Electromagnetic Angular Momentum and Relativity

TL;DR

This paper examines the electromagnetic angular momentum and torque in different frames, demonstrating consistency with special relativity for magnetic monopole pairs and resolving apparent paradoxes for point dipoles.

Contribution

It clarifies the relativistic behavior of electromagnetic angular momentum and torque for different dipole models, reconciling them with special relativity.

Findings

Magnetic monopole-antimonopole dipole has zero torque in all frames.

Point dipole experiences non-zero torque balanced by electromagnetic field angular momentum.

Results resolve apparent inconsistencies with Lorentz force law and relativity.

Abstract

Recently there have been suggestions that the Lorentz force law is inconsistent with special relativity. This is difficult to understand, since Einstein invented relativity in order to reconcile electrodynamics with mechanics. Here we investigate the momentum of an electric charge and a magnetic dipole in the frame in which both are at rest, and in an infinitesimally boosted frame in which both have a common velocity. We show that for a dipole composed of a magnetic monopole-antimonopole pair the torque is zero in both frames, while if the dipole is a point dipole, the torque is not zero, but is balanced by the rate of change of the angular momentum of the electromagnetic field, so there is no mechanical torque on the dipole.