# Is momentum conserved relative to all reference frames?

Assuming that there is an observer S in a train that is equipped with a cannon moving to the right relative to another observer S' in a train moving to the left relative to S, which is also equipped with a cannon.

Note: the situation assumes force of gravity = 0.

At some point the S train fires a cannon ball towards S'.

S' fires its cannon ball at exactly the same time, the goal is to collide the two balls with equal momentum so that each repel and return back to their train.

1. Is momentum conserved in both the S and S' reference frames? Would S observe that the work done on his ball is equal to that on the S' ball?

2. The big picture: When would momentum be conserved in relativity?

• every frame will see the momentum as computed in their frame is conserved. S and S' will see that one ball will have much more momentum, and that would be exchanged during collision and return. Apr 22, 2023 at 14:52

Assuming both $$S$$ and $$S’$$ are inertial, yes.