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Does the light speed change? The Theory of Relativity says that the speed of light in vacuum is the same and unchangeable, while I read that the speed of light in glass is lower than in air, and that it's the maximum in vacuum.

If so that the speed of light in media changes, then we can conduct the following suppose a media as air, and a body is moving through it in a uniform velocity, we get that time relative to this body dilates because of it's motion, $t = \dfrac{t'}{ \sqrt{1- \dfrac{v^2}{ c^2}}}$

Now suppose another media as $CO_2$ gas, and the same body is moving through it with the same regular velocity, time also dilates relative to it. So, since the velocity is the same, Time must dilate with the same value, but the speed of light is different, So time dilation has to be different. So which one is correct? Does this dilation of time change or no? I'm really confused.

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marked as duplicate by John Rennie, Kyle Kanos, jinawee, Brandon Enright, Stan Liou Mar 15 at 2:19

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Relativity says that the speed of light in vacuum is invariant. That's all. –  David H Mar 14 at 18:17
    
Also related: physics.stackexchange.com/q/44115 –  John Rennie Mar 14 at 18:43

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Relativistic effects like time dilation only depend on how close you are to the speed of light in vacuum.

This may make it sound like relativistic effects have something to do with the light itself, but that's not the case. What it means is that there is a speed, c, to which no mass can be accelerate, no matter how much energy you dump into it. Light happens to travel at c because photons have no mass.

Light slows down when it interacts with a medium, but that doesn't affect time dilation in a moving reference frame at all. In fact, matter particles can and do travel faster than light in media, causing a phenomenon called cherenkov raditaion

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Actually, relativity does say that massless particles can't travel slower than $c$. –  David H Mar 14 at 18:54
    
ahh, good point, I'll edit that –  George G Mar 14 at 18:56
    
@DavidH. Yes, but in a medium, such as a dielectric, c is not equal to its vacuum value. In case the medium is dispersive c even depends on the frequency. –  Urgje Mar 14 at 21:59
    
Dispersion is a macroscopic phenomenon though, so it's not really right to say that dispersion slows down particles. Is it? I'm not 100% sure here –  George G Mar 15 at 0:56

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