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 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.

 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.

 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".

 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...).

 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.

 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.

 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).

 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...

Recognitions:
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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

 Quote by ttn [...] it is rather Dr C who totally misunderstands the issue. There is absolutely no *assumption* of (what Dr C means by) "realism" in Bell's 1964 paper. And Bell makes this even clearer in his many subsequent papers.
While I also don't fully agree with DrChinese, you seem to claim that Bell's referral to the "nature of reality" doesn't relate to realism at all. Sorry that doesn't make any sense to me.
 The relevant money quote here is something I partially quoted earlier in this thread, from the B's sox paper: "It is remarkably difficult to get this point across, that determinism [aka, DrC's "realism"] is not a *presupposition* of the analysis. [..]
Determinism should not be confounded with realism. Bells' equation to which DrC referred imposes the particular restrained form of realism that was discussed there - not determinism. Counterfactual definiteness isn't the same as determinism.
 [..] They simply *miss* that the argument begins with the EPR argument *from locality to* "realism". They look only at the *second* part of the argument, which shows that "realism" + locality implies a contradiction with experiment. So they *mistakenly* think that we get to choose which of "realism" or locality to reject, in order to avoid the conflict. But in fact there is no such choice. Locality already entails "realism". So to have to choose one to reject is to have to choose locality. [..]
That's an interesting take! However, Bell starts in 1964 with exactly the approach that you say to be a misunderstanding of Bell: "These additional variables were to restore to the theory causality and locality". And your argument doesn't seem to relate to the issue that I discovered there (after everyone else).
 I think the sock is actually on the other foot.
I also think that the solution of the puzzle is likely in correcting the question (as so often).

 Quote by rubi I'm not referring to Jaynes. I've searched the forums, but unfortunately i there's too much results for me to look through. Can you point me to the thread you are referring to? [..]
 Quote by ttn This really isn't the place for a big technical discussion of this kind of thing. [..]
Physicsforums is THE place for big technical discussions of this kind of thing.

 Quote by harrylin While I also don't fully agree with DrChinese, you seem to claim that Bell's referral to the "nature of reality" doesn't relate to realism at all. Sorry that doesn't make any sense to me.
As I have said about 30 times, "realism" is used to mean a number of different things. If I understand correctly, you are referring to the title of Bell's "Bertlmann's socks and the nature of reality". The "nature of reality" part clearly refers to the question of whether reality (i.e., nature) is local or not, which is what the paper is about. It is really not possible to talk about the question of locality vs nonlocality without talking about reality in this generalized sense. Surely there would be no point having a debate about whether unreality was local or nonlocal (i.e., whether the non-existing causal influences that propagate around between non-existing parts of a non-existing universe do or do not obey relativity's speed limit). But the point is that *this* sort of "realism" -- believing that there is a real physical world out there with causal influences propagating around in it -- is simply *not* the "realism" that (at least) DrC has in mind when he says Bell's theorem refutes realism. Is this really so hard to understand???

 Determinism should not be confounded with realism. Bells' equation to which DrC referred imposes the particular restrained form of realism that was discussed there - not determinism. Counterfactual definiteness isn't the same as determinism.
The "realism" in question here means, specifically, deterministic non-contextual hidden variables. This *is* precisely what is assumed if one just jumps in and says:

"Suppose the particles carry hidden variables λ that determine the outcome for any possible measurement, so that functions A(a,λ) and B(b,λ) exist."

That is absolutely just exactly what DrC and others mean by "realism" and it is exactly what Bell was referring to when he said people mistakenly thought the argument started here instead of earlier, with a *derivation* of this "realism" from locality.

 That's an interesting take! However, Bell starts in 1964 with exactly the approach that you say to be a misunderstanding of Bell: "These additional variables were to restore to the theory causality and locality". And your argument doesn't seem to relate to the issue that I discovered there (after everyone else).
So you think Bell was lying when he said people missed the first part of the argument? This is more plausible to you than the possibility that you, too, missed the first part of the argument? Give me a break. Incidentally, you have to actually read the *words* and *think* -- not just skip to the equations.

As to the issue that you "discovered there", do you mean DrC's old saw about "c" being a third angle? This is a complete and total misunderstanding on his part. First off, "c" is an *angle*, not a property or hidden variable or any such thing. To say there are three possible angles along which somebody might orient their SG device, is hardly to commit to anything like "realism". And even if what is meant is not "c" itself but the pre-determined value "along c", i.e., A(c,λ), then still -- why in the world would somebody only object when a *third* angle is introduced? Surely introducing even a *single* one -- the pre-determined value A(a,λ) -- already goes against orthodoxy by adding a pre-determined value that is nowhere to be found in QM. And if it's counter-factual definiteness that somebody is worried about, then surely introducing a *second* such pre-determined value -- the value A(b,λ) -- already commits this sin. So -- anybody who thinks that, with respect to "realism", everything is fine (i.e., no such assumption has been made) until that *third* angle "c" gets introduced, simply doesn't know what they're talking about.

That's all I'll say about this, because it's been covered ad nauseum before. If my repeated explanations here, and my invitations to go learn about all these issues from the scholarpedia article, don't make you understand then nothing ever will.

 Quote by harrylin Physicsforums is THE place for big technical discussions of this kind of thing.
Maybe so, but not this thread. Let's just say that the set of people who voted "anti-realism" in the poll *because of some issue having to do with the measureability of the space of hidden variable states* is almost certainly of measure zero.

Look, there are two categories of issues here. First, there are the "elementary issues" such as what you raised in your previous post. For example: do you understand that, contrary to how most textbooks present it, Bell's theorem does *not* simply begin with the *assumption* of deterministic non-contextual hidden variables, but instead begins by *deriving* these from locality and the perfect correlations? Do you understand that therefore you cannot avoid the conclusion of nonlocality by denying determinism or hidden variables or non-contextuality or counter-factual definiteness? Do you understand that there is also a "no conspiracies" assumption that is made in proving the theorem? Do you know where this comes in (already in the first, EPR part!) and do you understand that it has nothing to do with literal human freewill? Do you understand that the "locality" from which the inequality flows is *not* defined by some statement like A(a,b,λ) = A(a,λ) but is rather something that Bell gave an extremely careful, general, non-proprietary formulation of?

People suffering from confusions about issues like these simply need to go and read a bit more until they understand the issues.

Now, admittedly, there are also "advanced issues", some of which have come out in this thread. For example, isn't there a kind of inconsistency between the "no conspiracy" assumption and Bell's formulation of locality? Doesn't Bell tacitly assume that the space of physical states λ is measureable, in deriving the inequality? And: doesn't Bell's formulation of locality become somewhat difficult to apply to theories whose ontologies include nonlocal beables?

 Quote by ttn [..] The "nature of reality" part clearly refers to the question of whether reality (i.e., nature) is local or not, which is what the paper is about. [..] But the point is that *this* sort of "realism" -- believing that there is a real physical world out there with causal influences propagating around in it -- is simply *not* the "realism" that (at least) DrC has in mind when he says Bell's theorem refutes realism. Is this really so hard to understand??? [..]
We agree about that but apparently you didn't understand that; sorry if you somehow ascribed to me something that I disagree with. What I referred to is the facts of Bell's derivation that DrChinese pointed out in the other thread; Bell's derivation is not subject to DrChinese's interpretation of "realism".
 "Suppose the particles carry hidden variables λ that determine the outcome for any possible measurement, so that functions A(a,λ) and B(b,λ) exist." That is absolutely just exactly what DrC and others mean by "realism" and it is exactly what Bell was referring to when he said people mistakenly thought the argument started here instead of earlier, with a *derivation* of this "realism" from locality.
You seem to be beating a strawman and I'm not interested in that.
 So you think Bell was lying when he said people missed the first part of the argument?
No, see above...
 As to the issue that you "discovered there", do you mean DrC's old saw about "c" being a third angle? [..]
Once more no, see above, I only referred to Bell's derivation.

 Quote by ttn Maybe so, but not this thread. Let's just say that the set of people who voted "anti-realism" in the poll *because of some issue having to do with the measureability of the space of hidden variable states* is almost certainly of measure zero.
I certainly agree with that.

 Look, there are two categories of issues here. First, there are the "elementary issues" such as what you raised in your previous post. For example: do you understand that, contrary to how most textbooks present it, Bell's theorem does *not* simply begin with the *assumption* of deterministic non-contextual hidden variables, but instead begins by *deriving* these from locality and the perfect correlations?
I don't believe that you are right about that. If you're claiming that Bell's "Theory of Local Beables" is his definition of locality, then he's already assumed essentially that hidden variables exist. He hasn't derived it from locality, because he doesn't even offer a way to state locality in the absence of such hidden variables.

 Quote by ttn Maybe so, but not this thread.
Ah yes, due to the title of this thread I had forgotten that it was just meant for an opinion poll!
 [..] Bell's theorem does *not* simply begin with the *assumption* of deterministic non-contextual hidden variables, but instead begins by *deriving* these from locality and the perfect correlations? Do you understand that therefore you cannot avoid the conclusion of nonlocality by denying determinism or hidden variables or non-contextuality or counter-factual definiteness? [..]
You are here summarizing a claim (with "therefore") that I have not seen discussed on this forum; as you said, this is not the thread for elaborating on such things. It would make for an interesting thread on itself!
 how many people voted for "anti-realism" because of anything like this? The answer is: one or two at most. The rest voted for "anti-realism" because they are simply confused (like DrC) about elementary points. My goal here has been to try to help make people aware that they might be confused. This is admittedly sometimes hard to figure out, since lots of seemingly reputable people, even books, are confused in exactly the same ways. [..]
The main problem (which I think is often recognized) is that there are too different (disagreeing) understandings about the meaning of words. Consequently such opinion polls can never be more than an indication of along which lines people are currently thinking.

 Quote by stevendaryl I don't believe that you are right about that. If you're claiming that Bell's "Theory of Local Beables" is his definition of locality, then he's already assumed essentially that hidden variables exist. He hasn't derived it from locality, because he doesn't even offer a way to state locality in the absence of such hidden variables.
Let me describe a toy model of EPR measurements that I think illustrates that it is possible to have locality without realism, so locality doesn't imply realism.

We have Alice at her detector, and far away, we have Bob at his detector. They each do the following things, over and over:
1. Pick a detector orientation.
2. Measure the spin of one of the particles from a twin pair source for that orientation.
3. Record the results and the detector orientation on a piece of paper.
4. Send the results in a letter to the other experimenter.

Here's the twist in the story: Alice and Bob both have terrible handwriting and/or terrible vision. So when Alice writes "I measured spin up along the z-axis", Bob sometimes reads it to say "I measured spin down along the z-axis", and vice-verse. Similarly, Alice occasionally misinterprets what Bob wrote.

If we further assume that the probability of a misinterpretation depends on (A) what was actually written, and (B) the state of the experimenter doing the reading, then it is certainly possible to reproduce the EPR results without faster-than-light influences.

This resolution does not deny locality, it denies realism, in that it doesn't assume that the words "Alice measured spin-up along the z-axis" is a reliable record of anything real in the world.

This is not a serious suggestion as to what is going on in quantum mechanics, but just a demonstration that no single experimental result, such as the EPR result, can be taken to show nonlocality, without additional realism assumptions.