In the notes I am using, it states that if two observables A and B are measured simultaneously, then the measurement of A does not affect the measurement of B, and vice versa. However, why does the frame of reference seem to be neglected in this explanation? For another observer, it seems that if A and B are measured simultaneously in the first frame, they will not be simultaneously measured in the second frame; thus the measurement of B should affect the measurement of A? Is this due to some change in the observable due to the relative motion that I am not aware of?
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2$\begingroup$ Can you provide more context? In particular, are the measurements of A and B performed on the same system? $\endgroup$– probably_someoneDec 12, 2018 at 18:46
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$\begingroup$ Although not specified in the notes, I would assume that they are? $\endgroup$– EigenFunctionDec 12, 2018 at 19:20
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2$\begingroup$ Also, is there a reason to suspect that these notes are using a relativistic extension of quantum mechanics? Because if not, quantum mechanics is non-relativistic, which means there's an absolute notion of simultaneity. $\endgroup$– probably_someoneDec 12, 2018 at 19:27
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$\begingroup$ It’s possible the notes do not account for relativity, since I don’t seem to see any mention of it; however, why would this not lead to paradoxes if the process of measurement is non-commutative? $\endgroup$– EigenFunctionDec 13, 2018 at 1:47
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$\begingroup$ Which notes? Which page? $\endgroup$– Qmechanic ♦Dec 20, 2018 at 20:05
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In relativity there exists a notion of a "space-like separation", that is, a separation between two events that cannot be viewed in any frame as happening at the same place, only at a different time. Additionally, you can show that events at these separations cannot be connected by light signals. Last but not least, there will be a frame in which these events happened at exactly the same instant.
That is, if we observe an event $A$ influencing an event $B$ at a space-like separation, there will be a frame in which this will look like instantaneous action at a distance, and in every physical frame this will look as an influence propagating at superluminal speeds. In other words, for causality, you have to require no influence of measurements over space-like separations, and this is indeed one of the building blocks of quantum field theory, the relativistic extension of quantum mechanics.
