= Galilean invariance of collision elasticity
{c}
{title2=$\Delta K'=\Delta K$}
For fixed particle <masses>, a <Galilean boost> by $\mathbf U$ changes total <kinetic energy> to $K'=K-\mathbf U\cdot\mathbf P+M_TU^2/2$. An isolated collision conserves total <momentum> $\mathbf P$ and total nonrelativistic <mass> $M_T$, so its final-minus-initial <kinetic energy> change is independent of the <inertial frame>. An <elastic collision> in one such frame is elastic in all of them. Conservation of <momentum>, rather than invariance of the numerical value of K, is essential to the argument.
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