Electromagnetic energy and momentum in moving media

TL;DR

This paper reviews the longstanding debate over electromagnetic energy-momentum tensors in moving media, clarifies the relation between Minkowski and Abraham tensors, and discusses their physical implications within a relativistic framework.

Contribution

It provides a comprehensive analysis of the Minkowski and Abraham tensors using a Lagrange-Noether approach and clarifies their roles in electromagnetic systems involving moving media.

Findings

Minkowski tensor is recovered as a canonical energy-momentum tensor.

Energy-momentum balance equations hold for open systems despite tensor asymmetry.

The Abraham tensor is relevant when the medium's 4-velocity is the primary covariant variable.

Abstract

The problem of the electromagnetic energy-momentum tensor is among the oldest and the most controversial in macroscopic electrodynamics. In the center of the issue is a dispute about the Minkowski and the Abraham tensors for moving media. An overview of the current situation is presented. After putting the discussion into a general Lagrange-Noether framework, the Minkowski tensor is recovered as a canonical energy-momentum. It is shown that the balance equations of energy, momentum, and angular momentum are always satisfied for an open electromagnetic system despite the lack of the symmetry of the canonical tensor. On the other hand, although the Abraham tensor is not defined from first principles, one can formulate a general symmetrization prescription provided a timelike vector is available. We analyze in detail the variational model of a relativistic ideal fluid with isotropic electric and magnetic properties interacting with the electromagnetic field. The relation between the Minkowski energy-momentum tensor, the canonical energy-momentum of the medium and the Abraham tensor is clarified. It is demonstrated that the Abraham energy-momentum is relevant when the 4-velocity of matter is the only covariant variable that enters the constitutive tensor.