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A discussion is given on the interpretation and physical importance of theMinkowski momentum in macroscopic electrodynamics (essential for theAbraham-Minkowski problem). We focus on the following two facets: (1) Adoptinga simple dielectric model where the refractive index $n$ is constant, wedemonstrate by means of a mapping procedure how the electromagnetic field in amedium can be mapped into a corresponding field in vacuum. This mapping waspresented 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. Acharacteristic property of this procedure is that it shows how natural theMinkowski energy-momentum tensor fits into the canonical formalism. Especiallythe spacelike character of the electromagnetic total four-momentum for aradiation field (implying negative electromagnetic energy in some inertialframes), so strikingly demonstrated in the Cherenkov effect, is worthattention. (2) Our second objective is to give a critical analysis of somerecent experiments on electromagnetic momentum. Care must here be taken in theinterpretations: it is easy to be misled and conclude that an experiment isimportant for the energy-momentum problem, while what is demonstratedexperimentally is merely the action of the Abraham-Minkowski force acting insurface layers or inhomogeneous regions. The Abraham-Minkowski force is commonfor the two energy-momentum tensors and carries no information about fieldmomentum. As a final item, we propose an experiment that might show theexistence of the Abraham force at high frequencies. This would eventually be awelcome optical analogue to the classic low-frequency 1975 Lahoz-Walkerexperiment.

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