Reply to “Comment on ‘Analysis of recent interpretations of the Abraham-Minkowski problem’ ”

The Comment of Partanen and Tulkki [Partanen and Tulkki, Phys. Rev. A 100, 017801 (2019)] claims that my criticism [Brevik, Phys. Rev. A 98, 043847 (2018)] of the earlier paper of Partanen et al. [Partanen et al., Phys. Rev. A 95, 063850 (2017)] was incorrect. Now, there are essentially three points involved here: (i) The first one regards the physical interpretation of the radiation pressure experiment of Kundu et al. [Kundu et al., Sci. Rep. 7, 42538 (2017)]. My mathematical analysis of this situation was certainly simplistic, but yet it was able to illustrate the main property of the experiment, namely that it showed the action from the radiation forces on the dielectric boundaries, and from the Lorentz force in the interior, but it did not have any relationship to the Abraham-Minkowski momentum problem as was originally stated by the investigators. (ii) The second and most important point was my emphasis on the fact that in an electromagnetic pulse in a medium, there cannot be an accompanying mechanical energy density of the same order of magnitude as the electromagnetic energy density itself. The electromagnetic wave carries with it a mechanical momentum, but not a mechanical energy (the latter being of second order in the particle velocity). Here, I illustrate this point by a simple numerical analysis. (iii) When going to a relativistic formulation of the electromagnetic theory in matter, care must be taken to secure that fundamental conditions from field theory are satisfied. In particular, one cannot in general take the electromagnetic total energy and momentum of a radiation pulse to constitute a four-vector; such a property holds only if the electromagnetic energy-momentum tensor is divergence free. For the Minkowski tensor, this condition is satisfied, whereas for the Abraham tensor, it is not. As a conclusion, my earlier standpoint on the Abraham-Minkowski problem remains unchanged.