Decomposition of the Total Electromagnetic Momentum in a Linear Dielectric into Field and Matter Components

TL;DR

This paper resolves the Abraham--Minkowski controversy by deriving a microscopic model of a linear dielectric, showing that both energy and momentum are purely electromagnetic without matter contributions.

Contribution

It provides a microscopic derivation of the electromagnetic momentum decomposition in a linear dielectric, clarifying the nature of energy and momentum.

Findings

Energy and momentum are entirely electromagnetic in a simple linear dielectric.

The dielectric can be modeled as driven harmonic oscillators producing polarization.

The macroscopic fields travel as a combined electromagnetic pulse.

Abstract

The long-standing resolution of the Abraham--Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using a microscopic model of a simple linear dielectric, we derive Lagrangian equations of motion for the electric dipoles and show that the dielectric can be treated as a collection of stationary simple harmonic oscillators that are driven by the electric field and produce a polarization field in response. The macroscopic energy and momentum are defined in terms of the electric, magnetic, and polarization fields that travel through the dielectric together as a pulse of electromagnetic radiation. We conclude that both the macroscopic energy and the macroscopic momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.