Electromagnetic force density and energy-momentum tensor in an arbitrary continuous medium

For more than a century, physicists have searched for a unique and general form for the force density that an electromagnetic field imposes on a medium. The existing equations for this quantity, obtained, e.g., by Minkowski, Einstein and Laub, Abraham and Helmholtz, are manifestly different and, as such, give different predictions in some particular physical situations. The cases of real media with dispersion, dissipation and nonlinearities as well as materials with optical gain have not been addressed much. Here we present an unambiguous general equation for the force density expressed in terms of a new energy-momentum tensor of the field. The equation can be applied to almost any natural or designed material. We show how the results obtained by Minkowski, Helmholtz, Einstein and Laub, and Abraham appear as special cases of this general treatment. Surprisingly, our result turns out to be physically very close to the almost forgotten result of Einstein and Laub.