John Bell Workshop 2014

Bell on Bell’s theorem: The changing face of nonlocality

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    Christopher Timpson

    Between 1964 and 1990, the notion of nonlocality in Bell’s papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality’) became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation. Full text


    I hope I’m not violating protocol by posting comments/questions so soon, but I already read, with significant interest, this contribution by Timpson and Brown and wanted to share some thoughts while they were still fresh in mind.

    To begin with, I don’t understand the claim (in section 0.9.1, case 1) that there is no non-locality (or is it no action-at-a-distance?) in the EPR case (where experimenters measure the spins of a pair of particles in the singlet state along parallel axes). The claim seems to be that the physics is local because it is deterministic: “Given the initial state that was prepared, and given the measurements that were going to be performed, it was always going to be the case that a spin-up outcome for system 1 would be correlated with a spin-down outcome for system 2 and vice versa…” Wouldn’t these same words apply to the de Broglie – Bohm pilot-wave theory’s account of the correlations? Do the authors think that the dBB theory provides a local explanation of the perfect correlations in the EPR case? (My sense is that the authors are letting too much of the work here be done by taking “the measurements that were going to be performed” as *given*, rather than as somehow freely-chosen variables.)

    And then, second, I was also confused by the authors’ claim that there is no nonlocality in the more general Bell case (of non-aligned measurements). The key point seems to be that “we can only think of the *correlations* between measurement outcomes on the two sides of the experiment actually obtaining in the overlap of the future light-cones of the measurement events — they do not obtain before then and — a fortiori — they do not obtain instantaneously.” I think I don’t understand the argument here because it is not clear to me what the authors are taking as the ontology (the beables) of the theory. But assuming the ontology includes the quantum state, the authors’ claim seems wrong. Let me explain. I think the authors want to say that, after the third (comparison) measurement in the overlapping future light cones, the quantum state becomes something like their (0.10), from which we can read off the total branch weights associated with the four different joint outcomes. So, I guess, at that point the correlations are real. But… surely we can do this just as well at an earlier stage, e.g., from the state written in equation (0.9). So I don’t understand why the authors suggest that the correlations in question don’t yet exist (when the state is 0.9) but do exist (when the state is 0.10). What criterion is being used to decide, by looking at the quantum state, whether the correlations really “obtain”? It seems to me the authors must have, tacitly in mind, some vision of an ontology of local beables that is either extracted somehow from, or postulated in addition to, the quantum state, and that whatever difference they are seeing between (0.9) and (0.10) is somehow manifested in different dispositions of the local beables associated with each state. I wish they would make this vision more explicit so we could all understand it and scrutinize it.

    On a closely-related note, I was also confused by the authors’ implication (e.g., on page 30: “Everett interpretation shows that a theory can be local in the sense of satisfying no-action-at-a-distance, whilst failing to be locally causal…”) that the Everett theory can be seen to violate Bell’s “local causality” condition. Bell’s condition is of course formulated explicitly in terms of the local beables posited by a theory. (The authors even quote, in their footnote 25, Bell’s lovely remark that “If local causality in some theory is to be examined, then one must decide which of the many mathematical entities that appear are supposed to be real, and really here rather than there.”) But I was under the impression that, for Everettian quantum theory, there were no local beables — the quantum state (or wave function) alone provided the complete ontology. So I simply don’t understand what the authors could possibly mean when they say that the Everettian theory violates “local causality”. It seems again that they must have some ontology of local beables secretly in mind…

    Howard Wiseman

    Likewise (regarding posting early). Thanks for the stimulating piece Harvey and Chris – some interesting history and perspectives.

    I have a shorter question/comment than Travis: Why go so far as Everett’s theory as an example violating local causality (LC) but respecting locality/no-action-at-a-distance? Why not simply consider operational quantum mechanics, in which nothing exists but settings and outcomes. This satisfies Bell’s original concept of locality, at least once is formulated in the obvious way for probabilistic theories, as Jarrett and maybe others before him pointed out (as well as similar but more rigorously motivated concepts, but that’s a different topic.)

    Is it that you do not see operational QM as providing an explanation for the correlations it predicts, whereas you think Everettian QM does? I had some of the same concerns as Travis about the explanatory account you say that Everettian QM offers, regarding the difference between (0.9) and (0.10).


    Thanks to Harvey and Chris for their stimulating paper, and to Travis and Howard, whose comments have kicked off the John Bell Workshop 2014. I hope everyone will be inspired by these discussions, either via email notifications or by online text chat.

    H. Dieter Zeh

    Much of Christopher Timpson’s paper is ´´philological´´ or historical and about the different or changing use of concepts and words. This is quite intersting and potentially important, but not what I am mainly interested in. However, in the context of Everett, the concept of (non)locality seems to be quite clear to me. If you accept the ontic nature of the wave function or of a general superposition, this evidently defines a ´´kinematical nonlocality´´. (I assume this is what people usually call ´´non-separibility´´, when they are not necessarily regarding the wave function as ontic.) However, if you also assume the existence of a fundamental local basis for this Hilbert space (such as the configuration space for particle positions and/or spatial fields), you may still define local dynamics – no action at a distance – by means of local interaction Hamiltonians and relativistic propagators (see ).

    This definition is obviously model-dependent, but I do not know any (explicitly defined) proposal for how possibly to replace the successful wave function. (This is indeed my basic point.) So it all depends on whether or not we need an additional collapse dynamics, which in my opinion is an illusion – in agreement with Everett (see Sect. 4 of my contribution to the book).

    H. Dieter Zeh

    If my link does not work, please use (or insert the missing slash before nonlocality in the replaced website by hand)!
    Sorry for the inconvenience!


    Hi Travis,

    I think the authors are right in suggesting that the correlations in question don’t yet exist (when the state is 0.9) but do exist (when the state is 0.10). The reason is that in Everettian theory a measurement result exists only relative to the systems which are decoherent with respect to the measurement result, and it does not exist for nondecoherent observers who does not make the measurement or know the result. Although people including me may not like such relativity of worlds, it is required by the theory, for which I have given a simple argument based on protective measurements (



    PS. It is a fundamental and widely accepted assumption that a measurement result exists universally, and in particular, it exists for every observer, independently of whether the observer makes the measurement or knows the result. But the Everettian theory violates this assumption.


    Shan, I find your suggestions interesting and surprising. I would have thought that Everettians would say: what exists is the wave function, period. So anything that is there, in the wave function, is real. (And to me this seems to include the “correlations in question” both for 0.9 and 0.10.) But maybe the thing to do is agree that there is some question about what, exactly, is physically real in Everett’s theory. You think there are some extra restrictions about measurement results, and I am confused because there are no local beables so I don’t know how to find an image of the familiar 3D world at all. Hopefully the authors will clarify some of these things.

    H. Dieter Zeh

    There seems still to be some confusion about terminology (such as the meaning of nonlocality and reality). So I also hope that the authors will clarify terms for their purpose. However, the situation apears completely clear in the Everett picture if based on decoherence, while the concept of relative states makes sense only with respect to individual (subjective) observers:

    Since the pointer states A and B are assumed to immediately decohere after measurement, there are objectively four ´´autonomous´´ Everett branches after both measurements. Only in the parallel case, two pairs of them are identical (In each branch there would then be a second measurement with predetermined outcome). According to Everett (or global unitarity), all four (or two) branches ´´exist´´. The branching becomes relevant to an observer only if and when he receives a (classical) message about the outcome. Only then will he ´´split´´, too. First into two and then (possibly) into four versions – with subjective(!) probabilities according to the empirically known (Born’s) weights. Measured spinors and pointer positions are according to this picture in their ´´relative states´´ with respect to these different versions of the observer, where they may be objectivized between different observers in one branch by means of their entanglement in the global Everett state.

    If this observer is a pragmatist, he will assume that the wave function had already collapsed (twice) into one single branch at the time of the first irreversible decoherence of each measurement result. This is the pragmatic ´´collapse by convention´´.

    I have precisley discussed this example on pp. 16/17 of (in case you would like to have a look).


    Hi Travis,

    I agree that finding an image of the familiar 3D world is an issue for the Everettians. I also hope Chris can clarify some of these things.



    Hi Dieter,

    Thanks for your clarification! I will look at your paper later.


    Christopher Timpson

    Hi folks,

    First, many thanks for these interesting comments and questions. Second, humble apologies for being so slow to reply (not least considering Travis’ and Howard’s getting the ball rolling so promptly): I can only plead the end of term and the whirlwind of the seasonal holidays.

    But to the business:

    In reply to Howard’s query – why not take operational QM as a simpler counterexample than Everett to the claim that failure of local causality entails the presence of nonlocal cause (action-at-a-distance)? – my answer is that certainly one can do this, it’s just that to my (and I am sure, to Harvey’s) mind Everett is by far a more interesting counterexample. And this for essentially the reason Howard surmises, namely that operational QM, so far as it is a theory at all (as opposed to a mere algorithm – but perhaps we should not get side-tracked with tendentious name-calling 🙂 is not a theory which offers explanation of the correlations, this being an instance of the more general property (or fault) that it seems not to offer explanations of physical phenomena across the board, in so far as it fails to offer any descriptive claims about the micro-constituents of the world and their behaviour. (This last very plausibly being a necessary condition for adequate explanation in a vast array of circumstances.) Moreover, I think that Bell himself already dealt very poignantly and clearly with the case of operational QM (not least in ‘Against Measurement’, but throughout Speakable and Unspeakable), whilst (for all I enjoy Bell’s writings on Everett – or on the state of Everett in the late 70s and 80s as it was often understood then) I think there is more to be said on Everett’s part than Bell’s discussions cover.

    Turning briefly to the first of Prof. Zeh’s comments: yes, I would take ‘kinematical nonlocality’ and ‘non-separability’ to mean the same thing.

    Now to Travis’ several points, queries or concerns.

    I agree, Travis, with part of the thrust of your first observation, that determinism on its own does not suffice to ensure no-action-at-distance, and that, moreover, one needs to be careful about what sphere of possibilities one is considering—what modal freedom one is allowing (e.g., is it possible—in some pertinent sense of ‘possible’—that the measurement settings might be, or could have been, otherwise than they will be, or in fact were?). Both of these things are of course plainly true. (There are plenty of theories which are deterministic but have action-at-a-distance, cf. de Broglie-Bohm as standardly assessed (though note Dickson 1998 for a slightly heterodox reading based on modal considerations); whilst if one is considering a sufficiently impoverished set of possibilities, it may be easy to construct a local theory to account for all the phenomena being allowed, as Bell himself pointed out in ’64 for example.) But the reference to the determinism of the evolution in the case we are considering takes place within the scope of the stipulation that we are considering all the measurement outcomes to be realised (this rules out the de B-B case, of course), and its purpose, in the parallel-settings case, is to highlight how un-mysterious, un-puzzling, non-conspiratorial, and not requiring of any collusion-at-a-distance-between-outcomes, the obtaining of EPR correlations is (in the Everettian setting).

    Perhaps there might be a worry if there were no action-at-a-distance in the parallel settings case, but there were to be in the non-parallel settings case. Then if we were free to move from one case to the other (by local free choices of settings), action-at-a-distance could be introduced. But our claim is that in neither case is there action-at-a-distance, thus our separation of the two cases is harmless. (The point of separating the two is that they differ in some details: in the parallel case, no appeal needs to be made to the Born rule to ground the claim that the pertinent correlations obtain, whilst in the non-parallel settings case, the correlations don’t obtain as soon as the pair of local measurements are made (i.e. do not obtain on any spacelike hypersurface cutting the two measurement events).)

    Next it is perhaps best if I simply say something about local beables in the Everettian context, as I think about it. Travis: you are of course right that for the Everettian, the ontology of the theory (apart perhaps from the spatio-temporal arena) is completely determined by the quantum state alone. It doesn’t follow that there are no local beables for the Everettian. Suppose we take a given background spacetime, then we can simply take the local beable in a given region of spacetime to be given (in whole) by the reduced density operator associated with that region. This will lead overall to a non-separable picture of the world: the beable associated with unions of disjoint spacetime regions will not be determined by the local beables of the various parts. But, pace Einstein, I see nothing wrong with, still less unintelligible about, a non-separable fundamental ontology. Note that the measurement outcomes in a given region (where a measurement has taken place) will supervene on the local beable (given by the reduced density operator) and in particular, typically a plurality of measurement outcomes will supervene on the local beable for a given region where a measurement has taken place.

    David Wallace and I call this kind of view ‘spacetime state realism’ and discuss it (and some alternatives) in our 2010 BJPS paper (also it is discussed in Chpt 8 of David’s 2012 book). (But note that this is not the only way to understand Everett in a spacetime setting – Bacciagaluppi (2002) uses an explicit branching spacetime structure.)

    Now: as to Harvey’s and my story about the non-parallel settings case. You are puzzled, Travis, I think, about how it can be that the correlations are `in the state’ at the time of the pair of measurements but do not (we claim) obtain at that time, if the state completely determines what there is in reality. (Is that a fair way to put it?)

    I am thinking about it like this: a branching structure for Alice’s measurements supervenes on the local beable for region A; a branching structure for Bob’s measurements supervenes on the local beable for region B. (These will be small bits of branching structure if A and B are relatively small.) Since the relations between things in region A and things in region B are not determined by the states of A and B individually (non-separability), these local branching structures do not suffice to determine what relations, if any, obtain between definite outcomes in A and definite outcomes in B. Relations between outcomes will be determined by the relative states with respect to measurement-outcome bases in A and B respectively. It is because the relative state of things in B is an entangled mess, with respect to a measurement basis element in A, and vice versa, that there is no definite outcome in B with respect to a definite outcome in A (and vice versa). The relations between outcomes are determined by the global state and there can be definite outcomes in A and definite outcomes in B, without there being definite relations between outcomes in A and B. To see this properly we of course need to recognise that talk of a definite outcome in A (say) is (typically) only partly to characterise the full state of affairs in A—the underlying local beable—for that later typically supports a superposed (but independently evolving) plurality of definite outcomes in A.

    Does this talk of relative states and measurement-bases (as a way of characterising the actual obtaining of definite relations between states of affairs in spacelike separated regions) reintroduce the kinds of worries that so exercised Bell about choosing a preferred basis? No. As is the common view in modern Everettianism, what we chose to call a measurement basis is in fact determined by the contingent facts of the actually obtaining dynamics: it is a basis which is robust against decoherence. This will necessarily be a somewhat rough-and-ready characterisation—does that fall foul of Bell’s quite proper injunctions against vagueness in fundamental physics? No: for branching and measurement aren’t fundamental physics, but parochial processes of interest only to creatures such as ourselves, not to the clean and neat laws of physics.

    That’s a stab at saying a little more about the kind of thing we have in mind—I hope it addresses a least a little of people’s puzzlement. There’s more I could say at various points, and on various points, but perhaps best to leave it at that for now.


    Hi Chris, Thanks for your comments in response to my queries. I’ve already said a lot about all of these issues in my own contribution to the Bell volume, so for the most part I’ll just invite you (and whoever else is interested) to check that out if you want to see what I think about several of the points you raised. I’m not convinced, for example, that the local density operators provide an adequate/appropriate set of local beables, nor that, even granting for the sake of argument that they do, the theory is actually local. But, like I said, see my paper for the longer version of those discussions.

    Here I’ll thus limit myself to the one point about the correlations existing, or not, in equations (0.9) vs (0.10). Your answer would make perfect sense if, according to spacetime-state-realist Everettism, the entire ontology was given by the local density operators (for some set of small regions). That is to say, I completely agree with you when you write: “Since the relations between things in region A and things in region B are not determined by the states of A and B individually (non-separability), these local branching structures do not suffice to determine what relations, if any, obtain between definite outcomes in A and definite outcomes in B.”

    But then, don’t you agree that there is more to the ontology than just the individual states of A and B? In particular, isn’t the “local beable” (?! — i.e., the density operator) for the joint region A+B also part of the ontology? And/or, isn’t the full universal quantum state part of the ontology? Either of these allow one to see perfectly well that the outcomes are “already” correlated (when the state is as in 0.9). So if either of these things is real — as real as the individual states of A and B are supposed to be — then surely the correlation “already exists” before Alice and Bob get together later to compare notes over tea, or whatever.

    So, it seems to me, your claim that the correlations only come into existence in the overlapping future light cones of the individual measurements, is based on something like confusion or forgetfulness about the ontology of the theory.

    Christopher Timpson

    Hi Travis,

    Thanks for these further comments. And yes – I’m keen to read your mentioned papers.

    “Confusion or forgetfullness about the ontology” Are these really the only two diagnostic options 😉 Of course we agree that the universal state grounds the ontology and indeed the local density operators for individual regions of spacetime generally don’t determine the universal state. I think you may have missed where I refer above to use of the apparatus of relative states to read-off facts about definite relations between things in the Everettian picture.

    It is because in 0.9 the state of the far apparatus is not definite relative to a definite measurement state of the near apparatus that we say that the correlations do not obtain at this stage, whereas they do in 0.10.

    But perhaps it would be helpful too to introduce a bit of further terminology to help here. Thus let us distinguish between occurrent correlations' andmodal (subjunctive) correlations’. Correlations between the outcomes of measurements are occurrent (on a given space-like hypersurface) iff relative to a definite measurement-indicating state of one apparatus, the other apparatus is also in a definite measurement-indicating state (on that hypersurface). That is, relative to things over here being some definite way, the things over there are also some definite way. This is the case of 0.10 (and 0.6 – the parallel measurements case). Correlations are modal, or subjunctive, on a given spacelike hypersurface, however, if they are not occurrent, but the state on the hypersurface entails that certain (non-trivial) occurrent correlations would obtain under certain future conditions (as in 0.9). So one *can* say that there are correlations in 0.9 if one wants to, but they are *modal* or *subjunctive* (to do with what would be observed were certain future conditions to obtain) rather than occurrent (having to do with how things actually are at a given time).

    We don’t use this explicit terminology in the paper since we feared it might be off-putting, but the distinction is present in the discussion. (As e.g. when we talk at the end of Section 0.9.1 of merely `formal’ joint probability statements.)



    Hi Chris. First, I hope you know I was just being playful with “confusion or forgetfulness about the ontology”. At any rate, *I* remain quite confused about the ontology of this Everettian theory, and your latest comments only add to that (with this new — and to me weird and metaphysical — distinction between occurrent and merely modal/subjunctive facts).

    Maybe the following will help clarify things. Take the simpler case in which Alice and Bob measure along the same axis. Here you want to say that (as examination of the local density operator for a spacetime region including Alice’s measurement will show) Alice’s measurement induces a splitting, and similarly for Bob. So there are two splittings in these two spatially separated regions. What is the status of the correlations between Alices’ results and Bobs’ results? That is, is the pairing-up of the branches REAL as soon as the two measurements have been completed? Or does it remain somehow “not really yet fully real” (which is more or less what I take your category of modal/subjunctive facts to mean) until some Charlie observes both Alice’s and Bob’s results in the overlapping future light cones?

    Christopher Timpson

    Hi Travis,

    Actually, I suspect that you are more familiar with the distinction between the occurrent and the modal than you realise – you (as all of us) will operate with the distinction hundreds, if not thousands, of times a day, in our ordinary thinking about, e.g., how things currently are in the world and how they would be were such-and-such to happen. Thus – my coffee is currently quite cold; if I were to go and put it in the microwave then it would be hotter, and I might then drink it and finish the cup. This isn’t weird and metaphysical but humble and familiar. (Of course, there are many philosophical debates about how occurrent and modal facts relate to one another—and especially whether facts of the latter kind might be reducible to facts of the former kind (as Hume, famously, thought). But that debate is not germane to our concerns.)

    In the parallel measurements case—the example you ask about—then as I stated above, the correlations will be occurrent correlations on any spacelike hypersurface containing both Alice’s and Bob’s measurement events. And this is because the measurement states of one apparatus are already definite relative to measurement states of the other on any such hypersurface.

    (N.B. I wouldn’t myself use the terminology of ‘not fully real’: existence (like truth) is an all or nothing affair and doesn’t come in degrees. The relevant distinction is a modal, rather than an ontological, one.)



    Hi Chris, Sorry, it’s not the distinction as such that I find “weird and metaphysical”, but rather your use of it in this context. Let me try to step back and explain what’s bothering me. On the one hand, I thought I understood you Everettian types to be ontologically monist about the quantum state. But then, in the discussion that arose about equations (0.9) and (0.10), it seemed like your position amounted to: yes, the correlations in question are there, already, in the quantum state, but they aren’t yet really real because they haven’t yet manifested in (some only-very-vaguely circumscribed subset of) the local beables. That is, it feels as if you are not taking the quantum state as exhausting the ontology. Indeed, it feels as if you are taking a very Bohmian sort of perspective on the quantum state — that it’s real, yes, but somehow a strange behind-the-scenes thing whose role (so to speak) is more to choreograph the dance of the primitive ontology (which, for you, seems to be this vaguely-defined subset of the local density operators). (By the way, in case it’s not clear, I’m referring to a “vaguely-defined subset” of local beables because it seems that what you are saying is based on taking the local density operators of the separate regions A and B as “appropriate to look at to decide what’s ‘occurrent’,” but excluding the local density operator for the joint region A+B.)

    Let’s step back even further. This whole thing came up because you argued that the non-existence of the correlations (on a hypersurface where (0.9) obtains) is evidence for the *locality* of the theory. I’m assuming you’d agree (but perhaps not?) that if the correlations in question really do exist, already, on that hypersurface, it becomes harder to claim that the theory is local in the relevant sense. But, to me, naively, and thinking that Everettians are serious about wave function monism, the correlations are just clearly there in (0.9). You can of course play games with parentheses, but (0.9) is a state with four branches, each of which has definite outcomes for each experiment and a definite overall branch weight. So — assuming wave function monism — it seems fair to say that the correlations are as real as they can ever possibly be in an Everettian picture. (That is, let’s leave aside questions about exactly what we even *mean* by correlations, how branch weights relate to what we’d normally describe as probabilities, and all that sort of business.) This is why I’m puzzled by — and trying to press you to elaborate and clarify — your suggestion that, no, really, the correlations (on the slice where (0.9) obtains) don’t exist. Your view seems to be that the quantum state (0.9) tells us something about which correlations are inevitably destined to later come fully into existence, but that this shouldn’t be confused with their really existing already (in your “occurrent” sense). Surely you can appreciate why it seems to me that something interesting is going on here, vis a vis the ontology of the theory — in particular why it seems that you are tacitly treating this vaguely-defined subset of the local density operators as somehow capturing the *true* ontology, with the quantum state not only not exhausting the ontology but indeed playing some kind of background, secondary, subsidiary ontological role.

    Re: the parallel measurements case, you said what I would have expected you (qua wave function monist) to say. I just wanted to clarify in that simpler case first to make sure. Hopefully now you can see, from the above two paragraphs, what I’m really concerned about here, and maybe the parallel-measurements-case sub-thread can just die. But I’ll mention that now I’m again worried about one of the points I raised initially — your seemingly artificial separation between the parallel and non-parallel cases. If I’m right to have understood you as saying that the case for the locality of the theory hangs, at least in part, on the correlations not really being real until some appropriate events in the overlapping future light cones, then you can see why I’d want to now follow up the parallel-settings case, in which it’s now clear that you agree that the correlations are fully real / occurrent right away. Does that mean we should worry after all that there is some nonlocality already in that simpler case? I think so — especially if (as I suggested originally) we treat Alice’s and Bob’s choices of measurement axes as “free” in the usual relevant sense, so that your (to me strange) argument about the correlations in that case being *determined* no longer really applies.

    Christopher Timpson

    Hi Travis,

    We seem to be going in circles, or talking past each other, which is disheartening. Of course, internet message boards aren’t the most subtle medium of communication ever devised, especially when it comes to nuances—perhaps we should convene over a beer at some point to thrash out whatever still needs thrashing out.

    But let me have a further (possibly final!) stab at trying to help clarify things.

    “Surely you can appreciate why it seems to me that something interesting is going on here, vis a vis the ontology of the theory — in particular why it seems that you are tacitly treating this vaguely-defined subset of the local density operators as somehow capturing the *true* ontology, with the quantum state not only not exhausting the ontology but indeed playing some kind of background, secondary, subsidiary ontological role.”

    No, I can’t really appreciate that, I have to say. I think there are perhaps two things obscuring our communication.

    First: you use the phrase ‘primitive ontology’. Harvey and I are not working in a primitive ontology framework. [For those unfamiliar with the phrase, this is (now) a technical term: the primitive ontology approach holds (roughly) that in order for any fundamental physical theory to be intelligible, or potentially acceptable, or susceptible to empirical verification, it must postulate at the ground-level of the fundamental variables of the theory items which inhabit 3-d physical space and evolve over time (no commitment to a preferred foliation), and are such that they can readily be identified with the determinate macroscopic goings-on of our experience (often simply by straightforwardly *composing* the things, or the goings-on, of our macroscopic experience). Examples are the definite positions of fundamental fermions of de Broglie-Bohm theory, matter-density fields in that version of GRW theory, or localisation events (‘flashes’) in the flash-version of GRW.]

    We are not postulating any primitive ontology at all. Which is not to say that we are not allowing local beables, nor to say that we are denying that events are locatable in spacetime; rather it is just to say that we are not adopting a certain rigid approach to the conception of what either of these things entails. I am of course aware that there is a school of thought which insists that any theory must postulate primitive ontology (in the special technical sense) to be acceptable or to be intelligible, but I am unpersuaded that such a thing is obligatory. (And since we are reflecting on 50 years of Bell, I add, for what it’s worth, that neither do I find in Bell’s writings an insistence on primitive ontology: what I do find is an insistence on precision in fundamental ontology; but these two need not be the same thing.)

    So: in the kind of Everettian view that Harvey and I are exploring (essentially a Saunders/Wallace view, as we understand it) there is no primitive ontology which enters at the fundamental level to ground the familiar features of the world of our experience. There *is* a fundamental ontology, and it *can* be conceived in a spacetime manner, as a non-separable field, but the connection to the macroscopic world of our experience is not written into the fundamental ontology. (The fundamental ontology doesn’t—on this view—care about such prosaic things as creatures like ourselves, nor about such prosaic regimes as the quasi-classical.) Rather, macroscopically determinate features *emerge* in a somewhat complex and somewhat messy (at least at the edges) way, under certain conditions, due to decoherence on a sufficient scale. The Everettian branching structure of worlds is not fundamental; the worlds within the branching structure are not fundamental: they are simply structural features, which emerge under certain conditions, of the fundamental ontology. (I make no claim of novelty in saying this—I am merely repeating the kind of view that David Wallace has so powerfully put.)

    Thus let me reiterate: nothing that I have said is inconsistent with, nor, I submit, in the least in tension with, full-blooded adherence to the view that the universal quantum state grounds the ontology. The universal state, plus spacetime (or maybe even without spacetime, if we want to go in for a Leibnizian reduction of spacetime to relations between stuff, a la Barbour-Bertotti) is all that there is in the fundamental ontology. We’re not putting anything else in. You say above that you think I am really appealing to the local density operators to determine what correlations are occurrent: this isn’t the case, and I don’t understand why again and again you seem to be neglecting my appeal to the concept of the relative state to determine relations between the things of our interest (e.g. determinate measurement outcomes in spacelike separated regions).

    Second: I think you are misreading the role of the discussion of the parallel and non-parallel cases, and the absence of definite outcomes at the far side relative to definite outcomes at the near side, in our paper. The discussion of these two cases is not intended to be key in proving that Everettian quantum mechanics is local.

    By contrast, we take it to be utterly straightforward that Everettian quantum mechanics is local—in the sense of not incorporating any action-at-a-distance (dynamically local)—for the simple reason that there is no source of action-at-a-distance in the theory. There is no collapse of the quantum state, and the unitary dynamics is local. Or again, put it this way: to be local in the sense of no action-at-a-distance is for it not to be the case that any locally-defined properties in one spacetime region are affected by any goings-on in a spacelike separated region. This just *obviously* holds for the fundamental ontology in Everettian quantum mechanics (since it is unitary): local density operators will not be affected by spacelike goings-on.

    Why, then, is there anything more to say? Well, there remains a puzzle, or a point of interest, regarding how it is in detail that this dynamically local theory manages to violate a Bell inequality: what actually *happens* in the EPRBB experiment in this theory? Put another way, there remains a point of interest regarding how the non-fundamental, emergent, ontology behaves; for the story of the EPRBB experiment will be a story involving the non-fundamental level of pointer states of measuring apparatuses, and so on. The main purpose of our 0.9.1 is just to give this story of how in fact, in this already dynamically (but not kinematically) local theory, Bell-inequality violation is achieved.

    Why, within this, is it interesting to highlight the fact (or alleged—by us!—fact) that in the non-parallel case (required for Bell experiments) there is no determinate outcome on the far side with respect to a determinate outcome on the near side, at the time of Alice’s and Bob’s measurements? Because this highlights the fact that worlds (emergent structure, or ontology) are generally locally defined (world-structure depends on what’s entangled with what, and how: what has a definite-value, in terms of the relative state, with respect to what), and it highlights that world-branching is a local process (since it is driven by local decoherence processes). [Granted, not all versions of Everett have taken worlds to be locally defined, or branching to be a local process; but the Saunders/Wallace view does, again, as I understand it; and this is the conception we are working within.] Within this, the EPR-Bohm parallel case is a special case. Here the correlations are not due to probabilities; the pointer states of the measuring apparatuses become perfectly (anti-)correlated one with another because the measurement interactions on both sides are those special interactions which are such that a definite measurement outcome state on one side bears a definite relation to a definite parallel spin-state on the far side. This isn’t a (dynamically) non-local feature, though; it is just a feature of the fact that being-value-definite-with-respect-to is a transitive relation: in the singlet state, spin-up for one system is value-definite with respect to spin-down (in the parallel direction) of the other system; the measurement interactions are then such that locally the pointer states become value definite with respect to the local spin states, and in this special case, *also* value definite with respect to the far spin states. But this is a matter of both measuring apparatuses each locally being brought into a particular relation with their local system, and thus being brought into relation with each other, on the basis of a pre-existing relation, rather than a matter of a measurement in Alice’s region having an effect on the locally defined (intrinsic) features of Bob’s region (and vice versa).

    The story of the emergent ontology (involving measurement outcomes, macroscopically distinct states of the lab, states of observers, etc.) *must* be (dynamically) local, given that the fundamental ontology is (dynamically) local. But even so, it is interesting to see how things play out in detail.



    Hi Chris, Yes, I agree, we’re not making any progress, and it seems a good time to wrap this up and agree to continue over beers someday. I feel I should wrap up some loose ends, but this will be my last post so you can take the author’s prerogative of having the last word.

    First, just to clarify, I understand perfectly well that you’re not “working in a primitive ontology framework.” I merely remarked that you seemed to be tacitly adopting certain elements of that perspective. I continue to think that you are doing so, unwittingly, and in a way that conflicts with your explicit disavowal of that perspective. But obviously we’re not going to resolve that here.

    Second, I should say something about “relative states” which you say I keep ignoring. I just don’t see how this idea is helpful or relevant. I believe you noted above that, when the state is described as in (0.9), the state of Bob relative to a particular definite-outcome state of Alice is an “entangled mess”. That’s true. But whenever a single person makes a single measurement, the state afterwards is an entangled mess, and I thought it was Everettism 101 to regard this as a description of several parallel branches/worlds. Why shouldn’t I adopt that perspective here, and say that for each definite outcome state of Alice, there are two branches, one in which Bob saw “up” and one in which Bob saw “down”. So we would understand (0.9) as describing a world with four branches. Which, mathematically and prima facie, is just obviously exactly what it is. Yet you think this perspective is wrong, and that something important changes between (0.9) and (0.10). Essentially my whole goal in this thread has been to try to understand what you think changes that is relevant, and unfortunately I never managed to understand that. But it sure looks and feels strongly as if, for you, what changes has something crucially to do with the local density operators for smallish regions: whereas the local density operator for region A, together with the local density operator for region B, do not “contain the correlations” between the definite outcomes on the two sides, the local density operator for region C will. What I continue to not understand is why anything like that should matter if, as you claim, you disavow anything like the “primitive ontology” approach but are instead genuinely monist about the quantum state.

    But finally, and most importantly, your last post makes it clear that we are really just in very different places regarding what “locality” means and how one might try to decide if Everettian quantum theory is or is not “local”. You seem to just take it as obviously local (on grounds, I’ll note, which would seem rather in danger of establishing with equal validity that Bohmian mechanics is local!). Whereas for me, as for Bell (see for example the statement you quote in your footnote 25), it is literally meaningless to even begin a discussion of locality/nonlocality until one is quite clear and explicit about the local beables of one’s theory, about the 3D/spacetime ontology. So to whatever extent you insist that Everettian quantum theory is just obviously and clearly “local” (and that grasping this doesn’t require sorting out any of the kinds of things I’ve been trying to press you on in this thread), I have to confess that I simply don’t understand what in the world you mean by “local”.

    All right, that’s my attempt at summarizing and wrapping up. Obviously lots of questions remain on the table for that future hashing out over beers. Thanks again for the enjoyable, if frustratingly unproductive, discussion.

    Christopher Timpson

    Thus: to exercise my gratefully-received author’s last-word prerogative.

    I have a better understanding of where you’re coming from now Travis (I also managed to skim very quickly some parts of your paper—which I shall return to properly in hopefully not too long—and that helped me see better where some of our differences are emerging).

    I take it as part of the kind of Everettian view I am considering that the relational properties of sub-systems are given by the relative states: importantly, though, these are not relational properties at the level of the fundamental ontology. At the level of the fundamental ontology, all that there is to say about how things in Alice’s region stand to things in Bob’s region is that there is a certain (typically, entangled) density operator for the union of the two regions. Talk of relative states is useful, by contrast, when one wishes to pick-out more familiar features—derivative and structurally emergent, but nonetheless real, features—from the fundamental (non-separable) field-like ontology. In particular, following a measurement in Alice’s region, we can discern a particular structure in the density operator for her region, given by an incoherent superposition of measurement-pointer states. Then, singling out one of these branches, which is just picking out a *part* of the fundamental state of her region (but it is picking-out an interesting and independently-evolving part of the fundamental state of her region) we can ask how things elsewhere stand relative to that part. It is this kind of job that the relative state is for—reading-off structural features of the overall quantum state. Where structural features are of the right kind: robust and enduring (at least relatively so), of suitable extent, and obeying quasi-classical dynamics, then they will warrant world-talk.

    Certainly it is Everettism 101 (as Travis puts it) to consider a post-measurement entangled state for a given region as a branching into distinct worlds (emergent features of the monistic underlying ontology). But this is a matter of the intrinsic features of that given region. It doesn’t settle how relational features, and in particular, relations to definite measurement outcomes (if any) in other regions, should be understood. I take it to be part of the kind of Everettian view Harvey and I are exploring that the relative state is the tool to use for questions of relational features (if one is going to go beyond just talking of the joint state of pairs of regions). Travis is perhaps suggesting that some other rule ought to be adopted (or at least *could* be adopted) for reading-off relational features, but I’m not sure whether there is some concrete alternative proposal on the table, whose merits might then be assessed, or whether it is just being proposed as an open question whether there might be some other alternative way than the relative state to approach questions of relations between subsystems in Everett. What’s clear, however, is that appealing to the Everettism 101 point doesn’t settle anything about how relations between things in Alice’s and Bob’s regions should be understood, because the Everettism 101 point is about intrinsic (non-relational) features of given spacetime regions. To suppose that we learn about relational properties by seeing what the intrinsic properties are perhaps leans dangerously towards neglecting the fact that we are dealing with a non-separable theory.

    Then to address Travis’ final point about our differing conceptions of what locality means. (N.B. I don’t see at all the worry about how de Broglie–Bohm might end up looking local by a parallel argument; de B–B is usually understood to have explicitly non-local *dynamics* for its hidden variables. I must be missing something.)

    “for me, as for Bell…it is literally meaningless to even begin a discussion of locality/nonlocality until one is quite clear and explicit about the local beables of one’s theory, about the 3D/spacetime ontology.”

    I note a number of things here:

    1.’Quite clear and explicit.’ People might have differing views as to what adequate clarity and explicitness would consist in. The local beables in the version of Everett we are discussing are given irreducibly and in toto by the local density operators. (No specifiation of a preferred basis or decomposition of the density operator, no further local beables, nothing. Just the density operator determined by the universal density operator). Measurement outcomes are localised (even if superposed) within specific spacetime regions. That seems quite sufficiently clear and explicit for me in order to get a discussion of locality off the ground. We could put it this way: the (primitive, irreducible) intrinsic (locally-defined) property of a given spacetime region is given by its local density operator. What it is for a theory to be dynamically local is for the intrinsic properties of regions only to depend on things in their past light cone (or inside the region of causal-connectability, if these are different things). This holds in Everett, since the local density operators aren’t affected by spacelike goings-on in this theory.

    2. It so happens in this theory that the local beable for a given region might support a plurality of emergent branching goings-on: a plurality of (emergent) macroscopic determinate events. It is within these emergent branches (whose features and behaviour are wholly determined by the local fundamental ontology and the dynamics driving it) that one will find familiar 3d ontology, including 3d measuring apparatuses having definite readings. The 3d ontology of our experience, or of experiment, need not enter at the fundamental level, at the level of the fundamental local beables of the theory. Thus we should beware a slide which goes from saying that we must have a fundamental ontology within which we can frame a debate about locality, to saying that we must have at the fundamental level of the ontology of the theory a familiar 3 dimensional ontology.

    3. Thus I want to urge that one does not need primitive ontology (in the technical sense) in order to frame a debate about locality. Nor, I think, would Bell have been committed to that view. He wanted local beables, yes, if one is to discuss locality; and he wanted precision in fundamental ontology. But I don’t think he insisted that the fundamental local beables needed to be the beables of our familiar 3-dimensional experience. (Though it had better be the case that the fundamental ontology does at least ground the facts of our familiar 3-dimensional experience; but as I have said before, the relation between the fundamental ontology and the emergent level of the macroscopically determinate world of our experience is not fundamental physics, so would not fall under Bell’s ‘precision’ rubric.)

    In sum, then, I’m not sure that the difference between Travis and me is really to do with a differing conception of locality (or of not having given adequate meaning to this word), but rather to do with differing conceptions of what intelligible fundamental physical ontologies could in principle be like, and of how it is permissible to go about telling a story about how the fundamental ontology relates to the everyday world of our experience.

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