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THE DUALITY OF MATTER AND WAVES Frank Znidarsic*

ABSTRACT A 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.

THE UNIVERSE IS COMPOSED OF PARTICLES

THE UNIVERSE IS COMPOSED OF WAVES

Sir Isaac Newton proposed that light consists of particle like corpuscles. Arthur Compton measured the angle of rebounding X-rays and discovered that they bounce like particles. This result confirmed Newton’s hypothesis. In the late nineteenth century, it was discovered that the spectrum of a black body contains much less ultraviolet radiation than classical wave theory predicted. Max Planck came up with a solution to this problem. His solution employed particles of light. These particles are called photons. The energy of these photons varies directly with their frequency. Planck’s particle construct solved the ultraviolet problem by showing that the higher frequency ultraviolet photons are not energetically accessible. Albert Einstein applied Planck’s constant to the photo-electric effect and showed that the maximum energy of an ejected electron equals the energy of the absorbed photon. These observations demonstrate that light is composed of particle-like things. The ancient Greek philosopher Democritus proposed that matter is constructed of particles. These particles are the smallest unit of the substance that still retains the properties of the substance. Chemist John Dalton offered some of the first theoretical proof of Democritus’ proposition. His experiments revealed that particles (elements) combine in whole number ratios to form compounds. Ludwig Edward Boltzmann extended this idea and showed that a gas consists of a collection of particles. Boltzmann discovered that the properties of a gas are established through a statistical interaction of its particles. Robert Millikan experimented with electrically charged droplets. His experiments revealed a first sub-atomic particle, the electron. Ernest Rutherford’s particle scattering experiments detected a few alpha particles that bounced directly back. This result disclosed a second subatomic particle, the nucleus. In the twentieth century, the tracks of a host of sub-atomic particles were directly observed in a bubble chamber. These observations demonstrate that matter is composed of particle-like things.

Christian Huygens proposed that light is a wave. He suggested that the amplitude of the wave determines its intensity and that the frequency of the wave determines its color. The diffraction of light by a prism seemed to support this hypothesis. The dispersion of light which passes through a pinhole also indicates that light is a wave. Thomas Young offered some of the first theoretical proof of Huygens’ proposition. Young passed light through two closely spaced slits. An interference pattern was produced as the light was projected on a screen. This interference pattern revealed the wave-like nature of light. Radio technology was developed in the twentieth century. This technology directly displays the amplitude and frequency of a radio wave (a form of light) on an oscilloscope. These observations demonstrate that light is composed of wave-like stuff. Louis de Broglie proposed that matter is a wave. In 1927, Clinton Davisson and Lester Germer of Bell Labs conducted an experiment in which an electron was passed though finely divided slits.1 An interference pattern was produced. It was discovered that the electron exhibits wave-like properties. These observations demonstrate that matter is composed of wave-like stuff. It appears that the substance of the universe simultaneously exists as both particles and waves. The property that emerges depends upon the bias of the observer. This duality has been a fundamental mystery.

1

INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

PROPOSED RESOLUTIONS Niels Bohr produced an atomic model that contained a particle-like nucleus. Particle-like electrons orbited around this nucleus. These electrons carried an amount of angular momentum that is an integer multiple of Planck’s constant. Angular momentum is the product of length, velocity and mass. These terms did not emerge from a fundamental analysis and are empirical. Bohr’s model described the radii of the atomic orbits and the frequency of the emitted pho-

ton. The model did not disclose the mechanism that binds the electron to a state, determine the probability of transition, or explain the intensity of the atomic spectra. Werner Heisenberg extended Bohr’s particle-like analysis and developed a mathematical technique that produced intensity of the spectral lines. His technique employed matrix mechanics and the mathematical function known as the Hamiltonian.2 The Hamiltonian describes particle interactions as a function of their energy. The correspondence principle was invoked. It states that the energy drop in a quantum system is equivalent to the amplitude of a classical system. The position of the particle was obscured within the Hamiltonian and the amplitude of the particle’s vibration was brushed aside with the help of the correspondence principle. The question of the fundamental nature of a substance was avoided. Erwin Schrödinger proposed that matter is a wave. His solution was slightly better than Heisenberg’s in that it incorporated de Broglie’s electron waves. The use of the de Broglie wave presented a conceptual problem. The de Broglie wave consists of a packet of waves that travel together at the group velocity V. The length of the packet decreases as its velocity increases. It is a curious mathematical construct with no classical analog. It has become accepted because it produces results. Schrödinger encountered a second conceptual problem. How do the discrete properties of matter naturally emerge from a continuous wave? He proposed that the superposition of an infinite number of waves localized the wave function.3 Wave patterns repeat at intervals. The solution suggests that the particle appears at intervals in remote locations. Matter’s particle nature did not spontaneously emerge 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 Copenhagen interpretation. It proposes that matter’s de Broglie wave is not real. It is a subjective construct that exists only in configuration space. The amplitude of this wave represents the probability that a particle of matter will reside at certain locations. A particle emerges, from the probability wave, upon the immediate collapse of the wave function. The solution attempted to extract a particle out of a wave and resolve the problem of wave particle duality. The interpretation did not provide for a mechanism to bind the electron to a state, disclose the whereabouts of configuration space, or explain how a continuous wave collapses at velocities greater than light speed. Schrödinger and Einstein never accepted this interpretation. The nature of the substance of the universe remained a mystery. The duality of nature remained irreconcilable.4

pilot and replaces Heisenberg’s and Schrödinger’s superposition of waves construct. The use of a single binding mechanism is a simplification, in accordance with the principle of Occam’s razor. Charles Coulomb studied the force between electrical charges. He qualified the energy E contained by the interaction of two electrical charges Q. Coulomb’s formulation (Equation 1) did not disclose the mechanism that binds an electron to a state.

ZNIDARSIC’S INTERPRETATION

The product of the harmonic frequency and the particle’s displacement is the velocity Vt. This velocity, as expressed by Equation 5, was extracted from the results of cold fusion experiments. The first term in Equation 5 equals the diameter of the active nuclear environment. The second term represents the natural frequency of an active environment.

My model reveals the mechanism that bundles a wave with a particle. The binding mechanism is classical. Classical systems are constructed by fastening components together. Fasteners are mechanical discontinuities. The same binding mechanism can attach a field. The electromagnetic field is, for example, pinned into the structure of a superconductor by introduced defects (discontinuities). This interpretation states that the natural force fields are pinned into the structure of matter at elastic discontinuities. Discontinuities naturally emerge when the intensity of a field exceeds the ability of space to support that field. The discontinuity acts as a

E=

2Q2 (1/r) 4πeo

(1)

The energy contained by a classical spring is proportionate to the product of the spring constant K and the square of the displacement x (Equation 2). This formula is usually employed with a fixed spring constant K and a variable displacement x. E=

1 Kx2 2

(2)

I regrouped the constants in Equation 1 into the form that expresses the elastic energy of a spring. This formulation, Equation 3, expresses both wave-like and particle-like properties. It describes electrical energy in terms of the movement of the fixed (particle-like) displacement 2rp within the variable elastic medium K-e. E=

1 K (2r )2 2 -e p

(3)

The displacement 2rp is twice that of the maximum extent of the proton. It equals the classical radius of the electron. Mass and kinetic energy are pinned into the structure of matter at this discontinuity. The phase velocity of disturbances within the pinned fields is luminal. The group velocity V of the packet is that of the discontinuity. The condition resembles that of stuck light. de Broglie suggested that the matter wave naturally emerges from the superposition of the Compton wave and its Doppler shifted reflection, under this condition.5 The properties of special relativity also emerge as a condition of stuck light.6,7 The variable elastic constant K-e (Equation 4) also emerged as a result of the regrouping of the electrical constants. I employed this elastic constant and produced the atomic energy levels and the intensity of the spectral emission.8 This analysis showed that the wave-like properties of matter emerge from its mass and elasticity. This harmonic is real; no configuration space is required. K-e =

Fmax r

Vt = (2πnrp)(fc/n)

(4)

(5)

I presented my theorem at a conference of the American Nuclear Society in 2000.9 It describes the action of Vt: “The constants of the motion tend toward the electromagnetic in a Bose condensate that is stimulated at a dimension freJULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY

2

quency of Vt.” The convergence of the motion constants is an effect of an equalization in the strength of the magnetic component of the electrical, gravitational and nuclear forces. The equalization in the strength of the forces matches the impedance of the interacting states and allows the fields to slip into a new configuration. Energy flows, the wavefunction collapses and the quantum transition proceeds. The constant Vt, like Planck’s, has produced the atomic energy levels and the intensity of spectral emission. The convergence of the motion constants provides a clue as to the origin of Vt. It is a condition where the velocity of light within the electronic structure of the atom equals the velocity of sound within the nuclear structure of the atom. In the case of cold fusion, the velocity of sound within the nuclear structure is determined by the vibration of the optical phonons within the mass of the dissolved deuterium. In the nucleus this velocity appears, as shown in Equation 6, as the product of the harmonic motion of the nucleons and the spacing of the nucleons rn within the nucleus. Vt = 1/2π

√ Z(Fmax/2nrn)/nMn x 2nrn

(6)

The equalization of the velocity of light and sound within the transitional atomic state is the effect that pulls the motion constants together. Vt is an emergent classical property and, as such, it is fundamental to Planck’s constant.

THE PARTICLE OF A LIGHT WAVE This paper extended the prior analysis and produced the energy of the photon. It was accomplished through the use of a fundamental analysis that did not require an ad hoc injection of Planck’s constant. The geometry a photon experiences during emission is approximately that of a flat plate capacitor. The capacitance C of a flat plate capacitor of area A and spacing D is given in Equation 7. C=

eo A D

(7)

The area A was set equal to the displacement of the photon squared. The displacement between the peaks in the amplitudes, D, equals one half wavelength. The capacitance experienced by a cycle of light is given in Equation 8. C=

eo λ2 .5λ

(8)

The reduction of Equation 8 produced Equation 9. C = 2eo λ

(9)

Equation 9 describes the capacitance of the captured photon. The capacitance of the “in flight” photon is indeterminate. Its energy is strictly a function of its momentum and, as such, it is independent of the photon’s displacement. The lack of restriction allows the displacement λ to vary. The geometry of the traveling photon is that of a boundless wave. This variability may produce, as Einstein called it, “a spooky interaction at a distance.”10 Its state is, as Feynman called it, the sum of every possible history.11 This is the state of the light that simultaneously passed through the two slits in Young’s experiment. The Heisenberg Uncertainty Principle associates the precise velocity of Vt with a boundless wave.12 This uncertainty in position couples the quantum transitions to a change in 3

INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

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

(10)

The strength and range of the natural forces converge as the quantum transition proceeds. The wavefunction’s negative gravitational potential increases to the point where it equals its positive mass energy. The zero energy wavefunction then collapses without restriction. Deterministic classical reality emerges, from probabilistic quantum waves, at this instant. One half of the quantum information is lost in the crash. Equation 10 was solved for length. This is the range at which the natural force fields strongly interact.

λ=

Vt f

(11)

The amplitude of light, as expressed by its capacitance, was given in Equation 9. The action of the transitional quantum state (Equation 11) fixes the geometry of the light. The simultaneous solution of Equations 9 and 11 produced Equation 12. It expresses the relationship between the capacitance and the frequency of the photon.

C=

2eo V t f

(12)

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

E=

Q2 2C

(13)

The great scientists described the energy of a photon in terms of its frequency. The energy of a classical wave is a function of its amplitude, not its frequency. This discrepancy has been a long-standing mystery. The principle of quantum correspondence was invented in an attempt to circumvent this problem. It proposes, with some slight of hand, that the frequency of a quantum system appears as an amplitude in a classical system. I have rejected this proposition and shown that the energy of light is an effect of the light’s displacement. The energy, of the captured photon was qualified through the simultaneous solution of Equations 12 and 13. The result (Equation 14) expresses the relationship between the energy and frequency of the photon. Equations 12 and 13 reveal that the energy of captured light is a function of charge and capacitance. The voltage produced by an electrical charge increases as its capacitance decreases. The energy of a photon is proportionate to the amplitude of its voltage. The action of this voltage replaces the principle of quantum correspondence. This is the state of the light that produces Einstein’s photoelectric effect.

E=[

Q2 ]f 4eoVt

(14)

Planck’s constant emerged from the terms within the brackets [ ]. Planck’s constant was substituted for the quantity within the brackets. Einstein’s famous photoelectric relationship was produced.

E = hf

(15)

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

cal function of its longitudinal displacement. The photon does not physically exist. The coupling of a light wave to the nuclear velocity of sound produces an artifact that appears as the photon.

CONCLUSION The nature of the substance of the universe has been the subject of debate since antiquity. Some philosophers have suggested that the universe is composed of particle-like things. Others have suggested that the universe is composed of wave-like stuff. In the twentieth century, it was discovered that the quantum realm consists of wave-like stuff. This “stuff” is governed by pure chance and exhibits many unusual properties, such as quantum entanglement. This realm can never be directly observed and its properties are subjective. This wave-like stuff is converted into particle-like things through a process of quantum transition. These things obey Newton’s laws and interact in a deterministic clock-like fashion. The properties of these things can be objectively measured. It is believed today that size is the divide that separates the wave-like continuum from the particle-like reality. The process of cold fusion was discovered in the late twentieth century. Scientists have suggested that the cold fusion reaction proceeds at the fringes of our contemporary understanding. I have shown, to the contrary, that the process of cold fusion rests squarely at the center of a debate that has been raging for hundreds of years. The observable results of the cold fusion experiments have exposed the nature of the divide that separates the quantum and the classical realms. A quantum wave is transformed into a classical particle as it follows a path through the divide. The speed of the passage, Vt, invokes the magic of a convergence in the motion constants. The range and strength of the natural force fields are adjusted, by this convergence, to the dimensions of the opening. The opening is large enough, under the condition of cold fusion, to encompass a cluster of nucleons. The terms that describe this passage have produced, in a past publication, the energy levels of the hydrogen atom and the probably of transition. This paper extends the analysis to the energy of a photon. These constructs form the foundation of our contemporary understanding of the natural universe. The path of the quantum transition has been exposed and a new perspective on the nature of reality has emerged.

3. Fourier, J.-B.-J. 1827. “Les Temperatures du Globe Terrestre et des Espaces Planetaires,” Mémoires de l’Académie Royale des Sciences de l’Institut de France VII, 570-604. 4. Einstein, A., Podolsky, B., and Rosen, N. 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev., 47, 777-780. 5. de Broglie, L.D. 1924. Ph.D. Thesis, “Recherhce sur la Theorie des Quanta,” U. of Paris. 6. Einstein, A. 1905. “Does the Inertia of a Body Depend upon Its Energy-Content?” Annalen der Physik, 18, 639-641. 7. Znidarsic, F. 2005. “A Reconciliation of Quantum Physics and 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 Quantum Mechanics, Cambridge University Press (original 1964). 11. Feynman, R.P. 1948. “The Space-Time Formulation of Nonrelativistic Quantum Mechanics,” Reviews of Modern Physics, 20, 367-387. 12. Heisenberg, W. 1927. “Over the Descriptive Contents of the Quantum Kinetics and Mechanics,” Zeitschrift für Physik, 43, 172-198. About the Author Frank Znidarsic graduated from the University of Pittsburgh with a B.S. in Electrical Engineering in 1975. In the 1980s, he went on to obtain an A.S in Business Administration at St. Francis College. He studied physics at the University of Indiana in the 1990s .He is currently a Registered Professional Engineer in the state of Pennsylvania. Frank has been employed as an engineer in the steel, mining and utility industries. Most recently he was contracted by to start up power plants in North Carolina. *Email: [email protected]

NOMENCLATURE eo Fmax fc Mn rp rn Q Vt

8.854 x 10-12 A2 s4 kg-1 m-3 29.05 Newtons 1.236 x 1020 hertz, the Compton frequency 1.67 x 10-27 Kg 1.409 x 10-15 m, half the classical radius of the electron = 1.36 x 10-15 m, the nuclear spacing = 1.602 x 1019 Coulombs = 1.094 x 106 m/second = = = = =

REFERENCES 1. Clinton Davisson received the Nobel Prize in Physics in 1937, with George Thomson. 2. Hamilton, W.R. 1853. Lectures on Quaternions, Royal Irish Academy. JULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY

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ABSTRACT A 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.

THE UNIVERSE IS COMPOSED OF PARTICLES

THE UNIVERSE IS COMPOSED OF WAVES

Sir Isaac Newton proposed that light consists of particle like corpuscles. Arthur Compton measured the angle of rebounding X-rays and discovered that they bounce like particles. This result confirmed Newton’s hypothesis. In the late nineteenth century, it was discovered that the spectrum of a black body contains much less ultraviolet radiation than classical wave theory predicted. Max Planck came up with a solution to this problem. His solution employed particles of light. These particles are called photons. The energy of these photons varies directly with their frequency. Planck’s particle construct solved the ultraviolet problem by showing that the higher frequency ultraviolet photons are not energetically accessible. Albert Einstein applied Planck’s constant to the photo-electric effect and showed that the maximum energy of an ejected electron equals the energy of the absorbed photon. These observations demonstrate that light is composed of particle-like things. The ancient Greek philosopher Democritus proposed that matter is constructed of particles. These particles are the smallest unit of the substance that still retains the properties of the substance. Chemist John Dalton offered some of the first theoretical proof of Democritus’ proposition. His experiments revealed that particles (elements) combine in whole number ratios to form compounds. Ludwig Edward Boltzmann extended this idea and showed that a gas consists of a collection of particles. Boltzmann discovered that the properties of a gas are established through a statistical interaction of its particles. Robert Millikan experimented with electrically charged droplets. His experiments revealed a first sub-atomic particle, the electron. Ernest Rutherford’s particle scattering experiments detected a few alpha particles that bounced directly back. This result disclosed a second subatomic particle, the nucleus. In the twentieth century, the tracks of a host of sub-atomic particles were directly observed in a bubble chamber. These observations demonstrate that matter is composed of particle-like things.

Christian Huygens proposed that light is a wave. He suggested that the amplitude of the wave determines its intensity and that the frequency of the wave determines its color. The diffraction of light by a prism seemed to support this hypothesis. The dispersion of light which passes through a pinhole also indicates that light is a wave. Thomas Young offered some of the first theoretical proof of Huygens’ proposition. Young passed light through two closely spaced slits. An interference pattern was produced as the light was projected on a screen. This interference pattern revealed the wave-like nature of light. Radio technology was developed in the twentieth century. This technology directly displays the amplitude and frequency of a radio wave (a form of light) on an oscilloscope. These observations demonstrate that light is composed of wave-like stuff. Louis de Broglie proposed that matter is a wave. In 1927, Clinton Davisson and Lester Germer of Bell Labs conducted an experiment in which an electron was passed though finely divided slits.1 An interference pattern was produced. It was discovered that the electron exhibits wave-like properties. These observations demonstrate that matter is composed of wave-like stuff. It appears that the substance of the universe simultaneously exists as both particles and waves. The property that emerges depends upon the bias of the observer. This duality has been a fundamental mystery.

1

INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

PROPOSED RESOLUTIONS Niels Bohr produced an atomic model that contained a particle-like nucleus. Particle-like electrons orbited around this nucleus. These electrons carried an amount of angular momentum that is an integer multiple of Planck’s constant. Angular momentum is the product of length, velocity and mass. These terms did not emerge from a fundamental analysis and are empirical. Bohr’s model described the radii of the atomic orbits and the frequency of the emitted pho-

ton. The model did not disclose the mechanism that binds the electron to a state, determine the probability of transition, or explain the intensity of the atomic spectra. Werner Heisenberg extended Bohr’s particle-like analysis and developed a mathematical technique that produced intensity of the spectral lines. His technique employed matrix mechanics and the mathematical function known as the Hamiltonian.2 The Hamiltonian describes particle interactions as a function of their energy. The correspondence principle was invoked. It states that the energy drop in a quantum system is equivalent to the amplitude of a classical system. The position of the particle was obscured within the Hamiltonian and the amplitude of the particle’s vibration was brushed aside with the help of the correspondence principle. The question of the fundamental nature of a substance was avoided. Erwin Schrödinger proposed that matter is a wave. His solution was slightly better than Heisenberg’s in that it incorporated de Broglie’s electron waves. The use of the de Broglie wave presented a conceptual problem. The de Broglie wave consists of a packet of waves that travel together at the group velocity V. The length of the packet decreases as its velocity increases. It is a curious mathematical construct with no classical analog. It has become accepted because it produces results. Schrödinger encountered a second conceptual problem. How do the discrete properties of matter naturally emerge from a continuous wave? He proposed that the superposition of an infinite number of waves localized the wave function.3 Wave patterns repeat at intervals. The solution suggests that the particle appears at intervals in remote locations. Matter’s particle nature did not spontaneously emerge 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 Copenhagen interpretation. It proposes that matter’s de Broglie wave is not real. It is a subjective construct that exists only in configuration space. The amplitude of this wave represents the probability that a particle of matter will reside at certain locations. A particle emerges, from the probability wave, upon the immediate collapse of the wave function. The solution attempted to extract a particle out of a wave and resolve the problem of wave particle duality. The interpretation did not provide for a mechanism to bind the electron to a state, disclose the whereabouts of configuration space, or explain how a continuous wave collapses at velocities greater than light speed. Schrödinger and Einstein never accepted this interpretation. The nature of the substance of the universe remained a mystery. The duality of nature remained irreconcilable.4

pilot and replaces Heisenberg’s and Schrödinger’s superposition of waves construct. The use of a single binding mechanism is a simplification, in accordance with the principle of Occam’s razor. Charles Coulomb studied the force between electrical charges. He qualified the energy E contained by the interaction of two electrical charges Q. Coulomb’s formulation (Equation 1) did not disclose the mechanism that binds an electron to a state.

ZNIDARSIC’S INTERPRETATION

The product of the harmonic frequency and the particle’s displacement is the velocity Vt. This velocity, as expressed by Equation 5, was extracted from the results of cold fusion experiments. The first term in Equation 5 equals the diameter of the active nuclear environment. The second term represents the natural frequency of an active environment.

My model reveals the mechanism that bundles a wave with a particle. The binding mechanism is classical. Classical systems are constructed by fastening components together. Fasteners are mechanical discontinuities. The same binding mechanism can attach a field. The electromagnetic field is, for example, pinned into the structure of a superconductor by introduced defects (discontinuities). This interpretation states that the natural force fields are pinned into the structure of matter at elastic discontinuities. Discontinuities naturally emerge when the intensity of a field exceeds the ability of space to support that field. The discontinuity acts as a

E=

2Q2 (1/r) 4πeo

(1)

The energy contained by a classical spring is proportionate to the product of the spring constant K and the square of the displacement x (Equation 2). This formula is usually employed with a fixed spring constant K and a variable displacement x. E=

1 Kx2 2

(2)

I regrouped the constants in Equation 1 into the form that expresses the elastic energy of a spring. This formulation, Equation 3, expresses both wave-like and particle-like properties. It describes electrical energy in terms of the movement of the fixed (particle-like) displacement 2rp within the variable elastic medium K-e. E=

1 K (2r )2 2 -e p

(3)

The displacement 2rp is twice that of the maximum extent of the proton. It equals the classical radius of the electron. Mass and kinetic energy are pinned into the structure of matter at this discontinuity. The phase velocity of disturbances within the pinned fields is luminal. The group velocity V of the packet is that of the discontinuity. The condition resembles that of stuck light. de Broglie suggested that the matter wave naturally emerges from the superposition of the Compton wave and its Doppler shifted reflection, under this condition.5 The properties of special relativity also emerge as a condition of stuck light.6,7 The variable elastic constant K-e (Equation 4) also emerged as a result of the regrouping of the electrical constants. I employed this elastic constant and produced the atomic energy levels and the intensity of the spectral emission.8 This analysis showed that the wave-like properties of matter emerge from its mass and elasticity. This harmonic is real; no configuration space is required. K-e =

Fmax r

Vt = (2πnrp)(fc/n)

(4)

(5)

I presented my theorem at a conference of the American Nuclear Society in 2000.9 It describes the action of Vt: “The constants of the motion tend toward the electromagnetic in a Bose condensate that is stimulated at a dimension freJULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY

2

quency of Vt.” The convergence of the motion constants is an effect of an equalization in the strength of the magnetic component of the electrical, gravitational and nuclear forces. The equalization in the strength of the forces matches the impedance of the interacting states and allows the fields to slip into a new configuration. Energy flows, the wavefunction collapses and the quantum transition proceeds. The constant Vt, like Planck’s, has produced the atomic energy levels and the intensity of spectral emission. The convergence of the motion constants provides a clue as to the origin of Vt. It is a condition where the velocity of light within the electronic structure of the atom equals the velocity of sound within the nuclear structure of the atom. In the case of cold fusion, the velocity of sound within the nuclear structure is determined by the vibration of the optical phonons within the mass of the dissolved deuterium. In the nucleus this velocity appears, as shown in Equation 6, as the product of the harmonic motion of the nucleons and the spacing of the nucleons rn within the nucleus. Vt = 1/2π

√ Z(Fmax/2nrn)/nMn x 2nrn

(6)

The equalization of the velocity of light and sound within the transitional atomic state is the effect that pulls the motion constants together. Vt is an emergent classical property and, as such, it is fundamental to Planck’s constant.

THE PARTICLE OF A LIGHT WAVE This paper extended the prior analysis and produced the energy of the photon. It was accomplished through the use of a fundamental analysis that did not require an ad hoc injection of Planck’s constant. The geometry a photon experiences during emission is approximately that of a flat plate capacitor. The capacitance C of a flat plate capacitor of area A and spacing D is given in Equation 7. C=

eo A D

(7)

The area A was set equal to the displacement of the photon squared. The displacement between the peaks in the amplitudes, D, equals one half wavelength. The capacitance experienced by a cycle of light is given in Equation 8. C=

eo λ2 .5λ

(8)

The reduction of Equation 8 produced Equation 9. C = 2eo λ

(9)

Equation 9 describes the capacitance of the captured photon. The capacitance of the “in flight” photon is indeterminate. Its energy is strictly a function of its momentum and, as such, it is independent of the photon’s displacement. The lack of restriction allows the displacement λ to vary. The geometry of the traveling photon is that of a boundless wave. This variability may produce, as Einstein called it, “a spooky interaction at a distance.”10 Its state is, as Feynman called it, the sum of every possible history.11 This is the state of the light that simultaneously passed through the two slits in Young’s experiment. The Heisenberg Uncertainty Principle associates the precise velocity of Vt with a boundless wave.12 This uncertainty in position couples the quantum transitions to a change in 3

INFINITE ENERGY • ISSUE 92 • JULY/AUGUST 2010

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

(10)

The strength and range of the natural forces converge as the quantum transition proceeds. The wavefunction’s negative gravitational potential increases to the point where it equals its positive mass energy. The zero energy wavefunction then collapses without restriction. Deterministic classical reality emerges, from probabilistic quantum waves, at this instant. One half of the quantum information is lost in the crash. Equation 10 was solved for length. This is the range at which the natural force fields strongly interact.

λ=

Vt f

(11)

The amplitude of light, as expressed by its capacitance, was given in Equation 9. The action of the transitional quantum state (Equation 11) fixes the geometry of the light. The simultaneous solution of Equations 9 and 11 produced Equation 12. It expresses the relationship between the capacitance and the frequency of the photon.

C=

2eo V t f

(12)

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

E=

Q2 2C

(13)

The great scientists described the energy of a photon in terms of its frequency. The energy of a classical wave is a function of its amplitude, not its frequency. This discrepancy has been a long-standing mystery. The principle of quantum correspondence was invented in an attempt to circumvent this problem. It proposes, with some slight of hand, that the frequency of a quantum system appears as an amplitude in a classical system. I have rejected this proposition and shown that the energy of light is an effect of the light’s displacement. The energy, of the captured photon was qualified through the simultaneous solution of Equations 12 and 13. The result (Equation 14) expresses the relationship between the energy and frequency of the photon. Equations 12 and 13 reveal that the energy of captured light is a function of charge and capacitance. The voltage produced by an electrical charge increases as its capacitance decreases. The energy of a photon is proportionate to the amplitude of its voltage. The action of this voltage replaces the principle of quantum correspondence. This is the state of the light that produces Einstein’s photoelectric effect.

E=[

Q2 ]f 4eoVt

(14)

Planck’s constant emerged from the terms within the brackets [ ]. Planck’s constant was substituted for the quantity within the brackets. Einstein’s famous photoelectric relationship was produced.

E = hf

(15)

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

cal function of its longitudinal displacement. The photon does not physically exist. The coupling of a light wave to the nuclear velocity of sound produces an artifact that appears as the photon.

CONCLUSION The nature of the substance of the universe has been the subject of debate since antiquity. Some philosophers have suggested that the universe is composed of particle-like things. Others have suggested that the universe is composed of wave-like stuff. In the twentieth century, it was discovered that the quantum realm consists of wave-like stuff. This “stuff” is governed by pure chance and exhibits many unusual properties, such as quantum entanglement. This realm can never be directly observed and its properties are subjective. This wave-like stuff is converted into particle-like things through a process of quantum transition. These things obey Newton’s laws and interact in a deterministic clock-like fashion. The properties of these things can be objectively measured. It is believed today that size is the divide that separates the wave-like continuum from the particle-like reality. The process of cold fusion was discovered in the late twentieth century. Scientists have suggested that the cold fusion reaction proceeds at the fringes of our contemporary understanding. I have shown, to the contrary, that the process of cold fusion rests squarely at the center of a debate that has been raging for hundreds of years. The observable results of the cold fusion experiments have exposed the nature of the divide that separates the quantum and the classical realms. A quantum wave is transformed into a classical particle as it follows a path through the divide. The speed of the passage, Vt, invokes the magic of a convergence in the motion constants. The range and strength of the natural force fields are adjusted, by this convergence, to the dimensions of the opening. The opening is large enough, under the condition of cold fusion, to encompass a cluster of nucleons. The terms that describe this passage have produced, in a past publication, the energy levels of the hydrogen atom and the probably of transition. This paper extends the analysis to the energy of a photon. These constructs form the foundation of our contemporary understanding of the natural universe. The path of the quantum transition has been exposed and a new perspective on the nature of reality has emerged.

3. Fourier, J.-B.-J. 1827. “Les Temperatures du Globe Terrestre et des Espaces Planetaires,” Mémoires de l’Académie Royale des Sciences de l’Institut de France VII, 570-604. 4. Einstein, A., Podolsky, B., and Rosen, N. 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev., 47, 777-780. 5. de Broglie, L.D. 1924. Ph.D. Thesis, “Recherhce sur la Theorie des Quanta,” U. of Paris. 6. Einstein, A. 1905. “Does the Inertia of a Body Depend upon Its Energy-Content?” Annalen der Physik, 18, 639-641. 7. Znidarsic, F. 2005. “A Reconciliation of Quantum Physics and 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 Quantum Mechanics, Cambridge University Press (original 1964). 11. Feynman, R.P. 1948. “The Space-Time Formulation of Nonrelativistic Quantum Mechanics,” Reviews of Modern Physics, 20, 367-387. 12. Heisenberg, W. 1927. “Over the Descriptive Contents of the Quantum Kinetics and Mechanics,” Zeitschrift für Physik, 43, 172-198. About the Author Frank Znidarsic graduated from the University of Pittsburgh with a B.S. in Electrical Engineering in 1975. In the 1980s, he went on to obtain an A.S in Business Administration at St. Francis College. He studied physics at the University of Indiana in the 1990s .He is currently a Registered Professional Engineer in the state of Pennsylvania. Frank has been employed as an engineer in the steel, mining and utility industries. Most recently he was contracted by to start up power plants in North Carolina. *Email: [email protected]

NOMENCLATURE eo Fmax fc Mn rp rn Q Vt

8.854 x 10-12 A2 s4 kg-1 m-3 29.05 Newtons 1.236 x 1020 hertz, the Compton frequency 1.67 x 10-27 Kg 1.409 x 10-15 m, half the classical radius of the electron = 1.36 x 10-15 m, the nuclear spacing = 1.602 x 1019 Coulombs = 1.094 x 106 m/second = = = = =

REFERENCES 1. Clinton Davisson received the Nobel Prize in Physics in 1937, with George Thomson. 2. Hamilton, W.R. 1853. Lectures on Quaternions, Royal Irish Academy. JULY/AUGUST 2010 • ISSUE 92 • INFINITE ENERGY

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