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

[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]

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 ?

.

 

[stevendaryl]

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?

 

[ttn]

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".

 

[stevendaryl]

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.

 

[ttn]

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.

 

[audioloop]

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 ?

 

[rubi]

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.

 

[ttn]

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.

 

[ttn]

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.

 

[ttn]

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

 

[stevendaryl]

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

 

[DrChinese]

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?

 

[ttn]

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's_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.

 

[stevendaryl]

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.

 

[stevendaryl]

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".

 

[ttn]

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...).

 

[ttn]

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.

 

[ttn]

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.

 

[stevendaryl]

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).

 

[ttn]

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...

 

[bohm2]

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/seevinck/Bell_LC_final_Seevinck_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/seevinck/Polkinghorne_white_paper_Seevinck_Revised3.pdf

 

[harrylin]

[...] 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).

 

[harrylin]

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? [..]

For example https://www.physicsforums.com/showthread.php?t=581193

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.

 

[ttn]

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.

 

[ttn]

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?

That is, there are legitimate and difficult and controversial questions about this stuff. But, seriously, 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. So here is my final plea. If you are somebody who voted for "anti-realism", please simply dismiss/ignore everything I'm saying -- if I strike you as somebody who doesn't know what he's talking about, who hasn't read and understood Bell, who hasn't thought seriously and carefully about these issues, etc. That is, if you think I'm a crackpot, then just ignore me. On the other hand, if you get the impression that I have studied these issues carefully, that I do seem to know something about what I'm talking about, etc. -- then take it seriously that I am saying YOU ARE CONFUSED. Go read some of the stuff I've been linking to, so that next time there's a poll like this, we don't have to again witness the embarrassing spectacle that we have witnessed here!

 

[harrylin]

[..] 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.

 

[stevendaryl]

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.

 

[harrylin]

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.

 

[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.

 

[ttn]

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.

I believe you must be thinking that "beables" is synonymous with "hidden variables"? That is not the case. Bell is super careful and explains his terminology. "Beables" means "whatever a certain candidate theory says one should take seriously, as corresponding to something that is physically real." (Those are my words, but it's his idea.) He gives examples like the E and B fields in classical electromagnetism, as against the potentials V and A. He also applies his formulation to ordinary QM, in which (at most!) the wave function is the only beable in the picture for microscopic things. So it simply is not the case that "beable", as Bell uses the term, means the same as "hidden variable". If you think that, you're confused and should go back and read Bell again.

 

[ttn]

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".

Perhaps I misunderstood you to be agreeing with DrC's criticism, where in fact you were pointing to the place you thought you had refuted his criticism? If so, I'm sorry for my misunderstanding. But in any case, I'm tired of arguing this point and so will simply leave it at that. I've made my view clear, or at least as clear as I know how to do, and have given references for people who want to think about it more.

 

[stevendaryl]

I believe you must be thinking that "beables" is synonymous with "hidden variables"? That is not the case.

How is it different from hidden variables?

Bell is super careful and explains his terminology. "Beables" means "whatever a certain candidate theory says one should take seriously, as corresponding to something that is physically real."

But does quantum mechanics necessarily have such "beables"? I don't see that it does. A candidate such as "the electric field" doesn't work as such a beable, because the electric field depends on locations of charged particles, and quantum mechanics doesn't assume that particles have definite positions. So what's an example of a beable in quantum mechanics?

 

[ttn]

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.

Well, thank you for at least *attempting* to address the challenge! But I don't think this really does it. What we are looking for is a local-but-non-realist explanation of the actual results that the experiment will give (in the special case where a=b, or equivalently for those particle pairs for which a happens to = b). My claim is that, if the underlying *physics* model is local and non-realist, then it will predict that at least sometimes, when a=b, the results will not be perfectly correlated. (For example, if we are calibrating things such that QM says the results should always be the *same* when a=b, then this local-but-non-realist model will say that, at least sometimes, the results will be *different* when a=b.) Now undoubtedly you can cook up a goofy story like the one here in which a sequence of conspiratorial accidents and misinterpretations fools Alice and Bob into believing that the experiment exhibited perfect correlations. But come on, that's not serious. What we are interested in is explain the actual, QM-predicted and experiment-verified correlations... not cooking up a "perfect correlations" delusion in the mind of some imaginary person.

Also, what you said above about the sense in which the proposed model is non-realist makes no sense. At best, this is yet another distinct sense of "realism". But it has nothing to do with the deterministic non-contextual hidden variables sense of "realism" that DrC and others who voted "anti-realism" in the poll think is relevant here.

 

[ttn]

How is it different from hidden variables?

See my "Bell's concept of local causality" paper where there is a whole section discussing this with copious quotes from Bell.

But does quantum mechanics necessarily have such "beables"? I don't see that it does.

You can say it doesn't if you want. But that theory will still be nonlocal.

A candidate such as "the electric field" doesn't work as such a beable, because the electric field depends on locations of charged particles, and quantum mechanics doesn't assume that particles have definite positions. So what's an example of a beable in quantum mechanics?

The wave function, at least for people who think (following Bohr) that the wave function provides a complete description of (microscopic) physical reality. It's true, there are people who don't think the wf in ordinary QM should be understood as a beable, as corresponding to some physical reality. The question for them is: what, then, does? Let them specify what their theory is. If their theory is ordinary QM -- but with *no beables* for the microscopic world -- OK, that's a perfectly clear theory, but it is *really* nonlocal since in effect it has direct, unmediated causal influences between spacelike separated hunks of measuring equipment.

But... seriously... take some time to look into Bell's formulation of locality before you keep coming up with all these alleged objections to it. Note that it is also a mistake to think that one will learn too much by scrutinizing an "unprofessionally vague and ambiguous" theory like orthodox QM...