Task id16705

Here is one of the “refutations” of the relativistic law of addition of velocities. Let two bodies be at one point, and then begin to move relative to the Earth in opposite directions (Fig. 6.4). The total movement of bodies dl=dl1 - dl2=v1·dt1 - (-v2·dt)=(v1 + v2)·dt. Hence the speed of approach u=dl/dt=v1 + v2. We obtained the classical law of addition of velocities, and not the relativistic one. Is there an error in the reasoning?