# Invariance and conservation

Why in a collision between particles is the four-momentum conserved within a frame of reference but not invariant between frames of reference?

• I'm not really sure what you're asking. Four-momentum transforms like any four-vector under Lorentz transformations. The magnitude of the four-momentum vector is the invariant mass, which is clearly invariant between frames. – Evan Rule Oct 8 '15 at 1:17

$$E_{\text{rest}}=mc^2 \rightarrow E_{\text{moving}} = \gamma mc^2,$$
if $E$ were invariant then a moving particle would have no kinetic energy.