Special theory of relativity and universal boundary conditions on uniformly moving surfaces

Abstract

The knowledge of the boundary conditions, which interrelate the field values observed on different sides of interfaces between different bodies, has crucial importance for the study of the electromagnetic phenomena created by a given source configuration. During the last century these conditions were discussed rather extensively in cases when the boundaries are at rest with respect to the observer. When the boundary is in motion with respect to the observer, the situation is still rather obscure and causes to tough difficulties. For example, the shape of the boundary seems differently, in general, for an observer moving with it and for an observer to which it is in motion. Hence, it is not an exact approach to try to reveal the boundary conditions on a moving body by assuming that its geometrical shape is known beforehand. The correct approach is the derivation of the boundary relations first in a reference system which moves with the boundary and then to transform the relations into the reference system of the observer. This can be done by the principles of the Special Theory of Relativity if the motion is uniform. The present paper aims to this end for the most general case and derive the universal boundary conditions and compatibility relations. Some illustrative examples show how the compatibility relations are elaborated in obtaining the particular forms of the boundary conditions.