= Equal-angle elastic scattering with unequal masses
Equal laboratory recoil angles constrain outgoing <momenta>, not equality of masses. In units $c=1$, take an incoming mass $m$ with <energy> $2m$ striking a stationary mass $2m$. The final <momenta> $m(13/8,\sqrt3/2,\sqrt{57}/8,0)$ and $m(19/8,\sqrt3/2,-\sqrt{57}/8,0)$ conserve <four-momentum> and have mass shells $m^2$ and $4m^2$. Both trajectories make angle $\arctan(\sqrt{19}/4)$ with the incident axis. This is a concrete counterexample to inferring equal masses from equal outgoing angles alone.
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