Is the speed of light constant to all observers?

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Ibix
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There are at least three different things one can call the "speed of light".

The first is the speed of light in a medium. This is variable. Hau's experiment is a modern and extreme example in a Bose Einstein condensate (which I wouldn't call a crystal, by the way), but the effect was well known long before Einstein. For example, Fermat was able to derive Snell's Law from the principle of least time.

The second thing is the coordinate speed of light. This is also variable. Shapiro delay is an example. But this is an effect analogous to looking at the shadow of a rod on bumpy ground - it will most certainly be curved, and regularly spaced notches on the rod may well be irregularly spaced on the shadow. This is an effect of the shape of the ground (analogous to your choice of coordinates), not the rod itself (analogous to the 4d path of a light ray).

Finally, there's the locally measured speed of light in vacuum. This is not variable. All observers will always see light pass them at c. Even in the presence of gravity, spacetime is locally flat (this is the meaning of the equivalence principle), so gravity does not have any effect on this measurement.

No one disputes that the first two are variable. But the last one cannot be variable in general relativity.
 

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