An Effective Photon Momentum in a Dielectric Medium: A Relativistic Approach

TL;DR

This paper uses a relativistic approach to define an effective photon momentum in a dielectric medium, concluding it should be the Abraham momentum, which is inversely proportional to the refractive index.

Contribution

It introduces a relativistic framework to derive the Abraham photon momentum in a dielectric medium, providing a theoretical basis for its validity.

Findings

Effective photon momentum is proportional to p/n.

The Abraham momentum is supported as the correct form.

Relativistic arguments justify the inverse relation with n.

Abstract

We use a relativistic argument to define an effective photon that travels through a transparent (non-absorbing) nondispersive dielectric medium of index of refraction $n$. If $p$ is the momentum of the photon in a vacuum, then the momentum of an effective photon inside the medium may be of the form $p_{\rm eff}=pn^\alpha$ and still reproduce the observed transverse relativistic drift when the medium is in motion. We employ an energy argument to determine the value of the exponent to be $\alpha =-1$, so that the effective photon momentum is $p_{\rm eff}=p/n$, which is the Abraham momentum.