Electromagnetic potentials and Aharonov-Bohm effect

TL;DR

This paper demonstrates that the Aharonov-Bohm effect, traditionally considered quantum, can be derived from classical Hamilton-Jacobi theory, challenging its supposed quantum uniqueness and explaining experimental observations.

Contribution

It shows the Aharonov-Bohm effect has a classical origin, undermining its status as a purely quantum phenomenon and providing a new classical perspective.

Findings

Aharonov-Bohm effect derived from classical Hamilton-Jacobi equation

Classical analogues of the effect explained

Questioning the unique quantum role of electromagnetic potentials

Abstract

Hamilton-Jacobi equation which governs classical mechanics and electrodynamics explicitly depends on the electromagnetic potentials (A,{\phi}), similar to Schroedinger equation. We derived the Aharonov-Bohm effect from Hamilton-Jacobi equation thereby having proved that this effect is of classical origin. These facts enable us to arrive at the following conclusions: a) the very idea of special role of potentials (A,{\phi}) in quantum mechanics (different from their role in classical physics) lost the ground, and becomes dubious, as this idea is based on the Aharonov-Bohm effect, b) failure to find any signs of a special role of these potentials in the appropriate experiments (Feinberg, 1963) is thereby explained, and c) discovery of classical analogues of the Aharonov-Bohm effect (Berry et al., 1980) is also explained by a classical nature of this effect. Elucidation of the "unlocal" interaction problem was made.