The conservation of momentum states that when two objects collide the resulting vector is the sum of the other two vectors.

 

Say you have Object A that is 5 kilos and Object B that is 5 kilos. They are moving in a one dimensional path, opposite each other at 5 and -5 m/s, respectively. They then collide with one another in a elastic collision (sticking together the conservation of momentum says that they will stop moving.

 

What happens if I have an electron for object A, with a mass e, and a positron for Object B, with a mass e. They are also moving in a one dimensional path, opposite each other with velocity v and -v, respectively. They then collide with one another and annihilate. Upon annihilation they produce photons in equivalence with E=mc^2.

 

However, the net momentum is 0. I know photons have momentum, so this means that the photons themselves would be stationary, but this seems to violate special relativity.

 

What am I missing here?

The momentum of photons moving in opposite directions cancels out just as the momentum of particles moving in opposite directions.

Thanks!

However, the net momentum is 0. I know photons have momentum, so this means that the photons themselves would be stationary, but this seems to violate special relativity.

 

What am I missing here?

 

You can conclude that you can never get one photon from this interaction. As Mr Skeptic points out, two photons traveling in opposite directions will have zero momentum. Other conservation laws come into play (e.g. angular momentum) that tell you that three photons are possible for aligned spins of the electron/positron pair.