Talk:Bell's theorem/Archive 8

The Born rule
The Born rule is usually introduced for an experiment with a very feeble beam with detectors arranged so that only one will click at a given time, indicating the presence of a single particle in a single output channel of the several output channels of a quantum analyzer (for example a Stern—Gerlach apparatus). Such channels, all outputs from a single quantum analyzer, are mutually compatible. If other analyzers are in the set-up, for other particles of the system, they can be chosen in various ways, by an external agent. Those chosen ways should be listed in the statement of the experimental result. The choice of the analyzers is not ordinarily described by the Schrödinger equation. It is in some respects analogous to a thermodynamic operation, not part of the usually considered internal dynamics of the system. This needs to be taken into account for Bell experiments with a delayed-choice protocol, which are crucial for the Bell reasoning. The Born rule then needs to be stated so as to account for the coexistence of the several analyzers.Chjoaygame (talk) 19:03, 11 October 2015 (UTC)


 * Surely, the Born rule is intended for very simple, highly idealized experiments. In less simple cases, I'd say, we have two ways: (a) include all relevant macroscopic apparatus into the quantum system and then apply the Born rule to an (unproblematic) "secondary" measurement of the outcomes of these (fully decohered) macroscopic apparatus; or (b) use quantum operations and quantum instruments. Hopefully now I use the Latin "apparatus" better. :-) Boris Tsirelson (talk) 19:23, 11 October 2015 (UTC)


 * My intention was to be vague. I just wanted to note that with several detectors, as in the Bell experiments, the simplest version of the Born rule needs to be suitably upgraded, not intending to say how that should be done.


 * My present understanding of the Born rule in its usual simple form is that it refers to the probability of detection of a particle by a detector sitting in an output channel of a single quantum analyzer. For example, a detector in an output channel of a polarizing beam splitter. I imagine more complicated cases of several particles in the system, with several analyzers (with their respective detectors), one for each species of particle, for example. At least that seems to be how they do Bell experiments. For this purpose, I don't envisage considering the analyzers as other than, for example, several macroscopic polarizing beam splitters; not treating them as internal parts of the quantum mechanical system and trying to describe them through their contributions to the Schrödinger equation of the system. I am not familiar with talk of 'quantum operations', but it would make good sense, I guess, to say that switching the orientation of a polarizer is a 'quantum operation'?


 * Looking at the articles you link, I see that the terms 'quantum operation' and 'quantum instrument' have been pre-empted, and defined in more or less abstract mathematical terms that hide or avoid or elide the simple physical kind of meaning I have in mind. Khrennikov has a footnote: "The quantum formalism does not account this sort of randomness. Random generators used in the experimental tests based on the Bell-type inequalities are not described by operators in the complex Hilbert space. They are considered as “technicalities”; often this sort of randomness is related to the freewill of an experimentalist." My guess is that it is beneath the dignity of quantum theory to talk about such practicalities. Some very careful thermodynamic texts (e.g. Tisza) talk deliberately and explicitly about thermodynamic operations in the sense that I mean here. They are essential to a logical treatment of macroscopic thermodynamics.


 * If one really wants to emphasize that one is talking about several distinct devices, I think it is natural enough to treat the word as English and to write 'apparatuses', but others might disagree.  Chjoaygame (talk) 21:44, 11 October 2015 (UTC)Chjoaygame (talk) 22:16, 11 October 2015 (UTC)


 * Do you really mean "thermodynamics" rather than "statistical mechanics"? Why?
 * About "beneath the dignity of quantum theory", this is up to you. If you can unite all the physics into a single consistent all-embracing theory able to analyze real-life experiments out of the first principles without drastic simplifications, just do it, urgently. :-)
 * As far as I know, use of temperature and other thermodynamical variables in relation to quantum measurement theory, as inherently classical variables, started in 1960:
 * H. Wakita, "Measurement in quantum mechanics", Prog. Theor. Phys. 23, 32-40 (1960);
 * A. Daneri, A. Loinger, G. Prosperi, "Quantum theory of measurement and ergodicity conditions", Nucl. Phys. 33, 297-319 (1962).
 * (Refs taken from Khalfin & Tsirelson 1992, see [52] and [244] there; also [53]. Mentioned on pages 901 and 905 there.)
 * Boris Tsirelson (talk) 05:53, 12 October 2015 (UTC)


 * I was not seeking there to cover a major area of physics, or to settle a deep question. I just intended to say that, in accounts of Bell practical experiments, the switching of the orientation of the polarizing beam splitter is not usually considered as a dynamical process described by the Schrödinger equation. Macroscopic thermodynamics is no more here than an instance of a subject where there is an explicit distinction between the internal adventures of the system (the process), on the one hand, and things that are done to it from the outside (the operation), on the other, but how that difference is carried out is not discussed in detail.


 * As I think about it, the following question comes to my mind. Allowing unprejudged in logic the contemplation of the possibility that the delayed-choice setting of the orientation of the polarizing beam splitter might affect the result, should one properly include the beam splitter as a component of the quantum system and put its dynamics into the Schrödinger equation for the system? I guess that might have been what you had in mind in a comment you made just above? If, following the orthodox view, one defines one's 'system' as separate from one's 'observational apparatus', and then inquires as to the 'effect' of a delayed-choice orientation switch, has one not moved the goal-posts while the ball is in flight, changed the rules of the game in the middle of play? Is that permitted in soccer?Chjoaygame (talk) 08:52, 12 October 2015 (UTC)


 * But wait. Bell theorem does not need quantum theory to be correct (correctly used) at all.  All we need from quantum theory is advice, how to arrange experiment that will give CSHS>2.  After successful experiment of this kind, even compete collapse of the quantum theory would not harm Bell theorem.  Thus I wonder, what do you really want to say. Boris Tsirelson (talk) 11:17, 12 October 2015 (UTC)
 * Ah, no, there is a problem, The real experiment differs from the thought experiment. In the thought experiment, Alice is on the Earth, while Bob is on the Moon. They have some seconds to exercise their free will.  In the real experiment, we are asked to believe in some apparatus, that it is indeed nothing but classical randomizers.  Yes, clearly a loophole.  Boris Tsirelson (talk) 11:27, 12 October 2015 (UTC)


 * I'm not working from a well-thought-out plan here, I'm just feeling my way. The CHSH inequalities involve several different expectations, that each rely on random polarizer settings. Are we dealing with a single experiment on one singlet system, or with several incompatible experiments on differently tested singlet systems? How do these various items fit into a single probabilistic and physical scheme?Chjoaygame (talk) 12:01, 12 October 2015 (UTC)


 * Each singlet is prepared, measured once, and lost (destroyed). This happens many times, with randomly chosen settings. Thus, we accumulate statistics for the four cases (2x2=4 settings); these cases get different sample sizes, but all four sizes are reasonably large. Now we calculate the four approximate probabilities, and finally, calculate CHSH. Well, in addition we probably calculate also confidence interval or something like that. Boris Tsirelson (talk) 12:54, 12 October 2015 (UTC)
 * Or maybe not; really, I never checked, since asymptotically, for large n, it is all the same. Maybe we treat each outcome as "win" or "loss" in the game (randomization of the inputs is the part of the game), and then calculate the approximate wining probability; if it clearly exceeds 0.75, we get excited... Boris Tsirelson (talk) 13:00, 12 October 2015 (UTC)


 * By the way, the game form of CSHS appears in "Quantum nonlocality". Boris Tsirelson (talk) 16:48, 12 October 2015 (UTC)


 * We are thinking of a 'classical' scheme when we intend to derive the Bell and congener inequalities. 'Classical' schemes are deterministic and admit neither randomizers nor random experimental results. Classical physics does not admit that Alice or Bob has free will. So I think we are blocked from the very beginning from our intention to carry out the Bell derivation as an example of a classical scheme. Only quantum physics admits random physical processes. An assumption of free will is already a huge metaphysical leap of faith. The existence of randomizers is another metaphysical leap. Assuming these things, it it no surprise that we can then overthrow causality. Our argument has assumed that it doesn't hold.


 * Classical physics assumes continuity, while the Bell and congener inequalities assume discontinuity. No wonder the consequences of the Bell assumptions rule out classical causality.Chjoaygame (talk) 20:13, 12 October 2015 (UTC)


 * Not so simple. Classical physics is not only classical mechanics but also classical statistical physics. Molecular chaos is a huge reservoir of pseudo-randomness that is the same as randomness for all practical purposes. This is the harmony between determinism and free will in classical physics. In quantum physics this harmony is broken, and now Gerard 't Hooft is brave enough for rejecting free will; see "'t Hooft's views" in Talk:Superdeterminism. Boris Tsirelson (talk) 20:30, 12 October 2015 (UTC)


 * Starting from your link to Talk:Superdeterminism, I followed some further links. I reached the following in the article Hard problem of consciousness:

Consciousness is fundamental or elusive Some philosophers, including David Chalmers and Alfred North Whitehead, argue that conscious experience is a fundamental constituent of the universe, a form of panpsychism sometimes referred to as panexperientialism.


 * This is a fine example of the misleading effect of the regrettable custom of inventing terms that end in '-ism', and conducting further discussion in those terms . For this example, one can easily understand how the writer reached his statement, and how it might be seen as accurate, assuming his '-ism' mind-set. But the overall effect of his statement is almost to make black into white. The expression 'Chinese whispers' comes to mind. Each step of '-ism' talk leads a little further into muddle, with near-nonsense the eventual outcome. (Of course, I hardly need say that '-ism'-ism intends to be "quick and efficient".) I will likely try to chat more, but not, I think, right here and now.Chjoaygame (talk) 06:31, 13 October 2015 (UTC)

Question from Martin
Chjoaygame, can your argument be summarised by saying that, in classical mechanics (without giving humans some special properties outide known physics) nothing can be truly random. Things can be chaotic or pseudorandom but ultimatley, in classical mechanics, everything is fundamentally deterministic. On this basis, because the two random number generators are not truly random, and share the same ancestry, so to speak, a greater than expected correlation between spacelike separated events is possible in classical mechanics? Martin Hogbin (talk) 15:33, 13 October 2015 (UTC)


 * (This anxiety is often called "conspiracy".) Boris Tsirelson (talk) 15:54, 13 October 2015 (UTC)


 * Yes, thanks for reminding me of that. We did briefly talk about it before, it is one of the ways out of the EPR/Bell problem that people do not like very much. I have not had time to study the Khrennikov paper properly so I was just taking a stab in the dark.  Martin Hogbin (talk) 17:31, 13 October 2015 (UTC)


 * Basic rule of life: when wondering whether something is due to conspiracy or mistake, go for mistake every time!!Chjoaygame (talk) 16:20, 13 October 2015 (UTC)


 * I guess you asked a fair question, but, no, Editor Martin Hogbin, that's not, repeat not, my argument here. Far from it. My argument here is: the fact that the orientation of the polarizing beam splitter is changed in some effectively random way needs to be taken account of in the calculations. The result of the calculations depends on whether or not the orientation was moved. It doesn't matter why or how it is moved, but it is an unpredictable thing and that unpredictability is part of the randomness of the experiment.Chjoaygame (talk) 16:27, 13 October 2015 (UTC)


 * Thanks for your reply. I will carry on thinking about the problem.  Martin Hogbin (talk) 17:31, 13 October 2015 (UTC)


 * I agree that it seems to call for some thinking. It occurred to me this evening as follows. Would an equivalent to the delayed-choice analyzer-rotation protocol be as follows? One of the twin photons passes though a randomized beam deflector. The deflector passes the photon either to analyzer $a$ or to analyzer $b$, both at the same station number 1. Come think of it, it seems to come to mind that indeed that's how the Bell experiment is sometimes done? Instead of randomly rotating one analyzer, the equipment randomly sends the photon to one of two relatively rotated fixed-orientation analyzers. Now there are four detectors for the station 1 that has the delayed-choice between two analyzers. Two detectors for the station 2 that has only one analyzer, with a fixed orientation. Six detectors altogether. Provided the beam is very feeble, only one of the four choice-side (station 1) detectors will click at the time of clicking of one of the two fixed-orientation detectors. I think this makes it easier to see why the delayed-choice protocol needs probabilistic analysis different from that for the no-switch protocol.Chjoaygame (talk) 18:57, 13 October 2015 (UTC)

Superdeterminism - "Least" popular?
I really like your lede, which I only just now read because in the past I was combing for calculations. But this sentence bothers me:

I am not claiming that this is a "popular" way to address the theorem, but that no view is "popular". The statement in question seems to imply that popular views exist. It also implies that scientists disfavor this view when I think they are sublimely neutral to it. I think the most common view among experts is bewilderment that ranges from mild to extreme. I don't think any philosophical view is "popular", except perhaps that looking for a hidden variable theory is a waste of time. If people agree, then we can look for a subtle change in the wording. Perhaps this:

In conclusion, the phrase "least popular" carries the connotation of "disliked". Personally, I found this view fascinating for a few days, and then decided to live the rest of my life as if I had free will-Guy vandegrift (talk) 14:19, 19 October 2015 (UTC)


 * I even thought about creating a one-dimensional universe with a big bang that consists of N identical non-interacting pairs of entangled particles travelling at different speeds (with Gaussian probability for position/momentum, centered spatially at the origin). The initial orientation of the observing filters would be predetermined, but the outcome of each measurement would determine the next measurement's orientation.  This would be a trivial but tedious problem to solve, made complicated by the possibility of the "slow" particles arriving at the detector before the "fast" ones did.  Sounds like a nice project for a gifted young student, but not worthwhile for an adult.--Guy vandegrift (talk) 14:33, 19 October 2015 (UTC)

I do not think we should editorialise in this manner at all. We should write:

Martin Hogbin (talk) 18:59, 19 October 2015 (UTC)


 * I agree. Strictly speaking, we shouldn't say "obscure" unless a source labels it as somehow "less popular" (if there is such a source, I'm certain the author meant "less common" instead of "less will-liked"). Feel free to change it. I am a Wikiversity writer and avoid editing WP whenever possible.--Guy vandegrift (talk) 19:16, 19 October 2015 (UTC)


 * Not sure about source, but it seems to me that it EVIDENTLY is MUCH less popular. Look for example at articles about games using entangled states. Almost all authors call them "nonlocal games", "nonlocal strategies" etc. So much so, that I, in my Citizendium article, was forced to emphasize that there are three principal assumptions, and locality is one ("first") of them, but there is also "second" (my pet), and, well, "third". Last years the third one is taken seriously by 't Hooft; and is discussed, after him, by several other authors. I do not know the future, but for now still most physicists did not hear about "second" and, the more so, "third" option. Boris Tsirelson (talk) 19:25, 19 October 2015 (UTC)
 * Sorry, I changed it before I read this. Martin Hogbin (talk) 19:35, 19 October 2015 (UTC)
 * Could we say something more specific like 'least studied'. Of couse that is because it is beyond the scope of physics but it is at least an indisputable fact.  Martin Hogbin (talk) 19:37, 19 October 2015 (UTC)
 * According to 't Hooft, it is not "beyond the scope of physics". But for now he still has few followers. And, I guess, Richard Gill will claim (with sources) that Bell did not take the third option seriously. (I remember he did already.) Boris Tsirelson (talk) 19:43, 19 October 2015 (UTC)
 * More information about 't Hooft and superdeterminism may be found in archived discussion here: Dispute_resolution_noticeboard/Archive_123. Boris Tsirelson (talk) 19:52, 19 October 2015 (UTC)
 * No, even better, this discussion: Articles_for_deletion/Superdeterminism. Boris Tsirelson (talk) 19:55, 19 October 2015 (UTC)
 * I do not think that 't Hooft he says that superdeterminism is not beyond the scope of physics, he says, ' The definition usually employed is clearly invalid in strictly deterministic theories' and then he propses an alternative model of free will. He does not say that 'The definition usually employed' is within the scope of physics.


 * Anyway, if we put something clearly factual like 'least studied' ther is no need to discuss this point. Martin Hogbin (talk) 21:26, 19 October 2015 (UTC)

I reverted back to referring to superdeterminism as "one of the least popular ways" because no consensus has been reached. Bell himself refered to it as implausible, and Boris Tsirelson gave evidence. My suggestion was not that we change the meaning of the sentence, but merely the word chosen to convey that meaning. "Unpopular" when referring to humans means annoying or lacking friends. The word just had too many connotations for me, and I though "obscure" was better suited.--Guy vandegrift (talk) 09:54, 20 October 2015 (UTC)

Aug 2015 experiment Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
New experiment, results to be peer reviewed. May be a future addition after peer review agrees with the results. http://www.nature.com/news/quantum-spookiness-passes-toughest-test-yet-1.18255?WT.mc_id=TWT_NatureNews http://arxiv.org/abs/1508.05949 JScience 17:04, 29 August 2015 (UTC)jcardazzi


 * Very nice, thank you!
 * And please sign your remarks (on talk pages) with four tildas: ~ . Boris Tsirelson (talk) 17:44, 29 August 2015 (UTC)

See also https://en.wikipedia.org/wiki/Bell_test_experiments (and perhaps also https://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experiments) Richard Gill (talk) 06:34, 5 September 2015 (UTC)


 * Final Loophole David Kaiser Additional thought:The experiment has closed two of the three major loopholes beautifully, but two out of three isn’t three,” Dr. Kaiser said. “I believe in my bones that quantum mechanics :::is the correct description of nature. But to make the strongest statement, frankly we’re not there.”


 * A potential weakness of the experiment, he suggested, is that an electronic system the researchers used to add randomness to their measurement may in fact be predetermined in some subtle way that is not easily detectable, meaning that the outcome might still be predetermined as Einstein believed.


 * To attempt to overcome this weakness and close what they believe is a final loophole, the National Science Foundation has financed a group of physicists led by Dr. Kaiser and Alan H. Guth, also at M.I.T., to attempt an experiment that will have a better chance of ensuring the complete independence of the measurement detectors by gathering light from distant objects on different sides of the galaxy next year, and then going a step further by capturing the light from objects known as quasars near the edge of the universe in 2017 and 2018."
 * http://www.nytimes.com/2015/10/22/science/quantum-theory-experiment-said-to-prove-spooky-interactions.html?:::emc=edit_th_20151022&nl=todaysheadlines&nlid=58413496&_r=0
 * --CuriousMind01 (talk) 13:56, 22 October 2015 (UTC)

Confusing terminology


We have Determinism, Superdeterminism, Hard determinism, Fatalism, and Predeterminism.

For a start, can anyone put them in order of 'hardness'.

Is there agreement on the correct term for the philosophy that the future of the universe and everything in it, including human actions and though is absolutely fixed and immutable?

In Bell's statement, '...absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the ‘decision’ by the experimenter to carry out one set of measurements rather than another,...',which of the above is he referring to? Martin Hogbin (talk) 21:46, 19 October 2015 (UTC)


 * As I stated above, I like this lede. The boxes put me off as I skimmed it because I thought they were attempts at rigorous definition.  Instead they are well-known attempts to explain the unexplainable.  Not all these people chose the right words, or they might have chosen the right words at a time or place when these words carried different connotations.  Bell was speaking in a radio interview when he used the words "implausible" and "superdeterminism".  Did Bell publish any papers on the subject?--Guy vandegrift (talk) 10:16, 20 October 2015 (UTC)


 * On Wikiversity, where it is the custom to start a parallel article instead of editing the writing of others, I replaced the content of this article's lede by one sentence: Bell's theorem has no more business than sunsets and sunrises to be paradoxical. It conveys the wide range of views one can legitimately take, and is sort of a portmanteau of comments by Marmin and Tovey. --Guy vandegrift (talk) 10:26, 20 October 2015 (UTC)


 * I can't rank in order of "hardness", but I now understand the lede:  Bell was was looking for a theory to replace Quantum mechanics in which variables "existed" before they were measured. He characterized his "superdeterminism" as "implausible", and the idea is "not popular" for good reason.  In this scenario, the universe is a gigantic "clock" in which all the variables are predetermined to obey what we know as quantum mechanics.  The same initial conditions that caused the polarization of an entangled photon to lie in a given direction also cause the humans to construct the experiment to measure that photon's polarization along that prescribed direction.  It is a clock where the behavior of every single atom was choreographed from the beginning.  It was implausible to Bell and not popular in the eyes of the editors of this article.  The phrase "one of the least popular" should stand, IMHO.  previous comment by same user was stricken --Guy vandegrift (talk) 14:25, 21 October 2015 (UTC)
 * What meaning do you intend to convey my the word 'unpopular'? Do you mean that it is not studied by physicist much (if at all)?  If so then I agree with you, but why not state that fact more clearly.  Do you mean that physicists, or mathematicians, or the public at large find the idea umpalatable or disturbing?  If so who says this?  Did Bell dislike this idea?  Does 'unpopular' refer just to the editors of this article.  If so, in my opinion it is unjustified and vague editorialising.  Words like 'implausible' do not have any meaning in this context.


 * I know perfectly well what Bell meant. Exactly as you say, the universe is an already-written and immutable book. That philosphy is a very ancient idea that has been discussed for centuries.  The generally  opinion on the subject is that there is no conceivable way of testing the idea experimentally; it is a logical impossibility in that, whatever results may be obtained from whatever experiment it is always possible to say, 'that is what was ordained'.  For that reason Bell's superdeterminism (or whatever we agree to call it) lies outside the scope of physics is therefore, by definition. 'unpopular' with physicists.


 * My dictionary defines 'determinism' as 'the philosophical doctrine that all events, including human actions and choices, are fully determined by preceeding events and states of affaires, so that freedom of choice is illusory'. This seems to me to be what Bell meant.  In order to get some experimentally testable predictions many people seem to have 'softened' the meaning of some of the the various words for this concept so that we now need to invent new ones for the original idea. Martin Hogbin (talk) 15:18, 21 October 2015 (UTC)


 * As I stated when I re-introduced this discussion of the lede, I am concerned with the connotations associated with the word "least popular". I agree with you that "implausible" is not an appropriate word, but it is the word that Bell chose.  Also, I am not comfortable with the Bell's mention of free will.  I think what Bell was referring to was the extreme sensitivity to initial conditions.  I don't know if Bell was thinking about the butterfly effect, but if he was, it's a pretty "implausible" butterfly that can simultaneously change what happens near a detector, and what happens inside the atom that created the entangled particles.  We can't edit Bell's words, but perhaps we can come up with a brief paragraph that expresses Bell's sentiments.  I know Wikipedia frowns on long footnotes, but I would put Bell's words in a footnote.  Personally, I frown on long ledes.   As is often the case, I am not entirely comfortable with the lede, but can't think of a better one.  One option might be to improve Wikipedia's Superdeterminism.  Does the word "superdeterminism" have any meaning outside the context of Bell's interview?  I have no idea.


 * As for the word "superdeterminism", how do you get more deterministic than "deterministic"? I think it's just a superlative prefix that Bell added to emphasize how amazingly implausible a Newtonian "clock" universe would be if it also obeyed quantum mechanics. All this is why I prefer to write in Wikiversity where I am free to express ideas in my own words.


 * I guess we should put it to a vote. I reverted your edit because I felt responsible for triggering the edit and also felt guilty for raising the question before I managed to understand what the lede was trying to say.  If you revert my revert, there will be no edit war from me.--Guy vandegrift (talk) 16:47, 21 October 2015 (UTC)


 * I am not going to fight about 'unpopular' either. There is a common misconception though that I believe should be dealt with in the article somewhere though, and that is the idea that QM is incompatible with determinism.  The odd thing is that it is fully compatible with the most extreme form of determinism (whatever we choose to call that) but lesser forms, in which the actions of inanimate objects are fully deterministic, but humans (and maybe cats?) are able to act in some way independently of the physical world (I think Bell is on record as not liking that possibility much either.) is incompatible with QM.  Martin Hogbin (talk) 17:34, 21 October 2015 (UTC)


 * About "humans and cats" etc...
 * As long as we think about physics (rather than, say, hard problem of consciousness, philosophical zombie etc.), free will is not really relevant. What is really relevant is, existence of local pseudorandom number generators that are, for all practical purposes, random (and local). In classical physics (mechanics plus statistical physics), such generators are abundant (the so-called molecular chaos). Accordingly, one may well believe that the future is predetermined, but only in principle, while for all practical purposes we have free will. But in quantum physics, this harmony is undermined by Bell theorem. This is the context in which the term "superdeterminism" is used by Gerard 't Hooft and some others. Boris Tsirelson (talk) 17:54, 21 October 2015 (UTC)
 * Note also that the (very important in physics) Einstein locality principle cannot even be formulated without local randomizers. But it is usually considered true in the classical physics. Think, why... Boris Tsirelson (talk) 17:57, 21 October 2015 (UTC)
 * The recent ideas of 't Hooft are the first (in the history) attempt to build a physical theory that stipulates the so-called "conspiracy", thus making the determinism (thus, failure of local randomizers and free will) visible "in practice", not only "in principle". If you like: visible to mortals, not only to immortals. Boris Tsirelson (talk) 18:00, 21 October 2015 (UTC)
 * It is fundamentally impossible to disprove the theory that everything is preordained. 'Random' has no meaning in this model of the world.  Whatever the result of any experiment the answer is always that it was already decided.  Martin Hogbin (talk) 19:06, 21 October 2015 (UTC)
 * Yes, I agree. But (a) this fact itself does not imply existence of any meaningful physical theory with "conspiracy"; and (b) the conjecture that everything is preordained is not falsifiable, but its negation is also not falsifiable, which means, it is, forever, a matter of belief. Boris Tsirelson (talk) 19:20, 21 October 2015 (UTC)
 * That is what I have said all along, I was not sure if you agreed or not. It is purely a matter of belief and is therefore outside the scope of physics.  On the other hand it is something that we should make clear in this article, not because it is directly relevant to Bell's theorem but to dispel the common misconception that QM and Bell's theorem experiments can disprove this belief.  One of the problems in making this fact clear is the confused terminology that I refer to below.  Martin Hogbin (talk) 22:07, 21 October 2015 (UTC)

Does anybody like the idea of briefly paraphrasing Bell's "superdeterminism" comment and using the link to Wikipedia's article of Superdeterminism? Something like this: ''In a radio interview Bell introduced what he called superdeterminism as another way to address the theorem. In this scenario the behavior of all particles, including those involved in choosing the measurements is predetermined by initial conditions. This removes the need for faster-than-light communication. Bell himself referred to this idea as "implausible"''--Guy vandegrift (talk) 18:18, 21 October 2015 (UTC)


 * For now, this article is much more professional than "Superdeterminism" (not sure this one will stay professional, but sure, the other one will often be attacked by cranks). Boris Tsirelson (talk) 18:29, 21 October 2015 (UTC)
 * Apart from making the agreed facts a little clearer here, as I suggest above, I agree that it is the other articles that need improving rather than this one. Whether we can improve those articles is another matter.  Even Superdeterminism contains this statement, ' It is conceivable, but arguably unlikely, that someone could exploit this loophole to construct a local hidden variable theory that reproduces the predictions of quantum mechanics'.  Superdeterminism is not a theoretical loophole in physics, it is a belief that is outside the scope of physics and cannot therefore be used to construct a theory of physics any more than Christianity can. Martin Hogbin (talk) 22:17, 21 October 2015 (UTC)
 * As for me, this article is, and should remain, a matter of physics. The other one also should be first of all about physics, namely 't Hooft, but may give more attention to philosophy. For genuine philosophic matters we already have philosophically oriented articles (linked above). Boris Tsirelson (talk) 06:33, 22 October 2015 (UTC)
 * Also, Martin, we had a discussion on these matters in Dec 2013 - Jan 2014, see archive 6 and archive 7 of this talk page. Anything new now? Any reason to reconsider? Boris Tsirelson (talk) 09:01, 22 October 2015 (UTC)
 * Yes, there was a rather long discussion, including Richard and others. At one point we had:


 * I do hope that you understand my point though. Making invalid claims for Bell's theorem brings physics into disrepute and causes people to lose faith in it. Martin Hogbin (talk) 09:52, 2 January 2014 (UTC)


 * Happy editing. Boris Tsirelson (talk) 12:47, 2 January 2014 (UTC)


 * So you were not against some clarification then. This also shows my rationale for wanting to clarify things here.  I do not think that I actually made any edits to the article at that time as I wanted to work with another editors if posible.  Maybe Guy would be interested in working with me on this subject. Martin Hogbin (talk) 10:59, 22 October 2015 (UTC)


 * You actually made edits yourself on Jan 30: this diff. Boris Tsirelson (talk) 17:28, 22 October 2015 (UTC)
 * Yes you are correct. Maybe that is enough then, unless anyone else thinks that we need to make it any clearer.  Martin Hogbin (talk) 17:47, 22 October 2015 (UTC)


 * "Making invalid claims brings physics into disrepute" — but I feel it differently. For a reader X that takes physics seriously, the formal logical consistence between facts and superdeterminism is of little importance. Such X is bothered, rather, whether or not the mainstream physical theory (or at least a serious alternative physical theory) supports superdeterminism. And for a reader Y that takes superdeterminism much more serious than physics, physics is already in disrepute anyway. This is why I do not share your concern. Boris Tsirelson (talk) 19:09, 22 October 2015 (UTC)
 * In other words: reader X hears from physics the voice: "as far as we understand, randomness exists"; and reader Y is attentive to different voice(s). This is the life, and you cannot change it by any edits to physical articles. Boris Tsirelson (talk) 19:47, 22 October 2015 (UTC)
 * Since you have pointed out that I have already made edits about this subject (which I forgot about) I am happy to leave things as they are and I will not be pushing for further changes. Martin Hogbin (talk) 21:28, 22 October 2015 (UTC)

Correction to the substitutions from CHSH (4 term) inequality to the simplified (3 term) version of Bell's inequality
I'm not sure how to perform/commit the correction, so I'll just post it here, in the hopes that a "guru" can fix the main article. The correct substitutions for transforming Eq(1) in §CHSH inequality
 * $$ \quad \rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') \leq 2$$

into the (un-numbered) equation at the top of §Original Bell's inequality
 * $$ \rho(a, c) -\rho(b, a) - \rho(b, c) \le 1,$$

are: b+π ← a, a+π ← a', a ← b, c ← b'. Also, might be useful to note that in order to reproduce the version of the CHSH inequality in this article from that in the main article on the CHSH Inequality,
 * $$S = E(a, b) - E(a, b^\prime) + E(a^\prime, b) + E(a^\prime, b^\prime)$$

one needs to perform a 180° rotation of b', that is: b'+π ← b'.
 * ProfessorJohnFrink (talk) 01:42, 20 January 2016 (UTC)


 * Here is my understanding of this matter.
 * Treatment of the parameters in CHSH and Bell inequalities is different.
 * In CHSH inequality, there are two settings $$a,a'$$ on Alice side, and two settings $$b,b'$$ on Bob side. Nothing special (like perfect anticorrelation) is assumed; thus, it is pointless to ask whether $$a=b$$ etc. The parameters are just (labels of) settings of measuring devices (possibly, of quite different type), not necessarily angles; thus, one should not try to rotate them. CHSH is purely informational. Accordingly, for proving it we introduce observables $$A,A',B,B'$$ such that $$\rho(a,b)=E(AB)$$ etc; assume they all commute (according to the local realism); and get $$\rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') = E(AB + AB' + A'B - A'B') \le 2$$.
 * In CHSH inequality, there are two settings $$a,a'$$ on Alice side, and two settings $$b,b'$$ on Bob side. Nothing special (like perfect anticorrelation) is assumed; thus, it is pointless to ask whether $$a=b$$ etc. The parameters are just (labels of) settings of measuring devices (possibly, of quite different type), not necessarily angles; thus, one should not try to rotate them. CHSH is purely informational. Accordingly, for proving it we introduce observables $$A,A',B,B'$$ such that $$\rho(a,b)=E(AB)$$ etc; assume they all commute (according to the local realism); and get $$\rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') = E(AB + AB' + A'B - A'B') \le 2$$.
 * In CHSH inequality, there are two settings $$a,a'$$ on Alice side, and two settings $$b,b'$$ on Bob side. Nothing special (like perfect anticorrelation) is assumed; thus, it is pointless to ask whether $$a=b$$ etc. The parameters are just (labels of) settings of measuring devices (possibly, of quite different type), not necessarily angles; thus, one should not try to rotate them. CHSH is purely informational. Accordingly, for proving it we introduce observables $$A,A',B,B'$$ such that $$\rho(a,b)=E(AB)$$ etc; assume they all commute (according to the local realism); and get $$\rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') = E(AB + AB' + A'B - A'B') \le 2$$.


 * Labels $$a,a'$$ are assigned to the two Alice settings arbitrarily. Equally well we may swap them, getting $$\rho(a',b) + \rho(a',b') + \rho(a,b) - \rho(a,b') = E(A'B + A'B' + AB - AB') \le 2$$. There are four such inequalities. In addition, labels $$+1,-1$$ are assigned to the two possible outcomes arbitrarily, and may be swapped for (say) Alice but not Bob, which changes the sign: $$\rho(a',b) + \rho(a',b') + \rho(a,b) - \rho(a,b') \ge -2$$ (and therefore $$|\rho(a',b) + \rho(a',b') + \rho(a,b) - \rho(a,b')| \le 2$$). These are symmetries of the CHSH inequality.


 * In Bell inequality, there are three angles (not just "settings") $$a,b,c$$; two of them, $$a,b$$, are used by Alice, and two of them, $$a,c$$, are used by Bob; note that $$a$$ is used by both. Denoting the two corresponding observables of Alice by $$A,B$$ we see that the first observable of Bob is $$-A$$ due to the perfect anticorrelation. The second observable of Bob may be denoted by $$-C$$ or by $$C$$; both options are legitimate. Let us choose the former one. Then $$\rho(a,c)=E(A(-C))=-E(AC)$$, $$\rho(b,a)=E(B(-A))=-E(BA)$$, $$\rho(b,c)=E(B(-C))=-E(BC)$$, thus, assuming commutativity (as before) we get $$\rho(a,c)-\rho(b,a)-\rho(b,c) = E(AB+BC-AC)$$.


 * In order to reduce Bell inequality $$ \rho(a,c)-\rho(b,a)-\rho(b,c) \le 1$$ to CHSH inequality, we subtract $$\rho(b,b)=E(B(-B))=-E(B^2)=-1$$, thus rewriting Bell inequality as $$ \rho(a,c)-\rho(b,a)-\rho(b,c)-\rho(b,b) \le 2$$, that is, $$E(AC-AB-BC-BB) \le 2$$. Taking into account the symmetries of CHSH we see that the latter is its special case.
 * Boris Tsirelson (talk) 19:32, 20 January 2016 (UTC)


 * In the presence of such august editors, I should perhaps not say too much. But in response to Editor Tsirel's comment "assume they all commute (according to the local realism)", I feel it could be mentioned that 'local realism' is an item of Bellspeak. At stake here are two things: a metaphysical principle, and a religious principle. The metaphysical principle is about causality. The religious principle is that Albert Einstein is a silly old goat, not nearly as clever as his critics. The causality thing is translated by his Bellspeaking critics into a matter that is exactly stated by classical mechanics, which is not a metaphysical principle, but something downstream from there, a physical theory. We don't need Bellspeakers to tell us that classical mechanics is unable to account for the existence and behaviour of atoms. That was apparent by 1920. The Bellspeakers muddle the metaphysical principle with the physical theory, and crow that because the physical theory is inadequate, they have overthrown the metaphysical principle and can thereby see in the dark and walk on water; well, at least they will be able to do so given one more research grant. But anyway, they are cleverer than Albert Einstein; the religious principle stands.Chjoaygame (talk) 22:47, 20 January 2016 (UTC)


 * No comment. :-) Boris Tsirelson (talk) 06:14, 21 January 2016 (UTC)


 * On the metaphysical front, a wise move. :-)


 * I may add that the actual discussion on the formulas offered here by Editor Tsirel is helpful and illuminating.11:51, 21 January 2016 (UTC)


 * Thanks for the compliment. If your "august" was toward me, you are (to the best of my knowledge) the first to call me this way. Another very generous compliment "great magician" is here. What a collection! Boris Tsirelson (talk) 13:21, 21 January 2016 (UTC)

Let's vote on whether to remove an external link.
I move that we remove the external link http://quantum.kelca.cz/LocalRealisticEntang-Kelca04-2016.pdf that was inserted by Pave69.
 * Support--Guy vandegrift (talk) 02:18, 8 April 2016 (UTC)
 * Question Is the author of the article Pave69? &mdash; Charles Stewart (talk) 07:37, 8 April 2016 (UTC)
 * Apparently yes, see c:File:3D_set_of_possible_angles_for_spin_measuring.png. I am deleting as self-promotion.  As there was no discussion, I will hide it here. See also this draft.--Guy vandegrift (talk) 10:46, 8 April 2016 (UTC)


 * Support - apparent case of self-promotion. &mdash; Charles Stewart (talk) 11:01, 8 April 2016 (UTC)
 * (implied) Support by User:Sławomir Biały who has already removed the link. Case closed? --Guy vandegrift (talk) 16:47, 8 April 2016 (UTC)
 * Support - need to be reliable, published source.--LaoChen (talk) 06:27, 9 April 2016 (UTC)

Two questions
Absolute signs are not present in the inequalities. This had me confused for a while. The statement without inequalities are, on the face of things, stronger. Should we have inequalities? Original references and introductory QM texts I might add as references (below) have them. If not, then some explanatory remarks are warranted for. YohanN7 (talk) 09:49, 29 April 2016 (UTC)

Is it desirable to have sample hidden variable theories? The ones I have in mind are
 * 1) Spin $1/2$ one-particle theory that fails to reproduce predictions of QM. (From introductory QM texts.)
 * 2) Spin $1/2$ one-particle theory that reproduces QM predictions. (From Bell's original paper.)
 * 3) Spin $1/2$ two-particle theory that fails to reproduce predictions QM. (From introductory QM texts.) Bell's trick that works in one-particle theory doesn't work for two-particle theory because it is non-local.

I believe that this could be illustrative. I estimate it would occupy about one screen. YohanN7 (talk) 09:49, 29 April 2016 (UTC)


 * About the absolute values, I am neutral.
 * About the sample hidden variable theories, I like this idea. Boris Tsirelson (talk) 20:28, 29 April 2016 (UTC)

Is this site safe?
Quantum Entanglement, by Dr Andrew H. Thomas. Archived version. Includes a simple explanation of Bell's Inequality. This site needs to be checked for safety. I went to the first one (ipod.org) and an obvious virus is involved. It might have come from another source--a few hours earlier I had logged into a server in a department store while a friend did some shopping.--Guy vandegrift (talk) 14:07, 10 June 2016 (UTC)


 * Indeed, it redirects to something irrelevant. Boris Tsirelson (talk) 19:07, 10 June 2016 (UTC)


 * When I went to the ipod.org site, my laptop froze and it looked like a virus. By the way, I do like the link to Doctor Chinese that I believe the same editor added. One of his (Dr Chinese's) other "calculations" (not linked from Wikipedia) proposes negative probability, but I think his intent was to be humorous.  Such humor would be inappropriate on Wikipedia though.  Should I delete one or both the external links that I de-wikied?  I am afraid to take my laptop to those sites.--Guy vandegrift (talk) 01:47, 11 June 2016 (UTC)


 * I finally found a library computer where I can click external links with minimal risk. The ipod.org site is dysfunctional so I removed it.  I have reservations about the other site (Quantum Entanglement, by Dr Andrew H. Thomas). It appears to be legitimate but a bit long winded.  I have no objection to anybody removing it.--Guy vandegrift (talk) 15:00, 13 June 2016 (UTC)

External links modified
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Puzzled
“Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the ‘decision’ by the experimenter to carry out one set of measurements rather than another, the difficulty disappears.”

But that's exactly what Laplacian determinism is all about, isn't? Provided that our thoughts are merely an epiphenomenon if the natural processes. (Which is, apparently, the standard view, anyway.) So what's the problem? That piece of article leaves people in quite a puzzled mood, I'd say. - 37.9.29.40 (talk) 19:03, 3 November 2016 (UTC)
 * It's all here, though: https://en.wikipedia.org/wiki/Talk:Bell%27s_theorem/Archive_6 . Oh my. Looks like a brief note that was needed was transformed into a long and prominent quote in the lede. And I did misunderstand what super-determinism meant or implied, just like one disputer (Boris Tsirelson?) predicted any casual reader would. A big uncanny game made to fool people who would otherwise believe that objects have constant properties. Puzzling, indeed. - 37.9.29.40 (talk) 21:39, 3 November 2016 (UTC)

Compliments!
Usually I offer constructive suggestions to improve an article, but in this case, my comment is that I consider this article to be very well-written. The earlier part of it is accessible to non-expert readers, and the later part goes into more technical detail. Well done!77Mike77 (talk) 01:20, 7 January 2017 (UTC)

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Simple pictorial proof of Bell theorem
I believe this article would benefit from a simple proof of Bell theorem, preferably a pictorial one. One can be found here: http://www.johnboccio.com/research/quantum/notes/paper.pdf Yesterday I have created even a simpler one - just using Born rule (for https://arxiv.org/pdf/0910.2724v2.pdf ) - if you think it is appropriate, you can take it to the article (or suggest modifications I can make). Jarek Duda (talk) 11:34, 1 August 2017 (UTC)

New explanation of Bell's theorem
New explanation of Bell's theorem added recently by Joseph Boone is nice, but I have a terminological objection. The mathematical proposition as formulated is but a special case of Boole–Fréchet inequalities (as noted in the article), well-known long ago before Bell, rather trivial, and unrelated to quanta. I feel it rather humiliating for Bell, to say that this trivial remark IS his great achievement. If THIS is called Bell theorem, then, what is the name for "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics"? Boris Tsirelson (talk) 06:22, 29 August 2017 (UTC)


 * Bell's corollary? YohanN7 (talk) 10:16, 29 August 2017 (UTC)
 * I also struggle with this terminology, and decided Bell's theorem is "No physical theory of local hidden variables can ever reproduce ...", and Bell's inequality is what everyone seems to understand. And, I refer to a "Bell's theorem experiment" as any effort to investigate this spookiness (regardless of whether the experimentalists even know that  a local hidden variable is).  I for one, would be hard pressed to define "local hidden variable", but have no great desire to do so.  This is all just my opinion--I am no expert on this junction between physics and philosophy.--Guy vandegrift (talk) 16:06, 30 August 2017 (UTC)

Local pilot-wave theory
The article implies exclusion of pilot-wave theory with local hidden variables, but I am not sure that is the latest thinking, at least among fluid dynamics experimenters like MIT's John Bush.

John Bush conducted experiments with oil droplets floating on fluids, generating pilot-wave and quantum behavior analogs consistent with Bell's theorem, not before thought possible in classical local systems(1). Article below also includes quotes from Frank Wilczek calling the idea "mind expanding" and interestingly John Bell believed his theorem was consistent with pilot-wave theory (2).

James Tankersley Jr (talk) 05:51, 24 May 2018 (UTC)
 * (1) The New Quantum-Reality Quanta Magazine 06.30.2014 by Natalie Wolchover, fluid dynamicists convinced there is a classical, fluid explanation of quantum mechanics.
 * (2) Fluid mechanics suggests alternative to quantum orthodoxy Quantum Physics 09.12.2019 by Larry Hardesty MIT, John Bell proponent of pilot-wave theory

A resolution of the measurement problem has been published in Measurement (link below)
In Relative Measurement Theory (RMT at: https://www.sciencedirect.com/science/article/pii/S0263224117306887) all measurement results are relative. In metrology this relative relation is established by a calibration process defining the difference between an interval of the measuring apparatus and a reference. The figure (https://commons.wikimedia.org/wiki/File:Bell.svg) shows the angle of rotation (polar coordinates) of one measuring apparatus to another measuring apparatus. In this figure each measuring apparatus is the reference to the other. The setting of the angle between these two measuring apparatus is a calibration process. In the examples in RMT, which formalizes a measurement in Cartesian coordinates, calibration defines an interval relative to a reference. Conversion between polar and Cartesian coordinate systems is a trigonometric function.

In RMT (Section 3) the digital voltmeter example of a classical measurement is shown to produce a Gaussian distribution, not a linear distribution (as shown in the reference figure inverted V or red curve). In the referenced figure the classical measurement (red curve) is shown without the calibration or resolution effects. It is common to present classical measurements without including calibration or resolution with the assumption that these effects are small. However, in the referenced figure the measurement system specifically varies the calibration (resolution is ignored in both curves as it is small), so ignoring calibration in the classical measurement creates the difference between the red and blue curves. The difference between the red and blue curves is exactly the difference between the Gaussian and linear measurement curves. At the zero or 360 degree setting the calibration is inverse, at 90 or 270 degrees there is no calibration/correlation and at 180 degrees the calibration is perfect. All the rest of the points on the Gaussian must differ from the linear curve exactly as shown in the referenced figure. The Bell theorem has been experimentally proven correct. The apparent discontinuity between classical and quantum measurements occurs when calibration is not treated in a classical measurement.

Krechmer (talk) 02:09, 14 July 2018 (UTC)

section on hydrodynamic quantum analogs
extracted into its own section on Oct 12th to get back to improving the article: I find the paragraph beginning with "Local hidden variable models have some experimental support in the form of hydrodynamic quantum analogs. [...]" (which follows the one mentioning 't Hooft) questionable: the cited sources only talk about "single-system" QM, so nothing where Bell comes into play; later (unpublished) work extended this to a Bell-type scenario (see: arXiv:1306.6822) but then also explained that these hidden variables are not local (since they represent the fluid surface on which the oil-droplets bounce (cf. arXiv:1401.4356) . Therefore I would advocate removing this paragraph, since as it stands it suggests support for "local hidden variable models violating Bell's inequality", which it does not.--Qcomp (talk) 14:37, 6 October 2018 (UTC)
 * in view of these results, that reports several experiments which fail to reproduce the original oil-droplet double-slit experiment, I'll now remove the section.--Qcomp (talk) 12:55, 12 October 2018 (UTC)

criteria for discussing a non-standard theory in WP
added a sentence referring to Joy Christian's new and controversial model as an example local hidden variable models violating Bell inequalities. (Paragraph beginning: A few advocates of deterministic models have not given up on local hidden variables.). I undid the change for two reasons: first and mainly, in contrast to 't Hooft's contributions (that were previously the only ones mentioned here), those of Christian are quite controversial (as can be seen both from the arXiv preprints on his "Disproof" of Bell's theorem and the comments on this and the referee reports on the Open-Science-paper cited and have not found any constructive echo in the discussion on Bell's theorem (at least up till now): there are zero citations of the Open Science paper and 3 to the IJTP one  - two by Christian himself and one essentially stating that it is false). In my opinion this debatable original research is not (yet) material for an encyclopedia. It is much more "fringe research" than 't Hooft, because the latter is regularly cited (several of his papers on deterministic/realistic QM have tens of citations, he contributed to respected books on the subject (like ), and the free-will/superdeterminism loophole is recognized by the community. The same is not true for Christian's model. The other point is that the representation of Christian's results seems contradictory: Bell's Theorem is a mathematical theorem, so to get around it you need to avoid some of the assumptions made, i.e., you need some "loophole" (such as superdeterminism in 't Hooft's case, which negates the independent choice of the measurement settings), but the edit stated/states that Christian "does not rely on any loopholes". But given all its assumptions, Bell's Theorem stands. Hence, either there's a loophole or Christian's model is not local-realistic. The edit by UstadIqbal was undone twice (once by me with the argument "fringe theory") and UstadIqbal has reverted both. Therefore I propose to clarify the issue here. --Qcomp (talk) 20:25, 24 September 2018 (UTC)
 * These are all excuses to justify your prejudice against Christian's work. There is a lobby to control the forum against his work in this manner and then claim that it is not being discussed or cited. The work is published in two highly respected journals. It is being discussed all over the internet (including on arXiv and several journals) since 2007. Your comments about Christian's work show that you have not read his papers. Bell's theorem, on the other hand, does depend on several assumptions as you state. It is not simply a theorem independent of assumptions. Thus it is perfectly possible to evade Bell's theroem as Christian has shown in the cited papers. — Preceding unsigned comment added by UstadIqbal (talk • contribs) 20:53, 24 September 2018 (UTC)
 * I'm not "pre"judiced against his papers. I have read some of them and discussed them with my colleagues. Concerning the present paper (which I have not read) my argument is not that it is not correct, but that it represents a quite controversial result ("a local-realistic model violating Bell's inequality", a "flaw in Bell's argument", see the reply letter of Christian to one of his reviewers in Open Science) and has so far no documented acceptance in the quantum foundation community. WP is not the place to advertise such scientific results. Those convinced by them should advocate in teh scientific community and they will succeed if the result in question is correct. Once this has lead to broad acceptance or even just stirred broad and fruitful debate (as did, e.g., the collapse models regarding interpretations of QM) that is reflected in secondary or tertiary literature, the results are suitable and welcome in WP.
 * Of course (as I state) Bell's theorem rests on assumptions. If one argues that some of them do not hold that opens what is usually called a loophole. Some of them can be closed in careful experiments (e.g., fair sampling), others can't (superdeterminism). Your edit stated that Christian's local-realistic model does not rely on a loophole - then we have a contradiction, namely a proven theorem that no local-realistic model can violate Bell's inequality and a (claimed) local-realistic model that does. I'm not an expert on the mathematics used by Christian (and here is not the place to discuss it), but my impression is that by describing space with non-commutative objects such as Grassmann vectors, quaternions, octonions he is redefining the usual concepts of locality. Whether that's a loophole or whether the model then is not local-realistic in the usual sense should be discussed in journals, conferences, and seminar rooms. But for the moment it is debatable original research far outside (not to say at the fringe of...) the accepted mainstream and not material for an encyclopedia article. PS: I indented UstadIqbal's comment for better readability. --Qcomp (talk) 21:51, 24 September 2018 (UTC)
 * I agree with Qcomp. In fact, I had a discussion with Joy Christian here, and got from him a gift - his book... Boris Tsirelson (talk) 04:00, 25 September 2018 (UTC)
 * "There is a lobby to control the forum against his work in this manner and then claim that it is not being discussed or cited." — A usual complaint of fringe scientists. "The lobby" is just the mainstream; and "this manner" is just the standard mechanism of science to be more selective than (say) youtube.
 * In exchange, I can quote a (usual?) complaint of a mainstreamer (myself): "In the last decade of the 20th century I was usually able to convince a skeptic. Frustratingly, in the first decade of the 21th century I faced a small serried cohort of “Bell-deniers”. My gut feeling was telling me that most (but not all) of them realize in the depth of their hearts that they are wrong, but cannot afford to acknowledge defeat and exchange a high status in the opposition for a low status in the coalition." (Here)  :-)   Boris Tsirelson (talk) 04:53, 25 September 2018 (UTC)
 * Boris Tsirelson, language like "cohort of Bell-deniers" is not the language respectable scholars use in any discourse. Such words are the tactics used by those who wish to control scientific forums to protect their own vested interests. It is best not to engage in such political tactics, which are well known to sociologists of science (at least) since the work of Thomas Kuhn. The people you call "Bell-deniers" are perhaps people like Christian who have recognized the flaws in the reasoning by Bell and his followers (like yourself). But the main issue of scientific significance here is that Christian's work is no more fringe than 't Hooft's work and no less cited or accepted than 't Hooft's work. It is now published in respectable physics journals despite having faced initial resistance from the Bell community. That is how science progresses. Science does not progress by prohibiting and discriminating against certain "heretical" works to protect one's own intellectual investments in the opposite point of view, in the manner the Catholic Church did in the darker times of Galileo Galilei. Since you are not arguing for a removal of 't Hooft's work, your position is politically inconsistent. UstadIqbal —Preceding undated comment added 07:54, 25 September 2018 (UTC)
 * Sorry if you feel insulted. But my "cohort" here is reaction to your "lobby". Back to the point, see above: "It is much more "fringe research" than 't Hooft, because..." and "a proven theorem that no local-realistic model can violate Bell's inequality and a (claimed) local-realistic model that does". Boris Tsirelson (talk) 11:41, 25 September 2018 (UTC)
 * (in answer to UstadIqbal): you write: But the main issue of scientific significance here is that Christian's work is no more fringe than 't Hooft's work and no less cited or accepted than 't Hooft's work. which is not correct: the two works by Christian that you cite have just 3 citations between them, only one of them not a self-citation and that single one refutes the paper. Earlier work by Christian has not been published in peer-reviewed journals and has been (to me: quite convincingly). On the other hand, 't Hooft's research on deterministic models for quantum physics (the correctness of which I cannot judge) is regularly cited by other researchers, e.g., with 51,  with 12, or  or his  (15, no self-citations) and is engaged in discussions about the subject by mainstream researchers and journals, . In contrast, Christian's  is cited 14 times among them 3 from published articles (one sound refutation) and 5 self-citations. This is not to argue that 't Hooft's position is not also considered "fringe" - but there are relevant distinctions within  the fringe, too. --- And if you want to question whether 't Hooft's work is adequate to be mentioned in a WP article: go ahead; I think it is, since he is addressing a valid loophole, which has even had part in motivating research  aiming to push the limit of how far back superdeterminism must go. But in a very concise article on Bell's theorem, his specific work might be omitted as well, in my opinion, while the superdeterminism loophole clearly has to be mentioned. --Qcomp (talk) 12:51, 25 September 2018 (UTC)
 * Boris Tsirelson, you are free to use any unprofessinal language you wish. That does not affect me. But let me take the liberty to correct some of the misconceptions here. The so-called theorem of Bell is based on an inequality that was discovered by George Boole some 100 years before Bell misused it within the context of the Einstein-Bohr debate. Thus Bell's claim is hardly a "theorem" in the mathematical sense. This is because Boole's inequality (which is of course mathematical) is misused by Bell and his followers within *physical* concepts. Let me quote from a recent paper published in Nature Communications to make a related point: "Any no-go result, as for example Bell’s theorem, is phrased within a particular framework that comes with a set of built-in assumptions. Hence it is always possible that a theory evades the conclusions of the no-go result by not fulfilling these implicit assumptions (https://doi.org/10.1038/s41467-018-05739-8)." Now, as for some of the claims made by Qcomp, it is important to note that no legitimate refutation of Christian's work exists to date. To be sure, some have claimed to have refuted his work, but if you look closely it is not difficult to recognize that the supposed critics of his work have only refuted their own caricatures of Christian's work, not his actual local-realistic model. Philosophers call such misleading refutations straw-man refutations (or straw-man arguments). Straw-man tactic is quite popular among politicians. UstadIqbal —Preceding undated comment added 14:53, 25 September 2018 (UTC)
 * Well, this is your point of view. I understand that we cannot agree, just as I was unable to agree with Joy Christian in 2012. I do not intend to start another frustrating discussion now. You are free to compare me to Catholic inquisitor (which make me smile), if you like. And if needed, I'll argue against you in a mediated discussion etc. Boris Tsirelson (talk) 18:19, 25 September 2018 (UTC)
 * Here are some very pertinent policy issues being criticised that are relevant to this discussion: https://qz.com/1410909/wikipedia-had-rejected-nobel-prize-winner-donna-strickland-because-she-wasnt-famous-enough/?platform=hootsuite UstadIqbal —Preceding undated  —Preceding undated comment added 07:50, 3 October 2018 (UTC)
 * That's a laughable comparison. I applaud Boris for being so patient with this discussion; needless to say I do not agree that the discussed content be included within the article. Porphyro (talk) 15:57, 4 October 2018 (UTC)
 * I am not laughing. This is not a laughing matter. Perhaps your opinion also stems from the same ignorance and bias Tsirelson has exhibited. Perhaps you too have vested interests or ideology to protect. For why else would you object to including legitimate research published in two respected journals? What are you afraid of? UstadIqbal —Preceding undated comment added 15:43, 5 October 2018 (UTC)
 * What are we afraid of? For the answer see above: "just the standard mechanism of science to be more selective than (say) youtube." Nothing personal; nothing political; just science. The matter is published, and does not get traction. A catholic inquisition? Boris Tsirelson (talk) 18:07, 5 October 2018 (UTC)
 * What you are afraid of, Boris Tsirelson, is Truth. You are so afraid of Truth that you have resorted to comparing two respected journals (RSOS and IJTP) with youtube. How is this not personal? How is this not political? Controlling intellectual forums (or Media) in this manner to protect personal interests is a standard political tactic employed by many organizations and individuals (a good example of it is the current political climate in the USA). As I have noted above, such tactics within science are well studied by the sociologists of science, at least since Thomas Kuhn:  UstadIqbal  —Preceding undated comment added 20:04, 5 October 2018 (UTC)
 * What I am afraid of is passionate pompous demagoguery instead of thoughtful logic. Boris Tsirelson (talk) 06:07, 6 October 2018 (UTC)
 * Wow! Now *that* is truly laughable. It is the pot calling the kettle black. Not only thoughtful logic but also stark evidence dictates that Bell's supposed "theorem" is physically a fundamentally flawed argument. What was claimed to be impossible by the supposed "theorem" is shown to be possible with --- you guessed it --- thoughtful logic. But accepting that truth would destroy your carelessly constructed and politically sustained ideology. So you resort to name-calling, such as "cohorts of Bell-deniers", and compare respected journals with "youtube." What could be a better example of "passionate pompous demagoguery" than what you have exhibited here? UstadIqbal —Preceding undated comment added 08:18, 6 October 2018 (UTC)
 * :-(  Boris Tsirelson (talk) 09:52, 6 October 2018 (UTC)
 * Bell's 1964 paper (published in an unknown, short-lived journal) did not have "traction" for decades (Clauser has even published his complaints about how badly his papers on Bell's paper were treated by the physics community). The same is true of Tsirelson's own paper --- no "traction" for many years. Therefore, according to Tsirelson's current logic, both of these papers were "youtube" material. :-) UstadIqbal —Preceding undated comment added 14:21, 6 October 2018 (UTC)
 * I'm afraid this discussion leads nowhere; currently the forums to advocate Christian's approach (if you wish to do so) are scientific conferences and journals and not WP. If this is done convincingly and the approach is found to be correct and interesting, people will cite the work, it will be discussed in secondary literature, and WP will take notice. Getting published in a research journal does, by itself, not make a result encyclopedically relevant. The discussion here is not about the science, but about the relevance of this result for WP: (1) Wikipedia articles should be based on reliable, published secondary sources and, to a lesser extent, on tertiary sources and primary sources. (see WP:No original research), but here, only primary sources exist; (2) there are many researchers who have (or think they have) a hidden-variable theory that somehow gets around Bell's theorem. Usually -if it's not simply wrong- it turns out to not fulfill all the assumptions of the theorem; I don't think the article "Bell's Theorem" is the place to list specifically all approaches that question the assumptions of the theorem. It suffices to state which assumptions have been questioned and mention the main recognized approach that does so. This discussion has not brought forth a single argument in favor of mentioning Dr. Christian's work in this article. That he (supposedly) refutes refutations of his original (unpublished) article in other (unpublished) articles just shows (independently of the correctness of these claims) that the subject is not yet mature enough for WP. And comparing Dr. Christian to Nobel prize winners is not an argument, neither are baseless claims of political or ideological conspiracies against this work.
 * regarding the "traction" of Bell's Theorem: it took about a decade to become impactful (see Google Ngram). I doubt that you'll find it in the encyclopedias of the 70s (or even 80s). That has nothing to do with "youtube material" (and neither had Boris' statement): this shows that you have to do more than "upload" (i.e.: publish) to become scientifically relevant or recognized. --Qcomp (talk) 14:37, 6 October 2018 (UTC)

I think we should also remove the references to Gerhard 't Hooft. I don't know of anyone who takes his views on this issue seriously. Also, superdeterminism has its own WP entry; it could go there. 84.213.47.175 (talk) 17:42, 3 November 2018 (UTC)
 * Hmmm... Not knowing who are you, we cannot fully appreciate your phrase "I don't know of anyone who..." Boris Tsirelson (talk) 21:03, 3 November 2018 (UTC)


 * I won't object, though I don't see it as urgent. I have not met physicists who consider 't Hooft's approach promising (Gill mentions it as the one "most likely" (out of a very unlikely bunch) to lead to progress), but given his reputation and the mathematical soundness of his approach, he seems to somehow serve as a reference point for the exotic hidden-variable approaches (being invited to foundations of QM (Quantum (Un)Speakables, Beyond the Quantum) and related philosophy conferences (International Ontology Congress, and being interviewed about his views in Physics today.
 * I think superdeterminism as a marginal, but unrefuted approach to reconciling local realism with Bell violations should be mentioned in the "metaphysics" section, although one may not need to mention proponents. Maybe s.th. like
 * A few advocates of deterministic models have not given up on local hidden variables, for example relying on the superdeterminism loophole.
 * would do -- although I'm not very comfortable with "for example" since I'm actually not aware of other valid local-realist approaches.
 * I find the whole "metaphysics" section strangely unbalanced: no word on giving up "realism", a lengthy paragraph on a paper by Jaynes that may be mistaken and in any case does not seem to be important in this discussion (I have only access to the abstract). Going into the detail that Gill cites Jaynes' strange fascination with the result by Gull (that apparently is no news at all) seem very out of place. But I don't feel competent (or tempted) to tackle improving the whole section. --Qcomp (talk) 21:55, 3 November 2018 (UTC)
 * I'm pretty much in full agreement with Qcomp on this. t' Hooft's approach is mature in the sense that the way it works is well-understood, and people can debate how meaningful the result is. Other explorations of superdeterminism haven't met with the same reception- I recall one that was based on p-adic distances to compare physical systems. The only way I know of that Bell's theorem can otherwise be meaningfully sidestepped is by moving to an Everettian viewpoint, and even so those models have features that make them poor candidates for the actual ontology of the universe- principally extraordinarily large state-spaces even when compared to Hilbert space. The article doesn't mention these approaches either, perhaps because they are not mature fields of study. Porphyro (talk) 14:11, 5 November 2018 (UTC)

Question
Wait a minute! Which term should be negated: (a,b') or (a',b')? U can't have it both ways. Can U? — Preceding unsigned comment added by 220.101.38.242 (talk) 05:35, 11 May 2019 (UTC)

Time-Varying Hidden Variables
Bell's 1964 paper is fairly short and it's available on the open Internet for anyone to read.

The meat of the paper is a mathematical derivation of Bell's Inequality.

Experiments carried out by Alain Aspect and others have confirmed that Bell's Inequalities do not hold in our cosmos.

Why not, and what does it mean that Bell's Inequalities do not hold?

Bell posits a hidden variable (which could be a constant or a function of time) and carries out a derivation in which any such imaginable hidden variable vanishes in the course of the derivation.

It's fairly easy to carry out Bell's derivation if you consider the case where the presumptive hidden variable is a constant (not time-varying).

But what about the case where the presumptive hidden variable is posited to be time-varying? Then you can still carry out Bell's derivation provided you assume there is a single uniform cosmic clock that keeps precisely the same time everywhere and everywhen.

But in our cosmos, there is no such thing as uniform timekeeping everywhere and everywhen. The rate at which clocks tick varies with the strength of the local gravitational field and with the motion of the clock.

Because there is no such thing as uniform time-keeping in our cosmos, the hidden variables do not vanish. Instead, they produce a "beat frequency" term that survives to the bottom line of Bell's derivation.

In short, the hidden variable is time itself, or any variable that is a function of time.

In Alain Aspect's experiments with photons, the not-so-hidden variable is the E-Field which varies in a manner spelled out by Maxwell's Equations.

And this is why Bell's Inequalities do not hold in our cosmos. — Preceding unsigned comment added by 100.17.20.31 (talk) 06:55, 3 June 2019 (UTC)

Parallel and anti-parallel directions
All these rants make sense only for spin ½. Isn’t the fact that photons have the spin 1 alarming? These are photons which are measured in most experiments. Incnis Mrsi (talk) 19:25, 24 June 2019 (UTC)

Simple explanation needed
Could someone please explain what Bell's inequality means in understandable words instead of math? I've been trying to find out what it means for 30 years and understand exactly NOTHING about it. — Preceding unsigned comment added by 2600:8807:C100:13C0:11ED:3D77:F4D0:DE0A (talk) 16:51, 2 March 2020 (UTC)
 * A big problem with Bell are these "realism" and "locality" assumptions - which usually are explained with words, and if you ask about details, you don't really get any. Much better is Mermin's inequality: for 3 binary variables, Pr(A=B) + Pr(A=C) + Pr(B=C) >= 1, what is practically "tossing 3 coins, at least 2 are equal", but it is violated by QM formalism: https://arxiv.org/pdf/1212.5214 . Its trivial derivation just requires "there exists probability distribution on Omega" assumption - that's all. To violate it in QM, we need to replace it with "there exists amplitude on Omega" - to be added over unmeasured variables, then multiplied to get probabilities in Born rule. Its origin nicely appears in Feynman path integrals formulation, or mathematically nearly the same: Boltzmann sequence ensemble, which is realized in Ising model - also getting Born rule and Bell violation: https://physics.stackexchange.com/questions/524856/violation-of-bell-like-inequalities-with-spatial-boltzmann-path-ensemble-ising Jarek Duda (talk) 18:20, 2 March 2020 (UTC)

Hopelessly outdated
This article is hopelessly outdated. In the early to mid 1980s there were numerous clarifications of the types of theories ruled out by Bell's inequality together with strengthenings of it to any theories that had the same underlying mathematical structure as the theories Bell had considered. This culminated in Arthur Fine's characterization of such theories as precisely those based on a single underlying probability space for all variables under consideration. Such theories are precisely the ones ruled out regardless of whether they are realist or non-realist and regardless of whether they are local or non-local. Around the same time it was observed that Bell's inequality and Fine's result were in fact well known results in the field of statistics going back to George Boole in the 19th century and applicable to any application of statistics not merely physics. Of major significance is the fact that Bell had not actually proven any of the points he had set out to do. In fact the Consistent Histories formulation of QM (supported by leading physicists such as Hartle, Omnes, Griffiths, Gell-Man) is both realist and local but not ruled out by Bell's results. — Preceding unsigned comment added by 197.234.164.85 (talk) 14:57, 13 April 2020 (UTC)
 * I have added material (previously blanked from the EPR article) that covers the points I mention. This is all sourced and referenced material, please no blanking.
 * I've undone your edit. How many times must this be discussed? Yes, Bell did manage to prove what he wanted to prove. No, you're not adding crackpots claiming otherwise to this article. Tercer (talk) 20:21, 13 April 2020 (UTC)


 * In John Bell's 1964 paper, the derivation of his inequalities is mathematically valid if one of these two crucial assumptions is met:


 * 1) The presumptive hidden variables are static (not time-varying), or


 * 2) The presumptive hidden variables are time-varying and time ticks at the same rate everywhere and everywhen in the cosmos.


 * Neither of those essential assumptions is valid. General Relativity, in particular, reveals that there is no universal cosmic clock. The rate at which time ticks varies from one location to the next and (among other things) depends on the strength of the local gravitational field.


 * Instead of the presumptive hidden variable vanishing in the middle of the derivation of Bell's Inequalities, there arises a non-vanishing "beat frequency" term that survives to the bottom line.


 * The presumptive hidden variable turns out to be time, itself (and any parameter that is time-varying).


 * The fact that Bell's Inequalities do not hold in our cosmos is confirmation that any hidden variables are necessarily time-varying and Einstein's GR is right about time-keeping being a function of the local gravitational field strength.


 * What Einstein derided as "spooky action at a distance" turns out to be not-so-spooky time-keeping at a distance.


 * Moulton (talk) 00:20, 16 August 2020 (UTC)
 * Please see WP:NOR and WP:NOTFORUM. Cheers, XOR&#39;easter (talk) 18:11, 16 August 2020 (UTC)

Experimental validation
The text currently says: "Experimental results match the curve predicted by quantum mechanics[3]". I propose to add a comma, and the words "though many experiments in the field do not actually try to create the singlet state. In any case, usually noise is also present."

The reference [3] is to a pretty ancient encyclopedia article. Two of the loophole-free experiments of 2015 did not use the singlet state at all, but used less than fully entangled, but more noise-resistant states, discovered by Eberhard. Other experiments create and see the singlet state + noise, and therefore recover a less than full amplitude cosine. For instance, the Delft experiment of 2015 got a value of S of 2.4 - half way between Bell's bound of 2 and the singlet state's 2.828... Richard Gill (talk) 15:22, 1 August 2021 (UTC)
 * That seems a fair point to make, though maybe it goes more with the following paragraph, which talks about closing loopholes. And I kind of like the somewhat-longer explanation you give here, rather than the shorter addition you first proposed; mentioning caveats without explanation in this area can start to sound like Bell denial. XOR&#39;easter (talk) 16:24, 1 August 2021 (UTC)
 * Thanks. I agree, this connects very much to the next paragraph. I came across this problem in heated discussion with a Bell denialist who insisted that according to Wikipedia all Bell tests produce the cosine. I think it was my denialist friend who reverted my edit. The problem is: Bell’s theorem is proven by providing one example of conflict between QM as a theory and local realism. A Bell experiment it meant to show a conflict between local realism and laboratory reality. There are good reasons that experimentalists use different states from theoreticians. Richard Gill (talk) 16:34, 1 August 2021 (UTC)
 * Gill wants to make insertions to cloud this wikipedia article to allow for his own personal interpretations of Bell's Theorem. He  is  vandalizing  the  wikipedia  article for  self interest. I request the article be protected. 47.205.198.247 (talk) 17:33, 1 August 2021 (UTC)

Well, that is 47.205.198.247’s personal opinion. I believe they have a conflict of interest. I hope that some knowledgable Wikipedia editors will take a look at this. I think the article could be improved on this point. The whole point of the 2015 experiments was that experiments which at that time had found the cosine, had found it usually after massive post-selection of data. Or only in situations where two subsystems were not physically separated at all. The 2015 experiments did not attempt to produce the cosine curve for very sound experimental reasons. Their intention was to demonstrate that local realism fails to describe physical reality, in an experimental context which is so stringent as to exclude alternative explanations. They didn’t need to, and didn’t try to, recover the cosine correlation curve. Richard Gill (talk) 17:46, 1 August 2021 (UTC)
 * Gill is not a physicist, and he is trying to read the technical reports to try to interpret them according to what he wants to see in them. I request this wikipedia article be protected. 47.205.198.247 (talk) 18:02, 1 August 2021 (UTC)
 * Technical reports? The papers cited by the editors who wrote the article. For instance: the paper by Hensen et al. in Nature, 2015, which even cites work by myself. Anyway, I plan to ‘let this be’ for a while. Richard Gill (talk) 18:26, 1 August 2021 (UTC)
 * Yes you just  let  it  be,  and  I request this Wikipedia article be protected. 47.205.198.247 (talk) 19:07, 1 August 2021 (UTC)
 * There's no need to protect the article. Vandalism has a specific meaning on Wikipedia, which does not apply to Richard Gill's edits in the slightest. XOR&#39;easter (talk) 21:01, 1 August 2021 (UTC)
 * of course (not that it really needs repeating), there's nothing wrong with Richard Gill's edits. I agree that it might be useful to add a statement that the exact cosine is not what is needed (nor predicted by QM if noise is included). I would, however, not mix noise and other state in the same sentence (and maybe leave the other states out completely in this paragraph, which I view as talking specifically about experiments related to the curve seen in the figure). E.g. one could write: "Experimental results contradict the classical curves and match the curve predicted by quantum mechanics if the noise present in the experiment is included." Now one could add: "Using states different from the singlet state discussed here will lead to a different angular dependence of the correlations. In certain cases the separation from the classical prediction is more resilient to experimental noise." though I'm not sure it's better to do that here or in the next paragraph when experiments using these different states are discussed. --Qcomp (talk) 22:54, 1 August 2021 (UTC)
 * I incorporated the first suggestion; I'm not quite sure where the latter would fit best. XOR&#39;easter (talk) 00:49, 2 August 2021 (UTC)
 * I would say "Experimental results contradict the classical curves and match the curve predicted by quantum mechanics if the noise present in the experiment is taken account of". But I'm not sure if "noise" is the best word. A "non-detection" is an experimental short-coming, but I wouldn't call it "noise". The old experiments had massive losses alongside of more or less random noise. This was taken account of by just omitting trials where either particle was not detected. How about: "Experimental results contradict the classical curves and match the curve predicted by quantum mechanics as long as experimental shortcomings are taken account of". The reference to the McGraw Hill encyclopedia of physics is useless. I think it sends one to a three page article entitled Hidden Variables which contains some ancient literature references and certainly does not say what it is quoted as saying. There is no separate article on Bell's theorem.I didn't find an article on the singlet state, but I will have another look in the index. One can consult the encyclopedia for free on the Internet Archive where it is available from some public library in the US. Not a very convenient link. Richard Gill (talk) 05:00, 2 August 2021 (UTC)
 * Don't Gill touch it. XOR'easter  has  it  right now,  with  his word  shortcomings.  47.205.198.247 (talk) 13:07, 2 August 2021 (UTC)
 * That's not how editing works here. I happen to have made the most recent change, but I'm not holding the conch shell. Please read the Civility policy. XOR&#39;easter (talk) 16:25, 2 August 2021 (UTC)