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Consider an elastic head-on collision between a projectile, with mass m1 and velocity v1, and a stationary target of mass m2. So, in the lab frame, the target m2 is at initially at rest and mass m1 moves toward it with v1. In the center of mass frame, m1 and m2 move toward each other with equal and opposite momentum. Taylor says the only effect of the collision is to reverse the three-momentum of each particle (in CM frame), which means m1's mass is still m1, and m2's mass is still m2, there is no change of the particle's mass. How do you prove this relativistically?