## The CHSH inequality as a weakly objective result

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### The CHSH inequality as a weakly objective result

Hi everyone.
This is the first topic I initiate in this forum. Similar issues were already discussed in other threads, however, it is sufficiently interesting and I believe that it deserves a separate thread of its own.
In 2001 Guillaume Adenier published a refutation of Bell's theorem that is extremely interesting and in my opinion relevant to the field https://doi.org/10.1142/9789812810809_0002
Adenier's paper was largely ignored by the physical community as it usually happens with papers rejecting the Bell theorem. The reason I believe Adenier's paper is relevant is that it is based on a widespread mistake that many "Bell-believers" think is correct.
Ironically the people noticing it is a mistake assume that it is the only way of interpreting Bell's derivation and conclude that the Bell inequality is immense nonsense.
I explain how the Bell inequality can and should be interpreted, in Adenier's parlance, as a weakly objective result. The explanation can be found in section 4 of my paper https://arxiv.org/abs/2012.10238v5

I already discussed in this forum the arguments upholding the strong objective interpretation, however, I am open to here where my weakly objective interpretation fails.
Justo

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### Re: The CHSH inequality as a weakly objective result

Justo wrote:Hi everyone.
This is the first topic I initiate in this forum. Similar issues were already discussed in other threads, however, it is sufficiently interesting and I believe that it deserves a separate thread of its own.
In 2001 Guillaume Adenier published a refutation of Bell's theorem that is extremely interesting and in my opinion relevant to the field https://doi.org/10.1142/9789812810809_0002
Adenier's paper was largely ignored by the physical community as it usually happens with papers rejecting the Bell theorem. The reason I believe Adenier's paper is relevant is that it is based on a widespread mistake that many "Bell-believers" think is correct.
Ironically the people noticing it is a mistake assume that it is the only way of interpreting Bell's derivation and conclude that the Bell inequality is immense nonsense.
I explain how the Bell inequality can and should be interpreted, in Adenier's parlance, as a weakly objective result. The explanation can be found in section 4 of my paper https://arxiv.org/abs/2012.10238v5

I already discussed in this forum the arguments upholding the strong objective interpretation, however, I am open to here where my weakly objective interpretation fails.

Well Justo, it fails because it doesn't even matter any more.

viewtopic.php?f=6&t=481&p=15064#p15063
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

@Fredizzx the correctness of your computational model belongs to a different discussion and, of course, if you think it is unquestionably correct, nothing else matters.
Justo

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### Re: The CHSH inequality as a weakly objective result

Justo wrote:@Fredizzx the correctness of your computational model belongs to a different discussion and, of course, if you think it is unquestionably correct, nothing else matters.

You asked where it fails. I let you know that you are just wasting your time. Pardon me. Ya know, Bell's junk theory has been dead for years now.
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

Justo, you are dancing on the head of a pin.
local

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### Re: The CHSH inequality as a weakly objective result

local wrote:Justo, you are dancing on the head of a pin.

Hi, local each one of those who deny Bell's theorem has his own reasons, FrediFizzx has a computational model, Gordon has his own mathematical proof, Joy now holds that Bell committed the same mistake he criticized in von Neumann proof, Essail has a counterexample, and so on. I do not know your arguments against Bell but the thing is that the reasons that motivate one person are different from what motivate others and is natural that each one is willing to discuss only his own reasons.
I brought up the case of Adenier because it is a widespread claim.
Justo

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### Re: The CHSH inequality as a weakly objective result

Justo wrote:
local wrote:Justo, you are dancing on the head of a pin.

Hi, local each one of those who deny Bell's theorem has his own reasons, FrediFizzx has a computational model, Gordon has his own mathematical proof, Joy now holds that Bell committed the same mistake he criticized in von Neumann proof, Essail has a counterexample, and so on. I do not know your arguments against Bell but the thing is that the reasons that motivate one person are different from what motivate others and is natural that each one is willing to discuss only his own reasons.
I brought up the case of Adenier because it is a widespread claim.

You have a point, Justo. There is no agreement among those who think Bell's claims are wrong. However, there is not necessarily always a disagreement why they are wrong. In fact, I believe there are multiple reasons, both theoretical and experimental, why Bell's claims are wrong. Over the years I have provided at least three serious reasons why Bell's claims should not be accepted:

(1) "The first of these shortcomings, which is discussed in greater detail in §4.2, amounts to averaging over measurement events in the derivation of the experimentally violated absolute bound of 2 on the CHSH string of expectation values that are impossible to occur in any possible world, classical or quantum, stemming from a mistaken application of the criterion of reality propounded by EPR." This argument can be found in my RSOS paper: https://royalsocietypublishing.org/doi/ ... sos.180526 (open access).

(2) "The second shortcoming of Bell’s argument stems from the unjustified identification of the image {+1, −1} of the measurement functions, which represents the actual measurement results in Bell’s prescription, with the co-domain of these functions, which is neither specified by Bell explicitly nor observable directly in the so-called Bell-test experiments. An explicit specification of the latter, however, is a prerequisite for the very definition of a mathematical function." This argument can be found also in my RSOS paper linked above.

(3) "...what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values." This argument is found in my arXiv preprint: https://arxiv.org/pdf/1704.02876.pdf

(4) In addition to the above, I have proposed a comprehensive local-realistic framework explaining the origins and strengths of all quantum correlations, a summary of which can be found in my recent talk at a conference in honor of Prof. David Hestenes (the creator of Geometric Algebra): https://www.researchgate.net/publicatio ... d_Hestenes

There is no disagreement between my views against Bell's theorem and those of Fred Diether. In fact, we are going to publish a joint paper on the subject. I also agree with the essential parts of Michel Fodje's views against Bell's theorem, which he has expressed many times in this forum.

But I appreciate your post and the issue you have raised in this thread is worthy of discussion. In fact, I believe you and I agree on this particular point about the misuse of counterfactuals in Bell-type arguments.
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Joy Christian
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### Re: The CHSH inequality as a weakly objective result

Justo wrote:Hi everyone.
This is the first topic I initiate in this forum. Similar issues were already discussed in other threads, however, it is sufficiently interesting and I believe that it deserves a separate thread of its own.
In 2001 Guillaume Adenier published a refutation of Bell's theorem that is extremely interesting and in my opinion relevant to the field https://doi.org/10.1142/9789812810809_0002
Adenier's paper was largely ignored by the physical community as it usually happens with papers rejecting the Bell theorem. The reason I believe Adenier's paper is relevant is that it is based on a widespread mistake that many "Bell-believers" think is correct.
Ironically the people noticing it is a mistake assume that it is the only way of interpreting Bell's derivation and conclude that the Bell inequality is immense nonsense.
I explain how the Bell inequality can and should be interpreted, in Adenier's parlance, as a weakly objective result. The explanation can be found in section 4 of my paper https://arxiv.org/abs/2012.10238v5

I already discussed in this forum the arguments upholding the strong objective interpretation, however, I am open to here where my weakly objective interpretation fails.

There are a few reasons why your paper is mistaken,

1) Going from Equation (20) to equation (21). You make an assumption that the domain of each of the functions A(ai, λj ), B(bk, λj ) is the same as the domain of their product. The effect of this assumption is that it gives you $\sum p(\lambda_j) = 1$ later when you go to equation (29). This assumption is not always true and you have no valid reason to assume that it is true for EPRB. Physically, in EPRB an angle is being changed and an outcome $\in \pm1$ is observed. But actually $\pm1$ is an arbitrary simplification of the real physical situation. At some angle, you expect the outcome to jump instantaneously from -1 to +1, without any transition! This doesn't normally happen in physics. If the functions are undefined for some angles where a transition happens the domains of A(ai, λj ) and B(bk, λj ) will not be the same as the domain of the product A(ai, λj )*B(bk, λj ) and $\sum p(\lambda_j) \neq 1$ because some lambdas are unmeasurable at some angles.

2) On the issue of Freedom, you say in section 2.3 that
Justo wrote:The freedom of the experimenters to choose their settings is a fundamental hypothesis for obtaining the Bell inequality

It is not. There are only 4 expectation values that are measured in the Bell-test experiment. When Alice and Bob measure $E(a_1, b_1)$. The settings are constant, and their average is a constant for which QM has a specific prediction of $\frac{1}{\sqrt{2}}$. For a weakly objective result, each of those expectation values is obtained from a different set of particle pairs in the singlet state. Therefore there is nothing about one set that influences the other set in any way. The only requirement is that each set of pairs is in the singlet state. Therefore the freedom of Alice and Bob is irrelevant for the expectation value $E(a_1, b_1)$ and $\rho(\lambda|a,b)=\rho(\lambda)$ is completely superfluous. Perhaps what you are calling freedom is not really freedom because it has nothing to do with the freedom of Alice and Bob. Alice and Bob's freedom to do what? Certainly not in picking settings because the settings are constant as already explained. So what do you mean by freedom? It is possible that what you mean is that Alice and Bob have the freedom to pick the same hidden variables when measuring $E(a_1, b_1)$ as when measuring $E(a_1, b_2)$. But this is unreasonable. They have no such freedom and should not be expected to have such freedom because the hidden variables are random and hidden. Instead, you are invoking the fair sampling assumption and using the misleading term "freedom" to describe it. It has nothing to do with freedom. A fair sample of a hidden distribution is an oxymoron.

3) In your paper equation (29) is the following.
$C(\lambda_j) = A(a_1, \lambda_j)B(b_1, \lambda_j) - A(a_1, \lambda_j)B(b_2, \lambda_j) + A(a_2, \lambda_j)B(b_1, \lambda_j) + A(a_2, \lambda_j)B(b_2, \lambda_j)$

You state after the equation: "None of the terms present in (29) are assumed to have originated from incompatible experiments, neither materialized out of counterfactual reasoning
nor pre-existed before actually measured"
. But this is very misleading because in writing that expression, you've already made a whole bunch of hidden assumptions. Let us examine that a bit.

You claim the expression is weakly objective, therefore you arrived at it starting from measurements on disjoint particle pairs. These measurements can be conceptualized as being represented on 2xN spreadsheets, where one column represents the value of $\lambda$, and the other column represents the corresponding outcome $\pm 1$. For a weakly objective result on disjoint particle pairs, we have 8 such spreadsheets:

$(A_1, \Lambda_w), (B_1, \Lambda_w), (A_1, \Lambda_x), (B_2, \Lambda_x), (A_2, \Lambda_y), (B_1, \Lambda_y), (A_2, \Lambda_z), (B_2, \Lambda_z)$

Where $(A_1, \Lambda_w)$ is the spreadsheet of data obtained by Bob for setting $a_1$, etc. I use spreadsheets because these are ordered sets and we are multiplying corresponding rows across the spreadsheets. This is the proper starting point for the weakly objective analysis.

One hidden assumption involved in equation (29) is the assumption of fair sampling. That is, the assumption that the probability distribution of $\lambda$ is the same for $\Lambda_w, \Lambda_x, \Lambda_y, \Lambda_z$. This is not necessarily true but let us grant that assumption.

Secondly, in $C(\lambda_j)$ we are doing arithmetic with functions, not plain numbers. and we don't just have the addition of functions above, we have the addition of products of functions which we eventually factorize! This means not only do the distributions match, but the ordering of the values in our spreadsheets must match also. The $\Lambda_w$ column may contain the same elements as $\Lambda_x$ (cf fair-sampling assumption), but the ordering will be almost certainly different for a weakly objective result. Therefore equation (29) contains another hidden assumption that

$\Lambda_w \equiv \Lambda_x \equiv \Lambda_y \equiv \Lambda_z = \Lambda_j$

That is the assumption that not only do the columns contain the same set of lambda values, but also that they contain the same ordering, or can be re-ordered into the same ordering. This assumption is false. Without this assumption, we cannot factorize the functions in equation (29) and the derivation does not proceed in the weakly objective scenario.

To see this, let us say you reshuffle the rows of $A_{1x}$ so that the $\Lambda$ columns match those of $A_{1w}$. Since column $\Lambda_x$ is shared by two spreadsheets, we must apply any such permutation not just to $A_{1x}$ but also to $B_{2x}$. However, you also have to make the lambda columns of $B_{2x}$ to match those of $B_{2z}$ and the lambda columns of $A_{2y}$ to match those of $A_{2z}$, each time making sure to rearrange the corresponding spreadsheet from the same particle pair. This is obviously not possible. The cyclic recombination of pairs of terms means you keep undoing the order as you go around. Again it is very important to note that the fair sampling assumption (which we've granted above, only says the probability distribution of values in the lambda column is the same for all the 8 spreadsheets. It says nothing about the ordering of those values. Therefore the Fair sampling assumption does nothing to resolve the real problem. Alice and Bob do not have the freedom to select lambda columns that can be easily rearranged. Randomization makes things worse, not better.

Let us pretend that what I just demonstrated was not the case. Let us pretend that as soon as the first two permutations are done, then all the pairs of spreadsheets that need to be rearranged will automatically match and we won't have any problems and for the sake of argument, let us evaluate it for a moment. If these permutations are able to be done (despite my proof that they can't), it would mean that at the end of the day, there are effectively only 4 2xN spreadsheets with identical lambda columns on all the spreadsheets. In other words, it would mean that there are only 4 functions $A(a_1, \lambda_i), B(b_1, \lambda_i), A(a_2, \lambda_i), B(b_2, \lambda_i)$ with exactly the same domain! (cf Justo's equation (29)). And it would mean, the four columns of outcomes can be combined into a single 4xN spreadsheet of outcomes! This is for all practical purposes exactly the strongly objective scenario! And therefore the derivation of an upper bound of 2 follows directly. Hopefully, now you may appreciate why Justo's equation (29) is loaded with hidden assumptions that are false.

In summary:
- The transition between (20) and (21) involves a hidden assumption about the domains of the functions, which is not necessarily true and very likely false for the physical situation of EPRB. Without this assumption, $\sum p(\lambda_j) \neq 1$ and the derivation can't proceed.
- Even if we grant the above, (29) includes the hidden assumption that disjoint random hidden variable sets can be re-ordered. An assumption that is false.
- If we grant that the hidden variables can be reordered, the weakly objective scenario is transformed to the strongly objective one. Therefore the derivation of the inequality from the weakly objective scenario involves a hidden assumption that the weakly objective scenario is the same as the strongly objective one.
minkwe

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### Re: The CHSH inequality as a weakly objective result

Justo wrote: I do not know your arguments against Bell...

I don't argue against Bell. I believe that QM does not in fact predict -a.b for EPRB, and that the experiments do not in fact show -a.b. That puts me in a very small club. I suppose you could say I agree with Fred that nothing can violate the CH inequality (absent information transfer between the sides), but for different reasons than Fred. All roads lead to Rome.

local

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### Re: The CHSH inequality as a weakly objective result

local wrote:
Justo wrote: I do not know your arguments against Bell...

I don't argue against Bell. I believe that QM does not in fact predict -a.b for EPRB, and that the experiments do not in fact show -a.b. That puts me in a very small club. I suppose you could say I agree with Fred that nothing can violate the CH inequality (absent information transfer between the sides), but for different reasons than Fred. All roads lead to Rome.

He is dancing on the head of a pin. All this debating about Bell is pure nonsense.

6 million trials; one degree resolution.

viewtopic.php?f=6&t=481&p=15064#p15063

Nothing more needs to be said. Bell's junk theory and Gill's junk theory are dead!!!
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

There is no Gill theory.
local

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### Re: The CHSH inequality as a weakly objective result

local wrote:There is no Gill theory.

Unfortunately there is or this would have been all over in 2007.
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

What theory? C'mon man. It's all derivative nitpicking, pretending. Don't dignify it. We have dragons to slay.
local

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### Re: The CHSH inequality as a weakly objective result

FrediFizzx wrote:
local wrote:There is no Gill theory.

Unfortunately there is or this would have been all over in 2007.

local wrote:What theory? C'mon man. It's all derivative nitpicking, pretending. Don't dignify it. We have dragons to slay.

Yes, I agree. All Gill has done is derivative nitpicking. But Fred is right. Gill does have a claim, if not a theory, which he imposes on the physics community by sheer, unmitigated aggression (I can provide plenty of evidence of his aggressive and unethical off-line activities against me personally, but I don't want to distract too much from the main topic of this thread).

So what is Gill's claim? It is that an event-by-event numerical simulation of the singlet correlations -cos(a, b) is impossible without exploiting loopholes or succumbing to nonlocality. He has gone to extreme lengths to undermine anything that threatens this claim. You can say this is Gill's theory or challenge. But Fred has defeated it and he and I are going to write a paper on it.
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Joy Christian
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### Re: The CHSH inequality as a weakly objective result

local wrote: ... We have dragons to slay.

LOL!! We have slayed the dragons; they are dead forevermore!!!
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

I content myself with slaying only Adenier's (well explained) dragon. BTW that includes slaying Richard Gill, I'm sorry Richard but is not personal is only about your senseless argument.

@minkwe, thank you for your criticisms and explanations. I will read them carefully and try to respond to them later.
Justo

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### Re: The CHSH inequality as a weakly objective result

FrediFizzx wrote:
local wrote:There is no Gill theory.

Unfortunately there is or this would have been all over in 2007.

There are quite a few Gill publications, some of them have had quite a lot of impact. I'm interested to hear what are the alleged errors in them.

In my opinion, all I did was to understand what Bell had already said. I proceeded to sharpen his results by adding to his bounds on "S", bounds on the probability of exceeding those bounds by any given positive amount. My probability bounds depended on the probability (randomness) involved in choices of measurement settings. My first results of this kind were published in 2001 and 2003. The group behind the Delft experiment of 2015 vastly improved, and simplified, my bounds. All the experimental groups in 2015 (Delft, Munich, Vienna, and NIST) cited my early work. It took care of the time- and memory- loopholes. Fred's simulations do not contradict my mathematical results. He moves the goalposts by collecting different data and analysing it in a different way from state-of-the-art experiments. He has created his own strawman.

Justo, it is not clear to me what you think we disagree about. Perhaps about terminology? You think you have slain me, but for the time being, I am alive and well. I suspect you have slain a straw-man. An illusion created by yourself. No problem.

"local", indeed you are a special case. You think that conventional QM predictions are wrong because entanglement does not continue to exist at large distances. Quite a few people used to think the same, and Donald Graft is a recent author who indeed recently argues that this is the case. But I am not interested in QM predictions. Bell's reasoning can be applied to experimental results without any reference to QM at all. Whether or not all that quantum entanglement stuff is non-local nonsense, is not the issue. The question is now: how can you explain the findings of state-of-the-art experiments? You can of course point out the imperfections of the 2015 experiments. You can stick by your belief that those imperfections can never be removed. OK. We will see.
Last edited by gill1109 on Mon Oct 18, 2021 8:55 am, edited 1 time in total.
gill1109
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### Re: The CHSH inequality as a weakly objective result

@gill1109 LOL!! We have slayed the dragons; they are dead forevermore!!!
Your so-called theorems are a bunch of junk theories now. Your're a pansy. Can't take down our latest simulation without a different strawman model.
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FrediFizzx
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### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:
The question is how: how can you explain the findings of state-of-the-art experiments?

Do state-of-the-art experiments contradict the predictions of quantum mechanics and thus refute quantum mechanics? If they do, then that is a bigger revolution than a Nobel Prize-worthy experiment. If all they do is confirm quantum mechanical predictions, then all any Bell-sceptic has to do is reproduce quantum predictions in a local-realistic framework, as I have done.
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Joy Christian
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### Re: The CHSH inequality as a weakly objective result

gill1109 wrote: "local", indeed you are a special case. You think that conventional QM predictions are wrong because entanglement does not continue to exist at large distances.

That's a lie. Don't tell me what I think, loser. I have several times told you that I do not appeal to loss of coherence as the particles separate. DG said that just as we would not expect quantum correlations if coherence is lost, we should not expect it when separated measurements are performed. Unless we conclude that Gill's pea-brain is incapable of understanding that that doesn't mean DG or myself are claiming that coherence is lost, we'll have to conclude that he is a shameless liar.

Forum members, read what I have said here and don't rely upon the motivated misrepresentations of this despicable liar.

Quite a few people used to think the same, and Donald Graft is a recent author who indeed recently argues that this is the case.

Another lie from the forum liar. DG never argued that. Narcs have no shame.

But I am not interested in QM predictions.

LOL. Then you cannot claim that Nature (ruled by QM) can violate the inequality. If you want to claim that, you have to show the QM prediction (for separated measurements) that implies that. But you won't, because you know I am right about it and you are a coward.

The question is now: how can you explain the findings of state-of-the-art experiments? You can of course point out the imperfections of the 2015 experiments. You can stick by your belief that those imperfections can never be removed.

Now the liar is equivocating. If the experiments have disqualifying issues then they prove nothing and there is nothing to explain. Whether what you call "imperfections" can be removed is irrelevant. I ask you again, Gill, which is the definitive experiment that you hang your hat on? There is no such experiment and you know it.

Amazing the contortions this bumbling incompetent (https://www.youtube.com/watch?v=cbkdhD6BsoY) is willing to twist himself into to defend his arrant nonsense.
local

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