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?