Wednesday, November 26, 2014

Bell's and sycophants' criticism of von Neumann's hidden-variable no-go theorem is misguided

John Preskill wrote a blog post, Bell’s inequality 50 years later, which argues that "without Bell, the broader significance of quantum entanglement would have unfolded quite differently and perhaps not until much later." Preskill concludes: "We really owe Bell a great debt."

Is every catchy song or paper written using modern tools "intrinsically original"?

Your humble correspondent is much less convinced that the 1964 Bell's paper was either new or pushing the physics research in the right direction. I am closer to Feynman who would say that it is not a theorem that anybody considers of any particular importance in quantum mechanics. Everyone knew that it [the difference between the/any classical local and quantum predictions] would happen, he just demonstrated it mathematically, Feynman says. (See also page 485 here where Feynman just mentions Bell's inequality without even calling it in this way.

It is a nice undergraduate textbook example very explicitly showing the differences between the quantum mechanical predictions and predictions of some simple "local realist" theories a beginner could expect to be relevant. Some people could have still believed that the question whether the probabilistic character of the physical predictions has to be intrinsic would become forever undecidable and that was shown to be wrong.

However, I strongly believe that
  1. the fathers of quantum mechanics could collectively solve the particular thought experiment and see the incompatibility of the quantum vs local realist predictions; even without that, the amount of evidence they had supporting the need for the new, quantum core of physics has been overwhelming since the mid 1920s
  2. much of the explicit findings and slogans about entanglement had been known for 29 years, since the 1935 works by Einstein, Podolsky, Rosen; and Schrödinger
  3. Bell's results didn't really help in the creation of the quantum computing "engineering industry" which would only start in 1970 and which has little to do with all the quasi-philosophical debates surrounding entanglement
  4. most frustratingly, Bell's correct results were served in a mixed package along with lots of wrong memes, unreasonable expectations, and misleading terminology and the negative price of these "side effects" is arguably larger than the positive price of Bell's realizations
Concerning the last point, Bell really remained a champion of the fundamentally flawed Bohmian ways to think about – or classically model – quantum mechanics. He was the man who made it popular for the laymen and deluded physicists to think that quantum mechanics was new because it was "non-local" even though the truth is that the quantum laws controlling Nature are local, thanks to relativity – but they are "non-classical" or "non-realist", if you wish. He has proved that "locality" and "realism" couldn't have been simultaneously true – but he kept on making the fundamental error in deciding which of these two principles is actually right and which of them is wrong.

In some sense, while the anti-quantum movement should have been almost completely killed by Bell's results, it was actually re-energized because one of its members, the quantum mechanics hater called John Bell, was able to write a moderately famous paper. So a cult of personality of a sort was created around this mediocre physicist. The fact that the paper was just another piece of evidence that the main idea underlying the movement is fallacious wasn't a problem for these folks.

More generally, Bell was arguably the main person who helped to degenerate much of the physics culture into the popular-book-driven and media-tainted contest between media fads of the current, postmodern type whose success is being decided by millions of readers who don't have a clue and who routinely interpret physical results exactly in the opposite way than what the results actually imply.

But I want to discuss a particular aspect of the claims that Bell's result – which disproves a sociologically important class of hidden-variable theories – was truly new: John von Neumann's 1932 anti-hidden-variable no-go theorem. Bell and his sycophants have argued for half a century that this theorem can't be counted because it was either completely wrong or didn't eliminate a damn thing.

John von Neumann's proof against the hidden-variable theories appeared in Chapter 4 of
John von Neumann: Mathematische Grundlagen der Quantummechaniek,
Springer, Berlin, 1932 (deutsch)

John von Neumann: Mathematical foundations of quantum mechanics, Princeton
University Press, Princeton, 1955 (English).
I will discuss it momentarily but let me begin with the criticisms. In the 1960s, Bell would offer some strong (and repetitive) words:
Yet the von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, its silly! ... When you translate [his assumptions] into terms of physical disposition, they’re nonsense. You may quote me on that: The proof of von Neumann is not merely false but foolish!
It was not hard to restore the original italicization of the words – the italicized words are "nothing", "silly", and "foolish". Did the mediocre physicist John Bell have some actual reasons to trash the result by one of the true geniuses of the 20th century?

(The Bell cultists typically worship Bell for this criticism as well – but it turned out that Bell just literally repeated a criticism written by an unknown female physicist Grete Hermann in 1935. While the cultists are mostly SJWs and self-described feminist warriors, when it comes to the worshiping of true flagships of their culture, such as John Bell, the fact that he just plagiarized a woman who wrote the same thing 3 decades earlier has to be forgotten.)

The critics generally agree that von Neumann's proof is mathematically valid – that his assumptions do imply the conclusions and there is no logical mistake in the derivation. But they have a problem with the proof, anyway. What is it?

If you study these folks' criticism of von Neumann's theorem (and they copy more than 90 percent from a text by Bell: that's true for Elemer E Rosinger 2004, too), about 95 percent of the texts are repeated expletives and non-technical mudslinging. The remaining 5 percent may be summarized by the following three claims:
  1. von Neumann was implicitly assuming that any two observables \(A,B\) have to commute when he was discussing their sum \(A,B\)
  2. he claimed that the spectrum of \(A+B\) is the set of the sum of eigenvalues of \(A\) and eigenvalues of \(B\)
  3. von Neumann's theorem fails to eliminate the "truly interesting" models of hidden variables such as Bohmian mechanics
You may read von Neumann's original text to see that none of these criticisms is fair. Alternatively, open the 2010 analysis by Jeffrey Bub of University of Maryland:
Von Neumann's 'No Hidden Variables' Proof: A Re-Appraisal
It is not my goal to copy the content of the paper but I do believe that what I would say about the criticism is largely equivalent to Bub's comments.

I will discuss why the criticisms are indefensible momentarily. But before I do so, it may be a good idea to sketch what the theorem actually assumes and says.

In 1932, John von Neumann assumed that for every observable we know in quantum mechanics, there is a function of the "beables" – observables in an intrinsically classical theory with hidden variables – and asked how the expectation value of the observable \(O\) may be calculated from the state \(\psi\). Quantum mechanics tells us its answer to this question,\[

E_\psi(O) =\bra \psi O \ket\psi.

\] The hidden-variable theory should allow you to calculate the expectation value differently, i.e. to have a map\[

E: \HH \times \O \to \RR

\] The expectation value \(E\) has to satisfy three axioms, von Neumann's assumptions. First, for the "unit observable" (one, a constant), we have to have\[

\forall\psi\in \HH: \quad E(\psi,{\bf 1})=1.

\] That's sort of trivial. Second, for a projection operator \(P\in \O\), we have\[

\forall\psi\in\HH:\quad E(\psi,P)\geq 0.

\] That's because the expectation value of the projection operator quantifies the probability of the corresponding No/Yes question and the probability can't be negative. Most nontrivially, we have some linearity in the observables:\[

\forall \psi\in\HH,\,\,A,B\in\O, \,\,\alpha,\beta\in \RR:\\
\qquad E(\psi, \alpha A+\beta B ) = \alpha E(\psi,A)+ \beta E(\psi,B).

\] Fine. Right afterwards, von Neumann straightforwardly proves that \[

E(\psi,O)={\rm Tr}(U_\psi O)

\] where \(U_\psi\) is a positive operator on \(\HH\) with a unit trace. When he applies this partial result on the projection operators \(P_\chi\) projecting on one-dimensional spaces generated by the state \(\chi\), he sees that\[

E(\psi,P_\chi) \in \{0,1\}.

\] You know, in an intrinsically classical theory, the state \(\psi\) is either the same as \(\chi\) or different, so the expectation value must be equal to a sharp eigenvalue that squares to itself. But none of these two values of the function works because they produce the trace of \(U_\psi\) that is either equal to zero or the dimension of the Hilbert space. But it should be one.

The intrinsically probabilistic character of the wave function is needed for quantum mechanics to avoid this paradox. We can no longer say that \(\chi,\psi\) are mutually exclusive. Instead, the probability that a normalized \(\psi\) is the same state as a normalized \(\chi\) is equal to\[

P_{\chi=\psi} = \abs{ \bra \psi \chi\rangle }^2

\] which depends on the state continuously, despite the rule \(P^2=P\) that implies discreteness of the eigenvalues! You may look for the original sources if you need a more detailed treatment or analysis of what von Neumann actually did say. But I think that the broad strategy is rather clear.

Why the criticism is idiotic

I've mentioned that the criticism is a mixture of three points. The first point, the claim that von Neumann forgot about the uncertainty principle, is completely stupid. The nonzero commutator of \(A,B\) is really the key novelty that makes quantum mechanics differ from any classical theory and John von Neumann has appreciated this fact. From the very beginning, he is very careful about the difference between pairs of observables that are simultaneously measurable and pairs that are not. See pages 297-309 of the English translation.

He says that in general, he can't write down a precise description of the procedure to measure \(f(A,B)\) if he has procedures to measure \(A\) and \(B\) but if \(A,B\) refuse to commute with one another. However, even if \(A,B\) have a nonzero commutator, one may talk about their sum and the expectation values of \(A+B\) in a given state may be constrained by his linearity rule.

Some of the critics of von Neumann – and perhaps John Bell himself – even claim that the linearity in the operators doesn't hold in quantum mechanics if \(A,B\) fail to commute. But of course that it does!\[

\bra \psi (A+B) \ket\psi = \bra\psi A \ket \psi + \bra\psi B \ket \psi.

\] Be sure that this holds in quantum mechanics so the critics are making an elementary mistake! What is true is that \(A+B\) cannot be measured by a "multi-staged" measurement in which we would measure \(A\) and \(B\) after each other, in the same repetition of the experiment (i.e. when the initial state is only set once). But von Neumann has never claimed such a thing. Even though \(A+B\) can't be measured in this "multi-staged" way, it corresponds to a Hermitian operator and according to quantum mechanics, it may be measured.

The original 1925 hit above was just "modernized" by the musicians who recorded the 2011 song at the top. Similarly, the 1925 insights about the new quantum mechanical foundations have been just remarketed many times in the following decades but nothing really new has ever been found about the foundations of quantum mechanics.

And quantum mechanics, much like any hypothetical competing theory, has to predict the odds what may happen if we measure \(A\) or \(B\) or \(A+B\). We may end up measuring something else but the theory must have some ready-to-use predictions for either scenario! In particular, a theory must be able to predict the expectation values of \(A\), of \(B\), and of \(A+B\), simply because we may prepare the system in the same state many times and measure \(A\) (or the other two operators) many times to find the expectation value as the average!

So this whole criticism of von Neumann is indefensible, much like the claim that he would think that the spectrum of \(A+B\) is the set of numbers \(a+b\) where \(a,b\) are eigenvalues of \(A,B\), respectively. Such a mistake could be done by a critic of quantum mechanics but John von Neumann really wasn't an idiot!

Bell himself would notice that \(\sigma_x\) and \(\sigma_y\) have eigenvalues \(\pm 1\) but \((\sigma_x+\sigma_y)/\sqrt{2}\) which corresponds to \(\sigma\) along the axis "in between" \(x\) and \(y\) has eigenvalues \(\pm 1\) as well – and not eigenvalues \((\pm 1\pm 1)/\sqrt{2}\). John von Neumann, like any competent physicist after 1925 or 1926, realized that perfectly. He would never claim that the eigenvalues of \(A+B\) may be obtained in this wrong way and his theorem has never implied or suggested such a claim.

So far, my point was that all the criticisms linked to the observation that \(A,B\) usually refuse to commute and John von Neumann would contradict this fact in one way or another – all these criticisms have been spectacularly idiotic.

The final part of the criticism was that von Neumann's theorem failed to disprove the "really interesting hidden-variable theories" such as Bohmian mechanics – which emulate the predictions of quantum mechanics by a theory within the "realist" framework that needs some non-local mechanisms, however.

Indeed, von Neumann's theorem doesn't eliminate such theories. But von Neumann has never made such a claim and these theories are not interesting or viable, either. The main reason why such theories are not viable candidate theories in physics is that they violate the theory of relativity. But von Neumann's proof had nothing to do with relativity – so of course it didn't discuss the problems of similar theories, and they're primarily problems with relativity.

But even if you ignore relativity, there's one purely epistemic reason why von Neumann didn't consider theories such as the pilot wave theory – a reason why it's totally OK to assume that we're not dealing with a theory of this kind. What is the reason? What is the assumption that von Neumann made?

The assumption is that the theory includes a particular set of "beables" and that this set may be mapped, in a one-to-one way, to the observables of quantum mechanics. Bohmian mechanics doesn't satisfy this assumption because there are some extra variables that might be in principle measurable in Bohmian mechanics but they aren't measurable according to the state-of-the-art quantum physics. So these Bohmian theories contradict the known list of "things that may be measured" that was extracted from the experiments. That's a serious problem!

Even if you ignore the state of the experiments, there is still a problem with the "list of beables". Bohmian mechanics needs to assume that there are classical observables that are completely physical because they do influence all other observations; but they cannot be measured themselves. And that's a problem because these observables are "operationally meaningless" yet "physically consequential" at the same moment. These variables resemble God who may affect others but can't be seen or affected – and natural physical theories simply don't allow such one-way "interactions".

Whenever you eliminate this problem, a highly contrived character of the candidate theory that requires some physical observables as well as a waterproof mechanism that keeps them unmeasurable, you're back to the assumptions of von Neumann's theorem and the proof of the theorem applies. You may conclude that given the known values of all the expectation values, quantum mechanics can't be replaced by any realist hidden-variable theory using an isomorphic "list of observables".

A great new cover of the 1925 song was recorded in Czechia because we've had some continuity and decades to think about the theme. The 1925 U.S. song has been used as the jingle of a program for motorists, "Beware the Curve", on the Slovak radio during communism. ("Pozor, zákruta" in Slovak; "Achtung, die Kurve" in East Germany LOL.) The musicians would have never forgotten about the theme; and the physics community would never forget about the discoveries in 1925. People who think that they found something really new and true only think so because they were living in a less educated or sensible corners of the community.

If one looks at all these aspects of von Neumann's proof, it is mostly a consistency check on quantum mechanics and a way to show that certain deviations from the precise quantum mechanical rules would ruin the consistency, indeed. All the "competing theories" are required to work with the sane "list of observables". But this "trivial character" of von Neumann's proof is largely inevitable because quantum mechanics may be shown to be the only "consistent alternative" to classical physics, indeed.

Bell's theorem is just a homework exercise analyzing a simple thought (or, later, real) experiment. And the actual reason why the Bell cultists are worshipping it is not what Bell has proved – but what he hasn't proved, namely all the extra philosophical gibberish that he added into his package and that he defended by his newly earned "political capital" rather than evidence. They worship him because they love to celebrate things like Bohmian mechanics – and so did Bell. But Bohmian mechanics is incompatible with relativity and utterly stupid for many other reasons, especially because it tries to completely revise the "list of observables" and introduce lots of observables (from the mathematical viewpoint) that must be kept unobservable by lots of fine-tuning and conspiracies at the same moment (because we know from the experiments that there's no way to measure them).

In 1932, John von Neumann didn't consider these candidate theories – like the 1927 Louis de Broglie pilot wave theory, currently known as Bohmian mechanics – because he considered it a low-brow conspiracy theory and a contrived set of demagogic ideas by which some people want to reject even the most obvious changes of the physics paradigm that were forced upon us by quantum revolution. John von Neumann shouldn't be criticized just because he wasn't proving theorems about completely deluded ideas and John Bell shouldn't be celebrated for promoting them.

And that's the memo.

I must preemptively say that while the song "If you knew SUSY like I know SUSY" was also recorded in 1925, physicists actually know much more about SUSY than their predecessors did in 1925. That's because there's quite some new nontrivial beef, new maths (first SUSY formulae only began to emerge in the 1970s), and that makes a difference. The "new interpretations of quantum mechanics" are mostly about philosophizing babbling measured by the ability to brainwash the ignorant listeners and if someone claims that some "progress" along these lines has been made, this "progress" is almost certainly bogus.


  1. Lubos - It's even worse than you have written. The so called Bell inequalities were found first (as far as I know), and 100 years before Bell, by George Boole as a condition for the existence of certain marginal distributions.

  2. An excellent point, RAF!

    Your comment really goes to the essence - which is that what Bell did was only to solve a simple problem in old, good, common-sense classical physics - which is what his inequality has to assume. That's why it's so silly to associate him with the most important revolutions in the new physics.

  3. Dear Lubos, Assuming he got it right, I thought Allan Adams' discussion of Bell's Inequality in this introductory lecture on quantum mechanics was almost ridiculously easy to understand for a layman like me. Right up there with Feynman's exposition of the double slit experiment, at least in my opinion.

  4. Hi Lubos, maybe I am mistaken, but you believe that QM is anti-realism because it is local but non realist, is that correct. ans In case is that a personal or a school of thought. and if it is a school of thought, do you have a reference paper/s. Thanks

  5. Quite so! The canonization of guys like Bell and Everett has been like a burr under my saddle for forty years. In a rational world it would be inexplicable.

  6. Good to hear about Allan's clarity.

  7. Dear Qsa, the first sentence isn't about a "belief", you just repeated the same thing twice. Anti-realism is the same as believing that something is non-realist, I believe.

    The papers first deriving that the right underlying theory has to be non-realist are papers by Heisenberg and others from 1925, and the formulation of the insights gets completely clear by 1930 or so. So a canonical reference where all these things are established and comprehensibly presented is e.g. Paul Dirac's Principles of Quantum Mechanics, 1930

    None of these papers and textbooks uses the same terminology, like "realist", because it's a terminology introduced by folks like Bell who were no longer making new discoveries in physics.

  8. This starts at 1:10 and is in practice explained by 1:16.

    So essentially Bell's inequality is that given a set of stuff with binary properties a,b and c, those who are (a but not b) plus those who are (b but not c) are always equal to or more than those who are (a but not c)?

    The last ones are obviously always included in one of the first two, while the first also includes (a, not b, c) and the second (not a, b, not c). Easy enough, but seeing how quantum mechanics breaks the inequality might be harder.

  9. I think your point 1 is partially wrong, Heisenberg could do it alone. In fact there is a book by Heisenberg named "Physical Principles of Quantum Theory", where he shows the result (I didn't read his arguments but result was clearly stated).

  10. Bertlemann's SocksNov 24, 2014, 10:40:00 PM


    I just have to disagree that Bell's result isn't extremely deep. Also, you're not quite correct about Bell "choosing" non-locality over realism. Actually, I don't know what realism means, but if it means pre-existing properties to explain the correlations Bell was looking at, then Bell himself placed an end to realism and fully understood this. That's why he wrote the essay "Bertlemann's Socks". You're correct that Bell adopted non-locality, but not for the reason you say, in Bell's own words, ""It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of local causality' -- or no action at a distance'. Of course, mere correlation between distant events does not by itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles go up or down. For any residual undeterminism could only spoil the perfect correlation."

    -- J.S. Bell

  11. Jolly - "seeing how quantum mechanics breaks the inequality might be harder.

    The point, I think, is not "seeing how" QM breaks it but rather the experimental fact that it does.

  12. Hi Lubos, maybe I am wrong, but you believe that QM is anti-realism because it is regional but non realist, is that appropriate. And In situation is that a individual or a approach. and if it is a approach, do you have a referrals paper/s. Thanks

    Incinerador de Grasa

  13. Thanks for an insightful blog, Lubos, as always. I have long been uncomfortable with Bell’s “contribution" to physics and I am now satisfied that what he did was of little positive significance and his work surely led to a massive increase in the popular confusion regarding QM.
    Theoretical QM is surely one of the greatest accomplishments of the human mind in its beauty and perfection; isn’t it?

  14. Dear Lubos, you shouldn't be so modest -- no one can disagree about the shallowness of Bell.
    But I have a question about the appraisal of von Neumann -- Isn't this 1932 book of his the place where the "collapse of the wave-function" was first enshrined as an axiom of quantum mechanics? I have not opened the book in a long time, but one often sees it quoted by the Everettian fanatics (and perhaps less so by the Bohmians?) as a starting point for their suicidal attacks and silly ramblings. On the other hand, the earliest writings (by Bohr, Heisenberg, Born) seem to show a much better appreciation of the subtleties involved. I might believe that as a physicist he understood what was going on, but am sometimes wondering whether we shouldn't give the "mathematician in Neumann" at least a little bit of the blame for the current desolate situation with "interpretations of QM".

  15. I didn't know that about the largely self-taught genius, George Boole. The physical instantiation of his logic/algebra was done mostly by Claude Shannon in his astonishing paper--A Mathematical Theory of Communication

  16. I cannot say it is my opinion, since I just picked it from reading 'around', plus I am no historian of science, but I would estimate that quite a few QC researches would not agree with the point 3.

  17. And it comes from Preskill, who, by his own admission, is much more interested in QC, than in fundamental physics, these days. So count me as not surprised.

  18. Right. I have not read every piece of literature the QM founding fathers would write but I've read enough to make the prediction that a text of the kind you mention does exist. They had the spirit, all the required technical tools, and knew about all the consequences concerning questions what happens in arbitrary experiments where a small number of qubits (or finite, small, discrete amount of quantum information) is measured, using a semi-modern jargon.

  19. Tony, I know. The set of people does include John Preskill, I think, and this fact was the actual main reason why this blog post was written.

    Look what the timeline of quantum computing in a generic encyclopedia looks like:

    Before 2012 and ignoring "Belle", "Bell" only appears twice - in Bell Labs. And I feel the urge to point out that Bell Labs were named after a man called Alexander Graham Bell, not John Bell. ;-)

    If one reads the individual entries in the history above, it's very clear that the advances that led to realistic quantum computing had nothing to do with Bell's mostly popular writing on foundations of QM.

  20. Thanks, Johannes, and I have the same understanding for the history of the collapse. This notion wasn't discussed, at least not prominently, before the von Neumann 1932 book. And the von Neumann 1932 comments were just catchy or provoking enough and people would associate the new things with the Copenhagen school. But while he was extremely close, I don't really count von Neumann as a member of the Copenhagen school (owning the interpretation) anymore. He was a slightly idiosyncratic guy with an immensely good understanding of the new QM, doing lots of mathematical things about it, but not really one of the true fathers of the new physical theory.

  21. Thank you, Gene, for showing me that this feeling may have been "out there" for quite some time. The amount (and I would even say, near-monopoly) of the misleading popular writings about quantum mechanics seems overwhelming today but its growing trend may only be fully seen with the hindsight. And I think that with the hindsight, John Bell's approach was crucial for the rise of the "popular for masses" writing about physics and its increased influence over the preferred language among the professional physicists, too.

  22. Dear Socks, I don't think that the particular quote you copied reveals whether he would believe that locality or realism is wrong in Nature. It's a typical quote in which he doesn't really distinguish these two assumptions.

  23. Well, Luke, there may be many points.

    My point would be exactly the opposite of yours. The most important point here - the bulk of the truly nontrivial knowledge connected with the experiment - is to understand how to derive the correct prediction (which disagrees with Bell's inequality) from the right theory, quantum mechanics.

    Being able to measure that a number is something - and outside an interval - is trivial, and so is the inequality derived assuming classical local physics. The hard part is the theoretical part of quantum mechanics, and that's exactly the part that the people who are focusing on Bell's writing never learn properly.

  24. I've often wondered what exactly it is that goes wrong if it were found possible to send information via entanglement (say one could skew the randomness slightly in some unusual but controllable circumstance). Obviously this is speculative, would require a modification of QM and relativity, and has never been observed (maybe that is already enough for it to not be worth considering :) ), but light would still travel at light speed, and clocks would still not be able to be universally synchronised, as a clock at one end of the communication channel could be ticking at a different rate than a clock at the other end (say in a different gravitational field). So what would be the real killer argument from a physics point-of-view that shows this could never happen?

  25. OT - John T. Neer attended Feynmann's lectures at the Hughes Aircraft Company from 1966 to 1971. He has made his extensive notes on these lectures available here:

  26. Sorry, I am not able to respond to such a sequence of emotions. You made about 12 different statements and each of them is wrong. To answer doesn't mean to answer one partial thing, or to fix one or two errors in your thinking. To answer means to teach you about 10 years worth of physics because you are ignorant about completely everything that is relevant here.

    It is wrong to suggest that a contradiction with relativity - the speed limit - is no big deal. Relativity is one of the 2-3 main pillars of physics as we know it, and physics is the most fundamental discipline of natural science. So it surely *is* a big problem and a killer argument. It's wrong to suggest that a contradiction with QM is no big deal. Similar comments, years of your missing knowledge.

    It's wrong for you to say that in a world contradicting the Lorentz symmetry, light would still move by the same speed. Massless particles and waves move the preferred speed because this speed plays a preferred speed in the structure of the spacetime - because of the Lorentz symmetry. If the world didn't respect special relativity - and it wouldn't if superluminal propagation of information were possible - then there would be even no reason for light of different colors to propagate by the same speed. Every different thing in the world would propagate by a different speed, and the speed would also be affected by the speed of the source and the speed of the observer.

    Of course that if you say that not even relativity, quantum mechanics, or any insight or observation known about about Nature is a strong or "killer" argument for you and you are ready to dismiss any argument like you, there won't be a way to convince you about any claim about Bell's inequality - or anything else in the world. But that's not a proof of a defect of physics or some arguments - only about defects of yours.

  27. Could you please elaborate on this? Perhaps give an example?
    Sorry, but on the face of it, I don't understand how what you write can possibly be true.

  28. J. Bell : a mediocre physicist ? Do you talk about the same guy who discovered with R. Jackiw (and independently S. Adler) chiral anomaly, such an important phenomenon in quantum field theory? I can agree with all your technical arguments to support QM against classical zealots but the pedagogical value of this post is greatly devalued if you would not recognize the pedagogical one of the Bell's theorem and do not differentiate the old-fashion conceptions or words of Bell from the sixites with the loosely-defined concepts of a large number of contenders of QM nowadays.

  29. We are likely talking past one another because what I said is easy to see:

  30. Of course breaking QM and relativity is a big thing, and I am happy working within those frameworks. The motivation to try and break them was to see if there would be any way that free will could possibly operate in the universe (which according to QM, relativity and string theory seems not possible). One hypothetical is that free will could produce an experimental outcome deviating from chance. If that could be applied to entangled particles, that would imply FTL information transmission. Sure, it would mess things up, but there is some small (and not convincing to some) evidence that free will exists (in the sense that it feels like it does, and would support ideas that we have responsibility for our actions, make choices, etc). Ultimately it is observation that is the decider, and it is the observable consequences that are the killer. Would you say that free will is an illusion?

  31. I think the book Consistent Quantum Theory by Robert Griffiths is a better book for a beginner. It is really written for people who are uneasy with quantum mechanics. Of course everything Dirac says is true but Griffths emphasize important things again and again and point you where people do mistakes when discussing so called paradoxes in quantum mechanics. He calls wave function as "pre-probability", gives a well defined mathematical statement of the fact that realism is not true called "single framework rule" and so on. Of course I agree with you that all of important things are understood people like Dirac, Heisenberg, and Feynman but Consistent or Decoherent Histories presents clearer discussion. Consistent Histories says things like properties before measurement that you don't like but the formalism gives completely true predictions for all observations so there is no problem. I am upset that you decided not to emphasize consistent histories after viewing interview of Gell-man. I actually understood quantum mechanics thanks to many posts of you and you were the one who pointed out consistent histories to me (really thanks).

  32. Thanks. You're right! It IS easy to see when given the correct reference!

  33. Free will is a complex word game but a simplification of the issue is to simply ask if higher order machinery can have emergent properties that render bottom up reductionism moot?

    “No, this trick won't work... How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love? ”
    ― Albert Einstein

  34. Dear Luboš,

    I have a new book coming out soon based on things such as I have seen on the internet, heard at dinner parties (after lots of alcohol has been consumed by the suburban philosopher guests), read in esteemed publications such as Scientific American, New Scientist and various other comics quality outlets, and seen on TV programmes produced by the BBC.

    I was wondering if you'd write a nice preface to it for me to give the thing added intellectual clout, and of course to help it sell better?

    It's called Quantum Quackery For Dummies.

    You wouldn't have to work hard at it. All you need do is sling a heavy smattering of technical terms into some pretty turgid prose and say what a wonderful book it is. Yes, just chuck in plenty about entanglement spaces, Hilbert uncertainty, government vectors, Caesarian operators, Bell's ringpiece ... that kind of thing. Just make it look good to your average dummy. You can sign it by whatever name you like (best avoid using your own). The publisher will add the bit about you being a five-times Nobel Physics & Gender Studies Laureate and Bingo! We could both get rich quick!

    Whaddya say? :)

    BTW, if you say no I'm gonna have to approach John Carrol. Sorry, I mean Sean Carrol. That is his name isn't it? Is it? Anyhow, I figured he'd try to muscle in on the content too and want to add his own shit. That's why I approached you first — I know you wouldn't touch shit with a bargepole so I can claim full credit for the content. We'll split the money 50/50 though, and you have my word no one will ever find out it was you. OK? Deal?