I know that the Lorentz factor is given by: $$\gamma=1/\sqrt{1-v^2/c^2}$$ However $c$ is a function of the medium parameters $\epsilon_0$ and $\mu_0$. Does the Lorentz factor change for the interior of materials or is it always dependent on the speed of light in vacuum. My guess is that it is, because even the interior of a material is mostly vacuum. Have experiments to verify this been done?
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$\begingroup$ It's an accident of history that we first discovered $c$ as the speed of light, but its true significance (according to SR) is that it's the space / time conversion factor. See physics.stackexchange.com/q/436315/123208 and physics.stackexchange.com/q/98564/123208 $\endgroup$– PM 2RingCommented Apr 6, 2019 at 12:26
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3$\begingroup$ Possible duplicate of Does the speed of light in different mediums affect the lorentz transformation? $\endgroup$– PM 2RingCommented Apr 6, 2019 at 13:55
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Lorentz factor arises in the Lorentz transformations, and the Lorentz transformations are derived using c. Therefore, the answer is:
it is always dependent on the speed of light in vacuum.
The speed of light in different media do not cause us to modify Lorentz transformations. A slowdown is just a slowdown.
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$\begingroup$ I don't quite understand. Doesn't that mean that the speed of a particle in a medium can surpass that of light in the medium, because the speed limit is set only by the vacuum speed of light? $\endgroup$– eeqesriCommented Oct 2, 2019 at 14:03
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$\begingroup$ Because if the speed limit is set by the speed of light in vacuum and not the speed of light in the medium, then massive particles should be able to surpass the speed of light in the medium. I think this is how cerenkov radiation can be produced. $\endgroup$– eeqesriCommented Oct 6, 2019 at 11:24