Scholarpedia article on Bell's Theorem

[ttn]

Your latest post indicates that Jarrett's analysis is naive in an important sense. Would you (and ttn if he reads this) recommend focusing on that, or something else?

I personally wouldn't recommend focusing on Jarrett per se, but I would recommend focusing on Bell's formulation of locality and maybe reading some Jarrett (or my paper on Bell vs. Jarrett) will help there. But how about just reading Bell??

 

[ttn]

Travis, I have just carefully read your article http://arxiv.org/pdf/0808.2178v1.pdf and it is just great!

Thanks. I appreciate that you took the time to read it, and even more so that you "got it".

 

[ThomasT]

And one is not *calling* the correlations "non-locality". One defines a notion of "locality" that captures just the idea of only-slower-than-light-causal-influences, and then finds that no theory respecting this condition can make the QM predictions. It has nothing whatsoever to do with correlations or any comparison to classical physics.

I think this is a most clear way of putting it. I've come to agree that it's been definitively shown that no theory respecting this condition can make the QM predictions. So, the only remaining consideration is how this locality condition might be related to the reality underlying instrumental behavior. That is, what inference(s) might be made wrt an underlying reality from the math. This is what isn't clear to me yet. Anything you might offer wrt clarifying that will be most appreciated.

 

[ThomasT]

I personally wouldn't recommend focusing on Jarrett per se, but I would recommend focusing on Bell's formulation of locality and maybe reading some Jarrett (or my paper on Bell vs. Jarrett) will help there. But how about just reading Bell??

Thanks, and your suggestions are noted.

I'm not yet finished with your paper on Bell vs. Jarrett. I've only done one fast reading of your Scholarpedia article. I'm pretty familiar with Bell 1964. And, I should add, that I'm not a scholar wrt this stuff or a physicist or a mathematician. So, if I'm ever to really understand this, then it's going to take more time for me than I suppose it would for most of the commenters here. So, if, at any time, you feel it's possible to explain anything in laymen's terms, then that would be most appreciated. I assume that much (most?) of this might not be explainable in ordinary language, so it's just going to take me longer than the other contributors here to formulate some definite opinions regarding aspects of your work -- because I have to look almost everything up to make sure I understand it.

 

[ttn]

So, the only remaining consideration is how this locality condition might be related to the reality underlying instrumental behavior. That is, what inference(s) might be made wrt an underlying reality from the math. This is what isn't clear to me yet. Anything you might offer wrt clarifying that will be most appreciated.

Put it this way. We consider all conceivable candidate theories. (One of them has to be true!) Now divide all the theories into two classes -- those that respect Bell's locality condition and those that don't. Now the theorem and the experiments show that none of the theories in the "respect Bell's locality condition" category can be correct. (They all make predictions in accord with the inequality, but the experiments show that in fact the inequality is violated.) Hence, the true theory is in the other category, the category of theories that don't respect "locality".

But that last is just another way of saying that *the world* is nonlocal.

So there is no particular further/additional/separate question about what you can infer about the real world. If no local theory is true, the world is nonlocal.

 

[ttn]

I'm not yet finished with your paper on Bell vs. Jarrett. I've only done one fast reading of your Scholarpedia article. I'm pretty familiar with Bell 1964. And, I should add, that I'm not a scholar wrt this stuff or a physicist or a mathematician. So, if I'm ever to really understand this, then it's going to take more time for me than I suppose it would for most of the commenters here. So, if, at any time, you feel compelled to explain anything in laymen's terms, whenever possible, that's most appreciated. I assume that much (most?) of this might not be explainable in ordinary language, so it's just going to take me longer than the other contributors here to formulate some definite opinions regarding aspects of your work -- because I have to look almost everything up to make sure I understand it.

Bell's 1964 paper is, I would say, somewhat technical and hard to follow. After that he spent 3+ decades trying to clarify the issue, and a number of his later papers are far less technical, and far more accessible, than the 1964. I would recommend especially "Bertlmann's Socks..." and "La Nouvelle Cuisine". Both are in the 2nd edition of "speakable and unspeakable".

Whether you are a scholar/physicist/mathematician or not, there is no better way to understand Bell than by reading Bell. He was truly a master at clear, accessible exposition.

 

[harrylin]

[..] One defines a notion of "locality" that captures just the idea of only-slower-than-light-causal-influences, and then finds that no theory respecting this condition can make the QM predictions. It has nothing whatsoever to do with correlations or any comparison to classical physics.[..]

??! It has everything to do with correlations between measurements at two locations, and certainly you know that. I wonder why you would contradict this most basic point?

 

[ThomasT]

Put it this way. We consider all conceivable candidate theories. (One of them has to be true!)

True wrt what?

Now divide all the theories into two classes -- those that respect Bell's locality condition and those that don't. Now the theorem and the experiments show that none of the theories in the "respect Bell's locality condition" category can be correct. (They all make predictions in accord with the inequality, but the experiments show that in fact the inequality is violated.) Hence, the true theory is in the other category, the category of theories that don't respect "locality".

True theory wrt what?

If no local theory is true, the world is nonlocal.

That's the assertion in question. Bell-LR theories of quantum entanglement are mathematically proven to be incompatible with QM, and, subsequently, to be incompatible with experimental results. There's no reasonable question about that, afaik. But you promise that this means that the world is nonlocal, which I don't yet see. So, either I'm missing something important, or you are. And, in my mind, I don't know which is the case.

 

[harrylin]

Put it this way. We consider all conceivable candidate theories. (One of them has to be true!) [..]

Hmm no, it's of course quite possible that none of the theories that we can conceive is true; and it would be very unreasonable to assume that an existing model of things that we know little about and which we cannot directly observe has to be true.

 

[ThomasT]

Bell's 1964 paper is, I would say, somewhat technical and hard to follow. After that he spent 3+ decades trying to clarify the issue, and a number of his later papers are far less technical, and far more accessible, than the 1964. I would recommend especially "Bertlmann's Socks..." and "La Nouvelle Cuisine". Both are in the 2nd edition of "speakable and unspeakable".

Whether you are a scholar/physicist/mathematician or not, there is no better way to understand Bell than by reading Bell. He was truly a master at clear, accessible exposition.

Thanks. I don't have the Socks or Cuisine articles. All I have is Bell's 1964. The more I read it, and take in what commenters here have to say about it, the more I seem to understand it. I now feel that I understand the math and the logic behind the math. So, there's no question in my mind that Bell's LR form is incompatible with QM and entanglement setups.

That took me a few years. Understanding your scholarpedia article might take even longer ... for me. Hey, there's no hurry. I'm pretty sure nature doesn't care if I understand any of it or not. But, as I mentioned, anything you can offer that might speed up the process will be most appreciated.

 

[malreux]

Hi, have followed most of this thread. Here's some reading material to supplement the article, if your arriving at this whole area for the first time (apology's if these references have already come out & I didn't spot them):

Maudlin, Quantum Non-Locality & Relativity
Healey, Gauging What's Real (for discussion of non-sep)
Cushing & McMullin (ed's), Philosophical Consequences of Quantum Theory - this collection is old now, but it is a classic, and includes important papers by Jarret, Mermin, Redhead, Shimony & Van Fraassen

For those in the field and or interested, some recent preprints:

http://philsci-archive.pitt.edu/9068/
http://philsci-archive.pitt.edu/9008/
http://philsci-archive.pitt.edu/8864/
http://philsci-archive.pitt.edu/8753/
http://philsci-archive.pitt.edu/8617/
http://philsci-archive.pitt.edu/5371/
http://philsci-archive.pitt.edu/8946/

PS Also noted a lot of people on here are interested in dBB - wondered if any of you chaps had read the 2004 paper by Wallace and Brown arguing for the superiority of the Everett I over dBB? Here's the preprint: http://philsci-archive.pitt.edu/1659/

 

[ttn]

??! It has everything to do with correlations between measurements at two locations, and certainly you know that. I wonder why you would contradict this most basic point?

Correlations are "involved", of course -- e.g., Bell's inequality is a constraint on correlations. But my point was that, at the level of formulating "locality", one is deliberately capturing what it means for something to *influence* something else -- *as opposed to* their merely being correlated. So in that sense, the whole argument is from the beginning about causal influence, *not correlation*. Also, nothing at all in the argument depends on asking the question "Could these correlations arise in a classical theory?"

 

[ttn]

True wrt what?

Uh, wrt the same thing truth is always wrt -- the world. (I am taking here for granted the correspondence theory of truth -- a theory is true if its description of how the world works is correct, if it corresponds to the way the world actually is.)

 

[ttn]

Hmm no, it's of course quite possible that none of the theories that we can conceive is true; and it would be very unreasonable to assume that an existing model of things that we know little about and which we cannot directly observe has to be true.

I think you misunderstand "conceive". It doesn't mean we have to think the theory up and write it down.

I take it for granted that there is *some* true theory, some correct description of how things work. And hey look! Just in that last sentence I already conceived of the true theory! Yes, I wish I knew more about it so I could win a Nobel prize, but I don't need to know more about it to know that it's not a local theory!

 

[ThomasT]

Uh, wrt the same thing truth is always wrt -- the world. (I am taking here for granted the correspondence theory of truth -- a theory is true if its description of how the world works is correct, if it corresponds to the way the world actually is.)

You asserted that at least one candidate theory had to be true. What are these candidate theories about? They predict instrumental behavior. Right? But your assertion wrt Bell's theorem is about the reality underlying instrumental behavior -- which no theory predicts. So, I asked: true wrt what?

 

[ttn]

You asserted that at least one candidate theory had to be true. What are these candidate theories about?

Particles, fields, strings... who knows what else.

They predict instrumental behavior. Right?

Yes, insofar as these things you call "instruments" are made of particles or fields or strings or whatever the theory is fundamentally about. Perhaps I should have clarified that we're thinking here about candidate *fundamental* theories -- theories that purport to describe nature at the most basic microscopic level. Such a theory of course won't include postulates about "measurement" or "instruments" or any such vague anthropocentric ideas, but will end up saying things about "instruments" in the same way it says things about cats, galaxies, ham sandwiches, etc.

But your assertion wrt Bell's theorem is about the reality underlying instrumental behavior -- which no theory predicts. So, I asked: true wrt what?

No theory says anything about the reality underlying instrumental behavior? That's certainly not true. There are plenty of extant theories that do. (MWI, GRW, dBB, etc.) But even if there weren't, it wouldn't matter. We could still imagine such theories. I think you're missing the point that Bell's theorem is in no way a constraint merely on "theories we happen to already know about" or "theories that have been published so far" or anything like that. It's a constraint on *all possible theories*.

 

[ttn]

Thanks for the links malreux. The book by Maudlin that you mentioned is particularly good.

PS Also noted a lot of people on here are interested in dBB - wondered if any of you chaps had read the 2004 paper by Wallace and Brown arguing for the superiority of the Everett I over dBB? Here's the preprint: http://philsci-archive.pitt.edu/1659/

I've read it. I think they're wrong. But this thread probably isn't the place to get into that!

 

[malreux]

No worries ttn!

Your right, this isn't thread to discuss that. If you think people would be interested maybe its an idea for a thread?

 

[harrylin]

Correlations are "involved", of course -- e.g., Bell's inequality is a constraint on correlations. But my point was that, at the level of formulating "locality", one is deliberately capturing what it means for something to *influence* something else -- *as opposed to* their merely being correlated. [..]

Ah yes - agreed (that is: with emphasis on "merely").

 

[ThomasT]

Particles, fields, strings... who knows what else.

Well, that's the language associated with the mathematics. But (and my question was a rhetorical one) what any theory is actually about is the prediction of instrumental behavior. Isn't it?

Yes, insofar as these things you call "instruments" are made of particles or fields or strings or whatever the theory is fundamentally about. Perhaps I should have clarified that we're thinking here about candidate *fundamental* theories -- theories that purport to describe nature at the most basic microscopic level.

Instrumental behaviors are the fundaments of physical science. Aren't they? Any theory can purport to be about anything that we have no way of ascertaining or verifying sensorily. Isn't direct objective sensory apprehension the basic criterion of empirical science?

Do we have any way of knowing how or if any of the mathematical constructions involved in models of quantum phenomena correspond to an underlying reality that's outside the purview of our senses?

No theory says anything about the reality underlying instrumental behavior? That's certainly not true.

I think you might well be right. The problem is that we have no way of knowing.

I think you're missing the point that Bell's theorem is in no way a constraint merely on "theories we happen to already know about" or "theories that have been published so far" or anything like that. It's a constraint on *all possible theories*.

I agree. It's a constraint on all possible Bell-LR models of quantum entanglement. And the question remains: what might this have to do with an underlying reality? I'm not saying we can't infer something about a presumed underlying reality from the conceptual content of theories that correctly predict instrumental behavior. But what you're saying is that we can infer something about a presumed underlying reality from the literal content of a theory that doesn't correctly predict instrumental behavior.

Ok, no problem. Nature is either exclusively local or it isn't. A theory assumes exclusive locality, and encodes that assumption in a certain way. The theory is proven wrong.

One conclusion might be that, ergo, there's some nonlocality in nature. Another conclusion might be that, ergo, the theory incorrectly models the experimental situation in a way that has nothing to do with whether or not nature is exclusively local.

The latter is my working hypothesis. But I'll keep an open mind while rereading and attempting to understand your article.

And thanks for the replies. Everything helps.

 

[harrylin]

[..] No theory says anything about the reality underlying instrumental behavior? That's certainly not true. There are plenty of extant theories that do. (MWI, GRW, dBB, etc.) But even if there weren't, it wouldn't matter. We could still imagine such theories. I think you're missing the point that Bell's theorem is in no way a constraint merely on "theories we happen to already know about" or "theories that have been published so far" or anything like that. It's a constraint on *all possible theories*.

MWI etc. are interpretations or models of physical theories, just like the Lorentz ether. But yes indeed, Bell's theorem is an extremely far-reaching claim, not just about existing theories but about possible theories including those that haven't even been conceived yet.

 

[harrylin]

[..] I agree. It's a constraint on all possible Bell-LR models of quantum entanglement. [..]

That may be true, but if that is true then Bell's theorem is wrong - for his theorem is an assertion about the incompatibility of any possible local model of nature with QM.

 

[ThomasT]

That may be true, but if that is true then Bell's theorem is wrong - for his theorem is an assertion about the incompatibility of any possible local model of nature with QM.

No. His assertion has to do with the form specified in equation 2 of his 1964 paper. Which form, he proved, cannot reproduce the QM predictions for the singlet state wrt the Stern-Gerlach experiment. This has been subsequently extended to apply to any quantum entanglement setup, and has been verified mostly wrt optical entanglement setups.

Of course, you can maintain that there is no other possible way to explicitly encode locality other than the way Bell did it. I can't think of one.

 

[harrylin]

No. His assertion has to do with the form specified in equation 2 of his 1964 paper. [...].

Sorry but I think we should let Bell speak for himself - and that is not what he asserted. Let's first check if ttn's article explains this well:

"Bell's theorem states that the predictions of quantum theory (for measurements of spin on particles prepared in the singlet state) cannot be accounted for by any local theory"

Yes, that is exactly what Bell's theorem states. But regretfully the article doesn't contain a link to Bell's statement... Here are two citations of Bell's assertion (his "theorem"):

"In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measurement device can influence [instantaneously] the reading of another instrument, however remote"
- Bell 1964
"Could we device a model that which reproduces the quantum formulae completely? No it cannot be done, so long as action at a distance is excluded. [...] the quantum correlatations are locally inexplicable"
- Bell 1980

 

[ttn]

But (and my question was a rhetorical one) what any theory is actually about is the prediction of instrumental behavior. Isn't it?

Forgive me for answering a rhetorical question, but ... NO.

Instrumental behaviors are the fundaments of physical science. Aren't they?

No. I mean, they're important, especially in the sense that our evidence for/against the truth of various candidate theories comes largely from "instrumental behaviors". But why in the world should that mean that "instrumental behaviors" is all theories can say anything about? That's insane. Is paleontology required to be only about the location of bone scraps in the dirt, never about dinosaurs themselves? Do we not know something about (say) the temperature in the core of the sun? How species evolved? It is completely and totally commonplace, normal, and proper for theories to say all kinds of things going far far beyond "instrumental behaviors".

 

[harrylin]

On a side note, I saw that the special relativity in Scholarpedia to which your article refers contains at least one misrepresentation (faulty description of second postulate, a misunderstanding that was discussed in the AJP). As this forum isn't the place to discuss that topic (and thus I won't), you could suggest those authors to bring their article up for discussion in the relativity forum.

 

[martinbn]

Well the claim is of course, contrary to what you claim here, that these correlations can not be modeled with no influence at a distance and that instead they are only compatible with instantaneous influence at a distance. That's what is meant with "non-locality".

But why should there be any influence?

 

[martinbn]

The proof allows one to specify only the complete state of a the particle pair as a single (perhaps holistic) thing. You don't *have* to break it apart into "the state of the subsystem over here" and "the state of the subsystem over there".

The proof of what? There is no QM involved in Bell's inequalities.

We are interested in faster-than-light causation, not faster-than-light messages. You really think the relativistic causal structure knows about (or only cares about) "messages"??

Well, I clearly said 'for example', nothing about _only_ messages.

And one is not *calling* the correlations "non-locality". One defines a notion of "locality" that captures just the idea of only-slower-than-light-causal-influences, and then finds that no theory respecting this condition can make the QM predictions. It has nothing whatsoever to do with correlations or any comparison to classical physics.

But what causal influences are we talking about here?

"La nouvelle cuisine" is I think his clearest presentation of all this stuff. If you read his preface to the first edition of "speakable..." he says he regrets never having put everything together in a certain way for publication. That's what he subsequently did with "la nouvelle cuisine".

So I have to go to the library.

 

[malreux]

But why in the world should [...] "instrumental [behavior]" [be] all theories can say anything about?

Quite, and what a miracle it would be if, knowing nothing about the world in itself, our theories being merely useful tools, yet our tools work so often and so well? QM is so successful it would be a miracle if it did not approximate the truth, even slightly. I don't believe in miracles. Besides, the real question here is 'why is QM so successful?' -part of the answer, presumably, is that human theory has managed to latch onto a bit of reality, or at least approximates it.

 

[ttn]

The proof of what? There is no QM involved in Bell's inequalities.

Uh, the proof of Bell's theorem. I agree that "there is no QM involved", if I understand correctly what you mean. The point is just that, in deriving the inequality from the assumption of locality, one doesn't have to assume that the state of the particle pair can be broken up as "the state of the first particle" and then, separately, "the state of the second particle". It is perfectly compatible with the derivation for the state to be somehow "holistic" (i.e., not "separable") as is basically the case in ordinary QM.