Quantum Mechanics without Measurement

DevilsAvocado

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Except being an excellent physicists, Feynman is also known for being a good lover. (That can also be said for Schrodinger, but let us stick with Feynman.)

So, we can say that Feynman is a good physicist, and we can also say that Feynman is a good lover.
But can we say that Feynman is a good scientist and a good lover?
This could be hard to prove, however with Schrödinger the case is a little bit ambiguous... Schrödinger discovered quantum theory while hunkered down with a lover in a Swiss chalet... and when pressed to write about his creative life... he protested, saying that he felt the part his lovers played in it was crucial, but discretion would require him to leave that out.

This opens a possibility for Schrödinger actually 'multitasking' in the Swiss chalet... :smile:

Seriously, everything that does not happen simultaneously cannot be proven true?? :bugeye: What a joke...
 
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Quantum Mechanics without Measurement

also known as 'superposition'
 

stevendaryl

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So! There is not claim that all conjunctions are meaningless. But you have completely changed the experimental set up. This is a different scenario.
I don't think so. The Feynman is precisely understood in terms of "hidden variables". Even though you have to make a choice whether to test his lover ability or his physics ability, we an assume that both abilities exist in him at the same time, although we can't demonstrate this.

So there is no contradiction that arises from assuming "hidden variables" in the Feynman case, while in the quantum mechanics it leads to a contradiction (or to a violation of something else important, such as locality).
 

stevendaryl

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Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...
He is definitely not crackpot. You can disagree about whether he has solved the conceptual problems of quantum mechanics through his approach without saying he's a crackpot.
 

atyy

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Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...
If Griffiths has made a mistake, where could it be? On the one hand, CH is not a realistic theory, so it seems that it could escape the Bell theorem.

In http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf (p289) he writes that "Thus the point at which the derivation of (24.10) begins to deviate from quantum principles is in the assumption that a function ##\alpha(w_{a}, \lambda )## exists for different directions ##w_{a}##."

Well, so far I think what he says is ok, since Bell's point is indeed that these exist only if local realism holds, and quantum mechanics is not a local realistic theory.

Then he says "The claim is sometimes made that quantum theory must be nonlocal simply because its predictions violate (24.10). But this is not correct. First, what follows logically from the violation of this inequality is that hidden variable theories, if they are to agree with quantum theory, must be nonlocal or embody some other peculiarity. But hidden variable theories by definition employ a different mathematical structure from (or in addition to) the quantum Hilbert space, so this tells us nothing about standard quantum mechanics."

This seems fishy, because http://arxiv.org/abs/0901.4255 argues that the Bell theorem is compatible with quantum mechanics, since the wave function itself can serve as the hidden variable. It is simply that if one accepts "realism", then the wave function is nonlocal. So I don't think the Bell inequality is incompatible with quantum mechanics. Perhaps it is here that Griffiths has made a mistake.

Nonetheless, in the broader sense, it seems that Griffiths could be right, and CH could be local since it does seem to reject realism (ie. Griffiths's definition of "realism" is not common sense realism). Hohenberg's introduction to CH http://arxiv.org/abs/0909.2359, for example, says CH is not realistic theory - which given how some versions of Copenhagen don't favour realism - CH could I think be argued to be Copenhagen done right.

But exactly how is locality retained in CH? Hohenberg says it's because there is no single framework in CH in which Eq 11 http://arxiv.org/abs/0909.2359 is satisfied. Can that be the explanation? It seems it is not satisfied in the orthodox shut-up-and-calculate Copenhagenish view, but that doesn't make shut-up-and-calculate local. So is the explanation instead that P(A,B,a,b), where a and b range over non-commuting observables does not exist in any single framework?

What I'm asking is: in CH is the Bell inequality violated in any single framework?
 
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stevendaryl

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It's accurate. There are many ways to define 'measurement'.
But "superposition" certainly doesn't mean the same thing as "Quantum Mechanics without Measurement".
 

stevendaryl

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Regarding Griffiths; the urge to 'eradicate' measurements altogether, I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview – and the easiest thing to do is just to get rid of the whole enchilada, by some preposterous word-salad, that no one can take seriously.
I think that is way too harsh. I don't see it that way at all. As someone else said, I see it as a way of doing Copenhagen without making measurement devices primary to the formulation. Instead, it makes histories of observables primary. That is a little bit of an improvement, because observables do have a definite definition within the framework of quantum mechanics, which is not true of "measurement".

I think that there is a sense in which what is being done is just systematizing the practice of quantum mechanics, which is basically Copenhagen, with as few non-physical, fuzzy elements as possible.
 

stevendaryl

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I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview.
I don't know why you say that EPR "doesn't fit in his worldview". EPR experiments can perfectly well be analyzed from the point of view of consistent histories. All the possible outcomes of an EPR experiment form "consistent histories", and the consistent histories approach would allow you to compute the probabilities of those outcomes. At least, I would assume that to be the case---if it's not, then I agree with you that consistent histories is complete garbage.

Let me do some Googling to see if there is a good analysis of EPR from the point of view of consistent histories. I would think that would be the very first thing that would be tried with any new foundation for quantum mechanics.
 

DevilsAvocado

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If Griffiths has made a mistake, where could it be? On the one hand, CH is not a realistic theory, so it seems that it could escape the Bell theorem.

In http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf (p289) he writes that "Thus the point at which the derivation of (24.10) begins to deviate from quantum principles is in the assumption that a function ##\alpha(w_{a}, \lambda )## exists for different directions ##w_{a}##."

Well, so far I think what he says is ok, since Bell's point is indeed that these exist only if local realism holds, and quantum mechanics is not a local realistic theory.
(24.10) is the CHSH inequality:

[itex]\rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') \leq 2[/itex]

"Thus the point at which the derivation of (24.10) begins to deviate from quantum principles is in the assumption that a function ##\alpha(w_{a}, \lambda )## exists for different directions ##w_{a}##."

To me this means that as long as we only deal with the simplest case of parallel settings (i.e. the deterministic 1935 EPR picture), we're okay and LHV would still work, but as soon as we introduce more and 'tougher' settings for the measuring apparatus (polarizer), LHV does not work anymore, only NLHV does.

[my bolding]
Then he says "The claim is sometimes made that quantum theory must be nonlocal simply because its predictions violate (24.10). But this is not correct. First, what follows logically from the violation of this inequality is that hidden variable theories, if they are to agree with quantum theory, must be nonlocal or embody some other peculiarity. But hidden variable theories by definition employ a different mathematical structure from (or in addition to) the quantum Hilbert space, so this tells us nothing about standard quantum mechanics."

This seems fishy, because http://arxiv.org/abs/0901.4255 argues that the Bell theorem is compatible with quantum mechanics, since the wave function itself can serve as the hidden variable. It is simply that if one accepts "realism", then the wave function is nonlocal. So I don't think the Bell inequality is incompatible with quantum mechanics. Perhaps it is here that Griffiths has made a mistake.
Fishy indeed... or maybe worse...

The first bold part above is where things start to go quite wrong. Bell's theorem is not a description or definition of quantum mechanics; instead it sets a limit for a theory of local hidden variables, aka Bell's inequality, which is violated both theoretically and experimentally by quantum mechanics, hence leading to this simple form:

No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Bell's theorem is an abstract mathematical formulation for the limit of theories of local hidden variables; it does not say anything specific about QM. And to use the Hilbert space as an argument is nothing but ridiculous – we have experiments for god's sake! And as I mentioned in a previous post, we could substitute QM for "Barnum & Bailey Circus", and Bell's theorem would still hold (though be it a little bit 'peculiar'):

No physical theory of local hidden variables can ever reproduce all of the predictions of "Barnum & Bailey Circus".

Bell's theorem is only about theories of local hidden variables; it does not say anything fundamental about theories violating the inequality (and of course the definition of local realism comes from the original 1935 EPR paper).

I don't know what to say about the second bold part... quantum mechanics violates Bell's inequality... it cannot be 'compatible' with it, Griffiths must have misunderstood the whole thing...

Nonetheless, in the broader sense, it seems that Griffiths could be right, and CH could be local since it does seem to reject realism (ie. Griffiths's definition of "realism" is not common sense realism). Hohenberg's introduction to CH http://arxiv.org/abs/0909.2359, for example, says CH is not realistic theory - which given how some versions of Copenhagen don't favour realism - CH could I think be argued to be Copenhagen done right.
Well, here is when things get so perplex that it is almost justified to talk about 'crackpotish' ideas...

If CH is local and non-real there is no problem whatsoever!

But then... when Griffiths claim that CH is also consistent (which the name indicates), we're back in the rabbit hole of total confusion: What consistency is he talking about?? In which way is CH more consistent than any other QM interpretation?? I just don't get it. :bugeye:

CH is surely not consistent according to the classification adopted by Einstein and EPR:

[PLAIN said:
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics]The[/PLAIN] [Broken][/PLAIN] [Broken] current usage of realism and completeness originated in the 1935 paper in which Einstein and others proposed the EPR paradox. In that paper the authors proposed the concepts element of reality and the completeness of a physical theory. They characterised element of reality as a quantity whose value can be predicted with certainty before measuring or otherwise disturbing it, and defined a complete physical theory as one in which every element of physical reality is accounted for by the theory. In a semantic view of interpretation, an interpretation is complete if every element of the interpreting structure is present in the mathematics. Realism is also a property of each of the elements of the maths; an element is real if it corresponds to something in the interpreting structure. For example, in some interpretations of quantum mechanics (such as the many-worlds interpretation) the ket vector associated to the system state is said to correspond to an element of physical reality, while in other interpretations it is not.
But what finally put the nail in the coffin for me, are statements like this:

http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf (p289) said:
If quantum theory is a correct description of the world, then since it predicts correlation functions which violate (24.10), one or more of the assumptions made in the derivation of this inequality must be wrong.
:surprised Wow... "If" and "must"... looks like he's refuting QM and/or Bell's theorem in one sentence... not bad at all!

What I'm asking is: in CH is the Bell inequality violated in any single framework?
I don't know atyy, all this looks like a mess to me, but of course, I could be wrong (and then I will put on my red face, bowing to the floor, apologizing)...

This is what Wikipedia has to say:

[PLAIN said:
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics]The[/PLAIN] [Broken][/PLAIN] [Broken] consistent histories interpretation generalizes the conventional Copenhagen interpretation and attempts to provide a natural interpretation of quantum cosmology. The theory is based on a consistency criterion that allows the history of a system to be described so that the probabilities for each history obey the additive rules of classical probability. It is claimed to be consistent with the Schrödinger equation.

According to this interpretation, the purpose of a quantum-mechanical theory is to predict the relative probabilities of various alternative histories (for example, of a particle).
It just makes it worse, the rules of classical probability can't possibly be non-realistic... a complete mess...
 
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DevilsAvocado

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I think that is way too harsh. I don't see it that way at all. As someone else said, I see it as a way of doing Copenhagen without making measurement devices primary to the formulation. Instead, it makes histories of observables primary.
Okay, maybe too harsh (I do have my red face ready, in case you find anything ;), but I don't understand how you are able to make any 'consistency' whatsoever of things you know absolutely nothing about, except probability densities (before measurement)??

Let me do some Googling to see if there is a good analysis of EPR from the point of view of consistent histories.
Great!
 

atyy

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It just makes it worse, the rules of classical probability can't possibly be non-realistic... a complete mess...
I think it's alright as long as it is not logically inconsistent, ie. one doesn't incur a contradiction by adding an additional axiom. Since you brought up Goedel earlier, an analogy would be that the Goedel statement is true if we are talking about the natural numbers. However, at the syntactic level, since neither the statement nor its negation are provable from the Peano axioms, one could consistently add the negation of the Goedel statement as an axiom. We wouldn't have the natural numbers any more, but it would still be a consistent system with a model.
 
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stevendaryl

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I don't know what to say about the second bold part... quantum mechanics violates Bell's inequality... it cannot be 'compatible' with it, Griffiths must have misunderstood the whole thing...
That was not a quote from Griffiths, that was another paper by a different author.

If CH is local and non-real there is no problem whatsoever!

But then... when Griffiths claim that CH is also consistent (which the name indicates), we're back in the rabbit hole of total confusion: What consistency is he talking about??
I think you misunderstood what Griffiths is talking about. The word "consistent" is a property of a set of histories. A "history" for Griffiths is a sequence of statements, each of which refers to a fact that is true at a particular moment in time. Basically, a history amounts to a record of the sort:

History [itex]H_1[/itex]:
At time [itex]t_{1 1}[/itex] observable [itex]\mathcal{O}_{1 1}[/itex] had value [itex]\lambda_{1 1}[/itex]
At time [itex]t_{1 2}[/itex] observable [itex]\mathcal{O}_{1 2}[/itex] had value [itex]\lambda_{1 2}[/itex]
...

History [itex]H_2[/itex]:
At time [itex]t_{2 1}[/itex] observable [itex]\mathcal{O}_{2 1}[/itex] had value [itex]\lambda_{2 1}[/itex]
At time [itex]t_{2 2}[/itex] observable [itex]\mathcal{O}_{2 2}[/itex] had value [itex]\lambda_{2 2}[/itex]
...

So history [itex]H_i[/itex] says that observable [itex]\mathcal{O}_{i j}[/itex] had value [itex]\lambda_{i j}[/itex] at time [itex]t_{i j}[/itex], where [itex]i[/itex] is used to index histories, and [itex]j[/itex] is used to index moments of time within that the history.

The entire collection [itex]H_1, H_2, H_3, ...[/itex] of possible histories is said to be a consistent collection if the histories are mutually exclusive. That is, it is impossible (or vanishingly small probability) that more than one history in the collection could be true. (Mathematically, each history corresponds to a product of time-evolved projection operators, and the condition of consistency is that the two histories, as projection operators, result in zero when applied to the initial density operator, or something like that).

So the word "consistent" is not talking about any particular history being consistent, or about Griffiths' theory being consistent. It's talking about it being consistent to reason about that collection of histories using classical logic and probability.

But what finally put the nail in the coffin for me, are statements like this:

Quote by http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf (p289)
If quantum theory is a correct description of the world, then since it predicts correlation functions which violate (24.10), one or more of the assumptions made in the derivation of this inequality must be wrong.​

:surprised Wow... "If" and "must"... looks like he's refuting QM and/or Bell's theorem in one sentence... not bad at all!
You're a lot harsher than I would be reading that statement. To me, it's only saying "If the conclusion of a theorem is false, then one of the assumptions must be false."

Bell's theorem is of the form: If we assume that we have a theory of type X, then that theory will satisfy inequality Y. Since quantum mechanics does not satisfy inequality Y, then the assumption that it is a theory of type X must be false.

That's all he's saying. He's not "refuting" Bell. To say that an assumption is false is not to refute the theorem.
 

Demystifier

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Why don't you consider CH to be a version of local nonrealism without a measurement problem?
First, it is not clear to me whether CH is supposed to be about realism or nonrealism. Second, even if I accept CH to be a version of local nonrealism without a measurement problem, I do not consider it to be a very satisfying version. That's because I cannot easily diggest a change of the rules of logic (unless it is absolutely necessary, which in the case of QM is not).
 
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First, it is not clear to me whether CH is supposed to be about realism or nonrealism. Second, even if I accept CH to be a version of local nonrealism without a measurement problem, I do not consider it to be a very satisfying version. That's because I cannot easily diggest a change of the rules of logic (unless it is absolutely necessary, which in the case of QM is not).
Surely, we must consider the laws of logic to be a purely mathematical construct and not given to us as a feature of nature. That must mean that we're free to define them how we like.

Provided that we're clear about which set of logical rules we are using, their selection should be arbitrary and I can't see how we can arrive at an unsatifsying conclusion.

If a set of logical rules is complete and self-consistent then I would expect it to arrive at the same conclusion as any other.

The set of logical rules that we use is so deeply ingrained in our way of thinking, that an attempt to use another set is very likely to fail into the trap of mixing and matching rule sets, which would give rise to inconsistencies and unsatisfying conclusions.
 
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DevilsAvocado

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I think it's alright as long as it is not logically inconsistent, ie. one doesn't incur a contradiction by adding an additional axiom.
Yes, maybe you're right. Still I find it very confusing, and what 'bothers' me (that is never explicitly spelled out), is that maybe the most straightforward name of this interpretation should be "Classical Histories"... There's no doubt that Griffiths does not like what Bell is telling us:

[PLAIN said:
http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf]In[/PLAIN] [Broken] summary, the basic lesson to be learned from the Bell inequalities is that it is difficult to construct a plausible hidden variable theory which will mimic the sorts of correlations predicted by quantum theory and confirmed by experiment. Such a theory must either exhibit peculiar nonlocalities which violate relativity theory, or else incorporate influences which travel backwards in time, in contrast to everyday experience. This seems a rather high price to pay just to have a theory which is more “classical” than ordinary quantum mechanics.
And maybe most mindboggling is that he makes the correct conclusion regarding premises for LHV, but do not [here] present his "third alternative" of "subjective logic" and "forbidden frameworks", but just conclude that "this seems a rather high price to pay".

And what on earth is "a theory which is more “classical” than ordinary quantum mechanics", I'm totally lost...

Since you brought up Goedel earlier, an analogy would be that the Goedel statement is true if we are talking about the natural numbers. However, at the syntactic level, since neither the statement nor its negation are provable from the Peano axioms, one could consistently add the negation of the Goedel statement as an axiom. We wouldn't have the natural numbers any more, but it would still be a consistent system with a model.
Yes, but it could still never be proven to be complete and consistent from within itself. :wink:
 
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DevilsAvocado

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I think you misunderstood what Griffiths is talking about. The word "consistent" is a property of a set of histories. A "history" for Griffiths is a sequence of statements, each of which refers to a fact that is true at a particular moment in time. Basically, a history amounts to a record of the sort:

History [itex]H_1[/itex]:
At time [itex]t_{1 1}[/itex] observable [itex]\mathcal{O}_{1 1}[/itex] had value [itex]\lambda_{1 1}[/itex]
At time [itex]t_{1 2}[/itex] observable [itex]\mathcal{O}_{1 2}[/itex] had value [itex]\lambda_{1 2}[/itex]
...

History [itex]H_2[/itex]:
At time [itex]t_{2 1}[/itex] observable [itex]\mathcal{O}_{2 1}[/itex] had value [itex]\lambda_{2 1}[/itex]
At time [itex]t_{2 2}[/itex] observable [itex]\mathcal{O}_{2 2}[/itex] had value [itex]\lambda_{2 2}[/itex]
...

So history [itex]H_i[/itex] says that observable [itex]\mathcal{O}_{i j}[/itex] had value [itex]\lambda_{i j}[/itex] at time [itex]t_{i j}[/itex], where [itex]i[/itex] is used to index histories, and [itex]j[/itex] is used to index moments of time within that the history.

The entire collection [itex]H_1, H_2, H_3, ...[/itex] of possible histories is said to be a consistent collection if the histories are mutually exclusive. That is, it is impossible (or vanishingly small probability) that more than one history in the collection could be true. (Mathematically, each history corresponds to a product of time-evolved projection operators, and the condition of consistency is that the two histories, as projection operators, result in zero when applied to the initial density operator, or something like that).
Thank you for explaining this; however what use do we have of this in providing "a natural interpretation of quantum mechanics"? If we take EPR-Bell test experiments, this is the Bell state:

[itex]\frac{1}{\sqrt{2}} \left( | \uparrow \rangle_A |\uparrow \rangle_B + |\rightarrow \rangle_A |\rightarrow \rangle_B \right)[/itex]

In standard QM this is interpreted as a quantum superposition in the shared wavefunction. Now, if CH wants to make consistent histories out of this, I guess it is okay, but afaik this can only happen afterwards, right? And what "prediction power" has CH then?

And most interesting of all:

Exactly how does CH explain the outcome of EPR-Bell test experiments if the "hidden observables" did have definite values all along??

So the word "consistent" is not talking about any particular history being consistent, or about Griffiths' theory being consistent. It's talking about it being consistent to reason about that collection of histories using classical logic and probability.
Thank you very much for this, and I'm sorry if I went too far in my criticism of CH.

However, I believe it is not possible to explain EPR-Bell experiments outcome, using only classical logic and classical probability.

You're a lot harsher than I would be reading that statement. To me, it's only saying "If the conclusion of a theorem is false, then one of the assumptions must be false."

Bell's theorem is of the form: If we assume that we have a theory of type X, then that theory will satisfy inequality Y. Since quantum mechanics does not satisfy inequality Y, then the assumption that it is a theory of type X must be false.

That's all he's saying. He's not "refuting" Bell. To say that an assumption is false is not to refute the theorem.
Okay, we are interpreting this differently. To me "If quantum theory is a correct description of the world", means that the writer questions if quantum theory is correct, and "one or more of the assumptions made in the derivation of this inequality must be wrong", to me means that the writer questions Bell's theorem.

We all know the outstanding precision and validity of QM, the gadget world of today would simply stop if there was slightest error in QM's "description of the world". John Bell was nominated for the Nobel Prize in Physics the same year he died (without ever knowing it). Anton Zeilinger and Alain Aspect will get it any year now.

Then to write this kind of 'insinuations' is just not right.
 

atyy

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John Bell was nominated for the Nobel Prize in Physics the same year he died (without ever knowing it).
For his inequality or for the chiral anomaly?
 

DevilsAvocado

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Inequality

Edit:
I can't find an exact verification... I just took it for granted... it seems illogical not to reward him for what many agrees is one of the most profound discoveries in science, but you never know with these old farts in Stockholm, they've done bigger mistakes...


A Chorus of Bells
http://arxiv.org/abs/1007.0769
 
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