## Bell’s-inequality-denialist Joy Christian offers me $200K if scalable quantum computers are built Joy Christian is the author of numerous papers claiming to disprove Bell’s theorem. Yes, that Bell’s theorem: the famous result from the 1960s showing that no local hidden variable theory can reproduce all predictions of quantum mechanics for entangled states of two particles. Here a “local hidden variable theory” means—and has always meant—a theory where Alice gets some classical information x, Bob gets some other classical information y (generally correlated with x), then Alice and Bob choose which respective experiments to perform, and finally Alice sees a measurement outcome that’s a function only of her choice and of x (not of Bob’s choice or his measurement outcome), and Bob sees a measurement outcome that’s a function only of his choice and of y. In modern terms, Bell, with simplifications by Clauser et al., gave an example of a game that Alice and Bob can win at most 75% of the time under any local hidden variable theory (that’s the Bell inequality), but can win 85% of the time by measuring their respective halves of an entangled state (that’s the Bell inequality violation). The proofs are quite easy, both for the inequality and for its violation by quantum mechanics. Check out this problem set for the undergrad course I’m currently teaching if you’d like to be led through the proof yourself (it’s problem 7). In case you’re wondering: no, Bell’s Theorem has no more been “disproved” than the Cauchy-Schwarz Inequality, and it will never be, even if papers claiming otherwise are stacked to the moon. Like Gödel’s and Cantor’s Theorems, Bell’s Theorem has long been a lightning rod for incomprehension and even anger; I saw another “disproof” at a conference in 2003, and will doubtless see more in the future. The disproofs invariably rely on personal reinterpretations of the perfectly-clear concept of “local hidden variables,” to smuggle in what would normally be called non-local variables. That smuggling is accompanied by mathematical sleight-of-hand (the more, the better) to disguise the ultimately trivial error. While I’d say the above—loudly, even—to anyone who asked, I also declined several requests to write a blog post about Joy Christian and his mistakes. His papers had already been refuted ad nauseam by others (incidentally, I find myself in complete agreement with Luboš Motl on this one!), and I saw no need to pile on the poor dude. Having met him, at the Perimeter Institute and at several conferences, I found something poignant and even touching about Joy’s joyless quest. I mean, picture a guy who made up his mind at some point that, let’s say, √2 is actually a rational number, all the mathematicians having been grievously wrong for millennia—and then unironically held to that belief his entire life, heroically withstanding the batterings of reason. Show him why 2=A2/B2 has no solution in positive integers A,B, and he’ll answer that you haven’t understood the very concept of rational number as deeply as him. Ask him what he means by “rational number,” and you’ll quickly enter the territory of the Monty Python dead parrot sketch. So why not just leave this dead parrot where it lies? Anyway, that’s what I was perfectly content to do, until Monday, when Joy left the following comment on my “Whether or not God plays dice, I do” post: Scott, You owe me 100,000 US Dollars plus five years of interest. In 2007, right under your nose (when you and I were both visiting Perimeter Institute), I demonstrated, convincing to me, that scalable quantum computing is impossible in the physical world. He included a link to his book, in case I wanted to review his arguments against the reality of entanglement. I have to confess I had no idea that, besides disproving Bell’s theorem, Joy had also proved the impossibility of scalable quantum computing. Based on his previous work, I would have expected him to say that, sure, quantum computers could quickly factor 10,000-digit numbers, but nothing about that would go beyond ordinary, classical, polynomial-time Turing machines—because Turing himself got the very definition of Turing machines wrong, by neglecting topological octonion bivectors or something. Be that as it may, Joy then explained that the purpose of his comment was to show that there is absolutely nothing that would convince you to part with your 100,000. You know that, and everyone else knows that … The whole thing is just a smug scam to look smarter than the rest of us without having to do the hard work. Good luck with that. In response, I clarified what it would take to win my bet: As I’ve said over and over, what would be necessary and sufficient would be to convince the majority of the physics community. Do you hope and expect to do that? If so, then you can expect my$100,000; if not, then not. If a scientific revolution has taken place only inside the revolutionary’s head, then let the monetary rewards be likewise confined to his head.

Joy replied:

[L]et us forget about my work. It is not for you. Instead, let me make a counter offer to you. I will give you 200,000 US dollars the day someone produces an actual, working, quantum computer in a laboratory recognizable by me. If I am still alive, I will send you 200,000 US Dollars, multiplied by an appropriate inflation factor. Go build a quantum computer.

I’m grateful to Joy for his exceedingly generous offer.  But let’s forget about money for now.  Over the past few months, I’ve had a real insight: the most exciting potential application of scalable quantum computers is neither breaking RSA, nor simulating quantum physics, nor Grover’s algorithm, nor adiabatic optimization.  Instead, it’s watching the people who said it was impossible try to explain themselves.  That prospect, alone, would more than justify a Manhattan-project-scale investment in this field.

Postscript. If you want something about quantum foundations and hidden-variable theories of a bit more scientific interest, check out this MathOverflow question I asked on Monday, which was answered within one day by George Lowther (I then carefully wrote up the solution he sketched).

Updates (May 6). Depending on what sort of entertainment you enjoy, you might want to check out the comments section, where you can witness Joy Christian becoming increasingly unhinged in his personal attacks on me and others (“our very own FQXi genius” – “biased and closed-minded” – “incompetent” – “Scott’s reaction is a textbook case for the sociologists” – “As for Richard Gill, he is evidently an incompetent mathematician” – “I question your own intellectual abilities” – “your entire world view is based on an experimentally unsupported (albeit lucrative) belief and nothing else” – “You have been caught with your pants down and still refusing to see what is below your belly” – “let me point out that you are the lesser brain among the two of us. The pitiful flatness of your brain would be all too painful for everyone to see when my proposed experiment is finally done” – etc., etc).  To which I respond: the flatness of my brain?  Also notable is Joy’s Tourette’s-like repetition of the sentence, “I will accept judgement from no man but Nature.”  Nature is a man?

I just posted a comment explaining the Bell/CHSH inequality in the simplest terms I know, which I’ll repost here for convenience:

Look everyone, consider the following game. Two players, Alice and Bob, can agree on a strategy in advance, but from that point forward, are out of communication with each other (and don’t share quantum entanglement or anything like that). After they’re separated, Alice receives a uniformly-random bit A, and Bob receives another uniformly-random bit B (uncorrelated with A). Their joint goal is for Alice to output a bit X, and Bob to output a bit Y, such that

X + Y = AB (mod 2)

or equivalently,

X XOR Y = A AND B.

They want to succeed with the largest possible probability. It’s clear that one strategy they can follow is always to output X=Y=0, in which case they’ll win 75% of the time (namely, in all four of the cases except A=B=1).

Furthermore, by enumerating all of Alice and Bob’s possible pure strategies and then appealing to convexity, one can check that there’s no strategy that lets them win more than 75% of the time.  In other words, no matter what they do, they lose for one of the four possible (A,B) pairs.

Do you agree with the previous paragraph? If so, then you accept the Bell/CHSH inequality, end of story.

Of all the papers pointing out the errors in Joy Christian’s attempted refutations of the simple arithmetic above, my favorite is Richard Gill’s.  Let me quote from Gill’s eloquent conclusion:

There remains a psychological question, why so strong a need is felt by so many researchers to “disprove Bell” in one way or another? At a rough guess, at least one new proposal comes up per year. Many pass by unnoticed, but from time to time one of them attracts some interest and even media attention. Having studied a number of these proposals in depth, I see two main strategies of would-be Bell-deniers.

The first strategy (the strategy, I would guess, in the case in question) is to build elaborate mathematical models of such complexity and exotic nature that the author him or herself is the probably the only person who ever worked through all the details. Somewhere in the midst of the complexity a simple mistake is made, usually resulting from suppression of an important index or variable. There is a hidden and non-local hidden variable.

The second strategy is to simply build elaborate versions of detection loophole models. Sometimes the same proposal can be interpreted in both ways at the same time, since of course either the mistake or the interpretation as a detection loophole model are both interpretations of the reader, not of the writer.

According to the Anna Karenina principle of evolutionary biology, in order for things to succeed, everything has to go exactly right, while for failure, it suffices if any one of a myriad factors is wrong. Since errors are typically accidental and not recognized, an apparently logical deduction which leads to a manifestly incorrect conclusion does not need to allow a unique diagnosis. If every apparently logical step had been taken with explicit citation of the mathematical rule which was being used, and in a specifi ed context, one could say where the first misstep was taken. But mathematics is almost never written like that, and for good reasons. The writer and the reader, coming from the same scienti c community, share a host of “hidden assumptions” which can safely be taken for granted, as long as no self-contradiction occurs. Saying that the error actually occurred in such-and-such an equation at such-and-such a substitution depends on various assumptions.

The author who still believes in his result will therefore claim that the diagnosis is wrong because the wrong context has been assumed.

We can be grateful for Christian that he has had the generosity to write his one page paper with a more or less complete derivation of his key result in a more or less completely explicit context, without distraction from the author’s intended physical interpretation of the mathematics. The mathematics should stand on its own, the interpretation is “free”.  My fi nding is that in this case, the mathematics does not stand on its own.

Update (5/7): I can’t think of any better illustration than the comment thread below for my maxim that computation is clarity.  In other words, if you can’t explain how to simulate your theory on a computer, chances are excellent that the reason is that your theory makes no sense!  The following comment of mine expands on this point:

The central concept that I find missing from the comments of David Brown, James Putnam, and Thomas Ray is that of the sanity check.

Math and computation are simply the tools of clear thought. For example, if someone tells me that a 4-by-4 array of zorks contains 25 zorks in total, and I respond that 4 times 4 is 16, not 25, I’m not going to be impressed if the person then starts waxing poetic about how much more profound the physics of zorks is than my narrow and restricted notions of “arithmetic”. There must be a way to explain the discrepancy even at a purely arithmetical level. If there isn’t, then the zork theory has failed a basic sanity check, and there’s absolutely no reason to study its details further.

Likewise, the fact that Joy can’t explain how to code a computer simulation of (say) his exploding toy ball experiment that would reproduce his predicted Bell/CHSH violation is extremely revealing. This is also a sanity check, and it’s one that Joy flunks. Granted, if he were able to explain his model clearly enough for well-intentioned people to understand how to program it on a computer, then almost certainly there would be no need to actually run the program! We could probably just calculate what the program did using pencil and paper. Nevertheless, Bram, John Sidles, and others were entirely right to harp on this simulation question, because its real role is as a sanity check. If Joy’s ideas are not meaningless nonsense, then there’s no reason at all why we shouldn’t be able to simulate his experiment on a computer and get exactly the outcome that he predicts. Until Joy passes this minimal sanity check—which he hasn’t—there’s simply no need to engage in deep ruminations like the ones above about physics or philosophy or Joy’s “Theorema Egregious.”

### 625 Responses to “Bell’s-inequality-denialist Joy Christian offers me $200K if scalable quantum computers are built” 1. Matt Leifer Says: Very nice MathOverflow post, which is only obvious in retrospect. One question that remains is whether we can construct a “maximally nontrivial” psi-epistemic theory such that every ontic state appears in the support of distributions representing more than one quantum state. If not, it would still be the case that sometimes the ontic state determines the wavefunction. 2. Scott Says: Thanks, Matt! But did you mean it was only obvious in retrospect that the post was nice? 🙂 3. Steve Flammia Says: Did Joy give necessary and sufficient conditions for him to pay up? 4. Scott Says: Steve: I don’t know anything more than what he posted here. 5. Joy Christian Says: Scott, Many thanks for advertising my work. I have reciprocated by advertised your post on a FQXi blog: Dear All, Scott Aaronson — yes, our very own FQXi genius — has joined in the battle of words over my refutation of Bell’s former theorem. And I do mean just words, because Scott has never read a single paper of mine, let alone understood that Bell’s so-called theorem was a theorem about physics, not mathematics. And yet he has a loud opinion about my work just as he has a loud opinion about almost everything on earth. To be fair to Scott though, he is not the first person to have an opinion about my work without knowing the first thing about either it or Bell’s former theorem. But, hey, if that is the way our genius wants to do science, then who am I to argue? Joy Christian The battle of words: http://feedworld.net/toc/. 6. Mike Says: Scott, I ask this on Matts Google+ post, but I thought I’d ask you as well. The Lewis paper says that the Pusey paper shows that it is not possible to construct psi-epistemic models of quantum theory, given an assumption that independent preparations produce uncorrelated ontic states. The Lewis paper shows that such models are possible if that assumption is given up. My questions are (i) whether the assumption is reasonable, and (ii) how the Lowther solution, or Matts comment about “maximally nontrivial” psi-epistemic models, impact whether the assumption is or is not reasonable? 7. Scott Says: Mike: The PBR assumption seemed perfectly reasonable to me, but you can decide for yourself! Personally, psi-epistemic theories never did and still don’t hold any appeal for me as possible descriptions of “what’s really going on.” I view the study of which assumptions do or don’t suffice to rule them out as basically a mathematical game … but it turns out to be an interesting and fun game! 🙂 8. Matt Leifer Says: Cross-posting my response to Mike from Google+, since he has asked the same thing here: I think that the factorization assumption is reasonable. I view it as a kind of time reverse of the “no superdeterminism” assumption that is needed in Bell’s theorem. I haven’t exactly made this precise yet, but that is my intuition. There are also a few weakenings of the assumption that still allow the theorem to be proved, such as the one given in http://arxiv.org/abs/1203.4779 Whether or not the assumption is reasonable is not impacted by any investigations we do without making the assumption. Of course, if we can come up with an elegant psi-epistemic theory without the factorization assumption then this might change my mind about its reasonableness. However, the lack of factorization is going to cause problems with composition of subsystems, so I view this as an unlikely possibility. For me, the interest in these investigations has more to do with whether we can derive a PBR-like no-go theorem involving just a single system, perhaps using slightly stronger but still reasonable assumptions than those used in the PBR paper. Since this sort of theorem can be used to derive nonlocality, preparation contextuality and perhaps other quantum phenomena, it would be nice if we could view it as a kind of meta-theorem from which other types of quantum weirdness are derived. The factorization assumption is a bit too strong for this purpose, because we already have proofs of Bell and Kochen Specker that don’t require it. If what I suggested in my comment is not possible then I think that would be sufficient for this purpose. It is a bit tricky because the ontic state space has to be continuous, so you have to be careful not to identify an ontic state being impossible with it having measure zero. Unlike Scott, I do view psi-epistemicism + realism as a plausible candidate for “what is really going on” with quantum theory. However, we knew even before PBR that this type of theory is implausible within the standard framework (because of Bell, Kochen Specker, ontic excess baggage, etc.). Therefore, the thought has always been that a radical change to what we mean by an ontic model has to come first, with my preferred candidate being the introduction of retrocausal influences. The current discussion is therefore more in the vein of toy-theories, which we know are wrong a priori, but which may lead to ideas that are useful in a less restrictive framework.﻿ 9. Joy Christian Says: With hopes that not everyone reading this blog is as closed-minded about Bell’s former theorem as Scott is, let me point out that all one needs to read is this one-page paper of mine http://arxiv.org/abs/1103.1879 to decide who is right. If this is not enough, then I do have more to offer elsewhere: http://arxiv.org/abs/1201.0775 If this too fails, then there is always the option of believing every word Scott says. 10. Roger Says: No matter how many flaws Joy Christian’s papers might have, they do not make quantum computing any more likely. Only some convincing qubit computations will do that. 11. MathOverflow – huh? | Gordon's shares Says: […] Link. “If you want something about quantum foundations and hidden-variable theories of a bit more scientific interest, check out this MathOverflow question I asked on Monday, which was answered within one day by George Lowther (I then carefully wrote up the solution he sketched).” […] 12. Shehab Says: I just checked out the list of references mentioned in the paper on the disproof. It looks Joy Christian doesn’t stand on the shoulder of any other giant. Only reference other than him is to Bell himself. I am now curious to read it! 13. Scott Says: Joy Christian #9: Sure, your suggestion is fine. Let anyone who’s interested read both your article and Richard Gill’s rebuttal—as I did—and then make up their mind. 14. Joy Christian Says: Scott, In that case, they should also read my reply to Gill: http://arxiv.org/abs/1203.2529. By the way, FQXi has just awarded me yet another grant to continue my work on this subject. Joy 15. rrtucci Says: Sure, with a name like Christian Joy, how can they not give you a grant. 16. Mateus Araújo Says: @Scott: Thanks for asking that question on MO and blogging about it! I was also intrigued by it. @Leifer: Do you have something more concrete about ontological models that allow retrocausal influences? I would be very interested in it. 17. Chris Says: @Joy: is there some experimental test that differentiates your physical model from our current ones? 18. Scott Says: By the way, FQXi has just awarded me yet another grant to continue my work on this subject. It’s funny, Joy: just this morning I was toying with the idea of resigning my FQXi membership, to protest its role in legitimizing your crackpot “research.” But then I thought: why should I turn down free cruises, or lovely trips to Iceland or the Azores? I can use my blog anyway, to let the world know exactly what I think about your Bell-icose papers. See you at the next conference! 🙂 19. Joy Christian Says: @Chris: Yes, there is an experimental test. It is a difficult, macroscopic experiment, but I have been told by David Wineland (yes, the famous David Wineland) that it is doable. You can find the experiment described here: http://arxiv.org/abs/0806.3078 Note that Bell and Scott predict that my proposed experiment will not violate the Bell-CHSH inequality. My model for the EPR experiment on the other hand predicts that it will violate the Bell-CHSH inequality, in a purely classical, macroscopic domain. In other words, if performed, my experiment could finally test the validity of Bell’s theorem experimentally. So far there has been absolutely no evidence for the validity of Bell’s theorem in a purely classical, macroscopic domain. 20. John Sidles Says: In the concluding chapter of Tony Zee’s Quantum Field Theory in a Nutshell we read: “In all previous revolutions in physics, a formerly cherished concept has to be jettisoned. If we are poised before another conceptual shift, something else might have to go. Lorentz invariance perhaps? More likely, we will have to abandon strict locality.” Researchers attracted to the Extended Church Turing Hypothesis (ECTH) can regard Zee’s conclusion as suggestive that the chief experimental obstruction to ECTH-disproving quantum computation will prove to be the factorization of physical systems, that is, it will prove to be technologically infeasible to control high-order quantum correlations among qubits, for reasons broadly similar to those that, in the 20th century, led first to theoretical appreciations, and then to experimental demonstrations, that it is physically infeasible to construct right-triangles of arbitrary size and accuracy. Precisely as Scott says, the most exciting application of practical, scalable quantum computers would be their disproof — by disproving the ECTH — that Nature obligates us to seek for Zee-type quantum dynamical theories. 21. Joy Christian Says: Scott, All you know are words. If you have the guts to face up the truth then have my experiment done at MIT. Let Nature speak for herself. You are so biased and closed-minded, Scott, that the only paper you ever read about my work was that of Gill. He is so incompetent that he does not even know the difference between a bi-vector and a multi-vector. Just read his abstract to see for yourself. See you at the next conference. Joy 22. Vadim Says: I’m not qualified to judge your claims, Joy, but I’m curious why they haven’t (apparently) been accepted by the wider physics community. Scott is but one person, and not a physicist, so never mind him for the moment, but surely claims that can be stated in a one page paper should be understandable by most people with a physics PhD. Where are the supporting papers referencing your results? 23. rrtucci Says: Correction: according to http://arxiv.org/abs/1203.2529 his real name is Joy Christian (Oxford) 24. Henning Dekant Says: @Joy, Supposedly Einstein coined the “local is beautiful” phrase for physics. I think he might reconsider after looking at your papers. Like the proposed experiment though. I strongly feel that anything that involves exploding colorful toy balls deserves to be funded. 25. Alex Says: Well, I wouldn’t describe Richard Gill precisely with the word incompetent. By the way, does Joy point out the flaw in Bell’s proof? That would settle it, wouldn’t it? 26. Joy Christian Says: Hi Vadim, Very good questions indeed; but a bit naive I am afraid. Sociologists of science know all too well how claims like mine are received by a mainstream scientific community. Scott’s reaction is a textbook case for the sociologists. But let me give you a more direct and specific example. It is generally believed that in 1963/4 John Bell discovered an error in von Neumann’s theorem against all (local and non-local) hidden variable theories. But in fact the error was actually discovered 30 years before Bell by a mathematician called Grete Hermann. Heisenberg and others were well aware of that discovery. Nevertheless von Neumann’s theorem (despite the existence of Bohm’s theory as an explicit counterexample) was believed in by the physics community for 30 years! For 30 years physicists continued to believe in von Neumann’s theorem and completely ignored and ridiculed Grete Hermann. She was marginalized and ostracized by the likes of Scott. So, I am afraid, the real picture of the sociology of science is a bit more complicated than what we are brought up to believe in. The fact that Scott has chosen to react to my work is a very positive development for it indeed. Joy 27. Richard Gill Says: The claims in Joy Christian’s one page paper are understandable, and understandably wrong, by anyone with a good bachelor’s degree in mathematics (I don’t know how that compares to a physics PhD). I wrote this note: http://arxiv.org/abs/1203.1504 to help the physicists. It concentrates on the pure mathematical error. This saves you from worrying about the sense of the whole program. That’s another issue, on which everyone can easily make up their own mind. But if the maths is wrong, no need to waste time arguing about the rest. Actually, the assumptions in Christian’s many papers are not always the same. Like a bump under the carpet, the basic error gets shifted around, sometimes hidden under the sofa, but it never disappears. Florin Moloveanu earlier wrote a comprehensive analysis, uncovering this error and many more. It’s amusing that Christian also has proposed an experiment. Actually, it is Perez’ Gedankenexperiment, in which macroscopic objects following Newtonian mechanics perform an analogy of a Bell-CHSH experiment. Two brightly coloured halves of a sphere fly off in equal and opposite directions. Their angular momentum lambda (equal and opposite) gets measured using a battery of TV cameras and image analysis software. Next, binary outcomes A, A’, B, B’ are calculated by formulas A=sign(-a.lambda), A’=sign(-a’.lambda), B=sign(b.lambda), B’=sign(b’.lambda). This is repeated N times, generating 4N numbers +/-1 which could be arranged in an N x 4 table with columns labelled A, A’, B, B’. In other words, this is Bell-CHSH (the Aspect experiment) in which we can measure the “spin” of the two “particles” in two different directions at the same time. Christian claims that the four correlations will violate CHSH, because his “topological” explanation of the singlet correlations is not restricted to the quantum domain. However, row wise AB+AB’+A’B-A’B’ 28. Fred Says: @Vadim, “Whenever you find yourself on the side of the majority, it’s time to pause and reflect.” — Mark Twain 29. Richard Gill Says: … =A(B+B’)+A'(B-B’)=A(B+B’)+A'(B-B’)=+/-2, so the average of this quantity over the rows lies between -2 and +2, hence … the four correlations satisfy CHSH. People were wondering whether Christian was a hoaxer or just a crackpot. Having seen a total failure of understanding of simple maths and logic in several different areas I come to the working assumption that he’s a mathematical dyslectic. The formulas he writes do not correspond to what he thinks he writes. His experimental paper (on arXiv) is from 2008. It’s very short and worth reading. It was already back in ca. 2008 that Abner Shimony, David Hestenes, and probably others, pointed out Christian’s main error on the theoretical side. The affair is sociologically and psychologically interesting. But that’s all. 30. David Says: @Joy, you have been at this disproof or quite some time now and I do not see ANYONE supporting your conclusions. Even most crackpots tend to have a few supporters… @Leifer What is really so wrong with superdeterminism? How is retrocausality more tenable? 31. Bram Cohen Says: It seems very odd to deny Bell’s Theorem. It is, you know, a theorem. I can see denying that the experiments have a measurement problem, or that it’s misapplied to the real world, but to deny the theorem is like trying to deny noncomputability, rather than claiming that reality has some extra-turing component. Oddly, although I still am skeptical that quantum computation can be pulled off in the real world, I have a hard time imagining that there’s anything wrong with Bell inequality violations. All explanations of what’s going on which don’t involve weirdo quantum stuff are basically along the lines of trying to deny relativity on the grounds that there’s aether and the relativistic effects are just a bunch of spooky coincidences, or that the devil put dinosaur bones in the ground to try to trick people into believing in evolution. At some point an Occam’s razor violation becomes so egregious that you just have to give in. 32. Scott Says: Joy #21: Interesting! So then, your experimental prediction is that the Bell/CHSH inequality can still be violated, even in a certain “macroscopic” experiment where physicists would say there’s nothing quantum-mechanical going on. The obvious question is: if such an experiment were done and Bell/CHSH were not violated, would you admit that you were wrong? (For my part, if Bell/CHSH were violated by such an experiment, then I wouldn’t say Bell’s Theorem had been disproved—that’s just not the way I use language—but I would readily admit that my understanding of the laws of physics had been wrong in a super dramatic way.) Alas, notwithstanding your detailed understanding of the sociology of science, I don’t actually have the power to “have your experiment done at MIT,” which is a large, heterogeneous institution. Why don’t you talk to specific people, at MIT or elsewhere, with the relevant experimental expertise? FWIW, I completely agree with Henning Dekant that anything involving exploding colorful toy balls should absolutely be funded. If someone takes up a collection, I’ll be pleased to put in$20 of my personal money.

33. Scott Says:

Richard Gill #27,29: Thanks for chiming in! Of all the Joy Christian refutations I saw, yours was far and away the clearest. In fact, I might add some extracts from it to the OP.

34. Joy Christian Says:

Scott # 32 “The obvious question is: if such an experiment were done and Bell/CHSH were not violated, would you admit that you were wrong?”
Yes, I would. Do this experiment http://arxiv.org/abs/0806.3078 and prove me wrong. Let no man but Nature bestow her verdict on herself.
As for Richard Gill, he is evidently an incompetent mathematician. One only needs to read his abstract to recognize this fact. This was confirmed by Joseph Doob, who thought that Gill was a third-rater. Scott, if you think that Gill’s critique of my one-page paper is anything but silly, then I question your own intellectual abilities. Just read my reply to him, http://arxiv.org/abs/1203.2529, and see for yourself. For once try to suspend your biases against my work just for ten minutes and read my reply to Gill. You owe that much to yourself. Let alone my model, the guy has absolutely no understanding of geometric algebra. All his arguments against my work have been systematically debunked, not only by me but also by others on the FQXi blogs.

35. Joy Christian Says:

Alex # 25 “…does Joy point out the flaw in Bell’s proof? That would settle it, wouldn’t it?”

First point, which Scott has not understood, is that Bell’s so-called theorem was not just a mathematical theorem. It was a theorem about physics and metaphysics, and as such it was always a legitimate target for disproof. This is just a linguistic issue and Scott should get over the word “disproof.”

As for the flaw in Bell’s argument, I indeed bring it out explicitly, in several of my papers and my book. You can find it detailed it in this paper, http://arxiv.org/abs/1201.0775, for example. See the discussion around Eq. (1.3). For more details, see the discussions in my book: http://www.brownwalker.com/book.php?method=ISBN&book=1599425645

36. Scott Says:

Joy #35: I’ve spent a decade interacting with physicists, and most of them are perfectly happy to say things like, “of course the Coleman-Mandula Theorem is true, and not disprovable, but I reject the following assumption of the theorem, and advocate the following alternative assumption…”

If you were willing to use language in a similar way, it would make it 1000 times easier for other people to evaluate your claims on their merits.

Having said that: OK, fine, I’m willing to set aside what I consider your perverse misuse of the word “theorem.” I’m now happy to consider our disagreement to be entirely centered around the experimental question of whether the Bell/CHSH inequality can be violated in purely classical situations.

37. Richard Gill Says:

According to Joy Christian, Richard Gill is an incompetent mathematician, and he cites Joe Doob to support this opinion. I am honoured by the lengths Christian now goes to discredit me!

Joseph Doob died in 2004. He was a brilliant probabilist. I am a mathematical statistician. I have made use of Doob’s martingale theory in survival analysis, and incidentally, also in quantum foundations – taking account of time (possible memory effects) in Bell type experiments. Doob had zero interest in mathematical statistics. Totally different area. Interesting that Joy Christian can report here that Joe Doob thought that Richard Gill was a third-rater. I wonder what the context was of their discussion?

I suspect a connection through the Univ. of Illinois to the famous anti-Bellists Karl Hess and Walter Philipp (deceased). Nowadays Karl Hess has joined up with Hans de Raedt, doing event based (local realistic) simulation of quantum phenomena by clever use of the detection loophole and the coincidence loophole. Christian nowadays claims that de Raedt’s philosophy fits in with his.

38. David Says:

@Joy I propose that you contact Sheldon Goldstein and his collaborators, they are experts on Bells Theorem and knew Bell personally.

Here is perhaps the most extensive article ever written on Bells Theorem: http://www.scholarpedia.org/article/Bell's_theorem
It’s written by them and others, surprisingly, your name is not even mentioned.
So contact them and get them into a discussion… FQXi is not really the place to weigh your revolutionary ideas.

If there is anything to your ideas, these people will recognize it immediately.
If you’re unwilling to do so, I actually think that hints in the direction that this shit is just a scheme to get grant money…

0. Somehow, I feel sure that this comment will be treated by most of the usual comment repliers as if it had never been written. (And, I also feel sure that Dr. Aaronson would not moderate it out.)

… Still…

1. The most important question: Is everyone on the same page, in the sense:

Is everyone sure that he will be able to establish the nature of the 1:1 correspondence of all the important concepts he is using to their supposed referents in reality?

If yes, the next question: Are both the parties (Joy and his detractors/opponents/debaters/whatever) sure that what they address is one and the same question?

… Suggesting the two questions to an audience like this might look silly, but we all know the second happens often enough—and the first, almost never! Or, (still speaking of the first), at least, not often enough when mathematicians and “theorem”-makers are/get involved.

2. @Joy: Re. our emails exchange a while ago. How has been the progress on the simulation program to illustrate the main points you have, and the differences of what you say and what Bell, according to you, had said? Just curious.

I think, folks could write computer programs faster than they could perform experiments.

More imporantly, the activity will also “force” them to be detailed enough about most every aspect of their understandings—and differences from each other.

Again, it looks silly to suggest such a simple thing as that, but it’s worth attempting (or setting some UG/PG students on the pursuit). Programs are known to behave unexpectedly oddly for some odd set of inputs, or, what might be much more likely in this case: the unthought of (“undocumentd”) hard-codings and the implicit assumptions built into programs, e.g., if some part of the system is deterministic/probabilistic, if a conclusion is to be taken to apply only to in the “global” sense: as integrated over the entire domain/system as in contrast to a part of it, only in the large-flux situation as against in the transient sense, etc.

3. Where I stand re. Joy’s papers: I do not know the mathematics of much of what he writes, not even the Clifford algebra. To the extent I understand his writings (esp. passages in arXiv:0806.3078), I think he has some very reasonable points.

As to Bell’s theorem and me. I have had some thoughts on similar lines (after somewhat extending my approach), but won’t publish on it for some (indefinite) time. It would be fun to implement my approach for this problem, though (which I haven’t done, yet)!

Ajit
[E&OE]

40. Joy Christian Says:

Richard Gill # 37 “Christian nowadays claims that de Raedt’s philosophy fits in with his.”

Another shameless lie from Richard Gill; but who is counting. All one needs to know is that he is an incompetent mathematician, and this is easy to see from his paper itself. No need to dig too deep into gossip.

41. Scott Says:

David #38: When Joy gave a talk at the FQXi Azores conference in 2009 on his “disproof of Bell’s theorem”, Shelly Goldstein and I were the two people in the audience loudly protesting his bullshit (Shelly much more so than me!). I only wished the other people there were half as outspoken as Shelly was.

42. Joy Christian Says:

@ David # 38
I did my PhD with Abner Shimony (the “S” of CHSH) and learned about Bell’s theorem partly from Bell himself. Another Bell pioneer, Eugene Wigner, was my intellectual grandfather. Mike Horne (the first “H” of CHSH) is my intellectual brother. Young Lucien Hardy is one of my best friends (I was the Best Man at his wedding). I have known several other Bell pioneers like Greenberger, Zeilinger, and Gisin for many years, since my days at BU in the 1980’s. The point here is that I know the best of them all. I do not recognize Goldstein and company as experts on Bell’s theorem any more than I recognize Richard Gill as an expert on geometric algebra (ROTFL).
“If you’re unwilling to do so, I actually think that hints in the direction that this shit is just a scheme to get grant money…”
The scheme is working.

43. Joy Christian Says:

@ Scott # 40 “Shelly Goldstein and I were the two people in the audience loudly protesting his bullshit (Shelly much more so than me!).”

My memory is that Shelly was quite polite, whereas you were rude and obnoxious. You were both wrong, however.

44. Scott Says:

Joy #41: Have any of the fine folks you mention—Abner Shimony, Lucien Hardy, Greenberger, Zeilinger, Gisin—found anything of merit in your Bell disproof? Have they gone on record as saying so?

45. Joy Christian Says:

@ Scott # 43

No and no. It took 30 years to recognize von Neumann’s error. It may take at least that many to recognize Bell’s.

In the mean time, let no man but Nature bestow her verdict on herself. Do this experiment, http://arxiv.org/abs/0806.3078, and prove me wrong.

46. Alex V Says:

Could someone explain how Joy Christian ideas about Bell related with impossibility of quantum computer? I would expect that, contrary, if Bell experiment may be modelled by classical system, we could expect that quantum computer may be simply implemented, because it does not differ much from a classical device.

47. aris Says:

I am so internally divided! One part of me says Joy Christian is a reactionary metaphysician with a bug up his butt. The other part, however, has long suspected Scott Aaronson to be a smug narcissist deserving of dramatic comeuppance.

48. Scott Says:

aris:

I am so internally divided! One part of me says Joy Christian is a reactionary metaphysician with a bug up his butt. The other part, however, has long suspected Scott Aaronson to be a smug narcissist…

I really don’t see the conflict between those two claims, nor do I strongly deny the second one… 🙂

49. rrtucci Says:

I am a conspiracy theorist too.

I’ve often wondered if FXQI and Templeton are fronts for italian criminal organizations. Their actions sound dumb, but underneath, maybe they are the ones that are having the last laugh.

50. Joy Christian Says:

@rrtucci #46

“I’ve often wondered if FXQI and Templeton are fronts for Italian criminal organizations. Their actions sound dumb, but underneath, maybe they are the ones that are having the last laugh.”

We are laughing.

Oops… I shouldn’t have said that out loud.

51. David Brown Says:

John Bell gave a fairly precise definition of a “hidden variable”. If one accepts his definition, then Bell’s theorem is true. However, does quantum field theory (QFT) now have an acceptable axiomatization? If we are not in agreement on an axiomatization of QFT then how can we be sure that (A) Bell’s meaning of a “hidden variable” is the most appropriate meaning of “hidden variable” and (B) Bell’s proof might have overlooked something in the correct axiomatization of QFT?
http://www.scottaaronson.com/papers/nks.ps http://wolframscience.com/reference/quick_takes.html
I claim that Wolfram’s “A New Kind of Science” (NKS) Chapter 9 is empirically valid if and only if the Rañada-Milgrom effect is empirically valid and the Space Roar Profile Prediction is empirically valid. Can someone explain to me why my claim about NKS Chapter 9 is wrong?

52. Joy Christian Says:

@David Brown #48

“John Bell gave a fairly precise definition of a “hidden variable”. If one accepts his definition, then Bell’s theorem is true.”

I use precisely the definition provided by John Bell for local hidden variables and show that Bell’s theorem is false. You can find the summary of my argument here
http://arxiv.org/abs/1103.1879
and further details here
http://arxiv.org/abs/1201.0775

QFT adds nothing to either Bell’s argument or my unambiguous and decisive refutation of Bell’s argument.

53. John Sidles Says:

A wonderful mathematical thrill in learning any dynamical framework comes at the moment when causality is reconciled with locality. For example, in Nielsen and Chuang’s Quantum Computation and Quantum Information, this thrilling reconciliation is associated to Theorem 8.2: Unitary Freedom in the Operator Sum Representation.

Joy Christian, I took the trouble to download arXiv:0806.3078, but did not find within it any mathematical discussion — thrilling or otherwise — of how this reconciliation is accomplished. Is there any such reconciliation, and (most vitally!) what mathematical theorem(s) and physical insight(s) are associated to it?

In engineering simulations, we simply dial-up the algebraic rank of the simulation until the surviving non-causal correlations are of sufficiently high order as to be submerged in noise (noise being present in any physical system) in which event the non-causality is immaterial.

This working reconciliation is adequate for today’s engineering purposes, but philosophers and physicists rightly desire a more fundamental and rigorous reconciling of causality and locality … and even we engineers wish that we had a better, deeper understanding of these matters.

Therefore, I think it is reasonable, Joy, to enquire where a discussion of causal aspects of your theories may be found, and to regard these theories (or any dynamical theories) as incomplete if they do not concretely address these matters … hopefully via thrilling mathematical theorems and illuminating physical insights!

54. Hal S Says:

Scott is right, Bell’s inequalities shouldn’t be questioned at this point, athough the ongoing debate is whether you dump localty or realism. There is some debate about whether you dump locality or realism http://arxiv.org/pdf/0909.0015v3.pdf (and the answer is realism :-).

What I think is hard for people to understand is that classicality itself is increasingly unfounded as anything other than as a useful approximation.

If there is a moment, it is worth reading J.E. Gunn’s thesis http://thesis.library.caltech.edu/4408/1/Gunn_je_1966.pdf (be sure to look for the shout out to Feymann amongst others).

The image that one should have in one’s mind is the idea trying to determine statistical distributions on photographic plates. If one thinks about the double slit experiment, where one sees the development of interference patterns on a photographic plate as photons pass through slits, then one can think similarly about looking for statistical distributions on photons hitting a photographic plate from a snapshot of the cosmos. One should quickly see the similarity in these endeavers.

The point being (although apocryphal to some), there are approaches to deriving statistical laws governing cosmological observables, so it is possible to imagine gravity at the cosmological scale as a statistical phenomenon (although not, for various reasons, an entropic phenomenon).

Since Gunn’s thesis makes explicit use of the cosmological principle, this puts us in a nice position to say that locality does matter, the universe is observer dependent, and it is realism that must be dropped.

55. Joy Christian Says:

@John Sidles # 50

Perhaps you may find this paper of mine mathematically more inspiring:
http://arxiv.org/abs/1101.1958

A gentler introduction to it can be found here: http://arxiv.org/abs/1201.0775

56. Joy Christian Says:

aris:
I am so internally divided! One part of me says Joy Christian is a reactionary metaphysician with a bug up his butt. The other part, however, has long suspected Scott Aaronson to be a smug narcissist…

I too really don’t see the conflict between those two claims, nor do I deny the second one…

57. David Brown Says:

I quote from Wikipedia, “The conditions Bell imposes on any “reasonable” local hidden variables have been similarly criticized in the work of Masao Nagasawa and Jörg Shröder. In addition to demonstrating that Bell’s conditions are overly restrictive, Nagasawa has proven that local hidden variable theories are possible by developing such a theory.”
http://en.wikipedia.org/wiki/Bell_theorem
Who agrees (or disagrees) with the Wikipedia entry concerning Nagasawa?
I have the impression that both Steven Weinberg and Sheldon Glashow think that I am crackpot. I say that they are correct if and only if the Space Roar Profile Prediction is false. Where did Einstein go wrong? I say that Einstein’s mistake can be found in “The Meaning of Relativity”, 5th edition, page 84.
Is Milgrom the Kepler of contemporary cosmology?
http://vixra.org/pdf/1202.0083v1.pdf “Anomalous Gravitational Acceleration and the OPERA Neutrino Anomaly”
http://vixra.org/pdf/1202.0092v1.pdf “Finite Nature Hypothesis and Space Roar Profile Prediction”
http://vixra.org/pdf/1203.0034v1.pdf “Does the Rañada-Milgrom Effect Explain the Ecliptic Alignment of CMB Anisotropy?”
http://vixra.org/pdf/1203.0036v1.pdf “Does the Rañada-Milgrom Effect Explain the Flyby Anomaly?”
http://vixra.org/pdf/1204.0095v1.pdf “Seiberg-Witten M-theory as an Almost Successful Predictive Theory”
If nature is finite and digital , then I have to be very concerned about Bell’s theorem. Recently I posted 3 pieces of appalling drivel online that seem to prove that I fail to understand physics and mathematics (OOPS!). Can anyone give me some feedback (however negative) on my vixra postings?
QUESTION1: If Bell’s proof of Bell’s theorem is wrong, then where is the first line of the proof in which Bell went wrong?
QUESTION2: What does Nagasawa think about all this?
Any response from Joy Christian or anyone else?

58. John Sidles Says:

To be candid, Joy, I was stimulated by Scott’s post to download all of your arxiv preprints and search them for the keyword “causality”, with a view toward mining them for techniques useful in engineering simulation.

Success was mixed. On the one hand, your geometric methods and notation are naturally compatible to efficient numerical simulation methods. But on the other hand, for large-$latex n$ spin systems, it is far from evident (to me) that the $latex S^k$ state-spaces of your preprints adequately support the low-order quantum dynamical entanglements that … as Scott rightly emphasizes! … innumerable experiments have exhaustively verified as reflecting the true dynamics of nature.

So like Oliver Twist, my final reaction is: “Please sir, I want some more!” In particular: (1) more dynamical dimensions, (2) state-space geometry that supports physically valid descriptions of low-order quantum entanglement dynamics, and (3) theorems governing the reconciliation of causality, locality, and separability.

Moreover, and needless to say, the more beautiful these theorems are, and the more surprising, useful, and accessible the physical dynamics that they govern, the better!

`Cuz heck … how hard can it be? 🙂

59. Mateus Araújo Says:

According to my calculations, Joy Christian scores 85 on Baez’s crackpot index: http://math.ucr.edu/home/baez/crackpot.html

60. Joy Christian Says:

@David Brown #57

“If Bell’s proof of Bell’s theorem is wrong, then where is the first line of the proof in which Bell went wrong?”

Bell went wrong in the very first equation of his famous paper. For a full understating of this please see the discussion from Eq.(1.1) to Eq.(1.3) in this paper: http://arxiv.org/abs/1201.0775

61. David Brown Says:

@Joy Christian #60: You write, “What is responsible for the EPR correlations is the set of all measurement results.” Do you mean to say that your theory precisely accounts for all the measurements that are attributed to “quantum entanglement”? If in your “Theorema Egregium” I replace the words “classical, local-realistic” by “Fredkin-Wolfram” then what difference would it make in terms of physics? If nature is finite and digital then I need a “Fredkin-Wolfram measurement topology” to make the theory work — can your mathematical method provide this?

62. David Brown Says:

Oops, I wrote “set of all measurement results” instead of “topology of the set of all measurement results”.

63. Joy Christian Says:

@Scott # 36:
“I’m now happy to consider our disagreement to be entirely centered around the experimental question of whether the Bell/CHSH inequality can be violated in purely classical situations.”
I am happy that you are happy. But should you be happy? Isn’t there a BIG data point missing from your cherished world view? Without my proposed experiment done and our disagreement settled one way or other experimentally, your entire world view remains based on a pure belief that Bell-CHSH inequality cannot be violated in a classical, macroscopic domain, in any physical situation. You have convinced yourself of this by buying into the discredited Bell ideology, but in the end, without my experiment done, your entire world view is based on an experimentally unsupported (albeit lucrative) belief and nothing else.

64. Joy Christian Says:

@Mateus Araújo #59
“According to my calculations, Joy Christian scores 85 on Baez’s crackpot index.”
Pity! I would have thought I would score at least a 1,000. I will try harder.

65. Scott Says:

Joy #63: Aha! But you see, I happen to think that, if the entire Grand Canyon were filled with honey, then an enchanted bear would magically appear, slurp up all the honey, and then finally explain to you why you were wrong in a way able to penetrate your skull. You might believe that if the Grand Canyon were filled with honey this would not happen. But until the experiment is actually done, who is to say which one of us is right? Doesn’t your entire world view remain based on pure belief—experimentally unsupported belief—in the bear’s nonexistence?

(Just to clarify, since we have a few professional point-missers on this thread: yes, I would regard Joy’s “macroscopic CHSH violations,” supposing they were found, as neither more nor less amazing than my honey-loving, Bell-explaining bear.)

66. Hal S Says:

@John #58

I want to make sure I understand the pullback operation you discuss in your link as well as here

http://mathoverflow.net/questions/66506/in-quantum-dynamical-simulations-what-is-the-symmetric-riemannian-analog-of-a

It looks like the theorem is that one can map the large space of states into a smaller space of states and still retain a relationship between the commutators of those states, so when one simulates dynamics in the smaller space one can still draw conclusions about the dynamics in the larger space. Is that a correct characterization?

67. Hal S Says:

@ John #58
p.s. very admirable work by the way

68. Jason Says:

Scott: this has been a very entertaining thread, thanks!

Joy: You are nothing like Grete Hermann. Her result went unnoticed for 30 years. Your result has been analyzed by several physicists and mathematicians and rejected by all of them. Please give us more examples from physics and mathematics in the last 200 years of figures who:

1) Claimed to discover a flaw in a widely accepted mathematical proof
2) Had their work *universally* rejected by all qualified physicists and mathematicians who examined it for at least 5 years after the work was initially presented
3) Were ultimately proven right

Please provide estimates of the size of this population relative to the population of people who satisfy 1) and 2) but not 3).

69. Hal S Says:

@ Jason #68

http://www.hcs.harvard.edu/~hrp/issues/1999/Hermann.pdf

Thanks, now I know where Zurek’s word “pointer” seems to have come from.

70. John Sidles Says:

Jason #58: I agree that the scenarios you describe are exceedingly rare … but they *do* exist.

Example: @article{Author = {Harold S. Black}, Journal = {IEEE Spectrum (USA)}, Month = {December}, Number = {12}, Pages = {54–60}, Title = {Inventing the Negative Feedback Amplifier}, Volume = {14}, Year = {1977}}

In particular, Black’s patent application “Wave Translation System” (US #2102671) was held-up in review for almost ten years, on the grounds that its theoretical foundations were manifestly “impossible.”

If you’ve ever wondered about Bell Lab’s primary revenue source, well for about 30 years, this was it.

71. Ankur Says:

The only thing missing from this is Rafee Kamouna!

72. Henning Dekant Says:

@Joy, I am fascinated with you earlier claim of credibility by association with esteemed individuals. Too bad they did just not see fit to endorse your research at this point. Science sociology is most certainly rather pesky.

This reminded me that I once rubbed shoulders with Vasclav Havel when he made a surprise appearance in a public square in Prague and that my grand-aunty once met Einstein lake-side when he was about to get into his sail boat.

Obviously these associations make me an expert on everything relativity, as well as give me deep insight into what it means to have lived a life as intellectual dissident to a totalitarian regime. It’s amazing how this works.

@Scott, I am thinking of setting up a non-profit Paypal acount to collect your $20, and will generously match your contribution. Exploding toy balls are surely worth it. Maybe we can get the Mythbusters to conduct the experiment if the MIT won’t listen to you? 73. anon Says: long time reader, first time commenter. this blog rules. that’s all i have to say. 74. Teresa Mendes Says: Scott: Joy intuition is right when he says there is a problem. But the problem is not on Bell’s theorem, the problem is on the generalizations Bell’s theorem. Anyone of the readers of this post analyzed the paper of J. Especial ‘Bell inequalities under non-ideal conditions’, recently published in the journal Annales de la Fondation Louis de Broglie (http://aflb.ensmp.fr/AFLB-371/aflb371m746.pdf) and would like to comment? And of course: extraordinary claims require extraordinary evidence. We estimate$200k for doing a conclusive experiment.
You offered 100k. Can you “find” the other 100k?
With or without you we will pursue this path.
Would any reader be wiling to to ship in?
Will FQXi award a grant?

75. David Brown Says:

After reading Joy Christian’s paper “On the Origins of Quantum Correlations” my estimate of the situation is this: Bell and Christian are using totally different meanings for the phrase “hidden local variables”. Christian wrote, “As we shall see however, Bell’s prescription is not only false, it is breathtakingly naïve and unphysical. It stems from an incorrect underpinning of both the EPR argument and the actual topological configuration involved in the relevant experiments [4].” Physical experiments show that Bell used a correct underpinning of the EPR argument. I think that Christian has implicitly used a concept of “quantum state” that is extremely interesting but it is some sort of topological decomposition of a quantum state. However, Christian’s mathematics might be important in finding a physical interpretation of M-theory.

76. Jason Says:

@Hal S: thanks, I stand corrected! @John Sidles: interesting story! I didn’t mean to imply it had never happened, was curious if people would come up with examples.

77. Mike Says:

Hey Scott, I’m wondering how you got the courage to post that question on MO. In truth it wasn’t that hard of a question and if you have trouble solving it then…well, no offense, but you see what I mean. Reputation matters.

78. Joy Christian Says:

I posted this on the FQXi blog:

Scott Aaronson is rigging his blog. He is blocking the posts that are not too flattering for him. In particular he is blocking my posts and refusing to read my arXiv reply to Gill. It is simply too painful for him to admit that he has been wrong all these five years. He has an ego of the size of Mount Everest.

79. David Says:

You claim this is so self-evident and that you have illustrated it time and time again. Then why are these people you appeal to as authority not seeing it?

I also think it is not fair to compare the time it took for people to notice errors in the 50s and today.
Today we have rigorus peer review (at least some journals) and we got a TON more physicists.
Bells Theorem has been scruitinized so heavily that there is virtually zero chance for anyone to ever find “fault” with it.

I can imagine, like ‘t Hooft, that maybe the “no conspiracy” assumption should be questioned further though

80. Joy Christian Says:

@ Scott #65
Aha! You have been caught with your pants down and still refusing to see what is below your belly. Well, eventually you will have to look. If it is still not clear to you, let me point out that you are the lesser brain among the two of us. The pitiful flatness of your brain would be all too painful for everyone to see when my proposed experiment is finally done. Until then, do keep your head buried in the sand.

81. John Sidles Says:

Joy, although my files contain sufficient case histories of STEM enterprises as to encompass exceptions to almost any rule, please let me say that *no* case histories (known to me) show that any benefits accrue to personal criticism.

Rather, effective innovators devote their energies wholly to improving, extending, and applying their own work, and to communicating it more clearly, and to sharing it more effectively, and to creating enterprises based upon it.

A terrific quotation in this regard is Arnold Shoenberg’s appreciation of Charles Ives:

“There is a great man living in this country — a composer. He has solved the problem of how to preserve one’s self and to learn. He responds to negligence by contempt. He is not forced to accept praise or blame. His name is Ives.”

82. Thomas H Ray Says:

@ Scott #65
” … yes, I would regard Joy’s ‘macroscopic CHSH violations,’ supposing they were found, as neither more nor less amazing than my honey-loving, Bell-explaining bear.)”

I suppose that means you have secret knowledge of the point that demarcates discrete quantum results from classical continuous functions. Where is it, and do you plan to publish?

83. Scott Says:

Joy Christian #78: The flatness of my brain? I suppose that would make it easier to bury in sand…

84. Scott Says:

Thomas Ray #80: No, I don’t have any “secret knowledge” about the so-called boundary between quantum and classical—just the public knowledge that, wherever you take that boundary to be, for experimental purposes it’s certainly below the level of Joy’s exploding toy balls, for which the decoherence times would be way too small to measure.

85. Wouter van Doorn Says:

Joy Christian: If you have a few minutes to spare, please read http://lesswrong.com/lw/i9/the_importance_of_saying_oops/ and the two posts that follow.

Scott: You are awesome.

86. Richard Gill Says:

The great thing about Joy’s exploding colourful toy balls (which in fact are due to Peres, I believe) is that his paper proposing his experiment simultaneously shows that the experiment is totally pointless. I mean: with probabiliy 100% it will prove Joy Christian wrong. This suggests that Joy Christian is not a Great Scientist but either a fool or a charlatan. So: please, let’s do it!

His topological ideas make great Science Fantasy, but his mathematics is quite simply *wrong*. Fundamental, stupid, errors, all over the place. Well enough hidden that most people don’t notice them.

It is nothing to do with the border between classical and quantum.

It is nothing to do with S^7.

The “experimental paper” is simply pure gobbeldygook, it proves that its author is either a simpleton or a sublime confidence trickster. Like a parrot he is extremely good at using a lot of difficult words and refering to unfamiliar mathematical concepts as if he is an expert, but actually the mathematics which he writes down has little correspondence to the “patter”. This led some people to imagine that maybe he was on to some very very deep important discoveries and that the reason it doesn’t make sense to them is just because the maths is too difficult for them. But it is not difficult. The mathematics of Clifford algebra is elementary. Christian makes elementary mistakes, probably caused by ambiguous notation. Lack of understanding of basic mathematical concepts. It’s undergraduate stuff.

It is not difficult, and quite simply, it is wrong. Full of mistakes. All over the place. Elementary mistakes.

For perhaps the simplest example of this, I highly recommend everyone takes a serious look at his so-called “experimental paper”. No need to spend an hour checking what Clifford Algebra is on wikipedia. You only need fifteen minutes and your plain common sense to completely understand the paper and to understand that it’s nuts. The reference is:
http://arxiv.org/abs/0806.3078 “Can Bell’s Prescription for Physical Reality Be Considered Complete?”
It’s only four pages. It has not been published in a peer reviewed journal and no-one is going to do the experiment, ever.

You see, Joy’s experiment would generate, in each of N runs, four binary outcomes of spin: measured in two different directions on each of two objects (a and a’, b and b’). In other words: in the n’th run we get an outcome +/-1 of A *and* of A’ and of B *and* of B’. Rather different from the situation in real CHSH experiments where in each run you have to choose between observing A or A’, B or B’.

The experimenters will end up with an Nx4 array of numbers +/-1. It’s a theorem of arithmetic, if you want to call it a theorem, that ave(AB)+ave(AB’)+ave(A’B)-ave(A’B’) will lie between -2 and +2, whatever the numbers.

Proof: rowwise, AB+AB’+A’B-A’B’=+/-2.

Does Joy understand this, or does he seriously imagine that 4N numbers +/-1 could generate four correlations violating the CHSH inequality? Difficult to tell. On the FQXi blog, Joy and his defenders have been making hysterical remarks about this, like “Richard Gill has rigged the experiment”, or “the correlations have to be computed separately”, or “the data can’t be analysed in an Excel spreadsheet”. Yet they agree that the experiment generates 4N numbers +/-1 and that by correlation they mean the average of the products of elements in the various columns.

Either way, this has certainly made Joy absolutely furious. The emperor was caught with his pants down. Still hard to know if he realizes this or not. Perhaps some of his best friends could have a word with him in private about this.

87. Hal S Says:

@ John Sidles

Hopefully these links help you on your quest, the second discusses recent advances in simulating fermion in 2d tensor networks. The claim is that this has been done at no computational cost, and that computational cost now scales with the level of entanglement (around time 33:40 in the video) but remains polynomial.

“…let me point out that you are the lesser brain among the two of us.” might be the best line ever delivered in these blog comments. I could practically hear the cackling.

89. Thomas H Ray Says:

Scott # 84

Exploding toy balls aside, by what warrant do you assume that quantum decoherence says anything about a measurement function continuous from an initial condition? In other words, can you answer Leslie Lamport’s question (“Buridan’s Principle,” Found. Phys. April 2012) that for a decision–i.e., a discrete measurement–in a bounded length of time, given nonzero probabilities for events x,y,z in which x < y < z , "Is the value greater or less than y?"

If Buridan's principle ("A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time") is a physical law, as Lamport claims, then without a counterexample to his question which is derived from this principle (tantamount to answering the question for any experimentally bounded length of time) the assumption of quantum decoherence cannot demonstrably apply to any but the quantum domain. Christian's analytical framework, however, does not recognize any boundary between quantum and classical domains.

90. Bram Cohen Says:

Does Joy Christian make a living off FQXi grants? It’s hard for people to give up their crank theories when they rely on them for money.

Scott, I happen to know that Joy Christian is a wonderful man. He wouldn’t post the outrageous, hurtful, and deeply ignorant comments appearing under his ‘name’ on this post. Let’s hold off judging him since there is no way to verify the identify of people posting on this blog.

92. Thomas H Ray Says:

Richard, I see that you still do not comprehend the difference between algebra and analysis.

93. Thomas H Ray Says:

Bram Cohen # 90, Do physicists still make a living verifying the Bell-Aspect result?

94. Richard Gill Says:

@Bram, I think the answer is yes, Christian depends for his living on FQXi. He just got a new mini-grant from them, maybe some kind of thank-you for the book and the publicity.

He has some kind of affiliation with Perimeter Institute and some kind of affiliation with Wolfson college, Oxford and/or the department of physics at the university of Oxford, but neither of these connections comes with a salary.

Perhaps he’s pulling in huge sums of money on the royalites of his book now?

95. Alex V Says:

Either something is wrong with my comment #46, or indeed nobody could explain how Joy Christian ideas about Bell are related with impossibility of quantum computer.

96. Scott Says:

Alex V #95: I don’t understand all that well either what the two have to do with each other, beyond that Joy denies the reality of quantum entanglement.

97. Alex V Says:

Frankly speaking I could suggest after reading of his works that he rather claims reality of classical analogues of entanglement …

98. John Sidles Says:

Hal #87, thank you for those very interesting fermionic simulation links! To answer your question of #66, which as I read it was (in essence):

When one simulates dynamics [by pullback] in the smaller space one can still draw conclusions about the dynamics in the larger space. Is that a correct characterization?

Yes. And this is true, even though the pullback is onto a (symplectic) manifold of states, rather than a (Hilbert) state-space.

Concretely, much of the microscopic spin physics that is developed in texts like Slichter’s Principles of Magnetic Resonance is restricted by well-verified conservation laws. Moreover from the microscopic physics one derives useful macroscopic physics (e.g., Onsager relations) and these macroscopic laws also depend upon microscope conservation laws. Thus in large-n numerical simulations of these systems, it is preferable to design the pulled-back lower-dimension dynamics such that these conservation laws are respected identically — this is the practicel motivation for the theorem.

A natural connection then arises to the fundamental issues that Joy and Scott care about, as follows:, it turns out to be infeasible to efficiently simulate quantum operations that exhibit exact dynamical separability, that is, it is infeasible to simulate measurement-and-noise operations whose (superluminal) interspin channel capacity is provably zero. At least, I for one don’t know how to prove such theorems, and to the best of my knowledge, no such theorems are known.

This thorny difficulty is entangled with many other thorny difficulties, and in consequence many researchers — including Scott as I understand his writings — agree with Steven Weinberg, who wrote:

I simply do not know how to change quantum mechanics by a small amount without wrecking it altogether.

This theoretical failure to find a plausible alternative to quantum mechanics, even more than the precise experimental verification of linearity, suggests to me that quantum mechanics is the way it is because any small change in quantum mechanics would lead to absurdities. If this is true, quantum mechanics may be a permanent part of physics. Indeed, quantum mechanics may survive not merely as an approximation of a deeper truth, in the way that Newton’s theory of gravitation survives as an approximation to Einstein’s general theory of relativity, but as a precisely valid feature of the final theory.

In engineering practice, in order to feasibly simulate large-n system dynamics — which we attempt despite the formidable difficulties that Weinberg mentions, because practical eninerring problems can’t wait upon practical quantum computers! — one resorts to the unaesthetic expedient of raising the algebraic rank of the state-space, to whatever rank is required for the ambient noise to quench the interspin superluminal signaling capacity that is associated to the non-Hilbert geometry of the state-space.

This expedient is unaesthetic both from an engineering point-of-view and from a philosophical and/or fundamental point-of-view … hence there is a natural connection between dissatisfactions with engineering practice and Joy and Scott’s interests in fundamental physics.

Although a full-text search finds a large set of arXiv preprints that mention “EPR”, “Bell”, and “superluminal” (454 of them at present), it is concerning that this set does not include any of Joy Christian’s works (in which the word “superluminal” is never mentioned). And so is not clear to me that in Joy’s replies to various critics like Florin Moldoveanu (arXiv:1109.0535), these (admittedly difficult) issues associated to superluminal channel capacity are being adequately respected, whether by reference or by analysis.

———————
Summary These issues exist at the intersection of math, physics, engineering, and philosophy. We may optimistically hope for progress, yet realistically, perhaps we should not be too confident of any near-term definitive resolution … if only because communication among these disciplines is so very challenging, and the applications of quantum physics are so very diverse.

We can all hope for discussions are fair, respectful, clear, and correct … and if we fall short in any one of these respects, by far the least important respect (in the long run) is “correct” … because Nature can take care of herself in this regard, but she declines to help us with the first three.   🙂

99. Thomas H Ray Says:

Alex V #97

Yes — orientation entanglement, as one uses for geometric analysis of spinor objects.

100. Alex V Says:

Thomas H Ray #98 – maybe and only problem I could imagine in such a case would be complexity n^2 instead of 2^n, but even that is not obvious

101. Thomas H Ray Says:

Alex V #99 — speaking strictly out of school in my personal opinion, the unique reciprocal relation n^2 = 2^n, where n = 4, has a strong connection to the 16 redundant points (6 of 3 space and 10 of 4 space) of the metric tensor of Minkowski space.

This makes sense to me because the geometric calculus that Joy Christian employs (due to David Hestenes) is fully translatable to Minkowski space. So instead of speaking as we do of increasing degrees of complexity in relation to discrete modeling, we can speak of a self-limiting model where the complexity of a continuous and nondegenerate measurement function increases near the singularity (which exists in every continuous topological function). What we mean by “complexity,” then, stays true to the meaning of local physical dynamics.

102. Joy Christian Says:

Since scepticism about my proposed experiment continues, I would like to quote the following paragraph from an early history of Bell’s theorem. It shows how expectations of even one of the most competent theorist and gifted experimentalist like John Clauser can turn out to be wrong when it comes to the verdicts of Nature.

[Begin quote

It is interesting that among the three quantum dissenters, Clauser and Bell were more optimistic about the possibility of obtaining results violating quantum mechanics than Shimony, and that Clauser was by far the most optimistic among them. Before they met each other, Shimony wrote to Clauser: “Incidentally, I am amazed at your estimate of the probabilities of the possible outcomes of the experiment. I would estimate a million to one in favor of the quantum mechanical correlation function. Needless to say, I hope I am wrong in this.” “Do keep imagining that it will come out against quantum theory; that makes it very interesting!” were words from Horne to Clauser. Shimony kept these memories of Clauser’s hopes, “… he was absolutely convinced that the experiment was going to come out for the local hidden variable theory and against quantum mechanics, and it was going to be an epoch-making experiment.”

end quote]

Let no man but Nature bestow her verdict on herself.

Perform my experiment now and prove me wrong.

I will accept judgement from no man but Nature.

103. Greg Jones Says:

Joy Christian # 102

Here’s an idea: take some of your FQXi money and perform your own damned experiment. Since everybody else accepts Bell, the onus is on you to disprove Bell’s Theorem and not the other way around.

104. John Sidles Says:

Greg, the assertion in #102 that “everybody else accepts Bell” so that “the onus is on you [Joy]” inspired a full-text search of the arXiv for ‘onus Bell quantum’ — which would be a great name for a band! — that happily found a recent analysis by Peter Evans, Huw Price, and K. B. Wharton, titled “New Slant on the EPR-Bell Experiment” (arXiv:1001.5057).

Please let me urge you to consider whether this delightful article (and its 42 references) constitutes a counterexample to the thesis of your post.

105. Joy Christian Says:

Since many participants here are unaware of the long, acrimonious, ugly, and months long conflict between myself and Richard Gill that took place (much of which is documented on several of the FQXi blogs), let me reproduce here our private email correspondence that started it all. Actually, the email correspondence took place after a month long pedagogical session in which Richard Gill came to Oxford to learn about geometric algebra from me. He came to Oxford pretending to be a friend and brought with him a gift of Trojan Horse. Enjoy:

>> On Fri, March 9, 2012 7:15 am, Joy Christian wrote:

>>> Dear Richard,

>>> Thank you for sending me the revised version. As you know, I do

>>> not accept your argument. I am still working on my rebuttal.

>>> Best,

>>> Joy

>> —–Original Message—–

>> From: Richard Gill [mailto:gill@math.leidenuniv.nl]

>> Sent: 09 March 2012 09:29

>> To: Joy Christian

>> Subject: RE: third version

>> PS *please* let me know in advance if there are any annoying errors of

>> terminology; I have done my best to make my terminology precise but it may

>> not correspond to what you are used to. I’d like our discussion to be free

>> of childish quarrels about moronic typos or sophomoric wording which

>> distract from the content. Your one page paper makes all this possible by

>> itself being absolutely precise about the context.

> On Fri, March 9, 2012 10:58 am, Joy Christian wrote:

>> Richard,

>> You have lost the right for this request by carelessly and irresponsibly

>> rushing into print without learning Clifford algebra properly. However,

>> as a fellow academic and a friend I will try to honour your request, as

>> long as it does not hinder my own argument against yours.

>> Best,

>> Joy

> —–Original Message—–

> From: Richard Gill [mailto:gill@math.leidenuniv.nl]

> Sent: 09 March 2012 10:12

> To: Joy Christian

> Subject: RE: third version

> thank you again for your patience!

> I want to learn.

>

106. Joy Christian Says:

@ Jason #68

I am not obliged to provide you anything.

However, I present a one-page summary of my disproof of Bell’s former non-theorem:
http://arxiv.org/abs/1103.1879

I present a link to my book for an extensive description of my local-realistic program
http://www.brownwalker.com/book.php?method=ISBN&book=1599425645

And I present an experimental proposal to test the central thesis of my local-realistic program
http://arxiv.org/abs/0806.3078

Let no man but Nature bestow her verdict on herself.

Perform my experiment now and prove me wrong.

I will accept judgement from no man but Nature.

107. Chris Says:

If it is “Bell’s former non-theorem”, does that make it a theorem again?

108. Chris Says:

Joy’s physical model must not be capable of being simulated by independently running classical computers. So let’s build an exploding-ball-computer (BEBPP, anyone?), or at least ask for money and say we will build one.

If this is your life’s passion and you truly believe in your result, you should try to raise the money to have the experiment conducted yourself. The only way I can imagine someone else going conducting it for you is if you’ve at least somewhat convinced them of the plausibility of your prediction; if you’re going to go that route I suggest working on your people skills a bit. I doubt any serious scientist will be goaded into conducting an experiment that they think is a waste of time.

110. Hal S Says:

Thanks John! The note on practical engineering challenges is interesting.

111. Joy Christian Says:

I can do people skills if you can find me people.

112. Scott Says:

Scott, I happen to know that Joy Christian is a wonderful man. He wouldn’t post the outrageous, hurtful, and deeply ignorant comments appearing under his ‘name’ on this post. Let’s hold off judging him since there is no way to verify the identify of people posting on this blog.

LOL! Let me ask you something: did the same Joy Christian impersonator also insert the outrageous, deeply ignorant comments—completely consistent with the comments that appear here—into Joy’s “research papers”? Was it the impersonator who gave the outrageous, deeply ignorant “Joy Christian” talk that I attended in the Azores in 2009? If so, then I think the “real” Joy really needs to do something about such a nefarious and persistent identity thief… 😀

113. Joy Christian Says:

Scott Aaronson is the deeply ignorant lesser brain here. He thinks that the idiotic paper written by Richard Gill is mathematically sound and not silly.

114. rrtucci Says:

I have important misgivings about the foundation of quantum mechanics FQXi.

What percentage of the FQXi budget goes into funding crackpot leading edge scientific research and what percentage goes to the “managers”?

The evidence seems to be that the “managers” are doing a “lackluster” job

From their website, I see that:

Contact FQXi

Kavita Rajanna
Managing Director

I don’t know, rrtucci. Compare his grants to the budget of a Hollywood movie. The Avengers, for example, was made for $220 million. I would argue that for a mere fraction of that, Dr. Christian provides far more entertainment. 116. Henning Dekant Says: @Richard Gill, you write that nobody will ever perform the experiment proposed by Joy. I find this deeply insulting since we allready have$40 dollar in firmly pledged moneys (by Scott and myself).

We are talking about exploding colorful toy balls preferably in space. It’s almost as awesome as sharks with frikken lasers and <a href=http://www.wired.com/gadgetlab/2012/05/wicked-lasers-shark/that has been done.

117. Henning Dekant Says:

118. Henning Dekant Says:

Since my earlier comment that the link belongs to is in moderation purgatory and broken. Let’s try this again:

@Richard Gill, you write that nobody will ever perform the experiment proposed by Joy.

I find this deeply insulting since we allready have $40 dollar in firmly pledged moneys (by Scott and myself). We are talking about exploding colorful toy balls preferably in space. It’s almost as awesome as sharks with frikken lasers and that has been done: http://www.wired.com/gadgetlab/2012/05/wicked-lasers-shark/ 119. aris Says: BT is entirely sound (inviolable) as a description of what happens here in the macroworld when you conduct experiments with sets of separable objects (determined however you wish … people in a room, a pile of coins or keys, people in a room with some keys thrown in, Venn diagrams etc.). It’s a beautiful, pristine statement of classical logic which also defines the (or, at least, defines a) fundamental ontology of the macroworld. All you need to do is state three yes/no variables applicable to your set of separable objects. Then set up your truth table and follow the inequality. Under those conditions BT’s never violated. Along with everything else Bell came up with something brand-new: a statement of experimental logic, readily testable. He demonstrated that the logical and the physical are one. BT is inapplicable when, quoting Nick Herbert, “In a truly non-causal world, Bell’s Theorem cannot be formulated because in such a world elemental events are not stable enough for Bell-type non-locality to even be defined.” Of course we wouldn’t even know how to conduct an experiment in such a world. In what other kind of world would BT be comparably meaningless? Well, in ours, that platform we’re required to operate from, according to Joy Christian. 120. Raoul Ohio Says: I am a bit confused. Does “I will accept judgement from no man but Nature.” imply that Nature is a man? That seem incompatible with the usual title of “Mother Nature”. 121. Raoul Ohio Says: Re #112: BTW, any stupid things posted by “Raoul Ohio” were actually posted by an imposter. All the clever things were from the real Raoul Ohio. 122. Joy Christian Says: @Raoul Ohio #120 I would accept judgment from a woman any day over a judgment from a man. In the end you all will have to accept the judgment of Nature whether she is a mere man or a woman, and whether you are a mere computer geek or a gifted physicist. 123. Richard Gill Says: @Vadim: Joy’s experiment generates outcomes +/-1 of *both* A *and* A’ on one “particle”, and of *both* B *and* B’ on the other. N times four binary outcomes. The averages of AB, AB’, A’B, and A’B’ will satisfy CHSH, whatever they are. Strangely, Joy did not realize this in advance, and does not admit it now. He can be a nice guy, he certainly has the gift of the gab, but what he writes is nonsense. @John Sidles: as far as I can see, the paper you mention uses the coincidence loophole to generate singlet correlations. The times of detections are determined by the particles. The experimenter decides that two events belong to the same pair of particles if the difference between the two detection times lies in a specified “coincidence window”. Unpaired events are rejected. This is the same trick used by de Raedt et al. to engineer event by event, local realist, simulation models which reproduce the statistics of famous experiments. You let particle A and B agree at the source how they want to be measured and what outcomes they will then exhibit. If particle A arrives at its detector and sees the “wrong” setting, it lets itself to be measured faster, with an earlier measurement time than on average. The other one does the opposite: its measurement time is later when it doesn’t like the setting it sees. This way, the pairs which finally get selected by the experimenter are a biased sample from all pairs. They are biased to amplify their correlation in the desired direction, depending on the pair of settings. The “coincidence loophole” was named by Jan-Ake Larsson and myself in a 2004 paper in Europhysics Letters, http://arxiv.org/abs/quant-ph/0312035 We show that it is a more serious loophole than the detection loophole, and more relevant to real experiments. Most “refutations of Bell” either depend on exploiting the detection or the coincidence loophole, or are built around elaborately concealed simple errors. Joy’s model is also built around a silly little error. But the “idea” in it is nutty, too. The actual outcomes predicted by his model are perfectly anti-correlated, whatever the measurement settings. To get the singlet correlations, Joy divides by two theoretical standard deviations (quaternionic roots of -1, each determined by the corresponding setting). Unfortunately he gets the signs mixed up while doing the calculation. It’s gorgeous nonsense. I wondered for a time whether the whole thing was not a deliberate hoax, as in the famous Sokal article about post-modern hermeneutic quantum gravity. Unfortunately, sad to say, it seems that Joy is sincere. 124. Joy Christian Says: Richard Gill is evidently an incompetent mathematician. He is clueless about many things. One only needs to read his abstract to recognize this fact. This was confirmed by no other than the famous and gifted Joseph Doob, who thought that Gill was a third-rater. This fact is now well known among many of my colleagues. Gill’s critique of my one-page paper is a documented evidence of his idiocy. Just read my reply to him, http://arxiv.org/abs/1203.2529, and see for yourself. The guy hasn’t a clue what he is talking about. Let alone my model, the guy has absolutely no understanding of geometric algebra, or even the underlying assumptions of Bell’s theorem. He is a third-rater through and through. All his arguments against my model have been systematically debunked, not only by me but many other people on several of the FQXi blogs. 125. Alex V Says: Thomas H Ray #101 I am not sure, I guess what do you mean, but the relation is not unique, because valid also for n=2. 126. Alex 'qubeat' Says: Oh sorry, I should change the nick – user Alex V no longer exists already few hours after his profile has gone with whole theoreticalphysics.SE 127. Richard Gill Says: I think Joy’s vitriolic and hysterical hatred shows that I hit some sore points. Yes, for a good laugh, you could amuse yourself reading Joy’s reply to my note. Turning a bug into a feature, he now claims that the mistake in the chain of inequalities going from (5) to (7) in his one page paper was actually the introduction of a daring new postulate. Daring indeed, to make use, in the middle of a tricky computation, of a completely new postulate, without any announcement thereof in the whole paper. Especially daring to introduce a new postulate which contradicts those apparently made early. But incredibly daring to build a whole theory on a new set of postulates which are mutually inconsistent! In the version of the theory in Christian’s one page paper, the key calculation was wrong. (And the axioms were stupid, but that’s another matter). In the revised version the calculation is correct, but the model is empty. Its axioms are inconsistent. The whole theory has now vanished in a puff of smoke. I’m grateful to Joy for pointing out to me his one page paper a few months ago, and for giving me a nice introduction to Clifford algebra during a pleasant meeting in Oxford, and for pointing out to me an error which I made when I first calculated his E(a,b) using an easier route. I had actually got *his* answer, so I was pleased that the calculations did not need to go such a roundabout way. But I had made an obvious mistake! And J.C. himself pointed it out to me! The point was, the mistake had to be made in the middle of the more difficult route, so that nobody would notice it. Weird science. 128. Alex V Says: Thomas H Ray #101 Indeed I should write 4^n – it is dimension of unitary group acting on n qunits. n^2 is relevant with widely known case of non-universaliry in quantum information science, then instead of whole group we have subgroup isomorphic to Spin(2n). 129. Thomas H Ray Says: Richard Gill #122, “It’s gorgeous nonsense. I wondered for a time whether the whole thing was not a deliberate hoax …” Many who miss the point of mathematical completeness in string theory call that gorgeous nonsense, too. Unless they have no love of mathematics, in which case it’s just nonsense. The strength of Joy’s framework, however, is the same feature that powers interest in SUSY string theory as a fundamental theory of nature. That is, its ability to retrodict what we already know about how nature behaves, in a way that preserves 1 to 1 correspondence of mathematical theory to physical result. Although Joy’s research has not attained the status of scientific theory (and neither, in fact, has string theory despite the name historically given to it), Joy’s framework has the additional advantage of experimental falsifiability. As far as the funding question goes, I’m a bit taken aback by the brazen display of petty jealousy on this blog and others–from those who fail to realize that FQXi was founded for the specific purpose of funding projects that are unlikely to receive support from traditional sources. 130. John Sidles Says: Richard Gill, as it happens, I agree with you (and with Scott) about very many things: • quantum mechanics on Hilbert spaces — we can call it QM-H — is provably separable and causal, yet non-local, and • all experiments done to date respect the predictions of QM-H and moreover “no one knows how to change QM-H by a small amount without wrecking it altogether” (in Tony Zee’s lovely phrase), and • although engineers commonly (and successfully) alter QM-H by a large amount (namely, by pullback methods), these methods unaesthetically introduce an adjustable parameter (namely, the state-manifold rank) that has no evident grounding in fundamental physical theory, and • Joy Christian’s alternative QM-nonH theory contains multiple elements that are unclearly explained, many of which are regarded by most folks (including me) as being just plain wrong. E.g., some folks assert that Joy’s works contain arithmetic errors, others note that the mathematical reasoning contains inconsistencies, still others (including me) regard Joy’s definition of “correlation” as differing substantially and unphysically from Bell’s definition. Logically speaking, it is quite possible that all of the preceding elements are present in Joy’s work, and yet it is arguable that none of these elements are the most important aspect of the present discussion, for the reason that I posted above (#98): We can all hope for discussions that are fair, respectful, clear, and correct … and if we fall short in any one of these respects, by far the least important respect (in the long run) is “correct” … because Nature can take care of herself in this regard, but she declines to help us with the first three. A justly celebrated cartoon that reminds us of the proper ordering of our priorities is xkcd’s Duty Calls, popularly known as “Someone is wrong on the internet.” Whenever “Someone is wrong on the arXiv server”, that’s a particularly good time for us all to scrupulously respect STEM traditions of fairness, respect, and clarity. Not necessarily for any moral reason, but for the pragmatic reason that the STEM enterprise can’t work any other way. 131. Calgon Says: Presumably he recognizes the University of Southern California’s Information Sciences Institute? If so I think he owes you$200K, as they have an actual, working quantum computer that dozens of people are using now.

132. Henning Dekant Says:

@Thomas H Ray, so in the spirit of getting Joy’s experiment performed how much are you willing to pledge?

So far we have $40 in the jar. 133. Henning Dekant Says: @Wouter van Doorn, very insightful link. 134. Thomas H Ray Says: Alex V #125 Yes, I should have said the least square integrable value, which rules out sqrt 2, for n = 2. What I’m getting at, is that the arithmetic limit 4 is identical to the equation degree limit (Abel-Ruffini theorem) for solving polynomial equations by methods of rational arithmetic and extraction of roots. Why does it matter? Consider the smallest NX4 array squared has a square root of 4. This is the least square integrable term > 1. Joy’s bound of 2(sqrt2) = sqrt8, which I find significant in other ways than those he used to arrive at the term: The integer 8 happens to be one unit less than the second least square integrable term. This suggests to me that there is more to the summation of terms on a simply connected compact surface than one finds by averaging terms on a one dimension interval oriented in the plane. For this reason: It’s a theorem of arithmetic that a point external to a set of points can approach any point of the set simultaneously, provided that the point is far enough away. (You can find this discussed in the introduction to Rozsa Peter’s classic book, Playing with Infinity.) From there, it’s easy to prove that a point at infinity such as that which differentiates R^3 from S^3, maps to the entire set of points in R^3. In other words, the distance of one point to another is finite, except one. So when we speak of a dynamic physical system finite in space and unbounded in time, every time interval except one is identical to every other (as Leslie Lamport shows by Buridan’s Principle: every measure function continuous from an initial condition in a bounded length of time contains a singularity of uncertain position). Quantum mechanical descriptions of reality lack the feature of the point at infinity (thus the need for renormalization to restore the N – 1 physical measure result). Continuous function models based on Minkowski space or other tensor metric techniques prescribe arbitrary boundary conditions. So I think that mathematical methods that combine the best of algebraic and continuous function techniques (particularly Hestenes’ spacetime algebra) are the best bet for mathematical completeness of a physical theory. 135. Thomas H Ray Says: Richard Gill #127 If you understood E (a,b) = -a.b as the input argument to a measurement function continuous from the initial condition, you wouldn’t make bonehead claims. 136. David Brown Says: I am confused. Is Joy Christian claiming that his mathematical method can take 4-dimensional spacetime and a 7-sphere of information and deterministically simulate quantum field theory? 137. Raoul Ohio Says: I knew not squat of FQXi, so I took a quick glance at their home page. I quote (copy and paste, actually) the first two lines I read: “To expand the purview of scientific inquiry to include scientific disciplines fundamental to a deep understanding of reality, but which are currently largely unsupported by conventional ” When I am reading fast, I have a bad habit of guessing words to complete sentences, and my internal reading system added a third line “evidence”. This caused a “WTF? exception” to be thrown a few seconds later, and I returned to the page and found that the third line is actually “grant sources”. Too bad, they might have missed their calling. 138. James Putnam Says: #131, Quoting Tom: “If you understood E (a,b) = -a.b as the input argument to a measurement function continuous from the initial condition, you wouldn’t make bonehead claims.” Scott Aaronson, is there a response to this please? James 139. Thomas H Ray Says: Raoul Ohio # 133 ” … my internal reading system added a third line “evidence”.” Your internal reading system is deficient in the knowledge that scientific judgments are made not on evidence, but on measured correspondence between mathematical theory and physical result. That’s the difference between the inductive logic of philosophy and the closed logical judgments of a scientific theory. 140. Joy Christian Says: For those of you who are unaware of the history of Richard Gill’s desperate attempts to find an error in my work only need to consult some of the blogs on FQXi. When all his attempts to find an error failed, he transformed himself into a bad cop. What the cop desperately wanted was to find a smoking gun. The boss had put fire under his you-know-what: “Where on earth is that gun? Where the hell has he hidden the damned thing?” But, alas, there was no gun to be found. So the bad cop did what all bad cops do: “Just plant the bloody thing and be done with it. We know the guy is guilty, so let him rot in the cell. Why do we care? The boss will be please anywise.” So that is what Richard Gill has been up to. He has been manufacturing errors and planting them on me. When his first attempt was exposed, not only by me but several other people on the FQXi blogs, he manufactured a different error and tried to plant that one on me. When that one was exposed, he manufactured another one, and so on. This has been going on for over three months. Just check out some FQXi blogs to see for yourself. Either the guy is a total maniac or a total idiot. No one needs to spend these many months of posting comments every single day on a one-page paper he or she thinks is wrong. As I said, the guy is either a total maniac or a total idiot. I go for the latter choice… 141. Alex V Says: Thomas H Ray #134 Thank you for expressing your point, but it is not about things I sayd. Roughly speaking, I am talking that if his model reproduces all results of QM and we know, that at least for 4-5 qubits quantum computer could be built, then how his model can prove impossibility of quantum computer 142. Joy Christian Says: @John Sidles #133 “Joy Christian’s alternative QM-nonH theory contains multiple elements that are unclearly explained, many of which are regarded by most folks (including me) as being just plain wrong.” John Sidles you are plain wrong, and you shall realize that in time. To expedite your enlightenment I suggest you first invest in John Bell’s two famous papers, and then to complete your enlightenment invest in my book: http://www.brownwalker.com/book.php?method=ISBN&book=1599425645 Nirvana awaits you. 143. Thomas H Ray Says: Richard #127 I dug up my email response to you from a couple of weeks ago: “Richard, the critical difference is whether the average — i.e., the time aggregated — results as represented in your table differs from the prediction of what the result would have been as N approaches infinity. I have been trying to get across to you the importance of Lamport’s discovery, that the singularity of uncertain position (“is the value greater or less than y”) in every measurement function continuous from an initial condition makes it impossible to decide the result of any measurement in a bounded length of time by probability (in this case coin toss, on the assumption of equally likely outcomes). The input argument of Joy’s function is – a.b. The measurement function continuous from that argument (initial condition) is angle preserving to infinity.” Where do you find that explanation lacking? Tom 144. Thomas H Ray Says: Alex V #141 Yes, I know it isn’t about what you said. I’m not convinced that Joy’s model disproves the possibility of quantum computing. I do know, however, that it disproves the possibility of modeling complete physical results by any machine language method, because no such method — quantum or classical — includes the point at infinity. What I’m getting at is the difference between a static solution programmed to arbitrary accuracy, and one that substitutes a dynamic solution based on random variables. 145. Ben Lund Says: Scott – I think you are not entirely correct that Joy denies entanglement – instead, he has devised a method of entangling classical computers! Bell’s inequality is fundamentally a statement about classical, not quantum, mechanics, and Joy’s proposed experiment is strictly classical, so it is not conceivable that his claims are strictly quantum. Imagine, for a moment, that we have two classical databases, such that projecting the state of one database onto some basis affects measurements made on the other. Since we can monitor the entire classical state of the database, this could easily be used for superluminal communication, and that’s just a start! Exploding balls in space may seem like a complicated way of preparing classical computers, but once we understand the phenomenon of entangled classical states better, I’m sure simpler methods of entangling computers will be devised. 146. David Brown Says: Joy Christian #141: In Bell test experiments the term “quantum correlation” has come to mean the expectation value of the product of the outcomes on the two sides. In other words, the expected change in physical characteristics as one quantum system passes through an interaction site. http://en.wikipedia.org/wiki/Quantum_correlation I think that quantum theorists use the term “quantum correlation” according to what Scott Aaronson says and not what you say. I think that in your Theorema Egregium you should replace “quantum mechanical correlation” by “quantum mechanical Christian-correlation” and replace “classical local-realistic correlation” by “non-local, objective Christian-correlation”. Do you understand my point? I think that I might be able to use your Theorema Egregium to create a Christian-Brown quantum theory of gravity. Do you understand what I mean? 147. David Brown Says: Joy Christian #141: Can the Bell/CHSH inequality be violated in purely classical terms? Prof. Aaronson says that the answer is NO! AARONSON IS CORRECT!!! — OR WE CAN BUILD SPACESHIPS THAT TRAVEL FASTER THAN THE SPEED OF LIGHT! To deny the validity of Bell’s Theorem is like Kary Mullis saying that HIV does not cause AIDS. 148. Thomas H Ray Says: Henning Dekant #132 You’ve certainly got my$20 pledge. Realistically, I predict a huge ROI for whoever does actually fund the experiment.

149. Bram Cohen Says:

After watching some footage of Joy Christian, I have to wonder if FQXi wouldn’t take him seriously if he didn’t look like a guru and instead looked like an aging geek.

Given how successful Joy Christian has been at demonstrating a classical exception to CHSH, he should also try to find counterexamples to Fermat’s Last Theorem and the Four Color Theorem. I’m sure those would be taken just as seriously.

150. Henning Dekant Says:

@David Brown #147: In defense of Joy Christian: Saying that HIV does not cause AIDS is worse than denying the Bell Theorem. Although it generally falls into the same class of stupid.

My baseline assumption is that there will be no increase in the death rate due to unsafe sex as a result of Joy Christian’s papers. Fortunately he just male-practices math.

Regardless, I want the exploding toy balls experiment.

151. John Sidles Says:

As a web search shows, numerous students and researchers have attempted to computationally simulate your theory. To date, all such simulation attempts have ended in confirming the correctness of Bell’s Theorem, and many simulation authors express frustration with the imprecision of your exposition.

In text-searching your recent book for a discussion of “simulation” (for which, thank you Google), we find the following illuminating passage (Section 9.7):

In my view the whole fashion of simulating EPR experiments on a computer is completely wrong headed. … a simply-connected model such as mine cannot possibly be proved or disproved by its numerical simulation.

For us engineers, this assertion is sobering, since any theory whose predictions cannot be computationally simulated even in principle, is (for engineers) not a physical theory at all.

In this regard Donald Knuth has written a beautiful essay, which appears as the introduction to a beautiful book of mathematics by Petkovsek, Wilf and Zeilberger titled A=B, that includes this celebrated passage:

“Science is what we understand well enough to explain to a computer. Art is everything else we do.”

Thus did Nirvana arrive as following revelation: John Bell’s works are science, whereas your works are art … albeit highly mathematical art … at least until such future time as your ideas mature to a form that (1) is explicitly amenable to computational simulation, and (2) can be communicated with clarity to students who successfully code those simulations.

Of course, we engineers apply Knuth’s principle backwards: whenever our computer simulations work unexpectedly well, we set to wondering whether some science may have accidentally crept into them. 🙂

152. David Brown Says:

Joy Christian #141 & John Sidles #152: I think that Christian’s Theorema Egregium (when properly formulated) might be a work of genius if it is mathematically correct. Do the 2 papers “What Really Sets the Upper Bound on Quantum Correlations?” and “On the Origins of Quantum Correlations” contain the gist of the basic ideas? If nature is finite and digital, then I need to define a Nambu transfer machine that simulates quantum field theory. My advice to Joy Christian is:
(1) Avoid invective and ad hominem attacks.
(2) Consult with quantum computing experts to understand how to properly formulate the Theorema Egregium.

153. Joy Christian Says:

@John Sidles #156

I am not a computer engineer. I am a physicist, interested in foundations of physics. In my view the whole issue of computer simulation of the EPR-Bohm correlation is misguided. It has nothing to do with Bell’s theorem or the argument of EPR. Bell’s theorem is not about what you can or cannot simulate on a computer. It is about the nature of physical reality. It is about whether or not Einstein’s conception of local reality is viable in physics. That is the question I am interested in. I am interested in this question because I do not believe we can succeed in constructing a theory of quantum gravity without addressing this question. I am interested in this question because nonlocal gravity is an oxymoron. You have to be a physicist to appreciate this.

What you seem to have achieved is a ghost of nirvana. May the real force be with you soon.

154. Mitchell Porter Says:

By now there is no point in debating whether Christian has “disproved Bell’s theorem” – we all agree that he hasn’t. What I would like to know is whether his construction is of interest as the prototype of a new form of nonlocal hidden variables theory. Can it be scaled up to describe the real world of fermions and fields, or is there an obvious barrier to this?

155. Thomas H Ray Says:

David Brown #152

“Consult with quantum computing experts to understand how to properly formulate the Theorema Egregium.”

And consult with a plumber to understand how to do your heart surgery.

156. John Sidles Says:

It is instructive that, for many decades, tests of quantum mechanics and general relativity have always compared experimental data-sets against high-precision computational simulations. That is why it is concerning to encounter a class of theories, purporting to link quantum dynamics to gravitational dynamics, that holds forth no hope, even in principle, of such computational simulations.

Two precedents for such a situation come to mind — both partial. One is Scott Aaronson and Alex Arkhipov’s The Computational Complexity of Linear Optics (arXiv:1011.3245), which describes a class of experiments whose computational simulation is feasible … but not with (classical) resources in P. In my personal opinion, this conception is outstandingly creative, and its analysis in arXiv:1011.3245 is a model of clarity … and most important of all, its predictions are (inefficiently) testable.

The other “untestable” precedent is humorous: Grothendieck primes. 🙂

A little more seriously, to my knowledge there has never been any scientific theory that cannot be computationally simulated, and it is arguable that any theoretical construct having this property, however attractive philosophically and/or mathematically, is not experimentally testable, and therefore is not a physical theory.

157. David Brown Says:

According to Richard Gill, comment #29, “The affair is sociologically and psychologically interesting. But that’s all.” If you want to deterministically simulate quantum entanglement in an approximately empirically valid way, then you must come to grips with SU(3) X SU(2) X U(1) physics and with quantum Markov branching in some manner. I see no evidence that Christian has done this so I’m afraid I must agree with Gill.

158. Joy Christian Says:

@Thomas H Ray #160

“And consult with a plumber to understand how to do your heart surgery.”

Absolutely brilliant! The naysayers and computer engineers in this forum trying to do dabble into fundamental physics are no better than plumbers trying to do heart surgery.
None, including Gill, has any understanding of Bell’s theorem, let alone the subtleties of the EPR argument it must comply with. In his own words Bell insisted that it is not possible to find local functions of the form

A (a, L) = +1 or – 1

and

B(b, L) = +1 or − 1

which can give the correlation of the form

= – a ・ b,

where L is a common cause and the measurement context b has no effect on what happens, A , in a remote region, and likewise the measurement context a has no effect on what happens, B. “This is the theorem”, he insisted.

But one does not have to be Einstein and one does not have to understand the mathematics of more than my one-page paper to see that I have accomplished exactly what Bell claimed to be impossible. The plumbers in this forum are not able to appreciate this because they haven’t got a clue what the Bell’s theorem (and especially the EPR argument) was all about.

159. Bram Cohen Says:

John Sidles #156: The linear optics paper isn’t the first proposed test of quantum computation, it was preceded by Shor’s algorithm, which was preceded by some other much less dramatic and much more artificial results. But the linear optics paper proposes an experiment which is both much more plausible and much more dramatic in its time reduction than Shor’s algorithm, and as such should be viewed as an important theoretical result. Noone’s managed to perform the experiment yet though, so whether the result will actually bear out the quantum mechanical predictions or demonstrate some unforeseen inaccuracy in quantum mechanical theory is unclear. Of course, it might be hard to differentiate between an error in the theory and a physical problem with the experimental apparatus. Not everyone has the same prediction as to how this will eventually play out, Aaronson is on the extreme edge of confidence that QM will hold up when and if the experiment manages to be done.

This stands in stark contrast to the Bell inequality, where the experiment has been done, the math is straightforward and well understood, and everyone who isn’t a crank accepts what is going on. Christian’s position is basically like claiming to have a solution to A^3+B^C=C^3 in the positive integers and then getting irate that people don’t repeatedly find the errors in his calculations just because they have one of those fancy-schmancy ivory tower elitist ‘proofs’ that there can’t be any such thing.

160. David Brown Says:

Joy Christian #160: Can you explain your ideas in a manner comprehensible to string theorists? Are you claiming that your Theorema Egregium is a misunderstood work of genius? Are you replacing two quantum states by two Christian SU(8) states?

161. Richard Gill Says:

@Tom #143. You asked ““Richard, the critical difference is whether the average — i.e., the time aggregated — results as represented in your table differs from the prediction of what the result would have been as N approaches infinity. I have been trying to get across to you the importance of Lamport’s discovery, that the singularity of uncertain position (“is the value greater or less than y”) in every measurement function continuous from an initial condition makes it impossible to decide the result of any measurement in a bounded length of time by probability (in this case coin toss, on the assumption of equally likely outcomes).

The input argument of Joy’s function is – a.b. The measurement function continuous from that argument (initial condition) is angle preserving to infinity.”

Where do you find that explanation lacking?”

That is not an explanation. We were not discussing the “input” to Joy’s function. We were discussing the experimental measurement outcomes +/-1 arranged in an Nx4 array, eg in an Excel file, in the computer of the experimentalist who has performed Joy’s experiment in the hope of getting a Nobel prize. The four correlations computed from those numbers will satisfy all the CHSH inequalities.

BTW I’ll contribute $20 too. 162. John Sidles Says: Bram, your post makes many good points. One of the nice things about this discussion is the many opportunities it affords to quote aphorisms, and your post reminded me of Henry George Forder’s “Logical investigations, besides being of interest in themselves, often point the way to extensions of knowledge previously unthought of. It was from such investigations that the classical non-Euclidean Geometries arose, and they freed the mind from its age-long bondage to the obvious, and made possible the bolder conceptions of space reached in our day. The virtue of a logical proof is not that it compels belief but that it suggests doubts.” Thus (for me and many) the chief merit of quantum computing research of the past 20 years is its proofs, which by their remarkable number and strength have helped focus our doubts upon physical hypotheses that otherwise we might not have been inspired to doubt, which helps greatly to “free us from our age-long bondage to the obvious.” And in this respect proofs that are incorrect — but ingeniously so — can be similarly helpful as rigorous proofs. This is a healthy situation overall … provided that we are scrupulous in sustaining the primary academic virtues of fairness, respect, and clarity, so that we don’t get too upset just because (in the happy phrase of xkcd) “someone is *wrong* on the arXiv server.” 163. David Brown Says: Mitchell Porter #155: I think perhaps Christian is using teleparallel gravitational equations to simulate quantum field theory. Consider s(1) X(1) + … + s(N) X(N), where each s(j) belongs to the the 7-sphere, each X(j) is a point in an alternate universe, and means tensor product. If each s(j) represents, in terms of energy-density, a 3-dimensional linear momentum, a 3-dimensional angular momentum, and a 1 dimensional quantum spin, then non-local, objective variables might describe the time evolution of dynamics in each alternate universe. The smoothing of what I call the Nambu transfer machine might be described by Christian’s scheme or some modification of the scheme. 164. Thomas H Ray Says: Bram Cohen #159 ” … just because they have one of those fancy-schmancy ivory tower elitist ‘proofs’ that there can’t be any such thing.” The main problem with Bell’s theorem is that it rests on the flimsiest of proofs — double negation — which is nothing more than proving what what assumed in the first place. Joy’s framework is constructive. If one wants to do science by induction, we can burn all our texts of the last 500 years and go back to Aristotle. 165. Hal S Says: Sidney Coleman I think still had the best understanding of this matter. Quantum Mechanics In Your Face http://media.physics.harvard.edu/video/?id=SidneyColeman_QMIYF 166. David Brown Says: I think that both Joy Christian and Thomas H. Ray do not understand what the rest of us mean by the term “quantum correlation”. However, I think that the following MIGHT be a work of genius: Christian’s Theorema Egregium (with correct terminology): Every quantum Christian SU(8) correlation among a set of measurement results can be understood as an objective Christian SU(8) correlation among a set of points of a parallelizable 7-sphere. 167. Joy Christian Says: I repeat: The plumbers in this forum are not able to appreciate my work because they haven’t a clue what the so-called Bell’s theorem — or the EPR argument on which it was based — was all about. I bet most of them have never read the original EPR paper, or even Bell’s first two important papers on the subject. 168. Richard Gill Says: Bram Cohen #159: everyone who actually checks Joy’s maths finds serious but elementary math. Thomas Ray #164: there’s no double negation in proving Bell’s theorem. Suppose in a CHSH style experiment, we believe that the unmeasured variables also possess values, independently of which of the directions we choose to measure in each run. Suppose our choices are made by independent fair coin tosses, for every run, anew. Per run there therefore exist A, A’, B, B’ with values +/-1; we get to observe A or A’, and B or B’, independently and each with probability 1/4. In each of the N runs AB+AB’+A’B-A’B’ 169. Richard Gill Says: (continued) In each of the N runs, AB+AB’+A’B-A’B’=A(B+B’)+A'(B-B’)=+/-2, as a little thought will convince you. So the average over the N runs of this quantity lies between -2 and +2. But that equals ave(AB)+ave(AB’)+ave(A’B)-ave(A’B’). Now the experimenter doesn’t get to see ave(AB), the average of the product of A and B over all N runs. She gets to see the average of the product of A and B over a random sample of about one quarter of the runs; the sample taken independently of the 4N actual measurement outcomes. Hence by some simple probability theory, well within the grasp of a third-rate mathematician or physicist, the observed average over the approximately N/4 runs in which A and B is measured, is very close to the average over all N. (within epsilon with probability exponentially close to 1). So in the long run, ave(AB)+ave(AB’)+ave(A’B)-ave(A’B’), where “ave” now refers to the long run experimentally observed average, also lies between -2 and +2. No double negations here. All assumptions explicitly spelt out. No mathematics beyond high school level. Joy Christian disagreed with Bell’s assumptions, not Bell’s proof. Joy redefines “local”, “realistic”, and “correlation” in ways which I think stupid, but everyone can make their own choice … and even then, he still can’t get a simple Clifford algebra calculation right. And he’s known this (or at least been told it, by the best experts) for four years already. In the meantime he goes on accepting FQXi grants to write his book. You can find the fatal error in his mathematics in the first 20 pages of the book -the bit you can download for free. He writes nice poetry, and knows all politicians’ cheap debating tricks, but that’s all. 170. Richard Gill Says: [sorry for typos in #166: first sentence: serious but elementary math errors. Last completed sentence: each with probability 1/2.] 171. Joy Christian Says: Since Gill continues to go on and on about his silly and discredited argument, let me point out once again that CHSH inequality is a figment of imagination, a result of an unjustified rigging, refuted by actual experimental observations, and discredited in my book and papers as born out of topological ignorance of John Bell. Equation (16) of my experimental paper describes exactly how the expectation values E(a, b), E(a’, b), E(a, b’), and E(a’, b’) are to be computed in my proposed experiment. Four separate sums are to be calculated as follows E(a, b) = 1/N Sum_j A_j B_j , E(a, b’) = 1/N Sum_j A_j B’_j , E(a’, b) = 1/N Sum_j A’_j B_j , and E(a’, b’) = 1/N Sum_j A’_j B’_j . It is a matter of indifference whether N here is chosen to be the same or different for each of the four alternatives. My model then unambiguously predicts that the observed correlations will be E(a, b) = -cos(a, b), E(a, b’) = -cos(a, b’), E(a’, b) = -cos(a’, b), and E(a’, b’) = -cos(a’, b’). Moreover, my model predicts that these correlations will give rise to violations of the Bell-CHSH inequality of the form | E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) | less or equal to 2 x sqrt{ 1 – (a × a’).(b’ × b) } The predictions of my model are unambiguous. The experimental procedure described in my paper is unambiguous. One does not have to be Einstein to understand my argument. All one has to do is to read a few pages of a few of my papers. 172. James Putnam Says: Scott Aaronson, What do you think about Tom Ray’s #143 and Richard Gill’s response #161? James 173. Thomas H Ray Says: Richard Gill #161, “We were not discussing the “input” to Joy’s function. We were discussing the experimental measurement outcomes +/-1 arranged in an Nx4 array, eg in an Excel file, in the computer of the experimentalist who has performed Joy’s experiment in the hope of getting a Nobel prize. The four correlations computed from those numbers will satisfy all the CHSH inequalities. ” Sorry, Richard, one CANNOT speak of Joy’s model without speaking of a continuous range of input values. Let me try to put it yet one more way: Chaitin’s omega exists on a 1 dimension line and yet is not algorithmically compressible, because the output depends on the machine language in which the program was written. One never knows whether the last binary digit of the number is 0 or 1. That’s a clear example of the limitation of digital computing to deal with models whose output is continuous from the initial input condition. If we assume probabilistic measure criteria from the beginning, it should be no surprise to get the P = 1/2 result. Tom 174. Joy Christian Says: It should be noted ALL of Richard Gill’s fallacious arguments against my model have been repeatedly debunked, not only by me but also by several other people on several of the FQXi blogs. He is evidently an incompetent mathematician. He is clueless about many things. One only needs to read his abstract to recognize this fact. This was confirmed by no other than the famous Joseph Doob, who thought that Gill was a third-rater. This fact is now well known among many of my colleagues. Gill’s critique of my one-page paper is a documented evidence of his stupidity and ignorance. Just read my reply to him, http://arxiv.org/abs/1203.2529, and see for yourself. The guy hasn’t a clue what he is talking about. Let alone my model, the guy has absolutely no understanding of geometric algebra, or even the underlying assumptions of Bell’s theorem. He is a third-rater through and through. 175. John Sidles Says: Hal S #165, the Sidney Coleman lecture you provided is an outstandingly witty and self-evidently cogent contribution to this discussion. To balance it, please let me contribute two stupifyingly mundane links: • the Wikipedia page “Cross-correlation“, • the discussion of “measuring cross correlation” in the manuals for the Agilent/HP Dynamic Signal Analyzers, and/or the SRS model 785 Dynamic Signal Analyzers (a Google search finds them on-line). How do these mundane discussions tell us “where to concentrate our doubts” (in Morris Klein’s phrase)? The first respect has to do with the two incompatible definitions of cross-correlation given on the Wikipedia page (1) linear, versus (2) normalized. Already this helps us, because the former definition is used by John Bell’s articles, and by the HP-3562A and SR-785 signal analyzers, and by all Bell-testing experiments (known to me). Whereas the latter definition, that Wikipedia calls “normalized cross-correlation”, is used in Joy Christian’s articles (see, e.g., the normalizing denominator of eq. 5 of arXiv:1103.1879) … and so, this definitional difference in itself suffices to decouple Joy’s framework from John Bell’s theorem and from the experimental quantum literature. Deeper questions arise when we consider that these mundane off-the-shelf HP and SRS signal analyzers, together with the photon-emitting and photon-absorbing diodes to which they are coupled, concretely accomplish the mysterious process that Sidney Coleman’s lecture calls “observation” (starting at around 8:45 or so). By what dynamical processes do they accomplish this, we wonder? What focuses our 21st century doubts in new directions, is the experimental difficulties that we encounter when we attempt to couple photon sources and photon sinks to these correlation meters, and simultaneously attempt to achieve near-unit efficiency in the photon sources and photon sinks. In contrast to 21st century experiments, in the Bell-type experiments of the 20th century (and in Hanbury-Brown and Twiss experiments, etc.) there was no serious attempt to achieve high efficiency and/or strong coupling of sources and sinks; indeed 20th century physics quantum optics experiments are prolifigately wasteful of photons. Nowadays, as we try harder and harder to realize high-efficiency quantum experiments (in GHZ photon experiments for example), we find that Nature fights back harder-and-harder, such that the quantum computers whose advent that we foresaw so confidently back in the 1990s, today seem technologically little closer than they did a decade ago. We wonder, why is this? Perhaps there is room for Tony Zee to be right, in suspecting (as quoted in #20) “we will will have to abandon strict locality” … if only because the quantum dynamics of the currents in high-efficiency photon source at point A is necessarily perfectly coupled (via Maxwell’s equations) to the quantum dynamics of the currents of high-efficiency photon sink at point B. In any case, the experimental methods and devices that we understood completely (for all practical purposes) in the low-efficiency quantum experiments of the 20th century, now are far less perfectly understood (and immensely harder to design and operate) in the high-efficiency quantum experiments of the 21st century. A very great contribution to physics pedagogy (it seems to me) would be an updated version of the Feynman lectures, in which the high-decoherence experiments and instruments of the original lectures (e.g., two-slit experiments) are replaced by low-decoherence cavity QED experiments … with source, sink, renormalization, and thermalization effects all treated with reasonable rigor. It is arguable that we are similarly far from conceiving such 21st century Feynman Lectures, as we are from constructing practical quantum computers — and perhaps our pedagogic incapacity to accomplish the former, is correlated to the practical difficulties that we encounter with regard to the latter. 176. Thomas H Ray Says: David Brown # 166, “I think that both Joy Christian and Thomas H. Ray do not understand what the rest of us mean by the term ‘quantum correlation’.” The rest of you assume quantum entanglement as a quasi physical law. It turns out, however, that one cannot support that assumption in a mathematically complete way. That’s what Joy’s program is all about — demonstrating that a constructive, mathematically complete framework obviates the assumption of quantum entanglement, and recovers quantum correlations as results of a measurement function continuous from the initial condition. A simple way to put it is — as in Einstein’s theory — the experiment drives the conclusion, rather than the conclusion driving the experiment. Quantum theory has made no strong foundational assumptions since Young’s 1803 two-slit experiment. 177. Bram Cohen Says: Richard Gill #168: Yes of course there are elementary math errors. There *have* to be elementary math errors. I think it’s extremely generous of you to go through the actual effort of finding the errors and trying to explain them, sort of like taking a proposed counterexample to fermat’s last theorem which is hard to check because the numbers are so huge and going ‘look – this isn’t a solution, I can compute the values modulo 7 and show you that it doesn’t add up’, and then getting told that you don’t know what ‘modulo’ means. For that matter, can anyone extract what exactly is the experiment which Christian claims will violate CHSH? Once it’s removed from its justification and rephrased in concrete classical terms, Christian’s math errors will of necessity have been de-obfuscated, and the probabilities will be well within elementary school math checkability. 178. Thomas H Ray Says: Richard # 168, “Thomas Ray #164: there’s no double negation in proving Bell’s theorem.” I have asked you repeatedly to show me a proof of Bell’s theorem not based on proof by double negation. (You won’t find one.) I am wondering if you even know what that means. You write, “Suppose in a CHSH style experiment, we believe that the unmeasured variables also possess values, independently of which of the directions we choose to measure in each run. Suppose our choices are made by independent fair coin tosses, for every run, anew.” Your assumption is that you can ASSIGN values to “the experiment not performed.” If you cannot do that, your argument is finished. The argument indeed relies on double negation: i.e., if the measurement theory were not probabilistic, there would be no probabilistic measure results. That’s double negation. If, on the other hand, we assign no value to the experiment not performed, we are compelled to substitute a range of measurement values continuous from the initial condition. These values are all real and local, whether the experiment is performed or not, which we can infer statistically — i.e., in a bounded length of time for an experimental run — from the experiment that we do do, using random variables in an entirely objective framework. 179. Bram Cohen Says: Thomas Ray #174: Is it your assertion that minus one times minus one is not equal to one? What is your issue with double negation? 180. Ben Lund Says: Joy 171, Given ANY 4 numbers A, A’, B, and B’, each in {-1,1}, we have (1) -2 \leq AB + A’B + AB’ – A’B’ \leq 2. Thus, for any ANY 4xN table of numbers, (2) -2N \leq \sum_j A_jB_j + A’_jB_j + A_jB’_j – A’_jB’_j \leq 2N. Confirming inequality (1) can be done using elementary methods, for example the following table: A, A’, B, B’, AB + A’B + AB’ – A’B’ 1, 1, 1, 1, 2 1, 1, 1, -1, 2 1, 1, -1, 1, -2 1, 1, -1, -1, -2 1, -1, 1, 1, 2 1, -1, 1, -1, 2 1, -1, -1, 1, -2 1, -1, -1, -1, -2 -1, 1, 1, 1, -2 -1, 1, 1, -1, -2 -1, 1, -1, 1, 2 -1, 1, -1, -1, 2 -1, -1, 1, 1, -2 -1, -1, 1, -1, -2 -1, -1, -1, 1, 2 -1, -1, -1, -1, 2 Notice (2) holds for ANY 4xN table of numbers; how the numbers are chosen doesn’t matter. Ben 181. Thomas H Ray Says: Bram Cohen #176 Arithmetic parity is not equivalent to a mathematical proof by double negation. The former is axiomatic. The latter is a proof of the form A = ~~A without specifically constructing A. In the case under discussion — Bell’s theorem — the mathematical proof does not survive beyond its own tautological assumptions; i.e., a probabilistic measure space is not not identical to a probabilistic measure result. A constructive argument would clearly construct the measure space independent of the assumed measurement outcome, therefore providing an objective measurement scheme . And that’s what Joy has done (“We construct a pair of dichotomic variables …”). 182. David Brown Says: In comment #171, Richard Gill writes, “Joy redefines “local”, “realistic”, and “correlation” …” Are we all agreed on this particular point? Do Christian and Ray claim that we, “the ignorami”, are plumbers because we do not understand the theory of teleparallel gravity? 183. Joy Christian Says: Ben Lund # 186 Please tell me something I do not already know. 184. Scott Says: James Putnam #172: What do you think about Tom Ray’s #143 and Richard Gill’s response #161? I completely agree with Gill. Tom Ray, like Joy Christian, seems to be showing a remarkable ability to complicate and obfuscate a simple mathematical point. Look everyone, consider the following game. Two players, Alice and Bob, can agree on a strategy in advance, but from that point forward, are out of communication with each other (and don’t share quantum entanglement or anything like that). After they’re separated, Alice receives a uniformly-random bit A, and Bob receives another uniformly-random bit B (uncorrelated with A). Their joint goal is for Alice to output a bit X, and Bob to output a bit Y, such that X + Y = AB (mod 2) or equivalently, X XOR Y = A AND B. They want to succeed with the largest possible probability. It’s clear that one strategy they can follow is always to output X=Y=0, in which case they’ll win 75% of the time (namely, in all the cases except A=B=1). Furthermore, by enumerating all of Alice and Bob’s possible pure strategies and then appealing to convexity, one can check that there’s no way for them to win more than 75% of the time: no matter what they do, they’ll lose for at least one of the four possible (A,B) pairs. Do you agree with the previous sentence? If so, then you accept the Bell/CHSH inequality, end of story. 185. Joy Christian Says: @Bram Cohen #183 Have you actually read my reply to Gill? Here it is again, if are willing to wake up just for ten minutes from your dogmatic slumber: http://arxiv.org/abs/1203.2529 186. Joy Christian Says: @Scott #190 “I completely agree with Gill.” Then you are as ignorant and closed-minded as Gill. That actually is not news to me, for I remember your reactions from 2007 and 2009: Brain wide shut. 187. Chris Says: @Scott #184: I’ve always preferred the CHSH game variant of the theorem because it highlights the operational significance of entanglement. However, it also illustrates the need for “loop-hole” test of CHSH; if the game were played with the quantum strategy and our current technological resources, I doubt the players would win any more than 50% of the time. In fact, the next group planning on experimentally violating the CHSH inequality should be willing to accept a bet at cos^2(pi/8) odds of winning the CHSH game. 188. Scott Says: Chris #187: Yes, the detection loophole and other loopholes are indeed central issues for experiments aiming to violate the Bell/CHSH inequality. There’s been great progress over the past couple decades in closing the loopholes—though as I understand it, it remains open to perform a single experiment that closes all the known loopholes simultaneously. (Here I’m not counting “superdeterminism” as a genuine loophole. If you have to resort mind-controlling demon to evade the implications of a physics experiment, at that point I’d say you’ve lost the debate! 🙂 ) Crucially, though, unlike the more “mainstream” Bell skeptics, Joy Christian isn’t talking about any of these known experimental loopholes. Instead, his beef is with the few lines of arithmetic that constitute the Bell/CHSH inequality itself! As a result, he thinks that Bell/CHSH can be violated even in purely classical situations. 189. Joy Christian Says: @Scott #194 “Crucially, though, unlike the more “mainstream” Bell skeptics, Joy Christian isn’t talking about any of these known experimental loopholes. Instead, his beef is with the few lines of arithmetic that constitute the Bell/CHSH inequality itself! As a result, he thinks that Bell/CHSH can be violated even in purely classical situations.” Very good, Scott. There hope for you after all. 190. Alex V Says: Scott #188 Indeed, and I would like to know, why using such kind of ideas we may not break RSA on classical analogue devices? 191. Alex V Says: Alex V #190 Sorry, it was stupid question, cf http://rjlipton.wordpress.com/2012/02/26/the-bourne-factor/ 192. Fred D Says: I’m really baffled by those that think the correlations between two points on S^0 would be the same as the correlations between two points of S^3 or S^7. Joy’s model of the EPR-Bohm scenario using parallelized S^3 topology definitely predicts the correlation will be -a.b. There are no math errors contrary to what Gill says. Gill (and others) are simply trying to deny Joy the right to make his physics postulate. There is now only one way to decide the issue; a real test of Bell since we do know that Nature does in fact violate the inequalities. Scott is correct that the loopholes are not an issue in the quantum experiments related to Joy’s model. There is nothing wrong with the quantum predictions. Joy has simply discovered the real underlying mechanism for quantum correlations. 193. Hal S Says: John #175 You make a good point about how important it is to use consistent definitions when addressing deep questions. I think there is a decoupling between what Bell was trying to do and what Christian is trying to do. It also highlights the importance of making sure one’s assumptions are actually coupled to the problem one is trying to solve, so not all assumptions can be arbitrary. As far as the more general points, this question of non-locality needs to be very carefully approached. If you look at some of the motivations behind string theory, you will see that non-locality does enter into any discussion when we replace traditional point particles with vibrating strings. However, that non-locality enters in a very fundamental way and is something that is intrinsic to the nature of the string itself and is effectively occuring out of sight (and I would offer that this way of managing the problem is what causes incredulity amongst most critics even if only at a subconscious level). The point here though is not to discuss the merits of string theory, but only to agree that there is a question of non-locality that one wants to manage, and people have worked hard to find ways to manage it. In the most general sense, the non-locality is an artifact of the need to consider non-periodic waves. In order to do that analysis, we must assume that our boundaries are t = +/- infinity. All discussion that similarly use infinite potential wells and other artificialities introduce similar problems. Conceptually we have a problem because their is overwhelming evidence that shows that everything evolved out of the big bang. So everything we observe has at least one correlated element. The flipside to the argument is that everything we see is self consistent within some space-time volume. So my analyzer should never make an observation that violates the probabilities and eigenvalues determined by the wave function. The wave function itself, as pointed out in the lecture, is not evolving in time, but actually is defined for all time. So from the day a person is born, all possibilities are already captured in the wave function. Nothing escapes it. What is even more important is that all environmental events that could happen in that person’s life are also captured. When on thinks of cross correlation, one has to keep that thought in mind. There are states in the Hilbert space that are mathematically feasible. That we experience them the way we do is just an artifact of our perception (and also remember, that humans, like analyzers, only construct a picture or existence from very limited frequency and intensity data http://wiki.answers.com/Q/How_does_the_Human_eye_see_things). The point is that if there is a state in Hilbert space that allows for the existence of quantum computers, then there is no a priori reason to say they can not be constructed. So the challenge to those who say it can not be done is to show that there is no possible state in Hilbert space that can contain a quantum computer (or that there are no states that exist within suitable constraints). If those states exist, then it is just a matter of our choices that will eventually find them. As far as sources and sinks, it is appropriate to think along similar lines. The creation of a photon is just the transfer of some average amount of energy between fields within some time envelope. Its destruction is just a similar transfer of energy. If two entities are created in a way that requires a correlation, then that correlation will be conserved until it is extracted from the field. There are several options on how that will occur, however because the observer is certainly causally seperated from the creation event their portion of the wave function can be treated as an independent and the decisions are also independent (to borrow from Einstein, in a very bastardized sense, the tidal effects of the distant creation event on our local decision process are negligible and only arise due to common distant origin). In any case, I would agree that it would be nice to update Feynmann’s lectures, and I am sure it will happen at somepoint. 194. Richard Gill Says: Bram #177. Joy’s experiment? It’s a four page paper on arXiv from 2008. Actually it’s a Gedankenexeriment due to Peres. Two halves of a colourfully painted sphere fly apart in equal and opposite directions, rotating with equal and opposite angular momentum. A battery of TV cameras and accompanying image processing software enable us to measure the angular momenta lambda and -lambda of the two pieces. Next our computers calculate for us A=sign(lambda.a), A’=sign(lambda.a’), B=sign(-lambda.b), B’=sign(-lambda.b’). Repeat N times. Calculate ave(AB), ave(AB’),ave(A’B), ave(A’B). Joy says that Nature will prove him right by these four correlations violating CHSH. David Wineland thought the experiment could in principle be done though had some doubts whether people nowadays have the suitable facilities. Joy insists the four correlations are computed *separately* and got really cross with me when I suggested the 4N numbers +/-1 might be stored in an Excel spreadsheet. I don’t know what “separately” means. On four different days, by a different lab assisistant? (The 4N numbers stay the same). I also don’t know why Nature has a problem with Excel. I predict that no-one is going to do this experiment. However, it’s nice proof that Joy is round the bend, which even third-raters can understand. 195. Richard Gill Says: PS There’s also an amusing requirement to pick a and b at random independently of one another. Joy thinks that real space has a point at infinity so that we live on a kind of Möbius strip. The randomness of the outcome of these measurements of spin direction is because Nature has to choose between a right-handed and a left-handed bivector basis every time we do a measurement. Or something like that. I’m afraid only first-raters can understand, and they are few and far between. 196. Joy Christian Says: “I predict that no-one is going to do this experiment.” Good, Richard Gill. Then I will never be proven wrong! But just in case someone is crazy enough to want to try, equation (16) of my experimental paper describes exactly how the expectation values E(a, b), E(a’, b), E(a, b’), and E(a’, b’) are to be computed in my proposed experiment: http://arxiv.org/abs/0806.3078 Four separate sums are to be calculated as follows E(a, b) = 1/N Sum_j A_j B_j , E(a, b’) = 1/N Sum_j A_j B’_j , E(a’, b) = 1/N Sum_j A’_j B_j , and E(a’, b’) = 1/N Sum_j A’_j B’_j . It is a matter of indifference whether N here is chosen to be the same or different for each of the four alternatives. My model then unambiguously predicts that the observed correlations will be E(a, b) = -cos(a, b), E(a, b’) = -cos(a, b’), E(a’, b) = -cos(a’, b), and E(a’, b’) = -cos(a’, b’). Moreover, my model predicts that these correlations will give rise to violations of the Bell-CHSH inequality of the form | E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) | less or equal to 2 x sqrt{ 1 – (a × a’).(b’ × b) } The predictions of my model are unambiguous. The experimental procedure described in my paper is unambiguous. One does not have to be Einstein to understand my argument. All one has to do is to read a few pages of a few of my papers. 197. Hal S Says: Stephen Lee actually built a simulation program of the experiment. http://tachyos.org/bell/bell1.html 198. Joy Christian Says: @Hal S # 203 “Stephen Lee actually built a simulation program of the experiment.” Despite the claim made by Stephen Lee, what he has simulated is Bell’s own local model of 1964, not my model. My model cannot be simulated that trivially. 199. David Brown Says: Do Christian and Ray claim that there is a “classical, local-realistic” interpretation of the double-slit experiment? http://en.wikipedia.org/wiki/Double-slit_experiment Does Ray claim that physicists should reject not(not(A)) if and only A because classical logic should be replaced by intuitionist logic? 200. David Brown Says: Prof. Aaronson thinks that Christian’s work is merely a “Monty Python Dead Parrot Sketch” situation. I am not entirely sure that I agree with Prof. Aaronson. I think that Christian might be a sort of Kary Mullis with an idée fixe. I address the following question to Joy Christian: In the acknowledgements in your paper “On the Origins of Quantum Correlations”, you thank David Coutts, Fred Diether, Azhar Iqbal, Edwin Eugene Klingman, Rick Lockyer, Ray B. Munroe, and Thomas H. Ray. Do all of these people think that your Theorema Egregium is mathematically correct? 201. jake Says: the endless game of “i’m smarter than you” is why i left my physics phd. the smartest thing anyone can do is ignore joy, he’s clearly nuts. 202. James Putnam Says: Jakes #201, “the endless game of “i’m smarter than you” is why i left my physics phd. the smartest thing anyone can do is ignore joy, he’s clearly nuts.” You can’t claim it, you must prove it. If you wish to be the expert on who’s nuts, then, put forward your own un-nutty accomplishments. What have you done or what do you know that makes you so self-special? The fact that you left your phd is not what makes you special. It is what makes me pose this question. Please explain, I mean actually say something meaningful, why: “…the smartest thing anyone can do is ignore joy, he’s clearly nuts.” James 203. Scott Says: the endless game of “i’m smarter than you” is why i left my physics phd. jake #201: While Joy has been constantly belittling my and others’ intelligence here, I just went through the entire thread, and was unable to find even a single example of the other side responding in kind (though it’s possible that I missed something). To me, calling Joy’s ideas crackpot nonsense, which they are, is completely different from calling Joy himself unintelligent (which, incidentally, I don’t believe for a second: I’m sure he does just fine on IQ tests). Granted, we need look no further than Lubos Motl to find a prominent example of a physicist who regularly ridicules his opponents’ intelligence even when making (sometimes!) correct points. And while Lubos might be record-setting in his nastiness, he’s obviously not the only disagreeable character in physics. But as a computer scientist who regularly interacts with physicists, Lubos’s and Joy’s behaviors have never struck me as the norm, and it seems like a shame to me for anyone to leave physics purely because of behaviors that occur around the edges of any human community. (Of course, you may have had other reasons for leaving physics, or found yourself in a particularly nasty department or research group, etc. etc.) 204. David Brown Says: From Wikipedia, “Two assumptions drove the desire to find a “local realist theory”: 1. Objects have a definite state that determines the values of all other measurable properties, such as position and momentum. 2. Effects of local actions, such as measurements, cannot travel faster than the speed of light (in consequence of special relativity). Thus if observers are sufficiently far apart, a measurement made by one can have no effect on a measurement made by the other. In the form of local realism used by Bell, the predictions of the theory result from the application of classical probability theory to an underlying parameter space. By a simple argument based on classical probability, he showed that correlations between measurements are bounded in a way that is violated by QM. Bell’s theorem seemed to put an end to local realism.” http://en.wikipedia.org/wiki/Bell_theorem Mainstream Bell’s theorem deniers look for loopholes within the context of accepted definitions of “quantum correlation” and “local realism” — but Christian insists on his own definitions. My guess is that Christian has a higher IQ than many Nobel prize winners, but his idea for a macroscopic test of his Theorema Egregium seems to me beyond eccentric. If his Theorema Egregium is mathematically correct then I think the theorem is dealing not with “local realism” but instead “Christian SU(8) realism”, which would be highly non-local because alternate universes would be needed to make it work. Does anyone agree with me? 205. John Sidles Says: Searching the arXiv server and Google books for quantum-relevant usages of “crackpot” yielded two good fine quotes and one instructive personal example. The first quote is from (field theorist) James Bjorken: “A theorist working within the Standard Model feels like an engineer, and one working beyond it feels like a crackpot.” Of course, we could restate Bjorken’s aphorism in the logically equivalent form “Every quantum physicist is either an engineer or a crackpot” … but what would be gained by that? 🙂 It is interesting too that John Bell was (to my knowledge) the very first STEM professional to proclaim himself “a quantum engineer” (arXiv:quant-ph/0104140v1) … perhaps Bell was aware of Bjorken’s distinction! The second quote is by Stephen Parrott (arXiv:gr-qc/0502029v3): “It is not clear to me that significant harm is done by letting a few misguided individuals post papers which some might regard as “crackpot”. Also, the line between “crackpot” and “brilliant but inarticulate” is not always clear.” And finally, an personal example is revealed by a Google search for books authored by Richard Feynman that contain the word “crackpot.” It appears the Feynman wrote that word only once in all his career … and then without reference to any specific individual or school of thought. It seems to me that that Bjorken, Bell, Parrott, and Feymann, by their words and by their personal examples, have imparted several good lessons to us. Perhaps we should all resort to terms like “crackpot”, about as often as Feynman did. 206. Fred D Says: David Brown said, “Does anyone agree with me?” No. Joy’s criteria for correlations and “local realism” are exactly the same as Bell’s. If you don’t think so then please quote something from Joy’s papers that say that they aren’t the same as Bell’s. 207. David Brown Says: Fred Diether #208: Look at page 3 of Christian’s “On the Origins of Quantum Correlations”. Bell defines a quantum correlation using criterion (1.1) whereas Christian defines a quantum correlation using criterion (1.3). This makes a HUGE DIFFERENCE. If Alice and Bob are working with 2 different quantum states then we understand a linear superposition of quantum states but in experimental terms what does Christian’s 3-sphere definition mean? 208. nickmann Says: Scott #188 “As a result, he thinks that Bell/CHSH can be violated even in purely classical situations.” Oddly enough, it can … as a gedanken — but ONLY if you simulate quantum entanglement. Dirk Aerts made an avocation of this (which both Bell and Aspect took it seriously) back in the early eighties. He took separables (two vessels of water) and made them into an “entangled system” by connecting the vessels with a tube. Of course they were no longer definable as two vessels. The main point he was making was that the Bell inequality isn’t as “fundamental” as the Heisenberg inequality. Bell apparently didn’t disagree, nor did Aspect. Bell was mainly concerned that Aerts might make a confusing issue even more so. Long discussion which I facilitated on the late GUTalk site. HTMLs available. But who needs a debate about an isomorphism? 209. David Brown Says: Fred D. #194: Is Christian a genius with several erroneous idées fixes? Fred D. writes, “Joy has simply discovered the real underlying mechanism for quantum correlations.” I think the preceding statement is wrong, but if Christian’s Theorema Egregium is mathematically correct, then I think that Christian may have discovered something profound in terms of theoretical physics. I think that the corrected form of Christian’s Theorema Egregium might be an essential part of developing what I call the “Nambu transfer machine”. The smoothing of the Nambu transfer machine would somehow have to simulate quantum entanglement, a very difficult undertaking indeed. 210. John Sidles Says: Regarding David Brown #204, and Fred D #206. Please count me among those who agree with David Brown, at least with regard to issues of math and logic. In particular answer to Fred #206, one concrete discrepancy is that Joy Christian’s one-page recipe “Disproof of Bell’s Theorem” (arXiv:1103.1879v1 [quant-ph]) includes a normalizing correction to the correlation — specifically the denominator of Eq.5 — that is neither present in Bell’s Theorem nor in any experimental test of it. With regard to larger issues, everyone should watch the Monty Python sketch “The Argument Clinic” 🙂 211. Fred D Says: @David Brown: Bell never actually specified eq. (1.1) like Joy has but perhaps he should have. All Bell ever specified was A(n, lambda) = +/- 1. That is a *condition* specification which Joy adheres to strictly with his model. Of course the topology does make a huge difference since that is the foundation of Joy’s argument. 212. Bram Cohen Says: Joy Christian #198: Perhaps you should write a simulator for your own experiment? Or is there some deep reason why it can’t be simulated using a computer? 213. Henning Dekant Says: @Joy Christian, never fear about your experiment. So far already$60 have been pledged.

Certainly we should be able to turn exploding colorful toy balls into an Internet sensation.

214. Raoul Ohio Says:

For evidence of Joy Christian’s mastery of General Relativity, note that in post #158 he answers post #160. I wish I could have talked to him before the Kentucky Derby yesterday!

215. Ben Lund Says:

Joy #183,

So you do agree that your experiment won’t show a violation of the CHSH inequality of the form
| E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) | less or equal to 2?

I’m curious about the inequality you claim to refute:
| E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) | less or equal to 2 x sqrt{ 1 – (a × a’).(b’ × b) }

I haven’t seen it before, but it does strike me as trivially false as written, even in two dimensions.

For example, let a=b’, let a’=b, and assume a 90 degree angle between a and a’. Then (a × a’).(b’ × b) = 1, and, as I understand it:

(1) E(a,b) = E(a’,b’) = 0, since these measurements are made at right angles to each other, and

(2) E(a’,b) = E(a,b’) = -1, since each measured spin at B will be exactly opposite of the spin measured at A.

216. Joy Christian Says:

@David Brown # 213

“Bell defines a quantum correlation using criterion (1.1) whereas Christian defines a quantum correlation using criterion (1.3). This makes a HUGE DIFFERENCE.”

Neither Bell nor I define “quantum” correllation. We are both working within a purely classical, local-realistic framework. Both (1.1) and (1.3) define local-realistic functions A(a, L) = +1 or -1. There is no difference as far as local realism and individual measurement results are concern. The key difference between (1.1) and (1.3) is in the co-domain of the functions A(a, L). Bell and his followers implicitly assume the co-domain to be a subset of the real line, where as I take it be a parallelized 3-sphere (more generally 7-sphere),
and take it to represent our physical space. This correction does not affect either Bell’s criterion of local realism or his measurement criterion.

217. Joy Christian Says:

@Bram Cohen #218

“Joy Christian #198: Perhaps you should write a simulator for your own experiment? Or is there some deep reason why it can’t be simulated using a computer?”

http://arxiv.org/abs/1110.5876

218. Joy Christian Says:

@Ben Lund #221

You seem to need to learn a lot more about Bell-CHSH inequalities. Please learn them properly before you can go on to more advanced topics like my model.

219. Bram Cohen Says:

@Joy Christian #217: Are you saying that there’s something outside of classical physics involved in your experiment, or that you’ve found an exception to the extended church-turing thesis, which states that a computer can simulate not only any classical physics experiment, but any ‘reasonable’ variant on classical physics?

220. Bram Cohen Says:

Thomas Ray #164: Do you believe the Brouwer fixed point theorem to be true?

221. David Brown Says:

Joy Christian #218: I afraid that I disagree you with about your assumptions on “local realism”. I think that if you talk with experimentalists then they might well agree with me and not you. However, I think that your Theorema Egregium might be mathematically correct. Do both Fred Diether and Lucien Hardy think that your Theorema Egregium is mathematically correct? Among the group of men consisting of David Coutts, Fred Diether, Azhar Iqbal, Edwin Eugene Klingman, Rick Lockyer, Ray B. Munroe, and Thomas H. Ray, which of them think that the Theorema Egregium is mathematically correct? I think that the conventional meaning of “quantum correlation” is not what you say, but that you have introduced “quantum Christian SU(4) correlation” and “quantum Christian SU(8) correlation” — have you asked experimentalists about this? I think you might have an idea of genius in the Christian hidden-variable identity found in (5) of page 2 of “Refutation of Some Arguments Against my Disproof of Bell’s Theorem”, v2, Nov 2011, arXiv.org .

222. Thomas H Ray Says:

Scott # 184

“Do you agree with the previous sentence?” One can agree with what you’ve said, without agreeing on the way you got there.

You’re talking about the choices that A and B make in their cooperative game strategy, and Joy is talking about the objective choice that everyone can agree that nature made, or could have made, were the game determined in an unbounded length of time. Of all the criticisms I have read of Joy’s framework, Marc Holman’s is the only one I have read that recognizes this extra degree of freedom (although he rejects the possibility).

That the bounded length of time in which decisions are made renders all time intervals identical does not imply that “God plays dice.” A measurement function continuous from the initial condition compels mathematical completeness (1 -1 correspondence between mathematical theory and physical result) rather than assuming probabilistic measure.

223. Thomas H Ray Says:

David Brown # 199

“Does Ray claim that physicists should reject not(not(A)) if and only A because classical logic should be replaced by intuitionist logic?”

Only if there’s not a constructive alternative, which in this case, there is. One has to accept that Joy’s framework is mathematically complete, even if he is proven wrong.

224. Alex V Says:

… extending co-domain most likely make the model similiar with Deutsch et.al MWI(-like) models. Is it ocassionally that state space of three qubit coincides with generalized Hopf fibration on S^7? In fact I already wrote about that possibility more than year ago. It is known that MWI interpretation is local

225. Alex V Says:

I asked about quantum computer also because after claim about impossibility my idea expressed in previous comment may not be valid.

226. David Brown Says:

Alex V #225: “It is known that MWI interpretation is local … ” I do not agree with the preceding statement. In my opinion, “local realism” excludes faster-than-light travel by particles AND alternate universes (which are not accessible except possibly by faster-than-light travel by particles). In my opinion, “local realism” and “MWI realism” are two distinct categories, although many physicists disagree with me. If Joy Christian says that “local realism” includes alternate universes then he should explicitly say so.

227. Thomas H Ray Says:

Bram Cohen # 220

“Do you believe the Brouwer fixed point theorem to be true?”

A theorem is true whether one believes it or not. Yes, I do have the same reservations about the proof method that Brouwer himself had. That one prefers a proof to be constructive, however, does not invalidate weaker methods of proving a mathematical conjecture.

The problem with Bell’s theorem is that it is mathematically based on the weakest possible proof method — double negation. Because of this, the proof cannot survive criticism that the domain and the measure space are defined to be identical. As a result, the theorem concludes that reality is observer-created (there is no measurement independent of a measurer). Experiments of the Bell-Aspect type validate the conclusion, but they validate only what was assumed true in the first place.

We should know from quantum field theory, however, that the necessity of renormalization falsifies that conclusion. Renormalization clearly implies the impossibility of mathematically complete measurement results on an infinite spatial domain in a finitely bounded length of time. That does NOT imply the converse — the possibility of complete measurement results on a finite space in an unbounded length of time still stands.

That we do not have access to an experimentally unbounded length of time does not harm the premise. By constructing the finite space (as Joy has explicitly done) we can account (by statistical inference) for the “experiment not done” in a metaphysically real manner from a continuous range of input values.

228. Thomas H Ray Says:

David Brown #226

“In my opinion, “local realism” and “MWI realism” are two distinct categories …”

Whether he actually said it or not, I agree with a statement attributed to Stephen Hawking that many-worlds is “trivially true.” Metaphysically real measurement results are still local.

229. John Sidles Says:

It’s both fun and instructive to see the very different personal styles with which people approach the non Church-Turing world-model that Joy’s preprint (arXiv:1110.5876v2) describes:

A simply-connected model such as mine cannot possibly be either proved or disproved by its numerical simulation. … Reality is mathematically far richer and profounder than what a computer can fathom.

The point is that in any non Church-Turing world:

Philosophy: definitely feasible
Mathematics: possibly feasible (?)
Theoretical Physics: identical to mathematics (?)
Experimental Physics: pointless
System Engineering: impossible

In contrast, Nicolas Gisin’s enjoyable monograph “Sundays in a Quantum Engineer’s Life” (arXiv:quant-ph/0104140v1) — which includes personal memories of John Bell — exemplifies the opposite ordering:

System Engineering: definitely feasible
Experimental Physics: serves to verify design
Theoretical Physics: serves to validate design
Mathematics: serves to optimize design
Philosophy: guides the moral elements of design

If the idea of computationally simulating Joy’s model attracts you, then likely you are suited to the second style of investigation; otherwise the first. As usual, it is neither necessary, nor feasible, nor desirable that everyone think alike in these matters. 🙂

230. David Brown Says:

Thomas H. Ray # 223: You write, “One has to accept that Joy’s framework is mathematically complete, even if he is proven wrong.” Among the group of men consisting of David Coutts, Fred Diether, Azhar Iqbal, Edwin Eugene Klingman, Rick Lockyer, Ray B. Munroe, and Thomas H. Ray, which of them think that Christian’s Theorema Egregium is mathematically correct? Scott Aaronson and I believe that Joy Christian’s contention that “Bell’s theorem is wrong” has already been disproved mathematically. Bell’s Theorem involves at least 4 different domains: (1) mathematics, (2) physics, (3) metaphysics, and (4) semantics. Aaronson has compared Christian’s contentions to the “Monty Python Parrot Sketch”. Consider Christian’s paper “Disproof of Bell’s Theorem” with the statement “We illustrate an explicit counterexample to Bell’s theorem by constructing a pair of dichotomic variables that exactly reproduce the EPR-Bell correlations in a manifestly local-realistic manner.”
http://arxiv.org/abs/1103.1879
If I wrote that “I have constructed a counterexample to Gauss’s reciprocity law for primes” then would you believe me? If Bell’s theorem fails in terms of physics, then constructing some mathematical counterexample CANNOT IN PRINCIPLE prove that Bell’s theorem fails physically. Why am I spending my time on this debate? I believe that I have identified 5 erroneous idées fixes in Christian’s work and perhaps two ideas of genius. However, I need to know if Christian’s Theorema Egregium is mathematically correct.

231. Alex V Says:

David Brown, I am using “MWI-like” term as not very rigour characterization of QM without reduction.

232. Joy Christian Says:

@David Brown #236

“… Joy Christian’s contention that “Bell’s theorem is wrong” has already been disproved mathematically.”

Anyone who believes that has to be as blind as a bat.

All Scott has done is reveal his ignorance of what Bell’s theorem was all about and proclaim his dogmatic adherence to the orthodox opinion without bothering to understand the profundity of my argument. Unlike Gill, Scott is certainly capable of understanding my argument, but so far he has only proved that he is not capable of freeing himself from the clutches of his deep-seated prejudices.

233. Raoul Ohio Says:

T.H. Ray says: ““Do you believe the Brouwer fixed point theorem to be true?”

A theorem is true whether one believes it or not. Yes, I do have the same reservations about the proof method that Brouwer himself had. That one prefers a proof to be constructive, however, does not invalidate weaker methods of proving a mathematical conjecture.”

As a student I learned to prove BFPT type theorems, and of course they are true. BUT, do they mean anything? The BFPT proof and usage depend on an idealized axiomatic framework that is a plausible map of “reality, what ever that is”. But there is no reason to think that topological notions such as compactness and continuity have more than a superficial resemblance to the “real physical world, whatever that is”.

A simpler example of the same idea: Q: Are the real numbers a faithful approximation for space and time? A: Maybe. They have been defined for the convenience of mathematicians wanting to do things like give meaning to transcendental functions (say, the square root of 2). They gain additional plausibility because two reasonable ways to do this (dedikind cuts, cauchy sequences) turn out to be equivalent. But this does not mean they are the only, or best, framework for time and space.

234. David Brown Says:

@Joy Christian #234: You write, “Unlike Gill, Scott is certainly capable of understanding my argument …” Does Lucien Hardy understand your argument? I think that you think that you are an immensely great theoretical physicist, on a level with Einstein and H. Weyl. You might possibly be correct. Can you give me the names of at least 3 people who believe that you are an immensely great theoretical physicist? Can you very briefly describe what you believe to be your 3 greatest ideas?

235. Thomas H Ray Says:

David Brown # 230

“Scott Aaronson and I believe that Joy Christian’s contention that ‘Bell’s theorem is wrong’ has already been disproved mathematically. Bell’s Theorem involves at least 4 different domains: (1) mathematics, (2) physics, (3) metaphysics, and (4) semantics.”

Those philosophical “domains” are independent of the one domain that actually matters to a mathematical proof of Bell’s theorem: the measurement domain. Applying the equally primitive mathematical notions of limit and function, we easily find that the measurement function is limited in range to a domain that is not defined on any space except the infinite 1-dimension real line oriented in the plane. That is not semantics, metaphysics, or physics; it is a mathematical fact.

Joy and I have had both private and public discussions over what “disproof” means to a mathematician vice physicist. To a mathematician it is transparent nonsense — a disproof can only be a proof which disproves itself, which is not useful, because that disallows any closed logical judgment, in principle. I would never say that Bell’s theorem is mathematically wrong, and have never said so — what I have said is another simple fact, that the proof assumes a priori that which it aims to prove. In its own specious domain of infinite range, the proof is valid.

Do I think that Joy’s theorema egregium is mathematically correct? My personal answer is that it’s not incorrect — what I mean by that, is that it’s a physicist’s interpretation of certain topological facts. It’s very easily translated to a mapping theorem that should satisfy a topologist’s logically closed judgment that all points of parallelized S^7 map completely to parallelized S^3. Now, the question of whether or not this is the physical space in which we live — being independent of the mathematical judgment — is the question Joy’s experiment wants to answer. We *know* to a certainty, however, that the 1-dimension line oriented in the plane is *not* the complete physical space in which we live. Bell’s theorem leaves us with no conclusion but that we live in an observer-created world — that cannot be physically true if the moon really is there when no one is looking at it. My bet is on objective reality.

236. John Sidles Says:

David Brown #230 asks: “I need to know if Christian’s Theorema Egregium is mathematically correct.”
—————-

David Brown, if by “know” you mean Feynman’s extended sense in which “What we cannot create, we do not understand”, then I would suggest the following arduous yet rewarding path.

Begin in the middle, with a modern article on dynamical simulation such as Kambergaj et al. “Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules.” (JCP v124, p224114, 2005). This article’s quaternionic state-manifolds — which are very commonly used in molecular simulation nowadays — will provide you with a practical computational handle on Joy’s exploding-sphere model.

Two well-written (and best-selling) texts that will help you grasp the key ideas of Kambergaj’s article — and also help you translate that article’s index notation into Joy’s abstract notation — are John Lee’s Introduction to Smooth Manifolds and Vladimir Arnold’s Mathematical Methods of Classical Mechanics.

To assess whether you are making progress toward a Feynman-level creative understanding, code-up a simulation of Joy’s proposed experiment, using the methods (and even the computer codes) of yet another well-written (and best-selling) text: Frenkel and Smit’s Understanding Molecular Simulation: from Algorithms to Applications.

When you have finished traveling this path, you will appreciate what everyone agrees: Joy’s preprints contain (1) many new ideas, and (2) many ideas of genius … and you can decide for yourself whether there is any substantial overlap between the “new” elements and the “genius” elements.

More important, you will be able to decide for yourself the relative merits of the various arguments that have been presented here on Shtetl Optimized. And you will have a keener appreciation of the merits of clarity and rigor in exposition, from the study of accomplished authors (John Lee in particular).

Therefore, under all circumstances and outcomes, this effort will equip you with a better understanding (in Feynman’s creative sense of “understanding”) of the modern literature of mathematics, science, and engineering. Specifically, you will find yourself equipped with a computational toolkit that is sufficient to handle a broad domain of practical dynamical simulation challenges (classical, quantum, or hybrid), and encompassing in particular Joy’s exploding sphere model.

Summary: Regardless of whether Joy’s preprints are correct, the mathematical toolkit that his preprints use is essential to modern research in dynamical simulation, and so effort spent learning this toolkit is certain to be rewarded. Good luck to students!

237. Alex V Says:

John Sidles #236
Let me disagree with you summary: due to all these efforts currently many innocent researchers may have problem with rejection of papers from Q-Info science related journals just because they are using quaternions or Clifford algebra with absolutely justified reasons

238. Joy Christian Says:

@David Brown #240

David Brown,

I most certainly do not think that I am a great theoretical physicist. I have had a few ideas and some of them have been recognized by the physics community whereas others have been ignored by the physics community. This is the usual story of any average physicist, and in that sense I am an average physicist. However, here and elsewhere on forums like these I and my ideas have been attacked irrationally and incorrectly by ignorant and prejudiced men. As a result I have been forced to defend myself and my ideas, and in doing so I am forced to say things that might sound arrogant and egotistical. If, however, you ask anyone who actually knows me personally you will get a very different picture. Having said that, I will not tolerate false attacks on me or my work by anyone, under any circumstances, even if that makes me look like an ass.

239. David Brown Says:

@Joy Christian #240: I now think that your Theorema Egregium is either mathematically correct or more-or-less mathematically correct. My problem is that I need your theorem or something like it. Is Milgrom the Kepler of cosmology? If the answer is no, then I am a crackpot. Is Wolfram a serious rival to Newton and Einstein? If the answer is no, then I am a crackpot. I am very much afraid that I am a crackpot, and the sooner I figure out my Milgrom/Wolfram hypotheses the better for me. Good luck in all your efforts.

240. Scott Says:

David Brown #239:

Is Milgrom the Kepler of cosmology? If the answer is no, then I am a crackpot. Is Wolfram a serious rival to Newton and Einstein? If the answer is no, then I am a crackpot.

Dude, my friend. I wish I had a gentle way to break to you the result of applying Modus Ponens to the above… 🙂

On the bright side, all it takes to stop being a crackpot is to decide to stop!

241. Henning Dekant Says:

David Brown #240: Wolfram clearly towers over Einstein and Newton in terms of wealth amassed. He could fund exploding toy ball experiments with the change you’d find in one of his sofas.

Clearly if he was to rival Einstein and Newton then we are actually living in a world imagined by Ayan Rand as a sequel to Atlas shrugged. Not a very pleasant thought. So with all due respect I prefer to think you are a crackpot.

242. Joy Christian Says:

@David Brown #245

It is million times better to be an eccentric crackpot than a dogmatic idiot. There are plenty of plumbers in this forum belonging to the latter category. Just ask them what they have accomplished in their lives to deserve the arrogance they are dripping with.

243. Bram Cohen Says:

Joy Christian: Trying to read your paper, you’re saying that the concern is ‘topological’. If your model of the world involves things at a distance being directly connected to each other, then that’s not topological, and you’re just reiterating that you can violate CHSH if you entangle the particles, but claiming that your entanglement is actually classical because the rest of us have been misunderstanding how the distance function works in 3-space this whole time.

244. James Putnam Says:

Scott Aaronson,

Thank you for your response. I asked my question because I feel it is important to know what you think and why. I appreciate the time you gave in answering my question.

“I completely agree with Gill. Tom Ray, like Joy Christian, seems to be showing a remarkable ability to complicate and obfuscate a simple mathematical point.”

My impression of Richard Gill’s response was that he insists on discussing the matter from his viewpoint. He avoided Tom’s description. Tom’s description is more complete to me. I have read many other messages by Tom. I find them to be enlightening and not obfuscating.

Richard’s description is very restricted so much so that it seems evasive. I interpret his response as pertaining to a problem that is not representative of Joy’s work. He evaluates Joy’s math independently of that which it is intended to model.

The model dictates the meaning and correctness of the math. It is the model to which the values and their variations pertain. It is the model that establishes the properties that are represented by the math.

How can one properly evaluate the math separate from the physics. I think the debate must be about the physics. If the physics is wrong then the math doesn’t need to be evaluated. If the physics is valid then the math is valid. I am certain that neither Joy nor Tom tolerate or attempt to cover up mathematical errors.

Richard Gill is invited to correct or clarify his position. I do not wish to be guilty of misrepresenting it.

“Look everyone, consider the following game. Two players, Alice and Bob, can agree on a strategy in advance, but from that point forward, are out of communication with each other (and don’t share quantum entanglement or anything like that). After they’re separated, Alice receives a uniformly-random bit A, and Bob receives another uniformly-random bit B (uncorrelated with A). Their joint goal is for Alice to output a bit X, and Bob to output a bit Y, such that

X + Y = AB (mod 2)

or equivalently,

X XOR Y = A AND B.

They want to succeed with the largest possible probability.

It’s clear that one strategy they can follow is always to output X=Y=0, in which case they’ll win 75% of the time (namely, in all the cases except A=B=1).

Furthermore, by enumerating all of Alice and Bob’s possible pure strategies and then appealing to convexity, one can check that there’s no way for them to win more than 75% of the time: no matter what they do, they’ll lose for at least one of the four possible (A,B) pairs

Do you agree with the previous sentence? If so, then you accept the Bell/CHSH inequality, end of story.”

I don’t disagree. However, that cannot be the end of the story. The reason I say this is because of Tom’s pointing out that Joy’s work cannot be properly evaluated through probability analysis. Rather it must be evaluated through statistical inference.

Tom is invited to correct me if I have misrepresented his position. If you are familiar with his position, and if I have properly represented it, then I value reading your opinion about it.

James

245. Bram Cohen Says:

I meant to say ‘that’s not classical’ in that last post, not ‘that’s not topological’.

246. Bram Cohen Says:

Tom Ray, could you clarify what you mean by ‘double negation’? Also, why do you keep bringing up quantum phenomena in the discussion of the Bell Inequality, which makes no reference to quantum mechanical physics whatsoever?

247. Ben Lund Says:

James Putnam –

Richard Gill’s point is very clear – it is impossible that Joy’s proposed experiment will violate the Bell inequality if you admit that he can do all of the measurements a, a’, b, and b’ on each recorded pair of vectors.

Each of these measurements gives a result in {-1,1}, and we can calculate

ab + a’b + ab’ – a’b’

directly for each pair of exact measurements.

This can’t be outside the range [-2,2] for any values of a,b,a’,b’, so the average taken over many measurements also can’t be outside that range – this follows from simple arithmetic.

Ben

248. Scott Says:

The central concept that I find missing from the comments of David Brown, James Putnam, and Thomas Ray is that of the sanity check.

Math and computation are simply the tools of clear thought. For example, if someone tells me that a 4-by-4 array of zorks contains 25 zorks in total, and I respond that 4 times 4 is 16, not 25, I’m not going to be impressed if the person then starts waxing poetic about how much more profound the physics of zorks is than my narrow and restricted notions of “arithmetic”. There must be a way to explain the discrepancy even at a purely arithmetical level. If there isn’t, then the zork theory has failed a basic sanity check, and there’s absolutely no reason to study its details further.

Likewise, the fact that Joy can’t explain how to code a computer simulation of (say) his exploding toy ball experiment that would reproduce his predicted Bell/CHSH violation is extremely revealing. This is also a sanity check, and it’s one that Joy flunks. Granted, if he were able to explain his model clearly enough for well-intentioned people to understand how to program it on a computer, then almost certainly there would be no need to actually run the program! We could probably just calculate what the program did using pencil and paper. Nevertheless, Bram, John Sidles, and others were entirely right to harp on this simulation question, because its real role is as a sanity check. If Joy’s ideas are not meaningless nonsense, then there’s no reason at all why we shouldn’t be able to simulate his experiment on a computer and get exactly the outcome that he predicts. Until Joy passes this minimal sanity check—which he hasn’t—there’s simply no need to engage in deep ruminations like the ones above about physics or philosophy or Joy’s “Theorema Egregious.”

249. Henning Dekant Says:

@Joy Christian @245, I really don’t like to tell on people but I am on the verge of reporting your blatant disregard for plumbers to the Ontario association of plumbers (assuming you are still based in Waterloo).

Really don’t think that with this kind of attitude anyone should help you if you ever were to be confronted with a stubbornly plugged toilet.

250. Edwin Eugene Klingman Says:

Having been mentioned above, in the context of “who agrees with Joy Christian’s framework”, I will state that I find his mathematical framework credible. There has been considerable discussion on another blog about the calculations that result in the cancellation of the a^b term in the final correlation. Even those who aggressively argue against this result have agreed that if there are physics reasons that this term vanishes, then the rest of his framework appears to be coherent. I have strong reservations about Joy’s interpretation of the physics, but am currently trying to embed my own physics interpretation into his mathematical framework. In my opinion the mathematical arguments seem to come from those who apply the math out of the context of the physics and those who apply it as Joy has specified in his various writings.

251. Edwin Eugene Klingman Says:

Reading the immediately preceding comments, I would like to clarify that my comment #250 applies to the EPR experiment and I have not explored the CHSH simulation and proposed experiment that is also under discussion in these comments.

252. Joy Christian Says:

@Ben Lund #253

“Richard Gill’s point is very clear.”

And so is Scott Aaronson’s point. They both make a very clear point, which has nothing whatsoever to do with physics. Scott, Gill, and their supporters need to check their own sanity before worrying about anyone else’s. No matter how they pitch it, their argument leads to one inevitable conclusion — i.e., the upper bound on the CHSH combination of expectation values is restricted by +/-2:

-2 is less than or equal to CHSH is less than or equal to +2.

Well, there is just one tiny problem with this wonderful result. IT HAS BEEN REFUTED A MILLIONTIMES OVER IN EVERY EXPERIEMTNT EVER PERFORMED. Nature does not respect it. Nature is crying out and telling us that the derivations of Bell and CHSH are based on at least one bad physical assumption. I have identified this assumption explicitly and in great detail in my papers and my book. The Bell-CHSH argument is based on an unjustified and unphysical rigging of the measurement results. This is as clear as a daylight to anyone with any understanding of physic. It is evident by now, however, that some people in this forum are not going to understand the difference between physics and mathematics.

253. Scott Says:

Joy #252:

Well, there is just one tiny problem with this wonderful result. IT HAS BEEN REFUTED A MILLIONTIMES OVER IN EVERY EXPERIEMTNT EVER PERFORMED. Nature does not respect it. Nature is crying out and telling us that the derivations of Bell and CHSH are based on at least one bad physical assumption.

And could the bad assumption in question possibly be … oh, let me see here … the assumption of local hidden variables? Which was the crazy, unorthodox conclusion of a certain Bell’s-inequality-denier back in the 60s named … John Bell? No, of course not: that would be too clear and comprehensible. Sorry I even brought it up.

254. David Brown Says:

Scott #250; “Until Joy passes this minimal sanity check …” Clearly, Christian’s macroscopic prediction is totally wrong because it amounts to predicting that signals can be sent and received faster than the speed of light. If that sense, the sanity check light is blinking. So far, I have identified at least 5 erroneous idées fixes in Christian’s writings. However, Kary Mullis is a genius. Tesla predicted that planet Earth’s ionosphere could be used for global power distribution. Linus Pauling published a crackpot model of DNA, And so on. The probability that Milgrom is a crackpot is zero. Study the work of McGaugh and Kroupa.
http://en.wikipedia.org/wiki/Pavel_Kroupa
I say that Wolfram’s “A New Kind of Science” Chapter 9 is crackpot stuff if and only if the Space Roar Profile Prediction is false. I think there is a decisive empirical test that might prove beyond doubt that I am a crackpot. However, I think that Wolfram really is a genius on a level with Galileo, Kepler, Newton, and Einstein. I might be VERY WRONG on this point. To hope that there is a finite automaton that simulates all of quantum field theory is a long shot, but Wolfram might be as great as he thinks he is … and HE at least believes that he is a serious rival to Newton and Einstein. If Wolfram is the captain of the Titanic then I intend to busy myself in the engine room until the water pours in.

255. Joy Christian Says:

@Scott #260

“And could the bad assumption in question possibly be … oh, let me see here … the assumption of local hidden variables? Which was the crazy, unorthodox conclusion of a certain Bell’s-inequality-denier back in the 60s named … John Bell? No, of course not: that would be too clear and comprehensible. Sorry I even brought it up.”

I am glad you caught your own error. Indeed, there is nothing bad about the assumption of local hidden variables at all. In fact, nothing could be more rational than the assumption of local hidden variables. What is bad and irrational is the mystical belief in the mysterious action-at-a-distance of quantum mechanics. There was a similar action-at-distance in Newton’s theory gravity which Einstein exorcized. It is high time we exorcize the non-locality from our contemporary physics.

Oh, wait. I have just done that.

256. Henning Dekant Says:

This plumber is actually sympathetic to the idea that there may be a topological resolution to the Bell inequality, but given Joy’s antics in this forum I don’t think one could have invented a worse champion for this idea. God forbid Joy would have to sit down with a CS plumber to figure out how to efficiently simulate his model (assuming it is mathematically sound).

And there I always thought Perimeter was about working inter-disciplinary.

257. wolfgang Says:

>> Joy Christian Says:
>> Comment #255 May 7th, 2012 at 4:11 pm

>> @Scott #260

One thing I find fascinating is that Joy keeps referencing comments
in the future.
First I thought it was simply a typo, but it happened so many times that the only explanation is that Joy lives beyond space and time,
which might explain his attitude towards Bell and all that.

258. Joy Christian Says:

Scott Says:

Comment #260 May 7th, 2012 at 3:59 pm

So may be my IE is from beyond space and time.

259. James Putnam Says:

Scott Aaronson & Henning Dekant:

I asked for your opinion and you gave it. Thank you. I will read the other messages that have been posted and think some before responding. However, I do see Henning Dekant’s message immediately above.

Henning Dekant: I have read the messages of both sides for months now in different locations. The level of hostility in messages from both sides was unexpectedly offensive to me. Enough messages have passed before my eyes that I suggest that it not be considered important at this time. I do not say this because I think it is not important. I say it because its importance pales compared to the importance of properly evaluating Joy’s work. Besides, it definitely is not confined to one side. Lets look at the physics first and then work on returning to the professional courtesy of bygone days.

James

260. Thomas H Ray Says:

Scott # 248

“Math and computation are simply the tools of clear thought. For example, if someone tells me that a 4-by-4 array of zorks contains 25 zorks in total, and I respond that 4 times 4 is 16, not 25, I’m not going to be impressed if the person then starts waxing poetic about how much more profound the physics of zorks is than my narrow and restricted notions of ‘arithmetic’.”

I am similarly unimpressed when someone tells me that reality consists of nothing more than random zorks in a row,

In any case, I have not addressed the physics of zorks — just the mathematics of a measurement function continuous from the initial condition. Zork for zork complete.

261. David Brown Says:

@Joy Christian: “It is high time we exorcize the non-locality from our contemporary physics. Oh, wait. I have just done that.” If you have really done this, then you are a great theoretical physicist in the same ballpark as Einstein and H. Weyl. Can you briefly describe your 3 most important ideas? (I sincerely want to know.)

262. wolfgang Says:

But we know that Joy is a careful man who checks his numbers and arithmetic, so this only leaves us with the ‘beyond space and time’ explanation.

263. Thomas H Ray Says:

Bram Cohen #246

“Tom Ray, could you clarify what you mean by ‘double negation’? ”

See my reply to you, # 181. If it isn’t clear, pick up a book on proof theory and technique, like Solow or Polya.

“Also, why do you keep bringing up quantum phenomena in the discussion of the Bell Inequality, which makes no reference to quantum mechanical physics whatsoever?”

I don’t know that I have done that. What I have said is that Bell’s theorem is not supported by a constructive proof (and I don’t think can be).

264. Joy Christian Says:

@David Brown #267

I am nowhere near Einstein or Weyl (and of course I am not being modest).

You can find most of my paper here: http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1

If I have to pick three ideas, then (1) I quantized Newton-Cartan theory of gravity, (2) I generalized Special Theory of Relativity to incorporate the objective passage of time, and (3) I exorcized non-locality form contemporary physics. Of these three, only the first one is widely known and accepted. The second one is hardly known or understood, and third one is viciously contested.

265. David Brown Says:

TO JOY CHRISTIANS AND THOSE WHO SUPPORT HIS VIEWS:
In quantum information processing and the study of quantum entanglement, a pure quantum logical qubit state is a linear superposition of the “basis states” |0> and |1>. If you use a NEW TOPOLOGY to change the meaning of quantum states and qubits then you are NO LONGER USING THE ACCEPTED LANGUAGE OF THE EXPERTS ON QUANTUM INFORMATION PROCESSING. If you say the parrot in the cage is alive, and all the experts say the parrot in the cage is dead, then who is correct? WHO GETS TO DEFINE THE PARROT AND ITS STATE?

266. Henning Dekant Says:

Tested this blog’s comment numbering with IE6 and IE9 without seeing the comment off-set that Joy apparently experiences. The HTML source does not indicate that the numbering in generated client side. A trivial yet intriguing plumbing problem.

Anyhow, if Jay talked to a plummer recently (as in the last five years) any self-respecting plumber would have recommended he switches to a different browser than IE.

267. Henning Dekant Says:

@Jay, #264 is the “Absolute Being vs Relative Becoming” paper the one with regards to generalizing special relativity?

268. Thomas H Ray Says:

David Brown #265

“WHO GETS TO DEFINE THE PARROT AND ITS STATE?”

The parrot.

269. James Putnam Says:

Scott Aaronson,

“The central concept that I find missing from the comments of David Brown, James Putnam, and Thomas Ray is that of the sanity check.

Math and computation are simply the tools of clear thought. …”

I agree. The mathematics helps us to keep our thoughts straight. It is the orderly processing of our thoughts about relationships between properties. In the case of physics, it is the relationship of physical properties. The math does not tell me what those properties are. I tell the math those conditions. I tell the math the correct form that it should take in order to accurately represent my thoughts so that I can proceed with the math in my quest to understand the full precise implications of my thoughts.

If my thought is that the magnitude of electric charge does not represent the source of a fundamental force, but, rather is a measure of time, then the math will properly carry the units of seconds for the magnitude of electric charge. If my thought is that thermodynamic entropy is simply a measure of the time required for heat to be absorbed at a constant temperature, then the math I employ will need to carry units of seconds to represent a quantity of thermodynamic entropy. It then even becomes possible for me to add electric charge to thermodynamic entropy. I find no reason to do that, but, the math would accept it. If someone finds this paragraph to be so ridiculous that it should be immediately dismissed as crackpottery, then, please say so. I may not be able to change fundamental theoretical physics, but, I can demonstrate the mathematical implementation of the ideas expressed above.

“…For example, if someone tells me that a 4-by-4 array of zorks contains 25 zorks in total, and I respond that 4 times 4 is 16, not 25, I’m not going to be impressed if the person then starts waxing poetic about how much more profound the physics of zorks is than my narrow and restricted notions of “arithmetic”. There must be a way to explain the discrepancy even at a purely arithmetical level. If there isn’t, then the zork theory has failed a basic sanity check, and there’s absolutely no reason to study its details further. …”

I can’t agree with this. I refer back to my beginning statement about electric charge and thermodynamic entropy. The mathematics of acceptable theoretical physics will say that my thoughts fail the ‘sanity check’, but, I can provide math that will say that my thoughts pass the sanity check. What does mathematics know about sanity? The math would have to be set up to represent someone’s thoughts about what properties and corresponding quantitative values constitute sanity.

“Likewise, the fact that Joy can’t explain how to code a computer simulation of (say) his exploding toy ball experiment that would reproduce his predicted Bell/CHSH violation is extremely revealing. This is also a sanity check, and it’s one that Joy flunks. Granted, if he were able to explain his model clearly enough for well-intentioned people to understand how to program it on a computer, then almost certainly there would be no need to actually run the program! We could probably just calculate what the program did using pencil and paper. Nevertheless, Bram, John Sidles, and others were entirely right to harp on this simulation question, because its real role is as a sanity check. If Joy’s ideas are not meaningless nonsense, then there’s no reason at all why we shouldn’t be able to simulate his experiment on a computer and get exactly the outcome that he predicts. Until Joy passes this minimal sanity check—which he hasn’t—there’s simply no need to engage in deep ruminations like the ones above about physics or philosophy or Joy’s “Theorema Egregious.””

Joy will address his thoughts and the mathematics required to correctly represent them. He will explain his own view about attempts to computer simulate his work. My own view on this is that the computer only tells us back that which we told it. Therefore, the computer must be told what Joy thinks. Also, it must be possible for Joy’s thoughts to be correctly represented by digital means. If not, then perhaps an analog computer might be employed. Joy would have to say whether or not his thoughts can be represented by any kind of computer and explain why or why not.

“…there’s simply no need to engage in deep ruminations like the ones above about physics or philosophy…”

I see ‘engaging in deep ruminations’ about physics as being the first requirement to be met before establishing the suitable mathematics for representing those deep ruminations. The math knows what I want it to know. The computer knows what i want it to know. What I think I know comes first because it is required to establish the proper use of the other two. That is what I think.

James

270. David Brown Says:

Thomas Ray #270: I think that I am beginning to understand Christian’s basic argument somewhat. The parrot seems to me to be the definition of “local realism”. What in, your opinion, is the parrot?

271. Scott Says:

James #269: I think you missed my point. In this particular case, I completely agree, as I said, that we’re unlikely to learn anything from computer programs or formal mathematical manipulations that we didn’t already put into them. The point that interests me, rather, is that Joy is manifestly unable to clarify his own thoughts to the point where verifying his claims would be an uncontroversial matter of running a computer program, or of well-defined mathematical manipulations that can be performed by someone other than him (!). If, like me, you regard Joy’s claims as pure, unredeemed delusional garbage, then there is no difficulty whatsoever in accounting for this.

272. David Brown Says:

@Joy Christian #266: You have NOT disproved Bell’s Theorem. I think that I can explain what you have done. You have reformulated string theory with a 7-sphere of superstring uncertainty. In your paper, you write, “… contrary to Bell’s claim, a local realistic model can indeed be constructed to exactly reproduce quantum mechanical correlations (4) without necessitating remote contextuality or backward causation.” The construction does not necessitate remote contextuality with respect to 4-dimensional spacetime but the construction DOES necessitate contextuality with respect to the 7-sphere of superstring uncertainty. Therefore your model is a non-local realistic model. However, your model is a great work of genius.

273. James Putnam Says:

Scott Aaronson,

Thank you for your response. I don’t evaluate Joy’s work. I do not claim to understand Joy’s work. I am interested in the potential importance of it. Joy and everyone seriously interested can speak for themselves.

My understanding is that there is a case to present with legitimate reasons why a computer simulation is not useful. I already know that those reasons can be expressed by both Joy and Tom. Perhaps others, I don’t know that. Both of them are quite capable of intelligently addressing the computer question.

I leave it to them to clarify their positions. No, I have seen no reason to think that Joy’s claims are ‘pure, unredeemed delusional garbage’. You have been generous with your time. Your opinion remains of value to me. There are many interesting opinions beng expressed here. I will see what is written.

James

274. asdf Says:

Story I heard about a well-known smart physicist I won’t name (call him B) who is a professor at a top research university. He was known all around as a kind, soft-spoken guy who talked with a slight stammer and who liked unorthodox approaches to problem solving. One day someone showed up at his office, saying he had a new discovery in particle theory that he wanted to share. The visitor was concerned though, that other physicists he had told the theory to had thrown him out of their offices, and he was afraid B would do the same.

B says, “no no, it’s fine, have a seat, there is a ch-ch-ch-chair”.

Visitor sits down, still a bit nervous, B asks a few friendly questions to make the guy comfortable.

B then says, “ok, tell me about your new particle discovery”. Visitor says, “I have a proof that the proton is flat”.

V (pleasantly surprsied): “I’m right?”

B. Yes–GET OUT OF MY OFFICE!!!

275. John Sidles Says:

The first two panels of today’s xkcd “Every Major’s Terrible” speak directly to the theme of this Shtetl Optimized.

Moreover, xkcd panels #19-20 of this same strip read:

Though physics seems to promise you a Richard Feynman-like career …

… the Wiki page for “physics major” redirects to “engineer.”

Yes, xkcd has got its facts right … the Wikipedia Page for “physics major” has been redirected twice in recent weeks, first to “engineer” and then to “physics educator.”

Ouch! Perhaps xkcd’s artist Randall Munroe has been reading James Bjorken? Or perhaps Randall knows that during the war, Richard Feynman (and Paul Dirac too) worked largely upon the nuts-and-bolts of transport mechanisms in isotope separation?

The necessary scrupulous respect for engineering norms seemingly did no lasting harm to either of their imaginations. 🙂

276. Florin Moldoveanu Says:

Scott,

I don’t want to get involved too much into this again, I burned way to many hours on it and I am really busy now, but I have a question I would like your opinion on.

I recently gave a talk at UMCP explaining Joy’s “disproof” and his mistakes in an easy and pedagogical way deriving everything from the fundamental Clifford algebra identity.

Now Joy has “replied” on the archive to my and Richard papers and he is making more confusions and mistakes and obfuscating trivial things quite well (like adding row with column vectors from direct and adjoint representations of Clifford algebras). So I ponder the wisdom of uploading the content of my talk to the archive and I have pro and con arguments.

Pro: Joy continues to obfuscate and deny the obvious and continues to receive research support on this nonsense.
Con: Proving +1 is not -1 is not really a noteworthy result for the archive.

So I am thorn and currently stuck on what to do. What would be your advice?

Thanks,

Florin

277. Joe Fitzsimons Says:

It is probably not entirely sensible to contribute anything to this thread, given some of the preceding comments. However there seems to be significant confusion over what theorems are, and their relation ship to physics.

Theorems do not say anything about nature, and are not subject to testing by nature. Rather they are a statement about mathematics, and are entirely independent of physics. We believe that certain mathematical objects well descibe physical ones, but this is certainly not something we can ever hope to prove for sure. That’s simply not the way physics works.

Bell’s theorem is a statement not about physics, but about a particular mathematical model. The question then becomes whether this model is a good fit for nature, and we know (as much as one can know these things) that it is not, due to the observed violations of Bell’s inequality. You can’t test Bell’s theorem, or any other theorem, via physics experiments. If you find a descrepancy it can always be due to associating an incorrect mathematical model with nature, and ultimately we never know if this is the case.

The talk of various physics experiments in this thread seems to be totally misguided. If the question is whether or not Joy has shown a flaw in the proof of Bell’s theorem, then this is not a question that can be answered by performing experiments. Experiments are about determining which physical model underpins nature, not about proving mathematical statements about any specific model.

278. Raoul Ohio Says:

asdf,

A related note:

Check out “Numerical methods that (Usually) work”, by Forman Acton. Between Parts 1 and 2, there is “Interlude — what not to compute — a brief cathartic essay”. He ends his (1970ish) discussion of dealing with social scientists wanting to upgrade their paper and pencil 3×3 model to a 300×300 system of linear equations with: “… the impasse finally has to be broken by violence — which therefore might as well be used in the very beginning.”.

That is about my favorite passage in a math book. Also, the “Usually” in the title has no ink applied to it, so the title appears to be “Numerical methods that work”, and a close look shows the printing mechanism used pressed a non inked “Usually” into the book cover.

Both “Numerical methods that work” and “Real computing made real” have been recently reprinted in paperback and are full of wisdom about scientific/engineering computing that is entirely relevant today. They are also funny. He also presents lots of little problems for the reader. If you think you understand math and how computers work, you might be surprised.

279. David Brown Says:

@asdf #275: Niels Bohr said, “Every statement I utter should be understood as having a question mark at the end of it.” Are we are on the same page here?

280. ScentOfViolets Says:

Joy’s ideas would be fantastic reading if they were part of a plot device as imagined by A. E. van Vogt. Hey, maybe this is what “similarity to twenty decimal places” really means 🙂

281. Richard Gill Says:

Simulation of Joy’s model is childishly simple. Pick unit vectors (directions) a, b. Think of them as quaternionic roots of -1: write a=a_x i + a_y j + a_z k. Check that a^2=-1. Similarly for b. Now let lambda=+/-1, a fair coin toss. Define A=lambda -a a = lambda a^2=lambda and B= lambda b b= -lambda. Now repeat N times.

Now the naieve reader will notice that ave(AB)=-1. The measurement outcomes are perfectly anti-correlated, whatever the settings a, b.

However as everyone knows you get a correlation by dividing by standard errors. It’s clear we have to divide -1 by -a on the left and by b on the right. The result is of course -ab

282. Richard Gill Says:

[sorry hit “submit” before I was done]. And I think the result is ab, not -ab. Anyway, as long as the number of sign errors I make is even, it doesn’t matter.

An easy calculation shows ab=-a.b -a x b where by a x b, I mean the cross product c of a and b (thought of as real 3-vectors), but as before encoded quaternionically as c_x i + c_y j + c_z k; while a.b is the usual real number dot product of a and b seen as real 3-vectors. A quaternion with both real and imaginary part. But how to get rid of the imaginary part?

We have nearly what we want. We just have to get rid of that pesky axb. Joy has tried all kinds of tricks to get rid of this. One idea is to have the right-handed or left-handed convention about axb also be random, so that in the large N limit the cross product term vanishes. But once you have decided if ijk = -1 or +1 in the algebra, everything is fixed. There is also a trick called Hodge duality in which you use the other 4 dimensions of a standard Clifford algebra. This gives lots of scope for sign errors. He has different tricks in various versions of the model (Florin Moldoveanu has documented them exhaustively) but it never works out, it is just a bump under the carpet (a dead budgerigar, I think) which gets shifted about.

In short, simulation is easy. Toss N coins. Compute the correlation between coin, and minus coin (it will be -1). Divide by the quaternionic roots of unity -a and b. Take the real part of the answer. It’s -a.b.

283. Scott Says:

Florin Moldoveanu #276:

Pro: Joy continues to obfuscate and deny the obvious and continues to receive research support on this nonsense.
Con: Proving +1 is not -1 is not really a noteworthy result for the archive.

So I am thorn and currently stuck on what to do. What would be your advice?

That’s a tough call, but on balance, I would say go ahead and post to the arXiv. 1 != -1 is indeed a triviality, but locating the trivial error within Joy’s highly obfuscated papers is not. More to the point, someone ought to be maintaining a paper trail documenting Joy’s childish errors, so that folks like me don’t have to! 🙂 And if you’ve already gone to the effort of locating the error in Joy’s latest “research,” no reason not to share it. Thanks for the great work! (But on the other hand, don’t feel obligated to continue doing this forever—you’ve already done more than enough!)

284. Scott Says:

Joe Fitzsimons #277: Everything you write about theorems, and their relation to physics, is 100% true (of course) and music to my ears!

However, to fill you in on the “moves” that Joy Christian makes:

First, he redefines Bell’s theorem to be “theorem of physics and metaphysics, not a theorem of mathematics.” To me or you, of course, that’s simply a forehead-banging misuse of the word “theorem”! However, this nonstandard language then opens the door for Joy to start talking about experiments, including his experimental prediction that the Bell/CHSH inequality can be violated even in purely classical settings (!!).

Once I learned about the above prediction, I decided that I did want to focus on it, since at least it was (somewhat) interestingly insane—in contrast to Joy’s various math errors and his redefinition of the word “theorem” meant to conceal those errors, which are merely boringly insane.

285. Joy Christian Says:

I too can fabricate and plant errors in someone else’s research and spread false and malicious rumours about their groundbreaking work, but instead I prefer to concentrate my efforts on the more constructive side of my own work rather than set out to falsely destruct someone else’s.

286. Thomas H Ray Says:

Scott #271

“Joy is manifestly unable to clarify his own thoughts to the point where verifying his claims would be an uncontroversial matter of running a computer program, or of well-defined mathematical manipulations that can be performed by someone other than him (!).”

Scott, what is it specifically that you find ill defined in Joy’s one-paper paper? http://arxiv.org/abs/1103.1879

287. Joy Christian Says:

Simulation of what? Let me reproduce Sec. VII of this paper
of mine: http://arxiv.org/abs/1110.5876

A SIMPLY-CONNECTED MODEL CANNOT BE SIMULATED BY ITS DESCRETIZED IMITATION:

As we saw above, within my framework quantum correlations are explained as topological effects, not contextual effects, and that Moldoveanu has overlooked this obvious fact. This is reflected, for example, in his failed attempts to simulate my model on a computer by expecting some sort of contextual variation in the measurement results. The usual idea behind a computer simulation of EPR correlations is to program how a measurement function, say A (a, L), changes when its context is changed, say from a to a’, and likewise for the function B(b, L). But in my model these functions do not change with their contexts at all. It is the topology of the physical space that brings about the sinusoidal correlation between A (a, L) and B(b, L), not the contextual variations within A (a, L) and B(b, L) themselves. As counterintuitive as this may seem, that is what the mathematics of my model implies, and it matches exactly with the experimental evidence. Consequently, most unsophisticated simulation attempts are bound to fail.

In fact, quite independently of Moldoveanu’s failed attempts, in my view the whole fashion of simulating EPR correlations on a computer is completely wrong headed. It is based on serious misconceptions about the true physical and mathematical reasons for the existence of EPR correlations in Nature [5]. In all real-life demonstrations of the correlations, Alice and Bob are known to always observe truly random outcomes of their measurements: A = +1 or -1 and B = +1 or -1. Therefore, as correctly recognized by Bell, no local functions of the form A (a, L) and B(b, L) can reproduce the observed correlation, unless the topological properties of the physical space itself are taken into account. In the language of my model this means that one must first model the physical space, not as R^3, but as S^3, which differs from R^3 only by a single point at infinity [4]. By contrast, what is usually tried in attempts to simulate my model is a completely wrong headed approach, based on an implicit assumption that the numbers A and B are only apparently but not truly random, and if only one can somehow discover the correct functional dependence of these numbers on the disposition of the apparatus and hidden variables then the correct correlation between them would emerge. However, as Bell convincingly demonstrated long ago [1], one can never reproduce the sinusoidal correlation in this manner. For the EPR correlation are what they are because of the topological properties of the physical space itself [10], not because there exists some as-yet-uncovered hidden order in the randomness of A and B. Moldoveanu would have saved himself a lot of time and effort had he appreciated this basic message of my framework.

In any case, a simply-connected model such as mine cannot possibly be either proved or disproved by its numerical simulation. A simulation of a model is an implementation of its analytical details, not an experiment that can either prove or disprove its validity. If reality can be so simply simulated then there would be no need for the staggeringly expensive actual experiments. Reality is mathematically far richer and profounder than what a computer can fathom.

288. Thomas H Ray Says:

I don’t think any mathematician can disagree with Joe Fitzsimons’ (well-written) points on the sharp demarcation between theorem and physical model.

On the other hand, I don’t think a scientist of any sort can disagree that the difference between conjecture and theory is measured correspondence between the mathematical theory and the physical result. Joy has proposed nothing short of this.

The only mathematical criticisms I have read don’t recognize Joy’s framework as analytical. That’s a big mistake on the critics’ part, and a misunderstanding that alone supports their remarks.

289. Joy Christian Says:

It should be noted that ALL of the incompetent and erroneous arguments by Richard Gill, as well as those by the other even lesser brain, have been debunked systematically many times over, not only by me but also by several other people on the FQXi blogs. See, in particular, the following two papers of mine:
http://arxiv.org/abs/1203.2529
http://arxiv.org/abs/1110.5876
Gill and his sidekicks do not have a leg to stand on.

290. David Brown Says:

@Joy Christian #287: In reference to your “groundbreaking work” PLEASE carefully read my comment #274. I AM NOT BEING SARCASTIC — I AM PERFECTLY SINCERE. You have NOT disproved Bell’s Theorem. Your model is NOT local realistic. Your model is non-local realistic because you have replaced quantum states by quantum Christian SU(8) states. YOU REALLY HAVE FOUND A REFORMULATION OF SUPERSTRING THEORY. Your 7-sphere consists of quantum superstring information. The 11-dimensional fundamental domain of M-theory consists of 4-dimensional spacetime together with your 7-sphere. Your model is non-local BUT IT REALLY IS A WORK OF GENIUS! Please consult with an M-theorist. YOU HAVE FOUND A PHYSICAL INTERPRETATION OF M-THEORY. Scott Aaronson is correct that: (1) the mathematical proof of Bell’s theorem is valid and (2) there is enormous (but perhaps not air-tight) empirical evidence that Bell’s theorem is true in terms of physics — several physicists have won Nobel prizes based on the physics of Bell’s theorem. You have an erroneous idée fixe that you need to overcome.

291. Joy Christian Says:

David Brown,

I do not doubt your sincerity, but my model is both local and realistic in precisely the senses defined by both Bell and EPR.

292. John Sidles Says:

There are plenty of lessons for students in the discussion so far, and it seems to me that opinions differ substantially (if they differ at all) only in the priority of the following four essential elements:

(1) master the toolset needed to decide these questions for yourself,

(2) scrupulously practice the ideals of fairness, respect, clarity, and correctness,

(3) respect Tony Zee’s dictum “any self-respecting physicist should learn about the history of physics,”

(4) computationally simulate (in detail, as a ‘sanity check’) everything that you *think* you understand, per Feynman’s dictum “what you cannot create, you do not understand.”

And since all four elements are essential, perhaps the priority ordering does not matter very much.

So what comes next? A powerful ‘sanity check’ is to upgrade one’s understanding of the Bell relations to an understanding of the Onsager relations, on the grounds that the latter naturally extends the former’s (1) mathematical toolset, (2) scientific ideals, (3) scientific history, and (4) computational practices.

As background, when Bell-type correlations are extended to depend continuously upon space and time, then — under certain assumptions that most researchers regard as mathematically and physically natural — these correlations respect certain symmetry relations that were first propounded by Lars Onsager, for which he received the Nobel Chemistry Prize in 1968.

History shows us that not everyone was pleased by Onsager’s Nobel. In particular, the school of “Rational Thermodynamics” that was led by Clifford Truesdell and propounded in a textbook of the same name, for many decades attacked Onsagerism (as they called it) root-and-branch. And this conflict was resolved in the usual way: after decades of bitter dispute, Onsager and Truesdell both died, following which Onsager’s formalism (mostly) prevailed, for the pragmatic reason that it was more powerful, and more naturally extensible, than Truesdell’s.

If we seek a faster path to enlightenment (and one having a lower mortality rate) then an illuminating ‘sanity check’ (in Scott’s phrase) of one’s understanding of the Bell relations is to work through, in full computational detail, a parallel understanding of Onsager relations. In this respect one good overview (of many) is provided by Kromnes and Hu’s “General theory of Onsager symmetries for perturbations of equilibrium and nonequilibrium steady states” (Physics of Fluids B, 1993), which includes in Section VIII.C a critique of Truesdell’s school. Regardless of one’s preferred formalism for discussing correlations among measurements, deriving the Onsager relations is an instructive ‘sanity check.’

A certain flexibility of conception turns out to be necessary in this exercise. For example, physicists tend to regard space and time as fundamental notions, from which transport theory arises, whereas engineers tend to regard transport as fundamental, from which notions of space and time arise. To calculate effectively, one needs to be familiar with both cognitive frames, choosing whichever is more natural for the computations at-hand.

One final crucial question is: After Bell, and after Onsager, what comes next? Insofar as we focus upon experimentally observable correlations, then it seems (to me) that one natural further exploration are the high-order correlations associated to linear quantum optics … continuing the explorations begun so admirably by Aaronson and Arkhipov (arXiv:1011.3245).

Everyone has their own conceptions regarding the seminal class of experiments that Aaronson and Arkhipov propose. For me, they suggest an Onsager-type reciprocity relation: “For any physically realizable dynamical system, the problem of verifying that a purported dataset of experimental observations is not a simulation belongs to the same computational complexity class as simulating that dataset.” Needless to say, this hypothesis is concretely on the Gil Kalai side of the (wonderful!) ongoing debate between Gil and Aram Harrow, that is being hosted on Dick Lipton’s and Ken Regan’s weblog Gödel’s Lost Letter and P=NP.

Far more important, however, than mundane questions like “Who’s winning the debate?” are the teachings of history with respect to the Bell relations and Onsager relations. Namely, pursuing new classes of questions always requires that we master new mathematical toolsets, respect the ideals of our profession, study history, and ‘sanity check’ our computations. As Scott has aptly written of this process: “We welcome it as the scientific adventure of our lives.” 🙂

293. Thomas H Ray Says:

David Brown #290

I understand how you get the nonlocal/real connection to string theory (string theory is said to be a nonlocal hidden variables theory). However, I never have quite understood why any actual experiment that could possibly be formulated to falsify string theory could be called “nonlocal.” A measurement result (click, flash, track) is ALWAYS local. The problem with the Bell-Aspect interpretation is the value of nonlocality assigned to “the experiment not done.”

294. Florin Moldoveanu Says:

Thanks Scott,

It’s a go then. But instead of uploading another paper I’ll write an appendix on the first one. I’ll let you (and everyone else) know as soon as is announced (I have a few editing to do and I hope to have it in a few days).

Florin

295. John Sidles Says:

Joy Christian Says:

David Brown, I do not doubt your sincerity, but my model is both local and realistic in precisely the senses defined by both Bell and EPR.

Joy, for students it is easier to verify that your correlations are not normalized in accord with the conventions of Bell and EPR. This in itself suffices to disconnect your work from the literature of Bell inequalities, both theoretical and experimental. It is concerning that you write article-after-article without addressing this point. In this objective respect, your (numerous) critics are entirely correct.

296. David Brown Says:

@John Sidles #294: When you suggest that we “computationally simulate” there is nothing to simulate.
@Thomas H. Ray #295: You write, “A measurement result … is ALWAYS local.” A measurement result might IN PRINCIPLE be evidence for non-local realism. A measurement result might IN PRINCIPLE be evidence for local realism. The definition of “local realism” involves mathematics, physics, metaphysics, and semantics. I contend that Christian has replaced “quantum correlation” by “quantum Christian SU(8) correlation” and has replaced “local realism” by “Christian SU(8) realism”. The basic definition of Christian’s model for his Theorema Egregium is non-local, realistic. Is there at least one expert on quantum information processing who thinks that Christian’s alleged disproof of Bell’s theorem HAS ANY MERIT WHATSOEVER?

297. David Brown Says:

Joy Christian, comment #289, writes “… within my framework quantum correlations are explained as topological effects, not contextual effects …” NO! NO! NO! Within the Christian framework, quantum Christian SU(8) correlations are explained as topological effects AND contextual effects relative to the 7-sphere of superstring uncertainty. PLEASE TRY TO UNDERSTAND THE PRECEDING SENTENCE. Christian, Ray, and the rest need to consult with an M-theorist. Christian and Ray fail to grasp the basic contention of Scott Aaronson and Bram Cohen: If I claim that, first, I have a proof that HIV does not cause AIDS and, second, I have some mathematical equations that prove that HIV does not cause AIDS, then would you think that I have gone off the deep end?

298. Joy Christian Says:

@John Sidles:

“Joy, for students it is easier to verify that your correlations are not normalized in accord with the conventions of Bell and EPR.”

They are.

John, instead for superficially and impressionistically reading my papers I wish you actually spend some time with it to realize what exactly I am doing. For the specific question you raise, I suggest you read two things. First, read this paper in full (from first sentence to last sentence): http://arxiv.org/abs/1106.0748

After you have done that, please do also consult Sec. XI of this paper: http://arxiv.org/abs/1110.5876

I need not remind someone as informed as you are that a new idea in science takes considerable time to digest, and it is not always author’s fault why it takes such a long time to digest.

299. wolfgang Says:

The halteproblem: Will this thread ever end on it own? Will it be stuck in an endless loop? Does John Sidles have an infinite supply of quotes? Is Scott’s patience finite after all?

300. Joy Christian Says:

David Brown,

Before consulting anyone else, pleases consult Bell himself. Please read the first two papers of Bell from his book. When you understand the contents of those two papers, you will understand my claim. It is evident that most people in this forum have never read either of Bell’s papers. Ideally they should also read the original EPR paper, but that would be too much to ask from people in this forum.

301. Raoul Ohio Says:

ScentOfViolets:

Excellent observation. I read some van Vogt when I was a kid. I could never understand what he was talking about, but suspected it was deep stuff.

302. John Sidles Says:

Wolfgang #299, my vein of quotations is far from exhausted!   🙂

Here is an affectionate story of Clifford Truesdell told by his colleague Ingo Müller, that illustrates how theoretical isolation from practical experimental concerns arises:

Truesdell was a consummate theoretician. He showed nothing but disdain for experiments, be they conducted in the laboratory or on the computer.

So when Truesdell visited me in Berlin, on the first day he came and said: “Ingo, can I ask you for a favor?” And I, eager to please my visitor and one-time mentor, say: “Of course, Clifford, what can I do for you?”

🙂   🙂   🙂

Although Truesdell was bull-headedly on the wrong side of the great 20th century debate regarding Onsager relations, his overall contributions were respected by many. For example, Truesdell wrote more than 500 well-regarded Mathematical Reviews, of which the present Shtetl Optimized discussion might perhaps be summarized by this one, which directly bears upon Joy Christian’s concerns:

Bearing in mind that really new ideas are not only difficult for a reader to grasp but also difficult for an author to express, the reviewer has long and earnestly sought to grasp what it is that the author spreads out in a maze of complicated diagrams, ungainly new words, quotation marks for phrases which are not quoted, italics, and innumerable dark symbols including a fantastic mournful black letter in some cases hardly identifiable. The reviewer’s effort has not been successful.

Although few research articles are retracted, many are ignored, commonly for the reasons that are given in Truesdell’s Mathematical Reviews.

And finally, my own interest in these topics arises not from expecting that the history of science will repeat itself, but from sincerely hoping and even systematically planning that history will repeat itself … warts and all … if we work hard and reasonably respect traditional STEM norms … and we are very, very, lucky.

303. Bram Cohen Says:

Joy Christian: How could a single point at infinity make a difference for a simulation of a finite-sized system? Since it’s at infinity, can’t it never be reached?

Also, I still don’t understand your problem with computer simulations. Do you not believe that the random number generators in computers work properly? Do you not think that, say, racing games can be extremely accurate physics simulators of real-world cars?

304. Sniffnoy Says:

David Brown:

I get the idea you’re going to have to do this consulting with an M-theorist yourself…

305. David Brown Says:

@Sniffnoy #306: This thread is the quantum information theorists’ version of the Monty Python Dead Parrot Sketch.
According to Bell’s 1964 paper, “It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty.”
http://www.drchinese.com/David/Bell_Compact.pdf “On the Einstein Podolsky Rosen Paradox”
According to Christian, in the first equation of Bell’s 1964 paper, Bell made the mistake of using the 1-sphere instead of the 3-sphere or the 7-sphere (in the most general case) as the co-domain.
http://arxiv.org/pdf/1201.0775v4.pdf “On the Origins of Quantum Correlations”
I say that Christian is suggesting that instead of talking about quantum states we should talk about quantum Christian SU(8) states. I say that if you use a 7-sphere of superstring uncertainty or superstring quantum information, then you are NOT talking about local realism. Christian insists that I am wrong and that the 7-sphere is not superstring uncertainty but is PART OF LOCAL REALISM. Christian claims that he proved:
Christian’s Theorema Egregium: Every quantum mechanical correlation can be understood as a classical, local-realistic correlation among a set of points of a parallelized 7-sphere.
I say that Christian’s claim is false. I say that Christian proved:
Corrected Form of Christian’s Theorema Egregium: Every quantum mechanical Christian SU(8) correlation can be understood as a realistic, non-local Christian SU(8) correlation among a set of points of a parallelized 7-sphere.
Why do I care? I need the corrected form of the Theorema Egregium to define the smoothing of the Nambu transfer machine. I say call in the M-theorists. I say that Christian is a great genius of theoretical physics but suffers from an erroneous idée fixe (or several erroneous idées fixes).

306. James Putnam Says:

Scott Aaronson,

This is a recent addition to Scott Aaronson’s opening statement:

“Update (5/7): I can’t think of any better illustration than the comment thread below for my maxim that computation is clarity. In other words, if you can’t explain how to simulate your theory on a computer, chances are excellent that the reason is that your theory makes no sense! The following comment of mine expands on this point:

The central concept that I find missing from the comments of David Brown, James Putnam, and Thomas Ray is that of the sanity check.

Math and computation are simply the tools of clear thought. …”

This quote first appeared in Scott Aaronson’s comment #248. Since it has reappeared in his opening statement, I want here to emphasize its connection to my response comment #269. Scott Aaronson responded in comment #273 that I missed his point. In my last comment #273 I did not object to that. I asked for his opinion and he gave it and I appreciated receiving it.

However, since I have become referrenced in his opening statement, I do wish to emphasize that I responded to his comment #248 in my comment #269. Furthermore, I will amend my last comment #273 by adding that I do not think that I missed his point. I think that I addressed it accurately and effectively. That is my opinion.

None of this is meant to imply that Scott Aaronson’s opinion is not valued by me. I value his opinion and look forward to learning more of what he thinks as well as from the many other learned contributors.

James

307. Joy Christian Says:

Bram Cohen,

The issue is not so much about a point at infinity, but about the compactness of S^3 as a physical space versus non-compactness of R^3 as a physical space.

Another issue is: what is it that we want to simulate, and what difference does it make whether we can simulate it or not? Unlike what seems to be the general view of people in this forum, Bell’s theorem was *not* about what we can or cannot simulate on a computer. It was about the nature of the physical reality. It was about whether Einstein’s conception of local reality is viable in physics or not. For this question computer simulations are irrelevant. As James once put it, computers can only tell you back what you tell *it*. In other words it cannot tell you back what you cannot tell it.

Now you may say: Then, tell us what to tell our computer. Well, I have already told you. It is all contained in my papers. According to my model EPR correlations are what they are because of the topological structure of our physical space itself, not because of the contextual variations in the apparently random numbers observed by Alice and Bob. If you can simulate the physical space S^3 (which has to be parallelized) on your computer and then let Alice and Bob play their game in that space, then you will find that the correlations between their measurement results are quantum, or stronger-than-classical. Can you do this?

308. Thomas H Ray Says:

David Brown,

“Christian, Ray, and the rest need to consult with an M-theorist.”

Is that, like, a priest with a physics PhD? Just kidding — but seriously, David.

“Christian and Ray fail to grasp the basic contention of Scott Aaronson and Bram Cohen: If I claim that, first, I have a proof that HIV does not cause AIDS and, second, I have some mathematical equations that prove that HIV does not cause AIDS, then would you think that I have gone off the deep end?”

I would think that you are a quack. One can’t prove by experiment that HIV does not cause AIDS — one can only possibly show that the correlation between HIV infected patients and those with full blown AIDS is tenuous; i.e., that there are a significant number of HIV positive folks who never get sick with AIDS. By the same token, no mathematical proof of such a relation is possible — one could only speak of a practical model predicting that among a certain population of HIV patients, x percentage will suffer with AIDS. I don’t know how meaningful that is, however — a similar argument is used to claim that marijuana smoking leads to hard drug abuse.

At any rate, your point here escapes me.

309. James Putnam Says:

David Brown #305,

“…I say that if you use a 7-sphere of superstring uncertainty or superstring quantum information, then you are NOT talking about local realism. Christian insists that I am wrong and that the 7-sphere is not superstring uncertainty but is PART OF LOCAL REALISM. Christian claims that he proved:
Christian’s Theorema Egregium: Every quantum mechanical correlation can be understood as a classical, local-realistic correlation among a set of points of a parallelized 7-sphere.
I say that Christian’s claim is false. I say that Christian proved: …”

Thank you for presenting this interesting challenge.

James

310. Thomas H Ray Says:

David Brown #296

“A measurement result might IN PRINCIPLE be evidence for non-local realism.”

Describe to me a real measurement that was made nonlocally. If by “in principle” you mean that the experimenter assigned some value to the experiment not done, that argument is contentious. Even tendentious, considering the flimsy proof on which Bell’s theorem is founded.

“A measurement result might IN PRINCIPLE be evidence for local realism.”

Not might. Is. In principle and in the correspondence of mathematical theory to physical event.

“The definition of ‘local realism’ involves mathematics, physics, metaphysics, and semantics.”

The definition of local realism involves the moon being there when no one is looking at it. Proving that objectively worded conjecture is why we’re here.

311. Thomas H Ray Says:

Bram Cohen #303

“How could a single point at infinity make a difference for a simulation of a finite-sized system? Since it’s at infinity, can’t it never be reached?”

Can the North Pole never be reached?

That’s not the problem for simulating a measurement function continuous from an initial condition.

312. Jim Says:

Sorry if this comment contributes to the noise-to-signal ratio here but: Joy, I wonder if you can clarify the physical meaning of your 3-sphere. In #307 you call it “physical space”, which makes it sound like you’re saying that the topology of a spatial slice of our universe is S^3, just as it is in a closed Friedman-Robertson-Walker spacetime. But, that can’t be what you mean, can it? Having skimmed your papers it appears that you’re saying the outcome of a measurement of spin-orientation is to be considered, somehow, a vector in parallelized S^3. This may be a stupid question but on the other hand it seems crucial for simulating, and thus understanding, your theory: what is the physical meaning of your 3-sphere?

313. David Brown Says:

@Thomas H. Ray #310: According to Scott Aaronson, “… Bell’s Theorem has no more been ‘disproved’ than the Cauchy-Schwarz inequality, and it will never be, even if papers are stacked from here to the moon.” Changing the definitions of “quantum correlation” and “local realism” changes everything.
I think that introducing the 7-sphere is NON-LOCAL but you and Joy Christian say it is LOCAL.

314. Richard Gill Says:

James Putnam #269: if you actually read the details of Joy’s model you will find out it is not about Bell and all that. His measurement outcomes are perfectly anti-correlated independently of the settings. His correlation is not the correlation calculated in experiments. Instead, he divides the raw product monent -1 by two functions of the measurement settings a and b respectively. The reasoning for this (he appeals to statistical theory! Not physics) is nuts. If you actually read the details of his experimental paper you will see it too is just plain nuts. Any experimentalist who performs that experiment will end up with 4N numbers +/-1 (N measurements of A and A’, B and B’) and by arithmetic necessity, all CHSH inequalities will be satisfied. Whatever the outcomes. Whatever N. Whatever a, a’, b, b’.

The reason why despite this I actually went to the trouble to refresh my memory of Clifford algebra and all that, was because I had the feeling that though the guy obviously doesn’t actually have a clue what Bell is all about, it could still be that his pure mathematical insight was so deep that he’ld tumbled upon a geometric alternative to the usual Hilbert space set-up. A deep isomorphism between two wonderful mathematical structures. I can forgive him for silly mistakes about what Bell is all about, if on the other hand he has found a deep mathematical result using his extraordinary skills in geometric algebra. In other words, though his work is not about Bell, it could be about something else, perhaps even more exciting!

But what did I find? Elementary logical contradictions! Stupid sign errors!

I was once by accident present at a string theory seminar. It was really deep stuff, all the big guys were listening attentively, nodding from time to time. At some point the speaker made an error. After all, whatever weird space he was in, he was merely doing a formal second order Taylor expansion and he forgot the half. I was the only one who noticed, the speaker had to do a lot of work to recover from the error, everyone thought I was a string theory expert. (The speaker was extremely grateful by the way).

Sometimes it helps *not* to know what it is *supposed* to be about. It enables one to spot errors, logical contradictions, and so on, which the person who knows what it’s about and is excited about where it is going, simply does not notice.

Whatever Christian’s maths might be supposed to be a model for in physical reality, it has to stand on its own feet. He can’t write down an assumption on line 1, use it on line 2, and then use a contradictory assumption on line 3. (I’m talking here about assumptions whose scope is global, not local. Assumptions about mathematical objects which are fixed throughout some long derivation.)

Usually when one mathematician points out a mistake in another mathematician’s work, they quickly come to agreement, one admits his or her mistake (everyone makes mistakes) and mathematical science makes progress. Joy’s work is not maths. It’s not physics either. It is science fantasy.

Everyone who actually knows the mathematical structures Joy is working with, sees the fatal errors. They do vary from paper to paper, some are better hidden than others. The extraordinary thing is that he can’t or won’t admit to any inconsistency. He never answers a direct question but evades the issue, says something irrelevant. Is he infinitely cleverer than everyone else, and onto something really great, which unfortunately is just hard to express? Or does he just have a vivid imagination, quick pen and sharp tongue, and has long ago fooled himself by an easy mistake to make by someone with lack of mathematical discipline but a gift for the gab, that he’s a genius?

315. David Brown Says:

@Thomas H. Ray #312: “Describe to me a real measurement that was made nonlocally.” The issue in Bell’s theorem is NOT the locality or nonlocality of the measurements made but instead the locality or nonlocality of the mathematical model of reality. “The definition of local realism involves the moon being there when no one is looking at it.” The metaphysical definition of local realism does indeed involve that but the PHYSICAL definition of local realism involves technical issues concerning quantum states, qubits, quantum correlations, etc. Scott Aaaronson is using one definition of local realism while you and Christian are using another definition of local realism.

316. Henning Dekant Says:

@Joy, based on the noise in this forum I suggest it should be self-evident at this point that you’d bolster your case immensely if you were to run a simulation of your proposed experiment in a simulated universe that adheres to a S^3 topology.

317. David Brown Says:

@Thomas H. Ray #312: To clarify my position, I make the following 2 claims:
(1) The mathematical assumptions made by John Bell are PART OF THE DEFINITIONS of “quantum correlation” and “local realism”. (2) These definitions are used by those who do experiments concerning quantum entanglement.

318. Joy Christian Says:

Once again I am compelled to point out that ALL of the incompetent and erroneous arguments by Richard Gill against my model have been systematically debunked many times over, not only by me but also by several other people on the FQXi blogs. See, in particular, the following two papers:
http://arxiv.org/abs/1203.2529
http://arxiv.org/abs/1110.5876
After having spent so many months on my one-page paper Richard Gill has yet to understand the first thing about my model.

319. David Brown Says:

Consider two arguments (A) and (B):
(A) Christian’s introduction of the 7-sphere involves measurement. Measurement is always local. Therefore, Christian’s model is local-realistic.
(B) Christian’s introduction of the 7-sphere involves 7 dimensions of quantum uncertainty. Quantum uncertainty is fundamentally nonlocal. Therefore, Christian’s model is nonlocal, realistic.
Which of the two arguments is correct? The answer involves highly technical issues involving quantum correlations and measurements. Both arguments are, to a large extent, metaphysical bilge.

320. Joy Christian Says:

Jim,

Your question is not at all stupid. In fact yours is probably the most pertinent question about my model in this entire thread. I am indeed saying that the topology of the spatial slice of our universe is a 3-sphere, but this 3-sphere is NOT the one which is usually assumed in a closed FRW spacetime. The difference is in its topology. The 3-sphere I am talking about is parallelized. It is the one that appears in teleparallel gravity. Its Riemann tensor is zero, but torsion non-zero (and constant).

321. Sniffnoy Says:

David Brown:

My point is, if you are correct (I would have no idea), it seems you’re going to have to talk to an M-theorist about it yourself, because it seems unlikely you’re going to convince Joy Christian.

322. David Brown Says:

@Richard Gill #316: If Christian is as you say, then how did he get a PhD with Abner Shimony as thesis advisor?

323. Henning Dekant Says:

One aspect that has been lost in this busy forum is that either Scott or Joy will have to pony up a lot of money. If Joy can keep his $200K than it is save to assume that Scott will have to pay$100,000 to whoever can explain why that is.

On the other hand if the IBMs of the world succeed in building a scalable quantum computer Joy owes Scott $200,000. Certainly we should keep an eye on this and make sure that these bets are properly honored in the future. So I added a “QC Bet Tracker” page to my blog and will pledge myself to keep monitoring this. After all gambling debt is a debt of honor. I am sure neither Scott nor Joy just frivolously threw this out to garner attention. 324. Thomas H Ray Says: David Brown #316 “(1) The mathematical assumptions made by John Bell are PART OF THE DEFINITIONS of ‘quantum correlation’ and ‘local realism’. ” Then they are merely metaphysical claims, aren’t they? “(2) These definitions are used by those who do experiments concerning quantum entanglement.” Which is why they can assign the value of nonlocality to experiments not done, and call it a day. Fatal error — assuming what one wants to prove, and proving it by induction alone. And look, I’m not saying that these assumptions are not useful. They do not, however, come up to the level of compromising a complete physical theory. 325. Jim Says: Joy, if the outcome of a local measurement depends on the global topology of the universe, in your theory, then it would seem to be, in essence, a nonlocal hidden variable theory. 326. Henning Dekant Says: @Joy, you wrote: Its Riemann tensor is zero, but torsion non-zero (and constant). If torsion is constant I’ll take it you simply assume this background for the sake of simplicity? My understanding is you are working in a strict teleparallel picture i.e. the torsion tensor is the sole expression for gravity, isn’t it? 327. David Brown Says: @Thomas H. Ray # 326: YOU MAKE VERY GOOD POINTS HERE. @Jim #327: You make an absolutely wonderful point. Is Joy Christian a genius who has discovered one of the essential prerequisites for a physical interpretation of M-theory? I think the whole issue depends upon whether the introduction of the 7-sphere is a NON-LOCAL or a LOCAL physical (and/or metaphysical) hidden variable theory. 328. Bram Cohen Says: Joy Christian, by S^3, are you referring to the surface of a hypersphere? If your contention is that the universe is on the surface of a hypersphere or a projective plane, can you refer to some evidence in cosmology that that’s the case? Also, why would the geometry of the universe as a whole matter for an experiment run in a miniscule section of space, which approximates R^3 so closely that it’s nearly impossible to measure the difference? Finally, what is your beef about compactness? Obviously computers use rational approximations for everything, but can you give an experiment (related to your experiment for the Bell inequality or not) where the real world experiment will yield a dramatically from the simulated experiment because of the limits of floating point approximations? 329. Bram Cohen Says: I meant to say ‘dramatically different from’ in that last post. 330. Bram Cohen Says: Er, ‘dramatically different result from’. I don’t copy edit so well. 331. John Sidles Says: Although I am keen as anyone regarding the beautiful mathematics of dynamical trajectories on curved manifolds, students (especially) are invited to examine the “Channel 1” and “Channel 2” inputs to a HP-3562a Dynamic Signal Analyzer (specifically, these inputs are the two BNC connectors at lower right in the image). The HP-3562a (or its functional equivalent) computes the correlation function in all experimental tests of the Bell inequalities. Unsurprisingly, the HP-3562a accepts 0-1 measurement inputs with aplomb, and it computes their correlation via Bell’s conventions. But the HP-3562a does *not* accept the quaternionic measurement inputs of Joy’s formalism; neither does any photon detector (known to me, or to any physicist) supply quaternionic measurements outputs. Moreover, according to Joy, quaternionic measurements cannot be converted to conventional 0-1 measurements … because otherwise numerical simulation of Joy’s formalism would be feasible. It is in this concrete experimental sense of requiring quaternionic measurement inputs, that Joy’s formalism is wholly disconnected from Bell’s Theorem, and disconnected also from experimental measurements of Bell-type inequalities. 332. Henning Dekant Says: @David Brown, I find it entirely fascinating that you think you can find a pony in Joy’s work yet he immediately refutes it and leads it to the slaughterhouse. This is all the more astounding as this seems to be mostly over terminology. @Bram Cohen #328, IMHO you are asking exactly the right question. Joy’s section on why this cannot be handled by a computer is all prose. A bit more mathematically motivated argument that demonstrates essential non-computability would be appreciated. 333. Joy Christian Says: @Jim: You wrote: “Joy, if the outcome of a local measurement depends on the global topology of the universe, in your theory, then it would seem to be, in essence, a nonlocal hidden variable theory.” Local measurements do not depend on the global topology of the universe. Only the correlation between the measurement results of Alice and Bob are dictated by the topology of the 3-sphere. Neither are we concerned about the universe as a whole. There seems to be much confusion about what is local and realistic within the context of my model. David Brown in particular seems to be very confused about this. My model is realistic precisely in the sense specified by EPR and it is local precisely in the sense specified by Bell. Bell had a very simple and clear-cut way of defining a local-realistic model. He would call a model local-realistic if the product AB(a, b, L) of the simultaneous measurement results A(a, L) = +/-1 and B(b, L) = +/-1 of Alice and Bob can be factorized as AB(a, b, L) = A(a, L) B(b, L). In other words, if the result A(a, L) of Alice would be independent of both the measurement context b and the measurement result B of Bob, and likewise if the result B(b, L) of Bob would be independent of both the measurement context a and the measurement result A of Alice. My model manifestly satisfies this criterion both for the raw scores (scalars) as well as the standard scores (bivectors). Thus my model for ALL quantum correlations is manifestly local and realistic. @Henning Dekant, You asked: “If torsion is constant I’ll take it you simply assume this background for the sake of simplicity?” No. The torsion of a 3-sphere happens to be constant (unlike that of a 7-sphere). You asked: “My understanding is you are working in a strict teleparallel picture i.e. the torsion tensor is the sole expression for gravity, isn’t it?” Yes, that is correct. @Bram Cohen You asked: “…by S^3, are you referring to the surface of a hypersphere?” Yes, but we are not concerned about cosmology. We are only concerned about the topology of a closed region where the experiment is taking place. There is no need to hypothesize anything about the universe as a whole. You eat elephant one bite at a time, not as a whole. You are asking a lot of simulation questions. But I am saying that the whole idea of a simulation is misguided. What makes you think that we can simulate the physical reality that easily? In my opinion a real experiment is inevitable to test my hypothesis. 334. David Brown Says: Thomas H. Ray #326: I think that Christian’s theory of local realism makes interesting predictions. According to the M-theorists the fundamental domain of physical reality has 11 dimensions. According to Christian, physical reality has 4 dimensions in the form of spacetime and 7 dimensions in the form of measurement. Therefore, according to Christian’s theory, it should be impossible to detect extra spatial dimensions. Do you agree? 335. David Brown Says: Thomas H, Ray #326: More importantly, if Christian’s theory of local realism is true then SU(8) should be the gauge group for physical reality — a far from obvious conclusion. 336. James Putnam Says: Richard Gill #314, I did say in comment #273: “I don’t evaluate Joy’s work. I do not claim to understand Joy’s work. I am interested in the potential importance of it. Joy and everyone seriously interested can speak for themselves.” No matter what I think I know, there is only one person who’s opinion is the benchmark, that is Joy’s. Whatever I might say has the risk of misrepresenting, and thereby being harmful to, Joy’s work. Joy represents Joy. The second reason is the one I wish to avoid interjecting the most. It concerns my reservations about theoretical physics. Those reservations have no place in this discussion. Joy’s work is based upon his expert knowledge of theoretical physics. Richard Gill: “James Putnam #269: if you actually read the details of Joy’s model you will find out it is not about Bell and all that. His measurement outcomes are perfectly anti-correlated independently of the settings. His correlation is not the correlation calculated in experiments. Instead, he divides the raw product monent -1 by two functions of the measurement settings a and b respectively. The reasoning for this (he appeals to statistical theory! Not physics) is nuts. If you actually read the details of his experimental paper you will see it too is just plain nuts. …” Theoretical physicists must decide the value of Joy’s work. “…Any experimentalist who performs that experiment will end up with 4N numbers +/-1 (N measurements of A and A’, B and B’) and by arithmetic necessity, all CHSH inequalities will be satisfied. Whatever the outcomes. Whatever N. Whatever a, a’, b, b’. …” This is a part of what you keep repeating while Joy says otherwise. It is the physics that determines the correct use of the math. Theoretical physicists must judge this. “…The reason why despite this I actually went to the trouble to refresh my memory of Clifford algebra and all that, was because I had the feeling that though the guy obviously doesn’t actually have a clue what Bell is all about, …” You are a mathematician declaring that a theoretical physicist “… doesn’t actually have a clue what Bell is all about…” Theoretical physicists will have to make that judgement. If they do not step forward and do it, then it is not done. “…it could still be that his pure mathematical insight was so deep that he’ld tumbled upon a geometric alternative to the usual Hilbert space set-up. A deep isomorphism between two wonderful mathematical structures. I can forgive him for silly mistakes about what Bell is all about, if on the other hand he has found a deep mathematical result using his extraordinary skills in geometric algebra. In other words, though his work is not about Bell, it could be about something else, perhaps even more exciting! …” Again, Joy’s understanding of “…what Bell is all about…” is a matter for theoretical physicists to address. “…But what did I find? Elementary logical contradictions! Stupid sign errors! …” I think that there is no way that Joy would tolerate, defend, or pretend to justify stupid sign errors in his work. Perhaps what you found is that you are misinterpreting Joy’s work. Joy has addressed this matter over and over again and I leave it to him to speak to. I wan’t no part in it. “…I was once by accident present at a string theory seminar. It was really deep stuff, all the big guys were listening attentively, nodding from time to time. At some point the speaker made an error. After all, whatever weird space he was in, he was merely doing a formal second order Taylor expansion and he forgot the half. I was the only one who noticed, the speaker had to do a lot of work to recover from the error, everyone thought I was a string theory expert. (The speaker was extremely grateful by the way). …” I would have thanked you also. There is no way that my talk could succeed so long as the audience is thinking about my math error and my inability to recognize its existence. “…Sometimes it helps *not* to know what it is *supposed* to be about. It enables one to spot errors, logical contradictions, and so on, which the person who knows what it’s about and is excited about where it is going, simply does not notice. …” I don’t agree with the point you are making here. “…Whatever Christian’s maths might be supposed to be a model for in physical reality, it has to stand on its own feet. …” It has been debated over and over again that his math does stand on its own. I play no part in that debate. Joy and Tom have played the principal roles in opposing your claim. I leave it to Joy and ultimately to theoretical physicists to address. “…He can’t write down an assumption on line 1, use it on line 2, and then use a contradictory assumption on line 3. (I’m talking here about assumptions whose scope is global, not local. Assumptions about mathematical objects which are fixed throughout some long derivation.) …” What is or is not contradictory is to be spoken to by Joy and ultimately judged by theoretical physicists. “…sually when one mathematician points out a mistake in another mathematician’s work, they quickly come to agreement, …” This is not difficult to agree to. It makes sense to me. “…one admits his or her mistake (everyone makes mistakes) and mathematical science makes progress. …” Here you are mixing a logical statement about mathematicians into a statement about Joy’s theoretical physics. I don’t see how they mix except through your personal opinion. “…Joy’s work is not maths. It’s not physics either. It is science fantasy. …” Can you quote enough theoretical physicists in support of what you say here to give it credibility? “…Everyone who actually knows the mathematical structures Joy is working with, sees the fatal errors. …” Can you name and quote some of these ‘everyones’? “…They do vary from paper to paper, some are better hidden than others. The extraordinary thing is that he can’t or won’t admit to any inconsistency. He never answers a direct question but evades the issue, says something irrelevant. Is he infinitely cleverer than everyone else, and onto something really great, which unfortunately is just hard to express? Or does he just have a vivid imagination, quick pen and sharp tongue, and has long ago fooled himself by an easy mistake to make by someone with lack of mathematical discipline but a gift for the gab, that he’s a genius? …” Your opinion is your opinion. I want nothing to do with associating myself with remarks such as these. James 337. David Brown Says: Thomas H. Ray #326: Perhaps Christian is totally correct! But perhaps Aaronson is totally correct! QUESTION 1: Are metaphysically possible measurements composed of quantum uncertainty? QUESTION 2: Are metaphysically possible measurements composed of virtual mass-energy? If Q1 <— yes and Q2 <— no then is the traditional form of Bell’s theorem favored? If Q1 <— no and Q2 <— yes then is Christian’s theory of local realism favored? 338. Fred D Says: Richard Gill says, “His measurement outcomes are perfectly anti-correlated independently of the settings.” You still have no comprehension of what Joy’s model is. It is a statistical model. You are hung up on some basic algebraic outcomes and can’t see the forest for the trees. And I see you still want to rig the game for Joy’s proposed experiment. http://www.fqxi.org/data/forum-attachments/2_Richard_said.pdf 339. David Brown Says: EVERYONE: Maybe we all have been too hasty and vituperative. We know that quantum entanglement occurs for pairs of particles such as photons, electrons, and even buckyballs. Does quantum entanglement occur for pairs of quantum entanglements in ways that yield decisive tests of the Aaronson view versus the Christian view? Let us think carefully about the preceding question. 340. Fred D Says: Jim says, “Joy, if the outcome of a local measurement depends on the global topology of the universe, in your theory, then it would seem to be, in essence, a nonlocal hidden variable theory.” I do believe the topology in Joy’s model is from the so-called “entangled” particles’ creation to detection only. And any particular outcomes due to topological “action” are completely random from the choice of handedness at creation. The only hidden variable in Joy’s model is mu = lambda*I where I is an oriented volume element and lambda is +/- 1 a fair coin toss. There is no variable for topological “action”. It is not required or needed; it is just a feature of the parallelized 3-sphere topology. So I believe Joy’s model is still local realistic. 341. David Brown Says: Joy Christian #5: “Scott Aaronson — yes our very own FXQi genius — has joined in the battle of words over my refutation of Bell’s former theorem.” Are Aaroson and Christian 2 geniuses like Bohr and Einstein? Aaronson’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Bell states can reproduce all of the predictions of quantum theory in the sense of the Copenhagen interpretation. Christian’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Christian SU(8) states can reproduce all of the predictions of quantum theory in the sense of the Christian interpretation of quantum theory. The Christian interpretation means the extension of the Copenhagen interpretation based upon Christian local realism. Brown’s Principle of Semantics in Physics: In physics the ultimate arbiters of the meanings of words should be the physicists who actually do the experiments. Brown’s Thesis of Quantum States: There are 3 fundamental categories of quantum states: quantum Bell states, quantum Christian SU(4) states, and quantum Christian SU(8) states. Brown’s Thesis of the Physical Interpretation of M-theory: There are 3 basic alternatives for a physical interpretation of M-theory: Seiberg-Witten curling-up (or compactification) of extra superstring dimensions, Christian local realism, and Fredkin-Wolfram building-up of time, space, and energy from Fredkin-Wolfram information below the Planck scale. 342. Fred D Says: There seems to be some computer science folks on this blog so I am wondering if a parallelized 3-sphere topology could be faithfully simulated on a computer using Geometric Algebra? If the answer is no, then Joy’s model for sure couldn’t be simulated on a computer. If the answer is yes, then maybe it is possible. And you would for sure find that the correlation between two points of the parallelized 3-sphere would produce -a.b after many runs. 343. David Brown Says: Do Aaronson and Christian have strong opinions? Are Aaronson and Christian 2 geniuses like Bohr and Einstein? Aaronson’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Bell states can reproduce all of the predictions of quantum theory in the sense of the Copenhagen interpretation. Christian’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Christian SU(8) states can reproduce all of the predictions of quantum theory in the sense of the Christian interpretation of quantum theory. The Christian interpretation means the extension of the Copenhagen interpretation based upon Christian local realism. Brown’s Principle of Semantics in Physics: In physics the ultimate arbiters of the meanings of words should be the physicists who actually do the experiments. Brown’s Thesis of Quantum States: There are 3 fundamental categories of quantum states: quantum Bell states, quantum Christian SU(4) states, and quantum Christian SU(8) states. Brown’s Thesis of the Physical Interpretation of M-theory: There are 3 basic alternatives for a physical interpretation of M-theory: Seiberg-Witten curling-up (or compactification) of extra superstring dimensions, Christian local realism, and Fredkin-Wolfram building-up of time, space, and energy from Fredkin-Wolfram information below the Planck scale. Is Brown a crackpot? Consider 6 questions: Is Milgrom the Kepler of contemporary cosmology? Is Wolfram a serious rival to Newton and Einstein? Is Fredking one of the greatest philosophers of our age? Is Aaronson a genius somewhat in the ballpark of N. Bohr and A. Turing? Is Christian a genius somewhat in the ballpark of A. Einstein and H. Weyl? Is Christian local realism essential for understanding M-theory? If the answer to any of the preceding 6 questions is no, then Brown is a crackpot. Is M-theory essential for understanding quantum gravity, D-wave superconductivity, and several other topics in physics? Does M-theory make many interesting TESTABLE PREDICTIONS in quantum information processing? Can we all learn something from the Monty Python Dead Parrot Sketch? 344. Richard Gill Says: James Putnam #336, I suggest you carefully read Joy’s one page paper, and then carefully read my critique of it. By “carefully read” I mean carefully check the maths, line by line. You may want to refresh your memory concerning things like Clifford algebra, quaternions, bivectors. These things have absolutely precise definitions, properties. In Joy’s one page paper, certain mathematical objects are defined. Their properties are specified. A calculation is made. The calculation is wrong. There is no room for maneuver, no room for opinion or debate. But if you want an argument from authority: ask David Hestenes. Ask Abner Shimony. Ask Reinhard Werner. Ask Michiel Seevinck. Ask Hans Maassen. Ask Marek Zukowski. Ask Lucien Hardy. … Note that not one of Joy’s papers on this topic passed peer review (several were submitted to top journals, according to his home page at Perimeter Institute). Note that after five years already, no peer reviewed article has appeared further developing Joy’s theory. Joy’s supporters never descend to the nitty-gritty level of specific definitions. Joy’s one-page paper says A=-lambda, B=lambda, lambda=+/-1 is a fair coin toss. Joy’s supporter Fred simply denies the actual unambiguous content of Joy’s paper. He admits that he recognizes the big picture, recognizes genius. He doesn’t check details. Joy’s supporter Tom says I don’t take account of the analytic nature of Joy’s model. Well, I take account of what Joy actually writes, the actual lines of mathematics. Joy’s refutation of my critique of his one-pager consists of changing his assumptions and then making a different mistake. Don’t believe me. Don’t believe Joy. Check yourself. It’s actually rather easy. This is the strength of mathematics: you don’t have to rely on authority, you can check for yourself. 345. David Brown Says: Fred D #340: “You still have no comprehension of what Joy’s model is.” One problem is that Christian, Ray, Klingman, and you have failed to explain Christian’s model in any proper sense to THOSE WHO REJECT YOUR BASIC ASSUMPTIONS. I would characterize N. Bohr’s viewpoint as “irreducible quantum agnosticism.” Here is my limited understanding of Christian’s viewpoint: The Copenhagen interpretation of physics should be replaced by an interpretation of physics based upon Christian’s model of topological measurement. Physical reality consists of 4 dimensions of spacetime together with a 7-sphere of topological measurement. ALL QUANTUM PHENOMENA are really EPR correlations based upon the parallelized 7-sphere model. IS THIS A FAIR ASSESSMENT? 346. John Sidles Says: Fred D, it just so happens that I *have* personally simulated the dynamical motion of rigid bodies on a quaternionic state-space manifold, and as an example, I have just now released a trajectory simulation (under a Creative Commons License) as the YouTube video “Dynamics of a water molecule” (with a tip-of-the-hat to Prof. James Moriarity). Computationally speaking, both the dynamical state-manifold of this animation, and the trajectory simulated on that state-manifold, are identical to the state manifold and the dynamical trajectory of outgoing fragments of Joy Christian’s “exploding sphere” experiment. It is instructive that all who have reduced Joy’s framework to concrete computations, have ended by rejecting the notion that this framework has any natural connection to Bell inequalities or to experiments that test them. Why is this? Perhaps it is because (as Scott says) “Computation is clarity.” ———— As a confection, follow the URL that the video provides to astronaut Michael Foale’s Mathematica Conference address “Navigating on MIR” (1998). The trajectory of the water molecule exhibits the same tumbling instability that, as Foale vividly describes, came near to destroying the space-station MIR. Also, and needless to say, the classical dynamical phenomena that this water molecule trajectory exhibits have higher-dimensional analogs on the complex state-manifolds of quantum simulations — these phenomena are what the burgeoning field of quantum simulation is all about. 347. David Brown Says: @Joy Christian #335: “Local measurements do not depend on the global topology of the universe.” IN THE COPENHAGEN INTERPRETATION, local measurements DO depend on the global topology of the universe and EVERYTHING ELSE in the universe. IN YOUR INTERPRETATION of physics, local measurements do not depend on the global topology of the universe. YOUR SO-CALLED DISPROOF OF BELL’S THEOREM is valid if and only if your interpretation of physics is valid. I think that you are a genius and your interpretation of physics might be valid MIGHT BE VALID. However, you foolishly and arrogantly dismiss experimentalists as plumbers. (Plumbers are more useful than theoretical physicsts.) YOU NEED TO EXPLAIN YOUR IDEAS BETTER. 348. Thomas H Ray Says: Bram Cohen #328 ” … why would the geometry of the universe as a whole matter for an experiment run in a miniscule section of space, which approximates R^3 so closely that it’s nearly impossible to measure the difference?” That’s actually the measurement problem with Bell-Aspect experiments. We know that unless quantum mechanics applies to the whole universe, it is not coherent. So we assume that every conceivable flat space in which we measure correlated pairs is identical to every other conceivable flat space in which a measurement could be made, and we assign the value of nonlocality to measurements not made. Joy’s flat measure space is parallelized S^3, which differs from R^3 by a point at infinity. This introduction of topology to the problem is a critical departure from previous assumptions — because it obliterates the local-global distinction one finds in ordinary geometry. The generalization of geometry — topology — is concerned only with global properties of space, which is what I think confuses many into believing that Joy’s model cannot be local even if realistic. Remember, though, that the measurement function over the manifold of S^3 is continuous from the topological initial condition of parallelized S^7. So the measure space is just as flat as Euclidean R^3, but is now COMPLETE. All measure results are correlated to infinity on the continuous function input argument – a.b. Classical time reverse symmetry is built into the framework, so we can no longer assume that every measurement interval is identical every other — there is one interval in which the result could be reversed. (Answers Einstein’s question of whether nature had a choice in creating the universe: she did.) Although Joy doesn’t use this terminology — I had to verify early on for the sake of my own sanity (yes, despite claims made here, I do my own regular mathematics “sanity checks”) that what I took to calling the physical space of S^7 being simply connected to the measure space of S^3 made a complete physical space. As I learned more, I realized that there is no need for a local-global distinction between these spaces, just as Joy had always said. It really isn’t an easy thing to get one’s mind around. Because we are used to thinking of ANY extradimensional framework (string theory, Randall warping, etc.) as “nonlocal,” we overlook the power of the topological property of simple connectedness to “localize” all measurement functions. Indeed, these concepts are on the very leading edge of topology research; it’s been only a half dozen years since we’ve been convinced by Perelman’s proof (and the important work of Richard Hamilton and conjectures of Thurston that support it) that S^3 is simply connected. 349. is Says: @Henning Dekant #334: “I find it entirely fascinating that you think you can find a pony in Joy’s work yet he immediately leads it to the slaughterhouse.” IT IS OBVIOUS TO ME that Christian is a great genius more-or-less in the same ballpark as Einstein and H. Weyl. The reason is that Christian’s parallelized 7-sphere model solves a problem that I have been trying to solve for 2 years. I need his model for my work on the physical interpretation of M-theory. However, Christian has many ideas WHICH HE ABSOLUTELY KNOWS ARE RIGHT and he won’t listen to objections and counter-arguments. 350. Thomas H Ray Says: Richard Gill #344 “Joy’s supporter Tom says I don’t take account of the analytic nature of Joy’s model. ” Joy’s supporter Tom still says that. Analysis is strong enough to generate arithmetic elements; arithmetic assumptions, however, don’t contain analytical elements. That’s why your averaging scheme doesn’t work in the context of Joy’s framework. 351. Joy Christian Says: Here is what Bill Schnieder wrote on Physics Forums long time ago: Richard Gill’s refutation is not a new critique. It is essentially the same as one of the critiques advanced by a certain Florin Moldoveanu in the fall last year to which Joy Christian has already replied. It originates from a misunderstanding of Joy’s framework which admittedly is not very easy to understand, especially for those who have blinders of one kind or another. Gill thinks Joy is using a convoluted more difficult method to do a calculation and prefers a different method which ultimately leads him to a different result, not realizing/understanding that the calculation method Joy used is demanded by his framework. This is hardly a serious critique, not unlike his failed critique of Hess and Phillip. He should at least have read Joy’s response to Moldoveanu which he apparently did not, since he does not cite or mention it. It’s been available since October 2011, one-month after Moldoveanu posted his critique. I remember Florin came here to boast about his critique and I pointed out his misunderstanding at the time in this thread: “… you are missing the point because Joy Christian is not using handedness as a convention but as the hidden variable itself.” This is the same error Gill has made. See section (II) of Joy’s response to Moldoveanu.” Enough said. 352. Joy Christian Says: If that was not enough, have a look at this explanation: http://fqxi.org/data/forum-attachments/JoyChristian_FAQ.pdf 353. is Says: @Joy Christian #351: “.. you are missing the point because Joy Christian is not using handedness as a convention but as the hidden variable itself.” YES! This is one of Christian’s genius-level ideas. However, consider the following: Aaronson’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Bell states can reproduce all of the predictions of quantum theory in the sense of the Copenhagen interpretation. Christian’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Christian SU(8) states can reproduce all of the predictions of quantum theory in the sense of the Christian interpretation of quantum theory. The Christian interpretation means the extension of the Copenhagen interpretation based upon Christian local realism. Does Joy Christian understand the point here? Is David Brown totally confused? 354. Joy Christian Says: And this is what I wrote elsewhere on the Internet 40 days ago: On the FQXi blog Gill now admits that he has lied in his paper. In his paper he claimed that his equation (2) is my equation (4). He did this either because of his incompetence in mathematics, or deliberately and calculatedly to derail my research program. The simplest explanation is that his equation (2) is a silly mistake because he is an incompetent mathematician. One only has to read his abstract to recognize this fact. Further lies (or at least assertions without evidence) appear in what he has writen above. He is abusing the good name of David Hestenes whom he has never met or spoken to. I, on the other hand, have been in touch with David since 2008, and have discussed my paper with him only a few months ago at a FQXi conference. Gill writes that I have introduced “a daring new postulate” “without any mention of the fact.” This is yet another lie. What Gill calls “a daring new postulate” is explicitly stated right at the start of my model, both in my one-page paper and my very first paper, which was written in 2007. The same postulate in the first paper is stated in two different ways. First in words: “Thus, in essence, the intrinsic freedom of choice in the initial orientation of the unit pseudoscalar mu would be our “local hidden variable.”” And then as an equation (cf. eq.(15) of the 2007 paper): mu . n = +/- I . n = L { n_j B_j }. This is the same as the equation B_j(L) = L B_j appearing in the one-page paper. Gill does not recognize that these two equations are one and the same equation, because he does not know anything about geometric algebra. I am amazed how shamelessly Gill is able to spread such a lie. One has to wonder what could be the real motivation behind spreading such a patent lie. 355. Joy Christian Says: Joy Christian does understand the point, but David Brown is at least partially confused. 356. is Says: @Joy Christian #355: “… David Brown is at least partially confused.” YES! David Brown is at least 75% confused. Are you saying to us that quantum theory should be replaced by EPR theory in the form of Christian local realism based upon the parallelized 7-sphere model? 357. Bram Cohen Says: Tom Ray, if our understanding of space is so flawed, maybe you could explain why rendering engines which work by doing projections in R^3 do such a good job of producing realisting-looking images and animations? 358. David Brown Says: @Joy Christian #355: David Brown is at least 98% confused 99% of the time. I have 5 pieces of advice for you: (1) Imitate N. Bohr, who said, “Every statement I utter should be understood as having a question mark at the end.” (2) Forget about Gill, Moldoveanu, and others who fundamentally do not understand your model. (3) Give a physical interpretation of M-theory in terms of your model. (4) Show that the Copenhagen interpretation reduces to the Christian interpretation of physics as the Planck length approaches zero. (5) Try to get those who understand what you are doing into the business of explaining your ideas to the typical physicist. 359. Shtetl-Optimized » Blog Archive » Waterman behind the scenes! Partying hard with the National Science Board Says: […] away for a minute to moderate my blog comments on my iPhone, where I’d invariably find a fresh round of insults about my “deeply ignorant lesser brain” from entanglement denier Joy […] 360. Joy Christian Says: David Brown, I am pleasantly surprised. Your 5 pieces of advice to me is at least 60 to 80% sensible. 361. Thomas H Ray Says: Bram Cohen #357 “Tom Ray, if our understanding of space is so flawed, maybe you could explain why rendering engines which work by doing projections in R^3 do such a good job of producing realisting-looking images and animations?” Sure. I didn’t say our understanding of space is flawed, especially our understanding of Euclidean R^3 in which static models are rendered and animations are programmed. The lack of understanding is over the analytical nature of Joy’s model — a measurement function continuous from the initial condition. Every such n-dimension function contains a singularity that is not measurable as discrete output, so the real measured result of the real valued continuous function has to be output as + 1 or – 1 for measurements made in a bounded length of time. Predicting this output using a pair of random variables, by statistical inference, is what Joy’s framework is about. In other words, instead of allowing random outcomes by probabilistic measure for every throw of the dice (every individual experiment) we allow deterministic output in a model of continuous measurement functions. 362. Richard Gill Says: Here are two interesting statements by Joy Christian, which he repeated here a couple of days ago. Interesting and unusual, because they are actually both true. (1) “However, as Bell convincingly demonstrated long ago [1], one can never reproduce the sinusoidal correlation in this manner” (2) “As counterintuitive as this may seem, that is what the mathematics of my model implies, and it matches exactly with the experimental evidence.” Statement (1) confirms that Joy does agree with Bell’s mathematics. You cannot recover the sinusoidal correlation in that particular manner. Joy disputes the physical relevance of the Bell’s mathematical concepts. Bell’s choice of “manner”. Now this is an interesting contradiction with his so-called experimental paper (from 2008) in which he claims that you *can* reconstruct that particular sinusoidal correlation in *precisely* that manner! Don’t believe me. Don’t believe Joy. Read the paper carefully and decide for yourself. Statement (2) underlines the point that his model is of no interest if its *mathematics* is internally fatally flawed; if it doesn’t stand on its own feet. After all, anyone can write down mathematically *incorrect* derivations of any correlation you like, in particular, those observed in certain quantum experiments and predicted by QM. The internal mathematical/logical coherence of the model is essential. Unfortunately, to date, no single mathematician has confirmed Joy’s mathematics, while a host of mathematicians have agreed that his mathematics is plain wrong. Does this mean that the guy is such a great genius that all those pedantic mathematicians haven’t got round to inventing the good mathematical formalism to encapsulate his brilliant insights? Sure, it’s often been the case in the past, that physics was in advance of mathematics. However, this particular case is a bit different. Geometric algebra is not difficult and it’s not new. In fact, Joy only uses the easy part of it, the basic definitions and properties! He doesn’t use the topology and the analysis, he only uses the algebra (I refer to the “hard” mathematical content, not to the surrounding sales talk). And … he demonstrably contradicts himself on a daily basis, he never gives a straight answer to a straight mathematical question, he gets the algebra wrong (David Hestenes has confirmed this), he replies to criticism by personal slander of the critic. This is not the typical reaction of the true mis-understood genius! This is the reaction of the charlatan whose trickery has been exposed. So I’m inclined to other thoughts. But that’s not important. The important thing is that anyone with some basic mathematical intelligence and a bit of mathematical self-discipline can check for themselves, by checking the details. So if you’re interested: don’t believe what I say; don’t believe what Joy says. Decide for yourself by checking the details of his one page paper. 363. Bram Cohen Says: Tom Ray, I don’t see why any measurement function on the initial input must have a singularity, or what that would have to do with later correlations. And doing monte carlo simulation should always give the same result as calculating the aggregates exactly. But that aside, if the thing which is interesting is a measurement function on the state of the system, then doing an ordinary simulation in R^3 will work just fine. Honestly, I get the feeling from his silence that I threw Christian by bringing up the highly esoteric concept of 3d rendering, and that the mathematics of that subject is beyond him. 364. James Putnam Says: Richard Gill #362, “…it’s often been the case in the past, that physics was in advance of mathematics. However, this particular case is a bit different. Geometric algebra is not difficult and it’s not new. In fact, Joy only uses the easy part of it, the basic definitions and properties! He doesn’t use the topology and the analysis, he only uses the algebra (I refer to the “hard” mathematical content, not to the surrounding sales talk). …” I look to understand your point of view and then you write things such as this. It appears to me to lack consistency. Perhaps, as you say, the physics is ahead of the math. Then you deny this is the case by pointing strictly to the math while discounting the role of the physics which is what I presume you mean by “the surrounding sales talk”. It is the physics that determines how the math must be used. Do you deny the correctness of specifics about Joy’s physics? I think I asked this question, without receiving a response, sometime ago in another forum: Where does David Hestenes confirm that Joy has the algebra wrong? I asked it because I knew it would be of great importance. If it is heresay based upon a private conversation that did not include Joy, then it does not count. If I am misunderstanding your position about possible ‘math errors’ then would it be possible for you to restate your case by addressing the union of the physics and the math? Thank you. James 365. Joy Christian Says: Bram Cohen, I have already answered your question above (in my answer primerily addresed to Jim). 366. Joy Christian Says: As Richard Gill continues his three-months long Trojan horse campaign against me, I cannot but agree with his suggestion that everyone should check my physics and my mathematics for themselves, especially those summarized in my one-page paper: http://arxiv.org/abs/1103.1879 As for my experimental paper, http://arxiv.org/abs/0806.3078, there is no issue if you understand my argument against bell’s theorem. This has been summarized in this introductory chapter of my book: http://arxiv.org/abs/1201.0775 As for my proposed experiment, Gill is rigging the game but too stupid to realize it even after it has been repeatedly pointed out to him by me and Fred on the FQXi blogs. He keeps asserting CHSH inequalities as if they were some sort of physical law. In fact they are a figment of imagination, a result of unjustified rigging, refuted by actual experimental observations, and discredited in my book and papers as born out of topological negligence of John Bell. Once this is appreciated, it is straightforward to understand my experimental paper. It describes exactly how the expectation values E(a, b), E(a’, b), E(a, b’), and E(a’, b’) are to be computed in my proposed experiment. Four separate sums are to be calculated as follows E(a, b) = 1/N Sum_j A_j B_j , E(a, b’) = 1/N Sum_j A_j B’_j , E(a’, b) = 1/N Sum_j A’_j B_j , and E(a’, b’) = 1/N Sum_j A’_j B’_j . It is a matter of indifference whether N here is chosen to be the same or different for each of the four alternatives. My model then unambiguously predicts that the observed correlations will be E(a, b) = -cos(a, b), E(a, b’) = -cos(a, b’), E(a’, b) = -cos(a’, b), and E(a’, b’) = -cos(a’, b’). Moreover, my model predicts that these correlations will give rise to violations of the Bell-CHSH inequality of the form | E(a, b) + E(a, b’) + E(a’, b) – E(a’, b’) | less or equal to 2 x sqrt{ 1 – (a × a’).(b’ × b) } The predictions of my model are unambiguous. The experimental procedure described in my paper is unambiguous. One does not have to be Einstein to understand my argument. All one has to do is to read a few pages of a few of my papers. 367. Henning Dekant Says: To better facilitate physics online discussions such as this one I suggest the following corollary to Godwin’s law: “Anybody who calls somebody else a genius or implies this by for instance comparison with Einstein lost the debate.” 368. Henning Dekant Says: @Joy, you should retain as Thomas H. Ray as your science advocate. He makes a very good case on your behalf. 369. David Brown Says: @Joy Christian #362: You write, “I am pleasantly surprised.” At this stage, there are probably only 5 to 10 people in the world who understand what you are doing. If I were to choose 7 of the 10 world’s greatest living theoretical physicists, they would be: Anderson, Weinberg, Glashow, Gell-Mann, Witten, Wolfram, and Christian. The fact that you have been viciously attacked shows that you have done something truly great. For Aaronson and me, when you attack Aaronson’s version of Bell’s Theorem and the Copenhagen Interpretation then that is like you attacking our religion. In your 2008 paper “Can Bell’s Prescription for Physical Reality Be Considered Complete?”, you write “It should be fairly clear by now that topologically the EPR elements of reality have far deeper structure than has been hitherto appreciated.” YES! I now believe you. I think that the 3 greatest achievements in all of theoretical physics are Einstein’s general relativity theory, Witten’s M-theory, and Christian’s parallelized 7-sphere model. I think that your model is what I call the “smoothing of the Nambu transfer machine with the infinite nature hypothesis.” Your model is fantastic news for the success of M-theory. If you live another ten years, you shall win the Nobel prize. 370. Joy Christian Says: Henning Dekant, I hope you did not miss my answer to your questions as Bram Cohen did (it is in my answers primarily addressed to Jim). 371. Edwin Eugene Klingman Says: @David Brown #345, you say “One problem is that Christian, Ray, Klingman, and you have failed to explain Christian’s model in any proper sense to THOSE WHO REJECT YOUR BASIC ASSUMPTIONS.” I believe that Joy has done an excellent job of describing his model, although it does require study of several of his papers to get the description in toto. As mentioned above, I have strong reservations about the physics, but I believe his mathematical framework presents a new and valid approach to analysis of the correlation problem. A blog is not the place to present a new theory, but I hope to provide an alternative physical explanation couched in Joy’s mathematical framework within the next few months. Judging by the last year or so of discussion, there will still be interest in a few months. 372. Bram Cohen Says: Joy Christian, I can’t find an answer from you to any ‘Jim’ in the comments here. The closest I can find is your answer to John Sidles, in which you say ‘I’m not a computer engineer’ and ‘Bell’s theorem isn’t about what can be simulated by a computer, it’s about the nature of reality’. Both of which make no pretense at answering my question. Seriously, do you even know the math behind reorienting objects in 3-space? Maybe you should learn some fundamentals before claiming to have a revolutionary physics idea. 373. David Brown Says: @Joy Christian #154: “… nonlocal gravity is an oxymoron. You have to be a physicist to appreciate this.” YES! I now believe that your disproof of Bell’s theorem is 100% correct. You need good publicity. One way to do this is to tell the world that Milgrom is the Kepler of contemporary. The results of McGaugh and Kroupa prove beyond a reasonable doubt that Milgrom is correct. http://en.wikipedia.org/wiki/Pavel_Kroupa You are going to having heavy sledding ahead of you in getting physicists to believe that Bell’s alleged theorem is false and that you have successfully overthrown the Copenhagen interpretation. Good luck. 374. James Putnam Says: Bram Cohen #372 Joy Christian, I can’t find an answer from you to any ‘Jim’ in the comments here. … I believe it is comment #333 James 375. Joy Christian Says: Bram Cohen, I am not using the traditional math behind reorienting objects in 3-space? I am working within the algebra of orthogonal directions in the physical space initiated by Grassmann and Clifford and further developed by Hestenes. This algebra I have explicitly introduced in the introductory parts of this paper: http://arxiv.org/abs/1106.0748 To learn the math behind reorienting objects in 3-space for my model you therefore first need to learn Grassmann-Clifford-Hestenes algebra, perhaps from this book: http://www.amazon.com/Geometric-Algebra-Computer-Science-Revised/dp/0123749425/ref=sr_1_1?s=books&ie=UTF8&qid=1336593002&sr=1-1 Good luck. 376. David Brown Says: @Edwin Eugen Klingman # 373 “A blog is not the place to present a new theory …” I think that there needs to be an Oxford interpretation of quantum theory and M-theory. Have you looked over my arxiv.org papers? I say that I am a crackpot if and only if the Space Roar Profile Prediction is true. Have you studied the work of Milgrom, McGaugh, and Kroupa? You, Christian, and your little group are attempting to overthrow the Copenhagen interpretation. If I am not a crackpot, then I think that you need my help. I certainly need help from somewhere — either to convince me that I am a crackpot or to get publicity for my ideas on the foundations of physics. If the empirical facts show that I am a crackpot, then I shall practice my crackpottery in a field other than physics. 377. David Brown Says: OOPS! In the preceding post I meant “Space Roar Profile Prediction is false”. I am still in shock over Christian’s disproof of Bell’s theorem. 378. David Brown Says: @Scott #32: You write, “… your experimental prediction is that the Bell/CHSH inequality can still be violated, even in a certain ‘macroscopic’ experiment where physicists would say that there’s nothing quantum mechanical going on.” Christian and his supporters are far more radical than that. They claim that the Copenhagen interpretation is only approximately true. They do not use language quite as precisely as you do. On page 11 of Christian’s “On the Origins of Quantum Correlations”, he uses the term “classical correlations” when I think that he should use the term “M-theoretical local realistic correlations”. When Christian says he has “disproved Bell’s theorem” he means he has used Bell’s physical assumptions with Christian’s HYPOTHESES about general quantum states to refute Bell’s theorem AS A THEOREM IN PHYSICS (not necessarily as a theorem in mathematics given the assumption that the Copenhagen interpretation is true). I now think that Christian is the greatest physicist since Einstein — you can believe it or not. 379. Thomas H Ray Says: Bram Cohen, “I don’t see why any measurement function on the initial input must have a singularity, or what that would have to do with later correlations. And doing monte carlo simulation should always give the same result as calculating the aggregates exactly. But that aside, if the thing which is interesting is a measurement function on the state of the system, then doing an ordinary simulation in R^3 will work just fine.” No it won’t. You misunderstand a measurement function continuous from the initial condition, i.e., an analytical framework. Implementing a model in R^3 tacitly amounts to prescribing arbitrary boundary conditions, similar to curve-fittting. What I mean is, that one cannot actually draw — i.e., simulate — a point. To arrange or program sets of points in relation is not the same thing as finding a singular value that represents such physical properties as position or momentum, because that point is unique. Somewhere in here, I think I referred to the theorem that a set of points can be approached simultaneously by another point, provided that the point is far enough away. When we are speaking about a function that includes the whole universe, yet holds that all measurements are manifestly local and real, it’s the point at infinity of S^3 that distinguishes the flat space of R^3 from the flat space of parallelized S^3. This topological difference breaks down the local-global distinction. I have not yet been convinced that any computer simulation can integrate the global initial condition. 380. Henning Dekant Says: @David Brown, there are a couple of David Browns with various middle initials in arxiv.org so I have a hard time figuring out which papers are yours. @Joy, thanks for pointing out that you answered my questions in an earlier comment, given how busy this thread is I would have overlooked it. 381. Bram Cohen Says: Joy Christian, I see no comment #133 by you, or a ‘Jim’, or anything near it. Perhaps you could take the effort to repeat yourself instead of just saying repeatedly that if people were to simply read a couple books and painstakingly go through your papers then everything would be clear. You seem to fundamentally not understand what a preposterous statement you’re making about space being in S^3. If the topology of 3-space were off, that would only have effects on the universe as a whole, and would be extremely obvious in cosmology, and would have absolutely no impact whatsoever on local experiments, or if it did then the effects would be so obvious you couldn’t pick up an orange without noticing them. You apparently have learned some terms for some algebra, but don’t have the most basic understanding of what it actually means. 382. Bram Cohen Says: Okay, the comment in question is apparently #333, and the response to me is buried at the end of it. The entire meat of that comment appears to be: “What makes you think that we can simulate the physical reality that easily? ” There’s this game called quake you might want to try playing. Get back to me after you’ve done that bit of ‘research’. 383. James Putnam Says: From comment #333 written by Joy Christian: “@Bram Cohen, You asked: “…by S^3, are you referring to the surface of a hypersphere?” Yes, but we are not concerned about cosmology. We are only concerned about the topology of a closed region where the experiment is taking place. There is no need to hypothesize anything about the universe as a whole. You eat elephant one bite at a time, not as a whole. You are asking a lot of simulation questions. But I am saying that the whole idea of a simulation is misguided. What makes you think that we can simulate the physical reality that easily? In my opinion a real experiment is inevitable to test my hypothesis.” 384. David Brown Says: @Henning Dekant #382: I have nothing on arxiv.org — I have 6 papers on vixra.org and 5 of them can be found listed on this thread under David Brown #57. I have no published physics papers but I do have 9 published papers on theoretical biology in refereed journals. If you look at my vixra.org papers then you see why I can’t get my work published. I claim that Milgrom is the Kepler of contemporary cosmology, the multiverse is finite and digital, the Higgs field does not exist, Einstein’s field equations are slightly wrong, and several other bizarre things. I fear that even Fredkin thinks that I am a crackpot. http://en.wikipedia.org/wiki/Edward_Fredkin By the way, I think that Fredkin is the world’s greatest living philosopher. 385. David Brown Says: @Bram Cohen #383: “If the topology of 3-space were off, that would only have effects on the universe as a whole …” YES! Joy Christian has not explained his ideas well to the typical physicist. Why is the M-theoretical fundamental domain 11-dimensional? There might be 4 dimensions of spacetime and 7 dimensions of topological measurement. The 7 dimensions of topological measurement somehow come from Christian’s parallelized 7-sphere model. What good is all that, you might ask? The 7-dimensions of topological measurement allow the simulation of linear momentum, angular momentum, and quantum spin by a deterministic flow of information through Christian’s model. How is that Bell’s theorem is not violated? Well, Bell’s theorem IS VIOLATED! Christian convincingly demonstrates that Bell’s alleged theorem is false as a physical theorem (although it might be true as a mathematical theorem assuming that the Copenhagen interpretation is 100% correct.) Where did Bell go wrong? Bell used quantum SU(1) states whereas Christian correctly uses quantum SU(8) states. Christian got his PhD with Abner Shimony as thesis advisor, and Christian really knows his stuff — Christian is very meticulous. 386. Alex B. Aible Says: Dear Professor Aaronson, Count me among those who think that betting actually provides a useful service, one where both the bettor and the scientific community gain. I also agree with those who believe that it is most appropriate in the general case for the author of a proof to be willing to pay a price to have his work examined, i.e., to make his own bet that his proof is correct (with a guarantee of a publicly documented payment if it is not correct). As an unknown researcher, I am willing to do just that. I have written a conventional proof of the 4-color theorem which has been rejected by every organization where it has been submitted without so much as a hint of analytical comment. A brief introduction to the proof, with an offer of$500.00 to the first person who can provide a counterexample (necessarily a checkable physical object), is contained on “Alex Aible’s blog.” This can be brought up by any search engine. An interested party can then click on the Bluehost address given in the blog to download the entire proof, which contains a clear preview (so a person will only have to read the first 15 double-spaced pages to understand how the proof works) along with a full description of the monetary challenge.

The proof is serious and I would like it to be subjected to
serious scrutiny.

Thanks,

Alex B. Aible

387. Bram Cohen Says:

Ahem, calming down a bit here, the justification for our model of 3-space is this thing called the Pythagorean Theorem, and while it’s true that the Pythagorean Theorem isn’t really a ‘theorem’ per se, and there’s an interesting question of which observations exactly serve as justifications for it, I’ve never encountered an actual Pythagorean Theorem denialist before.

It was entertaining prodding Joy Christian to get at what the actual center of his belief system is, since he has this amusing characteristic of being wrong instead of not even wrong, but pythagorean theorem denialism is just sad and pathetic.

388. Henning Dekant Says:

@David Brown, thanks for setting me straight on this.

Certainly don’t share your inclinations but to each their own 🙂

Fredkin’s ideas to me are reminiscent of how in the 19th century the universe was imagined to be the spit image of a fine tune mechanical machine (hence Laplace demon).

I wonder if as our technology matures there will always be a philosophy that claims the the universe is just like our latest and greatest machines.

The cosmic quantum computer has a nice ring to it doesn’t it ?

389. asdf Says:

Tom #361, that post makes no sense to me. Are you guys saying that the Church-Turing thesis is wrong, i.e. that Joy’s theory of physics is of a physics that can’t be simulated with a computer? If not, it seems perfectly reasonable for people to be asking for results of simulating Joy’s suggested experiment.

Thanks.

390. Fred D Says:

Henning says, “The cosmic quantum computer has a nice ring to it doesn’t it ?” LOL!

Sounds good but I am afraid that Nature is both classical and quantum. It’s a duality; one does not exist without the other.

391. David Brown Says:

@Henning Dekant #388 “… cosmic quantum computer …” Until I read Christian’s work, I thought that the Copenhagen interpretation would never be refuted … not in 10 billion years. Has Christian’s disproof of Bell’s alleged theorem opened up vast vistas for research on quantum entanglements? Are quantum entanglements of quantum entanglements actually 5-dimensional? Are quantum entanglements of quantum entanglements of quantum entanglements actually 6 dimensional? And so on, layering quantum entanglements until physicists reach 11 dimensions, exhausting the superstring domain’s complexity? Can we build quantum computers that are provably 11-dimensional? Joy Christian made the challenge, “Go build a quantum computer.” Perhaps he should have said, “Go build an 11-dimensional EPR computer based upon my disproof of Bell’s now-discredited former theorem.” My mind is still reeling. All quantum phenomena are really EPR phenomena?!? When I said that I thought that Christian is the greatest physicist since Einstein, I was not using hyperbole in any sense. If Christian’s work leads to convincing empirical proof that physical reality is 11-dimensional and deterministic, then superconductivity is very ill-understood by contemporary physicists.

392. David Brown Says:

@Fred D. #389 “… Nature is both classical and deterministic.” I think that your use of the word “classical” is actually wrong. I think that you should use the term “M-theoretically locally realistic.” I think that “classical” means either classical in the sense of Newton or classical in the sense of the field theory of Faraday and Maxwell. “… Nature is both Joy-Christian-explained and deterministic” — that I would agree with.

393. Thomas H Ray Says:

Bram Cohen #382

“You seem to fundamentally not understand what a preposterous statement you’re making about space being in S^3. If the topology of 3-space were off, that would only have effects on the universe as a whole, and would be extremely obvious in cosmology, and would have absolutely no impact whatsoever on local experiments, or if it did then the effects would be so obvious you couldn’t pick up an orange without noticing them.”

Patently untrue, Bram. Perhaps it will help to think of the problem this way: Where does CMBR originate? — i.e., what point of space? When we speak of the origin of the big bang, we find that the added dimension of time caused by the expanding universe allows us to place the origin at any point we choose. One wouldn’t call the CMBR nonlocal, would one?

It isn’t necessary to invoke nonlocal causes to explain local effects. All that’s required is the point at infinity. Standard QM chooses the point as a point set of infinite distance and infinite orientation in the flat plane embedded in R^3. That is, however, a line and not a true point — hence, the necessity of mathematically describing quantum events and dynamics by complex analysis in the Hilbert space.

The true point of origin described by a measurement function continuous from the initial condition has to be by real analysis in a topological space (all real functions of a real valued variable are continuous) defined by the initial condition. All the criticism of Joy’s framework citing a phantom “algebra error” is complete nonsense — the algebra, from Hamilton to Cayley to Hestenes, is simply a vehicle to convert the complex analysis to real analysis, in order to seamlessly connect with physical reality.

Then when one speaks of a pair of random variables (” … we construct a pair of dichotomic variables …” in Joy’s words) one does not prescribe, or know, the direction of orientation (LH or RH). One does know, however, that in the analysis of some run of discrete experimental events, the measurement is oriented, IN AN OBJECTIVE WAY, not necessarily the direction CHOSEN BY THE EXPERIMENTER. This is the crucial difference between the observer-created reality of standard quantum mechanics, and the non-mystical experimental result of combined classical-quantum analysis.

Unless nature had a choice in creating the world, the moon isn’t there when no one is looking. And if nature did have a choice in creating the world, then the topological initial condition that commands gravity to be attractive also deems that it could have been otherwise. That’s hardly preposterous, and it is an entirely local phenomenon.

394. Joy Christian Says:

David Brown,

Unlike some computer geeks in this forum, you seem to have the understanding of the mathematics of M-theory etc. I think you are ready to read this paper of mine (if you have not already done so): http://arxiv.org/abs/1101.1958

395. Thomas H Ray Says:

asdf # 389

“Tom #361, that post makes no sense to me. Are you guys saying that the Church-Turing thesis is wrong, i.e. that Joy’s theory of physics is of a physics that can’t be simulated with a computer? If not, it seems perfectly reasonable for people to be asking for results of simulating Joy’s suggested experiment.”

I think that’s an excellent question, with a subtle answer.

The Church-Turing thesis doesn’t assume that the world is algorithmically compressible. It just implies that algorithmically compressible functions are computable.

That the world may not be algorithmically compressible is a proposition, if proven, that would falsify standard quantum mechanics (one would not be able to assign a value to nonlocality). OTOH, what do we mean by “algorithm?” Chaitin gives us an algorithm that produces the halting probability (Omega) of a Turing machine, whose output is not computable. This is disturbing on at least two levels: 1. If a function is algorithmically compressible, how can it not be computable? 2. Is arithmetic itself untrustworthy?

The web is wonderful. In looking for a compact source on Chaitin’s own view of the Church-Turing thesis, I came across a delightful conversation between Chaitin and Cristian Calude, http://www.rutherfordjournal.org/article020103.html,
from which I excerpt:

“Calude: Are you talking about a physical Church-Turing Thesis?

Chaitin: Yes I am—but I think the notion of a universal Turing machine changes in a more fundamental way if Nature permits us to toss a coin, if there really are independent random events.(*note) If Nature really lets us toss a coin, then, with extremely high probability, you can actually compute algorithmically irreducible strings of bits, but there’s no way to do that in a deterministic world.

Calude: Didn’t you say that in your 1966 Journal of the ACM paper?

Chaitin: Well yes, but the referee asked me to remove it, so I did. Anyway, that was a long time ago.

(*the article notes: Quantum mechanics supplies such events, but you can postulate them separately, without having to buy the entire QM package.)”

” … there’s no way to do that in a deterministic world.” That’s the rub. I would never be one to say that new computing methods might not overcome the problem. After all, as recently as 18 months or so ago, I didn’t believe that Einstein’s ambition to have a continuous function model of the universe free of singularities and without arbitrary boundary conditions was possible, either. I am convinced that Joy Christian’s framework succesfully does the job.

396. Richard Gill Says:

James Putnam #364. You asked some good questions there, maybe you could send me an email and I can answer you directly?

In particular about David Hestenes’ verdict: I corresponded with him, and in private correspondence with you, I’m happy to share with you what he told me. But I am not going to post “private” correspondence on this blog. If I wanted to quote from him in a publication, I’d ask him first. I only wrote to him because Joy had boasted in public that David had given Joy’s work the seal of approval. This surprised me since even a third-rater like me can see it is wrong. Was I missing something? Answer: no.

About the maths and the physics: Joy Christian is using 150 years old maths, and only the elementary parts thereof, and he’s making beginner’s mistakes. He also regularly contradicts himself on simple issues of logic. This should have been obvious to anyone who cares to check the details of these landmark papers for 5 years. What rather surprises me is not that he has fooled himself into believing he’s the new Einstein, but that he fools anyone else. Sure, he is great with the science patter. Anyone thinking of script-writing some new sci-fi TV series or movie franchise, should consider hiring him. This is a question of being intelligent with words and imagery, and having a vivid imagination, and doing a lot of reading.

People keep asking him to explain how to simulate his model and he says this can’t be done.

I say it can be done. Preparatiry to this, read the Wikipedia articles on quaternions and on Clifford algebra. You now know how to encode real 3-vectors as bivectors, by the mapping (x,y,z) goes to ix+jy+kz. Learn the multiplication rules, don’t forget that multiplication is not commutative.

Simulation experiment. See Joy’s one page paper. Let a and b be two real unit 3-vectors. Encode as bivectors. Toss a fair coin N times. Denote the outcomes +/-1 by lambda_n, n=1…N. Define
A_n = -lambda_n a a = lambda_n
B_n = lambda_n b b = – lambda_n.
Compute ave(A_n B_n). You don’t have to be a genius to see the answer is -1. Divide on the left by -a and on the right by b. The answer is – a b = a.b + a x b, the part a.b is real, the part a x b is purely quaternionic. Take the real part. The singlet correlation!

Joy has to cheat with his algebra in order to get the “a x b” term to vanish in a more subtle way. In different papers he achieves this in different ways. I refer here just to the version of the model described in the one page paper.

So you asked: what do I think about Joy’s physics? I don’t. There is none. The mathematics is trivial and either empty or wrong, depending on what assumptions he commits himself to (that varies from day to day). Joy’s definition of correlation is stupid, and irrelevant to the whole Bell discussion. All the chit-chat about the parallelized 3-sphere is just chit-chat. Noise. Diversionary tactics. Window dressing. This is not an emperor with no clothes. It’s some clothing with fundamental design errors, with no emperor inside.

Joy got a PhD with Abner Shimony, but Abner Shimony thinks Joy’s work on Bell is nuts. I’ve heard that Joy’s income comes from privately teaching English in Oxford, and from FQXi, and from royalties of his book. His associations with PI and with Wolfson College Oxford and with the Physics Dept Oxford are just that: … associations. Zero publications on this Bell project in peer reviewed journals, despite five years’ labour, five years to correct the errors, five years to learn mathematical rigour, five years to learn how to communicate his ideas to professionals.

397. Richard Gill Says:

PS is it a coincidence that Joy sends his challenge to Scott, just after Joy’s book came out? Joy certainly is getting the publicity which he wanted. He’s a very very smart salesman.

398. Thomas H Ray Says:

Bram Cohen, there’s a Pythagorean theorem for 4 space (Riemannian geometry, Minkowski space), as well as an n-dimensional Pythagorean theorem.

“It was entertaining prodding Joy Christian to get at what the actual center of his belief system is, since he has this amusing characteristic of being wrong instead of not even wrong, but pythagorean theorem denialism is just sad and pathetic.”

It doesn’t have anything to do with belief, nor with a nonexistent “pythagorean theorem denialism.” Joy’s model is angle-preserving (conformal) to infinity.

399. John Sidles Says:

Please let me commend, to students especially, the practice of understanding experimental tests of Bell inequalities by computationally simulating that experiment.

One especially suitable candidate for computational simulation — by virtue of its concision, clarity, practicality, and technical sophistication — is S. Pironio et al. “Random Numbers Certified by Bell’s Theorem” (arXiv:0911.3427), hencforth “RNC-by-BT’)

Attention is directed particularly to RNC-by-BT’s figure 1, in which |1| a total of 3016 detection events are described in full detail, and |2| the CHSH observable is explicitly computed, and |3| the observed CHSH violates a Bell inequality.

For Joy’s theory to have any connection to this (wonderful!) experiment, it must be possible to |1| prepare an Excel table of 3016 lines (one for each event), |2| append to each line the value of a Joy variable “J”, and then |3| factor the inferred probability distributions to satisfy locality, via the equation that Joy gives (correctly) in his Comment #333 as “AB(a,b|J) = A(a|J) B(b|J)”.

What Scott calls “the clarity of computation” is concretely instantiated in the granular appreciations that are gained via this exercise. Philosphers especially are encouraged to attempt it! 🙂 Because this exercise helps greatly to remediate understandings that are global but not granular.

It is notable that all who attempt this exercise come away with an appreciation that Joy’s theoretical framework — to the extent that this framework has any consistent computational interpretation at all — is entirely disconnected from the literature of Bell-type experiments.

More broadly, this example illustrates concretely how computational simulations — of any STEM framework — help advance us more rapidly, reliably, and rigorously toward the primary objective of computing as defined by Richard Hamming:

“The purpose of computing is insight, not numbers.”

Also, congratulations to Scott on his (well-earned) NSF Waterman award!   🙂

400. Gil Kalai Says:

Dear all, I wonder if some of the experts can kindly explain for us the motivation, context and content of the loopholes research regarding Bell inequalities. Many thanks!

401. Thomas H Ray Says:

John Sidles #399

” … factor the inferred probability distributions to satisfy locality …”

We always come back to this, don’t we? In principle, this operation does not differ from the renormalization of a measurement result in quantum field theory, to make it behave according to our own notion of locality. Problem is, the operation tacitly assigns a probabilistic value to NONlocality. There is no value of nonlocality in Joy’s framework, no probabilistic measure function at all.

In the Calude-Chaitin dialogue I linked above, I spotted another relevant comment:

“In a universe in which the axiom of choice is not true one cannot prove the existence of Lebesgue non-measurable sets of reals (Robert Solovay’s theorem).”

I recognized this problem in a paper for NECSI ICCS 2006, and showed how to derive a well ordered set of continuous functions from discrete random functions (which renders such functions pseudo-random) without assuming AC. It further validates the theorem that all real valued variables of a real function are continuous.

Point is — all the computer simulations I have seen proposed for Joy’s model assume a nondeterministic universe of probabilistic measure functions. That’s no fair test of the model.

This conundrum may be stated as a corrollary to the real continuous functions theorem: “All probabilistic functions are nonlocal.”

402. Bram Cohen Says:

Here’s an animation done on S^3 –

And here’s some discussion of the math behind such things –

http://stackoverflow.com/questions/5147526/navigating-though-the-surface-of-a-hypersphere-in-opengl

You’ll notice how much like normal space they appear.

Christian seems to really honestly believe that space doesn’t work the way we think it does, that his two particles aren’t ‘entangled’ because they actually aren’t all that far from each other. Ignoring that that wouldn’t imply S^3 at all, but instead a space made of frothy bubbles, it has this problem of being inconsistent with the Pythagorean Theorem. When this is pointed out, Christian says that he isn’t a computer scientist and the rest of us should learn M-theory.

By the way, I asked my daughter about it and she said she learned the Pythagorean Theorem in the third grade.

403. John Sidles Says:

Gil, there are of course many motivations for “loopholes” research regarding Bell inequalities … and this diversity is of course a great catalyst for STEM creativity.

For me, one motivation is associated to the (wonderful!) debate that you and Aram Harrow have been conducting on Gödel’s Lost Letter and P=NP. As that debate approaches its (eagerly anticipated!) closing arguments, you can anticipate that I will summarize a case for the following Church-Turing-type thesis (per comment #292):

“For any physically realizable dynamical system, the problem of verifying that a purported data-set of experimental observations is not a simulation belongs to the same computational complexity class as simulating that data-set.”

This thesis derives its plausibility from a granular analysis of the problem of simulating Bell-type experiments in their large-n instantiation as Aaronson-Arkhipov experiments.

Although the granular elements of this thesis are pretty solidly worked-out, its global elements are as yet discerned only indistinctly … comments #52 and #292 briefly review some literature and history in this regard. Perhaps by the time that Gil and Aram present their summary arguments, there will be more to say.

In the meaning, we all owe appreciation and thanks to Gil Kalai and to Aram Harrow, for sharing quantum physics arguments that are exemplary of the ideals of fairness, respect, and clarity. Thank you, Gil and Aram!   🙂

404. David Brown Says:

@Joy Christian #396: OK, I’ll stop the Einstein/Weyl comparisons. Have you looked at the following 2 papers?
http://vixra.org/pdf/1202.0083v1.pdf “Anomalous Gravitational Acceleration and the OPERA Neutrino Anomaly”
http://vixra.org/pdf/1203.0036v1.pdf “Does the Rañada-Milgrom Effect Explain the Flyby Anomaly?”
Assume that the “finite nature hypothesis” is wrong. Can you use your GRT skills to clean up the two preceding papers and get the polished versions published? If so, I believe your effort would enormously reward both of us. The Rañada-Milgrom effect is approximately correct based upon an easy scaling argument and the work of McGaugh and Kroupa.

405. Shtetl-Optimized » Blog Archive » I was wrong about Joy Christian Says:

[…] response to my post criticisms his “disproof” of Bell’s Theorem, Joy Christian taunted me that […]

406. David Brown Says:

@Thomas H. Ray #397 “I am convinced that Joy’s framework successfully does the job.” What about explaining dark matter, dark energy, and the space roar? Can you convince Joy Christian that he should polish up my work on the Rañada-Milgrom effect? I say that BOTH CHRISTIAN AND BROWN DESPERATELY NEED TO HAVE CHRISTIAN PUBLISH IN REFEREED JOURNALS ON ******The Rañada-Milgrom effect*******. IT IS NOT WRONG … IT IS MERELY BEING IGNORED.

407. Joy Christian Says:

As Richard Gill continues his three-month long Trojan horse campaign against me, once again I am compelled to point out that ALL of his fraudulent arguments against my model have been systematically and thoroughly debunked many times over, not only by me but also by several other people on the FQXi blogs. See, for example, the following three documents:

http://arxiv.org/abs/1203.2529

http://fqxi.org/data/forumattachments/JoyChristian_FAQ.pdf

http://fqxi.org/data/forum-attachments/Richard_said.pdf

It is evident from these documents that after having spent so many months of his malicious campaign against my one-page paper Richard Gill has yet to understand the first thing about my model. This is because he is well known among my colleagues to be a third-rate mathematician.

I cannot but agree with his suggestion, however, that everyone should check the physics and mathematics of my model themselves, summarized in this one-page paper:
http://arxiv.org/abs/1103.1879

As for my proposed experiment, http://arxiv.org/abs/0806.3078,
there is no issue of interpretation once you understand my topological argument against Bell’s theorem. This has been summarized in this introductory chapter of my book:
http://arxiv.org/abs/1201.0775
My compete argument against Bell’s theorem can be found in my book itself:
http://www.brownwalker.com/book.php?method=ISBN&book=1599425645
I urge all of you to THINK FOR YOURSLEF.

408. Joy Christian Says:

Bram Cohen,

You need to sit-in with your daughter for math lessons. You have yet to understand the difference between a 3-sphere and a parallelized 3-sphere. But don’t feel so bad. M-theory is not meant for computer geeks.

409. David Brown Says:

@Joy Christian #396: Richard Gill totally does not understand your proof. The same is true of Aaronson and Moldoveanu. You have not explained your proof well enough. You need to separate out the mathematical part from the physics part. WHEN YOU ATTACK THE COPENHAGEN INTERPRETATION THAT IS LIKE SAYING THAT HIV DOES NOT CAUSE AIDS. YOU MUST EXPLAIN YOURSELF EXTREMELY CLEARLY. If you examine my work on the Rañada-Milgrom you will find that I am correct. IN THE STRONGEST POSSIBLE TERMS I SUGGEST YOU CLEAN UP MY WORK AND GET IT PUBLISHED IN A REFEREED JOURNAL. Replacing quantum SU(1) states by quantum SU(8) states is a genius-level idea but you must explain yourself extraordinarily clearly. DO NOT SAY THAT QUANTUM COMPUTERS DO NOT EXIST. Say that quantum computers exist within the Copenhagen interpretation but not within the EPR local realism interpretation.

410. Bram Cohen Says:

Joy Christian, a parallelized 3-sphere is a 3-sphere with some stuff added to it. It doesn’t change the underlying 3-sphere in any way shape or form.

Your refusal to even engage with me other than trying to use fancy words which you think I don’t know and using ‘computer geek’ as a pejorative is downright bizarre. Seriously, do you or do you not understand how to use the pythagorean theorem to find the distance between two points in space?

411. Richard Gill Says:

Gil Kilai #400. Loopholes. A good CHSH experiment consists of a source sending particles to two detectors. At the two detectors, Alice and Bob each toss a coin to determine whether to measure A or A’, and B or B’. It’s important in order to be able to draw the conclusion that local realism is false from observation of correlations violating CHSH, that information concerning whether Alice measured A or A’ can’t possibly reach the other measurement station before the outcome of Bob’s measurement has been completed.

Trouble is, measurement takes time, and some measurements are unsuccessful. Photons can be measured fast, and far apart, but not all photons actually get detected.

Imagine many pairs of photons conspiring to generate a particular collection of four correlations in such an experiment. At the source, the photons decide what pair of settings they want to be measured in, and what pair of outcomes they’ll then generate. When each photon arrives at the measurement station, it looks to see how it is going to be measured. If the pair had decided in advance on (A,B’) and -1, -1, the if Alice’s photon sees that Alice wants to measure A’ instead of A, then it decides to go undetected instead. Only if Alice actually is measuring A, does the photon get detected, and is the outcome -1.

Half of the photons are lost on each side of the experiment. Only one quarter of all the pairs are both measured. They are only both measured when both photons are being measured just how they wanted to be.

At this level of attrition, they could generate correlations +1, +1, +1, and -1; and violate CHSH by going all the way to ave(AB)+ave(AB’)+ave(A’B)-ave(A’B)=+4. They could easily violate Tsirelson’s 2 sqrt 2.

But they could in particular easily generate 2 sqrt 2. Suppose we restrict the amount of attrition. Can we still hit 2sqrt 2? Obviously, yes. How far can we go? I forget the exact answer, but it’s something like the following: only if for every pair of settings, the probability there’s no measurement on Alice’s side given there is one on Bob’s side is at most 10% (and the same with Alice and Bob interchanged) can we conclude from observing 2 sqrt 2 that a local realist mechanism can’t generate the observed correlations.

In other words, we must demand that at least 90% of the time that we get an outcome on one side of the experiment, we also get one on the other side (whatever the settings, whatever side). Only then, is an experimental result “2sqrt 2” incompatible with local realism.

Weihs’ experiment only has 5%. It’s a long way to go, before we reach 90%.

Now this was relevant for a clocked or pulsed experiment. There are definite times when the photons are supposed to arrive and get measured. In real experiments, photons arrive at the detectors at unpredictable times. We say that two photons are part of a pair if nd only if their measurement times are within a certain small time interval.

This requires a different analysis. Photons can cheat by arriving a bit earlier or a bit later if they don’t like the settings they see on arrival at the detectors. All photons can be detected but many are not counted as part of a pair, because their arrival times are too far apart.

It turns out that it is now twice as easy for local realism to fake QM. In other words: we must demand that at least 95% of the time that we get an outcome on one side of the experiment, it is paired with one on the other side (whatever the settings, whatever side). Only then, is an experimental result “2sqrt 2” incompatible with local realism.

412. Henning Dekant Says:

@Fred D. #389, Quantum Computers are also classical Turing complete, so there’s nothing stopping my new religion.

Although, to attract Wolfram fans, maybe I should go with: “The universe is a quantum cellular automaton”?

I think I will decide this using a Scientology focus group.

413. Joy Christian Says:

Bram Cohen,

“Joy Christian, a parallelized 3-sphere is a 3-sphere with some stuff added to it. It doesn’t change the underlying 3-sphere in any way shape or form.”

Whether or not I know Pythagoras’s theorem or not, it is abundantly clear from the above statement of yours that you haven’t a clue what a parallelized 3-sphere is, let alone the difference between a parallelized sphere and a non-parallelized sphere. Learn these concepts first before we can have a dialogue.

414. Bram Cohen Says:

In case anyone reading along is curious what a parallelization is, there’s a great writeup here – http://en.wikipedia.org/wiki/Hairy_ball_theorem

Adding a parallelization has no impact on the distance function whatsoever.

415. Gil Kalai Says:

Many thanks, Richard, and thanks as ever, John…

416. David Brown Says:

@Joy Christian: “M-theory is not for computer geeks.” YES! But I don’t have the knowledge and skills to work at your level. Can you give me a brief description of your work as it relates to the M-theoretical 11-dimensional domain? I need the (matter SU(8)) X antimatter SU(8)) gauge group put together. How do you do this?

417. David Brown Says:

@Joy Christian: I might be crazy, but it seems to me that unless the M-theoretical 11-dimensional fundamental domain can be fully realized in terms of D-wave superconductivity, then both you and I are completely wrong about the failure of the Copenhagen interpretation. Do you agree or disagree?

418. Joy Christian Says:

Since Scott continues to block my attempts to respond to his criticism, let me spell out here how grossly mistaken his criticism really is.

What Scott fails to recognize is that EPR correlations are statistical correlations between measurement results A(a, L) and B(b, L), where the initial state L is a *random* variable, not an algebraic variable. The measurement results A(a, L) and B(b, L) are thus functions of the random variable L, and are therefore random variables themselves, not algebraic variables. The correlation between the numbers A(a, L) and B(b, L) is then given by the average of the number AB(a, b, L), which is also a function of the random variable L and a product of the random variables A(a, L) and B(b, L), and therefore it is also a random variable, not an algebraic variable. Scott’s failure to understand these basic facts is well hidden under his vitriolic but fallacious attack on my work. Further details of how these statistical concepts work within my model can be found in the attached paper.

419. Joy Christian Says:

David Brown,

I would like to respond to your call but at the moment I am distracted by the vicious and unjustified attack on my work launched by Scott Aaronson and his yes-men. I my opinion he and his yes-men are ignorant, dogmatic, and closed-minded, but the current climate in physics is on their side so these facts are difficult to prove. Time will come, however, when it will be evident to everyone that I have been right.

420. Henning Dekant Says:

@Joy, #419 you called Scott some not so nice things. On his very own blog. This predictably tends to piss people off.

421. Joy Christian Says:

Henning Dekant,

“@Joy, #419 you called Scott some not so nice things. On his very own blog. This predictably tends to piss people off.”

I do not care.

422. Henning Dekant Says:

“@Joy, #419 you called Scott some not so nice things. On his very own blog. This predictably tends to piss people off.”

I do not care.

423. David Brown Says:

@Joy Christian #421: “The time will come, however, when it will be evident to everyone that I have been right.” I agree. However, you should never have said: Bell’s theorem is wrong. You should have said that Bell’s theorem is valid within the paradigm in which the Copenhagen interpretation works, and the Copenhagen interpretation can sometimes fail, causing the failure of Bell’s theorem as a consequence. Your statement of the Theorem Egregium is very confusing to people. The experts think in terms of quantum SU(1) correlations and not quantum SU(8) correlations. The fact that you are right is irrelevant if no one understands what you are saying. Your model’s 7-sphere is obviously identifiable, in some sense, with the 7 extra superstring dimensions. Your theory predicts that 11-dimensional knot theory can be fully realized within D-wave superconductivity — if that were not the case, then Seiberg-Witten would be correct about the nature of the universe and you would be wrong. However, it seems to me that your Theorema Egregium strongly suggests that you are correct. However, the knot theory is VASTLY EASIER TO TEST than the suggested test that you published. Scott Aaronson has no understanding of your model, or what you attempting to do. However, Aaronson is a genius in his own field and understands quantum information processing extremely well and you need to talk to him in the language that he understands, i.e., quantum SU(1) correlations and the Copenhagen interpretation.

424. Fred D Says:

Scott says, “…this is what it boils down to. A(a,λ) = λ and B(b,λ) = -λ.”

Sorry, that is not what it boils down to at all. You, like Gill and Moldoveanu, are hung up on some *algebraic* outcomes of a *statistical* model. Here are all the possible algebraic outcomes of Joy’s statistical model.

Even though Joy’s model is statistical, it can have two different sets of possible algebraic outcomes. With mu = L*I with I being an oriented volume element and L =+/- 1 fair coin toss, the first part of the set is for all a and b except when b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (I.b)(mu.b) = – 1 if L = +1 and +1 if L = -1

And for b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

Then we have the following possible algebraic outcomes due to the parallelized 3-sphere topology when b is not equal to a or -a,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (I.b)(mu.b) = -1 if L = +1 and +1 if L = -1

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(I.b)(mu.b) = +1 if L = +1 and -1 if L = -1

And then when b = a for the topological sign flip algebraic possibility,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

And then when b = -a for the topological sign flip algebraic possibility,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1

——————————————————————
Then we have a different set of algebraic possibilities if the handedness of the detectors, (I.n), is reversed,

A(a, mu) = (I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (-I.b)(mu.b) = +1 if L = +1 and -1 if L = -1

And for b = -a,

A(a, mu) = (I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (I.a)(mu.a) = -1 if L = +1 and +1 if L = -1

Then we have the following due to the parallelized 3-sphere topology when b is not equal to a or -a,

A(a, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (-I.b)(mu.b) = +1 if L = +1 and -1 if L = -1

A(a, mu) = (I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(-I.b)(mu.b) = -1 if L = +1 and +1 if L = -1

And then when b = a for the topological sign flip algebraic possibility,

A(a, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1

And then when b = -a for the topological sign flip algebraic possibility,

A(a, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

Now, it is easy to see why we have special cases for when b = a or -a. Because the topology and model are symmetrical, the sign flips due to the topology will be on both A and B equally in those two cases so that you always have the product AB = -1 when b = a and the product of AB = +1 when b = -a. So I think the above covers all the algebraic possibilities of the statistical model.

Now, I would suggest and recommend that you actually take the time to read and study *all* of Joy’s papers thoroughly so as to avoid yourself great embarrassment in the future.

425. James Putnam Says:

Richard Gill #396,

Thank you for taking the time to write that response. I will need time to follow through on it. Here is quick question:

“…So you asked: what do I think about Joy’s physics? I don’t. There is none. The mathematics is trivial and either empty or wrong, depending on what assumptions he commits himself to (that varies from day to day). Joy’s definition of correlation is stupid, and irrelevant to the whole Bell discussion. All the chit-chat about the parallelized 3-sphere is just chit-chat. Noise. Diversionary tactics. Window dressing. This is not an emperor with no clothes. It’s some clothing with fundamental design errors, with no emperor inside. …”

Are you saying that the math, due to its own required rules, is inescapably wrong and therefore the physics part is irrelevant? Or, are you saying that the physics part is so clearly contrived that it cannot justify the mathematical steps, and, therefore the math steps must be judged as if they form purely a mathematical problem: “… In Joy’s one page paper, certain mathematical objects are defined. Their properties are specified. A calculation is made. The calculation is wrong. There is no room for maneuver, no room for opinion or debate. …” I suppose you might be saying both.

“… Joy got a PhD with Abner Shimony, but Abner Shimony thinks Joy’s work on Bell is nuts. …”

I pursue the authority question mainly because I see it used. It could refer to “serious sicentists”, “reputable physicists”, and sometimes “names”. I have hesitated to try communicating with anyone because if they have not made their opinions public, then I would be surprised if they would share them with me even privately. Also, they have probably been plagued with such requests for some time now. Public opinions, or opinions that can be made public, are most desirable. If I did try, it would be to ask Abner Shimony first.

James

426. Joe Fitzsimons Says:

Gil Kalai:

There are essentially 3 loopholes in current Bell experiments. These loopholes are basically escape clauses which allow a local hidden variable model to fit the experimental data.

Richard Gill explains perhaps the most complicated: the detector efficiency loophole.

There are also two others, which are much less subtle.

The first of these is the separation loophole. If the measurements are not made sufficiently close in time, then it would be possible for a message to be sent from one to the other containing the measurement basis of the first particle. This extra information would be enough to allow faking of the statistics. To remove this possibility, the measurement events need to be spacelike separated, so that no communication is possible between events (unless superluminal signalling were possible).

The other loophole is the really silly one. Bell’s procedure requires measurement bases to be chosen independently at random for each of the two measurements. But the question is how do you make a choice at random? If quantum mechanics is correct then it is fairly simple, but if hidden variables are real, and nature is fully deterministic, then it would be possible to imagine a state of the universe such that the state of the particles depended on which experiment would later be performed, since the measurement basis would already be predetermined, and hence the statistics could mimic quantum mechanics without being quantum. Thus if an adversary got to choose the state of the early universe, they could convince you of pretty much anything by predetermining all the experiments you would later perform, if quantum mechanics were not correct.

The former can be closed, and has been in careful experiments, but the latter is not closable even in principle, but I doubt too many people take it seriously.

427. Joy Christian Says:

Let us not forget what kind of scientist Scott Aaronson really is. He knew about my work on Bell’s theorem from day one. He was there at Perimeter Institute on the 20th March 2007 and heard people talking about it. He even asked me to explain my argument to him briefly during a lunch. However, upon his own admission, he never read a single page of any of my papers on the subject until 10th of May 2012. Thus, for more than five years Scott Aaronson held an extremely strong, vehemently negative opinion about my work without ever having read a single line of my argument. Let this fact be on the record.

428. Richard Gill Says:

James Putnam #425. I am saying both, but since I’m a mathematican, I start with the maths. If the maths were coherent then Joy would have discovered something important. But if it contains blooper after blooper, then something is badly wrong. Joy has a lot of fans who think he’s the new Einstein. But Einstein didn’t make mistakes like that. I think those people are being fooled, and I point out the bloopers so they can think for themselves. It’s just a question of familiarizing yourself with the basic rules of the game and then carefully checking line by line. Joy’s one page paper is just one page! All elementary stuff! But it seems that committed Joy Christian followers are too far committed to the genius idea, to be able to perform independent thought.

If the mathematical foundation is irreparably flawed, if the guy can’t carry through an elementary Clifford algebra calculation without making major, irreparable, elementary mistakes, then it seems to me that his metaphysical ideas are reduced to science-fantasy, fairy tales, poetry.

If you don’t like checking algebra, you can also check logic, at those points where Joy is connecting his science fantasy to the real world. For instance: the one page paper is completely explicit in defining the experimental outcomes in such a way that they are perfectly anti-correlated. The four correlations are all -1. Joy has a cock and bull story about bivectorial standard errors, the need to normalize covariance to get correlation. But Aspect, Weihs and so on don’t normalize covariances to correlations. Bell doesn’t.

Here Joy exploits the mismatch between the statistician’s definition of correlation coefficient, and the physicist’s. This is really funny since I happen to be a mathematical statistician (working at the moment on forensic DNA); I can tell you that everything he says about statistics is pure bullshit.

Another example. Joy’s experimental paper. Read it for yourself. That data is going to satisfy all CHSH inequalities, as a simple arithmetic fact.

Since the guy can’t do maths, and doesn’t understand simple logic, is there any point in taking his “physics” seriously? In my opinion (but I’m not a physicist), no. But the whole story is an interesting case-study in the sociology of science.

429. David Brown Says:

@Joy Christian #266: “I exorcized non-locality from contemporary physics.” I believe that you have, but if you have then you are the greatest theoretical physicist since *******. I think that your bomb fragment test is theoretically possible but would be horribly difficult and expensive in practice — I might be wrong here. However, there are 3 and only 3 plausible physical interpretations of M-theory: (1) Seiberg-Witten compactification; (2) Christian parallelizable 7-sphere model as final word; and (3) Fredkin-Wolfram-Brown automaton feeding into the parallelizable 7-sphere model. Both (2) and (3) imply that 11-dimensional knot theory can be fully realized in tests of D-wave superconductivity. Do you agree or disagree?

430. Nick Says:

@Joy: “Whether or not I know Pythagoras’s theorem or not, it is abundantly clear from the above statement of yours that you haven’t a clue what a parallelized 3-sphere is, let alone the difference between a parallelized sphere and a non-parallelized sphere. Learn these concepts first before we can have a dialogue.”

Thanks for that, Joy. I’m a math PhD student studying differential topology and it would have been far to much work to find out how math illiterate you really are since I don’t know any physics. Thanks for the succinct demonstration.

431. Joy Christian Says:

David Brown,

You said: “@Joy Christian #396: Richard Gill totally does not understand your proof. The same is true of Aaronson and Moldoveanu.”

One only needs to read the abstract of Richard Gill’s paper to see how incompetent and clueless a mathematician he is.

How can one explain to someone as clueless as these three the significance of my papers? How can one show blind people like these three the beauty of a rainbow?

As they say, there are none so blind as those who will not see.

432. David Brown Says:

@Richard Gill #430: Christian’s idea of replacing quantum SU(1) correlations by quantum SU(8) correlations is GREAT! This one idea makes him an incredible genius. THERE IS OVERWHELMING EVIDENCE that Milgrom is the Kepler of modern cosmology. Do you understand this?
http://en.wikipedia.org/wiki/Pavel_Kroupa

433. Joy Christian Says:

Thank you, Nick.

But it is Roger Penrose whom you should really thank, for I learned these concepts from him.

434. David Brown Says:

For those who are in doubt on the Aaronson versus Christian debate, merely read Christian’s papers prior to 2005, and you will see who is correct.
http://arxiv.org/find/all/1/au:+Christian_Joy/0/1/0/all/0/1

435. David Brown Says:

@Joy Christian: “As they say, there are none so blind as those who will not see.” YES … but. My understanding of physics is from the computer nerd perspective. Your understanding of physics is from the H. Cartan perspective. Computer nerds want to know what your theory predicts AND WHAT IT MEANS IN DUMBED-DOWN TERMS. What are the MOST FUNDAMENTAL PREDICTIVE consequences of your parallelized 7-sphere model? I say that your model predicts that 11-dimensional knot theory can be fully realized in empirical tests of D-wave superconductivity. FOR COMPUTER NERDS the testable predictions are everything while the mathematical beauty and the intellectual coherence are nothing. Do we agree or disagree on the D-wave superconductivity tests?

436. Joy Christian Says:

David brown,

You keep asking: “Do we agree or disagree on the D-wave superconductivity tests?”

I cannot agree or disagree without understanding your argument in full. Can you provide a link for the test you are talking about? I am in discussion with an experimentalist about realizing my proposed experiment, but the test you are suggesting may be easier to realize. Please provide a link.

Thanks.

437. David Brown Says:

@Joy Christian #438
http://gow.epsrc.ac.uk/NGBOViewGrant.aspx?GrantRef=EP/G009678/1 “Knot Solitons in Superconductors? A definitive test of the Babaev-Faddeev-Niemi Hypothesis”
The hypothetical BFN knot solitons are 4-dimensional. My guess is that your quantum SU(8) state/Theorema Egregium hypothesis is valid if and only if there exist superconductivity knots in dimensions 4 through 11. The reason is that Christian local realism implies that the 7 extra superstring dimensions represent local measurement in some forms of superconductivity. On the other hand, Seiberg-Witten M-theory implies that the 7 extra superstring dimensions represent quantum uncertainty and quantum non-locality. However, I have no mathematical models, and I am a third-rate mathematician at best. If you could get 1 or 2 of your general relativity pals to polish up my Rañada-Milgrom paper and my flyby anomaly formula paper on vixra.org and then submit them to refereed journals then I think that both you and I would be helped immensely.
Thanks.

438. Thomas H Ray Says:

Joe Fitzsimons #426 says it all: “The other loophole is the really silly one. Bell’s procedure requires measurement bases to be chosen independently at random for each of the two measurements. But the question is how do you make a choice at random? ”

Right. There’s no such thing, in principle. That’s why the extra degree of freedom (nature’s choice) in Joy’s framework returns objectivity to the measurement function.

“If quantum mechanics is correct then it is fairly simple, but if hidden variables are real, and nature is fully deterministic, then it would be possible to imagine a state of the universe such that the state of the particles depended on which experiment would later be performed, since the measurement basis would already be predetermined, and hence the statistics could mimic quantum mechanics without being quantum.”

That is not the ONLY valid way to interpret the measurement basis, however. In a relativistic universe, the illusion of time that demarcates past and future events is obviated by a topology that obliterates the distinction between global and local states. In other words, non-relativistic quantum mechanics in which every time interval is identical to every other (t = T = 1) is replaced by a relativistic quantum mechanics that is event-based rather than time-based. This means that “future” events conventionally assumed as global states are causally correlated with local states. (Somewhere in the back of my foggy mind, it seems to me that ‘t Hooft has done something with deterministic quantum mechanics along this line.) So a macroscopic, or classical, demonstration of this relation would give us the local — the least-action — state of the maximally ordered future state. For simple quantum particle properties like spin or parity, this doesn’t mean much. Bell-Aspect results also tell us that those quantum properties are correlated to infinity.

Point is, determinism in a relativistic universe doesn’t simply mean predicting future states by specifying the initial condition and boundary conditions (as in Newtonian physics). It means on a more foundational level, that randomized elements that were in contact at one time are correlated for all subsequent time intervals by identical rates of change. This would be demonstrable by reversing trajectory to the least-action state.

“Thus if an adversary got to choose the state of the early universe, they could convince you of pretty much anything by predetermining all the experiments you would later perform, if quantum mechanics were not correct.”

Easy to say (and no one is implying that quantum mechanics is incorrect, just incomplete) — but like the prime factorization problem, probably NP-complete. The least-action state of the universe is not determined by the least-action state of a local experiment — we can only say that whatever boundary condition (pseudo-random choice) we make is maximally correlated with its least-action partner compromising a future boundary condition. That the future boundary condition is LOCAL (every experiment is performed in a locally bounded interval of time), however, tells us that the universe is always in its lowest energy state possible — and that is an OBJECTIVE state, not the result of our pseudo-random choice, and not probabilistic. Were it otherwise, we woud not find it POSSIBLE to choose boundary conditions from which future states can be determined.

A more poetic way to put it is that we have no free will unless nature has free will. Nature had a choice in creating the world.

“… I doubt too many people take it seriously.”

I do.

439. Richard Gill Says:

@David Brown #432. If Joy’s idea is so great, then I’m sure that someone who has some mathematical self-discipline as well as a great imagination will will recognise it and take it up. Science is a multi-person, multi-discipline, human enterprise. Joy hasn’t had much success communicating his ideas to other competent scientists. It’s a pity he can’t listen to, or learn from, criticism.

Apart from that I don’t understand a word you write (nor do I have much interest in the topics).

It’s amusing how discussions of Joy’s work attracts other crackpots, like flies buzzing around a carcass. This too puts off serious people.

440. Thomas H Ray Says:

Gill, I think the set of “serious people” in the world is quite a bit larger than the subset who happen to agree with you.

441. David Brown Says:

@Richard Gill #441: I am a crackpot if and only the Space Roar Profile Prediction is empirically false. The issue is empirically decidable.
Christian’s book “Disproof of Bell’s Inequality” should be entitled “Challenge to the Copenhagen Interpretation”. Christian claims that quantum entanglement, quantum non-locality, and all other quantum phenomena are really illusions explained by his parallelized 7-sphere model. He doesn’t mean that “Bell’s theorem is false” IN THE STANDARD SENSE USED BY THE EXPERTS — he really means “Bell’s theorem is valid when the Copenhagen interpretation is applicable but can fail when some esoteric tests are applied to the Copenhagen interpretation.”
Aaronson’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Bell states can reproduce all of the predictions of quantum theory in the sense of the Copenhagen interpretation.
Christian’s Version of Bell’s Theorem: No physical theory of local hidden variables based upon quantum Christian SU(8) states can reproduce all of the predictions of quantum theory in the sense of the Christian interpretation of quantum theory. The Christian interpretation means the extension of the Copenhagen interpretation based upon Christian local realism.
Corrected Form of Christian’s Theorema Egregium: Every quantum mechanical Christian SU(8) correlation can be understood as a realistic, Christian SU(8) correlation among a set of points of a parallelized 7-sphere in the sense of teleparallel gravity. (The Christian SU(8) correlation is NON-LOCAL in terms of the Copenhagen interpretation and LOCAL in terms of Christian local realism.)
Brown’s Principle of Semantics in Physics: In physics the ultimate arbiters of the meanings of words should be the physicists who actually do the experiments.
THOSE WHO IGNORE BROWN’S PRINCIPLE OF SEMANTICS IN PHYSICS SHALL BE SEVERELY PUNISHED. This is part of Joy Christian’s problem. I strongly believe that Joy Christian’s work shall be recognized and rewarded within 2 to 3 years. If Christian and I can convince Wolfram that we are probably correct, then we are in the catbird seat. If physicists realize that there is now overwhelming evidence in favor of the Rañada-Milgrom effect then everyone will take Christian’s work very seriously indeed. YOU CAN BELIEVE IT OR NOT. Christian is ABSOLUTELY NOT a charlatan. His work is of the highest caliber. Time shall vindicate him.

442. Joy Christian Says:

Richard Gill,

You are a third-rate mathematician who cannot do even the simplest of mathematical calculations. This is amply demonstrated in your paper criticising my work. Just have a look again at my reply to you and you might just see your error after all these months: http://arxiv.org/abs/1203.2529

Over on the other blog Scott has invited a lynch mob to systematically demonize me in every which way possible, without allowing me to respond to the wild speculations about me they are indulging in. Not a single one of the mobsters has the slightest clue about my work (most have never read a single line of it), and yet they all have an opinion about me, including speculations about my ethnic origins and psychological makeup. This is what you wanted to achieve for the past three months, Richard Gill, but you didn’t even have the talent to achieve that simple goal. If I were you I wouldn’t give up my day job of a third-rate mathematician.

443. Henning Dekant Says:

Joy #442, this is Scott’s blog i.e. he has full control over it and can do with it as he wishes. It’s like a virtual home and Scott owns it. Locking you out of the other thread is like keeping you out of the kitchen while he still tolerates you in his house.

444. Joy Christian Says:

After reading some of the comments in the other blog of Scott’s,
http://www.scottaaronson.com/blog/?p=1028#comment-44742
I must stress that one has to be mind-numbingly, excruciatingly, revoltingly stupid to think that there is an error of some kind in my one-page paper: http://arxiv.org/abs/1103.1879
You really, really, really have to be extraordinarily stupid to think that. So if you are thinking that, then you know what you are.

445. Joy Christian Says:

Henning Dekant,

“Joy #442, this is Scott’s blog i.e. he has full control over it and can do with it as he wishes.”

Not really. To deliberately, manipulatively, wrongly, and systematically defame someone on a public domain such as the Internet is a crime. Therefore in my eyes Scott Aaronson is a criminal. You heard it, Scott Aaronson is a criminal.

446. Henning Dekant Says:

Joy #445, since your case against Scott hinges on the correctness of your model, where are you going to find an attorney smart enough to understand your papers?

447. David Brown Says:

@Joy Christian #448: “To … defame someone on a public domain …” Aaronson has crossed over a line. I was pretty bad with regard to you, but Aaronson seems eager to destroy your reputation and career. Welcome to the wonderful world of paradigm changing. I think both of us need help from Wolfram. Your theory of Christian local realism with the infinite nature hypothesis is ABSOLUTELY ESSENTIAL to what Wolfram and I hope to achieve. I am unsure why Aaronson is still letting us express our opinions on his blog.

Joyless #445,

Accuracy is an absolute defense against defamation and libel, so Scott is clearly not a criminal; your papers are devoid of content.

449. David Brown Says:

TO SCOTT AARONSON: Look at Christian’s comment #444 and CAREFULLY STUDY Christian’s “Refutation of Richard Gill’s Argument Against my Disproof of Bell’s Theorem”. In some sense I would say that Christian’s argument hinges on “freedom of choice of the orientation of a Clifford algebra” — the problem with Christian’s argument is NOT the mathematics. If the introduction of the 7-sphere means “7 dimensions of quantum uncertainty” then Christian has NOT refuted Bell’s theorem in TERMS OF quantum SU(1) correlations. If the introduction of the 7-sphere means “7 dimensions of local measurability (i.e., 7 dimensions of local reality)” then Christian HAS refuted Bell’s theorem in the sense that Christian has REFUTED THE COPENHAGEN INTERPRETATION of quantum mechanics. To say that Bell’s theorem has been disproved is like saying that quantum theory disproves Maxwell’s equations. THE PROBLEM IS NOT WITH BELL’S THEOREM, IT IS WITH THE COPENHAGEN INTERPRETATION ITSELF. Thomas H. Ray and Fred Diether are correct about the mathematics while you and Richard Gill are wrong. Consult someone like Michael Atiyah if you don’t believe me. By the way, I have an M.A. in mathematics from Princeton (1975). I was at Princeton at the same time Witten was at Princeton, but I flunked out with an M.A. However, I still know enough mathematics to understand that in the Gill versus Christian dispute, THE MATHEMATICS is what Christian says it is. The issue is physics not mathematics.

450. Joy Christian Says:

Henning Dekant,

Nature is my attorney and she will expose Scott for what he is.

451. Simon J.D. Phoenix Says:

OK – let me sketch some initial thoughts on this – they may well be a bit wrong (won’t be the first time, and I can pretty much guarantee it won’t be the last).

We can obtain the mathematical inequality we call Bell’s theorem from consideration of just a single particle. The physical interpretation is different but the mathematical form is the same.

So imagining we prepare a spin-1/2 particle in one of 3 specified spin direction, chosen at random and then measuring the spin in the same 3 directions, also chosen at random – we’ll find that there is a correlation between state preparation and measurement that violates the inequality.

We can use this in a single-particle QKD scheme in which the eavesdropper screws things up and restores the inequality.

Of course we don’t have any locality issues here because the interpretation is very different. So at the risk of throwing the baby out with the bath water, let’s proceed.

There’s a lovely article by D’Espagnat in Scientific American (1979) in which he uses straightforward triangle inequalities for quantum probabilities to derive the mathematical form of the Bell inequality. The mathematical form of the inequality therefore depends upon complementarity. So it’s no surprise to me that a non-commuting algebra can reproduce a violation of the inequality – having a non-commuting algebra would be a requirement, in fact!

So implicitly, somewhere, I think the ‘disproof’ of BT depends on a model of classical reality that depends on non-commutativity.

In other words, we have to have a classical reality that, for a single particle, will give the violation of BT in order for the disproof to make sense. I don’t reckon we do have such a classical reality 🙂

Anyway – these are just some thoughts off the top of my head as to another way of approaching the issues under discussion. I could be, and history has shown that there’s a fair probability, entirely wrong!

452. David Brown Says:

453. Gil Kalai Says:

Thanks, Joe

Regarding the loopholes, one thing that I dont understand is this: Is the motivation behind the loophole research aimed at bringing experimental physics to a place where there is a demonstration of the Bell phenomenon which stands these statistical conspiracy possibilities. Or perhaps the motivation is really to refute Bell’s theorem or to propose an alternative “classical” explanation.

Also, Richard is quoted in Wikipedea as experssing the idea that there are physical reasons (within QM, I suppose) for why basic loopholes like the detection one cannot be “closed” as a matter of principle. Why is that?

454. Joy Christian Says:

“Accuracy is an absolute defense against defamation and libel”

Then Scott Aaronson has absolutely not defense.

Scott Aaronson is a criminal.

“…your papers are devoid of content.”

One has to be mind-numbingly, excruciatingly, revoltingly stupid to think that my papers are devoid of content. You really, really, really have to be extraordinarily stupid to think that.

455. Joy Christian Says:

David Brown,

I attack people because I have been wrongly attacked by lesser brains. But you are right. I should learn from Jesus and Gandhi to turn the other cheek.

I looked at some of your arguments on the Internet. You have some good ideas but you are not a professional physicist, if you don’t mind my saying so. I am nevertheless beginning to understand your argument. I am investigating your suggestion about the Rañada-Milgrom effect in relation to my work. If you are right, then what you are saying is extremely significant.

I had a brief correspondence with Michael Atiyah some months ago. He was intrigued by my argument involving the parallelized 7-sphere. I will send him a copy of my book.

Thank you for being a voice of reason amidst the sea of stupidity.

456. Alex V Says:

Gil Kalai #453
Where it is quoted in relation with detection loophole? I am aware about troubles with something like that, but such thing would have extremally strong argumentation, because in such a case, indeed, why we should do all these experiments?

TO: All the mathematicians and/or computer scientists and/or other thinkers who do understand the kind of mathematics that is used in Joy’s papers:

Here is what Dr. John Siddles wrote in his comment # 346 above:

“Computationally speaking, both the dynamical state-manifold of this animation, and the trajectory simulated on that state-manifold, are identical to the state manifold and the dynamical trajectory of outgoing fragments of Joy Christian’s “exploding sphere” experiment.”

Since I am not at all trained in the kind of mathematics that Joy’s work and the above statement involves, I have the following request for you:

Could someone of you please provide a second opinion as to whether John’s statement is alright in this context? I mean to ask: can I take John’s statement as is, without any significant (and relevant) addition or qualification having to be made for it to be a valid description of what Joy’s mathematics entails (in this context)? (Thus, in other words, I don’t at all doubt John’s competence; I just want a second opinion.)

Oh, BTW, another question, through relatively far minor: If I were to substitute the words “mathematically speaking” in place of “computationally speaking” in the above quoted statement of John’s, would it significantly alter the meaning of the statement? I think not. After all, the ideas like a dynamical state manifold and a trajectory defined on it, are basically mathematical ideas, even if their can be simulated on a computer, right? I mean it’s something like saying that, speaking in overall terms, for an upwardly thrown ball (high school problem), we can talk of a parabolic trajectory in both mathematical and computational senses, without any significant loss/gain of meaning as we go from one sense of the term to another, right?

[PS: My ‘net connection was down for a few days from 4th May through 9th (India time), and then I took some more time to “take in” all the further development on this blog since the last time I had checked it out.]

Ajit
[E&OE]

458. Thomas H. Ray Says:

Ajit #457

I think it boils down to the question of whether the simulation of a continuous function is a continuous function.

I think not.

459. Joe Fitzsimons Says:

Gil: I’m not quite sure what you mean be loophole research. It’s simply a case that current experiments don’t perfectly match the theoretical model, and so you have these escape clauses creeping in, but they tend to be well understood for a given experiment. Most of the current research I’m aware of tends to be experimentalists trying to make better experiments with less such caveats.

I believe that both the detection loophole and the separation loopholes have been closed in separate experiments, but not together in a single experiment. I could be wrong on this though, since I don’t keep up with that area. I don’t really consider it even remotely likely that nature exploits one of these loopholes, as I simply don’t think nature is that adversarial. I can’t find the quote you mention, and I don’t know which Richard you are referring to, but as I have said in my previous answer the free will loophole is not something that can ever be closed.

460. Richard Gill Says:

Gil Kilai, Joe Fitzsimmons, on loopholes. My paper http://arxiv.org/abs/quant-ph/0301059 “Time, Finite Statistics, and Bell’s Fifth Position” put forward the possibility that Nature herself through quantum physics might prevent simultaneous closure of the detection and the separation loophole. You can close the detection loophole by doing a CHSH experiment on close-by neutrons, or on ions in an ion trap, but the measurements take a long time and fail the separation criteria. Or you can do it rapidly with far-apart photons but then the photons tend not to be there when you want them. This is reminiscent of quantum uncertainty relations. Indeed it is all about simultaneously controlling time and location. You can try to create entanglement between distant ions using entangled photons but the detection loophole comes back through the photons, which don’t always do their work.

It turned out that others have had this idea is before and there is even some theoretical support from quantum field theory.

I don’t have an opinion one way or another whether or not this will turn out to be the case. It does mean that a loophole-free experiment (ie free of these two loopholes) is an exciting challenge to experimenters. I know they are starting to talk about it.

But suppose we can never ever do a loophole-free CHSH type experiment. Then we can never build secure quantum cryptography protocols on the foundation of Bell tests of quantum entanglement. We can never know, for instance, whether an adversary has replaced the quantum detectors with local realist computer software (Trojan horse attack).

In fact, Accardi and Ohya already successfully sold fake quantum cryptography hardware to a Japanese telecommunications company. They used the detection loophole to emulate a succesful Bell-CHSH experiment on classical computatation and communication hardware.

de Raedt et al could also consider earning money from their “event by event simulations” of Weihs et al experiment in this way. I can’t see any other use for it.

For an entrance to the literature on the detection and related coincidence loophole see http://arxiv.org/abs/quant-ph/0312035 , “Bell’s inequality and the coincidence-time loophole”, Jan-Ake Larsson & Richard Gill

461. Henning Dekant Says:

David Brown #447:

I am unsure why Aaronson is still letting us express our opinions on his blog.

Remarkable, isn’t it? Shouldn’t be overlooked that you are still welcome in the other thread as well.

When my little boy graduated from Kindergarten the principal pointed out that this is the place where you learn the most important lessons of your life. Seems rather pertinent in light of this thread.

462. David Brown Says:

@Joy Christian #458: Brown is “… not a professional physicist …” CORRECT! My work in some sense merely skims the surface of Wolfram’s intuition. However, Milgrom’s work has been ignored since 1983 — an unbelievable rejection of the greatest work in astrophysics. The Rañada-Milgrom effect is approximately correct because: when gravitational accelerations are low then an easy scaling argument shows that the effect is approximately equivalent to Milgrom’s acceleration law; when gravitational accelerations are high then the empirical facts about gravitational lensing show that the effect is approximately correct. According to Steven Weinberg, “String theory is the only game in town.” Standard physics cannot explain the Rañada-Milgrom effect. Plausible guesses show that the Rañada-Milgrom effect is strong empirical evidence for both M-theory AND Christian’s theory of local realism. Thus, I claim that there is ALREADY OVERWHELMING EMPIRICAL EVIDENCE in favor of your theory. YOU MUST EXPLAIN THE MEANING OF THE 7-SPHERE IN TERMS OF THE 7 EXTRA SUPERSTRING DIMENSIONS … at least that’s the way I see things. Carefully study Prof. Dr. Pavel Kroupa’s work and form your own opinions.
http://en.wikipedia.org/wiki/Pavel_Kroupa
I now clearly perceive that your parallelized 7-sphere model shall, sooner or later, be enshrined in the pantheon of theoretical physics.

463. Alex V Says:

Simon J.D. Phoenix #451
If I understand the example with a single particle correctly, the correlation should have opposite sign in comparison with the Bell experiment with two-particles singlet state.

464. James Putnam Says:

“Simon J.D. Phoenix Says:
Comment #85 May 12th, 2012 at 12:17 am

“A(a,λ) = something complicated = (as Joy correctly observes) λ

B(b,λ) = something complicated = (as Joy correctly observes) -λ”

Oh my word – thanks Scott – I hadn’t actually noticed this being somewhat befuddled with the mathematical decoration on show. Oh Lordy, Lordy, Lordy . . . .

If anyone still needs convincing after this then may I suggest Philippe Grangier’s beautiful dissection of the physics behind why Joy is wrong which can be found on Arxiv.”

“From Scott’s opening remarks in his other thread: ‘I was wrong about Joy Christian’

Update (May 11): A commenter pointed me to a beautiful preprint by James Owen Weatherall, which tries sympathetically to make as much sense as possible out of Joy Christian’s ideas, and then carefully explains why the attempt fails (long story short: because of Bell’s theorem!).”

The comment: “(^.^) Says:
Comment #59 May 11th, 2012 at 3:37 am
Pardon me…. dont even bring the previous comment to the front. I found something.. http://books.google.com/books?id=_V4MEYAENKwC&pg=PR13&dq=James+Owen+Weatherall&hl=en&ei=TM-sT_PXJIWUiAKT4bjqBg&sa=X&oi=book_result&ct=book-thumbnail&resnum=4&ved=0CEAQ6wEwAw#v=onepage&q=James%20Owen%20Weatherall&f=false

looks like Weatherall and Christian have had prior communication.”

Ok, two physicists to check: Philippe Grangier and James Owen Weatherall.

James

465. John Sidles Says:

Dear Ajit (#457)

Thank you for both the graceful manners of your post, and for its substantive content.

To answer your questions with regard to post #346, the water molecule dynamics in that post are integrated using the dynamical equations that (to my knowledge) were first given in the chemical simulation literature by Denis Evans, “On the representatation of orientation space”, Molecular Physics v34, 317–25 (1977). As an exercise, Evans’ equations were re-derived (and found to be correct) via pullback methods, in the context of a geometric formulation of constrained dynamics upon a symplectic state-manifolds, as set forth (for example) in Vladimir Arnold’s Mathematical Methods of Classical Mechanics (3rd edition, 1998). The pullback was automated in Mathematica, adhering strictly to the notation and toolkit of John Lee’s Introduction to Smooth Manifolds (2003).

This practical exercise was a portion of a broader practical exercise, to systematically rederive in a modern geometric framework not only Arnold’s classical dynamics, but also the general quantum dynamics of Michael Nielsen and Isaac Chuang’s Quantum Computation and Quantum Information (2003), encompassing in particular the large-n spin physics of Charles Slichter’s standard text Principles of Magnetic Resonance (3rd edition, 1989), and moreover encompassing also Lars Onsager’s transport theory, along the statistical physics lines set forth in Hendrik Casimir’s “On Onsager’s principle of microscopic reversibility” (Rev. Mod. Phys. v17, 343–50 (1945)), and along the thermodynamic lines of R. K. Zia, Edward Redish, and Susan McKay’s highly recommended “Making sense of the Legendre transform” (Am. J. Phys. v77, 614–622 (2009)), and along the quantum informatic lines that are set forth in Carlton Caves on-line notes “Completely positive maps, positive maps, and the Lindblad form” (2000).

From a historical point-of-view, this exercise’s strict adherance to ideals of geometric naturality continues a tradition that begins with J Willard Gibbs’ seminal “A method of geometrical representation of the thermodynamic properties of substances by means of surfaces” (1873), and continues in (for example) George Ruppeiner’s “Riemannian geometry in thermodynamic fluctuation theory” (Rev. Mod. Phys. v67, 605–659 (1995)).

Obviously the preceding spans spans a sufficiently broad range of ideas, that the whole enterprise of embracing strict mathematical naturality would make little practical sense, were it not that the aggregate mathematical toolkit can be boiled-down to one synoptic page whose mathematical expressions *do* prove to be exceedingly useful — indeed essential — in guiding the practical design of quantum technologies and experimental trials of those technologies (at least, that’s what we use them for). The algorithm for constructing this one-page outline is simple: take any article dealing with dynamics, and ask “How might Vladimir Arnold and John Lee collaborated to explain this dynamics?”

One could conceive an alternative-universe Feynman Lectures that sought to convey a unified naturality of understanding — via the frameworks of Gibbs / Onsager / Casimir / Arnold / Lee / Slichter / Nielsen & Chuang / Caves, etc. — as incrementally consolidated from granular exercises in computational simulation. Regrettably, for so long as students insist upon learning QM as soon as possible, and as rapidly as possible — and I was one of these students — students necessary will pay the heavy price of learning mathematically and computationally immature versions of QM, that are needless restrictive, and are arduous to broaden, and moreover are wholly at odds with Feyman’s own philosophy:

It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship.  … It was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. I think it is somehow a representation of the simplicity of nature. … Maybe that is a way of defining simplicity. Perhaps a thing is simple if you can describe it fully in several different ways without immediately knowing that you are describing the same thing.

Summary Two main lessons of this affair (for me) are:

(1) In striving to achieve both naturality of understanding (via mathematical frameworks) and granularity of appreciation (via computational simulation), in the long run we achieve either plenty of both, or little of either.

(2) In striving to achieve fairness, respect, clarity, and correctness, in the long run we achieve either plenty of all, or little of any.

And so there is a lot of work ahead of us. Practical work, creative work, fundamental work. Good! 🙂

466. Joy Christian Says:

Henning Dekant,

I fail to understand why you keep defending the actions of the juvenile delinquent Scott Aaronson. How do you justify the fact that he is grossly misrepresenting my work on the other blog without having understood the first thing about it and without letting me correct the perpetuation of his misrepresentation? He is deliberately feeding false information to people. I think it is about time you recognize that

Scott Aaronson is a criminal.

The crimes of Scott Aaronson are not only against me, but also against physics, and against science in general.

467. Joy Christian Says:

James Putnam,

(1) Simon J.D. Phoenix hasn’t a clue what he is talking about. He has bought into Scott’s misrepresentation of my model without thinking it through himself. Please see the explanation of Scott’s mistakes in one of my posts above, as well as the detailed and explicit calculations of my measurement functions A and B by Fred.

(2) Philippe Grangier’s criticism is old, outdated, and wrong. It has been thoroughly answered by me in this paper: http://arxiv.org/abs/quant-ph/0703244

(3) James Owen Weatherall is talking about his own model, not mine. His model has little or nothing to do with my model. Just like Scott, Jim has not understood my model at all.

When will people (excluding you) recognize the difference between a genuine criticism and a straw-man criticism?

468. Gil Kalai Says:

You wrote “My paper http://arxiv.org/abs/quant-ph/0301059 “Time, Finite Statistics, and Bell’s Fifth Position” put forward the possibility that Nature herself through quantum physics might prevent simultaneous closure of the detection and the separation loophole.”

This is an interesting possiblity while of course very bold.
(Am I correct that your thoughts do not involve breakdown of quantum physics of any kind?)

“But suppose we can never ever do a loophole-free CHSH type experiment. Then we can never build secure quantum cryptography protocols on the foundation of Bell tests of quantum entanglement.”

Usually these tasks are considered easier than universal quantum computing. Do your ideas have any baring on universal quantum computing? –best Gil (Kalai not Kilai 🙂 )

469. Simon J.D. Phoenix Says:

“Simon J.D. Phoenix hasn’t a clue what he is talking about.”

Well, that’s not something I’m going to disagree with over much, because it’s often true 🙂

But Joy – I know you feel a bit attacked, but wouldn’t a more professional and adult response be to rise above the attacks and display some dignity?

People are only disagreeing about a bit of physics and maths for heaven’s sake – with a little bit of name-calling and hyperbole thrown in. It should be fun.

Well on to the fun then 🙂
(1) do you agree that the correlations between state preparation and measurement on a single spin-1/2 particle can produce a violation of the mathematical inequality known as Bell’s inequality?
(2) Do you agree that the fundamental component in this interpretation is complementarity?
(3) Do you agree that in order to describe this with some non-QM based model we have to have a model that involves non-commutation?

I’d be interested in your perspective on this – genuinely.

470. James Putnam Says:

Fred D Says:
Comment #424 May 10th, 2012 at 8:20 pm
Scott says, “…this is what it boils down to. A(a,λ) = λ and B(b,λ) = -λ.”

Sorry, that is not what it boils down to at all. You, like Gill and Moldoveanu, are hung up on some *algebraic* outcomes of a *statistical* model. Here are all the possible algebraic outcomes of Joy’s statistical model.

Even though Joy’s model is statistical, it can have two different sets of possible algebraic outcomes. With mu = L*I with I being an oriented volume element and L =+/- 1 fair coin toss, the first part of the set is for all a and b except when b = -a, … ” (Fred’s message continues by presenting ‘…all the possible algebraic outcomes of Joy’s statistical model.)

I was wondering why there was no response to Fred’s message. Was waiting and watching.

James

471. Joy Christian Says:

Simon J.D. Phoenix,

I have been ostrasized, demonized, ridiculed, and under vicious attacks for the past five years, only a fraction of which has been in the public domain. When these things affect where your next meal is going to come from, it is no longer fun.

But let me try to be funny:

“(1) do you agree that the correlations between state preparation and measurement on a single spin-1/2 particle can produce a violation of the mathematical inequality known as Bell’s inequality?”

Yes.

“(2) Do you agree that the fundamental component in this interpretation is complementarity?”

“component”, yes, but not necessarily “fundamental.”

“(3) Do you agree that in order to describe this with some non-QM based model we have to have a model that involves non-commutation?

Yes, but not necessarily non-commutation of the *raw* measurement results.

472. Joy Christian Says:

James,

“I was wondering why there was no response to Fred’s message. Was waiting and watching.”

You already know the answer from what you have witnessed during the past many months.

Very few people are interested in knowing what my model actually is. They are not interested in Fred’s explanation. They are interested in convincing themselves that I must be wrong.

473. Scott Says:

James #470: The reason I didn’t respond to Fred’s comment is that it made no sense to me. What is a “statistical model,” in this context? What’s an “algebraic outcome,” and how is it different from a “statistical outcome”? I’ll need straight mathematical definitions of these concepts, not definitions in terms of other words that themselves have hidden meanings. If no one can define these concepts in a satisfactory way (as they haven’t so far, in 470 comments!), that’s an enormous red flag.

Or is the math just too advanced for me? Well, that’s fine: there are plenty of more sophisticated mathematicians reading this blog. Just explain it to one of them, so that they can give me the dumbed-down version.

I should confess at the outset, though, that I don’t see how any verbal maneuvering could possibly salvage things. When you do a physics experiment, you see an outcome—it makes no difference whether you describe the outcome as “statistical,” “algebraic,” “chocolicious,” etc. So ultimately, the only question that matters is: what outcomes does Joy’s model actually predict for the actual measurements that are actually performed in the lab? The text of his paper seems pretty unambiguous that the answer is A=λ, B=-λ. If it’s something else, then what is the something else, and why hasn’t Joy corrected or clarified his paper to say so?

The irony is that I, Richard, and others stand accused of being mathematical pedants, ignorant of the “deep physical meaning” of Joy’s model. Yet here we’re the ones repeatedly asking about the actual outcomes that would be recorded in an experiment, while the other side throws around formal manipulations without spelling out their connection to reality.

474. Fred D Says:

Hi James,

Let me provide the link back to the comment from me that you are referring to since I think it would be good to discuss it,

http://www.scottaaronson.com/blog/?p=993#comment-44530

What I have presented for the algebraic outcome possibilities of Joy’s model were not just pulled out of thin air. They come from the model itself if one does take the time to understand the parallelized 3-sphere topology involved in the model. What is more, if one is to completely analyze the content of those outcome possibilities for a large number of runs, they will find that,

A() = +/-1 randomly
B() = +/-1 randomly
AB = -1 when b = a
E(a) = E(b) = 0
E(a,b) = -a.b

Those are the conditions of Bell / EPR. Joy’s model is a local realistic counterexample to Bell’s theorem.

475. Raoul Ohio Says:

Talk about being fasttracked, Scott was promoted to juvenile delinquent, then criminal, then criminal against physics, and finally criminal against all science — in only a few lines!

This does not leave a lot to aspire to, maybe criminal against knowledge?

476. Joy Christian Says:

Scott Aaronson,

Your comments reveal a deep misunderstanding of the so-called Bell’s theorem, let alone the subtleties of the EPR argument it must comply with. In his own words Bell insisted that it is not possible to find local functions of the form

A (a, L) = +1 or – 1

and

B(b, L) = +1 or − 1

which can give the correlation of the form

average(AB) = – a ・ b,

where L is an initial state determining the numbers A and B, and the measurement context b has no effect on what happens, A , in a remote region, and likewise the measurement context a has no effect on what happens, B. “This is the theorem”, Bell insisted.

But one does not have to be Einstein and one does not have to understand the mathematics of more than a half a page of my one-page paper to see that I have accomplished exactly what Bell claimed to be impossible.

What you fail to recognize is that EPR correlations are statistical correlations between measurement results A(a, L) and B(b, L), where the initial cause L is a *random* variable, not an algebraic variable. The measurement results A(a, L) and B(b, L) are thus functions of the random variable L, and are therefore random variables themselves, not algebraic variables. The correlation between the numbers A(a, L) and B(b, L) is then given by the average of the number

AB(a, b, L) = A(a, L) B(b, L),

which is also a function of the random variable L and a product of the random variables A(a, L) and B(b, L), and therefore it is also a random variable, not an algebraic variable. Further details of how these statistical concepts work within my model can be found in this paper: http://arxiv.org/abs/1106.0748. It is easy to recognize from this paper that nothing can be more connected to reality than my model. What you have failed to recognize so far is that quantum correlations are understood in my model as purely topological effects, not contextual effects.

477. David Brown Says:

@Joy Christian #474: “I have been ostracized, demonized, ridiculed, and under vicious attacks for the past five years, only a fraction of which is in the public domain. When these things affect where your next meal is coming from, it is no longer fun.”
Consider:
“The paradigm was: crystals were ordered and periodic — no exceptions. … For a couple of years I was alone, I was ridiculed, I was treated badly by my peers and colleagues … ‘You are a disgrace to our group ….’ … People were hostile. The community of nonbelievers was very large in the beginning … in fact, it included everybody.” — Prof. Dan Shechter
http://www.youtube.com/watch?v=EZRTzOMHQ4s “Prof. Dan Shechter 2011 Nobel Prize Chemistry Interviewed by ATS”
Paradigm breakers get busted in the beginning.
THE EVIDENCE IS OVERWHELMING IN FAVOR OF MILGROM’S ACCELERATION LAW FOR GALACTIC ROTATION CURVES.
http://en.wikipedia.org/wiki/Stacy_McGaugh
Is Prof. McGaugh a crackpot?
The Rañada-Milgrom effect is strong evidence in favor of BOTH M-theory and Christian’s parallelized 7-sphere with local realism. THERE IS NOTHING ELSE IN THEORETICAL PHYSICS THAT CAN EXPLAIN THE EFFECT!

478. Simon J.D. Phoenix Says:

OK – let’s assume I’m an idiot – an assumption that may not be far from the truth. Now as far as I can determine from equations (1) and (2) of Joy’s one page ‘counter example’ paper we have

A(a, lam = 1) = 1
A(a, lam = -1) = – 1

B(b, lam = 1) = -1
B(b, lam = -1) = 1

where a and b are unit vectors describing the orientation of the measurement devices. Lam is a random variable that can take the values +1 or -1.

A and B are functions that represent the measurement outcomes. So if our hidden variable is lam = 1 for a particular run, then Alice’s detector ouputs A(a, lam = 1) = 1
and Bob’s detector outputs B(b, lam = 1) = -1

Am I missing something here? If I’ve interpreted equations (1) and (2) of Joy’s paper correctly then **whatever** the orientations of Alice’s and Bob’s detectors the clicks will always be anti-correlated??

If that’s not what Joy actually means – could someone explain what the heck it does actually mean in simple terms – without all the bi-vector nonsense.

It seems pretty clear cut to me – A and B are just functions that take as input some vector and a random variable that can take the values plus or minus one – and the definition of the output of these functions seems very clear in Joy’s paper – it’s given as above.

Note that the random variable must have the same value for both Alice and Bob for each run, because it is the random variable that is supposed to represent the hidden element of reality that pre-determines the results of our measurement. So you can’t have lam = 1 for function A and lam = -1 for function B on the same run.

If the above interpretation of what equations (1) and (2) actually mean are correct – then of course this model in no way reproduces the correct experimental results from actual spin-1/2 particles – or violates Bell’s inequality – it’s just a fancy version of Bertlemann’s socks.

479. Simon J.D. Phoenix Says:

Joy wrote : “I have been ostrasized, demonized, ridiculed, and under vicious attacks for the past five years, only a fraction of which has been in the public domain. When these things affect where your next meal is going to come from, it is no longer fun.”

OK – I understand the frustration, but seriously I don’t think you’re helping yourself much by fighting back in a similar vein – although I perfectly understand the temptation to do so.

I’ve only recently had a look at this whole issue and been reading these blogs and comments – and if I’m brutally honest I’ve seen you react very badly to moderate criticisms made in a polite, but sometimes robust, manner [and to be fair to you I’ve also seen a few pretty rough comments directed to you too, although I have to say that my impression is that the balance is against you]. OK – I now understand why – but once again – you’re not helping yourself here 🙂

OK – the point I’m trying to make with the single spin example is that if your model is correct it should also provide a non-QM model for this situation. Now I know that rotations do not commute – but the point is that these are operations – not variables. If you’re going to have a model for even a single spin particle then somewhere you’re going to have to have non-commuting variables – not operations. In essence this is repeating the argument of Peres (chapter 6 of his textbook on Quantum theory).

So if your model is correct it will also have profound implications for non-entangled QM too 🙂

480. Joy Christian Says:

Raoul Ohio,

“…maybe criminal against knowledge?”

Sorry I missed that.

Thank you!

481. Fred D Says:

Hi Simon,

It is just plain common sense that AB = -1 *always* is not the end of the story with Joy’s *statistical* model as many want to believe. I have given all the possible algebraic outcomes of Joy’s model above,

http://www.scottaaronson.com/blog/?p=993#comment-44530

And these are not hard to deduce from the model once you understand the parallelized 3-sphere topology. Joy’s eq. (1) and (2) are correct as presented and those are the outcomes for the core functions presented for A and B in those equations. And as you can see from what I have shown above, the core functions never change. All the sign flips cancel out in the correlation calculation via the proper statistical procedure. But since you are looking at the one page paper, let me make sure you understand the connection from the notation there to the notation used in my example above.

{-a_j beta_j} = (-I.a)
{a_k beta_k(lam)} = (mu.a)
{b_j beta_j(lam)} = (mu.b)
{b_k beta_k} = (I.b)

482. Joy Christian Says:

Simon J.D. Phoenix,

The mistake both you and Scott are making is this: You are ignoring how the functions A(a, Lam) and B(b, Lam) are defined in my model. It is in what Scott calls “something complicated” where the real beef of the model is.

Please first read the Appendix 1 starting on page 20. This will give you the conceptual understanding of what is going on in the model. After that please go to the actual model, described on page 4 onwards. Thank you.

483. Simon J.D. Phoenix Says:

So let me get this straight. We have 2 functions whose ouput depends purely on some random variable L which can take on 2 values +1 or -1 (the measurement directions a and b are superfluous) – the outcome of the function is defined **purely** in the following terms

The output of function A is 1 if L = 1
The output of function A is -1 if L = -1

The output of function B is -1 if L = 1
The output of function B is 1 if L = -1

Now L represents some hidden parameter that completely predetermines the outcome of a given experiment – and it can only have ONE value per experimental run – so L either equals 1 for that run or L equals -1 for that run.

So we have A(L = 1)B(L = 1) = -1 by definition

and we have that A(L = -1)B(L = -1) = -1 by definition

The product AB is not a random variable. It never can be.

So the entire scheme really depends on the normalization that’s applied to define what is meant by correlation in equations (5)-(7)? And that normalization depends on the value of L.

But the fact that AB is a constant – and not a random variable shows that A and B, which are random variables, are perfectly correlated always. So the sinusoidal result is an artefact of whatever has been put in the denominator – the {…}{…} term in the paper.

I really don’t see why this new definition of correlation that is used has anything to do with the correlation functions that are usually used to derive the Bell or CHSH inequalities – which are correlations between actual experimental outcomes.

So really (always assuming the maths is correct :-)) the entirety of the argument rests on whether this new correlation function that has been defined is (a) meaningful as a correlation or more importantly (b) related to the standard correlation used in the usual derivations of the inequalities.

Can you show that your new correlation function and the standard one are indeed the same thing in the appropriate limit?

So, if I’ve understood things correctly, we have an embedding of the usual 3 dimensional space in some higher-dimensional space – and when we consider higher dimensions we need to consider a different definition of correlation? The Bell inequality being seen as some result of this embedding that disappears when we extend to higher dimensions?

So we have experimental results (the A and B) that are always perfectly correlated – and yet you’ve used a definition of correlation that does not always yield perfect correlation. Curious.

I thought the Bell inequality was a statement about correlations between experimental RESULTS??

484. Sandro Says:

Joy #482: would you care to describe the Möebious example in your arxiv paper a bit better? First, why should the correlation depend continuously on the angle, given that there is a precise twisting point in this geometry? It should be -1 before and 1 after. Also, if you assume that the opposite faces of the paper strip correspond to the same 2D local space (as otherwise there is no turning of left into right), it would be possible for Bob travel on the other side of the strip, meet Alice, and find out that they don’t agree on right and left. What is the physical meaning of that?

Thanks

485. Simon J.D. Phoenix Says:

Joy wrote : “It is in what Scott calls “something complicated” where the real beef of the model is.”

Forgive me for being dense Joy, but you have something that looks like

A = G = E

and you define E by saying it is +1 when L = +1 and -1 when L = -1.

Well I don’t actually CARE what form G takes – I have all I need because A = E. The details of G are completely irrelevant. If I calculate something using G I’d better be damned sure I get the same result when I calculate the same thing using E.

Problem is – when you calculate a correlation from your definition E – it’s always perfect.

Somehow, when you use G not only do we lose this perfect correlation but we also recover the dependence on the measurement directions – and E quite explicitly does not depend on the measurement directions.

486. Sandro Says:

Joy #482: last point, which is also what others are pointing out. If the outcomes of A and B do not depend on a and b, and you are very clear about that, how can the correlation, which is a function of the outcomes, depend on a and b?

487. Joy Christian Says:

David Brown,

I saw your post on the other blog. Since Scott would not allow me to post a response there, let me respond to your post here:

(1) It is impossible for Abner Shimony to be objective or open-minded about Bell’s theorem. The reasons for this are obvious to anyone who knows the role he played in the entire Bell saga.

(2) Abner Shimony knew nothing about Clifford (or geometric) algebra back in 2007, and I doubt very much if he knows anything about it now.

But most importantly,

(3) James Owen Weatherall is talking about his own model, not mine. His model has little or nothing to do with my model. Just like Scott, Jim has not understood my model at all. When will people recognize the difference between a genuine criticism and a straw-man criticism? http://www.youtube.com/watch?v=v5vzCmURh7o

488. Scott Says:

I’m eagerly awaiting Joy’s reply to the questions of Simon #485 and Sandro #486.

489. Joy Christian Says:

Scott,

It is past midnight here in Oxford. You will have to wait for my response to Simon and Sandro until tomorrow. I am eager to respond too, because FINALLY we are getting into the real substance of my model.

Goodnight everyone.

490. Fred D Says:

Simon,

I see that you did not look at my list of possible algebraic outcomes for Joy’s model. But no matter, Joy’s model is very flexible. Watch what happens even if we are to take the very silly notion that the product AB = -1 *always*. I will suppress the limit and summation notation and use a B’ for beta and L for lambda. For the left side of eq. (6) of the one page paper,

{A(a,L^i)B(b,L^i)} = -1

Make the replacement in eq. (6)

E(a,b)= {a_j B’_j}{-1}{-b_k B’_k}
= {a_j B’_j}{b_k B’_k}

And since,

B’_j = B'(L)/L and L^2 = 1

We obtain,

E(a,b) = {a_j B’_j(L^i}{b_k B’_k(L^i)}

Which is exactly the same as right side of eq. (6) QED.
You can find the above in Joy’s arXiv paper that is a response to Gill’s nonsense. I highly suspect that the above result is simply due to the fact that the correlations between two points of a parallelized 3-sphere = -a.b is probably a topological theorem of sorts that Tom Ray has pointed out on FQXi.

491. Sandro Says:

Joy #489: and just to make the question mathematically precise: you have A(a,lambda)=f(lambda) and B(b,lambda)=g(lambda). As lambda is a random variable, the above are equality statements about random variables. For any correlation function c then c(A(a,lambda),B(b,lambda))=c(f(lambda),g(lambda)). As the second term depends only on lambda, there is some function d for which c(f(lambda),g(lambda))=d(lambda), and hence c(A(a,lambda),B(b,lambda))=d(lambda). The only way for d(lambda) to depend on a and b is if lambda depends on a and b, in which case it cannot be a fair coin toss.

492. David Brown Says:

@Joy Christian #490: Note that Abner Shimony did not allege obvious, absurd errors as Gill and Aaronson did. I think that you have not yet realized the significance of the Rañada-Milgrom effect for your parallelized 7-sphere model. Here is my reasoning:
(1) According to the work of Milgrom, McGaugh, and Kroupa, there is overwhelming evidence in favor of Milgrom’s acceleration law for galactic rotation curves.
(2) An easy scaling argument shows that the Rañada-Milgrom effect is approximately equivalent to Milgrom’s acceleration law.
(3) M-theory is, in Steven Weinberg’s words, the only game in town so that some form of M-theory is needed to explain the Rañada-Milgrom effect.
(4) Your deterministic model is THE ONLY WAY to get a form of M-theory that does not suffer from runaway Markov branching.
What do (1) throught (4) imply? The Rañada-Milgrom effect is empirical evidence in favor of both M-theory and your parallelized 7-sphere model. Do you agree or disagree with the preceding line of reasoning? I strongly suggest that you study the Rañada-Milgrom effect — I believe that you will agree with me in terms of the AVAILABLE evidence. In other words, I claim that empirical evidence ALREADY supports your theory of local realism. To Scott Aaronson’s credit, I believe he is giving us blog space because he really believes in airing all sides of an argument. On the other hand, maybe he views us as circus animals.

493. Sandro Says:

Silly me. Of course there is another way for d(lambda) to depend on a and b, and that is for a and b to be constants. Any combination of a/b constant or parameters of lambda will work. Just to be sure I covered all options available.

494. Fred D Says:

Sorry; allow me to fix the typos above.

B’_j = B’_j(L)/L and L^2 = 1

We obtain,

E(a,b) = {a_j B’_j(L^i)}{b_k B’_k(L^i)}

495. Henning Dekant Says:

Joy Christian #466, for consistency’s sake you should stick with only one of the insults that you are hurling at Scott:

(a) He is too stupid to understand your work.
(b) He criminally misrepresents your work.

The latter implies intend i.e. you can only criminally misrepresent if what you say or write is actually not what you believe to be true. So if (b) was true we would have to accept that Scott actually sees merit in your work, but for whatever reasons chooses to lie about it.

At any rate it is quite surprising that Scott lets you still comment here.

Let me explain, but let’s first get our terminology straight: Just as there are not multiple Internets there is only one Scott Aaronson blog. Everything under the domain http://www.scottaaronson.com/blog is Scott’s blog.

This is not a public domain space on the web, it is owned by Scott and he has full control over what appears here. This is not a matter of theory or justice but a technical fact. He can moderate and filter any comment on his blog, as well as change and delete them just like any other content that’s in his WordPress db (as I use the same blog engine I am familiar with the mechanics).

Yet, he still lets you make your case in this comment thread. If been perusing blogs of all sorts for many years, my wife blogged long before I started mine, and I can assure you very few bloggers tolerate insulting comments on their own blog.

The other thread is about you, but your work is not the focus, and Scott decided that he doesn’t want you in on this discussion.

We are all here at Scott’s discretion. You can either accept that or leave.

@Thomas H. Ray #458

Nope. Take a points series to stand as a simulation of a continuous curve. Now, regard the simulation function as a collection of Dirac’s deltas continuously connected by some piecewise defined functions having their values equal to zero in the interconnecting intervals.

And, I notice, you addressed my minor question, not major. Tch.

– – – – –

@John Sidles #465

Wow! That’s an amazing sweep of topics! And, BTW I have appreciated your attempts to introduce some calm- and cool-ness in this thread.

Personally, the comments I most enjoyed have come from James Putnam. And, to be honest, also some of the digs that Scott and Joy have been publicly taking at other! Reason? Neither ever replies anything to what I say. LOL! (1 lakh dollars fighting 5 lakh dollars or vice versa, and ~8 years of joblessness. Hmmm… OK. Forget that part…)

OK.

– – – – –

@All

Nope, contrary to what so many (in fact a dominant majority) of you think, Dr. Joy Christian isn’t a crackpot, full stop. In fact, he certainly does have some very valid ideas.

I wanted to say so right on May 5th, but my ‘net connection went down just at that time (out of the ISP’s apprehension whether I would be able to pay my bills or not; the service was disconnected before the generation of bill at the end of month despite normal usage pattern; and it was restored only after I coughed up entire claimed bill money in advance). Then, I was busy with catching up with everything else on the ‘net, too.

John’s simulation helped in dissolving any lingering doubts about the nature of Joy’s mathematics. So, today, I say it with even greater confidence.

To repeat: Dr. Joy Christian isn’t a crackpot; on the other hand, he does have some very valid ideas.

At the same time, he doesn’t offer very good explanations—either in his papers or here in the discussion threads (and, he didn’t also offer me any, in our personal though brief email exchange). He does not offer satisfactorily enough by way of connecting his abstractions to the concretes. Not in as much details as one would like to see. In fact, he seems to go in a shell and to divert topics whenever a thing like that comes up in discussion threads. This *is* a flaw on his part, but, as far as I can see it is a flaw of communication, not of physics theory (or at least the valid elements of one)—let alone an evidence of his being a crackpot, even if people on this thread seem to be gravitating to the last conclusion a bit too fast.

Notice, establishing 1:1 correspondence of abstractions to concretes is, epistemologically speaking, a proper responsibility of the physicist who puts forward the idea himself, not of others. Joy must be firmly asked to pick up this part of his responsibility and deliver on it—but it must be done without getting into name-calling etc.

Since so many of us are so impressed with Feynman, recall what he said. You don’t really understand something, he would tell professional theoretical physicists, unless you can explain it to high-school students in a way that they can understand.

When what you say can’t be understood by a PhD in mechanical engineering having a couple of publications on QM, think for yourself the distance by which you fall short of the goal Feynman urged you to keep. Even if not to high-school students, you should at least be plain and clear to physics/engineering UGs. Let alone to an engineering PhD. If not in formal paper, then at least via your slides, Web site contents, and, blog entries and replies. That’s what a rational epistemology would demand of you.

Here, you simply are not being so. None of you. Not just Joy but also not Scott (w.r.t. Joy’s papers). And, none else either—except for John coming in with his simulation. (Though somewhat unrelated, the one honorable mention I must additionally make is of James Putnam. The clarity he shows in spelling out the nature of the relationship between physics and mathematics, in a thread like this, is simply astounding.)

Since I do say that Joy Christian does have some valid ideas, it can and does raise another issue, viz., that of priority and apportionment of credit etc. These are relatively minor considerations to me, and they can be dealt with later on.

Ajit
[E&OE]

497. Simon J.D. Phoenix Says:

Fred,

I’m sorry, I feel like I’m being really thick – but don’t we actually have some function A(a,L) in equation (1) – and then some complicated definition and then another ‘=’ and then we have a curly bracket thing { and then the words
+1 if L = +1
-1 if L = -1

So, once again forgive my mathematical naivete, but I read this as “if the value of the random variable is 1, then the value of the function is 1 and if the value of the random variable is -1 then the value of the function is -1”.

We have the same definition for the function B but with a ‘bit’ flip in the value.

I’m going crazy here 🙂 but I fail to see how something so well-defined and clear as this can lead to the range of products you describe – since just from this basic definition AB is always equal to -1. If AB does not always equal 1, but is itself a random variable, then the RHS of equations (1) and (2) make no sense – because, clearly we (sometimes) have that A does NOT equal 1 when L=1 and B does NOT equal -1 when L=1.

But even that is not the real problem – the real issue is that the RHS, the last equals, has values that do not depend on a and b. The final outputs of A and B do not depend in any way on the orientations of the analyzers.

Yet by making the replacement you suggest – this L^i term in the LHS – we end up with an a and b dependence for the function AB – but the values of A and B individually do not depend on a and b.

I mean suppose one were to reword the paper a bit and start with

A=E
B=E’

where E and E’ are the statements about the values of A and B given the actual value of L in a given run. Then anyone would calculate the product AB = -1. There would be no controversy about it. It’s clear and well-defined – a mapping of the domains of the functions A and B to the range.

If we used a coin toss as our random variable then we could write down the only two possible outcomes:
{A(a,1)=1, B(b,1)=-1} and {A(a,-1)=-1 and B(b,-1)=1}

Can we agree that this is what we would have if we just started with A=E and B=E’ with the definitions, as written, in equations (1) and (2) of Joy’s paper?

If we just used these definitions for A and B then we’d interpret this as having experimental results that could never violate the Bell inequality.

Aha! we now say, let’s construct some functions G and G’ so that
A=G=E
B=G’=E’

All of a sudden our simple interpretation of our first equations A=E and B=E’, goes out of the window. I can’t for the life of me make any mathematical sense of this – and I think resorting to some replacement of L with L^i and some high-falutin’ notions of parallized 3 spheres just obfuscates things. Why does the mathematical equals sign mean one thing when we first write it down and then something else when we put the intermediate step G and G’ in there?

When we work things out using G and G’ – we obtain some dependence on a and b. None of this makes any sense to me I’m sorry.

498. Richard Gill Says:

Simon and Sandro: good work!

The typical Joy reaction is illuminating: “The mistake both you and Scott are making is this: You are ignoring how the functions A(a, Lam) and B(b, Lam) are defined in my model. It is in what Scott calls “something complicated” where the real beef of the model is”.

In fact, the mistake you are making as far as Joy is concerned is that you *are* actually reading how A and B are defined. How they are actually defined does make them identically equal to lambda and -lambda, independently of a and b. Joy wants you to be impressed by the poetic ideas; the maths formulas are just decoration. He counts on most people *not* knowing what Geometric Algebra is all about. But an hour on Wikipedia will teach you all you need to know in order to understand every single bit of maths he does.

The rest is just sales talk. Like the pseudo science in a third rate sci-fi movie.

499. Joy Christian Says:

David Brown,

You said: “I think that you have not yet realized the significance of the Rañada-Milgrom effect for your parallelized 7-sphere model.”

You are right, but I am working on it. I find the idea of a possible connection intriguing, to say the least. But you must realize that I am a professional physicist, and as such extremely skeptical about any new and farfetched idea. The irony in what I am saying is not lost on me here, but the fact is that I will not jump to accepting your reasoning without a proper investigation. And that will take time.

I am willing to accept steps (1), (2), and (3) of your reasoning as reasonable hypotheses. It is your step (4) that seems to be a pure conjecture at the moment: “Your deterministic model is THE ONLY WAY to get a form of M-theory that does not suffer from runaway Markov branching.” This is hard to believe and difficult to prove. But you have got me interested in the problem.

500. Simon J.D. Phoenix Says:

OK let’s forget Bell’s inequality and Joy’s paper for the moment.

Suppose I set the following examination question for my students :

Consider the functions A(a,L) and B(b,L) in which a and b are 3 dimensional unit vectors and L is a random variable that can take the values +1 or -1.

We define the functions A and B to be the following mappings

A=+1 when the value of L is +1
A=-1 when the value of L is -1

B=-1 when the value of L is +1
B=+1 when the value of L is -1

Consider the product AB. What is the probability that AB=1?

Unless I’ve missed something here (always quite likely) then the answer to this question is zero – the probability that the product AB=1 is zero.

If I’m wrong here then maybe someone could explain why.

OK I now I have the second part of the question and I say that I have an alternative definition for A and B – and then proceed to give some complicated expression – I now ask the students to calculate the same probability for the value AB=1 and they get a different answer.

I now ask the question whether the alternative definition of A and B is consistent with my previous definition. I would hope they’d give me the answer that the two definitions are not equivalent.

I’m really struggling here guys – someone help me out. Have I been using maths and the meaning of equality wrongly for the past few decades?

501. Joy Christian Says:

Here is my reply to the questions of Simon #485 and Sandro #486:

What is actually observed in the ideal EPR-Bohm experiment is the following:

A(a, L) = +1 or -1 with exactly 50/50 chance for any a.

B(b, L) = +1 or -1 with exactly 50/50 chance for any b.

(The above two results are equivalent to E(a) = 0 = E(b).)

AB(a, b, L) = -1 always only when b = a.

E(a,b) = -a.b.

These are the *only* conditions that are demanded by quantum mechanics, EPR, Bell, and the actual observations. Bell thought that local and realistic functions of the form A(a, L) and B(b, L) satisfying the above conditions are mathematically impossible to exist. He called this his theorem. Bell was wrong. Such functions do exist, provided their co-domain is taken to be a parallelized 3-sphere:

+/-1 = A(a, L) : R^3 x H maps to S^3

and

+/-1 = B(b, L) : R^3 x H maps to S^3,

with the initial state L belonging to the space of hidden variables H. On the other hand, if the co-domain of A(a, L) and B(b, L) is taken to be anything other than a parallelized 3-sphere, the completeness criterion of EPR cannot be satisfied, and then Bell’s theorem is again a non-starter for that reason.

Using such functions my one-page paper provides an exact, classical, local, realistic, and deterministic model for the observed EPR-Bohm correlations. It thus provides the most faithful representation of the actual empirical facts, conceptually more satisfactory than what is provided by quantum mechanics.

Here is how it works:

Let w(a), w(b), w(a, L), and w(b, L) be four unit bivectors belonging to the even subalgebra of the algebra of the orthogonal directions in the physical space, where L = +1 or -1 is a fair coin and

w(a, L) = L w(a)

and

w(b, L) = L w(b).

Note that w(a) and w(b) do not depend on the random variable L. They are thus “fixed” for the given directions a and b, and thus represent the detectors of Alice and Bob.

On the other hand the random bivectors w(a, L) and w(b, L) represent the physical spins, originating with the initial state L.

Next, define the functions A(a, L) and B(b, L) as products of these bivectors as follows:

A(a, L) = -w(a) w(a, L) = +/-1 if L = +/-1

and

B(b, L) = +w(b) w(b, L) = -/+1 if L = +/-1

Note that unit bivectors square to -1. Note also what is happening physically: The spins such as w(a, L) interact with the detectors w(a) to produce the measurement result A(a, L) = +/-1.

The question now is what is the correlation between the observed numbers A(a, L) and B(b, L). But these numbers are products of two numbers such as w(a) and w(a, L), where w(a) is a fixed number and w(a, L) is a random number. Remember that in geometric algebra bivectors are numbers no different from scalars apart from their grade.

Moreover, it is clear that the scalars A(a, L) and B(b, L) are generated with *different* bivectorial scales of dispersion.

Therefore the correct correlation between the raw scores A(a, L) and B(b, L) can only be determined by the covariance of the corresponding standard scores (this is basic statistics). But standard scores w(a, L) and w(b, L) are easy to read off (or calculate) from the raw scores A(a, L) and B(b, L). The covariance of the standard scores w(a, L) and w(b, L), which are of course bivectors, is then easily computed using the geometric product of w(a, L) and w(b, L). This is what you will find done in most of my papers, including my one page paper.

It is instructive to understand what is going on in the model geometrically. Note that all the elements we defined above, scalars as well as bivectors, specify nothing but different points of a unit parallelized 3-sphere. Thus EPR correlations are understood in my model as correlations among the points of a parallelized 3-sphere. They are thus understood as purely topological effects, not contextual effects. In other words, in my model the observed results A(a, L) and B(b, L) do not change with the measurement contexts a and b at all. And that is exactly what is observed in the actual physical experiments corresponding to the singlet state.

I fail to see why such a simple and straightforward result is so difficult for some people to understand. But given that it is difficult for many people to understand, I urge you to read the following three papers carefully.

http://arxiv.org/abs/1106.0748

http://arxiv.org/abs/1203.2529

http://arxiv.org/abs/1201.0775

502. Joy Christian Says:

It should be noted that ALL of Richard Gill’s arguments against my model have been systematically and thoroughly debunked many times over, not only by me but also by several other people on the FQXi blogs. See, for example, the following three documents:

http://arxiv.org/abs/1203.2529

http://fqxi.org/data/forum-attachments/JoyChristian_FAQ.pdf

http://fqxi.org/data/forum-attachments/Richard_said.pdf

It is evident from these documents that after having spent so many months of his failed campaign against my one-page paper Richard Gill has yet to understand the first thing about my model.

503. Joy Christian Says:

Henning Dekant Says:

“If I read Anthony A. comment #17 correctly then I think it seems rather unlikely that Joy will ever enjoy the benefits of another FQXi mini-grant once this one runs out.

Wow!

I thought lynch mobbing was a thing of the past.

Henning Dekant,

if you think that starving me from mini-grants or other academic privileges will prevent me from speaking out against dogma, ignorance, and closed-mindedness in some parts of the intellectual community, then you are in for a big surprise.

504. David Brown Says:

@Joy Christian #505: What are “local and realistic” functions? If quantum SU(1) states and Seiberg-Witten M-theory are empirically valid, then “local and realistic” means one thing. If quantum SU(8) states and deterministic M-theory with the parallelized 7-sphere model are empirically valid, then “local and realistic” means quite another thing. Do you understand how you are contradicting Seiberg and Witten? Do you understand what your theory means in terms of M-theory and the Rañada-Milgrom effect? Do you understand how the Rañada-Milgrom effect has ALREADY PROVED your theory of local realism?

505. Simon J.D. Phoenix Says:

Thank you for the reply Joy – your time and effort is much appreciated.

I still have some very fundamental issues with the basics, probably more a reflection of my own ineptitude.

OK – if I’ve understood your reply correctly you are confirming that A(a,L) = L and B(b,L) = -L.

Now consider what the A and B are physically. These are the actual recorded results for the spin-up or spin-down measurement (or whatever other phsyical system we wish to pick). The point of the hidden variable is to suggest that these results have some pre-determined value before the measurement is made – thus there is an element of reality.

The Bell inequality relates the actual measurement results by forming expectations – this is what is called ‘correlation’. This is the equivalent quantity to the quantum mechanical expectation value. We may wish to choose a more appropriate measure of statistical correlation, and there are many, but the Bell inequality only uses this one. We’re not really allowed to choose anything other than the one that is the average of the product of the detector results.

Sure we can pick any other, but then it’s not the equivalent quantity to the QM expectation – and we wouldn’t expect it to be so. We could use any old measure of correlation we like and I daresay we could select one that would give us the result we’re looking for – but it ain’t comparing the same quantities – Bell’s inequality says nothing about some other correlation functions – only the one that is the equivalent of the QM expectation value.

The one that is the correct quantity to use is the average value of the product AB – and this is always equal to -1 in your model whatever the directions we choose for our measurement, as you have appeared to have confirmed above. All this talk of raw scores seems to me to be a red herring. The A and B **are** the measurement results – and the Bell inequality is a relation between straightforward averages of products of these results – not some processed version of these into raw and standard scores – however appealing that might be to a statistician.

The problem still boils down to the fact that when the hidden variable L=1 then A=1 and B=-1, and when L=-1 then A=-1 and B=1. These are the actual experimental readings that your model predicts. There are only two possible outcomes for each experimental run. The terms that appear in the Bell inequality are calculated by taking averages of products of these experimental results – not some other average that is only based upon these direct results, or the results divided by some measure of covariance – but the actual results themselves.

Thanks again for your time and efforts, but the more I look at this the more I am satisfied that Bell was absolutely correct.

506. Joy Christian Says:

David Brown,

“What are “local and realistic” functions?”

Bell had a very simple and clear-cut way of defining local-realistic model. He would call a model local-realistic if the product AB(a, b, L) of the simultaneous measurement results A(a, L) = +/-1 and B(b, L) = +/-1 of Alice and Bob can be factorized as

AB(a, b, L) = A(a, L) B(b, L).

In other words, if the result A(a, L) of Alice would be independent of both the measurement context b and the measurement result B of Bob, and likewise if the result B(b, L) of Bob would be independent of both the measurement context a and the measurement result A of Alice.

If the functions A(a, L) and B(b, L) do not satisfy such a factorizability condition, then they are not local-realistic functions according to Bell. I agree with Bell on this point.

“Do you understand how you are contradicting Seiberg and Witten?”

Yes. That is not surprising.

“Do you understand what your theory means in terms of M-theory and the Rañada-Milgrom effect?”

No, not yet.

507. Aram Says:

@JC #501:
I shouldn’t wade into this, but when you write

“Bell thought that local and realistic functions of the form A(a, L) and B(b, L) satisfying the above conditions are mathematically impossible to exist. He called this his theorem. Bell was wrong. Such functions do exist, provided their co-domain is taken to be a parallelized 3-sphere:”

then you don’t need any math to know that this isn’t a refutation of Bell’s theorem.

Bell’s theorem says that {+1, -1}-valued functions A,B satisfying (…) do not exist. You say that {parallelized 3-sphere}-valued functions A,B do exist. You may be right, but even if you are, it doesn’t make Bell wrong.

508. Henning Dekant Says:

Joy #503, you misread the intention of my comment. The purpose is to highlight to Scott that I don’t think there is a point to escalate this further, it is formulated as a question, but the answer from my point of view is that there is no need for further action.

509. Joy Christian Says:

Simon J.D. Phoenix,

http://arxiv.org/abs/1106.0748

http://arxiv.org/abs/1203.2529

http://arxiv.org/abs/1201.0775

Thank you.

510. Thomas H. Ray Says:

Ajit #457

I think it boils down to the question of whether the simulation of a continuous function is a continuous function.

I think not.

Ajit # 496

“Nope. Take a points series to stand as a simulation of a continuous curve. Now, regard the simulation function as a collection of Dirac’s deltas continuously connected by some piecewise defined functions having their values equal to zero in the interconnecting intervals.

And, I notice, you addressed my minor question, not major. Tch.”

Ajit, your minor question IS the major question. The only better way I know to show where your reasoning is lacking, without a lot of calculation, is the case I made previously for the point at infinity that differentiates S^3 from R^3.

To a measurement function continuous from the initial condition, let us apply the theorem that informs us that any point may be simultaneously mapped to every point of another set, provided that the point is far enough away from the set.

The point at infinity on S^3, which is compact, is the only point not in R^3 that meets this requirement. So even though one may simulate a continuous function without the point at infinity, using arbitrary boundary conditions — a real measure in a bounded length of time that falls to either “side” of infinity is not arbitrary; in an oriented space, the measure is continuous from the initial condition, not continuous, as a simulation, from arbitrary boundary conditions. That’s why I asked the question: is a real measurement function continuous from the initial condition identical to the simulation of a continuous function? If a simulation were sufficient, how would one know that there is a point at infinity that maps completely to every point? — the measurement space, as in all quantum mechanical models, is compelled to be incomplete.

There is absolutely no reason to assume, however, that nature’s measure space is incomplete, i.e., probabilistic.

511. Joy Christian Says:

Henning Dekant,

512. David Brown Says:

@Joy Christian #510: If you accept what I have alleged about the Rañada-Milgrom effect, i.e., replace the -1/2 in the standard form of Einstein’s field equations by -1/2 + dark-matter-compensation-constant, where this constant is approximately sqrt((60±10)/4) * 10^-5 then what? If the alleged “constant” is not quite a constant then there must be dark matter particles such as neutralinos, axions, etc. If the alleged “constant” really is a constant then we must give up on the Seiberg-Witten interpretation of M-theory. In other words, we need a deterministic model of M-theory, and your model seems to be the only hope. Do you agree or disagree with the preceding?

513. Joy Christian Says:

Aram,

“…but even if you are, it doesn’t make Bell wrong.”

It makes Bell irrelevant for the future theory of physics, and it makes Bell inapplicable to the argument of EPR.

What is more, his theorem is stated by one of his staunch supporters, namely Abner Shimony, as follows:

“…no physical theory which is realistic as well as local
in a specified sense can reproduce all of the statistical predictions of quantum mechanics.“

As stated, Bell’s theorem is no longer valid. I have no problem with Bell being right in some technical sense that is irrelevant to physics. I am a physicist, not an information or communication engineer.

514. David Brown Says:

@Joy Christian #510: “Bell had a simple clear-cut way of defining local-realistic model.” You say that Bell made an obvious error, i.e., he used quantum SU(1) states when he should have used what YOU call “general quantum states” or quantum SU(8) states. Your change to general quantum states, more-or-less, amounts to changing quantum field theory (QFT) based on commutative geometry to QFT based on noncommutative geometry. A GREAT IDEA … but what precisely does it mean it terms of physical predictions? What does the parallelized 7-sphere model mean in terms of M-theory? Does the noncommutative geometry mean that 11-dimensional knot theory can be realized in terms of tests on D-wave superconductivity? Perhaps so … perhaps not. It is unclear what your theory really means.

515. Lev Goldfarb Says:

Scott,

I just want to mention that the fact that all this ‘controversy’ (together with the unbelievable insults) has been evolving for a long time at FQXi is not surprising to me *at all*.

I have participated at two of their ‘essay competitions’ and have been incredibly appalled by the extremely low quality of their organization. And this is in addition to the almost non-existent supervision of their blogs.

Only now, I noticed, did the administration began to clean much of the insulting stuff.

516. David Brown Says:

@Joy Christian #317: “… it makes Bell inapplicable to the arguments of EPR.” You should say, “Bell’s theorem is true within the paradigm of the Copenhagen Interpretation” and “I have disproved Bell’s theorem within the paradigm of deterministic M-theory, i.e., M-theory with the parallelized 7-sphere model.” Do you agree or disagree with the preceding statement?

517. James Putnam Says:

Aram & Simon J.D. Phoenix & Thomas Ray:

Aram Says:
Comment #507 May 13th, 2012 at 9:26 am
@JC #501:

Aram quoting Joy: “…“Bell thought that local and realistic functions of the form A(a, L) and B(b, L) satisfying the above conditions are mathematically impossible to exist. He called this his theorem. Bell was wrong. Such functions do exist, provided their co-domain is taken to be a parallelized 3-sphere:”

… then you don’t need any math to know that this isn’t a refutation of Bell’s theorem.

Bell’s theorem says that {+1, -1}-valued functions A,B satisfying (…) do not exist. You say that {parallelized 3-sphere}-valued functions A,B do exist. You may be right, but even if you are, it doesn’t make Bell wrong.”

Simon J.D. Phoenix Says:
Comment #505 May 13th, 2012 at 8:42 am

“…The Bell inequality relates the actual measurement results by forming expectations – this is what is called ‘correlation’. This is the equivalent quantity to the quantum mechanical expectation value . We may wish to choose a more appropriate measure of statistical correlation, and there are many, but the Bell inequality only uses this one. We’re not really allowed to choose anything other than the one that is the average of the product of the detector results.

Sure we can pick any other, but then it’s not the equivalent quantity to the QM expectation – and we wouldn’t expect it to be so. We could use any old measure of correlation we like and I daresay we could select one that would give us the result we’re looking for – but it ain’t comparing the same quantities – Bell’s inequality says nothing about some other correlation functions – only the one that is the equivalent of the QM expectation value. …

…Thanks again for your time and efforts, but the more I look at this the more I am satisfied that Bell was absolutely correct.”

Simon J.D. Phoenix: I understood your message as making the point that Bell’s theorem has not been disproved by Joy. I hope I didn’t remove too much of your message when I quoted you. It is the point of your message that is of interest to me and I don’t wish to misrepresent it. You may have been saying more than this.

Aram & Simon J.D. Phoenix: Assuming that the points of both of your messages is that Bell’s theorem has not been disproved, Thomas Ray has also had this disagreement with Joy. However, I believe he is satisfied that Joy’s math is correct and that Joy’s physics is correct.

The reason I mention this is that the matter of the use of the word disproof may not be formally correct, but, the opinions you might share that I am most interested in would have to do with: Has Joy successfully introduced new physics theory?

Thank you both for sharing your thoughts.

James

518. Simon J.D. Phoenix Says:

Sorry, the formatting of my previous message was a bit wonky.

Thanks for the response Joy.

Thanks for trying Joy, but I have to say I’m still not grokking anything.

No one has yet explained to me how you can have relations of the form

A = G = E
B = G’ = E’

where A and B are models of actual experimental results that give different answers when you compare the two ways of calculating things. If I use A=E and B=E’, which is quite legitimate, then I would predict a perfect anticorrelation for the actual data I observe. This is just straight from (1) and (2) of your counter-example – the RHS are clear, unambiguous and well-defined – there are only two possible experimental outcomes possible corresponding to the two different values of the hidden variable. That’s what the maths says – that’s what you have written.

However, if I use A=G and B=G’ to calculate the predictions for the observed data I get a different result. That should be enough on its own to raise alarm bells.

However, using A=E and A=E’, again it is unambiguous, clear and well-defined, that there is no dependence whatsoever on the orientation of the analyzers. This isn’t something I’ve derived – it’s there written in black and white on the RHS of your equations. Unless you’re telling me that statements of the form “when L=1 then A=1” don’t mean what they always used to in maths.

The correlation function you’ve used, whilst no doubt a perfectly good measure of correlation, is meaningless in the context of Bell’s theorem in which the term correlation has a very clear and well-defined meaning as the average of the product of experimental results – not raw scores or standard scores – but the actual real results we measure. You are not free to define some **other** measure of correlation and then use it to claim a ‘violation’ of the Bell inequality. Your violation of the inequality is an artefact of this correlation function you’ve introduced.

Taking a very naive view, non-locality is already built into QM from the outset. Take a particle with a well-defined velocity and measure its position – then instantaneously a wavefunction spread throughout space collapses to a well-defined location in space (according to the standard interpretation). You may disagree with the way Bell has illuminated this feature, but even if he was wrong (and so far you haven’t convinced me that he was, quite the reverse in fact) then you haven’t removed non-locality from QM 🙂

I’ve seen enough – good luck Joy – I wish you all the best.

519. David Brown Says:

@James Putnam #521: “Has Joy successfully introduced new physics?” I say the answer is yes. Why? I claim that the empirical validity of the Rañada-Milgrom effect strongly supports Christian’s theory of local realism.
(1) According to Steven Weinberg, “String theory is the only game in town.” Attempts to introduce new physics probably must use M-theory in some form.
(2) Dark matter exists either in the form of particles (approximate Rañada-Milgrom effect) or Milgrom’s MOdified Newtonian Dynamics (MOND) (precise Rañada-Milgrom effect).
(3) The precise Rañada-Milgrom effect looks promising based upon the empirical evidence.
(4) Dark matter particles are necessary for the empirical validity of Seiberg-Witten M-theory and perhaps any nondeterministic form of M-theory.
(5) The precise Rañada-Milgrom effect implies the failure of nondeterministic (i.e. quantum mechanical) M-theory.
(6) The failure of nondeterministic M-theory implies the success of deterministic M-theory, which in turn implies the success of deterministic M-theory with Christian’s parallelized 7-sphere model, because the latter is the simplest way to get a deterministic form of M-theory.
Is there any feedback on this?
http://en.wikipedia.org/wiki/M-theory

520. Simon J.D. Phoenix Says:

James, let me preface my remarks by saying that physics is not a democracy and I don’t have quite as much right to an opinion as a Bennett or a Deutsch or a Zeilinger (or even an Aaronson :-)) I am frequently wrong and usually slow on the uptake – so it’s entirely possible that I’ve completely missed the point of Joy’s analysis. I don’t think so – but it’s possible.

There are for me just too many basic and fundamental questions and problems with Joy’s work. I’m not yet getting the “aha” moment when the physics and maths all combines to make a coherent whole.

In my personal view neither the physics or maths makes much sense in Joy’s work – but that, as I have said, may be more my failing than his.

I’m actually interested in this because of the single-particle thing I mentioned. We can use the fact that there is a Bell inequality violation between state preparation and measurement for a single particle to provide us with another protocol for quantum key dsitribution. The eavesdropper, in effect, performs the role of a hidden variable and his intervention causes the inequality to be satisfied again – and this can be detected by the end users of the channel thus the presence of the eavesdropper can be inferred. If a hidden variable model exists, and provides a correct description of reality, then there might be a way for the eavesdropper to avoid detection.

The physics of what this is all about is pretty fundamental and interesting. QM seems to be a theory in which there exist no elements of reality until measurement. This is quite an uncomfortable fact, but it is the consequence of the formalism and the usual interpretation of it. So in order to try to make ourselves more comfortable we postulate that actually these elements of reality do exist, but we just can’t access them.

So in the Bell set up we might have two correlated particles that fly off in opposite directions. We imagine that, in fact, what we eventually measure is actually governed by some hidden parameters. In Joy’s case the hidden parameter is just a single random variable that can take the values +1 or -1 uniformly at random. So the hidden variable is just 1 classical bit of information.

Now the really important thing about Bell’s work is that we can freely, and randomly, change the orientation of our detectors – even deciding to change our mind about what we’re going to measure at the last minute. The hidden variable model has to cope with that and still provide the correct experimental prediction. Now it turns out you can have these elements of reality, these hidden variables, but in order for them to cope with this last minute possibility of changing your mind about what you measure, they have to be non-local.

Joy claims to have found a counter-example and claims to have explicitly constructed a local hidden variable model that will reproduce the experimental results. I think it’s wrong, for all the reasons that have been discussed.

In Bell’s proof he assumed the existence of these hidden variables and modelled the experimental results with two functions A and B. These functions depend on the detector directions and the hidden parameters. The A and the B give the predictions of the hidden variable model for the actual experimental results. Bell then showed that if we take averages of the products AB over many results and choosing 3 different orientations then a certain combination of them should satisfy an inequality.

The important thing to note is that the average is taken over experimental **results** – that’s all we need to figure out whether the inequality has been violated or not. We just make measurements, form the required averages, and plug the values in to the form of the inequality and see if it holds.

The averages have been called ‘correlations’ – but ultimately there is a well defined procedure for constructing these averages. Now we look at how we’d calculate the very same quantities using a full QM description and we find that, for certain choices of detector orientation, the inequality doesn’t hold.

But if we use the simple form of Joy’s functions A and B – and remember that these are the predicted experimental results – then Joy’s model predicts that we’re either going to get A=1 and B=-1, or A=-1 and B=1 for our measurement results. These are the only two possibilities allowed by his model. The simple form doesn’t predict the correct experimental results even before we try to do our statistical averaging.

But if we try to calculate these predicted experimental results using the more complex form in Joy’s model then all proverbial hell breaks loose and we seem to be able to perform mathematical magic. The simple and complex descriptions are not consistent with one another.

It all boils down to whether the interpretation of his simple form is correct, but there really is little room for doubt. If you write A(a,L)=1 if L=1 and A(a,L)=-1 when L=-1 then how many different ways can we interpret this? I think Joy would say that this interpretation is not correct, but unless the meaning of mathematical terms and expressions such as equals signs has changed whilst I haven’t been looking then there really isn’t any ambiguity here. We have a random variable that is supposed to be a factor in determining our experimental results – this hidden variable – but in Joy’s description it’s the **only** factor. The value of L completely specifies the value of A and B. In fact the predicted experimental results ARE the hidden variable – in effect we’re actually making a measurement of the hidden variable in Joy’s model.

Anyway I’m sure Joy will provide you with an alternative view, but the above is only one of the issues I have with the model – I’ve outlined some of the others. There are just too many for me at the moment to have any confidence in the model – it’s just not hitting the right buttons. When you read Bell’s original papers you just think “wow” – when I read Joy’s stuff all I’m getting at the moment is “WTF?”

(sorry Joy)

521. James Putnam Says:

David Brown #519,

Thank you for expressing your opinion. As far as I am concerned, the important question is: Did Joy successfully introduce new physics theory? Along with this for affirmative answers is: What did it accomplish? You have answered both questions.

I think that this matter can be resolved in a timely manner if it is evaluated by theoretical physicists who carefully consider Joy’s explanations. I am not implying that I know what the result will be. I am emphasizing only that I think theoretical physicists should not be distracted by matters that are not the theory. New ideas are still needed and will continue to be forthcoming. Wouldn’t they each want their own new ideas evaluated objectively by their peers?

I suppose that by saying all this that I am inviting the criticism that Joy’s work was not submitted through peer review channels. There is strength in that argument. My interest though is focused on: Is the theory a positive contribution to scientific learning?

James

522. Fred D Says:

Simon said, “…then Joy’s model predicts that we’re either going to get A=1 and B=-1, or A=-1 and B=1 for our measurement results. These are the only two possibilities allowed by his model.”

Sorry, but that is NOT what Joy’s model predicts. People only see what they want to see.

523. Henning Dekant Says:

Joy, #511

No harm done, but I wished, for your own sake, that you’d tone down your language.

This kind of online media is notorious for easily descending into the gutter as you don’t get all the additional non-verbal or intonation cues that’ll indicate how a statement is to be understood.

The fact that you cannot edit a comment after you hit the submit button emphasizes that careful self-editorial control is highly recommended. You cannot take back anything once it’s posted.

524. Joy Christian Says:

“I like Joy personally…

“I think he’s wrong and confused and that Scott, Richard and others are doing a service in pointing out Joy’s errors and confusions…”

I too like Adrian. We have known each other for many years. But I strongly object to his comments. There is no confusion in my work on Bell’s theorem. The only thing wrong with it is the fact that what I am saying is very inconvenient for many people. Scott Aaronson, Richard Gill, and others have done great disservice to physics and to intellectual inquiry in general. Richard Gill, to date, has not understood the first thing about my argument, and Scott Aaronson had not read a single line of any of my work on Bell’s theorem until the 10 of May 2012.

There are no confusions or errors in my work. To say that there are without any supporting argument is very disappointing.

As for my recent vitriol towards my critics, not many people know what kind of harassment Richard Gill, in particular, has put me through during the last three months. What appears on the computer screen is not always the full picture of the reality. I am also disappointed by Adrian’s implicit endorsement of Scott’s juvenile and unprofessional behavior through his comments.

525. Henning Dekant Says:

Joy, it is quite apparent that you believe your “Bell disprove” papers to be beyond reproach, although many people who are generally considered reasonably smart find them erroneous.

Obviously, I cannot really speak for Scott, but to me it seems he very much extended an olive branch when he wrote very early in the thread:

The obvious question is: if such an experiment were done and Bell/CHSH were not violated, would you admit that you were wrong?

(For my part, if Bell/CHSH were violated by such an experiment, then I wouldn’t say Bell’s Theorem had been disproved—that’s just not the way I use language—but I would readily admit that my understanding of the laws of physics had been wrong in a super dramatic way.)

IMHO Scott would have just gone back to ignoring your work if you’d had agreed to let an experiment settle it and left it at that. He’s apparently not that into your work, believes it to be incorrect and considers looking at your papers a waste of time.

You can’t force somebody to pay attention, it always backfires.

526. John Sidles Says:

It seems (to me) that there is a steadily increasing prevalence of posts on this topic that combine clarity, creativity, and politeness. Good!

Upon surveying the preceding 50+ posts it seemed to me that posts like those of James Putnam, Simon J.D. Phoenix, Henning Dekant, Aram, Ajit R. Jadhav, Sandro, and Gil Kalai are particularly deserving of appreciation and thanks. More please!   🙂

527. David Brown Says:

@Joy Christian #528: “There is no confusion in my work on Bell’s theorem.” The vast majority of experts on quantum information processing use the term “proof of Bell’s theorem” to mean “proof of Bell’s theorem within the paradigm of the Copenhagen Interpretation of quantum theory.” J. Christian uses the term “proof of Bell’s theorem” to mean “proof of Bell’s theorem using the definitions used by Bell in Bell’s first 2 papers” as interpreted by J. Christian. The problem is not confusion WITHIN the work of J. Christian. There are 2 problems: (1) refusal to use the definitions of “local” and “quantum correlation” as these are NOW used by the majority and (2) insistence that “general quantum state” (or quantum SU(8) state) is nature’s way instead of Bell’s quantum state (or quantum SU(1) state) — this might be true (I personally now believe it) BUT IT REQUIRES EMPIRICAL PROOF IF IT IS TRUE.

528. James Putnam Says:

Simon J.D. Phoenix,

Thank you for that comprehensive reply. I just finished Mother’s Day and will be reading it now. I noticed Fred’s message to you:

“Fred D Says:
Comment #522 May 13th, 2012 at 3:53 pm
Simon said, “…then Joy’s model predicts that we’re either going to get A=1 and B=-1, or A=-1 and B=1 for our measurement results. These are the only two possibilities allowed by his model.”

Sorry, but that is NOT what Joy’s model predicts. People only see what they want to see.”

“… Here are all the possible algebraic outcomes of Joy’s statistical model.

Even though Joy’s model is statistical, it can have two different sets of possible algebraic outcomes. With mu = L*I with I being an oriented volume element and L =+/- 1 fair coin toss, the first part of the set is for all a and b except when b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (I.b)(mu.b) = – 1 if L = +1 and +1 if L = -1

And for b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

Then we have the following possible algebraic outcomes due to the parallelized 3-sphere topology when b is not equal to a or -a, …” Fred continues on giving “…all the possible algebraic outcomes of Joy’s statistical model.”

James

529. Joy Christian Says:

Henning Dekant,

http://www.scottaaronson.com/blog/?p=993#comment-43488

People are of course free to ignore my work. But then they have no right to have an opinion about it as Scott did for five years. Neither do they have the right to mock it publicly as Scott did before reading a single line of my argument.

530. James Putnam Says:

Simon J.D. Phoenix,

Sorry, I remember now that Fred already communicated directly with you about his message.

James

531. John Sidles Says:

Ajit R. Jadhav’s well-written comment #496 reminds us that serious attempt to reformulate quantum mechanics … or even to alter it slightly … or even to understand it at all! … must encompass “an amazing sweep of topics.”

My BibTeX database contains literally hundreds of quotations that can be construed as bearing upon this observation. One large class of quotations — generally to be found in introductory texts and/or course notes — confidently affirms that:

“Non-physicists often have the mistaken idea that quantum mechanics is hard. Unfortunately, many physicists have done nothing to correct that idea. But in newer textbooks, courses, and survey articles, the truth is starting to come out: if you wish to understand the central ‘paradoxes’ of quantum mechanics, together with almost the entire body of research on quantum information and computing, then you do not need to know anything about wave-particle duality, ultraviolet catastrophes, Planck’s constant, atomic spectra, boson-fermion statistics, or even Schrödinger’s equation.” (from arXiv:quant-ph/0412143v2).

But if that statement were simplistically true, then the discussions here on Shtetl Optimized would hardly be so confused and even acrimonious.

Yet on the other hand, countervailing quotations to the effect that “quantum mechanics really is hard” strike us as being comparably lacking in useful sensibility. So let’s see if Nature can show us — without words or even equations — some of the reasons why quantum mechanics is simulataneously easy-and-hard to understand.

To make appreciate the remainder of this little essay, we must now visit YouTube and watch the eight-minute simulation of sphere eversion titled The Optiverse (http://youtu.be/cdMLLmlS4Dc). Are we done?

Now, after viewing The Optiverse, what ought we to think of a geometer who asserted:

“Non-geometers often have the mistaken idea that the geometry of a sphere is is hard. Unfortunately, many geometers have done nothing to correct that idea. But in newer textbooks, courses, and survey articles, the truth is starting to come out: if you wish to understand the central ‘paradoxes’ of spherical geometry, together with almost the entire body of research on surface geometry, then you do not need to know anything about immersion, orientation, projective planes, complex manifolds, conformal invariance, Boys’ surface, or even elastic energy.”

Now, there is a certain sense in which this “geometrized” quotation is a fair synopsis: namely, the geometry of the initial and final spheres of The Optiverse is (at least superficially) easy to appreciate, and moreover these two spheres related by a regular homotopy of immersions (as the video shows).

However, an appreciation of the entire eversion homotopy is by no means trivial, and a great many of the “hard” aspects of geometry necessarily enter into this appreciation. Speaking metaphorically, just as two spheres can have opposite orientations with respect to the immersing manifold, such that showing their equivalence is highly nontrivial, it has often happened that contrasting interpretations of quantum mechanics have opposing orientations with respect to their “immersion in our understanding”, such that establishing their dynamical equivalence has been very difficult indeed. Indeed I have had precisely this experience (as recounted in ##465) in the sense that working through all the granular details of transforming Nielsen and Chuang’s Quantum Computation and Quantum Information into Ashtekar and Schilling’s Geometrical Formulation of Quantum Mechanics (arXiv:gr-qc/9706069v1), most definitely embraced at the midpoint of that translation the “amazing sweep of topics” to which Ajit Jadhav’s post referred. As Ian Durham remarked (on the other thread) in quoting Matt Liefer: “Foundations is hard.” Yes, it is.

There are plenty of folks posting here on Shtetl Optimized who share the opinion that Joy Christian’s writings have no concrete bearing upon Bell-type theorems and/or experiments … heck, I myself am among these folks. Yet perhaps only those folks who are capable of watching The Optiverse and say “this entire simulation makes perfect sense to me” are qualified to say “the foundational ideas that Joy is pursuing make no mathematical sense, because the foundational ideas of quantum mechanics cannot possibly be that hard, or that broad, or that deep, or that subtle” — and I am not among these folks.

And that is why I am wholly in accord with Gil Kalai’s posts, which affirm humility and respect as values that are central to the culture of science, and essential too to the enduring value of science, and vital also to progress in science … and that these values ought to be scrupulously respected in responding to the challenge that Joy’s work presents to our understanding.

532. Fred D Says:

Since we are watching videos here; for those that are interested in learning more about the 3-sphere topology, I highly recommend this lecture by Nils Johnson of the University of Georgia about “Visualizations of the Hopf Fibration”.

533. Regular Blogging Will Resume Shortly | Wavewatching Says:

[…] on Scott Aaronson's blog where the Joy Christian "Bell Inequality Disproof" controversy is still in full swing.  The latter also inpsired me to the new "QC Bet Tracker" page on this […]

534. asdf Says:

Joy #529 and elsewhere: “People are of course free to ignore my work. But then they have no right to have an opinion about it as Scott did for five years.” Sorry but that is bogus. Knowledgeable people like Scott (and even less knowledgeable ones like me) see crap papers all the time, and are familiar enough with the phenomenon to recognize them for what they are. It is perfectly reasonable and normal to skim a paper or listen to the author, and quickly conclude “this sounds like crap, it’s not worth spending more time on”. That is, to form an opinion based on reasonable inference from past experience, and assign a high probability to it being accurate (it would of course be bad to consider it infallible).

It’s probably best to keep that type of opinion quietly to one’s self, but that’s much different than saying one shouldn’t have the opinion in the first place. It’s a perfectly valid opinion based on reasonable informed judgment. So your criticism has no validity at all unless Scott has been dissing you in public for the six years you mention.

Once Scott started discussing this in public, he did read your paper, and (by his standards) it was even worse than he expected, so you have nothing to complain about. The opinion he held for 6 years was apparently higher rather than lower than it would have been if he actually read your paper.

535. Simon J.D. Phoenix Says:

James,

Yes I’ve been mulling over how to reply to Fred. In essence my problem is very simple. Suppose I wrote the following :

A(a,L) is equal to 1 when the value of L is 1 and is equal to -1 when the value of L is -1

B(b,L) is equal to -1 when the value of L is 1 and is equal to 1 when the value of L is -1

Then anyone would conclude that the product AB is equal to -1 always. L is just a random variable, a coin toss, that on each run of an experiment takes either the value 1 OR the value -1.

There would be no controversy – and if A and B were supposed to model experimental outcomes in which the outcome depended in some way on this random variable L then we would conclude that there only 2 possible outcomes for each experimental run (how can there be more when the random variable only has 1 bit of information?)

Think of each experiment as a communication channel – in order to have 4 possible outcomes the random variable would have to be capable of encoding 2 bits of information.

Now the definition of A and B I have given above is precisely that which occurs in Joy’s paper (if we ignore the more complex term sandwiched between 2 equals signs)

So Joy’s paper contains the statement A=G=E and B=G’=E’ where A and E and B and E’ are given as above. Conventionally, the equals sign is understood to mean that A=E and A=E’. So I can stick a post-it note over G and G’ and just focus on this. If I do this, and read what Joy has **actually** written there – then it is the same as I have written above in the definitions of A and B. I can’t see how this could ever be interpreted in any other way mathematically. If you use the construction A=1 if L=1 and A=-1 if L=-1 then really it couldn’t be much clearer.

Yet somehow, and I really don’t see why, if we use the more complex construction we are invited to believe that now the RHS the A=E and B=E’ no longer means this – but means that we can have 4 possible outcomes. In other words if we use the complex middle form then it’s as if we are to interpret the RHS as if there were actually 2 hidden variables, say L and M, which can each independently take on the values 1 or -1. NOW we can have 4 possible experimental outcomes.

Somehow we’re being invited to consider A=E and B=E’ as meaning one thing when they’re just written like this and yet to mean a **different** thing when the extra term is added so that A=G=E’ and B=G’=E’. When we add the G and G’ terms we pick up an extra bit of information (apparently) that isn’t accounted for in our single 1 bit parameter L.

Mathematically (to me) it just doesn’t make any sense – it’s a use of the equal sign of which I’m not aware. It doesn’t make any sense when we view it from the perspective of information theory. The correlation function used doesn’t make any sense when we compare it to the actual correlation function used in Bell’s inequality.

Nothing about it makes any sense to me – and unfortunately Fred’s answer is dependent on using this middle G and G’ term – which, it is claimed, is where all the beef is. But if we have A=G=E, then there’s the same amount of beef in E as there is in G 🙂

536. Simon J.D. Phoenix Says:

Sorry – there’s a typo in the above. I should have written:

So Joy’s paper contains the statement A=G=E and B=G’=E’ where A and E and B and E’ are given as above. Conventionally, the equals sign is understood to mean that A=E and B=E’

537. Henning Dekant Says:

John Sidles #531, thanks for the sphere inversion video link. For reasons not entirely clear to me, my 5 and 7 year olds love to watch this sphere in-side out video:

Will see how they’ll take to the one you linked to (probably not quite as enthusiastically as the narration is less suitable for kids).

538. Jacques Says:

James (comment 528) says:

for all a and b except when b = -a,
A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (I.b)(mu.b) = – 1 if L = +1 and +1 if L = -1
And for b = -a,
A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

So A(a, mu)B(b, mu) is a continuous function of a and b which is equal to -1 for all a≠-b (independent of mu !!!), but is equal to +1 for a=-b (again, independent of mu).

I see two problems with that assertion

1) It’s still true that the value of A(a, mu)B(b, mu) is completely independent of mu (and hence not a random variable at all).
2) It’s not a continuous function of a and b, even though it was manifestly defined to be such.

I suggest that you think some more, because what you have said is neither self-consistent, nor does it lead to the conclusion Joy Christian would like it to.

P.S.: Thanks to all for a completely hilarious comment thread.

539. Henning Dekant Says:

Joy #529, I know that you agree to the experiment being the ultimate test. Again, my comment was not meant as an accusation that you did not. My point was that this should have been the end of the argument, as Scott and you can at least agree on this.

As with regards to opinions, they are just that opinions. You have to form an opinion of a line of research in order to decide if you want to spend time understanding its details. Scott’s scientifically informed opinion was that your work did not meet his criteria (i.e. your math looks off to him and the claimed impossibility to simulate it on a computer does not make sense to him either).

A personal blog is very much were you express your opinions. Of course you will not like the opinion that Scott has with regards to your work. But coming here and challenge him if he simply is not interested in pursuing the subject will not help.

You may think that this discussion will garner some attention for your efforts. When Scott made his $100,000 bet I thought it was brilliant marketing, so why would I think otherwise with regards to your$200,000 counter bet?

Any marketeer will tell you there are three necessary aspects to create the desired positive attention:

1) A hook
2) The message
3) Promise of Delivery

In both cases, Scott’s and your bet, the hook is the same. It works well. A big dollar bet and science controversy draws a crowd.

The message is simpler in Scott’s case: Tantalizing new computing capabilities. Everybody and their dog understand that’s important. Nevertheless your message of a “Disproof of Bell’s theorem” certainly turns heads in science circles, but already has some problematic connotations.

But the real problem is the promise of delivery. Scott has a lot of momentum on his side, as there is a race on for the first scalable universal quantum computer and dedicated machines like D-Wave’s One are already preparing the market.

On the other hand your promise of delivery hinges solely on your proposed experiment, the quality of your papers and your reputation. An experiment is a long way off (despite my \$60 in the tipping jar), and the other factors are not convincing enough for many of your fellow scientists to even pay attention. I can see how this must be very frustrating, but I strongly doubt that the way you’ve approached this conundrum here will help.

540. Bram Cohen Says:

Aram, Christian believes that real space is actually in S^3, or something unspecified which has the topological properties of S^3 on a local rather than global scale. When it’s pointed out to him that that violates the pythagorean theorem, he says that he isn’t a computer geek and us computer geeks should cut it with our fancy talk.

541. Joy Christian Says:

Scott: The “average” symbols did not go through in what I submitted before. Please replace it with this corrected version:

Here is what Bill Schnieder wrote on a FQXi blog. I hope he will forgive me for reproducing his counterexample here without his permission. The credit for it should go entirely to him:

[Begin quote

I appreciate Joy’s effort to explain his model despite a long line of detractors. Mostly I have found that the physicists are silent, and the mathematicians are crying foul without having understood the physics.

What you have shown convincingly in my opinion is that the QM expectation value can be reproduced in a local and realistic manner, contrary to the claims of Bell’s theorem. Obviously, this raises other questions about the validity of Bell’s inequalities which on the surface appears to be a slam-dunk mathematical identity. This, I believe is the lacuna where mathematicians and many “mainstream” physicists stumble. The following example which I’ve used often illustrates both the mathematical validity of Bell’s inequalities and their violation by an obviously locally realistic experiment.

Violation of Bell’s inequality by coins.

THEORETICAL:

For any three coins “a”, “b”, “c” toss a very large number of times (Heads = +1 Tails = -1). It follows that the inequality |ab + ac| – bc \leq 1 will never be violated for any individual case and therefore for averages | ave(ab) + ave(ac) | – ave(bc) \leq 1 will also never be violated.

Proof:

a,b,c = (+1,+1,+1): |(+1) + (+1)| – (+1) \leq 1, obeyed

a,b,c = (+1,+1,-1): |(+1) + (-1)| – (-1) \leq 1, obeyed

a,b,c = (+1,-1,+1): |(-1) + (+1)| – (-1) \leq 1, obeyed

a,b,c = (+1,-1,-1): |(-1) + (-1)| – (+1) \leq 1, obeyed

a,b,c = (-1,+1,+1): |(-1) + (-1)| – (+1) \leq 1, obeyed

a,b,c = (-1,+1,-1): |(-1) + (+1)| – (-1) \leq 1, obeyed

a,b,c = (-1,-1,+1): |(+1) + (-1)| – (-1) \leq 1, obeyed

a,b,c = (-1,-1,-1): |(+1) + (+1)| – (+1) \leq 1, obeyed

BELL CHALLENGE:

Find a locally realistic situation which violates the above inequality. In other words, find a locally realistic situation which gives perfect anti-correlations for all possible measurements. According to Bell and proponents, this is impossible.

EXPERIMENTAL TEST:

We have 3 coins labelled “a”,”b”,”c”, inside a special box. A button on the box releases only two of the coins at random when pressed. The coins must be returned to the box before the next press, therefore only two of the three coins can ever be outside of the box at the same time.
Since we cannot toss all three at once, we decide to perform the experiment by tossing just the pairs a very large number of times. We decide to group the results into 3 runs such that the first run contains tosses for the (a,b) pair, second the (a,c) tosses and the third the (b,c) tosses. From the experimental results we calculate ave(ab), ave(ac) and ave(bc). Even though the data appears like a random collection of (+1 and -1), we then calculate ave(ab), ave(ac) and ave(bc) and substitute in our expression and find that ave(ab) = -1, ave(ac) = -1 and ave(bc) = -1 (i.e 3 \leq 1 according to the inequality), thus violating the inequality and providing perfect anti-correlation which was supposed to be impossible according to the challenge!!! We are baffled, does this mean “local causality” is false or something spooking is happening?

THE EXPLANATION:

Consider the following: Each coin has a programmable bias which can be changed by the box just before it is released but not after. The box has an internal clock which keeps track of the time in seconds.

The above scenario [ ave(ab) = -1, ave(ac) = -1 and ave(bc) = -1 ] can then easily be realized if the special box operates as follows:

Every time a button is pressed, calculate sin(t) where t is the time read off the internal clock. If sin(t) greater than 0, program coin “a” to be biased for heads (+1) and coin “c” to be biased for tails (-1). Then randomly pick two of the three coins. If coin “b” is one of the picks, program coin “b” to be biased for tails (-1) if the other pick is coin “a”, otherwise program coin “b” to be biased for heads (-1). If sin(t) \leq 0 reverse all the signs.

CONCLUSION:

There is nothing spooky or weird about the mechanism of the box. It produces perfectly anti-correlated pairs which violate Bell’s inequality. The Bell challenge only proves that lack of imagination is mainstream.

End quote]

[ From Bill Schnieder (posted on a FQXi blog on 13 May 2012) ]

542. Bram Cohen Says:

Christian, that ‘experiment’ requires that the values be retroactively changed based on what coins the person chooses. It’s like you go in for a tarot reading, and the ‘psychic’ first asks you about yourself, then says ‘hold on a minute’ and starts carefully sorting together a deck in front of you. Not so impressive.

543. Thomas H Ray Says:

Simon # 518

“Taking a very naive view, non-locality is already built into QM from the outset.”

That’s not naive, that’s the PROBLEM with QM as a complete physical theory. And it’s a problem — of mathematical incompleteness — that Bell’s theorem assumes nonlocality in order to prove nonlocality.

544. Thomas H Ray Says:

Wonderful example by Bill Schneider. The statistics described in his penultimate paragraph correspond exactly to those I posted to FQXi in my “Ferryman puzzle” slide 5. That is, the singularity of zero measure probability in state 2 compels the real measure to biased states 1 or 3 (+ 1 or – 1).

There is at least one more way to show that a tripartite measure function allowing only bipartite data in a bounded length of time is uniformly biased, real and manifestly local. Leslie Lamport’s “Buridan’s principle,” Found. Phys. April 2012, takes as physical law that “A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time.” That is, given a measurement function continuous from an initial condition where x < y < z, and nonzero probability for a value in each neighborhood of x,y and z, a counterexample to "Buridan's law of measurement" has to answer the question "Is the value greater or lesser than y?" As Lamport allows, there appears to be no quantum mechanical theory of measurement that can answer the question.

As Schneider examples, there certainly does exist a classical measure example that can answer the question.

As a result, I think Joy's theorema egregium can be simply stated: "For every discrete observation of a classical state, there exists at least one correspondent quantum state." This is both sufficient and necessary to demonstrate mathematical completeness and to undermine the perceived boundary between quantum and classical measurement theory.

545. Richard Gill Says:

Simon J.D. Phoenix #535. Maybe it helps you and James Putnam to understand the so-called difficult middle terms. They are not difficult! Joy’s derivation of A=lambda, B=-lambda is completely correct and completely elementary!

The bonus of getting to understand this, is that now you’ll easily see that the rest is nonsense.

Step one: get yourself a copy of Joy’s famous one page paper

http://arxiv.org/abs/1103.1879

Step two: familiarize yourself with the quaternions. (Wikipedia is fine). These can be considered as real 4-vectors, just as ordinary complex numbers z=x+iy can be thought of as real 2-vectors (x,y), … as far as addition and scalar multiplication are concerned. For multiplication we use the following multiplication rules:

ij=-ji=k
jk=-kj=i
ki=-ik=j
i^2=j^2=k^2=-1

(For the complex numbers we just have i^2=-1)

FINAL EXAM: check that for any reals b,c,d with b^2+c^2+d^2=1, it holds that (bi+cj+dk)^2=-1

Thus we don’t have just three square roots of -1 (i, j and k), we actually have a whole 2-sphere’s worth. (You might ponder on the similarities with the Pauli spin matrices at this point).

Joy talks about Geometric algebra (aka Clifford algebra) and bivectors but this is diversionary chit-chat, at least, as far as the one page paper is concerned. Standard Clifford algebra is an 8 dimensional real vector space with multiplication tables extending what I just wrote down. In the one page paper, Joy only uses a four-dimensional sub-space, closed under multiplication … it can be identified with the quaternions, as Joy’s explicitly made assumptions make clear, and has also been well known for 150 years. There is no room for doubt, it is all written down completely explicitly by Joy in his one page paper, and Joy hasn’t retracted it.

Note how Joy maps unit 3-vectors to purely quaternionic numbers by the mapping (b,c,d) -> (bi+cj+dk).

His beta_x, beta_y, beta_z are i, j, k

His beta_x(lambda), beta_y(lambda), beta_k(lambda) are lambda i, lambda j, lambda k.

You are now well prepared to completely understand the first half of the one-page paper: all the way up to (but not including) equation (5). This also enables you to see that what Fred says about A B not always being equal to -1 is nonsense. You can do the algebra, but he manifestly cannot. He needs to go back to school.

Now that you are half way through the one-page paper, I recommend you press on and get to the end. The expression at the beginning of (5) is the limit of the empirical correlation between A and B, divided by two quaternionic square roots of minus one. This is a nutty definition of correlation, it has got nothing to do with Bell’s theorem whatever. However, it would be cute if the result were equal to -a.b. This would generate a pretty connection between the singlet correlations and Clifford algebra which was not known before. Such mathematical connections between previously unconnected mathematical objects can be powerful tools and they could also point to powerful new physics insights.

So to test your understanding of quaternions, replace the numerator of first big fraction in (5) with -1, and see if you can simply it. Joy will get angry with you for doing this substitution, but he can’t forbid you from doing algebraic substitutions according to the rules and assumptions which he wrote down himself.

Looks scary, I told you how to multiply, but not how to divide, right? But it isn’t scary at all!

Multiply numerator (top) and denominator (bottom) from the left by {- sum_j a_j beta_j}. Multiply numerator and denominator from the right by {sum_j b_j beta_j}. This is legal, these quaternionic numbers are not equal to zero. The denominator (bottom) now transforms into the product of two square roots of -1, so it’s transformed into +1. The numerator becomes the product of {- sum_j a_j beta_j}, -1, and {sum_j b_j beta_j}. Use the quaternionic multiplication table to work this out. The real part of the result is the desired -a.b. The purely quaternionic part is, embarassingly, the result of representing the real 3-vector -a x b with its purely quaternionic companion.

Amusingly, it was Joy who first pointed this out to me, a few months ago in Oxford! He’s a very nice guy, as long as you agree with him.

It seems that he has been spending 5 years trying to cover up this little mistake. You can hide it better by making things more complicated. The critic then has to have more technical knowledge. Florin Moldoveanu has (before me) catalogues all the variants of Joy’s conjuring trick. However, in the one page paper, the patter is almost absent, so just about anyone can see how the trick is done. I guess the conjuror was getting over-confident.

546. Thomas H Ray Says:

Bram Cohen #542

“Christian, that ‘experiment’ requires that the values be retroactively changed based on what coins the person chooses. It’s like you go in for a tarot reading, and the ‘psychic’ first asks you about yourself, then says ‘hold on a minute’ and starts carefully sorting together a deck in front of you. Not so impressive.”

You managed to intepret exactly the opposite of what the experiment says. It’s the bias that QM builds into an observer-created reality that leads to the psychic “Randi challenge” nonsense that falsely attends critiicism of Joy’s research.

Anti-correlation represented as the input argument, -a.b, is a completely objective feature of a measurement function continuous from the initial condition. It perfectly corresponds to classical time symmetry and angle-preserving transformations.

547. Sandro Says:

Joy #501: Joy, you reply is really not answering my question. My question was, and is, what is wrong about the argument chain I propose. I don’t want to enter into the details of your calculations before the abstract issues raised by its supposed outcome are cleared out on a formal level, which very much is independent on what your model is, but only on what your resulting claim are. So, please, tell me at which point in the following chain the reasoning is either wrong in general or inapplicable to your case.

1) We have variables L, a, and b. What their domains are doesn’t matter. Neither it matters whether they are random variables or algebraic variables.

2) We have functions A(a,L) and B(b,L). What their codomains are doesn’t matter.

3) We have functions f(L) and g(L) for which we can write A(a,L)=f(L) and B(a,L)=g(L) for the whole domain of the variables L, a, and b. Clearly to state this equality, the codomains of A and f, as well as those of B and g, have to be the same.

As far as my reading skills go, 1) 2) and 3) is what you state in your papers. The argument of James and Fred seems to be that 3) is not valid for the entire domain, but if this is the case then you should modify your papers accordingly.

You also seem to have the following assumption:

a) L is independent of a, independent of b, and independent of a and b. And all of them are variables, not constants in disguise.

If we agree on 1-3), then let’s continue.

4) You introduce a function c (your correlation function), whose domain is the cartesian product of the codomain of A and that of B. That is, this is not a functional operator, which might look at what the arguments of A and B are, but a plain standard function. What the function c is doesn’t matter.

If we agree on 1-4), then let’s continue.

5) Due to 3) we can write c(A(a,L), B(b,L)) = c(f(L), g(L)).

6) As a basic property of composition of functions, we can write c(f(L), g(L)) = d(L) for some function d.

7) By chaining the above equalities we get c(A(a,L), B(b,L))=d(L)

If we agree on 1-7), we can then look at your final claim. You claim to have some function e for which

8) c(A(a,L), B(b,L)) = e(a,b)

What the function e doesn’t matter. Putting 1-8) together we can conclude that

9) d(L) = e(a,b)

I assume that in all definitions all variable dependencies were explicit. So, is there something wrong in the above chain? Because if not, then the conclusion 9) is very much at odd with the assumption a), unless d(L) = e(a,b) = k, for some constant k.

If we can agree on what in the above chain is either wrong in general or inapplicable to your case, we might have a starting point for a further discussion. Any calculations starting at 1), 2) and 3) and arriving at 8), be them wrong or correct, will not be an answer to my question.

548. Thomas H Ray Says:

Bram Cohen #542

“When it’s pointed out to him that that violates the pythagorean theorem …”

Complete nonsense. In what way do you imagine that Joy’s framework violates the Pythagorean theorem?

549. Sandro Says:

Of course that symbol 8) was supposed to be point 8.

550. Sandro Says:

Typo: in 3) it clearly is B(b,L)=g(L) and not B(a,L)=g(L). I hope there are not (too many) other typos.

551. Simon J.D. Phoenix Says:

Thomas wrote : “that Bell’s theorem assumes nonlocality in order to prove nonlocality.”

That’s not my reading of Bell’s work. He basically asked the question whether there existed a local theory with hidden variables that could reproduce the results of a certain quantum experiment. He then showed that the results (those pesky actual measurement results) predicted by these kinds of theories had to obey a certain inequality.

So nowhere did he assume non-locality to prove non-locality.

Well that’s my reading of it anyway 😉

552. Joy Christian Says:

Sandro,

“My question was, and is, what is wrong about the argument chain I propose.”

It has nothing to do with my model. I have explained how my model works here: http://www.scottaaronson.com/blog/?p=993#comment-44967

I think it is inappropriate to radically change my model (as Gill and Aaronson insist on doing), or even try to fit it in some formal scheme as you are proposing to do. You must learn MY language to understand my model, which describes the experimentally observed facts within the geometro-algebraic framework I am using.

The only experimental requirements are

A(a, L) = +1 or -1 with exactly 50/50 chance for any a.

B(b, L) = +1 or -1 with exactly 50/50 chance for any b.

AB(a, b, L) = -1 only when b = a.

and

E(a,b) = -a.b.

Nothing else matters. My model fulfills these requierments.

If you really want to understand my model, then I urge you to invest some effort in geometric algebra, and then read at least some of my papers:

http://arxiv.org/abs/1106.0748

http://arxiv.org/abs/1203.2529

http://arxiv.org/abs/1201.0775

553. Scott Says:

Joy:

I think it is inappropriate to radically change my model (as Gill and Aaronson insist on doing), or even try to fit it in some formal scheme as you are proposing to do. You must learn MY language to understand my model…

And … there’s our problem right there! I can’t think of a single counterexample to the following thesis:

When a valid, important mathematical argument is discovered (be it Gödel’s incompleteness proof, Einstein’s path to general relativity, etc.), other people quickly figure out how to re-express the same idea in their own language. The math stands independently of the author.

By contrast, obscurantist bullshit—Hegel, Derrida, Judith Butler, etc.—can almost always be recognized by the property that no one besides the author can even re-express the original arguments without “destroying their true meaning.”

554. Joy Christian Says:

David Brown Says:

“@Joy Christian #528: “There is no confusion in my work on Bell’s theorem.” The vast majority of experts on quantum information processing use the term “proof of Bell’s theorem” to mean “proof of Bell’s theorem within the paradigm of the Copenhagen Interpretation of quantum theory.” J. Christian uses the term “proof of Bell’s theorem” to mean “proof of Bell’s theorem using the definitions used by Bell in Bell’s first 2 papers” as interpreted by J. Christian. The problem is not confusion WITHIN the work of J. Christian. There are 2 problems: (1) refusal to use the definitions of “local” and “quantum correlation” as these are NOW used by the majority and (2) insistence that “general quantum state” (or quantum SU(8) state) is nature’s way instead of Bell’s quantum state (or quantum SU(1) state) — this might be true (I personally now believe it) BUT IT REQUIRES EMPIRICAL PROOF IF IT IS TRUE.”

Empirical proof is indeed desirable. I have proposed an experiment that could decide the matter for the simplest case of EPR correlation. http://arxiv.org/abs/0806.3078

I also have an experimental idea for testing my 7-sphere hypothesis. I also find your argument relating M-theory, MOND, and my local-realistic framework intriguing, but in my eyes it remains a speculation so far.

555. John Sidles Says:

Here I have to agree entirely with Scott’s #553. And more, the process of translating theorems and physics from one context to another context, typically is productive of creative insights that lead us to more good theorems and physics. “Wherefore by their fruits ye shall know them” (good theorems and good physics, that is).

556. Bram Cohen Says:

Tom Ray said: “In what way do you imagine that Joy’s framework violates the Pythagorean theorem?”

In the earlier comments you can read Christian quite directly claiming that reality is in S^3, and that this is why his stuff can’t be modeled on a computer. Of course, S^3 can be modeled on a computer, making for nifty graphics demos as a link I posted does, but he’s clearly saying that space produces local phenomena different from R^3, which implies that space is quite unlike R^3, which is basically saying that the pythagorean theorem is wrong.

I have no idea what this has to do with Christian’s basic thesis. It seems to be a complete diversion to try and claim that his proposed experiment can’t be simulated on a computer.

557. Sandro Says:

Joy #552: Very good, it has nothing to do with your model. But you still have to tell me where it starts not to adhere with your model, and why. You still use functions and variables, and manipulate them according to mathematical rules. And although I’m not an expert in geometric algebra, as far as I know it still complies with what I’ve done in my abstractions.

So, please, at which point does my scheme diverg from your model, and why?

558. James Putnam Says:

Thomas Ray,

I remember that several weeks back you were preparing an ‘Eab_proof’. That was to be a very different presentation about Joy’s model. Have you worked more on that?

James

559. Alex V Says:

Richard Gill #545
There are two methods to introduce multiplication for quaternions. As I guess, Joy used both. For different
lambda are used different multiplications. It is nice trap.

560. Thomas H Ray Says:

James #556

“Thomas Ray,

I remember that several weeks back you were preparing an ‘Eab_proof’.”

I posted a sketch of it in the FQXi “disproofs of …” blog. About a month ago? I don’t remember. I’ll email you a copy if you’d like.

561. Simon J.D. Phoenix Says:

Richard,

Thank you – I suppose I ought to get round to this bit at some point. Mind you, part of me asks myself why bother? There are enough problems with the scheme as it is!

Still, it would be interesting to shed some light on where this extra bit of entropy that’s required to get 4 experimental outcomes comes from (or doesn’t come from :-))

Question is, if we let L be generated by a biased coin then would we still obtain any randomness in the output when it was completely biased 😉

562. James Putnam Says:

Jacques Comment #538 & Fred D.

I was quoting that math from Fred D.’s comment #424. I was looking for Simon’s opinion about what Fred had written. I have communicated at length with Fred about other matters elswhere. I respect his opinion. I imagine he has seen your comment. Thank you for expressing your opinion. Your message was substantative.

James

563. James Putnam Says:

Thomas H Ray Comment #560

I found the link for it. Thanks.

James

564. Michael Kovarik Says:

Resources for science is limited, especially for theoretical physicists.

We can’t allow this crackpot to cipher the little funds that ought to be provided for scientific research, you know, those that actually follow the scientific method.

I just find it hilarious that both Oxford and Perimeter associate themselves with this man.

Mike

565. Joy Christian Says:

Sandro Says:

“Joy #552: Very good, it has nothing to do with your model. But you still have to tell me where it starts not to adhere with your model, and why. You still use functions and variables, and manipulate them according to mathematical rules. And although I’m not an expert in geometric algebra, as far as I know it still complies with what I’ve done in my abstractions.

So, please, at which point does my scheme diverge from your model, and why?”

“(1) We have variables L, a, and b….”

I am pretty sure we already have very different understanding of what “L, a, and b” means. I am not being postmodernist here (Scott’s comment above is a total hogwash). For me L is the initial orientation of the parallelized 3-sphere modelling our physical space. But more importantly, a and b for me are vectors within the even sub-algebra of the algebra of the orthogonal directions in the physical space, NOT vectors as understood within the Gibbs-Heaviside vector (non-)algebra. Thus, for me, a and b are the solution of the equations

I /\ a = 0

and

I /\ b = 0

where I is the volume form of the physical space and /\ is the outer product of Grassmann.

So, you see Sandro, we are already talking about two completely different models.

Now I am sure I will be accused of all sorts of obfuscation and naughtiness for these comments. Let the hell turn loose…

566. James Putnam Says:

Richard Gill Comment #545

Thanks for the guidance. I printed off your message to save.

James

567. Thomas H Ray Says:

Bram Cohen #556

“In the earlier comments you can read Christian quite directly claiming that reality is in S^3, and that this is why his stuff can’t be modeled on a computer. Of course, S^3 can be modeled on a computer, making for nifty graphics demos as a link I posted does, but he’s clearly saying that space produces local phenomena different from R^3, which implies that space is quite unlike R^3, which is basically saying that the pythagorean theorem is wrong.”

Well, I don’t know that Joy has said that his model CAN’T be simulated on a computer — just that the models so far fall short, and I agree. I’m one who does conjecture, however, that the point at infnity obviates a (classical) computer simulation, for this reason:

R^3 is of course “quite like” S^3, but for the fact that R^3 is not compact. Because this compact surface of S^3, when sufficiently large, cannot locally differentiate a closed loop from an open curve, local continuous measurement functions on R^3 are compelled to be incomplete.

Now consider the theorem I brought up earlier, that a point can approach a set of points simultaneously, provided that the point is far enough away. This is both a necessary and sufficient condition to map an isolated point completely to all points of R^3, because without the point at infinity, independent of the scale of measurement, there is simply no means to close a judgment on the presence or absence of endpoints. I comprehend what this means, mathematically — though I admit that I don’t completely understand how a physicist uses the term “local.” Topological properties are always global. The leap I have to make is that because the model is mathematically complete (elements of the mathematical theory map 1 to 1 to elements of the physical measure) and because the singularity is independent of scale — and present in every real continuous function — there is no distinction (as Joy claims) between quantum and classical domains.

As for the Pythagorean theorem, it is always n-dimensional local.

568. Thomas H Ray Says:

Scott # 553

“When a valid, important mathematical argument is discovered (be it Gödel’s incompleteness proof, Einstein’s path to general relativity, etc.), other people quickly figure out how to re-express the same idea in their own language. The math stands independently of the author.”

Heck, that’s what I’ve been doing. It’s the only way I ever understand anyone else’s mathematical language. And I think Joy’s framework does have that power of translation — e.g., Hestenes’ spacetime algebra is fully translatable to Minkowski space; Hestenes shows explictily how to do it. As I told Richard Gill, who claims Hestenes’ authority in opposition to Joy’s framework, it seems to me that IF Joy’s framework is fully relativistic — (and I do agree that it is) — THEN he HAS correctly applied geometric algebra. It would otherwise contradict Hestenes’s program.

569. Richard Gill Says:

Simon J.D. Phoenix #561. Why bother? Well, Geometric Algebra is pretty cool, it’s always good to learn new things. Also it’s good to be able to stand on your own feet. That’s what mathematics is about. You don’t have to accept things on authority. The author states what he is talking about. Writes down definitions and assumptions. After that everyone is equal. Joy Christian can’t forbid you from taking a different legal route to calculate the same thing. And I was interested in the question whether or not he had actually discovered some exciting new mathematical connection between standard quantum formalism, and Clifford algebra. It’s obvious straight away that his model is nothing to do with Bell’s theorem. Bell does not forbid you to embed the two point set {-1,+1} in a larger space. Your hidden variables may live in Clifford algebras if you like. But Bell’s theorem is about the expectation of products of variables taking the values -1 and +1. Joy’s theoretical correlation has got nothing to do with this at all. His model generates perfectly anti-correlated outcomes independent of the settings!

If you do want to rely on an argument by authority, then I can tell you (as a pretty respected mathematical statistician) that everything that Joy says about statistics is nonsense.

Alex V #559. Sure there are different ways to do quaternions. If you define i’=j, j’=i, k’=k and write down the multiplication table for i’, j’, k’, it looks similar to that for i, j, k but is definitely different. A minus sign has crept into some, but not all, of the formulas. Different multiplication tables can define the same algebra.

If on the other hand you define i’=j, j’=k, k’=i, and write down the multiplication table for i’, j’, k’, you’ll find out that it looks exactly the same as that for i, j, k. But this doesn’t make i=i’, j=j’, k=k’.

Joy repeatedly writes: “the basis is defined by the algebra” but this shows that he does not know what he is talking about, and helps one to understand how he might have made these silly mistakes. The relationship between an algebra and the multiplication table of a basis of an algebra (I use the word basis here in its vector space sense) is more subtle than Joy suggests. The multiplication table of *a* basis defines the algebra, but apart from this, the relationship is not one to one.

Joy uses this interplay between algebra and basis in different ways when trying to hide the errors more deeply in the mathematics. In the one page paper the error is rather visibly exposed. In longer papers he uses the full 8-dimensional Clifford algebra: this gives more opportunity (another four dimensions) to confuse the reader and sneak in an illegal sign switch, since there are more isomorphisms (Hodge duality!) which you can use to make simple things complicated.

Joy’s problem was how to get the embarassing term to vanish. His solution is to confuse the reader by making things more complicated, and on the way secretly insert a sign flip, by switching to a different convention when no-one is looking. In his many papers over the years he tried many different variations on this theme. Florin Moldoveanu has patiently catalogued them all. That’s why Joy’s one page paper is such a godsend. Minimalist nonsense.

570. Alex V Says:

Richard Gill #569
Notation used in the one-page paper is ambiguous (or else one page likely would not be enough, yet I may not guess, why such limit of the size were used), but as I already wrote http://www.scottaaronson.com/blog/?p=1028#comment-44736 it is indeed there is some reason to a x b disappear for infinite n.

It is strange a bit to search for trivial mathematical errors a work already analysed during 5 years by many researchers and objected by physical, not mathematical reasons.

571. Joy Christian Says:

Since Richard Gill continues his misrepresentation of my work ad nauseam, I once again note that ALL of his arguments against my model have been systematically and thoroughly debunked many times over, not only by me but also by several other people on the FQXi blogs. See, for example, the following three documents:

http://arxiv.org/abs/1203.2529

http://fqxi.org/data/forum-attachments/JoyChristian_FAQ.pdf

http://fqxi.org/data/forum-attachments/Richard_said.pdf

It is evident from these documents that even after having spent so many months of his failed campaign against my one-page paper Richard Gill has yet to understand the first thing about my model.

572. Simon J.D. Phoenix Says:

Richard wrote : “Why bother? Well, Geometric Algebra is pretty cool, it’s always good to learn new things.”

🙂

You are quite right – I think I came across more negatively than I intended. I’ve actually been meaning to learn more about topology and geometric algebras for some time, for other reasons.

I could use this as an exercise!

I see more fundamental problems with the model Joy uses, and that’s before we delve into the formalism. I still haven’t understood what the RHS of his equations (1) and (2) are supposed to mean – how something that unambiguous can lead to 4 possible experimental outcomes I’ll never know – lol! I’m still trying to figure out if there are different ways I can interpret a mathematical statement of the form if L=1 then A=1 and if L=-1 then A=-1 (with the flipped version for the value of B).

And then I’m still trying to figure out why anyone would think that putting in a different correlation function to the one used in the Bell inequality should tell us anything at all about whether the Bell inequality is violated or not.

And why a single bit of randomness could accomodate the experimental outcomes that one observes. A single bit of randomness is sufficient to generate perfect anti-correlation whenever a=b and also the sinsoidal probablities when a does not equal b? Can’t be true. The single binary hidden variable L doesn’t have enough wiggle room to generate the stastistical richness required.

Anyway – it’ll take a me a week or so to learn the algebra to my satisfaction so that I can reproduce Joy’s calculations – or not as the case may be (I am slow and like to be very careful). I’ll get back to you 🙂

573. James Putnam Says:

Thank you for your very kind remark. It is a pleasure to be communicating with you here. This thread needs opinions of the kind that you share in your message.

James

574. Simon J.D. Phoenix Says:

To me there’s a sense in which this concentration on a certain theorem is not the central issue here. I mean if Bell’s theorem were to fall, either at Joy’s hand, or someone else’s, QM is still manifestly a non-local theory. It just means that Bell’s theorem is not a sufficient test of that.

Also, the rich features of entanglement don’t depend on non-locality. If we actually could find a locally realistic way of reproducing the results of the Bell experiment (and others in a similar vein), it doesn’t mean that this hidden variable description IS the way the world works. It just means that there’s a cute way of getting the same predicted results in some experiments using a local hidden variable description. After all, the point about hidden variables is that they purport to reproduce the results of QM.

What is interesting is the hints I’m getting from the bits and pieces of Joy’s work that I’ve looked at (and I’ve only skimmed them to get to the particular points I was interested in for the purposes of this discussion).

Joy, would I be right in thinking that you’re viewing entanglement as a result of some embedding of our world in some higher dimensional space? That when we view things from this higher perspective then the entanglement unravels?

I may be odd, but I think that’s much more interesting than whether Bell’s theorem is true or not. I still wouldn’t believe it without a fight, but it would be a fascinating perspective.

575. Richard Gill Says:

Alex V #570. The notation in the one page paper is completely *unambiguous*. You don’t have to search for mathematical errors: *the* error shouts at you!

I took no notice at all of Joy Christian’s work for 5 years precisely because conceptually it is nonsense, and completely irrelevant to Bell’s theorem. But then through some coincidences I got in email conversation with Joy through a mutual aquaintance, and later had an opportunity to chat with him at Oxford. My aquaintance is a Bell denier, by the way, with an enormous respect for Joy. So I did have an ulterior motive: to undermine my friend’s regard for his hero Joy Christian, in the hope that he might learn to see the light of Bell.

Now it could be that though his physics is nonsense, and in particular the relevance to Bell is zero, that Joy had discovered some interesting pure mathematics. Maybe even a way to replace the usual Hilbert space structure of QM with alternative but more intuitive mathematical structures (reproducing the same predictions)? Anyway, I wanted to find out what this Geometric Algebra was all about. Joy gave me a nice intro to the topic, which it turned out I was already familiar with under different names, and he recommended me his one page paper. When I read that, and found out that his maths was fundamentally flawed too, it seemed a pity not to write up the results. Especially after all attempts to discuss this with Joy by email ended in failure.

Later I found out that Florin Moldoveanu had already patiently written up a big catalogue of mathematical errors throughout all of Joy’s works, but it seemed to me that this careful and comprehensive analysis is rather hard reading, and requires a lot of technical knowedge, while Joy’s one page paper can be worked through in half an hour, after half an hour of “revision” (wikipedia’s article on quaternions is enough, really). I was surprised to find that the other critics of Joy’s work on arXiv seem all to trust him on the maths, and focus on conceptual issues.

Why argue about the physics, or tricky conceptual issues, when the maths shows that the author can’t handle elementary algebra?

Later I got a lot of compliments from people who had had their doubts about Joy’s work, but somehow imagined that it was their fault they could not understand a word he wrote, through their inadequate maths background. So it seems it was worth while to share my findings with the world.

576. John Sidles Says:

Simon, your post suggests that you are in a receptive frame of mind to appreciate Bill Thurston’s hugely-rated (110!) reply to the Math Overflow question: What’s a mathematician to do?. Have fun! 🙂

577. Fred D Says:

Hi James,

Concerning Jacques’ Comment #538 that you mention. You can’t just take part of the list of algebraic possible outcomes and think that it represents Joy’s model like Jacques is doing. The whole list has to be considered. I will reproduce the list of algebraic possibilities here again for just one of the sets for detector handedness.

For mu = L*I with I being an oriented volume element and L =+/- 1 fair coin toss, the first part of the set is for all a and b except when b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (I.b)(mu.b) = – 1 if L = +1 and +1 if L = -1

And for b = -a,

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

Then we have the following possible algebraic outcomes due to the parallelized 3-sphere topology when b is not equal to a or -a,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (I.b)(mu.b) = -1 if L = +1 and +1 if L = -1

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(I.b)(mu.b) = +1 if L = +1 and -1 if L = -1

And then when b = a for the topological sign flip algebraic possibility,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1

And then when b = -a for the topological sign flip algebraic possibility,

A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1

And as I mentioned before it should be clear to anyone that knows about EPR-Bohm why there are special cases for when b = a and b = -a. Please reproduce at least this much of the set of algebraic possibilities if mentioning in the future so as to avoid misunderstandings. The above gives all the outcomes necessary to show that,

A(a,mu) = +/- 1 randomly
B(b,mu) = +/- 1 randomly
AB = -1 when b = a
E(a) = E(b) = 0
E(a,b) = -a.b

for Joy’s model. Those are the conditions for EPR-Bohm / Bell. Joy’s model is a counterexample to Bell’s theorem.

578. David Brown Says:

@Simon J.D. Phoenix #578: “… entanglement as a result of some embedding of our world in some higher dimensional space.” According to J. Christian, entanglement and all quantum phenomena are explained by the Theorema Egregium, which is “proved” on the basis of higher quantum states. I claim we might as well beg the question mathematically because the significance of the Theorema Egregium is really all about physics. It seems to me that the objections of Gill, Moldoveanu, and Aaronson are wrong mathematically but that is fundamentally irrelevant because the Theorema Egregium is really something that needs to be empirically tested (and how it was derived mathematically is a secondary issue).

579. Henning Dekant Says:

Thomas H Ray, #568; Your comment highlights why I recommended you as Joy’s science attorney 🙂

Your one of the few people here who say they can follow Joy’s winded mathematical path.

Curious to see if Simon J.D. Phoenix can also find a pony in this minefield.

580. Jacques Says:

Fred (Comment #576) sez:

Then we have the following possible algebraic outcomes due to the parallelized 3-sphere topology when b is not equal to a or -a,
A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (I.b)(mu.b) = -1 if L = +1 and +1 if L = -1
A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(I.b)(mu.b) = +1 if L = +1 and -1 if L = -1
And then when b = a for the topological sign flip algebraic possibility,
A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
And then when b = -a for the topological sign flip algebraic possibility,
A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1

Sigh. OK. Not entirely consistent with what James transcribed, but still subject to exactly the same objections.

A trivial computation, from what you wrote, yields

A(a,mu)B(b,mu) = +1 for b≠±a
A(a,mu)B(b,mu) = -1 for b=±a

Ergo:

1) A(a,mu)B(b,mu) is completely independent of mu and hence not a random variable at all.
2) A(a,mu)B(b,mu) was, by construction, a continuous function of a,b, but your answer is clearly not continuous.

The first point means that all the blah-blah about expectation values is completely irrelevant (since A(a,mu)B(b,mu) is not a random variable, but a completely deterministic function of a,b).

The second point means that there’s something bogus about your computation, but I’ll leave you to sort out your mistake.

In any case, this clearly cannot lead to Joy’s claimed result.

581. Simon J.D. Phoenix Says:

Fred,

Thanks again for trying to explain the maths. I’m still not getting it. However, are you sure that there isn’t a typo in the following expression you wrote for when b is not equal to a or -a :

“A(a, mu) = -(-I.a)(mu.a) = -1 if L = +1 and +1 if L = -1
B(b, mu) = (I.b)(mu.b) = -1 if L = +1 and +1 if L = -1

A(a, mu) = (-I.a)(mu.a) = +1 if L = +1 and -1 if L = -1
B(b, mu) = -(I.b)(mu.b) = +1 if L = +1 and -1 if L = -1”

What these results seem to be suggesting to me (although I am clearly having problems with the precise mathematical meaning of what someone means when they write a construction of the form A = +1 if L=+1 and -1 if L=-1) is that if the random variable were to be generated by a biased coin and we let it become perfectly biased then we’d still obtain some randomness in the output.

I’m still not getting how you can generate 2 bits of entropy, per run, from a single binary random variable.

582. Richard Gill Says:

Notice that Fred #577 is using different assumptions from those of Joy’s one page paper. He carefully does *not* state which assumptions he’s using. He’s gone into 8 dimensional Clifford algebra using Hodge duality, an isomorphism between two 4 dimensional sub-algebras (that’s where the “I” lives). His list of possible outcomes contradicts Joy’s. So if he is following Joy, he’s yet again proving that Joy’s results are self-contradictory. If he’s not, he’s proving that even Joy’s truest supporters don’t have a clue about Joy’s model.

I forgot to mention that apart from actually making a mistake with a sign, Joy sometimes uses the alternative strategy of assuming several mutually contradictory assumptions at the same time. This is a cunning mathematical trick because now any desired result whatever is true, given the assumptions. If you’ll allow me to assume 1=2, then I can quickly derive P=NP and claim my millenium prize from the Clay institute. That’s how he dealt with the mistake in the one-page paper at the FQXi blog: the mistake has been elevated to a new assumption. It contradicts the already made and used assumption, silently introduced in the middle of a chain of inequalities. Unfortunately this does not help: the new assumption contradicts the already made and used assumptions.

Of course he is not going to revise the one page paper in order to list all the assumptions he actually does use. That would make the contradiction too obvious.

583. Joy Christian Says:

David Brown,

You wrote:

“@Simon J.D. Phoenix #578: “… entanglement as a result of some embedding of our world in some higher dimensional space.” According to J. Christian, entanglement and all quantum phenomena are explained by the Theorema Egregium, which is “proved” on the basis of higher quantum states. I claim we might as well beg the question mathematically because the significance of the Theorema Egregium is really all about physics. It seems to me that the objections of Gill, Moldoveanu, and Aaronson are wrong mathematically but that is fundamentally irrelevant because the Theorema Egregium is really something that needs to be empirically tested (and how it was derived mathematically is a secondary issue).”

Well said. Very well said.

Why is it that for someone like you who is neither a professional physicist nor a professional mathematician it is so easy to see what I am doing? And why is it that for professional physicists and mathematicians it is so hard to follow a half-a-page document of elementary mathematics? Because you are like a child, free of intellectual vanity, who is able to read my four-line argument without the fear of any academic impunity. You, David Brown, have earned my respect. If you are a crackpot as you sometime claim, then I am very very proud of being your fellow crackpot.

584. David Brown Says:

@Fred D. #581 “Joy’s model is a counterexample to Bell’s theorem.” The parallelized 7-sphere model is a counterexample to what J. Christian defines to be Bell’s theorem based on the definitions in Bell’s 1st 2 papers AND Christian’s assumption that nature uses quantum SU(8) states instead of quantum SU(1) states. I say that the latter assumption really amounts to claiming that nature’s model of M-theory is deterministic (which might or might not be true). BUT what the experts on quantum information processing NOW mean by “Bell’s theorem” is “Bell’s theorem proved within the paradigm of the Copenhagen interpretation”. J. Christian’s model implies that SU(8) is the fundamental gauge group of our universe — this is far from obvious in term of experimental physics. It is impossible to prove that SU(8) is the fundamental gauge group of our universe merely by offering a sound mathematical argument. It is impossible to “physically disprove” the “physical content of Christian’s version of Bell’s theorem” merely by offering a sound mathematical argument. Abner Shimony has good reasons for doubting the validity of J. Christian’s work. I suggest that such validity is fundamentally a question of experimental physics. Einstein’s field equations are valid because of physics and not because of any kind of mathematical argument.

585. Sandro Says:

Joy #565: Well, as I wrote the domain of the variables is yours to choose, so as far as point 1) is concerned we are on the same page. But, as the devil is in the details, there is something concerning me with respect to my assumption a), which is that these variables are independent from each other. As L encodes some global information on our space, it seems to me this will affect the domain of a and b, so that they will not be independent on the actual value of L. Can you comment on this?

586. Thomas H Ray Says:

Simon # 372

“I still haven’t understood what the RHS of his equations (1) and (2) are supposed to mean – how something that unambiguous can lead to 4 possible experimental outcomes I’ll never know – lol!”

There are actually 3!, or 6 possible outcomes, but 2 are null. This is a result of simple combinatorics applied to a pair of random variables. The null values describe the orientation of a measurement function continuous from the initial condition. Did you understand Joy Christian #565?

587. Thomas H Ray Says:

Richard Gill #

“Standard Clifford algebra is an 8 dimensional real vector space with multiplication tables extending what I just wrote down. In the one page paper, Joy only uses a four-dimensional sub-space, closed under multiplication … it can be identified with the quaternions, as Joy’s explicitly made assumptions make clear, and has also been well known for 150 years. There is no room for doubt, it is all written down completely explicitly by Joy in his one page paper, and Joy hasn’t retracted it. ”

The eight dimension space described by O incorporating the four dimension space of H, derived from the two dimension space of C, subsuming the one dimension real line R — are division algebras that correspond precisely to the parallelizable spheres S^0, S^1, S^3, S^7. One cannot simply pick an algebra from any of these spaces and apply those rules to the whole. Joy’s analytical framework is all of a piece — a continuous measurement function and not algebraic.

“The expression at the beginning of (5) is the limit of the empirical correlation between A and B, divided by two quaternionic square roots of minus one. This is a nutty definition of correlation, it has got nothing to do with Bell’s theorem whatever.”

So what? Joy’s claim is a counterexample to the conclusions of Bell’s theorem. It doesn’t — despite the unfortunate choice of the word “disproof” — question the mathematical integrity of the theorem.

“However, it would be cute if the result were equal to -a.b. This would generate a pretty connection between the singlet correlations and Clifford algebra which was not known before.”

No. The input argument doesn’t do anything to the algebra. It just says that of a continuous range of input variables, measurement results are perfectly anticorrelated by the symmetry of a measurement function continuous from the topological initial condition.

“Such mathematical connections between previously unconnected mathematical objects can be powerful tools and they could also point to powerful new physics insights.”

Yes indeed.

588. Thomas H Ray Says:

David Brown # 583

“Einstein’s field equations are valid because of physics and not because of any kind of mathematical argument.”

I would say that the mathematical argument is independent of the physics. That’s what mathematical completeness means — 1 to 1 correspondence between mathematical theory and physical result. Einstein was always conscious of this relation; the conclusions of relativity are all completely closed logical judgments. For this to apply, the mathematics must be valid.

That’s why Joy’s critics attack the validity of the math. They know that if Joy’s model is mathematically compete, it is far, far stronger than the demonstrably incomplete quantum mechanical framework. I agree with Joy — the attacks are strawmen arguments.

@James Putnam #574: Cool.

– – – – –

@Thomas #568:

“… Well, I don’t know that Joy has said that his model CAN’T be simulated on a computer — just that the models so far fall short, and I agree. I’m one who does conjecture, however, that the point at infnity obviates a (classical) computer simulation …”

Now, that clarifies much more about the nature of Joy’s theory. However, I do wonder: Why can’t Joy state his position on this point and end this business of conjectures?

– – – – –

@All:

That precisely is the problem I have with Joy. If someone tries to concretize his theory even just a bit, he is not to be found addressing many of the important resulting issues. For instance, no detailed comments are forthcoming from me as to why *he* thinks the simulations by others are wrong.

But, oppose his theory, and he is very certain to respond, perhaps asking us to learn his language first.

This method or style of communication on Joy’s part has now begun to make me actually become bored of this thread.

And, further, when I tried to re-read his papers again, I have begun questioning myself if I have not read more into his papers than what he had intended.

Just the way understanding too little of his papers is a strong possibility with me, reading too much into his papers also is an easy possibility with me, and that’s because: (i) I do have the essentials of a local physics theory to reproduce violation of Bell’s inequalities (though not much abstract mathematics with which to describe it); (ii) I don’t understand his mathematics, and (iii) he won’t supply a C++ program to simulate a physically possible experiment, a program which I could then use to assure myself that I wasn’t reading too much into his papers.

Anyway, it’s been nice getting acquainted with quite a few thoughtful gentlemen, even on this thread.

However, as I said, this thread now has become boring to me. So, let me quit it, at least for the time being. … In the meanwhile, in the unlikely event that Joy begins distributing a C++ program of the abovementioned kind, I would appreciate if someone could drop a line to me to that effect.

Best,

Ajit
[E&OE]

590. John Sidles Says:

Richard Gill #545 “The expression at the beginning of (5) … [as a] definition of correlation  … has got nothing to do with Bell’s theorem whatever.”

Thomas H Ray #586: “So what?”

Just to remind folks, Richard Gill’s post could have stated — equally correctly and with augmented cogency — that J. Christian’s definition of correlation has got nothing to do with experimental physics practice either.

We thus appreciate that Joy’s nonstandard “correlations” are disconnected from Bell-type theorems … and are disconnected too from experimental physics practice … and moreover cannot be computationally simulated, even in principle … and so what is left?

Well, plausibly there is a residuum of pure mathematics, just as Ray #586 suggests. And if that mathematics were carefully explained, without reference to the words “Bell” or “physics” or “correlation” or “quantum” — and with arithmetic errors corrected — then plausibly these findings would arouse less controversy.

Error correction.

In my immediately above message, instead of:

“For instance, no detailed comments are forthcoming from _me_”

“For instance, no detailed comments are forthcoming from _him_”

I have no honest idea how I could commit *this* mistake! Anyway, evidently, I have!!

Good bye.

Ajit
[E&OE]

592. Simon J.D. Phoenix Says:

Thomas wrote : “There are actually 3!, or 6 possible outcomes, but 2 are null. This is a result of simple combinatorics applied to a pair of random variables.”

What you say makes perfect sense if we actually diid have a pair of random variables – but we don’t have a pair of random variables – only one, and that is L (the lambda in the paper).

We don’t have A(a,L) and B(b,M) where L and M are random variables, but A(a,L) and B(b,L). The parametrization is in terms of the single random variable L – which splits the world into the two choices of helicity in the model.

Where is the other source of randomness?

593. Richard Gill Says:

Thomas H Ray #587. As usual you show that you do not have the faintest idea what you are talking about.

The octonions O are not only non-commutative but also non-associative. Clifford algebra is associative. Joy works in Geometric algebra, i.e., with Clifford algebra Cl_{0,3}(R). Which is the direct sum of two copies of the quaternion algebra H.

Secondly, you keep saying that Joy’s model is analytic. Joy’s one page paper does not use any analysis at all (except for the law of large numbers). He only does algebra, and he remains entirely within H. In other papers, attempting to move the bump (dead parrot) under the carpet to somewhere under the sofa where no-one will see it, he works in Cl_{0,3}(R) or H+H.

The fact that these algebras turn up all over the place in differential geometry and elsewhere, doesn’t change the fact that in Joy’s one page paper, he only uses the algebra of the quaternions, and he gets it wrong. His definitions are completely explicit. He leaves himself no room to maneuvre.

Well: he just has the choice whether he is making a stupid mistake in the middle of line (7), or silently introducing a daring new postulate there – very daring since it contradicts the postulates of (1) to (4). Either way, the maths does not stand up on its own. Internally inconsistent. Glaring errors in elementary algebra.

Tom, you should spend more time reading up the basic definitions on wikipedia, and less time displaying your incredible ignorance of the basic matters under discussion on serious discussion fora.

594. Thomas H Ray Says:

Henning # 578

“Thomas H Ray, #568; Your comment highlights why I recommended you as Joy’s science attorney

Your one of the few people here who say they can follow Joy’s winded mathematical path.”

LOL. I was a reluctant participant 18 months or so ago — I was as incensed as any mathematician to have the idea of “disproof” waved in my face, inviting a charge. When most of the counterarguments turned out to be based on the belief that Joy committed the mathematical sin of arriving at “+ 1 = – 1”, it was a game changer for me, because I find no such error. What I liked right away about Joy’s framework was the method — I had been trying myself for years to get a relativistic model to work on a closed, compact surface. For relativists, the reason should be obvious: adding dimensions to a field theory won’t solve the problem of doing away with arbitrary boundary conditions.

With Joy’s framework, the continuous measurement function without such boundary conditions is exactly as Einstein predicted: the product of improvement in the algebraic methods since Einstein’s day.

“Curious to see if Simon J.D. Phoenix can also find a pony in this minefield.”

It takes a village.

595. Thomas H Ray Says:

Simon # 591

“We don’t have A(a,L) and B(b,M) where L and M are random variables, but A(a,L) and B(b,L). The parametrization is in terms of the single random variable L – which splits the world into the two choices of helicity in the model.

Where is the other source of randomness?”

The variables are dichotomous. I have gotten the impression over the past couple of months of online exchanges that this isn’t the easiest thing to understand.

The parameters in Joy’s model that, like Bell-Aspect, respect both remote parameter independence and remote outcome independence, are dual — not independent in the sense of Bell-Aspect such that the world splits into a binary choice with probability 1/2 for remote outcome and local outcome. Bell assumes, as you, that parametrization is over the field of real numbers on the interval {- oo, + oo}. This is but a single classical parameter, as you say — true.

Joy makes a different, topological, assumption. He replaces the field assumption with an input argument of a continuous measurement function that guarantees anti-correlation of particle properties from a continuous range of input values. Even though the discrete ouptut is described by real numbers (all real valued variables of a real continuous function are real), the local measurement is dual to the global. In other words, while Bell-Aspect assigns the value of nonlocality to “the experiment not performed,” dropping the assumption of nonlocality produces the dichotomous variables of Joy’s model and therefore obviates the arbitrary distinction between local and global domains. The measure space is complete.

596. Thomas H Ray Says:

Richard Gill #592

“Tom, you should spend more time reading up the basic definitions on wikipedia, and less time displaying your incredible ignorance of the basic matters under discussion on serious discussion fora.”

I’ll do that, Richard, the day you consult Wikipedia to learn the difference between algebra and analysis.

597. Alex V Says:

Richard Gill #592
I supposed it is Cl_{3,0}(R) , i.e. realification of Pauli algebra

598. Simon J.D. Phoenix Says:

Henning wrote : “Curious to see if Simon J.D. Phoenix can also find a pony in this minefield.”

lol! I only just noticed that Henning. It’s a long, long time since I had a play with quaternions – so it will take me a while to get myself enough up to speed to satisfy myself.

But there are, for me, enough problems without delving into the formal maths. But unfortunately I can’t fully understand the counters to the problems that have been raised because they’re all in terms of this relatively unfamiliar mathematics. I am deeply suspicious of this continual appeal to the formalism, but then maybe it’s because I don’t consider that I’ve understood something until I have every last i dotted and t crossed. Which means that, in my own terms, I don’t understand very much 🙂

599. Thomas H Ray Says:

Richard Gill #592

” …you keep saying that Joy’s model is analytic. Joy’s one page paper does not use any analysis at all (except for the law of large numbers). He only does algebra, and he remains entirely within H.”

Were that true, we could forget about topology and call it a day. It’s ridiculous to say that Joy’s domain is limited to H. What we do know to a certainty, however, is that Bell’s domain is limited to R. You’re not going to be able to maintain this charade, Richard.

600. Sandro Says:

Simon #591: in his 2D Möebius example (http://arxiv.org/abs/1201.0775, page 22), Joy is very candid about the fact that the product of the measurements being always -1 is an “illusion”. He claims that this product will “fluctuate inevitably between the values -1 and +1”. The reason of this is because L, while the measured object travels from its origin to the measurement point, might “flip”, due to the topology of the considered space (passing on the other side of the strip makes left become right). As to why/when the flip occurs, and most importantly why the flip probability should depend continuously on a and b, that is so far beyond me.

So, what I concluded out of this is that his measurements are not A(a,L) and B(b,L) but rather A(a,L_A) and B(b,L_B), and the main point is there how L evolves into these two values. And as it seems, either L_A and L_B depend somehow on a and b, or viceversa a and b depend somehow on L. This is what I’m currently trying to understand.

601. Scott Says:

Sandro #599: Right, insofar as I was able to make sense of that section, Joy thinks that Alice and Bob’s actual spatial positions on the Möbius strip somehow depend on their choice of detector settings. In other words: as Alice adjusts the detector in her lab, unbeknownst to her, she’s also whirling herself around the entire universe. Since the universe is a Möbius strip, that means she’s also changing the probability that the hidden-variable L’s sent to her by the gremlin are going “flip their orientation” on their way over!

This is truly a sad and pathetic invocation of “topology.”

602. Simon J.D. Phoenix Says:

Thomas, thanks for the reply – I appreciate it. It will take me a while to understand and digest what you have written.

I undertand that the variables A and B are dichotomous – which simply means that they can have two possible values. Lambda is also a dichotomous variable. On each run Lambda takes the value +1 or -1 uniformly at random. I’m assuming that lambda represents just a good old-fashioned number that we can generate by tossing a fair coin.

Now if A and B were two bog standard random variables we could enumerate the 4 possible outcomes we could obtain and we could work out the joint probabilities P(A=+1, B=+1) etc. However, the randomness in A and B is through the use of the input L – which has the same value for both. So we only have two possibilities

{A(L=1), B(L=1)} and
{A(L=-1), B(L=-1)}

The randomness in A and B is as a result of the randomness in L. There is, at most, 1 bit of entropy here. There is no other source of randomness here.

Now we could have A and B to be functions defined, for example, like

A(L) = 1 with prob p when L=1
=-1 with prob (1-p) when L=1
=1 with prob q when L=-1
=-1 with prob (1-q) when L=-1

which is equivalent to defining A as before such that A is 1 with with probability (p+q)/2. If B is defined in a similar fashion (with p’ and q’) we now have our two sources of randomness. But this is equivalent to simply defining A(L) and B(M) where L and M are two binary random variables where the values of L and M are governed by the probabilities p,q, p’ and q’ that we have defined.

I may be assuming something about a parameterization over the field of reals – but lambda is just a coin toss isn’t it? I’m still not seeing another source of randomness other than this in the model. Joy’s model is generating entropy!

603. Alex V Says:

Scott #600
Anyway, where is denominator in the one-page work coming from??

604. Simon J.D. Phoenix Says:

Sandro wrote :”The reason of this is because L, while the measured object travels from its origin to the measurement point, might “flip”, due to the topology of the considered space (passing on the other side of the strip makes left become right).”

Ah – so the **other** source of randomness is whether we travel in one space or another – so we have another hidden variable in there (heck, it might even be non-local!)

Thanks Sandro

605. James Putnam Says:

Scott Aaronson #600,

“… as Alice adjusts the detector in her lab, unbeknownst to her, she’s also whirling herself around the entire universe. Since the universe is a Möbius strip, that means she’s also changing the probability that the hidden-variable L’s sent to her by the gremlin are going “flip their orientation” on their way over!

This is truly a sad and pathetic invocation of “topology.” ”

In this message are you objecting solely to the physics? Is the discussion about the possible incorrectness of the math predicated on rejection of the theory? I recognize that in some cases, the math may look wrong due to one’s inability to correctly understand the physics. That is not what I am asking about from you:

If, for the sake of argument, the physics, as you have stated it in the above quote from comment #600, is accepted would the math be correct in your opinion? Might the debate, at its true core, be about the reasonableness of the theory?

I recognize that objections to your description may arise, but, I am interested in your assessment of your description in your message. Thank you.

James

606. Thomas H Ray Says:

Richard,

Speaking of what kind of people should be allowed to participate in “serious discussion fora,” let me point out your support of this sterling example of scientific gravitas:

“I would especially like to draw attention to Sascha Vongehr’s ‘quantum Randi challenge’ on science20.com, see Vongehr (2011). The idea is to insist that those who believe Bell got it all wrong, to deliver by providing computer programs which simulate their local realistic violation of Bell’s inequality. A successful simulation will get the attention of science journalists and science communicators and educators, and thereby of the whole scientific community, without having to pass the barrier of hostile peer review.”

Yes, let’s not let hostile peer review interfere with the carnival midway show. Fact is, psychic guessing games are as far removed from Bell’s theorem and Joy’s model as spots are from a spotted puppy. Correlation is not causation. It should be obvious that anyone who buys into the Randi challenge nonsense has little grasp of the meaning of physically correlated pair properties, and prefers the unconstrained quantum mysticism of observer-created reality.

607. Thomas H Ray Says:

Sandro #599

” … why the flip probability should depend continuously on a and b, that is so far beyond me.”

For a measurement function nondegenerate near the singularity, discrete experimental output in a bounded length of time — given a continuous range of input values — does depend on a continuous coin-flip probability. For an experimental run of n Bernoulli trials, compare the random coin flip events to the predicted output for a measurement function continuous from the initial condition.

608. Richard Gill Says:

Alex V #597. You’re right. Sorry, typo.

Thomas H Ray #599. You say “It’s ridiculous to say that Joy’s domain is limited to H. What we do know to a certainty, however, is that Bell’s domain is limited to R. You’re not going to be able to maintain this charade, Richard.”

I’m not the one maintaining a charade! Joy is the one doing that. Joy’s one page paper defines everything explicitly in terms of scalars and bivectors, ie elements of the even sub-algebra of Cl_{0,3}(R) known as H. Moreover, by exhibiting explicit relations between all these objects, he himself puts everything into one and the same copy of H.

So Tom, as well as checking the basic definitions of Geometric Algebra on wikipedia or somewhere (I recommend the very nice book by Doran and Lasenby), you’ld better also *read* Joy’s one page paper.

Bell on the other hand discusses binary measurements which are conventionally labelled -1, +1. Bell’s correlations (the correlations measured by experimentalists) are ratios of counts: number equal minus number unequal, divided by total number of pairs.

There is nothing whatever in Bell disallowing you to imagine those two outcomes, the outcomes whose combinations the experimenters just count, as being points in any space whatever. Nothing whatever in Bell disallows the hidden variables to be elements of whatever weird and wonderful space you like.

Bell-CHSH is not about R. It’s about counts of outcomes in 2×2 tables – a pair of dichotomous variables – under four different (joint) measurement conditions.

These are the reasons why already 5 years ago anyone could see that Joy’s “model” was not actually about Bell and local realism and all that, at all. That’s the reason no one in the field paid it any serious attention. But some people imagined that he might have discovered some impressive new mathematics, which then could come in useful elsewhere.

Those people were disappointed.

609. Alex V Says:

Richard Gill #607
But eq(4) in the one-page paper defines two algebraic structures. Loosely speaking sign of lambda swaps Alice and Bob, so indeed, that is locality we are talking about

610. Sandro Says:

Thomas #606: Where is the singularity in a Möebius strip?

611. Joy Christian Says:

Sandro,

You ask: “Joy #565: Well, as I wrote the domain of the variables is yours to choose, so as far as point 1) is concerned we are on the same page. But, as the devil is in the details, there is something concerning me with respect to my assumption a), which is that these variables are independent from each other. As L encodes some global information on our space, it seems to me this will affect the domain of a and b, so that they will not be independent on the actual value of L. Can you comment on this?”

a and b are vectors, not bivectors. Vectors do not have handedness, unlike bivectors. So they cannot, and do not, depend on the actual value of L, which specifies the handedness of all bivectors for each run of the EPR-Bohm experiment.

The confusion you are having here again has to do with the fact that, as you confessed, you are unfamiliar with the language of geometric algebra my model is based on. One is unlikely to articulate a sentence correctly if one does not know the language one is trying to use to articulate the sentence. The confusions I see in many, many, many, comments on this thread stem from this very simple fact.

612. Thomas H Ray Says:

Richard #607,

“Bell-CHSH is not about R. It’s about counts of outcomes in 2×2 tables – a pair of dichotomous variables – under four different (joint) measurement conditions.”

I buy that. Now, why should any 2 X 2 table differ from any other?

It doesn’t.

Any N X N measurement space, assumes its boundary N on orthogonal axes, in which discrete measures in each direction are taken in time intervals assumed to be independent, discrete and identical to all other time intervals. So actually, it is ultimately about R after all, i.e., R in C, where we can use the Hilbert space or extend C to quaternionic algebra, etc., to describe static relations among sets of differentiated points. OTOH:

A measurement function continuous from an initial condition and given a continuous range of input values, cannot treat time intervals as identical — because the output will always be recorded in a bounded length of time. So there remains at least one quantum state for any table that is not in the table, given an unbounded length of time. If that’s all there were to say, we could not avoid a probabilistic reality — however, because Joy’s framework allows a complete measure space of continuous functions with a specified input argument, the provable extra degree of freedom — a nondegenerate measure near the singularity which attends every continuous function — compels a measure that reveals the extra quantum state at the arbitrary end of an experimental run. This state is not probabilistic, but follows from the iniitial condition.

613. Thomas H Ray Says:

Sandro #609

“Where is the singularity in a Möebius strip?”

A Mobius strip IS a singularity. That is, the object being nonorientable, one cannot differentiate a Mobius strip from a singularity in a continuous function model of d > 3. Past the point of torsion, though (the “twist”), reversed chirality tells us that the measurement function is nondegenerate, because for that to happen, the function must pass near a singularity.

614. David Brown Says:

@Joy Christian #475: “Very few people are interested in knowing what my model is. They are not interested in Fred’s explanation. They are interested in convincing themselves that I must be wrong.” YES … this is precisely the problem.
@Scott #605: “In other words: as Alice adjusts the detector in her lab, unbeknownst to her, she is also whirling herself around the entire universe.” From the viewpoint of the Copenhagen interpretation, this is a fairly good description of what is happening in the model. From the viewpoint of Christian’s theory of local realism, the universe’s topology of allowable measurements forbids Alice from making a measurement that would provide a counterexample to Bell’s theorem. Alice does not need to whirl herself around the universe because the problem does not arise — there is a tricky continuous measurement function that explains quantum theory. Is David Brown wrong here?

615. Thomas H Ray Says:

Simon #601

“I may be assuming something about a parameterization over the field of reals – but lambda is just a coin toss isn’t it? I’m still not seeing another source of randomness other than this in the model. Joy’s model is generating entropy!”

There’s no probability function in Joy’s framework. Classical randomness represented by a coin toss probability is a convention. Pair correlations of orientation entangled particles are exactly determined.

The question of entropy is an interesting one. I think there’s no loss of information in Joy’s framework, because it is perfectly symmetric, angle preserving.

(I have my own ideas of information loss, however. According to some of my calculations, there is just the slightest loss necessary to keep the universe in a metastable state. But that’s another discussion.)

616. Sandro Says:

Joy# 610: Dear Joy, as you very correctly remarked, I could not make an articulate sentence in the language of geometric algebra, and I won’t even try to, don’t worry. I wouldn’t say that mine was a confession, as I never stated I am an expert on the topic, or tried to hide the fact that I’m not. But let’s not diverge. All I want is to understand what you mean on a rather basic notational level, and hence I’ll let your comments guide the discussion.

So, so far it seems like we concluded that:

1) We have variables L, a, and b, each living in some fixed domain, as by you specified.

a) L, a, and b are mutually independent. That is, neither a or b depend in any way on L, neither L depends on a and b.

If you agree, as you seem to do, we can move on points 2 and 3, which were the following.

2) We have functions A(a,L) and B(b,L). As far as I’m concerned, you can define their codomains as you whish. Their domain is clearly the cartesian products of the domains of the corresponding variables.

3) We have functions f(L) and g(L) for which we can write A(a,L)=f(L) and B(a,L)=g(L). These functions are your cases definitions. What is important is that these equalities hold for the whole domain of the variables L, a, and b. Clearly to state this equality, the codomains of A and f, as well as those of B and g, have to be the same.

Can you comment?

617. Sandro Says:

Too bad, same typo as before (should avoid copy and paste). B(a,L)=g(L) should read B(b,L)=g(L).

618. Richard Gill Says:

Alex V #609. Eq. (4) defines two different bases of the same algebra. Different multiplication tables, same algebra. Nothing to do with Alice vs. Bob.

Tom #612. You are talking about your own private fantasy, not about Joy’s model. You talk about your imagination, your heartfelt desire and deep belief, that this would be what it’s about. Unfortunately your poetic science-fancy is even further dissociated from the actual maths which Joy writes down, than his own sales patter is.

619. Joy Christian Says:

David Brown asks: “Is David Brown wrong here?”

David Brown is more right than most wrongs on this blog.

620. James Putnam Says:

Joy and David Brown,

David Brown Says:
Comment #613 May 15th, 2012 at 1:23 pm

“From the viewpoint of Christian’s theory of local realism, the universe’s topology of allowable measurements forbids Alice from making a measurement that would provide a counterexample to Bell’s theorem. Alice does not need to whirl herself around the universe because the problem does not arise — there is a tricky continuous measurement function that explains quantum theory. Is David Brown wrong here?”

I found David’s remark compelling and waited for an authoritative response.

Joy: “David Brown is more right than most wrongs on this blog.”

I need more to be said. “… Alice does not need to whirl herself around the universe because the problem does not arise — there is a tricky continuous measurement function that explains quantum theory. What about that “…tricky continuous measurement function…” Anyone is invited to help with this.

James

621. Joy Christian Says:

Sandro,

I agree up to your point 2).

Your point 3) is not quite right. Let me rephrase it in my words:

3) We have functions w(a)w(a, L) and w(b)w(b, L) for which we can write A(a, L) = w(a)w(a, L) and B(b, L) = w(b)w(b, L). These functions are [ my ] cases definitions. What is important is that these equalities hold for the whole domain of the variables L, a, and b. Clearly to state this equality, the codomains of A and w(a)w(a, L), as well as those of B and w(b)w(b, L), have to be the same.

They are the same. It is the parallelized 3-sphere, S^3.

622. Thomas H Ray Says:

Richard, glad to see you admit that you’ve run completely out of argument. Thanks.

623. James Putnam Says:

My last message was not properly punctuated:

“…that explains quantum theory.”

What about that “…tricky continuous measurement function…” Anyone is invited to help with this.

James

624. Elevated Doofus Activity « Pink Iguana Says:

[…] I was Wrong about Joy Christian, here. Sometimes the snark has go to eleven. In response to my post criticizing his “disproof” of Bell’s Theorem, Joy Christian taunted me that “all I knew […]

625. Tsirelson’s bound | MyCQstate Says:

[…] of the EPR paradox and Bell’s work were still being debated (well, they still are even today…). As we saw in the previous post, 20 years earlier Bell had demonstrated that the set of […]