On the energy-momentum tensor of light in strong fields: an all optical view of the Abraham-Minkowski controversy

Abstract

The Abraham-Minkowski controversy is the debate surrounding the "correct" form of the energy-momentum tensor of light in a medium. Over a century of theoretical and experimental studies have consistently produced conflicting results, with no consensus being found on how best to describe the influence of a material on the propagation of light. It has been argued that the total energy-momentum tensor for each of the theories, which includes both wave and material components, are equal. The difficulty in separating the full energy-momentum tensor is generally attributed to the fact that one cannot obtain the energy-momentum tensor of the medium for real materials. Non-linear electrodynamics provides an opportunity to approach the debate from an all optical set up, where the role of the medium is replaced by the vacuum under the influence of a strong background field. We derive, from first principles, the general form of the energy-momentum tensor in such theories, and use our results to shed some light on this long standing issue.

Light-to-Plasma Momentum Transfer

“…Equation ( 10) corresponds to the Minkowski description of the photon momentum [16], while Equation ( 11) corresponds to the Abraham description of the photon momentum [17]. The Abraham-Minkowski controversy has been generally resolved if an appropriate phase or group refractive index is employed, respectively, in the Minkowski and Abraham expressions [31,32], though this conclusion has been obscured by associating Minkowski's interpretation with the words "canonical or wave momentum" and Abraham's interpretation with the "kinetic momentum", rather than referring directly to the phase (Minkowski) or group (Abraham) velocities of light (see [19,20,33,34]). For example, the diffraction of light was determined by the phase of the light, so in diffraction calculations, the Minkowski photon momentum should be used (see, for example, the diffraction "thought experiment" discussed by Padgett [35]).…”