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

[GeorgCantor]

Does the violation of Bell's inequalities and Alain Aspect's experiment lend support to the idea that there is no mind-independent world?

 

[akhmeteli]

Just to demonstrate a specific example that this makes no sense. The below reference was submitted this week by a highly respected research group. It demonstrates nonlocality, see the title. Now, according to your thinking, this is actually evidence of locality rather than non-locality as it states. Are you following any of this, or am I wasting my time? I don't expect you to change your position, rather to simply stop writing what has already been refuted here.

Is this the first-ever article with "nonlocality" in the title? As I said, they say absolutely nothing about absence/presence of loopholes. I think they would certainly claim a first-ever loophole-free demonstration of nonlocality, if they could.

And I do believe that the failure to demonstrate nonlocality for 45 years suggests locality.

So, with all due respect, if you say that you refuted something, that does not necessarily mean you refuted it.

 

[ThomasT]

Imho, nonlocality only exists via the manipulation of terms and misinterpretation.

IMHO Most people, myself included, believe that your viewpoint only exists through those means in bold; I might add a forcefully willful ignorance that borders on the religious.

That's a curious belief.

Certainly there's more to reality than meets the eye. However, the assumption of nonlocality wrt an underlying reality is based on our ignorance, not our knowledge, of that underlying reality.

People can read what they want into QM formalism and technique, and Bell's theorem, and attribute EPR-Bell correlations to nonlocal whatevers. People can see the Virgin Mary in a splatter of spilled gazpacho and attribute that to a personal God giving a sign, or they can attribute the composition and appearance of natural objects to the will of an intelligent designer who they can pray to for free hockey tickets.

For me no-FTL and locality is something which emerges only macroscopically.

Does this macroscopic emergence require the prior assumption that there's an underlying physical medium which propagates disturbances ftl?

So locality, while it is observed in most cases and is only "weakly" violated in EPR is not "natural"

Locality is what we experience ... exclusively. So it's certainly natural. And, since Bell's locality condition isn't a locality condition, then locality isn't contradicted by Bell tests.

QM projection along transmission axis of polarizer transmitting detected disturbance is based on assumption of local common cause.

Please explain this somewhat cryptic statement in more detail. Do you mean that the interpretation assumes that the photon has to interact locally with the polarizer in order for the measurement at a given detector to occur? Or do you mean something else?

The assumption is that the optical disturbances incident on the polarizers have an emission-produced, common property which is being jointly analyzed by the crossed polarizers. Interaction of each disturbance with its associated polarizer is local.

There are only two values for angular difference of polarizers wrt which A and B are perfectly correlated (anticorrelated). These correlations at these settings have a local common cause explanation. There are no other A<->B correlations to explain.

Please elaborate on the "local common cause explanation" in this case, not in terms of the Aspect '82 experiment you have mentioned before, but rather in terms of a modern experiment where both polarization components are detected at each detector, so that in the ideal case (100% detector efficiency) there would be no missed detection events.

The type of experiment doesn't matter. A<->B type correlations have a local common cause explanation. The problem for the local realist isn't explaining correlation (anticorrelation) between A and B, it's reproducing the full range of QM predicted and observed experimental results.

... as I stated in my last post, your "broken entanglement" source produces results that are fundamentally different from the predictions of QM ...

The result that you (and I) posted is the QM prediction for that setup.

... I guess you don't dispute that SQM predicts some non-local phenomena? Are those predictions "manipulations of terms" or "misinterpretations" in your view, and why?

Whether or not SQM predicts non-local phenomena depends on how SQM is interpreted. There are no, per se, nonlocal phenomena.

 

[Frame Dragger]

@ThomasT: You are the undisputed master of copy-pasta... more so even than Akhmeteli. Sadly, you're lacking in even his meager content. Your response is not meaningful given the context of the quote you're using.

This is what comes of endless discussions of "Interpretations"... and it's not science.

 

[DrChinese]

DrChinese,

I admit that I don't know much about GHZ. However, in the article by Zeilinger e.a., Nature 403, 515-519 (3 February 2000),
Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, I found the following quote:
"However, we realize that, as for all existing two-particle tests of local
realism, our experiment has rather low detection efficiencies.
Therefore we had to invoke the fair sampling hypothesis21,22,
where it is assumed that the registered events are a faithful
representative of the whole."
So, at least on the face of it, fair sampling is used in GHZ experiments. Of course, the article is relatively old. However, in the following article (GHZ and Shimony, Bell's theorem without inequalities, Am. J. Phys., 58 (12), 1990) I found the following: (the authors discuss a possible GHZ experiment):
"The second step is to show how the test could be done even with low-efficiency detectors, provided that we make a plausible auxiliary assumption, which we call fair sampling. Finally, we show that the auxiliary assumption is dispensable if detector efficiencies exceed 90.8%." So it looks like you need 90% efficient detectors to do without fair sampling in GHZ. To the best of my knowledge, there are no such optical detectors. Please advise if I am wrong.

As for your latest reference (12.4 km experiment), the authors seem to be remarkably reticent on the issue of absence/presence of loopholes.

Another thing. At http://www.quantum.at/fileadmin/Presse/2008-07-01-MG-PW_A_Quantum__Renaissance.pdf Aspelmeyer and Zeilinger (Physics World July 2008, p. 22) write the following:

"But the ultimate test of Bell’s theorem is still missing:
a single experiment that closes all the loopholes at once.
It is very unlikely that such an experiment will disagree
with the prediction of quantum mechanics, since this
would imply that nature makes use of both the detection
loophole in the Innsbruck experiment and of the
locality loophole in the NIST experiment. Nevertheless,
nature could be vicious, and such an experiment is desirable
if we are to finally close the book on local realism." Then they discuss GHZ and do not claim that a loophole-free experiment had been performed. This article is recent, unlike the 1998 article in arxiv that I quoted before, so it looks like I did not misrepresent Zeilinger's opinion.

I would say again that you have substantially misrepresented Zeilinger's position by pulling out a early quote from a historical narrative prior to his reaching the end. He goes on to say (regarding 3 particle GHZ and then summarizing the results of both GHZ and Bell tests):

"...three entangled particles can produce an immediate
conflict in a single measurement result because
measurements on two of the particles allow us to predict
with certainty the property of the third particle.
The first experiments on three entangled photons
were performed in late 1999 by AZ and co-workers, and
they revealed a striking accordance with quantum theory
(Nature 403 515). So far, all tests of both Bell’s inequalities
and on three entangled particles (known as
GHZ experiments) (see figure 1) confirm the predictions
of quantum theory, and hence are in conflict with
the joint assumption of locality and realism as underlying
working hypotheses for any physical theory that
wants to explain the features of entangled particles."

and later:

"One such question concerns once again the notions
of locality and realism. The whole body of Bell and
GHZ experiments performed over the years suggests
that at least one of these two assumptions is inadequate
to describe the physical world (at least as long
as entangled states are involved). But Bell’s theorem
does not allow us to say which one of the two should
be abandoned."

Next time, try sticking to the gist of the article. Zeilinger goes on to mention Leggett (as I have as well) and the fact that this rules out even many forms of non-local realism. In the meantime, I noticed you have also failed to produce any of the following:

a) Decent reference for Bell being dependent on QM theory or the measurement problem.
b) A dataset that matches the QM predictions that is realistic.

And referring to your post stating the absurdly illogical "And I do believe that the failure to demonstrate nonlocality for 45 years suggests locality." At least you finally mention it is your opinion in the statement, a position to which you are entitled and I would not bother to try to change your mind about. (Perhaps I should state the highly insightful: "And I do believe that the failure to demonstrate non-existence of leprechauns for 45 years suggests the leprechaun exists.")

Honestly, I think our dialogue has reached an end. I simply ask that from here on out, you label your opinions as such. And please, do not misrepresent the opinions (or general scientific acceptance thereof) of other authors. You are entitled to your opinion, but you are not entitled to misled others who may not know as much about the area.

 

[DrChinese]

Does the violation of Bell's inequalities and Alain Aspect's experiment lend support to the idea that there is no mind-independent world?

As far as I know, the answer is NO. But there are others who disagree. There is no meaningful evidence on this question.

 

[akhmeteli]

I would say again that you have substantially misrepresented Zeilinger's position by pulling out a early quote from a historical narrative prior to his reaching the end. He goes on to say (regarding 3 particle GHZ and then summarizing the results of both GHZ and Bell tests):

"...three entangled particles can produce an immediate
conflict in a single measurement result because
measurements on two of the particles allow us to predict
with certainty the property of the third particle.
The first experiments on three entangled photons
were performed in late 1999 by AZ and co-workers, and
they revealed a striking accordance with quantum theory
(Nature 403 515). So far, all tests of both Bell’s inequalities
and on three entangled particles (known as
GHZ experiments) (see figure 1) confirm the predictions
of quantum theory, and hence are in conflict with
the joint assumption of locality and realism as underlying
working hypotheses for any physical theory that
wants to explain the features of entangled particles."

and later:

"One such question concerns once again the notions
of locality and realism. The whole body of Bell and
GHZ experiments performed over the years suggests
that at least one of these two assumptions is inadequate
to describe the physical world (at least as long
as entangled states are involved). But Bell’s theorem
does not allow us to say which one of the two should
be abandoned."

Look, people ask you if GHZ produced loophole-free evidence against LR. You choose to keep silence on this point. I gave you a 2008 quote by Zeilinger that there had been no loophole-free experiments ruling out LR by that time. (Nobody claimed such experiments since then, as far as I know, and there are no such claims in work referenced by you). So who misrepresents him?

Next time, try sticking to the gist of the article. Zeilinger goes on to mention Leggett (as I have as well) and the fact that this rules out even many forms of non-local realism.

See above

In the meantime, I noticed you have also failed to produce any of the following:

a) Decent reference for Bell being dependent on QM theory or the measurement problem.
b) A dataset that matches the QM predictions that is realistic.

First you demand a reference, now you demand what you call a "decent reference", next you'll require a "perfect reference"? I reject your demand. The rules demand that I present a published reference, I did just that. You refuse to criticize the quotes from the reference I offered or my arguments supporting them, you prefer to criticize the author of the reference - it's your decision.

Neither am I under any obligation to produce any "dataset". I state that LR has not been ruled out so far. To this end, I proved by references that no violations of the genuine Bell inequalities had been demonstrated experimentally and that the Bell theorem itself uses mutually contradictory assumptions from standard QM (or, if you wish, consequences of these assumptions), thus it cannot be considered a no-go theorem for LR. If you have other proofs that LR has been ruled out, then YOU are supposed to present them. I indicated a general approach demonstrating at least appearance of entanglement in local theories. I don't have to accept any "challenges" you may wish to offer. Again, you would not understand if I demanded that you conduct a loophole-free experiment. So either put up a proof that LR has been ruled out, or...

By the way, how about Euclidian geometry?

Honestly, I think our dialogue has reached an end.

As you wish.

I simply ask that from here on out, you label your opinions as such. And please, do not misrepresent the opinions (or general scientific acceptance thereof) of other authors. You are entitled to your opinion, but you are not entitled to misled others who may not know as much about the area.

I reject your allegations that I misrepresented "the opinions (or general scientific acceptance thereof) of other authors".

 

[zonde]

and later:
"One such question concerns once again the notions
of locality and realism. The whole body of Bell and
GHZ experiments performed over the years suggests
that at least one of these two assumptions is inadequate
to describe the physical world (at least as long
as entangled states are involved). But Bell’s theorem
does not allow us to say which one of the two should
be abandoned."

Suggests but does not prove. So nothing new here.

a) Decent reference for Bell being dependent on QM theory or the measurement problem.

Why separate reference when Bell's paper can be used instead:
"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."
And anyone wishing to confirm that this statement has crucial role for Bell argument can examining his paper. http://www.drchinese.com/David/Bell_Compact.pdf"

 

[Demystifier]

Do the authors of the paper reporting the actual GHZ experiment explicitly claim that this disproof of LR does not contain any experimental loopholes?

I asked it Dr Chinese, but now Akhmeteli answered it in #385. Not only that they do not claim that, but they explicitly claim the opposite. Of course, it does not change my opinion that nature is nonlocal, but it's fair to say honestly how much the existing evidence for it is certain. The evidence is indeed strong, but there is no need to exaggerate that it is even stronger than it really is.

 

[Hans de Vries]

And entanglement is not so easy to explain these days with some of the newer experiments. EPR is completely lost on these. Please explain, for example, how photons become entangled when they are not in each other's light cones - and never have been - and originate from different lasers. Meanwhile, QM can..

It would be a totally sensational result if there was any correlation outside the
lightcone but I can't draw this conclusion from these experiments.

If there is correlation between pair A1,B1 and independently there is correlation
between pair A2,B2. Then the (random) relation between A1 and A2 is also
expected between B1 and B2 even if B1 and B2 have never met.Regards, Hans

 

[SpectraCat]

Why separate reference when Bell's paper can be used instead:
"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."
And anyone wishing to confirm that this statement has crucial role for Bell argument can examining his paper. http://www.drchinese.com/David/Bell_Compact.pdf"

I don't really see how this is crucial for his *argument*. In section II, he sets up the test cases for his proof in terms of the predictions of QM, which have been adequately supported by experimental measurements (EDIT: although not at the time, and this is my opinion of the modern experimental results). However everything concerning the proof in section IV is completely independent of how those test cases were determined. So, the only way that Bell's paper "depends on QM", is for the generation of the test case. Since this is outside the scope of the rest of the derivation, the idea of a "Bell test" certainly seems valid outside the scope of the initial test case it was devised to explain.

 

[DrChinese]

Suggests but does not prove. So nothing new here.


Why separate reference when Bell's paper can be used instead:
"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."
And anyone wishing to confirm that this statement has crucial role for Bell argument can examining his paper. http://www.drchinese.com/David/Bell_Compact.pdf"

That is a prediction of QM. Maybe it was wrong. It doesn't matter HOW the prediction was arrived at for Bell. The important thing is the QM and LR are incompatible as to their predictions.

 

[SpectraCat]

It would be a totally sensational result if there was any correlation outside the
lightcone but I can't draw this conclusion from these experiments.

If there is correlation between pair A1,B1 and independently there is correlation
between pair A2,B2. Then the (random) relation between A1 and A2 is also
expected between B1 and B2 even if B1 and B2 have never met.


Regards, Hans

Yes, but the correlations between the non-interacting photons (B1 and B2 in your example) violate a Bell inequality, which means that they cannot be explained in terms of simple random coincidences. Whether or not these results are proof of quantum non-locality is still open for discussion .. it depends on if you accept the assumptions of the experiment (i.e. independence of initial entangled pairs, fair sampling assumption), which some are not prepared to do yet. (that is the whole reason for this thread)

 

[DrChinese]

I asked it Dr Chinese, but now Akhmeteli answered it in #385. Not only that they do not claim that, but they explicitly claim the opposite. Of course, it does not change my opinion that nature is nonlocal, but it's fair to say honestly how much the existing evidence for it is certain. The evidence is indeed strong, but there is no need to exaggerate that it is even stronger than it really is.

You should re-read my response or look at the original. Akhmeteli takes the comment out of context. As per usual. It is clear by the end of the article that they do not consider LR viable per experiment.

From my #395:

"...three entangled particles can produce an immediate
conflict in a single measurement result because
measurements on two of the particles allow us to predict
with certainty the property of the third particle.
The first experiments on three entangled photons
were performed in late 1999 by AZ and co-workers, and
they revealed a striking accordance with quantum theory
(Nature 403 515). So far, all tests of both Bell’s inequalities
and on three entangled particles (known as
GHZ experiments) (see figure 1) confirm the predictions
of quantum theory, and hence are in conflict with
the joint assumption of locality and realism as underlying
working hypotheses for any physical theory that
wants to explain the features of entangled particles."

I don't think that this in any way deviates from what I have been saying, of course Zeilinger says it much more clearly.

 

[DrChinese]

It would be a totally sensational result if there was any correlation outside the
lightcone but I can't draw this conclusion from these experiments.

If there is correlation between pair A1,B1 and independently there is correlation
between pair A2,B2. Then the (random) relation between A1 and A2 is also
expected between B1 and B2 even if B1 and B2 have never met.


Regards, Hans

It is not random as you suggest. They are entangled, and exhibit statistics to match. Correlated but unentangled photons do not show those statistics.

 

[Frame Dragger]

It is not random as you suggest. They are entangled, and exhibit statistics to match. Correlated but unentangled photons do not show those statistics.

I read this paper and I don't see how there can be this apparent level of confusion regarding these entangled photons. We can parse the language to fit our agendas (ahkmeteli) or be genuinely confused (ThomasT), or truly believe (DrChinese) or not (Demystifier).

Some relevant questions about the laser source for supposedly "never met each other" photons seem germaine. This endless meandering about ERB and Bell has become so cyclical and predictable that I set my clock by them now. Can we please jettison disruptive elements (akhmeteli and any like), and get back to the real questions about the LR or not?

The next person who says "loophole" is going to be on the wrong end of a slap to the face, or maybe a botnet. I'm tired, so it'll be a coinflip. I'm kidding, or am I? Ahhh...

 

[DrChinese]

I read this paper and I don't see how there can be this apparent level of confusion regarding these entangled photons. We can parse the language to fit our agendas (ahkmeteli) or be genuinely confused (ThomasT), or truly believe (DrChinese) or not (Demystifier).

Some relevant questions about the laser source for supposedly "never met each other" photons seem germaine. This endless meandering about ERB and Bell has become so cyclical and predictable that I set my clock by them now. Can we please jettison disruptive elements (akhmeteli and any like), and get back to the real questions about the LR or not?

The next person who says "loophole" is going to be on the wrong end of a slap to the face, or maybe a botnet. I'm tired, so it'll be a coinflip. I'm kidding, or am I? Ahhh...

Ha!

A note about the "photons that never met each other". This is something of a misnomer (of course perpetrated by the article's author), and I will direct my comments to the other thread we have on the subject so that we can reserve this one for discussion of LR.

 

[zonde]

I don't really see how this is crucial for his *argument*. In section II, he sets up the test cases for his proof in terms of the predictions of QM, which have been adequately supported by experimental measurements (EDIT: although not at the time, and this is my opinion of the modern experimental results). However everything concerning the proof in section IV is completely independent of how those test cases were determined. So, the only way that Bell's paper "depends on QM", is for the generation of the test case. Since this is outside the scope of the rest of the derivation, the idea of a "Bell test" certainly seems valid outside the scope of the initial test case it was devised to explain.

For Bell's argument it is crucial that all single measurements are predictable.
Say if there are measurements that are more predictable and others are less predictable it will spoil the whole picture.

 

[DrChinese]

For Bell's argument it is crucial that all single measurements are predictable.
Say if there are measurements that are more predictable and others are less predictable it will spoil the whole picture.

QM only makes 1 prediction for a Bell test, and it is statistical. cos^2 theta. If there is any other, I have never seen it.

 

[SpectraCat]

For Bell's argument it is crucial that all single measurements are predictable.
Say if there are measurements that are more predictable and others are less predictable it will spoil the whole picture.

I have no idea what you mean here ... how does anything that is written in that paper even imply that, "all single measurements are predictable"? The whole point of QM is that, in the general case, the results of single measurements are NOT PREDICTABLE. The only thing that *is* predictable for the case in Bell's paper is the coincidence rate, which is a statistical relationship that is built up from the observation of MANY measurements.

Anyway, as I said, even if you were correct, it wouldn't affect the logic of Bell's deduction at all ... it would only affect whether or not QM predicted violations of the Bell inequality. Those "more and less predictable measurements" you are talking about are completely covered by Bell's LHV formulation AFAICS, so they are handled generally in the proof without any reference to or assumption of the correctness of QM.

 

[Demystifier]

I read this paper and I don't see how there can be this apparent level of confusion regarding these entangled photons. We can parse the language to fit our agendas (ahkmeteli) or be genuinely confused (ThomasT), or truly believe (DrChinese) or not (Demystifier).

Just for the record, I also truly believe in nonlocality. However, I allow for a possibility (with a very very small probability) that my belief may be incorrect.

 

[Frame Dragger]

Just for the record, I also truly believe in nonlocality. However, I allow for a possibility (with a very very small probability) that my belief may be incorrect.

I stand corrected; I share your view with the same modest belief in it possibly being wrong.

 

[yoda jedi]

a new experiment

on pre-determined (polarization values) polarizers ?

but what about ten particles (previous pre-entangled) up and the other ten, down, then make the ten particles up to spin down, and see how spin the other ten particles....
if change the spin, well that`s no-locality, but i wish to see that...

I read this paper and I don't see how there can be this apparent level of confusion regarding these entangled photons.

We can parse the language to fit our agendas (ahkmeteli) or be genuinely confused (ThomasT), or truly believe (DrChinese) or not (Demystifier).

Some relevant questions about the laser source for supposedly "never met each other" photons seem germaine. This endless meandering about ERB and Bell has become so cyclical and predictable that I set my clock by them now. Can we please jettison disruptive elements (akhmeteli and any like), and get back to the real questions about the LR or not?

The next person who says "loophole" is going to be on the wrong end of a slap to the face, or maybe a botnet. I'm tired, so it'll be a coinflip. I'm kidding, or am I? Ahhh...

...laughs...​

Very Concise !
and for me, the answer have to be developed (for locality).

as for REALITY

...existing a long time before us...

 

[Hans de Vries]

It is not random as you suggest. They are entangled, and exhibit statistics to match. Correlated but unentangled photons do not show those statistics.

Maybe I didn't express myself clear enough. If A1 and A2 meet then they have a
random relation ship because they are not entanglement. Upon determining the
relation between A1 and A2 you know that B1 and B2 will have a similar relation.Regards, Hans

 

[Frame Dragger]

a new experiment

...laughs...​

Very Concise !
and for me, the answer is beyond (for locality).

as for REALITY existing a long time before us...

Thank you ;) ... I become downright expressive when I'm cranky. While it seems that LR is out, like you once that ruling is on the table as a strong possiblity, I feel out of sorts as a seemingly local and real meat-puppet.

 

[SpectraCat]

Maybe I didn't express myself clear enough.

perhaps ...

If A1 and A2 meet then they have a random relation ship because they are not entanglement. Upon determining the relation between A1 and A2 you know that B1 and B2 will have a similar relation.

Unfortunately, that doesn't make your point a whole lot clearer (at least not to me). In the "normal" interpretation of the experiment we are discussing (i.e. the one put forward by the authors of the paper), photons A1 and A2 (in your notation) become entangled when they interfere at the fiber beam splitter. This entanglement is then teleported to the "non-interacting" pair B1 and B2, as confirmed by violation of a Bell inequality.

Are you proposing an alternative explanation of the experiment, whereby A1 and A2 do not become entangled at the beamsplitter, or are you saying that their entanglement is not required for observation of a Bell violation for B1 and B2? Or are you saying something else entirely?

 

[DrChinese]

Maybe I didn't express myself clear enough. If A1 and A2 meet then they have a
random relation ship because they are not entanglement. Upon determining the
relation between A1 and A2 you know that B1 and B2 will have a similar relation.


Regards, Hans

You might think so, but that doesn't work unless the photons are actually entangled. Remember that you need the so-called "perfect" correlations when you have the same settings for Alice and Bob. That doesn't happen in the case you describe. You only have to try a few data points to see what I am talking about. The best you can get out of the scenario you describe is Product state statistics, not Entangled State statistics.

 

[ThomasT]

@ThomasT: You are the undisputed master of copy-pasta... more so even than Akhmeteli. Sadly, you're lacking in even his meager content. Your response is not meaningful given the context of the quote you're using.

This is what comes of endless discussions of "Interpretations"... and it's not science.

Your commentary is amusing, but please feel free to contribute an idea or to comment on some specific aspect of the thread discussion other than the styles, etc. of the other contributors.

 

[Frame Dragger]

Your commentary is amusing

Thanks

...but please feel free to contribute an idea or to comment on some specific aspect of the thread discussion other than the styles, etc. of the other contributors.

Awww, I just knew there was a catch. I've made my views clear in this thread, and then when it started to run I commented. Other than your response and this counter-point, I'd say the thread has improved since.

 

[zonde]

I have no idea what you mean here ... how does anything that is written in that paper even imply that, "all single measurements are predictable"? The whole point of QM is that, in the general case, the results of single measurements are NOT PREDICTABLE. The only thing that *is* predictable for the case in Bell's paper is the coincidence rate, which is a statistical relationship that is built up from the observation of MANY measurements.

Anyway, as I said, even if you were correct, it wouldn't affect the logic of Bell's deduction at all ... it would only affect whether or not QM predicted violations of the Bell inequality. Those "more and less predictable measurements" you are talking about are completely covered by Bell's LHV formulation AFAICS, so they are handled generally in the proof without any reference to or assumption of the correctness of QM.

I will try a bit differently. I understand that analogy is not the best argument but let me use one this time.

Let's consider an experiment.
You and I each take ten pebbles. We arrange them so that we can later identify pairs from our pebbles (say we number them from 1 to 10 and my n-th pebble makes pair with your's n-th pebble).
Now each of us picks one pebble and we compare them and identify if they are from the same pair. If they do not make pair we discard them. If they make a pair then we record whether your pebble is bigger than mine or not.
After that we repeat from start - you and I each take ten pebbles ...
When we have collected some amount of data we find out that your pebble is bigger in almost all cases (or more precisely there is on average one exclusion for every 200 000 successful runs).
Now there are two observers that analyze this data.
Observer A says that this result indicates that your pebbles are bigger than mine.
Observer B says that this result does not indicate anything particular about our pebbles but it shows that I am picking smallest pebble out of my ten but you are picking biggest pebble out of yours.
However observer A insists that he is correct because as he speculates if we modify the experiment so that we take only one pebble instead of ten then we will observe the same result.

Now do you agree with observer A?