Thursday, October 12, 2017

Experts dispute meaning of Bell's theorem

I mentioned 'tHooft's new paper on superdeterminism, and now Woit links to an email debate between 'tHooft and philosopher of physics Tim Maudlin over it and Bell's Theorem.

The debate is very strange. First of all, these two guys are extremely smart, and are two of the world's experts on quantum mechanics. And yet they disagree so much on the basics, that Maudlin accuses 'tHooft of not understanding Bell's theorem, and 'tHooft accuses Maudlin of sounding like a crackpot.

Bell's theorem is fairly elementary. I don't know how experts can get it wrong.

Maudlin says Bell proved that the quantum world is nonlocal. 'tHooft says that Bell proved that the world is either indeterministic or superdeterministic. They are both wrong.

I agree with Maudlin that believing in superdeterminism is like believing that we live in a simulation. Yes, it is a logical possibility, but it is very hard to take the idea seriously.

First of all, Bell's theorem is only about local hidden variable theories being incompatible with quantum mechanics. It doesn't say anything about the real world, except to reject local hidden variable theories. It is not even particular important or significant, unless you have some sort of belief or fondness for hidden variable theories. If you don't, then Bell's theorem is just an obscure theorem about a class of theories that do not work. If you only care about what does work, then forget Bell.

I explained here that Bell certainly did not prove nonlocality. He only showed that a hidden variable theory would have to be nonlocal.

Sometimes people claim that Bell should have gotten a Nobel prize when experiments confirmed his work. If Bell were right about nonlocality, and if the experiments confirmed nonlocality, then I would agree. But Bell was wrong about nonlocality, and it is highly likely that the Nobel committee recognized that.

At most, Bell proved that if you want to keep locality, then you have to reject counterfactual definiteness. This should be no problem, as mainstream physicists have rejected it since about 1930.

I am baffled as to how these sharp guys could have such fundamental disagreement on such foundational matters. This is textbook knowledge. If we can't get a consensus on this, then how can we get a consensus on global warming or anything else?

Update: Lubos Motl piles on:
Like the millions of his fellow dimwits, Maudlin is obsessed with Bell and his theorem although they have no implications within quantum mechanics. Indeed, Bell's inequality starts by assuming that the laws of physics are classical and local and derives some inequality for a function of some correlations. But our world is not classical, so the conclusion of Bell's proof is inapplicable to our world, and indeed, unsurprisingly, it's invalid in our world. What a big deal. The people who are obsessed with Bell's theorem haven't made the mental transformation past the year 1925 yet. They haven't even begun to think about actual quantum mechanics. They're still in the stage of denial that a new theory is needed at all.
I agree with this. Bell's theorem says nothing about quantum mechanics, except that it helps explain why QM cannot be replaced with a classical theory.
Free will (e.g. free will of a human brain) has a very clear technical, rational meaning: When it exists, it means that the behavior affected by the human brain cannot be determined even with the perfect or maximum knowledge of everything that exists outside this brain. So the human brain does something that isn't dictated by the external data. For an example of this definition, let me say that if a human brain has been brainwashed or equivalently washed by the external environment, its behavior in a given situation may become completely predictable, and that's the point at which the human loses his free will.

With this definition, free will simply exists, at least at a practical level. According to quantum mechanics, it exists even at the fundamental level, in principle, because the brain's decisions are partly constructed by "random numbers" created as the random numbers in outcomes of quantum mechanical measurements.
I agree with this also. No one can have perfect or maximum knowledge, so free will is not really a scientific concept, but it clearly exists on a practical level, except for brainwashed ppl.

But I don't agree with his conclusion:
Maudlin ends up being more intelligent in these exchanges than the Nobel prize winner. But much of their discussion is a lame pissing contest in the kindergarten, anyway. There are no discussions of the actual quantum mechanics with its complex (unreal) numbers used as probability amplitudes etc.
No, 'tHooft's position is philosophically goofy but technically correct. Maudlin accepts fallacious arguments given by Bell, when he says:
Bell was concerned not with determinism but with locality. He knew, having read Bohm, that it was indeed possible to retain determinism and get all the predictions of standard non-Relativistic quantum theory. But Bohm's theory was manifestly non-local, so what he set about to investigate was whether the non-locality of the theory could be somehow avoided. He does not *presume* determinism in his proof, he rather *derives* determinism from locality and the EPR correlations. Indeed, he thinks that this step is so obvious, and so obviously what EPR did, that he hardly comments on it. Unfortunately his conciseness and reliance on the reader's intelligence have had some bad effects.

So having *assumed* locality and *derived* determinism, he then asks whether any local (and hence deterministic) theory can recover not merely the strict EPR correlations but also the additional correlations mentioned in his theorem. And he finds they cannot. So it is not *determinism* that has to be abandoned, but *locality*. And once you give up on locality, it is perfectly possible to have a completely deterministic theory, as Bohm's theory illustrates.

The only logically possible escape from this conclusion, as Bell recognized, is superdeterminism: the claim that the polarizer settings and the original state of the particles when they were created (which may be millions of years ago) are always correlated so the apparatus setting chosen always corresponds—in some completely inexplicable way—to the state the particles happen to have been created in far away and millions of years ago.
No, Bell and Maudlin are just wrong about this. All of that argument also assumes a hidden variable theory, and therefore has no applicability to quantum mechanics, as QM (and all of physics since 1930) is not a hidden variable theory. If Bell and Maudlin were correct about this, then Bell (along with Clauser and Aspect) would have gotten the Nobel prize for proving nonlocality. 'tHooft is correct in accepting locality, and denying that Bell proved nonlocality.


  1. The quantum double slit experiment demonstrates the nonlocality of quantum mechanics, predicted by the equations.

    Bell's Inequality is also used to demonstrate the nonlocality of quantum mehcanics.

    Bell's Inequality, and all the surrounding experiments, did not really add to the notion of nonlocality seen in the double slit experiment.

    And too, all the "quantum eraser" and "quantum teleporation" hype add little new physics to the physics observed in the quantum double slit experiment. :)

    1. Double-slit interference does not prove any non-locality. No single-particle experiment can. You need two or more entangled particles, with experiment on them done at spacelike separation.

  2. Yes, the double slit experiment shows a sort of nonlocality in the sense that you can think of electrons going thru both slits and once. But Bell and his followers wanted to show some kind of action-at-a-distance, and you are right that those experiments do not show additional nonlocality.

    1. Yes!!! :) :) You have the best signal/noise physics blog out there! :)

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  4. The reason you are having so much trouble understanding the fuss over Bell's Theorem is that, unfortunately, you don't understand it either. In particular, it is not about "hidden variable" theories. Indeed, the very phrase "hidden variable theory" has no meaning at all outside of quantum theory, and there it is often as misleading as it could possibly be. (In the pilot wave theory, for example, the particle positions are called "hidden variables" even though they are the very variables that are manifest empirically. It is the wave function that is hidden.) Anyway, Bell's theorem is not about "hidden variables" or even about quantum theory: it is about *any local theory at all*. No local theory, of any sort, can predict violations of Bell's inequality for experiments done a space like separation. (Excluding superdeterminism as incompatible with science, which is what some of the debate with 't Hooft is about.) So if you accept that such experiments really do show these correlations at spacelike separation (and a Many Worlds person might deny that), then you accept that no local theory can be correct: the world itself uses non-local physics. Period.

    What does this show about quantum theory? If you understand it so that it predicts violations of the inequality at spacelike separation then you understand it as a non-local theory. So you should just accept that.

    If you dispute this, as I am sure you will, here is your next task. Go look up Bell's theorem, and identify the step in the theorem where an assumption of "hidden variables" (as opposed to an assumption of just locality) is made. And explain how the theorem fails without that assumption. If you can't do that, stop and think. If you can, we can discuss what you have found.

  5. One more comment. EPR shows that locality implies determinism. This is rather trivial: if anything really indeterministic happened in one of the distantly separated labs, then the only way for the result in the other lab to always anti-correlate with it is for information about the indeterministic outcome to be transmitted superluminally. On the other hand, explaining the EPR correlations locally with a deterministic theory is a piece of cake: that was Einstein whole point. And once you have determinism, you get counterfactual definiteness for free: the theory tells you what would have happened had things been different. But really counterfactual definiteness plays no role in the theorem. The CHSH inequality applies to local indeterministic theories with no perfect correlations. Indeterminism does not get you out of Bell's result, as you mistakenly believe.

  6. I am not the only one saying that Bell's theorem depends on local hidden variables. That is also what the Wikipedia article says, it is what Bell said, and it is what my textbooks say. Local hidden variables are essential to the proof. I really do not see how you can deny that.

    Bell later said that he just needed locality, but that was because he redefinied locality to mean a local hidden variable theory.

    If Bell nonlocality has been proved, then why hasn't anyone gotten a Nobel prize for it?

    My textbooks also deny that EPR proves determinism. You're right that EPR shows that certain experimental outcomes are determined once the emission has occurred, but most textbooks say that there is an inherent randomness in the process.

    1. Wikipedia? Are you serious? Your textbooks?

      I gave you a simple, straightforward task if you think you actually understand what you are claiming: look at Bell's proof and identify the step (it isn't a long proof) where he assumes hidden variables, show how, then show that the proof fails without the assumption. And you respond by saying that Wikipedia says something? And what your textbooks say?

      Bell's work has been almost uniformly misunderstood and misreported, as I document in "What Bell Did". But if instead of thinking for yourself you regard quoting Lubos Motl(!) as evidence of anything then it is clear what the situation is: you don't understand the theorem. You are simply parroting what other people, who also don't understand the theorem, say.

      Of course Bell non-locality has been proved. Over and over. And all of the other obviously non-local phenomena: the GHZ phenomenon, teleportation (which is be really not a violation Bell locality per-se but indicates the information-theoretic transmitting properties of the wavefunction) etc.

      One more time: if you understand what you keep saying, show the step in the proof. If you can't, just be honest and admit you are simply repeating things that you don't really understand. You might get interested enough to learn something.

  7. The key Bell assumption is quoted in that 2014 paper, What Bell Did, by Tim Maudlin: "Let this more complete specification be effected by means of parameters λ. It is a matter of indifference in the following whether λ denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous."

    The "parameters λ" are the local hidden variables.

    You argue that this "makes no contentful physical supposition that can be denied." That is the belief of the hidden variable theorists. The belief might have seemed reasonable before 1925, but not since.

    1. You must be joking again. Where do you find either "local" or "hidden" in that description? And the only reason Bell adds "additional" is that EPR already made clear that if the quantum mechanical description is complete, then the theory is non-local. That's the whole point of EPR (see title). As far as Bell is concerned, you can throw away the wave function and build a theory on whatever grounds you like. As long as it is local it can't violate his inequality (modulo hyperfine tuning, which we are discussing with 't Hooft). So are you saying that if Bell had started this way: "Take any local theory. Let the terms in which the theory describes systems be designated lambda. Lambda can be anything you like: it is a matter of indifference in the following whether lambda denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous", or you actually say that that constitutes a contentful physical assumption that can be denied? Is that your assertion? Yes or no.

  8. No, I am not joking. I am not saying anything radical here either, as I am just defending orthodox textbook quantum mechanics.

    Quantum mechanics uses non-commuting observables. If you identify observables with measured values, calling them lambda or whatever you like, then you get Bell's inequality. But then you have left the quantum world and entered the world of hidden variable theories, because those lambdas commute.

    As you say, it doesn't matter "whether lambda denotes a single variable or a set, or even a set of functions, and whether the values are discrete or continuous". As long as they are non-quantized variables that commute in the lingo of quantum mechanics, then you get a hidden variable theory. If they are also local, then the theory contradicts the Bell test experiments.

    I think Bell switched from calling them "hidden variables" to "beables", but they amount to the same thing.

    If you don't like Wikipedia, an excellent book on the Bell test experiments is The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics. What I say is consistent with that book.

  9. Here are some more links.

    I posted a criticism in 2014 of Maudlin's 2014 paper.

    Reinhard F. Werner also criticized it, with a paper starting: "The Editors of this special issue have asked me to give a comment on Maudlin’s contribution[Mau]. The background is that the paper is rather polemical and takes issue with views which are widespread in the physics community and probably also shared by most of the other authors of this volume." Maudlin replied here.

    I post this quote to show that criticism of Maudlin is not just ignorance of what Bell did. Maudlin's view is contrary to most physicists with expertise in the subject. That does not make him necessarily wrong, of course. A lot of physicists say funny things about quantum mechanics.

    1. Look, this is very clearcut. If you want to talk about Bell's theorem because you actually think that you, personally, understand the theorem then talk about the theorem. If you want to talk about sociology, then that is an entirely different matter. I do not dispute a word about Werner's sociology. The paper is polemical. It is polemical exactly because the vast majority of physicists—even those who style themselves experts—do not understand the first thing about the theorem. In "What Bell Did" I cite a video put out by Physics World, as mainstream physics as you can get, that claims that Bell proved that hidden variables are impossible and hence that the probabilities derived from quantum theory are fundamental randomness, not mere ignorance. And I demonstrated that that could not possibly be the case, since Bell was a strong proponent of the pilot wave theory, which employs hidden variables and is deterministic. These are just plain facts. Don't believe me? Watch the video and read "On the Impossible Pilot Wave".

      This is proof—absolute and irrefutable proof—that the "common wisdom" about Bell is completely and utterly false. They literally have no idea what they are talking about. So citing books and Wikipedia and so on is just pointless.

      If your position is this—you don't really understand Bell's theorem, and you know you don't really understand it, and instead of studying it you intend to just repeat what you hear the most—then fine, just admit it. I will recommend that people not pay attention to what you say, since you acknowledge that you have no first-hand understanding. I will recommend that they read, say, the Scholarpedia article on the subject, not just because it exists but because I know first hand that it is accurate and well written and complete,

      But if you claim to actually understand the theorem, and how quantum mechanics somehow gets around the theorem and remains a local theory despite predicting violations of the inequality at space like separation, then I can inform you that you are deluded.

      As for the lambdas, when you say they have to commute and so one, notice that Bell says not a word about that. You want to use Grassman variables? Be my guest. The theorem still goes through. It might occur to you, looking at the actual proof, that all Bell does with lambda is conditionalize on it and integrate over the distribution of lambdas. And on top of that, the GHZ phenomenon does not even need the integration, since the predictions are not statistical.

      Anyone can see that all you are doing is citing sources, not giving arguments. I assert that every one of your sources is wrong. If you want to defend your claims with actual arguments, do so. If you are only going to make sociological observations, then just admit that's all you have.

  10. I cite authorities because you keep accusing me of not understanding Bell's theorem. It is not just me. You are accusing most expert physicists of not understanding it either, from 'tHooft on down.

    1. Yes I am. Did I really fail to make that clear? That 't Hooft does not understand it, or GHZ, is patent in the exchange I am having with him.

      My point is that you confidently pronounce that I am wrong here, as if you have an informed opinion on the matter. Do you claim you do, or you are just repeating what you read elsewhere? If you think there is a way out of Bell's result for quantum theory, then let's get down to brass tacks and identify what it is. If you are just parroting what you read without any understanding, then just fess up and we can move on.