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(06192016, 09:56 AM)gill1109 Wrote: So according to definition (4) the correlation is "1". Hence there must be mistakes in Christian's calculations (5) to (12).
I am accepting Christian's postulates. For the definitions of D and L Christian refers to http://arxiv.org/pdf/1501.03393v6.pdf, see in particular equations (5) and (9) in that paper. We find D(n) = I n, L(n, lambda) = lambda I n. One needs to know the standard multiplication rules of geometric algebra; in particular, the pseudoscalar I commutes with everything and its square is 1.
Sorry, but you are not accepting the \(S^3\) postulate. Ya take eq. (4) and you substitute the A and B functions to get eq. (5). It is a very simple thing; not sure why you are having trouble with it.
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06192016, 11:20 PM
(This post was last modified: 06192016, 11:22 PM by secur.)
(06192016, 07:36 PM)FrediFizzx Wrote: It is a very simple thing; not sure why you are having trouble with it.
Suppose something is very simple  in your opinion. Suppose someone else has trouble understanding it  in your opinion , after years of effort. How could you be unsure of the reason? Isn't it obvious  in your opinion?
Say the first thing that comes to mind: what kind of person can't see something very simple, no matter how many times you explain it? He must be an [ fill in the blank ]. What other reason could there possibly be  in your opinion?
Just wanted to clarify that, hope it helps move the discussion forward
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06202016, 12:35 AM
(This post was last modified: 06202016, 01:02 AM by FrediFizzx.)
(06192016, 11:20 PM)secur Wrote: Suppose something is very simple  in your opinion. Suppose someone else has trouble understanding it  in your opinion , after years of effort. How could you be unsure of the reason? Isn't it obvious  in your opinion?
Say the first thing that comes to mind: what kind of person can't see something very simple, no matter how many times you explain it? He must be an [ fill in the blank ]. What other reason could there possibly be  in your opinion?
Just wanted to clarify that, hope it helps move the discussion forward
Hmm, strange... I guess you are having trouble with it also. Let me help. Just add this next sentence after eq. (4). Now we will take the A and B functions defined in eqs. (1 and 2) and substitute them in eq. (4) to arrive at eq. (5). That seems pretty simple to me and is usually understood from the context of the equations. You would think a mathematician wouldn't have any problem with that. If that is not done, then the \(S^3\) postulate is being rejected. I suspect Gill is mixing up \(S^3\) with geometric algebra. ???
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I have to confess, at first I thought S3 meant the permutation group  that's the (at least, "a") standard mathematical (Abstract Algebra) notation. Couldn't make heads nor tails of it. Finally realized my mistake, gave up in disgust, should give it another shot. Physics can be a lot more confusing if you know (nonphysics) math. Happened often that I think  incorrectly  I know what they mean. Might be better to start with a blank slate.
Can you give a ref that defines exactly, and concisely, how these terms are being used in this context? Probably not. For instance, I don't (yet) know what you mean by "geometric algebra". The term didn't exist when I went to school. Undoubtedly it's something very simple, with a new name conferred by physicists, for jobsecurity purposes. (Admittedly there's been a lot of new terms made up by mathematicians also, always for some standard thing that we used to have some other name for.) Another one is "quaternion"  I know what Hamilton thought they were, but apparently physicists sometimes use only the 3 nonreal ones and call those, casually, quaternions. Frustrating.
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C. Doran and A. Lasenby, "Geometric Algebra for Physicists" (Cambridge University Press, Cambridge, 2003)
https://en.wikipedia.org/wiki/Geometric_algebra
One of the main features of GA is that it has outer products in addition to inner or dot products. It is a very rich algebra geometrically. Basically, geometric objects are all on the same footing algebraically. Thus you can have things like a "directed plane". IOW, a plane that points in a certain direction. It is not limited to just vectors.
\(S^3\) means 3sphere topology. In the case of Joy Christian's EPRBohm model, he uses specifically parallelized 3sphere topology.
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06202016, 02:14 AM
(This post was last modified: 06202016, 02:30 AM by secur.)
Okay, it helps to begin at the beginning. First sentence of Christian's "Local Causality in a FriedmannRobertsonWalker Spacetime" :
"A local, deterministic, and realistic model within a FriedmannRobertsonWalker spacetime with constant spatial curvature (S3) ..."
Previously I just started reading it, and, as mentioned, thought S3 meant permutations. But  just to show how messedup physicsspeak can be  I looked through the first 5 ref's google gives for FriedmannRobertsonWalker. Not one of them uses the notation S3!
Furthermore, Christian says it's the curvature  surely that's not right. But he can't mean FLRW itself, since that has 4 dimensions.
FF: S3 means 3sphere topology
I guess that's right. It's the 3sphere spatial part of FLRW  which is questionable also since it presupposes we know the time axis. But this is GR, where we pretend there's no predefined time axis, but go ahead and use it anyway.
Looked at Wikipedia, they never define S3! They just start using the notation after a while, and one can guess it means a topological 3sphere  which is not, after all, a 3sphere per se. Apparently physicists use it casually for either purpose; or, also to mean the curvature property, if they're in the mood. And now I'm wondering what it means to "parallelize" it, when you consider that Grigori Perlman proved all topological 3sphere's equivalent. I suppose it will become apparent. You know, I'm willing to bet he also uses it to mean SO(3) at some point. Any takers?
Turns out "Geometric Algebra" is just a Clifford algebra! As I suspected, something common with a new name. ... Why does it suddenly need a new name?
At least Joy Christian has the mark of a good physicist: utter contempt for rigorous definitions. Drives a mathematician crazy. QM makes perfect sense, because Dirac (who had the mind of a mathematician) and von Neumann (who was a mathematician) defined it. But GR is a mess. Bell, having a QM background, is clear as a Bell. But now Christian's dragging in GR concepts, that's why it's confusing.
Someone above said QM is poorly defined, but not GR; wrong, it's the other way around. Well, Einstein's paper is fine but modern GRworld seems to be full of halfunderstood concepts and definitions.
David Hilbert was right, physics is too important to leave to the physicists.
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secur wrote: "Looked at Wikipedia, they never define S3!"
Look where? Ya got a link?
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06202016, 08:13 AM
(This post was last modified: 06202016, 08:40 AM by gill1109.)
(06192016, 07:36 PM)FrediFizzx Wrote: (06192016, 09:56 AM)gill1109 Wrote: So according to definition (4) the correlation is "1". Hence there must be mistakes in Christian's calculations (5) to (12).
I am accepting Christian's postulates. For the definitions of D and L Christian refers to http://arxiv.org/pdf/1501.03393v6.pdf, see in particular equations (5) and (9) in that paper. We find D(n) = I n, L(n, lambda) = lambda I n. One needs to know the standard multiplication rules of geometric algebra; in particular, the pseudoscalar I commutes with everything and its square is 1.
Sorry, but you are not accepting the \(S^3\) postulate. Ya take eq. (4) and you substitute the A and B functions to get eq. (5). It is a very simple thing; not sure why you are having trouble with it.
I have no problem with (5) and no problem with the \(S^3\) postulate. According to the right hand equalities of (1) and (2), the product of the two limits inside the summation in (5) is identically equal to 1. So (5) evaluates to 1.
Christian's derivation in http://arxiv.org/pdf/1103.1879v2.pdf goes wrong with (6), which makes no sense unless a and b happen to be equal. His problem at this point is with calculus, not algebra. Things go crazy regarding algebra at (11) where a new "postulate" is introduced.
Christian's geometric algebra context is indeed just Clifford algebra; specifically, the particular Clifford algebra \(Cl_{(3,0)}( R)\). The even subalgebra consisting of the scalars and the pure bivectors and their sums can be identified algebraically with the quaternions. The length one quaternions can be identified topologically with \(S^3\).
(06202016, 12:35 AM)FrediFizzx Wrote: (06192016, 11:20 PM)secur Wrote: Suppose something is very simple  in your opinion. Suppose someone else has trouble understanding it  in your opinion , after years of effort. How could you be unsure of the reason? Isn't it obvious  in your opinion?
Say the first thing that comes to mind: what kind of person can't see something very simple, no matter how many times you explain it? He must be an [ fill in the blank ]. What other reason could there possibly be  in your opinion?
Just wanted to clarify that, hope it helps move the discussion forward
Hmm, strange... I guess you are having trouble with it also. Let me help. Just add this next sentence after eq. (4). Now we will take the A and B functions defined in eqs. (1 and 2) and substitute them in eq. (4) to arrive at eq. (5). That seems pretty simple to me and is usually understood from the context of the equations. You would think a mathematician wouldn't have any problem with that. If that is not done, then the \(S^3\) postulate is being rejected. I suspect Gill is mixing up \(S^3\) with geometric algebra. ???
Yes do that. Take the A and B functions defined in equations (1) and (2) and substitute them in equation (4) to arrive at equation (5). Now substitute the evaluation of the two limits also given in (1) and (2) to get ... 1.
That is certainly legal mathematics. On the other hand, Christian's step from (5) to (6) is problematic.
Christian is mixing up \(S^3\) with geometric algebra. He can do that since the quaternions are contained in his geometric algebra and the unit length quaternions can be identified with the threesphere https://en.wikipedia.org/wiki/3sphere
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06202016, 09:28 AM
(This post was last modified: 06202016, 09:45 AM by secur.)
(06202016, 02:19 AM)FrediFizzx Wrote: secur wrote: "Looked at Wikipedia, they never define S3!"
Look where? Ya got a link?
Conveniently enough, gill1109 just posted the link above, "3sphere". Not important.
I've gotten a good reeducation in Clifford algebras now and I thank you for that. OTOH a couple hours are gone and I have a headache.
gill1109, and Schmelzer, are right. You and Christian are, OTOH, not.
The paper linked to above by gill1109, "Disproof of Bell’s Theorem" contains elementary errors, as he says. You can blame it on taking the limit of s as it goes to both a and b; Schmelzer gave another way to look at it a while ago, I believe. The correlation is 1, not (a.b).
Joy Christian should not have published those onepagers, they're too easy to figure out; even I can do it. ref. [1], is much harder and I still don't know where the error is. Unfortunately I started with that one; should have started with the onepagers.
There's only one way I can see for Christian to have anything worthwhile here. First, assume that [1] is valid. (I doubt it.) Then assume the poor guy literally went crazy under the pressure of the last few years, and that's why those onepagers are so bad.
Another alternative  which I seriously propose  the whole thing is an elaborate joke. Christian, and you (FreddiFizzx) are laughing at Gill and others as they waste all this time. I recommend you take this way out. That's very clever and my hat is off to you guys!
Only way I'm going to spend any more time is this. You must admit those onepage papers are trash, that something went wrong with Mr. Christian when he wrote them. But, nevertheless, his [1] is good. In that case I'll investigate further. But if you continue to uphold the validity of "Disproof of Bell’s Theorem", I can only assume the whole thing's a joke. And it's not going to be on me!
Sorry if I sound a bit annoyed, but ...
1. "Local Causality in a FriedmannRobertsonWalker Spacetime", JC, 2016
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06202016, 01:09 PM
(This post was last modified: 06202016, 01:12 PM by gill1109.)
(06202016, 09:28 AM)secur Wrote: Joy Christian should not have published those onepagers, they're too easy to figure out; even I can do it. ref. [1], is much harder and I still don't know where the error is. Unfortunately I started with that one; should have started with the onepagers. An error in ref. [1] "Local Causality in a FriedmannRobertsonWalker Spacetime"? How about equation (23) of http://arxiv.org/pdf/1405.2355v3.pdf . The set Lambda is empty.
But it hardly matters, the paper is pretty incoherent from beginning to end. It even includes the nonsense onepage paper more or less verbatim in the last two pages.
