I suspect it would be a valuable exercise, but I’d need some direction if I were going to “try it”.
Well lets start with "time" which in the classic physics you can conjecture if it exists for the photon or not.
QM does not give you a "no time" choice, that photons behaviour is described by a probability wave (as is everything)
and that wave requires time. You do not get to conjecture if "time exists" it is implicit in the description. So when you send the photon thru a double-split experiment QM can predict what is going to happen because it is implicit time exists for the photon which describes it's probability wave ... no time ... no QM ... no probability wave ... no predicted answer.
That is why I get cross at people who say they accept QM but then talk about time being something that is "experienced" like the classic physics trash version. I had a go at Bill G a couple of times over that when he tried to pull his consensus science garbage. I don't care how many science magazines and/or sites run trash like that it's wrong unless you can overturn QM.
So if you accept QM then a photon experiences time it isn't up for conjecture. As to why GR breaks down I gave you the answer the photon or anything moving at the speed of light isn't a classic physics object and the theory isn't valid for it, hence SR/GR exclude a reference frame at the speed of light.
If you want it in science speak:
Quantum physics sees time as an intrinsic variable and not extrinsic as in classical relativistic physics.Now in QFT you have fields everywhere and the probability waves must traverse that worldscape so time at a minimum must be everywhere the field is. You can also describe the E/B fields even when its moving at the speed of light (Quantum electrodynamics) something all classic theories fail at.
Now I can't help some people don't get classic physics is wrong and often misleading
An illusion can not describe itself hence my rainbow joke, what does a rainbow look like to itself?
Do you see why a photon can not classically describe itself?
Now you spent the time to follow the logic and evidence and you should now get the current science position on time. You can play silly games with time in classic physics but don't mistake that for thinking it is something science says is consistent with ALL THE DATA, which is a key point of science. My complaint of the classic physics zealots is they exclude data and are no better than religious zealots excluding data they don't like. If one is a quantum zealot at least you are consistent with all the data and it's still science
