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Time is not "hidden". Perhaps you mean that the hidden variables can be timedependent? This shouldn't affect Bell's theorem. For instance it could be done with different timing for the two measurements  probably has been done that way, with same results.
I don't see the relevance of prime numbers. Some  I think all  of the properties you mention are standard properties of primes investigated and understood in Number Theory. Doesn't mean it can't be relevant to Bell, somehow. But you haven't explained that relevance.
You say "As we demonstrated, regarding the algebraic closure of the complex plane...". No, you haven't demonstrated any such thing, haven't even mentioned complex plane before this.
This post has a tantalizing air of making some sort of sense but I can't see what it is. Perhaps it would help if I had Hess' work handy but don't.
Can you relate this more directly to Bell's theorem? For instance, run through one detection event and show how QM correlations are achieved via prime numbers.
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Reversibility is hidden. When tested against the requirements of relativity, quantum theory has always failed.
If quantum numbers are supposed to exploit all the properties of the natural and real line of numbers (notably proportion and recursion), they fail. If Bell theorists appeal to the algebraic completeness of the complex plane, they fail.
The detectorsetting dependence of BellAspect truncates the function. HessPhilipp restored time reversibility via timelike correlated parameters: "We propose the following definition: TLCPs are parameters that exhibit correlations because they are related to periodic processes. They may depend on the setting of the station in which the periodic process occurs. The correlations are caused not by any information transfer over distance but by the fact that the stations are subject to the same physical law." http://www.pnas.org/content/98/25/14228.full
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Thanks for the reference  Hess and Philipp. I don't know if it's correct, yet, but it's well written; no "handwaving". I'll have to study it more.
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I would say relativity has failed when tested against quantum theory.
I do not see any reason why the hidden parameters \(\lambda\) allowed by Bell would not include some "timelike correlated" or whatever correlated hidden variables. Ok, in principle one could argue that the way how the parameters a and b are chosen it not an ideal random way.
The obvious problem with introducing some time dependence is that a measurement in direction a by Alice predefines the measurement of a by Bob with certainty and independent of the time when Bob makes the measurement.
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06172016, 08:14 PM
(This post was last modified: 06172016, 08:51 PM by secur.)
Schmelzer: I would say relativity has failed when tested against quantum theory.
Right.
Schmelzer: I do not see any reason why the hidden parameters λ allowed by Bell would not include some "timelike correlated" or whatever correlated hidden variables.
Right, but there's a difference with the TLCP's of the paper. They're associated with the stations (Alice and Bob) not the two particles, like Bell's λ's.
Schmelzer: The obvious problem with introducing some time dependence is that a measurement in direction a by Alice predefines the measurement of a by Bob with certainty and independent of the time when Bob makes the measurement.
Hess and Philipp: Notice also that the time operations and mixing of parameters occur (in quantum mechanical terms) during the collapse of the wave function.
They're assuming TLCP's at both stations are determined simultaneously. Of course this violates relativity and is a variety of "spooky action at a distance".
To answer your objection, when Alice measures in direction a Bob's TLCP parameters are fixed right then. In particular his RV will determine that if, later, Bob sets his direction b equal to a, he will definitely (actually, in the “overwhelming majority of cases") equal Alice's result. No matter when Bob makes his actual measurement. (I think)
I'm figuring that this collapse is where the "trick" comes in. True, Station A is not communicating the setting a, or the result of the measurement. But it's (in effect) telling Station B that "right now" is when the measurement actually occurs. That allows the TLCP variables to coordinate enough to produce the right correlations. But it's not clear to me how that works.
I'm Ok with the idea of "instantaneous collapse", personally; but it does violate relativity.
[EDIT] I'm not sure if they mean the wave function collapses in both stations at once, or there are two separate collapses, at each station. Above I was assuming the former, but reading further it's not clear. If they mean the latter then Schmelzer's objection is hard to answer. Have others things to do now, I hope someone figures it out before I get back!
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Ok, if you have interpreted this correctly, then so what.
In quantum theory, the collapse is global. But, of course, they are free to invent whatever they like.
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(06172016, 09:39 PM)Schmelzer Wrote: Ok, if you have interpreted this correctly, then so what.
Well, it's just a puzzle, that's all. I'm not worried about Bell being invalidated. If the paper is correct it constitutes another "loophole" which would be interesting. If not one could perhaps get a refutation published. There are, certainly, more useful things to do.
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(06182016, 01:54 AM)secur Wrote: Well, it's just a puzzle, that's all. I'm not worried about Bell being invalidated. If the paper is correct it constitutes another "loophole" which would be interesting. If not one could perhaps get a refutation published. There are, certainly, more useful things to do.
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There are no loopholes since it is mathematically impossible for anything to "violate" a Bell inequality. Come on folks, it is really simple math!
Besides, "loopholes" implies that you think that quantum mechanics is not correct as far as the predictions for the EPRBohm scenario goes. Bell's theorem is just a word statement that is based on a faulty interpretation of the inequalities.
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QM predicts strong correlation, cos^2, in the EPR  type experiment. You don't need Bell to see that it appears logically impossible to do that without something "spooky" going on, although admittedly I needed Bell to help me understand this fact. I'm not interested in parsing the grammar here; it's not important exactly how Bell's theorem needs to be phrased; the math speaks for itself. Hess and Philipp obviously agree there's a puzzle here, else why do they go to all that trouble to show a way around it? At the moment I'm thinking the way they do it is by postulating, in a sense, time itself as the hidden variable. Clever!  and it may work. I'd call that a loophole in the sense the word is used by scientists working in this field.
If you take the word "loophole" to mean I don't believe QM predictions for EPRBohm scenario, either I'm miscommunicating or you're misunderstanding. It doesn't matter which. Let me assure you, that's not what I mean to imply.
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06182016, 05:29 AM
(This post was last modified: 06182016, 05:29 AM by Schmelzer.)
(06182016, 02:57 AM)FrediFizzx Wrote: There are no loopholes since it is mathematically impossible for anything to "violate" a Bell inequality. Come on folks, it is really simple math!
For anything which has the mathematical form \(E(a,b) = \int A(a,\lambda) B(b\lambda) \rho(\lambda)d\lambda\) with \(A(a,\lambda), B(b\lambda)\in\{1,+1\}\). But that a theory of a particular type (an Einsteincausal realistic theory) has to be of this type is something which needs a proof. Which was given by Bell based on the EPR argument.
(06182016, 02:57 AM)FrediFizzx Wrote: Besides, "loopholes" implies that you think that quantum mechanics is not correct as far as the predictions for the EPRBohm scenario goes.
No, loopholes refers to the experimental tests of Bell's inequality, which are not necessarily ideal realizations of the original thought experiment. The most serious "loophole" was detector efficiency.
