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We know that the Lorentz transformation is derived using the speed of light in vacuum. But if we were to use it in water, would it change since the speed of light in water should also remain constant for every observer.

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No. The speed of light is always c. And only that is constant to every observer. You use only c in Lorentz transformation. In some medium light would appear to slow down because it would jiggle electrons of atoms in that medium which would generate electromagnetic waves themselves. The combined result is a wave traveling slower in a medium. You can see it classically (waves) or quantum-mechanically (photons), but the result is the same in this case. The resultant wave moves slower and is not constant to every observer. There are experiments where light slows down to snail pace and we certainly do not observe any weird time dilation effects in this case.

I don't know if it appropriate to link a youtube video here, but the video below sheds some "light" on to the issue using only simple words (no complex equations).

http://www.youtube.com/watch?v=CiHN0ZWE5bk

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The medium (the water or whatever else) has a preferred frame, that is its frame of rest. In that medium, the speed of light is not the same for all observers and it doesn't have to be because there is a special restframe now. In vacuum there is no such preferred restframe, that being the root of the principle of relativity.

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