I am considering a case of collision in special relativity in which there is a change in the number of particles; for example, two particles colliding and sticking together to form a single particle. I was thinking about approaching a problem like this from the zero momentum frame, but then I realised that I did not know whether to consider the initial scenario (two particles approaching each othet) or the final scenario (a single particle travelling with speed v) to obtain the velocity of my zero momentum frame.
Something tells me that it should not matter which I choose, as if it did I could tell whether I am moving relative to some other frame, which would violate one of the principles of relativity. However mathematically I cannot see why it would be the case that these two considerations would lead to the same result for the velocity of the ZM frame.