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Generate an entangled pair of qubits. Send to Alice and Bob far away from each other. Both measure along basis in one of two possible orientations. The result is sent to Charlie at some later time, who compares the corellations and concludes the Bell inequalities have been violated.

But in Copenhagen, Charlie can say, the pair of results didn't become real until I collected both observations from Alice and Bob. They weren't real when either of them measured them. They only became real once I observed them. Then, both results, when they materialized, materialized at the same place. So, no nonlocality?

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Maybe Charlie can say the results aren't real yet if he believes that Alice and Bob were still in superposition states until they report their findings to him (like Wigner's friend). But I don't think that Alice and Bob, who have seen the outcome of the measurement apparatus, would be of the opinion that the measurements aren't real yet. But I've never been completely clear on the exact beliefs of the Copenhagenists. –  Dan Stahlke Sep 4 '12 at 1:41

4 Answers 4

In CHSH we can explain why quantum violate the inequality but it tells nothing about nonlocality :

The operator S=AB-AB'+A'B'+A'B

The measurement process in Copenhagen is used : the wavefunction collapses in an eigenstate of A remeasuring A will give the same result noted a The same for A' noted result a'

Then a strange thing happens for the B side the first measurement gives b the two next b'

And the last one finally explains the violation : since we measured B' before, the wavefunction is in an eigenstate of B', but those are not eigenstates of the last B hence the result for the last B can be b or -b thus the measurement result of S is

$$s=ab-ab'+a'b'\pm a'b$$

This lead to the possible value of measurement 0,2,4,-2,-4

Hence using quantum axioms and not Bell's hidden variables violates the inequality since with hidden variables it should be 2,-2.

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Hi Julien, Weclome to Physics! Note that this site has MathJax enabled, which means you can use Latex-like syntax to add in equations for readability. You may also want to take the time to fix up some of the grammar & formatting in the post here (e.g., only proper nouns & first letter of sentences are capitalized). –  Kyle Kanos Aug 3 at 19:24

If it's really all just a manifestation in Charlie's mind (What!? Is He God, or what?), then why can Alice and Bob only score at most ${1\over 2} + {1\over 2\sqrt 2}$ in the CHSH game? Why would Charlie impose such a limitation on himself? OK, let's just suppose for the moment that Charlie has self-imposed limitations on his mind. Wouldn't that limitation be none other than "quantum locality" by another name?

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It depends how they communicated the results to Charlie. Compenhagen interpretation makes a distinction between the classical and quantum world. So if they communicated the results to Charlie using a classical device then a Copenhagenist Charlie would have to conclude that the results must have been real at the time Alice and Bob sent them. On the other hand, if they sent the results using quantum communication, then they only became real when he measured the received system. My conclusion from this is that a Copenhagenist can still demonstrate nonlocality by communicating results classically.

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Yes, this restores locality, and is sometimes called "Solipsistic Copenhagen". It is described on the first page of Everett's thesis and paper on many worlds. The solipsistic Copenhagen interpretation is the only you can collapse the wavefunction, everyone else is in superposition.

From this interpretation to many worlds is only the step of moving the collapsing entity away from youself, and noting there is no contradiction with experiment, so the whole collapse thing is not really required, and one can logical positivistically remove it from the theory, at the cost of saying that the notion of reality and definite events is not physics, but how the branches get selected by the memories of observers. It moves the question away from physics to philosophy of mind.

While I think this is a neat trick, it might not be nature's trick. One has to be sure quantum mechanics is exact before declaring it so.

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protected by Qmechanic Aug 3 at 19:31

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