (original 1964).11. Feynman, R.P. 1948. “The Space-Time Formulation ofNonrelativistic Quantum Mechanics,” Reviews of ModernPhysics, 20, 367-387.12. Heisenberg, W. 1927. “Over the Descriptive Contents ofthe Quantum Kinetics and Mechanics,” Zeitschrift für Physik,43, 172-198.

cal function of its longitudinal displacement. The photondoes not physically exist. The coupling of a light wave to thenuclear velocity of sound produces an artifact that appears asthe photon.

CONCLUSIONThe nature of the substance of the universe has been the sub-ject of debate since antiquity. Some philosophers have sug-gested that the universe is composed of particle-like things.Others have suggested that the universe is composed ofwave-like stuff. In the twentieth century, it was discoveredthat the quantum realm consists of wave-like stuff. This“stuff” is governed by pure chance and exhibits manyunusual properties, such as quantum entanglement. Thisrealm can never be directly observed and its properties aresubjective. This wave-like stuff is converted into particle-likethings through a process of quantum transition. Thesethings obey Newton’s laws and interact in a deterministicclock-like fashion. The properties of these things can beobjectively measured. It is believed today that size is thedivide that separates the wave-like continuum from the par-ticle-like reality.

The process of cold fusion was discovered in the late twen-tieth century. Scientists have suggested that the cold fusionreaction proceeds at the fringes of our contemporary under-standing. I have shown, to the contrary, that the process ofcold fusion rests squarely at the center of a debate that hasbeen raging for hundreds of years. The observable results ofthe cold fusion experiments have exposed the nature of thedivide that separates the quantum and the classical realms.A quantum wave is transformed into a classical particle as itfollows a path through the divide. The speed of the passage,Vt, invokes the magic of a convergence in the motion con-stants. The range and strength of the natural force fields areadjusted, by this convergence, to the dimensions of theopening. The opening is large enough, under the conditionof cold fusion, to encompass a cluster of nucleons.

The terms that describe this passage have produced, in apast publication, the energy levels of the hydrogen atom andthe probably of transition. This paper extends the analysis tothe energy of a photon. These constructs form the founda-tion of our contemporary understanding of the natural uni-verse. The path of the quantum transition has been exposedand a new perspective on the nature of reality has emerged.

NOMENCLATUREeo = 8.854 x 10-12 A2 s4 kg-1 m-3

Fmax = 29.05 Newtonsfc = 1.236 x 1020 hertz, the Compton frequencyMn = 1.67 x 10-27 Kgrp = 1.409 x 10-15 m, half the classical radius

of the electronrn = 1.36 x 10-15 m, the nuclear spacingQ = 1.602 x 1019 CoulombsVt = 1.094 x 106 m/second

REFERENCES1. Clinton Davisson received the Nobel Prize in Physics in1937, with George Thomson.2. Hamilton, W.R. 1853. Lectures on Quaternions, Royal IrishAcademy.

About the AuthorFrank Znidarsic graduated from theUniversity of Pittsburgh with a B.S. inElectrical Engineering in 1975. In the 1980s,he went on to obtain an A.S in BusinessAdministration at St. Francis College. He

studied physics at the University of Indiana in the 1990s.He is currently a Registered Professional Engineer in thestate of Pennsylvania. Frank has been employed as an engi-neer in the steel, mining and utility industries. Mostrecently he was contracted by to start up power plants inNorth Carolina.

*Email: fznidarsic@aol.com