View Poll Results: What do observed violation of Bell's inequality tell us about nature? Nature is non-local 10 30.30% Anti-realism (quantum measurement results do not pre-exist) 15 45.45% Other: Superdeterminism, backward causation, many worlds, etc. 8 24.24% Voters: 33. You may not vote on this poll

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

 Quote by ttn Now that's an interesting set of statements! So, you agree that, for whatever reason, the Bohm theory precludes signalling (i.e., basically, it agrees with the empirical predictions of QM, including that Bob's marginal shouldn't be affected by Alice's setting). And you want "locality" to just *mean* this no-signalling condition. But then... what in the world do you mean when you say that, despite the no signalling, there ARE nonlocal interactions in the Bohm theory?
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.

 Quote by ttn This idea ... 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.

[ ... snip silly analogy ... ]

 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.
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.

 Quote by ttn Aspect's experiment (and other more recent and better versions of the same thing) experimentally prove that nature is nonlocal. They falsify locality.
They falsify local theories of quantum entanglement based on Bell's locality condition. They don't prove that nature is nonlocal.

 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.
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.

 Quote by ttn Quantum teleportation?
There's no physical superluminal transmissions involved in quantum teleportation.

 Quote by ttn 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.
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.

 Quote by ttn That's got to be the strangest argument (for the inapplicability of Bell's formulation of locality to ordinary QM) that I've ever heard. Suffice it to say I disagree. Yes, there are lots and lots of different possible ψs. But I don't think there is any technical problem with this of anything like the sort you suggest here.
I'm sorry, but then you are wrong. If you think you are right, then here's a challenge for you: Take the space $L^2(\mathbb R)$ and define some arbitrary example of a probability measure (let's call it $\mu$) on it (you are absolutely free). Give a meaning to probabilities like for example $P(\psi(3) = 5) = \int_{\psi(3)=5}\mathrm d\mu(\psi)$. 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 $\mathbb R^{6N}$ and the measure could be given by any probability distribution $\rho(x_1,p_1,\ldots,x_{3N},p_{3N})$ for example.

 But rather than get into the details of that, just think about how silly this is. If the space of λs is too big for QM, then surely it's too big for Bohm's theory as well, since the physical states in Bohm's theory include everything they include in QM, plus more stuff. Indeed, each particular ψ corresponds to just one possible physical state in QM, whereas it corresponds to an infinite number of possible physical states in Bohm's theory (since there are an infinite number of different ways the particles could be arranged for that ψ)! So evidently you also think that it is impossible to say whether Bohm's theory is local or not? (I consider that a reductio of your argument.)
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.

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

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

 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.
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 physical superluminal transmissions involved in quantum teleportation.
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.

 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 something that you can't make sense of.
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.
 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.

 Quote by ttn Interesting question. So, which is it? Actually both are true! The key point here is that, according to the pilot-wave theory, there will be many physically different ways of "measuring the same property". Here is the classic example that goes back to David Albert's classic book, "QM and Experience." Imagine a spin-1/2 particle whose wave function is in the "spin up along x" spin eigenstate. Now let's measure its spin along z. The point is, there are various ways of doing that. First, we might use a set of SG magnets that produce a field like B_z ~ B_0 + bz (i.e., a field in the +z direction that increases in the +z direction). Then it happens that if the particle starts in the upper half of its wave packet (upper here meaning w.r.t. the z-direction) it will come out the upper output port and be counted as "spin up along z"; whereas if it happens instead to start in the lower half of the wave packet it will come out the lower port and be counted as "spin down along z". So far so good. But notice that we could also have "measured the z-spin" using a SG device with fields like B_z ~ B_0 - bz (i.e., a field in the z-direction that *decreases* in the +z direction). Now, if the particle starts in the upper half of the packet it'll still come out of the upper port... *but now we'll call this "spin down along z"*. Whereas if it instead starts in the lower half of the packet it'll still come out of the lower port, but we'll now call this *spin up along z*. And if you follow that, you can see the point. Despite being fully deterministic, what the outcome of a "measurement of the z-spin" will be -- for the same exact initial state of the particle (including the "hidden variable"!) -- is not fixed. It depends on which *way* the measurement is carried out!
i agree.
I can think of another example, "position" position respect to ?

.

 And if you follow that, you can see the point. Despite being fully deterministic, what the outcome of a "measurement of the z-spin" will be -- for the same exact initial state of the particle (including the "hidden variable"!) -- is not fixed. It depends on which *way* the measurement is carried out!
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?

 Quote by 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 $L^2(\mathbb R)$ and define some arbitrary example of a probability measure (let's call it $\mu$) on it (you are absolutely free). Give a meaning to probabilities like for example $P(\psi(3) = 5) = \int_{\psi(3)=5}\mathrm d\mu(\psi)$. 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.
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.

 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.
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".

 Quote by 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.
I think it does. Bell assumed a probability distribution on the "hidden variable" $\lambda$. 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.

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

 Quote by 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.
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 ?

 Quote by 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.
As far as i'm concerned, his definition of locality requires the existence of the probabilities of the form $p(a,b,\lambda)$, 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, $p(a,b,\psi)$ 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.

 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".
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 $p(a,b,\lambda)$, then it's not applicable.

 Quote by stevendaryl I think it does. Bell assumed a probability distribution on the "hidden variable" $\lambda$.
Not in the definition of locality! (Yes, such a thing does come up in the derivation of the inequality, though.)

 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.
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.

 Quote by 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 ?
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.

 Quote by rubi As far as i'm concerned, his definition of locality requires the existence of the probabilities of the form $p(a,b,\lambda)$, 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, $p(a,b,\psi)$ is only a purely formal expression void of any precise meaning. In particular, it's not a probability.
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 $p(A,B,\lambda)$ but rather $p(A,B|\lambda)$ -- or, as I indicated before, slightly more precisely, $p_{\lambda}(A,B)$.

 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.
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

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

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

The proof of the theorem assumes that the unknown hidden variable $\lambda$ is measurable; in particular, that it makes sense to talk about things such as "the probability that $\lambda$ lies in some range such that $A(\hat{a},\lambda) = B(\hat{a},\lambda)$" for various choices of $\hat{a}$ and $\hat{b}$. Pitowky showed that if you don't assume measurability of $\lambda$, then the EPR correlations can be explained in terms of a non-measurable function $F(\hat{r})$ where $\hat{r}$ 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):
• $F(\hat{r})$ is always either +1 or -1.
• $\langle F \rangle = \frac{1}{2}$: The expectation value, over all possible values of $\hat{r}$, of $F(\hat{r})$ is 0.
• If $\hat{r_1}$ is held fixed, and $\hat{r_2}$ is randomly chosen so that the angle between $\hat{r_1}$ and $\hat{r_2}$ is $\theta$, then the probability that $F(\hat{r_1}) = F(\hat{r_2})$ is $cos^2(\dfrac{\theta}{2})$

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.

 But anyway, were it true, then wouldn't it follow that it was impossible to meaningfully assert that Pitowsky's model is local?
It's explicitly local: When a twin pair is created, a hidden variable, $F$ is generated. Then when Alice later measures the spin along axis $\hat{a}$, she deterministically gets the result $F(\hat{a})$. When Bob measures the spin of the other particle, he deterministically gets $-F(\hat{b})$

 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!
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

Recognitions:
Gold Member