# Why do we believe local gauge invariance (that tells us photons are exactly massless)? [duplicate]

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?

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:

1. How does a massive photon make QED non-renormalizable?
2. 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.

• isn't 1) and 2) related? Finite mass breaks U(1) gauge invariance, which is crucial to charge conservation via Noether's theorem. Because I only took a first semester's worth of field theory, I do not understand how breaking gauge invariance leads to failure of renormalization. However, I think there have been several Physics SE questions on why massless of photon is required by gauge invariance (my understanding is that gauge invariance and massless work together to remove two unphysical degrees of freedom from the four-potential). – wcc Mar 17 at 20:05
• A CERN lecture series linked by anna v in this post seems useful (physics.stackexchange.com/q/328861) – wcc Mar 17 at 20:05
• A critical attitude towards gauge invariance is very well defensible. I showed that classic electromagnetism can be formulated without gauge invariance in this peer reviewed paper: arxiv.org/abs/physics/0106078 – my2cts Mar 17 at 22:39
• Possible duplicates: physics.stackexchange.com/q/31994/2451 , physics.stackexchange.com/q/296975/2451 , physics.stackexchange.com/q/328861/2451 and links therein. – Qmechanic Mar 19 at 21:56