Hidden momentum and the Abraham-Minkowski debate

TL;DR

This paper explores how different models of electric and magnetic dipoles affect the electromagnetic momentum in media, clarifying the Abraham-Minkowski debate by linking specific models to established momentum expressions.

Contribution

It demonstrates the compatibility of Abraham and Minkowski momenta with different dipole models using an extended electrodynamics framework including magnetic charges.

Findings

Abraham's expression aligns with electric charges and magnetic charges models.

Minkowski's expression aligns with magnetic currents and electric currents models.

The expression ε₀E×B is compatible with natural electric and magnetic dipole models.

Abstract

We use an extended version of electrodynamics, which admits the existence of magnetic charges and currents, to discuss how different models for electric and magnetic dipoles do or do not carry hidden momentum under the influence of external electromagnetic fields. Based on that, we discuss how the models adopted for the electric and magnetic dipoles from the particles that compose a material medium influence the expression for the electromagnetic part of the light momentum in the medium. We show that Abraham expression is compatible with electric dipoles formed by electric charges and magnetic dipoles formed by magnetic charges, while Minkowski expression is compatible with electric dipoles formed by magnetic currents and magnetic dipoles formed by electric currents. The expression $\varepsilon_0\mathbf{E}\times\mathbf{B}$, on the other hand, is shown to be compatible with electric dipoles formed by electric charges and magnetic dipoles formed by electric currents, which are much more natural models. So this expression has an interesting interpretation in the Abraham-Minkowski debate about the momentum of light in a medium: It is the expression compatible with the nonexistence of magnetic charges. We also provide a simple justification of why Abraham and Minkowski momenta can be associated with the kinetic and canonical momentum of light, respectively.