The Equations of Maxwell for a Medium in Prefered and Non-Prefered Reference Frames

TL;DR

This paper derives Maxwell's equations for a medium in both preferred and non-preferred reference frames, introducing a tensor-based proper time and transformation methods to extend classical electromagnetism to anisotropic geometries.

Contribution

It presents a new derivation of Maxwell's equations in a medium within non-preferred frames using tensor transformations and introduces a tensor-based proper time concept.

Findings

Maxwell's equations in a medium are derived for preferred frames.

Transformation formulas are used to obtain equations in non-preferred frames.

A Lagrangian similar to that in empty space is formulated for media.

Abstract

Let us consider a reference frame for which the pseudo-Euclidean geometry is valid (prefered frame). The equations of Maxwell in empty space have a simple form and are derived from a Lagrangian. In a medium magnetic permeability and electric permittivity exist. The equations of Maxwell are also well-known in a medium but they cannot be derived as in empty space. In addition to the pseudo-Euclidean geometry a tensor of rank two is stated with which the proper time in a medium is defined. The theory of Maxwell now follows along the lines of the empty space. Reference frames which are uniformly moving with regard to the prefered frame which have an anisotropic geometry are studied by many authors and are called non-prefered reference frames. The equations of Maxwell of a medium in a non-prefered reference frame are derived by the use of the transformation formulae from the prefered to the non-prefered frame. A Lagrangian for the equations of Maxwell of a medium similar to the one in empty space is also given.