## My Challenge to All Bell-Believers --- Meet it or Beat it:

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

### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

Joy Christian wrote:Let me note that for the 4-particle GHZS state the condition E(a, b, c, d) = << ABCD >> = +1 or -1 for some specific settings for all runs and thus even for a single run is similar to the familiar condition E(a, b) = << AB >> = +1 or -1 for the 2-particle EPRB state for some specific settings (i.e., for a = b and a = -b, respectively) for all runs and thus even for a single run. In the latter example, it is the condition of perfect correlation (or perfect anti-correlation), which is predicted by quantum mechanics.

For completeness, let me prove this here for the EPRB case, parallelling the proof below which I provided in response to the counterchallenge to me by Tim Maudlin:

For the EPRB case, let us follow the construction of my 3-sphere model presented in this paper: https://arxiv.org/abs/1405.2355. The proof goes through as follows:

What I want to show is AB = -1 for a = +b and AB = +1 for a = -b even for a single run. It would suffice to prove AB = +1 for a = -b since the case AB = -1 for a = +b follows quite similarly. We start with equations (54) and (55) of the above paper, which define the binary valued functions A = +/-1 and B = +/-1, subject to the conservation of the spin-0 defined in equations (65) and (66). The expectation value E(a, b) = < AB > = - a . b is then derived in equations (67) to (75) of the paper using these functions A and B. In fact, the expectation value (75) or (76) follows from the very construction of the functions A and B in the equations (54) and (55), as a geometrical identity within my 3-sphere model. Therefore we can use this geometrical identity to prove that AB = +1 for a = -b. In fact, for the chosen settings this identity reduces simply to E(a, b) = < AB > = +1. But E(a, b) = < AB > = +1 tells us that the average of the number AB is a constant, and it is equal to +1. This is mathematically possible only if AB = +1 for all runs, for a = -b. But if AB = +1 for all runs, then AB = +1 holds also for any given run. Therefore AB = +1 for any single run, for the chosen settings a = -b. QED.

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Joy Christian
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

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Joy Christian
Research Physicist

Posts: 1752
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

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I rarely use my twitter account. But sometimes the opportunity to twit is just too sweet to let go:

https://arxiv.org/abs/1704.02876

http://philsci-archive.pitt.edu/14305/

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Joy Christian
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

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I posted my original challenge above more than two years ago: viewtopic.php?f=6&t=275#p6681.

To date no one has been able to meet this challenge. And yet, many continue to believe in the traditional interpretation of Bell's theorem: viewtopic.php?f=6&t=342&p=8222#p8221.

The traditional interpretation of Bell's theorem is based on the claim that in the actual experiments such as the above the Bell-CHSH inequality with the upper bound of 2 is "violated." If so, then the claimant(s) should be able to provide actual experimental data --- event-by-event --- that violates the Bell-CHSH inequality. In other words, they should be able to provide actual experimental data for which the absolute value of the following sum,

E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) ,

exceeds the bound of 2, where

E(a, b) = << A(a)B(b) >> ,

E(a, b' ) = << A(a)B(b' ) >> ,

E(a', b) = << A(a' )B(b) >> ,

and

E(a', b' ) = << A(a' )B(b' ) >> .

So this is my new (or perhaps not so new) challenge. Please do not try to insult my intelligence by obfuscating the issue with statistics or probabilities. Just face up the challenge!

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Joy Christian
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.
FrediFizzx
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

FrediFizzx wrote:Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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Joy Christian
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

Joy Christian wrote:
FrediFizzx wrote:Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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The actual data from the experiments do violate the bound of 2. You can probably get the data from Weihs, et al (1998) to confirm that.

But they don't violate the real bound of 4 or even the QM bound of 2*sqrt(2) for CHSH.
FrediFizzx
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### Re: My Challenge to All Bell-Believers --- Meet it or Beat i

FrediFizzx wrote:
Joy Christian wrote:
FrediFizzx wrote:Joy, that has been done. The problem is that for that particular CHSH sum, the bound is not 2 for experiments. It is 4 not 2. Of course they never "violate" that.

Exactly! ..... But the Bell-believers keep claiming that they are violating the bound of 2 in the experiments! If so, then I say to them: Please demonstrate that by providing actual data.

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The actual data from the experiments do violate the bound of 2. You can probably get the data from Weihs, et al (1998) to confirm that.

But they don't violate the real bound of 4 or even the QM bound of 2*sqrt(2) for CHSH.

Indeed. We are both saying the same thing with different words. My point is that the actual data do not violate the absolute bound of 2 on the CHSH sum

E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) ,

where

E(a, b) = << A(a)B(b) >> ,

E(a, b' ) = << A(a)B(b' ) >> ,

E(a', b) = << A(a' )B(b) >> ,

and

E(a', b' ) = << A(a' )B(b' ) >> .

But the experimenters and people like Richard D. Gill are claiming that the latter violation is what is happening in experiments, which is of course false.

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Joy Christian
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