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Recall that the spin components of a spin-entangled pair do not exist until one of the pair undergoes quantum observation, at which time both of the pair immediately obtain quantum random opposing quantum spin components.

Alice and Bob ceremoniously split a pair of spin-entangled electrons. Alice and Bob each carry their respective entangled electron along with them on a trip in their respective spaceships. Each pilots their craft to a separate previously-arranged location and velocity (inertial reference frame.) These inertial reference frames have been selected such that, observed locally in Alice's inertial reference frame, her time tau precedes time tau in Bob's inertial reference frame. And observed locally in Bob's inertial reference frame, his time tau precedes time tau in Alice's inertial reference frame.

At her local time tau, Alice observes the component of her electron's spin parallel to the galactic axis of rotation. Observing her electron before Bob observes his, Alice simultaneously breaks her electron's entanglement and observes its spin to be oriented galactic North. At time tau in his reference frame, Bob also is first to observe his still-entangled electron. Bob also observes the component of his electron spin parallel to the galactic axis. As luck would have it, simultaneous to breaking its entanglement, Bob also observes his electron's spin to be oriented North.

After making these quantum observations, Alice and Bob radio their results to each other. Much later, when the transmissions arrive at each others' spacecraft, Bob and Alice are both surprised to find that they have obtained conflicting results.

How may this contradiction be resolved?

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  • $\begingroup$ I can't see at the moment how the entanglement would survive the transport in a magnetic field... $\endgroup$ – CuriousOne Apr 9 '16 at 6:15
  • $\begingroup$ Thank you. Good point. Correction: Edited to remove superfluous sentence suggesting hypothetical technology used to transport electrons. $\endgroup$ – godot Apr 9 '16 at 6:40
  • $\begingroup$ I don't do hypothetical technology in Gedankenexperiments. You have to show me that the entanglement actually survives your physically implementable transport technology of choice and how it acts on the spins. If you want to clean it up, you can remove all the scifi elements and do it in a normal size lab. The question doesn't depend on the distance. What it does depend on, though, is what interactions that can move the spins will do to them. I am not sure I fully understand that part. $\endgroup$ – CuriousOne Apr 9 '16 at 6:44
  • $\begingroup$ The contradiction in physics is described well; the gedanken stands. Can anyone address the elephant in the room? Has anyone a resolution to the contradiction? An answer to the fundamental underlying question? Perhaps there is a hint here: arxiv.org/pdf/1007.3977v1.pdf, although I do not know how entanglement can be independent of time if it has a precise onset and termination. $\endgroup$ – godot Apr 10 '16 at 1:04
  • $\begingroup$ I don't have an elephant standing here but a mouse: I simply don't know if your assumptions about the transport of massive particle spins are even borderline valid. Unless someone convinces me with a QFT calculation that one can transport unmeasured spins this way without destroying entanglement, I am not feeling much pressure. $\endgroup$ – CuriousOne Apr 10 '16 at 1:17
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Even if Alice and Bob are both first to measure their spin (according to their respective reference frames), two spins entangled into the singlet state will still give opposing results. That's what quantum mechanics predicts.

Finding out that the entangled spins gave agreeing results would falsify a prediction of quantum mechanics. People would be very surprised, check that the experiment was repeatable and done correctly, then start looking for a more comprehensive theory that didn't fail in this case.

Bell tests have been performed with space-like separated measurements. They confirmed the predictions of quantum mechanics. It would be very surprising if tweaking the speeds made a difference. You probably shouldn't spend your Bayes points on that.

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  • $\begingroup$ This is what I also would guess from arxiv.org/pdf/1007.3977v1.pdf, but does anyone KNOW the answer? Aspect, Copenhagen, et al. say the 1st to observe collapses the wavefcn. But in this case there is no 1st. Yet empirically the spin is known to be undetermined prior to collapse. Which observer triggers the collapse? Can we tell? When does it remotely occur? $\endgroup$ – godot Apr 10 '16 at 1:08
  • $\begingroup$ @godot Even in instantaneous collapse interpretations, changing the order doesn't affect the overall expected results. The two possible collapses commute with each other. $\endgroup$ – Craig Gidney Apr 10 '16 at 20:13
  • $\begingroup$ Not sure it's germane. Empirical evidence (in the form of Complex vs. Real statistics) tells us that at some point in the past, the resultant state is unknown. At a later time after at least one observation, the projected state becomes known to both observers. Prior to observation, it remains possible for any results to be introduced into the universe of classical physics – including results due to an impromptu measurement on an axis orthogonal to the planned measurement (which would not commute.) The results need not agree until AFTER the wavefcn has collapsed at BOTH locations. When is that? $\endgroup$ – godot Apr 12 '16 at 1:18
  • $\begingroup$ BTW, Dr. Gidney, "Bayes points" is an excellent descriptive term. A tip of my hat to you, Sir! $\endgroup$ – godot Apr 12 '16 at 1:19
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This is one of the most misunderstood things about entanglement, which is that it doesn't matter who goes first. Neither measurement actually affects the other one, contrary to the intuitive implications of "wave function collapse". Entanglement is correlation, not causation.

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  • $\begingroup$ The spins have been empirically shown to be undetermined prior to collapse. I fail to conceive of what it means for entanglement to be independent of time, yet collapse have a precise shared moment of onset. Does the collapse, perhaps, occur in an inertial reference frame in which the two observations occur simultaneously no matter when+where they occur? I believe it can be shown that for any pair of observations in spacetime, there exists a reference frame in which the observations occur simultaneously. This solution has a satisfying elegance. Is it allowed? $\endgroup$ – godot Apr 10 '16 at 1:11
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Your question has nothing to do with entanglement. You might as well ask this instead:

Physics predicts that two positive charges will repel each other. Suppose I bring two positive charges into close proximity and find that they attract each other instead. How can this contradiction be resolved?

Or you could posit any other experimental result that contradicts known physics and ask for a "resolution".

Your assumption about Alice and Bob's measurements is as contrary to both theory and evidence as an assumption that like charges are observed to attract.

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  • $\begingroup$ If you are saying you know independent of wavefunction collapse the orientation of each observer's spin, as you always know like charges repel, that would be the "Purloined Letter" version of a hidden rule! All 3d spin orientations are possible prior to the collapse. Since the wavefcn has not yet collapsed prior to either observation, there is a 50% probability that Bob will observe the same N-S orientation as Alice. Perhaps a time-reversed action "subsequently" creates consistency. Which observer collapses the wavefcn, and when does it collapse? $\endgroup$ – godot Apr 10 '16 at 1:12
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    $\begingroup$ All I'm saying is that if alice and bob choose to measure spin in the same direction, they will observe opposite spins. We know this from theory and we know it from experiment. So your assumption that they observe the same spin is in the same category as an assumption that someone observes like charges attracting. There's no need to explain this because it won't happen. $\endgroup$ – WillO Apr 10 '16 at 1:26
  • $\begingroup$ If we pose the analogous GR question re: systems under acceleration, it is a different situation altogether: (from: en.wikipedia.org/wiki/Unruh_effect) "If those observers are accelerating, there may be no shared coordinate system....this comes about because the two vacua lead to unitarily inequivalent representations of the quantum field canonical commutation relations." It seems your same argument applies if A & B are under acceleration relative to each other. If so, it appears your argument does not fare well in that context. $\endgroup$ – godot Apr 12 '16 at 9:13

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