How do we know photons are stable? For something to decay time must have passed for that object. If I were to grab a block of super unstable material and look at $t=0$ none of it would have decayed. Now Einstein posits that time moves slower the faster you move (relative to another observer). Taken to the extreme an object at the speed of light would experience no time at all, thus everything would be instant. Of course massive objects can't travel at the speed of light, but light can. So I was wondering, if no time has passed from the point of view of a photon for it to decay before it is absorbed by something, is it stable? How do we know it wouldn't decay given the time to do so? An alternative is that my understanding of all this is wrong, but in that case please enlighten me.
 A: A simple argument for the stability of photons comes from the algebra of special relativity, that is the backbone in the standard model of particle physics.
In mainstream physics theories, photons are described by a special relativity four vector,

This is the energy-momentum four vector for a particle.
Particles have an invariant mass,


The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.

$m_0$ , fixed for each particle/(or system of particles described by the four vector).
A zero mass particle in an inertial frame has  $E=pc$.
The conservation laws of energy conservation and momentum conservation are axiomatic. If a zero mass particle could split into two particles,in an inertial frame, there will be an angle between them, and the addition of the two four vectors will have an invariant mass, leading to a contradiction, as the four vector before the decay has zero invariant mass, while the added four vector after the decay has an invariant mass. The decay of a photon cannot be consistent with the algebra of special relativity.
As special relativity has been validated with innumerable experiments of particle physics, mainstream physics does not accept a decay for a mass zero particle.
