The momentum-energy tensor of the electromagnetic field

Abstract

The question of the form of the momentum-energy tensor of the electromagnetic field (in a medium) remains debatable to this day. The dilemma of whether the photon momentum in a medium is equal to nhf/c (Minkowski) or hu/nc (Abraham) therefore remains unresolved (n is the refractive index). Simple considerations based on the law governing the motion of the center of gravity of the "field + medium" system lead, however, to a unique choice of Abraham's tensor. The Jones-Richards experiments do not contradict this, although they do not lead to a solution of the problem. In principle, measurements of the Jones-Richards type (of the pressure of light in media) in the pulsed regime would yield the solution of the problem. Considerable space is allotted to an analysis of the question of the "rejection" of Abraham's tensor, a question advanced by Laue and supported by many authors. It is shown that the use of the Laue criterion is based on an error in the very formulation of the question. The arguments advanced in this connection are illustrated by using as an example analogous relations in the case of the motion of a simple static system, namely a charged capacitor. The conservations laws applied to a static electromagnetic field having angular momentum also lead to Abraham's expression for the field momentum density.

Reexamination of the Abraham-Minkowski dilemma

“…A few now classical experiments attempted to settle the dispute (e.g., [6]- [8]) and their results at first sight suggest that Minkowski's momentum gives the correct answer. However, careful consideration of all the forces acting on the relevant material bodies shows that the experimental results are fully compatible with Abraham's momentum [9][10]. A seminal experiment was performed by Walker [1,11] and verified the so-called Abraham component of the Lorentz force, thereby providing rather strong experimental evidence in favor of Abraham's theory.…”

“…Thus, the timeaveraged Lorentz force is independent of the electromagnetic momentum: it is simply determined by the stress-tensor at the material boundary, which has an unequivocal form in the air region, even in the framework of macroscopic electromagnetism. In fact, the Abraham-Minkowski dilemma has relevant physical consequences mainly in the context of transient phenomena [9,11], and this explains some of the difficulties in settling the The point of view of this article is that the macroscopic kinetic electromagnetic momentum density EM g should ideally be some function of the macroscopic fields that -8-when integrated over some generic region V of space gives a momentum that agrees with the microscopic theory:…”

Complex Form of Classical and Quantum Electrodynamics

“…In this methodological note, we discuss a complex version of Minkowski's phenomenological electrodynamics (at rest or in a moving medium) without assuming any particular form of material equations as far as possible. Lorentz invariance of the corresponding differential balance equations is emphasized in view of long-standing uncertainties about the electromagnetic stresses and momentum density, the so-called "Abraham-Minkowski controversy" (see, for example, [5], [15], [19], [22], [24], [30], [31], [32], [34], [36], [51], [62], [63], [67], [68], [69], [72], [73], [74], [78], [80], [85], [89], [92], [93], [94], [95] and the references therein).…”

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

“…The discrepancy between these two forms, which both have a sound theoretical basis, 5 led to numerous investigations through the latter half of the century which attempted to pin down the "correct" form. This led to experimental and theoretical work supporting Minkowski [6][7][8][9][10] and Abraham, [11][12][13][14][15] and it is this conflicting evidence which has been the source of much of the confusion surrounding this subject. What many of these studies did not fully take into account was the importance of the energy-momentum tensor of the material itself.…”