The title sums up the question. Given two events separated by a spacelike interval, say one takes place after the other in an inertial frame, then by a suitable boost we may invert the time order of both events.(This of course is not possible for timelike separated events) My question is hence: is there is any direct experimental evidence of this? And if not direct, then somewhat indirect.
Relativity of simultaneity is a logical consequence of c's invariance. Time order reverseals have not been tested directly as far as I know, but since the invariance of c from which the relativity follows has been tested in a lot of experiments I would say that the thought experiments regarding this issue are solid.