Talk:Bell's theorem/Archive 7

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What is an example of an "impossibility proof" that Bell mentioned?

I don't know many "impossibility proofs" One I do know involves simple plane geometry: "It is impossible to trisect an angle using only a compass and a straight edge." The proof is that only linear and quadratic (but not cubic) operations are possible using these simple tools.

I think there should either be a link to another section on such proofs, or else reference specific examples of the kinds of impossibility proofs that betray a "lack of imagination". — Preceding unsigned comment added by Danshawen (talk • contribs) 15:29, 23 April 2014 (UTC)

The article has a link to (freely available) Bell's text [16]. There, on pages 2-3, Bell mentions impossibility proofs in [3], [4], [7]-[14]. See these sources, according to his References. On Wikipedia, see Kochen–Specker theorem and John Stewart Bell#Bell's critique of von Neumann's proof. Boris Tsirelson (talk) 18:17, 23 April 2014 (UTC)

A quote about (in)determinism

"In summary, I think it’s fair to say that physical indeterminism is now a settled fact to roughly the same extent as evolution, heliocentrism, or any other discovery in science. So if that fact is considered relevant to the free-will debate, then all sides might as well just accept it and move on!"

(Scott Aaronson "The Ghost in the Quantum Turing Machine", page 23)

Boris Tsirelson (talk) 06:29, 28 April 2014 (UTC)

Freedom

The article currently says, 'Freedom refers not to the philosophical concept of free will but to the physical possibility to determine settings on measurement devices independently of the internal state of the physical system being measured'.

Can someone explain exactly what this statement means. In particular, what is meant by 'the internal state of the physical system'? Does this refer to the values of the presumed hidden variables? Martin Hogbin (talk) 09:39, 29 January 2014 (UTC)

Yes. For more details: Freedom = no-conspiracy, see Boris Tsirelson's article on entanglement on Citizendium, [1]. Or read my article "Statistics, causality, and Bell's theorem", [2]. I use the *consequence* of the assumption, that when an experimenter chooses settings of a measurement device by tossing coins, then those coin toss outcomes are statistically independent of the counterfactual outcomes of each possible measurement. Richard Gill (talk) 11:57, 1 February 2014 (UTC)

See also Free will theorem. Richard Gill (talk) 12:07, 1 February 2014 (UTC)

I cannot find a clear description of what 'no-conspiracy' means anywhere. Martin Hogbin (talk) 14:23, 1 February 2014 (UTC)

Boris and I have done our best, but not succeeded. Maybe you need to study a whole lot more physics and philosophy of physics before you can begin to appreciate what we are on about? It is rather subtle. I have been working intensively on Bell's theorem and all that for 20 years now. The longer I studied it, the more I learnt that it is impossible to explain to outsiders in a few sentences what is going on.

Von Neumann said that anyone who claims to understand quantum physics clearly doesn't. This is very very true. Only after you have studied it deeply enough to truly understand that it is un-understandable, can you begin to appreciate the significance of the various quantum paradoxes. The reason for this is quite simple: quantum physics violates the basic understanding of the world which is hard-wired (by evolution) in our brains. So far we didn't need it.

But surely you do understand what it means to suppose that the outcomes of coin tosses (used to determine measurement settings) are statistically independent of all those hidden variables which determine what the outcome of the measurement will be, given each possible setting? Richard Gill (talk) 18:24, 1 February 2014 (UTC)

Sorry for being a bit not nice, but I guess that Martin will say (again) that under absolute determinism there is no randomness at all and therefore "statistically independent" means nothing.

I only wonder, what is his attitude to the fact of (seemingly) statistical behavior of coins tossed (and many other objects)? He never told us. He always did something else. Boris Tsirelson (talk) 21:06, 1 February 2014 (UTC)

Yes Boris you are quite right that I would say something along the lines you state but I think we have all agreed that absolute determinism does not falsify Bell's theorem. Please do say if either of you do not agree with this.

I have now moved on to asking exactly what is meant by 'freedom' and 'no-conspiracy'. Freedom, as far as I can see, is intended to replace the philosophical and ill-defined term 'free will' with a more objective and well-defined term. I have my doubts that it succeeds is doing this and I am asking you to tell me in some clear way exactly what 'freedom' means. The use of the term 'no-conspiracy' does not, in my opinion help. It is a term that seems to be intrinsically based on human emotion.

Regarding your coin tossing question, I think that it leads to a circular argument if used regarding Bell's theorem. If we assume that a local classical theory of physics is possible the tossing of a coin is deterministic. Tossing it in exactly the same way will always produce the same result. If, on the other hand, we assume that there is some inherent and fundamental randomness in the process due to QM then we have already abandoned classical physics. Martin Hogbin (talk) 21:53, 1 February 2014 (UTC)

No! This is the root of our absence of mutual understanding during the long time! As I wrote many times, randomness and determinism coexist in classical physics in full harmony! This fact is very important for physics. You cannot just ignore it when discussing physics. The chaotic motion of atoms acts like a huge Pseudorandom number generator. Its outcomes are fixed beforehand, but if you do not know them beforehand you never discover a statistically significant deviation of randomness. Think on this seriously. If this big obstacle will disappear, our discussion will be much more smooth and (hopefully) successful. Boris Tsirelson (talk) 06:52, 2 February 2014 (UTC)

But pseudorandom numbers are not random numbers. The WP article on the subject starts [my italics], 'A pseudorandom process is a process that appears to be random but is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process'.

I fully appreciate that psuedorandom processes may exhibit many of the properties of a random process and may, for example, be arbitrarily sensitive to initial conditions but the outcome of such processes can, in principle, be calculated even if such a calculation is currently impossible or would require exact knowledge of the initial conditions.

I would even accept that there is an interesting philosophical discussion to be had here over the difference between something that is likely to be forever incalculable and something which is fundamentally unknowable but the WP article shows that there is not a clear consensus that you are right. Martin Hogbin (talk) 09:51, 2 February 2014 (UTC)

Who says that pseudorandom numbers are random numbers?? Me?? Not at all. Never. They are not. And this is very good! For this reason they are compatible with deterministic classical mechanics. Boris Tsirelson (talk) 12:00, 2 February 2014 (UTC)

OK, I misunderstood you. We agree that pseudorandom and random are not the same. I think we also agree that true randomness is hard to find when hidden in pseudorandomness. Am I right about that?

Yes. --Boris

What I do not understand is what you mean by 'freedom' and 'conspiracy'. I do not even understand what kind of concepts they are. Are the philosophical concepts like free will, in other words things that can never be subject to the scientific method?

Are they measurable quantities? Martin Hogbin (talk) 13:51, 2 February 2014 (UTC)

Not philosophical. Yes, subject to the scientific method. Measurable, with some reservations. "Freedom" (as used by Richard) means exactly "no conspiracy" (as used by me and some others). Here is a quote from my Citizendium article:

"However, is the result really unpredictable in principle (not just in practice)? Not necessarily so. Moreover, according to classical mechanics, the future is uniquely determined by the past! In particular, the result of the coin tossing exists in the past as a complicated function of a huge number of coordinates and momenta of micro particles.

It is logically possible, but quite unbelievable that the future result of coin tossing is somehow spontaneously singled out in the microscopic chaos and transmitted to the apparatus B in order to influence yB. The no-conspiracy assumption claims that such exotic scenarios may be safely neglected."

Boris Tsirelson (talk) 14:12, 2 February 2014 (UTC)

You say, 'It is logically possible, but quite unbelievable...'. I do not understand how unbelievabilty can be considered measurable. Is there some mathematical measure of believability or does that just represent your personal opinion about how nature should be? Martin Hogbin (talk) 14:44, 2 February 2014 (UTC)

Tastes differ. Beliefs differ. Only logic... no, logics also differ (classical and intuitionistic, for instance). What can I say? Still, people manage to communicate. Somehow. Sometimes. Yes, it just represents my personal opinion about how nature should be. So what? Do you think it is possible to make physics (or any science) on the basis of logic only? If you do, read Feynman's The Character of Physical Law. This my personal opinion is shared by quite many. But I understand that maybe the opposite opinion is shared by even more people. In fact it was my old proposal: to present the controversy to the reader and let him/her decide, which opinion to share. WP articles on politics typically represent opposite opinions with some comments. Your personal opinion is as personal as mine. Boris Tsirelson (talk) 15:14, 2 February 2014 (UTC)

But for now this is not the point. You ask what do we call "freedom". I answer. Whether we (me, you, ...) consider it believable or not is a separate question. Boris Tsirelson (talk) 15:39, 2 February 2014 (UTC)

I do not necessarily even disagree with you. Human laws of physics are, to some degree, what we want them to be. I too would find it hard to believe in some apparent conspiracy of nature to confound an experiment. On the other hand I would find it hard to say what exactly would constitute a conspiracy or, as Richard would call it a lack of freedom. I do not think that non-conspiracy is any less of a philosophical concept than free will.

What I might consider a conspiracy you might not. Also, what might appear to be a conspiracy to both of us might turn out to have some simple explanation when viewed in the right light. Martin Hogbin (talk) 18:09, 2 February 2014 (UTC)

In the same way that randomness might be hidden behind pseudo randomness, non-conspiratoral complexity might be hidden behind presumed conspiracy. Martin Hogbin (talk) 18:16, 2 February 2014 (UTC)

Well... you may hope on such scenarios of the future of physics... But as for now, the following fact (copied from Richard's message a lot above, modified by me) should find its place in the article:

while two logical possibilities, non-locality and non-realism, correspond to well-developed interpretations of quantum mechanics, and have many supporters, this is not the case for the third logical possibility, non-freedom.

Boris Tsirelson (talk) 20:25, 2 February 2014 (UTC)

I would support that proposal. We might also perhaps mention free will which might be regarded as the more traditional third possibility. Martin Hogbin (talk) 21:05, 2 February 2014 (UTC)

OK, I got bold and did the change, in the hope that Richard will not be disturbed by his own words, even if somewhat modified. About free will I feel very unsure, just because different people interpret it very differently. (I recall a note that free will contradicts both determinism and randomness...) Boris Tsirelson (talk) 21:36, 2 February 2014 (UTC)

That is all fine with me. If Richard wants to change the wording a little that would be fine also. I am not going to fight over free will. Richard, what is your view on this? Martin Hogbin (talk) 00:22, 3 February 2014 (UTC)

I am not fighting about free will. I would like to show you here some slides of a recent talk by someone I admire: Klaas Landsman. http://www.math.leidenuniv.nl/~gill/Klaas_Landsman_Bell_talk.pdf Richard Gill (talk) 11:45, 15 February 2014 (UTC)

An interesting paper but I am very suspicious of the concept of freedom. It seems to me just to be a restatement of Bell's theorem itself. Martin Hogbin (talk) 17:30, 17 February 2014 (UTC)

Which paper? Anyway: all there is, is one or two very simple mathematical results, which can be dressed up as (mathematical) "theorems" if you like (tautologies), and there is the interpretation of what these might mean for physics and for the understanding of quantum physics and for metaphysics ... and so we get into a vast territory, where there are no "theorems", only opinions, experience, matters of taste, culture ... and if you want to leave physics altogether and get "purely" into philosophy, then I'm afraid you'll be spending most of your time trying to figure out what words mean, and what it means to say a word means something, and so on ad infinitum. Good luck.

Einstein: "As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality." Richard Gill (talk) 19:38, 19 February 2014 (UTC)

(Rather off-topic; and edit conflict) My brother, a much more humanitarian person than me, told me: you mathematicians (seemingly) use words, and nevertheless do not depend on the (natural) language. Boris Tsirelson (talk) 19:58, 19 February 2014 (UTC)

What makes you think that I want to leave physics? Martin Hogbin (talk) 19:52, 19 February 2014 (UTC)

I really do not believe the "Freedom" assumption belongs in top section of Bell's Theorem along with the other two. First, it actually has absolutely nothing to do with Bell's Theorem specifically. It could be applied (as a hidden assumption) to virtually any quantum (or other for that matter) experiment ever performed. Second, it completely waters down the Bell paper, which of course does not mention it at all. Anyone who reads the paper after reading the Wikipedia article will be quite confused. Third, it is a relatively new area of discussion which would be better served placed in a different section. Yes, it is true that Bell mentioned it himself in talks. However, I don't think he or most anyone took it seriously until 't Hooft started writing about it. So it really relates more to the viewpoint of 't Hooft and his "Cellular Automata" interpretation of QM. There are a number of interpretations of QM which attempt to address Bell. Each interpretation makes an assumption of some type, and each of those do not deserve equal footing with "locality" and "realism" in a discussion of Bell. (Time Symmetry/Asymmetry is such an example.) As a point of reference, the Stanford/Plato discussion (updated 2009) does not mention Freedom (or Superdeterminism) as a Bell assumption. So I propose that Freedom be demoted. DrChinese (talk) 22:27, 12 May 2014 (UTC)

Rather convincing. Boris Tsirelson (talk) 05:23, 13 May 2014 (UTC)

As a non-expert I tend to agree too. These rather philosophical concepts are rather like mirages in that when you try to define exactly what you mean, you just move on to another concept that needs explanation. Martin Hogbin (talk) 08:21, 13 May 2014 (UTC)

Thanks for your comments/feedback. I will do some drafting on it and post the edit in a few days. Richard Gill and I have spoken in the past about the Bell page, and how to best fend off those who have used this page to dilute the main topic. (Several of us had a go of it with one of Joy Christian's followers a couple of years ago who wanted Christian's work to be featured here.) DrChinese (talk) 22:09, 13 May 2014 (UTC)

Some sources for improving the article

I'm not familiar enough with the concept to dare edit the article, but I think the claims in doi:10.1038/510467a should be given some space. In particular that Bell revised his own theorem in 1976 (Bell, J. S. Epistemol. Lett. 9, 11–24 (1976)) and that localists argue the 1964 formulation while non-localists argue the 1976 formulation.

Yes, thank you, I agree that this is worth mentioning. Let me think... Boris Tsirelson (talk) 19:51, 22 July 2014 (UTC)

After reading Wiseman's article I'd say, its message is that Bell did not really revise his own theorem in 1976. Bell's "beables" in the common past are the hidden variables. True, they need not uniquely determine the future event, but they do so up to a local randomization, which is well-known to lead to the same Bell inequalities.

From the section "Reconciling the camps" of Wiseman's article:

Thus Bell's 1976 theorem can be restated as: either causal influences are not limited to the speed of light, or events can be correlated for no reason. [...] It enables them to agree on a single Bell's theorem, and what logical options it offers, even if they prefer different options.

These two options are: reject the "locality", or reject the "realism" (in terms of our article). The third option, rejection of "freedom", is mentioned in the last section "The path forward" of Wiseman's article:

the only things correlated with free choices are their effects...

In fact, the three options were discussed in "An exchange on local beables" (by J.Bell, A.Shimony, M.Horne, J.Clauser), "Epistemological Letters" 1976-1978, reprinted in: "Dialectica" 39:2, 85-110 (1985).

Boris Tsirelson (talk) 06:41, 23 July 2014 (UTC)

Two more quotes from Wiseman could interest us. From the first paragraph:

The first [option] is that reality is irreducibly random ... The second option is that reality is 'non-local' ... Most physicists are localists: they recognize the two options but choose the first ...

From the section "Another theorem":

Bell himself was a non-localist ...

Boris Tsirelson (talk) 08:35, 23 July 2014 (UTC)

What is called correlations

To Jochen Burghardt and Arthur Rubin: isn't it better to first discuss the matter here rather than edit forth and back? Boris Tsirelson (talk) 07:19, 7 January 2015 (UTC)

Probably you're right - I didn't expect the issue to be that much complicated. Also, I can't help much in answering questions, as I'm not a physicist, but just a mathematician who wants to understand the article. Arthur Rubin is right in that the caption of File:Bell's theorem.svg explicitly mentions "spin-half". On the other hand, section Bell's_theorem#CHSH inequality speaks about "binary (+/-1 valued) outcomes". Maybe, the "outcome" is a normalized (i.e. scaled by 2 in our case) version of the measured "spin"? As another suggestion, the easiest way to obtain consistency might be to stick with the statistical notion of correlation, unless this is absolutely unusual in quantum physics. - Jochen Burghardt (talk) 18:15, 7 January 2015 (UTC)

I do not think it is complicated (and I am a kind of expert in it). Artur Rubin is right if the spin is treated as mechanical (the angular momentum); in this sense it is really neither 1 nor 1/2 but (plus-minus) a half of the Planck constant. But! This mechanics is rather irrelevant. Here the spin is treated informationally, as just a yes-no observable, encoded (for convenience) as plus-minus 1. (And by the way, the Stern–Gerlach experiment gives just this: splits the electron beam in two beams, without indicating "plus-minus how much" is it, really.)

About the statistical notion of correlation: the quantum calculation in the singlet state shows that the average spins (the expectations) are zero, and therefore there is no conflict between the two "correlations". However, when discussing Bell inequalities, it is usual indeed to call "correlations" the expected product in every case, whether or not the expectations are zero. Boris Tsirelson (talk) 19:14, 7 January 2015 (UTC)

Section "Two classes of Bell inequalities" is too technical

This section departs from the previous sections by suddenly being full of unexplained technical terms such as "fair sampling", "inhomogeneous", "homogeneous", "dark rate", "dead time", "resolving times".

Nobody needed to perform the experiment, because singles rates with all detectors in the 1970s were at least ten times all the coincidence rates.

Does this mean, performing the experiment would have been futile or inconclusive? The sentence uses irony where declaration would be clearer. I would correct it myself, but I can't be sure of my interpretation.

(I also don't understand why this factor of ten even matters or what it means here, but this is only one of many things that are unclear in this section.)

178.38.79.96 (talk) 07:34, 12 April 2015 (UTC)

Psychological Aspects

This article makes no mention of the psychology of the observers. Such factors as memory, subjectivity, and interpretation influence the results that each observer perceives and what they can agree on. Even without a many-worlds interpretation, each observer only perceives part of the entire reality. Which part they perceive affects the correlation. — Preceding unsigned comment added by 153.203.90.130 (talk) 20:05, 23 March 2015 (UTC)

I hope it depends strictly on the mathematics of tensor products and projection operators, and not on literary constructions. Otherwise I have no chance of understanding this gadget ! 178.38.79.96 (talk) 07:44, 12 April 2015 (UTC)

Unclear on the intuition of some text

The article reads,

"Suppose the two particles are perfectly anti-correlated—in the sense that whenever both measured in the same direction, one gets identically opposite outcomes, when both measured in opposite directions they always give the same outcome. The only way to imagine how this works is that both particles leave their common source with, somehow, the outcomes they will deliver when measured in any possible direction. (How else could particle 1 know how to deliver the same answer as particle 2 when measured in the same direction? They don't know in advance how they are going to be measured...)."

The above is an unsourced (perhaps OR) intuitive argument the intuition of which dose not jibe with my own understanding.

The particles in question are photons which are observed. Thus, they are photons that have been both emitted and absorbed. When a photon is emitted and absorbed, it has traveled at the speed of light and, from the photon's perspective, the emission and absorption have happened simultaneously, coupling and conserving mass-energy and spin angular momentum from the emitter to the absorber.

Similarly when a pair of entangled photons is emitted and absorbed, the emission event, and the two absorption events happen simultaneously, again from the photons' perspective, and again conserving spin angular momentum. So the photon does not have to "know" what these angular momenta are while in transit, as from the photon's perspective, the entire coupling event has happened in a single instant, is a single event and there was no concept of being "in transit".

The fact that the two distantly separated absorbers are measured as not being co-located, by some observer, who is neither of the photons, is explained because that's how special relativity works. In different frames you measure different distances and times. The coupling must make sense from the frame of the force-coupling carrier(s), but not from anybody else's frame. So there is no FTL communications paradox, at least not in this example involving photons in a vacuum.

Spope3 (talk) 06:03, 7 May 2015 (UTC)

Maybe. But the effect is the same on electrons and even heavy ions, that are far not massless. That "the emission and absorption have happened simultaneously" is itself not a well-established point of view. Moreover, bare photons are massless but do not exist in reality. Dressed photons are not quite massless because electron-positron virtual pairs matter. Boris Tsirelson (talk) 07:16, 7 May 2015 (UTC)

== (Reply to Boris re. "unclear intuition")

I have two points here:

1) Although the effect "is the same" for electrons and heavy ions, the article makes it clear that the most serious experimental results come from studying the behavior of photons. So it is at this point speculative to say that similar results hold for electrons (although I personally believe they do).

2) It is true that all real-world photons behave as dressed photons. But I'm not sure this means undressed photons don't exist, to me it means that a perfect vacuum does not exist, at least in our section of the universe/multiverse. So a photon might scatter off particles other than its Bell-experiment target (including virtual particles, and this effect can be translated into a mass expression for a dressed photon, but if this happens the Bell-experiment outcome is different whether or not one leans towards my point of view or the article's statements. — Preceding unsigned comment added by Spope3 (talk • contribs) 02:02, 8 May 2015 (UTC)

Looking at recent work from the Hanson group in Delft I see that a Bell test experiment is presently underway using electrons in diamonds. "Entanglement swapping" uses entangled photons to create entanglement between electrons in widely separated in locations in imperfections in carbon crystals (diamonds). Replace one carbon atom with a nitrogen atom and you have an addressable electron. Take a look at http://hansonlab.tudelft.nl/publications/ and at http://www.tudelft.nl/en/current/latest-news/article/detail/beam-me-up-data/ Richard Gill (talk) 16:43, 4 August 2015 (UTC)

I'm probably missing something, but your Bell's inequality seems wrong

From http://www.drchinese.com/David/Bell_Compact.pdf I have:

$1+\rho _{BC}\geq |\rho _{AB}-\rho _{AC}|$

Replacing B by c, C by b, and A by a:

$1+\rho _{cb}\geq |\rho _{ac}-\rho _{ab}|$

It seems you are missing the absolute value sign.--Guy vandegrift (talk) 04:03, 6 September 2015 (UTC)

On one hand, that is all the same. From $\forall a,b,c\;\;\rho (a,c)-\rho (a,b)\leq 1+\rho (b,c)$ it follows that also $\rho (a,b)-\rho (a,c)\leq 1+\rho (b,c)$ and therefore $|\rho (a,c)-\rho (a,b)|\leq 1+\rho (b,c).$

On the other hand, indeed, the absolute value appears in Bell's original text, equation (15) there; why not do the same in this article? Boris Tsirelson (talk) 19:15, 6 September 2015 (UTC)

Anyway, Mermin's form is rather $0.5(1-\rho (a,c))\leq 0.5(1-\rho (a,b))+0.5(1-\rho (b,c)),$ that is, $\rho (a,b)+\rho (b,c)\leq 1+\rho (a,c).$ Boris Tsirelson (talk) 19:37, 6 September 2015 (UTC)

Since you don't need the minus sign, you removed it. But removing the absolute value sign weakens the result and also confuses the reader who is looking for it. Before I read a paper, I scan the equations to see what the paper is about. Removing the minus sign interferes with that initial assessment of whether or not I need to read the article. BTW, I am drafting a simple derivation on Wikiversity at v:Bell's theorem/Guy vandegrift. You are welcome to join in.--Guy vandegrift (talk) 09:28, 7 September 2015 (UTC)

The inequality with absolute value sign is two inequalities, depending on whether the thing we take the absolute value of is positive or negative. Those two inequalities are actually (from a mathematician's point of view) the same inequality - prove one, and you have proved the other too, by symmetry. The inequality without the absolute value sign is the one which you need to understand and it is the one with the simplest proof. But actually the CHSH inequality is just as simple to prove and it implies Bell's original and it is the one actually used in experiments. So I recommend you look for a simple proof of CHSH. We know that this inequality is very fundamental, for instance from Fine's theorem which says that one can come up with a local hidden variables model for an experiment with two parties, each with two settings, for measurements each with two outcomes, if and only if the probabilities P(A, B| a, b) satisfy all 8 CHSH inequalities (apply the obvious symmetries to transform one CHSH inequality into others). My favourite proof is the one on my slide 7 of my slides http://www.slideshare.net/gill1109/epidemiology-meets-quantum-statistics-causality-and-bells-theorem Richard Gill (talk) 19:47, 7 September 2015 (UTC)

Wow, that was easy! I will use it at Wikiversity:Bell's theorem/Inequality (but not till Thanksgiving when I have another few days to do as I please).--Guy vandegrift (talk) 03:47, 8 September 2015 (UTC)

No, thanks, I do not join in, for two reasons. First, I already did my best elsewhere. Second, one may write down a lot of various necessary conditions, but they are at best of historical interest, since we know the necessary and sufficient conditions: Bell-CHSH inequalities. All necessary conditions follow from Bell-CHSH. Boris Tsirelson (talk) 10:45, 7 September 2015 (UTC)

I will look at your website. FYI - I just found an extremely simple proof in a textbook by Griffiths. http://www.physics.umd.edu/courses/Phys270/Jenkins/Griffiths_EPR_BellInequality_Excerpt.pdf --Guy vandegrift (talk) 16:37, 7 September 2015 (UTC)

Your link seems not to work. Martin Hogbin (talk) 17:14, 7 September 2015 (UTC)

Try the link now. I had the signature touching the file: ..._Excerpt.pdf--(signature)--Guy vandegrift (talk) 03:17, 8 September 2015 (UTC)

Sister links to Commons categories

I created a category in Commons, not knowing exactly what I was doing. When I went to put a sister link here, I discovered that you already have one. I presume that you don't want two such links and I presume this is resolved by using subcategories at Commons. I will post the question on commons and place a link here so you can verify the status. If anybody knows how commons does categories, let me know. You may remove the link to the Bell's theorem category if you wish (obviously). See this post on commons.--Guy vandegrift (talk) 23:04, 15 September 2015 (UTC)

The category on commons seems OK. See c:Category:Bell's theorem. You can add or not add. I will move on to other projects. --Guy vandegrift (talk) 01:26, 16 September 2015 (UTC)

Delete new section "Alternative Analysis"?

I question the recent addition of the section Bell's_theorem#Alternative_analysis. It certainly needs to be stated that papers have been published in refereed journals suggesting that Bell's theorem experiments are flawed. But keep in mind that an experiment demonstrating that nature never violates Bell's inequality would be the greatest event in the history of quantum mechanics. In the minds of most, the only question is whether experiments to verify the violation of the inequality have minor flaws that need to removed before we have (almost) refutable evidence that nature can violate Bell's inequality.--Guy vandegrift (talk) 22:46, 2 October 2015 (UTC)

Thank you for this comment

Thank you for this comment. May I say, contrary to it, that the new section does not (repeat NOT) suggest, nor (repeat NOR) does Khrennikov suggest, that the "Bell's theorem experiments are flawed". For the sake of definiteness, I can add here that the section, and Khrennikov, gladly accept that the Bell's theorem experiments are not (repeat NOT) flawed. For more explicitness, perhaps I may add that the section and Khrennikov gladly accept that "we have (almost) [ir]refutable evidence that nature can violate Bell's inequality". The section and Khrennikov gladly accept that "an experiment demonstrating that nature never violates Bell's inequality" is not at all likely to be validly conducted. If by now there remains unclarity about this, please let me know, and I will try to clarify.

For support of my just foregoing comment, may I observe that the only use of the word 'experiment' in the section is as follows:

According to Bell, it is essential for the establishment of the causal implications of his inequality, that the experimental protocol be of the delayed-choice structure.

For definiteness, may I say that this sentence intends to agree completely with Bell on this point, and does not intend to impugn any experiment that might be performed.

No, the point made is about the theory in Bell's paper, his reasoning and argumentation, that generates the inequalities that the experiments test. It is the theoretical generation of the inequalities, not the experiments, that are the subject of the section and that are addressed by Khrennikov.

Since my just foregoing remarks interpret your comment as seeming to indicate that you are concerned that Khrennikov might be challenging the experiments, when the section intends that such is not his proposal, perhaps I may stop at this point, and see if we can review the situation, before going further.Chjoaygame (talk) 00:59, 3 October 2015 (UTC)

Thank you for clarifying your position. It was a relief to learn that you understand Bell's theorem. I now modify my complaint by stating that the following sentence is misleading:

When this factor is taken into account, the resulting inequalities are far less stringent, and are not violated by quantum mechanical predictions.

I assumed that the words "the resulting inequalities" refer to some modification of Bell's inequality that makes it more realistically model the experiment, for example by including missed photons or false detection of entangled photons. These complications were neglected in Bell's original paper. The phrase "not violated by quantum mechanical predictions" sounds like Bell's inequality is NOT violated when these effects are taken into account. First time readers will find it extremely confusing that Bell "derived" an inequality that is violated by both theory and experiment. Virtually all theoretical work focuses on deriving equations that are consistent with theory and experiment. So even if your section is technically correct, it is misleading.

When you write about Bell's theorem always keep in mind this peculiar fact: Bell's inequality is a quote-"prediction"-unquote that is violated by experiment and by quantum mechanics. Ironically one of the greatest discoveries in the recent history of quantum mechanics is an equation that is wrong. I often talk to students about Bell's theorem, and that is a big stumbling block. --Guy vandegrift (talk) 03:09, 3 October 2015 (UTC)

Thank you for your prompt and apposite response.

In my opinion, you are right to have "assumed that the words "the resulting inequalities" refer to some modification of Bell's inequality that makes it more realistically model the experiment". On the other hand, I should say that Khrennikov is not remotely imagining or suggesting that the modification is about "missed photons or false detection of entangled photons", or anything along those lines. Neither is Khrennikov suggesting that "Bell's inequality is NOT violated when these effects are taken into account". Khrennikov fully accepts that Bell's inequality is violated when these effects are taken into account.

Thank you for emphasizing the point that I (and, perhaps I may guess, Khrennikov) agree with, that "First time readers will find it extremely confusing that Bell "derived" an inequality that is violated by both theory and experiment." But the question is 'why will they find it confusing?'

The reason why they will find it confusing is not that Khrennikov is mistaken, nor that my posting of Khrennikov is wrong or misleading. They will find it confusing because they have already in their minds the idea that Bell validly derived an inequality that refers to the experiments. The reality is, according to Khrennikov, that Bell's inequality does not validly refer to the experiments. First time readers, and many readers who have read it a hundred times in the past, suppose that Bell's inequality and its congeners are validly applicable to the experiments.

Khrennikov is pointing out that the inequality that validly applies to the experiments is different from Bell's, and more particularly, from the CHSH, inequality. Bell's 1964 paper gives the reason for this. The last words of the conclusion of Bell's text are as follows:

Of course, the situation is different if the quantum mechanical predictions are of limited validity. Conceivably they might apply only to experiments in which the settings of the instruments are made sufficiently in advance to allow them to reach some mutual rapport by exchange of signals with velocity less than or equal to that of light. In that connection, experiments of the type proposed by Bohm and Aharonov [6], in which the settings are changed during the flight of the particles, are crucial.

It is evident, from the fact of these being the last words of his conclusion, and from the idea they express (the need to follow the delayed-choice protocol) not being expressed earlier in his paper, that Bell's derivation does not take that idea into account. Uniformly, other writers, following Bell, produce derivations of congeners of Bell's inequality that also do not take that idea into account. Khrennikov's paper, that is reported in the section, shows how to take it into account through valid orthodox probabilistic reasoning. The result is an inequality that indeed validly refers to and applies to the experiments, but is different from Bell's and its congeners'. The experiments do not come near violating the inequality that Khrennikov validly derives.

That the inequality that Khrennikov derives is not violated by the experiments is consistent with the validity of Khrennikov's derivation. As it happens, Khrennikov's working with conditional probabilities was to a degree anticipated, though not completed, by Edwin Thompson Jaynes.

The problem is not with Khrennikov's derivation, nor with his result, nor with the section's report of them. The problem is that Bell's inequality, as derived by Bell, and of its congeners as derived by his followers, makes no pretence to take into account the last words of Bell's 1964 paper that I have quoted just above. Those Bell inequalities and their congeners, accordingly, cannot pretend to apply to experiments that follow the delayed-choice protocol. Readers who supposed the contrary would be confused.

But their confusion does not arise from a mistake by Khrennikov, nor, I submit, from the section that I posted being misleading or mistaken. To find the source of their confusion, they must look not there, but instead must look at their supposition that Bell's inequality and its congeners refer validly to the experiments. The bulk of the article would, of course, support their supposition. That is why the section is headed 'Alternative analysis'.Chjoaygame (talk) 05:28, 3 October 2015 (UTC)

Is the Khrennikov paper freely available online or can anyone send be a copy please? Martin Hogbin (talk) 13:07, 3 October 2015 (UTC)

what is happening?

I do not understand, what is happening. Yes, of course, "experiments ... in which the settings are changed during the flight of the particles, are crucial"; doing otherwise is one of the loopholes well-known since 1964, isn't it? So, what could be the new point made by Khrennikov in 2015? Maybe this matter (if at all) should go to "Loopholes in Bell test experiments"? Boris Tsirelson (talk) 06:11, 3 October 2015 (UTC)

Thank you, very much admired and respected Editor Tsirel, for your very welcome comment.

Perhaps I may approach the question again. I think all agree that, broadly speaking, the so-called "Bell" experiments are sound when considered as experimental facts. The agreed experimental facts are that the observations violate the Bell and congener inequalities. So far as I can see, all will agree on that. If not, please let me know, and I will consider the reasons offered.

The questions arise as to interpretation of this violation.

I think most will agree that because the experimental facts contradict the Bell inequalities, there must be something very wrong with any purported "derivation" of those inequalities. This means that, in particular, there must be something very wrong with Bell's derivation. So far as I can see, all will agree on that. If not, please let me know, and I will consider the reasons offered.

What is wrong with the Bell derivation?

I guess the currently most celebrated diagnosis, of the fault in Bell's "derivation", is that Bell's "derivation" makes some wrong physical assumptions, more or less along the lines that 'nature would follow classical physical thinking'.

Under the heading 'Alternative analysis', the section takes the line that such a currently celebrated diagnosis differs profoundly from the diagnosis that is to be found in Khrennikov's paper. No, Khrennikov's paper does not endorse that currently celebrated physical diagnosis of the fault in Bell's "derivation". Instead, Khrennikov's paper diagnoses a logical, not a physical, defect that makes Bell's "derivation" inapplicable to the experiments. That is to say, Bell's "derivation" does not use conditional probabilities when they are needed for a valid derivation that can refer to the experiments. The diagnosis is not physical failure; it is logical, failure to conduct valid probabilistic reasoning.Chjoaygame (talk) 07:52, 3 October 2015 (UTC)

I still guess that our "Metaphysical aspects" section mentions all known ways to escape Bell inequality. What does it mean here, "logical, not physical"? When the physical assumptions are carefully formulated, Bell theorem becomes just this: a mathematical theorem that is a logical consequence of the assumptions. Rigorously. Do you want to say that Khrennikov is able to be more rigorous than the mainstream mathematics (including, of course, the probability theory, as is)? Even though the mathematics is now available to formal computerized verification? Boris Tsirelson (talk) 10:06, 3 October 2015 (UTC)

Thank you for this response. It is good to see that you take this seriously. Nevertheless, you do not make it clear, as to whether or not you have read Khrennikov's paper; at face value, your reply gives me the impression, perhaps mistaken, that you have not read Khrennikov's paper; please tell me this impression is mistaken, or please read the paper. As a piece of persuasive rhetoric, your response is fine. But your response does not pretend to address explicitly and directly the logical issue raised by Khrennikov.

Instead, your response just asks me what do I want to say, asking my opinion about Khrennikov's rigour? Your response presupposes, but does not offer reasons for, the idea that Khrennikov is not using "mainstream mathematics, including probability theory , as is". My answer is that Khrennikov is indeed using mainstream mathematics including probability theory, as is. The failure of Bell's "derivation" to use mainstream conditional probability where it is needed, as in this case, was pointed out in 1988 by none other than E.T. Jaynes, as cited and linked above. For the benefit of this discussion, may I point out that a major element in Khrennikov's presentation is his approving citation of the contribution of one Boris Tsirelson. I do not know if you are that Boris Tsirelson; perhaps you may wish, or not, to enlighten me on that point; by default, I am supposing you are he. I am nowhere near qualified to pass judgment on Tsirelson's work, because I am nowhere near him in knowledge and scholarly stature, but my unquestioning personal assumption is that Tsirelson's work is undoubtedly correct.

For definiteness, it may be useful if I here quote Khrennikov's paper:

Therefore “quantumness” is characterized not by a violation of the inequality (34), i.e., not by the experimentally confirmed fact that |Q₁₁ + Q₁₂ + Q₂₁ − Q₂₂| can be larger than 2, but by the Tsirelson bound 2√2. This cannot be explained in the classical Kolmogorov framework.

For clarity, I should add that by the "the classical Kolmogorov framework", Khrennikov means 'the most basic form of the Kolmogorov framework', that does not explicitly deal with conditional probability. Of course, Khrennikov accepts the basic form of the Kolmogorov framework, as do all, including me. Conditional probability is of course an established mainstream offspring of the basic Kolmogorov framework. As a detail, it seems that Khrennikov assumes that the reader is so well familiar with the work of Tsirelson, that, most regrettably, Khrennikov does not actually give the reference for the relevant paper by Tsirelson; I here supply the latter for the English translation, according to my reading: Tsirelson, B. (1985/1987). 'Quantum analogues of the Bell inequalities. The case of two spatially separated domains', Journal of Soviet Mathematics, 36(4): 557–570. This can easily be downloaded from the internet for free. If I am mistaken here, of course I will defer to proper correction.

The Khrennikov diagnosis is that the Bell derivation does not refer to the experiments because of a logical disqualification, namely failure to use conditional probability when it is needed. Consequently, the physical assumptions of the Bell derivation have no applicability, and no relevance.

In a nutshell, the choice of each occasion of analyzer setting is part of the physical content of the experiments, and should be taken into account as conditioning the relevant probabilities, a thing not done by the Bell derivation and its followers. So to fail is an error of logic, not a physical error.

With great respect for your fine erudition, I feel that this matter may best be advanced here if you tell us what you think of Khrennikov's reasoning when you have read his paper.Chjoaygame (talk) 13:41, 3 October 2015 (UTC)

Well, for now, just two simple bits of information that you like to know: (a) indeed, I did not see Khrennikov's work (yet); (b) really, I am that Tsirelson; proof: "his" website (in Tel Aviv university) contains a link to "my" userpage here. Boris Tsirelson (talk) 16:19, 3 October 2015 (UTC)

Thank you for this. I await your further post.Chjoaygame (talk) 17:23, 3 October 2015 (UTC)

OK, I saw his article. First of all, I know that my opinion is not a reliable source; no matter which Tsirelson I am, here I am just one of numerous editors of WP. This being said, here is my first impression.

It was my preconception that Bell inequalities follow evidently from Bell's assumptions; and therefore someone that fails to get these inequalities, necessarily uses different, nonequivalent assumptions. And this is the case. By conditioning on the pair of inputs, the author opens the door for contextuality. And so, not unexpectedly, he escapes Bell's framework. Such a model generally cannot be embedded into the framework of local hidden variables ( = "local realism" = "counterfactual definiteness + relativistic local causality + no-conspiracy" = ... ). It is of course important that Bob's input cannot influence Alice's hidden variables. If someone chooses to escape Bell theorem by admitting that Bob's input does influence Alice's hidden variables, well, he'd better say so explicitly. Just to be more clear to physicists in his position, than speaking about Kolmogorov's probability theory etc. As usual, by admitting this hidden faster-than-light communication, he gets CHSH=4 (rather than 2) and then wonders, why we never observe this.

So, what about the article in Wikipedia? The question is, how notable is this reliable source. My impression is that, if out threshold admits this source, then it admits quite a lot of other sources that discuss (non)contextuality and many other possible thoughts inspired by Bell theorem. Or maybe "Quantum contextuality" is the right place for it? See his first phrase on his last page 723: "It seems that there the key word is contextuality". Boris Tsirelson (talk) 17:36, 3 October 2015 (UTC)

Sad to say, your last added fragment has created an edit conflict which makes my last half-hour's work inaccessible to my machine's editor. I would need to re-type every word again in order to reproduce it. I will think it over.Chjoaygame (talk) 19:11, 3 October 2015 (UTC)

Oops... I am really sorry, but not guilty. I was many times in such situations, the last time - just here, today, because of you! (You are not guilty, of course.) But, seeing the edit conflict, I did "copy" of my text (by mouse) and later, "past"; my text was not long. I would never create a long text with no backup. Maybe, because I worked 10 years as a programmer? :-) Boris Tsirelson (talk) 19:39, 3 October 2015 (UTC)

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Partially offtopic... There is no problem to work with conditional probabilities in Bell's framework. This was made many times. But it was still assumed that Bob's input cannot influence Alice's hidden variables (in contrast to Khrennikov). In fact, I did once such conditional-probability reformulation in the quantum framework, in my work that is justly forgotten,

It seems evident that the immediately foregoing was left incomplete. It was written on this occasion by Editor User:Tsirel.

With much respect for Editor User:Tsirel's opinion, I differ. At present, I think Khrennikov does not, repeat not, think, or use an assumption, "that Bob's input can influence Alice's hidden variables". Perhaps Editor Tsirel may very kindly, if he has time and inclination, say more here that may persuade me that Khrennikov does endorse and make use of that idea. It is conceivable that Editor Tsirel thinks that Khrennikov uses such action at a distance because Khrennikov regrettably uses the very risky and unreliable word 'context' in the present context. Indeed that word 'context', in the present context, is sometimes defined to include an assumption of such action at a distance. But Khrennikov points out the risks of using the word, and he says he is defining it himself for the present purposes, not following the definitions of others. It is a pity that words can be appropriated by factions in the way that has befallen 'contextuality', and I think Khrennikov made a regrettable mistake in letting himself be lured into using the word 'context' in the present context. But I think Khrennikov's argument does not depend on the use of the word 'context', and that Khrennikov's argument does not assume or suggest an assumption of such action at a distance as is implied in in the words "that Bob's input can influence Alice's hidden variables".Chjoaygame (talk) 15:06, 13 October 2015 (UTC)

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Whatever this conversation is about, it is far too complicated for Wikipedia. Bell's theorem is breathtakingly simple. One could go on and on about what the assumptions mean -- they are hidden variables and that's all the reader needs to know in this article. Other ideas belong in a different article.--Guy vandegrift (talk) 19:17, 3 October 2015 (UTC)

With respect, Guy vandegrift, this conversation intends to consider the proposal that Bell's theorem is not just breathtakingly simple. This conversation intends to consider a paper that means that Bell's theorem is a gross and intolerable oversimplification . There is no suggestion by me or by Khrennikov that there are 'hidden variables'. I, and I think Khrennikov, fully accept quantum mechanics. The present point is rather that Bell's physical assumptions are irrelevant because they are treated wrongly in logic for the crucial delayed-choice protocol.Chjoaygame (talk) 19:41, 3 October 2015 (UTC)

I am now feeling better. I worked out how to access what I had written.

Thank you for your comment, Editor Tsirel. It calls for several lines of response.

It is appropriate here to remember that an ultimate aim of the Bell industry is to establish that quantum mechanics' success is enough to overthrow the idea of causality, and in effect to establish instead a kind of action at a distance, for some cases. Of course, when it is put like that, there is clever word-play to evade the starker implications. Nevertheless, the stakes are high. The standards of reasoning need to be correspondingly high. By such criteria, Bell's derivation fails in logic to deal with what he recognizes as the crucial case, the delayed-choice protocol.

The Bell industry, represented for example by the present Wikipedia article, has set up a special ad hoc vocabulary. Examples of that are in your words 'contextuality' and 'hidden variables'. I think Khrennikov works in a different way. Though he mentions it, he does not mainly rely on a special ad hoc vocabulary, but instead he relies on ordinary mainstream mathematics and logic. I think the special ad hoc vocabulary has been invented for lack of adequate attention to to the need for ordinary mainstream mathematics and logic. What Khrennikov has done ought to have been done forty or even fifty years ago.

Bell's derivation uses probabilistic reasoning that does not condition on the last-moment choices of analyzer setting. We can say this, not only because it is not there in Bell's text, but also because Bell refers to the delayed-choice protocol only in the very last paragraph of his 1964 paper. This means that Bell's derivation cannot refer to experiments of which interpretation needs to rely on delayed-choice reasoning. Khrennikov proposes that for such experiments, explicit account needs to be taken, in the probabilistic reasoning, of the fact that choice means unpredictability, which is mathematically represented as stochasticity; this calls for conditional probability, which is absent from Bell's derivation. I think that talk in terms of 'contextuality', 'hidden variables', and suchlike, is using a special vocabulary that obscures rather than clarifies. I prefer Khrennikov's direct talk in terms of established mainstream probability theory. I think Khrennikov's way makes the logic safer and clearer.

Be that as it may, a more cogent concern here is your question about reliable sourcing and notability. I am no Wikilawyer. My instinct is that if the Khrennikov paper were reliably sourced, then it would well and truly pass the notability test, because it works through ordinary mainstream mathematics and logic, not relying on the special ad hoc vocabulary. More questionable is whether the Khrennikov paper is by itself a reliable source. I think one could well argue that it is primary research, not yet supported or rejected by secondary sourcing, and this would make it inadmissible on the grounds of lack of reliable sourcing. But I am no Wikilawyer and so I will not try to decide that issue by myself.

Perhaps other editors may have opinions here.Chjoaygame (talk) 19:44, 3 October 2015 (UTC)

I see. Well, now I have nothing to say. We appear to think so much differently that our discussion degenerates. It remains to me only to join your last phrase: Perhaps other editors may have opinions here. Boris Tsirelson (talk) 19:54, 3 October 2015 (UTC)

Thank you for this comment. I now reply to your just previous one. I think that there are no such things as hidden variables, and so no thought arises of their being influenced or not influenced at a distance. I think Khrennikov's reasoning avoids entanglement with such ideas, even if he mentions them. The key here is that Khrennikov's method removes putative grounds for a belief that quantum mechanics somehow licenses a sort of action at a distance that is exhibited in the Bell experiments. The experiments are valid, but, when properly interpreted, they do not support ideas of action at a distance. Yes, we will see what others might say.Chjoaygame (talk) 20:04, 3 October 2015 (UTC)

Strangely or not, this time I nearly agree: The experiments are valid, but, when properly interpreted, they do not support ideas of action at a distance; rather, they disprove counterfactual definiteness. In fact, I've voiced this opinion here. Boris Tsirelson (talk) 20:55, 3 October 2015 (UTC)

Yes. Counterfactual definiteness is a metaphysical position. It holds that definite prediction is possible because of a sufficiently deterministic world. Counterfactual definiteness does not hold for phenomena for knowledge of which one needs essentially quantum techniques. In other words, in general, the result of an observation of a quantum phenomenon is not predictable. Perhaps I am mistaken, but I think we know that without needing to rely on Bell experiments? It is evident in the Heisenberg uncertainty principle? But yes, Bell experiments exhibit quantum unpredictability.

Please excuse my edit conflict whinge! I was tired, and I was not familiar with the editing resources of my machine! I soon learnt how to do it.Chjoaygame (talk) 21:31, 3 October 2015 (UTC)

I'd say, quantum mechanics gives us

• predictions;
• point of view.

Accordingly, a physicist can

• be happy with the predictions and the point of view;
• be shocked by the point of view but accept the predictions;
• be shocked by the point of view and hope that some "outrageous" predictions are wrong.

It seems, you belong to the first group (happy with the predictions and the point of view). Indeed, you write "It is evident in the Heisenberg uncertainty principle?" etc. That is OK, of course. But then, what do you seek on this page?? Bell theorem means nothing for the first group. Just work in the quantum mechanics, do the calculations and be happy. Bell theorem is of interest for the shocked. Boris Tsirelson (talk) 05:44, 4 October 2015 (UTC)

thank you

Thank you for this very interesting comment. Beyond saying that I think the sources that I have so far encountered fail miserably to provide an even remotely adequate, consistent, and coherent point of view about which one could be either happy or unhappy, and I am very unhappy about that failure, for the present I will refrain from further reply because it is forbidden to use this page as a discussion forum as distinct from an article forge. I will think about it. Perhaps personal talk pages suggest themselves?Chjoaygame (talk) 10:07, 4 October 2015 (UTC)

As a physcist (of sorts) I fit firmly into the 'be happy with the predictions and the point of view' camp but I am stll interested in the results of Bell tests.

I have just seen the Khrennikov paper and have not followed all the maths yet but my initial impression, from reading just the abstract, is that there might be something in it. It would be a pity if Bell tests were made even harder but if that is the case we just have to accept it. Martin Hogbin (talk) 16:57, 4 October 2015 (UTC)

Hmm. I read it the other way !! As I read it, the Khrennikov view is that the tests, properly analyzed, are so easy you can drive a truck through them. The customarily celebrated tight tests are just artefacts of mistaken logic, if construed as tests of metaphysical positions, such a 'locality'. The Bell tests, as they are celebrated, just corroborate that every experiment can be analyzed, though only up to a point, in terms of waves, and in terms of particles, and no experiment, with genuine quantum phenomena, can be fully analyzed by either waves or particles alone.Chjoaygame (talk) 17:40, 4 October 2015 (UTC)

Now I see

Now I see. The ad hoc term 'context' is a way of using Jeffreys' idea that a statement of the data on which it is based must accompany every statement of a probability, without acknowledging Jeffreys' priority. In more detail, for example, the expression 'the probability of detecting a prescribed position state of a particle, given the detection of its prescribed momentum state' has no meaning, because the prescriptions are inconsistent and inadequate. On the other hand, it does make sense to speak of 'the probability of detecting a prescribed position state of a particle, given its preparation in a prescribed momentum state', because the prescriptions are consistent and adequate.Chjoaygame (talk) 14:56, 4 October 2015 (UTC)Chjoaygame (talk) 15:30, 4 October 2015 (UTC)

Well, now I understand the direction of your (and Khrennikov's, and some other's) thinking. The direction is itself OK, but this is not about Bell inequalities! Bell inequalities, BY DEFINITION, are inequalities that must be satisfied under LOCAL REALISM (there are several equivalent terms, choose any one, this one is the shortest, if not the best). If you are not interested at all in local realism, OK, this is your right. But then, you are not interested at all in Bell inequalities. Thus, again, this part of the discussion (as well as Khrennikov's work) should go to the article on contextuality. (There you may argue that the term is historically wrong, if you like.) Boris Tsirelson (talk) 16:15, 4 October 2015 (UTC)

Hmm. I am not quite in agreement with some of this. I guess that's because I don't have any confidence that the metaphysical term LOCAL REALISM has a definite physical meaning. I would define Bell inequalities as inequalities proposed by Bell. Since I don't trust his logic, I have no confidence that they have definite physical or metaphysical import. If local realism means the same as 'no action at a distance', I am interested in it. But the "realism" side of it leaves me distrustful, because I am not confident what it might mean. The fallacy of misplaced concreteness hovers all over it. Perhaps I should follow your advice and go to the article on "contextuality". Let's see.Chjoaygame (talk) 17:53, 4 October 2015 (UTC)

It seems you know what is meant by 'no action at a distance' in a universe without counterfactual definiteness! I do not. The no-signaling condition seems to me rather a surrogate, or an implication, of 'no action at a distance'. Boris Tsirelson (talk) 19:36, 4 October 2015 (UTC)

Touché! I guessed you might ask what does one mean by 'no action at a distance', but thought I would wait till you asked. I have to concede I don't have an answer any better than I do about 'local realism'. I'm sure I don't know any better than you or the next man! It's just that I prefer, without a very strong reason, the more traditional wording, rather than the newfangled term 'local realism'!! I suppose what I mean by 'no action at a distance' is the same as 'finite speed of propagation of causal efficacy'; I guess that would raise a laugh from some!

The orthodox quantum doctrine, with which I agree, is that if you want to find out something from nature, you have to design a question and a set of experiments that explicitly and directly address that something. So if one wants to find out the speed of propagation of "influence", one should do an experiment that measures speed. But time and distance appear nowhere in the Bell story: so it doesn't allow a deduction about speed, infinite or not. Another way of looking at it is to remember the rule against arbitrary deduction from a contradiction.

It seems, you take "the Bell story" quite literally: just the text of the Bell 1964 article. Why? I do not. For me "Bell story" is the great story initiated by that article. Including later articles by Bell, and numerous articles by others. Accordingly, (1) for me "Bell inequality" means every inequality on observed probabilities that follows from local realism; (2) time and distance do appear. (Just look at my article on Citizendium, linked above.) For example, it is well-known during decades that Bell inequalities are violated in the vacuum state; this is interpreted within the quantum field theory; needless to say, space/time/relativity is crucial. Boris Tsirelson (talk) 06:02, 5 October 2015 (UTC)

Near enough. I speak of 'Bell inequalities and their congeners'. I think we refer to the same inequalities. I am not, however, comfortable in speaking in terms of "hidden variables" and "local realism", as I suppose is by now obvious. I am unpersuaded by the methods of reasoning that rely on those terms.

We are getting close to some deep water. I haven't yet looked at your article but will do so quite soon. Perhaps it may help here if I quote from the Wikipedia article on Hidden variable theories and comment on the quote:

Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance.

Let me comment on that sentence. I think it puts words into mouths of the authors which they did not speak, and I find that procedure a recipe for endless consequent muddle. I think the EPR 1935 paper suffers from grave logical problems that are not well criticized by the usual literature on "hidden variables". At a rough guess, perhaps more useful criticism may be found in terms of Jaakko Hintikka's 'Independence Friendly' (IF) logic. I previously claimed that I wanted orthodox logic and here I am proposing something that might be seen as slightly different. So we are, as I said, getting close to some deep water. I guess I have to say I find the usual literature on hidden variables (how shall I put it?) not to my taste. For this kind of work, one needs serious cosmology in the sense of Alfred North Whitehead. Whether Whitehead's own cosmology is adequate for the present kind of work, I am not confident. But I am confident that seriously professional cosmology (in that sense) is needed. I will look at your article on Citizendium, linked above. I think we will not sort out the present questions very easily or quickly.Chjoaygame (talk) 08:18, 5 October 2015 (UTC)

Oh yes; we will not. Here is a kind of a proof of this no-go theorem. :-) Looking at my reminiscence on IQOQI blog here you can see that the shock from the Bell theorem is a fundamental fact of my biography. An intellectual drama (or even tragedy?) of my youth. It is possible, in principle, to convince me that the inequalities hold, or not, conform to views of Einstein, or not, etc.; or even, that I am very stupid, from my youth onward. But it is impossible, in principle, to convince me that they are not shocking, since the assumptions are not reasonable. For me they are, absolutely. Boris Tsirelson (talk) 09:54, 5 October 2015 (UTC)

I too was rather surprised to learn of the Bell story. My immediate reaction was to think there must be something wrong with the reasoning. This was because I don't believe in action at a distance, and I do, in general, believe in causality. Dare I say it, I have a suspicion that much of our difficulty derives from the way Niels Bohr set the tone of the thinking. I am not disagreeing with any particular thing he said. Rather I am saying that I think he set our thinking in an unfruitful frame, from which we can't easily escape. I have to accept that this is a nearly meaningless thing to say. But it's my best guess.

Quantum mechanics has the isolated system obey the Schrödinger equation. That is deterministic. The stochastic element comes in when one makes the isolated system collide with another system, the observing apparatus. I suppose the observing apparatus might have been obeying its own Schrödinger equation, again deterministic, until the collision. But we don't pretend to know a Schrödinger equation jointly for the two after the collision. I think our lack of knowledge of a suitable joint Schrödinger equation does not make the physical world lack obedience to a joint Schrödinger equation, which again is deterministic. A closely related problem, I think, is in thermodynamics. A thermodynamic process is initiated by a thermodynamic operation. The thermodynamic operation just appears out of nowhere, a true deus ex machina. Thermodynamics makes no effort to deal with it. Perhaps it is the work of Maxwell's demon? This doesn't shock me. I think something along these lines may help with the Bell problem.Chjoaygame (talk) 11:24, 5 October 2015 (UTC)

If the physical world, accurately described as it is by quantum mechanics, really were weird and magical as too many try to persuade us, it wouldn't let itself be restricted by Tsirelson's bound; it would go all out, as in this story about toy systems. If someone isn't bound by such constraints as Tsirelson's bound, why would he stop there? Might as well be hung for a sheep as for a lamb. For me, this points to a physical world that obeys causality, even though it cannot be verified by singular direct observation.Chjoaygame (talk) 12:02, 5 October 2015 (UTC)

Oh, the quantum/classical boundary is a vast and complicated matter... But! My admiration for Bell is first of all due to the fact that his argument disentangles us from this vast and complicated matter. Bell theorem shows that Nature is not a classical mechanism; and what is the input from the quantum theory? Only a single prediction, of purely informational nature (thus, no matter what kind of particles we use, and whether they are particles, at all). Bell theorem establishes a direct connection between fundamental assumptions and empirical facts, over the head of the quantum theory. As long as the prediction is experimentally verified, I can forget all ideas of Bohr, Schrödinger etc.

Thus, I think, seriously, that these ideas of Bohr, Schrödinger etc should not be discussed here. (On personal talk pages, they may.) This is not wikilawyering, this is the essence of Bell's approach. Boris Tsirelson (talk) 12:22, 5 October 2015 (UTC)

This is sometimes called "experimental metaphysics": a single experiment can give us a fundamental knowledge about Nature irrespective of any theory at all (in particular, of quantum theory). Bell have discovered the very existence of experimental metaphysics. Unprecedented! Boris Tsirelson (talk) 12:53, 5 October 2015 (UTC)

It looks as if we have gone as far as we can for now? We have aired some ideas which may develop. Perhaps some further progress may come in future. I will look forward to that. It has been a great privilege and pleasure for me to chat as we have. Thank you.Chjoaygame (talk) 12:46, 5 October 2015 (UTC)

Happy editing. Boris Tsirelson (talk) 12:53, 5 October 2015 (UTC)

I am not quite sure which article you are indicating. I have now downloaded and will shortly read this one. Is it the one you mean?Chjoaygame (talk) 08:56, 5 October 2015 (UTC)

Oops, no, sorry for being misleading; I mean this. Boris Tsirelson (talk) 09:44, 5 October 2015 (UTC)

No worries. I am learning all the while. Thank you for this. I will read it.Chjoaygame (talk) 10:20, 5 October 2015 (UTC)

Ah, yes, now I recall glancing at this, but it slipped my mind. I will now read it with attention.Chjoaygame (talk) 10:32, 5 October 2015 (UTC)L

Yes, I now recognize that I did read this, but it didn't all lodge in my memory. There is quite a lot in it. My own approach to these puzzles is to try to hold close to a physical picture, if such is possible. What is a physical picture? I don't have a ready answer. I won't try to answer right now.Chjoaygame (talk) 10:46, 5 October 2015 (UTC)

There, "bibliography" and "external links" are separate pages. Boris Tsirelson (talk) 10:56, 5 October 2015 (UTC)

Coming back to 'contextuality'. I have to say that I think that the rule proposed by Jeffreys, that a statement of the data on which it is based must accompany every statement of a probability, is normal ordinary routine logic, not something special and peculiar that justifies a new label and a separate article "contextuality". My instinct is that a breach of the Jeffreys rule is automatically wrong and a violation of ordinary logic. One encounters, on the other hand, an attitude that I find bizarre and crazy, that somehow a quantum experiment or theory could overthrow ordinary logic and justify a new "quantum logic". The quantum theory is written in the language of ordinary logic. To overthrow ordinary logic is to send everything back to the drawing board, including quantum theory; not for me, thanks very much! A departure from the Jeffreys rule is, I think, mere carelessness or incompetence. I think it safer to take the Jeffreys rule as part of normal reason.Chjoaygame (talk) 00:38, 5 October 2015 (UTC)

If it is contemplated that last-moment switching of the near analyzer setting might affect what happens at the far observation station, it would be natural to expect that such switching would have potentially far greater effects on what happens at the near station. Once it is contemplated as effective, who knows what might be the effects of the switching? It is part of the experiment.Chjoaygame (talk) 02:37, 5 October 2015

If anyone has had so much time to spare as to have glanced at my above comments, perhaps it may help if I quote Khrennikov as follows:

I have had numerous conversations with outstanding physicists. A rather common opinion is that it is totally meaningless to pay attention to foundations of probability theory.Typically such a viewpoint is motivated by considering probability as a “physically well-defined quantity.” Therefore one need not seek a mathematically rigorous probabilistic formalization.

I totally disagree with such a viewpoint. In the same way one might say that physicists need not take note of mathematical models of space and geometries.

And from Kolmogorov:

In consequence, one of the most important problems in the philosophy of the natural sciences is—in addition to the well­ known one regarding the essence of the concept of probability itself—to make precise the premises which would make it possible to regard any given real events as independent. This question, however, is beyond the scope of this book.

Khrennikov does a lot of talking, and it takes a while to find the core of what he is on about. Much of his basic thinking is hardly different from that of Harold Jeffreys, and it disappoints me that it seems Khrennikov did not read Jeffreys.

Or perhaps for some very odd reason Khrennikov did not see how close are his and Jeffreys' ideas on probability. The key is simple, as above: a statement of the data on which it is based must accompany every statement of a probability. Chjoaygame (talk) 03:18, 7 October 2015 (UTC)

article on quantum contextuality

I have now followed your advice and had a look at the article entitled Quantum contextuality. I am not sure what I should say as a result.Chjoaygame (talk) 04:57, 5 October 2015 (UTC)

In the opinion of Khrennikov:

     The main terminological problem is related to the notion of contextuality.The use of the term “contextual” is characterized by a huge diversity of meanings, see Bell [34], Svozil [296] or Beltrametti and Cassinelli [35] for the notion of contextuality in quantum physics ...

     ... In quantum physics the contextuality is typically reduced to a rather specific contextuality—“Bell contextuality.” J. Bell invented this notion in the framework of the EPR-Bohm experiment [34, 35]. We recall that such quantum contextuality (“Bell’s contextuality”) is defined as follows.

     The result of the measurement of an observable a depends on another measurement of observable b, although these two observables commute with each other.

     It should be emphasized that the nonlocality in the framework of the EPR-Bohm experiment is a special case of quantum contexuality. ...

     Our contextuality is essentially more general than Bell’s.

On looking at the reference Beltrametti & Cassinelli (1984), one finds that built into their definition of "contextuality" is the presupposition of "hidden variables".

On looking at the reference to Svozil, I can only say it confirms my view that the term 'contextuality' is a recipe for muddle.

Speaking more generally, it seems to me that the term 'contextuality', though used just barely reasonably but still unfortunately, perhaps to satisfy the watchdogs, by Khrennikov, is a brilliant masterpiece of obfuscation or intellectual coersion that puts George Orwell's 1984 Newspeak in the shade.

For those unfamiliar with Orwell, Newspeak is a synthetic language, enforced by the state, so constructed that it is practically impossible in it to express thoughts other than those authorized by, or pleasing to, Big Brother. It ensures that ordinary truth is inaccessible, and that nonsense prevails unchallengeably, making doublethink seem natural.

Khrennikov uses the term 'contextuality' in a safe way, though I think he would have done better to avoid it because it is saddled with crippling handicap in the wake of Bell's use of it.

Once one starts using the term 'contextuality' as if it were an ordinary-physical-usage word in the present context, without very particular and well-advertised precautions (such as, for example, Khrennikov's), one is almost sure to talk nonsense.Chjoaygame (talk) 18:27, 11 October 2015 (UTC)

Maybe. I can only add that I was always bored by contextuality, and has never been willing to think seriously in this direction. Boris Tsirelson (talk) 19:06, 11 October 2015 (UTC)

section deleted

I have thought it over, and have deleted the section because it relies only on primary research in a journal, which is not adequate as a reliable source.Chjoaygame (talk) 21:02, 3 October 2015 (UTC)