(a) Use the results of Problem 15.69 to prove that for any number of material particles there exists a CM frame, that is, a frame in which the total three-momentum is zero. (b) Relative to an arbitrary frame 8, show that the velocity of the CM frame is given by β=.
Problem 15.69
(a) Show that the four-momentum of any material particle (m > 0) is forward time-like.
(b) Show that the sum of any two forward time-like vectors is itself forward time-like, and hence that the sum of any number of forward time-like vectors is its self forward time-like.