It seems that all books about special relativity only include discussion about perfectly elastic and perfectly inelastic collisions. The notion of the coefficient of restitution, $e$ in classical physics doesn't seem to appear in relativistic collisions.

My question is: how do we formulate newton's experimental law in special relativity? To be more specific, let particles $1,2$ collide to form particles $3,4$. Then (Let $P$ denote 4-momentum,$m$ denote rest mass) $$ {P_{1}}_r+{P_{2}}_r={P_{3}}_r+{P_{4}}_r,{P_{1}}^r+{P_{2}}^r={P_{3}}^r+{P_{4}}^r\\ {P_{i}}^r=\gamma_i m_iV_i^r,r={1,2,3,4.} $$ Here I have used tensor notation. Then the question is: how can I find $V_3,V_4$ in terms of $m_i,e,V_1,V_2$, where $e$ is the resititution coefficient? Or can we obtain any other meaningful relations?

  • $\begingroup$ I am not a specialist on this, but maybe if SR books don't contain your answer you need to look into General Relativity books. I would imagine that modelling collisions of stars cannot be done under perfect elastic or non-elastic constraints. $\endgroup$ – Cryo Jul 11 at 21:24
  • $\begingroup$ Also, don't expect to get away with a single coefficient (of restitution). I would expect it to become a full tensor, and probably even relative tensor once the real treatment begins. $\endgroup$ – Cryo Jul 11 at 21:28

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