Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

TL;DR

This paper critically examines the Einstein box thought experiment, deriving relativistic expressions for Abraham and Minkowski momenta, and highlights assumptions that challenge the uniqueness of Abraham momentum as the light's momentum in matter.

Contribution

It provides a detailed relativistic analysis of the Einstein box, clarifies the roles of different energy-momentum tensors, and questions the traditional preference for Abraham momentum.

Findings

The total energy-momentum tensor is crucial for understanding light momentum in matter.

Relativistic expressions for Abraham and Minkowski momenta are derived.

The Abraham momentum is not uniquely determined as the momentum of light in matter.

Abstract

We analyse the "Einstein box" thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.