## Pedagogical proofs of Bell's theorem

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

### Re: Pedagogical proofs of Bell's theorem

Justo wrote:@Heinera, the urn model is interesting. As far as I know the first one to come up with the idea was no other than the nobel Laureate Eugene Wigner.
It would be interesting to produce a simple model of it in an excel spreadsheet so that everyone can see it and shoot down(or not) Bell's theorem for everyone to see.
Ii is not necessary for the simulation to reproduce QM predictions. It just has to violate the bound two (modulo finite statistics).

Yes, the nice thing about this urn experiment is that it will indeed be very easy to simulate in Excel or any other computer program. But I'm afraid the Bell deniers wouldn't touch such a spreadsheet with a barge pole, because deep down they know what the results would be.
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
Joy Christian wrote:
Justo wrote:
Obviously, data from experiments violate it.

Demonstrate, event by event, using only the experimental data, how experiments violate the bound of 2 on the CHSH inequality. Do this, because all the rest of what you say is nonsense.
.

What? Aspect et al., for starters. And then a rush of others over a 40 year period. What is your point here?

Argument from authority is a logical fallacy. Demonstrate, event by event, as I asked. One has to be brainwashed to believe that a mathematical inequality can be violated by something.

Let me help you out here: You can write down the experimental data on an Excel spreadsheet. Then you can show us how it violates the bound of 2 on the CHSH inequality. Very simple!
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:Let me help you out here: You can write down the experimental data on an Excel spreadsheet. Then you can show us how it violates the bound of 2 on the CHSH inequality. Very simple!
.

Are you serious? You don't think eight datasets, in four pairs, can give a CHSH value larger than 2?
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
Joy Christian wrote:Let me help you out here: You can write down the experimental data on an Excel spreadsheet. Then you can show us how it violates the bound of 2 on the CHSH inequality. Very simple!
.

Are you serious? You don't think eight datasets, in four pairs, can give a CHSH value larger than 2?

Ah ... so you are saying that the experiments are done for a different inequality with the bound of 4. Good. You finally get it.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:Let me help you out here: You can write down the experimental data on an Excel spreadsheet. Then you can show us how it violates the bound of 2 on the CHSH inequality. Very simple!
.

Are you serious? You don't think eight datasets, in four pairs, can give a CHSH value larger than 2?

Ah ... so you are saying that the experiments are done for a different inequality with the bound of 4. Good. You finally get it.
.

The experiments are not done for any inequality, they are just done. And then the results are compared to theory.
If you think the CHSH inequality does not mean eight datasets, in four pairs, then no wonder you are confused.

Where, in the CHSH urn experiment, do you think that the data is anything but eight datasets in four pairs?
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:One has to be brainwashed to believe that a mathematical inequality can be violated by something.
.

I have no idea of what you are talking about. But whatever it is it can't be what Bell-believers call the Bell inequality. It is obvous that you are not talking about the result of 4 different series of experiments.
Would care to tell us? or perhaps I am the only one here who doen't know.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:Let me help you out here: You can write down the experimental data on an Excel spreadsheet. Then you can show us how it violates the bound of 2 on the CHSH inequality. Very simple!
.

Are you serious? You don't think eight datasets, in four pairs, can give a CHSH value larger than 2?

Ah ... so you are saying that the experiments are done for a different inequality with the bound of 4. Good. You finally get it.
.

The experiments are not done for any inequality, they are just done. And then the results are compared to theory.
If you think the CHSH inequality does not mean eight datasets, in four pairs, then no wonder you are confused.

Where, in the CHSH urn experiment, do you think that the data is anything but eight datasets in four pairs?

I don't know. You tell me. Better still, produce the data and demonstrate what I asked. Why are you avoiding the demonstration? Could it be that you are incapable of demonstrating?

For anyone not brainwashed by Bell, the experiments are never done in accordance with the CHSH correlator that satisfies the bound of 2. They are done by the bait-and-switch tactic of switching to the CHSH correlator with the bound of 4. It is then no wonder that the experimental data "violates" the bound of 2 because that bound was never respected in the first place.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:I don't know. You tell me. Better still, produce the data and demonstrate what I asked. Why are you avoiding the demonstration? Could it be that you are incapable of demonstrating?
.

You have to be kidding with me. I will of course oblige with your request. In what format do you want the data?
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
Joy Christian wrote:I don't know. You tell me. Better still, produce the data and demonstrate what I asked. Why are you avoiding the demonstration? Could it be that you are incapable of demonstrating?
.

You have to be kidding with me. I will of course oblige with your request. In what format do you want the data?

Good.

The CHSH inequality requires the experimental data to be collected in a 4 x N table with entries, A(a, k), B(b, k), A(a', k), and B(b', k), with k running from 1 to N >> 1.

So first produce such a 4 x N table from any real experiment and then demonstrate that the data in it "violates" the bound of 2 on the Bell-CHSH inequality.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:The CHSH inequality requires the experimental data to be collected in a 4 x N table with entries, A(a, k), B(b, k), A(a', k), and B(b', k), with k running from 1 to N >> 1.

So first produce such a 4 x N table from any real experiment and then demonstrate that the data in it "violates" the bound of 2 on the Bell-CHSH inequality.
.

No, the CHSH expression refers to eight data sets grouped in four pairs, in other words four 2 x N tables. I can produce that. And by the way, this is also the data structure that is produced by the CHSH urn experiment.
If you think otherwise, no wonder you are confused.
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

Heinera wrote:
Joy Christian wrote:The CHSH inequality requires the experimental data to be collected in a 4 x N table with entries, A(a, k), B(b, k), A(a', k), and B(b', k), with k running from 1 to N >> 1.

So first produce such a 4 x N table from any real experiment and then demonstrate that the data in it "violates" the bound of 2 on the Bell-CHSH inequality.
.

No, the CHSH expression refers to eight data sets grouped in four pairs, in other words four 2 x N tables. I can produce that.
If you think otherwise, no wonder you are confused.

Complete nonsense. The CHSH expression requires a 4 x N table of entries I specified above. If you think otherwise, then no wonder you are confused.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:The CHSH inequality requires the experimental data to be collected in a 4 x N table with entries, A(a, k), B(b, k), A(a', k), and B(b', k), with k running from 1 to N >> 1.

So first produce such a 4 x N table from any real experiment and then demonstrate that the data in it "violates" the bound of 2 on the Bell-CHSH inequality.
.

No, the CHSH expression refers to eight data sets grouped in four pairs, in other words four 2 x N tables. I can produce that.
If you think otherwise, no wonder you are confused.

Complete nonsense. The CHSH expression requires a 4 x N table of entries I specified above. If you think otherwise, then no wonder you are confused.
.

You need four different 2 x N spreadsheets containing data for the 4 settings as Heinera said.
You can also have one 4 x N spreadsheet as Joy says but in each row only two columns can have data, one corresponding to Alice and the other to Bob. Both are equivalent forms of collecting the experimental data.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: Pedagogical proofs of Bell's theorem

Justo wrote:
Joy Christian wrote:
Heinera wrote:
Joy Christian wrote:The CHSH inequality requires the experimental data to be collected in a 4 x N table with entries, A(a, k), B(b, k), A(a', k), and B(b', k), with k running from 1 to N >> 1.

So first produce such a 4 x N table from any real experiment and then demonstrate that the data in it "violates" the bound of 2 on the Bell-CHSH inequality.
.

No, the CHSH expression refers to eight data sets grouped in four pairs, in other words four 2 x N tables. I can produce that.
If you think otherwise, no wonder you are confused.

Complete nonsense. The CHSH expression requires a 4 x N table of entries I specified above. If you think otherwise, then no wonder you are confused.
.

You need four different 2 x N spreadsheets containing data for the 4 settings as Heinera said.
You can also have one 4 x N spreadsheet as Joy says but in each row only two columns can have data, one corresponding to Alice and the other to Bob. Both are equivalent forms of collecting the experimental data.

The 2 x N spreadsheet of data for 4 settings corresponds to the bound of 4 on the CHSH correlator, not the bound of 2. Nothing can exceed the bound of 4, and no experiment ever has.

The 4 x N spreadsheet of data is what CHSH inequality is all about, derived using either CFD or local realism. You just confirmed that no experiment can produce that data, and thus no experiment has ever violated the Bell-CHSH inequality. As I said before, all claims of "violation" of Bell-CHSH are based on the bait-and-switch tactic employed by the experimentalists.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:The 2 x N spreadsheet of data for 4 settings corresponds to the bound of 4 on the CHSH correlator, not the bound of 2. Nothing can exceed the bound of 4, and no experiment ever has.
.

Of course, it is a trivial mathematical truism. But please don't call it Bell inequality when the bound is 4 because is very confusing when you say nothing can violate the Bell inequality and perhaps you are implicitly meaning the bound is 4.

Joy Christian wrote:The 4 x N spreadsheet of data is what CHSH inequality is all about, derived using either CFD or local realism. You just confirmed that no experiment can produce that data, and thus no experiment has ever violated the Bell-CHSH inequality. As I said before, all claims of "violation" of Bell-CHSH are based on the bait-and-switch tactic employed by the experimentalists.
.

Of course, when you use CFD the spreadsheet becomes a silly tautology. However, in that case, you all four columns need to have values in it. You just can't do that with real data. Experimental data can only fill two columns leaving blank the other two, it is another way of storing the same data instead of using 4 different 4 x N spreadsheets.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: Pedagogical proofs of Bell's theorem

Justo wrote:
Joy Christian wrote:The 2 x N spreadsheet of data for 4 settings corresponds to the bound of 4 on the CHSH correlator, not the bound of 2. Nothing can exceed the bound of 4, and no experiment ever has.
.

Of course, it is a trivial mathematical truism. But please don't call it Bell inequality when the bound is 4 because is very confusing when you say nothing can violate the Bell inequality and perhaps you are implicitly meaning the bound is 4.

It does not matter. Both inequalities are tautologies due to the rules of arithmetic and nothing can violate either one.

Joy Christian wrote:The 4 x N spreadsheet of data is what CHSH inequality is all about, derived using either CFD or local realism. You just confirmed that no experiment can produce that data, and thus no experiment has ever violated the Bell-CHSH inequality. As I said before, all claims of "violation" of Bell-CHSH are based on the bait-and-switch tactic employed by the experimentalists.
.

Of course, when you use CFD the spreadsheet becomes a silly tautology. However, in that case, you all four columns need to have values in it. You just can't do that with real data. Experimental data can only fill two columns leaving blank the other two, it is another way of storing the same data instead of using 4 different 4 x N spreadsheets.

The CHSH inequalities deals with a spreadheet $A$ containing 4 columns of actual data labelled $a_1, b_1, a_2, b_2$. There are N rows of data in the spreadsheet. The columns are rearranged in pairs and used to calculate the correlations $E(a_1,b_1), E(a_1,b_2), E(a_2,b_1), E(a_2,b_2)$. Where

$E(a_1,b_1) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A_i^{a_1} A_i^{b_1}$
$E(a_1,b_2) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A_i^{a_1} A_i^{b_2}$
$E(a_2,b_1) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A_i^{a_2} A_i^{b_1}$
$E(a_2,b_2) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A_i^{a_2} A_i^{b_2}$

It is for this scenario that
$E(a_1,b_1) - E(a_1,b_2) + E(a_2,b_1) + E(a_2,b_2) \leq 2$
The terms are not independent. This relationship is a mathematical tautology. It is impossible to find a 4xN spreadsheet that will violate this relationship.

You calculate correlations from values, not empty spaces. If you start from four independent 2xN spreadsheets you now have Spreadsheets $A1, A2, A3, A4$ you can't use the CHSH. Instead, you have

$E_1(a_1,b_1) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A1_i^{a_1} A1_i^{b_1}$
$E_2(a_1,b_2) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A2_i^{a_1} A2_i^{b_2}$
$E_3(a_2,b_1) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A3_i^{a_2} A3_i^{b_1}$
$E_4(a_2,b_2) = \lim_{N \rightarrow \infty} -\frac{1}{N}{}\sum_{i=1}^{N} A4_i^{a_2} A4_i^{b_2}$

And you end up with a correlator:

$E_1(a_1,b_1) - E_2(a_1,b_2) + E_3(a_2,b_1) + E_4(a_2,b_2) \leq 4$
The terms in this expression are independent. This is a mathematical tautology. It is impossible to find four 2xN spreadsheets of data that will violate this relationship.

What Bell believers do is to take experimental data in the form of four 2xN spreadsheets, calculate $E_1(a_1,b_1) - E_2(a_1,b_2) + E_3(a_2,b_1) + E_4(a_2,b_2)$, and then claim that it violates $E(a_1,b_1) - E(a_1,b_2) + E(a_2,b_1) + E(a_2,b_2) \leq 2$.

They are comparing oranges with rocks. By doing this underhanded substitution, they are making an additional assumption. The assumption is simply that it is possible to take the 4 distinct independent spreadsheets $A1, A2, A3, A4$ and reduce them to the single spreadsheet $A$, through permutation of rows. But as I've shown previously. This assumption is false and the key reason why is because of the peculiar use of cyclic recombination of columns used in the original inequality. You will note that the way the settings are chosen for each of the terms follows a cyclic pattern. This is a very important feature of the inequality. Why did Bell use that feature? How come nobody has ever demonstrated so-called "non-locality" by using measurements at pairs of settings that do not have this peculiar cyclic recombination feature? Is it possible that perhaps that's where the magician's trick is hidden? It turns out the cyclic recombinaton is also the undoing of Bell. You can't complete the required re-permutation of rows in a cyclic manner because you will have to undo a previously performed re-permutation.

BTW, I didn't say anything about CFD.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: Pedagogical proofs of Bell's theorem

gill1109 wrote:
Joy Christian wrote:.
None of the above. No proof of Bell's argument (which is not a "theorem") exists without the assumption of the additivity of expectation values. But the additivity of expectation values is an invalid assumption for any hidden variable theory, regardless of its specific characteristics such as locality or realism. Therefore Bell's argument is not valid for any hidden variable theory.

I have no time to discuss this any further. The full details of my argument can be found in my paper: https://arxiv.org/pdf/1704.02876.pdf.

A one-page summary of my argument can also be found in Section II of my paper published in IEEE Access: https://ieeexplore.ieee.org/stamp/stamp ... er=9418997.
.

@Joy: It is been explained to you by myself and by others numerous times that the additivity of expectation values is not an assumption. It holds true for QM. So any theory which reproduces QM statistical predictions has to reproduce the linearity.

Wrong. Read my paper to understand why your claim is the stupidest thing anyone has ever said in this forum.
.
Joy Christian
Research Physicist

Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

### Re: Pedagogical proofs of Bell's theorem

I'm starting to suspect that minkwe and Joy Christian might actually believe that the long run upper bound for the CHSH urn experiment is 4, and not 2.

Then there is nothing more to do, except suggesting that they get themselves an urn and start testing.
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: Pedagogical proofs of Bell's theorem

@Heine It is quite irrelevant anyways since Bell's junk physics theory has been shot down dead for years. And the final nail in its coffin,

viewtopic.php?f=6&t=481&p=14290#p14249

RIP!!!
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

### Re: Pedagogical proofs of Bell's theorem

Joy Christian wrote:
Justo wrote:@Heinera, the urn model is interesting. As far as I know the first one to come up with the idea was no other than the novel Laureate Eugene Wigner.
It would be interesting to produce a simple model of it in an excel spreadsheet so that everyone can see it and shoot down(or not) Bell's theorem for everyone to see.
Ii is not necessary for the simulation to reproduce QM predictions. It just has to violate the bound two (modulo finite statistics).

Justo, the urn model is not interesting. It does not represent how the Bell-test experiments are performed. If it did, then there would be no point in performing the expensive experiments. It is extraordinary that you think anything can violate the bound of 2 on CHSH. Nothing can. And that fact makes Bell's argument ridiculously silly. Wigner, by the way, was the Ph.D. mentor of my Ph.D. mentor Shimony. But in my opinion, both of them were wrong in believing in the validity of Bell's argument.
.

Whether something is interesting or not is to some extent a matter of taste. I think the urn experiment may be useful for those whom the topic is new and who are trying to understand it. The urn experiment is easy to understand and to perform. One could naively believe that it is analogous to Aspect's and similar experiments. However, the results of the urn experiment are different which demonstrates that what happens in Aspect's experiment is not analogous to the urn experiment and therefore not to the naive belief.
Mikko

Posts: 163
Joined: Mon Feb 17, 2014 2:53 am

### Re: Pedagogical proofs of Bell's theorem

@Mikko The urn junk is not really interesting at all anymore since it is quite irrelevant anyways because Bell's junk physics theory has been shot down dead for years. And the final nail in its coffin,

viewtopic.php?f=6&t=481&p=14290#p14249

RIP!!!
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

PreviousNext