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

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.

18 pages, no figures. Minor changes; a reference added

References in corpus (6)

• Observation of a push force on the end face of a nm fiber taper exerted by outgoing light
• Resolution of the Abraham-Minkowski Controversy
• Momentum exchange between light and a single atom: Abraham or Minkowski?
• Comment on "Observation of a push force on the end face of a nanometer silica filament exerted by outgoing light," Phys. Rev. Lett. 101, 243601 (2008)
• On the Possibility of Measuring the Abraham Force using Whispering Gallery Modes
• Nonlinear Laser-Induced Deformations of Liquid-Liquid Interfaces: an Optical Fiber Model

Cited by in corpus (6)

• Mass-polariton theory of light in dispersive media
• About the Abraham force in a conducting medium
• Remarks on the Abraham-Minkowski problem, from the formal and from the experimental side
• Very Special Relativity: Cherenkov Effect and an Analogy with Minkowski's Electrodynamics of Continuous Media
• About conservation the angular momentum for asymmetric tensors in electrodynamics
• Electromagnetic energy, momentum and forces in a dielectric medium with losses