Mathematica Mathematical expression of Bell's local realism

[DrChinese]

Huh? I thought you said (what you call) Bell Locality is experimentally disproved, not verified.

1. Would you say there is experimental evidence in favor of signal locality? Sure there is.

Would you say there is experimental evidence against the separability condition (PI+OI)? Sure there is.

Would you say there is experimental evidence in support of MY Bell Locality condition (7)? Sure there is.

So it depends which definition we are talking about.

2. Now let's agree about this much too...

(5 - entanglement) needs to be proven before we can do a valid test of (6 - Bell's Inequality). We agree on that much. And we also BOTH agree that there is in fact another condition which needs to be considered or confronted: that there might be improper skewing of the results if we perform (6). The disagreement is how strict the definition should be and at what level "skewing" is allowed.

a. In my program, I want a looser definition that is proven true (no improper skewing) - so that a test of (6) is meaningful - and then we will know if realism is viable. My definition matches Bell's verbatim words.

b. In your program, you want a stricter definition that can be proven false which supports your contention that WF collapse is non-local. You definition matches Bell's separability condition.

Assuming Bell's Inequality is violated: Your program excludes all fully* local theories. My program agrees with that, and also excludes all realistic theories.

*where "Fully" local = signal local plus local WF collapse.

 

[ttn]

Would you say there is experimental evidence against the separability condition (PI+OI)? Sure there is.

That's what I'm so surprised to hear you say. PI+OI is Bell Locality. So you are saying that there is experimental evidence against Bell Locality. Well, what is that evidence? You've always disagreed with my argument that EPR + Bell + experiment proves that Bell Locality is false... now you're "sure there is" experimental evidence disproving Bell Locality?

a. In my program, I want a looser definition that is proven true (no improper skewing) - so that a test of (6) is meaningful - and then we will know if realism is viable. My definition matches Bell's verbatim words.

Um, OK, suppose you make up some weaker condition: DC Locality. And suppose, combined with the assumption of "realism", you can derive some sort of inequality (or whatever) which turns out to be consistent with experiment. You think somehow from this you're going to conclude: aha, realism is false! That makes no sense.

b. In your program, you want a stricter definition that can be proven false which supports your contention that WF collapse is non-local. You definition matches Bell's separability condition.
Assuming Bell's Inequality is violated: Your program excludes all fully* local theories. My program agrees with that, and also excludes all realistic theories.
*where "Fully" local = signal local plus local WF collapse.

Given your definition of "realism", we already know it's false from (eg) Gleason's theorem. What more are you going for here?

If your program agrees with my claim that Bell Locality is false, why do you always disagree with me when I say that? Or maybe the problem is your footnote: what my program excludes is Bell Locality. There can be no Bell Local theory that agrees with experiment. But you are wrong that this kind of locality " = signal local plus local WF collapse." But I applaud your creativity in dreaming up so many new attempts to define "locality."

 

[Rade]

I never said the particles themselves don't exist. I simply state that the particles did not have definite values for all possible observables. That is the definition of realism.

Thank you for your answer--perhaps this is the basis of my confusion. When I say that some "thing" is "real", what I mean is that it "exists". But it is not clear to me that then this must mean that what exists must have, as you say, "definite values for all possible observables". Why must this be true to say that something is real ? I do not understand. Why cannot a thing have "probability values" and not "definite values" yet still be real -- for example, is that not what QM tells us, that what is out there is a probability type reality, not a definite reality. Any help with my confusion is appreciated.

 

[DrChinese]

That's what I'm so surprised to hear you say. PI+OI is Bell Locality. So you are saying that there is experimental evidence against Bell Locality. Well, what is that evidence? You've always disagreed with my argument that EPR + Bell + experiment proves that Bell Locality is false... now you're "sure there is" experimental evidence disproving Bell Locality?

If your program agrees with my claim that Bell Locality is false, why do you always disagree with me when I say that? Or maybe the problem is your footnote: what my program excludes is Bell Locality. There can be no Bell Local theory that agrees with experiment. But you are wrong that this kind of locality " = signal local plus local WF collapse." But I applaud your creativity in dreaming up so many new attempts to define "locality."

Well, first my priority is to learn. So no harm there.

Second, I think what I have been trying to say is that Bell's Theorem is not so much about locality as reality. And I am pretty comfortable with that at this point. But the great thing is, my journey has greatly aided me in understanding your position. Thank you very much for taking the time to critique my posts.

And I don't ever recall consciously trying to deny that WF collapse is non-local. I just don't happen to think that is the criteria that one should apply when calling a theory Bell Local - whether Bell did or did not himself. But that is mostly for theoretical reasons - and by that I mean strictly from the perspective of theory construction. A weaker theory of locality means a stronger Bell Theorem, no question about that. So in my mind, I believe I have the weakest definition of locality possible that leads to a meaningful version of Bell's Theorem. And I do not think the traditional definition is required for that one.

 

[DrChinese]

Thank you for your answer--perhaps this is the basis of my confusion. When I say that some "thing" is "real", what I mean is that it "exists". But it is not clear to me that then this must mean that what exists must have, as you say, "definite values for all possible observables". Why must this be true to say that something is real ? I do not understand. Why cannot a thing have "probability values" and not "definite values" yet still be real -- for example, is that not what QM tells us, that what is out there is a probability type reality, not a definite reality. Any help with my confusion is appreciated.

I do not believe that there are definite values for all possible observables of a particle. I believe that there is something fundamental about the act of measurement. So I am more in the "probability" camp than the "definite" camp. We know what we observe, and this shapes reality.

 

[DrChinese]

Summary of points about realism and locality

I will summarize a few of the points I have made during the course of my recent posts.

a. I defined realism by way of 2 assumptions:

Rule 1 Assumption:
1 >= p(a+, b+, c+) >= 0
(..and similar for all permutations of the above.)

Rule 2 Assumption:
p(a+) = p(a+, b+) + p(a+, b-)
= p(a+, b+, c+) + p(a+, b-, c+) + p(a+, b+, c-) + p(a+, b-, c-)
(…and similar for all permutations of the above.)

b. I used those alone, without any reference to locality, to develop a Bell-type Inequality for a single particle:

(3) corr(Alice.a, Alice.b) + noncorr(Alice.a, Alice.c) – corr(Alice.b, Alice.c) ) / 2 >= 0

And proved that:

(4) No realistic theory can be internally consistent if Malus’ Law is accepted.

c. We discussed why tests a la Malus would or would not be appropriate for (3). We looked at ways to develop a form of (3) that was an indirect test of correlations, using an entangled photon pair. This introduced a new experimental requirement (not an assumption):

(5) Alice.a = Bob.a, or generally: corr(Alice.a, Bob.a) = 1
Alice.b = Bob.b, or generally: corr(Alice.b, Bob.b) = 1
Alice.c = Bob.c, or generally: corr(Alice.c, Bob.c) = 1

We then used this to develop a true Bell Inequality that makes no reference to locality at all:

(6) corr(Alice.a, Bob.b) + noncorr(Alice.a, Bob.c) – corr(Alice.b, Bob.c) ) / 2 >= 0

d. We discussed the feasibility of using this for an experiment, and determined that there is a potential flaw that can be addressed if we could prove:

(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)

(7) can be experimentally verified, and matches verbatim one of Bell’s definitions of locality. In fact, it already has been verified; it is sometimes called parameter independence (PI). Therefore it is possible to test the viability of all realistic theories via (6) - without the usual assumption of locality present.

e. However, we encountered criticism, valid, that (7) was not a faithful representation of Bell Locality as expressed mathematically by Bell; (7) is in fact the weakest definition we could have and still come to a meaningful version of Bell’s Theorem.

Additional criticism expresses doubts that (7) would be sufficient to lead to a convincing proof, primarily because outcome independence (OI) should also be included as an assumption. At this point, opinion diverges with the majority opinion probably being that (6) will not be convincing without assuming PI+OI - although I can always hope I shaped someone's opinion on this.

I stand by my assessment, but respect the opinions of my learned friends and fellow PF participants. Additional comments are welcome, and thanks to all who patiently followed.

-DrChinese

 

[DrChinese]

This is intended for Vanesch and other MWIers out there:

The definition of Bell locality (as PI only) I used to set up for a test of a Bell Inequality (6 above) is more restricted - weaker - than the definition often used as being PI+OI. My definition (7 below) does not factor in Alice's outcomes, only Alice's measurement settings. I believe this is correct, ttn and many others do not.

(7) p(Bob.b+) = p(Bob.b+, Alice.a+) + p(Bob.b+, Alice.a-)
= p(Bob.b+, Alice.b+) + p(Bob.b+, Alice.b-)
= p(Bob.b+, Alice.c+) + p(Bob.b+, Alice.c-)
= .500
(…and similar for all permutations of the above.)

Here is the advantage of this definition - if you can accept it, and also accept MWI as reasonable:

The definition of BL=PI+OI is demonstrably false. That requirement is that there is NO correlation between the outcomes at Alice and Bob other than the "perfect" correlation it takes to establish that entanglement is present (expressed as my 5 above). This is experimentally false. If you accept that definition, then MWI cannot be local because the WF collapse is non-local. But that was one of the advantages of MWI - the locality.

My definition (7) neatly solves this as follows: (7) is experimentally true. It also matches to what I think MWI would predict. So by this particular definition - which was designed to both be true and dovetail into Bell's Theorem - locality holds. (Just as it holds if your definition of locality is signal locality.)

So with (5) and (7) true by experiment, we are cleared to test (6) by experiment - which is a test of Bell's Inequality based ONLY on the assumption of realism and not based on locality in any way. The inequality is violated; therefore realism is not viable.

MWI is not a realistic theory, as I understand it, because each measurement causes a branching. All non-commuting observables do not have simultaneous real values. Is my understanding correct on how MWI would address the issue of realism? I don't want to speak wrongly...

 

[ttn]

And I don't ever recall consciously trying to deny that WF collapse is non-local. I just don't happen to think that is the criteria that one should apply when calling a theory Bell Local - whether Bell did or did not himself.

He didn't! And I never did either! Ugh, I don't know where you get all these weird new ideas every 30 seconds about who defines locality how. Bell Locality doesn't just mean something about wf collapse. It's true that in OQM the wave function collapse postulate violates Bell Locality. But Bell Locality is a perfectly clear test that doesn't in any way require wf collapse.

But that is mostly for theoretical reasons - and by that I mean strictly from the perspective of theory construction. A weaker theory of locality means a stronger Bell Theorem, no question about that. So in my mind, I believe I have the weakest definition of locality possible that leads to a meaningful version of Bell's Theorem. And I do not think the traditional definition is required for that one.

Well, I still think you are missing the main point, which is related to EPR. The reason "Bell Locality" is a useful and relevant criterion (in addition to its prima facie plausibility as a requirement of relativistic causality) is that *from it* follows the exact "local hidden variables" that permit the rest of Bell's Theorem to go through. You're probably right that if you just assume those hidden variables from the beginning, some weaker locality condition would permit you to derive an inequality. So then, assuming the inequality is empirically violated, you'd have to conclude that either the lhv's don't exist, or the weaker locality assumption is false. That is precisely the kind of reasoning that is the standard mis-understanding of what Bell proved (but with Bell Locality in place of the weaker locality condition). It is precisely why people erroneously think of Bell's theorem as a proof that hidden variables aren't viable, which we *know* is false because Bohm's theory *exists*. The correct approach starts with the EPR type argument which shows that the existence of the lhv's *follows* from (Bell) Locality, and only then passes to Bell's Theorem (which shows that the lhv's are in conflict with experiment).

If your point in this thread has been to argue that lhv's don't exist, you're barking up the wrong tree. Everybody agrees they don't exist. That's just what Bell's Theorem proves, and there's no controversy about that. The controversy is over why anybody wanted to believe in those lhv's in the first place. If it's only to save some philosophical bias for "realism", then you'd be right: so much the worse for realism. But if the reason for believing in the lhv's is because they're required by *locality*, then the conclusion is: so much the worse for locality. That latter is, in my opinion, the correct perspective.

 

[DrChinese]

He didn't! And I never did either! Ugh, I don't know where you get all these weird new ideas every 30 seconds about who defines locality how. Bell Locality doesn't just mean...

Bell's words, not mine: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Quoted from one of my previous posts. So I am not sure I follow the 30 seconds thing.

I think he knew why this definition - which is PI and is as identical to my (7) as I could make it - was the weakest possible definition that would be convincing. I would have formulated a weaker version if I could have and gotten away with it, but I also think this is the minimal definition that works. If Alice's measurement apparatus is not affecting Bob's results (and vice versa), and I am correlating Alice and Bob's outcomes, I assert I have a valid test. I do not claim there is no relationship between the outcomes of Alice and Bob; the nature of the relationship is the very thing I determine for use with my Inequality.

 

[ttn]

Bell's words, not mine: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Quoted from one of my previous posts. So I am not sure I follow the 30 seconds thing.

I think he knew why this definition - which is PI and is as identical to my (7) as I could make it - was the weakest possible definition that would be convincing. I would have formulated a weaker version if I could have and gotten away with it, but I also think this is the minimal definition that works. If Alice's measurement apparatus is not affecting Bob's results (and vice versa), and I am correlating Alice and Bob's outcomes, I assert I have a valid test. I do not claim there is no relationship between the outcomes of Alice and Bob; the nature of the relationship is the very thing I determine for use with my Inequality.

Yes, in the paper you have in mind, Bell says what you say he says -- that the outcomes on each side can't depend on the distant setting. But this is *not* what is technically known in the literature as PI (parameter independence). You have to be extremely careful about what all these things mean precisely, mathematically -- in particular, you have to be careful about what the probabilities involved are conditionalized on. To say something like "the outcome here doesn't depend on the parameter there" is indeed a kind of "parameter independence". But it simply is *not* the same as the "PI" satisfying "PI + OI = Bell Locality".

These things are very subtle and you can't just plow through them at light speed. For example, you say: "If Alice's measurement apparatus is not affecting Bob's results..." Well what do you mean exactly that Bob's results aren't affected? That in a given run of the experiment (i.e., for a given particle pair) the outcome is the same as it would otherwise have been? That the probabilities for different outcomes are the same as they would have been? Or that the long-time-average of Bob's results over many runs are the same as they would have been? Or that the correlation coefficient for Alice's and Bob's outcomes are independent of Alice's settings? etc. The point is, there are a ton of subtly different things that might plausibly be thought of as a kind of parameter independence. Being clear about which is which and which is justified/relevant in a given context, however, is crucial to this discussion.

I still think you need to read La Nouvelle Cuisine. Is there something preventing you from doing this? Or maybe you read it and didn't find it clarifying?

 

[DrChinese]

I still think you need to read La Nouvelle Cuisine. Is there something preventing you from doing this? Or maybe you read it and didn't find it clarifying?

I would purchase & enjoy it if it were at Barnes & Noble, which it's not. Or if someone gave me a copy for Christmas, which probably won't happen. So I guess I will have to get from Amazon...

 

[DrChinese]

The point is, there are a ton of subtly different things that might plausibly be thought of as a kind of parameter independence. Being clear about which is which and which is justified/relevant in a given context, however, is crucial to this discussion.

I agree. And I have tried to discuss this point. I think the context is: what does it take to test Bell's Inequality.

 

[Sherlock]

But the point is that Bell Locality is a stronger condition that signal locality. Bell Locality can be violated, even by a theory that still respects signal locality.
...
... details like the speed of light don't appear in Bell's locality condition. It is just a condition saying that one thing is independent of another. Then, from that condition, the inequality follows -- so it is an indirect test of whether or not the one thing depends on the other. If it doesn't so depend, the inequality should be respected by the experimental results. If there is some dependence on the distant setting/outcome, the inequality will be violated.
...
If entanglement simply meant that the initial spins of the particles were correlated (such that there was, later, no influence of Alice's measurement on Bob's outcome or vice versa) Bell's inequalities would *not* be violated. That's the whole point here. The violation of Bell inequalities proves that testing one affects the other.
The correlations can *not* be accounted for in terms of pre-correlated properties which locally determine the outcomes.

So, what does it mean for the correlations to violate Bell locality but not signal locality? It means that the measurements at A and B are related to each other, but not causally. This is what quantum non-locality means, an acausal relationship between A and B, and because the relationship is acausal there is no conflict with special relativity.

Bell locality is a more encompassing condition than signal locality. Bell locality encompasses correlations as well as causal relationships. So, a violation of Bell locality does not necessarily discern the presence of a causal relationship between A and B.

As DrChinese has mentioned, it's been shown experimentally that the results at one end don't depend on the settings at the other end.

We know that the statistics at A and B aren't independent of each other, because the observations at A and B aren't independent of each other. What is sampled at one end depends on what is sampled at the other end. "Testing one affects the other" in that a detection at one end gates open the coincidence circuitry, and therefore determines what is selected for sampling at the other end.

The sampling method is of primary importance, because it's assumed that the spins of the photons are correlated upon creation of the entangled state, which occurs during emission, and exists prior to filtration by the polarizers. And it's not just the spins, and therefore the polarizations, of the incident disturbances associated with suitably paired detection attributes that are related. The phase relations and relative amplitudes of the emitted disturbances also determine the strength of the correlations.

Now, I don't see in any of this where it is necessary to postulate the existence of superluminal propagations to account for the correlations. QM doesn't do that, and it accounts (approximately, quantitatively) for the correlations. I have to conclude that it hasn't been shown that non-locality is a fact of nature.

Via EPR we can think of local hidden variables as, in some sense, existing. However, because of limitations on what can be experimentally determined, which limit the content of any, explicitly local, hidden variable formulation, the development of an experimentally viable local hidden variable theory which matches or exceeds the accuracy of qm is disallowed. Maybe it's worth noting again that it is local hidden variable theories, not locality, and not non-local hidden variable theories which are ruled out. But since locality isn't ruled out, and therefore the assumption of locality is retained, then developing an explicitly non-local hidden variable theory wouldn't make much sense (unless you just wanted to show that some, any, hidden variable formulation was possible).

 

[Sherlock]

Yes, in the paper you have in mind, Bell says what you say he says -- that the outcomes on each side can't depend on the distant setting. But this is *not* what is technically known in the literature as PI (parameter independence). You have to be extremely careful about what all these things mean precisely, mathematically -- in particular, you have to be careful about what the probabilities involved are conditionalized on. To say something like "the outcome here doesn't depend on the parameter there" is indeed a kind of "parameter independence". But it simply is *not* the same as the "PI" satisfying "PI + OI = Bell Locality".

The "PI satisfying PI + OI = Bell Locality" is,
P(A|a) = P(A|a,b) and P(B|b) = P(B|b,a), isn't it?
If so, then this is just a shorthand way of saying that the "outcomes on each side can't depend on the distant setting", isn't it?
If this isn't "the same as the PI satisfying PI + OI = Bell Locality", then what is the PI that satisfies PI + OI = Bell Locality?

These things are very subtle and you can't just plow through them at light speed. For example, you say: "If Alice's measurement apparatus is not affecting Bob's results..." Well what do you mean exactly that Bob's results aren't affected? That in a given run of the experiment (i.e., for a given particle pair) the outcome is the same as it would otherwise have been? That the probabilities for different outcomes are the same as they would have been? Or that the long-time-average of Bob's results over many runs are the same as they would have been? Or that the correlation coefficient for Alice's and Bob's outcomes are independent of Alice's settings? etc. The point is, there are a ton of subtly different things that might plausibly be thought of as a kind of parameter independence. Being clear about which is which and which is justified/relevant in a given context, however, is crucial to this discussion.

I think the definition I wrote above is ok. But if not, let me know.
Parameter independence is the part of the Bell Locality condition that isn't violated. Parameter independence means that the rate of detection, A, does not vary with the setting, b, of the distant polarizer, and that the rate of detection, B, does not vary with the setting, a, of the distant polarizer.
What is violated is outcome independence, which is equivalent to statistical independence. A and B are not statistically independent. So, the Bell Locality condition (which is not, strictly speaking, a locality condition) is violated.
The idea that there is a common cause explanation for the correlations, rather than a non-local causal link between space-like separated filtration and detection processes and events, is further supported by the joint detection schemes and experimental protocols of the tests of Bell inequalities.

 

[ttn]

The "PI satisfying PI + OI = Bell Locality" is,
P(A|a) = P(A|a,b) and P(B|b) = P(B|b,a), isn't it?
If so, then this is just a shorthand way of saying that the "outcomes on each side can't depend on the distant setting", isn't it?
If this isn't "the same as the PI satisfying PI + OI = Bell Locality", then what is the PI that satisfies PI + OI = Bell Locality?

You *have* to also conditionalize on a complete specification of the state of the system prior to measurements. Otherwise, it just isn't Bell Locality you're talking about. P(A|a,b,B,L) = P(A|a,L). That's Bell Locality. (L here is a complete specification of the state.)

Note that this is *not* something you can just go into a lab and measure. How would you ever know that you had conditionalized on a *complete* specification of the state? That's why I've said that this is a condition that only (directly) applies to *theories* -- because a given theory gives an account of what a complete specification consists of.

Parameter independence is the part of the Bell Locality condition that isn't violated.

I don't know how you could possibly know that. The inequality is derived from Bell Locality (both OI and PI) and is violated. Which is to blame? There's no way to answer. All one can say is that Bell Locality is violated.

So, the Bell Locality condition (which is not, strictly speaking, a locality condition) is violated.

Yes, it is. (Bell Locality is a locality condition, I mean. If you leave out the idea of conditionalizing the probabilities on L, then I can see why you'd think it's merely a statistical correlation condition. But once you have specified that complete state description, the *additional* dependence of a probability on some spacelike separated event implies a nonlocal causation.)

The idea that there is a common cause explanation for the correlations, rather than a non-local causal link between space-like separated filtration and detection processes and events, is further supported by the joint detection schemes and experimental protocols of the tests of Bell inequalities.

No. You've been repeating this mantra for years, but it's just wrong. You need to rethink it.

 

[Sherlock]

You *have* to also conditionalize on a complete specification of the state of the system prior to measurements. Otherwise, it just isn't Bell Locality you're talking about. P(A|a,b,B,L) = P(A|a,L). That's Bell Locality. (L here is a complete specification of the state.)

Afaik, parameter independence doesn't mean something different as a component of Bell's Locality condition, P(A|a,L) = P(A|a,b,B,L), than that the outcome, A, doesn't depend on the distant setting, b.

But if it does, then I would like to learn what it means.

Note that this is *not* something you can just go into a lab and measure. How would you ever know that you had conditionalized on a *complete* specification of the state?

Exactly. How would you ever know? So, we ask the physically meaningful question: does P(A) -- ie., the detection rate, A --vary with the distant setting, b, or P(B) with a? The QM answer is no, and the QM answer has been experimentally corroborated.

Parameter independence is the part of the Bell Locality condition that isn't violated.

I don't know how you could possibly know that. The inequality is derived from Bell Locality (both OI and PI) and is violated. Which is to blame? There's no way to answer. All one can say is that Bell Locality is violated.

I believe that PI isn't violated because of the physical evidence that it isn't, and also because the theory that does make correct predictions wrt Bell tests, QM, doesn't violate PI --- and, afaik, there isn't any physical evidence to suggest that PI is violated.

On the other hand, we know that OI is violated (A and B are not statistically independent) because the sampling method imposes an observational dependency. (The sampling method is based on the assumption, which is part of the experimental design of all Bell tests that I'm familiar with, that measurable properties of the incident disturbances are related due to common cause or common interaction prior to filtration and/or detection.)

So, I think more can be said than just that the Bell Locality condition is violated. There are pretty good indications of which part of it is violated.

If you leave out the idea of conditionalizing the probabilities on L, then I can see why you'd think it's merely a statistical correlation condition. But once you have specified that complete state description, the *additional* dependence of a probability on some spacelike separated event implies a nonlocal causation.

The more complete state description promised by L only works if nature is non-local. But, there's no reason to believe that nature is non-local.

There are two classes of spacelike separated events involved in Bell tests, polarizer/analyzer settings and detector registrations. The setups and results have been analysed enough to show, pretty convincingly I think, that parameter independence is not violated and outcome independence is violated --- and from this we can't conclude that non-locality is a fact of nature.

The idea that there is a common cause explanation for the correlations, rather than a non-local causal link between space-like separated filtration and detection processes and events, is further supported by the joint detection schemes and experimental protocols of the tests of Bell inequalities.

No. You've been repeating this mantra for years, but it's just wrong. You need to rethink it.

The experimental protocols reveal a lot. They're what tell you that OI is violated, that PI isn't violated, and that Bell tests are not a test of locality vs. non-locality, but rather are only testing the viability of realistic or hidden variable theories of quantum phenomena. The conclusions (so far) are that nature is local, and that hidden variable theories of nature's quantum processes are ruled out --- and while non-local hidden variable theories can be constructed which are quantitatively viable, they represent a departure from the conceptual direction that the extant experimental evidence indicates should be taken.

 

[ttn]

Afaik, parameter independence doesn't mean something different as a component of Bell's Locality condition, P(A|a,L) = P(A|a,b,B,L), than that the outcome, A, doesn't depend on the distant setting, b.
But if it does, then I would like to learn what it means.

Yes, it means the (probability of the) outcome on one side doesn't depend on which measurement is performed on the other side -- *given* the pre-measurement complete state description *and* the outcome on the far side.

Exactly. How would you ever know?

If you were a mindless drone in a lab doing the experiment, you *wouldn't* know. That's why I keep saying that violation of Bell Locality (or PI) isn't something that you can directly test in a lab. You can only test it subject to an *assumption* about the completeness of one's state description.

This is all just a different perspective on the importance of recognizing that Bell's proof of nonlocality has two parts. The first part is essentially the EPR argument: Bell Locality *requires* the existence of a certain type of local hidden variables which determine the outcomes of the measurements on each side. The second part of the argument is then Bell's Theorem: these HV's entail something which can be directly tested empirically, and is found to be false.

So, we ask the physically meaningful question: does P(A) -- ie., the detection rate, A --vary with the distant setting, b, or P(B) with a?

You can certainly ask this question, but it isn't the same as the original question (namely: is Parameter Independence true). Just because the original question is unanswerable in the way you hoped, doesn't mean that the question you ask instead is the same question you started with.

I believe that PI isn't violated because of the physical evidence that it isn't,

What evidence is that exactly?

and also because the theory that does make correct predictions wrt Bell tests, QM, doesn't violate PI

But other theories which *also* make correct predictions *do* violate PI! So you definitely cannot say that the experimental results show that PI isn't violated!

On the other hand, we know that OI is violated (A and B are not statistically independent) because the sampling method imposes an observational dependency.

Either what you say is false, or you've switched to your alternate definition of OI. I really don't know, and don't care, which. In either case, it simply is not true that "we know that OI is violated."

What we know for sure is violated is Bell Locality, because of the combination of the two parts of Bell's argument (EPR and Bell's thm). Whether OI or PI is to blame is not known -- and, as Maudlin has very convincingly argued, not even a meaningful question.

So, I think more can be said than just that the Bell Locality condition is violated. There are pretty good indications of which part of it is violated.

As I've said, I don't agree. But even if this were right, to say that one "part" is violated is to confess that Bell Locality *is violated* -- which seems to be something you deny -- e.g., here:

But, there's no reason to believe that nature is non-local.

 

[Sherlock]

Yes, it [parameter independence wrt the Bell Locality condition] means the (probability of the) outcome on one side doesn't depend on which measurement is performed on the other side -- *given* the pre-measurement complete state description *and* the outcome on the far side.

This isn't quite clear to me. Are you saying that how, or whether, the rate of detection, A, varies with the distant polarizer setting, b_hat, depends on whether a pre-measurement complete state description accompanies the test *and* on the rate of detection, B --- or what?

If you were a mindless drone in a lab doing the experiment, you *wouldn't* know [that you had conditionalized on a *complete* specification of the state].

And if you do, or don't, "conditionalize on a *complete* specification of the state" --- how does that affect the detection rate? Why should it, for that matter?

That's why I keep saying that violation of Bell Locality (or PI) isn't something that you can directly test in a lab. You can only test it subject to an *assumption* about the completeness of one's state description.

Why should an assumption about the completeness of one's state description affect the results? In fact, the results, A, don't vary with b_hat, or with a_hat either. Same with B. The results, A or B, don't vary at all, ever, in Bell tests. The rate of detection at A is the same as B in every run, and doesn't vary from run to run.

This is all just a different perspective on the importance of recognizing that Bell's proof of nonlocality has two parts. The first part is essentially the EPR argument: Bell Locality *requires* the existence of a certain type of local hidden variables which determine the outcomes of the measurements on each side. The second part of the argument is then Bell's Theorem: these HV's entail something which can be directly tested empirically, and is found to be false.

What is being directly tested are the predictions of an LHV theory. There seems to be some disagreement as to whether it is the L part or the HV part, or both, that is responsible for the discrepancy between the LHV predictions and the experimental results.


The L part is usually identified as the Bell Locality condition which is further analysed into PI and OI. Neither PI nor OI are violated because the detection rates, A and B, at either end of the experimental setup remain constant.


Which leaves the HV part as the most likely, if not the usual, suspect in the non-viability of LHV theories.

But other theories which *also* make correct predictions *do* violate PI! So you definitely cannot say that the experimental results show that PI isn't violated!

Whether or not PI is violated depends on whether the observed detection rate varies with the polarizer setting, doesn't it? So if the detection rate doesn't vary with the polarizer setting, then how can a theory that says the detection rate does vary with the polarizer setting be making correct predictions?

... it simply is not true that "we know that OI is violated."

I agree. After thinking about this a bit, it became clear to me that all we can say is that, as far as can be ascertained, OI isn't violated.

What we know for sure is violated is Bell Locality, ...

What we know for sure is that, as far as can be ascertained, neither PI nor OI is violated experimentally. So, Bell Locality is not violated.


Wrt individual results and settings, there are no interesting correlations.

But if we impose a certain structure on the apparently causally unrelated individual events, then a correlational pattern is revealed. The rate of coincidental detection, AB, varies with the angular difference between the polarizer settings, Theta, as cos^2 Theta. How can this be, if the two sides of the setup are causally isolated from each other?


One answer is that the components (AB, Theta, and the disturbances that are jointly analyzed by the polarizers during a particular coincidence interval) of the structure that has been imposed, the combined context, all have some common cause. Individual A and B results are paired via their occurance during the same coincidence interval, and the combined AB result is then associated with the Theta in effect during that interval. Coincidence intervals are determined wrt the presumed elapsed time between the creation of an entangled pair of incident disturbances and a detection event at one end or the other which initiates the coincidence circuitry. In the case of eg. the Aspect et al. experiments, the presumed common cause of paired photons, and of their entanglement, is that they were emitted from the same atom -- in which case the observation of predictable correlation patterns between their joint detection and a common measurement operator doesn't seem too surprising --- even if somewhat resistant to a detailed explanation of exactly how it happens.

 

[ttn]

This isn't quite clear to me. Are you saying that how, or whether, the rate of detection, A, varies with the distant polarizer setting, b_hat, depends on whether a pre-measurement complete state description accompanies the test *and* on the rate of detection, B --- or what?

Look, the condition is what it is. It's just what I said before. No, this doesn't necessarily imply anything about the rates of detection. Those rates are some kind of averages over the probabilities involved in Bell Locality. The whole point here is that you can't just test Bell Locality by looking at emprical rates -- not without some subsidiary assumptions provided by a theory (which will tell you what a complete specification of the state consists of, and will tell you something about what initial state(s) are being produced by the setup procedure).

And if you do, or don't, "conditionalize on a *complete* specification of the state" --- how does that affect the detection rate? Why should it, for that matter?

The conditionalization isn't something that affects the detection rates. The probabilities we're talking about are not detection rates, not directly. They are the probabilities for some events predicted by a theory. Those can be related to detection rates with subsidiary assumptions.

Why should an assumption about the completeness of one's state description affect the results?

Of course it doesn't affect the results. But it affects whether the probabilistic dependence in question implies a causal influence. No causal influence is implied just because the probability of some event changes when you conditionalize on some other bit of space-like separated info. But if that probability changes even though one has already specified the contents of the past light cone of the event in question, there is clearly some sort of causal influence involved. That's why Bell thought Bell Locality was the proper mathematical test for "relativistic causality." And it's a test that can be applied directly to *theories* -- not to empirical correlation rates.

What is being directly tested are the predictions of an LHV theory. There seems to be some disagreement as to whether it is the L part or the HV part, or both, that is responsible for the discrepancy between the LHV predictions and the experimental results.
The L part is usually identified as the Bell Locality condition which is further analysed into PI and OI. Neither PI nor OI are violated because the detection rates, A and B, at either end of the experimental setup remain constant.

Wrong.

Which leaves the HV part as the most likely, if not the usual, suspect in the non-viability of LHV theories.

Except that L alone entails HV. So you can't "save" L by "blaming" HV for the violation of Bell's inequality. That's logic 101.

Whether or not PI is violated depends on whether the observed detection rate varies with the polarizer setting, doesn't it?

NO. PI is not simply the claim that the rate on one side doesn't depend on the distant setting.

What we know for sure is that, as far as can be ascertained, neither PI nor OI is violated experimentally. So, Bell Locality is not violated.

But if Bell Locality is true, then there must exist local hidden variables. But there can't exist local hidden variables, because there existence entails Bell's inequality, which is violated.

 

[Sherlock]

Look, the condition is what it is. It's just what I said before. No, this doesn't necessarily imply anything about the rates of detection. Those rates are some kind of averages over the probabilities involved in Bell Locality. The whole point here is that you can't just test Bell Locality by looking at emprical rates -- not without some subsidiary assumptions provided by a theory (which will tell you what a complete specification of the state consists of, and will tell you something about what initial state(s) are being produced by the setup procedure).
The conditionalization isn't something that affects the detection rates. The probabilities we're talking about are not detection rates, not directly. They are the probabilities for some events predicted by a theory. Those can be related to detection rates with subsidiary assumptions.

Ok, ttn ... I suppose I should reread your paper on this stuff, as well as the papers you reference (including Bell's La Nouvelle Cuisine). The comments being traded recently in this thread are not giving me a better understanding of the issues involved -- all of which are related to the larger question of what can be said about theoretical formulations and, especially, nature from experimental tests of Bell inequalities ... but I don't want to divert this thread from its specific program any longer.

Anyway I have some questions for DrChinese, which I want to post later ... and will also start a couple of threads on what I'm not clear about wrt the analysis (including yours) and meaning of Bell's formulation. But first, some reading and ... thinking. Thanks for your comments and Happy Holidays.