Talk:Bell's theorem

As a mathematician, I don't know much about the physics underlying quantum mechanics. However, I believe statistics would show that the example cited has a basic flaw, viz:

"Each row describes one type of electron pair, with their respective hidden variable values and their probabilites N. Suppose Alice measures the spin in the a direction and Bob measures it in the b direction. Denote the probability that Alice obtains +1/2 and Bob obtains +1/2 by"

   P(a+,b+) = N3 + N4

The probability of two independent statistical measurements is not the sum of their individual probabilities, it is their product:

   P(a+,b+) = N3*N4

An analogy can be made when Alice and Bob each have a coin. These are independent statistical devices with probability 1/2, similar to the quantum mechanical case. The probability that Alice and Bob both flip heads is not 0.5 + 0.5 as stated in the article, but 0.5 * 0.5, or 0.25.

With this correction, Bell's inequality would hold true in all cases, even when the directions of a, b, and c are not orthogonal.

Probabilities

It is right that the probability of two events related by AND is the product of their individual probabilities. But these probabilities are the Nk (k=1,...,8) and not the P(x,y), which are related by OR and therefore give the sum. Let's consider P(a+,b+), for which there are the events e3 and e4 (line 3 and 4 of the table) that Alice mesures + in direction a and Bob + in direction b:

e3 = Alice mesures + - + AND Bob mesures - + -

e4 = Alice mesures + - - AND Bob mesures - + +

From that follows:

P(a+,b+) = P(e3 OR e4) = P(e3) + P(e4) = N3 + N4.

Ulrich Utiger

Loopholes

I made a few edits the other day to correct the impression that experiments had conclusively backed QM. However, some more radical revision is needed. The article ought to start by saying what "Bell's Theorem" is! The section labelled Hidden Variables is really the derivation of just one version of the inequality. Somewhere in the article we need a statement of Bell's original version and of at least the main one used in actual experiments (the CHSH inequality). The CHSH inequality page, incidentally, might need re-writing from scratch. (Caroline Thompson 10:27, 4 Jul 2004 (UTC))

Looking at the inequality derived here, I notice that it is not the one Bell derived, nor one that is in fact used in any experiment I know of. Moreover the assumptions behind it make it completely unusable in practice. They include the assumption that there is never a non-detection. If the table of possible outcomes and their relative frequencies were to be expanded to include zero outcomes it would not be possible to derive the inequality. I can't prove this directly (too much algebra) but used to have a nice diagram illustrating a local realist case in which it failed. The diagram was a trivial application of my [Chaotic Ball model (http://arXiv.org/abs/quant-ph/9611037)].

Does anyone even begin to understand the derivation of the QM formula? Could it not just be taken as read, since Bell's arguments concerned only what happens under local realist assumptions.

I think the article should:

1. State what "Bell's Theorem" is, admitting the definition is ambiguous since Bell himself never called his result a theorem and there are many different inequalities masquerading as his.

2. Sketch the basic setup of a two-channel experiment.

3. State the critical assumption:

There exist hidden variables set at the source and the probability of registering a + count for a given particle is determined by the hidden variable value together with the detector setting. The detection events themselve are independent, so that the probability of detection of both particles can be obtained by multiplying individual probabilities. (I need to check back to what Bell actually said here. I'm probably influenced by Clauser and Horne's 1974 paper.)

4 Give Bell's own derivation of his inequality, as per the 1964 paper.

5 List other "Bell inequalities", with links to where they are derived and comments on where used, if at all.

6 Tests of Bell's theorem.

Might need another section or two. The whole task looks quite hard work. Caroline Thompson 09:13, 7 Jul 2004 (UTC)

I've replaced the page as promised. I think I've included all significant content from its predecessor, except that I've relegated the quantum-mechanical derivation of the prediction to a separate page, Quantum mechanical Bell test prediction, and used the version in Shimony's new article [1] (http://plato.stanford.edu/entries/bell-theorem/). This uses less specialised jargon than the version in the original paper. Caroline Thompson 09:00, 14 Aug 2004 (UTC)

Move here:

I don't think most physicists find accepting the consequences of Bell's theorem to be difficult.

Living with "Bell test violations"

Though most accept that experiments have indeed violated Bell's inequalities, few are finding it easy to live with the consequences. There are currently two main ways whereby reconciliation can be attempted between local realism and the facts. The logic of Bell's theorem itself can be disputed, or the experimental evidence challenged.

I like some of the new information, however I do have two problems with the new text....

1) First of all, the really, really important thing that Bell showed was that quantum mechanics was incompatible with local realism. This demonstration is theoretically very important not withstanding the experimental issue over which is correct.

2) Second, there is the wiki rule "no original research"

Roadrunner 03:18, 17 Aug 2004 (UTC)

I added a summary of the Bell theorem which is intended to give the non-technical reader some background before launching into the math.

Roadrunner 03:55, 17 Aug 2004 (UTC)

Roadrunner: I've edited your contributions slightly. Hopefully I have not changed the meaning too much, just clarified things. There was a reason for the short introduction in my version: I wanted the table of contents to be sure of displaying on the first page when printed. It only just does so now.

I don't think I've included any actually "original" research. I've merely tried to tell the world some less well known facts. These days you can find experts in, say, "quantum information", who know all about the aspects of their subject that they want to use and yet have never looked at the details of a Bell test experiment and take it for granted that the basic "resource" they employ — quantum entanglement — really exists. My own studies have strongly suggested that though the correlations they use are very real, the explanation of what is happening is incorrect. See for example http://arxiv.org/abs/quant-ph/9912082. Caroline Thompson 12:27, 17 Aug 2004 (UTC)

latex code more or less legible

If you don't think the image files generated by latex are more legible, then you are free to change your viewing preferences. That's what's so nice about the wiki math tag, it leaves the choice up to the reader. Unless the equation is in line with text, it should always go in a math tag. You shouldn't force your personal preferences on anyone.

I'd be glad to use Latex if only I could find out how to force it to produce smaller fonts! I think it makes for a more comfortable read if all equations are at least the same size.

Caroline Thompson 10:06, 23 Sep 2004 (UTC)

You can't make latex use smaller fonts, but you can turn off latex. just go to your preferences. (I feel like i just finished saying this). Here is a more detailed set of instructions: click on "preferences". then click on "rendering math". then choose from among a variety of options, for example, if you choose "HTML if possible", and then the wiki will only show you rendered latex equations whenever possible. Using math tags allows everyone the maximum flexibility, so please don't revert such changes. They are useful for the wiki. -Lethe | Talk

Loaded sentence

Lethe is right. The sentence on loopholes is loaded, POV and merits removal.CSTAR 23:37, 20 Nov 2004 (UTC)

Presentation

In reading this page, I'm struck by the same reaction I often have to Wikipedia articles - we aren't thinking enough about writing for our (non-specialist) audience, as opposed to the (specialist) writers of the article. This article remains heavy going for me, even though I have a technical education, and have been interested in the whole Bell/EPR/etc are for some decades now. I would like to draw people's attention to the following article:

N. David Mermin, Is the moon there when nobody looks? Reality and the quantum theory, in Physics Today, April 1985, pp. 38-47.

which to me remains, almost 20 years later, the best introduction to the issues at hand, and the one that best combines rigour and understandability. I would really encourage the maintainers of this article (and no, I don't have time to do it myself!) to obtain this work, review it, and see if they can't get to this level of approachability here. Noel (talk) 16:55, 22 Nov 2004 (UTC)

I'm afraid that you can either have "approachability" or something near to the true facts, which are complicated. Yes, I'm aware of Mermin's article, and, in its way, it is very good. But it is wrong! His thought-experiment does not allow for the kind of "stochastic" model (one in which the hidden variables predict probabilities rather than actual results) that is relevant to the real experiments. He introduces Aspect's experiments, complete with photo of the apparatus, but nowhere mentions the fact that not all "photons" are detected. The reader is left to assume that the real experiment produced infringements of Bell tests and followed the same, deterministic, rules as the thought-experiment. Yesterday I checked a more recent article by him: http://arxiv.org/abs/quant-ph/0207140. He is still, I'm afraid, disseminating a misleading picture in which it is implied that an experiment with no non-detections has been conducted and has infringed a rigorous Bell test. [Incidentally, in order to understand where Aspect's results come from there is, in my opinion, no way of avoiding the issue of "accidentals". See Bell test loopholes.] Caroline Thompson 11:42, 23 Nov 2004 (UTC)

Caroline Thompson's POV and Self Promotion in this topic

Caroline Thompson has added references to her own papers in Bell's Theorem, even though the papers have little to do with Bell's Theorem. This smacks of self-promotion.

In addition, she has modified the thrust of the Bell's Theorem topic to match her own non-mainstream point of view, violating Wikipedia's NPOV policy. Specifically, she states that there are no experiments supporting the quantum mechanical position over the local realistic position she espouses. In fact, the Aspect experiment (and others following) are considered definitive by most scientists in the field.

These deficiencies should be corrected as soon as possible.

-DrChinese (Dave@DrChinese.com)

Hi DrChinese

I have never made any secret of the fact that my point of view is a local realist one, but nor have a I made any secret of the fact that I have read Aspect's PhD thesis and discovered that the raw data from one of his experiments does not support quantum theory. I have received no response from him to various requests for raw data from other experiments, but it is clear from the published facts that the data adjustment in his third (time-switching) experiment would be even greater, so that I can confidently predict that here too, the claim that the experiment vioates the Bell inequality is, to a local realist, suspect. The accepted point of view is based on inferior information -- just the published papers and the opinions of a very few quantum theorists and experimenters who, for reasons best known to themselves, never seem to have looked into the question of the legitimacy of his adjustment to his data. The result has been a very serious bias on behalf of the establishment in favour of quantum theory.

But this is not really, I take it, what you are challenging? You are simply pointing out that I have presented the local realist point of view. [I don't think your statement that I have not discussed "Bell's Theorem" is really justified, but let that ride.] Perhaps the solution is to preface the page by a statement of my identity and point of view?

The reason why I reference several of my own papers is that, although they cover facts that are already available in the literature (in, for example, Pearle's 1970 paper and Clauser and Shimony's 1978 report), they explain things more clearly, as far as possible intuitively, so that considerably less specialist knowledge is needed to understand them.

Incidentally, though I consider it only right and proper that the Bell's Theorem page should be written by a local realist, I have left the EPR Paradox with its quantum-theoretical bias.

Caroline Thompson 19:35, 9 Jan 2005 (UTC)

Thank you for your honesty in admitting your biased POV. In addition, none of your work adds anything to understanding Bell - your work involves the postulation of significant loopholes in Bell test experiments and more significantly, denial of the existence of photons. Despite your strongly helds views, this topic should follow mainstream science. I will be reverting this topic to an earlier version prior to most of your edits this week after consulting with others on an appropriate version. I would ask you to refrain from interfering with this process.--DrChinese 00:24, 10 Jan 2005 (UTC)

I have gone ahead and placed a POV warning on the page. As it is, this page has almost nothing to do with Bell's Theorem. I count perhaps 3 good paragraphs about Bell and his famous paper. There really isn't even any meaningful presentation of the derivation of his conclusions.

Instead, this page is currently focused on: a) presentation of alternative formulations of the Bell Inequalities, and their deficiences; b) tests of Bell Inequalities, and their deficiences; c) the failures of the mainstream physics community, especially in regards to ignoring the local realistic view; and d) references to Caroline Thompson's non-mainstream work having nothing to do with Bell's Theorem at all.

I would like to solicit assistance from others out there who would be interested in helping to locate a suitable version of the page for reversion.--DrChinese 04:16, 10 Jan 2005 (UTC)

DrChinese. You certainly have my support in this matter; unfortunately I think there is no suitable reversion; the article may have to be written from scratch. CSTAR 05:52, 10 Jan 2005 (UTC)

and mine. -Lethe | Talk 06:41, Jan 10, 2005 (UTC)

DrChinese: I see that you have inserted a POV caveat. This is fair enough.

I think everyone was agreed that the previous, quantum-theory-biased, version of the page was unsatisfactory. It did not even state what the theorem was. Lethe and CSTAR are therefore right: the whole page could be re-written.

Hopefully, though, sufficient people agree that it is valuable, in its own way, as it stands. It does not deserve to be simply deleted! People ought at least to be told that when they read about a test of Bell's inquality the experiment is not in fact testing Bell's original inequality under the original restrictive conditions. The distinction between Bell's original test, or the effectively similar Wigner-d'Espagnat test, and the CHSH or the CH74 tests, and the adjustments and assumptions made in actual experiments, are critical.

Sorry, DrChinese. I wrote the above before reading your request to stay out of the matter! I'm not sure I am able to obey this. If people write anything misleading I am compelled to correct them.Caroline Thompson 09:22, 10 Jan 2005 (UTC)

There is always a problem with users on a mission.

AFAIK the old version of the article has been exiled by Caroline to Sakurai's Bell inequality, arguably in violation of GNU FDL as the author list got lost by cut and paste.

I'm sorry about this. It was entirely unintentional. The page was just part of the original Bell's Theorem page. Since this Bell inequality (more properly termed the Wigner-d'Espagnat inequality) is neither Bell's original one nor one that is used in any experiments I felt it did not deserve prominance. Caroline Thompson 18:39, 10 Jan 2005 (UTC)

See also: Bell test loopholes, Bell test experiments, Hidden variable theory (this one is mainstream), Local hidden variable theory, Loopholes in optical Bell test experiments, CHSH inequality, Clauser and Horne's 1974 Bell test.

Pjacobi 10:31, 2005 Jan 10 (UTC)

POV on quantum mechanics

The POV is unfortunately not limited to this article on Bell's inequalities; for instance the article Interpretation of quantum mechanics offers the following sentence in the 1st paragraph:

However it becomes philosophically troublesome once it is mathematically demonstrated that it cannot have all of the properties that one would intuitively expect for it to have.

This is nonsense ...

Please note that the above was not due to me! I am not the only contributor to wikipedia who is a local realist or challenges some aspects of quantum theory. Apart from the pages I virtually created from scratch, all I have done on most is correct statements that implied that quantum entanglement had been "conclusively confirmed" or similar. Caroline Thompson 18:45, 10 Jan 2005 (UTC)

Interpretation is deemed necessary (by some, although there are or were notable exceptions such as perhaps Asher Peres) for the same reason that modal logic might need interpretation: The abstract formulation of QM is sufficiently different form the formal structure of the physical theories preceeding it that some kind of interpretation (in the sense of semantics) is necessary. Interpretation can itself be a formal activity, in the sense that the defining semantics can be itself be given formally, such as is commonly done with programming languages or mathematical languages. To see what this means for physical theories look at for example the formal semantics that is given by the Many-worlds interpretation.

I will cross post this comment to the talk page of that article which also needs revision in my opinion.CSTAR 18:02, 10 Jan 2005 (UTC)

That sounds good to me. We will probably need to take a fuller inventory of the related pages, determine which are the most significant, which have had the most damaging revisionism, and then work from there. The first clue is that there are references to Caroline Thompson's papers. It shouldn't be too hard to locate those references. I believe most of those should be removed as they do not meet Wikipedia guidelines. --DrChinese 20:39, 10 Jan 2005 (UTC)

I do hope, DrChinese, that you will allow references to my work in the Bell Test Loopholes page and a few others, or is it now your aim to suppress all information regarding loopholes? I trust not, since you have previously given me a measure of support!

How can a valid "encyclopaedia" be built if certain classes of information are excluded solely on the basis of the belief of a group of people that they are unimportant? They are nonetheless facts, and readers should surely have the right to know these facts so that they can judge their importance for themselves. Facts are facts. They are not just points of view. To suppress them is, I think, to support the quantum theory point of view to the exclusion of the local realist one, which is contrary to wikipedia policy.

Caroline Thompson 22:32, 10 Jan 2005 (UTC)

Caroline:

I personally think it makes sense for you to provide input in the Bell Test Loopholes article; you are pretty familiar with these and you could probably make your POV fit with it if you will simply restrain yourself a bit. I do not understand why you use such charged language in your presentation, basically saying you are right and everyone else is wrong. Examples: NO EVIDENCE FOR BELL VIOLATION, etc. There is plenty of evidence, not all of it is of equal caliber. Maybe there are even loopholes. Can you accept that?

Sorry, DrChinese, but the answer is "No!". On the basis of what I know there is no room for doubt: the QM claims of "violation of Bell inequalities" are effectively false since no valid inequality has ever been tested. I use charged language because this matter is of such critical importance. Theoretical physics has taken a wrong path that must be corrected otherwise it has reached a dead end. Students these days are being taught that Bell tests have been violated and, in consequence, forced to make valiant attempts at understanding the impossible. This it cruel to them, and wasteful of their intellects! It would only be justifiable if the evidence was incontrovertible and it is not.

Caroline Thompson 23:30, 10 Jan 2005 (UTC)

OK, then let's give Archimedes Plutonium a say on this article. I'm sure he believes "Theoretical physics has taken a wrong path that must be corrected otherwise it has reached a dead end" as you claim. CSTAR 01:25, 11 Jan 2005 (UTC)

Archimedes! I remember him... I followed the link but I missed a reference to his most brilliant (LOL) idea, moving Venus into an earthlike orbit... Meanwhile, Caroline is telling us with a straight face that evidence supporting QM is actually proof QM is wrong (her Chaotic Ball paper). --DrChinese05:58, 11 Jan 2005 (UTC)

I'm sure we're all appreciative of your efforts to correct the path of physics. But Wikipedia is not the place for it. Your efforts to use wikipedia to promote fringe views here are not appropriate. -Lethe | Talk 00:00, Jan 11, 2005 (UTC)

Hmmm ... I've just checked again what the POV page actually says. It is "In a neutral representation, the differing points of view are presented as such, not as facts." I think our problem here is that we are not really talking of POVs but of facts, and it so happens that I know more facts re the actual Bell test experiments and their assumptions than most "mainstream" physicists. It is not so much "fringe views" that I am promoting as "fringe facts". Surely an encylopaedia is the right place to get the facts straight? I am not pretending anything. I state in several places that these facts are not well known. What more can you ask?Caroline Thompson 09:58, 11 Jan 2005 (UTC)

Surely an encylopaedia is the right place to get the facts straight?. No. The right place is the peer-reviewed literature.CSTAR 14:04, 11 Jan 2005 (UTC)

I am not trying to suppress anything, much less your voice. But Wikipedia has a POV policy for a reason; Wikipedia's says that you should sometimes write what is generally believed, not what is right. It is not the purpose of Wikipedia to act as a spot to debate (which should be done in academic circles), it is educational. All articles are summaries and putting in all POVs equally is not the purpose. There are plenty of other opinions out there besides yours and there simply isn't space to include them all. If you have a problem with the Wikipedia editorial policy, you should discuss it with them. It makes perfect sense to me.--DrChinese 23:08, 10 Jan 2005 (UTC)

Yes, there are plenty of other opinions, but only one set of facts and it is these that my contributions discuss. Caroline Thompson 09:58, 11 Jan 2005 (UTC)

There are one set of facts; the determination of those facts is the result of the scientific process. The published literature is the record of the scientific process. The published literature gives little to the significance to your facts.CSTAR 14:04, 11 Jan 2005 (UTC)

Fully agreed, CSTAR. Given that Caroline has indicated no desire to particpate within the bounds of NPOV, I would say let's continue the re-building process for Bell's Theorem et al. I do not plan to debate her in this forum. --DrChinese 21:35, 11 Jan 2005 (UTC)

DrChinese, how about the following compromise? We reduce the "Bell's Theorem" page to a very short one just stating the definition (if this can be agreed!) of the basic theorem followed by two links, one clearly labelled QM, the other local realism. These would cover the two opposing views of its current experimental status, its role in theoretical physics, its applications and philosophical consequences. I don't know what the QM pages would say, but the local realist ones would cover the actual experiments and their local realist interpretations, allowing for the loopholes.Caroline Thompson 21:56, 11 Jan 2005 (UTC)

Having separate pages per POV is strictly against Wikipedia policy. You can setup such pages at the Wikinfo project. --Pjacobi 22:08, 2005 Jan 11 (UTC)

Thanks! If the worst comes to the worst I shall transfer some of my pages to Wikinfo. I hope it will not come to this, though. I hope wikipedia will allow publicity to be given to the full experimental facts, despite the playing down of these inconvenient truths by the community.Caroline Thompson 22:43, 11 Jan 2005 (UTC)

Tsirelson

If your are going to do an rewrite anyway, you may also have a look at Tsirelson's bound which would need more links to it and an stylistic overhaul. --Pjacobi 16:53, 2005 Jan 12 (UTC)

Interpretation

I think the articles that we are talking about (this one and also interpretation of quantum mechanics) should be worked in tandem. There are a few others. In any case I am going to put an POV tag also on the interpretation article. Nevertheless I will precede that action by a warning on the Talk page of that article.

BTW I have no objection to CT contributing to any of these articles provided she sticks to an account of the accepted facts. Moreover, there is a clear procedure for determining what the accepted facts are, namely the scientific literature. If she wants in her spare time to demolish the prevailing view of QM that's fine, (and I encourage it. It's fun to see egg on people's faces -- even on my own) but the way for her to begin doing it is to clearly and fairly represent on WP what QM is. This is an important principle in argumentative dialogue.CSTAR 03:42, 14 Jan 2005 (UTC)

I'm glad you don't object to my contributions! Thanks for saying so. However, it's down to the quantum theorists to put their side of the story. I have not, except perhaps minimally, contributed anything to the interpretation of quantum mechanics page, regarding it as a QM preserve. Nor, you may notice, have I done more than the minimum on the main Quantum Mechanics page, or the EPR Paradox one. All I have done -- and all I feel qualified to do -- is (a) present the facts re the actual Bell test experiments and (b) stand up for common sense and the ideas of local causality that prevailed before QM took root. Caroline Thompson 09:30, 14 Jan 2005 (UTC)

Sorry, Caroline, but CSTAR does object to your (past) contributions if they are in Wikipedia and biased. That would be 100% of the contributions I have seen so far. He said he is willing to work with you if you stick to "an accepted account of the accepted fact". You have repeatedly said you will not do so, and so I do not see a role for you in the re-vamping process. There is NO BURDEN OF PROOF on our backs. In fact there is no burden of proof on the LR position either because it is not generally accepted. We are not going to debate you, and we do not need to "compromise" a generally accepted position. We plan to present material as you would expect it from a college textbook on the subject, in suitable summary form as to make it of use to someone who would come to Wikipedia. Since none of your own work has been accepted by the scientific community at large, there should be no references to it. Sorry if that sounds harsh, but Wikipedia is not the place for self-promotion. You have your own web site and other places to promote your ideas.--DrChinese 21:31, 17 Jan 2005 (UTC)

DrChinese, to say that none of my work has been accepted is simply not true! There is as yet very little public recognition, but in correspondence with theorists and experimenters I am far from feeling ignored.

At present I know of only two places where "establishment" physicists have mentioned my work -- a paper by Tittel (http://arxiv.org/abs/quant-ph/9806043) and Abner Shimony's encyclopaedia article on Bell's Theorem http://plato.stanford.edu/entries/bell-theorem/ -- but many others have taken note of what I say. Nobody, to my knowledge, disputes the content of any of my papers. Indeed, one of the main reasons given by the editors of PRL for rejecting http://arxiv.org/abs/quant-ph/9903066 was that I was not saying anything that was not already well known! It is not yet in the text books, but would you really like to see wikipedia propagating false claims? If you restrict information relating to the loopholes, you leave the way open for convinced quantum theorists to simply say that "general opinion" is that local realism is no longer an option, and the reader has no way checking for himself. And if you don't include quite a few refs to my work, you won't be providing anywhere near as much information as he needs. As I think you realise, what I have to say about the loopholes is fact. What I have to say about the actual Bell inequalities used is also fact. Fact, not opinion, is what ought to be in both wikipedia and the text books.

Caroline Thompson 23:34, 17 Jan 2005 (UTC)

Caroline, you can (mis)represent my position and over-estimate the importance of your own work all day long. I am not going to respond further to your baiting. You have abused horribly the Wikipedia system and now it is going to take a lot of work by others to repair the damage. Please do not waste further time explaining how the rightness of your position justifies your actions. It doesn't. You knew perfectly well what you were doing, and it is disingenuous to imply otherwise.--DrChinese 01:37, 19 Jan 2005 (UTC)

DrChinese, surely the wikipedia policy does not actually ban minority views? The guidelines merely say that when such are presented it should be made clear that they are not generally accepted. Caroline Thompson 13:32, 19 Jan 2005 (UTC)

Besides re-stating me general opinion, that some merges should to done, I've found a paper (Phys.Lett. A260 (1999) 323-327), which IMHO (I only have a very shallow exposure to this topic) can be used as reference for a sober representration of the BT/lhv/"loopholes" problematic. The paper http://arxiv.org/abs/quant-ph/?9905018

explains why detector efficencies open a "loop hole"
explicitely constructs a lhv theory in agreement with observations
demonstrates how "artifical" and vulnerable to the sharp side of Occam's razor such a theory is

Pjacobi 09:58, 2005 Jan 19 (UTC)

Yes, I'm familiar with this paper, and could use it maybe as the main ref for the detection loophole, but it only covers the one loophole. On second thoughts, I seem to remember that it does not make it clear that the loophole has only been open in its wide form since Aspect inaugurated the use of the now-standard version of the CHSH test, using total observed counts as divisor in the estimates. My own papers cover several others, at least one of which (the subtraction of accidentals) can be shown to be of empirical importance.Caroline Thompson 13:32, 19 Jan 2005 (UTC)

The article fails to mention

Bell's inequality is a (completely classical) inequality about correlations of random variables defined on probability spaces.
The inequality is meaningful in other situations in which pairwise correlations make sense.
The inequality can be used to test whether situations in which pairwise correlations can be imbeded in a classical probability space.

As the article currently reads it never explains the basic fact 1 above, at least not in any comprehensible way. It goes to great lengths to talk about seven different versions without ever saying the most important fact.

I hope to write this up carefully within in the next few days. CSTAR 06:28, 20 Jan 2005 (UTC)

Excellent, CSTAR. I noticed that the article is weighted heavily towards a discussion of the various inequalities that can be derived from Bell, as well as tests of these inequalities. There is a lot about the debate on local reality vs. QM which is probably over-emphasized here and should be largely moved elsewhere. There is relatively little about the historical context, EPR, Von Neumann, Bohm, etc. The Theorem is important, as you point out, on its own and regardless of the experimental tests. I would also like to see a little more on Bell, his comments on the paper, and its enduring value (how many times has this been cited, for example).--DrChinese 17:50, 20 Jan 2005 (UTC)

OK, there is something there now, although a bit more is needed on quantum correlation. The article is now too long. What should be removed? Do we need all this stuff on the various Bell inequalities other than just a passing mention? Bell test experiments probably should be in some other article as well as "loopholes". CSTAR 21:25, 20 Jan 2005 (UTC)

Reversion

Could CT at least please explain why my edits were incomprehensible?CSTAR 00:45, 21 Jan 2005 (UTC)

I'm sorry about this. I tried to explain yesterday but the server was playing up and my edit failed. What I wrote yesterday was (under the heading "CSTAR's new introductory section"):

I'm sorry, CSTAR. You've clearly put a lot of work into this, but the page is about Bell's Theorem, not about abstract quantum theory! The theorem does not depend on any of the special QM ideas on correlation that you introduce. When Bell says the correlation is the expectation value of the product of the outcomes, he means the ordinary statistical expectation, i.e. the sum of the probabilities times the product of "outcome values". I haven't time right now to check all your sections but feel that they add totally irrelevant QM spin to the matter. The theorem is essentially a local realist one. The only link with QM is in the fact that the inequalities conflict with it. Caroline Thompson 09:13, 21 Jan 2005 (UTC)

I'm afraid that what was there before clearly failed to explain Bell's inequality or why it was true. I made sure that some form of Bell's inequality was displayed in the first paragraph. The origin of Bell's work cannot be understood independenly from von Neumann's efforts to prove non-existence of hidden variables.

"I ... feel that they add totally irrelevant QM spin to the matter"

This is complete nonsense. I was very careful not to do that, outside the section on quantum correlation where the example requires I assume quantum theory.CSTAR 14:59, 21 Jan 2005 (UTC)

Caroline, I'm sure you don't like the way the consensus is leaning here on wikipedia, but CSTAR worked hard on these revisions, and well, this is the way wikipedia works. I think it's unspeakably rude for you to revert his hard work without any attempt to work with us, and I will undo your reversion everytime I see it. I know you've expressed the opinion here that you are unwilling to comprimise on this matter. I suppose if you cannot comprimise, you cannot contribute at all. This is how the wiki works. -Lethe | Talk

You're quite right -- see above. I still haven't had time to look at CSTAR's contributions carefully, but

(a) I should have filled in the link on "quantum correlation" ages ago! There is no question of re-defining the term "correlation" itself, or any other part of standard statistics when deriving Bell inequalities

(b) Bell's contribution to physics was in deriving local realist constraints on certain expressions. The QM prediction was already known. There is no need to put the reader off from trying to understand the Bell inequalities themselves or the experiments by giving such prominence to the QM story. If you have to have this, why not do as I have done elsewhere in the page and put it on a separate page with a link?

Once again, I'm sorry about the abrupt reversion. However, I don't think you can assume that the consensus is in favour of CSTAR's additions. I've got family commitments for the weekend but hope to find time to have another look at this matter. Caroline Thompson

Re: Your quote:

"I should have filled in the link on "quantum correlation" ages ago! There is no question of re-defining the term "correlation" itself, or any other part of standard statistics when deriving Bell inequalities"

Wrong again. Precisely, we're not dealing with standard statistics. If you read what I wrote, CHSH is trivial for standard statistics. The right model is either

A C*-algebraic model of of local observables which pairwise commute at long distances
The more informal operational model which I described (which is also more faithful to the original operational intent of quantum mechanics)

Whoa, I just this second made the connection CSTAR=C*!! Hey, lay off. I'm kinda slow. -Lethe | Talk 21:30, Jan 23, 2005 (UTC)

Well at least don't follow Lumidek and call me CDAGGER ---- particularly when he gets annoyed politically.CSTAR 19:41, 24 Jan 2005 (UTC)

And what link to quantum correlation are you talking about?

CSTAR 15:08, 21 Jan 2005 (UTC)

No, CSTAR. Bell and Clauser were dealing with standard statistics. Try re-reading their papers. But the most important thing about their inequalities was that they were concerned with how they applied in real experiments in the presence of real hidden variables. Your two sections on "correlation" and "correlation in quantum mechanics" are irrelevant to Bell's Theorem. Quantum-mechanics ideas, I repeat, don't come into the story except when you come to very end.

That's point one. Point two is that your discussion of the CHSH inequality, restricted as it is to cases where every measurement produces an outcome of +1 or -1, is no use in practice. Bell proved it in a more general form, and omitting his original assumption that correlations had to be perfect when detectors were parallel, in his 1971 paper, and this proof is reproduced in http://en.wikipedia.org/wiki/CHSH_inequality.

Possibly you are assuming that your definition of "realism" enables the CHSH inequality to hold even when some measurements do not produce an outcome, but this is a crazy way of going about things! It completely misses the point about the function of hidden variables, and reveals, I'm afraid, ignorance re the fact that all later versions of Bell inequalities in fact apply to "stochastic" hidden variables -- ones that do not (in conjuction with the detector setting) completely determine the outcome, only its probability.

This last matter is covered in some of Bell's papers. May I suggest that you re-read a few chapters in his book, "Speakable and Unspeakable" and then look again at your new sections. As I said, they are effectively incomprehensible. They are designed for those with a background in quantum theory. Bell's theorem was designed for realists, and his papers are not filled with QM jargon.

What do you mean by saying CHSH is true "in the operational interpretation of correlation"? What one needs to know is whether or not it is true in real experiments, and whether or not it is true when the terms are estimated in the standard manner! [See recent proposals for loophole-free Bell tests for evidence that the establishment is aware of the fact that it is not. My paper on the subject is at http://freespace.virgin.net/ch.thompson1/Papers/Homodyne/homodyne.htm]Caroline Thompson 23:46, 21 Jan 2005 (UTC)

We can do RfC for this article or a straw poll just here. --Pjacobi 09:22, 2005 Jan 21 (UTC)

Standard statistics

If the variables in the CHSH were defined on single underlying sample space, then as I pointed out the CHSH inequality is trivial. More significantly, the CHSH inequality in this case has nothing to do with locality. It doesn't matter whether Alice or Bob are sitting at the same bistro table or in different galaxies, it still is true. To emphasize the point about the single sample space, I referr to Shimoney's Stanford encyclopedia article [2] (http://plato.stanford.edu/entries/bell-theorem/), he produces a model with system state (defined in some abstract way, and not as a probability measure) and several associated transition probabilities resulting from measurement. This is one formalization of locality and realism.

Or you can look at Arthur Fine's article on Bell's Theorem in the Routledge Encyclopedia of Philosophy: I quote (p 713)

"...the system of Bell's inequalities above are the necessary and sufficient conditions for all of the given probabilities to be derivable from one distribution P(A A' B B'), for all for variables. Put differently, the Bell inequalities are the conditions that the given probabilities can be represented on a classical probability space where all outcomes (even for incompatbile mesurements) are defined."

Note that Shimoney's formalization is not the only one possible. It can be accomplished for instance, using C*-algebras of local observables as I suggested. This idea is not new; see for instance the article

Lawrence LandauOn the Violation of Bell's Inequality in Quantum Theory Physics Letters A 120 (1987) 54-56

which is available online in some form here (http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/bell.html). CSTAR 07:19, 22 Jan 2005 (UTC)

CSTAR, that reference has something wrong with it. Do you know is it possible to find it somewhere as a proper latex ps? -Lethe | Talk 21:32, Jan 23, 2005 (UTC)

CSTAR, you have not quite answered all my yesterday's points in the "Reversion" section, but let's concentrate on the CHSH inequality. Yes, it is trivially true when there are underlying hidden variables (almost equivalent to your above statements) but not quite as trivially as you make out. In real experiments you need a more general version, true even if some outcomes are zero.

More importantly, though, we need to say clearly what method we propose to use to estimate the various E terms. This is an issue that Bell did not address in his 1964 paper. Clauser and Horne addressed it indirectly in 1974 by saying, in effect, don't use the CHSH inequality unless you estimate the terms by dividing by the number of emitted pairs. But applications ever since Aspect have used an estimate in which division is by the total number of detected pairs. The CHSH inequality does not hold for these unless we make the fair sampling assumption, which, as has been known since 1970 or ealier, is liable to introduce bias.

No time for more now -- family commitments. Caroline Thompson 09:02, 22 Jan 2005 (UTC)

"but not quite as trivially as you make out." Excuse me? In the case there is an underlying probability space,proving the CHSH correlation involves nothing more than multiplication and using the fact that

<math> X \leq Y \implies \operatorname{E}X \leq \operatorname{E}Y.<math>

Fairness and time averages

There is a difference between time averages and spatial averages; as you know this was one of initially recognized problems in statistical mechanics. Besides the interesting mathematics, this also had a philosophical importance at the turn of the century because of the emergence of operationalism in works Bridgman, and earlier of Mach. Operationally, spatial averages make no sense or so at least it was thought.

The "fair sampling" loophole in those Bell test experiments that use the CHSH inequality has absolutely nothing to do with whether we're looking at time averages or spatial ones. It has to do with the fact that when we use detectors that don't detect every single particle, the ones that are missed out may not be a random sample. When the CHSH test is used in the accepted manner, estimating each term by a ratio in which the sum of observed coincidences is used as denominator, we are using a "post-selection" method that can easily involve a biased sample. Please do read one of my Chaotic Ball papers (e.g. http://arxiv.org/abs/quant-ph/0210150), or, if this goes against the grain, go back to Philip Pearle's original. Caroline Thompson 20:41, 22 Jan 2005 (UTC)

The "fair sampling" ... has to do with the fact that when we use detectors that don't detect every single particle, the ones that are missed out may not be a random sample.

Exactly. This means that a subsequence of a time averages is skewed! As I was trying to point out, in a classical probability setting this "sampling loophole" is usually accounted for by arguing that for almost all infinite sequences of trial runs, there is no sampling bias. This is the law of large numbers. However, it is still possible to argue that classically, in some weird run, there could be sampling bias. This "loophole" is hardly a serious criticism, although it does merit academic study. CSTAR 22:54, 22 Jan 2005 (UTC)

Many of the problems in (classical) probability reduce to determining properties of spatial averages or of the state of the world by using time averages. This is even true for instance in econometrics. The issue of sampling fairness for time averages I only partially addressed that in my discussion of classical sampling where "almost all" repetitions of the experiment are fair samples by the law of large numbers. In the general case, the fair sampling assumption must be made explicit: this has to be formulated as a strengthening of the assumption that the limit of averages exists; the stronger assumption is that for almost all trials the limit exists and is equal to the limit of taking a subsequence of trials.

However, for an expository article I don't think this is necessary, unless you have an agenda, namely to show that there is some arcane technical point which nobody has considered that proves QM has not been conclusively proven. It is also not true that these technical details have gone unnoticed: they have been noted and mostly dismissed, as I'm sure you're aware.

Unless someone objects, I will put this page up for RfC, after I delete the rest of the stuff in it which I think is irrelevant. CSTAR 15:46, 22 Jan 2005 (UTC)

PS I have not gone through the RfC process before, so if someone is more familiar with the details, they might provide advice on that.CSTAR 16:26, 22 Jan 2005 (UTC)

CSTAR, I really don't think you have understood what Bell was saying -- what the purpose of his theorem was! He was saying that any "reasonable" (in the old-fashioned sense of obeying local causality) theory had to obey his inequality. Quantum mechanics is merely an example of one that does not. Just how and why QM fails to agree with the inequality is not that important! What matters is whether or not the real world does. It is therefore absolutely crucial to know what has been tested, and your new sections are not relevant to this. The exact inequalities and their conditions of validity, and the details of the experiments, on the other hand, are. Caroline Thompson 20:41, 22 Jan 2005 (UTC)

Of course CSTAR knows that Bell's theorem was about local realist theories, that they had to obey the inequality. Why should you think otherwise? His edits clearly demonstrate that he knows this.

As for whether QM is "only an example" or the case of most interest to most people is a matter of opinion. The importance of how QM fails to satisfy Bell (i.e. the nonlocality of QM) is also a matter of opinion. Just because what CSTAR thinks is important is different from what you think is important does not mean he is ignorant, and is no excuse for you to impugn his edits, which I think have been of high quality. -Lethe | Talk 03:09, Jan 26, 2005 (UTC)

Any further dialogue is pointless if you fail to respond to what I say, and reply instead with what you believe I understand or don't understand. You have not responded to my comments on operationalism and its relation to time averages and fairness which were a direct response to another peripheral comment of yours regarding the issue of fairness. Your comment about Bell

"He was saying that any "reasonable" (in the old-fashioned sense of obeying local causality) theory had to obey his inequality."

is of dubious historical accuracy and in any case is a red herring in this argument.

"Just how and why QM fails to agree with the inequality is not that important!"

Aside from reproducing a well-known example in the quantum correlation section I added (and which I cited Nielsen and Chuang as a source) and its mention in regard to hidden variables (which Bell did write about also) I have not mentioned quantum mechanics elsewhere. I don't believe I mentioned it once in the correlation section.CSTAR 22:29, 22 Jan 2005 (UTC)

P.S. My remark above about the historical accuracy of your interpretation of Bell's work refers to your tendentious use of "reasonable"; of course Bell's inequality assumed locality and realism, but he never, to my knowledge, referred to QM as an unreasonable theory.CSTAR 22:43, 22 Jan 2005 (UTC)

Discussion

Lethe, I appreciate your support. Indeed, I thought carefully about what I wrote and didn't much appreciate CT's reversion.

Comments and revisions to what I wrote are welcome. However (and this is directed to CT) please read what I wrote before plunging into reversion. Please note that many of your criticisms are baseless, and reflect the fact (which you seem to admit) that you didn't actually read what I wrote. I have already given some examples of how your comments are without any merit. Here is another one:

You say above

"The theorem is essentially a local realist one."

Well yes, and if you read what I wrote, I stress that point! I thought I went to great lengths to distinguish the classical stochastic model in which CHSH can be trivially proved (and which is mostly irrelevant for this discussion) and the operational interpretation in which CHSH is true only under local realist assumptions.

I don't think I'm likely to be alone in totally failing to understand what you mean. See above. Caroline Thompson 23:51, 21 Jan 2005 (UTC)

See above? What do you mean? Are you referring to somebody that specifically objected to anything I wrote?CSTAR 23:59, 21 Jan 2005 (UTC)

Note that CT's earlier comments about her not interfering in other pages related to QM are irrelevant (it is my understanding that there are to be no private "preserves" in WP -- e.g., the local realist preserve and the QM preserve) and in some cases these remarks about non-interference are not true. For instance, a similar conflict occurred on the EPR article over a period of several months. In the end after much discussion, (mainly) CYD, Lethe and myself hacked out a revision against continual protestations by CT.CSTAR 18:16, 21 Jan 2005 (UTC)

[I thought we reached a successful compromise. All I wanted was to cut out false statements. Caroline Thompson 23:51, 21 Jan 2005 (UTC)]

Thank you CSTAR for your efforts. I'm not quite done with a careful reading of the new version, but I have a first impression, that there is now some redundany between "Correlation in quantum mechanics" and "Comparison with the quantum-mechanical prediction". --Pjacobi 22:58, 2005 Jan 21 (UTC)

Yes I agree there is redundancy, and I had planned to delete that part Comparison with the quantum-mechanical prediction which seems to be written with a totally different perspective. I had tried to use the viewpoint of th eEPR paradox article.CSTAR 23:30, 21 Jan 2005 (UTC)

What is the source for CSTAR's QM prediction section? The source for the present page http://en.wikipedia.org/wiki/Quantum_mechanical_Bell_test_prediction is Shimony's encyclopaedia article. Caroline Thompson 23:51, 21 Jan 2005 (UTC)

What is the source for CSTAR's QM prediction section? Nielsen and Chuang, Quantum Information and Quantum Computation p 116, on which my discussion is based. CSTAR 23:57, 21 Jan 2005 (UTC)

What's going to be done about this page? As it is, it is nonsense! Whilst correcting a spelling mistake, I came across the following sentence in "my" part -- a sentence that, if you look at Bell's original papers, clearly expresses what Bell intended his theorem to be all about:

"If the world has underlying local hidden variables, then Bell's inequalities must be obeyed by the "coincidence counts" from a Bell test experiment such as the optical one shown in the diagram ..."

Compare with the present introductory sentence by CSTAR:

"In foundational studies of quantum mechanics, Bell's theorem refers to a class of inequalities about correlations of real-valued random variables defined on probability spaces and extensions to other contexts where real valued-variables satisfy assumptions of locality and realism."

Which is nearer to what the theorem is all about? It was never intended as an abstract mathematical theorem but as a practical tool for testing experimentally between QM and local hidden variable theories.Caroline Thompson 17:36, 23 Jan 2005 (UTC)

First of all, your claim that I regard Bell's inequality as an "abstract mathematical theorem" is neither true nor relevant. Again this is a red herring.

Secondly, the sentence in "your part" doesn't say what Bell's inequalities are! The sentence you chose to criticize says exactly what it is. Moreover, it is followed by a clear example of one of those inequalities. In fact look at Shimony's opening sentence n the encyclopedia article.

"Bell's Theorem is the collective name for a family of results, all showing the impossibility of a Local Realistic interpretation of quantum mechanics. There are variants of the Theorem with different meanings of “Local Realistic.” "

or the first sentence in Arthur Fine's Routledge Encyclopedia of Philosophy article:

" “Bell's theorem“ is a generic name for a family of results that restrict the statistics for a certain type pf quantum mechanical “correlation experiment“"

Or from the section Bell's inequalities of Omnès book Understanding Quantum Mechanics, Princeton University Press 1999

"Von Neumann believed he could prove that hidden variables are impossible, but there was an error in his proof, which was first noticed by Magda Mugur-Schacter and later by Bell."

All these are relevant facts about Bell's inequality which are now stated immediately in the introductory paragraph, including the mention of local realism.CSTAR 18:04, 23 Jan 2005 (UTC)

Most of the above concerns second-hand opinions by quantum theorists about Bell's theorem. You have not addressed the fundamental reason why the world was so pleased with it -- that it provided a means for an experimental test of QM versus hidden variable theory. It does this by putting limits on what can be done with hidden variable theories. Your new introductory sections involve several pages of quite heavy maths that is not relevant to hidden variable theories and is sufficient to deter many readers from even attempting to understand the issues involved. They give the impression that you have to understand QM in order to understand the theorem, and this is simply not true!

All you need to understand the inequalities is some basic logic and ordinary properties of probabilities. All you need to know about QM is that it predicts a "quantum correlation" value that is greater than is possible under a hidden variable theory.Caroline Thompson 21:45, 23 Jan 2005 (UTC)

"second-hand opinions by quantum theorists". Please! They are authorities in the field, and there opinions are certainly relevant.

"All you need to know about QM is that it predicts a "quantum correlation" value that is greater than is possible under a hidden variable'"

Why not argue "All you need to know about Bell's inequality is that it is an inequality." CSTAR 22:07, 23 Jan 2005 (UTC)

Re the "second hand opinions" remark, I'm sorry. I was -- and still am -- frustrated by the failure of Bell's followers to take account of what both Bell in 1964 and Einstein in 1935 were trying to do. This was to find a test that discriminated between the QM nonseparable formula and the local realist separable one, preferably a test in the form of an actual experiment, not just a thought one.

Re my point about not needing to know about QM, it does not follow that you don't need to know where Bell's inequalities came from. The test between the two theories has no value unless everyone agrees it is valid test, and to decide this you need to know what assumptions were made and how it was derived. The assumptions and method behind the inequalities are purely local realist ones.Caroline Thompson 18:47, 24 Jan 2005 (UTC)

CSTAR, I'm afraid you still have't got anywhere near to what Bell's work was all about! In your opening para you imply that he produced an inequality that was purely of mathematical interest. No! Others did this! Kolmogorov and the like have produced mathematical inequalities, and though Bell's in fact follows from these, what he was talking about was random variables that were the outcomes of Bell test experiments. He was a physicist, not a mathematician. Caroline Thompson 22:02, 25 Jan 2005 (UTC)

It's quite plain that you will continue to assert that no-one "get" Bell's work. Indeed looking at your past edits on this article alone, it's clear you believe nobody (other than yourself) has understood what "Bell's work was all about! For example, the following remark you added to the article on 20 Nov 2004

Reminder: There are loopholes in all experiments to date. Few authors are aware of these, and even fewer understand them.

As to your claim

"In your opening para you imply that he produced an inequality that was purely of mathematical interest."

this assertion is patently false. Indeed, the first sentence opens with In foundational studies of quantum mechanics.

Out of curiosity is anybody else following this talk page?CSTAR 01:47, 26 Jan 2005 (UTC)

Hey CSTAR, yeah, I'm still following the talk page. I guess I haven't had the wherewithall to argue many of CT's claims (actually started drafting a couple of replies to her, and then thought better of it, and just butted out.) But anyway, I'm still following along. I sort of agree with something you said at some point, dialogue with CT is not very productive. But I am reading the talk page and also reading all the edits to the article. And I have your Landau reference printed out, waiting to be read. But what is there to say to CT, when she is the only qualified person in the world to write this article? -Lethe | Talk 03:09, Jan 26, 2005 (UTC)

Yep, always watching. At least it's more sane than Burkhard Heim. --Pjacobi 09:09, 2005 Jan 26 (UTC)

I put a lot of work into constructing a really informative wikipedia page and CSTAR, by that completly misleading first few pages, has ruined it! I suppose I just have to wash my hands of the whole thing. I can't see anyone other than quantum theorists bothering to read it.

Bell devised his theorem not in the abstract but, as I keep saying, with a mind to application in real experiments. The relevant papers were written from the local realist point of view. I just don't see how you can justify your QM bias. Caroline Thompson 20:22, 26 Jan 2005 (UTC)

Let's not get melodramatic. CSTAR does good work. -Lethe | Talk 03:33, Jan 27, 2005 (UTC)

Yes, but he does not know how the loopholes work! He has, it seems, not studied the experimental reports. He seems to think that all those apparent agreements with QM prediction mean something, ignoring the facts! The facts comprise the messy details of the experiments and the use of biased test statistics. I'll have a go at editing the page back to "science", as opposed to QM "belief". The first thing that has got to change is that first sentence! Does anyone else agree that it really expresses what Bell's Theorem is all about

What makes CSTAR think that it is only believers in quantum mechanics who will be interested in the page? Are not local realists in fact the majority out in the real world?Caroline Thompson 18:39, 27 Jan 2005 (UTC)

Caroline - as I understand this discussion, you have points to make about Bell's intention in developing this kind of inequality. This would be quite legitimate content; but needs to be supported by some material reporting those intentions, rather than just imputing them to him. I haven't gone back through the page history, to see if such things have been edited out; probably you know though what has been here. Charles Matthews 12:11, 28 Jan 2005 (UTC)

Reply to Charles Matthews

Charles, the problem here, is that CT makes different assertions, which all of us have been trying to address:

Bell's "real" intentions about his result
Bell's theorem has nothing to do with QM and in particular my discussion of Bell test violation is irrelevant
Bell's theorem is not mathematics
Bell's inequality has never been refuted
QM is not science is not ultimately supported by the evidence

Let me address these briefly again:

1) Who knows what Bell's real intentions were. However, if you look a t the papers written in the 60's and early seventies (all his papers related to Bell's theorem and QM are available in a single volume) it's absolutely clear that QM was a central issue. His insight was to have understood that the reason QM is different is because of correlations. In th e1964 paper which intriduces his inequality, the intro specifically raises th issue of Hidden variables and interpretation of QM

2) ET's assertions that Bell's theorem has nothing to do with QM is an extremely unusual one, certainly not a view which is available in almost all the peer-reviewed scientific literature. As you are well aware, NPOV does not mean saying "some believe the moon is made of green cheese, some don't".

3) I never said Bell's theorem is mathematics, but certainly mathematics is relevant to physics and has been for hundreds of years. ALso I discuss the measning of probability carefully as used experimentally. My idscussion on that is based on (Readhead, 1986).

4) That Bell's inequality has been shown to be violated, is shown by virtually all experimental tests. CT claims that the reports of these tests incorrectly interpret the experimental evidence e.g., this quote from her:

He has, it seems, not studied the experimental reports. He seems to think that all those apparent agreements with QM prediction mean something, ignoring the facts!

Now what does CT mean by that? Is she accusing the authors of lying in their papers? Is she some kind of scientific whistleblower? If that's the case, she should stop working on WP and immediately contact the authorities. This would be one of the major crimes of the last centuries.

5) QM is not science but belief. Well this assertion is not directly atttributable to this dialogue, but it is a paraphrase of CT's comment on one of the Bell-related artciles talk pages (possibly CH74). Do I need to answer this? Are we going to allow Green cheesers and flat earthers and Archimedes Plutonium a forum? CSTAR 14:59, 28 Jan 2005 (UTC)

OK, I suppose I was singling out #1 of these points. For myself, I'm quite happy that anything called 'theorem' be treated as mathematics. If there were some good quote from Bell, giving the context of his work as he saw it, why not have it here? I'm not in a position to comment on whether the experimental interpretation is correct. It is a familiar remark on some pieces of mathematical physics that they don't 'say' exactly what many people think they say. Charles Matthews 15:17, 28 Jan 2005 (UTC)

Charles,

If any of us thought there was a legitimate point in looking at Bell's personal position - which is interesting - that would be fine. But CT tries to find any angle which supports her POV and emphasize it excessively. Bell probably started off a local realist... I mean, don't we all when it comes down to it? It has never occurred to me that Bell questioned what the results of actual experiments would be. If he *had* questioned what they would be (i.e. supporting LR or not), that would not make his theorem any better or any worse. CT would like us to believe that Bell's position therefore supports her POV. As CSTAR stated, it is possible to selectively quote Bell and get a wide variety of positions, all of which ultimately have nothing to do with his legacy.--DrChinese 15:38, 28 Jan 2005 (UTC)

A small comment on "refuted": AFAIK most experiments have only ruled out the "natural" lhv theory. As explained in the paper, I mentioned on one of these zillion talk pages, unless the detector efficency can be improved, a highly contrived looking lhv theory can explain the outcome. Some progress on killing this last doubt has been made recently.

But even without these refined experiments, most physicists would judge the evidence as sufficent.

A somewhat limping anology: Even WMAP data doesn't rule out Young Earth creationism in the form of the Omphalos hypothesis, but nobody is really disturbed about this.

Pjacobi 15:50, 2005 Jan 28 (UTC)

Thanks for that reference. I did look at this paper. As you point out, and the authors themselves emphasize, (a) that the example is artificial (b) there purpose is to eventually construct completely airtight experimental support for Bell test violations. But the WP Bell theorem article, as it stands, very clearly acknowledges that these loopholes exist. Moreover there already is a Bell test loophole article in WP (who knows maybe even more than one). Any further discussion should be put there.CSTAR 18:30, 28 Jan 2005 (UTC)

I would also like to point out another element of the bias present in the article, and how it is affecting our discussions. It makes sense to reference tests of Bell's Theorem in this article. But WHY would it ever make sense to reference "loopholes" in those tests here? It is of little consequence to the Theorem itself what the actual results are! And it makes all the sense in the world to reference the "loopholes" a single time in the Bell Tests article. Harping on it here is a remnant of CT's influence. I will be making adjustments accordingly.--DrChinese 18:21, 28 Jan 2005 (UTC)

Oops, I guess we almost said the same thing, simultaneously.CSTAR 18:34, 28 Jan 2005 (UTC)

CT's new argument

"Are not local realists in fact the majority out in the real world?"

Now that's a new argument! We can call that the lynch mob at your door argument. Also called "know-nothingism".CSTAR 19:16, 27 Jan 2005 (UTC)

I heard that the vast majority of people in the real world doesn't believe in the Banach-Tarski paradox. I'm listing that on WP:VfD. -Lethe | Talk 19:46, Jan 27, 2005 (UTC)

Evolution ain't too popular either, particularly in these here United States.CSTAR 19:57, 27 Jan 2005 (UTC)

Oh dear! What is science all about? All I'm saying is that the experimental facts and also Bell's inequalities are part of our common heritage, not the private property of quantum theorists! Bell's inequalities put limits on what local realism can achieve. They put no limits on QM.

And, of course, is it not possible that you are suppressing the very information needed by a new Keppler? As I see it, the situation parallels that in cosmology, where way back before Christ we had Aristarchus, with his modern, heliocentric, universe. Then we had Ptolemy with his epicycles and whatever. Had Keppler not returned to Aristarchus' idea and gone back and checked the facts -- discovered that the orbits were, after all, not circles but ellipses -- we'd have been stuck with Ptolemy to this day.

Yes, I know QM has, in most areas, a lot more experimental support than Ptolemy's theory ever had, but it shares the property of failing to provide causal explanations. And, as it happens, in this key area of quantum entanglement, the experimental support is inconclusive.

Anyway, to conclude my lecture, I suggest you think hard about whether or not you are really acting as scientists when you defend "entanglement". As Koestler wrote re Aristarchus (p 51 of “The Sleepwalkers: a history of Man's changing vision of the Universe”, Penguin Arkana 1989):

" ... his correct hypothesis was rejected in favour of a monstrous system of astronomy, which strikes us today as an affront to human intelligence."

Caroline Thompson 10:19, 29 Jan 2005 (UTC)

Reply

All I'm saying is that the experimental facts and also Bell's inequalities are part of our common heritage, not the private property of quantum theorists!

No. That is not what you're saying at all. You are saying that nobody, other than yourself, has correctly interpreted the data.

As usual, you are bringing in irrelevant arguments. The historical facts are interesting, but seriously, they are totally irrelevant to this argument. Clearly, they would support continually revisiting every abandoned theory such as the phlogiston theory. While it is acceptable for individuals to entertain this possibility, there is no room for this in an encyclopedia.CSTAR 15:47, 29 Jan 2005 (UTC)

The issue at stake here is whether or not the real world makes sense! I think you will find that a majority of scientists in fact take that for granted. However, if you persistently misrepresent Bell's theorem and the experiments that are supposed to support it, you will be preventing the said majority from access to the facts that would enable them to make sense of it. Why not accept the compromise I was working on? Let the pages EPR Paradox and Quantum Mechanics represent the orthodox point of view, whilst Bell's theorem and related pages represent (mainly) Bell's original intentions?

Have you ever read Bell's papers on hidden variables etc, or are you basing your interpretation of his theorem on some other, later, accounts? Caroline Thompson 18:18, 29 Jan 2005 (UTC)

As was pointed out to you above by Pjacobi your proposal is against wikipedia policy.

"Have you ever read Bell's papers on hidden variables etc,"

Another one your irrelevant insinuations. Yes I have read them and I have repeatedly referred to them.CSTAR 18:46, 29 Jan 2005 (UTC)

The main article

Unless there are objections, I will delete most the last two sections of the article which already have articles of there own. Material from those sections should be moved over into the specialized articles.CSTAR 15:47, 29 Jan 2005 (UTC)

Hmmm ... it is your two sections at the beginning that need to be deleted! Why does the reader have to be introduced to random variables X and Y when Bell himself talked only in terms of the "outcomes", A and B, of an actual experiment? Almost every text on the subject talks only of A and B. Agreed, one can approach the subject by first deriving the mathematical inequality and then relating it to experiment. This is what Clauser and Horne did in 1974 (see Clauser and Horne's 1974 Bell test, but for most readers all this stuff about X and Y and the "operational definition of correlation" is totally out of place and confusing.

How many times do I have to say this? The important part of Bell's theorem is the local realist part. The QM theory was already known.Caroline Thompson 22:55, 29 Jan 2005 (UTC)

Re: Landau reference

Unfortunately, I can't seem to find the original Latex source. The version on his page was deLatexed but the program didn't do a great job. I think a straightforward gawk program could have done a better job.CSTAR 22:07, 23 Jan 2005 (UTC)

BTW: Of course, the author is not Lev Landau.CSTAR 22:47, 23 Jan 2005 (UTC)

Hidden variables

Von Neumann's "proof" was for hidden variables, period. No local. Moreover, Bell's 1966 paper is specifically concerned with the same problem (although he also addresses local hidden variables).CSTAR 23:03, 28 Jan 2005 (UTC)

But in real experiments outcomes are more often zero than +-1

CSTAR, I started to edit the page to replace the term "correlation" (which necessarily means the standard statistical kind) by "quantum correlation", but came across statements that are either just plain false or (as I've tried to say many times) irrelevant. They hinge around the fact that in real experiments outcomes are often zero, which is the reason Clauser and Horne in 1974 produced what should have been the definitive version of the Bell test -- one in which non-detections simply don't matter. If you read the 1969 CHSH paper carefully, you will find that test they actually recommend is not what is now known as the "CHSH test" but the 1974 version, relying on comparing counts with polarisers both sides with those with one or other or both absent.

Anyway, the relevance of the above to your two sections is that the following is wrong:

"Notice however, that the definition of quantum correlation makes sense more generally, regardless of whether or not there is an underlying probability space on which the variables X, Y are defined. The important conditions are that

The experiment which produces the values X and Y be repeatable;
That on each trial of the experiment, both variables X and Y can be observed."

I added the qualification "[which is not actually the case in real optical Bell test experiments]" then realised that the result was complete nonsense! What's the point of making this condition only to say that it is never met?

Your section goes on to say:

"The proof of the CHSH inequality for random variables taking only values -1 or +1 is trivial: for each sample point,

This holds since for each sample point one of the values

is zero."

But again, in real experiments this is not so! If, for example, X_B is 1 and Y_B is zero then the sum and difference are both 1.

What is the point of presenting in wikipedia a "proof" that bears no relation either to any usable Bell inequality or to the real world?

Caroline Thompson 18:58, 30 Jan 2005 (UTC)

Reply to Caroline Thompson

Caroline, please note that in this case the proof is trivial also. For in that case we are added two quantities with absolute value at most 1. Such a sum has to be less than or equal to 2.

It is with great regret that I make a public comment on WP about a fellow Wikipedian, something that in my 10 months here I have avoided until now. You have shown that

You have absolutely no idea what you are talking about
You are abusing WP to promote yourself and your POV
You are wasting everybody's time requiring them to read and judge whether to revert your edits.

Unless there is some compelling reason, I will no longer read anything you write and on this page at least, I will revert it once I see it. If you wish to be heard from me at least, please precede any proposed changes with a comment on the talk page explaining what you are doing.

I hope everyone else that reads this supports me on that point and also reverts.CSTAR 20:34, 30 Jan 2005 (UTC)

Well, that's your opinion, but I think you'd be surprised if you knew how many people respect my views. They respect my powers of logic as well as my knowledge. I have, for instance, read Aspect's PhD thesis from cover to cover. Have you? I have corresponded with many of the theorists and experimenters concerned ...

I think you'd be surprised if you knew how many people respect my views

I was expecting a list of people who respect your views to follow, but instead only heard about things you've read. I don't think reading any of those things makes your fringe views any more mainstream.-Lethe | Talk 03:49, Jan 31, 2005 (UTC)

Re your point above, I was not saying that the inequality did not remain trivial if some results were zero. I was merely saying that the existence of zeros meant your proof was illogical. Caroline Thompson 21:37, 30 Jan 2005 (UTC)

PS: What on earth does the sentence "CHSH is true in the operational of correlation" mean? Is it even English? Caroline Thompson 21:54, 30 Jan 2005 (UTC)

Caroline: Thanks to your wasting everyone's time, we have a difficult task restoring some meaning to these pages. Please do not waste more time, we'll manage somehow without you. I don't care who respects you - which is a laugh anyway since you bring up the subject (I wouldn't have) - your biased ideas do not belong here. I will be monitoring every EPR/Bell/QM related page I can.

So just what does that phrase of CSTAR's mean, then? I submit that his contributions are irrelevant. We don't need a proof here of the CHSH inequality (it is covered by the CHSH inequality page), especially not one that applies only to perfect experiments with no null outcomes. We don't need either a lecture on statistics, especially when that statistics contains unreasonably abstruse jargon, concepts that are not covered in any of the standard expositions of Bell's theorem, and generally serves no purpose other than to mislead the reader into thinking he can't hope to understand what the theorem is all about.

Caroline Thompson 20:03, 31 Jan 2005 (UTC)

Please read the phrase as it currently stands. Thanks you for pointing out that the phrase was ungrammatical.CSTAR 20:10, 31 Jan 2005 (UTC)

Re: The CHSH proof

The (or "your") proof of CHSH, in the Wikipedia CHSH article says

We start with the standard assumption of independence of the two sides,

This really requires clarification. As I'm sure you know, variables which are stochastically independent (and have zero mean) have zero correlation, which is certainly not true here. BTW, you incorrectly foisted your "independence" assumption on the Bell theorem page, which I will correct soon enough. The only assumption needed there is locality and realism.

In Bell's 1971 paper, which I have in front of me, particularly on section 4, immediately after eq (6), Bell indeed says that

<math> \overline{A} <math>

is independent of

but does not assert independence "of the two sides" which is much too vague and actually misleading. I suppose it would be too much to ask you to correct this?

ThanksCSTAR 20:50, 31 Jan 2005 (UTC)

Thanks CSTAR, I'll have to rephrase this. What I mean is that once the hidden variable has been fixed, that covers all the correlated factors. Given lambda, this determines the probability of detection at A and the probability at B. The detections at A and B are conducted independently, i.e. by detectors that have no connection with ("are independent of") each other. The consequence is that you can apply the usual rule of probability theory and multiply the two singles probabilities to obtain the joint probability. This is the standard assumption underlying hidden variable theories. Bell explains very carefully in one of his papers just what assumptions are involved. I haven't got it to hand but will look it up. Caroline Thompson 22:08, 31 Jan 2005 (UTC)

CSTAR's new diagram

CSTAR, what has become of the source in your new diagram?

CSTAR, this first diagram is still not displaying correctly. Moreover your notation is very misleading, as is your implication that the experimenters usually toggle between two detector settings. It has only been in two experiments that I know of (Aspect's last one (1982) and Weihs' of 1998) that they have done this. Assuming that X and Y in the diagram correspond to + and - detections (guessing from the notation you use later re the CHSH test), the experimenters don't toggle between them but count them simultaneously.Caroline Thompson 10:48, 7 Feb 2005 (UTC)

"X and Y in the diagram correspond to + and - "

They don't and I never said anywhere they did. CSTAR 00:31, 8 Feb 2005 (UTC)

Surely the existence of a common source is absolutely essential for the EPR setup? And, incidentally, Bell's description of his basic experiment is not restricted to just the two setting on each side! Some versions of Bell test (the "visibility" test, for example) require that you look at the whole "coincidence curve", i.e. the plot of coincidence rates for a range of values for the settings on each side. [Strictly speaking, we should be speaking not of coincidence curves but coincidence surfaces, to allow for the possibility that we don't have "rotational invariance" -- See Bell test loopholes.] Additionally, if you don't investigate more than just the "Bell test angles" (two on each side) there is no way you can test for fair sampling by the only method agreed by both quantum theorists and local realists, by checking for constancy of the total coincidence counts.

And, while I'm about it, what does the following mean?

There remain a number of technical details that need to be attended to. The first one is that the subsequences of actual measurements taken have the same limits of averages as the entire sequence. Since in each one of these averages, only a subset of values is actually observed, we need to assume that the each expression has the same value when taken on the subsequence of observed values.

I take it that what you mean is just that "fair sampling" assumption has to be made, i.e. we have to assume that the sample of detected pairs is a fair sample of those emitted. Why not say so? Caroline Thompson 12:05, 6 Feb 2005 (UTC)

Well yes, that's what I tried to explain in one of these zillion talk pages. It is the fair sampling assumption. That's why in one earlier version I discussed at length the probabilistic (= global hidden variable) fair sampling assumption. Fair sampling should link to some notion of fair sampling in statistics, not to Bell test loopholes. That's why the concept is not mentioned.

But this is just not appropriate! "Fair sampling" in the context of the Bell tests has nothing to do with the ordinary selection of a fair sample by a statistician! The samples are selected by Nature, and the experimenters have little control over them. The failure of the assumption is due to the failure of real detectors to "fairly" (with respect to the hidden variable space) record detections. The detectors are being asked to decide whether they are receiving a signal with a higher '+' component or a higher '-' one, and when the signal is weak they are more likely to be unable to decide, i.e. to register nothing. The unfairness does not show up in the singles counts since we can't look at just one hidden variable value at a time, but it does leave a trace in the coincidence counts: it causes the total to vary as you vary the detector settings. This is what "fair sampling" is all about in the Bell tests. I don't know of any parallel to this in ordinary statistical sampling.

"The samples are selected by Nature"

Please note, that even in polling, the pollster may have some control over who turns up to take a statistical poll, and how particular questions are interpreted, but there too, it is ultimately nature that does the choosing.

"Fair sampling" in the context of the Bell tests has nothing to do with the ordinary selection of a fair sample by a statistician!

They are not identical (and of course I never said they were), because, obviously one is assumes a local hidden variable theory and the other assumes a global hidden variable theory. However, Your claim that there is nothing to do with each other is not true. I can give you numerous examples, but I have wasted enough time on this already.

And please stop claiming you somehow know what Bell's thinking was and others don't.CSTAR 23:37, 6 Feb 2005 (UTC)

On second thoughts, since you are considering only the case of 100% perfect detectors, what you are talking about is not the same fair sampling problem that gives rise to bias. It is therefore very confusing to bring it into the story.

I shall stop claiming I know better than you what Bell meant when you give me some evidence of having understood the local realist position which he, when he wrote the papers, was advocating. I know that later he became persuaded that the real world was not local, but his logic in his 1964 paper was concerned with the local realist approach, with only a brief mention of quantum theory.

This matter of notation needs sorting out! What do you mean by X and Y in that first diagram? Caroline Thompson 10:48, 7 Feb 2005 (UTC)

Of course, if you, as a quantum theorist, don't believe it possible that hidden variables exist that can explain the results, the above explanation may make little sense. It would have made sense to Bohm or Bell, though. It is the essence of what Pearle wrote about in 1970. I suggest you take his word for it. Caroline Thompson 22:35, 6 Feb 2005 (UTC)

"CSTAR, what has become of the source in your new diagram?"

What do you mean? There are only PNG files here, and I have not destroyed or deleted any graphics.

In you first diagram it seems that some parts are not displaying. There is nothing showing except the words Alice and Bob and an indication of the two outcomes in each side. Caroline Thompson 22:35, 6 Feb 2005 (UTC)

You are of course right, Bell's test is not restricted to two settings, but (a) it suffices for the introductory discussion and (b) for the use made of it in the quantum mechanical example. This is an encyclopedia article on Bell's theorem not an article on Bell tests.

"there is no way you can test for fair sampling by the only method agreed by both quantum theorists and local realists, by checking for constancy of the total coincidence counts."

Again, this article is not about the experimental details of Bell tests. CSTAR 19:33, 6 Feb 2005 (UTC)

This is evidently how you think it should be. I think you are wrong, and Bell himself would have been bitterly disappointed. He would not have liked to see such prominence placed on irrelevant statistical matters or on the quantum-mechanical derivation either! But then, that's just my opinion. Caroline Thompson 22:35, 6 Feb 2005 (UTC)

We agreed no original research when we came here. I would hope that you would realize the importance of this rule, and out of respect for your fellow contributors, many of whom must similarly restrain themselves on areas where they have made original contribitutions, and refrain from inserting your own opinions into the page. Stirling Newberry 00:41, 8 Feb 2005 (UTC)

More of CT's scurrilous attacks on my talk page

For those that are still watching this show, it is now playing over at my talk page.

However, visitors are requested to send $10 to any Tsunami relief fund per visit.

Thank you!CSTAR 15:09, 8 Feb 2005 (UTC)

More CT

From some reason CT has decided to protest over at my talk page. My latest response to her:

Reply to CT

Why is this discussion taking place here on my talk page and not on the Bell theorem talk page?

"They look as if they mean orthogonal settings in your remaining diagram."

Well in the remaining diagram they refer to the specific quantum mechanical example discussed in that section in which they are orthogonal. That is clear from the surrounding text.

"I have as yet to see evidence that you understand the whole hidden variable approach."

Whoa, that's a pretty prickly response! Are you now qualified to issue exams?

"You might possibly be interested in the following,"

I've read enough of your theories already. No thank you. CSTAR 19:32, 8 Feb 2005 (UTC)

Sorry CSTAR, but you are wrong!

You really are confused about the interpretation of X and Y! Look at the text preceding your first equation. You say:

As an example consider a composite system consisting of two photons prepared in a special state one of which is sent to Alice and the other to Bob. Alice and Bob then each measure polarization of their photon along one of two perpendicular axes.

It is simply not true. In CHSH tests that use polarisation the angles used are, e.g., 0 and 45 deg for Alice, 22.5 and 67.5 deg for Bob. X and Y are not orthogonal. They would be orthogonal in tests using spin-1/2 particles but you are not talking about these.

In other words, a change of notation is essential. X and Y are not suitable for the job.

Thanks. I changed the example to conform to the EPR example that follows below in the article. The notation remains unchanged. CSTAR 13:59, 9 Feb 2005 (UTC)

OK, though I still think the choice of notation unfortunate.

In answer to your question in the discussion in Bell test experiments as to what is wrong with using X and Y, one part of the answer is that you can use it but only if you give the proper definition at the time. It is only later, when we come to the section on the derivation of the quantum-mechanical formula, that we have it clearly stated that:

"The operators XB, YB correspond to B's spin measurements along skew directions in the xz-plane."

But therein lies the rub! XB and YB are essentially quantum mechanical concepts. What is needed in an introduction to the Bell inequalities is just ordinary angles. We're talking about ideas that are intended to be applied to real experiments in which detectors are physically set at particular angles.

Surely the requirement to write the page from the QM point of view is not so strong that we have to make it completely inaccessible to local realists! As I've pointed out many times now, Bell derived his inequality from the local realist point of view. The page as it stands does not even introduce the hidden variables that were an essential feature of his model. The only place where you can find out the kind of way Bell approached the problem is from a similar derivation given in the CHSH inequality page. Caroline Thompson 08:56, 29 Mar 2005 (UTC)

How about the next inaccuracy -- the presumption that we toggle between two detector settings? Could we perhaps say something like:

"Each experimenter is free to choose any setting for their detector, just two settings on each side being needed for conduct of the CHSH Bell test".

I see no reason to put this in the intro. A suitable place is perhaps the Bell test experiments section, where an optical Bell test is discussed.CSTAR 20:28, 9 Feb 2005 (UTC)

As I've mentioned before, they don't constantly toggle between the two. In fact, even in Weihs' experiment and Aspect's "time-varying" one, it is important that they don't "toggle" (i.e. switch regularly back and forth) but choose between the two settings randomly. Caroline Thompson 20:03, 9 Feb 2005 (UTC)

And I never said "they constantly toggle between the two", implying that the setting is different on each trial.CSTAR 20:09, 9 Feb 2005 (UTC)

I'm afraid there are several other corrections needed to the introductory section before it reaches an acceptable level of "neutrality". As it stands, it is quite unreasonably biased towards the quantum theoretical POV. For a start, I suggest a very modest change that would perhaps make the page less off-putting and more informative. Could we re-arrange the first sentence to read:

"Bell's theorem refers to a class of correlation inequalities that hold under local realism but not under quantum mechanics."

I take it you do not like this proposal? Caroline Thompson

And you are still referring in the introduction to "correlation" where it should be quantum correlation, not quite the same thing. Caroline Thompson 10:42, 9 Feb 2005 (UTC)

I see no reason to change it, and I doubt anybody that follows developments on this page does either.CSTAR 14:28, 9 Feb 2005 (UTC)

Quite frankly I don't know what you are talking about; moreover it has aready been pointed out to you that it is bad etiquete to label section headings with a personal reference, which though falling short of qualifying as a personal attack, is still unnecesarily hostile.CSTAR 02:05, 30 Mar 2005 (UTC)

New "Bell inequalities" page

I've gone ahead and created a new page for the actual inequalities, since they did not really fit in with Bell test experiments. They are not all suitable for use in actual experiments and, besides, you don't really need to know how the inequalities are derived in order to be able to test them.

I don't know what happened to an edit for the Bell's theorem page I did this morning. I changed the relevant link to point to my new Bell inequalities page and also deleted a lot of the refs that were no longer referred to. I see the refs have now been re-formatted, but how many are really still relevant? Most relate parts of the page that have now been moved. Caroline Thompson 22:11, 10 Feb 2005 (UTC)

What's going on? Once again I edited Bell's theorem, apparently successfully, to link to my new page and once again my edit has vanished into thin air! Caroline Thompson 22:15, 10 Feb 2005 (UTC)

Don't look at me. CSTAR 22:24, 10 Feb 2005 (UTC)

It's just some kind of glitch, either with my machine or wikipedia. I'm sure I'll get there in the end.

However, it's time to move on to the next problem: what happens when there are some zero outcomes:

Effect of zero outcomes on formula

We all seem agreed the CHSH inequality holds equally when there are some zero values, but it is clear that it assumes the use full value for 'N' in estimates based on formula (2). It assumes we divide by the number of pairs we attempt to measure, not the number that we measure and which give a non-zero outcomes for both Alice and Bob. [The notation is still, incidentally, very confusing!] This, of course, is what lies at the heart of the detection loophole and I don't understand the explanation given of how to get around it -- how to justify use of formula (2) using the total observed coincidences (i.e. just the non-zero outcomes when both sides are non-zero at once) instead of N.

In their 1974 paper, Clauser and Horne say firmly that their CHSH test cannot be used unless N is known. As has been known since Pearle's time (1970), it can only be used replacing N by the observed coincidence total if it can safely be assumed that the non-detections all occur purely at random. This, to a local realist, is incredibly unlikely!

I don't see what can be done about it in the page, since the policy seems to be to avoid mention of "hidden variables" and the whole issue of fair sampling revolves around the concept. What we are talking about is whether or not we have a fair sample of the hidden variable values. Caroline Thompson 10:27, 11 Feb 2005 (UTC)

Can I take it, CSTAR, that you have moved on and do not intend further edits to this page? If so, is it OK if I prune down the refs to the ones actually used, leaving only three or four?

I remain unhappy about your treatment of zero outcomes. The fact is that an inequality that can be proved when we use the full value N is in practice used with a different value for N -- just the number of "successful" outcome pairs. Caroline Thompson 09:58, 15 Feb 2005 (UTC)

Do you mean "Am I not looking?" CSTAR 13:31, 15 Feb 2005 (UTC)

Re: References

All the Bell articles should be mentioned, in addition to CHSH, Griffiths, Redhead, Nielsen and Chuang as well as d'Espagnat's classic (it is currently not mentioned). Am I missing anything?

I see no reason to delete the others, but if you insist, I suppose go ahead and delete them.CSTAR 15:57, 15 Feb 2005 (UTC)

Reversion and deletion of talk pages

I also note that Caroline Thompson has deleted over a month of discussion on these talk pages. That is very much against WP practice if not policy.--CSTAR 02:13, 30 Mar 2005 (UTC)

I am unaware of having deleted anything on this talk page! If I did it was entirely unintentional. I'm sorry, too, about the personal reference in my last entry. It just happened to be the most relevant place to comment further on the use of X and Y. Where did you get the idea from? What have you got against using Bell's own notation? I don't much like that either but at least it does not come accompanied by any firm conventions! X and Y do. When talking about directions (which is the case here), they are assumed to be orthogonal. Indeed, when you come to the QM section, you take this for granted: clearly x, y and z are an orthogonal set.

Unless a few changes are made (as a minimum, inclusion of at least one derivation by something like Bell's own method, i.e. a method involving hidden variables, and inclusion of a statement of the actual formula used in the CHSH test, i.e. one dividing not by N but by the total coincidence count) the current page deserves a pov tag. It is strongly biased towards QM -- so strongly that it no longer represents "human knowledge". It does not at present satisfy the wikipedia requirement set out in the Neutral point of view page:

Wikipedia is a general encyclopedia, which means it is a representation of human knowledge at some level of generality.

Caroline Thompson 08:49, 30 Mar 2005 (UTC)

Caroline, why are you continuing this debate when it was already resolved against you and your biased POV? QM is the standard for the science of electrodynamics and physical theory. Therefore, it is in fact a neutral POV by definition. Your attempts to insert your revisionism into this area of Wikipedia are not welcome, as should be evident to even the most obtuse person. Attacking CSTAR's hard work - which was required as a direct result of your actions - is not only wrong, it is the ultimate irony. If some fine-tuning of the presentation is required, that would be normal and can be done more efficiently once you back off. Maybe you should get involved in the debate about whether the speed of light is a constant... anything that results in your leaving this area alone so we can finish cleaning up the mess you created.--DrChinese 16:12, 31 Mar 2005 (UTC)

Dr Chinese, I'll stop intruding if and when I consider that you've cleaned up the mess that you and CSTAR created! Why don't you get on with the job? [Or invite me to!]

The facts I'm asking to be included are just facts, essentially neutral, and in any event, as I've said many times, surely a neutral point of view is not the same thing as one that is unintelligible to anyone other than a trained quantum theorist? Don't we want wikipedia to be as far as possible accessible to the general reader? Bell's own work was. The reader of his papers is free to skip the QM parts and will still come away with a clear idea of what his theorem is all about. And, in case you hadn't noticed, it's all about hidden variables. Where do these feature in the current page? Only as casual links to other pages. Caroline Thompson 09:20, 1 Apr 2005 (UTC)

Talking about unnecessary added work, please note that the material CT deleted from this talk page (please compare the current version with those of a few days earlier) now has to be merged back in; it forms an important record for the article and should be available for readers. I'm not quite sure why CT deleted it (she claims it was a mistake).

Anyone else volunteer to do this? --CSTAR 16:49, 31 Mar 2005 (UTC)

CSTAR, I have added back a bunch of the deleted text, going back to 15 Feb. I hope this helps.--DrChinese 21:45, 31 Mar 2005 (UTC)

Not only bad notation: the derivation of the CHSH inequality is wrong!

The derivation currently presented for the CHSH inequality entirely misses the point and is wrong. It does not apply either to Bell's original idea or to the actual Bell test experiments! [I had been concentrating my attention on the use of poor notation and have only just got around to looking at the logic.]

The statement that Bell test trials consist of "An infinite sequence of values XAn, YAn, XBn, YBn, where n denotes the trial number" is simply not true, and cannot legitimately be used as a starting point.

Bell's idea was that by assuming hidden variables, with the source being at any one time in a given state and with a fixed probability distribution for those states, one can derive the inequality as a statistical result. The discussion currently given can at best be regarded as an argument for its plausibility, since in the actual experiments there is no meaning to the index n. As implied under "Remark 1", the actual Bell tests comprise a set of subexperiments, each investigating one setting for detector A, another for detector B. It is physically impossible to look at all four combinations of settings at once. [Even in Aspect's or Weihs'experiments, where the choice between the two settings on each side is random, they cannot physically be observed simultaneously.] The idea that we can somehow ensure that all the expressions have the "same value when taken on each one of the ... subsequences" is just wishful thinking.

Valid derivations are given in the CHSH inequality page. They employ (as far as possible) the standard notation -- that of Bell, Clauser and Horne's original papers -- which differs markedly from that of the current page.

Other faults with the page that urgently require correction include:

Bell's orginal inequality is not even stated
The diagrams print poorly
Some of the Latex expressions over-run the line so the end is not printed

Drastic revision is needed. My own suggestion remains that we base the new version on the one before CSTAR's intervention. I don't know where CSTAR got his material from but it is evidently not an authoritative one. No authoritative version would attempt a derivation based on an index n and not on hidden variables. Caroline Thompson 09:08, 9 Apr 2005 (UTC)

RFC some comments for Caroline Thompson and Dr Chinese

What I see is two people very passionate about the issues. I would recommend that you both make some restraint and allow that several POV should be shown with a fair statement about majority and minority view. It should also admit that it is a difficult area subject to unclear thinking in the past even by some acknowledged great men.

Caroline, please make your statements more in the nature of a POV not an absolute fact. Dr Chinese, please allow Caroline's statements to stand or only modify them to a POV as I suggested, and not just delete them. User:RayTomes 2005-04-16

While they may seem fair, your suggestions are not in line with WP policy. Caroline does not have a right to present her biased POV while I (and others) have an absolute right to present generally accepted scientific opinion on this subject.--DrChinese 03:08, 22 Apr 2005 (UTC)

Caroline is making it clear that the CSTAR is making statements claiming to be the accepted POV but which are quite inaccurate. Also, if you take the essence of Caroline's criticisms (but not all of them) you will find that they are shared by a number of knowledgeable physicists. That is why I ask for you both to be more moderate. User:RayTomes 2005-04-24

Reply to User:RayTomes

CT's claims have been discussed and refuted in this talk page and in other forums by other individuals, endlessly. Are you also making the claim that "CSTAR is making statements claiming to be the accepted POV but which are quite inaccurate" or are you simply trying to paraphrase CT? = As I have expressed many times, my presentation closely follows Asher Peres formulation in his standard textbook, which is also essentially the treatment given by Nielsen and Chuang in there now classic book.

Before making any claim , please note that CT has attempted to delete (at 08:56 29 March 2005 to be specific) the past record of this talk page: See [3] (http://en.wikipedia.org/w/index.php?title=Talk:Bell%27s_theorem&diff=11670481&oldid=11643516)

There you can quite clearly she has tried to obliterate an important part of the discussion, including past refutations of her position, contributions of many in the WP community and an explicit statement of my references, which she claims now to ignore. --CSTAR 03:35, 24 Apr 2005 (UTC)

Disputed pages can be seen from CHT's user page

I've put copies of versions of the three main pages that have (since January, 2005) either been lost or revised beyond recognition as subpages of my user page:

CHT version: Bell's theorem (http://en.wikipedia.org/wiki/User:Caroline_Thompson/Bell's_theorem)
CHT page: Bell test loopholes (http://en.wikipedia.org/wiki/User:Caroline_Thompson/Bell_test_loopholes)
CHT version: Bell inequalities (http://en.wikipedia.org/wiki/User:Caroline_Thompson/Bell_inequalities)

Some of the links will, unfortunately, not now be effective or will lead to redundancy, but readers may find there material of interest that deserves to be incorporated in the present pages. I admit the bias in the presentation is "local realist" (I'm not apologising! Why should it be otherwise?), but the facts themselves are neutral.

I'm afraid I still consider the faults in the present Bell's theorem page so serious that nothing short of complete replacement will suffice. Caroline Thompson 09:22, 21 Apr 2005 (UTC)

So noted. You now have links from here to your user page and you can say whatever you want there. So please stay away from here, Caroline; at least until the scientific community has a change of heart. I hope you don't feel the need to have the final word, although somehow I expect you will need to.--DrChinese 03:19, 22 Apr 2005 (UTC)

Note that the opinion of the scientific community cannot alter facts such as the methods used by Bell and others to derive inequalities or the existence and empirical importance (easily provable in the case of the subtraction of accidentals) of various "loopholes"/flaws in the experiments designed to test those inequalities.

Doesn't wikipedia take into account the opinion of the rest of the world -- people who have not been indoctrinated into the mysteries of quantum theory or carried away by the enthusiasm of the scientific journalists? Haven't they the right to expect to be told relevant facts? I trust you agree and will be editing the pages accordingly. Caroline Thompson 08:46, 22 Apr 2005 (UTC)

DrChinese, you sound like a real wanker to me.

Caroline, about your editing jinx

I've looked over some of this talk page change history and found that your problem edit made at 08:56, 29 Mar 2005 almost certainly occurred because you started editing on a very outdated revision of the page, that of 20:28, 9 Feb 2005 rather than the current version of the page (which was 10:09, 20 Mar 2005). This caused the following 16 edits to be thrown out:

10:09, 20 Mar Caroline Thompson (→Bell's original inequality - Where is lead to other Bell inequalities?)
10:13, 19 Mar Caroline Thompson (→Bell's original inequality)
10:10, 12 Mar Caroline Thompson (→Info on Bell's inequalities has been lost - Perhaps mostly OK now)
09:55, 12 Mar Caroline Thompson (→Info on Bell's inequalities has been lost)
18:23, 11 Mar Caroline Thompson (The redirect for both Bell inequalities and Bell's inequalities 
18:52, 16 Feb Caroline Thompson (→Re: References - Did some deletion and editing; repeated crit
15:57, 15 Feb CSTAR (→Effect of zero outcomes on formula)
13:31, 15 Feb CSTAR (→Effect of zero outcomes on formula)
09:58, 15 Feb Caroline Thompson (→Effect of zero outcomes on formula)
10:27, 11 Feb Caroline Thompson (→New "Bell inequalities" page - Back to the detection loophole)
22:24, 10 Feb CSTAR (→New "Bell inequalities" page)
22:15, 10 Feb Caroline Thompson (→New "Bell inequalities" page)
22:11, 10 Feb Caroline Thompson (→New "Bell inequalities" page)
22:00, 10 Feb Caroline Thompson (→New "Bell inequalities" page)
14:42, 10 Feb Stirling Newberry (Changing header, please do not direct talk page headers at individuals.)
10:35, 10 Feb Caroline Thompson (→Sorry CSTAR, but you are wrong!)

On the article page itself you have had similar problems (one symptom of which was your "links jinx"). At 18:40, 16 Feb 2005 you made an edit based on the out-of-date revision of 23:10, 9 Feb 2005, thus losing these edits:

09:56, 11 Feb Caroline Thompson (4th attempt at link to Bell's inequalities page! (My machine glitch?))
00:34, 11 Feb CSTAR (→Comparison to quantum mechanical prediction - Deleted redundant sentence)
18:25, 10 Feb CSTAR (→External Links)
18:25, 10 Feb CSTAR (→References -Format)
15:40, 10 Feb CSTAR (→Bell test experiments - Removed link. ALready have one link to that page)

The simplest explanation is that you sometimes click to edit while looking at an old revision. It would be good to be careful in the future, and also to check at the top of the editing page for this message:

WARNING: You are editing an out-of-date revision of this page. If you save it, any changes made since this revision will be removed.

Yours for more effective wikiing -R. S. Shaw 06:51, 24 Apr 2005 (UTC)

Thanks! I've no idea, though, how I could confuse a really old edition for the current one. I know my browser sometimes uses one from cache that is not quite up to date, and this can be cured by pressing Ctrl+F5, but it's most strange that I could have accidentally brought back an ancient edition of a talk page. Ah well, since the article has since been hacked around beyond recognition, most of this talk is now irrelevant. The problems on the article page were relatively minor and they, too, no longer matter. Caroline Thompson 10:03, 26 Apr 2005 (UTC)

Page is under dispute

I have put notes on the page to indicate that the CHSH inequality derivation is under dispute. The reputation of wikipedia is otherwise in danger. Dr Chinese has not responded to requests to refrain from reverting all my edits. If he does so for this one, I'm afraid I must accuse him of vandalism.

As I have repeatedly pointed out, the derivation is not valid. Moreover the notation is so seriously misleading that I see no alternative but to start again, going back to the edition of Bell's theorem from the beginning of January. This is reproduced on my user page. Caroline Thompson 09:08, 2 May 2005 (UTC)

CT, you are wrong. Please kindly remove your dispute headers yourself or this has to go to RfC. --Pjacobi 09:55, 2005 May 2 (UTC)

As CT fails to understand, there are many different formalizations of local realism. However, it should be now abundantly clear that it is pointless to maintain any discussion on the matter. The issue was resolved once. Yet another reference is Streater's article [4] (http://www.mth.kcl.ac.uk/~streater/lostcauses.html). CT's addition should be reverted immediately, preferably by her. --CSTAR 03:38, 3 May 2005 (UTC)

CSTAR, the issue is far from resolved. All that has happened is that a few people who, for one reason or another, believe quantum theory to be correct have failed to look carefully at the logic in your "correlation" section and failed to answer my point re the impossibility of defining your index 'n'. Nobody has commented at all. I assure you that whatever your source for this "derivation" it is in error. Valid derivations of the CHSH inequality are available, so there is no justification for including this invalid one. [What, BTW, was your source?]

The article by Streater adds nothing new, merely re-iterating what we already know: that Bell's theorem proves QM to be incompatible with the existence of hidden variables. He is wrong, though, in saying:

" ... the work of Aspect, Dalibrand and Roger (1982) shows that for some systems of two correlated photons, the best experimental estimates for certain spin correlations violate the Bell inequalities, and so cannot be explained by classical probability theory, with or without hidden variables"

without qualifying this by mentioning the existence of loopholes. As was at one time (in wikipedia pages now effectively erased) made clear, one of Aspect's experiments (his second) was subject to the fair sampling loophole, the remaining two at risk of severe bias due to the subtraction of accidentals (http://arXiv.org/abs/quant-ph/9903066). If these factors are taken into account, we see that it is possible that QM is in fact wrong in this area and that the opinion that hidden variables have been ruled out does not rest on solid experimental evidence. Caroline Thompson 10:33, 3 May 2005 (UTC)

At last! Thanks, CSTAR, you have dealt with one of the problems. Now for the others, e.g. better coverage of the loopholes (especially fair sampling, which I suspect you still have not understood), and at least a statement of what Bell's original inequality was -- and a note of the fact this has never been used.

Note: If you want to understand what the fair sampling loophole is all about, I continue to recommend my own work, e.g.:

C H Thompson and H Holstein , “The ‘Chaotic Ball’ model, local realism and the Bell test loopholes”, http://arxiv.org/abs/quant-ph/0210150

Caroline Thompson 09:23, 4 May 2005 (UTC)

I fear that though the page is now more accurate, it is far from deserving inclusion in an encyclopaedia. It needs drastic tidying up. And that notation is doomed to cause endless confusion! Why use X and Y as if they are going to correspond to the two sides when defining correlation, then switch back a few lines later to XA and YA corresponding to two different settings on the same side? Why use X and Y here at all, when there is later a further cuase for confusion, with x, y and z assumed to be orthogonal axes? Though Bell's notation may not have been the best possible, it was better than this. Caroline Thompson 08:58, 5 May 2005 (UTC)

Dr Chinese, you may well not care about my POV, but a considerable number of people do! John Bell himself would have been among them. He knew what he was doing when he derived his inequality on the basis of the assumption of hidden variables. As I see it, there were two reasons for requiring them:

the whole debate, ever since the 1935 EPR paper (http://fangio.magnet.fsu.edu/~vlad/pr100/100yrs/html/chap/fs2_14005.htm) had been about the existence of hidden variables (Einstein's "elements of reality"), and
he was creating an inequality that would be testable and he knew that it would only be possible in any one trial to measure one property on each side.

As it happens, it is possible that he himself never quite understood what the detection loophole was all about (witness his much-quoted statements about not thinking higher efficiency would fail to support QM), but others such as Philip Pearle did (see Physical Review D, 2, 1418-25 (1970)), and the only way to understand the problem is in relation to hidden variables. This, I'm sure, is the reason why many people dismiss it: they cannot understand it because the only derivation they have seen of a Bell inequality is one such as that in the present page, which CSTAR states follows Peres and others. It seems clear that these people were wrong. Since Bell was right and this is supposed to be about his theorem, wikipedia surely must present a correct derivation? Caroline Thompson 09:11, 6 May 2005 (UTC)

CT, you aren't claiming communications with the dead, I hope? --Pjacobi 10:20, 2005 May 6 (UTC)

She appears to understand his thinking from the grave. And it doesn't matter, because there is really no issue with Bell's Theorem. It is the experiments CT has the problems with. So leave this area alone, Caroline, we have already settled the issue and further interference is not appreciated. Cstar, I didn't mean to interrupt your development of the topic but I don't see any reason to give Caroline any free advertising in this area. I am certainly happy to make sure the material follows Bell if that is a question, but Bell's Theorem has nothing to do with purported loopholes.--00:16, 7 May 2005 (UTC)

Pardon me, but Bell's theorem surely has everthing to do with Bell's inequality, and it surely makes a difference whether you talk about a valid version or one that is valid only under assumptions that can easily be shown to be unreasonable. This is what I'm concerned about -- that the present page does not give Bell's original test, does not give a valid derivation of the test it does give (the CHSH test) and does not explain properly how the test is applied in practice or how the known loophole re fair sampling actually works. Of course, a lot of people don't know how it works, but this is no excuse in an encyclopaedia. Caroline Thompson 08:49, 27 May 2005 (UTC)

Making the page respectable

Would whoever suggested the need accept my idea of a reversion to the early January version,

CHT version: Bell's theorem (http://en.wikipedia.org/wiki/User:Caroline_Thompson/Bell's_theorem) ?

Note that it would be necessary at the same time either to expand (and rename!) the section in Bell test experiments on the loopholes or bring back the Bell test loopholes page that is currently re-directed to it. Caroline Thompson 08:49, 27 May 2005 (UTC)

CT, I will revert your attempts to roll back; this discussion has already been settled against you. Any improvements to this page can be made without your repeated (and clearly unwelcome) interference. -DrChinese 16:34, 31 May 2005 (UTC)

Fair enough, but I thought you had agreed that the current derivation of the CHSH inequality should be replaced by one that everyone agrees is valid? While we're about it, we might as well improve the notation, get back to Bell's definition of quantum correlation and make a few other improvements, possibly relegating the section on the quantum-mechanical prediction to a separate page. This would be in deference to Bell. His contribution was to provide the local realist inequality. The quantum-mechanical theory was already known.

Something needs to be done, and soon! The present page it not something wikipedia can be proud of. Caroline Thompson 09:12, 1 Jun 2005 (UTC)

So apparently CT has added a new page - quantum correlation - which we will now need to edit for her biased POV. Thanks for pointing this out so we can remove it. Caroline, have you created any others we should know about? -DrChinese 19:10, 1 Jun 2005 (UTC)

What if I have created another page or two? Since the pages I create are factually correct and are more comprehensible than ones such as the current Bell's theorem page, I really don't see why I should help you to remove them! The quantum correlation page is neutral, merely stating Bell's own definition and giving a few words to put it in context. It is equivalent to that given in Bell's theorem but put in words and so more readily digestible to the general reader. As you know, I consider the present page to be far too mathematical, most of the mathematics being irrelevant to Bell's theme, which was concerned with the fact that under local realism there are natural limits on the values of certain functions of coincidence rates in a suitably designed experiment. The mathematics needed to establish these limits comprises no more than a little basic probability theory, though, of course, it is the assumptions behind the maths that matters.

Incidentally, may I remind you, the derivation of the limit given in the current article does not apply to the experiments supposed to test it! It is high time it was replaced by one that does, for which see the CHSH inequality page. Caroline Thompson 08:47, 3 Jun 2005 (UTC)

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