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OK, yes, let’s wrap up. I appreciate your comments and they actually help me understand your view better. But I guess I would have to summarize by saying two things. One, you’re making a big fuss (as Dustin already pointed out) about the kinds of things (like schematic treatments of pointers and associated implied decoherence assumptions) that any quantum mechanical treatment of these issues will have to involve, at least for the forseeable future. Sure, we can all agree that it would be nice to have more realistic quantum mechanical treatments of macroscopic objects, with certain qualitative (but strongly motivated) assumptions about decoherence, etc., replaced by hard theorems. But it seems silly to me to think that there is going to be any kind of fundamental surprise here, and also silly to act as if these sorts of things are somehow uniquely or especially problematic for Bohm’s theory. And then two: it seems that the things that, in my opinion, Bohm’s theory does genuinely add to more orthodox treatments, you basically just dismiss with a shrug, on the grounds that, for you, the alleged problems that these alleged advances allegedly address, were never actually problems in the first place. I’m thinking here in particular of your remark that “operational QM does not have a measurement problem”. In so far as that’s true, it can only be true because what you mean by “operational QM” literally involves no attempt whatsoever to say what is actually going on physically in the quantum world. And to me it is just an expression of a very boring and stale and unscientific philosophy (think Osiander here), rather than some kind of insightful criticism of Bohm’s theory, to say that you elude all the problems that supposedly plague Bohmian mechanics simply by refusing to even try to aim at providing a realistic description. That’s not deep and it’s not insightful… it’s just a “betray[al of] the great enterprise”.
Anyway, that’s how I see things after this interesting exchange. Thanks again for your participation and, it being your thread, I think you should get the last word if you want it.
Reinhard, Could you elaborate on your statement that (even) position is not “directly observable” in BM? I don’t think you’re right, but then I’m not entirely sure what you mean. I would say that position is directly observable in BM in the sense that it is possible, according to the theory, to find out the actual position of some particle at some time. I’m guessing you wouldn’t dispute that (but I’m really not sure, because your ideas/criticisms tend to be obscured by a frothy layer of polemical rhetoric), but would consider it insufficient. That is, I think you assume that genuinely “directly observing” particle positions somehow has to mean monitoring them over time, with perfect accuracy, but without changing the trajectory from what it would have been in the absence of such monitoring. I would of course agree that if *that’s* what you mean by “directly observing” a Bohmian particle position, then you are right, you cannot do that. But I wouldn’t consider that an appropriate definition/standard for “genuinely observing particle positions”.
(And then similarly, vis a vis the “surreal trajectories” business, I think the situation there is just that, some experimental setup which you might have naively expected to constitute a “genuine observation of the particle position”, according to BM, actually turns out, according to BM, *not* to be that. I again wouldn’t consider that as refuting the claim that it is possible to genuinely observe particle positions in BM: “anything that seems to me, naively, without really considering in detail what the theory says, like it should constitute a valid position measuring device, must actually be a valid position measuring device” is not the appropriate standard. What’s relevant is just that it is in fact possible, according to the theory, to observe particle positions — and you cannot ignore what the theory itself says about exactly under what conditions, and with what accuracy, and for which kinds of setups, etc., this is possible.)
But all of this seems like the kind of stuff that you’ll just pounce on and denounce as worthless loose talk. So maybe it would be helpful to instead try to argue in the context of some simple but concrete example. Let’s take the “Einstein’s Boxes” setup, where there’s some particle that can either be on the left (psi_L) or on the right (psi_R), or perhaps a superposition of the two. Now imagine a position measuring apparatus with a pointer (initially in state phi_0) that is intended to swing to the left/right (phi_L/phi_R) to indicate the presence of the particle on the left/right. Let’s assume that the detector is ideal/perfect in the sense that, if the particle is prepared in the initial state psi_L, then the Schroedinger evolution of the combined particle/pointer system goes like this:
psi_L(x) phi_0(y) –> psi_L(x) phi_L(y)
and then similarly for the other case where the outcome should be certain:
psi_R(x) phi_0(y) –> psi_R(x) phi_R(y).
Now of course according to BM there is, in addition to the wave function, the actual particle positions X and Y. If we assume that the initial configuration X(0), Y(0) is random and |Psi|^2 distributed (where Psi = psi phi is the “Universal” wave function), then it is a theorem that this remains true over time. OK, so in the case that the particle is prepared in state psi_L(x), the final position of the pointer Y(t_f) ends up in the support of phi_L(y) with certainty. That is, the pointer definitely ends up veering left if the particle definitely started out on the left. And similarly for the other possibility.
Now what about the case where the initial quantum state has the particle in a superposition of psi_L and psi_R? Well in this case, the actual position X(0) of the particle will be either in the support of psi_L or in the support of psi_R. (I assume that these supports don’t overlap.) Then the Schroedinger evolution of the universal wf is as follows:
[ psi_L(x) + psi_R(x) ] phi_0(y) –> psi_L(x) phi_L(y) + psi_R(x) phi_R(y)
which can be understood as two disjoint lumps in configuration space. The actual particle/pointer positions at the end, X(t_f) and Y(t_f), will end up in the support of one lump or the other, just depending on whether X(0) was initially in the support of psi_L or psi_R. So the pointer indeed registers the actual pre-measurement (“Bohmian”) position of the particle, and with perfect faithfulness/fidelity.
That’s the kind of thing I have in mind when I say that “the position of a particle can be genuinely measured in BM”. I would be very interested to understand better exactly which parts of this you find wrong and/or so fraught with dubious handwaving as to be worthless. Is it for example that the measuring device is treated so schematically (as basically just a single particle, the pointer, with all the real details of the physical structure and operation of the device mocked up with some special interaction Hamiltonian between the “particle” and “pointer” which, to annoy you maximally, I didn’t even bother to write down)? Or is it the assumption that the two wave packets under consideration don’t overlap at all? So that, in a more realistic treatment in which there is some small overlap, it could occasionally happen that the pointer moves Right when the particle actually starts out on the Left, and vice versa, so the measurement is less than 100% faithful? Or is the problem that you think there’s some infinite regress, since the pointer position will be just as observable/unobservable as the original particle, so that this kind of schematic analysis just moves the problem back one level without really solving it? Or what? I’d really like to understand better exactly what you see as problematic.
And then let me also clarify (again in the context of this simple example) what I meant to be saying about ordinary/operationalist/orthodox QM, when I accused it of just making up ad hoc rules on the fly. I meant, specifically, the need to apply “measurement postulates” (such as the collapse rule). That is, instead of treating the particle+pointer in a fully quantum way, which would obviously produce the entangled post-measurement state I wrote above, in which there is no particular fact about which direction the pointer is pointing (which I would say contradicts, or at least appears to contradict, what we see with our eyes in actual labs in this kind of situation), we treat the particle-pointer interaction as a “measurement” in which the normal dynamical rules (namely Schroedinger’s equation) momentarily fail to apply. And so we just say — in flat contradiction to what the unitary Schroedinger dynamics would apply — that the pointer, being classical rather than quantum, just magically ends up pointing Left or Right, with 50/50 probability, as a result of its interaction with the particle, which interaction also results in the wave function of the particle collapsing to either psi_L (if the particle magically points Left) or psi_R (if instead the particle magically points Right). Now maybe you will disavow this kind of “orthodox” treatment as not capturing what you, Reinhard, think is going on. If so, I’d love to understand better what you think is going on. But what I just described really is the orthodoxy — it’s what all the textbooks say, for example. And I don’t think anybody could dispute the claim that, compared to this orthodox treatment, the Bohmian analysis really adds something. It explains how the pointer ends up pointing in a definite direction, which (under the admittedly idealized setup assumed) correlates perfectly with the pre-measurement position of the particle, purely as a result of the two basic dynamical postulates, without any need for additional ad hoc “measurement postulates”. So let me re-assert my point from before this way: anybody who accepts this orthodox account, but who also criticizes BM for the allegedly hand-wavy and un-rigorous and unconvincing and ad hoc character of its analysis of this kind of measurement, is a hypocrite. Hopefully you can clarify exactly why this does not apply to you. =)
Hi Ken. I think I agree with your description of the situation and the problem and even your statement of what the solution must be:
“Nevertheless, for consistency’s sake, it must be true that some internal interactions are treated as boundary constraints, of one subsystem on the other. That’s the only possible conclusion: effective boundary constraints cannot just be at the beginning and end of the universe, they have to occur periodically throughout.”
But I would put it this way (and I’m not sure if this is just exactly what you meant to be saying, or something else entirely): it better turn out that the boundary conditions on S’ *imply*, via the application of the basic dynamical postulates of the theory, the same sort of “internal facts” that were instead imposed by hand, as boundary conditions, when you analyzed S. That’s, I think, the “block universe consistency” that’s needed.
But then, I think unlike you, I’m not at all optimistic that this can be achieved. You mention Rod’s theory as one example of how it could be achieved, but to me Rod’s theory is instead a very clear cut example of this *not* working out, at all, in the desired way. But then I admit that I remain fuzzy on what his theory is supposed to be saying, exactly — none of the stuff about getting rid of config space wave functions in favor of “spacetime local beables” ever made any sense to me, and it is still not clear to me how he intends to resolve the interaction/measurement problem that you described so clearly (my sense is that he wants to say that every interaction is a measurement, but that can’t be right — you can’t make literally everything in the block a measurement boundary at which you simply stipulate, by hand, what’s going on… there’d be literally nothing left for the theory to say).
And then your other proposed solution (treating large-entropy systems as dynamically privileged w.r.t. small-entropy systems) also strikes me as not too promising — it seems like just another way of trying to hide the standard vagueness and ambiguity pea, from ordinary QM, under some macro/micro terminological shell. That is, I don’t see how all of your prose descriptions of how it might work out (which sound nice, but to me are riddled with exactly the same sort of vagueness and ambiguity that one finds in standard OQM talk about how quantum systems evolve one way when they’re not interacting with a measuring device, but another way when they are) can possibly be realized in clean mathematical terms.
I mean, it’s not like I’m claiming to see with certainty that this’ll never work. It’s just that it doesn’t look promising to me. But I’ll of course be interested to hear about any progress that is made.
Since the issue of a retro-causal qtwo came up, I thought this might be a good place to mention Rod Sutherland’s model. I’m not at all convinced by a number of the claims that he’s made with that, but I still find his model interesting, in the sense that it provides a simple example of a retrocausal qtwo. Just have two universal wave functions, the usual one evolving forwarad in time from some big-bang-ish initial condition, and then the second one, evolving backwards in time from some ???- (maybe heat-death-) -ish final condition. And then I think the dynamics of the particle configuration can be defined to depend in a kind of symmetrical way on the two wave functions.
(Note that, as I finally learned after lots of discussion and confusion, this is not actually how his model works. But I think you can generalize his one-particle toy model into a qtwo in this way.)
Two quick points about this idea:
1. I’m pretty sure that the picture will give nonsense for all but the earliest and latest times. The particle configuration in the middle will be a big mess. Nothing like the macro-world we actually observe. So I think that, while interesting in so far as it’s maybe an example of a true retrocausal qtwo (but see 2.), it’s not an empirically viable theory.
2. I’m not sure it’s even retro-causal. This is really the main point I wanted to get at. Despite how I described it above, I don’t see why one should think of this theory as any more retro-causal than ordinary BM. It’s just that there are two wave functions, which jointly influence the particle velocities, instead of one. But so what? Whatever differential equation the new, supposedly backwards-evolving wave function obeys could just as easily be read as normal, forward-in-time evolution. Just because you solve some problem by specifying a boundary condition at t_final, doesn’t make it retro-causal. You’d have, I think, exactly the same theory if you instead had two wave functions that jointly influence the particles, one evolving forward in time from some kind of thermodynamically low entropy initial condition, and the other evolving forward in time from some high entropy initial condition. So my point here is: I literally lose sight of what it’s even supposed to mean to call a theory like this retro-causal. And so part of the big worries that I meant to be expressing before, is the worry that, at the end of the day, and in the context of something like a qtwo where you don’t sneak things in by treating observation/measurement in a special way, I’m really not even sure what retro-causality means. At some very abstract level, the theory just says what happens “in the block” (or maybe gives some kind of probability distribution over possible histories of what happens “in the block”). It makes me a little uncomfortable that not only the idea of retro-causation, but also the idea of forward-causation, kind of crumbles to dust from this point of view. But it seems to me that it does. Or might. So that’s the other thing I’m worried about. Is there anything left for retro-causality to even mean, if we zoom out from the toy models to something like a qtwo, where there are no longer any “external interventions”??
Responses to the excellent responses you all gave to my previous post…
Dustin: I think I agree with everything you wrote about measurement being special in some thermodynamic sense, this being bound up with our sense of agency and macro-causality, etc. Obviously this is tricky stuff and nobody would claim to have a solid grasp on how it all fits together. In any case, I agree that in general it’s fine for a toy model to treat measurement/observation differently. My worry is that it “feels” to me (somewhat vaguely) as if it should be considerably harder to generalize from a toy model to a qtwo in a theory with retro-causation. I’m not sure I can say what that’s based on. Maybe it’s just the sheer mathematical issues associated with even defining appropriate initial data / boundary conditions.
Ken: yes, constructing a theory of exclusively local beables is a goal we share, but I’m really not at all convinced that retro-causality is going to somehow help on this front. (In the discussion with Rod S, we never even really got into this part, but I’ll just say that I couldn’t understand at all how he thought his theory was going to achieve this.)
Then re: your “one last point”, I guess I am pretty impressed by how Bell’s (time-asymmetric) notion of local causality rules out a certain class of phenomena, namely, those that violate Bell’s inequality. So you’re right to pick up on some element of that kind of hope in my comments. But really I didn’t mean to insist on something like that. I’m more just concerned that (if — like Nathan but apparently unlike Dustin? — you want to use retro-causality to preserve some notion of locality) you can’t use that notion of locality to cleanly and finally diagnose different candidate theories as either consistent, or inconsistent, with the notion in question. So it seems rather empty.
Good point about confounding factors. So maybe my China/Boston example isn’t probative. But then it was just kind of a joke anyway. I’ll have to think more about whether your response here really undercuts my whole worry, or just shows that this silly example isn’t the best one for expressing it.
I look forward to any further elaborations/comments you have on my point (4)!
Nathan: thanks for chiming in and nice to hear from you. I am, as I said before, genuinely sorry that our final edit of the scholarpedia thing fell off the back burner. (I also quite liked that expression when it occurred to me!) And I was sorry to hear that you felt frustrated by all the discussions about this stuff. Probably you can appreciate that we also felt somewhat frustrated by them (and that this probably contributed to our non-excitement to make final changes afterwards). I guess it would be fair to summarize by saying that, for you, retro-causality is a really important and central issue that you thought should be addressed and acknowledged and made into a really important and central thread in the article… whereas, for all of us, really, it’s not that important and basically the kind of thing that, sure, ought to be explicitly acknowledged, at least once (but maybe just in a footnote), but needn’t be made a big deal of. In any case, given this basic disagreement over what is really crucial and important and what isn’t, there was bound to be some mutual frustration there. And I bet if you had asked for less you would have ended up getting more, if that makes sense. But, that’s all behind us (at least until we fish the thing out from behind the stove and put it back on the back burner).
As to your actual comments here… I didn’t really understand your parsing of the old Bell vs Shimony et al thing. I think it’s clear that everybody was just taking for granted that there was no backwards-in-time causation. That’s a pretty standard and normal and reasonable assumption, in most contexts, you have to admit! And then given that assumption, the discussion was about the assumption that Bell makes explicitly in deriving the inequality (the independence of settings and lambda. I think Shimony et al didn’t really understand at first that there was a separate assumption here (separate from local causality) so they thought they were refuting the claim that violation of the inequality proved violation of local causality, period. Whereas in response Bell had the opportunity to clarify that there is just an additional assumption here. Anyway, I think — assuming no retro-causation — calling this additional assumption “no conspiracies” is completely reasonable (certainly better than “free will”). So I guess I see that exchange as just a normal and perfectly reasonable and comprehensible working out of the fact that there’s an additional assumption here. You are obviously upset that none of these guys ever bothered to question the even-further-in-the-background assumption of no retro-causation. But your comments almost read as if you see this whole thing as something like a deliberate attempt to wrongly diagnose retro-causation as conspiratorial. I just don’t see that at all. Retro-causation (often or maybe) violates the assumption that gets called “no conspiracies”, and quite reasonably so, by people who don’t really take retro-causation too seriously. When you press us we’re happy to acknowledge that that classification is somewhat misleading since there may not be anything “morally” conspiratorial (to use Dustin’s apt description) in such models. But that doesn’t necessarily make us take retro-causality any more seriously than we did before.
I’m glad to hear we’re in agreement about the ultimate need for a qtwo.
I was confused by your remark that “locality should be understood as … a notion which is to be defined only in the context of discussions in which the causal arrow of time has already been accepted.” Did you say, two posts up, that (unlike Dustin) you “would like to use retrocausality to save locality”? Did you mean a time-symmetric notion of “locality” in the earlier comment (which, for maximum confusion, I quoted second just now)? I’d be very interested to know how you might define/formulate this symmetric notion of “locality”.
And then finally, you asked me if I’m persuaded? Of what, exactly? I certainly didn’t find anything in all these comments (nice and thought-provoking though they were) that fundamentally changes my attitude about retro-causality, if that’s what you meant.
I just wanted to highlight two ironies that I found in catching up with this thread.
1. Re: the “surreal trajectories”, I find it somewhat amusing that people who basically think it’s impossible to say anything coherent about what’s really going on physically at the microscale, are nevertheless quite certain that (in certain cases) what BM says is going on is clearly wrong. By what standard, exactly, is it being decided that what BM says in these cases can’t be right? I’m happy to agree with Dustin and others that the story is somewhat surprising or unexpected based on some naive classical intuition or whatever. But isn’t it completely obvious to everybody that there are more options open to us than just (1) our naive classical intuition turns out to be exactly right in every detail, and (2) we have to completely give up and say nothing about physical reality at the microscale? BM provides a clear picture/story of what happens, which is occasionally surprising or counter-intuitive in its details, but which nevertheless gives exactly the right statistical predictions for things that are directly observable. I don’t claim to know whether BM is right or not, but I think it’s a near-certainty that whatever turns out to be right will have this exact character (rather than (1) or (2) above).
2. Re: Reinhard’s criticism of Bohmian mechanics and/or Bohmians for using assumptions / approximations / hand-waving, when analyzing measurement and the emergence of macroscopic behavior, I guess (as Dustin already said) there is some truth there and maybe the Bohmians should accept it as a good challenge that our position would be stronger if we could make these sorts of analyses more rigorous. OK. But still, come on. However hand-wavy and approximate and unrigorous one thinks the (extant) Bohmian analysis of measurement is, isn’t it 100% crystal clear that the orthodox/operationalist treatment favored (e.g.) by Reinhard — in which literally new ad hoc rules are just made up out of whole cloth and postulated on no grounds whatever except that they seem to be needed because the basic micro-dynamical axioms started to output nonsense — is far far worse? The truth is that Bohm’s theory provides a theory in which it seems possible in principle to give a rigorous *analysis* of measurement. That is, compared to orthodox/operationalist perspectives, an incredible advance and achievement, and I think it is quite hypocritical for anybody who endorses the orthodox/operationalist perspective (which is just obviously much much worse in *exactly* this same respect) to criticize BM for the allegedly approximate/hand-wavy character of its analysis.
Bob, can you give a simple concrete example of the kind of thing you have in mind when you say that BM sometimes “gives the wrong answers” and/or fails to make correct predictions for certain (two-time) correlations? I’m pretty sure you are forgetting that what we actually have direct access to, empirically, are “pointer positions” and such things. So for example if there is some particle (in the 2-slit experiment or something) and BM tells us its position x(t), you might think the theory gives “wrong answers” for (e.g.) the correlation between where it is at t_1 (say, when it’s going through one slit or the other) and where it is at t_2 (way, when it’s hitting the detection screen). But if you want to analyze this kind of situation and compare to empirically measured correlations, you must include the measuring equipment and the effects of that measuring equipment on the particle. In particular, for example, the distribution of particle positions at t_2 will be different if you say that, at t_1, a position measurement was made (in which the position of some macroscopic pointer was arranged to become correlated with whether the particle in question went through the top slit or the bottom slit). I’m pretty sure you are just forgetting/ignoring this, if you think that there is something “wrong” with BM’s predictions for 2-time correlations. (Reinhard has also tried to make this same criticism of BM.)
Anyway, maybe that’s already enough to help you appreciate why actually the theory’s predictions are not at all wrong. If not, if you can give a concrete example of what you have in mind, I think it would be fruitful to talk through in detail.
Thanks Daniel — Yes, I saw (and read with interest!) your earlier comments above. It seemed (from what you wrote in #2791) that you were still thinking of the argument as really strongly suggesting (if not quite rigorously proving) that there is retro-causation, but then also reconsidering this. I didn’t really have anything to say in response to that. Then in #2828 it seemed like you remained somewhat conflicted… on the one hand you were saying that the strength of your argument lies in the fact that it’s not tied to any particular interpretation, but on the other hand you acknowledge that the argument doesn’t actually prove retro-causation. I guess I just meant to be continuing to prod the part of you that still feels like the argument does show/suggest/whatever retro-causation in some interpretation-neutral sense. I just don’t think that’s right. I think you get to that conclusion basically by making various assumptions (something along the lines of locality, something along the lines of no hidden variables, etc.) that I would consider anything but interpretation-neutral.
But in so far as at least part of you acknowledges that, while this scenario *could* certainly be explained using retro-causation, it could also be perfectly well explained without any retro-causation, I’m happy and have nothing further to add. =)
Hi Dustin — I finally got around to reading through the new version of your paper. I again found it very clear and very thought-provoking. Here are some questions and half-baked thoughts, in no particular order:
(1) Now I understand better why there was a little bit of confusion/disagreement in our earlier comments (above) about whether your model violates “locality” or rather “no conspiracies” (in the usual, anti-retro senses of these terms that, e.g., we elaborate in the scholarpedia article). I think it depends on whether one is thinking in terms of Bell’s 1976 formulation of “locality” (where the “lambda” lives in the overlapping past light cones of the measurement events) or instead in terms of Bell’s 1990 formulation (where the “lambda” lives in a slice across the past light cone(s) that shields off the measurement events from where the past light cones overlap). I think you were saying that the model violates “locality”, but respects “no conspiracies”, because you’re thinking of the lambda as the initial state, the anti-correlated spins you describe in your equation (3). That state is, obviously, independent of the settings a and b, so you are right. But one could also note that, in your model, the state of a given particle — not initially, but at some random intermediate time prior to its being measured — *is* correlated with the setting that is later used to measure it. So, from that point of view, (this other thing that one might quite reasonably mean by) “lambda” is indeed not independent of the settings, and the model would hence count as “conspiratorial” in that sense. (It is of course *also* nonlocal, in the 1990 sense!) I have some further half-baked thoughts / concerns about what’s going on here, but I’ll separate those into comment (3) below and end here by saying: does that seem right to you, or have I misunderstood something?
(2) So one of my big (but admittedly slightly fuzzy) worries about retro-causation, generally, is that it kind of defeats itself, in the following sense. Basically the whole point is to avoid spooky/antirelativistic action at a distance, by confining causal influences to (inside?) the light cones, but allowing influences to go both ways in time. Of course everybody understands that, if you allow this, then you can string a few such influences together to get multi-step (“zig-zag”) influences across spacelike separations. So, in a rather obvious sense, one does not actually *avoid* the scary sort of non-local influences by introducing retro-causality — rather, the most one could possibly hope for is to *explain* those non-local influences in a less scary (more relativity-friendly) way. So far so good? The worry I have about all this is just that it seems to make the new, temporally symmetric notion of “locality” extremely, uh, fragile. This comes up in your article at the end when you say that “a more natural desideratum … would simply be the absence of *direct* influences between space-like separated events.” (Emphasis added.) The worry, then, is that you could always add stuff to a theory that had *direct* influences between spacelike separated points, to convert those direct influences into indirect (zig-zag) influences. And so it seems like — to ever actually reject a theory as “not consistent with this time-symmetric notion of locality” — you would have to interpret that theory as being in some sense “the final word”, i.e., not subject to additions/revisions. By comparison, what is to me so interesting about Bell’s theorem, at least as it is understood outside the context of discussions of retro-causality, is that it rules out local theories *period*. If Bell’s result were instead along the lines of “if you understand ordinary QM as the final word, then you are stuck with nonlocality” it would be far less interesting. It would just be: nonlocality — unless you add hidden variables in which case you can get rid of the nonlocality. (Indeed, then it would really just be equivalent to the old EPR argument.) So the worry is something like this: as soon as you allow retro-causality, you basically *guarantee* that it will be possible to explain anything you want in a “local” (meaning now time-symmetrically-local) way — just keep adding more hidden variables to convert any *direct* spacelike influences into acceptable, zig-zag/indirect influences. Now I admit it would be unfair to just abandon the whole program on the grounds that, in some sense, it is obvious from the beginning that it should be able to succeed. If, for example, somebody comes up with a really simple and elegant and relativistic retro-causal “quantum theory without observers”, I would definitely sit up and pay attention. But still perhaps you can see how at some level I feel like the whole exercise is slightly silly, on the grounds that basically the thing you are trying to achieve (namely, locality in the time-symmetric sense) can never really be defined in a way that actually rules something out: anything that appears to be in violation of that sort of locality can always be converted into something that respects it by adding more hidden variables and zigs and zags.
(3) So in a sense what I meant to be saying in (2) is that the idea of saving locality by allowing retro-causality doesn’t really make sense to me, because retro-causality undermines (or at least seems to threaten to undermine) any clean distinction between locality and nonlocality. And then I have exactly that same worry about the other — “no conspiracies” — assumption in Bell’s theorem. That is, I worry that the idea of retrocausality undermines (or threatens to undermine) any clean distinction between a theory that is conspiratorial and one that isn’t. So that, as you can now see, is kind of what I was starting to get at in (1) above. Is your theory conspiratorial? Well, it depends… But just in general, stepping back, whereas there is some kind of strong reason to believe (if one excludes the possibility of retro-causation) that the states of systems which have been “causally isolated” (to some reasonable extent) in the past should be uncorrelated, there is no reason at all to think that systems which *have* had intimate causal contact should be uncorrelated. And if you try to time-symmetrize that notion, then obviously you end up saying that the states of systems which will interact in the future should be expected to be correlated. And isn’t that just why you say your model isn’t conspiratorial? Sure, the state of a particle (at some intermediate time) is correlated with the setting of the device that will measure it, but there is a clear and non-conspiratorial causal chain to explain that correlation: the post-measurement state of the particle is affected by the device, and affects the spins earlier in time. So again the worry is just: isn’t it obvious, from the beginning, that literally anything that would be diagnosed as conspiratorial (using the no-retro sense of the concept) could be given a non-conspiratorial explanation if one introduces retro-causation? For example, I just read an article about how the price of tea in China last year correlates perfectly with the mosquito population in Boston… Conspiracy? No! Both sets of events were causally influenced by the article I just read, so the correlation is explained in a happy local non-conspiratorial way. So, again, the worry is along these lines: it seems important to you to be able to say “this model is interesting because it respects a certain time-symmetric notion of locality and a certain time-symmetric notion of ‘no conspiracies’.” But I’m not really clear that either of those time-symmetric notions even means anything (i.e., even cleanly rules out anything). So (despite being quite interested and definitely not feeling certain about any of this) I remain somewhat unimpressed. Can you help convince me that the proposed time-symmetric notions of locality and “no conspiracies” really mean something?
(4) And then finally, the thing I kind of mentioned in the earlier comment and which is, unfortunately, an even bigger and more sprawling and more philosophical thought than the previous ones: I am concerned at the extent to which this model (and every other retro-causal model I’ve ever seen) seems to suffer from a kind of measurement problem, just in the sense of introducing special dynamical rules that apply to the preparation and measurement ends of the process considered. Let me put it this way. One of the things that I appreciate most about Bohmian mechanics (in contrast to ordinary QM) is that it is possible (and indeed, in some sense, as has come up in the exchange with Prof. Werner, *mandatory*) to think of Bohmian mechanics as a theory of the whole universe, with observers included as part of what’s described by the theory. Basically I want to demand that theories should be understandable in that way — as “quantum theories without observers” (to use Shelly’s term) — or I won’t want to bother taking them seriously. Now of course in building theories it’s fine to start with toy models about single particles, but my point is we should always keep in the back of our minds the question: is it going to be possible to scale this up into a “quantum theory without observers”? And, after a kind of sprawling email discussion I’ve had in recent months with Ken Wharton and Rod Sutherland, I have really started to worry about retro-causal theories in general with respect to this issue. I don’t want to try to speak for them here (hopefully they will chime in!) but the kinds of things they kept saying kept hitting my ears like this: “well of course you’ll never be able to achieve that — the whole point of these sorts of models, the whole thing that’s going to make this maybe work, is that you have to impose these measurement/preparation-related boundary conditions on subsystems all the time”. So it just started to feel like what they were trying to tell me was that one could never scale up these toy retro models into a “qtwo” in the way I would be hoping for. Maybe they’ll tell me I misunderstood, but maybe I can just pose the question to you (Dustin) in a way that relates it to your model. So, for example, you assume that when your spinning particles get measured, they get annihilated, and this (as you acknowledge) plays an important role in your analysis: if the particles were still around after the measurement (and the same dynamical laws that apply in the middle continue to apply!) then their spins in the distant future would continue to influence their spins in the past (or whatever the right time-neutral way to say that is), and (probably??) all the predictions and analysis you do so nicely in the paper would come out completely different and, well, who knows what would happen. And then I think there are similar worries on the front end as well: you just impose a certain kind of t=0 condition on the state of the particle pair, but would this even be consistent with the dynamics if you allowed the particles to have existed prior to t=0? To me at least none of this is obvious, and it starts to feel like, as soon as you move even an inch in the direction of “pushing back the boundary conditions” (so that more stuff — here I’m focussing on “the same two particles but over a bigger spacetime region”, but I’m also similarly concerned about including “more particles, e.g., those composing the preparation/measurement equipment” — is included in “the system we analyze”) everything you thought you had established in the simpler case is totally out the window and you have to start over from scratch without any particular reason for optimism. So, uh, does this kind of worry make any sense to you and, if so, can you say anything that would give me hope that interesting little toy models (like yours) should be expected to be able to be scaled up into serious, viable “qtwo”s? Because at present I’m not convinced there’s any basis for hope there.
OK, phew, I’ll stop there and look forward to any comments you (or others) have!
Ah, sorry! Thanks for clarifying. But in any case, I still think there is some unacknowledged assumption in your argument that makes you think you’ve established retro-causation, when in fact faster-than-light (but perfectly forward-causal) influences (such as in orthodox QM with a preferred frame over which collapse occurs, or in Bohmian mechanics) can explain the phenomenology in your example perfectly well.
“I certainly don’t consider … exceeding the speed of light.” I think that is the problem. The setup/scenario in question here is exactly the sort wherein Bell showed — making a few other assumptions (like that the future cannot influence the past, that experimenters’ choices about what to measure can be considered “free” in the relevant sense, etc.) — that faster than light causation is *required*. So … *of course* … if you just decide a priori, up front, to refuse to consider the possibility of faster than light causal influences, you will end up convincing yourself that there is backwards in time causation, or that free will doesn’t exist, or some such thing. But arguments with unadmitted premises are never good/convincing.
And by the way, if the surprising conclusion one does end up endorsing in this situation is that there are backwards-in-time (but non-super-luminal!) causal influences, one really does not thereby elude causal influences that exceed the speed of light, because one can always “chain” or “zig-zag” backwards- and forwards-in-time influences to produce a net (indirect) influence across spacelike separation. So, while there are admittedly some other ways of looking at this, the idea of trying to avoid nonlocality (in Bell’s sense) by endorsing sub-luminal but retro-causal influences, always struck me as silly. You don’t actually succeed, that way, in avoiding the thing one wanted to avoid.
Hi Dustin — First, I don’t think you’re “interfering” at all. I’ve found all of your comments to be extremely illuminating and on-point! Second, I know the kind of Vaidman/Gisin argument you’re referring to, and (not surprisingly) I agree with you that it’s really no argument at all if you’re willing to just take BM seriously. And I do see why you interpret Reinhard as thinking along these same lines — clearly the occasionally “surrealistic” character of the trajectories is part of, or at least related to, what’s on Reinhard’s mind. But I’m not sure that’s really the main point. I’ve said what I think the essence of his, uh, mis-application is, and as of right now, I still continue to think that. But… only Reinhard can know for sure whether the problem, really, is that he’s thinking of BM in the Frankenstein way I described above, or if he’s instead worrying about the trajectories being surrealistic. Maybe he’ll elaborate and we can make some progress towards mutual understanding…
Hmmm. I guess I thought the first few sentences constituted a kind of argument for why “the existence of [whatever] remains a hope — it is not supported by the evidence”. That is, I thought what you were saying was: supposing the Bohmian trajectories (etc.) to exist may allow me to account for what I observe, but this doesn’t imply that those Bohmian trajectories really exist; who can ever know? So, my point was, if that’s what you meant, then it seems (troublingly, to me at least) that the same exact reasoning would have you dismiss the empirical-predictive successes of the atomic theory as not actually constituting evidence that the atoms really exist.
Now, I’m happy to concede that the situations of the two theories, vis a vis evidence, are not exactly parallel. There are, arguably, several different candidate quantum theories (Bohm, GRW, ???) that can all account for our observations — whereas there was nothing like a distinct competitor to the atomic theory that was able to account for the same very diverse set of observations equally well.
But still, I don’t really understand, from your point of view, how the two situations are different in principle. There’s a theory that accounts for a bunch of observed facts, and contradicts no observed facts. Isn’t that some (if not “strong” or “conclusive”) evidence that what the theory says is actually true? If not, what other kind of thing do you consider “evidence”?? What kind of thing did the atomic theory do, with respect to the phenomena it made predictions about, that Bohm’s theory fails to do with respect to the phenomena it makes predictions about??
Hi Reinhard, Re: “gravitationally and electrodynamically invisible”, I think I understand what you meant, but I still think you are misunderstanding (or maybe it would be better to say misapplying) Bohm’s theory here. It really is, I remain convinced, just what I said in my comments in response to Richard: you insist on thinking of Bohm’s theory as a replacement for just the quantum part of the Frankenstein picture of the world you’re accustomed to from ordinary QM (I mean with the quantum part and the classical part gruesomely stitched together); I agree that if you think of it that way, it will seem pointless and stupid; but you should really try to appreciate that that is not the right way to think of it (not, at any rate, if you want to give it a fair hearing and try to understand what people who like it like about it).
Let me try to elaborate this just to make it as clear as I can (and so you can point out any mistakes I’m making in understanding your point of view). You wrote that, according to Bohm’s theory, “you should not take these particles as a source for the respective fields”. By which I think you mean the following: if I have some particle (or, say, a planet) here in the classical world, and I want to know how it will move, I figure out what the gravitational/electric fields are in its vicinity and then solve F=ma; to figure out what the fields are like, I add up the contributions from all of the sources; but if I treat the Bohmian particles (over on the quantum side of the shifty split) as sources, there will be cases where I get completely wrong predictions for the motion of the particle/planet; so obviously I shouldn’t treat the hypothetical Bohmian particles as sources in this way; which then means that the hypothetical Bohmian particles have no effects at all on me and the particles and planets over here on this side of the shifty split; which means I might as well simplify my quantum theory by just eliminating them. Is that a fair summary of your thinking?
The reason I think it’s wrong is that Bohm’s theory should be understood not just as a theory about “the quantum part” of some hybrid Frankenstein world, but instead as a theory about the whole world, full stop. And so if you want to know how some one particle affects some other particle or planet (or instrument pointer or your brain or whatever) you need to at least start by treating everything involved in a uniformly quantum (here, Bohmian) way. I think at this stage you just give up and dismiss the whole thing on the grounds that any such treatment (of, say, two planets colliding) in a “uniformly quantum way” will necessarily involve lots of idealizations and approximations and will therefore be, in your opinion, so “fuzzy” as to be completely meaningless. The Bohmian people see it differently, though, maybe because they are more comfortable with fuzzy things, or maybe because they are more able to appreciate that the details that are fuzzed over will not change the crucial points of principle. But in any case, to me at least, and I think to a lot of other people (but not to you, or at least not yet!), it is completely clear and obvious that a uniformly Bohmian-quantum treatment of two planets colliding, or whatever, will make perfect sense and will perfectly correspond to what we see in the real world: if there is some long-range gravitational attraction, but, say, something like a short range electrostatic repulsion, and the initial state (of the relevant particle positions and the wave function) is the sort that would give rise, for each planet in the absence of the other, to some more or less classical motion (nice wide gaussian wave packets or whatever), then what Bohm’s theory says is that the planets will speed up as they get closer together but then bounce off each other… just exactly the kind of thing we in fact observe happening. As I said before, I think it would be crazy to say that, according to the theory, the planets don’t affect each other (even if their interaction is “via” the wave function). And they are predicted to behave in just the way we observe such things to behave in such situations. So it is simply false to say either that the particles are pointless (in the sense that they don’t affect other things, other particles) or that if you do what you need to do to have the particles not be pointless, then you get wrong predictions. The wrong predictions you have in mind are simply *not* what Bohmian mechanics actually predicts. They are instead what some crazy Frankenstein theory that you have in mind, and that you mistake for Bohmian mechanics, predicts.
Thanks Lev, it is so refreshing to get clear and simple answers to these kinds of questions! I continue to have concerns about the view you’re advocating, and would love to continue probing you about them if you’re game, but I just wanted to say that it’s nice to get straightforward answers!
So, can you tell me about how you think of the wave function (quantum state) ontologically? There’s no way I know of to mathematically formulate the wf/qs such that it can be understood as just directly representing some physical things/stuff in the 3D space we take ourselves to inhabit (and if this were possible we wouldn’t be having this discussion about “m”, etc.!). For example, to the extent one thinks about the wave function as something like a physical field, it’s evidently a field in a very high dimensional (so-called) configuration space. Is that how you think of it? If so, the idea that the m-field (in 3D space) is just an emergent property of the wf, really concerns me. How can an emergent property of a thing that lives in one space, live in a different space? Where does the new (3D) space come from?? Or maybe instead I shouldn’t think of the emergence of the m-field in this way (as if it really comes into existence) but should instead understand emergence in a more psychological sense, as in: the m-field is “what the wave function looks like, to us, who are also built of it, from the inside” if that makes sense. That avenue also really worries me, as it seems to basically imply that the whole 3D world we ordinarily take ourselves to live in, isn’t actually real, but is instead a kind of delusion… It has a “brain in a vat” flavor to me. I wrote about some of these worries here
https://ijqf.org/wp-content/uploads/2014/12/Norsen-Bell-paper.pdf
if anybody is really interested. But probably the short version above is enough to give the essence of the concerns. Can you shed any light on how you think about these things, Lev?
Tell me how the following is unfair:
“Pragmatism is not incompatible with the realist program: but it is flexible enough to make room for alternative programs. Its central insight is that concepts are intellectual tools for coping with the world, and that we can create concepts and use them in a variety of ways in pursuit of our goals. One way of doing this is to create theories that posit [atoms]: if the theory works, you can hope the [atoms] exist. That, I take it, is the [atomist] program. But the problem with that program is that even if the theory is empirically adequate the existence of the [atoms] remains a hope — it is not supported by the evidence.”
=)
Dear Reinhard, I don’t understand what you find “Platonic” about “claiming reality for the particles and their trajectories”. How is this, in principle, any different from the claims that people made in the 19th century about matter being made of atoms?
You ask: “how would you convince me that we live in such a world?” I guess I would start by pointing out that the story told by the theory about how big, directly-observable, macroscopic collections of particles move, is consistent with what we see in fact happening. That of course doesn’t prove that the theory is right. But surely it counts for something — it’s enough that it should make one take the theory very seriously as a real possibility. You say Bohmians “don’t give a rule of how to make the connection to the real world”. But the connection is crystal clear: what the theory says about how (macroscopic collections of) particles (like pointers, etc.) should move, matches how we in fact observe them to move. If that isn’t what you’re looking for, what in the world are you looking for? What kind of connection between a physical theory, and the real world of direct perception, would satisfy you??
Your paragraph starting “I suppose…” contains several confusions/misconceptions about the theory. 1. There is no “averaging” of the “point distribution” involved. The particles have actual positions. There’s a definite configuration. That (not some average of anything) is the “real world matter distribution” according to the theory. 2. You say “the interaction is always with the wave function”. I think you mean that, according to Bohm’s theory, you (who are, of course, according to that theory, made of particles) cannot interact with the other particles (also posited to exist by the theory); you can only interact with the wave function. That’s just not right. I suppose you could say that in some sense the interactions between particles are mediated by the wave function. But it’s just ridiculous to understand the theory as saying that particles can’t interact with each other. 3. You suggest in particular that “the BM particles themselves are gravitationally and electrodynamically invisible”. That’s simply wrong. Maybe what you mean here is that the particles do not move (and do not influence other particles) according to the laws of Newtonian mechanics (with gravitational/electromagnetic interactions). That’s true. But just because something has a new, quantum dynamics doesn’t make it invisible. If there are gravitational/electromagnetic interactions in the Hamiltonian, then the particles interact gravitationally/electromagnetically, and are simply not “invisible” in the sense you mean.
I’ll stop there (although there are more confusions/misconceptions). But I’ll just highlight this comment, which I think is quite revealing: “This is precisely the virtue of the Heisenberg/von Neumann/whoever cut: It allows you to come to a theory that actually allows predictions.” I think it is clear that you are continuing to think about Bohm’s theory in exactly the (wrong) way I outlined in my previously-linked-to comment on the thread started by Richard Healey.
Hi Richard — I read through your “open_question…” essay last night. I enjoyed reading it, as it contains a very nice collection of quotes from Einstein, Bohr, etc. But I really just don’t get the pragmatic turn you want to take. As I understand it, your pragmatism does not just mean “sometimes we should maybe try things out and see what works and learn from that without worrying, immediately, about what it implies about what it implies about reality”. That I would be all in favor of, sometimes. But to me, that attitude is 100% compatible with the *ultimate* goal remaining to describe the world as accurately and completely as possible. Instead, it seems like you want to permanently and irrevocably give up on the goal of describing the world as accurately and completely as possible. And I just don’t understand what could motivate this. I agree with what Dustin wrote above: this (“realist”) attitude has been central to the scientific enterprise since its inception, and has, I think, demonstrated itself to be quite practical. It seems like the kind of thing you’d only contemplate giving up if you were backed into some kind of corner where you just had no option but to give it up. And of course people have often claimed that this is exactly the situation that we are backed into by QM. But literally every such claim is wrong, and rather straightforwardly demonstrably wrong (in the sense that Bohmian mechanics is a living breathing inspectable counterexample to all of these claims). So why should I abandon the realist attitude and adopt your pragmatism instead??
Ah, so you understand MWI/Everett as what Allori et al call “Sm” in this paper:
http://arxiv.org/pdf/0903.2211.pdf
Is that right? I’m still a little confused by how you talk about the ontology, though. Do you think of the m-field as something like an emergent property of the wave function (such that it, the m-field, doesn’t count as an addition to the ontology beyond the wf)?
I would be very interested to hear your talk, so do send me a link if it’s recorded, etc. I hear what you are saying about the local density matrices, but presumably you can appreciate that there are further (subtle and challenging) questions. For example, if the local density matrix doesn’t exhaust the ontology, then it is hardly persuasive to say “the theory is local because interventions over there do not affect the density matrix over here”. And (as I have written about elsewhere) I think there are real questions about whether the local density matrices even capture the part of the ontology that I think you have in mind when you say that it is/captures “ALL what is in a particular location”. One of the crucial things that is real (in the sense of being there in the wave function) is that there are connections between terms in the local density operator over here, and the one over there. (That is, a certain “piece” of the density operator over here is, so to speak, “in the same world/branch” as a certain other “piece” of the density operator over there.) But, sort of by construction, the collection of local density operators leave precisely these connections out, and hence what they omit is in some sense exactly the thing that (in the context of other theories) causes problems for nonlocality. So the whole argument seems a bit like a swindle.
And then I really just don’t have any idea how I’m supposed to understand mathematical operators (associated with spacetime regions) as describing some physical “stuff”. If you tell me tables are made of particles, that makes sense as a possibility. Or a constellation of spacetime-point “flashes” — OK, that’s weird, but I can comprehend it. Or maybe a table is a table-shaped region in which some field has a different value from the background value. OK, yes, that makes sense as a possibility. But if you tell me a table is made out of mathematical operators that act on states in some abstract Hilbert space, I literally don’t know what you mean; I don’t understand what in the world it could mean for a table to be made of such things.
But maybe this is off-topic for this thread. =)
Lev, yes, in Bohm’s theory the nonlocality is clear: if you have a pair of entangled particles, the velocity of one of them (according to the theory) can depend on a free choice (say, about some external magnetic field that you might apply) at the location of the other one. That is, something over here (the trajectory of this particle) depends on some distant intervention, according to the theory. So it’s not locally causal.
The thing I don’t understand about MWI is: what *is* there “over here”, according to the theory, that might or might not depend on some distant intervention? What really exists, physically, “over here” (in 3D space) according to the theory? If all you have is a quantum state (or wave function) it’s just not clear what ontology there is, if any, in 3D space.
I think maybe you meant to suggest that the local (i.e., existing-in-3D-physical-space) ontology is the local density matrices. Is that right? So then the idea is that what exists physically, in 3D space, “over here”, is some local density matrix/operator, and then it’s easy to show that this isn’t affected by distant interventions. Have I got that right? Assuming so, I might have follow up questions (such as how I should understand a mathematical operator as a description of something physically real, and whether the local density operators *exhaust* the ontology even though they don’t capture all of the structure that’s in the wave function (which I thought was what the theory said was real), etc.). But maybe I’ll pause there and just make sure I’m on the right track so far.
Dear Lev, Two quick (and arguably off-topic) points about your previous comment to me above (#2744).
First, you seem to be using the word “beable” to mean something like “hidden variable” (i.e., stuff postulated to exist in addition to the wave function). I understand Bell’s term in a different way, though — as referring to whatever a theory says exists. So for you, as an MWI/Everett guy, it’s not that you don’t “feel a particular need for beables”, but, I think, rather, that you see no need for beables other than the wave function of the universe (which, for you, is the one and only beable). In a way this is just a pointless quibble about how to use a word, but I wouldn’t want there to be any kind of misunderstanding (on the part of other people reading this exchange) about the fact that MWI/Everett does postulate that the universal wave function (and only that!) is physically real, i.e., I’d say, a beable.
And then second (and relatedly) you indicated that you prefer MWI/Everett over Bohm in part because MWI/Everett does not include action at a distance. I have for a long time found this claim (which Everettians always make) very puzzling. “Action at a distance” refers, of course, to the sorts of faster-than-light causal influences (influences outside of the future light cone) that Bell took himself to have established. The point is that it really only makes any sense to apply this notion (or its absence, “local causality”) to physical goings-on in ordinary 3D physical space (or 4D spacetime). But I simply don’t understand how you can claim that MWI/Everett is a local theory in this sense (if that is what you meant to claim?), or what you would even take such a claim to *mean*, when it is so unclear (as I think you acknowledged?) how the beable posited by MWI/Everett (namely the universal wave function) relates to anything like a distribution of matter in 3D space / 4D spacetime. Do you have some specific model/idea in mind for how we go from the quantum state / wave function of the universe, to some kind of story about physical processes in 3D/4D to which notions like “local”, “action at a distance”, etc., can even be meaningfully applied? Or maybe when you say there’s no action at a distance in Everett’s theory, you don’t actually mean that the theory is locally causal (in anything like Bell’s sense) but you instead only mean something formal, like that the equations defining the theory’s dynamics respect Lorentz invariance. That I would probably agree with. But then to me it remains far from clear why I should care about that, or what it has to do with relativity theory (and its claims, e.g., about the structure of 4D spacetime), when it remains completely unclear what if anything the theory is even saying about physical goings on in 4D spacetime. Anyway, can you help me understand what you have in mind with this claim that Everett avoids the kind of nonlocality that is present in Bohm’s theory?
Hi Dustin. I read some earlier version of your paper about this a year or so ago (probably when it appeared on arxiv or something??). I found it interesting but now don’t remember the details. Your comments above motivate me to want to understand it better, so I’ll try to take a look at the paper you posted on this thread (which I haven’t looked at yet) in the next couple of days. And then I’ll be happy to try to elaborate some of the reasons for my hostility to retrocausation — unless your model refutes those reasons, in which case perhaps I’ll keep them to myself instead!
Hi Lev, Thanks for the elaboration/clarification. I think we agree, about two things. First, yes, this setup probably should not be described as “counterfactual communication” according to Bohm’s theory since *something* (the empty wave) goes along the path through 1/2 and then causally influences the motion of the Bohmian particle below. And second, yes, I agree, different fans of Bohm’s theory (and perhaps sometimes the same one person at different times!) sometimes think/talk about the ontological status of the wave function differently. For me personally, one of the things that makes Bohm’s theory really attractive is the clear, intuitive, causal explanations it provides in exactly this kind of situation (similarly the 2-slit experiment, etc.). So I definitely tend to think of wave functions as physically real things — so much so that I am troubled by the ontological status of multi-particle (and ultimately the universal) wave function(s), and want to try crazy things like reformulating the theory so that only 1-particle wave functions appear as beables. That is to say, the things that attract me most to Bohm’s theory make it rather difficult for me to understand wave functions, not as physical waves, but instead as laws.
On the other hand, I can definitely understand the point of view of the people who (looking more at the fundamental formulation of the theory, in which there is only really one wave function, that of the whole universe) think of the wave function as more law-like (than beable- or field-like) in character. But then I am troubled at losing the intuitive/causal understanding of things like the 2-slit experiment and your example here. Of course, it’s not completely clear that one has to really choose one or the other. For example, one might say that the wave function of the Universe is best understood as a law, but then the one-particle (so-called “conditional”) wave functions that would figure in a Bohmian analysis of the 2-slit experiment, or your setup here, can perhaps be thought of as beable-/field-like. But to me that’s a bit weird. The “conditional wave function” in Bohm’s theory is just the universal wave function, evaluated at the actual (Bohmian) position of all the other particles. It’s like a single “slice” out of the Universal wave function. And… how can a single “slice” of a law, be a beable/field? That’s weird to me.
Anyway, yeah, if you are motivated here by the feeling that you sometimes get mixed signals or contradictory answers from Bohmians about whether one should think of wave functions as physical fields, or instead something like a law, that makes sense and I agree that this is worth discussing further. On the other hand, it should be noted here that these sorts of questions about how to understand the wave function aren’t as pressing for Bohmian mechanics as they are for some other theories — e.g., MWI/Everett, according to which the wave function is the only thing in the ontology. For Bohm’s theory, the matter we see around us (tables, chairs, trees, planets, etc.) is made of *particles* which are just unproblematically in 3D and can hence unproblematically build tables, chairs, etc.; the wave function has a somewhat secondary, background role; so it’s possible to understand quite a lot about what the theory says and how it works and how it explains the distribution of matter we observe, etc., without ever really resolving these questions about whether the wave function should be thought of as a law, or a field, or what. Whereas MWI/Everett, I think, has a long way to go to explain how we end up with tables and chairs and planets in 3D, starting *just* from a universal wave function.
Hi Nathan and Dustin —
Nathan, when I read this paragraph…
“I was also dismayed by the fact that retrocausation had been charaterized as conspiratorial (when I learned about it). Clearly, those who adopt this charaterization are taking the causal arrow of time for granted. Apparently their intuition is so firmly grounded in the macroscopic world that they just can’t really think in any other way. Unfortunately, even in those discussions which aim to carefully lay out all the assumptions involved in Bell’s theorem, this simple fact – that they take the causal arrow of time for granted – is not pointed out. However, if you ask them – which I am bent on doing – whether or not they’re assuming the causal arrow, they’re usually happy to admit that they are.”
…I couldn’t help but suspect you were thinking of the scholarpedia article on Bell’s theorem here! =) Maybe it will help Dustin and other readers to explain the situation there a bit? So Shelly Goldstein, Nino Zanghi, Daniel Tausk, and I wrote, at some point a few years back now, a big review article on Bell’s theorem for the website scholarpedia. We were lucky enough to get Nathan as a referee, and he made (among other comments/suggestions) the point that we don’t acknowledge, as explicitly as we might, that we are assuming no retro-causation. One of the effects of this (un- or at least under-acknowledged) assumption is then that the types of retro-causal models you guys are discussing here would violate what we call the “no conspiracies” assumption in that article — even though, as I think you are both entirely correct to point out here, such models may in fact not involve anything “conspiratorial” in the everyday sense of that term.
In any case, the sad truth (for which I can only apologize rather than offer any good explanation) is that going back and making a few small wording changes to that scholarpedia article, in response to Nathan’s good suggestions, has been on our joint to-do list for, well, about 5 years now. Somehow we just never got around to tweaking it (after some good in-person conversations about this stuff in Sesto a few years ago) and then it sort of fell completely off the back burner and is now hidden completely in a pile of dust and dead bugs behind the stove. Anyway, that little piece of history/sociology maybe explains what might otherwise appear as a slightly puzzling tone in Nathan’s paragraph that I quoted above. Is that fair Nathan? =)
Regarding the actual issues under discussion here, as I said, I agree with you guys (1) that there need really be nothing conspiratorial about a correlation between “lambda” and the “settings”, in the context of a retro-causal model and (2) that the assumption of no retro-causation should be made more explicit when it is being made, to avoid miscommunication and false impressions. That being said, I think I am among the “hostile” people that Dustin mentioned in his previous comment. That is, I just can’t really get myself to take retro-causality very seriously. Part of the stumbling block, for me, is that I can only even really understand what retro-causality *means* in the context of these sorts of toy models that treat different kinds of variables (like “settings”) in different ways. My sense is that somehow the very idea of retro-causation sort of crumbles away to dust in your hands as soon as you imagine instead a true “quantum theory without observers”, i.e., a theory that treats the whole universe in a consistent and uniform way (without, for example, any ad hoc “settings” that are treated as outside the system being described by the theory). I’d be happy to elaborate the thinking (half-baked though it remains) behind this sense, if it’s not at all clear why I’d say something like that.
And if it is at least somewhat clear, but you disagree with it, I’d be interested in hearing arguments intended to persuade me out of my hostility…
That helps a little, but I remain confused. You say that particles (for example) exist, but that the function of the mathematical objects we use to characterize them (wave functions, etc.) “is not descriptive but prescriptive”. OK, sure — but then how *can* one (literally, accurately, and completely) describe these particles (if I should even understand that word, “particles”, literally — and if I shouldn’t I want to know what I should say instead)? If something really exists, shouldn’t it be possible in principle to provide a description of it? And shouldn’t a supposedly fundamental physical theory, about these things, provide such a description??
It just seems that what you are saying comes down to renouncing the goal of saying what physical reality is actually like on the micro-level, and instead adopting some kind of instrumentalist/operationalist view of the goal of physical theories. Maybe that’s it and our “metaphysical prejudices” (i.e., our ideas about what the goal of a scientific theory should be) are just different.
Hi Lev, Thanks for this interesting contribution to the forum. I didn’t follow the controversy in your Refs [1-5] so perhaps I’m just ignorant of the context and hence missing the point. But my initial impression is that the whole question here is based on a kind of equivocation on the word “particle”. You define “counterfactual communication” as “communication without particles present in the transmission channel”. OK, so then is it “counterfactual communication” if I send morse code to my friend (on the other side of the lake) by means of ripples that propagate across the lake? Or is communication by means of information encoded in electromagnetic waves (taking here the perspective that classical Maxwellian electrodynamics is true, i.e., ignore photons) “counterfactual”? If the answer to those questions is “yes” then I suppose you are right that this simple setup involves counterfactual communication according to Bohm’s theory. But then I’d wonder why in the world I should care about this strangely and arbitrarily defined notion, “counterfactual communication”.
On the other hand, presumably, to whatever extent the idea of counterfactual communication is actually interesting, we should understand the word “particle” in your definition more broadly — basically as meaning “anything physically real”. In which case, obviously, sending messages using waves (water or electromagnetic) rather than particles, would fail to count as counterfactual communication. And in that case it seems like this setup, from the point of view of Bohm’s theory, would also fail to count — because although the Bohmian particle may not go through the arm of the interferometer that takes it past your mirror 1/2, *something* physically real (namely the “empty half” of the wave packet) does take that route. So there is a perfectly clear physical mechanism by which Bob’s choice about whether to place the mirror at 1, or 2, influences the subsequent motion of the particle.
That is, my reaction to your final question “Is it counterfactual according to the Bohmian perspective?” is “It depends on exactly what you mean — but surely there’s nothing puzzling here?!” But like I said, maybe I’m just missing what makes this puzzling…
Dustin wrote: “there seems to be a misunderstanding”.
That is my sense as well. Reinhard, it seems like you have a number of simple factual misconceptions about how Bohm’s theory works and what it says. Did you read the long comment on the other thread that I linked to above? If you have questions about how/why/whether the sorts of things I was saying there are true, it would probably be quite helpful to hash them out here. On the other hand, to me it seems rather pointless to just ignore the claims of the people who understand the theory well, and continue with the straw man type rhetoric against the theory. If you think we’re wrong about something, by all means call us on it. We can argue about it and at least maybe somebody else reading the exchange will learn something. But what’s the point of saying things like “Bohmian trajectories are unobservable as a matter of principle” when you know Bohmians don’t accept that as an accurate characterization of the theory?
Hi Richard, I read your post several times trying to understand your point of view, but I’m still just not sure what you mean to be saying. Can you, for lack of a better phrase, dumb it down for me a bit? It sounds like you’re saying that, according to “observer-free quantum theory”, the ontology (i.e., the stuff that really exists physically according to the theory) includes settings of switches and knobs, and currents, and presumably a lot of other macroscopic things/properties described in classical terms. Whereas wave functions (meaning, presumably, the typically microscopic things like individual electrons or atoms whose states are, in QM, described by a wave function) are not part of the ontology. Am I at least close to right so far?
What I don’t get is how this kind of picture isn’t just drowning in the sorts of problems Bell identified by noting that ordinary qm is “unprofessionally vague and ambiguous”, i.e., part of what’s usually called the measurement problem. Is there some clean, unambiguous way of saying exactly what, according to the theory, is real? It seems like you mean to say that big, macroscopic, classical things (whose reality nobody (sane) ever doubted) are real. But where, exactly, is the boundary as we move along the continuum from big/macro to little/micro? To me, as long as you can’t specify *sharply* what the theory says is real, I can’t really take it seriously as a candidate fundamental theory. And then this same feeling applies as well to the dynamics, which, it seems to me, inherits and amplifies whatever vagueness/ambiguity there is about ontology: if you only say something like “big/macro things are real, but little/micro things described by wave functions aren’t real”, and there are some equations for how the big/macro stuff behaves, and some other equation for how wave functions behave, and maybe some other equations to describe how big/macro stuff interacts with wave functions, etc., you can’t possibly give sharp unambiguous rules about which equations apply in which situations, until/unless you’ve got some unambiguous way to decide which kind of thing (or non-thing) you’ve *got* — when, say, what you’ve got is something mesoscopic. And then of course there is the general worry about what in the world it could mean to say that big/macro things are real, but the smaller and smaller pieces that they are made of cease to exist at some sufficient level of smallness.
But really I’m just expressing my concerns with “ordinary QM”. My sense is that, while your view has some kind of overlap with that, you mean for it to be somehow different and immune to these sorts of concerns. Can you help me understand better what your view is and why you think it’s immune to such concerns?
Just briefly, re: the point that an “energy measurement” (of the sort discussed above) doesn’t reveal the true pre-measurement energy of the particle… First, I don’t think it’s even clear what the true pre-measurement energy of the particle would be, according to Bohm’s theory. There is, in some sense, no such dynamically meaningful property according to the theory. (Of course, one could just make something up — as people indeed do — and call that “the energy”… but it wouldn’t, for example, be a conserved quantity… so there’s really no particular reason to define it in any particular way, and hence no particular reason to define it, or talk about it, at all.)
And then the more interesting second point about this: it shouldn’t be surprising that not every measurement can just reveal some pre-existing value of some associated property. We know, from the various no-go theorems (Kochen-Specker, Bell considered in a certain way, etc.) that at least some properties in theories like this will have to be “contextual”. Now often, in discussions of such no-go theorems, the idea of properties being “contextual” is regarded as some very strange kind of thing that would require a lot of obviously-implausible ad hoc put-in-by-hand fix-ups. But one of the really wonderful things about Bohm’s theory is that it shows how exactly the required sort of “contextuality” can come out, trivially, from a kind of brutally obvious dynamics, without anything even remotely resembling “implausible ad hoc put-in-by-hand fix-ups”. The particle is just guided by the wave function in the standard way, and this turns out to imply that, for example, if you “measure the energy” using some “time of flight” type procedure, you’ll get exactly the QM-predicted outcome statistics, and the outcome will be determined (once the completely particle state *and the details of the procedure by which the “measurement” occurs* are specified), even though the “measurement” isn’t really a measurement at all in the sense of revealing some pre-existing value of some dynamically-meaningful quantity.
My paper “The pilot-wave perspective on spin” discusses this point in some depth in the case of spin measurements, where the “contextuality” manifests itself in the fact that two distinct setups, which would both be regarded as valid ways of “measuring the z-component of the particle’s spin”, can give *different* outcomes even for the exact same particle-state input:
http://arxiv.org/abs/1305.1280
And then, yeah, I completely agree with you that there are lots of different potentially promising jumping-off points for our shared goal. Perhaps more on that later… =)
Thanks, Werner, for your contribution — and thanks, Dustin, for your comments (which I agree with completely). I wrote some comments in response to Richard Healey’s contribution over on this other thread:
http://www.ijqf.org/forums/topic/comments-on-bohmian-mechanics
Basically I was there echoing/elaborating what Dustin expressed by noting above that “the whole empirical content of [Bohm’s theory] is in the particle positions, i.e. the distribution of matter in space.” So people interested in this thread might want to check out that other one as well.
Richard, thank you for your stimulating contribution. I think you raise a number of extremely important points (that overlap with the issues raised by Reinhard Werner and Shelly Goldstein and by implication Max Schlosshauer). Of course I don’t really agree with your conclusion (that Bohm’s theory is plagued by a number of pointless/unobservable/metaphysical idle wheels, and is therefore a bad/unpromising/implausible theory) — but I applaud your efforts at raising these important issues in a direct and clear and forceful way!
There is a lot that could be said in response to, for example, your point about the need (in Bohm’s theory) to posit a dynamically privileged but unobservable foliation of spacetime, and your point about the existence of distinct but empirically equivalent guidance formulas (for particles in a Bohmian version of NRQM and for field configurations or particles in a Bohmian version of QFT). But I want to (perhaps just temporarily) set those issues aside and focus on what I think is the most fundamental of your points, and also certainly the one that causes the most widespread confusion about the theory. I mean the claim that the particle positions/trajectories — the “hidden variables” that are added to the normal quantum wave function — are unobservable in Bohm’s theory.
To begin with, you are correct that (basically) the exact trajectories — such as the trajectories one always sees plotted in Bohmian discussions of the 2-slit experiment — are not measureable/observable, according to the theory. (I say “basically” because one can quibble with some of your comments about weak measurement. As Einstein pointed out, the theory decides what can be observed. For sure, if one adopts the perspective of some more or less orthodox version of QM, the alleged “weak measurement of velocity” is not at all a genuine measurement of the velocity of a particle… there are no particles according to that theory! But if one adopts the perspective of Bohmian mechanics, actually those same “weak measurements of velocity” *do* count as genuine measurements. But really that’s not what I want to talk about…)
OK, so the detailed trajectories are basically unobservable. From this, I gather, you basically infer that the particles (whose exact trajectories are basically unobservable) are pointless — we could get the same empirical predictions out by just dropping the particles entirely, and just basing the empirical predictions on the wave function alone, as in ordinary QM. This, I think, is completely wrong. It is based, I think, on a completely wrong way of understanding what Bohmian mechanics is and is trying to do. I mean the idea that Bohmian mechanics is a theory that is basically just orthodox QM, but with some “hidden variables” added. I mean the idea that, for example in the context of the 2-slit experiment, one thinks of the particle source and the slits and the screen and the lab bench on which all this equipment is laid out (and so on) as some kind of given, “classical” stuff which is *not* treated quantum mechanically and hence just unproblematically exists in an unproblematically observable way, while only the particles being shot through the slits are treated quantum mechanically, with that quantum description (for Bohm’s theory) involving *both* a wave function *and* a definite particle position.
I would agree that, as long as you are thinking of Bohm’s theory in that way, the particles (and hence their exact positions/trajectories) are pointless. But, as I said, that’s just not the right way to think about it.
Instead, I think, one really has to take seriously the idea that Bohm’s theory is a theory of the whole universe — not just some one tiny little corner of the universe that one segregates off as “the quantum system”. It’s not just the particles being shot toward the slits which one should be thinking of as described by Bohm’s theory, but also the particles composing the shooter, and the barrier with the slits in it, and the detection screen, the lab bench that all this is resting on, the experimenter who put all that stuff there this morning, the entire planet where all of this is occurring, and … *everything*. The whole physical world (of everyday macroscopic experience), that is, is — according to Bohmian mechanics — made of these Bohmian particles. So while it may be true that exact detailed microscopic trajectory of individual particles is (according to the theory) not observable, it is just completely and utterly wrong to suggest that the particles are unobservable, full stop. Literally every time you open your eyes and observe something — a chair, a friend, a distant planet through a telescope, etc. — you are (according to Bohmian mechanics) observing (some macroscopic features of a large collection of) Bohmian particle positions.
From the perspective of Bohm’s theory, then, the suggestion that one could just get rid of the particles and still have some sort of viable theory, is insane. By getting rid of the particles, you’d be getting rid, not just of some invisible microscopic thing whose detailed properties are unobservable anyway, but of all the furniture in your house, and your house, and your friends, and yourself, and the whole Earth, and indeed the whole observable physical universe! Crazy. (I don’t mean to suggest here that no theory other than Bohmian mechanics — no theory without particles with positions/trajectories — could account for our observation of tables and chairs and planets and whatnot. Maybe after all those things are not made of particles, but are instead made of fields or flashes or strings or some other sort of local beable. The point is rather just that all that stuff has to be made of *something*, and — to count as empirically viable — a theory better posit the existence of some such something and then better make predictions, for how that stuff moves around and interacts in physical space, that corresponds to what we in fact *observe* happening to the tables and chairs and pointers and planets and people… That is, the point is not that you have to have particles specifically, but rather that if you think you can just dispense with the particles, without replacing them with anything else, and maintain the kind of empirical adequacy that Bohmian mechanics enjoys, you have somehow grossly misunderstood — grossly underestimated — the role that the particles play in the theory.)
Thinking that the particles in Bohmian mechanics are unobservable — and can hence be simply dispensed with — would be like an oceanographer thinking (say, on the grounds that the exact phase space point, of the entire collection of water molecules composing the ocean, is unobservable) that he might as well just dispense with the water molecules in his theory. If he does that, he’s just dispensed with the whole ocean, the whole really-existing (and unquestionably observable) thing he’s trying to study!
So the point is that one has to be careful. It simply does not follow from “the precise trajectory of an individual particle is, according to the theory, unobservable” that “the particles are unobservable” — let alone “the particles basically play no role at all, they are just idle wheels, and we can get along just as well by simply dropping them”.
There is of course a lot more to say, and a lot of details that can and should be argued through, but I think that’s enough to steer the discussion toward the “big picture” point that I think is simply being misunderstood when you (and, for example, Reinhard Werner) suggest that the Bohmian particle trajectories (qua “hidden variables”) are just pointless, functionless, dispensable idle-wheels.
Hi Ken, I’m not really sure what needs explaining here. I mean, one should really understand (“orthodox”??) Bohmian mechanics as a theory of the entire universe, whose ontology is (a) all of the particle positions and (b) a single universal wave function evolving according to Schroedinger’s equation. And that universal wave function, to be sure, is a function on the very high-dimensional configuration space of the whole universe. So while of course you can apply the theory to sub-systems within the universe, such as individual particles that are suitably decoupled from the rest of the universe, and hence get by with a one-particle wave function (that can be thought of as a field in physical space) in this kind of context, it should be kind of obvious from the outset that you can’t do this in general. There is, according to Bohmian mechanics, such a thing as entanglement, and so in general one is never going to get rid of configuration space wave functions completely. And so to whatever extent one cannot accept configuration space wave functions as part of the ontology of a theory, one just won’t accept Bohmian mechanics, and it doesn’t really matter exactly how many different kinds of situations there are where one can avoid this thing one doesn’t like.
That said, as you know, I share your sense that there is something a bit indigestible about physically real configuration space wave functions. Here I am unusual among people who like Bohmian mechanics — most others I think tend to view the (universal) wave function as more like a “law” than a “field” and so the idea that it is mathematically a function on configuration space doesn’t bother them much… whereas I, influenced in no small part by the very sorts of one-particle phenomena you raise here for discussion, where there is a really clear and intuitive physical story taking place exclusively in physical space, tend to think of the wave function as more “field”-like, which means I am quite bothered indeed by the idea of a physically real field on (what seems obviously like) an abstract, non-physical, space. So I remain ultimately not-fully-satisfied by the “orthodox” version of Bohmian mechanics I meant to be talking about in the previous paragraph. But where you seem inclined to just dismiss the whole theory on the basis of its having configuration space wave functions, I actually see it as by far the most promising jumping-off point for people (like me/us) who are concerned about configuration space ontology issues and want a theory whose ontology is exclusively in physical space.
Here briefly is how/why I see it as a promising jumping-off point. First, in Bohmian mechanics, what we think of in everyday experience as the physical world (the tables and chairs and cats and trees and planets we see around us) are made of *particles*, not wave function. And of course the particles in Bohmian mechanics live in ordinary 3D physical space. So basically (and unlike a lot of other extant candidate quantum theories) Bohmian mechanics already gives a really clear and coherent (and empirically adequate) account of the comings and goings of material objects in 3D space. The worrisome thing — the config space wave function — is a kind of secondary, behind-the-scenes player (unlike in, e.g., Everett’s theory, in which whatever worries one has about config space ontology are completely front and center). And then the second point: Bohmian mechanics, uniquely and under-appreciatedly, makes it possible to define single-particle wave functions (and I mean in general — not just for unentangled particles) and it is then possible to understand the Bohmian guidance formula as defining each particle’s motion in terms of its associated single-particle-wave function. These single-particle wave functions (technically called “conditional wave functions” in the literature) can be understood as something like fields in physical space, and so it is possible — in a sense — to recover the intuitively sensible stories that you and I both like so much in certain simple one-particle situations, in complete generality. That is, one can tell the story of the universe (according to Bohmian mechanics) by describing the motion of each individual particle, and regarding each particle’s motion as determined/guided/piloted by its associated “conditional wave function” (thought of as a field in 3D physical space). The problem is, the set of N conditional wave functions doesn’t contain all the information that’s in the universal wave function. (Obviously!) So the particles and the set of conditional wave functions can’t really be regarded as a complete ontology — this would not constitute a closed dynamical system. But to me this is not so much cause for despair, as a promising research program: find some other stuff (that can also be understood as living in 3D physical space) that contains the “missing entanglement information” (i.e., the residue of the universal wave function that fails to be captured by the set of N conditional wave functions) to supplement the ontology with, to produce a closed dynamical system that reproduces the particle trajectories of “orthodox” Bohmian mechanics, but without the universal wave function (on configuration space) being, as such at least, part of the ontology. As you know, I wrote a paper a few years ago showing one (ugly/implausible) way this can be done, as a kind of “proof of principle”, and have been doing some work with Xavier Oriols and other people trying to push the idea forward. It remains very much a work in progress, but, again, I think there is room for optimism here to whatever extent one’s goal is to get rid of config space ontology. Rejecting Bohm’s theory out of hand (just on the grounds that it has, in general, a config space wave function in it), and starting over from scratch in some totally different way, seems unwise if one just wants a “theory of exclusively local beables”, since Bohmian mechanics is, in some sense, really close to what one wants already.
(But of course you probably wouldn’t agree with that last sentence since Bohmian mechanics has what you would regard as an additional problem, namely the *dynamical* nonlocality. My project of searching for a re-formulation which gets rid of the nonlocal *ontology*, in favor of exclusively local beables, will certainly not get rid of the dynamical nonlocality. So if for you that’s a deal-breaker, then none of this will be convincing. But for me, it’s again unwise to regard dynamical nonlocality as a deal-breaker since, I think, we know, with certainty, from Bell’s theorem and the associated experiments that we need dynamical nonlocality no matter what. Of course, you dispute that because Bell and I don’t allow retrocausality — or more precisely, classify retrocausality as just an example of dynamical nonlocality — whereas you think that one can save locality by embracing retrocausality…)
And then finally, going back to your original post and following up a comment I made to you last week, I think the class of “experiments/phenomena that can be understood in Bohmian terms without any config space wave function” is a bit broader than you acknowledge in your post. Basically anything which ends with a position measurement of the particle in question, can be understood in the way you have in mind. This of course involves things like the 2-slit experiment where, literally, one just measures the position of the particle when it hits the screen. But one can also, for example, understand spin measurements in this way: you shoot a particle through a Stern-Gerlach device and assign a value to its spin based on … where it hits a screen behind the magnets. (So “measuring spin” is, or at least can be, nothing but “measuring position” after some suitable external fields are applied.) And velocity/momentum can also be measured in this same way using the so-called “time of flight” technique: if the particle whose velocity you want to measure is initially localized (by some potential well, say), just turn off the potential, let the particle evolve freely for a long time, and then measure its position; the distance it went (from where the well was, to where it was later detected) divided by the time you let it evolve for, is its velocity, and it can be shown that (in the large-time limit) this constitutes a perfectly valid way of “measuring the velocity”. Same for energy, etc. As I said at the beginning, I’m not sure this really matters, since you really can’t avoid entanglement forever (unless you get on board with the project I outlined in the previous couple of paragraphs), but maybe it’s helpful to realize that a perhaps-surprising number of different types of measurements really do (or can) just come down to a position measurement of the particle in question, and can hence be understood in the perfectly intuitive config-space-free way that we both like.
Hi Daniel, I don’t agree with the claim that “retrocausality is intrinsic to QM” — if that means that any viable quantum theory has to involve backwards in time causation. I made some comments about this over in the “Bohm’s theory” forum (somewhat directly in response to your comments above and the earlier paper they refer to, but also as a way of answering Max Schlosshauer’s prompt there):
http://www.ijqf.org/forums/topic/in-what-specific-ways-is-bohmian-mechanics-helpful
I will definitely be interested to hear your thoughts.
So… Rohrlich’s argument that “retro-causality is intrinsic to QM”. For some details, see Section II of Rohrlich’s paper “A reasonable thing that just might work”, which is here:
http://physweb.bgu.ac.il/~rohrlich/Bell50titles.pdf
The basic idea is as follows. Consider three people, Alice, Bob, and Jim, who share a bunch of GHZ-state particle trios:
|GHZ> = ( |+z>|+z>|+z> – |-z>|-z>|-z> ) / sqrt(2).
Rohrlich points out that if Jerry measures the spin of his particle along the z-axis, the remaining two particles (held by Alice and Bob) will be left in a product state (one of two possible product states, really, depending on the outcome of Jerry’s measurement). Whereas if instead Jerry chooses to measure the spin of his particle along (say) the x-axis, the remaining two particles will be left in an entangled state. So the idea is that Jerry can *control* whether Alice’s and Bob’s particles are entangled, or not. And this of course has observable consequences: Jerry can control whether (at least once the data are later appropriately binned according to Jerry’s outcomes) Alice’s and Bob’s measurements are, on the one hand, totally uncorrelated — or, on the other hand, so strongly correlated that they violate a Bell inequality.
So far so good.
But then Rohrlich goes on to point out that the above remains true even if Jerry’s measurement on his particle happens *after* Alice and Bob have already made their measurements and recorded their data. So it seems that Jerry can control whether or not Alice’s and Bob’s particles were entangled (at the earlier time of Alice’s and Bob’s measurements) — i.e., Jerry can control whether or not Alice’s and Bob’s outcomes violate a Bell inequality — by his free and *later* choice about whether to *later* measure his particle in the z- or instead the x- direction.
Here is Rohrlich: “[All this] nicely illustrates the fact that quantum mechanics is retrocausal…. On the one hand, there is no reason to doubt that Alice, Bob, and Jim have free will. Indeed the results of Alice and Bob’s measurements are consistent with whatever Jim chooses right up to the moment when he decides to measure [spin along z] or [spin along x] on each of his particles and record the results. On the other hand, there is no doubt about the effect (in Jim’s past light cone) of Jim’s choice. After Alice and Bob obtain the results of Jim’s measurements (within his forward light cone) they can reconstruct from their data whether their particles were entangled or not at the time they measured them. Thus quantum mechanics is retrocausal….”
It’s maybe not clear whether Rohrlich means to claim that the particular candidate theory “orthodox quantum mechanics” is inherently retro-causal, or instead the more general claim that *any* empirically viable quantum theory will have to be retro-causal. If the latter claim is intended, though, it is definitely false, and we can see that it is false by considering what is going on in this experiment according to Bohmian mechanics.
I don’t want to write out all the technical details (which are trivial anyway), so here’s the gist of it. The important thing to consider is the “effective [or here, equivalently, conditional] wave function” of Jerry’s particle at the time he ends up making his measurement. This is the “one-particle wave function” that, in Bohmian mechanics, can be understood as guiding the particle in question along its deterministic trajectory through the Stern-Gerlach apparatus (or whatever). See, e.g., my paper on “The pilot-wave perspective on spin” if these concepts are unfamiliar:
http://arxiv.org/abs/1305.1280
Anyway, in the case that Jerry is the first to make a measurement, the conditional wave function of his particle is such that (for the standardly-assumed statistical distribution of possible Bohmian particle positions within the wave) his outcome is 50/50 random, no matter what axis he measures the spin along. As a result of his measurement, though, the conditional wave function(s) associated with the other two particles change (non-locally, to be sure) and hence the subsequent trajectories of Alice’s and Bob’s particles are different from what they would have been had Jerry instead made a different (or no) measurement.
In the other case, though, where Alice and Bob perform their measurements first, Jerry’s outcome turns out *not* to be 50/50 random for all measurement directions. For example: suppose Alice measures her particle along the x-axis and Bob measures his particle along the n-axis (60 degrees toward the y-axis from the x-axis… just the kind of measurements we’d expect them to be making if they planned on seeing later if a Bell inequality was violated) and suppose that Alice and Bob both find their particles to be “spin up” along the measured direction (this will happen, according to Bohmian mechanics, some of the time, depending on the exact initial positions of the various particles). Then it turns out that the conditional wave function of Jerry’s particle is such that, if Jerry measures along the z-direction, his outcome is 50/50 random… *but*… if Jerry measures along the x-direction, there is a 25% probability that his particle will be “spin up along x” and a 75% probability that his particle will be “spin down along x”. It’s not 50/50 random at all.
To be sure, there is nonlocality here: Alice’s and Bob’s measurements change the state (meaning, here, the conditional wave function) of Jerry’s particle and hence (sometimes, maybe) cause it to emerge in a different direction from the Stern-Gerlach device than it would have (even for the same initial position of Jerry’s particle!) had Alice’s and Bob’s measurements been different (or not been done at all or had they come out differently). So there is non-local (faster than light) causation, but no retrocausality. So the claim that the phenomena in question require retrocausality is simply wrong. The feeling that there is somehow something retro-causal going on, is in fact just a result of the false assumption that Jerry’s measurement outcome is “really 50/50 random” when, in fact, in the relevant cases, it’s not. What maybe vaguely looks like retro-causation from some perspective is instead, from the perspective of Bohm’s theory, just a matter of biased post-selection.
Some random notes about all this:
* Ordinary QM, with nonlocal collapse, also provides a (rather parallel) way of understanding why retrocausality isn’t required in this kind of situation. I say it’s “rather parallel” because what I said about the Bohmian conditional wave function of Jerry’s particle above is just exactly the same as what ordinary QM would say happens to “Jerry’s particle’s wave function” after Alice’s and Bob’s measurements collapse the overall 3-particle state. Of course, I prefer the Bohmian account, even for this polemical purpose, because, well, Bohmian mechanics might actually be true.
* The same exact ideas apply (in almost exactly the same exact way) to the delayed choice quantum eraser. There too, there is (at least according to Bohm’s theory) no backwards-in-time causation. There may be faster-than-light causation (depending on exactly what quantum eraser setup one is talking about) but really the appearance of retrocausation is fully explained in terms of biased post-selection.
* And finally note that the basic idea here is really quite simple. Roderich Tumulka linked above to Bell’s nice article about Wheeler’s delayed choice (thought) experiments, explaining how there’s really nothing retrocausal (or, frankly, nothing the least bit weird *at all*) going on, according to Bohm’s theory. That’s definitely worth reading/reviewing. And here’s another simple example that I think brings out (what is, from the Bohmian point of view) the error in Rohrlich’s reasoning quite simply. Consider the EPRB situation — a pair of spin-1/2 particles in the singlet state. Suppose Alice and Bob are just both measuring their particles spins along the z-axis. The outcomes are of course perfectly (anti-) correlated. Well, you might argue as follows: “suppose Alice measures first and Bob measures second; Bob’s measurement outcome is 50/50 random (because QM); but the results are perfectly (anti-) correlated; so it must be that Bob’s result retro-causally affects the state of Alice’s particle, prior to her measurement, and hence affects the outcome of Alice’s earlier measurement!!” But of course that is silly. I mean, that’s one logically possible story, I suppose, but it’s hardly required. It’s perfectly possible to explain everything without retrocausality — by just allowing that Alice’s measurement (which happens first!) non-locally influences Bob’s particle (and hence the outcome of his subsequent measurement). See my paper on spin, linked above, for details about this case. I think, when the dust clears, it really is equivalent to Rohrlich’s more complicated case — the error in both arguments comes down to assuming (unjustifiably and wrongly, from the Bohmian point of view) that some later measurement is “really 50/50 random”.
Hi Max, Thanks for your submission, which I think is an excellent one for stimulating some discussion about what people who like Bohmian mechanics find valuable about it. I have actually found Bohmian mechanics very illuminating in thinking about several of the things you mentioned, and when I first read your submission I thought “It would be good to write up a little note explaining, for example, how Bohmian mechanics helped me stop losing sleep over the delayed choice quantum eraser.” As it happens, I then went looking around some of the other discussion threads and found a nice post by Daniel Rohrlich, in the “time-symmetric theories” forum, where he claims that “retro-causality is intrinsic to quantum mechanics”. The example turns out to be closely related to the quantum eraser (and some other things) so I figured I’d kill two birds with one stone and talk about Rohrlich’s specific example instead.
But first, I wanted to say something more general about why I like Bohmian mechanics. It’s true that it provides, I think, a very illuminating concrete model against which to judge claims of the form “Quantum mechanics conclusively establishes X!” (where X is, for example, the failure of determinism, or the existence of parallel worlds, or the metaphysically creative role of observation or consciousness, or …). That is, Bohmian mechanics provides a very convenient way of seeing that many, many claims that one hears about what QM proves/establishes/requires, are actually just wrong. The available data simply do not require those things. This sort of debunking is the purpose to which I’ll put the theory in my comments about Rohrlich’s example below. But to me that’s kind of a polemical side benefit, rather than the central reason that one should actually like the theory. That central reason is: it might be true. And what I mean by that is: Bohmian mechanics is the kind of theory that might actually be “the final word” about how things really work (at least, to the extent that you pretend that non-relativistic QM is empirically adequate). Orthodox QM, by contrast, has no chance (in my opinion) of being that final word — it is to me just unbelievable that there are really two different worlds (one “quantum” and one “classical”) with distinct ontologies and dynamics and then only vaguely-defined ad hoc rules for how those two worlds interact when they meet. That just can’t be right. It’s instead clear that orthodox QM is some kind of phenomenological makeshift that, virtuous and accurate though it may be in terms of its predictions, simply can’t be the final description of what’s happening in the world.
Of course, Bohmian mechanics is not the only such viable candidate “description of what’s happening in the world”. There are a couple of different flavors of GRW type theories that are viable candidates; maybe (I’m skeptical, but maybe) Everett’s many worlds picture is such a candidate; and of course there are presumably many such viable candidate theories that we just haven’t thought of yet.
I’m not sure if Bohmian mechanics is (again leaving aside issues about extensions to QFT, etc.) true. But it *might* be true. And that mere possibility is a remarkable achievement — something that many/most extant “interpretations of QM” cannot match. This is, in a sense, the same point that people have in mind when they claim that Bohm’s theory solves the measurement problem. But that, to me, is too negative a way to put it, so I’m trying to rephrase that point in more positive terms. Anyway, that’s what I regard as the central virtue of the theory. It might actually be true.
Since this preamble got long, I’ll comment about Rohrlich’s example in a separate post…
Hey, I agree with Howard about something! Namely: the actual EPR paper is quite convoluted. Re: Matt’s #s 4 and 5, I actually think somebody would have a much easier time reconstructing a rigorous version of EPR+Bell by reading Bell alone (and perhaps the cited Einstein!) than by reading Bell plus EPR. Bell’s recapitulation of the EPR-ish argument, while imperfect, gives a much clearer sense of “how it basically goes” than the EPR paper itself.
Otherwise, I can agree with Matt’s 9 uncontroversial items, and I look forward to his writeup of EPR+Bell.
Matt, re: #1866, good, it seems like we’re basically on the same page. I suspect there remains some lingering disagreement having to do with whether Bell (in ’64) meant to define locality with his Einstein quotations and/or how similar the Einstein quotation (what Howard calls “no telepathy”) is to (Bell’s later formalized) “local causality”. But I can’t quite put my finger on what gives me the feeling there’s some unresolved dispute there, and, well, I’m a little exhausted by all of this. Oh, I also don’t quite understand what you’re alluding to in the PS. If at some point you want to take time to explain the “EPR-ish arguments based on `localistic’ premises weaker than local causality” business, I’d be quite interested.
Howard, Bell’s paper “AS IT IS WRITTEN” includes repeated references to Einstein’s Autobiographical Notes. Prima facie, Bell intends these to explain what he means by “locality”. I agree that he says things elsewhere in the paper that could also be interpreted as attempts to define “locality”, and that are definitely different, so there is something of an interpretive puzzle. I’ve repeatedly offered a candidate solution: the Einstein quote captures his *generalized* notion of “locality”, whereas the other remarks merely characterize the specific implication of locality that he applies to deterministic theories. It continues to baffle me that you can claim to be trying to understand Bell’s paper “AS IT IS WRITTEN”, but simply ignore the repeated Einstein citations. You pretty much said, on the other thread, that if you’d had a chance to edit the paper you would have simply removed those citations. It just increasingly seems to me as if you’ve done this editing in your mind and are working hard to interpret that fantasy version of the paper instead of the version Bell wrote.
I mention this here because, while I agree completely with Matt that there is an ambiguity about how to formalize and generalize some of Bell’s other remarks in the context of not-necessarily-deterministic theories, I don’t think that’s the important issue to be arguing about. It’s a pointless little side show. The crucial question is whether one regards these other remarks (which are unambiguous *only* for deterministic theories), or instead Bell’s repeated quoting of Einstein’s statement from Autobiographical Notes, as capturing his basic, generalized notion of “locality”. What exactly is your argument, based on the paper “AS IT IS WRITTEN”, against taking the Einstein citations as expressing a generalized notion of “locality” that Bell means to endorse?
Hi Matt. Yes, I agree with you. Refuting B’ (i.e., refuting Bohr’s “completeness doctrine”) and refuting B (i.e., establishing deterministic hidden variables) are distinct, though of course closely-related. (In case it’s not obvious, here by “refuting” I mean “subject to the assumption of locality”. Post-Bell — i.e., once it is established that locality is just false — one would no longer say that any EPR-ish argument actually proves that the completeness doctrine is false or that determinism is true.)
Anyway, note that just after the bit you quoted, Einstein goes on to say: “The statistical character of the present theory would then have to be a necessary consequence of the incompleteness of the description of the systems in quantum mechanics, and there would no longer exist any ground for the supposition that a future basis of physics must be based upon statistics.” I read this as implying that rejecting B’ somehow leads inevitably to rejecting B (and accepting A, i.e., a deterministic — not “statistical” — hidden variable model). So I think Einstein is not quite as careful as you suggest, “to say that he is only ruling out B’.”
In any case, the missing link is just the EPR paper/argument, which does of course explicitly involve the perfect correlations and makes it easy to see that, indeed, locality requires abandoning not just B’ but B. Your type of model “C” provides a nice way to see why. So consider a hidden variable type of theory in which there is some residual, local, randomness. That is, assume each particle (in some appropriately entangled and spatially separated pair) has its own “real factual situation” that generates probabilities for possible outcomes of a measurement (independently, of course, of what is done with the distant particle). Then the probability for a certain joint outcome will just be the product of the individual probabilities (independence). But we can only get perfect correlations out this way (i.e., joint probabilities of either 1 or 0) if all of the individual probabilities are themselves 1 or 0. We really need local hidden variables to *determine* the individual outcomes. Their merely “tilting the balance” in a certain direction (tilting, that is, “past” whatever probabilities would have been assigned on the basis of some quantum state) doesn’t help, if the goal is to explain the perfect correlations locally.
Of course, there are lots of ways to express that same basic argument. There’s a somewhat convoluted version of it in the actual EPR paper. It’s the same as the “Einstein’s boxes” argument that Einstein (and others) give in various places. And of course — most relevantly here — it’s the argument that Bell sketches in the first paragraph of section 2 of his 1964 paper.
Travis
Thanks for the comments, Matt. I’m of course happy to hear that you found the paper thought-provoking, and in particular happy to hear that it helped you realize that there is no basis for thinking Bell meant Parameter Independence by “locality”. As should be clear, I completely agree with what you say about the “mathematically rigorous part of the 1964 paper”.
Of course, as I imagine must also be clear, I would want to stress that this “mathematically rigorous part” is the second part of an overall two-part argument, the first part of which is indeed treated in a disappointingly non-mathematically-rigorous way. But just because the first part is not laid out very rigorously, doesn’t mean it isn’t there. As I have tried to argue, I think it is quite reasonable for an author who takes himself to be adding a further step to something that has been previously established by others, to merely summarize (and cite) the relevant earlier work, without feeling the need to rehearse it in meticulous detail. That’s how I read Bell’s 1964 paper. Of course, with the benefit of hindsight, we can now say that this was a huge mistake: Bell was quite naive to think that others would agree with him about Einstein/EPR having really previously *established* that *only* pre-determined values can explain the perfect correlations locally. But however clear it is that the first part of Bell’s 2-part-argument was presented in a disappointingly sketchy way, however clear it is that Bell was naive or foolish, etc., I think it is equally clear — indeed, perfectly and totally clear — that Bell in 1964 did take Einstein as having previously established that deterministic hidden variables are *required* by locality, such that one could not legitimately claim to avoid nonlocality by rejecting determinism. So if one simply ignores this part one is fundamentally misunderstanding what Bell did in 1964.
I stress this background point here because it seems extremely relevant to the question of deciding what Bell meant by “locality”, which seems to be your primary interest here. You write that “we can only speculate on how the 1964 Bell would have formally defined locality”. I disagree. I think he provided a quite explicit general definition of locality three times in his 1964 paper, by citing the quoted sentence from Einstein’s Autobiographical Notes. Maybe that’s not formal enough for your tastes (and of course I agree that it was really good progress when Bell later formalized this!) but you can’t reasonably deny that Bell intended this Einstein quote as providing a generalized definition of “locality”. Something like equation (3) in my paper — i.e., what he actually uses in the “mathematically rigorous part” of his paper — is merely an *implication* of this generalized concept of locality to the particular kind of deterministic theory that is under investigation in the “mathematically rigorous part”.
As to your last point, about whether Einstein’s A and B exhaust the possibilities, I think it’s pretty clear that he intended for the two options to be jointly exhaustive (and that they are!). Here is Einstein: “But what about the single measured value of q? Did the respective individual system have this q-value even before the measurement?” Note that it’s a straightforwardly yes-or-no type question. And then the options A and B are clearly identified with these respective answers: “A. The individual system (before the measurement) has a definite value of q … for all variables of the system, and more specifically, *that* value which is determined by a measurement of this variable.” And then: “B. The individual system (before the measurement) has no definite value of q…”
So I don’t see how there could be some third possibility. Either (to use more contemporary terminology) there is a hidden variable that determines the measurement outcome, or not.
I don’t really understand your concrete proposal for a third alternative (“the real factual situation of the individual system allows us to predict measurement outcomes better than ψ, but still not with certainty”) since it is phrased in terms of our ability to predict measurement outcomes. But if what you have in mind is a kind of model in which there is some hidden variable which “tilts the balance” in favor of a certain q value, but without determining it (say, it makes the probability 90% that a certain outcome will be realized if a measurement is performed), I just don’t think that will work. Such a model, if local, would fail to predict *perfect* correlations.
Travis
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.
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.
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?
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.
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.
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…
