Examples and Comments Related to Relativity Controversies

TL;DR

This paper uses simple relativistic charge systems to clarify controversies about the Lorentz force and conservation laws, confirming their validity and addressing recent claims of incompatibility with relativity.

Contribution

It provides clear relativistic examples that demonstrate the validity of conservation laws and refutes claims of Lorentz force incompatibility with relativity.

Findings

External forces can produce different torques in different inertial frames.

Conservation of angular momentum holds in all inertial frames.

Mansuripur's claims of Lorentz force incompatibility are invalid.

Abstract

Recently Mansuripur has called into question the validity of the Lorentz force in connection with relativistic electromagnetic theory. Here we present some very simple point-charge systems treated through order v^{2}/c^{2} in order to clarify some aspects of relativistic controversies both old and new. In connection with the examples, we confirm the validity of the relativistic conservation laws. The relativistic examples make clear that external forces may produce a vanishing torque in one inertial frame and yet produce a non-zero torque in another inertial frame, and that the conservation of angular momentum will hold in both frames. We also discuss a relativistic point-charge model for a magnetic moment and comment on the interaction of a point charge and a magnetic moment. Mansuripur's claims of incompatibiltiy between the Lorentz force and relativity are seen to be invalid.