for any trajectory t, there is an equivalent trajectory t’ which is exactly the same except everything moves with some given velocity, and it still follows the laws of physics
This describes Galilean relativity. For special relativity you have to shift different objects’ velocities by different amounts, depending on what their velocity already is, so that you don’t cross the speed of light.
So the fact that velocity (and not just rapidity) is used all the time in special relativity is already a counterexample to this being required for velocity to make sense.
I just realized,
This describes Galilean relativity. For special relativity you have to shift different objects’ velocities by different amounts, depending on what their velocity already is, so that you don’t cross the speed of light.
So the fact that velocity (and not just rapidity) is used all the time in special relativity is already a counterexample to this being required for velocity to make sense.