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Specified by Allah? It has nothing to do with the experiments, which measure some +1 or 1.
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06122016, 10:33 AM
(This post was last modified: 06122016, 03:14 PM by gill1109.)
(06122016, 03:26 AM)FrediFizzx Wrote: (06112016, 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. Fred: let's put it a different way. The numbers +/1 are also elements of the set of unit length quaternions S^3. The product of lambda and  lambda in S^3 is the same as their product as real numbers, namely 1.
I carefully computed \(A(a,\lambda)\) and \(B(b,\lambda)\) using geometric algebra, getting the same result as Christian himself, and I then took the geometric product of \(A(a,\lambda), B(b,\lambda)\). I was working throughout in S^3. The result is 1 in S^3.
You can check it yourself in GAViewer if you like.
Equations (1) and (2) (which seem to be correct) contradict equations (4) to (9). It is easy to see where (4) to (9) go wrong: s can't get closer and closer to a and at the same time get closer and closer to b unless a = b. So (4) to (9) is silently assuming that a = b. And if we evaluate (9) taking a equal to b, we do find 1.
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06122016, 11:22 AM
(This post was last modified: 06122016, 03:32 PM by gill1109.)
(06122016, 07:13 AM)Schmelzer Wrote: Specified by Allah? It has nothing to do with the experiments, which measure some +1 or 1.
Ilya: Christian's A(a, lambda) and B(b, lambda), as they are specified by him, are elements of the Geometric Algebra of three dimensional real space.
On closer inspection it turns out that A(a, lambda) and B(b, lambda) are members of the subalgebra containing the bivectors and the real numbers, which (as you probably know) can be identified with the quaternions, which is a real vector space of dimension 4. Moreover, it is easy to see that their lengths are equal to 1. So we may consider them elements of S^3.
On further evaluating the limits A(a, lambda) and B(b, lambda) actually turn out to be purely real numbers +lambda and  lambda, where lambda = +/ 1.
It's all in formulas (1) and (2) of the paper. This part seems to be correct. Though the model does not seem very interesting: A(a, lambda) = lambda, B(b, lambda) = lambda, lambda = +/ 1. We may think of +/1 as unit length quaternions if we like. We can go on to compute correlations by geometric algebra or by ordinary algebra; we will get the same answer. The real numbers are a subalgebra of geometric algebra. As I said, the first real mistake occurs in the step from (5) to (6). Equation (6) has no meaning in conventional mathematics: it includes a limit as s converges to a and to b. The same s, because "total spin is conserved" according to Christian. However, a and b can be different. In the subsequent algebra, the dependence on s conveniently disappears. It's not mathematics and it's not physics, it's a poor conjuring trick.
The first version of the model was much more sophisticated, there was a novel definition of correlation, and there was a much more subtle conjuring trick.
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06122016, 05:43 PM
(This post was last modified: 06122016, 06:12 PM by FrediFizzx.)
(06122016, 07:13 AM)Schmelzer Wrote: Specified by Allah? It has nothing to do with the experiments, which measure some +1 or 1.
S^3 is a postulate of the model. That postulate along with the left or right handed orientation postulate gives the prediction of the model of a.b.
QM as a model can't do what you think this model should be able to do either. Using only +/ 1 outcomes try to produce the negative cosine curve using only QM. Remember that there are no hidden variables in QM at all. You won't be able to do it because it is impossible.
IOW, we have two theories that give the same prediction for the EPRBohm scenario. One of them is a LHV model with physically sensible postulates (they could be possible).
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And how this model connects with reality of experiments, where we have only results +1 or 1, but Bell's inequality is violated anyway? I see no way to use a \(S^3\) model to explain the statistics of experiments which have results +1 or 1.
And I have, of course, de BroglieBohm theory, which is a realistic and causal interpretation, which is able to give violations of Bell's inequality because it is not Einsteincausal. Your LHV model simply has no connection with the experiments, and is therefore not viable.
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(06122016, 06:13 PM)Schmelzer Wrote: And how this model connects with reality of experiments, where we have only results +1 or 1, but Bell's inequality is violated anyway? I see no way to use a \(S^3\) model to explain the statistics of experiments which have results +1 or 1.
And I have, of course, de BroglieBohm theory, which is a realistic and causal interpretation, which is able to give violations of Bell's inequality because it is not Einsteincausal. Your LHV model simply has no connection with the experiments, and is therefore not viable.
Joy answers your question here,
http://arxiv.org/pdf/1405.2355v3.pdf
So the model is indeed viable.
It is true that a nonlocal hidden variable model can use +/ 1 outcomes to produce the negative cosine curve. But we have to reject all nonlocal behavior in the EPRBohm scenario as not physically sensible.
BTW, if you think Bell was right then how do you explain this published classical experiment?
https://www.osapublishing.org/optica/ful...&id=321243
Perhaps a new thread should be started for that?
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I have read Joy's papers and not found an answer. So, I see no reason to consider the model as viable.
That you use this strange term "nonlocal" for something violating only Einstein causality (as if a theory with a higher maximal speed of information transfer would be nonlocal) is a general error, not your. Nonetheless, this strange naming convention is the only justification for presenting theories which do not follow Einstein causality as somehow "not physically sensible".
First, this "classical" experiment uses simply quantum particles in a regime where the statistics are (or have seemed up to now) classical.
Quote:This means a source producing a field that is quantum mechanical (since we believe all light fields are intrinsically quantum), but a field whose quantum statistics are not distinguishable from classical statistics.
And, anyway, what forbids violations of Bell's inequality, and is necessary to prove Bell's theorem, is Einstein causality.
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Joy completely addressed the question that you posed in the paper that I linked. Apparently there is something you don't understand. Perhaps you should ask more questions?
Of course we expected you to try to rationalize the classical experiment away that exceeds the CHSH bound of 2. And of course the paper's authors had to be careful what in what they said in order to get it published. However note that +/1 outcomes were not necessary for this experiment. The experiment definitely proves that Bell was wrong. No need to follow his "rules" any longer about LHV models.
Are you sure you want to stay on a sinking ship? Save yourself before it is too late. You are way too smart to stick with Bell's junk physics. It is time for something way new in physics!
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My question is clear enough. We have a reality of an experiment where what is measured are valued +1 or 1. The statistical evaluation of the experiment does not use anything from \(S^3\) but, instead, multiplies these values like integer numbers.
Elementary logic is not a sinking ship. And I have no reason to explain something away  the proof of Bell's theorem needs Einstein causality, so why I should even care about the question if only quantum experiments or classical too show violations? Ok, I have no reason to expect that it is violated by a purely classical experiment, but the article itself is not really clear about this.
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(06132016, 07:14 AM)Schmelzer Wrote: My question is clear enough. We have a reality of an experiment where what is measured are valued +1 or 1. The statistical evaluation of the experiment does not use anything from \(S^3\) but, instead, multiplies these values like integer numbers.
Elementary logic is not a sinking ship. And I have no reason to explain something away  the proof of Bell's theorem needs Einstein causality, so why I should even care about the question if only quantum experiments or classical too show violations? Ok, I have no reason to expect that it is violated by a purely classical experiment, but the article itself is not really clear about this.
Sure the evaluation doesn't require anything from \(S^3\) but how those +1 and 1 outcomes happen does involve \(S^3\). Why are you mixing that up? That is what Joy's model is really showing. And from the classical optical experiment, you can see that +/1 outcomes are not required for an experiment anyways. So we do have an LHV model that produces the same prediction as QM for the EPRBohm scenario. I really think you should be asking other questions.
It is abundantly clear that the classical experiment that exceeds the CHSH bound of 2 is using classical fields. Perhaps you need to study it more thoroughly?
