Scholarpedia article on Bell's Theorem

[harrylin]

I've read Jaynes on Bell. I generally like Jaynes. But Jaynes is simply dead wrong when he writes, for example[..]

Yes we discussed that in this forum; and thus I wrote in my comment to you that "while Jaynes doubted it, I do think that Bell understood that." However your reply gives the impression that you don't understand it despite having read Jaynes (but perhaps it's just a misunderstanding about words), and for some strange reason you even reacted on my comment about your statement as if it was criticism on the way Bell formulated his theorem. If you cite the passage of Bell that you think is the same as what you said, we can verify it.

 

[harrylin]

I don't think there is any important difference, qualitative or otherwise. Bohm's version in terms of spin is just more directly related to Bell's theorem and the experimental tests of the inequality. But the argument is the same, whether you use x/p or s_x/s_y or whatever. Note that s_x and s_y (I am thinking of spin 1/2 here, but if you want to think about photons you should say instead "polarization along some axis" and "polarization along some non-parallel axis") don't commute and so there is an uncertainty principle relation between them the same way there is between x and p.

OK thanks for the clarification! As I have read some papers (but sorry, I forgot which) in which this point was criticised, a footnote of that kind could be useful.
But I still don't get it: If we know the position more accurately, we know the momentum less accurately. I would say that it is quite different with spin: if we know one spin more accurately, we also know the other spin more accurately and I'm not aware that there is anything that we would know less accurately. Perhaps you can elaborate?

 

[lugita15]

If we know the position more accurately, we know the momentum less accurately. I would say that it is quite the opposite with spin: if we know one spin more accurately, we also know the other spin more accurately. Perhaps you can elaborate?

If we know the spin along one direction more accurately, then we know the spin along another direction less accurately. Position and momentum bear the exact same relation to each other that (say) the x-component of spin angular momentum has to the y-component of spin angular momentum.

 

[DrChinese]

I would say that it is quite different with spin: if we know one spin more accurately, we also know the other spin more accurately and I'm not aware that there is anything that we would know less accurately. Perhaps you can elaborate?

Just to elaborate on lugita15's accurate answer:

For a spin 1/2 electron, there are 3 spin components which are mutually perpendicular (i.e. 3 axes): sx, sy, sz. If you know sx, then sy and sz are completely indeterminate. Any observation which involves some mixture of sx and sy (let's say 45 degrees between) will likewise be a mixture of a known outcome and an indeterminate one. And so on for all angles.

For a spin 1 linear polarized photon, the same kind of mixtures are possible (of known and indeterminate) but the indeterminate component is 45 degrees away from the known one (rather than 90 degrees as is the case with an electron).

All of this is because spin components do not commute, just as p and q do not commute. One of the advantages of working with spin observations is that you can easily obtain these combinations by simply rotating a part of the apparatus.

 

[billschnieder]

For the record: A(a,λ) does presuppose both locality and determinism. Yes, this "A" is not a probability. Bill thinks that there are more variables ("x") in addition to λ that might help determine the outcome. But this just shows that he -- like Jaynes and Jarrett, incidentally -- have not studied/understood Bell carefully. Bell is absolutely clear that "λ" denotes a *complete* specification of the state of the physical stuff in question (the particle pair, or whatever).

You are arguing with yourself here. This contradicts what you said previously:

... the λ refers to the state of the particles *before any measurements are made on them*. That, of course, is precisely what λ means in all the derivations. But why in the world should ρ(λ) -- the distribution of states of an ensemble of particles that have just been shot toward some polarizers -- depend on the orientation of the polarizers?

So which one is it. Does λ represent the COMPLETE specification of the physical state relevant for the outcome (including all hidden particle AND instrument properties), or does it represent ONLY the "state of the particles shot toward some polarizers"? Make up your mind already.

 

[ttn]

Does λ represent the COMPLETE specification of the physical state relevant for the outcome (including all hidden particle AND instrument properties), or does it represent ONLY the "state of the particles shot toward some polarizers"? Make up your mind already.

λ represents the complete specification of the physical state relevant for the outcome -- except the controllable "parameter settings" a and b. That is, the totality of things relevant to the outcomes needs to be broken apart into three parts: the part that is "freely set" by the experimenter on one side (at the last second, let's assume), the part that is freely set by the experimenter on the other side (at the last second), and then everything else. λ is the everything else. (And note that "freely set" here means the "no conspiracies" idea -- we assume the two settings can be made independent of λ such that the distribution of λ is the same no matter how the settings are made.) One usually thinks of λ as a complete description of the state of the particle pair (on which polarization measurements are to be made) but if there are relevant variables in the apparatuses too, ones that influence the outcomes somehow but are independent of the appratus settings -- no problem, throw them into λ as well. (Drawing the lines precisely will be subtle and theory-dependent, but it should be clear that in principle this can always be done. See the article for a more detailed presentation of all this.)

PS -- I am learning that there are two kinds of posters here: those that recognize a good opportunity to learn something and so ask intelligent questions in a polite way, and those that can't tell the difference between somebody who does and somebody who doesn't know what they're talking about and that tend to ask only sarcastic/hostile questions. The curious thing is that the first group understands the issues much better than the second.

 

[billschnieder]

PS -- I am learning that there are two kinds of posters here: those that recognize a good opportunity to learn something and so ask intelligent questions in a polite way, and those that can't tell the difference between somebody who does and somebody who doesn't know what they're talking about and that tend to ask only sarcastic/hostile questions. The curious thing is that the first group understands the issues much better than the second.

Oh, so you came here to teach us? I wonder which class of the above you place yourself in. I thought you came here so that your paper could be criticized. Now that explains a lot:

People who read this article and say "it's not neutral" really just mean "it disagrees with what I, personally, consider to be the truth". But such people should, first, actually read the article (not just skim the abstract to see whether it endorses their half-baked opinions)

How so polite of you -- anyone who disagrees with you certainly hasn't read the article and their opinions are half-baked

I quibbled about your mis-statement of the setup just for the sheer fun of it. But I know perfectly well what you should have said

If you can't stand the heat, don't start fires.

 

[harrylin]

If we know the spin along one direction more accurately, then we know the spin along another direction less accurately. Position and momentum bear the exact same relation to each other that (say) the x-component of spin angular momentum has to the y-component of spin angular momentum.

Lugita (and DrC), finally I understand the differences and similarities of EPR's vs Bohm's examples - thanks!

PS. ttn: as lugita showed, one precise sentence (the second one above) suffices to clarify that point in your article.

 

[ThomasT]

... I still don't get it: ... I would say that it is quite different with spin: if we know one spin more accurately, we also know the other spin more accurately and I'm not aware that there is anything that we would know less accurately. Perhaps you can elaborate?

This might be helpful:
https://www.physicsforums.com/showthread.php?t=563029

 

[harrylin]

This might be helpful:
https://www.physicsforums.com/showthread.php?t=563029

Thanks for the link!

 

[ttn]

...

Stay classy, Bill!

 

[harrylin]

[..] To me, the important thing (or at least the thing relevant to this thread), though, is that this dilemma is wrong. Bell's theorem doesn't offer you any such choice. Indeed, Bell's theorem doesn't speak to "realism" at all one way or the other. Nothing about "realism" need or can be inferred from Bell's theorem.

That's funny: while I disagree with a purposeful indoctrination of readers with one's own opinion of "the truth" in an encyclopedia article, we clearly agree on your main point which I also brought up in this forum. Bell discussed Einstein's "[spooky] action at a distance" which is also called "non-locality"; I have not seen a clear definition of "realism" or "non-realism" - whatever that is supposed to mean.

Perhaps the confusion/disagreement stems from the fact that Einstein discussed (and Bell cited) the existence of physical reality in this context, or that Bell had to define "beables" for truly existing physical entities, to which this locality refers?

 

[martinbn]

Of course I agree with what you say here, in the sense that it is a kind of minimalist statement of at least part of what's happening. But the whole point under discussion, when the discussion is about "locality", is to probe a bit deeper and not just say "they're correlated, end of discussion" but instead to ask how those correlations arose and in particular whether there was any nonlocal causation at work. Sure, you can just bury your head in the sand and refuse to talk about it. But refusing to talk about it is hardly the same as somehow proving there was no nonlocality!

I am not trying to prove that there is no nonlocality, just trying to understand why you are so hung up on a name that doesn't help nor captures the essence. After all, giving a name doesn't mean that you are probing deeper.

Well, then maybe "definition" is the wrong word. Call it a "formulation". The point is that we are trying to capture, in a mathematically precise way, an idea that we have a reasonably clear intuitive sense of -- roughly, all of the causal influences on a given event should be inside the event's past light cone. The difficult thing is precisely to formulate this in a way that gets at *causal influences* rather than mere correlations.

Well, I am not sure what 'reasonably clear intuitive sense' is, neither who you mean by 'we'. I might be wrong, but it seems that your intuition comes form a specific interpretation, not mathematics.

Seriously, reading "la nouvelle cuisine" is a good idea here.

I have started.

 

[lugita15]

I have not seen a clear definition of "realism" or "non-realism" - whatever that is supposed to mean.

Counterfactual definiteness seems to be a pretty clear criterion for realism (excluding superdeterminism): if experiment A is performed, then counterfactual definiteness says that the question "What would have happened if A had not been performed and B had been performed instead?" must always have a definite answer.

 

[ttn]

... purposeful indoctrination of readers ...

Big eyeroll. Look up "indoctrination" in the dictionary sometime. Then try actually reading the scholarpedia article.

Perhaps the confusion/disagreement stems from the fact that Einstein discussed (and Bell cited) the existence of physical reality in this context, or that Bell had to define "beables" for truly existing physical entities, to which this locality refers?

I'm not sure what "confusion/disagreement" you have in mind exactly. (Clearly, there are many in the mix.) The logic of EPR and Bell is clear enough: Einstein assumed locality and this led him to conclude that certain "elements of reality" (not acknowledged by ordinary QM) existed. Bell showed that these "elements of reality" implied disagreements with QM predictions, hence overall Bell proved that there is no way to account for the QM predictions with a local theory.

Re: Bell's needing to define "beables" in the context of formulating "locality", of course that needed to be done. The whole goal was to clearly distinguish *physically real* influences from mere correlations, influences on objects in a theory that shouldn't be taken as physically real (e.g., the scalar potential in coulomb gauge E&M), etc. So the very idea of "locality" presupposes a clear designation of what a given candidate theory says should be taken seriously, as corresponding to something physically real. That is all the concept of "beables" means, and it should be clear that without this idea it would be impossible to give a precise formulation of local/nonlocal causality.

 

[ttn]

I am not trying to prove that there is no nonlocality, just trying to understand why you are so hung up on a name that doesn't help nor captures the essence.

You'd only put it that way if you were already convinced there is no nonlocality!

Well, I am not sure what 'reasonably clear intuitive sense' is, neither who you mean by 'we'. I might be wrong, but it seems that your intuition comes form a specific interpretation, not mathematics.

The point is that we know, before we start looking into this Bell business, what "locality" and "nonlocality" are supposed to mean, especially in the context of relativity: in a "local" theory, causal influences *on* an event come from its past light cone, and causal influences *from* and event lie in its future light cone. Every student of relativity understands this. So the "we" just referred to anybody that knows a little relativity and hence is in a position to worry about whether relativity's alleged prohibition on faster-than-light causation is respected by other theories or not.

Neither of your proposed options for the source of the intuition is correct. It doesn't come from any specific interpretation (of QM, I assume you mean), nor does it come from mathematics. It comes from physics -- regular physics that no regular physicist thinks of as controversial. (Namely the idea that relativity implies a "fundamental speed limit".)

Let's talk more after you read about the great chef...

 

[ttn]

Counterfactual definiteness seems to be a pretty clear criterion for realism (excluding superdeterminism): if experiment A is performed, then counterfactual definiteness says that the question "What would have happened if A had not been performed and B had been performed instead?" must always have a definite answer.

Yes, that is probably what some people (who use dubious phrases like "local realism") mean by "realism".

Of course, nothing like "counterfactual definiteness" needs to be assumed to derive an empirically testable Bell inequality. So all the people talking about "realism" and "counterfactual definiteness" and other such things are for the most part just barking up the wrong tree.

 

[harrylin]

Big eyeroll. Look up "indoctrination" in the dictionary sometime. Then try actually reading the scholarpedia article.

By chance I checked that word before I gave my comment on your clarifications here in this forum that your article is not concerned with "the consensus of non-experts" but with (your view of) "the truth".
- http://dictionary.reference.com/browse/indoctrination

[..] Bell's needing to define "beables" in the context of formulating "locality", of course that needed to be done. The whole goal was to clearly distinguish *physically real* influences from mere correlations, influences on objects in a theory that shouldn't be taken as physically real (e.g., the scalar potential in coulomb gauge E&M), etc. So the very idea of "locality" presupposes a clear designation of what a given candidate theory says should be taken seriously, as corresponding to something physically real. That is all the concept of "beables" means, and it should be clear that without this idea it would be impossible to give a precise formulation of local/nonlocal causality.

Yes, I guess that we all agree on that.

 

[ttn]

By chance I checked that word before I gave my comment on your clarifications here in this forum that your article is not concerned with "the consensus of non-experts" but with (your view of) "the truth".
- http://dictionary.reference.com/browse/indoctrination

So, is your point that you didn't intend any of the usual negative connotations of the word, e.g., the implication that one is trying to get people to accept things *uncritically*? If really all you meant is that the article tries to teach a doctrine, OK, fine. But I suspect you meant, and certainly others have said openly, that they think the article is an attempt to indoctrinate in the usual sense of tricking people into accepting something. And that is just patently absurd. The article presents Bell's theorem *fairly*, explaining the reasons for everything in extensive detail, quoting extensively from primary literature, and acknowledging and critically reviewing different things that others have said. To call that "biased" or "indoctrination" is to confess that one cannot judge the scientific content for oneself but can instead only sense vaguely that lots of other people might feel that something controversial is being said.

As I suggested before, it's like accusing a biology textbook of being "indoctrination" on the grounds that it presents Darwin's ideas and gives only a short polemical footnote to creationism. To think that's wrong is to *presuppose* that creationism is a valid scientific alternative that deserves to be treated on an equal footing. And note that it doesn't matter whether 1% of people believe creationism, or 99%, or something in between. The way to decide what does and doesn't belong in a fair, objective, encyclopedic presentation of a topic is to look carefully at the issues and arguments, and decide where there is and where there is not *legitimate controversy*. You don't do this by taking public opinion polls, you do it by studying the science (and some history) in depth.

 

[mattt]

I'll try to explain what I meant in previous posts of mine.

At first I thought that a "naive or intuitive meaning of local causality" (with respect to these type of experiments) would be the following:

The outcomes predictions (of a "local theory") for a given setting HERE (for a totally specified state of the system, the pair, when it was created) should not depend (should be statistically independent) on what they later on choose to measure THERE (on what they choose to measure THERE; not the result predictions for a given setting THERE, that in fact may be correlated).

Mathematically:

For any "a", "b", "c",...and any value of the hidden variable \lambda (that completely specifies the state of the pair when it is created) :

P_{a}(A_1=1|\lambda)=P_{a,b}(A_1=1,A_2=\pm 1|\lambda)=P_{a,c}(A_1=1, A_2=\pm 1|\lambda)=...


For the moment let us call it "Mattt's naive notion of locality".

It is clear that "Travis factorizability condition" implies "Mattt's naive notion of locality", but the reverse is not true.

For example, orthodox quantum mechanics satisfies "Mattt's naive notion of locality" but does not satisfy "Travis factorizability condition".


For a deterministic hidden variable theory (a theory for which there is a funcion F such that (A_1,A_2)=F(\lambda,\alpha_1,\alpha_2) where \alpha_1 and \alpha_2 account for the setting HERE and THERE), "Mattt's naive notion of locality" and "Travis factorizability condition" are just the same.


Hence his "CHSH-Theorem" is, in particular, a correct mathematical proof that ANY deterministic theory that satisfies "Mattt's naive notion of locality" CAN NOT reproduce all predictions of Quantum Mechanics.


Obviously the question Travis would ask me is: why in hell do you call that mathematical expression of yours, "Mattt's naive notion of locality"?


I'll try to explain, and it is related to "weirdness":

For me, a (deterministic or stochastic, no matter) theory that DOES NOT satisfy my "Mattt's naive notion of locality" would seem to me very very strange (yes, I know Bhomian Mechanics is precisely a deterministic theory that does not satisfy my "Mattt's naive notion of locality" :) , I just say that for the moment it looks weird to me, just that).

The fact that (given a setting HERE and another setting THERE and the pair being prepared in a completely specified state when it was created earlier in the source) there may be statistical dependence among the distribution outcomes (for a completely specified state, I repeat) HERE and THERE, is not THAT surprising to me, (after all they both must be correlated with the state of the pair in the origin source, and thus may be correlated themselves). What would really surprise me is the violation of "Mattt's naive notion of locality".

Why?

Because I don't see ANY WAY their decision (of what parameter "a", "b"..to set) can be statistically correlated with the state of the pair when it was created, so if it (their decision) is correlated with the outcomes HERE, that would imply a kind of faster than light influence (between space-like separated regions).


Anyway, I still have to read all the rest of your scholarpedia article (I have only read till the CHSH Theorem) and maybe then (after reading about Bell's beables and their meaning in relativity theory) I may change my view about what looks to me "weird" and what not (after all I am a young mathematician, not a physicist, so I have not thought too much about the physical part yet).

In any case, I said since the first time that the CHSH-Theorem is correct, the only thing you and I (and martinbn I think) are now treating is "how do we call it" (specifically the "factorizability condition"), or "what anyone of us think "locality" should mean".

As I said, I have to read all the rest of your article. I'll be back in few days.

 

[harrylin]

So, is your point that you didn't intend any of the usual negative connotations of the word, e.g., the implication that one is trying to get people to accept things *uncritically*? [..]

No, my point, as I and others have sufficiently explained to you, is the inappropriateness of "teaching or inculcating a doctrine [..], especially one with a specific point of view" in an encylcopedia.

I happen to have experience with religious indoctrination and most religions use more refined methods to try to convince people of their teaching than attempting to get people accept things uncritically. Mostly what religions do is to present information and opinions - also contrary opinions - in such a way that the reader is likely going to agree with them. Usually they therefore critically review different things that others have said in a way and in so far as that supports the point of view that they want to teach. The problem is that such a biased presentation is often confused with a "fair" presentation - it can't be, by definition.
It would be the same as claiming that the defence summary in a court case is "fair and unbiased". And note that calling a defence summary biased is not to confess that one cannot judge the content for oneself, but - quite the contrary- that judgement is not for the defence. In science everyone must judge for himself after a fair hearing of the summaries from both sides.

 

[ttn]

... inappropriateness ...

OK, we disagree, so be it. Anybody who thinks the article is dangerously inappropriate is of course free not to read it. Though such people shouldn't be shocked if they try to discuss Bell's theorem here and I suggest they read the article and then get annoyed if they refuse!

 

[ttn]

At first I thought that a "naive or intuitive meaning of local causality" (with respect to these type of experiments) would be the following:

The outcomes predictions (of a "local theory") for a given setting HERE (for a totally specified state of the system, the pair, when it was created) should not depend (should be statistically independent) on what they later on choose to measure THERE (on what they choose to measure THERE; not the result predictions for a given setting THERE, that in fact may be correlated).

The issue is: what's so special about "what they later on choose to measure THERE"? What you want -- I mean, what you should want! -- is to formulate an idea of "local causality" in the context of a truly fundamental candidate theory. So ideas like "they" (i.e., people as opposed to other kinds of objects), "choose", "measure", etc., really shouldn't be showing up. It should be possible to formulate "locality" in non-anthropocentric terms.

Bell's approach is to simply say this: if you *completely specify* what exists in a slice of spacetime that closes off the back light cone of some event, then the probabilities assigned (by some candidate theory) to that event shouldn't be affected if you in addition specify stuff at spacelike separation from the event (more precisely, stuff that is outside the future light cone of the slice mentioned before).

You'll have to think through the details and see if you think it's reasonable. See my recent AmJPhys paper for lots of discussion about it. The point I am making here is just that Bell's formulation, unlike yours, has the virtue of being purely in terms of very general concepts (like "stuff" or "beable" or whatever) that don't sneak in any dubious (especially, anthropocentric) type distinctions.

Mathematically:

For any "a", "b", "c",...and any value of the hidden variable \lambda (that completely specifies the state of the pair when it is created) :

P_{a}(A_1=1|\lambda)=P_{a,b}(A_1=1,A_2=\pm 1|\lambda)=P_{a,c}(A_1=1, A_2=\pm 1|\lambda)=...


For the moment let us call it "Mattt's naive notion of locality".

I don't think that's quite the right way to express what you have in mind, but I think I understand what you have in mind. BTW, do you know that there is a huge literature from the 80s and 90s about "parameter independence" vs "outcome independence"? I think what you are expressing is that you think "parameter independence" is a reasonable requirement for locality, but not "outcome independence". I have written about this issue here if you're interested:

http://arxiv.org/abs/0808.2178

It is clear that "Travis factorizability condition" implies "Mattt's naive notion of locality", but the reverse is not true.

Right.

For example, orthodox quantum mechanics satisfies "Mattt's naive notion of locality" but does not satisfy "Travis factorizability condition".

Yup.

For a deterministic hidden variable theory (a theory for which there is a funcion F such that (A_1,A_2)=F(\lambda,\alpha_1,\alpha_2) where \alpha_1 and \alpha_2 account for the setting HERE and THERE), "Mattt's naive notion of locality" and "Travis factorizability condition" are just the same.

Yup.

All of this is standard stuff in the thread of literature I mentioned above.

Hence his "CHSH-Theorem" is, in particular, a correct mathematical proof that ANY deterministic theory that satisfies "Mattt's naive notion of locality" CAN NOT reproduce all predictions of Quantum Mechanics.

Yes, I agree, it should be absolutely clear to everybody that you cannot reproduce the QM predictions with a local deterministic theory. The question is: can you do it with a local non-deterministic theory? And you can't answer that question until you decide: what does "locality" mean for a non-deterministic theory?

Obviously the question Travis would ask me is: why in hell do you call that mathematical expression of yours, "Mattt's naive notion of locality"?

I'll try to explain, and it is related to "weirdness":

For me, a (deterministic or stochastic, no matter) theory that DOES NOT satisfy my "Mattt's naive notion of locality" would seem to me very very strange (yes, I know Bhomian Mechanics is precisely a deterministic theory that does not satisfy my "Mattt's naive notion of locality" :) , I just say that for the moment it looks weird to me, just that).

Well, OK, I won't criticize except to say that you'd have to do better than "it feels weird" to convince me.

The fact that (given a setting HERE and another setting THERE and the pair being prepared in a completely specified state when it was created earlier in the source) there may be statistical dependence among the distribution outcomes (for a completely specified state, I repeat) HERE and THERE, is not THAT surprising to me, (after all they both must be correlated with the state of the pair in the origin source, and thus may be correlated themselves).

My suspicion would be that it only seems "not too weird" for the things to be correlated because you start to forget what it meant that the state was specified completely! For sure, if the specification of the state is incomplete (or equivalently if you define "complete specification" to mean something epistemic!) there is no surprise, and no nonlocality, in the fact that the outcomes are correlated. But if you really meant it when you said the state was being specified completely, then you are basically in the position of having to say that something about the measurement over there influences the state over here, or the algorithm by which the state over here determines the probabilities for different possible outcomes over here, or ... *something* pertaining to over here.

What would really surprise me is the violation of "Mattt's naive notion of locality".

Well, of course I agree that violation of that should surprise you. We don't disagree about whether a violation of "Matt's ... locality" constitutes a violation of "real locality".

Why?

Because I don't see ANY WAY their decision (of what parameter "a", "b"..to set) can be statistically correlated with the state of the pair when it was created, so if it (their decision) is correlated with the outcomes HERE, that would imply a kind of faster than light influence (between space-like separated regions).

FYI, most of the people who argued this back in the 80s and 90s did so on the grounds that a violation of "Matt's ... locality" (aka, I think, "parameter independence") would allow faster-than-light *signaling*, whereas a violation of "Bell's locality" (but the sort of violation that respects "Matt's ... locality", i.e., a violation of "outcome independence") would not allow faster-than-light signaling. And, people argued, prohibiting such signaling is all relativity really requires. I think this was all wrong-headed on several counts. First, it is simply wrong to identify violations of OI/PI with no/yes on superluminal signaling. Bohmian Mechanics, for example, actually violates PI yet predicts it's impossible to send superluminal signals. The people just missed that "signaling" requires extra conditions. But second and more fundamentally, it's silly to think that "relativistic causal structure" is somehow ultimately about a human activity like sending signals. Again, a bare minimum requirement for a valid formulation should be that it doesn't contain anthropocentric concepts.

In any case, I said since the first time that the CHSH-Theorem is correct, the only thing you and I (and martinbn I think) are now treating is "how do we call it" (specifically the "factorizability condition"), or "what anyone of us think "locality" should mean".

Yes, as I said, I totally agree that the main issue is the one you're focusing on -- how "Locality" should be understood/formulated for non-deterministic theories.

 

[mattt]

Travis, I have just carefully read your article http://arxiv.org/pdf/0808.2178v1.pdf and it is just great!

It is a "must read" for everybody in my opinion. Now I fully understand many subtleties I missed when I just read the "CHSH-Theorem" statement and proof the other day.

It is funny that what I thought and partly wrote in earlier messages is basically exactly the same as what Jarrett thought years ago (I was not aware of anything of this, I just saw your thread some days ago and, because I am a mathematician, I could see that at least the CHSH-Theorem was a mathematical correct statement with a mathematically correct proof, and so I started to think about the whole issue the last few days for the first time in my life) about your "factorizability condition" being equivalent to "parameter independence"+"outcomes independence" and, as Jarrett, I naively thought of "locality" as just "parameter independence".

I think now that it is impossible to understand fully well the whole issue if someone has not read carefully your article I cited at the beginning.

Now I can understand much much better the meaning of both \lambda variables and parameter "a", "b"...variables.

It is clear ONLY after you read carefully all the stuff about beables, relativity, past light cone, regions 1,2 and 3, sufficiently specified beables in region 3, and Bell's own words, basically the whole first six pages of the article. And in fact the figures, specially figure 4 (on page 5 ) is just crucial to understand why "factorizability condition" is just exactly what Bell means about "local causality".

It is crucial (figure 4) because look how you drew it: both what would be "region 3" for A (and respectively "the other region 3" for B), don't overlap with the past light cone of B (respectively, with the past light cone of A), sorry you even label them in the picture, i.e. region 3a shields off region 1 from the overlap of the past light cones of 1 and 2 and region 3b shields off region 2 from the overlap of the past light cones of 1 and 2.

Look how the beables in these two regions 3a and 3b are not beables in the region (event) where the pair was created (that was an important point for me that I missed before reading this article) but any FUNDAMENTAL theory that satisfies this notion of "local causality" should be able to produce outcomes predictions for A and B just using the beables in regions 3a and 3b (even if those are not beables in the region/event of creation of the pair).

It is also very well explained why "parameter" (some material particles forming a device with a certain orientation) is as much a "beable" as "outcome" (some material particles forming a pointer with certain ubication).

So my "hypothetical theory" from previous posts (that satisfied "parameter independence" but did not satisfy "outcomes independence"), if thought of as FUNDAMENTAL, then would be violating the causal structure of relativity theory.

It is something remarkable.

I am just too tired to write anything else for the moment...maybe tomorrow I can comment something more. Tomorrow I will read it carefully again.

As I said, I think it is a great article, a must read for everyone.

 

[ThomasT]

@ mattt,
I'm appreciating your input, as well as others' input. Hope you (and ttn) check on this thread in the coming weeks. I'm still in the process, as time permits, of formulating some decent questions.

I don't understand the conclusion (that nature is nonlocal) yet, and I can't identify, much less approximate a clear statement of, exactly why I don't understand it. I have certain ideas, but they're more or less intuitive (ie., vague) and based on my expectation of the behavior of light wrt crossed polarizer setups.

Hopefully, another reading (or two) will help with that.

Your latest post indicates that Jarrett's analysis is naive in an important sense. Would you (and ttn if he reads this) recommend focusing on that, or something else?

One other question, for anybody, are Bell inequalities generally based on a linear correlation limit? This might be important, given the known behavior of light and the limits imposed by Bell's archetypal LR form, or it might not be important. I have no well-formed opinion wrt this.

 

[lugita15]

One other question, for anybody, are Bell inequalities generally based on a linear correlation limit? This might be important, given the known behavior of light and the limits imposed by Bell's archetypal LR form, or it might not be important. I have no well-formed opinion wrt this.

Bell inequalities are not derived from the ASSUMPTION that the correlation is at most linear for theories obeying the principle of locality. Rather, Bell inequalities follow from the assumption of the principle of locality and they yield the CONCLUSION that the correlation is at most linear.

 

[martinbn]

The point is that we know, before we start looking into this Bell business, what "locality" and "nonlocality" are supposed to mean, especially in the context of relativity: in a "local" theory, causal influences *on* an event come from its past light cone, and causal influences *from* and event lie in its future light cone. Every student of relativity understands this. So the "we" just referred to anybody that knows a little relativity and hence is in a position to worry about whether relativity's alleged prohibition on faster-than-light causation is respected by other theories or not.

Neither of your proposed options for the source of the intuition is correct. It doesn't come from any specific interpretation (of QM, I assume you mean), nor does it come from mathematics. It comes from physics -- regular physics that no regular physicist thinks of as controversial. (Namely the idea that relativity implies a "fundamental speed limit".)

Well, but this goes back to my 'problem'. If you have two systems (particles or not), which are spacelike separated and measuring one affects the other, then curtainly there is non-locallity. But, as said before, this is not the case. We have an entangled pair and it is meaningless to talk about the subsystems. There is just one system whose state is not a pure tensor and measurements on it. As far as I know you need entanglement in order to show that quantum mechanical predictions do not satisfy Bell's inequalities. And in those situations there is nothing transmitted faster than light. For example messages cannot be sent faster than light. Yes, the correlations are very different than anything in classical physics, but why call this property non-locality?

Let's talk more after you read about the great chef...

Actually which paper is it exactly? It says it is reprinted in "Speakables and ...", which I have and since I like Bell's style I'll probably try to read the whole thing, but just to know which one you are referring to.

 

[harrylin]

[..] entanglement [..] in those situations there is nothing transmitted faster than light. For example messages cannot be sent faster than light. Yes, the correlations are very different than anything in classical physics, but why call this property non-locality?[..]

Well the claim is of course, contrary to what you claim here, that these correlations can not be modeled with no influence at a distance and that instead they are only compatible with instantaneous influence at a distance. That's what is meant with "non-locality".

 

[ThomasT]

Yes, the correlations are very different than anything in classical physics ...

Are the correlations really very different than anything in classical physics? It doesn't seem so. Consider the QM correlation in the ideal. It corresponds to the classical Malus Law. I suspect that this isn't just happinstance. We're dealing, in both cases, with light directed through crossed polarizers.

In optical Bell tests, the rate of coincidental detection corresponds to the intensity of light transmitted by the analyzing polarizer in a polariscopic setup.

 

[ttn]

Well, but this goes back to my 'problem'. If you have two systems (particles or not), which are spacelike separated and measuring one affects the other, then curtainly there is non-locallity. But, as said before, this is not the case. We have an entangled pair and it is meaningless to talk about the subsystems. There is just one system whose state is not a pure tensor and measurements on it.

The proof allows one to specify only the complete state of a the particle pair as a single (perhaps holistic) thing. You don't *have* to break it apart into "the state of the subsystem over here" and "the state of the subsystem over there".

As far as I know you need entanglement in order to show that quantum mechanical predictions do not satisfy Bell's inequalities. And in those situations there is nothing transmitted faster than light.

Well that begs the question at issue.

For example messages cannot be sent faster than light. Yes, the correlations are very different than anything in classical physics, but why call this property non-locality?

We are interested in faster-than-light causation, not faster-than-light messages. You really think the relativistic causal structure knows about (or only cares about) "messages"??

And one is not *calling* the correlations "non-locality". One defines a notion of "locality" that captures just the idea of only-slower-than-light-causal-influences, and then finds that no theory respecting this condition can make the QM predictions. It has nothing whatsoever to do with correlations or any comparison to classical physics.

Actually which paper is it exactly? It says it is reprinted in "Speakables and ...", which I have and since I like Bell's style I'll probably try to read the whole thing, but just to know which one you are referring to.

"La nouvelle cuisine" is I think his clearest presentation of all this stuff. If you read his preface to the first edition of "speakable..." he says he regrets never having put everything together in a certain way for publication. That's what he subsequently did with "la nouvelle cuisine".