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

stevendaryl

Nonlocal in my sense is relative to a set of state variables. Quantum mechanics has no nonlocal interactions in terms of macroscopic variables (the locations, velocities and orientations of macroscopic objects, the values of macroscopic fields). But the Bohm model introduces additional variables (the positions of microscopic particles) that are subject to nonlocal interactions. IF there were some way to know the values of these microscopic variables, then you could signal through them.

So Bohm-type models explain macroscopic variables that have no nonlocal interactions in terms of microscopic variables that do.

nanosiborg

Yes, you've made that clear. I'm curious why you put experimental design in quotes.

[ ... snip silly analogy ... ]

That should already be clear to you. But, as you've indicated, it isn't. I don't know how to say it any clearer. This isn't your fault. I accept the responsibility for effectively communicating the ideas I'm exploring.

They falsify local theories of quantum entanglement based on Bell's locality condition. They don't prove that nature is nonlocal.

I'm wondering if you've actually read my posts and thought about the ideas (which are not mine by the way). I've said several times that I agree with you that Bell locality is definitively ruled out as a viable option for modeling quantum entanglement, and that I take Bell's formulation as general. Insofar as effectively exploring the suggestion that QM might be supplemented by LHVs so as to make it a more complete theory of physical reality there's nothing wrong with Bell's formulation. It does that and more, ruling out local theories of quantum entanglement whether HV or realistic or nonrealistic orwhatever.

What it doesn't do is prove that nature is nonlocal.

There's no physical superluminal transmissions involved in quantum teleportation.

I'm entertaining and exploring some ideas that I find interesting that you say you don't understand or can't make sense of. They're not 'loopholes' in the usual sense of that word, and I'm not "clinging" to them in the perjorative sense that I take you to mean.

Any clinging that's going on would more appropriately be used to characterize your holding on to the notion that Bell has proved that nature is nonlocal, and your repeated insistence that you simply can't understand or make any sense of the ideas being presented.

So, again, can we just agree to disagree for now? This will be my last post in this thread. You're free to have the last word in our discussion, although I don't see why it would be necessary to reiterate what you've already said unless you want to add some more ad hominems or whatever, as I understand that you can't very well argue (or argue very well) against, or agree with, something that you can't make sense of.

And yes, of course I'll read the papers you suggested. Thanks, sincerely.

rubi

I'm sorry, but then you are wrong. If you think you are right, then here's a challenge for you: Take the space [itex]L^2(\mathbb R)[/itex] and define some arbitrary example of a probability measure (let's call it [itex]\mu[/itex]) on it (you are absolutely free). Give a meaning to probabilities like for example [itex]P(\psi(3) = 5) = \int_{\psi(3)=5}\mathrm d\mu(\psi)[/itex]. I've given you complete freedom here, so if you think that it is possible, this task should be easy. You can provide an arbitary, completely exotic example if you like.

Bell's definition applies only to situations where such a measure is possible. In classical mechanics for example, the space could be [itex]\mathbb R^{6N}[/itex] and the measure could be given by any probability distribution [itex]\rho(x_1,p_1,\ldots,x_{3N},p_{3N})[/itex] for example.

Bohms theory isn't nonlocal with resprect to Bell's definition (because it can't be applied) but in the sense of whether there is an action at a distance or not.

ttn

Because it seems like what you actually mean is the *results of*, rather than the *design of*, the experiments. But this is just another way of saying I don't understand what you're getting at, and as you suggest below, it is perfectly reasonable to just leave it there for now.


I would put the first sentence this way: they falsify local theories of quantum entanglement, where "local" is defined in the way Bell defined it.

If we agree about that (and I'm honestly not sure), then the second sentence should read: "This *does* prove that nature is nonlocal (with "local" defined in Bell's way)."

I know you said you didn't want to post more, and trust me, I respect and understand that -- but what I was never able to understand was whether you were saying (a) that Bell's def'n of locality was fine, but that there was some subtle logical presupposition in the analysis *other* than Bell's def'n of locality, or (b) that there is some problem/flaw in Bell's def'n. So, maybe that expression of my confusion will help you sort out how to communicate your idea more effectively next time. Or possibly it's just that I'm dense.


Yes, I've read every word. And I've heard you say those things. But then I hear you saying "but..." with the "..." being stuff that, to me, contradicts the above. So I am continuously thinking that either you must not have meant what you said, or I didn't understand it correctly.

There's no transmission of useable *information*, to be sure. That is, you can't transmit a *message* superluminally this way. But you'd be hard pressed to explain the fact that quantum teleportation is possible, in terms of a local theory.


Of course. I'm sincerely sorry if my posts have come off as attacking you. That wasn't intended at all. I was just trying (perhaps too hard?) to understand what you were saying. And the reason I kept going back to the general points about Bell's theorem is not that I ignored your statements about where you agreed with me -- rather I was just trying to keep this part of the thread it's embedded in, i.e., connect it back, largely for the purposes of other people who might be reading, to the big issue at hand here, namely, whether Bell's theorem should be understood as refuting "realism" or "locality". Sorry if the attempt to keep both of those balls in the air (talking with you and arguing for a general audience about the main issue of the thread) made it seem like I was throwing balls at you undeservedly.

nanosiborg

T. Norsen, sorry if I came off as having taken offence. I actually enjoyed much of our discussion, and will continue to enjoy the other discussions in this thread from the sidelines. Thanks for clarifying, and I realize that it's up to me to put into clearly understandable form any ideas that I might want help in exploring. Of course, that's part of the problem I'm having, as I just have this vague intuitive notion that there might be something there, but am not sure how to state it most clearly. Maybe after reading the papers you suggested I won't have to worry about that.

audioloop

i agree.
I can think of another example, "position" position respect to ?

.

stevendaryl

This point, which I think I knew once upon a time, but forgot, is very interesting. It bears some similarity with Cramer's "Transactional Interpretation". In that interpretation, the result of a measurement was not completely random, but could depend on details in the future. The transactional interpretation is sort of nonlocal, as well, but the nonlocal interactions propagate along null paths into the future and into the past. Maybe the two theories end up being essentially the same?

ttn

This really isn't the place for a big technical discussion of this kind of thing. Suffice it to say that what you are saying here is totally irrelevant to Bell's formulation. Go read up on how he defines "locality" and you'll see that nothing like this comes up.


But it is precisely "the sense of whether there is an action at a distance or not" that Bell is concerned with, and that his definition captures. You should look into how he defines this idea, before you decide whether it's applicable to Bohm's (or some other) theory and before you decide whether or not it genuinely captures the notion of "no action at a distance".

stevendaryl

I think it does. Bell assumed a probability distribution on the "hidden variable" [itex]\lambda[/itex]. So technically, if the "hidden variable" is a function, with infinitely many degrees of freedom, then there can't be a probability distribution.

This technicality was exploited by Pitowsky, who developed a local hidden variables theory that makes the same predictions for the spin-1/2 EPR experiment as orthodox quantum mechanics. Where he escapes from Bell's clutches is exactly in using a "hidden variable" for which there is no probability distribution. He uses nonmeasurable sets, constructed via the continuum hypothesis.

ttn

Hmmm. Maybe I'm not entirely sure what you are intending to give another example of, but it is actually not true that position is "contextual" (in the way I explained spin was) for Bohm's theory. For position measurements (only!) there is, in Bohm's theory, a definite unambiguous pre-existing value (namely, the actual location of the thing in question) that is simply passively revealed by the experiment.

That's probably not what you meant. You meant something about the arbitrariness of reference frame -- e.g., what you call x=5, maybe I call x=-17. But that's a totally different issue than the one I was bringing up for spin in bohm's theory. There is an analog of your issue for spin -- namely, maybe what you call "spin along z = +1" I instead call "spin along z = +hbar/2" or "spin along z = 37". All of those, actually, are perfectly valid choices. We can disagree about what to *call* a certain definite outcome. But that is not at all the point of the example I explained for the contextuality of spin in bohm's theory. There, the point is not that different people might call the outcome different things, but that two different experiments (that happen to correspond to the same Hermitian operator in QM) can yield distinct outcomes (for exactly the same input). This isn't about calling the same one outcome by two different names; the outcomes are really genuinely distinct.

audioloop

i understand, but what is a definite value ? something defined by other definite value in turn defined by another value and so on.
in the case of position x,y,z axes in turn determined by other set of axes ? in turn determined by other set of axes ?

"coordinates" respect to ?

rubi

As far as i'm concerned, his definition of locality requires the existence of the probabilities of the form [itex]p(a,b,\lambda)[/itex], so if they don't exist (which definitely is the case in QM even for the simple case of a free 1D particle), then the definition can't be applied. Up to now, [itex]p(a,b,\psi)[/itex] is only a purely formal expression void of any precise meaning. In particular, it's not a probability.

By the way: I was looking for that paper you suggested, but i don't find it on the internet. (Apart from that, i don't know french, so i probably couldn't read it?) Can you point me to a source? I have access to most journals.

I'd like to like to look into this, but as i said: I don't find that paper anywhere. However, if it uses probabilities of the form [itex]p(a,b,\lambda)[/itex], then it's not applicable.

ttn

Not in the definition of locality! (Yes, such a thing does come up in the derivation of the inequality, though.)



I am highly skeptical of this. First of all, the claim that was made here was that Bell's definition of locality is inapplicable if the space of λs is unmeasureable. That is simply false, and the person making such a claim obviously hasn't actually read/digested Bell's formulation of locality. (Probably anybody making this claim simply doesn't yet appreciate that there's a difference between Bell's definition of locality, and Bell's inequality.) But anyway, were it true, then wouldn't it follow that it was impossible to meaningfully assert that Pitowsky's model is local? Yet that is asserted here. So something is amiss. Furthermore, if the space of λs is unmeasureable, I don't see how you could possibly claim that the theory "makes the same predictions ... as orthodox quantum mechanics".

I'd even be willing to bet real money that this isn't right -- that is, that there's no genuine example of a local theory sharing QM's predictions here. If it were true, it would indeed be big news, since it would refute Bell's theorem! (Something that many many people have wrongly claimed to do, incidentally...) But internet bets don't usually end well -- more precisely, they don't usually end at all, because nobody will ever concede that they were wrong. So instead I'll just say this: you provide a link to the paper, and I'll try to find time to take a look at it and find the mistake.

ttn

I don't think there's any serious issue here that has any relevance to Bell's theorem. Surely it is possible to specify a coordinate system in such a way that different people can adopt and use that same system and thus communicate unambiguously with each other about exactly where some pointer (indicating the outcome of an arbitrary measurement) is.

ttn

I'm sorry, but... what the heck are you talking about? Are you really saying that ordinary QM doesn't allow you to calculate what the probabilities of various possible measurement outcomes are, in terms of the state ψ of the system in question? That's the one thing that orthodox QM is unquestionably, uncontroversially good for!

Maybe the issue has to do with what I assume(d) was just a typo? Namely: it's not [itex]p(A,B,\lambda)[/itex] but rather [itex]p(A,B|\lambda)[/itex] -- or, as I indicated before, slightly more precisely, [itex]p_{\lambda}(A,B)[/itex].


You mean "la nouvelle cuisine"? First off, it's not in French. Only the title. =) The easiest place to find it is in the 2nd edition of "Speakable and Unspeakable in QM", the book collection of Bell's papers on the foundations of QM. The book is on google books, but unfortunately this particular paper isn't included. And I also couldn't find the paper online. If you don't have access to a library that has the actual book (though the book is cheap and brilliant so maybe it's a good excuse to spring for a copy), my paper quotes a lot from it and will certainly allow you to understand Bell's definition:

http://arxiv.org/abs/0707.0401

stevendaryl

I don't think he actually gave a definition of "locality". The way I interpreted what he was doing was describing a class of models, and then proving that no model in that class could reproduce the predictions of quantum mechanics. If he gave an explicit definition of what "local" means, I didn't see one.

Maybe it would help the discussion if you wrote down what you consider Bell's definition of "local". What I have seen is this:

• Assume in an EPR-type experiment (assume the spin-1/2 version for definiteness) involving Alice and Bob that there is a deterministic function [itex]A(\hat{a}, \hat{b}, \lambda)[/itex] giving Alice's result (+1 or -1) as a function of Alice's choice of detector orientation, [itex]\hat{a}[/itex], Bob's choice of detector orientation, [itex]\hat{b}[/itex], and some unknown parameter [itex]\lambda[/itex] shared by the two particles by virtue of their having been produced as a twin-pair. Similarly, assume a deterministic function [itex]B(\hat{a}, \hat{b}, \lambda)[/itex] giving Bob's result.
• Then, in terms of such a model, we can call the model "local", if [itex]A(\hat{a}, \hat{b}, \lambda)[/itex] does not depend on [itex]\hat{b}[/itex], and [itex]B(\hat{a}, \hat{b}, \lambda)[/itex] does not depend on [itex]\hat{a}[/itex]. In other words, Alice's result is [itex]A(\hat{a}, \lambda)[/itex] and Bob's result is [itex]B(\hat{b}, \lambda)[/itex].
• Theorem, there are no such functions [itex]A(\hat{a}, \lambda)[/itex] and [itex]B(\hat{b}, \lambda)[/itex].

The proof of the theorem assumes that the unknown hidden variable [itex]\lambda[/itex] is measurable; in particular, that it makes sense to talk about things such as "the probability that [itex]\lambda[/itex] lies in some range such that [itex]A(\hat{a},\lambda) = B(\hat{a},\lambda)[/itex]" for various choices of [itex]\hat{a}[/itex] and [itex]\hat{b}[/itex]. Pitowky showed that if you don't assume measurability of [itex]\lambda[/itex], then the EPR correlations can be explained in terms of a non-measurable function [itex]F(\hat{r})[/itex] where [itex]\hat{r}[/itex] is a unit vector (or alternatively, a point on the unit sphere), with the properties that:
(This is from memory, so I might be screwing these up):

• [itex]F(\hat{r})[/itex] is always either +1 or -1.
• [itex]\langle F \rangle = \frac{1}{2}[/itex]: The expectation value, over all possible values of [itex]\hat{r}[/itex], of [itex]F(\hat{r})[/itex] is 0.
• If [itex]\hat{r_1}[/itex] is held fixed, and [itex]\hat{r_2}[/itex] is randomly chosen so that the angle between [itex]\hat{r_1}[/itex] and [itex]\hat{r_2}[/itex] is [itex]\theta[/itex], then the probability that [itex]F(\hat{r_1}) = F(\hat{r_2})[/itex] is [itex]cos^2(\dfrac{\theta}{2})[/itex]

Mathematically, you can prove that such functions exist (with the notion of "probability" in the above being flat lebesque measure on the set of possibilities). Pitowksy called it a "spin-1/2 function".But it's not a very natural function, and is not likely to be physically relevant.

It's explicitly local: When a twin pair is created, a hidden variable, [itex]F[/itex] is generated. Then when Alice later measures the spin along axis [itex]\hat{a}[/itex], she deterministically gets the result [itex]F(\hat{a})[/itex]. When Bob measures the spin of the other particle, he deterministically gets [itex]-F(\hat{b})[/itex]

Not in any serious way. Physicists routinely assume things like measurability and continuity, etc., in their theories, and whatever results they prove don't actually hold without these assumptions, which are seldom made explicit.

In a brief Google search, I didn't see Pitowsky's original paper, but his spin-1/2 models are discussed here:
http://arxiv.org/pdf/1212.0110.pdf

DrChinese

Relational BlockWorld is local. I consider it non-realistic.

http://arxiv.org/abs/quant-ph/0605105
http://arxiv.org/abs/0908.4348

How much were we betting?