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  1. editor
    editor at |

    This paper has been sent out to peer review.

  2. Travis Norsen
    Travis Norsen at |

    Dear Howard,

    Rather than write another detailed rebuttal to the many points you raise here, I would like to simply re-frame the big picture and encourage interested people to make up their own minds on the basis of what has already been written.

    I will cut right to the chase. You wrote, in your original paper, that “there is only one plausible reading of `locality’ in Bell’s 1964 paper”, namely Parameter Independence (PI). This, in my view, is simply preposterous. PI is a statement about probabilities, but nowhere in his 1964 paper — either in his English prose or in his equations — does Bell indicate that what he means by `locality’ has something to do with probabilities. There is simply no evidence for your interpretation. Furthermore, your interpretation flies in the face of the direct, conclusive evidence that does exist: that Bell references Einstein’s Autobiographical Notes, 3 times, by way of specifying what he means by `locality’.

    I think any honest reader of Bell’s 1964 paper would have to recognize that Bell uses `locality’ to mean what Einstein expresses in his Autobiographical Notes — the condition you call “no telepathy” and concede has “the same force as local causality”. And once that is established, everything else falls nicely into place: Bell’s equation (1) and the surrounding prose are describing a narrower implication of locality, an implication relevant to the sort of deterministic theory that Bell (following Einstein) regards as required to locally explain the usual perfect correlations and which therefore figures crucially in the novel 2nd part of Bell’s overall two-part-argument.

    The fundamental dispute (between your so-called operationalists and realists) is about whether Bell *assumed* determinism, as a premise, in 1964, or instead saw determinism as following from locality via something like the EPR argument. But this dispute is trivially resolved: Bell says explicitly, in his EPR-recapitulation paragraph, that predetermined outcomes *follow* from locality and perfect correlations. Of course there are further questions about that argument (Is it really valid? Does Bell capture it adequately in his 2-sentence recapitulation? How exactly is `locality’ formulated in this argument? Are there any other prerequisite assumptions beyond `locality’ and perfect correlations?) but there can be no question about whether Bell took Einstein to have previously made a valid argument along these lines.

    And so the operationalists in question were simply *wrong* to think that determinism was, for Bell, an independent assumption which could be rejected instead of locality. All of this was of course made much clearer in Bell’s subsequent papers. But the problem was never that Bell proved two different things in two different decades, or changed what he meant by `locality’ and then dishonestly attempted to cover his tracks, or failed at first to even indicate that his novel result was the second part of a two-part-argument (i.e., that his novel result was crucially based “On the Einstein-Podolsky-Rosen paradox”). The problem was simply that the operationalists in question apparently never bothered to read and understand what Bell actually did.

    (Note that I am not saying that, had these operationalists actually understood what Bell was doing in his 1964 paper, they would have agreed with it. If they had understood that Bell’s notion of `locality’ and the crucial first part of the two-part-argument were sourced back to Einstein’s Autobiographical Notes, and followed up with that reference, they probably would have disembarked from the train of thought at the first sentence of the relevant passage: “Physics is an attempt conceptually to grasp reality as it is thought independently of its being observed.” But then we would hear them expressing a philosophical disagreement, about the very meaningfulness of Einstein’s — and Bell’s — notion of `locality’, or about the appropriateness of Einstein’s and Bell’s visions of the purpose and aim of science… not claiming, as you claim they do, that Bell assumed determinism and/or meant, by `locality’, Parameter Independence or — even less plausibly — No Signalling.)


  3. Travis Norsen
    Travis Norsen at |

    Howard, some further comments in response to your comments. (I follow your numbering scheme.)

    1. My view, as you must know by now, is that Bell’s *definition* of “locality” is provided by the passage he quotes from Einstein, and that some of his later words must be understood not as attempts to provide a general definition, but instead as characterizing the specific implication of locality (to deterministic theories) that is relevant to the second part of his two-part argument. It’s not that I think that “Bell’s vagueness” is helping my argument — I don’t actually think there is any vagueness. He cites the passage from Einstein by way of explaining what he means by “locality”. You and I will never convince each other; interested people will have to decide for themselves whether my reading is plausible.

    2. I find your comments here rather silly. Do you really think that your feelings about how “the grammatical and scientific clarity” could have been improved by omitting the references to Einstein, constitute a justification for simply ignoring those references? It seems quite clear to me that, in all three places where Bell cites that passage from Einstein, he is doing so in order to explain what he means by “locality”.

    3. I understand that you think it is misleading to suggest that (what you call) “no telepathy” *alone* “has the same force as local causality” since, you want to say, it is really only “no telepathy” *plus* “the assumption … that systems have real factual situations” which, together, “have the same force as local causality”. I agree that this other realism-type assumption is needed. But I think we disagree about the logical-hierarchical relation of the two assumptions. In my view (which is also Einstein’s view and Bell’s view) “the assumption that systems have real factual situations” is a pre-requisite for discussing locality. That is, one could not maintain a meaningful notion of locality (such as “no telepathy”) while rejecting this elementary sort of realism. Indeed, as I pointed out in my comment above, the relevant section of Einstein’s Autobiographical Notes begins with a statement about this sort of realism being an essential aspect of what “Physics is”. I thus find it quite misleading to list this as an assumption at the same level as locality, as if one could meaningfully choose to maintain *either* (by abandoning the other). You probably disagree with all this. I’m not trying to convince you to agree with me; I’m just explaining why, from my point of view, it is in fact quite accurate to identify Einstein’s formulation of locality (from the Autobiographical Notes) with what Bell would later call “local causality”. (Note by the way that an identical “realism” assumption underlies Bell’s “local causality”.)

    4. I wouldn’t (and didn’t) describe Bell’s EPR paragraph as “quite flawed”. For sure it could have been clearer, more precise, more formal, and longer. And, looking back, I wish it had been all of those things, so that (ongoing!) misunderstandings had simply been pre-empted. But there’s a big difference between writing something that is “quite flawed” and simply failing to adequately foresee and pre-empt misunderstandings.

    5. Your suggestion that “Bell in 1964 did not understand the EPR argument at a technical level” is based on your (I think, preposterous) interpretation of what Bell meant by “locality”. Of course we agree that Parameter Independence + Perfect Correlations do not imply deterministic hidden variables. And so we agree that *if* Bell took the EPR argument to be this, and thought it was a valid argument, he “did not understand the EPR argument at a technical level”. But of course I don’t agree that he did take the EPR argument to be this. Instead I think Bell understood the EPR argument to be the one given by Einstein — the one that Bell quotes from and cites 3 times — in which “locality” most certainly does not mean Parameter Independence.

    6. I wasn’t suggesting we *ignore* the “further questions” about the EPR part of the argument. They’re important questions. I just don’t think we should let a (subjective and highly anachronistic) obsession with “theoremhood status” blind us to parts of Bell’s paper which — whatever else we might think of them — were clearly important parts of what Bell was doing in 1964. The very phrase “Bell’s theorem” is a modern invention, and it is anachronistic to approach Bell’s 1964 paper as if Bell’s goal in the paper had been to “prove Bell’s theorem”. At the time, he wasn’t thinking in those terms at all. He was, rather, thinking that Einstein had already argued — convincingly to him — that deterministic hidden variables were required to explain certain QM-predicted correlations locally. He had also noticed and been impressed by the grossly nonlocal character of Bohm’s 1952 hidden variable theory, and wondered whether (as had been suggested earlier by Einstein et al.) it would be possible to construct an empirically viable, but *local*, hidden variable theory. After some failed attempts, he began to suspect that this might actually be impossible, and then managed to construct a proof that, indeed, it was impossible. The paper lightly sketches all of this background, and then presents the proof of the new result. To ignore or suppress this background, because it’s not presented in a rigorous way and hence not part of “Bell’s 1964 theorem” and hence irrelevant to the thing we are celebrating the 50th anniversary of, is just absurd. One shouldn’t let a contemporary name for an important historical discovery blind one to the actual content of that discovery.

    7. Is it really news that, for me, “operationalism itself is wrong”? Of course. Just as, for (you?) operationalists, “realism itself is wrong”. I wouldn’t exactly say I’m “opposed to finding a form of Bell’s theorem that operationalists would agree with” — I just think it’s hopeless since Bell’s theorem, as I understand it, centrally involves an inherently “realist” notion of locality (what you call “no telepathy” or “local causality”) which no operationalist could ever endorse as meaningful. Yes, this means that, in my opinion, your “aim” (“to seek common ground between realists and operationalists”) was misbegotten and doomed to failure from the beginning.


  4. Travis Norsen
    Travis Norsen at |

    3. Fair enough.

    6. Thanks. I suppose my feeling is that you are not managing to “keep it as background”, but are instead setting it completely aside as irrelevant. (Which makes sense, insofar as you define your mission as examining exclusively the thing you segregate off as “his theorem/result/proof”.) But then you are simply repeating and sanctioning precisely the misunderstanding that Bell later complained was “almost universal”. That is, as I see it, the problem all along has been that your “operationalists” failed to notice, or understand, or appreciate, the parts of Bell’s 1964 paper that are here being described as “background”. I am happy to agree that Bell shares in the blame for this, in the sense that he could have presented this “background” material more clearly, more explicitly, more consistently, more carefully, more formally, etc. But whatever. The real point is just that, to fix the problem, what’s needed is to clarify, to bring out more explicitly and consistently and carefully and formally, this background stuff — especially to the people who missed or misunderstood it originally. Telling the operationalists that, actually, they were right to miss it because it’s not really there — when it plainly is, even if in a disappointingly brief/informal/unclear/imprecise format — doesn’t seem right. Not, at any rate, if one’s goal is to spread a better understanding of Bell’s 1964 paper “AS IT IS WRITTEN”. =)

    7. First an aside: I dispute, actually, that PI is an “an inherently operational notion of locality”. But as to your main question, yes, sure, it’s possible to derive a “Bell type inequality” from lots of different sets of assumptions. And in general I would not think it appropriate to call all of them “Bell’s theorem” merely on the grounds that they arrive at some formula that is somehow obviously in the same category as Bell’s (original) inequality (or even identical to it). As to the specific example you mention, since I don’t think that Bell ever once constructed an argument whose premises were determinism and Parameter Independence, I would find it inappropriate to refer to that argument as “Bell’s theorem”. Off the cuff, it seems likely that Jarrett, or perhaps Shimony, first constructed such an argument, so probably (if you think the argument deserves a special name) it should get one of their names… or CHSH or whoever first actually ran it.

  5. editor
    editor at |

    Report of Referee A

    This manuscript is in reply to Norsen’s submission “Are there really two different Bell’s theorems?”, itself a response to the (current) author’s “The two Bell’s theorems of John Bell”. Since Norsen’s submission confronts the authors position directly it seems only fair that he has an opportunity to reply. Furthermore the manuscript is engagingly written and makes several interesting points on related topics, for example I particularly enjoyed the concluding discussion of who’s position does more credit to Bell. Overall then I recommend that if Norsen’s submission is published, this reply is as well.

    I would ask the author to reconsider some aspects of the second page, which in places teeters dangerously on the line between merely paraphrasing Norsen (for rhetorical effect) and putting words into his mouth. Additional caution seems wise in light of the author’s complaint that Norsen “misrepresents” him.

    More specifically, since Norsen does not use the word “flawed” in his paper, it seems a little strong to say he has admitted Bell’s EPR paragraph is flawed. How about something like this: “Some of the flaws in Bell’s argument in that paragraph, from ‘locality’ to determinism, are now acknowledged by Norsen. He therefore does not object to somebody like me withholding the word ‘theorem’ from that part of Bell’s work.”? Ultimately the point is best made by letting the Norsen quotes on page 4 speak for themselves.

    Similarly, I don’t see what in Norsen’s paper licenses saying “In Norsen’s view [Bell’s 1981 commentary] is proof enough that this is a misunderstanding.” Norsen does dwell on Bell’s 1981 commentary, and calls it an “important piece of evidence”, so why not just say that?

    I would like to conclude with a remark on section 4. I have made it clear in my report on Norsen’s submission that I find some of the “Are there really two different Bell’s theorems?” quotations on pages 8 and
    9 of the submission to be potentially misleading and hence unacceptable for publication. Hopefully Norsen will rectify these issues, and the present manuscript can then be updated in light of this. I think readers will appreciate it if we are able to avoid a discussion on what Bell and Einstein said degenerating into a discussion on what Wiseman said about what Bell and Einstein said!

  6. editor
    editor at |

    Author’s response:

    We thank the referee for the fair-minded and thoughtful report. We have made several changes in response to the report, as detailed below. We have also made numerous minor changes to reflect the change from I to we (as heralded in the previous version) and to improve the text in other ways. Finally, we have made two substantial additions belonging to none of the above categories: a long paragraph at the end of Sec. 2.1, and a short paragraph at the end of section 3. These strengthen our argument through further analysis of the text of Bell’s 1971 paper. We apologise to the referee for not having thought to include such arguments until now.

    For the convenience of the referee, all changes are in mauve, except for added quotes in the appropriate colour (which usually have some mauve text in the vicinity) and for trivial corrections, clarifications, and textual reorganisations. We will of course remove this mauve colouration upon acceptance.

    The referee says:
    [S]ince Norsen does not use the word “flawed” in his
    paper, it seems a little strong to say he has admitted Bell’s EPR
    paragraph is flawed. How about something like this: “Some of the flaws
    in Bell’s argument in that paragraph, from ‘locality’ to determinism,
    are now acknowledged by Norsen. He therefore does not object to
    somebody like me withholding the word ‘theorem’ from that part of
    Bell’s work.”? Ultimately the point is best made by letting the Norsen
    quotes on page 4 speak for themselves.

    We have followed the referee’s advice closely.

    Similarly, I don’t see what in Norsen’s paper licenses saying “In
    Norsen’s view [Bell’s 1981 commentary] is proof enough that this is a
    misunderstanding.” Norsen does dwell on Bell’s 1981 commentary, and
    calls it an “important piece of evidence”, so why not just say that?

    Again, we have followed the referee’s advice closely.

    I would like to conclude with a remark on section 4. I have made it
    clear in my report on Norsen’s submission that I find some of the “Are
    there really two different Bell’s theorems?” quotations on pages 8 and
    9 of the submission to be potentially misleading and hence
    unacceptable for publication. Hopefully Norsen will rectify these
    issues, and the present manuscript can then be updated in light of

    We are pleased that Norsen has removed one unreasonable claim (that I accused Einstein of having made a huge blunder), enabling us to remove one of the (originally) five points of Section 4. However, another unreasonable accusation he made has merely been reworded as a rhetorical question and a statement of suspicion. We felt this still required a response, so have rewritten, rather than removed, the first point of Section 4. In response to new statements and a new, lengthy, footnote by Norsen on the subject of what is ‘plain’ in Einstein’s 1949 work, we have added a sentence.

    I think readers will appreciate it if we are able to avoid a
    discussion on what Bell and Einstein said degenerating into a
    discussion on what Wiseman said about what Bell and Einstein said!
    We agree, but we have to comment on what Norsen said Wiseman said Einstein said when he (Norsen) misrepresents us. In particular we were disappointed that Norsen did not remove his gross misquotation (on p. 9) of a passage on p.11 of my 2014 paper. Until he does so, we will need to address that issue as we do, albeit briefly, in the Second point of section 4.

  7. editor
    editor at |

    Report of Referee A:

    My overall impression of the manuscript I gave in my previous report still holds for this revised version. The authors have revised it carefully in response both to my comments and the changes Norsen has made to his paper. The new discussion of Bell’s 1971 paper is also a useful addition. Although my aspiration for the debate not to be about what Wiseman said in 2014 has not been fully realised, I think we are probably as close as is reasonably possible, and so I support publication.

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