Minkowski Momentum Resulting from a Vacuum-Medium Mapping Procedure, and a Brief Review of Minkowski Momentum Experiments

TL;DR

This paper explores the Minkowski electromagnetic momentum in media through a vacuum-medium mapping, reviews related experiments, and proposes a new experiment to detect the Abraham force at high frequencies.

Contribution

It introduces a mapping procedure connecting medium and vacuum fields, clarifies the interpretation of experiments, and suggests a new high-frequency experiment to observe the Abraham force.

Findings

The Minkowski energy-momentum tensor fits into the canonical formalism.

The electromagnetic total four-momentum can be spacelike, implying negative energy in some frames.

Careful interpretation is needed for experiments on electromagnetic momentum.

Abstract

A discussion is given on the interpretation and physical importance of the Minkowski momentum in macroscopic electrodynamics (essential for the Abraham-Minkowski problem). We focus on the following two facets: (1) Adopting a simple dielectric model where the refractive index $n$ is constant, we demonstrate by means of a mapping procedure how the electromagnetic field in a medium can be mapped into a corresponding field in vacuum. This mapping was presented many years ago [I. Brevik and B. Lautrup, Mat. Fys. Medd. Dan. Vid. Selsk {\bf 38}(1), 1 (1970)], but is apparently not well known. A characteristic property of this procedure is that it shows how natural the Minkowski energy-momentum tensor fits into the canonical formalism. Especially the spacelike character of the electromagnetic total four-momentum for a radiation field (implying negative electromagnetic energy in some inertial frames), so strikingly demonstrated in the Cherenkov effect, is worth attention. (2) Our second objective is to give a critical analysis of some recent experiments on electromagnetic momentum. Care must here be taken in the interpretations: it is easy to be misled and conclude that an experiment is important for the energy-momentum problem, while what is demonstrated experimentally is merely the action of the Abraham-Minkowski force acting in surface layers or inhomogeneous regions. The Abraham-Minkowski force is common for the two energy-momentum tensors and carries no information about field momentum. As a final item, we propose an experiment that might show the existence of the Abraham force at high frequencies. This would eventually be a welcome optical analogue to the classic low-frequency 1975 Lahoz-Walker experiment.