Calculating Relative Motion of A, B, & C: Agree?

[wsellers]

This is indirectly addressed in some posts but I can't find a direct answer to the following: consider moving frames A, B, and C (e.g., A, B, and C are 3 trains moving at different speeds on the same track; or A is a train, B is a person walking inside the train holding a tray, and C is a wind-up toy moving along the tray; etc.). Now observers in each frame calculate the speed of the objects in the two other frames relative to them. Will these calculations always agree reciprocally--e.g., will a person in A calculate a speed for the motion of C that is the same (magnitude) as the speed calculated by a person in C for the motion of A? I believe the answer is "yes" but would like confirmation.

 

[Doc Al]

Yes. The speed of C with respect to A (as measured by A) is the same as the speed of A with respect to C (as measured by C).

 

[Jorrie]

What Doc Al mentioned can be accomplished by e.g. reciprocal (Doppler) radar measurements. Wsellers mentioned calculated speeds, for which the relativistic addition of velocities equation can be used to verify the answer in both directions, first with positive velocities and then with negative velocities.

 

[wsellers]

Thanks to both for your prompt replies! (I wasn't sure that all that was needed to do the calculation theoretically was the addition of velocities equation, so the post from Jorrie clarifies that.)