Quantum Mechanics makes predictions about the values of probabilities. I suppose the only empirical way to test these is to rely on "the law of large numbers". It says something about measuring frequencies and itself talks about probabilities, but I suppose this circular type of self-reference is inherent in probability theory. The way I visualize a QM experiment is that it would be a series of "independent trials". The experimenter must put a system into some well defined Quantum state and then make a measurement. Suppose this series of experiments has been done. In the experimenters frame of reference the experiment confirms that the "preparation" of the state and the equations of Quantum Mechanics correctly predict the probability of the observed data at a later time.Now imagine an observer in some frame of reference who (according to relativity) sees the experimenters chronology differently. He see some of the experiments where the time between "preparation" and measurement is different than the experimenter measured. Perhaps he sees some of the measurements of the observed data happening before the "preparation". This doesn't necessarily produce any contradiction about the laws of QM. The observer wouldn't count some of the experimenter's trials as relevant to predicting the law that the experimenter was trying to verify. So the statistics of what the experimenter observed would neither confirm or refute the predictions of QM, they would simply be irrelevant, in the opinion of the observer.So, how would one experimentally test the consistency or inconsistency of QM's predictions for the experimenter and the observer? Use a more complicated experimental design?