Talk:Bell's theorem/Archive 3

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Article contradicts itself

In the overview..

"Similarly, the results will be anti-correlated (+,-) (-,+) if their analyzers are aligned on orthogonal axes."
But then to the right the table says otherwise.
" Orthogonal axes: pair 1 pair 2 pair 3 pair 4 ...n
Alice, 0°: + − + − ...
Bob, 90°: − − + + ...
Correlation: ( −1 +1 +1 −1 ...)/n = 0.0
"Dave3457 (talk) 02:48, 11 June 2009 (UTC)

This overview was a huge mess, and contained multiple issues. I just spent a fat chunk of time revamping it. Much better now. Isocliff (talk) 08:46, 1 October 2010 (UTC)

Cute theorem but trivially refutable; why so much space?

In outline: Essentially QM argues that rather than having specific values miniscule objects and processes have probability distributions. These probability distributions are collapsed into specific values when various conditions apply. For instance a decaying tauon may decay into this that or the other thing with varying degrees of probability. Once it has decayed into (say) tauon neutrino + X + X antineutrino, then it is a specific value.

For any studied (historical) system there are no relevant probabilities left, there are only realized values. Given an appropriate ordering and mapping these can be expressed as a sequence of values on some more or less continuous interval.

It cannot be proven that the system was not the result of consulting such a sequence.

If the sequence is random then there are no hidden variables (there, at least).

If the sequence is pseudo-random then there are hidden variables.

It cannot be proven that the sequence is not pseudo-random without knowing the pseudo-random period.

So at most Bell has proven that some hidden variable models are insufficiently sophisticated. 76.126.215.43 (talk) 22:43, 11 July 2009 (UTC)

I don't think you really understand Bell's theorem. It has nothing to do with random versus pseudorandom measurement outcomes. You could assume the classical hidden-variable theory is truly random or the quantum-mechanical universe is pseudorandom, it doesn't matter. The important thing is that the quantum statistics of the measurement outcomes can't be simulated by any classical algorithm applied independently to the two subsystems that are measured. It can be simulated by a classical algorithm that gets to choose the outcome for both subsystems together, but you can set things up such that that requires faster-than-light communication. -- BenRG (talk) 21:18, 20 July 2009 (UTC)

Agree with BenRG. You're asserting the very thing that Bell's theorem, and the accumulating evidence and experiments since; a naive philosophical realism. Before you patronize a well-established scientific theory on purely philosophical grounds, it's good to understand the theory you're trying to criticize. If you can demonstrate your thought-experiment in the same manner as the EPR [which is Bell's starting point] to refute it, there's a nobel prize waiting for you. —Preceding unsigned comment added by 209.105.184.93 (talk) 03:00, 20 October 2010 (UTC)

The error of reasoning in naive philosophical realism is captured in "Essentially QM argues that rather than having specific values miniscule objects and processes have probability distributions." This presupposes that quantum wave functions are probability distributions over specific values, but that is not what QM asserts. In QM it is wave functions that are real, not the specific values found from measurement. Measurements lead to mixed states on subsystems that we interpret as probability distributions over specific measured values. However, this is only a mathematical artifact of the projection of a larger wave function onto a measurement subspace of interest. The wave function for the universe as a whole never collapses. Wave function evolution per QM is fully deterministic. It is only our interpretation of specific measured values on subsystems that are probabilistic. Quantum decoherence explains the physical processes involved. Non-local quantum correlations demonstrate that QM is inconsistent with naive philosophical realism. Experiments demonstrate that the universe is consistent with QM. Manawiz (talk) 23:01, 27 December 2010 (UTC)

Experiments: Where's the point?

Assuming that there's a hidden spin (or polarization) variable, then these measurements prove that when your spin (or polarization) detector's axis is not aligned exactly at the axis of an incoming particle, then there is a misalignment-angle-dependend probabilty that it will either output the same result like a correctly aligned device or not.

I can't see why this proves anything more but that a misaligned binary measuring device outputs fuzzy results, and that the statistical distribution of this fuzz is correctly stated by a certain equation. Any device mapping a linear input to a binary output will behave more or less like this. For example when you have a TTL circuit and the input voltage for a 1 signal is below the circuit's specifications, than it will take this input for either 1 or 0 (as is not allowed anything inbetween) with certain probabilities that depend on the input voltage and the circuit's physical properties.

This all looks like some circle argument about some statistical equations proofing themselves, not like valid a falsification of the local variables hypothesis.

Am I missing something!?

--217.87.172.196 (talk) 19:45, 24 November 2009 (UTC)

Relativity and Determinism

After EPR (Einstein–Podolsky–Rosen), quantum mechanics was left in an unsatisfactory position: either it was incomplete, in the sense that it failed to account for some elements of physical reality, or it violated the principle of finite propagation speed of physical effects. In a modified version of the EPR thought experiment, two observers, now commonly referred to as Alice and Bob, perform independent measurements of spin on a pair of electrons, prepared at a source in a special state called a spin singlet state. It was equivalent to the conclusion of EPR that once Alice measured spin in one direction (e.g., on the x axis), Bob's measurement in that direction was determined with certainty, with opposite outcome to that of Alice, whereas immediately before Alice's measurement, Bob's outcome was only statistically determined. Thus, either the spin in each direction is an element of physical reality, or the effects travel from Alice to Bob instantly.

Look at this in terms of Relativity. In every experiment like the one described above, for every individual measurement taken by Alice and Bob, there will be a frame of reference in which Bob's measurement happens first, one in which Alice's happens first, and one in which the measurements happen simultaneously. Logically, then it doesn't even make sense to talk about the possibility of one measurement affecting the other. In frames where the measurements happen simultaneously, the two have to be conspiring, simultaneously affecting each other. And since either measurement could come first and at any time after the creation of the entanglement, then the resolution has to be predetermined, even in cases where A or B "randomly" set their detectors or change their detector orientations while the particles are in transit.

Is there a hole in this reasoning? If not, does this mean the universe has to be deterministic? —Preceding unsigned comment added by 70.166.64.3 (talk) 22:19, 30 March 2010 (UTC)

The situation where the two distant measurements are close to each other in time excites a lot of talk about "quantum effects" (people seem to know better than to say "information") propagating faster than light, etc etc. But the times are totally irrelevant. The situation is this: If Alice and Bob measure the two entangled spins in the same direction they will get opposite results. If they measure the spins along orthogonal directions they will get uncorrelated results. It doesn't matter whether Alice goes first, or Bob, by how long. 76.102.80.158 (talk) 01:46, 31 December 2010 (UTC)

What is wrong with the Overview?

In today's edit by 128.143.100.177 (talk) (→Overview: This was just wrong...) a confusion (not a mistake) is revealed, to the effect that in the Overview a measurement is discussed using polarization measurements of two correlated photons (as performed by Aspect and coworkers in 1981). The discussion of these experiments is largely analogous to the discussion in terms of correlated spin-1/2 paricles in a singlet state (which the editor had in mind), be it that angles differ by a factor of 2. The confusion is enhanced by a picture in that section referring to spin rather than photon polarization, but nevertheless meant to illustrate the issue.WMdeMuynck (talk) 22:25, 31 March 2010 (UTC)

Overview 4th par.: 45°?

So far, (when the analyzers are aligned, orthogonal, or 45 degrees) the measurement results can be modeled by proposing physical attributes, -- but there's no discussion of 45°. ABS (talk) 17:19, 12 June 2010 (UTC)

Source lacks authority

In the overview, it is suggested that Bell's theorem is controversial in some way. 'Not everyone agrees with these findings' We'd really need a source of some notability to back this up. The source for this appears completely unreliable. It's not from any kind of peer-reviewed journal, but self-published by someone who appears to be a bit of a crank. I would just delete it but it appears to have already been deleted and promptly re-added.Steady unit (talk) 22:36, 2 September 2010 (UTC)Steady unit (talk) 23:25, 2 September 2010 (UTC)

Agreed. The lead-in paragraph, especially near the end, is using vocabulary that appears to be in doubt of the experiment's results, and then implies further doubt by appealing to a feigned controversy over interpretation. The experiment has been done repeatedly, and each time, the results have been the same. The burden of proof belongs to 'not everyone' and whoever 'interpretation of these experiments is still the subject of some debate' is; they are welcome to step up to the plate and design an experimental refutation, but until then, I will be going through the article and removing un-sourced [and political] assertions. —Preceding unsigned comment added by 209.105.184.93 (talk) 16:11, 18 October 2010 (UTC)

I regret the changes recently made to the overview, referred to above, because they substitute a majority view endorsing a nonlocality explanation of the Bell inequalities for a view leaving room for alternative explanations. An alternative explanation has been discussed in chapter 10 of my book, Willem M. de Muynck, Foundations of quantum mechanics, an empiricist approach, Fundamental theories of physics, vol.~127, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002, based on peer reviewed publications (see my website [1] for a list). I am not suggesting to explicitly deal with this alternative on the present Wikipedia page (which is not really necessary since at several places in Wikipedia there are references to my website), but I agreed with the previous version precisely because of its cautiousness, which is now lacking.WMdeMuynck (talk) 20:10, 18 October 2010 (UTC)

I appreciate the interest of the above two commenters in this article, but both of you seem to have gotten the wrong idea about the major rewrite I did of the overview on October 1st. To be abundantly clear, I ABSOLUTELY agree that any suggestion of controversy in the physics community with respect to Bell's theorem is ridiculous. The one sentence at the very end of my overview rewrite that refers to dissenting views was included solely in the hopes of avoiding future back-and-forth editing, due to the the presence of (as far as I can tell) a single user dedicated to casting doubt on Bell's theorem. If you check, you will see that the previous version was far more supportive of such dissent, to the point of being seriously misleading. The overly conciliatory sentence at the end was not ideal, but it is at least correct. So again, since we seem to be in agreement on this point, it should be fine to begin revising any phraseology that casts undue doubt on the theorem. (Edit: On further examination, it appears you are actually referring to the first section, before the overview, in which case we definitely agree. This part is even worse than I realized so I will edit it immediately, to at least be accurate.)

Now, WMdeMuynck, your comment does not seem to make much sense to me. Please be specific. I don't see how you can argue that my revision does not "endorse a nonlocality explanation" when I plainly said that the results demonstrate "the existence of superluminal effects".

Sorry, if my mastery of the English language is insufficient. When I said "a is substituted for b", I meant to say that "b is replaced by a". Hence, I certainly implied that your edit is endorsing a nonlocality explanation (as you plainly said). My criticism was about the suggestion of exclusivity of that view (which view, indeed, was widely held within the physics community, but currently meets with increasing criticism), and about the neglect of the possibility of alternative explanations.WMdeMuynck (talk) 09:12, 19 October 2010 (UTC)

My rewrite of the overview on Oct 1st was primarily to address three problems with the prior version: 1) the presence of errors and contradictions 2) the greatly exaggerated "disagreement" with the standard interpretation of BT, and 3) the fact that the description of BT was overly specific to the point of being incorrect. If you'd like to explain what you meant, Id be very interested to hear what you have to say, but please keep in mind that I cannot read your book. Isocliff (talk) 03:22, 19 October 2010 (UTC)

I agree that the former presentation of the problem was far from ideal, and should be improved. However, I found your edit not an improvement. The alternative you chose is the one developed by John Bell, introducing a kind of nonlocality that has triggered phantasies of superluminal communication, the latter, however, being recognized by the physics community to be unobservable. Hence, the nonlocality view has its own problems, which undermines the possibility of plain statements as presented by you. Unfortunately, a complete analysis of the problem needs an analysis of both the mathematical formalism of quantum mechanics as well as its interpretation, probably going beyond the level of sophistication aspired by a Wikipedia article.WMdeMuynck (talk) 09:12, 19 October 2010 (UTC)

I see. We'll your english seems pretty good to me, except for the one sentence that gave the reverse impression than was intended. Im certainly interested to hear your argument, but I dont see how you can reasonably describe the nonlocality of entangled systems as an "explanation", considering we experimentally observe the instantaneous statistical changes in measurement outcomes. Avoiding this conclusion, it seems to me, would require a departure from traditional assumptions so radical that it would be incumbent on you to state so explicitly (i.e. Superdeterminism, Solipsism), or else, in the words of someone much smarter than myself, a weird "conspiracy of nature". I don't think its necessary to think of the nonlocal effects as "communication" except in the most general sense, since I've never heard anyone suggest that entanglement results from particles sending signals to each other. I think the more common view is the one that parallels the quantum formalism: that both parts of the entangled system are simply described by the same information (the same quantum state). Your use of the word "phantasies" to describe this nonlocality leads me to believe that you flatly reject the mainstream consensus (perhaps that was your intention). But this wikipedia article's primary responsibility should be to convey the meaning and significance of Bell's theorem as it is understood and accepted by the physics community as a whole, otherwise very few articles would be able to say much of anything. Now I haven't conducted a formal survey of the literature, but the quantum mechanics textbook used at MIT, Harvard, my own school WPI, and a lot of other universities (Griffiths) refers to Bell's theorem and these experiments as demonstrating nonlocality, without any qualification, exactly as I did in the revision. So again, feel free to state your case tersely if you can, since Im interested. But I doubt I'll be comfortable accepting a major revision of physics understanding into the article without the demonstrated support of some major people in the field (who Im sure would also defend the mainstream view much better than I ever could). I dont mean disrespect, since your credentials dont seem insignificant at all, but you're still just citing yourself. Isocliff (talk) 04:42, 25 October 2010 (UTC)

You say: I dont see how you can reasonably describe the nonlocality of entangled systems as an "explanation". My answer: Nonlocality explains von Neumann projection in an EPR experiment (this is an explanation, although a bad one). Nonlocality is not part of "description" (entanglement is). In the wake of logical positivism physicists have learnt to make no difference between explanation and description: in talks you will often hear that something is explained when an adequate description is found (i.e. when it is subsumed under a physical theory, as is the case in the Deductive-nomological model).

You are right that I have strong doubts with respect to nonlocality precisely because it is unobservable (you can't use it to send messages). Violation of the Bell inequalities in EPR-Bell experiments only occurs if incompatible observables are involved. But incompatibility is a local affair (mutual exclusiveness of measurement arrangements). So it seems that violation of the Bell inequalities has a local origin.

I have discussed this extensively on my website [2] and in my book Willem M. de Muynck, Foundations of quantum mechanics, an empiricist approach, Fundamental theories of physics, vol.~127, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002. Unfortunately, the problem of nonlocality is entangled with many other aspects of the interpretation of the quantum mechanical formalism. I tried to find the most weak interpretation possible, which I refer to as the `empiricist interpretation', which does not try to bestow on the formalism more physical meaning than is strictly necessary. It is not my intention to burden Wikipedia with all these intricacies, but every now and then I try to venture a moderating word when a presentation in Wikipedia in my view becomes too one-sided.WMdeMuynck (talk) 17:01, 31 October 2010 (UTC)

First let me say, In regards to your last sentence, I'm not objecting to what you're doing on here, just expressing my own disagreement and trying to understand. I do think you've expressed your dissent in a respectful and responsible way, so I definitely appreciate that. At first you certainly piqued my interest with what you described as alternative formulations of Bell's inequalities, however after looking more closely it looks like there is a fatal flaw in your reasoning. Before I get into that, what I find most bewildering about your position, and what I have yet to find a satisfying explanation for in your work, is why you can ignore the physical evidence for nonlocality that has been demonstrated over and over. We directly observe the statistics of a particle changing dramatically after measuring its entangled partner in a spatially-dispersed system. The possible mechanisms for getting around this, which already seemed somewhat far-fetched (i.e. the communication loophole), have been all but experimentally ruled out. It just seems to me to me that an argument against nonlocality should be under some obligation to provide a specific explanation for the otherwise unambiguous evidence. You say that "incompatibility is a local affair". This is incorrect, and it precisely because it is a nonlocal affair that we can discern the existence of nonlocal correlations. Compatibility is determined by the detector settings of the respective distant observers, which can be chosen randomly after the photons (or whatever) are in flight, in mutually-exclusive lightcones. If you want to argue that the elaborate efforts undertaken to ensure this randomness have failed, okay. But then as more and more ways are found to randomize the settings, the more contorted and unlikely it seems to me any such theory would have to become. The above statement, combined with your describing nonlocality as "unobservable" makes me increasingly wonder if there isn't a fundamental misunderstanding somewhere. We can "observe" that the nonlocality occurred when, after an experiment, classical communication is used to exchange information about measurement results that occurred in the past.

Now here is where either I have misunderstood your argument, or your analysis has made a serious mistake. Bell's inequality is an expression of a condition placed on the expectation values of the products (correlations) of measurement results. It is derived by assuming definite values of physical quantities, whose expected value, as we see it, is given by the integral of the measurement results times the probability density of the hidden variable over all possible values of the hidden variable(s). On the other hand, you're inequality apparently involves probabilities computed as a function of which subsets of results $(S^{i})$ the various observables are confined to exhibit. So it seems that your result expresses something else entirely. To put it another way, BI is a limit on the expectation value of the product of two spin measurements made on two separated particles, as a function of the detector orientations, with the only other assumption being that when the axes of measurement are aligned (or anti-aligned), the results must be perfectly anticorrelated (correlated) which is the property we observe with pairs prepared in the state ${1 \over {\sqrt {2}}}(\left|\uparrow \downarrow \right\rangle +\left|\downarrow \uparrow \right\rangle )$. Your derivation doesn't seem to require this condition, or any hidden variables, but you apparently derive something that looks like Bell's Inequality expressing a limit on the probabilities of results as a function of the results, so again it seems both the domain and the codomain of the functions $P(S^{1},...,S^{n})$ which are the subject of your paper, are fundamentally different from those of Bell's theorem. As a final remark, because I cant seem to find any references to hidden variables in your derivation, your conclusion could be said to apply to any theory, realistic or not, which would plainly put it at odds with what we observe, since the BI is violated experimentally. Even if this is not a correct assumption, and you do reference hidden variables somewhere, and I assume you are correct that this result demonstrates the impossibility of hidden variables to account for quantum mechanical behavior, then the mere existence of Bohmian mechanics would seem to contradict your conclusion, since it is a hidden variable theory that reproduces the results of experiments and of QM. For this reason I am especially interested to see what remarks of Bohms you are referencing in this article, apparently in support of your thesis, but I cannot seem to find/access that article. Care to help provide the details on this, or otherwise explain where I go wrong in my analysis of your work? Isocliff (talk) 09:10, 1 November 2010 (UTC)

Let me first say that I appreciate very much your extensive reaction on my previous answer to you. Since this discussion does not seem to be about the editing process I will explain my point of view in more detail on your talk page.WMdeMuynck (talk) 03:35, 2 November 2010 (UTC)

Excellent edit Isocliff, and to Mr. WMdeMuynck; I'm not quite sure this is the proper place, either, as this page applies more concerning Bell's theorem and it's effects, as the lead-in states, than an explanation on whether the interpretation of quantum mechanics and it's overall philosophy is factual on particular points. However, I am by no means an important editor here, so I appeal to Isocloff's comments above. As a side-note: I am currently reading your work on your personal homepage (for personal enlightenment), and it is interesting thus far. —Preceding unsigned comment added by 209.105.184.93 (talk) 03:19, 20 October 2010 (UTC)

J-Wiki's edits

There have been a number of useful edits by J-Wiki. But it seems a pity to lose the mention of Aharonov. Bell refers to the paper by him and Bohm in 1957, not just Bohm. I think I linked to the wrong thing and so got him axed. Myrvin (talk) 10:51, 26 April 2011 (UTC)

Hello, Myrvin. Although Bell points to the Aharanov-Bohm paper of 1957 as advocating the example he uses, Bohm originally published his version of the EPR argument, using the example of quantum spin, in the conclusion of his 1951 book, Quantum Theory. I'm not sure of the best way to handle this, but for now I've now added a reference for the 1951 book to the article. J-Wiki (talk) 00:25, 28 April 2011 (UTC)

I have to agree with J-Wiki on this one... it seems that Bohm came up with his spin-based variant of EPR well before his contact with Aharanov. However, their 1957 paper does seem to be the first to put its finger on the importance of correlations and suggest that resolutions of the EPR paradox might be experimentally testable.--Sabri Al-Safi (talk) 09:00, 28 April 2011 (UTC)

Vandalism or Error?

Remark 1, third indent, under the CHSH Inequality section has the word "JEFF" on the left side of an equation. This was introduced in the Revision as of 07:20, 27 August 2011 which, otherwise, seems sensible (although IANAP so take that evaluation for what it's worth). — Preceding unsigned comment added by 24.239.181.139 (talk)

I removed the "JEFF =". I think it looks right now, but someone else might want to verify that. My edit was at 15:34, 21 October 2011‎ 199.68.65.235 (talk) 15:43, 21 October 2011 (UTC)

Typos

The diagram of the source, Bob and Alice has two typos: the y axis for both Bob and Alice should be a "z" axis in order for the diagram to be consistent with the rest of the text. In addition, in the text, please change "The operators B(b'), B(b)" to "The operators B(b), B(b')" so that it corresponds to the x-z plane being rotated 135 CC degrees into the x'-z' plane, with b corresponding to Bob's measurements along x' and b' to Bob's measurements along z'. Perhaps the figure should also prime the axes on Bob's side. Clejan (talk) 18:17, 14 September 2011 (UTC)

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Lede

The version reverted to here [3] reads more clearly for the lede. IRWolfie- (talk) 20:52, 25 June 2012 (UTC)

• Disagree...per Stanford University's much clearer -- and vastly more authoritative -- cited article on Bell's Theorem'. -- Updated: --FormerNukeSubmariner (talk) 13:52, 27 June 2012 (UTC)
• Agree. The original longstanding consensus version is much clearer. Sławomir Biały (talk) 11:53, 26 June 2012 (UTC)

• Comment. The old version of the lead is the consensus version. It has been stable for over 5 years, meaning that many editors have implicitly endorsed it (see WP:CON and WP:BRD). If this were a vote, not only would we have the implicit consensus that already existed, but in addition it is two to one against the new change. FNS, if you want this to be included, then you have to make your case here and convince somebody else that you are right. Sławomir Biały (talk) 21:24, 26 June 2012 (UTC)

• Agreed: clearer becuase

"No physical theory of local hidden variables can ever reproduce all of the predictions of Quantum Mechanics."

is very direct, the other is more wordy. I just reverted the last change by FormerNukeSubmariner; the prosy comment for an edit summary "two people doth not a 'consensus' make" (WTF?) is meaningless - now it’s 3. I don't have time to keep eyes on WP right now though... F = q(E+v×B)⇄ ∑_ic_i 22:21, 26 June 2012 (UTC)

I added a ref to the statement, which has a paragraph saying the exact same thing almost word for word. F = q(E+v×B)⇄ ∑_ic_i 22:34, 26 June 2012 (UTC)

• Final comment (clearly, speaking for myself): I do not engage in dialogues on Wikipedia that too-quickly slide into either slander or calling my words "meaningless." If the vastly superior (IMHO) clarity of the Stanford article isn't immediately apparent to the reader...then it isn't apparent to the reader. Clearly, not my problem to solve. Moreover, I can always simply refer my colleagues to the Stanford article to have corresponding dialogues...so I truly have no problem to solve (here). Cheers to All. --FormerNukeSubmariner (talk) 13:58, 27 June 2012 (UTC)

I apologize for any offense, just expressing myself - sorry... Thanks for at least being capable of conceding defeat and moving on instead of dragging the issue on forever, which is the right thing to do given that no-one was convinced. F = q(E+v×B)⇄ ∑_ic_i 22:04, 27 June 2012 (UTC)

Don't confuse disinterest in fixing other people's problems with defeat, my friend. You clearly don't know whom you are talking to, nor do you have the right life experience or capacity at a 90-rated IQ (your words, not mine) to be making such judgements. Such an attempt would be (my word) arrogant. Cheers to All...and Good Day. --FormerNukeSubmariner (talk) 22:21, 27 June 2012 (UTC)

Overconfident?

This article seems to imply that Bell's theorem has been proven definitively:

"John Clauser and Stuart Freedman (1972) and Alain Aspect et al. (1981) convincingly demonstrated that the predictions of QM are correct... one is forced to reject either locality or realism (or both)"

But other parts of wikipedia seem to contradict this:

http://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experiments

"In one of Alain Aspect's experiments, inter-detector communication at light speed during the time between pair emission and detection was possible, but such communication between the time of fixing the detectors' settings and the time of detection was not. An experimental set-up without any such provision effectively becomes entirely "local", and therefore cannot rule out local realism." Doubledork (talk) 22:52, 26 March 2013 (UTC)

Lead section

There is no indication against linking EPR paradox in the lead, but IMHO the current lead is too preoccupied with EPR and Alain Aspect and does not give a concise description of Bell's result (in any hidden-variable theory, for … measurements, the estimate … holds). In any case, current wording in Bell's theorem #Overview provides a better context for the EPR paradox link than current wording in the lead. Incnis Mrsi (talk) 17:06, 30 March 2013 (UTC)

LHV does not imply linear variation in the correlations

Hi All, In the article it says "With the measurements oriented at intermediate angles between these basic cases, the existence of local hidden variables would imply a linear variation in the correlation." But it is not correct. Yes, some LHV models produce a correlation as a linear function of the difference of angles but not all of them. On this page http://www.mathpages.com/home/kmath521/kmath521.htm there are examples of LHV models that produce different functions.

I'm not experienced in editing Wikipedia article hence brought the issue here in the talk page. Best, Sokratesla (talk) 14:56, 12 May 2013 (UTC)

Indeed. Only a Bell inequality can restrict all LHV theories at once. The linear correlation function is just an example. Boris Tsirelson (talk) 16:03, 12 May 2013 (UTC)

Thus, I've changed the text accordingly. Boris Tsirelson (talk) 18:24, 30 May 2013 (UTC)

Inconsistent notation?

It seems to me that there is disagreement between the three tables in the overview section showing annti-parallel, parallel and orthogonal correlation. The two first-mentioned denotes identical correlation (same sign for Alice and Bob) with a +1 and anti-correlation with a -1. However, the third table denotes same-sign with -1 and opposite-sign with +1. This puts the third table in agreement with the figure to the right, but is confusing when the three tables are compared. It should nbe corrected - or am I missing something? — Preceding unsigned comment added by Laererlund (talk • contribs) 07:12, 30 May 2013 (UTC)

Indeed. Thank you. I fixed the signs. Boris Tsirelson (talk) 18:12, 30 May 2013 (UTC)

About the (dis)agreement with the figure: I've reformulated the caption, and added some clarification to the text. Boris Tsirelson (talk) 18:39, 30 May 2013 (UTC)

Final comments

The final comments had a small reference to the detection loophole still being an issue for some. I have rewritten this to accord more with what I believe is mainstream current thinking: the mainstream view is *not* (and never was) that the nondetected photons are different from the others and local hidden variables still have a chance. The mainstream view was always that this is a hypothetical possibility which moreover most people did not take seriously, on general physical grounds. But the mainstream view is no longer that this is a minor philosophical nuisance which we shouldn't worry about. I think the mainstream view is that it *is* important to do an experiment which closes all "practical" loopholes simultaneously - I mean, loopholes which can be closed by practical arrangements in the experiment; not abstract philosophical loopholes which no-one can do anything about except make them appear ridiculous. In fact it is clear that the top experimental groups are now vying to be the first one to attain this goal so indeed it has in the last few years changed status from some kind of optional extra which no-one should worry about, into something important which will be a big step in physics. I reference two persons on this, their statements can be found in:

M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger (2013). Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227--230.

B.G. Christensen, K.T. McCusker, J. Altepeter, B. Calkins, T. Gerrits, A. Lita, A. Miller, L.K. Shalm, Y. Zhang, S.W. Nam, N. Brunner, C.C.W. Lim, N. Gisin, and P.G. Kwiat (2013). Detection-Loophole-Free Test of Quantum Nonlocality, and Applications. arXiv:1306.5772 [quant-ph]

Z. Merali. Quantum Mechanics Braces for the Ultimate Test. Science 18 March 2011: 1380–1382. Science Magazine

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner (2013). Bell nonlocality. arXiv:1303.2849 [quant-ph]

One reason for this importance is that quantum cryptographic applications depending on quantum entanglement are not safe if one can "fake" quantum entanglement with classical physical means. So various quantum communication protocols only become as secure as they are claimed to be once all practical loopholes have been closed simultaneously, and can be easily closed simultaneously in mass produced quantum communication networks. Richard Gill (talk) 14:27, 14 August 2013 (UTC)

Jaynes (undue weight)

The theoretical section near the end concludes with Jaynes' criticism of Bell's assumptions. However, Jaynes later agreed that Bell's conclusions seemed to be true, and indeed, shocking. I am hunting for a good literature citation to support this claim. Richard Gill (talk) 17:29, 9 August 2013 (UTC)

Thanks J-Wiki for adding some nice references here! I have asked Steve Gull for his proof. It is a two-page note (a really neat little argument, very different from standard proofs). He faxed me it some years ago, but I can't find it right now, but he'll send it me again. If I scan it and put it on internet then, together with the discussion at the end of Jaynes' paper where Jaynes explicitly refers to Gull's proof (it appeared in a conference volume at which they both presented papers) everything is properly referenced. Richard Gill (talk) 13:21, 14 August 2013 (UTC)

Thanks for further adressing this topic, and clarifying it. It would be great if the Gull proof could be made generally available.J-Wiki (talk) 01:27, 15 August 2013 (UTC)

Here's a link: [4]. I plan to LaTeX this and make it more generally available. Richard Gill (talk) 14:58, 22 September 2013 (UTC)

And Steve Gull has even posted it on his own webpage [5]: [6]. Richard Gill (talk) 15:07, 22 September 2013 (UTC)

Professor Gill, thanks to you and Professor Gull for posting the sketch proof. I've placed a question I have about it on your user talk page.J-Wiki (talk) 20:03, 28 September 2013 (UTC)