Main Question or Discussion Point
Suppose one scientist performs a series of experiments, and another scientist does the same thing. But unbeknown to either of them, a highly evolved alien measures all of the particles the first scientist is going to test, just before he does his measurements.A measurement of a particle property makes the value of a non-commuting property completely indeterminate (and independent of any prior value it had). All of the situations you are asking about can be answered using that rule. If you consider spin or polarization rather than momentum, you can construct a series of examples for yourself. That is because you can measure the spin over and over on the same basis and expect the same answer each time.
Question: Would the two scientists find different results from their experiments?