Continuum electrodynamics and the Abraham--Minkowski momentum controversy

TL;DR

This paper challenges the validity of traditional continuum electrodynamics and proposes a new formal theory based on a non-Minkowski spacetime to resolve the Abraham--Minkowski momentum controversy.

Contribution

It introduces a novel formal theory of continuum electrodynamics in a non-Minkowski spacetime, addressing fundamental flaws in existing axioms and resolving the momentum controversy.

Findings

Traditional theorems are proven false by relativity and conservation laws.

A new formal theory is derived for a non-Minkowski spacetime.

The theory addresses the Abraham--Minkowski momentum controversy.

Abstract

Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block of dielectric situated in free-space and illuminated by a quasimonochromatic field. We show that valid theorems of the formal theory are proven false by relativity and by conservation laws. Then the axioms of the formal theory are proven false at a fundamental level of mathematical logic. We derive a new formal theory of continuum electrodynamics for macroscopic electric and magnetic fields in a four-dimensional flat non-Minkowski material spacetime in which the speed of light is c/n.