Electromagnetic force density and energy-momentum tensor in medium

The force density imposed by an electromagnetic field on individual electric charges that compose a medium is unambiguously described by the so-called microscopic Lorentz force density. For practical purposes, a macroscopic theory is needed to describe nano- and larger-scale phenomena. Several different expressions have been proposed for the macroscopic force density during the last century, but which of them is correct or more general, seems to remain an open question. Some of the most famous of these expressions have been introduced by Minkowski, Abraham, Einstein and Laub, and Helmholtz. A correct expression for the force density is usually searched for in terms of macroscopic, and hence already averaged field and material quantities. We have, instead, chosen to derive the expression for the force density by spatially averaging the microscopic Lorentz force density.