The Charge-Magnet Paradoxes of Classical Electrodynamics

TL;DR

This paper demonstrates that charge-magnet paradoxes in classical electrodynamics can be resolved without hidden momentum by adopting Einstein-Laub laws instead of Lorentz law, providing a clearer understanding of electromagnetic conservation laws.

Contribution

It shows how Einstein-Laub laws address classical electrodynamics paradoxes, eliminating the need for hidden entities and clarifying conservation law applications.

Findings

Einstein-Laub formalism resolves charge-magnet paradoxes.

Conservation laws are satisfied without hidden momentum.

The approach aligns with experimental and theoretical evidence.

Abstract

A number of charge-magnet paradoxes have been discussed in the literature, beginning with Shockley's famous 1967 paper, where he introduced the notion of hidden momentum in electromagnetic systems. We discuss all these paradoxes in a single, general context, showing that the conservation laws of linear and angular momenta can be satisfied without the need for hidden entities, provided that the Einstein-Laub laws of force and torque are used in place of the standard Lorentz law. Einstein and Laub published their paper in 1908, but the simplicity of the conventional Lorentz law overshadowed the subtle features of their formulation which, at first sight, appears somewhat complicated. However, that slight complication turns out to lead to subsequent advantages in light of Shockley's discovery of hidden momentum, which occurred more than a decade after Einstein had passed away. In this paper, we show how the Einstein-Laub formalism handles the underlying problems associated with certain paradoxes of classical electrodynamics involving a static distribution of electric charges and a magnet whose magnetization slowly fades away in time. The Einstein-Laub laws of electromagnetic force and torque treat these paradoxes with elegance and without contradicting the existing body of knowledge, which has been confirmed by more than one and a half century of theoretical and experimental investigations.