Speed of Light vs Refractive Index: Does It Violate Relativity?

[dasher]

the speed of light relative to glass, still water, or other media is not 3*10^8 m/s (otherwise known as c). This is due to the refractive index, the refraction of light itself. Is this actually a violation of the theory of special relativity?

 

[Demystifier]

the speed of light relative to glass, still water, or other media is not 3*10^8 m/s (otherwise known as c). This is due to the refractive index, the refraction of light itself. Is this actually a violation of the theory of special relativity?

No.
Theory of relativity does NOT say that light always moves with the velocity equal to c=299792.458 km/sec. It says that IF SOMETHING moves with the velocity equal to c, THEN IT moves with that velocity for any observer.
The unfortunate fact is that c is called "the velocity of light", while such a terminology is actually misleading.

 

[dasher]

so does this mean that the statement (or fact): "The speed of light relative to still water is 2.25*10^8 m/s." does not violate the theory of special relativity? However, can a more elaborate explanation be given to why this is so?

 

[jtbell]

When we say "the speed of light is always c" according to SR, we always mean "the speed of light in vacuum." We're simply too lazy to write out the complete statement every single time we say it.

Light traveling through a medium does slow down, in effect. This is addressed in the Physics Forums FAQ (located in the General Physics forum):

https://www.physicsforums.com/showthread.php?t=104715

 

[OOO]

so does this mean that the statement (or fact): "The speed of light relative to still water is 2.25*10^8 m/s." does not violate the theory of special relativity? However, can a more elaborate explanation be given to why this is so?

The refractive index is frequency dependent. It may fall below 1 for certain frequency bands (resulting in c>c_0 for example) but it tends towards 1 for frequencies approaching infinity. The latter is a consequence of the observed fact that matter gets more an more transparent for ever higher frequency (x-ray goes through your flesh but not your bones, whereas gamma ray goes through all your body matter).

What really matters for special relativity is the propagation of events, i.e. pointlike instantaneous flashes. Those contain very large frequencies which therefore travel with c. Thus special relativity isn't violated even inside transparent media.