Relativity: Is "c" Speed in Vacuum Only?

[Jimber-Jaw]

Hi all. New to PFs. I deal in (exotic) human biology, which happens to have put me at the intersection of fields and, in this instance, conceptually more challenging physics. I'm presently involved in a comparative analysis of biological versus physical time contraction-dilation. I happen to have a question for the experts on relativistic time dilation, if I may cut-the-chase:

Does the speed of light term in relativistic calculations strictly only refer to its speed in a vacuum or could it also be that in a substance, say, e.g., water, where it's speed happens to be some 25 % less?

Thanks, much appreciated.

 

[DrClaude]

c is the speed of light in vacuum. The speed of light in a medium is < c.

 

[Jimber-Jaw]

Thanks

 

[DrStupid]

Does the speed of light term in relativistic calculations strictly only refer to its speed in a vacuum or could it also be that in a substance, say, e.g., water, where it's speed happens to be some 25 % less?

The question is not completely clear:

If you mean the speed of light than the answer is yes, it is less c in a medium.

If you mean the invariant speed in relatistic equations than the answer is no, it is always 299792458 m/s.

 

[Jimber-Jaw]

I meant the second one. Thanks.

 

[Dale]

Does the speed of light term in relativistic calculations strictly only refer to its speed in a vacuum or could it also be that in a substance, say, e.g., water, where it's speed happens to be some 25 % less?

It is possible for a particle to move faster than the speed of light in a material, but still slower than c (the speed of light in vacuum). When that happens you get a very characteristic radiation called Cherenkov radiation.

 

[Jimber-Jaw]

Thanks Dale. Specifically, I was wondering whether the speed of light term, c, was actually a constant, such that only it's value in a vacuum coukd be used for relativistic calculations or whether one could use its value through matter.

Thanks all, I think Dr. Stupid resolved it for me: if you tinker with relativity, always use the value for a vacuum.

... moving on and without sucking up more oxygen.

 

[Cutter Ketch]

To concur with previous posts the fundamental constant for the purpose of relativistic calculations etc is fixed. In another sense the speed of light doesn't really slow down.

The slowing of light as it passes through a medium can be thought of classically as the response of the charge in the material lagging behind the externally applied electric field so that the sum of the external field and the displacement field falls behind. The wave slows, but the wave isn't purely the free electric field. It includes the responding field from the moving charges which can be slow.

In a QM sense, if the electronic energy states in the material had a transition with the correct energy the light would be absorbed. By the uncertainty principle on a short enough time scale the allowed energies are not well determined. A photon will be temporarily absorbed into virtual electronic state for a period of time until the uncertainty in the transition energy falls to below the energy difference to the nearest allowed transition at which point the photon must be reemitted. The delay from the virtual absorption grows as the energy of the virtual state approaches the energy of a real allowed transition because it takes longer for the uncertainty to resolve that the virtual absorption is not allowed. Thus the speed of light slows ( and the index of refraction grows) as the photon energy approaches an absorption line (or edge, or let's say feature) which is one way to explain dispersion.

 

[Jimber-Jaw]

Your physical kung-fu just scared the bejesus out of my biological kung-fu