Simultaneous measurements of two entangled particles [duplicate]

Question

Experimental evidence reject the local hidden variable theory, so let's say quantum mechanics is right and the wave function does instantaneously collapse upon measurement.

Suppose we have two entangled particles A, and B spaced arbitrarily far apart, Alice measures A, then the wave function collapses which makes Bobs measurement of B definite. The same logic goes if Bob measures first and Alice measures second. But what if Alice and Bob happened to measure A and B simultaneously? When Alice is measuring A, Bob hasn't measured B so her result should be random, the same idea goes for Bob, so both of their results should be random. Please let me know if there are flaws in my logic or this is simply impossible.

Answer 1

The situation is even worse than that! In relativity, there is no universal definition of 'instantaneous' - it varies depending on your velocity. So the following situation can arise, where both measurements collapse the wavefunction of the other before the other measurement can occur.

The resolution of the paradox is that wavefunction collapse has no observable consequences, and indeed there is an interpretation of quantum mechanics (the Everett Interpretation) where no collapse takes place, and nothing propagates 'instantaneously' or faster than light. (See here for a longer discussion.)

Since the wavefunction collapse version makes exactly the same experimental predictions as a theory in which nothing travels instantaneously or faster than light, the collapse can have no observable instantaneous/FTL consequences. Long distance correlations arise, but they are only observable once the experimenters have got back together (at sub-lightspeed) to compare notes.

The fundamental problem here is the concept of wavefunction collapse, which does not work well with relativity. Quantum mechanics without collapse works fine with relativity. Although the Schrodinger equation is non-relativistic, the Dirac equation (that governs the motion of particles like electrons) is perfectly valid relativistic quantum mechanics.

Answer 2

The flaw is in quantum mechanics. Definite simultaneity doesn't exist thanks to special relativity. If Alice is stationary in her lab doing the simultaneous measurement with Bob, her grad student walking towards Bob say he's already done the measurement, while her post-doc walking away from him says Alice was first.

Of course, quantum mechanics is non-relativistic, and cannot resolve this.