Scholarpedia article on Bell's Theorem

[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.

 

[harrylin]

But why should there be any influence?

Bell's conclusion - which according to ttn has been perfectly proven - is that the predicted correlations cannot be explained without such an influence (a "spooky action at a distance", as Einstein called it).

 

[martinbn]

Bell's conclusion - which according to ttn has been perfectly proven - is that the predicted correlations cannot be explained without such an influence (a "spooky action at a distance", as Einstein called it).

I thought that the conclusion is that if you want to explain it with and influence it cannot be local. But why should there be an influence?

 

[martinbn]

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.

Yes, of course. So?

 

[ttn]

Yes, of course. So?

So, that answers the question you asked in 298.

 

[harrylin]

I thought that the conclusion is that if you want to explain it with and influence it cannot be local. But why should there be an influence?

No, nothing like that! Again, what is meant with "an influence" or "spooky action at a distance": Bell concluded that the measurement at one place - however remote - instantly affects what is measured at another place; according to him the predicted correlations cannot be explained without such an influence.

See also my citations in post #294.
martinbn, perhaps ttn's summary statement in his article is not clear enough and he should retain more of Bell's words? You are as an apparently "fresh" reader of this topic the best positioned to answer that question.

 

[lugita15]

ttn, would it be possible for you (or anyone else) to scan "La Nouvelle Cuisine" for those of us who don't have Bell's book handy?

 

[DrChinese]

Bell concluded that the measurement at one place - however remote - instantly affects what is measured at another place; according to him the predicted correlations cannot be explained without such an influence.

... perhaps ttn's summary statement in his article is not clear enough and he should retain more of Bell's words?

If you want to retain more of Bell's words, you would want to add this important phrase to your first sentence: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements". I.e. a theory "supplemented by additional variables". A hidden variable theory.

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

 

[lugita15]

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

DrChinese, I still don't understand why you don't agree with this. You said that EPR argument is only that "simultaneous perfect correlations" implies hidden variables, but it seems to me that perfect correlations implies simultaneous perfect correlations, assuming the no-conspiracy condition.

I claim that the following two statements together imply hidden variables:
1. There is perfect correlation at identical polarizer settings.
2. When you don't set the polarizers to identical angles, it is still true (and meaningful) that you WOULD have gotten perfect correlations if you HAD set the polarizers to identical angles.

Do you disagree with this?

 

[harrylin]

If you want to retain more of Bell's words, you would want to add this important phrase to your first sentence: "In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements". I.e. a theory "supplemented by additional variables". A hidden variable theory.

This distinction in phrasing probably wouldn't be so important to ttn, since he believes that perfect correlations imply hidden variables.

I had not elaborated on this as my comment there was directed at ttn and martinbn, and I suppose that ttn understands this well.

An important difference in the two papers that I cited is that the second paper clearly does not suggest that his conclusion would only be valid for the addition of variables. And his conclusion as expressed in his first paper evidently also applies to a null-variable. Therefore I hold that citing that other phrase without explaining the history (he was obviously simply referring to EPR) or without also citing his reformulation in a later paper (as I did in my post #294) can put people on a wrong track. My summary in post #305 for martinbn points to what I believe to be the essence of Bell's theorem.

 

[mattt]

After a second thought, I changed my mind. I think that the way Bell defines "local causality" for a fundamental theory to respect the causal structure of Relativity Theory, is correct for a deterministic fundamental theory, but I would not use that definition for a stochastic fundamental theory. I'll expand on this in the following days...

 

[DrChinese]

DrChinese, I still don't understand why you don't agree with this. You said that EPR argument is only that "simultaneous perfect correlations" implies hidden variables, but it seems to me that perfect correlations implies simultaneous perfect correlations, assuming the no-conspiracy condition.

I claim that the following two statements together imply hidden variables:
1. There is perfect correlation at identical polarizer settings.
2. When you don't set the polarizers to identical angles, it is still true (and meaningful) that you WOULD have gotten perfect correlations if you HAD set the polarizers to identical angles.

Do you disagree with this?

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

For Bell: That assumption (also along with locality, explicitly assumed) is necessary to arrive at the contradiction - see after Bell's (14) where we now have the 3 angles a, b and c in one equation simultaneously. (There were only 2 in the EPR program.) As with EPR, if either locality or realism are bad assumptions, then there is no contradiction. Because Bell extended the idea of realism from 2 (in EPR) to 3 simultaneous values, he was able to latch on to a tiebreaker in the debate.

 

[lugita15]

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

For Bell: That assumption (also along with locality, explicitly assumed) is necessary to arrive at the contradiction - see after Bell's (14) where we now have the 3 angles a, b and c in one equation simultaneously. (There were only 2 in the EPR program.) As with EPR, if either locality or realism are bad assumptions, then there is no contradiction. Because Bell extended the idea of realism from 2 (in EPR) to 3 simultaneous values, he was able to latch on to a tiebreaker in the debate.

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

 

[ttn]

It is the word "simultaneous" that is at issue here. So I agree with your 1 and 2. Certainly EPR *assume* that this is reasonable, as they explicitly said this is part of any reasonable definition of reality. Which is my entire point. A reasonable definition of reality (let's call that realism) requires you to assume your 2. Since it can never be proven, it must be assumed to make the EPR and Bell programs work.

For EPR: That assumption (along with locality) led them to their final conclusion that QM is incomplete and a greater specification of the system is possible (i.e. because you have the values of 2 non-commuting observables). Since I don't believe that a greater specification is possible, I call their assumption into question. However, that is just an opinion, and so there were 2 camps after EPR: those that followed EPR and those that followed Bohr on this particular matter.

http://www.scholarpedia.org/article/Bell%27s_theorem#Some_controversy_regarding_the_EPR_argument

 

[ttn]

OK, we're on the same page. So what ttn needs to understand is that for a given photon pair, Bell's argument involves meaningfully discussing not only the two polarization attributes that are measured but also a third polarization attribute that is unmeasured but that could have been measured had the experimenter chosen to. In other words, the argument assumes counterfactual definiteness.

No, it doesn't. The confusion giving rise to the impression that it does is called positivism -- i.e., the insistence that everything we're ever talking about has to be entirely reducible to directly measureable things.

But in fact the whole argument is about *candidate theories* and what predictions they make in various situations. There is nothing at all like "counter-factual definiteness" assumed in saying, e.g.: consider candidate theory A; in situation 1 it predicts such-and-such; in situation 2 it predicts thus-and-so; and so on. That is the structure of the argument. It's about what a theory predicts when various different things are measured. The question of whether some outcome of some experiment "really exists" even when that experiment isn't actually performed, is a completely and total philosophical red herring. Strictly speaking, this all means that, at the end of the day, the conclusions is that *no local theory can explain the quantum predictions*. So maybe there is some wiggle room if, for example, you think that you can explain the quantum predictions in a local way without using a theory, or some such thing. Good luck with that.

 

[ttn]

ttn, would it be possible for you (or anyone else) to scan "La Nouvelle Cuisine" for those of us who don't have Bell's book handy?

Sorry, no, I'm not comfortable doing that. This paper of mine quotes *extensively* from "la nouvelle cuisine", though, so maybe you could look at this if for some reason you really can't get a copy of Bell's book (2nd edition).

http://arxiv.org/abs/0707.0401