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 $$\rho^n_M=\frac{\rho^n_E}{v^2}?$$
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asked Jun 9, 2023 at 9:37
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1$\begingroup$ 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. $\endgroup$– naturallyInconsistentCommented Jun 9, 2023 at 13:49
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1$\begingroup$ 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. $\endgroup$– naturallyInconsistentCommented Jun 9, 2023 at 13:51
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$\begingroup$ @naturallyInconsistent - Those should be answers. $\endgroup$– mmesser314Commented Jun 9, 2023 at 15:24
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$\begingroup$ @mmesser314 Thanks, converted. $\endgroup$– naturallyInconsistentCommented Jun 9, 2023 at 15:27
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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.
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.
answered Jun 9, 2023 at 15:27
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$\begingroup$ But Newton’s gravitational law uses mass not energy and Einstein’s laws should be consistent with Newton in low curvature, low speed limit. In order to use photons in Newton’s law you need to convert their energy to mass. $\endgroup$ Commented Jun 9, 2023 at 15:30
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1$\begingroup$ You can't use $F=ma$ to get the speed of light in a material. What really causes light/photons to appear slower in media? $\endgroup$ Commented Jun 9, 2023 at 15:41
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$\begingroup$ And the very least you could try, is $F=\frac E{c^2}a$, which is wrong, but still at least going to get you somewhere $\endgroup$ Commented Jun 9, 2023 at 15:51
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1$\begingroup$ @JohnEastmond In order to use photons in Newton’s law … you should not do that. Newton's gravitational law is obtained in low curvature, low velocity limit so photons do not satisfy it. For example two parallel beams of photons experience no mutual attraction, while two antiparallel beams experience double gravitational effect than what Newton's law suggests. $\endgroup$– A.V.S.Commented Jun 11, 2023 at 6:35
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$\begingroup$ As I understand it a photon confined to a box with reflective walls has a relativistic mass $E/c^2$. If the box contains a material with refractive index $n$ then is the relativistic mass $En^2/c^2$? $\endgroup$ Commented Jun 11, 2023 at 16:57