Schrodinger's Dog said:
I'm surprised this thread hasn't gone that way, that's testament in itself to the people contributing. I once asked this question and eventually ended up with the answer, light has no mass, but there's no reason it couldn't have an infinitessimal one, it's just unlikely if we'll ever measure it, but anyway, that's of course extremely contraversial. But if light had a mass of say 3.2372878^-60 then would it violate GR is my question? And feel free to call the crank police

it's only a question
But you also need to examine your question and in what way would you accept an answer!
For example, ask anyone on the street if, let's say, you have a vase that has been broken into a thousand pieces, that if you throw these pieces onto the floor, will it assemble itself back into the original vase?
You will get
definite answer that no, it will not!
Yet, ask this in physics, and you will get an answer that the probability of it happening is extremely small, but it is definitely not zero.
When you ask for the "mass of a photon", do you expect an answer via standard, textbook physics (i.e. "NO, it has no mass"), or do you expect an answer at the forefront of cutting-edge physics research in which, by definition, we
challenge many of the things we know of in physics today?
It appears that even when the simple textbook answer is given, inevitably the question is THEN made more complicated by bringing in all of these exotica that is part of research-front physics. That is why something that can be answered easily never made it through to its clear conclusion. When you ask for something based on work that is still on-going, don't expect a clear, definite answer because there isn't any! However, if you want standard, textbook answer, then THAT is clear, because any textbook will have such a thing.
Now, while the question on what is the speed of gravity isn't a crank question, insisting that there is a definite answer is! We
expect that gravity travels at c, or at least, the
information that allows us to detect gravity travels at c. However, any good physicist will qualify that by saying that this has not been verified YET! This must always be the first check in any claims in physics - has that been empirically verified? So if you are insisting that there is one definite answer to this question, now that is inviting crackpottery.
Zz.