Calculating Relativity with Different Speeds: Vacuum or Medium?

[User11037]

Hi, this is probably a silly question but I can't seem to find the answer anywhere:

are the effects of relativity calculated with reference to the speed of light in a vacuum or the speed of light in the medium in which you are traveling? For instance, if traveling in water, would the Lorentz factor be calculated based on c ≈ 3e8 or c ≈ 2.2 e8?

 

[Nugatory]

Speed of light in a vacuum. The physics of light traveling through a medium are very different; the light is being continuously scattered, absorbed, re-emitted by the atoms of the medium. You could imagine the light being absorbed by an atom, then being re-emitted after a delay, traveling at c through the vacuum between atoms, then being absorbed and delayed again.

It's possible for a particle to travel through a medium at a speed greater than the speed of light in that medium; but not faster than c.

In fact, it would be more accurate to say that "c is the speed of a massless particle in a vacuum and light, being massless, travels at that speed in a vacuum" than "c is the speed of light". We don't, but that's for historical reasons - when relativity was being developed we didn't know about the other things that propagate with speed c.

 

[HallsofIvy]

As a result of the relativistic properties being based on the speed of light in vacuum, while it is not possible for an electron to move faster than the speed of light in vacuum, it is possible for an electron to move faster than the speed of light in water. That has been observed in water cooled nuclear reactors.

 

[nitsuj]

As a result of the relativistic properties being based on the speed of light in vacuum, while it is not possible for an electron to move faster than the speed of light in vacuum, it is possible for an electron to move faster than the speed of light in water. That has been observed in water cooled nuclear reactors.

How is that possible? Seems to violate causality, and I guess mass/energy equivalence since the electron has a mass.

Is it better said as An electron can move faster than a photon through a medium under xyz conditions; both speeds are less than c*.

*speed of light in a vacuum

 

[HallsofIvy]

Well, yes, the whole point is that the speed of light in water is less than the speed of light in vacuum. The whole point is that relativity uses the speed of light in vacuum and an electron can move faster than the speed of light in water. Look at https://en.wikipedia.org/wiki/Cherenkov_radiation

 

[robphy]

How is that possible? Seems to violate causality, ...

It seems to me that Causality is related to the maximum signal speed.
The "speed of light in vacuum" happens to equal that maximum signal speed.

The speed of light and of other particles in a medium is more about their interactions with the medium... with causality only playing a role in setting an upper speed limit.