Howard M. Wiseman, Eleanor G. Rieffel and Eric Cavalcanti
We address Gillis’ recent criticism of a series of papers (by different combinations of the present authors) on formulations of Bell’s theorem. Those papers intended to address an unfortunate gap of communication between two broad camps in the quantum foundations community that we identify as “operationalists” and “realists”. Here, we once again urge the readers to approach the question from an unbiased standpoint, and explain that Gillis’ criticism draws too heavily on the philosophical inclinations of one side of that debate — the realist camp. As part of that explanation we discuss intuition versus proof, look again at Bell’s formalizations of locality, and correct misstatments by Gillis of our views, and those of Bell and Einstein. Full text
This paper has been sent out for peer review.
Referee A’s report:
This manuscript is the 5th or 6th in a series of papers offering various conflicting readings of what Bell did in his 1964 paper. By this point, the discussion has almost certainly dropped below the interest threshold of the overwhelming majority of the Quantum Foundations community, with perhaps only the authors of these series of papers still paying attention. (And also us Referees, I suppose, who face a growing burden of papers to read with each iteration! 🙂
That said, I’d be inclined to give Wiseman and co-authors the chance to have the last word (Wiseman started this series, after all) — so long as I was convinced there was some reasonable hope of it actually *being* the last word. To this end, I have a number of suggested small changes. Each of these serves at least one of the following two purposes:
A) To tone down the stronger and less-defensible claims, so as not to provoke yet another response-paper.
B) To try to draw clear lines of agreed-disagreement, granting the strongest arguments from each side, and framing the (very few!) issues that remain under disagreement in a clear way.
Concerning various (quoted) passages from the new manuscript, my suggestions are:
1) “One of the key claims by some of the realist critics, including Gillis, is that the corect notion of locality has been clear enough since the 1935 paper of Einstein, Podolsky and Rosen [9] that other notions are not worth considering.”
I did not get any impression from reading Gillis’ paper that other notions of locality were not worth considering in any context whatsoever – simply that they aren’t relevant to what Bell was thinking and doing in 1964. If I missed something, it should be quoted at this point in the paper: otherwise, this final point (as used as motivation in the following sentences) seems to be substantially incorrect.
2) “What he offered in 1964 was a statement of locality that requires a little interpretation to be formalized, but by any plausible reading is quite different from local causality.”
“*any* plausible reading” is clearly overstating the situation, given the responses by Gillis, Norsen, etc.– Not to mention the previous sentence of this very manuscript! If Wiseman agrees that it’s plausible that Bell’s 1964 heuristic notion of locality was later (under much difficulty) formalized as “local causality” (1976), then surely it follows that there is a plausible alternate formalization of what Bell was trying to say in 1964 (i.e. the 1976 formalization) that is not at all different from local causality. Later in this manuscript, at the start of section 4, the authors grant that it is “possible” the key statement was not a definition at all, just an important consequence of Bell’s concept of locality.
3) ” In suggesting that the notion of local causality was there all the time, Gillis fails
to recognize the formidable intellectual effort, starting with Bell’s 1971 paper [15], then
the Clauser-Horne paper of 1974 [16], then Bell’s 1976 paper [14] and the subsequent
conversation about free will [17, 18], to develop the formal notion of local causality.”
I think more agreement could be reached on all sides if the word “notion”, used twice here (and often throughout) was replaced with a sharper word, especially in that first line. (Clearly, it is not being used in the same sense as “heuristic… notion” two paragraphs above.) A clear distinction should be drawn between a “heuristic-notion” and a “formal-notion”; everyone seems to agree that Bell might have plausibly had the former, but certainly lacked the latter. Better still would be “concept” and “formalization”, words that would need no explanation. (Elsewhere, I noticed the phrase “intuitive notion” used as well.) The word should certainly never be used on its own, such as in:
“(i) There is no notion of locality set out in 1964, or earlier, by Bell, which allows a rigorous derivation of his result without assuming predetermination of outcomes (or something like it).”
Again, the word “notion” here should be sharpened, along with the phrase “set out”. ‘There is no formalization of locality in 1964…’ would certainly be defensible.
4) “It is doubtful that Bell had even read the EPR paper [9],”
This is getting strangely close to an ad hominem attack on Bell, and should be rephrased to address the written record.
5) “these arguments instead provide support for the operationalist or AUR reading of Bell’s 1964 paper.”
I don’t follow how Gillis’s arguments might be thought to provide support for the very position he is explicitly arguing against. Some elaboration here would certainly be expected if this point is to remain. (Although, please keep in mind goal (A) above in the process!)
6) “No physicist had formulated any such principle, applicable to probabilistic theories such as quantum mechanics,”
Again, the goal (A) would be better served by the clearer statement that ‘no physicist had *precisely formalized* any such principle’. Better yet, the authors might consider granting that the “concept” may have been there, not the “formalization”. EPR had already come some distance towards showing how such a principle could eventually be precisely formulated. In the interest of goal (B), it might be worth requoting a previous paper: “Certainly, one could undertake to formalise Einstein’s assumptions so as to make the argument from predictability to determinism.” [4].
7) ” The strain is unavoidable because of the flaw in Bell’s logic itself, as others who disagree with Wiseman’s more general arguments have admitted [8].”
I am fairly sure that Norsen would not appreciate being linked to any “admission” of a “flaw in Bell’s logic itself”!
8) In the interest of my goals (A) and (B), expanding the conclusion would seem to be a very good idea. Laying out the general points of agreement, in particular, would go a long way. From my perspective, those key points seem to be:
a: Bell did not lay out an explicit formalization of locality in 1964.
b: Einstein had not explicitly formalized it either, but had laid out the general concept that would later become formalized as local causality.
c: Depending on which formal definition of locality one combines with Bell’s 1964 paper, one gets different theorems.
The remaining point of disagreement, then, seems to be which formal definition of locality (if any!) should be associated with Bell’s 1964 paper. And although I doubt any agreement will be reached on this point, if the paper concludes with some big-picture framing of the issue along these lines, I think it would greatly enhance the probability that this might be the final (published) word on the subject. =)
I support publication with the above changes and clarifications.
Authors’ reply to Referee A:
We would like to thank the referee for the careful and patient reading of our paper, and for the many constructive suggestions. We also would like to thank the referee for the inclination to give us a chance to have a last word on the subject, and agree that we should tone down the paper so as not to provoke yet another response. We have attempted to do that in the revised version, as detailed below. In response to the referee’s specific comments:
1) We agree that we have overstated our claim, and don’t want to imply that Gillis and others with similar realist dispositions think other notions of locality aren’t worth considering in any context whatsoever. They just think they are not worth considering as part of a formulation of Bell’s theorem. We have modified this paragraph to read: “One of the key claims by some of the realist critics, including Gillis, is that the correct notion of locality has been clear enough since the 1935 paper of EPR [9], with the implication that other formulations of Bell’s theorem are not worth considering”
2) The intention of this paragraph was to say that any plausible reading of what Bell formally defined in 1964 is quite different from local causality, according to our analysis. To make this clearer and to satisfy goal (A), we have modified that sentence to read “What he offered in 1964 as a definition was a statement of locality that requires a little interpretation to be formalized, but is quite different from local causality.”
3) We agree with the referee’s suggestions and have changed “notion” to “concept” and “formal notion” to “formalization”, in this sentence and the subsequent one, to read:
“In suggesting that the concept of local causality was there all the time, Gillis fails to recognize the formidable intellectual effort, starting with Bell’s 1971 paper [15], then the Clauser-Horne paper of 1974 [16], then Bell’s 1976 paper [14] and the subsequent conversation about free will [17, 18], to develop the formalization of local causality. Furthermore, the assurance with which Gillis asserts that this concept is the way to capture these intuitive notions runs counter to Bell’s own thinking on this subject”.
We have also followed the suggestion to modify the paragraph on page 5, to read: “Bell does not provide, in 1964 or earlier, a formalization of locality that allows a rigorous derivation of his result without assuming predetermination of outcomes (or something like it)”.
4) We have changed that passage to read “Bell does not engage at all with the technical content of the EPR paper [9]”.
5) We have expanded on this point and softened the claim, to read:
“On pp. 8–9, Gillis attempts to explain why Bell phrased his paper in terms of settings rather than a more general notion of locality. He suggests that “the reason is that it is the one aspect of the experimental arrangements envisioned that can be placed unambiguously outside the past light cone of the second measurement”, and recalls that “Bell was hugely influenced by Bohm’s theory”, in which it is the setting of one measurement that influences the distant outcome.
However, these arguments provide no support for the idea that Bell had a more general intuitive notion of locality; on the contrary, they can explain why Bell may have initially thought about locality primarily in terms of the settings, and why he was only able to formulate his notion of local causality at a later date”.
6) We have changed “formulated” to “precisely formalized”, and added the sentence “We grant, as in [4], that “one could undertake to formalise Einstein’s assumptions so as to make the argument from predictability to determinism”, but this had not been done in 1964”.
7) We agree and have changed “logic” to “exposition”, to read: “The strain is unavoidable because of the flaw in Bell’s exposition itself, as others who disagree with Wiseman’s more general arguments have admitted [8]”.
8) On the suggestion that we should lay out the general points of agreement, we have thought hard about this issue — indeed this is the main reason it took us so long to reply to the referee’s comments — and decided that it would not be a good idea to do this. We believe it would potentially work against the referee’s aim of reducing the probability of yet another reply, if Gillis or others turn out to disagree with the precise wording or with an implication of any “points of agreement” we may one-sidedly publish. We have decided therefore to not presume to know exactly what Gillis or others would agree with, but instead to put forward our best argument for our own point of view, while accepting the suggestions of the referee to try and be more conciliatory and charitable in this revised version.
Since the referee took the trouble to put together a short three-point summary of agreement, we thought we should explain why we could not go with this summary. It illustrates the difficulties we had with putting together a concise summary. We briefly discuss each of the three points in turn:
a) Bell did not lay out an explicit formalization of locality in 1964.
In our reading, Bell did lay out what he meant by locality in 1964. If he had not, there would simply be no theorem in 1964. Gillis would, we think, also say that Bell laid out what he meant by locality, although he would radically disagree with us as to what that meaning was. Perhaps we all agree that Bell’s exposition could have been clearer, and that at least a little work is required to obtain an explicit formalization.
b) Einstein had not explicitly formalized it either, but had laid out the general concept that would later become formalized as local causality.
We don’t agree that Einstein set out a concept that was later formalized as local causality. Einstein’s argument uses, not a single concept, but two assumptions (at least): “independent real situations” and what he elsewhere called “nahewirkung” (which can perhaps best be translated, contra Born, as “local agency”). Together they have, or at least would seem to have been intended to have, the same empirical force as local causality But the same is true, more or less, of the conjunction of Bell’s two assumptions from 1964. So we maintain that “local causality” did not exist as a unitary concept prior to the work of Bell in the 1970s.
c) Depending on which formal definition of locality one combines with Bell’s 1964 paper, one gets different theorems.
We don’t agree with this either. We certainly agree there are (at least) two correct theorems that are called Bell’s theorem. But what does it mean to “combine” a definition of locality with Bell’s 1964 paper? Bell’s 1964 paper is one theorem, with its definition of locality. Bell’s 1976 paper is a different theorem, with a different localistic assumption (local causality). If one were to insert the definition of local causality where Bell said locality in 1964 then Bell’s claim in that paper would become that quantum phenomena are incompatible with locally causal deterministic hidden variable theories. That is a theorem, it is true, but one with too many assumptions, clearly. And it is neither Bell’s 1964 theorem nor Bell’s 1976 theorem. Perhaps the referee is suggesting to remove the concepts Bell uses in 1964 (locality and determinism) and instead insert a single assumption (local causality) and rewrite Bell’s paper around that. This would certainly be possible, but that would result in a substantially different paper from the one which Bell gave us.
Other minor modifications:
i) “formal formulations” changed to “formal statements” on page 3.
ii) “intuitive notions of locality” changed to “localistic intuitions” on page 9.
This paper has been accepted for publication in IJQF.