# Conservation of three-momentum

1. Mar 8, 2014

### dipole

I'm blanking on this at the moment, but a quick application of Noether's theorem would imply that, aside from the momentum-four vector, $p_{\mu} = (E/c,-\vec{p})$ being conserved, that each component of $\vec{p}$ is also conserved due to invariance of the Lagrangian under translations - this is certaintly true in classical mechanics, but it also applies to special relativity, correct?

2. Mar 9, 2014

### Ben Niehoff

A vector being preserved is the same as all of its components being preserved.