Talk:WikiJournal of Science/A card game for Bell's theorem and its loopholes

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WikiJournal of Science is an open-access, free-to-publish, Wikipedia-integrated academic journal for science, mathematics, engineering and technology topics. WJS WikiJSci Wiki.J.Sci. WikiJSci WikiSci WikiScience Wikiscience Wikijournal of Science Wikiversity Journal of Science WikiJournal Science Wikipedia Science Wikipedia science journal STEM Science Mathematics Engineering Technology Free to publish Open access Open-access Non-profit online journal Public peer review

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Article information

Authors: Guy Vandegrift[i], Joshua Stomel

Vandegrift, G; Stomel, J. 




Author comments[edit]

Why I am placing this in draft space[edit]

  1. The primary reason is that Josh and I want sole credit for creating this resource. Others will be able to edit this after it has been accepted by the WikiJournal of Science. (Note that the license permits anybody to copy and develop a parallel page on any wiki).
  2. At the moment (and subject to change) my opinion is that virtually everything on Wikiversity should eventually be in Draft space. This is a radical idea, but none of the WMF wikis have peer-reviewed content. Perhaps the WikiJournals will evolve to fill this need. Perhaps Wikipedia will even create a peer reviewed namespace (see this discussion for yet another example of why the WMF needs something that supports peer review . See also for where peer reviewed documents might be situated on Wikiversity.)
  3. Finally, some people might whine when their articles are moved to draft space. There is nothing wrong with draft space. I have this article in draft space right now and it causes me no pain, concern, or discomfort.--Guy vandegrift (discusscontribs) 20:33, 17 February 2018 (UTC)
  • FYI, according to Wiktionary, "whine" when referring to "a complaint or criticism" is considered "derogatory". --Marshallsumter (discusscontribs) 16:25, 12 March 2018 (UTC)
  • Point well taken. I regret the uncivil tone of my comment. My only excuse is that since nobody has "whined" (or complained or objected) about being in draft space, nobody is the target of that remark. On the same topic, there are three plausible approaches to this problem: One is to highlight the best efforts (e.g. with WikiJournals or guilds); another is to place "drafts" in draftspace. Finally, the third plausible approach is to ignore the problem. I will never interfere with anybody's effort to implement any of these solutions. But, I have no idea which one is the best.--Guy vandegrift (discusscontribs) 18:40, 12 March 2018 (UTC)

Plagiarism check[edit]

Artículo bueno.svg Pass. WMF copyvio tool using TurnItIn. Trivial hits to the version hosted on a private wiki (link) and author's CV were found. Otherwise no plagiarism was detected. T.Shafee(Evo﹠Evo)talk 11:48, 22 February 2018 (UTC)

A reference that needs to be added[edit]

Bojić, Alan. "A new quantum game based on CHSH game." Journal of Information and Organizational Sciences 37.1 (2013): 15-22. https://bib.irb.hr/datoteka/868224.02.pdf

I just found out about this. In many ways a better paper, especially for the more advanced reader. The card game still has advantages though.--Guy vandegrift (discusscontribs) 21:36, 13 March 2018 (UTC)

First peer review[edit]

Review by Franck Laloë  
This review was submitted on 19 March 2018, and refers to this previous version of the article

As the text itself makes it clear, this is not a research article, since it contains nothing really new. It is rather a pedagogical contribution proposing a method to explain the Bell theorem to students, nicely illustrated with figures and drawings. I have never taught this part of quantum mechanics, and I cannot judge if this approach is the best to treat the subject. Personally, I would think that the traditional (more algebraic method) is not more difficult to follow, maybe even easier. Personally I did not find that easy to understand all the rules of this card game, and all these diagrams in the 13 pages, but this is just my personal taste.

In the field of fundamental quantum mechanics, one can enter endless discussions on the way to phrase ideas. So, I do not want to bother the authors with my own personal views, but I nevertheless with to express some disagreements.

The sentence "To some experts, a loophole is a constraint on any hidden variable theory that might replace quantum mechanics" is, to me, a very bad introduction to the notion of "loophole". A loophole is a logical possibility to evade the Bell inequalities by rejecting one of the (explicit or implicit) assumptions of the EPR paper and its continuation by Bell. It has nothing to do with hidden variable theory specifically, since it actually does not refer to any specific sort of theory. I would strongly recommend not to introduce the ideas of loopholes to students in this way.

Figure 1 is confusing for someone who is familiar with quantum optics. The text says that is shows two entangled photons but, with photons, it is impossible to have devices filtering three polarizations at 120 degrees as shown in the figure. The space of states of photon polarizations is 2-dimensional, and the filters shown in the figure will necessarily leak since they have three outputs.

Nicolas Gisin, in his recent book "Quantum chance", discusses something similar, which he calls "Bell's game" I believe.The authors might wish to include a reference to this book.

Please note that the first and last lines of several pages are missing in the pdf file you sent me, for some technical reason.

My conclusion is that, if this articles comes as a complement of another more traditional introduction to the Bell inequalities, it may probably be useful to some teachers. I would nevertheless not recommend it as the only introduction to the inequalities, but maybe just as a nice illustration of the Bell theorem once the students understand its logic.

Second peer review[edit]

The following review was transferred from the American Journal of Physics with permission from the reviewer. It refers to the version of the manuscript as submitted to the previous journal and so may not take account of changes that have already been made between submissions. T.Shafee(Evo﹠Evo)talk 22:47, 22 March 2018 (UTC)

Review by anonymous peer reviewer  

I have read the manuscript "A card game for Bell's theorem and its loopholes". The goal of the paper is to present a simple card game from which students can learn the impossibility of achieving the sorts of correlations that are forbidden according to Bell's theorem... and perhaps also understand, by figuring out how to "cheat" to win the game, several loopholes associated with the theorem and/or the associated experiments. I enjoyed reading the paper and applaud the general concept of trying to convey Bell's theorem to students in the form of a simple game. But I do have several reservations about the paper. First, there is a lot of confusion, in the physics literature generally, about what Bell's theorem means/proves, and (at best) this paper doesn't help address those confusions. (At worst, it adds to the inertia of the confusions.) I have in mind here things like the paper's first sentence, which says (vaguely and non-commitally) that Bell's theorem proves "that the laws of physics are not constrained to obey ... intuitive or common notions." There is confusion/controversy, though, about what notions those are, and I would expect newly-published papers on Bell's theorem to be more explicit about this. Another similarly off-putting remark is the following: "Since entanglement is so successfully modelled by quantum mechanics, one can argue that there is no need for a mechanism that 'explains' it." The difference between a mere "model" and an "explanation" is not exactly clear. But the frustrating thing here is again just that the authors remain completely vague about what is at stake. Is it, as many have claimed, the concept of determinism? Or "hidden variables" generally? Or "local causality"? The fact that the authors don't take (and, as necessary, defend) a position on the meaning of Bell's theorem is not necessarily a fatal flaw with the paper since that is not what the paper is all about, but the fact that the ultimate implications of the idea illustrated by the game remain completely unspecified, does seem to significant detract from the authors' aims (and, in particular, would seem to undermine students' motivation to care about the topic).

Another point that detracts from the pedagogical value of the recommended game, at least for me, is that it is not perfectly parallel to the physics experiments (testing Bell's inequalities) that it is supposed to illuminate. The authors acknowledge this, e.g., when they explain that "the card game reverses roles regarding probability: Instead of the investigators attempting to ascertain the photons' so-called hidden variables, the players are acting as particles attempting to win the game by guessing the measurement angles." Similarly: "a penalty must be deducted from the partners' score whenever they are caught using a forbidden strategy..." Again, the fact that the game doesn't perfectly mirror the structure of the real experiments is not necessarily a fatal flaw, but the differences do detract from the ability of the game to really illuminate, for students, what it's meant to illuminate.

Third, I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand (by which I largely have in mind the questions, referred to above, about exactly what minimal set of assumptions gives rise to Bell's inequality, but then also various details about the structure of the experiments and how those relate to the assumptions) are not illuminated by the card game. Instead, the card game focuses exclusively on the purely statistical aspects of deriving the inequality -- aspects which, in my experience, are the least controversial and easiest for students to understand properly. The authors seem to sort of acknowledge this when they write, in explaining the solitaire version of the game, that "It is evident that the player has a 2/3 probability winning a round." I agree, it is evident, and I think even students can understand clearly and easily why this is the case. But then, why bother with the game?

Finally, I felt like the discussion of the three "loopholes" did not quite live up to what I was hoping for based on the beginning of the paper. Re: the communications loophole, the authors state that "Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2." This is true (although I find it extremely confusing to describe this as a "loophole" -- surely "locality" is one of the central premises in the derivation of Bell's inequality.) But I was disappointed that the authors just say this but then all the subsequent discussion is about why superluminal communication is problematic vis a vis special relativity. (Incidentally, there are problems with this discussion. For one, there is really no meaningful notion of "nearly infinite speed". Any faster-than-light influence will appear to propagate with infinite speed in some inertial frame. Also, the whole argument is circular and unconvincing. If Bell's theorem and the associated experiments provide evidence that there is some nonlocality in nature -- and I think they do -- then we can hardly just assume any longer that special relativity, as ordinarily understood, is true. The same kind of theory that one might contemplate to reconcile Bell's result -- say, a theory in which the usual relativistic metric is supplemented with some additional structure such as a dynamically privileged spacetime foliation -- will automatically prevent the sorts of paradoxes discussed here. But my main point here isn't to complain about the content of this discussion of the relation between relativity and superluminal communication. Instead, I mean only to complain that this discussion is basically disconnected from the card game. It's the kind of thing one would find in any random website or popular book about Bell's theorem.)

I feel similarly about the second "loophole" discussed -- the "superdeterminism loophole". This is almost completely unrelated to the card game and is instead just a (not very good) discussion of the idea of superdeterminism. (The authors seem slightly confused about what the "super" in "superdeterminism" adds to mere "determinism". It does add something -- i.e., "superdeterminism" is not merely the idea that "nothing happens by chance". It is instead the idea that not only are the "randomly" or "freely" chosen measurement settings in the experiments determined, but that they are determined to be correlated in certain ways with the ("hidden variable") states of the photon pairs that are being tested. The idea is that there is a kind of cosmic conspiracy -- things that we have no reason to think should be correlated, and indeed things that experimentalists take explicit pains to ensure are not correlated, are nevertheless correlated in a conspiratorial way that, in effect, fools us into seeing violations of Bell's inequality. But again, my point here is not to complain about the content of the discussion, even though I find it somewhat wanting. Instead, I am just pointing out that it is somewhat disappointing that the discussion doesn't really relate to the card game at all.)

I liked the discussion of the 3rd loophole much more, since it is actually what I thought I was getting: a way of cheating at the game that helps me understand one of the Bell loopholes!

To summarize, what I thought I would find in the paper was a card game that closely paralleled the structure of the experiments testing Bell's inequality -- a game that would allow students to understand Bell's theorem itself by figuring out, after playing for a while, why they can never win... and which might also allow them to appreciate certain "loopholes" by finding creative ways to win the game (by stretching or violating the rules). I think I would really enjoy (and support the publication of) a paper that did that, and I enjoyed this paper to some extent because it did some of that. But at the end of the day I feel like it doesn't live up to that promise. It leaves too much of what's important about Bell's theorem (namely, understanding exactly what assumptions generate the inequality so one can understand what's at stake in the experiments) too obscure, the game is really only vaguely analogous to the relevant (local hidden variable) theories and experiments rather than perfectly reflecting them, and only one of the three loopholes really interacts significantly with the card game. If I was going to teach Bell's theorem and wanted to do so using a kind of "game", I would probably just keep it simple and do something that is more exactly parallel to the real experiments: make up 3 yes/no questions, have the students pair up and then answer one randomly-selected question at soundproofed stations on opposite ends of the room. Challenge them to find a strategy that will allow them to reproduce the QM correlations and see what happens... (Let them figure out that they cannot do it unless they carefully arrange to refuse to answer under certain conditions, or they somehow rig the question selection so it is not random at all but correlated with their answer-strategies on a given run, or if they simply use their cell phones to text each other and update their strategies after seeing what questions they're asked.)

Anyway, I think this paper has some value and I support its publication at the WikiJournal, but hopefully the above critical discussion will be useful for some readers and/or the authors.

Where and when do author's respond?[edit]

Is this the time and place for authors to respond? If the WJS has already answered this question, I'm sure that whatever format has been chosen will suit my needs. If no policy has been established, perhaps individuals can put their thoughts, almost in a blog format in subpages? I have taken the liberty of creating such a subpage, with the understanding that it can be easily moved or deleted. See:

Third peer review[edit]

Preprint - A card game for Bell's theorem and its loopholes (Reviewer 3).pdf

A

Preprint - A card game for Bell's theorem and its loopholes (Reviewer 3 further comments).pdf

B


Reviewer-annotated pdf file. A) First file B) Second file

Review by Natalia Sanchez Kuntz  
This review was submitted on 25 March 2018, and refers to this previous version of the article

Reviewer comments provided as annotated manuscript PDF (A) and further comments provided in additional PDF (B).

Author's initial responses[edit]

The simplicity of the Venn diagram for three symmetrical polarization angles was the initial motive for selecting this geometry.
Another reason to use polarization (instead of spin) is this: Hold two filters crossed to block the light with your clumsy hand and use your clever hand to insert third at 45°.

First, I thank the referees (including two who reviewed this manuscript in the American Journal of Physics.) All five reviews were expertly and carefully written, and quite frankly put to shame any referee report I have written. A theme common to all five reviews was concern about the loose and informal use terms such as Loophole, Hidden variable, Superdeterminism, and even Bell's theorem. Our target audience is far less sophisticated than one typically associates with the study of Bell's theorem, and my co-author and I both struggled with the need to find language that is both precise and simple. Both of us had previously seen an entry level textbook that used a messy bedroom to illustrate entropy. I still don't know if making your bed in the morning changes the room's entropy. Nor do I care -- we both consider that analogy to be pedagogically useless. To illustrate the difficulty we face in trying to bring Bell's theorem to this level, consider how WP defines hidden variable theory.

"A local hidden variable theory in the w:Interpretations of quantum mechanics is a w:hidden variable theory that has the added requirement of being consistent with w:local realism. It refers to all types of the theory that attempt to account for the probabilistic features of w:quantum mechanics by the mechanism of underlying inaccessible variables, with the additional requirement from local realism that distant events be independent, ruling out instantaneous (i.e. w:faster-than-light) interactions between separate events."
(a hypothetical) "w:complete theory" would "provide descriptive categories to account for (all observable behavior and thus avoid any w:quantum indeterminacy".

My main point is that these definitions might serve those familiar with quantum mechanics, we need to explain it differently to the non-expert.--Guy vandegrift (discusscontribs) 13:24, 6 April 2018 (UTC)

Author's response to First Review[edit]

The card game is not easier to follow than an algabraic proof[edit]

As the text itself makes it clear, this is not a research article, since it contains nothing really new. It is rather a pedagogical contribution proposing a method to explain the Bell theorem to students, nicely illustrated with figures and drawings. I have never taught this part of quantum mechanics, and I cannot judge if this approach is the best to treat the subject. Personally, I would think that the traditional (more algebraic method) is not more difficult to follow, maybe even easier. Personally I did not find that easy to understand all the rules of this card game, and all these diagrams in the 13 pages, but this is just my personal taste.

My response -Guy vandegrift (discusscontribs) 21:19, 14 May 2018 (UTC)
I agree. Nothing is simpler than the Venn diagram proof shown above.  But my experience is that the typical high school graduates has no understanding of "proof".  A card game they cannot win is immediately grasped, even if they cannot "prove" it to be unwinnable. Also, I recently showed this game to undergraduate science students (trig-based intro physics), and they could play the solitaire game directly from the paper, which I handed out to them.
See also #Article_would_serve_a_complement_to_traditional_introduction below.
Regarding the length, I propose to remove the appendix from the article and place it into this supplementary subpage

Definition of "loophole"[edit]

In the field of fundamental quantum mechanics, one can enter endless discussions on the way to phrase ideas. So, I do not want to bother the authors with my own personal views, but I nevertheless with to express some disagreements.

The sentence "To some experts, a loophole is a constraint on any hidden variable theory that might replace quantum mechanics" is, to me, a very bad introduction to the notion of "loophole". A loophole is a logical possibility to evade the Bell inequalities by rejecting one of the (explicit or implicit) assumptions of the EPR paper and its continuation by Bell. It has nothing to do with hidden variable theory specifically, since it actually does not refer to any specific sort of theory. I would strongly recommend not to introduce the ideas of loopholes to students in this way.

I agree that it is a bad introduction, I tried to change the wording to illustrate the fact that we will instead view a loophole as analogous to a way to cheat.  The problem is that a loophole and Bell's theorem need to mean different things to different people.  I am looking for the entry-level understanding but felt obligated to tell the reader that this is not how experts might view it.  I added an entire section "Conundrum" to help clarify

Figure 1 is confusing[edit]

Figure 1 is confusing for someone who is familiar with quantum optics. The text says that is shows two entangled photons but, with photons, it is impossible to have devices filtering three polarizations at 120 degrees as shown in the figure. The space of states of photon polarizations is 2-dimensional, and the filters shown in the figure will necessarily leak since they have three outputs.

Response: I don't understand this comment, and can only guess it means one of two things:
1. The suggestion of "leaking" might be a reference to an old version of the figure that simultaneously presented the atom with three different filters, with only one lying in the path of the photon.  To avoid cluttering Commons with outdated figures, I placed it here]
2. "Leaking" might refer to the loss of efficiency in using three symmetric angles of polarization when attempting to statistically establish violation of Bell's inequality.  Bell's inequality is better established with filters at (0°, 22.5°, 45°).  This lack of symmetry adds more steps to the analysis because one must analyze two pairs of orientations.  This Venn diagram proof of Bell's inequality leads one to immediately grasp the (0°, 60°, 120°) case.--Guy vandegrift (discusscontribs) 13:29, 6 April 2018 (UTC)

Reference to other efforts to create a Bell's theorem "game"[edit]

Nicolas Gisin, in his recent book "Quantum chance", discusses something similar, which he calls "Bell's game" I believe.The authors might wish to include a reference to this book.

Response
Whew! First I need to look at the book.  I also found another reference here: 
Bojić, Alan. "A new quantum game based on CHSH game." Journal of Information and Organizational Sciences 37.1 (2013): 15-22. https://bib.irb.hr/datoteka/868224.02.pdf
And I found Frąckiewicz, Piotr. "Application of the Eisert–Wilkens–Lewenstein quantum game scheme to decision problems with imperfect recall." Journal of Physics A: Mathematical and Theoretical 44.32 (2011): 325304. https://arxiv.org/pdf/1407.6757.pdf--Guy vandegrift (discusscontribs) 13:29, 6 April 2018 (UTC)

First and last lines missing from pdf file[edit]

Please note that the first and last lines of several pages are missing in the pdf file you sent me, for some technical reason.

See draft:A card game for Bell's theorem and its loopholes--Guy vandegrift (discusscontribs) 13:29, 6 April 2018 (UTC)

Article would serve a complement to traditional introduction[edit]

My conclusion is that, if this articles comes as a complement of another more traditional introduction to the Bell inequalities, it may probably be useful to some teachers. I would nevertheless not recommend it as the only introduction to the inequalities, but maybe just as a nice illustration of the Bell theorem once the students understand its logic.

Author's response
Quite to the contrary: Our goal is to make this a "stand alone" introduction for those who do not understand the logic.  As such, this last comment will take a lot of work to address.  But the referee and I agree on one point: The card game is a "non-traditional" approach.  And, one should never mix two different approaches when introducing a subject.  Advanced students should be taught the traditional approach, and then perhaps be shown the card game. If we are to bring Bell's theorem to a less sophisticated audience, we need this longer paper.
The editors and referees need to make a decision:  Is this a paper for the expert or the novice?  If experts are the target, the paper can be drastically reduced in length in a way that will remove almost all issues raised.  But I still think the article can be fixed so that novices can understand it.  That is the purpose of Wkiversity/Wikipedia, right?--Guy vandegrift (discusscontribs) 21:45, 14 May 2018 (UTC)

Author's response to Second Review[edit]

I enjoyed the paper (but have several reservations)[edit]

Referee's entire comment

I have read the manuscript "A card game for Bell's theorem and its loopholes". The goal of the paper is to present a simple card game from which students can learn the impossibility of achieving the sorts of correlations that are forbidden according to Bell's theorem... and perhaps also understand, by figuring out how to "cheat" to win the game, several loopholes associated with the theorem and/or the associated experiments. I enjoyed reading the paper and applaud the general concept of trying to convey Bell's theorem to students in the form of a simple game. But I do have several reservations about the paper.

I'm glad you enjoyed the paper and agree that your reservations have merit.  The solution is to focus at the introductory level and make that clear to the reader at the beginning--Guy vandegrift (discusscontribs) 13:37, 6 April 2018 (UTC)

Confusion about what Bell's theorem means/proves[edit]

Referee's entire comment

First, there is a lot of confusion, in the physics literature generally, about what Bell's theorem means/proves, and (at best) this paper doesn't help address those confusions. (At worst, it adds to the inertia of the confusions.) I have in mind here things like the paper's first sentence, which says (vaguely and non-commitally) that Bell's theorem proves "that the laws of physics are not constrained to obey ... intuitive or common notions." There is confusion/controversy, though, about what notions those are, and I would expect newly-published papers on Bell's theorem to be more explicit about this. Another similarly off-putting remark is the following: "Since entanglement is so successfully modelled by quantum mechanics, one can argue that there is no need for a mechanism that 'explains' it." The difference between a mere "model" and an "explanation" is not exactly clear. But the frustrating thing here is again just that the authors remain completely vague about what is at stake. Is it, as many have claimed, the concept of determinism? Or "hidden variables" generally? Or "local causality"? The fact that the authors don't take (and, as necessary, defend) a position on the meaning of Bell's theorem is not necessarily a fatal flaw with the paper since that is not what the paper is all about, but the fact that the ultimate implications of the idea illustrated by the game remain completely unspecified, does seem to significant detract from the authors' aims (and, in particular, would seem to undermine students' motivation to care about the topic).

Gill, Richard D. "Statistics, causality and Bell's theorem." Statistical Science (2014): 512-528. "quantum mechanics is incompatible with the principles of realism, locality and freedom". https://arxiv.org/pdf/1207.5103.pdf.  I just don't see how this belongs in an introductory paper--Guy vandegrift (discusscontribs) 13:29, 6 April 2018 (UTC)

Game not perfectly parallel to the physics experiments[edit]

Referee's entire comment

Another point that detracts from the pedagogical value of the recommended game, at least for me, is that it is not perfectly parallel to the physics experiments (testing Bell's inequalities) that it is supposed to illuminate. The authors acknowledge this, e.g., when they explain that "the card game reverses roles regarding probability: Instead of the investigators attempting to ascertain the photons' so-called hidden variables, the players are acting as particles attempting to win the game by guessing the measurement angles." Similarly: "a penalty must be deducted from the partners' score whenever they are caught using a forbidden strategy..." Again, the fact that the game doesn't perfectly mirror the structure of the real experiments is not necessarily a fatal flaw, but the differences do detract from the ability of the game to really illuminate, for students, what it's meant to illuminate.

Author's response-Guy vandegrift (discusscontribs) 21:36, 14 May 2018 (UTC)
The discrepency between the game and actual experiments is unavoidable because we need they three fold symmetry of the polarizers to give the player(s) a concrete goal.  How do you instruct card players to strive for certain correlations?  In the system introduced in the paper, the players try to maximize the sum of three correlations with the understanding that all three are inherently negative
I believe the referee and I have different students in mind.  Non-STEM students cannot grasp the concept of an "impossible correlation".  The fact that physicists didn't know these quantum correlations were impossible until 1964 illustrates the conceptual difficulties with the traditional way of introducing the topic
Finally, I wrote two subpage supplements that bring both the experiment and theory up to a higher level:
See Impossible correlations and Tube entanglement

Paper ignores the difficult questions and focuses on the easiest to understand[edit]

Referees entire comment

Third, I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand (by which I largely have in mind the questions, referred to above, about exactly what minimal set of assumptions gives rise to Bell's inequality, but then also various details about the structure of the experiments and how those relate to the assumptions) are not illuminated by the card game. Instead, the card game focuses exclusively on the purely statistical aspects of deriving the inequality -- aspects which, in my experience, are the least controversial and easiest for students to understand properly. The authors seem to sort of acknowledge this when they write, in explaining the solitaire version of the game, that "It is evident that the player has a 2/3 probability winning a round." I agree, it is evident, and I think even students can understand clearly and easily why this is the case. But then, why bother with the game?

I have two good responses:
1.  I like to emphasize technical writing skills and have used that as an excuse to have students read the procedures for both the solitary and partner's game.  They routinely grasp the solitaire game.  But it is not unusual for a student to say they never really understood the partner's game.  As I have already stated, the intended audience for this paper includes those who need the solitaire game.  That's why I focused on the easy questions.
2. See the two supplements.  This derives the CHSH inequality without calculus, and the this uses Maluss' law to explain much of what happens in a semiclassical way, with the introduction of a simple 2-particle system to get the 100% correlation (or anti-correlation) that seems to be possible only in a full quantum model.

The faster-than-light loophole (or not a loophole?)[edit]

Referee's entire comment

Finally, I felt like the discussion of the three "loopholes" did not quite live up to what I was hoping for based on the beginning of the paper. Re: the communications loophole, the authors state that "Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2." This is true (although I find it extremely confusing to describe this as a "loophole" -- surely "locality" is one of the central premises in the derivation of Bell's inequality.) But I was disappointed that the authors just say this but then all the subsequent discussion is about why superluminal communication is problematic vis a vis special relativity. (Incidentally, there are problems with this discussion. For one, there is really no meaningful notion of "nearly infinite speed". Any faster-than-light influence will appear to propagate with infinite speed in some inertial frame. Also, the whole argument is circular and unconvincing. If Bell's theorem and the associated experiments provide evidence that there is some nonlocality in nature -- and I think they do -- then we can hardly just assume any longer that special relativity, as ordinarily understood, is true. The same kind of theory that one might contemplate to reconcile Bell's result -- say, a theory in which the usual relativistic metric is supplemented with some additional structure such as a dynamically privileged spacetime foliation -- will automatically prevent the sorts of paradoxes discussed here. But my main point here isn't to complain about the content of this discussion of the relation between relativity and superluminal communication. Instead, I mean only to complain that this discussion is basically disconnected from the card game. It's the kind of thing one would find in any random website or popular book about Bell's theorem.)

As per previous comments, I need to be explicit about the focus on elementary pedagogy.  The (valid) suggestion that there might be something wrong with special relativity "as normally understood" would confuse the target audience.
Once the target audience is recognized, perhaps the reviewer will reconsider the relevance of the space-time diagram in this paper.  It is not easy to explain why most things cannot travel faster than light, and this argument using the two trains with "magic phones" is the most convincing and direct argument that I know.  The argument is based on the two postulates of relativity (with the nonexistence of a preferred frame used to argue that a magic phone would operate on the same way on train as on earth.)  A more sophisticated person might be satisfied with the velocity transformation rule, which says that superluminal messages travelling from Alice to Bob will be viewed as travelling in the opposite direction by a moving observer.  But first, that requires an equation, and second, the velocity transformation rule requires that the reader understand that a message delivered to the past to a remote observer causes a paradox.  
For evidence that we need a simple explanation of why superluminal communication is impossible, look at the current version of Wikipedia:Faster-than-light_communication.
Many years ago, the parent of a physics major told me they never understood special relativity until they learned about the light clock.  Though the explanation for the violation of causality associated with superluminal communication is a bit more involved, it is also based on something that can be visualized as a geometry problem.  I recently introduced Bell's theorem to instructor who teaches introductory college chemistry, and their first reaction is that the particles might be in "communication". For Bell's theorem, we don't need proof that all superluminal communication is impossible, just that "nearly infinite" communication is impossible (or at least inconsistent with special relativity.)  If anybody is concerned that "nearly instantaneous communication" is an artificial concept, I point out that "quasi-static equilibrium" is also an idealism designed to simplify things."--Guy vandegrift (discusscontribs) 13:29, 6 April 2018 (UTC)

Superdeterminisme "loophole"[edit]

Referee's entire comment

I feel similarly about the second "loophole" discussed -- the "superdeterminism loophole". This is almost completely unrelated to the card game and is instead just a (not very good) discussion of the idea of superdeterminism. (The authors seem slightly confused about what the "super" in "superdeterminism" adds to mere "determinism". It does add something -- i.e., "superdeterminism" is not merely the idea that "nothing happens by chance". It is instead the idea that not only are the "randomly" or "freely" chosen measurement settings in the experiments determined, but that they are determined to be correlated in certain ways with the ("hidden variable") states of the photon pairs that are being tested. The idea is that there is a kind of cosmic conspiracy -- things that we have no reason to think should be correlated, and indeed things that experimentalists take explicit pains to ensure are not correlated, are nevertheless correlated in a conspiratorial way that, in effect, fools us into seeing violations of Bell's inequality. But again, my point here is not to complain about the content of the discussion, even though I find it somewhat wanting. Instead, I am just pointing out that it is somewhat disappointing that the discussion doesn't really relate to the card game at all.)

 I think I repaired this by removing the confusing talk about superdeterminism.  The goal (as with the previusley relativity-causality-communication loophole) is to get students to analyize position versus time diagrams in a critical way.  It also points out that while (classical) wave equations are determinisitic, they can be used to model the non-deterministic nature of quantum mechanics in a way that does not seem to be contradicted by Bell's inequality or theorem--Guy vandegrift (discusscontribs) 22:00, 14 May 2018 (UTC)

Liked the 3rd loophole[edit]

I liked the discussion of the 3rd loophole much more, since it is actually what I thought I was getting: a way of cheating at the game that helps me understand one of the Bell loopholes!

Summary[edit]

Extended content

To summarize, what I thought I would find in the paper was a card game that closely paralleled the structure of the experiments testing Bell's inequality -- a game that would allow students to understand Bell's theorem itself by figuring out, after playing for a while, why they can never win... and which might also allow them to appreciate certain "loopholes" by finding creative ways to win the game (by stretching or violating the rules). I think I would really enjoy (and support the publication of) a paper that did that, and I enjoyed this paper to some extent because it did some of that. But at the end of the day I feel like it doesn't live up to that promise. It leaves too much of what's important about Bell's theorem (namely, understanding exactly what assumptions generate the inequality so one can understand what's at stake in the experiments) too obscure, the game is really only vaguely analogous to the relevant (local hidden variable) theories and experiments rather than perfectly reflecting them, and only one of the three loopholes really interacts significantly with the card game. If I was going to teach Bell's theorem and wanted to do so using a kind of "game", I would probably just keep it simple and do something that is more exactly parallel to the real experiments: make up 3 yes/no questions, have the students pair up and then answer one randomly-selected question at soundproofed stations on opposite ends of the room. Challenge them to find a strategy that will allow them to reproduce the QM correlations and see what happens... (Let them figure out that they cannot do it unless they carefully arrange to refuse to answer under certain conditions, or they somehow rig the question selection so it is not random at all but correlated with their answer-strategies on a given run, or if they simply use their cell phones to text each other and update their strategies after seeing what questions they're asked.

Anyway, I think this paper has some value and I support its publication at the WikiJournal, but hopefully the above critical discussion will be useful for some readers and/or the authors.

Author's final (?) response begins here.[edit]

I have now digested the three reviews shown here, which have a lot in common with two additional reviews from my original submission to AJP. A common theme among all five reviews was expressed by an AJP reviewer who wrote

...I worry that the things about Bell's theorem (and the associated experiments) that are actually difficult to understand ... are not illuminated by the card game. Instead, the card game focuses exclusively on ... aspects which, in my experience, are the least controversial and easiest for students to understand ...

This was a valid criticism that inspired me to write the supplement Draft:A card game for Bell's theorem and its loopholes/Guy vandegrift. I will refer to that document as I go through each review and edit accordingly. I begin with the third review because that person meticulously proofread the document.--Guy vandegrift (discusscontribs) 20:51, 2 May 2018 (UTC)

Third review[edit]

I begin with part 1 at File:Preprint - A card game for Bell's theorem and its loopholes (Reviewer 3).pdf

YesY Done: "Abstract" and "A simple Bell theorem expt"

Abstract[edit]

  1. The solitaire version of the game so simple it can be used to teach elementary statistics without mentioning physics or Bell's theorem. I agree and will change. ♦ R3 seen GV seen

A simple Bell's theorem experiment[edit]

  1. 1964 discovery I don't see the difference. It was a "discovery" of a proof that something is a great surprise.
    ♦ R3: It's ok. It doesn't appear in the text anymore.
  2. customary to name the particles in a Bell's theorem experiment "Alice" and "Bob" I would be happy to reference Bohm's book and Aharonov (Phys Rev 108 (4) 1957), provided it is ethical to reference something I never read. Many years ago I once read that this is considered improper. Waiting for clarification from editor
    ♦ R3: The purpose of my comment was to introduce the reader to the original development of the matter.
  3. "a "loophole" is a constraint on any "hidden variable" theory that might. I disagree with the need to define "hidden variable" theory. This is an introductory paper for students who are not at all ready to contemplate hidden variable theories. In my opinion, no reader or student should attempt to understand hidden variable theories until well after quantum mechanics is digested. 'Instead I will reduce the phrase "hidden variable" to the footnote. ♦ R3 seen GV seen
  4. spooky I included a link to wiktionary, which mentions einstein. I made it a permalink.
    ♦ R3: It is my view that the explanations in the second and third sentences of this paragraph do not explain anything to the untrained reader.
    GV: Perhaps the goal is not to explain, but to give the untrained reader a hint as to what is to come.
  5. It should be noted that the three loophole mechanisms introduced in this paper raise questions that are even spookier than quantum mechanics I agree with carefully preparing the reader for the three loopholes, but not that it is necessary to go into detail about how and why they are spooky, or whether QM is inherently spooky. The three questions posed are sufficiently and blatantly spooky.
    ♦ R3: You added a link to Loopholes in Bell test experiments from Wikipedia, and this link talks about eight loopholes (at least), so it is still unclear to which „three loophole mechanisms” you refer to. Also, the previous comment: How does each loophole imply each question? Are these precise questions not already implicit in any foundations of Quantum Mechanics revision? has not been addressed.
    GV: A footnote states the loopholes by name, and also uses a permalink to the WP article in case it changes. The footnote reads: In (permalink) these questions are associated with the "communication (locality)", the "free choice" and a "fair sampling" loophole, respectively. That is more than what a first-time reader needs.
  6. when the cards are unfavorable Need clarification from the editor/reviewers The WJS needs to establish the appropriateness of idiomatic language. I have seen enough lengthy debates about silly issues on Wikiversity and Wikipedia to want any part of this decision. My "spooky" question was whether the particles can "persuade" the detector to fail, which is already casual way to describe the situation. I have tentatively kept the idiomatic language an included a link to wiktionary:play the hand one is dealt. It wouldn't surprise me if other languages don't have card game idioms. Also, the virtue of wikitext is the ability to teach english to foreigners using wikilinks to explain the language. On the other hand, if the editors want clean scientific language, "who am I to argue?".--Guy vandegrift (discusscontribs) 10:32, 6 May 2018 (UTC)
    ♦ R3: The sentence read: „Do they persuade the measuring devices to fail when the cards are unfavorable?“ and since you are talking about photons and devices, you should refer to the settings of these devices, rather than the cards. (Given also, that in the game the cards play the role of the settings, i.e., device orientation).
    GV: I think it should be clear that this is an allegory to the experiment. The students are not physicists, and the intent is to teach the game. I see no reason for a footnote explaining that "cards" refers to "measurement", but have no objection if the editor wants one.
  7. Bell's theorem experiment Included permalink to WP #Overview to clarify As they say, "the person who invented it didn't really invent it". I clairified this with a link to the Overview. read the first line.
    ♦ R3: I think the concept „a Bell test“ is a case of what has become the way of refering to things; just a way of refering to an experiment that puts Bell's inequality (or the type) to test. The experimental design was first thought by EPR, through a measurment of position and momentum, and then redisigned by Bohm, through measurements of spin; his proposal is analogous to the polarization experiments carried nowadays. I think it is better to include the original reference, for readers to learn deeper, rather than just a superficial talk, but I leave this freedom to the writers. GV: seen.
  8. Since entanglement is so successfully modeled by quantum mechanics, one can argue that there is no need for a mechanism that "explains" it. This should stand. I never said that the sole reason for investigating loopholes was to look for a flaw in QM. And, no single experiment conclusively closes a loophole. (I did correct the spelling error "modelled"->"modeled")
    ♦ R3: I believe that there are reasons for investigating loopholes, but some may argue that the loopholes you talk about have already been closed. Please clarify why you don't think so.
    GV: Two comments: First, a loophole is only closed in the experiment that closes it. Future Bell's theorem experiments that look at other loopholes should, if possible, also "close" the communication loophole. Second, I was speaking about loopholes in general.
  9. "After the photons have been separated by some distance" Reviewer wanted to know if this was a "Bell state". I linked the word "entangled" in the previous sentence to WP.
    ♦ R3: The link talks about Quantum Entanglement in a very general way. This is ok, but what about the particular state of the photons? There exists an infinite quantity of entangled two-photon states.
    GV: The reader does not need to know about that. For more information, see Supplement:Tube entanglement. Also, it is nearly impossible to correctly describe the photon states because photons must be modeled by quantum field theory. So instead I modeled a pair of non-interacting classical particles confined to a narrow tube.
  10. Another complication is that the original form of Bell's inequality does not adequately model the partners' version of the game Referee is correct. This entire paragraph needs a rewrite. FYI: "original" form refers to Bell's original paper in which the correlations (anti-correlations) are enforced. The CHSH inequality repairs this. In this supplement I proved the CHSH identity using a trick I found on the internet to avoid using probability integrals over the "hidden variable(s)". I didn't change much: Links to "parity" and "original form" are all we need because this paragraph won't be read by novices who won't want to read a paragraph that begins "xxx is easy to prove". The expert can sort out the links. ♦ R3 seen
YesY Done: The solitaire cardgame

The solitaire cardgame[edit]

  1. This strategy in which one suit has a different answer (here the spade) shall be called the a-strategy . In the solitaire version, this is the only viable strategy , because the forbidden ß-strategy is not possible ... I agree w/ ref. This will be explained better ♦ R3 seen
  2. 3 choose 2 is now defined in a footnote that links to wikipedia. ♦ R3 seen GV seen.
  3. The conundrum of Bell's theorem is that ...particles maintain an average score of zero I suggest we keep it as is I have already introduced this card game in several occasions. We need to avoid conceptual overload here. We first establish that the solitaire game cannot be won (on average). Many students have told me that did not fully grasp the partner's version. See also the supplement: Draft:A card game for Bell's theorem and its loopholes/Guy vandegrift. It's a long story: First, we must do Maluss' law, then (without proof or explanion) claim the correlation (anticorrelation) for identical measurement angles for Alice and Bob. Then do the Venn diagram proof of Bell's original inequality. Finally, the correlation (anticorrelation) does not seem to have any counterpart in classical physics. I managed to find an analogy involving two non-interacting particles confined to a long tube. None of that belongs here.
    ♦ R3: Please see comments in second review. GV seen.
YesY Done: The game for entangled partners

The game for entangled partners[edit]

  1. Whenever asked the same question, Alice and Bob would always give the same answer , if they were entangled particles ... Yes, this needs work. First, the reader should note the footnote which clarifies that "same" and "different" lose their distinction if we rotate one of the detectors (by 90 degrees for photons or 45 degrees for spin). Nevertheless, the sentence was a bit abrupt. ....Also, I deleted the line It should be noted that actual Bell's theorem experiments can register such events due to detection error flaws (in response to the referees request that I explain it more.) The fact that the partner's version can simulate detection error flaws does not need to be introduced at this point.
    ♦ R3: Throughout the text I have been uneasy regarding the fact that there is no clarification concerning the specific experiment the authors refer to. Please see comments in second review.
    GV: By "specific experiment" does R3 refer to an experiment that used three symmetrically placed polarizing experiments? If so, that is a valid point. I changed to Figure 1 shows an idealized experiment... to Figure 1 shows a hypothetical and idealized experiment... . Also, does "second review" refer to the review by R2, or to the second pdf file submitted by R3. Just to be safe, I looked at both.
  2. Equation (1). The referee raised a number of points: First, it was pointed out that the equation was not actually derived. I believe the explanation in the appendix was sufficient for the expert to recover equation (1). But my target audience is not the expert, but the teacher and the student. I will make it more clear that the recommended strategy for the teacher is to adopt the 4 point penalty but to enhance the 25% odds of asking the same question beyond the shuffle shown in the figure. For the student, the important fact about both games is that there is a way to award and deduct points so the game cannot be won in the long run. Neither the student nor the teacher needs to actually understand equation 1; they just need to understand the consequences of making Q sufficiently large to discourage the beta strategy ♦ R3
  3. Premature introduction of equation 1 before the explanation of the alpha/beta strategies This was in part due to the articles format that places figures between the text, and not alongside, causing the caption to figure 3 to appear out of context. The referee seemed to acknowledge this problem by using reddish pink magenta to highlight the discussion of the alpha and beta strategies. This problem was alleviated by slightly simplifying the instructions in the top row of Table 2, and also moving the table to after it is discussed in the text ♦ R3 seen
  4. How eqn (1) explains why P>2/11 and Q=6 is biased is discussed in a footnote ♦ R3 seen
YesY Done: Cheating at cards and Bell's theorem "loopholes"

Cheating at cards and Bell's theorem "loopholes"[edit]

  1. Fixed a few typos: //his or her own//error detector loophole//of the each car//rear of the//with #2 from ♦ R3 seen
  2. Here is an interesting edit: My original draft began a sentence with And, without taking sides in the debate..., which led the referee to ask "What debate?". I guess I was talking about the religious "free-will" v "determinism" debate, but one could also bring up Bell's "superdeterminism" idea. It is not my intent to speculate on the philosophical implications of Bell's theorem. But I did want to show readers how "spooky" this all is. I have found that people who believe in psychic powers are almost bored by Bell's theorem...because they "knew" this was happening all along. Also, highly religious people see nothing wrong with God arranging for Bell's inequality to be somehow violated routinely in experiments. I want to allude to these issues, but strongly believe that people should work these things out with zero input from me. So, I replaced the original reference to a debate, with some brief speculation, followed by a snarky footnote suggesting that not the a matter that involves physics (or science). ♦ R3 seen
YesY Done: Magic phones: Communications loophole

Magic phones: Communications loophole[edit]

I wrote: Alice and Bob could win every round of the partners' version if they cheat by communicating with each other after seeing their question cards in phase 2. In an actual experiment, this loophole is closed by making the measurements far apart in space and nearly simultaneous, which in effect requires that these communications travel faster than the speed of light.

Referee#3 commented: If this loophole is closed, there is not a "communication loophole" anymore. There is not such thing as a "superluminal communication loophole" given that loopholes are designed to explain the violation of Bell's inequality by experiments in a way that is consistent with Special Relativity...Then, this section is devoted to explain what would happen to causality if we were to violate the limit c, within the causal structure of Special Relativity. Not to the discussion of the loophole and its benefit to Bob and Alice.

My response: First I must confess that my understanding of the word "loophole" is largely based on Wikipedia. Given that the intended audience for the paper includes those with minimal understanding of Bell's theorem, this might not be so bad. The current version of w:Loopholes in Bell test experiments vaguely states that the word "loophole" refers to any problem of experimental design or set-up that affect the validity of the experimental findings. It is clear from this article's context that to "close" a loophole is to repair this flaw in the experimental design (and in the process verify the predictions of Quantum mechanics in a way that violates Bell's inequality). I don't see how "closing a loophole" implies that it no longer exists. All I am trying to do in this section is explain why it was considered so important to ensure that the two remote measurements are designed to occur at nearly the same time. And key to this explanation is the fact that faster-than-light communication is inconsistent with special relativity due to issues with causality.

♦ R3: More than a flaw, a loophole in an experiment is a mechanism by which the results of measurements come to violate Bell's Inequality but still can be interpreted as the results of a local hidden variable theory. If one closes a loophole in the experiment, this loophole can no longer account for the violation of Bell's Inequality to be local (and this is what I meant with „no longer exists“), and in that way the loophole can no longer „help Bob and Alice” in exhibiting correlated results.

Finally, I don't understand what was meant by "the loophole and its benefit to Bob and Alice". To me, a "loophole" in a Bell's test experiment involves an effort by the experimentalist to change the outcome by tinkering with the experimental design (this outcome is predicted by QM but violates Bell's inequality). A "loophole" in the card game is an effort by Bob and Alice to win the game, presumably by cheating (since I seriously doubt that two human beings can achieve quantum entanglement.)

♦ R3: Again, a loophole is not an effort to change the outcome, a loophole is a mechanism through which QM can render entanglement in a local way. The effort one makes when studying a particular loophole is the effort to verify that quantum entanglement is not taking advantage of the particular studied loophole to exhibit the entangled behavior.

Also, the apparent typos involving commas in "simultaneity, which" and "January, as" seem to be flaws in the wikitext-to-pdf conversion. ♦ R3 seen

GV: In think R3 and I are OK on this section. I agree that defining "loophole" is not a trival matter.


YesY Done: Referee collusion:Determinism loophole

Referee collusion:Determinism loophole[edit]

More than one referee raised concerns about comments I made, and in retrospect, I decided to delete many of them. I did include the recent reference to 600 year old cosmic photons, and retained the use of figure 5 to discuss the deterministic nature of quantum mechanics in that it does predict probabilities. While there is no practical value in pondering a deterministic theory of the entire universe, students should recognize that any theory that predicts probabilities is is some sense deterministic. I removed most references to "superdetermisim" and "hidden variables" (but retained the references in the footnotes). The deleted section is archived at special:permalink/1865381. ♦ R3 seen GV seen.

YesY Done:The Rimstock cheat: Detector error loophole
table[edit]
event N=12 Theo N=40 Observed
lose (−3) 2 17% 6.67 7 18%
win (+1) 6 50% 20 20 50%
stop 4 33% 13.33 13 33%
don't stop 8 67% 26.67 27 68%
Total 12 100% 40 40 100%
flipWin* 2 17% 6.67 6.5 16%
flipLose* 2 17% 6.67 6.5 16%
favorable1* 4 33% 13.33 13.33 33%
favorable2* wins − flipWins 13.5 34%
favorable3* 2*wins/3 13.33 33%

The Rimstock cheat: Detector error loophole[edit]

  1. I repaired figure 6 and its caption as per instructions. The pair win/win states for the favorable situation is changed in the figure, and the figure now identifies that alice chose hearts to be the "different" even/odd choice, with clubs and spades getting the same answer. ♦ R3 seen
  2. I looked at figure 7 and think it matches the expected values. The simulation did not keep track of whether the partners won because the cards were favorable or they were lucky with unfavorable cards. Out of the fundamental probability space of 12 equally probable events in figure 6, the game will be stopped 4 times and will continue on 8 rounds. Of those 8, four are because the cards were favorable, leaving four rounds where they have a 50% chance of winning. FlipWin refers to winning 2 of these 4 rounds, and flipLose refers to losing 2 rounds. The N=40 columm multipliese these results by 40/12 to get expectations for the 40 rounds shown. Since the mechanism for winning was not recorded, we must rely on three estimates. The first estimate (or "prediction") is that a third of the hands (40/3=13.33) were favorable, which I called favorable1. But since we know the game was not stopped on 13 occasions, it is reasonable to guess that it was also stopped on 13 occasions. They would have lost half of those, so the estimate yields flipWin−flipLose=20−6.5=13.5=favorable2. A third estimate of the favorable wins is that 2/3 of the wins will be favorable: 10(2/3)=favorable3=favorable1. All the numbers work out. In fact we selected a case where they all work out. This might make a good class lab in a conceptual physics course. For that reason I added a footnote on the results, explaining that the Excel "recalculation" button is hit several times.
    ♦ R3: Ok. With this explanation I can see how the statistics is followed, nevertheless I think the graph could be misleading (as I experienced it) because of the way the results are grouped. When I see the 10 steps that make out one round, I think that this ten steps should follow the rules of stoping no more than 50%, and therefore I am led to believing that at least the same number of unfavorable cards (not stopped) as stops must have occurred within those ten steps.
    GV: looks like a candidate for Quizbank
  3. I corrected two other typos: "to calculated" and "(ignore) same questions" ♦ R3 seen
  4. Added explanation to why Bob stops only 1/3 of the time. ♦ R3 seen GV: we seem OK in this section.
YesY Done:Pedagogical issues

Pedagogical issues[edit]

  1. A number of simple suggestions have been implemented: spaces->spades // king 6,7 // Identify Q=6 or Q=4 // our->the // with // perhaps ♦ R3 seen
  2. I never defined Bell's theorem/loopholes I added a section at the beginning that might address this problem. This was a common theme among all the referee reports. ♦ R3 seen

GV: We seem to be OK here.

Appendix[edit]

  1. Figure 8: question->answer Done!
    ♦ R3: A typo still remains. Please see comments in the new PDF commented file.
    GV@R3: Is this the typo I already fixed?
  2. Confusion about Alice announcing alpha and Bob not following clarified. ♦ R3 seen

I think it's time to talk about subpages[edit]

In response to referee comments, I have created three "official" subpages with supplementary material. And I created a fourth subpage that begins an educational effort aimed at non-technical students. It is my guess that the educational effort should be moved into Wikiversity mainspace, but that is something for the WJS editor and/or board to decide without my input (see Wikipedia:COI.)

But as author, I wish to argue the case for the three supplementary pages already linked already present: One subpage, The car and the goats is the proof of equation 1 for the penalty for giving different answers. One referee commented that this material was not easy to understand. Moreover, it is not required for the first-time reader (which is why it was placed in an appendix). The other two Impossible correlations and Tube entanglement) were in response to referee remarks to the effect that very little was actually explained in the article. As a college teacher with many years of experience with introductory students, I can assert that "conceptual overload" is a serious problem. I wanted to focus the article on the card game, and state without proof or much explanation that it is isomorphic to experiments that involve quantum mechanics. This mismatch between the intended reader and the reviewers has motivated most of the recent edits to this article (see also https://www.ee.ucl.ac.uk/~mflanaga/thresholds.html.) I think the introduction of three subpages helps with this quite a bit.

Finally, some of the most recent comments by referee 3 cannot be resolved without going beyond the intended scope of this article. I suggest the future creation of "subpages" (official or unofficial) to resolve these issues. Personally, I consider the ability to freely append and comment upon journal articles to be a fascinating and largely unexplored aspect of the WikiJournal concept.

Before I go into Referee 3's latest comments, I need to clean up the subpage "Impossible correlations" by moving the practice quiz and discussion of Quizbank to a more appropriate location.--Guy vandegrift (discusscontribs) 11:45, 25 May 2018 (UTC)

YesY Done with the subpages --Guy vandegrift (discusscontribs) 21:42, 26 May 2018 (UTC)
The article currently contains three "official" subpages and a fourth subpage that perhaps should be moved into Wikiversity namespace.
  1. The car and the goats was originally the appendix, but since students need not read it, it is better as a supplement (that even the ɫteachers don't need to fully understand).
  2. Impossible correlations resolves complaints that Bell test experiments don't use the geometry introduced by the card game. The asymmetries associated with actual experiments will render the scorekeeping of any game more complicated. Nevertheless, I did find the transition from the symmetrical to actual configurations to make for interesting instructional materials (see #4 in this list below)
  3. Tube entanglement allows us to use Schödinger's equation to achieve a primitive entanglement. Lower division physics majors with little or no experience in quantum mechanics might find this accessible. And, I found a way to introduce Dirac notation to such an audience.
  4. Conceptual is a work in progress that the WJS will likely want to move into Wikiversity mainspace. Nevertheless, it is relevant to the evaluation of this article as non-technical introduction to the "spookiness" of Bell's theorem. Also, if at all possible I would like to invite a few readers of the article into the Quizbank effort (but understand that this decision must be made by the WJS with no input from me as a member of the board.). I will refer to this section often as I address the remaining referee comments.--Guy vandegrift (discusscontribs) 21:42, 26 May 2018 (UTC)

Editorial comment[edit]

Comments by Melanie Stefan
These comments were submitted on 31-05-2018, and refer to this previous version of the article

The article is well written, but the beginning (both of the "abstract" and the actual article) is a bit abrupt and confusing to the non-expert reader. Specifically, it does not explain what Bell's inequality is, what a card game has to do with it, what Bell's test experiments are and what the observed "spookiness" there is. I would suggest adding just a few introductory sentences of the following form: "Bell's inequality states that ... This is related to observations of ... We suggest a card game that can be used to teach the underlying concepts."

Response
I agree with the need for more explanation early on. I think the best way to achieve this is to move material from the "Conundrum" section that starts the article and move it to the beginning of the "Abstract". I added a few "live" (not permalinks) to Wikipedia articles that are so well established that I think they are stable (I use permalinks to more quirky or obscure places that are likely to be edited.)--Guy vandegrift (discusscontribs) 01:35, 1 June 2018 (UTC)