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

nanosiborg

So, what can be inferred from the predictability of distant correlations? Can it be said, for example, that there has been an invariant relationship between entangled particles created through the entangling process, ie., through common source, interaction, common motion imparted to particles that don't have a common source and have never interacted, etc.? If so, does this seem weird? It doesn't to me, and the fact that the totality of results of optical Bell tests are in line with the conservation laws and optics principles further supports that view.

stevendaryl

Yes.

My general feeling is that if you don't find quantum mechanics weird, you haven't thought about it enough. Conservation laws don't by themselves explain the correlations.

Think about the following situation: You prepare an electron with spin-up along some axis [itex]\vec{S}[/itex]. Then later you measure its spin along a different axis [itex]\vec{A}[/itex]. Then the result will be non-deterministic: with a certain probability, the electron will be found afterwards to have spin-up in the [itex]\vec{A}[/itex] direction, and with a certain probability, it will be spin-down. In either case, the angular momentum of the electron was changed by the measurement: its final angular momentum is not the same as its initial angular momentum. That isn't a violation of conservation of angular momentum, because you can attribute the change to the interaction between the detector and particle. The angular momentum of the particle changes, and the angular momentum of the detector changes in a complementary way, so that the total angular momentum is unchanged by the detection process. But note that there is a small amount of angular momentum, [itex]\delta \vec{L}[/itex] transferred from the electron to the detector.

Now, if that electron happened to have come from an EPR twin-pair experiment, then each of the two detectors can be expected to receive a tiny amount of angular momentum from whichever particle is detected. But in the case of perfectly aligned detectors, we know that the [itex]\delta \vec{L_1}[/itex] received by one detector must exactly correlate with the [itex]\delta \vec{L_2}[/itex] received by the other detector, so that the resulting spins of the twin particles are perfectly anti-correlated.

So the perfect anti-correlation is not simply a matter of conservation of angular momentum. Angular momentum would be conserved whether or not the twin particles are found to be anti-correlated--it's just that different amounts of angular momentum would be transferred to the detectors. The perfect anti-correlation of twin pairs is a matter of cooperation between nondeterministic processes involving distant macroscopic objects (the detectors).

bohm2

That's where the disagreement is with those who contend that Bell's formulation does not make those further assumptions, like hidden-variables, realism, etc. As one example of such authors making those arguments consider Norsen:
Norsen also discusses why Bell felt that his theorem does tell us something about nature:
Local Causality and Completeness: Bell vs. Jarrett
http://arxiv.org/pdf/0808.2178v1.pdf

With respect to a discussion of Bell's concept of local causality see this paper with this interesting quote:
J.S. Bell’s Concept of Local Causality
http://arxiv.org/pdf/0707.0401.pdf

morrobay

Pages 9 &10 of the Bell vs Jarrett paper are about the completeness of λ .
And from both these papers it seems that Bell presupposes that completeness holds.
While at the same time Bell limits and qualifies completeness of λ to properties of
candidate theories. So this is a conflict on completeness. And I cannot agree that because
no local casual theory agrees with experiment that nature is nonlocal, conclusion.
Rather it is that the description of λ the hidden variable that is not complete .
And when it is the violations of the inequalities can be understood.
And I voted to reject realism, in its limited definition

ttn

Hi folks. I voted for "non-locality". And so, incidentally, did Bell -- though, being dead, he is unable to vote in this particular poll. But here are his words (from the classic paper "Bertlmann's socks and the nature of reality"):

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other."

For the convenience of the people who are confused here (i.e., the people who voted that we should conclude, from Bell's theorem, that "realism" is wrong) I have bolded the relevant part of the argument above. Note that it is just the EPR argument. The point is that "realism" just means the existence of variables which determine, in advance, what the result on each side will be. What Bell points out here -- and what EPR already pointed out long ago -- is that such variables are (i.e., "realism" is) the *only* way to account *locally* for the perfect correlations that are observed "whenever the analyzers happen to be parallel". So the idea that we can still account for the QM predictions with a model that respects locality but denies "realism" is simply wrong. It will not, does not, and can not work.

Still don't agree? Still think that one can have a local explanation of even this small subset of the quantum predictions -- namely, the perfect correlations that are observed "whenever the analyzers happen to be parallel"? Let's see the model. (Note: the model should also respect the "free choice" aka "no conspiracies" assumption, if it is to be taken seriously.)

This is a serious challenge. Anybody who voted for (b) in the poll evidently thinks (or at least is unwittingly committed to thinking) that these perfect correlations can be explained by a local, non-realist model. Let's see it.

nanosiborg

@ bohm2, re your post #38

I agree with Norsen, and Bell, that it's Bell's locality condition that causes Bell's LHV formulation to be incompatible with QM and experiments, and that realism (hidden variable models) is not ruled out. Bell locality is necessarily realistic, but a realistic model need not be Bell local. We know from deBB that realism isn't ruled out. Which leaves only locality.

I disagree with Norsen, and Bell, that violations of Bell's inequalities tells us anything about nature. I think that the incompatibility with QM and experiment is determined by some feature of Bell's locality condition other than the assumption of locality.

nanosiborg

Do you find it weird that particles which have interacted or have a common source are measurably related? Or is it weird that the quantum correlations can only be approximated by classical preparations (and only approximately described by classical LHV models)? I suppose it's the latter. But is the creation of invariant relationships between and among particles, by the means described, beyond any sort of classical comprehension (ie., weird), or is it, as I suggested in an earlier post, just a matter of degree?

Some of the interpretations of QM are weird, but I don't think of standard QM as weird. Is it possible that those who find QM weird haven't thought about it enough?

On the other hand, some quantum phenomena (the physical, instrumental stuff, not the theory) do seem weird, but I wouldn't include entanglement correlations in there.

I agree, and I didn't say they do. But the conservation laws plus the applicable optics laws plus the repeatability of the preparations and the correlations don't seem so weird. The correlations are quite unsurprising when all those things are taken into consideration.

[... snip nice discussion ...]

OK.

As you said in your discussion, it's the individual results that are nondeterministic (ie., random). Because the correlations are predictable (and the unknown underlying processes therefore apparently repeatable) we can retain the assumption that the processes are deterministic.

So, I would change your last sentence to read: the perfect anti-correlation of paired (entangled) particles is a matter of a repeatable relationship between, and deterministic evolution of, certain motional properties of the entangled particles subsequent to their creation via a common source, their interaction, or their being altered by identical stimulii. Which doesn't seem weird to me.

ttn

I don't think that's right. Here's a model that non-realistic but perfectly Bell local: each particle has no definite, pre-existing, pre-scripted value for how the measurements will come out. Think of each particle as carrying a coin, which, upon encountering an SG device, it flips -- heads it goes "up", tails it goes "down". That is certainly not "realistic" (in the sense that people are using that term here) since there is no fact of the matter, prior to the measurement, about how a given particle will respond to the measurement; the outcome is "created on the fly", so to speak. And it's also perfectly local in the sense that what particle 1 ends up doing is in no way influenced by anything going on near particle 2, or vice versa. Of course, the model doesn't make the QM/empirical predictions. But it's non-realist and local. And hence a counter-example to any claim that being Bell local requires/implies being "realist".


I think you must be using "realism" in a different way than most other people. deBB is a hidden variable theory, to be sure, but it is *not* a hidden variable theory about spin! That is, there is no fact of the matter, in deBB, about how a given particle will respond to a measurement of some component of its spin. This is sometimes described by saying that, for deBB, spin is a "contextual" property. It would be more accurate, though, to say that, in deBB, the particles simply do not have any such property as spin.


I would be very interested to hear precisely what you have in mind. Have you carefully studied Bell's paper "la nouvelle cuisine" (where he is most explicit about how "locality" is formulated)? If you think the very formulation of "locality" smuggles in some other requirement, I want to know exactly what and how.

stevendaryl

As I thought I said, but maybe I just thought it it's certainly not weird that particles with a common history could share state information. For example, two people could agree on some random number, and then separate to large distances. Then there would be a nonlocal correlation due to shared state information from a common past.

It's weird that distant particles would be connected in any way other than shared state information.

Yes, I think it's weird.

I don't think you can separate entanglement from measurement. Or rather, entanglement is only weird to the extent that it implies nonlocal correlations between distant macroscopic measurements.

Are you saying anything different from: It's not weird, because it's predicted by quantum mechanics? Whether something is weird or not is a matter of taste, I suppose.

nanosiborg

I've been using 'hidden variable' to refer to any denotation (in a Bell test model) which refers to an underlying parameter which contributes to the determination of individual results. It doesn't have to include a pre-existing, pre-scripted value for how any specific measurement will come out. It's just included in the model to refer to any underlying parameter which contributes to the determination of individual results.

My understanding of Bell locality is that the denotation of Bell locality in a Bell test model requires some such hidden variable, whether the definition of that hidden variable includes a denotation about precisely how the hidden variable affects individual detection or not.

In other words, I would consider your example to be realistic in the same sense that Bell's λ is realistic, and therefore not a counter-example to my statement.

As per my above, the particles don't have to have any property in particular. They're underlying entities (that presumably have some property or properties) that are denoted in the deBB model. As such, and as you note, deBB is a hidden variable theory, and thus, in my lexicon, a realistic theory. But, due to the nonmechanical (ie., nonlocal vis the quantum potential) aspects of the theory it's also not a Bell local theory. I think of standard QM as a nonrealistic theory that is also not a Bell local theory, although not nonlocal in exactly the same sense that deBB is deemed nonlocal.

I haven't studied "la nouvelle cuisine". I have read a few of Norsen's papers, including the one where he discusses Jarrett's parsing of Bell's locality condition. I'm inclined toward Jarrett's interpretation that Bell locality encodes the assumptions of statistical independence (that paired outcomes are statistically independent of each other) as well as the independence defined by the principle of local action (that the result at A is not dependent on the setting at b, and the result at B is not dependent on the setting at a).

Since Bell tests are prepared to produce outcome dependence, and since this does not necessarily inform regarding locality or nonlocality in nature, and since this might be the effective cause of the incompatibility between Bell LHVs and QM, and between Bell LHVs and experimental results, then violations of Bell inequalities don't inform regarding locality/nonlocality in nature.

There is another aspect to the form that Bell locality imposes on LHV models of quantum entanglement to consider. Any Bell LHV model of quantum entanglement must necessarily denote coincidental detection as a function of the product of the independent functions for individual detection at A and B. So the relevant underlying parameter determining coincidental detection is the same underlying parameter determining individual detection. I think the underlying parameter determining coincidental detection can be viewed as an invariant (per any specific run in any specific Bell test preparation) relationship between the motional properties of the entangled particles, and therefore a nonvariable underlying parameter. I'm not sure how to think about this. Is it significant? If so, how do we get from a randomly varying underlying parameter to a nonvarying underlying parameter?

nanosiborg

I agree. That (eg., nonlocally connected) would be weird. But I hope I've made it clear that I don't think the particles are connected in any way other than statistically through shared information imparted through local channels (common source, interaction, common 'zapping', etc.).

Ok, so I take it that you find the invariance of the relationship between entangled particles in any particular run of any particular Bell test to be weird. But why should that be weird?

Consider, for example, the polarization entangled photons created via atomic cascades. Entangled photons are assumed to be emitted from the same atom (albeit a different atom for each entangled pair). Is it surprising (weird) that their spins and therefore their polarizations would be related in a predictable way via the application of the law of conservation of angular momentum? Is it surprising that each entangled pair would be related in the same way? After all, the emission process is presumably the same for each pair, and the selection process is the same for each pair.

Ok, I agree with this, and since I don't think the correlations imply nonlocal connections between distant macroscopic measurements (because I think they can be understood in terms of related properties produced via local channels, and because the correlations are in line with empirically based optics laws involving the analysis of polarizations via crossed polarizers), then I don't view the correlations as being weird.

I think so. I'm saying that we can understand why QM predicts what it does in the case of Bell tests by referring to the applicable (eg., conservation and optics) classical laws which are preserved in the QM treatment.

I would say that it's a matter of interpretation, and that interpretation isn't solely a matter of taste.

ttn

Yes, OK. So then the point is just that "hidden variable theories" (like, e.g., deBB) need not be "realist theories".

It's not correct that Bell's formulation of locality (i.e., "Bell locality") assumes the existence of hidden variables. Maybe we're still not quite on the same page about what "hidden variables" means, because we're not on the same page about what "underlying" means in your formulation above. Usually the phrase "hidden variable" is used to mean some *extra* thing, beyond just the standard wave function of ordinary quantum theory, that is in the mix. So then, e.g., deBB is a hidden variable theory because it uses not only the wave function, but also the added "definite particle positions", to account for the results. In any case, though, the point is that "Bell locality" does not presuppose "realism" and it also does not presuppose "hidden variables". You can meaningfully ask whether ordinary QM (not a hidden variable theory!) respects or violates "Bell locality". (It violates it.)


OK, but then you're using the word "realistic" in a different way than (I think) most other people here do. I think most people use that word to mean that there are definite values pre-encoded in the particles somehow, such that there are meaningful answers to questions like: "What would the outcome had been if, instead of measuring along x, I had measured along y?"


I certainly agree that it makes sense to call deBB "realist" by some meanings of the word "realist". But it is important to understand that the theory is *not* "realist" in the narrow sense I explained above. Stepping back, that's what I wanted to point out here. The word "realism" is a slippery bugger. Different people use it to mean all kinds of different things, such that miscommunication and misunderstanding tends to be rampant.

Me too, though I'm not sure what the two "senses" of nonlocality here might be. They both violate "Bell locality". What other well-defined sense does anybody have in mind?


I'm this "norsen" guy, by the way. So, you know what I think of Jarrett already.


I can't follow this. Are you just repeating Jarrett's idea that "Bell locality" is actually the conjunction of two things, only one of which really deserves to be called "locality"? So then, from the mere fact that "Bell locality" is violated, we can't necessarily infer the (genuine) "locality" is violated? If that's it, you know I disagree, but if the "Bell vs. Jarrett" paper didn't convince you, nothing I can say here will either. =)

ttn

Would it directly answer the "challenge" I posted above (to explain the perfect correlations locally but without "realism")? If so, I don't see why you shouldn't be permitted to post it here. That's perfectly relevant to this thread.

Nugatory

If the heads/tails value of Norsen's coin is considered realistic before we've flipped it, I'm not sure what you'd consider not to be realistic. Could I ask for an example?

That's a trick question, of course. If you do come up with such an example I'll use it instead of Norsen's coin in his example to produce a local but not realistic model. If you can't, then I'll argue that something is wrong with your definition of realism because it includes everything.

nanosiborg

I'm using hidden variable theory and realistic theory interchangeably. So, any hidden variable theory is a realistic theory. Any theory which does not incorporate hidden variables is a nonrealistic theory.

If Bell locality doesn't require hidden variable representation, then how would Bell locality be formulated and incorporated into a model of a Bell test without the explicit denotation of a hidden variable, such as Bell's λ, that contributes to the determination of individual results?

Ok, you could write A(a) = ±1 and B(b) = ±1, but then your formulation has already deviated from one of the primary requirements of the exercise aimed at finding an answer to the suggestion that QM might be made a more complete theory, perhaps a more accurate (or at least a more heuristic) description of the physical reality with the addition of supplementary 'hidden' variables.

To further clarify how I'm using the terms underlying and hidden variable, underlying refers to the sub-instrumental 'quantum realm' where the evolution of the 'system' being instrumentally analyzed is assumed to be occuring. Hidden variable refers to unknown variable parameter(s) or property(ies) of the quantum system being instrumentally analyzed that are assumed to exist 'out there' in the 'quantum realm' in the pre-detection evolution of the system.

A hidden variable, such as Bell's λ, need not provide a meaningful answer to a question such as, "What would the outcome at A have been if, instead of the polarizer being set at 20° it had been set at 80°?", because λ can refer to any variable underlying parameter(s) or property(ies) of the system, or any collection thereof. The denotation of λ in the model acts as a placeholder for any unknown underlying parameter(s) or property(ies) which, together with the relevant instrumental variable(s), contribute to the determination of individual results. The hidden variable is needed in this way in order to explicitly denote that something in addition to the instrumental variable, something to do with the 'system' being analyzed, is determining the individual results, because this is what the LHV program, the attempt to answer the question of whether or not QM can be viably supplemented with underlying system parameters and made explicity local, is predicated on.

I understand, I think. But I'm just using realistic synonymously with hidden parameter. If a theory includes explicit notation representing non-instrumental hidden (or underlying or unknown ... however it might be phrased) parameter(s), then it's a realistic theory, if not, then it isn't.

Yes, I agree that the fact that they both violate Bell locality is the unambiguous criterion and statement of their non-(Bell)localness. What I had in mind was that the way in which deBB is explicitly nonlocal (and nonmechanical) through the quantum potential is a bit different than the way standard QM is (to some) explicitly nonlocal (and nonmechanical) through instantaneous collapse and establishment and projection of a principle axis subsequent to detection at one end or the other.

Oh, cool. Yes, I read that paper some time ago. I think that I don't quite understand your reason, your argument for dismissing Jarrett's idea. Maybe after reading it again I'll get it. If you have time, would a brief synopsis here, outlining the principle features of your argument, be possible?

Yes, that's basically it. I would say, following Jarrett, that Bell locality encodes two assumptions, one of which, the assumption that paired outcomes are statistically independent, is the effective cause of the incompatibility between Bell LHV and QM, and the incompatibility between Bell LHV and experiment, and that this doesn't tell us anything about locality or nonlocality in nature.

But, as I mentioned, I still have this feeling that I don't fully understand your argument against Jarrett ... but will say that if your argument is correct, then there wouldn't seem to be anything left but to conclude that nonlocality must be present in nature. (Unless the idea that this nonlocality must refer to instantaneous action at a distance is also correct, and then I have no idea what it could possibly mean.)

ttn

Good point! But I think the real lesson here is again just that "realistic" is used to mean all kinds of different things by all kinds of different people in all kinds of different contexts. There is surely a sense in which the coin-flipping-particles model could be considered "realistic" -- namely, it tells a perfectly clear and definite story about really-existing processes. There's nothing the least bit murky, unspeakable, metaphysically indefinite, or quantumish about it. So, if that's what "realistic" means, then it's realistic. But if "realistic" means instead specifically that there are pre-existing definite values (supporting statements about counter-factuals) then the coin-flipping-particles model is clearly not realistic.

So... anybody who talks about "realism" (and in particular, anybody who says that Bell's theorem leaves us the choice of abandoning "realism" to save locality) better say really really carefully exactly what they mean.

Incidentally, equivocation on the word "realism" is exactly how muddle-headed people manage to infer, from something like the Kochen-Specker theorem (which shows that you cannot consistently assign pre-existing definite values to a certain set of "observables"), that the moon isn't there when nobody looks.

nanosiborg

How would you represent it in a model? Can it be one of many possible hidden parameters collectively represented by λ. Lets say that λ is the universal convention for denoting hidden parameters, and, following Bell, that λ refers to any relevant underlying parameter. (We have no way of knowing what the relevant underlying parameters are, but whatever they are, λ refers to them.) Theories which include λ would be called realistic, and theories which don't include λ would be called nonrealistic.

As I mentioned in my most recent reply to Norsen, I suppose you can make a model that's, in some sense, Bell local without λ. But that would pretty much defeat the purpose, which is to determine whether or not QM can be supplemented by hidden parameters, λ, and also be made explicitly local. (And of course Bell proved that it can't be. But Norsen maintains that Bell also proved that nature is nonlocal. Which I don't get.)

If you think that there's something wrong with λ including anything and everything, then your argument is with Bell's formulation ... I think.