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

nanosiborg

Ok. Thanks.

And my point is that nonlocality in nature doesn't necessarily follow from the generalized nonviability of the locality condition.

Well, no to both statements. The point is that every possible local theory can disagree with experiment in an exclusively local universe if the general locality condition is encoding something (in addition to locality) that's necessarily incompatible with the experimental designs of Bell tests but which has nothing to do with locality.

I take Bell's formulation as general, and assume that the QM treatment of quantum entanglement will always agree with experiment. So, insofar as Bell locality and QM have been mathematically proven to be incompatible, then there's no possible viable local theory of quantum entanglement.

But consider that Bell tests are designed to produce statistical dependence by the entanglement creation process (eg., common emitter, interaction of the particles, common 'zapping' of separated particles, etc.) and the data pairing process, both of which proceed along exclusively local channels.

Then consider that the locality condition codifies statistical independence. I'm just wondering if there's anything significant enough about that inconsistency so that it, and not nonlocality, might be the effective cause of the inconsistency between local theories and experiment.

ttn

True. That's also, for example, what Jarrett thought. But... I can't understand what exactly you are proposing this "extra illicit something" to *be*. If you have something definite in mind, I would enjoy hearing about it. Probably it will turn out that you haven't really fully understood Bell's locality condition (as Jarrett didn't when he made similar charges) and that actually whatever you have in mind is not at all smuggled in. But who knows, maybe you're right.

On the other hand, if you don't have anything definite in mind -- if it's just "well what if there's some illicit assumption smuggled in there? prove that there isn't such a thing!" -- then that would be quite silly and would certainly leave nothing to discuss.


If the claim is that there is some extra illicit assumption built into Bell's definition of locality, I don't see how you think it helps to bring up the experiments. Shouldn't you be talking about the mathematical proof of Bell's theorem, and arguing that there is an assumption in the theorem other than (genuine) locality?


I don't understand what you think you mean by that. What the locality condition codifies is ... locality. It certainly does *not* just say: A and B should be statistically independent. If you think that is the locality condition, you need to actually read Bell and understand what he did before you start criticizing him.

nanosiborg

Just an intuited possibility of something ('statistical' independence) that's sort of hidden by the causal independence (locality) that's codified in the locality condition, and that might be inconsistent with the experimental designs to a significant enough extent that it would be considered the effective cause of the inconsistency between local theories and experiment.

I'll agree that at this point the former seems much more likely than the latter.

I agree. Certainly no disproof is required of what I'm suggesting, rather vaguely, might be the case. It's along the lines of, I have this vague notion, help me explore it if you think there's any possibility that there might be something to it. You've indicated that you don't, and the more I get into it the more I think you're probably right. But I'd like to at least get to the point where I have a clearly formulated hypothesis instead of just a vague notion.

The mathematical proof only tells us that the locality condition is incompatible with QM. The possible incompatibility of the suggested extra illicit (and less visible) assumption can only be demonstrated when evaluated in relation to experimental design.

I just left out, "in addition to codifying locality (ie., causal independence)", which I thought was understood. Certainly the locality condition doesn't only codify statistical dependence. Part of what I'm wondering is if it codifies statistical independence. Or, in other words, does the locality condition only codify locality (causal independence)?

If the locality condition codifies statistical independence in addition to codifying locality, then the question becomes: is the inconsistency between the statistical independence codified by the locality condition and the statistical dependency necessitated by the experimental design significant enough that this inconsistency is the effective cause of the inconsistency between the predictions of models incorporating the locality condition and experimental results? .

Nugatory

I think this is a restatement of the detection and fair-selection "loopholes"...?

That doesn't make it ipso facto wrong, just gives us a starting point for considering whether, in any given experiment, the experiment might not completely preclude locality.

nanosiborg

If that's all it is, then I agree with T. Norsen that there's nothing there. But I think it's a different consideration than these loopholes, which have been more or less covered in more recent experiments, haven't they? Anyway, we're assuming that the applicable assumptions in the QM approach regarding the various usual experimental loopholes are correct and adequate so that when all the usual experimental loopholes are covered then the results will still be in agreement with QM predictions.

ttn

The mathematical proof tells us that the locality condition is incompatible with the *empirical predictions* of QM. QM, the theory, actually plays zero role whatever in Bell's argument. Or put it this way, it plays exactly the same role that the dBB pilot-wave theory plays. Here's what I mean. Bell formulates a careful definition of locality, and shows on its basis that local theories will always make predictions in accord with the inequality. OK, so now experimentalists go and do the tests and they find that the inequality is empirically violated. So locality is refuted. That's it. Now if you want you can also say: the theory called "QM" makes predictions that violate the inequality, which evidently shows that it must be a nonlocal theory and indeed, if you just look at the theory and test it against Bell's definition of locality, indeed, it's nonlocal. And the same is true for the pilot wave theory, the GRW theory, and all other empirically viable extant theories. But the point is that we never had to say anything -- or even *think* about -- any particular candidate theory in the course of proving that nature is nonlocal.


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, then there's a sense in which Bell's conditions does just assert statistical independence. Many people over the years have rejected Bell's conclusion on the grounds that, they say, it doesn't rule out *nonlocality*, it just rules out *nonlocal correlations* -- and, they say, two distant events can be *correlated* without one of them causally influencing the other. That's of course true, but such people fail to appreciate the special conditions that Bell described (e.g., that we completely specify the goings-on in the past light cone of one of the events, in a region with a certain special relationship to the other distant event, etc.) under which, actually, "statistical dependence" *does* necessarily require nonlocal causation. I always refer such people to Bell's last (and I think on this subject, best) paper, "la nouvelle cuisine", where he takes as an explicit theme the idea of needing to carefully distinguish causal connections from mere statistical correlations. To whatever extent this is what you're thinking, you would probably benefit from reading that paper too.

ttn

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.)

bohm2

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:
Quantum nonlocality: How does Nature perform the trick?
http://lanl.arxiv.org/pdf/0912.1475.pdf
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:
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:
Emergent spacetime and Empirical (In)coherence
http://arxiv.org/pdf/1206.6290.pdf

ttn

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.

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?

nanosiborg

Yes.

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.

ttn

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.

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


They've *assumed* that??!? That's the whole content of the theorem!


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.



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.

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:
Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

nanosiborg

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.

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.

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.

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.

Maui

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.

ttn

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.


Hogwash. Aspect's experiment (and other more recent and better versions of the same thing) experimentally prove that nature is nonlocal. They falsify locality.



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.



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.