Interaction of Photons with Electrons in Dielectric Media

The question of the field energy‐momentum tensor in a medium is not new and many workers, in the past, attempted to find the answer to it. Nevertheless, there was no general agreement about the form of such a tensor, thus resulting in a confusion involving the very fundaments of physics. Although the present work uses well established theories, the underlying philosophy is completely novel. Investigations are mainly centered around the collisionless plasma as, in that state, development of the argument is most transparent. On the basis of a simple theoretical reasoning, it is, first of all, postulated that the momentum of the photon in a plasma is given by the Minkowski expression. This hypothesis becomes more viable as it directly leads to the accepted form for the field energy density. Furthermore, utilizing the concepts of stimulated and spontaneous emission and absorption, it is confirmed that, in the equilibrium (between radiation and plasma), the transferred momentum has the value given by the Minkowski theory. However, as will be seen, this result is valid only in the region of high frequencies. Put otherwise, when conditions are such that the laws of geometrical optics apply, the momentum of the photon is, to a good approximation, given by the Minkowski theory. In order to arrive at a more general result, valid in the domain of wave optics, a similarity between the dispersion relation (describing the wave propagation through a medium) and the relativistic energy‐momentum of a particle moving through vacuum, is explored. Accepting the equivalence of these two relations implies that some of the properties of radiation in a medium, can also be described by a massive particle travelling through empty space. In other words, the task of analysing the behaviour of electromagnetic waves in a medium, can be replaced by the analysis of the free neutral vector meson field. Adoption of this equivalence results in the field energy‐momentum tensor being symmetrical. A thorough study of the field theory then provides the basis for interpreting the Abraham tensor as the sum of the “orbital” and “spin” tensors. The former is directly connected with the energy transport, whereas the latter one is not. Realising that the magnitude of the spin term increases towards the lower end of the frequency spectrum provides the resolution of the Abraham‐Minkowski dilemma: the energy‐momentum tensor, corresponding to the electromagnetic wave in a medium, is that given by Abraham, while the one of Minkowski is only an approximation valid at high frequencies. Although this conclusion stems from studies involving collisionless isotropic plasma, it is in excellent agreement with the experimental data.