Talk:Bell's theorem/Archive 10

Non-locality of quantum mechanics in lead
In his original 1964 paper, Bell made a connection between the violation of Bell's inequality and the violation of locality, shouldn't this be in the lead? I understand that the lead is already very long, but the current statement seems incomplete to me.

Let me be more specific. In the introduction to Bell's 1964 paper, he writes that EPR show that hidden variables need to be introduced to restore locality, and that he proves that this cannot be done, and concludes "It is the requirement of locality [...] that creates the essential difficulty". The logic being that EPR says locality => hidden variables and hidden variables => Bell's inequality, so a violation of Bell's inequality means no hidden variables (at least not for all observables at once), and therefore no locality. This is spelled out in more detail in many later papers by Bell (see for instance "Bertlmann's sock and the nature of reality", printed in Speakable and unspeakable in quantum mechanics on p.139, see in particular the last paragraph on page 149 of the book) but the idea was already there in 1964. Bell writes in the Preface to Speakable and unspeakable "I regret never having written up the version of the locality inequality theorem that I have been mostly using in talks on this subject in recent years" which suggests he had the non-locality in mind since the beginning (which, it seems to me, is clear from the 1964 introduction).

In its current state, the lead emphasizes the impossibility of "local hidden variable theories" and the phrasing that follows suggests a dichotomy: either we have hidden variables or we have nonlocality. But Bell's 1964 paper actually proves two much stronger statements: 1. there is no locality in quantum mechanics, 2. there are no hidden variables for all observables simultaneously. So the dichotomy is a false one: it is not that we have to choose between hidden variables and locality: there is no locality (A or B is always true if A is true). And whereas Bell's 1964 paper is not as explicit as his later publications about these two statements, they are both in there (statement 1 is in the introduction, statement 2 is proved in section II).

So, given that Bell's theorem (as presented in its original form in 1964) implies a statement that is much stronger than what is presented in the lead, shouldn't the lead be changed to reflect this? Ianjauslin (talk) 14:31, 24 May 2023 (UTC)
 * I'm not sure what article you are reading, but it is clearly not this one. The first two sentences currently state, and I quote "Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories' given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light."  (bold mine).  The thing you say isn't discussed in the lead is literally the very first thing the lead mentions.  -- Jayron 32 16:46, 24 May 2023 (UTC)
 * I have indeed been reading this article. The first sentence states that quantum mechanics is incompatible with local hidden-variable theories. Bell's theorem proves that quantum mechanics is incompatible with any local theory. There is no need to mention hidden variables. In fact, that sentence is misleading: it suggests a false dichotomy: either quantum mechanics is nonlocal or there are no hidden variable theories, but quantum mechanics is simply non-local, so the dichotomy is redundant. The fact that quantum mechanics is not local is not currently in the lead of this article. Ian Jauslin (talk) 17:10, 24 May 2023 (UTC)
 * You keep saying that. It doesn't make it true.  Indeed, before you correct Wikipedia, you should work on correcting John Stewart Bell himself.  It's the source at the end of the first paragraph.  Bell himself is the source of the quote that you seem so keen on disagreeing with.  -- Jayron 32 18:14, 24 May 2023 (UTC)
 * I do not disagree with that quote. I disagree with the presentation of Bell's theorem as ruling out local hidden-variable theories.
 * John Bell agrees. He has written on many occasions that quantum mechanics is non-local independently from hidden variables. The argument is in the 1964 paper: "It is the requirement of locality [...] that creates the essential difficulty", as well as in many of his subsequent publications (a number of which have been collected in the "Speakable and unspeakable in quantum mechanics" book). For instance, from the 1976 paper "The local theory of beables", which is on p.52 of the Speakable book, Bell has a section titled "Quantum Mechanics is not locally causal" and, later in that paper, writes "So quantum mechanics is not embeddable in a locally causal theory" (p.59 in the book). He gives a comprehensive review of locality in quantum mechanics in "Bertlmann's socks and the nature of reality" on p.139, in which he explicitly spells out the logic that I expressed in the last paragraph on p.149. Ian Jauslin (talk) 18:55, 24 May 2023 (UTC)
 * I urge you to read WP:PRIMARY. You are arguing that we should take Bell 1964 as gospel and ignore the half-century of research that came afterwards. Even more, you are arguing that we should take your interpretation of Bell 1964 as gospel. WP:PRIMARY is specially important in subjects as contentious as Bell's theorem, and Wikipedia should definitely not take a side when the experts do not have a consensus. And they emphatically do not have a consensus. On the occasion of 50 years of Bell's theorem we had a heated argument between Maudlin and Werner, two renowned experts. Two other renowned experts, Wiseman and Cavalcanti, tried to settle the argument, and succeed only in pouring petrol on the fire.
 * Instead of going down this rabbit hole, what the Wikipedia article is doing is following what the secondary sources do: presenting instead CHSH's version of Bell's theorem, that is both clear-cut and non-contentious. It explicitly says several times that are multiple versions of Bell's theorem, as it should.
 * That said, I am sympathetic to your argument. I think it's a valid interpretation of Bell 1964, and one that is hardly mentioned in the article. I think it would fit well in the "Bell (1964)" section. When properly referenced to secondary sources, of course.
 * On the other hand, I don't think the argument in Bell 1964 is quite relevant. It is not a theorem (Bell himself didn't call it a theorem), but rather an informal argument. I think a much better argument for the nonlocality of quantum mechanics is Bell 1976, which is where your terminology of local causality comes from. Tercer (talk) 18:41, 24 May 2023 (UTC)
 * I agree: wikipedia should not take positions on unsettled arguments. However, in its current form, it does take a position: that Bell's theorem is about ruling out local hidden-variable theories. But there is no consensus on the fact that this is what Bell's theorem is really about. Wouldn't a reasonable middle ground position be to keep the statement about the no local hidden-variable theories in the lead (it is technically correct after all) as well as the discussion following it, but to add a few sentences that explain that a consequence of Bell's inequality is non-locality in quantum mechanics, independently of hidden variables (the "independently of hidden variables" bit doesn't even need to be spelled out explicitly in my opinion). (I had made such a change before, but it was reverted).
 * I also agree that this statement is much more clearly exposited in Bell's 1976 paper.
 * I also completely agree with the presentation of the CHSH inequality rather than Bell's original. My only suggestion here is to add content to the lead, not change the content of the body of the article. Ian Jauslin (talk) 19:07, 24 May 2023 (UTC)
 * I think there is consensus that Bell's theorem does rule out local hidden-variable theorems. Pretty much all texts on Bell's theorem repeat this. A bit more controversial, but still widely supported, is the assertion that Bell's theorem implies that quantum mechanics is in some sense nonlocal. What there is absolutely no consensus about is what Bell's theorem is and what Bell himself meant, and this is what Wikipedia should steer clear from.
 * In any case, I'm emphatically opposed to adding any content to the lead. Just look at its current state. Doesn't it make you want to cry? Perhaps a sensible way forward would be to move the second and third paragraphs to the body of the text, so that there would be space in the lead for more content.
 * Remember, though, that the purpose of the lead is to summarize the body of the article. You can't add content to the lead that is not supported in the body. Tercer (talk) 19:36, 24 May 2023 (UTC)
 * I'd like to shorten the lead somehow. Some of the second and third paragraphs are perhaps important enough to keep (like the bit about how measurements are performed independently on the two separated particles of an entangled pair). But it may be possible to condense and combine those two paragraphs. XOR&#39;easter (talk) 19:41, 24 May 2023 (UTC)
 * I agree that the lead is too long. I also agree with XOR'easter that it would be better to condense them than move them.
 * What would you think about shortening them to:
 * 'The term is broadly applied to a number of different derivations, the first of which was introduced by Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox". Bell's paper was a response to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen proposed, arguing that, in order for quantum mechanics to be local, hidden variables (in the sense described above) need to be introduced for all observables. Bell considered a setting where measurements are performed independently on the two separated particles of an entangled pair, and proved that, should EPR's hidden variables exist, then a certain statistical inequality would have to hold true. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts violations of this inequality. Consequently, quantum mechanics is incompatible with a theory in which all observables have hidden values.'
 * What do you think? (should the term 'all observables' be replaced with 'non-commuting observables', or is that too technical?)
 * What would you think about adding a sentence at the end of this paragraph to the effect of:
 * 'Since these hidden variables were shown by EPR to be required by locality, Bell deduced that quantum mechanics is "nonlocal", in the sense discussed above.'
 * (maybe with a citation to Bell 1976?) Ian Jauslin (talk) 20:10, 24 May 2023 (UTC)
 * It's a start, but it needs more workshopping, I think. The idea of an entangled pair should be attributed to EPR, not Bell. Writing "the" Bell inequality in the singular is somewhat at odds with the rest of the article. "Observable" is already somewhat technical, even without the modifier "non-commuting" (if one isn't acclimated, it looks like a word like "quantity" is missing). Per the comments above, I think flat statements in Wikipedia's voice about what "Bell deduced" have to be made very, very carefully, if we make them at all. XOR&#39;easter (talk) 21:07, 24 May 2023 (UTC)
 * I am all for workshopping!
 * Actually do we need to mention the entangled pair at this level?
 * Good point about "observable". I am happy with "observable quantity".
 * Point well taken about "Bell deduced". I would be happy to replace it with "It follows that" with a reference to Bell 1976 at the end of the sentence.
 * How does this look:
 * 'The term is broadly applied to a number of different derivations, the first of which was introduced by Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox". Bell's paper was a response to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen proposed, arguing that, in order for quantum mechanics to be local, hidden variables (in the sense described above) need to be introduced for all observable quantities. Bell proved that, should EPR's hidden variables exist, then a certain statistical inequality would have to hold true. This constraint would later be called a Bell inequality (of which there are many formulations, see below). Bell then showed that quantum physics predicts violations of this inequality. Consequently, quantum mechanics is incompatible with a theory in which all observable quantities have hidden values. Since these hidden variables were shown by EPR to be required by locality, it follows that quantum mechanics is "nonlocal", in the sense discussed above. ' Ian Jauslin (talk) 21:25, 24 May 2023 (UTC)
 * The parenthetical aboves and belows are distracting, at least to me. Removing all mention of entangled pairs goes way too far and puts this summary out of sync with the text it is supposed to be summarizing. And the last sentence still has the problem that it advances a particular take on Bell's results as the implication of Bell's results. We simply aren't in a position to say it follows that quantum mechanics is "nonlocal". Without qualification, this is taking a side on an issue where the experts disagree (vehemently). With a qualification about the sense in which it is meant, it is redundant with the first paragraph. XOR&#39;easter (talk) 21:44, 24 May 2023 (UTC)
 * OK, how about:
 * 'The term is broadly applied to a number of different derivations, the first of which was introduced by Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox". Bell's paper was a response to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen proposed, in which they considered a setting where measurements are performed independently on the two separated particles of an entangled pair. They argued that, in order for quantum mechanics to be local, hidden variables need to be introduced for all observable quantities. Bell proved that, should EPR's hidden variables exist, then a certain statistical inequality would have to hold true. This constraint would later be called a Bell inequality. Bell then showed that quantum physics predicts violations of this inequality. Consequently, quantum mechanics is incompatible with any local theory in which all observable quantities have hidden values. Since these hidden variables were shown by EPR to be required by locality, Bell deduced that quantum mechanics is "nonlocal". '
 * On the last sentence, it seems to me that this is why it makes sense to have sentences such as "Bell deduced". That statement is immediately verifiable, and irrefutable: Bell wrote out a deductive reasoning that led him to write that quantum mechanics is nonlocal, as is shown in the reference. This whole paragraph is historical: it describes Bell's reasoning, so it makes sense for it to be tied to what Bell wrote. Would it be better not to have a description of Bell's reasoning?
 * edit: changed 'incompatible with a theory' to 'incompatible with any local theory' to stay closer to Bell's text and the Bell 1964 part of the body of the article.Ian Jauslin (talk) 22:11, 24 May 2023 (UTC)
 * It would be better to summarize what the field as a whole has taken as the message. Unfortunately, the field as a whole doesn't all agree. Can one take the jump from "a hidden-variable model of nature must be nonlocal" to "nature is nonlocal"? (shrug) That's for the literature to argue out, not for Wikipedia to decide. Worse yet, the experts don't agree with each other about what Bell meant at each point in time. This is all too much for the introduction of an article like this to get into. Shortening the lede's current description of the particles in an EPR scenario to entangled pair seems to be going too far. "Entangled" here has a specialized meaning and needs to be clarified in some way. XOR&#39;easter (talk) 00:52, 25 May 2023 (UTC)
 * I understand that this is delicate. However, since the disagreement is whether Bell's inequality implies that quantum mechanics is nonlocal, not mentioning that there are authors (including Bell) that claim that it does is taking a side. The lede as it is currently written does not represent the views of many experts in the field, including Bell, Maudlin (who was mentioned earlier), Goldstein, Bricmont... Having both views expressed in the lede seems like a good compromise to me.
 * As to debates on what Bell meant, I understand that some of his statements may have been ambiguous, but in the work I cited, Bell writes "Quantum mechanics is not locally causal" in bold letters. This is not ambiguous. And this point can be made even more unassailable by adding many more Bell quotes if you think this is necessary.
 * For the entangled pair, I'm not sure how much detail needs to be given (I'm still not convinced that it is an essential piece of information for the introduction). Could 'measurements are performed independently on two separated particles in a special quantum state called an "entangled pair"' be suitable? Ian Jauslin (talk) 02:10, 25 May 2023 (UTC)
 * I don't think there's room in the lede to cover the debate; certainly not as it stands, and perhaps not even with the shortening being considered. But that's OK; not everything has to fit into the first few paragraphs. If we are to include it, the right way to go would be to work on the main text first and then, once that is settled, write a workable summary. Otherwise, the intro just gets longer and longer as every little thing getting mentioned prompts somebody to add another little thing.... There's also the question of whether this article is the right place to get very far into that. We have a whole host of articles in this corner of the encyclopedia, and not much thought has been put into how to organize them on a larger scale. There's Bell's theorem, Bell test, Hidden-variable theory, Local hidden-variable theory, EPR paradox, quantum nonlocality, principle of locality, CHSH inequality, etc. What goes into which? XOR&#39;easter (talk) 02:28, 25 May 2023 (UTC)
 * Some do advocate nonlocality, but those views are already represented in the section titled "Non-local hidden variables". That is enough. It is not a mainstream view. Roger (talk) 03:52, 25 May 2023 (UTC)
 * Nonlocality is not discussed in that section. There, they talk about the possibility of having a nonlocal hidden variable theory, i.e. Bohmian mechanics, which is indeed not mainstream. Nonlocality is not Bohmian, it is a theorem about standard quantum mechanics. Ian Jauslin (talk) 04:46, 25 May 2023 (UTC)
 * The possibility of nonlocal hidden variables is the only nonlocality implied by Bell's theorem. Roger (talk) 17:39, 25 May 2023 (UTC)
 * Actually, Bell's inequality shows that quantum mechanics is a nonlocal theory. There are several argument that have been made that lead to this conclusion, some of which by Bell himself. He wrote a very accessible review entitled "Bertlmann's socks and the nature of reality" (you can find a PDF of the paper easily, for instance using Google Scholar; it is also reprinted in the book "Speakable and Unspeakable in quantum mechanics"). One argument, which is summarized on the next to last paragraph of section 3 (p.149 in the Speakable book), is that Bell's inequality implies that there are no local hidden variables, but EPR show that the only way to preserve locality is to have hidden variables. Therefore, the absence of local hidden variables implies no locality. Another argument Bell made is written out in section 4, where a Bell inequality is derived without the assumption of hidden variables, just locality, and quantum mechanics is shown to violate it. Therefore, quantum mechanics must be nonlocal.
 * Yes, Bell's later papers do include some peculiar beliefs about locality and hidden variables. This article is about Bell's theorem. Maybe those beliefs can be mentioned somewhere, if not already. Roger (talk) 05:16, 26 May 2023 (UTC)
 * Well, those beliefs are based on theorems. The 1976 version of Bell's argument is a formal one, with clearly stated hypotheses and a conclusion. The locality hypothesis is that the probabilities of the outcomes of A and B, conditioned upon a complete description of the state of the system being measured, factorize (in other words, conditioning on the complete description of the state of the system removes correlations). A violation of the inequality means that this factorization does not hold (or that one of the other assumptions fails, hence the possibility for superdeterminism). If the probabilities do not factorize, the ouctomes are not independent. Wouldn't that qualify as a breach of locality, in the sense laid out at the beginning of this wikipedia article? Ian Jauslin (talk) 12:57, 26 May 2023 (UTC)
 * Yes, the hidden variables are nonlocal in that sense. You could add to the section on nonlocal hidden variables, if you think it is needed. Roger (talk) 17:19, 26 May 2023 (UTC)
 * The 1976 version of Bell is extremely general: hidden variables are allowed by the theorem, but not required. So the statement applies to regular quantum mechanics as well as a theory with hidden variables. Ian Jauslin (talk) 17:25, 26 May 2023 (UTC)
 * Okay, go ahead and add it to the section, but be sure you have a secondary source saying that it is a generally accepted interpretation of the theorem. Or say it was just the opinion of Bell and a few others. Roger (talk) 00:54, 27 May 2023 (UTC)
 * Very good point, I will make sure to do that. Thanks! Ian Jauslin (talk) 03:50, 27 May 2023 (UTC)
 * (Strictly speaking there is one way out of nonlocality, which is superdeterminism, this is discussed briefly in the body of the article). Ian Jauslin (talk) 20:23, 25 May 2023 (UTC)
 * That's fair. I have a long flight coming up next week, and I might try my hand at a section on Bell 1976. Would that be of interest?
 * There are indeed many articles. Do you think some should be merged? But a discussion on Bell 1976 certainly seems to have a place here: it is another formulation of the Bell theorem. Ian Jauslin (talk) 04:53, 25 May 2023 (UTC)
 * I think a section on Bell 1976 would be most welcome. Also, I think the argument you're making about EPR + Bell implying nonlocality would fit well in the already existing section of Bell 1964. It's bizarre that it doesn't mention that, instead the whole section is about irrelevant mathematical details.
 * As for your discussion on shortening the lead, I'm afraid you both are attempting the impossible. It's just too much information. It needs to be cut down, not condensed. My suggestion is to remove any reference to EPR, as that is just history, and instead mention the different versions of the theorem with their different interpretations. Tercer (talk) 12:07, 25 May 2023 (UTC)
 * OK great, I'll take a whack at a section on Bell 1976 and add a couple sentences to Bell 1962. By the way is there a way that I can make changes to the page, but instead of publishing them, submit them for review? Something similar to a git pull request?
 * After that we can come back to the lede and discuss how to make it more of a summary of the contents of the article, and less expository?
 * And thank you so much Tercer and XOR'easter for all your help and your patience! Ian Jauslin (talk) 14:35, 25 May 2023 (UTC)
 * One way to do something like that is making a draft in your "sandbox" page to see how it looks and get feedback. XOR&#39;easter (talk) 18:21, 25 May 2023 (UTC)
 * Great! Thank you for the info! Ian Jauslin (talk) 20:23, 25 May 2023 (UTC)
 * It's probably worth looking at how the Stanford Encyclopedia entry discusses "local causality", "parameter independence", "outcome independence", etc. XOR&#39;easter (talk) 14:39, 31 May 2023 (UTC)
 * Thanks for the source! It seems quite thorough!
 * I've been working on a section on Bell 1976 (which I'm calling 1975 because it appeares in lecture notes from 1975 that was reprinted in a journal in 1976). In it, I simply state the assumption of local causality in the way Bell does it, which is parameter + outcome independence. I am still gathering some more bibliography, and will post it for review early next week.
 * I was thinking that a review of the different notions of locality would be better suited for the article Quantum nonlocality rather than this one. In this article, we could just have a statement of the locality condition, and let the reader decide for themselves what the philosophical implications of the assumptions are. What do you think? Ian Jauslin (talk) 17:50, 31 May 2023 (UTC)
 * That sounds generally reasonable. XOR&#39;easter (talk) 23:14, 31 May 2023 (UTC)
 * As long as it's clear that the locality in Bell 1976 is not the same as the one in Bell 1964 I'm fine with that. Over and over again my students have problems because what one source calls locality is not what another source calls locality. Tercer (talk) 06:54, 1 June 2023 (UTC)

The assumptions in Bell's theorem about "the nature of measurement" are not "basic" (and Supermeasured≠Superdetermism)
The assumptions made about measurement independence in the theorem are decidedly non-trivial, per the important clarifying details added in my recent edit, which I then made further follow-up edits in an attempt to preserve neutrality & be more concise.

From what I can glean, my edit was reversed for the reason that it's WP:UNDUE "as discussed extensively in the talk page". However I believe my topic is not related to the existing topic.

The existing topic is arguing for a literal reading of Bell's paper as it was written 70 years ago, I agree it's WP:UNDUE.

Whereas my topic is about updating the article from its current state (which I believe to be misleading), with respect to recent discoveries (2022) that are not refuted in the scientific community. I believe it is not niche to understand that measurement independence is critical (Bell later admitted this himself after the famous 1972 talks by John Clauser), it's simply that many people are not aware of it. And I believe it's Wikipedia's primary responsibility to be accurate, despite how many people know something is true.

If you agree with me on that point at least, but you still decide to keep out the info about "supermeasured" theories, I would be happy.

That said, I will still try to make an argument to keep all of it.

On reading WP:UNDUE, it says:

> "Giving due weight and avoiding giving undue weight means articles should not give minority views or aspects as much of or as detailed a description as more widely held views or widely supported aspects. Generally, the views of tiny minorities should not be included at all, except perhaps in a "see also" to an article about those specific views."

I see where you're coming from, since anyone proposing that local hidden variables can exist is often considered herecy despite the fact that it doesn't necessarily conflict with Bell's theorem. To be clear: My edit does not give any weight to superdetermism at all, in fact it's evidence that superdeterminism is not required for local hidden variable theories to exist.

In any case, my edit was not intended to talk about the views of tiny minorities, but rather the (updated) views of Bell himself, as well as the scientists who won the 2022 Nobel prize. They obviously weren't making predictions about superdeterminism and supermeasuring, but they were the cause of Bell reworking his theorem after the original theorem became known as Bell's inequality. Local hidden variable theories are at the crux of Bell's theorem, therefore understanding how they work or don't work under Bell's own assumptions is crucial for understanding the theorem's context in science today. Finally, this kind of research is a perfect example of scientists using Bell's theorem to make novel discoveries about the nature of the universe, which incidentally furthers our understanding of what it means for something to be "measurement independent", which Bell himself later admitted was a non-trivial assumption.

Finally, I want to add that if this article bothers to mention "free will", then it should at the very least clarify that this is not a valid argument against all local hidden variable theories, only ones like superdeterminism that violate measurement independence via correlation with hidden variables.

Thank you for considering. If you're still not convinced about why measurement independence is non-trivial, please watch this video. . This is about understanding the true nature of Bell's theorem, and if it's a minority opinion in the science community that measurement independence is important, I believe they are mistaken & need to brush up on their history. Dinosoeren (talk) 14:14, 13 July 2023 (UTC)
 * The extensive discussion in the talk page I was referring to is this one. It's in the archives of the talk page. And it's about precisely the same subject: Hossenfelder was trying to add mentions to her work in this page. The YouTube video you're linking to is also by Hossenfelder.
 * The "discoveries" you mention are not from 2022. It's the same old story about superdeterminism. Now they're using a different name, "supermeasured", but the underlying theory is the same. It's WP:UNDUE because it's a minority view. The mainstream sources either don't mention superdeterminism at all, or mention it only to immediately dismiss it. Tercer (talk) 15:04, 13 July 2023 (UTC)
 * I see, thanks for the context. Like I said, I wouldn't be opposed to excluding discussions about "supermeasured" theories in this article. If anything, that could go in Superdeterminism.
 * But how is it you don't agree that framing measurement independence as trivial seems antithetical to Bell's and others' understanding of the theorem after 1972?
 * In that regard, I would argue precisely the (non-niche) concept of "measurement independence" ```has``` been more rigorously defined by Hossenfelder's work - even if it happens to come from researching properties of a niche topic.
 * Scientists doing work on the fringe are often ignored simply because of the controversial topics they pursue, but if a side effect is that we now have a new mathematical model for describing violating measurement independence, I don't think it should be kept from people simply b/c this insight into previously poorly-understood complexities within the assumptions required for Bell's theorem came from somewhere unexpected. Do you see what I'm getting at? Dinosoeren (talk) 15:45, 13 July 2023 (UTC)
 * People have always known that no-superdeterminism is a necessary assumption. Bell himself did. There is however little discussion of it because the mainstream sources consider superdeterminism to be obviously false. There is also nothing new in a mathematical model for it. Not only that's very easy to construct, but also such models have been published decades before Hossenfelder's work. Tercer (talk) 16:06, 13 July 2023 (UTC)
 * Ok. Again I would say based on my understanding, being certain that no-superdeterminism is a necessary assumption is:
 * 1. probably accurate
 * 2. not necessarily related to supermeasuring or other models which don't rely on hidden variables for measurement setting
 * 3. based on an assumption that measurement independence is trivial, which I haven't seen any evidence that it's not. Dinosoeren (talk) 16:15, 13 July 2023 (UTC)
 * I meant I haven't seen any evidence that it is necessarily trivial. Dinosoeren (talk) 16:16, 13 July 2023 (UTC)
 * To be clear about #3, that's an argument against superdeterminism, not against believing no-superdeterminism. Again, I think claiming that measurement independence is non-trivial doesn't disprove anything about Bell's theorem... not even a little bit. Dinosoeren (talk) 16:45, 13 July 2023 (UTC)
 * Can you please tell me: why couldn't there be a local hidden variables model assuming a non-trivial implementation of measurement independence, which then is (perhaps later) proven to just be a special case of Bell's theorem? Similar to how Einstein proved General Relativity after proving Newton's theory was just an approximation of Special Relativity. Dinosoeren (talk) 17:17, 13 July 2023 (UTC)
 * I'm sorry, I'm really not interested in arguing about superdeterminism, I share the mainstream view that it's a complete waste of time. Tercer (talk) 17:51, 13 July 2023 (UTC)
 * I thought I was arguing about Bell's theorem, but what do I know. I'm just some guy who doesn't feel comfortable making assumptions that Bell himself said were non-trivial to make. Dinosoeren (talk) 19:44, 13 July 2023 (UTC)
 * Yes, the assumption is trivial. Many accounts of Bell's theorem do not even mention it. All you have cited is one fringe opinion in favor of superdeterminism. Roger (talk) 20:49, 13 July 2023 (UTC)
 * Thank you both for your replies but I also cited Hall, 2015 and Clauser, 2003. And I thought I made it clear in my first reply I have no problems with putting aside superdeterminism and even supermeasuring. Clearly it was a mistake including Hossenfelder's citation, it seems all the attention has gone there instead of what I've actually written. Dinosoeren (talk) 21:12, 13 July 2023 (UTC)
 * Are you ok with simply ignoring the fact that most "accepted" papers on Bell's theorem fail to consistently describe locality as either "spooky action at a distance" or "spatially unseparated knowledge updates"? It's not even that clear in this article which one is implied in which contexts, they are used interchangeably as the same word: 'locality'. This not only leads to confusion about quantum mechanics itself, but also leaves readers wondering if Bell's theorem proves anything about reality or only says something about the accuracy of our current quantum model. Superdeterminism and fringe theories aside, I believe both concepts of 'locality' and 'the nature of measurement' are not described adequately here. Dinosoeren (talk) 21:47, 13 July 2023 (UTC)
 * I meant 'non-locality'. Hopefully you get the gist. Dinosoeren (talk) 22:07, 13 July 2023 (UTC)
 * Yes, a lot of people misuse the term "nonlocality". Maybe you can take that up on the articles on that subject. The Hall paper is not even on quantum mechanics. The Clauser paper is behind a paywall, and I did not look at it. Bell's theorem does not say anything about reality or accuracy of quantum models. If readers get that impression, so much the better. Roger (talk) 01:13, 14 July 2023 (UTC)
 * How can you tell me with a straight face that the Hall paper isn't about quantum mechanics when it's mentioned explicitly in both the Abstract and the Introduction?
 * It's also mentioned several times throughout, e.g. here's an excerpt:
 * > "For example, in standard quantum mechanics λ may be taken to range over a set of density operators, with (2) for some density operator λP associated with preparation procedure P and some positive operator valued measure (POVM) {EmM ≡ Eabxy} associated with the joint measurement procedure M = (x,y)."
 * The Hall paper is clearly about measurement independence (in the title) as it relates to quantum mechanics.
 * As for the Clauser paper, here is a non-paywalled release of Chapter 6 of The Early History of Bell's theorem. This is written by a 2022 Nobel laureate. Are you going to tell me it's fringe?
 * Here is a noteworthy quote from pages 72-73:
 * > ...A very powerful secondary stigma began to develop within the physics community towards anyone who sacrilegiously was critical of quantum theory's fundamentals. This stigma long outlived the McCarthy era and persisted well into the 1970s and 1980s...
 * > This stigma was very real and had more than just a mild social impact on the conduct of physics. For example, even as late as the early and mid seven-ties, whenever a manuscript discussing the foundations of quantum mechanics (and especially one discussing hidden variables) was submitted to either the Physical Review or Physical Review Letters, editor Samuel Goudsmit would, in turn, enclose a one-page APS policy statement along with it to the manuscript's referee. That policy, in essence, urged the referee summarily to reject any paper on this subject, unless the paper was both mathematically based and gave new quantitative experimental predictions. Bohr's response to EPR certainly could not have been published under Goudsmit's stated criteria...
 * > As part of the “common wisdom” taught in typical undergraduate and graduate physics curricula, students were told simply that Bohr was right and Einstein was wrong...
 * > An obviously central figure in the development of Bell's Theorem is the hero of our story, John Bell, himself, who appeared to be keenly aware of the power and potential danger available within this stigma. Generally, he appeared to exercise great caution to avoid its wrath. Perhaps, for this reason, not much of his work on Bell's Theorem was formally published (see below) until it much of it was later collected into his book, Speakable and unspeakable in quantum mechanics [9]. John Bell clearly evidences his awareness of the stigma and its associated limitation to open discussion, via the double-entendre manifest in this book's title. His article, Against Measurement [10],is somewhat more poignant and outspoken on this issue. I offer here three anecdotes further supporting my opinion of his extremely cautious attitude towards the stigma...
 *  Do you see the irony here?... 
 * I believe in one of the later chapters about loopholes is when Causer explains Bell's response to his talks in 1972, pertaining at least partially to non-triviality of measurement independence.
 * Finally, I'm not the only one to make this connection.
 * I can easily quote another recent paper Kupczynski, 2022 (PhD in theoretical physics who, let me be clear, is NOT refuting the validity of Bell's theorem):
 * > "A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model, called a violation of measurement independence, would mean a violation of experimenters freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities... From two bad choices he chose nonlocality. Today he would probably choose the violation of statistical independence understood as contextuality.
 * So far I've given plenty of high quality sources to prove my point, most of which I gather the participants of this chat didn't even bother to read. Why am I the one with the burden of proof arguing against ppl not even willing to consider my point? I urge you to cite higher quality sources disproving the ones I've cited above, or please invite an expert PhD physicist into this thread (or make me aware of your own credentials), since at the moment I'm not convinced y'all are able to willing or able to discuss this topic in a Socratic discussion that respects my position without blatantly disregarding everything I say b/c you don't enjoy thinking about the complexities of your safe (and possibly wrong) assumptions about Bell's theorem. Dinosoeren (talk) 03:18, 14 July 2023 (UTC)
 * The Hall paper is trying to mimic QM with hidden variables. It is not studying QM. Clauser and others thought that QM was wrong, and complained about the top journals not wanting to publish untestable anti-QM papers. The Kupczynski paper is also rejecting QM, and speculating about how Bell might also reject it. These papers are not interesting to anyone who accepts QM. Clauser's paper is a little interesting for its history, as he got a Nobel prize for proving himself wrong, and conventional wisdom correct. The prize was just for his experimental work. Roger (talk) 05:46, 14 July 2023 (UTC)
 * These are not high-quality sources. They are rather obscure, which confirms the fringe status of superdeterminism. Hall's and Clauser's papers are published in conference proceedings, and have a grand total of 8 and 3 citations, respectively. Kupczynski has 6 citations, which is actually a good number for a 2022 paper, but when you look at them you see that they are all by himself or by people saying he is wrong. Tercer (talk) 07:32, 14 July 2023 (UTC)
 * Also, Kupczynski published in Entropy, which is basically like not being peer-reviewed at all. XOR&#39;easter (talk) 22:14, 14 July 2023 (UTC)


 * Superdeterminism is a fringe theory. It is supported by Hossenfelder and only a couple of others. There is no mainstream acceptance of it. It requires rejecting 99+% of science. There is no theory consistent with any experiments. Nobody has anything good to say about it, except that it is a theoretical possibility. The idea that we are all in a simulation is taken more seriously. The article already has a section on it, and there is no reason to say any more, except to say how ridiculous it is. Roger (talk) 17:41, 13 July 2023 (UTC)
 * I like how folks have just decided I'm arguing for superdeterminism when I'm not. Dinosoeren (talk) 19:40, 13 July 2023 (UTC)
 * To me, it looks like these edits vastly overstressed a point that the physics community and the relevant literature simply do not stress. XOR&#39;easter (talk) 22:12, 14 July 2023 (UTC)

Recent reverts
I have, like, no time or energy to put into this article now, but I did want to say that I think the text removed here is a bad addition. Squeezing every possible qualification into the paragraph that is supposed to be the most broadly comprehensible is a bad idea. The intro is already overlong; if anything, it needs to be condensed (and if we are to add any more to it, it needs to be condensed significantly first). Moreover, per house style, the intro is supposed to provide a capsule summary of the main article that follows, and putting emphasis upon a point that the main article doesn't is giving that point undue weight. (The article itself doesn't even say "noncontextual" until it gets into Gleason's theorem.) No doubt the page needs improvements, but I don't think this is one of them. XOR&#39;easter (talk) 20:56, 27 February 2024 (UTC)


 * Without mentioning noncontextuality, the conclusion drawn is literally incorrect. In order to describe a theorem, one must state all of the hypotheses of the theorem. As written the article is misleading. Physicalisms (talk) 18:58, 7 March 2024 (UTC)
 * This isn't an issue of mathematics, it's one of language and technical writing. No one disagrees as to what the theorem is or what it fundamentally requires, but we have to explain it in the format of an encyclopedia article. It's fine to have an incomplete description after the end of the first paragraph.
 * (This reminds me tangentially of the saga where Wikipedians came to heartache and an ArbCom decision over the ordering and treatment of explanations in the Monty Hall problem article.) Remsense  诉  19:37, 7 March 2024 (UTC)
 * The term "noncontextual" is confusing, and does not add anything. Roger (talk) 20:11, 7 March 2024 (UTC)

Mermin-Peres magic squares.
The Mermin-Peres magic square analysis seems missing here. As a simplified "game" it might make some of this more accessible.

Mermin and Peres both worked on simplified Bell models as summarized in: These models take the form of a "game" described in the common sense of a game but treated as in game theory. The wikipedia treatment of the Mermin-Peres magic square is buried inside Quantum pseudo-telepathy. Johnjbarton (talk) 17:59, 27 March 2024 (UTC)
 * Aravind, Padmanabhan K. "Quantum mysteries revisited again." American Journal of Physics 72.10 (2004): 1303-1307.


 * I disagree. The rules of the game are more complicated, the proof of the local bound is more complicated, and the quantum strategy is much more complicated. The only good thing about the magic square is that the quantum probability of victory is 1. Which is rather nice but conceptually irrelevant for Bell's theorem, and in any case already covered by the GHZ game here. Tercer (talk) 19:55, 27 March 2024 (UTC)