A Gedanken Experiment
Consider a glancing collision of two equal mass objects which are moving at relativistic speeds.
From the initial rest frame of B one sees:
After the collision B moves slowly at right angles to the initial direction of A.
From the initial rest frame of A one sees:
Consider motion ? to original direction of motion
The time it takes (in each object’s rest frame) to travel a fixed ? distance must be the same (since problem is the same for both A and B).