A photon speed / mass / etc question

[CuriousCanuck]

Let me start off with this: I'm not a physics guy. So this may be a silly question/observation.

According to Wikipedia (the best source out there, I know), a proton has mass, and in some theories it decays with a half life ot 10e36 years.

In unrelated news (so far) a photon travels at light speed which is said to be 'c', or the fastest possible speed. Also, it is theorized that a photon is massless,.

If a photon had any mass at all, it is also stated in places that 'c' would remain the fastest possible speed, just that photons would no longer be travelling at strictly c.

So...

If a photon were to have mass, would it not also be subject to decay? Would there be a way to experimentally test to see if a photon has mass by seeing if there were a decay, and from there infer its mass? (forgetting the near impossibility of witnessing said decay. I'm asking theory for now.)

Also, bonus question:

If a photon were to have mass, would we still have a good idea of the upper limit of 'c' or could it be 2x as fast as we believe? 1,000,000x the current projection, or 1.0000000000000000000000000000000000000000001x the current projection?

Thanks for indulging the non physics guy.

[OldGuy]

A particle can only decay into something lighter and with the same charge as far as we know (or lighter things whose charge add up to the original charge). A proton might be able to decay into a positron (anti-electron) or it might not. Theory says baryon number is conserved and the proton is the lightest baryon, so if that part of the theory is correct it can't decay. If a photon had mass and something else had lighter mass, I suppose it might be able to decay.

We're pretty sure that the universal speed limit is what is now measured as the speed of light (or very near to it) unless relativity is very wrong. The mass energy equivalence E = M C squared depends on the universal speed limit not the speed of light per se, and this predicts how particles can decay etc. They can measure how the energy (or mass if you prefer) of a particle increases as it speeds up and how the half-lives of particles change as they speed up. Both of these formulae depend on the universal speed limit. So without some major change in relativity, the universal speed limit has to be very close to what we now set it at. (I'm talking about changes in nth decimal places here and I'm not sure which one, but your last guess is possible I'd think and would be even if photons are massless.)

[Hari Seldon]

Remember that neutrinos were thought to be massless and travel at light speed. Turns out they have tiny mass, but they still travel so close to light speed that the difference cannot be detected. In that 1987 (I think that was the date), the neutrinos arrived at the same time, as far as anyone knows, as the light.

[MikeS]

As long as photons are lighter than any other particle, they can't decay. If a hypothetical particle is massive, then you can in general switch reference frames and describe the behaviour of the particle as it would appear to someone moving with said particle. In this reference frame, the hypothetical photon is at rest and has no momentum; in other words, its energy equals the (hypothetical) rest mass of the photon. If the hypothetical particle were to then decay, you would then see a particle-antiparticle pair emerge (due to the particle number conservation laws mentioned by OldGuy). The energies of each of these new particles can't be less than the rest masses of these new particles. So if the photon is lighter than all other particles, then you can't have the photon decay even if it has mass.

The current best limit on the mass of the photon (according to the Particle Data Group) is that it must be less than 10^-18 electron-Volts. (For comparison, the mass of the electron is about 5 x 10⁵ electron-Volts.) It's conceivable that one of the neutrino species could have a mass small enough so that the photon could decay into it — all we can currently measure about neutrino masses are the differences between the respective masses of the three type of neutrino. However, this would imply that one of the neutrinos would be many, many times lighter than the other two, and it seems much more likely to most physicists that all three neutrinos should be much closer in mass. So a massive photon decaying into neutrinos seems to be out.

That leaves the graviton. I'm pretty sure (though I'm not as used to dealing with gravitons in this context) that a single massive particle can't decay into gravitons without violating conservation of angular momentum. If that's the case, then the photon couldn't decay into other particles even if it had mass.

Theories in which the photon decays do actually exist; in general, they have the property that the "limiting speed of matter" for some species of particle — the speed c' that they approach as you give them more and more energy — is actually greater than the speed of light. If this occurs, the photon with a sufficiently high energy will decay into particle-antiparticle pairs. (To forestall questions: in such a theory, the "cosmic speed limit" is just c' instead of c.) Such a decay has never been observed, of course, which allows us to figure out just how much c' can differ from c (answer: very very little.)

[Pasta]

Originally Posted by MikeS

I'm pretty sure (though I'm not as used to dealing with gravitons in this context) that a single massive particle can't decay into gravitons without violating conservation of angular momentum.

As far as angular momentum is concerned, there isn't a fundamental problem. If the two gravitons have opposite spins and together have orbital angular momentum (L=1), conservation would hold.

[Chronos]

Remember that neutrinos were thought to be massless and travel at light speed. Turns out they have tiny mass, but they still travel so close to light speed that the difference cannot be detected. In that 1987 (I think that was the date), the neutrinos arrived at the same time, as far as anyone knows, as the light.

Actually, the neutrinos arrived before the light, but that's just because the processes that produced the neutrinos in the supernova occurred a little before the processes that produced the light, so we can't really compare the travel times of the light and neutrinos directly. Among the neutrinos, though, the higher-energy ones did in fact arrive a little earlier than the lower-energy ones, which can be used to estimate the neutrino mass at a few eV or less (the upper bound is much stronger than the lower bound).

That leaves the graviton. I'm pretty sure (though I'm not as used to dealing with gravitons in this context) that a single massive particle can't decay into gravitons without violating conservation of angular momentum. If that's the case, then the photon couldn't decay into other particles even if it had mass.

I don't know of any fundamental problem with a hypothetical massive photon decaying into gravitons. A fermion couldn't decay entirely into gravitons, but that's just because gravitons are bosons: A fermion also couldn't decay entirely into photons, for the same reason.

Oh, and I'm sure you know this, but for the benefit of everyone else, the products of decay of a particle need not in general be particle-antiparticle pairs. The pi+, for instance, usually decays into a mu+ and and a mu neutrino, while the muon will in turn decay into an anti-mu neutrino, an electron neutrino, and a positron. And if the proton does decay (most extensions of current theory have baryon number only approximately conserved, not absolutely), the most likely decay would probably turn out to be a pion and some sort of neutrino.