In a relativistic treatment of mechanics one can say, that momentum and energy are correlatively conserved. The argument I would use, is that the length of the four-momentum is lorentz-invariant, and therefore, if E is conserved in any frame of reference, so the momentum. But I don't know, if this argument is fully valid. The length of the four-momentum ( I mean pμpμ) is creating a relation between the Energy and the magnitude of the momentum, not the vectorial momentum itself. But I want a vectorial conservation... Where is the catch?