Microscopic derivation of electromagnetic force density in magnetic dielectric media

Macroscopic force density imposed on a linear isotropic magnetic dielectric medium by an arbitrary electromagnetic field is derived by spatially averaging the microscopic Lorentz force density. The obtained expression differs from the commonly used expressions, but the energy-momentum tensor derived from it corresponds to a so-called Helmholtz tensor written for a medium that obeys the Clausius–Mossotti law. Thus, our microscopic derivation unambiguously proves the correctness of the Helmholtz tensor for such media. Also, the expression for the momentum density of the field obtained in our theory is different from the expressions obtained by Minkowski, Abraham, Einstein and Laub, and others. We apply the theory to particular examples of static electric, magnetic and stationary electromagnetic phenomena, and show its agreement with experimental observations. We emphasize that in contrast to a widespread belief the Abraham–Minkowski controversy cannot be resolved experimentally because of incompleteness of the theories introduced by Abraham and Minkowski.