Elastic Collisions in Minkowski Momentum Space with Lorentz Transformations

We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.