The Minkowski and Abraham tensors, and the non-uniqueness of non-closed systems resolution of the controversy

Abstract

Non-uniqueness of the relativistic description of a non-closed system is studied. First on particular illustrative examples and later in more general manner, it is shown that Minkowski's and Abraham's energy-momentum tensors (together with Maxwell's equations) when used in their original sense, are in general, not well defined and, therefore, indeterminate quantities, due to the fact that their balance equations form a non-closed system. This implies the possibility of choosing the definition of the momentum leading to various expressions for the ponderomotive force and explaining Kastlers' and Peierls' unusual values for momenta. The covariant definition of the ponderomotive force density which is given in explicit form is based on the covariant decomposition of the 4-gradient in the energymomentum conservation equation. This contribution solves the last remaining problem with respect to the Minkowski-Abraham controversy.