# Superconductivity - speed of light change?

1. Jan 27, 2012

### Clever-Name

So my Cosmology prof (who does research in String Theory) mentioned something during class a few days ago that the driving factor behind Superconductivity is that the speed of light changes.

Someone in my class spoke to him after the lecture about it and he rambled on about something to do with cooper-pairs requiring a change in the electromagnetic force law and this demands that the speed of light changes.

I have never heard of this before, I have been to several rudimentary lectures on superconductivity and I have only ever come across Cooper Pairs and phonons being the driving force behind superconductivity.

Does anyone have any idea what my prof was talking about and could shed some light on it? I have done a few google searches and have turned up empty-handed. Was he just mumbling some higher-dimension mumbo-jumbo or is his statement valid.

2. Jan 28, 2012

### fzero

Photons inside a superconductor actually get a mass from the abelian Higgs mechanism. This phenomenon was actually discovered by Anderson and the later work by Higgs and others was about generalizing it to relativistic and nonabelian gauge theory. What happens is essentially that Cooper pairs behave like a scalar field with a nonzero vacuum expectation value. The U(1) gauge symmetry is broken and the would-be Goldstone boson adds to the 2 photon degrees of freedom to complete a massive vector field.

This seems more a consequence of superconductivity, while the formation of Cooper pairs is the cause. The photon mass does, however, explain the Meissner effect. Since the photon has a mass, the EM force in a superconductor is short-range (due to an exponential damping in the force law). External fields can only penetrate to a distance of $h/Mc$, resulting in the "expulsion" of a magnetic field from a superconductor.

This is discussed in many places, but if you have a QFT background, you might look at the discussion in Atchison and Hey's gauge theory text (the google preview is missing important pages).

3. Jan 28, 2012

### Clever-Name

@fzero Ahhhh, yes that is what he said, the photon gains mass. Interesting! I don't have QFT background but I'll take a look around now that I know what I'm looking for. Thanks!

4. Jan 28, 2012

### DrDu

Weinberg, Quantum theory of fields, (I think vol. 2) has also a very nice discussion of the subject which brings out the underlying symmetry principles very nicely.