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Joy Christian's LHV Model that disproves Bell
HVS has, I think, identified the (key) problem. FreddiFizzx may be right that eqn. 50 can be considered simply an identity, where a and b are any unassigned variables (although the identity seems to be wrong, as Gill1109 says). But it's used in eqn 66 to justify that crucial step. There a and b are the values of the detectors which are spacelike-separated so (one way or another) it requires non-locality.

If this paper were cleaned up it could be a perfectly valid treatment of the Bell-type experimental setup, using quaternions. s (a.k.a. s1 and s2) is the assumed "hidden variable", namely, the spin direction vector which is fixed at creation. Of course this isn't standard QM but it works. When the two complementary particles are detected we must assume they non-locally communicate.  s1 goes to a and s2 goes to b: that means they each collapse to their local setting. The result is either +1 or -1 depending on the angle between them.

The stuff about FLRW is just window dressing to introduce quaternions. Since a, b, s1 and s2 are all assumed known simultaneously for the calculations starting at eqn 60, the correlations would be correct. Someone ought to write it up; just a couple pages; that way the non-local step would be obvious.
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(07-08-2016, 01:50 AM)secur Wrote: HVS has, I think, identified the (key) problem. FreddiFizzx may be right that eqn. 50 can be considered simply an identity, where a and b are any unassigned variables (although the identity seems to be wrong, as Gill1109 says). But it's used in eqn 66 to justify that crucial step. There a and b are the values of the detectors which are spacelike-separated so (one way or another) it requires non-locality.

If this paper were cleaned up it could be a perfectly valid treatment of the Bell-type experimental setup, using quaternions. s (a.k.a. s1 and s2) is the assumed "hidden variable", namely, the spin direction vector which is fixed at creation. Of course this isn't standard QM but it works. When the two complementary particles are detected we must assume they non-locally communicate.  s1 goes to a and s2 goes to b: that means they each collapse to their local setting. The result is either +1 or -1 depending on the angle between them.

The stuff about FLRW is just window dressing to introduce quaternions. Since a, b, s1 and s2 are all assumed known simultaneously for the calculations starting at eqn 60, the correlations would be correct. Someone ought to write it up; just a couple pages; that way the non-local step would be obvious.

Double LOL!  I guess you missed the part previously in this thread that we are now discussing a paper that has been published in the journal Annals of Physics.  Some anonymous referees disagree with you.  Plus I am sure that the editor in chief, the famous Brian Greene, approves everything that goes into the journal.

HVS is just apparently confused as you are.  But if you keep studying it and ask the right questions, you might get it figured out.  There are no errors in the paper; you are only left with rejecting the postulates.  The FLRW "stuff" supports the \(S^3\) postulate.  As does that fact that Joy's classical local realistic model produces the same prediction as QM for EPR-Bohm.  It is a thing of quite elegant beauty.
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(07-07-2016, 12:32 PM)HVS Wrote:
(07-07-2016, 08:16 AM)gill1109 Wrote:
(07-07-2016, 06:45 AM)HVS Wrote: Is the right-most term of equation (50) in http://www.sciencedirect.com/science/art...1616300975 NON-local?

It contains the OUTER product of two detector orientations, the detectors being spacelike separated. (There is no problem with the INNER product and neither product has anything to do with space-time curvature.)

The right-most term of equation (50) is quite simply *wrong*: it contradicts (51) and (52) according to which \(L(a, \lambda) L(b, \lambda) = \lambda I a \lambda I b = - ab\), independent of lambda. I use here the facts lambda^2 = 1, I^2 = -1, and the fact that the scalar lambda and pseudo-scalar I commute with everything.
The sign is right BUT how does your calculation deliver the inner (scalar) product of a and b?
The calculation \(L(a, \lambda) L(b, \lambda) = \lambda I a \lambda I b = - ab\) independent of lambda, contradicting (50), does not deliver the (scalar) inner product of a and b. It delivers the geometric algebra product of a and b; in fact ab = a.b + I(a x b) = a.b + a^b, see (12) in http://arxiv.org/pdf/1405.2355v4.pdf. The geometric product of two vectors is a scalar plus a bivector. (The symbol "^" stands for the wedge product here, not "to the power". Notice that a^b = - b^a).

Christian has to find a way to get rid of the bivector part. His trick has always been to try to introduce a random sign: he would like to have ab = a.b + lambda I(a x b). Then when you average over many copies with independent lambda^k = +/-1 completely at random, the law of large numbers would take care that the bivector part asymptotically vanishes.

But it doesn't matter. We have so far discussed a whole list of errors. If (55) and (56) are correct, then E(a, b) = -1. If (51) and (52) are correct, then (50) is wrong. In the transition (62)-(63), Christian is effectively letting s_1 = s_2 = s converge to both a and b. That's three gross errors in the space of not much more than one page. Earlier in the paper, it is not difficult to check that the set Lambda in (23) is empty. The FRW stuff at the beginning of the paper does not connect to the Pearle model stuff in the middle, and neither connects to the geometric algebra at the end of the paper.
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From Don Graft's paper:

I also go much further in asserting that nonlocal correlations cannot
be obtained in EPR experiments, and that the experiments purporting to show nonlocal
correlations are incorrectly designed, analyzed, and/or interpreted.

Everyone else is assuming the experiments are correct, and the correlation found really is -cos(a-b). If that's not so all the rest of the discussion is irrelevant. But the paper gives no justification for this assertion. So it really is a completely different topic (for a new thread), and requires a new reference to support this statement.
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(07-08-2016, 05:02 PM)Don Wrote: And it's both hyperbole and incorrect to say "everyone else" assumes the experiments are correct.

I meant, of course, everyone else participating in this thread, not everyone else in the world.
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(07-08-2016, 05:43 PM)Don Wrote: Thank you for the clarification, secur. I'm definitely not the first or only researcher to challenge the experiments. Here is a recent example:

https://arxiv.org/abs/1606.00784

Adenier and Krennikov have done great work in quantum foundations.

Their program is just as misguided as yours is.  As soon as you assume "loopholes" you are assuming that the QM predictions are not correct therefore quantum mechanics is wrong.  If you assume non-locality is the only answer to explain quantum correlations, then you of course you will think that QM has to be wrong.  Fortunately we have Joy Christian's classical local realistic model that explains quantum correlations that is now published once again.  All you simply have to do is accept two physically reasonable postulates.  It's a no-brainer.  There is no EPR paradox.  Problem solved!
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Don, I'm aware of the research on various "loopholes" but haven't studied it. Bell-type experiments are technically very challenging, and the result is controversial, so it's very reasonable that they should be checked very carefully, and not accepted without a lot of replication under various conditions. So I don't blame anyone for questioning them, for a while anyway.

However "philosophically" I disagree with you. The issue can be framed as "QM vs. SR". If QM is right that seems to imply non-locality, which seems to violate SR. But in fact it doesn't since no information can be sent. You may say it violates the "spirit" of relativity but that means nothing. OTOH if QM does not have "instantaneous wave function collapse" that violates conservation of energy and other vital principles. The following thought experiment occurred to me long before I ever heard of EPR; and, it's interesting to note, it occurred to Einstein also long before 1935.

Consider an EPR-like experiment but involving only a single particle. The wave function spreads to the two detectors. According to QM one, and only one, will detect it - just like, in EPR, one and only one detects spin up if detector is aligned with spin vector. But if you reject "instantaneous wave function collapse", you have to figure there's 1/4 chance of both observers detecting the same particle, and 1/4 chance that neither will. Both of these are bad, violating conservation of energy, etc. The same reasoning led Einstein to doubt QM and, a decade or so later, write EPR paper; but evidently he was wrong.
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Don Graft's paper: "there is no way for side B to extract it (per the no-signaling theorem), but this is essentially irrelevant, ..."

The claim that this is "irrelevant" is not a statement about physics, it's a philosophical stance: an opinion. Neither SR nor anything else in physics prevents superluminal transfer of "information" if that information can't be accessed; and the no-signaling theorem proves that's the case. That's why I mentioned philosophy: this absolutely essential point of your paper is based on it. As you say, philosophy is not interesting - but then, what to make of this paper which relies on it?

As for starting a new thread, if ever I saw a thread that might as well be hijacked, this is it!
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My role is to review people's papers and help them see the error of their ways, or else commend and encourage them, as appropriate. (Usually, both are appropriate.) Their role, having written the paper, is to start threads.
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The mark of genius is to assert that an objection is easily refuted. Only small minds bother with the tedious and trivial task of actually producing the refutation.
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