Comment on "Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation"

TL;DR

This paper clarifies that the Lorentz force law is compatible with special relativity, countering recent claims of incompatibility, and emphasizes the importance of considering relativistic effects in such analyses.

Contribution

It demonstrates that the perceived paradox arises from neglecting the relativistic implications of the covariant Lorentz force, reaffirming its consistency with special relativity.

Findings

The supposed paradox is due to incomplete relativistic analysis.

The Lorentz force law remains compatible with special relativity.

Experimental validation is needed to determine the actual force law used by nature.

Abstract

It has been recently argued that the Lorentz force is incompatible with Special Relativity and should be amended in the presence of magnetization and polarization in order to avoid a paradox involving a magnet in the presence of an electric field. Here we stress the well-known fact among relativists that such an incompatibility is simply impossible and show that the appearance of such a "paradox" is a mere consequence of not fully considering the relativistic consequences of the covariant form of the Lorentz force. It should be mentioned, though, that this criticism does not invalidate the debate on which is the law of force followed by Nature, which is an experimental issue.