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OK, good. But I guess I’m inclined to stick to my guns here — the relative positions of the particles determine the measurement outcome. Suppose the first particle is the one whose spin is being measured, and the second particle marks the top of the detection screen. Then if the two particles end up close together, the incoming particle is spin-up, and if they end up far apart it is spin-down.
Your challenge is that since the spin-up and spin-down wave packets extend over the whole of space, the two particles might be associated with the spin-down wave packet even if they are close together. But I don’t know how to associate a Bohmian particle with a wave packet. A Bohmian particle is just a location in (configuration) space, and as such is influenced by all wave packets that are non-zero at that point. The particles aren’t associated with either packet, and neither packet picks out the “actual” measurement result (the particle configuration performs that job).
I think maybe the rhetoric of “empty” and “occupied” wave packets in the context of Bohm’s theory (which I’m as guilty as anyone for using) is misleading, and should be retired.
Thanks for the interesting post, Shan. Let me attempt to respond to your main argument. It is true that simply specifying the position of a Bohmian particle doesn’t pick out a measurement outcome. But neither does specifying the position of a classical particle. You need to specify the position of the particle relative to the apparatus — if it hits the top half of the detection screen it is spin up, and if it hits the bottom half it is spin down. But a Bohmian can interpret the screen as a set of particle positions too. That is, the outcome supervenes on a pattern among a number of particles . (And probably on the behavior of the particles over time, too.)
Thanks Ken. Maybe I should clarify my clarification: What I had in mind was something like the ontology I sketch in here:
http://bjps.oxfordjournals.org/content/57/2/359.short
The measurement direction constitutes the retrocausal influence from the measurement back to the source, and the actual spin value constitutes the forward-causal influence from the source to the measurement. Which sounds like what you meant by associating the hidden variables with particular directions, rather than the measured value. (Depending on what counts as the hidden variable.) If so, I’m fully on board with that. (This paper was written rather quickly, and some of the explanation is inadequate — sorry that it was so unclear!)I agree that it’s tricky to avoid trivializing the explanation in retrocausal stories (the explanation of the spin-up result is the spin-up result). And I agree with Travis Norsen that measuring devices can’t have a special role, so appealing to measurement to fix the boundary conditions has to be done carefully. But like you, I don’t see any reason it can’t be done. I touch on both these issues in the paper I mentioned above.
Anyway, basically I need to think more carefully about the ontology for retrocausal QM. But for present purposes, do you think it’s OK to say that there are several non-holistic options of the table, including your anomalous rotation account and Huw’s two-spin account?
Thanks, Ken, this is super helpful. I’ll definitely add the unconditional probabilities, as you suggest. And you’re right that I shouldn’t say that there’s NO sense in which preparation and measurement are the time-reverse of each other – I should say that they’re not entirely the time-reverse of each other.
Now on to your main point about intermediate measurements. First, I should clarify footnote 5 (and the sentence it attaches to). I shouldn’t say that the particle has spin properties for every direction in which its spin COULD be measured at R. Rather, what I meant to say is that it has spin properties for the direction in which its spin is ACTUALLY measured at R, whatever that direction might be (and footnote 5 provides the formula for assigning probabilities). Given that, I don’t feel so concerned that if you stick an intermediate measurement between S and R you change those probabilities. After all, you’ve changed the measurements that flank the source.
But you point out that the intermediate measurement can be “non-invasive” – it can simply divert the particle according to its spin in some direction, without any entropy-increasing action (like running it into a screen). You would rather not change the beables for such “measurements” (and, I assume reserve the term MEASUREMENT without the scare quotes for entropy-increasing interactions of a certain kind). It’s always a challenge to explain the role of measurement in retrocausal accounts without introducing a new measurement problem. I guess I’m committing myself to a particular view on measurement. Perhaps: a measurement of property p for a particle is any interaction in which the value of p becomes correlated with the position of the particle. This casts a pretty broad net (and has a special role for position, like Bohm does). So when you introduce a new SG device (even if there’s no entropy increase) then you introduce a new (genuine) measurement and you need to re-figure the probabilities. Are there problems lurking?
This is a very interesting idea. Here are a couple of questions about how it might work:
You write that “it seems natural to assume that the origin of the Born probabilities is the random discontinuous motion of particles”. Certainly some kind of reconciliation of your interpretation of the wave function with the Born rule is required. If a position measurement consisted of sampling the position of the particle at an instant in time, I can see how this might go. But measurements take place over finite intervals of time. How could that kind of process pick out one position (with the relevant probability)?
Second, how is interference handled in your approach. Presumably, in a two-slit context, the particle occupies the top-slit wave packet half the time and the bottom-slit wave packet half the time. But then how is interaction between the wave packets to be explained if the particle is always in either one or the other? The particle presumably can’t interact with itself (as you remark elsewhere). Any suggestions?
Thanks for your helpful comments, Robert. I should make it clear that Bell’s view of what the beables are is not the only view, or the best. Spontaneous collapse and Everettian theories I think agree with the consistent histories approach that subspaces of the Hilbert space are the beables.
And you are right that I should clearly distinguish retrocausation from retrodiction. The latter certainly doesn’t entail the former, and I don’t want to seem to be implying otherwise. I will read the article you suggest.
Good. I guess I don’t see why causality in a block world should (in general) be superfluous (or inconsistent). You can ask “Suppose this measuring device setting had been different — would anything earlier have been different?” If yes, then you’re retrocausal. But what I suspect is that it’s hard to answer this question in RBW because of the unmediated nature of the energy exchange. That is, I suspect that it’s not the block world that makes causal talk inappropriate, but something else about your model. Does that sound right?
Thanks, Matt, that’s helpful.
About Bell and K&S: You’re right that the theorems apply equally to theories in which the wave function is ontic. I should make that clear. They constrain property ascription in Everett, for example. But Everettians can shrug their shoulders – of course you can’t ascribe pre-measurement properties to systems corresponding to their unique outcomes, because measurements typically don’t have unique outcomes. But even if there’s no special obstacle for epistemic views (compared to ontic views), the theorems still constrain epistemic views. What’s more, epistemic views invite the picture (although they don’t mandate it) that the wave function represents our knowledge of pre-existing properties that are revealed on measurement. This is precisely the picture that the theorems make trouble for.
About interference: I confess that I don’t really know what to make of Spekkens’ toy models. Sure, you get interference, but how exactly? You start with a principle about knowledge – that knowing more than half the information is ruled out. But without knowing why that principle holds, it’s hard to judge whether this is really an epistemic view. Bohm’s theory has restrictions on knowledge too, but the way in which those restrictions are brought about involves the wave function pushing the particles around (on a literal reading at least). I’m not sure that Spekkens can simply assert that this kind of restriction on knowledge can arise without the state being a causal entity in some sense. So I guess I’m not convinced yet that Spekkens has shown that you can get interference out of a wave function epistemic theory.
OK, good. As long as we’re all clear on the differences between diachronic and synchronic holism, I have no objection! Thanks again for the input.
Aha! Now I get it. Sorry to be so slow!
Yes, that’s nice, thanks for the suggestion. Here’s my only worry. In the regular EPRB case (fig 2), we need a holistic property of the pair (of two points of space on a hyperplane) because Bell’s theorem tells us that you can’t make do with intrinsic properties of the two points alone. But in the retrocausal case (fig 1), there’s no apparent need for a temporally holistic property — of two points of time along a world-line — because Bell’s theorem doesn’t apply. So in what sense, exactly, is the retrocausal case temporally holistic? I know you have to treat the system as a temporal whole in assigning properties to the temporal parts, but the properties themselves don’t seem to involve any holism. Is ther a way to make the parallel between temporal and spatial holism closer?
(BTW this is very helpful!)
I have a bunch of questions and comments, but let me start with “Is RBW a retrocausal account?” You cite Geroch approvingly saying that nothing changes or moves in the blockworld. But that doesn’t seem right to me. Change/motion only make sense from the perspective of a world-line — the properties of one temporal part of the world-line are different from the properties of another temporal part. Of course the 4D world-line itself doesn’t move or change — that would be a conceptual confusion. But their contents change — in fact, that’s all that change means. But if you buy that, then why resist saying that RBW is retrocausal? Causation is something that appears from the perspective of a world-line. Of course, causation is a lot harder to characterize than change! But the fact that RBW explains a 4D situation “all at once” is no barrier in principle to characterizing the causation implicit in it. There may be other barriers to causal talk though, like the “unmediated” exchange of energy between emission and absorption, or the lack of counterfactual definiteness. But I’d be interested to hear what you think.
Thanks for the clarification! Some questions: Can I gloss “undirected spacelike link” (in figs 2 and 3) as “holistic property”? If so, then figs 2 and 3 have them, and fig 1 doesn’t. But you say fig 3 “strikes me as also ~holism”. It strikes me as holism!
But maybe you mean that fig 3 is holism and fig 1 isn’t (according to me), and yet (as you point out) fig 3 can be made as close to fig 1 as we like (by moving points p and q close to S). That’s right, but there’s still an absolute distinction between spacelike and null, and that’s what’s doing the work (it seems to me). Fig 1 has no undirected spacelike links, so that’s how it escapes holism.
Am I getting closer?
Thanks Mark. I agree that there’s something that smells like holism in retrocausal approaches. But it’s a dynamical something — as you say, it has to do with causal links, and whether they’re directed or undirected. There’s a different kind of holism that’s (arguably) absent in the retrocausal framework, namely property holism. There’s no need for properties of (spatial or temporal) wholes that are irreducible to the properties of the (spatial or temporal) points. Maybe what we need is a taxonomy of kinds of holism. (Maybe you know of one…)