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Japan Journal of Research

Classical Interpretation of Quantum Mechanical Concepts

Clymer, NY, USA, Richard Joseph Oldani

Published Feb 28, 2023• 0 citations
Publisher

Abstract

All of the mathematical formulations of quantum mechanics describe the interaction between radiation and atoms, but we show here that only Einstein has been able to establish a solid logical connection with classical theory. His methods are used to interpret the other mathematical models by requiring that observables be described in a physically-defined coordinate system and that there be strict adherence to the conservation of momentum. The properties of momentum exchange are included in a quantum oscillator, or clock, by replacing the non-relativistic Hamiltonian model with a relativistically correct Lagrangian model. Equal contributions are assigned to photon, electron, and nucleus; and field boundaries are defined that coincide with the electron shells. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The Lagrangian model accounts for the 720 degree rotation of a wave function as an initial 360 degree electromagnetic wave cycle (photon absorption) followed by a second wave cycle (photon emission), yielding two wave cycles to correspond with one complete electron cycle. The abstract space of quantum mechanics is replaced by a real classical space.

DOI
10.33425/2690-8077.1055

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All of the mathematical formulations of quantum mechanics describe the interaction between radiation and atoms, but we show here that only Einstein has been able to establish a solid logical connection with classical theory. His methods are used to interpret the other mathematical models by requiring that observables be described in a physically-defined coordinate system and that there be strict adherence to the conservation of momentum. The properties of momentum exchange are included in a quantum oscillator, or clock, by replacing the non-relativistic Hamiltonian model with a relativistically correct Lagrangian model. Equal contributions are assigned to photon, electron, and nucleus; and field boundaries are defined that coincide with the electron shells. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The Lagrangian model accounts for the 720 degree rotation of a wave function as an initial 360 degree electromagnetic wave cycle (photon absorption) followed by a second wave cycle (photon emission), yielding two wave cycles to correspond with one complete electron cycle. The abstract space of quantum mechanics is replaced by a real classical space.
Einstein showed in his seminal paper on radiation that molecules with a quantum-theoretical distribution of states in thermal equilibrium are in dynamical equilibrium with the Planck radiation. The method he used assigns coordinates fixed with respect to molecules to derive the A and B coefficients, and fixed relative to laboratory coordinates to specify their thermal motion. The resulting dynamical equilibrium between quantum mechanical and classically defined statistics is critically dependent upon considerations of momentum exchange. When Einstein’s methods relating classical and quantum mechanical statistical laws are applied to the level of the single quantum oscillator they show that matrix mechanics describes the external appearances of an atom as determined by photon-electron interactions in laboratory coordinates, and wave mechanics describes an atom’s internal structure according to the Schrödinger wave equation. Non-commutation is due to the irreversibility of momentum exchange when transforming between atomic and laboratory coordinates. This allows the “rotation” of the wave function to be interpreted as the changing phase of an electromagnetic wave. In order to describe the momentum exchange of a quantum oscillator the Hamiltonian model of atomic structure is replaced by a Lagrangian model that is formulated with equal contributions from electron, photon, and nucleus. The fields of the particles superpose linearly, but otherwise their physical integrity is maintained throughout. The failure of past and present theoretical models to include momentum is attributed to the overwhelming requirement of human visual systems for an explicit stimulus.
A fully relativistic formulation of quantum mechanics is derived by introducing a Lagrangian density of the fields between the excited and ground states and taking the action integral. The change in action, or photon, is a four-dimensional localization of fields that is defined symmetrically with respect to the field boundaries. Due to this photon model, we interpret the three mathematical formulations of atomic structure, matrix mechanics, wave mechanics, and path integrals, as different mathematical methods of describing the superposed physical components of an excited state: nucleus, electron, and photon. Recent experiments with slow and stopped light are shown to support this theoretical interpretation. The derivation of quantum theory with respect to fields requires new interpretations of the uncertainty principle, correspondence principle, complementarity, and force.
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It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Because he did not complete his own quantum theory its far-reaching, intuitively motivated derivations were never properly appreciated despite the fact that his is the only theory based on a relativistically correct foundation. The development of his arguments reveals that although non-relativistic theory correctly predicts what it is possible to observe (the emissions) with remarkable accuracy it neglects the other half of natural phenomena, that which cannot be observed (the absorptions), thereby violating the conservation of energy. The deficiencies in non-relativistic theory are corrected by applying Hamilton’s principle to derive relativistic equations of motion. This allows quantum mechanical formalism in abstract space to be interpreted as the juxtaposition of particle field geometries in real space. Direct application of the calculus of variations to an electron cycle reveals that the wave function is incomplete because it requires twice the allowable action minimum.
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A fully relativistic formulation of quantum mechanics is derived by introducing a Lagrangian density of the fields between the excited and ground states and taking the action integral. The change in action, or photon, is a four-dimensional localization of fields that is defined symmetrically with respect to the field boundaries. Due to this photon model, we interpret the three mathematical formulations of atomic structure, matrix mechanics, wave mechanics, and path integrals, as different mathematical methods of describing the superposed physical components of an excited state: nucleus, electron, and photon. Recent experiments with slow and stopped light are shown to support this theoretical interpretation. The derivation of quantum theory with respect to fields requires new interpretations of the uncertainty principle, correspondence principle, complementarity, and force.