Identical motion in relativistic quantum and classical mechanics

David C. Lush

It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schrödinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schrödinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schrodinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schrödinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schrödinger wavefunction.

В. В. Ласуков, Т. В. Ласукова, M. O. Abdrashitova

F. Reuse

Edward R. Floyd

Identical motion for classical and quantum mechanics is re-examined in order to include the effects of energy-dependent potentials in the equations of motion. Only free particles permit such motion.

Ya.I. Frenkel

Yu. A. Rylov

Abstract It is shown that non‐relativistic quantum mechanics can be treated as a kind of relativistic statistical theory which describes a random motion of a classical particle. The theory is relativistic in the sense that for the description of the particle behaviour the relativistic notion of the state is used. This is very important because a statistics is a state calculus and the result depends on the definition of the notion of state.