Could the speed of light be variable?

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Dremmer
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Could the speed of light be variable? (not always travel at the same speed)
 
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The speed of light (in current theory) in a vacuum is constant. However, some possibilities have been raised that it might have varied over time, but the evidence is at best scanty.
 
This is a related question...

Could the speed of light through water be exceeded by an object traveling through water. In other words does the C change for all of the relativistic equations if the experiment is conducted in a medium other then vacuum?