This is not problematic in pre-Einsteinian physics, where arbitrarily fast signals could be
used in place of light. As faster and faster signals are used, the interval between departure
and return shrinks toward a unique instant, which then must also be the time that is
simultaneous with the arrival of the infinitely fast signal atB. In SR, however, nothing can
travel faster than light.
2
In fact, if standard simultaneity is adopted in every inertial frame
of reference, then it follows in SR that every instant in the open interval between the
departure of the light ray fromAand its return is simultaneous with its arrival atBin some
inertial frame (where AandBstill refer to fixed spatial locations in the original frame).
The question is which instant atAin the interval between the departure and return
of the light ray is simultaneous with the ray’s arrival atB.