We used to think neutrinos were massless, and therefore traveled at c. Now we know that at least some types of neutrinos have mass, and travel at less than c. What about the photon? Section I.2 of Jackson has a description of the empirical limits on the mass of the photon. (This is the introductory chapter, letter "I", not chapter 1.) I have the 2nd ed., so this would be as of 1975. As of 1975, the 1/r2 form of the Coulomb force law had been tested to very high precision at scales of 10^-2 m to 10^7 m. (Section 12.9 of Jackson also has a lengthy description of why one particular method for testing for a nonzero photon mass doesn't work.) More recently, searches for dispersion of the vacuum have had negative results: http://arxiv.org/abs/0908.1832 , but this is at short wavelengths, whereas I assume the effects of massive photons would be felt at extremely long wavelengths. Now suppose that someone does an experiment tomorrow that finds that photons have a mass that's nonzero, although very small. Then photons would have the same status as neutrinos: particles that almost always travel very close to c, because they are hardly ever produced with energies small enough to make v significantly less than c. You would also be able to have real, longitudinally polarized photons, although I guess they'd be hard to manipulate in practice, since they'd have to have such low energies. Would this have any especially important implications? Do massive photons produce any technical problems in QED? Mandl and Shaw have the following remark, which I'm not sophisticated enough to understand, on p. 183: "...this [convergence] factor does not provide a suitable regularization procedure for QED, as it does not ensure zero rest mass for the real physical photon, nor the related gauge invariance of the theory." Does this mean that gauge invariance is somehow logically related to zero mass? From my limited understanding of gauge invariance in particle physics, one expects it to occur for any bosonic field, but I don't see how a nonzero mass affects anything. I'm inclined to believe that this would not have any particularly deep implications for relativity, but I'm open to arguments to the contrary.