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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.
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.
Cheers,
ChrisHi 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.)
Cheers,
ChrisHi 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.)
Cheers,
ChrisHi 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.
