Remarks on the Abraham-Minkowski problem, from the formal and from the experimental side

TL;DR

This paper examines the Abraham-Minkowski problem in classical electrodynamics through formal theoretical analysis and review of experimental evidence, highlighting Minkowski's theory as more consistent with optical experiments, while noting differences at low frequencies.

Contribution

It provides a formal covariant analysis linking Minkowski's photon momentum to the formalism and reviews experimental results favoring Minkowski's momentum in optical conditions.

Findings

Minkowski's photon momentum aligns with formal covariant analysis.

Experimental evidence supports Minkowski's momentum under optical conditions.

Differences emerge at low frequencies where Abraham's effects could be observed.

Abstract

We analyze the Abraham-Minkowski problem known from classical electrodynamics from two different perspectives. First, we follow a formal approach, implying use of manifolds with curved space sections in accordance with Fermat's principle, emphasizing that the resulting covariant and contravariant components of the photon four-momentum is a property linked to the {\it Minkowski} theory only. There is thus no link to the Abraham theory in that context. Next we turn to the experimental side, giving a brief account of older and newer radiation pressure experiments that clearly show how the Minkowski photon momentum is preferable under optical conditions. Under low-frequency conditions, where experimental detection of the individual oscillations predicted by the Abraham term are possible, the picture is however quite different.