The connection between electromagnetic stress tensors and the dielectric constant in a medium

TL;DR

This paper confirms the existence of a unique microscopic electromagnetic stress tensor in dielectric media and clarifies its relation to the macroscopic tensor, resolving previous ambiguities in the field.

Contribution

It explicitly demonstrates that the microscopic stress tensor is unique and that the macroscopic tensor is its spatial average, clarifying their physical significance.

Findings

The microscopic stress tensor $\sigma^{#}$ exists uniquely in dielectric media.

The macroscopic stress tensor is a spatial average of the microscopic tensor.

Both tensors have a well-defined physical meaning, contrary to some claims.

Abstract

We perform explicit calculations for microscopic models to confirm that a single, unique electromagnetic stress tensor exists in a dielectric medium: the microscopic tensor $\sigma^{#}$. We demonstrate that the conventional macroscopic stress tensor of continuum electrodynamics, which contains the derivative of the dielectric coefficient, is merely a representation of $\sigma^{#}$'s spatial average. This result establishes that, contrary to claims in the literature, both this averaged electromagnetic stress and the hydrodynamic pressure always possess a unique physical meaning.