SciPhysicsForums.com

[quote="gill1109"]

There are many proofs. Bell (1964) was the first one. Soon came CHSH with a different proof, some years later Gull with a very different one. There are yet more proofs since there are lots more Bell-type inequalities; and there are other arguments too. E.g. Lucien Hardy’s proof. [/quote]
I see that Gill has been un-banned for the n^th time. Let us hope that he keeps himself un-banned if only to keep us entertained with false propaganda such as the above.

It is true that Bell in 1964 claimed that no local and realistic model can reproduce the quantum mechanical prediction of the singlet correlations. That calm was further elaborated by Bell himself and by Clauser, Horne, Shimony, and Holt (CHSH) in 1969. But the Bell-CHSH claim has been proven wrong by me since 2007, and many times after 2007.

There is no such thing as Gull proof or Gull theorem. There is never going to be such proof or theorem. It is pure fantasy.

Lucien Hardy's proof was disproven by me as well, in 2009. My disproofs of Lucien's proof and GHZ's proof have been published in my book and discussed in [url=https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.180526]my [i]RSOS[/i] paper[/url].

Since 2007 what remains is a politically and sociologically sustained belief system called "Bell's theorem." Sadly, this belief system is often reinforced by extreme academic thuggery.
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[quote="FrediFizzx"]@Gordon You missed the whole point of my argument. Bell never defines the A and B functions other than equal to +/-1. So, substitute the +/-1's and you have nonsense.
[/quote]
Bell requires A and B to take values +1 and -1 as a, b and lambda vary. Obviously, for any a, b and lambda, A(a, lambda) is equal to just one of the possible two values, and B(b, lambda) too.
He requires rho to be nonnegative and integrate to 1.

Bell proves that whatever you take the functions A, B and rho to be, subject to those constraints, you’ll not be able to match the singlet correlations and singlet expectation values.

There are many proofs. Bell (1964) was the first one. Soon came CHSH with a different proof, some years later Gull with a very different one. There are yet more proofs since there are lots more Bell-type inequalities; and there are other arguments too. E.g. Lucien Hardy’s proof.

It is great that people keep trying out new ideas but I don’t give them any real chance at all.

@Gordon Unless you define the A and B functions, you are just talking more nonsense. The vectors [b]a[/b] and [b]b[/b] have dropped out of the equation. It doesn't matter if they are orthogonal, equal to each other or opposite each other.
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[quote="FrediFizzx"]@Gordon You missed the whole point of my argument. Bell never defines the A and B functions other than equal to +/-1. So, substitute the +/-1's and you have nonsense.
.[/quote]

Fred, no! Nothing missed and --- since I do not mimic Bell's erroneous analysis --- no nonsense here.

Bell gives us enough information to derive these expectations:

[tex]E[A(a,\lambda)]=E[B(b,\lambda)]=0[/tex] : since [tex]\lambda[/tex] is a random variable.

BUT:

[tex]E[A(a,\lambda)B(b,\lambda)]\neq 0[/tex] except when [tex]a[/tex] and [tex]b[/tex] are orthogonal:

since each [u]paired-result[/u] is correlated via a common [tex]\lambda[/tex].

Gordon

@Gordon You missed the whole point of my argument. Bell never defines the A and B functions other than equal to +/-1. So, substitute the +/-1's and you have nonsense.
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[quote="FrediFizzx"][tex]P({\bf a, b}) = \int\,d\lambda\,\rho(\lambda)\,\pm 1 = 0[/tex]

Easy to see if you just use the +/- 1's the [b]a[/b] and [b]b[/b] vectors drop out of the equation and you are left with just lambda and nonsense.
.[/quote]
Fred,

Bell (1964) is wrong: that's a fact.

But your comment above is not correct. In his eqn (2), Bell is simply giving the expectation (the average value) of the product [i]A(a,λ)B(b,λ)[/i] under the EPR-Bohm experiment.

It can equal zero when [i]a[/i] and [i]b[/i] are orthogonal; but not otherwise.

For the way to refute Bell's subsequent erroneous analysis, please see this draft:

[url]https://vixra.org/pdf/2010.0068v5.pdf[/url]

This draft is discussed at: [url]http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=451[/url]

HTH. All the best, Gordon
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[tex]P({\bf a, b}) = \int\,d\lambda\,\rho(\lambda)\,\pm 1 = 0[/tex]

Easy to see if you just use the +/- 1's the [b]a[/b] and [b]b[/b] vectors drop out of the equation and you are left with just lambda and nonsense.
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This should actually be in a new thread.

Here is the nonsense Bell did in his first paper eq. (2).

[tex]P({\bf a, b}) = \int\,d\lambda\,\rho(\lambda)\,A({\bf a}, \lambda)\,B({\bf b}, \lambda)[/tex]

Then Bell says,
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/bell1.jpg[/img]

You have two unspecified functions as a product and all we know is that they are +/-1. So, the product is going to be either +1 or -1. Taking lambda =1 and [tex]\rho(\lambda)=1[/tex] we will have,

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/bell2.jpg[/img]

So, you are averaging a bunch of +1's with a bunch of -1's which of course is equal to zero at infinity. Then we have,

[tex]P({\bf a, b}) = \int\,d\lambda\,\rho(\lambda)\,A({\bf a}, \lambda)\,B({\bf b}, \lambda) = 0[/tex]

There is one way around this dilemma and that is to do what Joy did. So, Bell was wrong because it is possible!
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