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

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

by bohm2
Tags: bell, inequalities, nature, violations
P: 1,397
 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.
P: 733
 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.
P: 415
 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 ?
P: 111
 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.
P: 733
 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.
P: 733
 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.
P: 733
 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
P: 1,397
 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
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P: 5,055
 Quote by ttn 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.
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?
P: 733
 Quote by 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.
Well I must have explained about 30 times here where you can find his careful and explicit formulation of the concept of locality, i.e., local causality.

 Maybe it would help the discussion if you wrote down what you consider Bell's definition of "local".
I wrote a whole paper about it, published recently in AmJPhys. Preprint here:

http://arxiv.org/abs/0909.4553

Or see Bells' papers, especially "la nouvelle cuisine" or "the theory of local beables".

 What I have seen is this: [...]
You're behind the times then. That's a standard textbook-ish sort of presentation. Bell was much better. See the above, or the systematic encyclopedia article:

http://www.scholarpedia.org/article/Bell%27s_theorem

which discusses all of the subtleties in gory, exhausting detail.

 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.
I don't understand what measureability of anything has to do with this. It sounds like the claim is just that each particle carries local deterministic hidden variables. Such a model can account for the perfect correlations when a=b just fine of course, but cannot reproduce the general QM predictions.

 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.
That is true, which is why I'm at least open to the possibility that such an assumption got made somewhere important. But so far I'm not seeing it.

 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
Well, OK, I'll try to take a look later.
P: 1,397
 Quote by ttn You're behind the times then. That's a standard textbook-ish sort of presentation. Bell was much better.
It's from Bell, "Locality in quantum mechanics: reply to critics" in Speakable and unspeakable in quantum mechanics

 I don't understand what measureability of anything has to do with this.
It's just a technical result that if you don't assume anything about measurability, it is possible to come up with a counterexample to Bell's theorem.

 It sounds like the claim is just that each particle carries local deterministic hidden variables.
It is. It's exactly the type of model that Bell claimed did not exist. I don't really consider it to be a refutation of Bell's theorem, it just means that Bell's theorem should really be stated in a slightly different way, making the assumption about measurability explicit. Not that anyone really cares, because the Pitowsky model is of more mathematical than physical interest.
P: 1,397
 Quote by ttn Or see Bells' papers, especially "la nouvelle cuisine" or "the theory of local beables".
I've read his "Theory of local beables", and it seems to me that he is defining a theory of "local beables", rather than defining locality. You can fail to have local beables either by jettisoning the "local", or jettisoning the "beables".
P: 733
 Quote by 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?
I've never even heard of "relational blockworld". I looked at one of the papers and couldn't make any sense of it -- it's just page after page of philosophy, metaphor, what the theory *doesn't* say, etc. So... you'll have to explain to me how it explains the EPR correlations -- in particular the perfect correlations when a=b. Recall that the explanation should be local (and that the "no conspiracies" assumption should be respected... something tells me this could be an issue in a "blockworld" interpretation...).
P: 733
 Quote by stevendaryl It's from Bell, "Locality in quantum mechanics: reply to critics" in Speakable and unspeakable in quantum mechanics
The point is that your'e jumping in mid-stream -- as if determinism was assumed, etc. See Bell's *full presentation* of the theorem, not some out of context snippet.

 It's just a technical result that if you don't assume anything about measurability, it is possible to come up with a counterexample to Bell's theorem.
I get that that's the claim. But I'm not buying it yet.

 It is. It's exactly the type of model that Bell claimed did not exist. I don't really consider it to be a refutation of Bell's theorem, it just means that Bell's theorem should really be stated in a slightly different way, making the assumption about measurability explicit. Not that anyone really cares, because the Pitowsky model is of more mathematical than physical interest.
Assuming a model of this sort actually does what you claim, I would agree. But I remain highly skeptical. Surely you are aware that all kinds of weird people (Joy Christian, for example... Hess and Phillip was another recent example) make wholly wrong claims of just this sort. Sometimes their mistakes are trivial/obvious. Sometimes they are hard to identify, for me at least. But in my experience (which is significant on this front) all of these kinds of claims always turn out to be wrong. Nevertheless, I've never heard of the one you're talking about here, and it's interesting enough to look into.
P: 733
 Quote by stevendaryl I've read his "Theory of local beables", and it seems to me that he is defining a theory of "local beables", rather than defining locality.
No, actually he's just defining locality. Look at it again. But "la nouvelle cuisine" is better. Note that he subtly tweaked how he formulated "locality" in between those papers. (See the footnote in "free variables and local causality" for some comments about why he made the change.)

 You can fail to have local beables either by jettisoning the "local", or jettisoning the "beables".
So, you think a theory without beables could be local -- or for that matter nonlocal? I disagree. So did Bell: "lt is in terms of local beables that we can hope to formulate some notion of local causality." That is, without beables (i.e., physically real stuff of some kind) the very idea of locality (which is a speed limit on the influences propagating around in the stuff) is incoherent/meaningless.
P: 1,397
 Quote by 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?
The papers on "Relational Block World" are very frustrating, because they don't give a succinct definition of what the "Blockworld interpretation of quantum mechanics" is. The entire paper reads like a very lengthy introduction.

The observation that the generators of boosts, translations and rotations obey commutation relations isomorphic to those of quantum mechanics is intriguing (and I've wondered for years whether there was some connection), but I still don't get it. For one thing, the classical commutation relations don't involve h-bar, so I don't understand how that constant can arise from a block world interpretation (even though I don't really know what the blockworld interpretation is).
P: 733
 Quote by stevendaryl The papers on "Relational Block World" are very frustrating, because they don't give a succinct definition of what the "Blockworld interpretation of quantum mechanics" is. The entire paper reads like a very lengthy introduction. The observation that the generators of boosts, translations and rotations obey commutation relations isomorphic to those of quantum mechanics is intriguing (and I've wondered for years whether there was some connection), but I still don't get it. For one thing, the classical commutation relations don't involve h-bar, so I don't understand how that constant can arise from a block world interpretation (even though I don't really know what the blockworld interpretation is).
There are a lot of crazy ideas for how to understand QM, and most of them simply do not make any sense. For me a useful rough litmus test is to ask the proponent of some such idea to explain what's going on in the 2-slit experiment with single electrons. Lots of theories can pass this test (Copenhagen, Bohm, MWI, GRW, for example). Ones that can't, I find I have no use for. Hopefully Dr C can give this sort of quick explanation of what this RBW thing is all about. Of course, something like this is inherent in the "challenge" I posed...
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P: 634
Two other interesting papers discussing Bell's concept of local causality and implications of violation of bell's inequality pursuing Bell's and ttn's positions (with many passages from Bell's work) are the following 2 papers by M.P. Seevinck:
 The starting point of the present paper is Bell’s notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen’s (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell’s condition of local causality.
Not throwing out the baby with the bathwater: Bell’s condition of local causality mathematically ‘sharp and clean’
http://mpseevinck.ruhosting.nl/seevi..._corrected.pdf
 Consider jointly the following two theorems: firstly, the so-called No-Signalling Theorem in quantum theory; and, secondly, Bell’s Theorem stating that quantum theory is not locally causal. Then, do quantum theory and the theory of (special) relativity indeed “peacefully coexist” or is there an “apparent incompatibility” here (J.S. Bell, 1984 [5, p. 172])? If we think the latter is the case—which we will argue one should—, does this ask for a radical revision of our understanding of what (special) relativity in fact enforces?
Can quantum theory and special relativity peacefully coexist?
http://mpseevinck.ruhosting.nl/seevi...k_Revised3.pdf

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