Violation of the center of mass theorem for systems with electromagnetic interaction

TL;DR

This paper demonstrates that the traditional center of mass motion theorem fails for systems with non-symmetric energy-momentum tensors, such as electromagnetic systems, and proposes a modified, valid version.

Contribution

It introduces a modified center of mass theorem applicable to systems with non-symmetric energy-momentum tensors, supported by an explicit electromagnetic example.

Findings

Standard theorem is invalid for non-symmetric energy-momentum systems.

Minkowski's momentum density aligns with total momentum conservation.

A simple electromagnetic system illustrates the violation of the standard theorem.

Abstract

In this letter we show that for isolated systems for which the energy current density is not equal to the momentum density, that means for systems with non-symmetric energy-momentum, the usual statements of the center of mass motion theorem are not valid. We also discuss the modified version of the theorem that is always valid. Then we present a simple and exactly workable example of an electromagnetic interacting system which illustrates the violation of those standard versions of the center of mass motion theorem. We show that for this system Minkowski's density of linear momentum which yields a non-symmetric electromagnetic energy-momentum tensor, but not Abraham's, is compatible with total momentum conservation.