Electrodynamics, topsy-turvy special relativity, and generalized minkowski constitutive relations for linear and nonlinear systems – abstract

An attempt is made here to integrate and consolidate foundational ideas of electrodynamics and special relativity theories into a consistent structure, from the point of view of the application-oriented applied scientist and engineer. A discussion of this kind is best served by minimizing the sophisticated mathematical tools to the bare minimum, and avoiding lengthy calculations. Some of the difficulties encountered in educating engineers and applied scientist are exactly of this kind, hence a topsy-turvy presentation of special relativity is used, in which fundamental postulates and conclusions exchange roles. With the recent interest in direct time-domain methods, the pre-sent discussion strives to elucidate the fundamental problems involved. Essentially it is argued that appending Maxwell's theory with constitutive relations is in general valid for systems homogeneous in time and space. Spatiotemporal constitutive relations are thus becoming differential operators. Strictly speaking, inhomogeneous systems in time and space are appropriate for non-dispersive systems, or as an approximation. Although Electrodynamics in moving media is often considered a purely academic subject, the understanding of its implementation as proposed by Minkwoski is a crucial cornerstone to our understanding of the physical models at hand. To that end, a generalized approach to the Minkowski method for electrodynamics in moving media is presented. This applies to linear as well as nonlinear media. Finally, a novel representation is proposed for nonlinear constitutive differential operators. This contributes to the spatiotemporal representation of Volterra type nonlinear constitutive parameters.