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

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.