How stable is the photon? Yes, the photon.
If the photon has a mass it can decay into other particles…
If the photon is unstable and decays into other particles, then the number density of photons in the cosmic microwave background (CMB) should decrease while the photons are propagating. But then, the energy density of the spectrum would no longer fit the almost perfectly thermal Planck curve that we observe. One can thus use the CMB measurements to constrain the photon lifetime.
Interesting approach to the problem. It’s weird to see the phrase “photon rest frame” as there’s no such thing for a massless photon, but once you hypothesize a mass it becomes a perfectly reasonable thing to do, and then you can put limits on what the mass could be.
This reminds me of an arxiv paper I was looking at recently.