6.5. Relativistic law of velocity addition

Let in the frame of reference K 'the material point moves along the x axis' at a constant speed System K 'moves relative to system K in the same direction with velocity v . We define what is equal to the velocity of the material point v _o , relative to system K, i.e. what is equal to . Let at mt is at the origin, and . For system K:

Substituting and t in the formula for v _o

Divide the numerator and denominator by t

This equality expresses the relativistic law of velocity addition. At low speeds and we have

those. the relativistic law of velocity addition goes over to the classical