View Poll Results: What do observed violation of Bell's inequality tell us about nature? Nature is non-local 11 32.35% Anti-realism (quantum measurement results do not pre-exist) 15 44.12% Other: Superdeterminism, backward causation, many worlds, etc. 8 23.53% Voters: 34. You may not vote on this poll

# What do violations of Bell's inequalities tell us about nature?

by bohm2
Tags: bell, inequalities, nature, violations
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P: 733
 Quote by Nugatory I think this is a restatement of the detection and fair-selection "loopholes"...?
That's kind of what I was thinking when I suggested earlier that he was doubting the "no conspiracy" assumption. (Although, really, the "no conspiracies" assumption that is used in the proof of the theorem, is not exactly the same thing as the fair-sampling assumption that experimentalists use when they interpret their data as violating the inequality. They're related, though.)
PF Gold
P: 675
 Quote by Maui The point is not why there could potentially be non-locality but why there is locality.
I'm not very knowledgeable about the various quantum theories of gravity but a number of them try to do away with spacetime. And some physicists, like Gisin, who are convinced that violation of Bell's implies that nature is non-local, further argue that nonlocal quantum correlations would appear to emerge, from "outside" space-time:
 To put the tension in other words: no story in space-time can tell us how nonlocal correlations happen, hence nonlocal quantum correlations seem to emerge, somehow, from outside space-time.
Quantum nonlocality: How does Nature perform the trick?
http://lanl.arxiv.org/pdf/0912.1475.pdf
 If so, whatever causes entanglement does not travel from one place to the other; the category of “place” simply isn't meaningful to it. It might be said to lie *beyond* spacetime. Two particles that are half a world apart are, in some deeper sense, right on top of each other. If some level of reality underlies quantum mechanics, that level must be non-spatial.
How Quantum Entanglement Transcends Space and Time
http://www.fqxi.org/community/forum/topic/994?search=1

But since only entities localized in spacetime can ever be observed, it's not clear if "progress" can be made on this issue which kind of hi-lites Einstein's concerns; nevertheless, I found these 2 questions/problems discussed in the paper below very interesting and would support what you are suggesting:
 ...we define a theory to be empirically incoherent in case the truth of the theory undermines our empirical justification for believing it to be true. Thus, goes the worry, if a theory rejects the fundamental existence of spacetime, it is threatened with empirical incoherence because it entails that there are, fundamentally, no local beables situated in spacetime; but since any observations are of local beables, doesn't it then follow that none of our supposed observations are anything of the kind? The only escape would be if spacetime were in some way derived or (to use the term in a very general sense, as physicists do) 'emergent' from the theory. But the problem is that without fundamental spacetime, it is very hard to see how familiar space and time and the attendant notion of locality could emerge in some way...at least without some concrete proposals on the table.
Maudlin quoted in that paper also makes this point which the author refers to and ultimately criticizes (e.g. the bolded part) as Maudlin's challenge:
 But one might also try instead to derive a physical structure with the form of local beables from a basic ontology that does not postulate them. This would allow the theory to make contact with evidence still at the level of local beables, but would also insist that, at a fundamental level, the local structure is not itself primitive...This approach turns critically on what such a derivation of something isomorphic to local structure would look like, where the derived structure deserves to be regarded as physically salient (rather than merely mathematically definable). Until we know how to identify physically serious derivative structure, it is not clear how to implement this strategy.
Emergent spacetime and Empirical (In)coherence
http://arxiv.org/pdf/1206.6290.pdf
 P: 733 Before this thread goes quietly into the night, I would just like to point out one last time that -- despite the fact that "anti-realism" won the poll by a large margin -- not a single person has been willing to answer my challenge. Here it is one last time in case anybody missed it... Bell's inequality, as everybody knows, is a constraint on the correlations that can be exhibited between the outcomes of spin measurements on pairs of entangled particles, as the alignments of the measuring devices are changed. In principle, to be empirically viable, a theory needs to be able to make the correct predictions for the statistics that will be observed for *all possible* alignments. But for the sake of discussion, let us focus here on a very small and simple subset -- namely, just the case where both Alice and Bob measure the spins of their particles along the z-direction. Clearly, to be empirically viable, i.e., to be able to make the right predictions for *all possible* measurements, a theory will have to at least make the right predictions for this particular case. As it turns out, experiment tells us that, in this case, there is a perfect (anti-) correlation of outcomes: whenever Alice's particle goes up, Bob's goes down, and vice versa. So here is the challenge. People who answered "anti-realism" in the poll evidently believe that there exists a theory that is (a) local and (b) non-realist and which is empirically viable. As noted, this theory must surely be able to explain what is empirically observed in the special case of parallel measurements, if it is really empirically viable. So... what theory is this? Explain how the perfectly anti-correlated outcomes (in just this case where Alice and Bob both measure along the z-direction) can be accounted for in a local but non-realistic model. Or, if you can't do that, please have the dignity to retract your vote. Thank you very much.
 P: 724 ttn, you make it sound like this is the first time that a classical explanation for a quantum phenomenon appears inadequate and incoherent. Of course, this is not the case - classical intuition is the number one barrier, you could raise the same newtonian objections towards the uncertainty principle for instance and the people voting anti-realism are merely acknowledging the reality of observations. Quite a number of experiements have been performed that prove that quantum particles do not have fixed properties at all times, as you would expect classically. I do not understand why a quantum physicist would ever go on a rampage about something as undefensible as realism in quantum physics unless he wanted to turn known physics upside-down. Do you?
P: 79
 Quote by ttn Statistical dependence/independence of what? Maybe that's what I'm missing. If what you mean is: statistical in/dependence of the outcomes, A and B, on the two sides, ...
Yes.

 Quote by ttn ... then there's a sense in which Bell's condition does just assert statistical independence.
Yes, and I think this might be significant for the following reasons.

The only way to make explicit, to codify, the assumption of locality in a model of quantum entanglement is via the formal expression of statistical independence.

Bell inequalities are based on the correlational boundaries imposed by this formal constraint, which means that any and all 'explicitly local' theories of quantum entanglement can't possibly violate a Bell inequality.

Bell tests are designed to produce statistical dependence (via entirely local means), and
a model explicitly based on statistical independence would not be expected to reproduce all the results of experiments based on statistical dependence.

All of this is fine for Bell's main purpose, which was to see if local (hidden variable, but as we've seen HVs are superfluous) theories of quantum entanglement can be compatible with QM. Or, in other words, if QM could be interpreted locally -- and he proved that it can't be.

However, many people want to extend the applicability of Bell's theorem to say that it means that nature is nonlocal. Which means that statistical dependence of the sort designed into Bell tests is impossible in a local universe. But that doesn't seem reasonable to me, so I wondered where it came from.

Those who believe that Bell's theorem proves that nature is nonlocal have assumed that (via codifying locality as statistical independence) in a local universe, we should expect the angular dependence (the correlation observed experimentally) to be bounded such that it can never reproduce the Malus' Law angular dependence that's observed experimentally.

Prior to the adoption of statistical independence as being formally synonymous with the assumption of locality, the Malus' Law angular dependence is what would have been expected from Bell tests. Following the adoption of statistical independence as being formally synonymous with the assumption of locality, and applying this in models of experiments designed to produce statistical dependence via local means, it was expected that the angular dependence produced in Bell tests would not only not be Malus' Law but would in some cases even be linear -- an expectation that runs contradictory to known empirical optics laws.

In considering this, it seemed to me then that the oddity wasn't the angular dependencies produced in Bell tests, but the fact that Bell inequalities are based on angular dependency expectations that have no foundation in physics. In fact, their sole foundation is the application of models based on statistical independence to experiments based on statistical dependence.

So, there seems to me to be a basic problem with extending the meaning of Bell's theorem to encompass nature. What Bell's theorem does, and the only thing it does (as far as I can tell), is definitively rule out local theories of quantum entanglement (a nonetheless monumental result).

And here I'll restate my position regarding bohm2's poll. Violations of Bell inequalities tell us nothing about nature.
P: 733
 Quote by Maui ttn, you make it sound like this is the first time that a classical explanation for a quantum phenomenon appears inadequate and incoherent. Of course, this is not the case - classical intuition is the number one barrier, you could raise the same newtonian objections towards the uncertainty principle for instance and the people voting anti-realism are merely acknowledging the reality of observations. Quite a number of experiements have been performed that prove that quantum particles do not have fixed properties at all times, as you would expect classically. I do not understand why a quantum physicist would ever go on a rampage about something as undefensible as realism in quantum physics unless he wanted to turn known physics upside-down. Do you?
Sure, I love turning stuff upside down. But what you say here doesn't seem relevant. The question (that the poll was about) was not: "is realism true?" It was rather "what do violations of Bell inequalities tell us about nature?" So saying that there is all kinds of evidence that realism is not true -- I agree, it isn't, at least with the silly meaning that people give to it here (namely, non-contextual hidden variables) -- is irrelevant. The point is that something *more* than this -- something *much more interesting than this* -- follows from the violations of Bell's inequality, namely: nonlocality.

Also, part of your comments above suggest that you misunderstood the challenge. I never said that people voting (b) should provide a "classical" (also local and non-realist) explanation of the perfect correlations. The explanation can be "quantum" (whatever that means exactly) or whatever flavor you like. It just has to be local.

Surely the reasoning here is clear? If somebody thinks we get to choose whether to reject realism or locality in the face of Bell inequality violations, and opts for rejecting realism, surely they believe that the empirical data can be explained locally. I'm just saying: put up or shut up. Show me a local non-realist way to explain the perfect correlations or retract your false vote. Simple.
P: 733
 Quote by nanosiborg The only way to make explicit, to codify, the assumption of locality in a model of quantum entanglement is via the formal expression of statistical independence.
No, there's a whole heck of a lot more to it than that. You should read "la nouvelle cuisine" or perhaps my paper on Bell's formulation:

http://arxiv.org/abs/0707.0401

 Those who believe that Bell's theorem proves that nature is nonlocal have assumed that (via codifying locality as statistical independence) in a local universe, we should expect the angular dependence (the correlation observed experimentally) to be bounded such that it can never reproduce the Malus' Law angular dependence that's observed experimentally.
They've *assumed* that??!? That's the whole content of the theorem!

 Prior to the adoption of statistical independence as being formally synonymous with the assumption of locality, the Malus' Law angular dependence is what would have been expected from Bell tests.
I don't see why. Malus' law has nothing to do with it. That law describes the fraction of photons passing through a polarizer at one angle, which then also pass through a subsequent polarizer at a different angle. It's the probability for a single photon to pass one polarizer, given that it's passed another. In the Bell tests there are two particles. Thinking that it's somehow just "obvious" that they should exhibit statistics that have something to do with Malus' law can only be a confusion.

 So, there seems to me to be a basic problem with extending the meaning of Bell's theorem to encompass nature. What Bell's theorem does, and the only thing it does (as far as I can tell), is definitively rule out local theories of quantum entanglement (a nonetheless monumental result). And here I'll restate my position regarding bohm2's poll. Violations of Bell inequalities tell us nothing about nature.
I find this bizarre. If we know that no local theory can be true, then the correct description of nature is nonlocal. If the true theory is a nonlocal theory, then nature is nonlocal. Yes, it's amazing that we can know that the true theory is a nonlocal theory without (yet) knowing what the true theory *is*. But, that is the situation. Saying that, yes, we know the true theory is nonlocal -- but we can't say anything about nature -- that's bizarre.
PF Gold
P: 675
 Quote by Maui I do not understand why a quantum physicist would ever go on a rampage about something as undefensible as realism in quantum physics unless he wanted to turn known physics upside-down.
Maybe I'm misunderstanding but ttn's argument doesn't have much to with realism. As I understand it, his basic argument with respect to violations of Bell's inequalities is the following:
 ...the role of Bell’s theorem is not to set constraints on how ‘realist’ we are allowed to be about quantum systems but rather, much more interestingly, to characterize a structural property of any theory that aims to cover the domain of validity covered so far by quantum mechanics, namely non-locality. As a consequence, whether a theory aiming to supersede quantum theory will be ‘realist’, ‘non-realist’, ‘half-realist’ or ‘one-third realist’, this will concern the further conceptual and formal resources of that theory and not at all the Bell theorem.
Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf
P: 79
 Quote by ttn No, there's a whole heck of a lot more to it than that. You should read "la nouvelle cuisine" or perhaps my paper on Bell's formulation: http://arxiv.org/abs/0707.0401
Yes, lots of details. But, for the argument I'm currently making, that's the essence of it. I will read those papers, thanks. Maybe they'll change my mind.

 Quote by ttn They've *assumed* that??!? That's the whole content of the theorem!
It's assumed that what explicitly local models predict is what should be expected in a local universe, ignoring the inconsistency of explicitly local models with experimental design, and what prior empirical optical results would lead us to reasonably expect the results of such tests to be.

 Quote by ttn I don't see why. Malus' law has nothing to do with it. That law describes the fraction of photons passing through a polarizer at one angle, which then also pass through a subsequent polarizer at a different angle. It's the probability for a single photon to pass one polarizer, given that it's passed another. In the Bell tests there are two particles. Thinking that it's somehow just "obvious" that they should exhibit statistics that have something to do with Malus' law can only be a confusion.
Or maybe it's a not so obvious insight. In Bell tests there are streams of photons, paired by time correlation and a relationship that's presumably produced through some common (local) emission process. What's recorded at both ends as rate of coincidental detection might be seen as analogous to the resulting intensity in Malus' Law setups involving crossed polarizers, and the angular dependence or correlation between rate of coincidental detection and θ seen as analogous (in the ideal) to the Malus' Law angular dependence. But, then again, maybe that's not a good analogy. As I said, I'm just exploring alternatives, because the interpretationally based theoretical 'inference' of nonlocality in nature from Bell test results seems to me to be on rather shaky grounds. Yes, the outcome independence of the locality condition seems to be the only way to make an explicitly local model of quantum entanglement, but it doesn't follow from that that nonlocal models of quantum entanglement are true and correct models of deep reality. The assumption that nature is nonlocal isn't a verifiable or falsifiable hypothesis, and, so far in my explorations, there are at least as many reasons to think that nature is exclusively local as there are to think it's nonlocal.

 Quote by ttn I find this bizarre. If we know that no local theory can be true, then the correct description of nature is nonlocal. If the true theory is a nonlocal theory, then nature is nonlocal. Yes, it's amazing that we can know that the true theory is a nonlocal theory without (yet) knowing what the true theory *is*. But, that is the situation. Saying that, yes, we know the true theory is nonlocal -- but we can't say anything about nature -- that's bizarre.
What we know is that experiments designed to produce statistical dependence can't be viably modeled by explicit statistical independence. We don't know that any theory is a true 'description' of deep reality. Strictly speaking QM is neither a local nor a nonlocal theory. It doesn't model quantum entanglement in terms of statistical independence and the fact that it takes into account the statistical dependency produced by the experimental designs doesn't make it a nonlocal theory, and anyway it's not designed to be a 'description' of what's happening in deep reality. Imho, it's quite bizarre to conjecture that nature is nonlocal from optical Bell test results, ignoring the inconsistency of explicitly local models with experimental design, and what prior empirical optical results would lead (at least some of) us to reasonably expect the results of such tests to be.

It seems we're at an impasse on this, so, for the moment, we can just agree to disagree. Of course I do agree with your opposition to the "2." ('anti-realism) votes and your clarification of the issue and (non)relevancy of 'realism'. I admire your contributions to your field.

I'm willing to conjecture, even bet on, that nothing that applied physics can actually use (ie., no physical faster than light anything) will ever come from the assumption of nonlocality in nature per se. The most parsimonious 'explanation' for this will remain simply that there's no 'nonlocality' in nature.
P: 724
 Quote by bohm2 Maybe I'm misunderstanding but ttn's argument doesn't have much to with realism. As I understand it, his basic argument with respect to violations of Bell's inequalities is the following: ...the role of Bell’s theorem is not to set constraints on how ‘realist’ we are allowed to be about quantum systems but rather, much more interestingly, to characterize a structural property of any theory that aims to cover the domain of validity covered so far by quantum mechanics, namely non-locality. As a consequence, whether a theory aiming to supersede quantum theory will be ‘realist’, ‘non-realist’, ‘half-realist’ or ‘one-third realist’, this will concern the further conceptual and formal resources of that theory and not at all the Bell theorem.

Bu we already know that non-contextual chairs and table do not exist according to quantum mechanics, so realism as is usually(naively) defined is broken at the level of atoms and electrons. Given that, who needs additional magic like non-locality at all costs and what does explain better? He has no qm explanation for the reality of chairs and tables that matches both the postulates of qm and our experience of them, so adding non-locality brings nothing substantial. Though it seems obvious that if realism fails, so does locality and nonlocality is implied by the consistence of the classical world and in the end both will be found to be incorrect and incompatible with qm.
P: 733
 Quote by nanosiborg It's assumed that what explicitly local models predict is what should be expected in a local universe, ignoring the inconsistency of explicitly local models with experimental design, and what prior empirical optical results would lead us to reasonably expect the results of such tests to be.
This idea that you keep repeating -- that there is some inconsistency between the theorem and the "experimental design" that makes it improper for us to conclude anything from the experiments -- really makes no sense to me. What you're saying strikes me as just like the following silly scenario. Suppose everybody still thought the world was flat, but somebody figured out that if you designed a rocket and flew up to a very great altitude and looked down and took a picture of the earth, you could really see what shape it is. OK, so they decide to build the rocket and perform the experiment, even though everybody expects that, when they get up there, they'll just see the flat earth stretching off forever in all directions. Then they run the experiment, take the picture, and -- lo and behold! -- it is immediately obvious that, actually, the earth is round! Everyone is shocked and surprised!

But then nanosiborg comes along and says: not so fast. There is an inconsistency between the assumption that everybody held (namely that the earth was flat) and the "experimental design" (meaning that the experiment actually shows that the earth is round). This inconsistency (which I guess is just the fact that there is a conflict between what many people *expected* and what the experiment actually *showed*) means that actually we cannot conclude from the experiment that the earth is round. The most we can say is that theories according to which the earth is flat are no longer viable. But this tells us nothing about nature.

Tell me how what you're saying isn't just parallel to that (I think, manifestly absurd) response to the hypothetical scenario.

 The assumption that nature is nonlocal isn't a verifiable or falsifiable hypothesis
Hogwash. Aspect's experiment (and other more recent and better versions of the same thing) experimentally prove that nature is nonlocal. They falsify locality.

 Strictly speaking QM is neither a local nor a nonlocal theory.
Hogwash. QM is a nonlocal theory, at least by the best definition of locality that we have going -- namely, Bell's as presented in "la nouvelle cuisine". You have a better/different formulation of "locality" to propose? I'm all ears. Or you think there's some flaw in Bell's formulation? I'm all ears.

 I'm willing to conjecture, even bet on, that nothing that applied physics can actually use (ie., no physical faster than light anything) will ever come from the assumption of nonlocality in nature per se. The most parsimonious 'explanation' for this will remain simply that there's no 'nonlocality' in nature.
Quantum teleportation?

Anyway, read the papers I mentioned. It's clear (to me at least) that you are clinging to loopholes that don't in fact exist, because you don't yet fully appreciate what Bell did. You need to study his work carefully before you take a strong position on whether he screwed up or not.
 P: 129 ttn: here is the paper by Wallace where he describes some of the ideas regarding ontology: http://arxiv.org/abs/1111.2189
P: 733
 Quote by Maui ... who needs additional magic like non-locality at all costs and what does explain better?
What non-locality explains better is the results of the Aspect (-type) experiments. The data from these experiments cannot be explained by any local theory. That is what Bell proved.

Don't agree? Then please please please address the challenge I keep posting: tell me how to explain even just the one simple subset of the data (namely, that there are perfect correlations when Alice and Bob measure along the same axis)

(You I think mean to be pointing out that we already know that "realism" is false. Presumably you are thinking of the Kochen-Specker and other similar "no-hidden-variable" theorems. I agree. Realism in that sense is already known to be false. But as bohm2 has explained, this is just a red herring here. To say that Bell's theorem does not prove nonlocality because we already know that realism is false, is like saying that the earth doesn't go around the sun because we already know the earth is round. It is just a total non-sequitur. It is possible to know more than one thing, so discovering X does not in any way preclude or automatically refute a purported later proof of Y.)

 Though it seems obvious that if realism fails, so does locality and nonlocality is implied by the consistence of the classical world and in the end both will be found to be incorrect and incompatible with qm.
So you agree that no local theory is consistent with experimental data? I can't exactly follow the comments here.
P: 733
 Quote by Quantumental ttn: here is the paper by Wallace where he describes some of the ideas regarding ontology: http://arxiv.org/abs/1111.2189
Thanks. I actually just ordered his book and am looking forward to reading it, but I'll check this out too.
P: 3,184
 Quote by ttn [..] Tell me how what you're saying isn't just parallel to that (I think, manifestly absurd) response to the hypothetical scenario.
Not sure what he means, but it doesn't seem fair to give him/her the disadvantage of the doubt; fair would be to give him/her the advantage of the doubt. For example, it could be more similar to MMX type experiments: contrary to the generalizing nonsense that one sometimes reads about it those merely disproved a specific set of hypotheses that was put to the test.
 [..] QM is a nonlocal theory, at least by the best definition of locality that we have going -- namely, Bell's as presented in "la nouvelle cuisine". You have a better/different formulation of "locality" to propose? I'm all ears. Or you think there's some flaw in Bell's formulation? I'm all ears. [..]
See the recent discussion here:
http://physicsforums.com/showthread.php?p=4236787
Thus, apparently Bell implied with "realism" that it "is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out."
IMHO that fundamentally disagrees with QM while it is not required for the concept of physical reality, as an electron could be extended as a wave without having a precise, single position. That it should have such a position is an unrealistic definition of "realism" as it only corresponds to a specific subset of models of reality.
P: 733
 See the recent discussion here: http://physicsforums.com/showthread.php?p=4236787 Thus, apparently Bell implied with "realism" that it "is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out." IMHO that fundamentally disagrees with QM while it is not required for the concept of physical reality, as an electron could be extended as a wave without having a precise, single position. That it should have such a position is an unrealistic definition of "realism" as it only corresponds to a specific subset of models of reality.
What part of that thread is supposed to be relevant? I mean, obviously, there are similar issues being discussed, but I don't know what specifically you meant to be pointing to.

I don't understand your sentence starting "Thus, apparently Bell implied..." Who are you quoting there? I'm pretty sure that isn't a statement of Bell's! Indeed, I don't recall Bell ever talking about "realism". The whole idea that "realism" is somehow relevant to Bell's theorem is an invention of the people who haven't actually studied/understood Bell.

I think I agree with your last couple of sentences, but again isn't the point just that "realism" is used to mean a number of rather different things, so people should be careful to define exactly what they mean whenever they use the term? For example, if the goal is to have what is sometimes described as a "realist interpretation of QM" -- that is, some kind of good old-fashioned style physics theory that makes postulates about what kind of stuff exists and how it acts (rather than, e.g., operationalist-style postulates about laboratory procedures) -- then, no doubt, it would be ridiculous to demand from the outset that electrons must have definite sharp positions at all times. Maybe it will turn out that electrons are like little fuzzy clouds, or like groups of ripples on a pond. Such models would be perfectly "realist" in this sense and certainly shouldn't be ruled out a priori at the outset. I think that was your point, and I totally agree.

But I think people who voted for "anti-realism" in the poll did *not* mean that *this* sort of "realism" is refuted by Bell's theorem. They meant instead the idea that there should exist deterministic non-contextual hidden variables for all (?) "observables" recognized by QM. They are correct that this other sort of "realism" is indeed false, but they are wrong to think that this is the lesson of Bell's theorem. We already knew this realism was wrong, from von Neumann, Kochen-Specker, etc. Bell taught something new, something that has nothing to do with realism.

Anybody who disagrees should explain how to account for the perfect correlations in a local but non-realist way. (Everybody knows you can explain the perfect correlations in a local way *with* this deterministic non-contextual HV sense of "realism". But then everybody also knows that you can't explain the *rest* of the QM predictions with that kind of theory. The question is whether the QM predictions can be accounted for by a theory that is local but non-realist. The challenge is to show that such a model can even account for the perfect correlations subset of the QM predictions. No takers so far, unfortunately.)
P: 141
 Quote by ttn QM is a nonlocal theory, at least by the best definition of locality that we have going -- namely, Bell's as presented in "la nouvelle cuisine". You have a better/different formulation of "locality" to propose? I'm all ears. Or you think there's some flaw in Bell's formulation? I'm all ears.
Bell's definition of "locality" just can't be applied to every possible theory of nature, because it assumes that nature can always be described by classical probabilities of the form $p(a,b,\lambda)$, where $\lambda$ are some unknown parameters. This requirement isn't fulfilled in quantum mechanics, so this definition of locality can't be applied to it in the first place. Quantum mechanics neglects the existence of functions $p(a,b,\lambda)$ entirely. It only predicts functions of the type $p(a,b)$. So it isn't even possible to decide whether QM is Bell-local or not. In other words: Bells definition of locality isn't general enough to cover all possible theories of nature (including QM) and thus isn't a useful criterion to classify theories at all.

A useful criterion to classify "locality" that covers both QM and classical probability theories is this: A theory is local if an event in one region of spacetime can't influence the experimental outcomes of an experiment in a spacelike separeted region.

In that sense, QM predictions can be explained by completely local quantum theories. Of course non-relativistic QM doesn't count, but relativistic theories like Wightman QFT's can explain the predictions. Locality is even an axiom there.

If you worry about the nonlocal correlations of QM, let's make a simple gedankenexperiment:

You have a green ball and a red ball and put them in two identical boxes. You send these boxes to two different people. These people know that you started with a green and a red ball. So the probability to get green/red is 1/2. When person 1 opens his box, he will get a definite result. Let's say he gets red. Then he knows immediately that person 2 has the green ball in his box, even if that box hasn't been opened yet. This is definitely a nonlocal correlation, but nobody would consider this as an action at a distance.

Up to now, this isn't quantum mechanics yet. But let's do the same experiment with qubits instead of bits. Instead of green and red balls, we put particles with spin into these boxes. We create 2 particled with orthogonal spin states, put them in the boxes and repeat the same experiment. Of course we get nonlocal correlations again, because we separated two particles that were created with correlation locally.

So all the weirdness concerning "nonlocality" is gone and what remains is the standard QM weirdness about the existence of superpositions of states.
P: 3,184
 Quote by ttn What part of that thread is supposed to be relevant? I mean, obviously, there are similar issues being discussed, but I don't know what specifically you meant to be pointing to. I don't understand your sentence starting "Thus, apparently Bell implied..." Who are you quoting there? [..]
That post (not that thread) refers to the clarification by DrChinese in post #49 there that Bell imposes the requirement to realism of post #48 that was brought up in the discussion and which for your convenience I also cited here. As discussed there, Bell didn't make that sufficiently clear.
 Indeed, I don't recall Bell ever talking about "realism". The whole idea that "realism" is somehow relevant to Bell's theorem is an invention of the people who haven't actually studied/understood Bell.
In view of those remarks of yours, DrChinese's clarification there as well as Bell's paper "Bertlmann's socks and the nature of reality" will be interesting for you.
 if the goal is to have what is sometimes described as a "realist interpretation of QM" -- that is, some kind of good old-fashioned style physics theory that makes postulates about what kind of stuff exists and how it acts (rather than, e.g., operationalist-style postulates about laboratory procedures) -- then, no doubt, it would be ridiculous to demand from the outset that electrons must have definite sharp positions at all times. Maybe it will turn out that electrons are like little fuzzy clouds, or like groups of ripples on a pond. Such models would be perfectly "realist" in this sense and certainly shouldn't be ruled out a priori at the outset. I think that was your point, and I totally agree. But I think people who voted for "anti-realism" in the poll did *not* mean that *this* sort of "realism" is refuted by Bell's theorem. They meant instead the idea that there should exist deterministic non-contextual hidden variables for all (?) "observables" recognized by QM. They are correct that this other sort of "realism" is indeed false, but they are wrong to think that this is the lesson of Bell's theorem. We already knew this realism was wrong, from von Neumann, Kochen-Specker, etc. Bell taught something new, something that has nothing to do with realism.
The issue that recently came up in the linked thread is that those two things are perhaps not unrelated; and in the abovementioned discourse Bell himself highlighted that his theorem has much to do with a certain "realism". Even, as it turns out, "counterfactual" realism. I don't know if it makes a difference but for the moment I'm not convinced about anything.
 Anybody who disagrees should explain how to account for the perfect correlations in a local but non-realist way. [..]
Suppose I don't know how a TV works but that I can believe that TV could work. Now you say that therefore I should believe that TV cannot work? That doesn't make any sense to me. A puzzle is just a puzzle, not a conclusion.
 The question is whether the QM predictions can be accounted for by a theory that is local but non-realist. The challenge is to show that such a model can even account for the perfect correlations subset of the QM predictions. No takers so far, unfortunately.)
Apparently Neumaier is a taker for a realistic explanation that you call "non-realist" (post #53 there), but not yet ready to deliver. I'm an interested onlooker.

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