There are experimental upper limits on the photon's mass, but they are finite. I heard that the reason we know that photons have exactly zero rest mass (and thus travel exactly at the universal invariant speed c) is local gauge invariance.
But why do we believe local gauge invariance?
This page from UC Riverside theorists says that
If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass.
But there's no further explanation. The question of local gauge invariance seems to require two explanations:
- How does a massive photon make QED non-renormalizable?
- How does a massive photon wreck charge conservation?
I would especially appreciate responses that minimize theoretical abstractions. I'm trying to get to the experimental basis of our belief that light is massless. These two questions connect to empirical basis because (1) QED, which works, needs apparently to be renormalizable and (2) charge is evidently conserved in the world as far as we can tell.
Please note: this is not the same question as Is it experimentally proven that photons travel at speed $c$ in vacuum?, as I'm asking not asking about measurements of the speed of light, but about the theoretical justifications (that have an experimental basis) that lights moves at exactly the universal invariant speed c.
