Conservation of energy and momentum for an electromagnetic field propagating into a linear medium from the vacuum

TL;DR

This paper examines the controversy over the correct form of the energy-momentum tensor for electromagnetic fields in linear media, highlighting inconsistencies in existing resolutions and proposing a detailed analysis of the total energy-momentum tensor.

Contribution

It demonstrates the self-inconsistency of the Abraham-Minkowski controversy resolution by analyzing the divergence of the total energy-momentum tensor in linear media.

Findings

The divergence of the total energy-momentum tensor depends on different powers of the refractive index.

Existing resolutions treat the electromagnetic and material subsystems separately, leading to inconsistencies.

The controversy remains unresolved due to these fundamental issues.

Abstract

The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame, remains controversial. The Minkowski energy-momentum tensor is the main component of the electromagnetic conservation law. It has been known for over a century that the electromagnetic conservation law is unsound as evidenced by alternative energy-momentum tensors that have been proposed to ameliorate known physical deficiencies (violation of conservation of angular and linear momentum) and by the various material energy-momentum tensors and coupling forces that have been introduced to repair or complete the law. The extant resolution is to treat the continuum electromagnetic system as a subsystem and add a phenomenological material subsystem energy-momentum tensor. We show that the four-divergence of the total, electromagnetic plus material, energy-momentum tensor produces an energy continuity theorem in which the two non-zero terms depend on different powers of the refractive index $n$. Then the extant resolution of the Abraham-Minkowski controversy is self-inconsistent.