Mass density of photons in a refractive medium

Question

The effective mass density of photons in a vacuum $\rho^{vac}_M$ is related to the photon energy density $\rho^{vac}_E$ by $$\rho^{vac}_M=\frac{\rho^{vac}_E}{c^2}.$$ Is it true that the mass density of photons inside a medium of refractive index $n$, $\rho^n_M$, with phase velocity $v=c/n$, is related to the photon energy density $\rho^n_E$ by $$\rho^n_M=\frac{\rho^n_E}{v^2}?$$

Answer 1

In no circumstance should you be needing the mass anything of photons. If you are trying to work out the gravitational effect of photons, just use the energy and momentum densities of the photons, written in the stress-energy tensor, and you can already get the correct answer. Gravity and inertia both couple to energy, not mass.

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As for the correct behaviour for light in materials, there continues to be hot debate in the literature on the correct way for the refractive index to appear. Is it by multiplication or by division? This Abraham-Minkowski controversy does not seem to want to end any time soon. If you can avoid it, avoid it.