Post #2135883

@quietmarc Yes there is a practical difference which you astutely point out in the other comment. The measurements can't be at the *same* time because that's a) very impractical experimentally, even if relativity isn't in the picture and b) not really even meaningful due to relativity. The measurements need to be a *short* time apart because wavefunctions (even ones that are collapsed into an eigenstate) evolve with time. So the system is in a definite state of some physical observable after measurement 1, but if you wait too long to do measurement 2 the wave function will undergo time evolution according to the Schrodinger equation and end up in some superposition that might give a different value for the 2nd measurement. You can still actually object on the same grounds as before: the time interval between the two measurements is still relative to reference frame (and since your initial question precluded communication between the two measurements, there are even reference frames where measurement 2 happens first!) but sorting this out requires developing relativistic quantum mechanics aka quantum field theory, which is a whole other can of worms. In quantum field theory the primary goal is to calculate the scattering matrix, which tells us the probability distribution over possible final states given an initial state. The task of quantum field theory is to construct interactions such that the scattering matrix is invariant under change of reference frame (among other things) so that all predictions and observations will be consistent across reference frames. To get back around to the main point, my first answer assumed the context of non-relativistic quantum mechanics, where energies and velocities aren't in the relativistic regime and we can kind of just ignore issues that might arise from relativistic questions and "measurements happen a short time apart" is more or less a meaningful thing to say lol