What consequenses would there be if the photon got mass?

[Hymne]

Hi, as I understand the photon can according to todays theory have a very small mass. What would this actually mean if it shows up to be true?
I now the we had to give the neutrinos mass to solve the solar neutrino puzzel, but since I don't got so much mathematical knowledge, I can't deduce it on my own.

Are there some interesting things that would happen or be possible?

 

[D H]

The photon has zero mass in every extant theory (QM, general relativity, string theories). Any attempt to prove this by measurement will have some experimental error. The best any experiment can do is establish some non-zero upper bound on the photon's mass. This upper bound is incredibly small and getting smaller as experiments improve.

Don't mistake a reported non-zero upper bound on the photon's mass as meaning the photon does have non-zero mass. No experiment to assess the photon's mass has shown a non-zero lower bound on the photon's mass. All measurements to date are consistent with the theoretical mass of zero.

 

[blechman]

**IF** the photon had mass (m), it would imply some rather remarkable things. Here are a few of them:

(1) It would break the gauge symmetry of E&M. This means that charge would no longer be conserved - you would be able to create or destroy charge.

(2) It would imply that the Coulomb force would no longer be infinite range, but would have a "Yukawa" potential:

$$V\sim\frac{e^{-mr}}{r}$$

(3) It would change the dispersion relation $k=\omega/c$, leading to violations of the laws of optics (law of reflection/refraction, etc); similarly, it would imply that light waves can be longitudinally polarized, rather than only transversely polarized.

(4) It would wreak havoc with our notions of causality, since signals would be able to travel "faster than light".

There are just a few consequences.