Local realism ruled out? (was: Photon entanglement and )

[ThomasT]

I am awfully sorry, I've read your post several times, but I just cannot understand a word.

Ok, I'll try to present the gist of how I've learned to think about this in a less scattered way.

1. Bell locality can be parsed to include statistical independence between A and B.

2. Statistical dependence between A and B is sufficient to cause experimental violation of inequalities which are based on the (formal) assumption of statistical independence between A and B.

3. The statistical dependence is produced via local channels.

4. So, experimental violation of inequalities based on Bell locality doesn't imply nonlocality.

5. Formally, Bell locality entails that the joint probability of the entangled state be factorable into the product of the individual probabilities for A and B.

6. Bell locality is incompatible with the QM requirement that the entangled state representation be nonfactorable.

7. This nonfactorability or quantum nonseparability reflects the (locally produced) statistical dependencies required for the experimental production of entanglement.

8. Experimental loopholes notwithstanding, no Bell local theory can possibly reproduce the full range of QM predictions or experimental results wrt entangled states.

9. None of this implies the existence of nonlocality in Nature -- which is contrary to your idea that, in your words:

Yes, that would certainly be a good evidence of nonlocality (I mean if violations of the genuine Bell inequalities, without loopholes, are demonstrated experimentally).

10. None of this implies that SQM (associated with Bell's theorem) is a nonlocal theory -- which is contrary to your idea that, in your words:

To get such nonlocality in the Bell theorem you need something extra - such as the projection postulate. And this postulate generates nonlocality in a very direct way: indeed, according to this postulate, as soon as you measure a projection of spin of one particle of a singlet, the value of the projection of spin of the other particle immediately becomes determined, no matter how far from each other the particles are, and this is what the Bell theorem is about..

11. In fact, the standard QM methodology and account (including the projection postulate and any quantum level models associated with a particular experimental setup) is based on the (at least tacit, but explicit in the case of some models) assumption that there's a locally produced relationship between quantum disturbances analyzed at spacelike separations. (eg., in the case of Aspect et al experiments using atomic calcium cascades to produce entangled photons, the entangling relationship is assumed to be produced at emission -- and the experimental design must entail statistical dependence between A and B in order to pair photons emitted by the same atom).

 

[akhmeteli]

Ok, I'll try to present the gist of how I've learned to think about this in a less scattered way.

Thank you very much for your patience with me. At least now I don't feel as if I were trying to decipher a text in double-Dutch:-)

3. The statistical dependence is produced via local channels.

What local channels, if there is enough spatial separation?

8. Experimental loopholes notwithstanding, no Bell local theory can possibly reproduce the full range of QM predictions or experimental results wrt entangled states.

Again, the fact that local theories cannot reproduce all QM predictions (which include contradictions) cannot be used as an argument against local theories - it's their strong point.

11. In fact, the standard QM methodology and account (including the projection postulate and any quantum level models associated with a particular experimental setup) is based on the (at least tacit, but explicit in the case of some models) assumption that there's a locally produced relationship between quantum disturbances analyzed at spacelike separations. (eg., in the case of Aspect et al experiments using atomic calcium cascades to produce entangled photons, the entangling relationship is assumed to be produced at emission -- and the experimental design must entail statistical dependence between A and B in order to pair photons emitted by the same atom).

"the entangling relationship assumed to be produced at emission" is one thing, but the choice of projection of spin or polarization measured at A seems to immediately change the situation at B. If it were indeed so, that would be a problem for locality. At least that's what I tend to think.

 

[DrChinese]

9. None of this implies the existence of nonlocality in Nature ...


11. In fact, the standard QM methodology and account (including the projection postulate and any quantum level models associated with a particular experimental setup) is based on the (at least tacit, but explicit in the case of some models) assumption that there's a locally produced relationship between quantum disturbances analyzed at spacelike separations. (eg., in the case of Aspect et al experiments using atomic calcium cascades to produce entangled photons, the entangling relationship is assumed to be produced at emission -- and the experimental design must entail statistical dependence between A and B in order to pair photons emitted by the same atom).

A comment just to make sure everyone is up on some of the refinements to the original Bell test regimen.

We now have the ability to entangle photons that have never met - this is called "entanglement swapping" (ES). Early versions of this protocol did not effectively allow the photons to be created sufficiently far enough to eliminate local interaction, but the newer ones do. For example:

High-fidelity entanglement swapping with fully independent sources
(2009) Rainer Kaltenbaek, Robert Prevedel, Markus Aspelmeyer, Anton Zeilinger

"Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fi delity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication experiments as well as for novel tests on the foundations of quantum physics."

Note that the experiment in this paper does not actually execute the variation where the photons are never in each other's light cones, but you can be sure that is coming (if not already published).

So basically, you have a pretty difficult time explaining the violation of a Bell Inequality by photon pairs that were never in a common light cone. Without having something being non-local, that is.
It is hard to imagine how you can have

 

[ThomasT]

What local channels, if there is enough spatial separation?

Statistical dependence refers to the fact that a detection at A changes the sample space at B, and vice versa.

This happens during the pairing process via the coincidence circuitry.

All very local, but sufficient to render Bell locality incompatible with QM and entanglement experiments.

Again, the fact that local theories cannot reproduce all QM predictions (which include contradictions) cannot be used as an argument against local theories - it's their strong point.

But QM predictions agree with experimental results, and Bell local theories don't. More importantly, Bell local theories can't possibly agree with experimental results ... ever -- because Bell's formal expression of locality encodes statistical as well as causal independence.

Bell locality contradicts an integral part of entanglement experiments, statistical dependence between A and B. The upside, for LHV advocates, is that this doesn't rule out local realist theories -- just Bell local theories. The downside, for nonlocality advocates, is that this tells us nothing about nonlocality wrt either Nature or standard QM.

... the choice of projection of spin or polarization measured at A seems to immediately change the situation at B. If it were indeed so, that would be a problem for locality.

Yes, that would be a problem for locality. But that's not what standard QM says, and that's not what happens experimentally.

 

[akhmeteli]

Statistical dependence refers to the fact that a detection at A changes the sample space at B, and vice versa.

This happens during the pairing process via the coincidence circuitry.

All very local, but sufficient to render Bell locality incompatible with QM and entanglement experiments.

But QM predictions agree with experimental results, and Bell local theories don't. More importantly, Bell local theories can't possibly agree with experimental results ... ever -- because Bell's formal expression of locality encodes statistical as well as causal independence.

Bell locality contradicts an integral part of entanglement experiments, statistical dependence between A and B. The upside, for LHV advocates, is that this doesn't rule out local realist theories -- just Bell local theories. The downside, for nonlocality advocates, is that this tells us nothing about nonlocality wrt either Nature or QM.

Yes, that would be a problem for locality. But that's not what QM says, and that's not what happens experimentally.

Sorry, ThomasT, you've lost me again. This time I cannot say I don't understand a word, but 30% is too little for a meaningful discussion - this is a physics forum, not a crossword contest. With all due respect, if you believe you're saying something well-known that I don't know, give me a reference, if not, try to be clearer. And I mean much clearer.

 

[yoda jedi]

"the entangling relationship assumed to be produced at emission" is one thing, but the choice of projection of spin or polarization measured at A seems to immediately change the situation at B. If it were indeed so, that would be a problem for locality. At least that's what I tend to think.

long time ago...​

...Quantum mechanics says that there should be a high correlation between results at the polarizers because the photons instantaneously "decide" together which polarization to assume at the moment of measurement, even though they are separated in space. Hidden variables, however, says that such instantaneous decisions are not necessary, because the same strong correlation could be achieved if the photons were somehow informed of the orientation of the polarizers beforehand......

...Quantum mechanics predicts that “non-local” correlations can exist between the particles. This means that if one photon is polarized in, say, the vertical direction, the other will always be polarized in the horizontal direction, no matter how far away it is. However, some physicists argue that this cannot be true and that quantum particles must have local values – known as “hidden variables” – that we cannot measure......




.

 

[DrChinese]

But QM predictions agree with experimental results, and Bell local theories don't. More importantly, Bell local theories can't possibly agree with experimental results ... ever -- because Bell's formal expression of locality encodes statistical as well as causal independence.

...

Yes, that would be a problem for locality. But that's not what standard QM says, and that's not what happens experimentally.

These are not standard expressions of theory or experiment. Experimentally: when Alice acts, it appears "as if" the situation changes non-locally for Bob (and vice versa). Theoretically: A Bell local theory is one in which Alice action does not appear "as if" the situation changes at Bob to match UNLESS there is a sub-c channel for propagation (or possibly a common earlier cause within a mutual light cone).

 

[ThomasT]

Sorry, ThomasT, you've lost me again. This time I cannot say I don't understand a word, but 30% is too little for a meaningful discussion - this is a physics forum, not a crossword contest. With all due respect, if you believe you're saying something well-known that I don't know, give me a reference, if not, try to be clearer. And I mean much clearer.

I don't know if it's a well known approach or not.

The argument is that Bell's locality condition isn't, exclusively, a locality condition. If it isn't, then what might this entail wrt the interpretation of experimental violations of inequalities based on Bell locality?

In a nutshell:

Bell locality doesn't just represent causal independence between A and B, but also statistical independence between A and B.

Statistical dependence between A and B means that a detection at A changes the sample space at B, and vice versa. The pairing process entails statistical dependence between A and B, and this statistical dependence can be accounted for via the local transmissions and interactions of the coincidence circuitry.

Statistical dependence between A and B is sufficient to violate inequalities based on Bell locality.

So, experimental violations of inequalities based on Bell locality, while they do rule out Bell local theories, don't imply nonlocality or necessarily rule out local realism.

 

[ThomasT]

These are not standard expressions of theory or experiment.

If not, they should be.

Experimentally: when Alice acts, it appears "as if" the situation changes non-locally for Bob (and vice versa).

This isn't the way that I've learned to think about it.

Theoretically: A Bell local theory is one in which Alice action does not appear "as if" the situation changes at Bob to match UNLESS there is a sub-c channel for propagation (or possibly a common earlier cause within a mutual light cone).

I'm not sure what you're saying. Bell local theories of entangled states don't match QM or experiments, do they?

 

[DrChinese]

I'm not sure what you're saying. Bell local theories of entangled states don't match QM or experiments, do they?

Bell local + Bell realistic = ruled out.

 

[Eye_in_the_Sky]

What about "Bell Locality" alone?

Bell local + Bell realistic = ruled out.

Dr. Chinese, I am wondering, do you not also agree that the following stronger statement is true as well?

Bell local = ruled out

 

[DrChinese]

Dr. Chinese, I am wondering, do you not also agree that the following stronger statement is true as well?

Bell local = ruled out

No, but I can certainly understand why you might feel that way.

The Bell argument - to me - centers around counterfactual reasoning (realism) more than locality (separability). Realism being the requirement that particles have definite values for observables regardless of their actually being measured. Without this critical requirement, the Bell Inequality cannot be derived, and therefore it cannot be violated.

But a reasonable person would also look at entanglement and say, gee, there must be *some* kind of non-local action occurring. I refer to that as "quantum non-locality" which to me simply encapsulates the idea that there are non-local correlations. But that does not strictly imply that Einsteinian (Bell) locality is violated.

 

[ThomasT]

Sorry, ThomasT, you've lost me again. This time I cannot say I don't understand a word, but 30% is too little for a meaningful discussion - this is a physics forum, not a crossword contest. With all due respect, if you believe you're saying something well-known that I don't know, give me a reference, if not, try to be clearer. And I mean much clearer.

I think I might have been presenting the argument the wrong way.

Bell locality applied to LHV representation of two photon entangled state entails this:

P(A,B) = P(A) P(B)

That is, it entails that the joint probability be factorable (separable) as the product of the individual probabilities.

From probability theory and statistics, if two (sets of) events, A and B, are independent, then their joint probability is the product of the individual probabilites, P(A) and P(B).

So, we start out by observing that Bell locality represents statistical independence.
(This is different from the previous approach of assuming that Bell's locality condition represents causal independence, and then parsing it to include statistical independence.)

Does statistical independence imply causal independence?

The answer is yes (causal dependence entails statistical dependence).

However, in order to ascertain whether or not Bell locality is viable (that is, whether or not its application allows us to deduce the presence of superluminal causality) we must ask:

Does statistical dependence imply causal dependence?

Ok so far?

 

[DrChinese]

I think I might have been presenting the argument the wrong way.

Bell locality applied to LHV representation of two photon entangled state entails this:

P(A,B) = P(A) P(B)

That is, it entails that the joint probability be factorable (separable) as the product of the individual probabilities.

From probability theory and statistics, if two (sets of) events, A and B, are independent, then their joint probability is the product of the individual probabilites, P(A) and P(B).

So, we start out by observing that Bell locality represents statistical independence.
(This is different from the previous approach of assuming that Bell's locality condition represents causal independence, and then parsing it to include statistical independence.)

1. I agree that P(A,B) = P(A) P(B) is a test of a local realistic theory. Certainly I look for that in any model claiming to be local realistic. Actually I look for something in which P(A)=f(A, v1, v2, etc) as long as B is not a variable, even indirectly.

Because of the advent of Bell, though, the meaning of independence has been blurred. Because it is obvious now that somehow or another, P(A) and P(B) must be connected some way to make the relationships work out. In the De Raedt computer simulation, for example, random variables and specially shaped functions are introduced to achieve a pseudo dependence on theta=A-B.

2. Of course, P(A,B) = P(A) P(B) alone does not lead to a violation of a Bell Inequality. That requires P(A, B, C)>=0 which is actually not true for all A, B, C. So that too is something I test for. I want there to be values produced for an A, B and C simultaneously using the same f(...). Now according to your line of thinking, this is automatically true if there is a separable f(). So 2. must not be necessary.

3. Lastly, I want the results to match QM predictions. I know, on the other hand, that this will not happen because of requirement 2 above. In the De Raedt simulation, it is false. So their argument is that the full universe does not, in fact, match the QM predictions. So you might conclude that we have demonstrated that 2. is not necessary.

--------

So where is the problem? Because I can ALSO start with 2 as well, ignoring 1. All I need to do is ask you to provide me with a data set of values for an A, B and C I select (such as 0, 120, 240 degrees). You can make them up any way you want, and you can use A, B and C to determine those values... they do not need to be separable! You cannot do that AND have them match requirement 3, which is that they match QM predictions for those same angles.

So are these requirements simply alternative requirements? In some sense they are. Travis Norsen, for one, would agree with you that Bell locality (he defines it somewhat differently) is sufficient for Bell's Theorem. I.e. he believes that realism is NOT a requirement of Bell's Theorem, and therefore all Bell tests prove that nature is non-local.

On the other hand, I argue that realism IS a requirement of Bell's Theorem. It is the requirement of a simultaneous value for A, B and C that makes it work. I personally think the separability requirement is not as important, but again it too IS a requirement.

And that is the standard view. You can try to prove Bell's Theorem without either requirement (locality or realism), but you won't be able to. You need both the ideas of f(variables) and values for A, B and C to get the result.

 

[Eye_in_the_Sky]

zooming in on "realism"

No, but I can certainly understand why you might feel that way.

The Bell argument - to me - centers around counterfactual reasoning (realism) more than locality (separability). Realism being the requirement that particles have definite values for observables regardless of their actually being measured. Without this critical requirement, the Bell Inequality cannot be derived, and therefore it cannot be violated.

But a reasonable person would also look at entanglement and say, gee, there must be *some* kind of non-local action occurring. I refer to that as "quantum non-locality" which to me simply encapsulates the idea that there are non-local correlations. But that does not strictly imply that Einsteinian (Bell) locality is violated.

In the above, you cite "realism" in connection with to different points:

CF ≡ counterfactuality

and

IS ≡ the existence of "instruction sets" .

How do you see the status of IS in Bell's derivation? Do you see it as a derived principle, or do you see it as an independent assumption? I see it as a derived principle in the following way:

BL Λ PC Λ CF → IS ,

where

BL ≡ Bell Locality

and

PC ≡ perfect (anti-)correlation for equal settings .

 

[DrChinese]

In the above, you cite "realism" in connection with to different points:

CF ≡ counterfactuality

and

IS ≡ the existence of "instruction sets" .

How do you see the status of IS in Bell's derivation? Do you see it as a derived principle, or do you see it as an independent assumption? I see it as a derived principle in the following way:

BL Λ PC Λ CF → IS ,

where

BL ≡ Bell Locality

and

PC ≡ perfect (anti-)correlation for equal settings .

This is a good point. When you really break down Bell, you see what he has given us is a road map. Once we have that map, we have the key to breaking apart any local realistic theory. The map points out a lot of features of the territory. Some of these features probably should have been obvious even without the Inequality itself. And your point about perfect correlations (PC) is a great example.

PC needs to be a requirement of a LR theory, and Bell points this out early. It turns out this is NO MINOR POINT at all! Here we have inherent randomness that itself defies modeling (as the entangled outcomes are random at all settings) and yet they must match. Now, how can there be separability with this characteristic? Yes, we must add yet another constraint to account for this - one I didn't explicitly mention. I said: "... somehow or another, P(A) and P(B) must be connected some way to make the relationships work out." And that is both the PC you mention and more generally, Malus.

1. Instruction set may be a slight misnomer (although it is a good visual), because as Bell says: "...it follows that the result of any such measurement must actually be predetermined..." Now, of course you can say "don't forget the interaction with the polarizer" but that really makes no sense. Polarizer, beamsplitter, or whatever optical system, the results are PC. That is also true with electrons so obviously it has nothing whatsoever to do with underlying nature of the interaction with the measurement apparatus per se. There must be complete predetermination of all settings in an LR model if there is PC. You also have random results (RR). So to me, PC + RR -> IS. And so this simple case is not so simple at all.

2. If you have predetermination, then presumably you have the separability we are asking for AND we have the realism we are asking for. Now you just need one final point, that there are angle settings for which no predetermined IS will work. If Bell simply supplied these settings out of thin air, without a proof, it would still be enough to provide a contradiction. Assuming for a moment - as Bell does - that QM predictions would match experimental results: IS <> QM.

3. You then don't even need Bell's Theorem to be valid if you accept the reasoning so far. Because who cares if the theorem is even valid? Once you know - as Bell figured out - what those angles are, you have everything you need to finish the picture. Bell mentions the predetermination in the second paragraph of his paper (i.e. the first paragraph of his argument). If he stopped there and said: PC -> IS <> QM we would already have a big mess on our hands for those who advocate the HV position.

4. We are now left to struggle to determine what element(s) of IS precisely is wrong. And that is where everyone gets into a tizzy. Is it locality? Is it realism? Is it contextuality? Is it separability? Clearly, there are a lot of issues to consider, and a lot rides on your definitions for these terms. It is obvious to me that the IS cannot exist "there" and "then". I.e. at the spacetime point that the entangled particle pair comes into existence, the IS cannot be restricted to that location at that time. There MUST be information entering into the equation from somewhere else and/or at some other point in time.

5. QM considers the "context" of the setup as part of its successsful predictions. So I would simply state that the context spans points in space (i.e. is non-local), and the context somehow spans a points in time (non-temporal, non-causal, or whatever you want to call it). That context violates our notions of local realism.

 

[yoda jedi]

No, but I can certainly understand why you might feel that way.

The Bell argument - to me - centers around counterfactual reasoning (realism) more than locality (separability). Realism being the requirement that particles have definite values for observables regardless of their actually being measured. Without this critical requirement, the Bell Inequality cannot be derived, and therefore it cannot be violated.

But a reasonable person would also look at entanglement and say, gee, there must be *some* kind of non-local action occurring. I refer to that as "quantum non-locality" which to me simply encapsulates the idea that there are non-local correlations. But that does not strictly imply that Einsteinian (Bell) locality is violated.

reality can have no definite values.

 

[zonde]

I don't know if it's a well known approach or not.

The argument is that Bell's locality condition isn't, exclusively, a locality condition. If it isn't, then what might this entail wrt the interpretation of experimental violations of inequalities based on Bell locality?

In a nutshell:

Bell locality doesn't just represent causal independence between A and B, but also statistical independence between A and B.

Statistical dependence between A and B means that a detection at A changes the sample space at B, and vice versa. The pairing process entails statistical dependence between A and B, and this statistical dependence can be accounted for via the local transmissions and interactions of the coincidence circuitry.

Statistical dependence between A and B is sufficient to violate inequalities based on Bell locality.

So, experimental violations of inequalities based on Bell locality, while they do rule out Bell local theories, don't imply nonlocality or necessarily rule out local realism.

I will try to describe the point of ThomasT a bit differently. I hope that I will be in line with what ThomasT is saying.

Lets take equation that describes correlations of photons from Type I PDC:
$$P_{VV}(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta\, cos^{2}\theta_{l} + cos^{2}\alpha\, cos^{2}\beta\, sin^{2}\theta_{l} + \frac{1}{4}sin 2\alpha\, sin 2\beta\, sin 2\theta_{l}\, cos \phi$$
This is equation (9) from paper - http://arxiv.org/abs/quant-ph/0205171/"

This relation produces $$\frac{1}{2}cos^{2}(\alpha-\beta)$$ law when $$\theta_{l}$$ is Pi/4 and $$\phi$$ is 0. But when for example $$\theta_{l}$$ is 0 it produces $$sin^{2}\alpha\, sin^{2}\beta$$ that is simply product of two probabilities from Malus law.

So let's rewrite this EPR state with $$\theta_{l}=\pi/4$$ and $$\phi=0$$:
$$P_{VV}(\alpha,\beta) = \frac{1}{2}sin^{2}\alpha\, sin^{2}\beta + \frac{1}{2}cos^{2}\alpha\, cos^{2}\beta + \frac{1}{4}sin 2\alpha\, sin 2\beta$$
First and second term have perfectly sensible physical interpretation - it's product of H (V) photon detection probabilities from Alice and Bob i.e. chance that we have a click at coincidence counter.
However if detection efficiency is not 100% then we have to make additional assumption that sample spaces of Alice and Bob for detected H(V) photons are completely uncorrelated (random).
But we have third - interference term that can be positive as well as negative. For me it seems that straight forward interpretation of this interference term is that sample spaces of detected photons can become correlated (as I understand this is the point of ThomasT). Say if $$sin 2\alpha$$ becomes non zero Alice's side has uneven distribution of sample space but as long as $$sin 2\beta$$ is zero (Bob has even distribution) Alice's uneven distribution has no effect. But if both sides have uneven distributions depending from correlation or anti-correlation of this unevenness this term becomes nonzero positive or negative.

Please note that this is just an interpretation of SQM and it confirms correctness of ensemble interpretation and denies correctness of other interpretations that unconditionally separate ensemble in individual photons.

 

[Eye_in_the_Sky]

on "instruction sets"

This is a good point. When you really break down Bell, you see what he has given us is a road map. Once we have that map, we have the key to breaking apart any local realistic theory. The map points out a lot of features of the territory. Some of these features probably should have been obvious even without the Inequality itself. And your point about perfect correlations (PC) is a great example.

PC needs to be a requirement of a LR theory, and Bell points this out early. It turns out this is NO MINOR POINT at all! Here we have inherent randomness that itself defies modeling (as the entangled outcomes are random at all settings) and yet they must match. Now, how can there be separability with this characteristic? Yes, we must add yet another constraint to account for this - one I didn't explicitly mention. I said: "... somehow or another, P(A) and P(B) must be connected some way to make the relationships work out." And that is both the PC you mention and more generally, Malus.

1. Instruction set may be a slight misnomer (although it is a good visual), because as Bell says: "...it follows that the result of any such measurement must actually be predetermined..." Now, of course you can say "don't forget the interaction with the polarizer" but that really makes no sense. Polarizer, beamsplitter, or whatever optical system, the results are PC. That is also true with electrons so obviously it has nothing whatsoever to do with underlying nature of the interaction with the measurement apparatus per se. There must be complete predetermination of all settings in an LR model if there is PC. You also have random results (RR). So to me, PC + RR -> IS. And so this simple case is not so simple at all.

2. If you have predetermination, then presumably you have the separability we are asking for AND we have the realism we are asking for. Now you just need one final point, that there are angle settings for which no predetermined IS will work. If Bell simply supplied these settings out of thin air, without a proof, it would still be enough to provide a contradiction. Assuming for a moment - as Bell does - that QM predictions would match experimental results: IS <> QM.

3. You then don't even need Bell's Theorem to be valid if you accept the reasoning so far. Because who cares if the theorem is even valid? Once you know - as Bell figured out - what those angles are, you have everything you need to finish the picture. Bell mentions the predetermination in the second paragraph of his paper (i.e. the first paragraph of his argument). If he stopped there and said: PC -> IS <> QM we would already have a big mess on our hands for those who advocate the HV position.

4. We are now left to struggle to determine what element(s) of IS precisely is wrong. And that is where everyone gets into a tizzy. Is it locality? Is it realism? Is it contextuality? Is it separability? Clearly, there are a lot of issues to consider, and a lot rides on your definitions for these terms. It is obvious to me that the IS cannot exist "there" and "then". I.e. at the spacetime point that the entangled particle pair comes into existence, the IS cannot be restricted to that location at that time. There MUST be information entering into the equation from somewhere else and/or at some other point in time.

5. QM considers the "context" of the setup as part of its successsful predictions. So I would simply state that the context spans points in space (i.e. is non-local), and the context somehow spans a points in time (non-temporal, non-causal, or whatever you want to call it). That context violates our notions of local realism.

Dr. Chinese, thank you for your reply. However, I cannot see in it an answer to my question.

From your reply to ThomasT (sitting right above the post in which I asked my question), I think I can see what your answer would be.

... he believes that realism is NOT a requirement of Bell's Theorem, and therefore all Bell tests prove that nature is non-local.

On the other hand, I argue that realism IS a requirement of Bell's Theorem. It is the requirement of a simultaneous value for A, B and C that makes it work.

And that is the standard view. You can try to prove Bell's Theorem without either requirement (locality or realism), but you won't be able to. You need both the ideas of f(variables) and values for A, B and C to get the result.

It appears to me that your answer is:

I see the existence of instruction sets as an independent assumption and not as a derived principle in Bell's derivation.

... Am I correct?

 

[DrChinese]

Dr. Chinese, thank you for your reply. However, I cannot see in it an answer to my question.

From your reply to ThomasT (sitting right above the post in which I asked my question), I think I can see what your answer would be.It appears to me that your answer is:

I see the existence of instruction sets as an independent assumption and not as a derived principle in Bell's derivation.

... Am I correct?

I think the Bell paper is a road map to a disproof of local realism. One of the paths is to to demonstrate that PC (perfect correlations) implies predetermination in a classical (local realistic) world. Bell makes several concurrent arguments, so I try not to specifically say X -> Y about too many things. To me, it is clear that the instruction set mentality cannot work, and there are several ways to arrive at that point - and it depends on which assumption you start with.

 

[yoda jedi]

So, experimental violations of inequalities based on Bell locality, while they do rule out Bell local theories, don't imply nonlocality or necessarily rule out [STRIKE]local[/STRIKE] realism.

imply nonlocality, but does not rule out realism.




http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

...the Bell theorem has demonstrably nothing to do with the 'realism' as defined
by these authors Leggett, Zeilinger, Gröblacher and that, as a consequence, their conclusions about the foundational significance of the Bell theorem are unjustified...

...the role of Bell’s theorem is not to set constraints on how ‘realist’ we are allowed to be about quantum systems...





http://arxiv.org/PS_cache/arxiv/pdf/0901/0901.4255v2.pdf

...In recent years the violation of Bell's inequality has often been interpreted as
either a failure of locality or of realism (or of both). The problem with such a
claim is that it is not clear what realism in this context should mean. Sometimes
realism is dened as the hypothesis that every physical quantity always has a
value and that measurements merely reveal these predetermined values. That
is, realism is identied with determinism. But if so, then, rst, why should
one use the word local realism instead of local determinism? And second, Bell's
inequality can be stated and proven without any assumption about determinism.
Consequently, determinism is not the issue......


...In conclusion, the claim that the observation of a violation of a Bell inequality
leads to an alleged alternative between nonlocality and non-realism....However, it is not specifc to Bell inequalities......Hence, all violations of Bell's inequality should be interpreted as a demonstration of nonlocality...





http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.4000v1.pdf

...There is hardly a result that is more widely misunderstood in the scientific
community than Bell’s theorem...

...To summarize, what can one conclude from the violation of Leggett’s
inequality ? ....That doesn’t tell us anything about determinism or any type of philosophical realism.





http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0958v1.pdf

...What really matters is the fact that the derivation of Bell’s inequality in no way whatsoever needs an assumption of realism...


....This being the situation we must conclude that in no way whatsoever Bell’s
inequality has something to do with realism. It simply identifies in a straightforward
and lucid way that what quantum phenomena impose to us is to accept the
unescapable fact that natural processes involving entangled states of composite
and far-away systems turn out to be unavoidably non-local...


....or by those who derive from experimental results inspired by not strictly convincing theoretical models unjustified conclusions concerning such an important issue as the one of the reality of the world around us.......

 

[nikman]

Paging DrC. Haven't really gotten my head around the Gisin paper. The Zeilinger group's Legget paper (arxiv 0704.2529) is titled "An experimental test of non-local realism" and starts out thus:

Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be aected by actions in spacelike separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply conrmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sucient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned [1].​

concluding in this wise:

We have experimentally excluded a class of important non-local hidden-variable theories. In an attempt to model quantum correlations of entangled states, the theories under consideration assume realism, a source emitting classical mixtures of polarized particles (for which Malus' law is valid) and arbitrary non-local dependencies via the measurement devices. Besides their natural assumptions, the main appealing feature of these theories is that they allow us both to model perfect correlations of entangled states and to explain all existing Bell-type experiments. We believe that the experimental exclusion of this particular class indicates that any non-local extension of quantum theory has to be highly counterintuitive. For example, the concept of ensembles of particles carrying denite polarization could fail. Furthermore, one could consider the breakdown of other assumptions that are implicit in our reasoning leading to the inequality. These include Aristotelian logic, counterfactual deniteness, absence of actions into the past or a world that is not completely deterministic [30]. We believe that our results lend strong support to the view that any future extension of quantum theory that is in agreement with experiments must abandon certain features of realistic descriptions.​

In addition there are a couple of Charles Tresser papers (arxiv 0501030 and 0608008v2) proposing that the locality assumption isn't even necessary for Bell: Occamize it out and what you have left are actually tests that violate "classical realism".

 

[DrChinese]

http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0958v1.pdf

...What really matters is the fact that the derivation of Bell’s inequality in no way whatsoever needs an assumption of realism...


....This being the situation we must conclude that in no way whatsoever Bell’s
inequality has something to do with realism. It simply identifies in a straightforward
and lucid way that what quantum phenomena impose to us is to accept the
unescapable fact that natural processes involving entangled states of composite
and far-away systems turn out to be unavoidably non-local...


....or by those who derive from experimental results inspired by not strictly convincing theoretical models unjustified conclusions concerning such an important issue as the one of the reality of the world around us.......

Yes I have seen some of these arguments and papers previously. There is, as I have mentioned, those such as Norsen that make the argument that realism is not assumed in Bell. Of course, it is but it is not marked as "Here is where the realism argument starts." So if you want to see it, look after Bell's (14). "It follows that c is another unit vector..." That is where the counterfactual argument begins, obviously with 2 photons there can only be 2 measurements (a and b).

So you can think whatever you want. On the other hand, there are plenty of other experiments - such as GHZ - in which the realistic position is demolished independently of Bell. So you might want to consider that as well.

As Gisin says, realism is often poorly defined. There is a reason for that, the fact is we don't know precisely how to define it. It could be considered akin to causality, non-contextuality, or something else. Experiments continue to probe the frontier.

 

[DrChinese]

Paging DrC. Haven't really gotten my head around the Gisin paper. The Zeilinger group's Legget paper (arxiv 0704.2529) is titled "An experimental test of non-local realism" and starts out thus:

Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be aected by actions in spacelike separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply conrmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of 'spooky' actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sucient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned [1].​

concluding in this wise:

We have experimentally excluded a class of important non-local hidden-variable theories. In an attempt to model quantum correlations of entangled states, the theories under consideration assume realism, a source emitting classical mixtures of polarized particles (for which Malus' law is valid) and arbitrary non-local dependencies via the measurement devices. Besides their natural assumptions, the main appealing feature of these theories is that they allow us both to model perfect correlations of entangled states and to explain all existing Bell-type experiments. We believe that the experimental exclusion of this particular class indicates that any non-local extension of quantum theory has to be highly counterintuitive. For example, the concept of ensembles of particles carrying denite polarization could fail. Furthermore, one could consider the breakdown of other assumptions that are implicit in our reasoning leading to the inequality. These include Aristotelian logic, counterfactual deniteness, absence of actions into the past or a world that is not completely deterministic [30]. We believe that our results lend strong support to the view that any future extension of quantum theory that is in agreement with experiments must abandon certain features of realistic descriptions.​

In addition there are a couple of Charles Tresser papers (arxiv 0501030 and 0608008v2) proposing that the locality assumption isn't even necessary for Bell: Occamize it out and what you have left are actually tests that violate "classical realism".

I am with you on the Gisin paper, I don't really follow what point he is making. Clearly, he is in the middle of some of the most fascinating research on delayed choice experiments and quantum teleportation. To me, any delayed choice experiment is automatically an attack on realism. After all: if you can change the past with a future decision, how much realism can there be?

See also Hall's: http://arxiv.org/abs/0909.0015"

Tresser's are good papers, I have seen his previously and I happen to agree with him: I don't think you need locality to obtain the main Bell result. But I also believe that Bell's final conclusion does include a locality condition and I think that is a generally accepted result.

Zeilinger and others have come up with a number of experiments showing a similar result: realism suffers from severe problems which are fundamentally in conflict with QM. I think the HUP is such, for example. I think entanglement, delayed choice, quantum erasers, GHZ, all of these are counterexamples to realism. Also Adan Cabello is invloved in some good work, here is a paper he was involved with demonstrating contextuality in single photons (i.e. against realism).

http://arxiv.org/abs/0907.4494"

"We present an experimental state-independent violation of an inequality for noncontextual theories on single particles. We show that 20 different single-photon states violate an inequality which involves correlations between results of sequential compatible measurements by at least 419 standard deviations. Our results show that, for any physical system, even for a single system, and independent of its state, there is a universal set of tests whose results do not admit a noncontextual interpretation. This sheds new light on the role of quantum mechanics in quantum information processing. "

 

[akhmeteli]

I don't know if it's a well known approach or not.

The argument is that Bell's locality condition isn't, exclusively, a locality condition. If it isn't, then what might this entail wrt the interpretation of experimental violations of inequalities based on Bell locality?

In a nutshell:

Bell locality doesn't just represent causal independence between A and B, but also statistical independence between A and B.

Statistical dependence between A and B means that a detection at A changes the sample space at B, and vice versa. The pairing process entails statistical dependence between A and B, and this statistical dependence can be accounted for via the local transmissions and interactions of the coincidence circuitry.

Statistical dependence between A and B is sufficient to violate inequalities based on Bell locality.

Sorry, was not able to answer for a few days.

OK, at least now it's in plain English. Thank you.

However, your statement "The pairing process entails statistical dependence between A and B" is not obvious, so it needs proof, as you admit you don't know if this reasoning is well-known. One would think that if experiments are performed infrequently, coincidence circuitry effect should not be important. Of course, this is hand-waving, but I don't think it's my duty to prove that your statement is wrong, it's your duty to prove it's correct.

 

[akhmeteli]

I think I might have been presenting the argument the wrong way.

Bell locality applied to LHV representation of two photon entangled state entails this:

P(A,B) = P(A) P(B)

That is, it entails that the joint probability be factorable (separable) as the product of the individual probabilities.

From probability theory and statistics, if two (sets of) events, A and B, are independent, then their joint probability is the product of the individual probabilites, P(A) and P(B).

So, we start out by observing that Bell locality represents statistical independence.
(This is different from the previous approach of assuming that Bell's locality condition represents causal independence, and then parsing it to include statistical independence.)

Does statistical independence imply causal independence?

The answer is yes (causal dependence entails statistical dependence).

However, in order to ascertain whether or not Bell locality is viable (that is, whether or not its application allows us to deduce the presence of superluminal causality) we must ask:

Does statistical dependence imply causal dependence?

In general, not necessarily. But if the Bell inequalities are violated, I guess yes.

 

[DrChinese]

Haven't really gotten my head around the Gisin paper.

Just to make it a little weirder, what about this one from Gisin which superficially seems to be in direct opposition to the other one (by ruling out more classes of non-local theories):

http://arxiv.org/abs/1002.1390"

"... Hence, any covariant nonlocal model is equivalent to a Bell-local model and, consequently, contradicts well tested quantum predictions, the violation of Bell's inequality. ..."

 

[nikman]

Just to make it a little weirder, what about this one from Gisin which superficially seems to be in direct opposition to the other one (by ruling out more classes of non-local theories)... "... Hence, any covariant nonlocal model is equivalent to a Bell-local model and, consequently, contradicts well tested quantum predictions, the violation of Bell's inequality. ..."

Gisin (kind of like our own Peter Morgan?) seems to be zeroing in on the measurement problem as the nexus of all our confusions? The inputting must be considered real, he says, and both Alice and Bob must be assumed to have freedom of choice -- but the reality of the physical measurement itself isn't obvious and this fact surely points to something deeply important although without suggesting specific questions to ask.

In a paper from a year ago Gisin's occasional colleague Suarez, sounding a bit quantum mystical, advances this:

It is argued that the quantum correlations are not maximally nonlocal to make it possible to control local outcomes from outside spacetime, and quantum mechanics emerges from timeless nonlocality and biased local randomness. This rules out a world described by NL (nonlocal) boxes. A new type of experiments is suggested.​

and continues a bit later:

The violation of Leggett inequalities was first interpreted as an experimental falsification of "nonlocal realism", where "realism" refers to the view that the single particles carry well defined properties when they leave the source. Such an interpretation is misleading: By testing models fulfilling Leggett inequalities one does not test "nonlocal realism", but rather models assuming both nonlocal randomness and outcomes that depend on biased random local variables. Nevertheless, it is the Colbeck-Renner theorem which clearly shows the relationship between nonlocality and biased local randomness in entanglement experiments.​

Any relationship(s) here?

 

[DrChinese]

Gisin (kind of like our own Peter Morgan?) seems to be zeroing in on the measurement problem as the nexus of all our confusions? The inputting must be considered real, he says, and both Alice and Bob must be assumed to have freedom of choice -- but the reality of the physical measurement itself isn't obvious and this fact surely points to something deeply important although without suggesting specific questions to ask.

In a paper from a year ago Gisin's occasional colleague Suarez, sounding a bit quantum mystical, advances this:

It is argued that the quantum correlations are not maximally nonlocal to make it possible to control local outcomes from outside spacetime, and quantum mechanics emerges from timeless nonlocality and biased local randomness. This rules out a world described by NL (nonlocal) boxes. A new type of experiments is suggested.​

and continues a bit later:

The violation of Leggett inequalities was first interpreted as an experimental falsification of "nonlocal realism", where "realism" refers to the view that the single particles carry well defined properties when they leave the source. Such an interpretation is misleading: By testing models fulfilling Leggett inequalities one does not test "nonlocal realism", but rather models assuming both nonlocal randomness and outcomes that depend on biased random local variables. Nevertheless, it is the Colbeck-Renner theorem which clearly shows the relationship between nonlocality and biased local randomness in entanglement experiments.​

Any relationship(s) here?

Not sure, I will need to look at the theorem you mention. I think it is interesting that NO model really seems to come close. You can start one place and rule out some things. Or start somewhere else and rule out what seems to be everything else. Maybe we should be considering non-local non-realistic solutions.

 

[Eye_in_the_Sky]

consulting the "atlas"

I think the Bell paper is a road map to a disproof of local realism.

Okay. I will look it up in the atlas.

In my atlas, the Bell map shows three roads converging into one main road called "local determinism" at which point there is a signpost reading "equation (1)". The three convergent roads are called:

"locality", "perfect anti-correlation for equal settings", and "counterfactuality".

The names of latter two roads are respectively abbreviated as "PC" and "CF". Now, in propositional terms, the convergence of these three roads into one means:

Proposition 1: locality Λ PC Λ CF → local determinism .

I invite anyone who wishes to verify the accuracy and validity of this proposition to do so. Here are Bell's own words:

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stem-Gerlach magnets, on selected components of the spins σ₁ and σ₂. If measurement of the component σ₁∙a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of σ₂∙a must yield the value -1 and vice versa. Now we make the hypothesis [2], and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of σ₂, by previously measuring the same component of σ₁, it follows that the result of any such measurement must actually be predetermined.
-------------------------
[2] "But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S₂ is independent of what is done with the system S₁, which is spatially separated from the former." A. EINSTEIN in Albert Einstein, Philosopher Scientist, (Edited by P. A. SCHILP) p. 85, Library of Living Philosophers, Evanston, Illinois (1949).

Next:

One of the paths is to to demonstrate that PC (perfect correlations) implies predetermination in a classical (local realistic) world.

Dr. Chinese, by this statement do you mean?

"Proposition 1" above is both accurate and valid.

Next, returning once again to the Bell map, I see that the road called "local determinism" eventually merges with another road called "QM". They merge into an unnamed dirt path. This path leads directly into the mouth of an abyss. In propositional terms, this means:

Proposition 2: local determinism Λ QM → CONTRADICTION .

Bell makes several concurrent arguments, so I try not to specifically say X -> Y about too many things.

Yes, and it is for this reason that you make a conceptual error in your reply to yoda jedi:

There is ... those ... that make the argument that realism is not assumed in Bell. Of course, it is but it is not marked as "Here is where the realism argument starts." So if you want to see it, look after Bell's (14). "It follows that c is another unit vector..." That is where the counterfactual argument begins, obviously with 2 photons there can only be 2 measurements (a and b).

No. That is not where the counterfactual argument begins. Counterfactuality has already been invoked in the first paragraph of the section II, "Formulation", of Bell's paper, the relevant part of which I have quoted above, whose argument therein I have summarized as "Proposition 1". But now we are in the section IV, "Contradiction", in the process of developing the validity of "Proposition 2". The premise of "local determinism" is now considered to be given, and therefore, at this stage, there is no difficulty with a counterfactual claim such as "It follows that c is another unit vector...". At this stage, there can be any number of simultaneous specifications of measurement outcomes.

That is to say, Dr. Chinese, any quarrel you may have with CF as it is used in Bell's original paper does not lie with an ad hoc simultaneous assignment of values to noncommuting observables, as you have been thinking it does; but, rather, any such quarrel you may have lies with the truth of CF as it is used as a premise in "Proposition 1" above.

 

[Demystifier]

http://arxiv.org/abs/1002.1390"

"... Hence, any covariant nonlocal model is equivalent to a Bell-local model and, consequently, contradicts well tested quantum predictions, the violation of Bell's inequality. ..."

Given the definition of the word "covariant" used in that paper, the conclusions of that paper are correct. However, his definition of the word "covariant" is, mildly speaking, quite unusual.

 

[yoda jedi]

Yes I have seen some of these arguments and papers previously. There is, as I have mentioned, those such as Norsen that make the argument that realism is not assumed in Bell. Of course, it is but it is not marked as "Here is where the realism argument starts."

So if you want to see it,

look after Bell's (14). "It follows that c is another unit vector..." That is where the counterfactual argument begins, obviously with 2 photons there can only be 2 measurements (a and b).

So you can think whatever you want.

On the other hand, there are plenty of other experiments - such as GHZ - in which the realistic position is demolished independently of Bell.

So you might want to consider that as well.


the fact is we don't know precisely how to define it.

pathetical ludicrosity, then, how can be demolished ?

if it is not definite yet....

...laughs...

in which the realistic position is demolished

wooowww DEMOLISHED !

 

[ThomasT]

... your statement "The pairing process entails statistical dependence between A and B" is not obvious, so it needs proof ...

It's not a matter of proof, it's just a matter of identifying the symbolic convention, statistical dependence, with the experimental setup. When a detection is registered at one end, then the sample space at the other end is altered. The matching of the separate data streams at A and B isn't done randomly. The matching process itself produces (via local interactions and transmissions) the statistical dependence between A and B -- and this is sufficient to violate Bell inequalities based on the assumption that the data set at A is statistically independent from the data set at B via Bell locality.

One would think that if experiments are performed infrequently, coincidence circuitry effect should not be important.

The separate accumulations of data at A and B have to be matched somehow. The point is that the designs of entanglement experiments contradict Bell locality.

Does statistical dependence imply causal dependence?

In general, not necessarily. But if the Bell inequalities are violated, I guess yes.

Statistical dependence between A and B doesn't imply a direct causal link between A and B whether Bell inequalities are violated or not.

Therefore, even though entanglement experimental designs and standard QM are incompatible with Bell locality, we can't conclude that violations of Bell inequalities require nonlocal propagations in Nature.

 

[Eye_in_the_Sky]

In the beginning ...

This thread began with a post in which it was written:

... the proof of the Bell theorem uses two mutually contradictory results/assumptions of quantum theory: unitary evolution and the projection postulate. Therefore, I argued, the Bell theorem is on a shaky ground ... on the theoretical ... level.

Hello, akhmeteli. It appears to me there may be some misconception in the way you are thinking about Bell's theorem.

Bell's theorem, per se, is nothing more than a proposition of the form

P → D ,

where "P" is the conjunction of some set of premises, the 'truth' of which does not in any way require the 'truth' of any of the premises of Quantum Mechanics, and "D" is a certain condition (e.g. a Bell inequality).
________________

Now, it happens that Quantum Mechanics (let us denote its premises by "QM") is such that

QM → ~D .

Therefore, the conjunction "P Λ QM" is inconsistent.
________________

In the weak version of Bell's theorem

P = local determinism .


In the strong version of Bell's Theorem

P = locality Λ PC Λ CF ,

where

PC ≡ perfect anti-correlation for equal settings

and

CF ≡ counterfactuality .


In the strong version, of course, "PC" has been employed as premise; but this means only that we are considering any theory which admits "PC" as a feature.
________________


... Do you see what I am saying?

 

[zonde]

Proposition 1: locality Λ PC Λ CF → local determinism .

I invite anyone who wishes to verify the accuracy and validity of this proposition to do so. Here are Bell's own words:

Can you tell where do you yourself see the problem?

As I understand the sentence you quoted from Bell ascribe counterfactuality to QM:
"If measurement of the component σ1∙a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of σ2∙a must yield the value -1 and vice versa."
This statement is taken as experimentally valid but on the other hand experiments with photons say that you can only detect 50% of photons maximum with one detector. So it is not conclusively true.
Then if we accept as empirical fact that only 50% of photons can be detected and we do not invoke counterfactuality then QM can not make prediction like that about photons.