Why Must a Particle Decay into Two or More Photons to Conserve 4-Momentum?

[thenewbosco]

Explain using 4-momenta, how if a particle of mass M decays into photons, it must decay into two or more photons. Does your explanation still hold if the particle is moving at high speeds while it decays?

I can see if the particle is at rest and decays how it would have to decay into two or more to conserve the 3 momentum part of 4 momentum, that is the two photons travel in opposite directions.

If the massive particle is moving, why must it decay into at least two photons? the speed is c, regardless for the photons, and since the massive particle must be traveling less than c, the resultant photons must be such that the various components cancel to leave the original velocity? is this correct? or is there some other angle i have not looked at?

thanks

 

[quasar987]

Don't speculate and hypothesize. Use the equations you know.

To orient you in the right direction, consider the following: "Suppose the particle decays into only one photon. Can momentum and energy be both conserved? ($E^2=(pc)^2+(m_0c^2)^2$)"

Another way to approach the question is simply by "noticing" that a particle moving in one referencial is at rest in another. And you've shown that if the particle is at rest, then it cannot decay in just one photon. So it must decay in 2 no matter the frame of reference.