Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles

TL;DR

This paper derives quantum wave mechanics from classical electrodynamics by modeling Dirac particles as relativistically circulating charges, showing that magnetic interactions can produce equations equivalent to Schrödinger's wave equation.

Contribution

It presents a novel derivation of quantum wave equations from classical relativistic electrodynamics, linking magnetic interactions of Dirac particles to quantum wavefunctions.

Findings

Magnetic force modulation behaves like the Schrödinger wavefunction.

The time-independent Schrödinger equation is exactly solved by the derived modulation.

The model extends to obtain the full complex Schrödinger wavefunction considering Minkowski-Osiak relativity.

Abstract

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 Schr\"odinger 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 Schr\"odinger 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 Schro\"dinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schr\"odinger 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 Schr\"odinger wavefunction.