Premetric electrodynamics

TL;DR

This paper discusses premetric electrodynamics, an approach that derives fundamental laws like Maxwell's equations without initially relying on a metric, emphasizing an axiomatic framework and observer effects.

Contribution

It introduces an axiomatic approach to electrodynamics that incorporates the metric only at a late stage and explores non-inertial observer effects on Maxwell's equations.

Findings

Premetric formulation isolates fundamental laws without metric dependence.

Axiomatic approach delays metric introduction, clarifying theoretical foundations.

Examines influence of non-inertial observers on Maxwell's equations.

Abstract

Classical electrodynamics can be divided into two parts. In the first one, with the use of a plenty of directed quantities, namely multivectors and differential forms, no scalar product is necessary. It is called premetric electrodynamics. In this part, principal laws of the theory can be tackled, among them the two observer-independent Maxwell's equations. The second part concerns specific media and requires establishing of a scalar product and, consequently a metric. We present an axiomatic approach to electrodynamics in which the metric enters as late as possible. Also a line of research is mentioned in which the notion of non-inertial observer is studied and its influence on observer- dependent Maxwell equations.