Electromagnetic momentum in a dielectric and the energy--momentum tensor

TL;DR

This paper addresses the Abraham--Minkowski controversy by demonstrating the conservation of Gordon electromagnetic momentum in dielectric media and proposing a revised energy-momentum tensor with new continuity equations.

Contribution

It introduces a new form of the energy-momentum tensor based on Gordon momentum and derives electromagnetic continuity equations using a modified four-divergence operator.

Findings

Gordon momentum is conserved in a thermodynamically closed system.

A new energy-momentum tensor form is proposed for dielectric media.

Derived continuity equations incorporate a material-specific four-divergence.

Abstract

The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon form of the electromagnetic momentum is conserved in a thermodynamically closed system. We regard conservation of the components of the four-momentum in a thermodynamically closed system as a fundamental property of the energy--momentum tensor. Then the first row and column of the energy--momentum tensor is populated by the electromagnetic energy density and the Gordon momentum density. We derive new electromagnetic continuity equations for the electromagnetic energy and momentum that are based on the Gordon momentum density. These continuity equations can be represented in the energy-momentum tensor using a material four-divergence operator in which temporal differentiation is performed with respect to ct/n.