The problem of effective parameters of a mixture of two isotropic dielectrics distributed in space-time and the conservation law for wave impedance in one-dimensional wave propagation

The problem of effective parameters of a composite medium assembled from the original constituents distributed in space-time is formulated in covariant tensor form. I introduce the fourth rank tensor of material constants using Maxwell's system for a moving dielectric medium as a model example. For one-dimensional wave propagation, if a mixture is composed from two dielectrics with the same ratio epsilon/mu of permittivity epsilon to permeability mu, then the ratio epsilon/M of an effective permittivity to an effective permeability of the mixture will preserve the value epsilon/mu. This statement may be rephrased as the conservation law for the relevant wave impedances root mu/epsilon; this is similar to the law known for two-dimensional polycrystals in an analogous elliptic situation. The tensor concept developed for a dielectric medium is based on the idea of a relativistic invariance of Maxwell's system. The idea of relativistic invariance is fundamental for an adequate description of the effective parameters of any material assemblage in space-time regardless of its physical embodiment. Problems related to structural vibrations or acoustics could be completely understood on the basis of the relevant relativistic equations.