Institutionalized Denial of the Disproof of Bell's Theorem

[minkwe]

Ok, I read again your description and you choose from each row four values to obtain wx-wz+yx+yz. If that is what you do, then I understand it.

(w,x,y,z) is an arbitrary set of 4 numbers belonging to the set . Incidentally, each row of the 4xN spreadsheet from scenario 3 is analogous to (w, x, y, z) and the expectation values that are estimated from the 4xN spreadsheet as explained experiment 3 are analogous to the averages <wx> - <wz> + <yx> + <yz>. Therefore, the proof showing that <wx> - <wz> + <yx> + <yz> <= 2 is also a proof that E(a1,b1) - E(a1, b2) + E(a2, b1) + E(a2, b2) <= 2 for scenario 3.


Note that this limit is not a statistical limit but a mathematical limit. It is impossible to violate it even by a tiny tiny bit. Not by experimental noise, nothing at all. Note also that the data from scenario 3 is not restricted anyway. The researchers are completely free to use any method to generate the data. They can use QM, magic, spooky non-local communication, conspiracy, backward causation or any other contrapment to generate the data and that limit can't be violated so long as the rules of scenario 3 are followed. I will assume that you agree with this and if you disagree you will object.

Then here is scenario 4:

Let us re-introduce Gill's "the particles must be created in the same way", to Scenario 3. In other words, Scenario 4 is just scenario 3 with the additional restriction that "the particles must be created in the same way", or as you explained the particles must be created in the singlet state. Do you believe adding this restriction can permit the data to violate the limits established in scenario 3?
Can you think of any additional restrictions (or freedoms) that can be imposed (or conferred) on the researchers, which will to permit them to violate the limits established in scenario 3?

[minkwe]

The interesting thing I did with my spreadsheet was imagining that each row of the spreadsheet is assigned to just one of the four experimental conditions, completely at random. Then four correlations are computed each on a different subset of rows, each using a different pair of the columns. I showed that CHSH would hold with probability exponentially close to 1, if N is large.

Certainly it is interesting, you presented another derivation of the Bell inequqlity. It would be good if you can write another paper generalizing it for arbitrary probability of chosing two columns. In that way your derivation would be completely ganeral.

What I'm doing has nothing to do with Gill's paper. But there is a fatal flaw in Gill's paper which we can discuss in another thread. To see it you have to understand the difference between sampling with replacement and sampling without replacement. You will also have to understand that there is a hidden assumption in Gill's paper that disjoint subsets are independent, which is false. But this should be discussed in a separate thread.

[Justo]

Ok, I read again your description and you choose from each row four values to obtain wx-wz+yx+yz. If that is what you do, then I understand it.

(w,x,y,z) is an arbitrary set of 4 numbers belonging to the set . Incidentally, each row of the 4xN spreadsheet from scenario 3 is analogous to (w, x, y, z) and the expectation values that are estimated from the 4xN spreadsheet as explained experiment 3 are analogous to the averages <wx> - <wz> + <yx> + <yz>. Therefore, the proof showing that <wx> - <wz> + <yx> + <yz> <= 2 is also a proof that E(a1,b1) - E(a1, b2) + E(a2, b1) + E(a2, b2) <= 2 for scenario 3.


Note that this limit is not a statistical limit but a mathematical limit. It is impossible to violate it even by a tiny tiny bit. Not by experimental noise, nothing at all. Note also that the data from scenario 3 is not restricted anyway. The researchers are completely free to use any method to generate the data. They can use QM, magic, spooky non-local communication, conspiracy, backward causation or any other contrapment to generate the data and that limit can't be violated so long as the rules of scenario 3 are followed. I will assume that you agree with this and if you disagree you will object.

Then here is scenario 4:

Let us re-introduce Gill's "the particles must be created in the same way", to Scenario 3. In other words, Scenario 4 is just scenario 3 with the additional restriction that "the particles must be created in the same way", or as you explained the particles must be created in the singlet state. Do you believe adding this restriction can permit the data to violate the limits established in scenario 3?
Can you think of any additional restrictions that can be imposed on the researchers, which will to permit them to violate the limits established in scenario 3?

The way the equation is mounted from 4 arbitrary values to give the Bell inequality is a tautology, i.e., it is valid for any values so it is irrelevant that the particles be prepared in the same way. It does not impose any restriction at all on the 4 values that gave it origin.

[minkwe]

The way the equation is mounted from 4 arbitrary values to give the Bell inequality is a tautology, i.e., it is valid for any values so it is irrelevant that the particles be prepared in the same way. It does not impose any restriction at all on the 4 values that gave it origin.

Good! At this point, we should review the derivation of the CHSH to confirm that it is done exactly like what I did in scenario 3. You take a look at this one from Bell's "Speakable & Unspeakable" if you like: https://en.wikipedia.org/wiki/CHSH_inequality.

Do the following substitutions and you will see that mathematically, this is exactly the same derivation.






Do you agree? Now the following question is being begged to be asked. What is the QM prediction for scenario 4? Is it the same as the QM prediction in scenario 1?

[Heinera]

Note that this limit is not a statistical limit but a mathematical limit. It is impossible to violate it even by a tiny tiny bit. Not by experimental noise, nothing at all. Note also that the data from scenario 3 is not restricted anyway. The researchers are completely free to use any method to generate the data. They can use QM, magic, spooky non-local communication, conspiracy, backward causation or any other contrapment to generate the data and that limit can't be violated so long as the rules of scenario 3 are followed. I will assume that you agree with this and if you disagree you will object.

The restriction is not on how the data is generated, it is on the method employed by the analyzer. As I wrote:

I guess minkwe means that while in the original case, the analyzer receives eight datasets in order to compute the CHSH value (four experimenters, two sides for each), he now only receives four datasets, and will have to use each twice.

Needless to say this restriction makes a huge difference of what results he can achieve.

The derivation of this algebraic upper bound of two by using your scenario 3 is not the proof of Bell's theorem, it's just an intermediate step. The final step in the proof (that relies on probability theory) takes us back to your scenario 1, and shows that for data produced by a LHV model, the bound is still 2 in the limit as N goes to infinity. It is this final step you don't understand.

[minkwe]

This question is for anyone who wants to participate in the discussion. It's a very simple question:

What is the QM prediction for scenario 4?

[Justo]

The derivation of this algebraic upper bound of two by using your scenario 3 is not the proof of Bell's theorem, it's just an intermediate step. The final step in the proof (that relies on probability theory) takes us back to your scenario 1, and shows that for data produced by a LHV model, the bound is still 2 in the limit as N goes to infinity. It is this final step you don't understand.

I agree that 3 is not what Bell did

[Heinera]

This question is for anyone who wants to participate in the discussion. It's a very simple question:

What is the QM prediction for scenario 4?

The QM prediction requires the singlet state. It is impossible to report corresponding results from the singlet state using only 4 datasets as you require in your scenario 4. Your question has no answer; there is no QM prediction.

[Justo]

The way the equation is mounted from 4 arbitrary values to give the Bell inequality is a tautology, i.e., it is valid for any values so it is irrelevant that the particles be prepared in the same way. It does not impose any restriction at all on the 4 values that gave it origin.

Good! At this point, we should review the derivation of the CHSH to confirm that it is done exactly like what I did in scenario 3. You take a look at this one from Bell's "Speakable & Unspeakable" if you like: https://en.wikipedia.org/wiki/CHSH_inequality.

Do the following substitutions and you will see that mathematically, this is exactly the same derivation.






Do you agree? Now the following question is being begged to be asked. What is the QM prediction for scenario 4? Is it the same as the QM prediction in scenario 1?

I agree it is mathematically equivalent. Of course scenario 3 has nothing to do with the way a Bell test is performed according to scenario 1.
The question is if the equation can represent the real experimental scenario 1.
At this point I can only refer you to one of my papers where I explain( with my coauthor) why and how your previous equations emerge in a real Bell test experiment: "A note on Bell's theorem logical consistency", it is on arXiv and the derivation is in section 4.

I appreciate your efforts to make me understand your point that I did not understand at some point. It was my fault, your explanations were clear.

[minkwe]

I agree it is mathematically equivalent. Of course, scenario 3 has nothing to do with the way a Bell test is performed according to scenario 1.

Exactly! I never claimed that it did.

The question is if the equation can represent the real experimental scenario 1.

It can't, but you are jumping the gun. (BTW: Claims about probability can be dispelled by reviewing Bell's original paper on the subject. You can also review this Wikipedia article https://en.wikipedia.org/wiki/Bell%27s_theorem under the section titled "Derivation of the classical bound"). But the question right now is what is the QM prediction for scenario 4.

At this point I can only refer you to one of my papers where I explain( with my coauthor) why and how your previous equations emerge in a real Bell test experiment: "A note on Bell's theorem logical consistency", it is on arXiv and the derivation is in section 4.

I'll be happy to discuss your paper after this.

I appreciate your efforts to make me understand your point that I did not understand at some point. It was my fault, your explanations were clear.

No worries.

[Justo]

It can't, but you are jumping the gun. (BTW: Claims about probability can be dispelled by reviewing Bell's original paper on the subject. You can also review this Wikipedia article https://en.wikipedia.org/wiki/Bell%27s_theorem under the section titled "Derivation of the classical bound"). But the question right now is what is the QM prediction for scenario 4.
.

If what you mean is the tautological combination of four values, the relsult is always bound by 4. Is that what you mean?

[gill1109]

The interesting thing I did with my spreadsheet was imagining that each row of the spreadsheet is assigned to just one of the four experimental conditions, completely at random. Then four correlations are computed each on a different subset of rows, each using a different pair of the columns. I showed that CHSH would hold with probability exponentially close to 1, if N is large.

Certainly it is interesting, you presented another derivation of the Bell inequqlity. It would be good if you can write another paper generalizing it for arbitrary probability of chosing two columns. In that way your derivation would be completely ganeral.

That is an easy exercise for anyone who knows a bit of elementary probability, it has been done by other authors to take account of biased setting choice in some actual experiments.

I deliberately specialised to the special case in which binary measurement settings are chosen by independent fair coin tosses. The point of my paper was not to derive Bell's inequality yet again. The point was to show that by taking advantage of random setting choices one could obtain probability bounds on the amount by which CHSH can be violated under local realism. This resolves a whole collection of loopholes (finite statistics loophole, time dependence and time shifts in measurement devices and source...). I obtained a powerful and experimentally valuable strengthening of Bell's inequality, by making assumptions about the way settings are chosen. Bell did not do that. I did it first in a paper twenty years ago, which was used by the experimenters of the 2015 experiments.

https://arxiv.org/abs/quant-ph/0110137

Accardi contra Bell (cum mundi): The Impossible Coupling
Richard D. Gill
An experimentally observed violation of Bell's inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allow a loophole for local realism, known as the memory loophole. We show that the randomized design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale differences. The results are used to specify a protocol for a public bet between the author and L. Accardi, who in recent papers (Accardi and Regoli, 2000a,b, 2001; Accardi, Imafuku and Regoli, 2002) has claimed to have produced a suite of computer programmes, to be run on a network of computers, which will simulate a violation of Bell's inequalites. At a sample size of thirty thousand, both error probabilities are guaranteed smaller than one in a million, provided we adhere to the sequential randomized design. The results also show that Hess and Philipp's (2001a,b) recent claims are mistaken that Bell's theorem fails because of time phenomena supposedly neglected by Bell.
Journal reference: pp. 133-154 in: Mathematical Statistics and Applications: Festschrift for Constance van Eeden. Eds: M. Moore, S. Froda and C. Léger. IMS Lecture Notes -- Monograph Series, Volume 42 (2003). Institute of Mathematical Statistics. Beachwood, Ohio
https://projecteuclid.org/ebooks/institute-of-mathematical-statistics-lecture-notes-monograph-series/Mathematical-statistics-and-applications/Chapter/Accardi-contra-bell-cum-mundi-the-impossible-coupling/10.1214/lnms/1215091935

See also
https://arxiv.org/abs/quant-ph/0301059

Time, Finite Statistics, and Bell's Fifth Position
Richard D. Gill
I discuss three issues connected to Bell's theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars Under Local Realism), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell's list of four positions to hold in the light of his results. Levy's (1935) theory of martingales, and Fisher's (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell's conclusions are independent of how one likes to interpret probability, and give a critique of some recent anti-Bellist literature.
Comments: 28 pages; proceedings of Vaxjo conference (2002) on foundations of QM and probability. Version 2: corrected a LaTeX error (\mathbb 1 did not work)
Subjects: Quantum Physics (quant-ph); Probability (math.PR); Statistics Theory (math.ST)
Journal reference: pp. 179-206 in: Proc. of "Foundations of Probability and Physics - 2", Ser. Math. Modelling in Phys., Engin., and Cogn. Sc., vol. 5/2002, Växjö Univ. Press, 2003

[minkwe]

It can't, but you are jumping the gun. (BTW: Claims about probability can be dispelled by reviewing Bell's original paper on the subject. You can also review this Wikipedia article https://en.wikipedia.org/wiki/Bell%27s_theorem under the section titled "Derivation of the classical bound"). But the question right now is what is the QM prediction for scenario 4.
.

If what you mean is the tautological combination of four values, the relsult is always bound by 4. Is that what you mean?

No that's not what I mean. Scenario 4 is the same as Scenario 3 (which is bounded by 2), except we have re-introduced Gill's requirement that the particles must be created in the singlet state. We still end up with 4 columns of data like in Scenario 3 except now the particles generating those data must be created in the singlet state. So in this case, what will QM predict for the linear combination of expectation values E(a1,b1) - E(a1, b2) + E(a2, b1) + E(a2, b2)? Will it be the same as in Scenario 1? Will it exceed the bounds of 2?

[Justo]

It can't, but you are jumping the gun. (BTW: Claims about probability can be dispelled by reviewing Bell's original paper on the subject. You can also review this Wikipedia article https://en.wikipedia.org/wiki/Bell%27s_theorem under the section titled "Derivation of the classical bound"). But the question right now is what is the QM prediction for scenario 4.
.

If what you mean is the tautological combination of four values, the relsult is always bound by 4. Is that what you mean?

No that's not what I mean. Scenario 4 is the same as Scenario 3 (which is bounded by 2), except we have re-introduced Gill's requirement that the particles must be created in the singlet state. We still end up with 4 columns of data like in Scenario 3 except now the particles generating those data must be created in the singlet state. So in this case, what will QM predict for the linear combination of expectation values E(a1,b1) - E(a1, b2) + E(a2, b1) + E(a2, b2)? Will it be the same as in Scenario 1? Will it exceed the bounds of 2?

I am sorry, now I realize that I incorrectly wrote 4 instead of 2 in my previous comment.
It doesn't matter how the particles are generated, it is irrelevant if they are in a singlet state or not. When you use only 4 vales instead of 8 and then conbine them in the form <wx> - <wz> + <yx> + <yz> you will always obtain the 2. That is "tautological" and meaningless it does not say anything about the experiment or nature. That is exactly what people who base the derivation on CFD do.

[gill1109]

If 4N particles, each one being one of a different pair together in the singlet state, is measured in any direction, then all outcomes are independent and equally likely to be +1 or -1. So those four correlations are all zero, up to 1/sqrt N random fluctuations. Necessarily, the CHSH quantity ‘S’ lies between -2 and +2, but it will usually be very close to zero if N is large.

By the way, just because there is institutionalised denial of anything, does not mean that thing is actually true. There is institutionalised denial that sqrt of 2 is a rational number. There is institutionalised denial that the earth is flat. There is nowadays, in physics, institutionalised belief that Bell’s theorem is true. Still, there are plenty of original thinkers who believe it is not true and enough of them keep getting papers published claiming the same, that one can certainly say that there continues to be a lively debate as to its meaning for physics and especially for the philosophy of science.

[minkwe]

If 4N particles, each one being one of a different pair together in the singlet state, is measured in any direction, then all outcomes are independent and equally likely to be +1 or -1. So those four correlations are all zero, up to 1/sqrt N random fluctuations. Necessarily, the CHSH quantity ‘S’ lies between -2 and +2, but it will usually be very close to zero if N is large.

By the way, just because there is institutionalised denial of anything, does not mean that thing is actually true. There is institutionalised denial that sqrt of 2 is a rational number. There is institutionalised denial that the earth is flat. There is nowadays, in physics, institutionalised belief that Bell’s theorem is true. Still, there are plenty of original thinkers who believe it is not true and enough of them keep getting papers published claiming the same, that one can certainly say that there continues to be a lively debate as to its meaning for physics and especially for the philosophy of science.

You can generate singlet state for the and column and a singlet state for the and columns. Then the QM prediction for



Which doesn't violate



So far QM has not violated anything. And we now have 2 different inequalities, each valid for a different scenario:

For scenario 1 and 2
For scenario 3 and 4

In both cases, the QM prediction for the specified scenario does not violate the inequality for the specified scenario.

[gill1109]

If 4N particles, each one being one of a different pair together in the singlet state, is measured in any direction, then all outcomes are independent and equally likely to be +1 or -1. So those four correlations are all zero, up to 1/sqrt N random fluctuations. Necessarily, the CHSH quantity ‘S’ lies between -2 and +2, but it will usually be very close to zero if N is large.

By the way, just because there is institutionalised denial of anything, does not mean that thing is actually true. There is institutionalised denial that sqrt of 2 is a rational number. There is institutionalised denial that the earth is flat. There is nowadays, in physics, institutionalised belief that Bell’s theorem is true. Still, there are plenty of original thinkers who believe it is not true and enough of them keep getting papers published claiming the same, that one can certainly say that there continues to be a lively debate as to its meaning for physics and especially for the philosophy of science.

You can generate singlet state for the and column and a singlet state for the and columns. Then the QM prediction for



Which doesn't violate



So far QM has not violated anything. And we now have 2 different inequalities, each valid for a different scenario:

For scenario 1 and 2
For scenario 3 and 4

In both cases, the QM prediction for the specified scenario does not violate the inequality for the specified scenario.

Of course not. However you fill that spreadsheet of mine, you won’t violate Bell-CHSH, as a matter of simple spreadsheet arithmetic.

[minkwe]

It doesn't matter how the particles are generated, it is irrelevant if they are in a singlet state or not. When you use only 4 vales instead of 8 and then conbine them in the form <wx> - <wz> + <yx> + <yz> you will always obtain the 2. That is "tautological" and meaningless it does not say anything about the experiment or nature. That is exactly what people who base the derivation on CFD do.

But do you realize that Bell derived his inequalities using just 4 values, not 8? Please take a look at the original references (see links in my previous post), how Bell did the derivation in multiple papers. If you are not convinced we can go through it here step by step. CFD is irrelevant to the discussion so far. I have not relied on any CFD so far. All the spreadsheets we are talking about are actual data from realizable real experiments.

[minkwe]

Of course not. However you fill that spreadsheet of mine, you won’t violate Bell-CHSH, as a matter of simple spreadsheet arithmetic.

But we are not talking about your spreadsheet. We are talking about scenarios 1 to 4 described above. QM has not violated any of the relevant inequalities that arose in Bell's work.

If you disagree, show me an inequality from Bell's work that has been violated by QM.

[gill1109]

Of course not. However you fill that spreadsheet of mine, you won’t violate Bell-CHSH, as a matter of simple spreadsheet arithmetic.

But we are not talking about your spreadsheet. We are talking about scenarios 1 to 4 described above. QM has not violated any of the relevant inequalities that arose in Bell's work.

If you disagree, show me an inequality from Bell's work that has been violated by QM.

Bell derived an inequality under an assumption called nowadays "local realism", also called "local hidden variables". The four values which are involved in his proof exist mathematically under a class of mathematical models called "local realistic models". According to conventional interpretations of QM they don't exist at all in reality; or they only exist in parallel worlds ("many worlds interpretation"; don't ask me what that means). Bell's point is that local realism would imply that a certain inequality would hold involving four observable correlations, each one coming from different experimental settings. QM predicts that those four correlations would not satisfy that inequality. Experiments have produced results which do not satisfy the inequality. In the experiments, one essentially performs four sub-experiments, each with a different pair of settings, and calculated four empirical correlations. Whether or not you find this remarkable depends on whether or not you think that the physical world operates according to the picture called "local realism". Clearly, Einstein did. Gerard 't Hooft does. Tim Palmer does.