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What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than speed of light with entangled, separated states when one wave function gets collapsed. I imagine this paradox has been resolved, but I don't know the reference.

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I believe most of these correlations are related to symmetries, or per Emmy Noether, conservation. Is this correct? Also, we are assuming 3 dimensions in assessing our distances. I'm sorry if I only added more questions. –  user16050 Nov 17 '12 at 16:24

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It's not possible to communicate faster than light using entangled states. All you get out of entanglement is a correlation between the values of two measurements.; the entanglement doesn't allow you to influence the value measured at another location in a non-causal way. In other words, the correlation only becomes evident after combining the results from the measurements afterwards, for which you need classical information transfer.

For example, consider the thought experiment described on the Wikipedia page for the EPR paradox: a neutral pion decays into an electron and a positron, emitting them in opposite directions and with opposite spins. However, the actual value of the spin is undetermined, so with respect to a spin measurement along a chosen axis, the electron and positron are in the state

$$\frac{1}{\sqrt{2}}\left(|e^+ \uparrow\rangle|e^- \downarrow\rangle + |e^+ \downarrow\rangle|e^- \uparrow\rangle\right)$$

Suppose you measure the spin of the positron along this chosen axis. If you measure $\uparrow$, then the state will collapse to $|e^+ \uparrow\rangle|e^- \downarrow\rangle$, which determines that the spin of the electron must be $\downarrow$; and vice versa. So if you and the other person (who is measuring the electron spin) get together and compare measurements afterwards, you'll always find that you've made opposite measurements for the spins. But there is no way to control which value you measure for the spin of the positron, which is what you'd need to do to send information. As long as the other person doesn't know what the result of your measurement is, he can't attach any informational value to either result for his measurement.

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Excellent answer, but I think there is something still missing. You can still naively argue that the results of all the measurements were predetermined when the electron and the positron were emitted, and therefor there is nothing "special" about the correlation. To answer this claim you need Bell's theorem, as explained by this great answer. –  Joe May 25 '11 at 9:00

Everybody misses the point Einstein was trying to make, which makes it all the more remarkable that it's been 80 years since he was working on spooky action at a distance. The no signalling theorems mean nothing, and it's a shame that most answers simply site: no signalling, nothing spooky about it. Bell emphasized that his theorem could be quickly summarized as: there is non-locality. Guess what? Bell was very well aware of the no signalling theorems. The point is not that we can send signals, the point is that there is a signal sent by the photons themselves -- they have to be communicating. How else could they always coordinate their spins? Einstein's whole critique of quantum mechanics was that it needed to be like Bertleman's socks -- e.g. that the spins were already determined before the experiment, or else there would have to be a non-local communication to coordinate the spins. Einstein called it telepathy, and it's been proven by Bell.

If you don't think there's spooky action, then how do you explain that the spins are always coordinated? If you gave Alice and Bob each a quarter and separated them by a large distance and tasked them with choosing heads or tells, and they always came back to you with one choosing heads, the other choosing tails, what might you think? Maybe they talked to each other on a phone and coordinated their results?

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Let's be more rigorous. No-signalling has been proven safely and shouldn't be worried about. Nevertheless, you'd notice that the point of EPR paper was to show that if quantum mechanics is considered to be a description of "reality", then it is "incomplete". There is an approach, such as in operationalism, to say quantum mechanics isn't meant to be a description of reality. It's a description of our knowledge of reality, due to Asher Peres. Another approach is to say we can give an ontological model of quantum theory using contextual hidden variables, such as the one in de Broglie-Bohm model. So conclusion: EPR argument hasn't been resolved if you mean it's gone! Because in fact orthodox quantum mechanics isn't a complete description of reality. However, it doesn't mean one can signal faster than light!

Some interesting extra information: There is an interesting paper which kind of analyses Einstein's argument. It bring historical facts that show Einstein didn't like the EPR and wrote another paper with the same title in correspondence with Schrödinger, and the one with Rosen and Podolsky was never reviewed by him.

This quotation is from a letter of Einstein to Schrödinger, dated June 19, 1935:

“For reasons of language this [paper] was written by Podolsky after many discussions. But still it has not come out as well as I really wanted; on the contrary, the main point was, so to speak, buried by the erudition.”

Update: A source of confusion in my answer has been pointed out by Marek. I'll try to clarify here: Scientific realism assumes there is an underlying objective reality which has attributes regardless of them being measured by an observer. One can suggest a model which ignores such reality and say "...there is no logical necessity for a realistic worldview to always be obtainable"(Fuchs and Peres, Physics Today 53 (3), 70-71.). On the other hand, one can offer an ontological model which in this case it can be located in 3 different category as in figure below: alt text

I believe Einstein had in mind to show that quantum mechanics can't give a picture of type (a). Which was successful. Because, even if there is an underlying reality, quantum states can't sharply specify them by any means.

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that's a great piece of historical trivia. Einstein's most highly cited paper (by a huge margin!) wasn't even written by him. –  Jeremy Dec 24 '10 at 3:09
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@Sine: nice overview but one thing has to be made more precise: "quantum mechanics is not complete description of reality" has to be specified as "quantum mechanics doesn't allow us to know everything we want to know". But that's because (as far as we know) reality is inherently quantum in nature (in particular, there can be no local hidden parameter theory) and so quantum theory certainly is complete description of reality in this sense. –  Marek Dec 24 '10 at 10:05
    
@Marek: The update is my attempt to clarify what I meant by completeness. –  iii Dec 24 '10 at 11:02
    
@Sina: uh, I have to say I am confused now. I think the picture a) is correct as long as one works in good interpretation of quantum theory (in particular, one has to dispose of the notion of wave-function collapse). Complete state of system indeed is specified by a ray in Hilbert space and there is no more information to be found anywhere. On the other hand, picture b) is surely incorrect if it means to be a hidden parameter theory. As for picture c), I am uncertain about what it means precisely. But again it feels like hidden parameter theory and so is ruled out. –  Marek Dec 24 '10 at 11:10
    
Hmmm... I understand it's not entirely clear from the figure only! It's derived from the paper I linked in the body of my answer. I was intending to point to where one should look at, in that paper to find an adequate answer. It is explained in page 5. Nevertheless, I guess all this is just complimentary information. I think I made the point by just saying No-signalling theorem shows that we can't signal faster than light using non-local features of quantum mechanics. :-) –  iii Dec 24 '10 at 13:38

Being silly, in the vein of the season, if you agreed before hand that if in David's example your colleague could open their christmas present on the other side of the world if their electron was spin up, and the same time they measured their electron you measured your positron as spin down, you now know they have opened their present, faster than the speed of light

Instantaneous data transfer!

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haha very nice indeed! (unfortunately i won't be giving a +1 because it's not really a correct answer) –  Cem Dec 23 '10 at 22:31
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-1 I guess this is a joke, but it's not instantaneous data transfer, and some people could find it confusing. –  Mark Eichenlaub Dec 23 '10 at 22:33
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sorry mark! was gonna qualify it as false, but i thought it was pretty self-explanatory. For those that don't understand - you have no 'proof' the present is open, only faith that those at the other end did whay they were told, and weren't drunk on egg nog, kissing the undergrad –  SoulmanZ Dec 23 '10 at 23:20
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@Soulman: you don't need quantum present for this, classical present would do just fine. If you put blue teddy bear in one box and red teddy in the other and then ask your friend to take one of them with them then as soon as you open your present and find blue teddy, BAM you instanteously know that your friend has the red one. I think people often don't realize, that classical physics can sometimes contain same paradoxes quantum physics can. And also that problem with entanglement and collapse lies in something completely different (cont). –  Marek Dec 24 '10 at 10:10
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This is Berkelmann's always-mismatched socks, used by Bell to demonstrate nonlocal correlation. When you see one is red, you instantly know the other isn't. This isn't how quantum entanglement works, because this type of thing is determined by local hidden variables (the color of the socks) and so can't violate Bell's inequality. –  Ron Maimon Dec 18 '11 at 7:07

Well, the problem in that paradox is that yes, one of the parties will measure the entangled particle to get the wave function collapsed and yes it will collapse for the other party. However, the other party will still have to measure the thing to learn what it is or has to wait for the initial party to send them a message telling what the wave function has collapsed to. The first method will result in a 50% +x and 50% -x(if it is spin you are measuring), as the wave function that collapsed can collapse to either one of these states. So the fact that the wave function collapsed does not really transfer any usable information to the other side. The second method is capped with the speed of light anyway.

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Of course they can't transfer information faster then the speed of light because of the no-signalling theorem. However, we should be careful of how we state the first scenario! In some games, for instance CHSH, you can win the game %75 of the times classically, whereas you can do ~%80 using quantum theory! –  iii Dec 24 '10 at 2:07

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