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Suppose two spacelike-separated measurement events take place on an entangled pair of particles, both of which events, in isolation, would cause the entanglement to collapse.

It is impossible to say which event occurs "first" and therefore it is impossible to say that either event causes the collapse by itself.

The cause of the collapse cannot be "both measurement events", because either one in isolation would have caused the collapse.

So, what does cause the collapse? It must have a definite, objective, attributable cause - otherwise why does it happen?

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  • $\begingroup$ This is relevant, though I'm not sure it will answer your question: delayed choice quantum eraser. $\endgroup$ – Sean E. Lake Sep 20 '16 at 16:52
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    $\begingroup$ "It must have a definite, objective, attributable cause - otherwise why does it happen?" - it's not even clear that it happens, since there are interpretations without collapse. Also, physics has no actual requirement for "effects" to have "causes". Your question comes from applying classical thinking to quantum mechanics, which just doesn't work. $\endgroup$ – ACuriousMind Sep 20 '16 at 19:54
  • $\begingroup$ So in the example above, either wavefunction collapse or causality can hold, but not both. Right? $\endgroup$ – Morgenstern Sep 21 '16 at 8:18
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One can distinguish among three things in the context of this question: (1) the experimental results, (2) the mathematical theory with which one predicts what one would see in such an experiment, and (3) the interpretation of the theory. The first two combine into what we call the scientific method. The third cannot be confirmed and is therefore not considered part of the scientific method. However, that does not mean people cannot and does not ponder these interpretations.

In the context of the question, the idea of collapse lies in the third category. There is currently no known way to confirm that there really is such a thing as quantum collapse.

As for the predictions and the experiment, when such observations are made as space-like separated events, which implies that neither could have dictated the outcome of the other, then one would simply find that whatever is observed is always mutually consist. How this works and why it works this way we cannot say with certainty.

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Magic can be used to coordinate but not to communicate.

Quantum entanglement lives in this middle ground. To resolve your paradox we must understand this middle ground.

Classical correlations: Suppose a machine splits a coin in half, separating the head and tail halves. It gives one half to Alice and the other to Bob, sealed tightly inside a box. Alice and Bob then separate. Once Alice opens her box, she immediately knows that Bob, who is lightyears away has the opposite face. However, each box already had it's face predetermined so nothing unusual happens. This is an example of local hidden variables. There is no causality.

Communication: After separation, Alice chooses whether she wants a heads or tails. Her box sends a radio signal to Bob's box which set's itself to the opposite of Alice's choice. This can only happen for causal time-like separations because of the radio signal.

Entanglement: Like the case of classical correlations, Alice can't choose whether she gets a heads (up) or a tails (down). No matter what she does she won't affect Bob. But unlike the classical choice, the entangled particles do what classical local hidden-variables (coins in boxes) can't, such as violating Bells inequality and playing coordination games.

Non-locality means that if we were to model the quantum state on the computer we would need to have Alice and and Bob modify and/or measure the same shared state no matter how far they are apart. However, they are restricted in what they can do to/with this joint state so they can't use it as a channel to send information. In addition, it does not matter who goes first, so no matter what frame we choose (which affects who is first if they are spacelike-separated), Alice and Bob's results will be the same. There is no paradox.

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  • $\begingroup$ I understand that the example above does not involve any superluminal communication between Alice and Bob, and from that perspective it is not paradoxical. $\endgroup$ – Morgenstern Sep 21 '16 at 8:00
  • $\begingroup$ My question is more of a philosophical one. If wavefunction collapse is a "real thing" then it must have a cause that triggers it. However in the example given there is no one measurement that can be said to unambiguously "cause" wavefunction collapse. $\endgroup$ – Morgenstern Sep 21 '16 at 8:02

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