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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!