Is there experimental evidence of RoS (relativity of simultaneity) available? According to Carl Popper something that cannot be falsified is metaphysics. Can the ALT (absolute Lorentz transformation) and absolute simultaneity be used instead of RoS?
Yes. There is lots of evidence that IF observers define simultaneity of remote events by comparing the arrival times of light signals from those events and adjusting for the light travel times, then they will NOT agree on which pairs of events are or are not simultaneous.
What cannot be falsified (and so, according to Popper, is not worthy of consideration as scientific) is the claim that one particular set of “stationary” observers are “correct” and the rest are “wrong” about the “actual” simultaneity (with the observations of the “wrong” ones being explained by effects of their “motion” on their clocks and measuring rods).
The “metaphysical” question of whether or not there is such a particular set of “stationary” frames is generally resolved by reference to “Ockham’s Razor” which advises us to prefer an explanation which involves fewer arbitrary choices. To the extent that the identification of a particular preferred set of “stationary” frames is arbitrary, we are therefore advised to treat them all as equally valid and make no choice of what constitutes “absolute” simultaneity.
Of course, any particular feature of the universe (such as for example, the cosmic background microwave radiation (CBMR)) can, if we like, be taken as defining an “absolute” rest frame (and so an “absolute” sense of simultaneity). And if I were moving at a noticeably high speed relative to the CBMR, then it might indeed be presumptuous to declare my own synchronization as more fundamental, but it would not in fact lead to any difference in anyone’s prediction of any testable event.