Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric

TL;DR

This paper clarifies the correct form of the energy-momentum tensor for electromagnetic fields in dielectrics, identifying the Gordon momentum as the conserved total momentum and resolving the Abraham-Minkowski controversy.

Contribution

It constructs a consistent energy-momentum tensor for electromagnetic fields in dielectrics using continuity equations, emphasizing the Gordon momentum as the conserved total momentum.

Findings

Gordon momentum is identified as the total conserved momentum.

A traceless, diagonally symmetric energy-momentum tensor is constructed.

The Abraham-Minkowski controversy is explained as a result of nonconserved quantities.

Abstract

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy-momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field and a negligibly reflecting dielectric. The Gordon momentum is easily identified as the total momentum by the fact that it is, by virtue of being invariant in time, conserved. We construct continuity equations for the energy and the Gordon momentum and use the continuity equations to construct an array that has the properties of a traceless, diagonally symmetric energy-momentum tensor. Then the century-old Abraham-Minkowski momentum controversy can be viewed as a consequence of attempting to construct an energy-momentum tensor from continuity equations that contain densities that correspond to nonconserved quantities.