## Archive for the ‘Bell’s Theorem? But a Flesh Wound!’ Category

### Bell’s-inequality-denialist Joy Christian offers me $200K if scalable quantum computers are built Wednesday, May 2nd, 2012 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.”