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Joy Christian's LHV Model that disproves Bell
#11
Hi everybody!
I do not know jack about this jargon on Bell Inequalities and mysterious QM interpretations. Even if some papers are not peer reviewed or not published in prestigious magazines that does not mean they should be discarded. I trust mostly my scientific intuition and empiricism and then I try to understand other or even accepted interpretations. The common mistake of Quantum Theory and most Science is that they discard the obvious. Something that is obvious supported with fundamental but unique arguments may lead to real understanding.

In regards to Quantum Entanglement is not a mystery (it became due to the injected maths involved) and it can be described as follow:
non-local effect (misinterpretation due to long range effects) = large scale chain (ignored) = local link (ignored) + local link (ignored) +  local link (ignored) ........

A change in phase on one local chain will create an extremely fast domino effect on other local chains that it is eventually seen as a non-local influence on the remote end (from one end to the other end).

Non-local realism is directly associated with the dimensions of the large scale chain. When one understands the technique (I have searched but nothing found about it) and the idea behind the setup of a Quantum Entanglement Experiment then, everything will become clear.

Maths do not always lead to right questions and answers.

Right questions may always lead to right maths, at least.
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#12
Ioannis, I have considered if and where they have been published, because this information is not completely worthless. But you may note that I have quoted those papers and rejected them as wrong because of the content.

The "non-locality" used in the Bell inequality business has nothing to do with some non-locality, it is simply a misleading word for Einstein causality, that means, that nothing can move faster than light. And, therefore, such a large chain consisting of a lot of local chains helps nothing. If all the local chains cannot send any information faster than light, then their combination is unable to do this too.
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#13
OK, but let's take a look at Joy Christian's model now. I propose we study the "one page paper" http://arxiv.org/pdf/1103.1879v2.pdf which is a 2015 revision (note: it is version 2) of the original from 2011.

You have to guess the definitions of D(n) and L(n, lambda), they are not given in the paper, but I think that D(n) = I n and L(n, lambda) = lambda I n. My guess is supported by (3) and by the fact that if n is a unit vector then I n and lambda I n are indeed bivectors whose squares equal -1. Formula (10) also supports my guess.

Let's start with formulas (1) and (2). It seems to me that (1) tells us that A(a, lambda) = lambda and (2) tells us that B(b, lambda) = - lambda. The two limits have been correctly computed, according to my guess for the definitions of D and L. (The pseudo-scalar I commutes with everything, and I^2 = -1).

In that case we find immediately that E(a, b) = -1. No need for the derivation from (4) to (9) on the way towards the hoped for result E(a, b) = - a . b. But the interested reader can track down a severe problem with the derivation (what does Christian mean by a limit as s converges both to a and to b?). There is also a problem with the subsequent claim (11). If it suits him, Christian reverses the order of terms in a multiplication (in geometric algebra, multiplication is not commutative). So finally Christian does reach the answer E(a, b) = - a . b by a succession of conjuring tricks which are not even interesting.

I guess that many readers are unfamiliar with geometric algebra. This might lead them to hesitate in forming a judgement. For an introduction to the tiny piece of geometric algebra which Christian is using here, see my http://vixra.org/pdf/1504.0102v2.pdf .
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#14
All of Gill's criticisms of Joy Christian's classical local-realistic model that produces the predictions of QM have been thoroughly debunked here,

http://challengingbell.blogspot.com/2015...f-joy.html
And here,
http://vixra.org/abs/1504.0102

Scroll to the comments sections. If any questions for further clarification, please ask.
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#15
Take a look at equation (1) of http://arxiv.org/pdf/1103.1879v2.pdf
The paper does not define the functions D and L, but I believe that the intended definitions are D(a) = I a and L(s, lambda) = lambda I s.
This makes - D(a) L(s, lambda) = - I a lambda I s = - I^2 a s = lambda a s
Now take the limit as s tends to a and we get lambda a a = lambda a^2 = lambda which is confirmed by the very last part of (1): Christian writes that A(a, lambda) = +1 if lambda = +1, A(a, lambda) = -1 if lambda = -1 (the hidden variable lambda is +/- 1 each with probability 50%.). Or more compactly: A(a, lambda) = lambda.
Similarly (2) gives us B(b, lambda) = - lambda.
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#16
(06-11-2016, 09:30 AM)gill1109 Wrote: Take a look at equation (1) of http://arxiv.org/pdf/1103.1879v2.pdf
The paper does not define the functions D and L, but I believe that the intended definitions are D(a) = I a and L(s, lambda) = lambda I s.
This makes - D(a) L(s, lambda) = - I a lambda I s = - I^2 a s = lambda a s
Now take the limit as s tends to a and we get lambda a a = lambda a^2 = lambda which is confirmed by the very last part of (1): Christian writes that A(a, lambda) = +1 if lambda = +1, A(a, lambda) = -1 if lambda = -1 (the hidden variable lambda is +/- 1 each with probability 50%.). Or more compactly: A(a, lambda) = lambda.
Similarly (2) gives us B(b, lambda) = - lambda.

Hmm... is there a specific question you have?  However, if you continue to do a simple algebraic product instead of a geometric algebra product of course you will always get the wrong answer. But thanks for getting the thread back on topic.
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#17
FrediFizzx
(06-11-2016, 05:50 PM)FrediFizzx Wrote:
(06-11-2016, 09:30 AM)gill1109 Wrote: Take a look at equation (1) of http://arxiv.org/pdf/1103.1879v2.pdf
The paper does not define the functions D and L, but I believe that the intended definitions are D(a) = I a and L(s, lambda) = lambda I s.
This makes - D(a) L(s, lambda) = - I a lambda I s = - I^2 a s = lambda a s
Now take the limit as s tends to a and we get lambda a a = lambda a^2 = lambda which is confirmed by the very last part of (1): Christian writes that A(a, lambda) = +1 if lambda = +1, A(a, lambda) = -1 if lambda = -1 (the hidden variable lambda is +/- 1 each with probability 50%.). Or more compactly: A(a, lambda) = lambda.
Similarly (2) gives us B(b, lambda) = - lambda.

Hmm... is there a specific question you have?  However, if you continue to do a simple algebraic product instead of a geometric algebra product of course you will always get the wrong answer.  But thanks for getting the thread back on topic.
I was working in the usual geometric algebra of three dimensional real Euclidean space. a, s and n are unit vectors in R^3. I is the pseudo scalar. The product is the geometric algebra product. Everything the same as in Christian's http://arxiv.org/pdf/1103.1879v2.pdf 

So it seems that FrediFizzx agrees that equations (1) and (2) of that paper state that Christian's LHV model defines A(a, lambda) = lambda and B(b, lambda) = - lambda where lambda = +/-1 is a fair coin toss. It would seem to follow that E(a, b) = -1, whatever the measurement directions a and b. So we do have a genuine local hidden variables model ... but it does not reproduce the singlet correlations and it does not contradict Bell's theorem. 


This means that there must be something wrong in the derivation from (4) to (12). In fact there are two serious anomalies. In equation (6) we see a nonsensical expression involving a limit as s converges both to a and to b. In equation (11) we see Christian reversing the order of multiplication of the bivectors L(a, lambda) = lambda I a and L(b, lambda) = lambda I b when lambda = -1

Actually since A(a, lambda) and B(b, lambda) are real numbers their product commutes so Christian could just as well have written them in the opposite order in (4) whenever lambda = -1. This means that the big error occurs in the step from (5) to (6) and the subsequent nonsensical (6), (7) and (8).
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#18
(06-11-2016, 06:35 PM)gill1109 Wrote: FrediFizzx
(06-11-2016, 05:50 PM)FrediFizzx Wrote:
(06-11-2016, 09:30 AM)gill1109 Wrote: Take a look at equation (1) of http://arxiv.org/pdf/1103.1879v2.pdf
The paper does not define the functions D and L, but I believe that the intended definitions are D(a) = I a and L(s, lambda) = lambda I s.
This makes - D(a) L(s, lambda) = - I a lambda I s = - I^2 a s = lambda a s
Now take the limit as s tends to a and we get lambda a a = lambda a^2 = lambda which is confirmed by the very last part of (1): Christian writes that A(a, lambda) = +1 if lambda = +1, A(a, lambda) = -1 if lambda = -1 (the hidden variable lambda is +/- 1 each with probability 50%.). Or more compactly: A(a, lambda) = lambda.
Similarly (2) gives us B(b, lambda) = - lambda.

Hmm... is there a specific question you have?  However, if you continue to do a simple algebraic product instead of a geometric algebra product of course you will always get the wrong answer.  But thanks for getting the thread back on topic.
I was working in the usual geometric algebra of three dimensional real Euclidean space. a, s and n are unit vectors in R^3. I is the pseudo scalar. The product is the geometric algebra product. Everything the same as in Christian's http://arxiv.org/pdf/1103.1879v2.pdf 

Nonsense.  You are doing simple algebraic products all the way through.  You have to do a geometric product of the functions A and B.  If after all this time you still don't understand what you are doing wrong, then I probably can't help you.  Perhaps you should be asking questions instead of making statements since it is pretty clear that you still don't understand geometric algebra.
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#19
Let's try a question: Why should we use a geometric product of the \(A(a,\lambda), B(b,\lambda)\) if we know that they are simple numbers, namely the measurement results, which are simply +1 or -1?
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#20
(06-11-2016, 08:28 PM)Schmelzer Wrote: Let's try a question:  Why should we use a geometric product of the \(A(a,\lambda), B(b,\lambda)\) if we know that they are simple numbers, namely the measurement results, which are simply +1 or -1?

Because S^3 was specified.
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