Does Bohm's Quantum Force Have a Classical Origin?

TL;DR

This paper explores whether Bohm's quantum force can be explained by classical electrodynamics, specifically through magnetic forces between particles with circulatory motion, suggesting a classical origin for quantum effects.

Contribution

It proposes a classical electrodynamics model with circulatory charges that reproduces the quantum force, linking Bohmian quantum mechanics to classical magnetic interactions.

Findings

Magnetic forces between circulatory charges can cancel Coulomb forces.

The magnetic force modulation matches the de Broglie wavelength.

Classical model reproduces features of Bohmian quantum force.

Abstract

In the de Broglie - Bohm formulation of quantum mechanics, the electron is stationary in the ground state of the hydrogen atom, because the quantum force exactly cancels the Coulomb attraction of the electron to the proton. In this paper it is shown that classical electrodynamics similarly predicts the Coulomb force can be effectively canceled by part of the magnetic force that occurs between two similar particles each consisting of a point charge moving with circulatory motion at the speed of light. Supposition of such motion is the basis of the {\em Zitterbewegung} interpretation of quantum mechanics. The magnetic force between two luminally-circulating charges for separation large compared to their circulatory motions contains a radial inverse square law part with magnitude equal to the Coulomb force, sinusoidally modulated by the phase difference between the circulatory motions. When the particles have equal mass and their circulatory motions are aligned but out of phase, part of the magnetic force is equal but opposite the Coulomb force. This raises a possibility that the quantum force of Bohmian mechanics may be attributable to the magnetic force of classical electrodynamics. It is further shown that non-relativistic relative motion between the particles leads to modulation of the magnetic force with spatial period equal to the de Broglie wavelength.