About conservation the angular momentum for asymmetric tensors in electrodynamics

TL;DR

This paper demonstrates that asymmetric energy-momentum tensors in electrodynamics still conserve angular momentum when considering their symmetric parts, challenging the common assumption of violation.

Contribution

It shows that conservation laws hold for asymmetric tensors when expressed through their symmetric components, clarifying misconceptions about Minkowski tensor invariants.

Findings

Conservation of angular momentum is valid for asymmetric tensors.

The total divergence of the antisymmetric part of the tensor is zero.

The Minkowski tensor's linear invariant does not match electromagnetic field invariants.

Abstract

It is customary to assume that the law of conservation of the angular momentum is violated for an asymmetric energy-momentum tensors. This is the reason for criticizing the Minkowski tensor and other asymmetric energy-momentum tensors. In this paper, it is shown that the laws of conservation of energy and momentum following from an asymmetric tensor in the form of its total divergence are equivalent to the divergence of its symmetric part. It is shown that the total divergence of the antisymmetric part of the asymmetric tensor is identically zero. From this, it follows that for the asymmetric energy-momentum tensor the law of conservation of the angular momentum is also fulfilled. It is shown that the linear invariant of the Minkowski tensor for a vacuum does not correspond to the quadratic invariant of the electromagnetic field. This indicates that the linear invariant of the Minkowski tensor and the three-dimensional stress tensor are not correct.