A Classical (Local) Account of The Aharonov-Bohm Effect

TL;DR

This paper presents a classical explanation for the Aharonov-Bohm effect, arguing that the vector potential has a fundamental role in classical physics, challenging the common view of its exclusively quantum significance.

Contribution

It offers a fully classical account of the Aharonov-Bohm effect, emphasizing the fundamental importance of the vector potential in classical physics.

Findings

Classical account reproduces Aharonov-Bohm phase effects

Vector potential is essential for local phase descriptions

Challenges the view that the effect is purely quantum

Abstract

It is frequently stated that the electromagnetic vector potential acquires a fundamental role in quantum physics, whereas classically it only represents a convenient, but by no means necessary, way of representing the electromagnetic field. Here we argue that this is a historical accident due to the fact that the electromagnetic field was discovered before photons, while the electron itself was discovered first as a particle, before it became clear that it must also be treated as a wave and therefore as an excitation of the underlying electron field. We illustrate the fact that the vector potential ought to play a fundamental role classically using the Aharonov-Bohm effect. This effect is considered as the strongest argument for the role the vector potential plays in quantum physics, however, here we offer a fully classical account of it. This is a consequence of the fact that any account, be it classical or quantum, must involve the vector potential in order to preserve the local nature of the Aharonov-Bohm (as well as all the other) phases.