Conservation of Relativistic Momentum

We are looking for coefficients c(m, b) which multiply velocity such that the linear sum is conserved before and after an elastic collision. A function of the particle mass and speed \(\beta\) is basically the only thing it can be subject to depending only on the current state of the particle. ie: being local in space (not dependent on properties of other particle) and time (not dependent on the future state of the particle)

QM provides a deep reason why we expect to be classically conserved quantities

Dual descriptions: inside vs boundaries… will focus here on the boundaries