I read recently that there may be (very slight) variations in the speed of light due to the nature of spacetime itself, I had the idea that this may be due to the photon having mass, but that's another discussion. Anyway, I was hoping for some maths/good physical reasons why this may or not be the case because it's confusing me quite a bit.
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Hi Sam. You may have meant your question to refer to the idea that propagation of light may be dispersive i.e. different frequencies might move at different speeds. If so have a look at Constancy of speed of light in vacuum?. – John Rennie Jun 23 '17 at 05:37
2 Answers
There are a few cases to my knowledge and one of them is the case ofCherenkov Radiation. The speed of light is decreased by making it go through a denser medium and what happens is amazing, When electrons flow at speeds much larger than the speed of light, they emit bluish glow and that's what we call Cherenkov Radiation. Hope it answers your question

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Cerenkov radiation is emitted by electrons that go through a medium faster than the speed of light in that medium (light speed is slower in media than in vacuum). – hdhondt Jun 23 '17 at 04:23
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Is there variation in the speed of light?
Light has a fixed speed c in vacuum but in a medium it can have a smaller speed, quantified by the refractive index.
It is photons, the building blocks of light that have always a fixed velocity c . You must be talking of alternative cosmological models.
The standard models of physics at present have the speed of zero mass particles at c in all local frames.

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