Depends on what you are willing to consider as "arbitrary". For inertial travelers, the frame where their velocities are equal and opposite would be one obvious non-arbitrary choice.Nugatory said:Is there any construction that can give an unambiguous answer when the two travelers are not colocated? To remove the ambiguity we need an additional arbitrary choice of a simultaneity convention, do we not?
I think this is one source of confusion in this type of scenario. From the point of view of any given scenario there is always (or often, at least) a fairly narrow selection of sensible frames to use. One where a velocity is zero, or two velocities are equal, and suddenly some bit of maths is trivial. But from the point of view of the physical laws any choice is completely arbitrary.jbriggs444 said:Depends on what you are willing to consider as "arbitrary". For inertial travelers, the frame where their velocities are equal and opposite would be one obvious non-arbitrary choice.