Special Theory of Relativity - Lecture-5

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5. The Relativistic Addition of Velocity :      In classical physics, if we consider a case of a train moving with velocity  with respect to ground and a passenger on the train moving with a velocity with respect to train, Then the velocity of passanger with respect to the ground is,                                  .......................  ( 1 ) This is simply Galilean or classical velocity addition theorem. Let us discuss how the velocities are added according to special theory of relativity. Consider for a special case, all velocities are along x -direction of two inertial frames  and , - is the laboratory frame and - is moving frame with constant velocity . A body moves in  frame with a velocity and its position can be written as . The speed of the body with respect to  frame can be calculated as follows,