The Classical Aharonov-Bohm Interaction as a Relativity Paradox

TL;DR

This paper examines the Aharonov-Bohm effect as a relativity paradox, highlighting misunderstandings due to overlooked acceleration fields derived from the Darwin Lagrangian in classical electromagnetism.

Contribution

It clarifies the role of acceleration fields in the Aharonov-Bohm effect, challenging common textbook explanations and providing a new perspective on the interaction.

Findings

Acceleration fields from the Darwin Lagrangian are crucial for understanding the effect.

The Aharonov-Bohm interaction involves relativistic considerations often neglected.

Misinterpretations arise from unfamiliarity with acceleration fields in classical EM.

Abstract

The situation of a charged particle passing down the symmetry axis through a magnetic toroid presents a relativity paradox; different inertial frames suggest different forces on the charge and on the toroid due to the unperturbed systems. We review the charge-toroid interaction and suggest that the magnetic Aharonov-Bohm situation is misunderstood because of unfamiliarity with the acceleration fields following from the Darwin Lagrangian, which go unmentioned in recent textbooks of classical electromagnetism.