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Before this thread is locked, let me make the point that Gill & Schmelzer ignore:
" ... the orientation λ of S3 is a fair coin ..."
Gill and Schmelzer would have us believe that every coin toss ends in heads and tails. How does that happen?
Tom
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This is what one somehow assumes if one talks about coins. The probability that it ends standing on the edge is, in principle, not exactly zero, but sufficiently small. Small enough to be ignored. And if one talks about this in theoretical considerations, one usually ignores it.
But 1.) why do you think I want to make you believe some claims about coins? I couldn't care less. 2.) What is the point? If I criticize something, for rejecting it it is sufficient to find a single error, and I'm free to ignore everything else until this error is corrected. I have found the \(\lim_{s\to a\,\,s\to b}\) nonsense which allows to prove 1=2, Gill has found that simply computing what follows from the definitions is sufficient. For me, my point is sufficient, for Gill, his point is sufficient, and we agree about the conclusion: The paper is wrong.
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(06232016, 07:10 PM)Thomas Ray Wrote: Before this thread is locked, let me make the point that Gill & Schmelzer ignore:
" ... the orientation λ of S3 is a fair coin ..."
Gill and Schmelzer would have us believe that every coin toss ends in heads and tails. How does that happen?
Tom 
See what you are up against? Ilja (Schmelzer) didn't even understand what you said. Further discussion with these guys is pretty pointless.
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(06232016, 06:28 PM)FrediFizzx Wrote: (06232016, 12:13 PM)gill1109 Wrote: (06232016, 05:09 AM)FrediFizzx Wrote: Forget about eq. (68); it is mathematically possible to just go directly from eq. (5) to eq. (9). Based on that fact, you have absolutely no argument.
Let's indeed forget about eq. (68). Let's go back to eq. (14) of http://arxiv.org/pdf/1103.1879v2.pdf.
Equation (1) says \(A(a, \lambda) = \lambda\), equation (2) says \(B(b, \lambda) =  \lambda\).
Equation (4) therefore says \(E(a, b) = 1\) since we are told that \(\lambda = \pm 1\).
Note that equations (1) and (2) contain definitions of \(A(a, \lambda)\), and \(B(b, \lambda)\) as certain limits, and an evaluation of those limits. You can easily check that these evaluations are correct using (3) and the facts that unit bivectors such as \(L(a, \lambda)\) square to 1, and \(\lambda = \pm 1\).
The only way to save the paper is to abandon equations (14). 
Yeah, we know that is your claim; you don't need to keep repeating it over and over. What it really means is that you simply reject the \(S^3\) postulate of the model.
Are you saying that (1) and (2) are wrong? A and B are defined as certain limits, and the limits are computed. I believe that the computation is correct. Simple calculus and geometric algebra. A and B are indeed elements of S^3, the unit length quaternions.
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06242016, 11:56 AM
(This post was last modified: 06242016, 12:12 PM by Thomas Ray.)
Gill wrote " A and B are indeed elements of S^3, the unit length quaternions."
At the same time?
(06232016, 07:29 PM)Schmelzer Wrote: This is what one somehow assumes if one talks about coins. The probability that it ends standing on the edge is, in principle, not exactly zero, but sufficiently small. Small enough to be ignored. And if one talks about this in theoretical considerations, one usually ignores it.
But 1.) why do you think I want to make you believe some claims about coins? I couldn't care less. 2.) What is the point? If I criticize something, for rejecting it it is sufficient to find a single error, and I'm free to ignore everything else until this error is corrected. I have found the \(\lim_{s\to a\,\,s\to b}\) nonsense which allows to prove 1=2, Gill has found that simply computing what follows from the definitions is sufficient. For me, my point is sufficient, for Gill, his point is sufficient, and we agree about the conclusion: The paper is wrong.
Like it or not, quantum theory is about coins, or balls in a urn.
What can it say about orientation?
Tom
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Schmelzer wrote: "I have found the lim s > a s >b nonsense which allows to prove 1=2, Gill has found that simply computing what follows from the definitions is sufficient."
And that is the fundamental error, in both cases. You are merely assuming what you intend to prove. This is no problem for the mathematics; proof by contradiction is a timehonored technique.
In the absence of a defined measure space, however, your conclusion amounts to meaningless manipulation of numbers.
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06242016, 04:11 PM
(This post was last modified: 06242016, 04:13 PM by Schmelzer.)
(06242016, 01:58 PM)Thomas Ray Wrote: Schmelzer wrote: "I have found the lim s > a s >b nonsense which allows to prove 1=2, Gill has found that simply computing what follows from the definitions is sufficient."
And that is the fundamental error, in both cases. You are merely assuming what you intend to prove. This is no problem for the mathematics; proof by contradiction is a timehonored technique.
In the absence of a defined measure space, however, your conclusion amounts to meaningless manipulation of numbers. I know that proof by contradiction is timehonored and valid, and that's why I have used it to show that \(\lim_{s\to a\,\, s\to b}\) is nonsense by proving 1=2 with it. In this proof by contradiction I have not used any measure space, so that your claim that there are none (where?) is irrelevant. I also do not use orientation, so I ask you why you ask about it.
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06242016, 10:27 PM
(This post was last modified: 06252016, 03:55 AM by Schmelzer.)
[unanswered fullquote removed]
(06242016, 04:11 PM)Schmelzer Wrote: (06242016, 01:58 PM)Thomas Ray Wrote: Schmelzer wrote: "I have found the lim s > a s >b nonsense which allows to prove 1=2, Gill has found that simply computing what follows from the definitions is sufficient."
And that is the fundamental error, in both cases. You are merely assuming what you intend to prove. This is no problem for the mathematics; proof by contradiction is a timehonored technique.
In the absence of a defined measure space, however, your conclusion amounts to meaningless manipulation of numbers. I know that proof by contradiction is timehonored and valid, and that's why I have used it to show that \(\lim_{s\to a\,\, s\to b}\) is nonsense by proving 1=2 with it. In this proof by contradiction I have not used any measure space, so that your claim that there are none (where?) is irrelevant. I also do not use orientation, so I ask you why you ask about it. Because the proof is not just simple contradiction  it is by double negation (proving A by proving notnot A, which is equivalent to A)  it can have no physical application. It is akin to philosophy.
When taking a physical measurement, and Joy Christian has been very specific about this, one unavoidably records the result in a direction. Direction implies measure space. Measure space implies orientation. Orientation is a topological property
Tom
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Of course it has no "physical application". The physics is unchanged: We have the violation of Bell's inequality, with the consequence that the fundamental, Einsteincausal variant of relativity  the one which would allow to prove Bell's theorem  is dead.
What has been refuted by the 1=2 proof is Christian's paper http://arxiv.org/pdf/1103.1879v2.pdf
What could be the point of your strange considerations  even if they would be true  is beyond me. Moreover, they are wrong. The result of the measurement is not a direction  the direction is a parameter of the measurement device, the result is +1 or 1. Then, a measure space does not imply orientation. And one can, of course, define a topology, which will also have some properties, on \(\{1,1\}\) too.
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Schmelzer wrote:
"What could be the point of your strange considerations  even if they would be true  is beyond me. Moreover, they are wrong. The result of the measurement is not a direction  the direction is a parameter of the measurement device, the result is +1 or 1. Then, a measure space does not imply orientation. And one can, of course, define a topology, which will also have some properties, on {−1,1}
too."
I went back over my previous comments to see if I had misspoken, and led you to believe I said 'the result of a measurement is a direction.' I could find no such statement. Which tells me that you have not gone beyond the coin toss, balls in an urn, dicethrowing formulation of quantum theory.
The direction of an observation does not determine a result. It guides the result  not as a parameter of the measurement device, where the 'equally likely' hypothesis applies as a function of the choice principle  rather, a perturbative continuous curve dependent on the time a measurement was made. Don't let Richard Gill persuade you that the time parameter (more technically, the 'timelike correlated parameters' of HessPhilipp) plays no role; he's a statistician committed to quantum discontinuity. As evidence of this, ask him to define a measure space  he won't, and for a very simple reason: if space is eliminated as a parameter, spacetime goes with it, which leaves only 'an attempt to breathe in empty space' as Einstein put it, a probabilistic vacuum where things just happen.
I believe you favor Bohmian mechanics, as a nonlocal theory. The only thing standing in the way of making it a local theory, however, is evidence of self similarity at multiple scales  as soon as one speaks of quantum trajectories as an observable, however, measure space enters as an absolute requirement and spacetime matters.
[ https://www.researchgate.net/publication...t_and_Back]
Tom
