Comment on “Analysis of recent interpretations of the Abraham-Minkowski problem”

In a recent paper [I. Brevik, Phys. Rev. A 98, 043847 (2018)], Brevik analyzed the experiment by Kundu et al. [A. Kundu et al., Sci. Rep. 7, 42538 (2017)] reporting deformation of a graphene oxide (GO) film after it has been irradiated by a laser beam. The two-dimensional atomic force microscope (AFM) line scanning of the deformation of the GO film after switching off the laser beam takes by far too much time for any elastic changes to remain in the AFM scans. Thus, the changes in the GO film are irreversible and the optoelastic model used by Brevik is not applicable. The rough estimates of the kinetic energy and displacement of atoms by the optical force of a light pulse calculated by Brevik are correct, but in making a comparison with the corresponding high-precision results for the kinetic energy and displacement of atoms in our work [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)], the kinetic energy of atoms is confused with their rest energy. The atoms and their masses are displaced forward by the field and their displaced rest energies give rise to an energy flux. The difference of arguments between ours and Brevik's culminates on the question whether the flux of rest energy caused by the displacement of the medium moving with light should be included in the total energy flux. We also show that the four-divergence of the stress-energy-momentum tensor of the mass polariton theory of light is zero.

Figure 1

Illustration of the mass transfer effect and the related different scales of mass shifts. The red solid blocks denote the energy $E_{\mathrm{field}}$ of the field (top) and the mass $M_{\mathrm{a}}=\rho A{v}_{\mathrm{l}}\tau$ of atoms (bottom) in the volume of a light pulse at $t=0$. The light pulse is propagating to the right. The blue dashed blocks denote the displaced positions of $E_{\mathrm{field}}$ and $M_{\mathrm{a}}$ at $t=\tau$. The mass $M_{\mathrm{a}}$ is moved due to the optical force. In time $\tau$, the field energy has moved a distance $v_{\mathrm{l}}\tau$ with velocity $v_{\mathrm{l}}=c/n$. In this same time, the center of mass $M_{\mathrm{a}}$ has moved a distance $l=v_{\mathrm{a}}\tau$ with small atomic velocity $v_{\mathrm{a}}$. However, if we compare the initial and final distributions of matter to each other, we observe that a small effective mass $\delta M=M_{\mathrm{a}}{v}_{\mathrm{a}}/v_{\mathrm{l}}$ (and the related rest energy $\delta M{c}^2$, not shown) in the left gray area has moved forward a distance $v_{\mathrm{l}}\tau \gg l$ with light. Therefore, the effective mass transfer with light is an unavoidable consequence of the optical force. The results of the detailed numerical OCD simulations are in full agreement with this simple schematic picture.