A famous result in Newtonian dynamics is that if a particle in motion collides elastically with an identical particle at rest, the two particles emerge from the collision on perpendicular trajectories. Does the same hold in the special theory of relativity? Suppose a particle of rest mass m and total energy E collides with an identical particle at rest, and the two particles emerge from the collision with new velocities. Are those velocities necessarily perpendicular? Explain.