(a) Write down the relativistic energy of a particle of rest mass and speed . Find the approximate form for when is small compared to , keeping all terms up to order . What new physical idea (when compared to Newtonian Dynamics) is revealed in this approximation?
(b) A particle of rest mass is fired at an identical particle which is at rest in the laboratory frame. Let be the relativistic energy and the speed of the incident particle in this frame. After the collision, there are particles in total, each with rest mass . Assuming that four-momentum is conserved, find a lower bound on and hence show that