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Consider the Bell state $|\psi\rangle =\frac{|00\rangle +|11\rangle}{\sqrt{2}}$.

When measuring one of the individual systems, the superposition is projected onto one of the eigenstates $|00\rangle$ or $|11\rangle$.

Imagine we measured the entangled systems at the same time. Which part will project the state? That is, at measurement one part of the system determines the outcome of the other. But if measured at the same time, which determines the outcome?

For the moment I neglect special relativity and think the observer to be in the rest frame of the experiment.

Zetaman
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The outcome is determined (probabilistically) by the state, and is either $|00\rangle$ or $11\rangle$ (assuming that's the observation you're making) equiprobably.

WillO
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  • No, the state doesn't determine the outcome. Before a measurement we have superposition. That's what the Bell test proves: The outcome is not determined before the measurement is made and thus rules out all hidden variable theories. (Given there are no loopholes and c is constant) – Zetaman Jul 06 '16 at 14:23
  • @JohannesFankhauser: It rules out some classes of hidden variable theories. It doesn't seem to rule out all hidden variable theories. Not that this matters. That's not a question to nature, anyway. – CuriousOne Jul 06 '16 at 14:25
  • I'm not familiar with these theories. Which are they? – Zetaman Jul 06 '16 at 14:29
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    @JohannesFankhauser : "No, the state doesn't determine the outcome". Perhaps you overlooked the word "probabilistically". – WillO Jul 06 '16 at 14:30
  • @JohannesFankhauser: You have to ask the quantum philosophers about that, it's certainly not a physics questions. – CuriousOne Jul 06 '16 at 14:33
  • If we take the 'measurement' on A and B as 2 events MA/MB, then when MA and MB are timelike-separated, we know which event happens first; if MA and MB are spacelike separated, then which event happens first is observer dependent. If the 'state collapse' concept is concerned, the 'collapse' happens instantaneously with the measurement for all observers (strange, this can only happen with MA/MB at the same spacetime point). Some papers on 'relativistic quantum information' might help. – XXDD Jul 06 '16 at 14:36
  • @X.Dong: There is no such thing as a collapse of the wave function and as such it is certainly not "instantaneous", which is a completely meaningless concept. – CuriousOne Jul 06 '16 at 14:38
  • OK. I just mentioned it since it's still a popular concept. But anyway we have no answer of the measurement problem so far and we do not know what happened exactly when we measure one of them. – XXDD Jul 06 '16 at 14:48
  • @X.Dong: And I simply replied that it's a useless concept. What happens when we measure something is that we alter the system from a closed, reversible one to an open, irreversible one. That's by definition of what a measurement is. – CuriousOne Jul 06 '16 at 14:49
  • But when does this happen on B if you measure A? I do not know. Decoherence can not answer this. I hope you can explain this. – XXDD Jul 06 '16 at 14:52
  • @X.Dong: Absolutely nothing physical happens on B when you measure A. That's the entire point. Decoherence doesn't claim that to begin with. That's just some classical ballast that you carry around while thinking about this stuff. Decoherence is not a way to make the quantum world classical. It's a way to explain the measurement process consistently within the rules of the quantum world. – CuriousOne Jul 06 '16 at 14:56
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To add on to WillO's answer, I think the key in entanglement is not "which measurement happens first" or "which measurement affects the other", but rather that $|00\rangle$ and $11\rangle$ are the only possible outcomes! No matter what frame you switch to, you will NEVER get $|01\rangle$ or $|10\rangle$.

Even if you consider the different frames in which the two events can have different chronological order, the Bell test still rules out local hidden variable theories because the two events are causally disconnected regardless of which frame you look at it from. So the causal disconnection is not affected by the chronological ambiguity.

Zhengyan Shi
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    I really believe the concept of 'locality' or 'causality' need to be reconsidered when entanglement is involved. Since entanglement is related with the spacetime geometry, on which our concept of 'locality' is built. – XXDD Jul 06 '16 at 14:44
  • @X.Dong: Locality is well defined and it works just fine. Causality is also well defined and it is not violated by entanglement. Entanglement simply doesn't exchange anything, even though it looks that way, and that's what throws people's minds off. – CuriousOne Jul 06 '16 at 14:47
  • I do not think so. Before we have a clear picture of the structure of spacetime, we can not have the correct concept of 'locality'. If Preskill is correct, the AdS/CFT is related with quantum error correcting code, then we have to reconsider these concepts. – XXDD Jul 06 '16 at 14:50
  • There are recent developments relating entanglement and wormholes by Maldacena and Susskind, but I don't understand the details of their argument at all, so I will not comment... Maybe you want to look at this SE post: http://physics.stackexchange.com/questions/34650/definitions-locality-vs-causality ? – Zhengyan Shi Jul 06 '16 at 14:54
  • At this point it seems that whenever Susskind doesn't understand something, he confabulates a wormhole into it. Don't fall for that stuff. – CuriousOne Jul 06 '16 at 14:58
  • Yes. I am also interested in their work. They built relationship between quantum computation concepts and spacetime geometry. Especially the 'speed of light', which plays a central role in the concept of causality. I am wondering if it's related with some concept of computation. Thanks for the information. – XXDD Jul 06 '16 at 15:00
  • @X.Dong: It looks almost like Susskind may not have made a single testable prediction in his life. Why don't you start with that. :-) – CuriousOne Jul 06 '16 at 15:02
  • @ CuriousOne It's worthy a try even it's dangerous. At least a school of brave birds are diving in it. Not everybody works in the same way. As you mentioned before, string scientists worked for 40 years with no observable predictions. – XXDD Jul 06 '16 at 15:02
  • @X.Dong: Physics is when you stick your head out and predict something that can be experimentally tested. If you can't do that, you are not doing physics and you aren't doing anything worthwhile within the definition of science. It's certainly not brave to hide behind stuff that's not even wrong. – CuriousOne Jul 06 '16 at 15:03
  • @CuriousOne I agree with you that physics is verified by observation. But it's not easy to judge if an idea can have an observable prediction. If we can not say "there is no wormhole in nature", then we have a reason to play with it. Be aware the first concept of black hole appeared 200 years ago. How can you be so sure that Susskind's work can not be verified 200 years later? – XXDD Jul 06 '16 at 15:14
  • @X.Dong: The definition of science is "a framework and method of rational explanations of nature". In other words: as a scientist you are being asked to explain the things that have been observed. Wormholes have not been observed and even the theory seems rather ambiguous about their existence. You are a smart guy but if you are not using your smarts to actually work on something that is, at least in principle, observable, then you are a smart mathematician, at best, but you are not a smart scientist. It doesn't take anything away from what you do, it just doesn't qualify for science. – CuriousOne Jul 06 '16 at 15:18
  • @X.Dong: What happens to Susskind's legacy is, at the moment, completely irrelevant. I am, by the way, pretty sure that there is a string regime inside black holes, it's just pretty narrow and it might be completely unobservable for anybody who is not suicidal. Now, the definition of science does not rule out suicide, so if you are willing to fly into a black hole to make the most important measurements of your life ten seconds before your death, that's OK, it's still covered by the scientific method. What is not covered is not to sacrifice yourself that way while pretending that you know. – CuriousOne Jul 06 '16 at 15:21
  • So according to your definition, mathematics is not science and I should not work with mathematics. That's strange. Is it not allowed to discuss pure mathematical concepts, even it's related with physics, here? I prefer to have concrete ideas but not simple judgement as "it's not science and it's a shame to touch it!" – XXDD Jul 06 '16 at 15:28
  • @X.Dong: Mathematics is not science. In science mathematics is a tool. In mathematics it's a method to derive ever more complex symbol sequences from sets of simple symbol sequences. The latter has some inherent beauty and it is very worthwhile doing, it just doesn't help with science proper if these symbol sequences can't connect to observations. The problem modern theory faces is the absence of data. Nobody says that you guys couldn't figure it out in a few months if you had the data. The simple truth is that you don't have the data, so there is nothing to figure out and you are floating. – CuriousOne Jul 06 '16 at 15:31
  • I agree with you on the concept of science as "a framework and method of rational explanations of nature". According to this, math is science since our physics is described in the framework of math. It seems that you are too brave to judge if we can have data someday. I do not like the idea that "If you have data to verify your idea, then you are scientist, if you have no data yet, then your idea should be abandoned". – XXDD Jul 06 '16 at 15:43
  • @X.Dong: Not all of mathematics has implementations in nature and no mathematics has a perfect implementation in nature, as far as we (can) know. Will we have data on everything some day? No. We will never have data on everything. We will have data on many things. Many things will stay hidden from us. That's the nature of science. That's also the nature of mathematics, by the way. One can never know everything about mathematics. One can, indeed, know much less about mathematics than about nature. How does that validate an entire generation of theoreticians who haven't been producing testables? – CuriousOne Jul 06 '16 at 15:48