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July 3, 2015 at 1:08 pm #2458
Quantum mechanics is often taken to entail holism. I examine the arguments for this claim, and find that although there is no general argument from the structure of quantum mechanics to holism, there are specific arguments for holism available within the three main realist interpretations (Bohm, GRW and many-worlds). However, Evans, Price and Wharton’s “sideways EPRB” example challenges the holistic conclusion. I show how the symmetry between the sideways and standard EPRB set-ups can be used to argue against holism. (Aside: This short paper is essentially me working out the SEPRB example to my own satisfaction. I hope I got it right!)July 5, 2015 at 11:59 pm #2497
Your understanding of SEPRB agrees with mine, so I’m hoping you’ve got it right 😉
In the context of Evans’ paper in this forum, we might depict the holism of EPRB you describe as an undirected space-like link between its space-like separated outcomes (a la the undirected links in Evans’ Fig 4). One could attribute a direction to that link perspectivally/subjectively from within the block universe, depending on whether Alice’s detection or Bob’s detection occurred first per one’s particular Lorentz frame. Since some observers would have that link directed from Alice to Bob, while others would have it reversed, the “objective” version of the link would be undirected. This is analogous to the subjectively ambiguous direction of the retrocausal links in Evans’ Fig 4, which are likewise undirected in their objective form. With this depiction of retrocausality in EPRB, one might say the retrocausal links of Evans’ Fig 4 depict “diachronic holism” (as Silberstein suggested).
In either case, the key to explaining EPRB is that classical causality as characterized by Wood and Spekkens is violated per undirected links in the relevant explanatory graph. That’s why RBW (https://ijqf.org/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf) employs fundamental explanation via an adynamical global constraint over spatiotemporally extended fundamental ontological entities we call “spacetimesource elements.” In that sense, RBW is “4D holism.”July 6, 2015 at 7:10 pm #2505
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…)July 7, 2015 at 5:54 pm #2513
Thanks for your reply, Peter. Please see attached a clarification of my point.July 7, 2015 at 6:16 pm #2515
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?July 8, 2015 at 1:34 pm #2527
Let me start by saying I believe the main claim of your paper is correct and perfectly in keeping with the conventional understanding of holism. What I’m proposing is a change to the conventional understanding of holism based on the example in your paper. Sorry if you thought I was trying to refute your main claim. Attached is a candidate for the taxonomy you requested. [I’m thinking out loud here, so correct me as necessary.]July 8, 2015 at 2:15 pm #2530
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!)July 8, 2015 at 4:03 pm #2531
I imagine local properties existing on p — B and q — A of Figure 3. So, on S — p and S — q you have holism and thereafter you have retrocausality. The two situations (holism and retrocausality) are, as you point out, distinct concerning local properties, but can be mixed (Figure 3) and transformed smoothly and continuously from one to another. So, in considering a term for the general situation I chose “spatiotemporal holism” with limits of synchronic and diachronic holism because, as you say, you have “a temporal whole” in retrocausality. And, I have an adynamical bias 😉July 8, 2015 at 5:14 pm #2534
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.July 14, 2015 at 1:36 pm #2726
Nice paper! Yes, I think you got the SEPRB example just about right… As you note, we didn’t really commit to an intermediate ontology, so that’s where things get tricky, but even without committing to a particular ontology I think you’re perfectly justified in making your conclusions.
Still, since I’m quite interested in the pros and cons of possible intermediate ontologies, and you’re proposing something a bit different starting on Page 8, I’d like to delve into the intermediate details, a bit…
First of all, before you start dealing with the L/R asymmetry on Page 9, you of course have a past-future asymmetry in SEPRB. One strange way that this manifests itself, that you might not have considered, is what happens in a series of consecutive measurements. You’re right in footnote 5 that it’s *possible* to assign the correct probabilities to all of these hidden properties. But as soon as one of them is measured, the rest of the properties have to shift their probabilities in a strange and time-asymmetric manner (in order to account for the distribution that would be observed at a future measurement).
Okay, then we get into the time-symmetric version where you note that all these w- and z- probabilities are conditional on each other. I think this part would be greatly enhanced by explicitly noting the unconditional (joint!) probabilities P(w,z), from which your conditional probabilities can be derived. You could even list the 8 equal-joint-probability cases:
w | z
If each of these 8 cases have an equal chance of jointly occurring, you can easily show that you get the correct marginal probabilities for w and z, as well as the correct conditional probabilities for P(w|z) and P(z|w). As it is now, you only really tell the conditional-probability account, leaving it somewhat unclear what the unconditional story you’re telling really looks like. I think having this explicit account would strongly support the epistemic/ontic distinction you’re making in the last paragraph of section 3.
Now, to the question of your ontology (having a built-in outcome associated with each possible measurement direction), and how it constrasts with the “real polarization” ontology that Huw and I have been using. The downside of our approach is that we either need *two* polarizations (one controlled from each side), or else an anomalous rotation from one to the other. You don’t have this problem, which seems like a plus.
But another issue is whether one needs a discontinuity at a given measurement. These Stern-Gerlach experiments can easily be staged, one after the other, simply by blocking one of the two output ports, and sending the open port directly into another experiment. If the blocked port doesn’t detect a particle, then you have “measured” the intermediate spin of the particle without an entropy-increasing interaction.
As I noted above, all of your beables would generally have to shift at such an intermediate measurement. Maybe this is okay, but I strongly lean toward stories where one doesn’t need any sudden change at all in such non-invasive scenarios. That’s why I don’t particularly like even the two-polarization stories (for which one polarization is unchanged, but the other one changes). I much prefer the anomalous rotation account, where there’s only one “beable”, and it doesn’t need to do anything at all when it passes through such an intermediate measurement.
But that point aside, I actually think your approach here is easier to analyze than our polarization examples… and I may be stealing it for general-audience summaries! 🙂
One last nitpick: I thought the statement “there is NO sense in which [preparation and measurement] are the time-reverse of each other” was too strong… I think there are lots of senses in which they are, even taking our human asymmetries into account.
Thanks for a thought-provoking paper!July 15, 2015 at 2:49 pm #2772
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?July 16, 2015 at 12:19 pm #2792
I guess I mis-read what you were doing here… But given your clarification, I think you should be careful about simply assigning the outcome of the future measurement as a hidden variable. Huw has already talked about exactly this kind of minimal-ontology (see section 5.2 of 1002.0906 ), and the obvious downside is that such accounts are doomed to fail as a deeper explanation of the outcomes (the outcomes are not “explained” by the hidden variables if they are simply identical!)
With this in mind, you may want to consider my mis-interpretation of your ontology, after all… There’s at least hope for some deeper explanatory account if you associated the hidden variables with particular directions, rather than just the actual measurements.
And yes, there are always “problems lurking” when one is talking about measurements – although at least in retrocausal block-universe scenarios everything lives in spacetime. But, problems still lurk. In order to get retrocausality, measurements can’t just be *correlations* between the device the system, they actually have to be *constraints* (or else one can’t recover retrocausation, right?).
Travis Norsen was mentioning on one of these threads (as he has to me, personally) that even for retrocausal accounts, he doesn’t see how there can be a special role for measurement devices, if those devices are supposed to obey the same rules as the systems themselves. Why are some interactions treated as external constraints, and other interactions treated as mere correlations?
This is an excellent and still unresolved question, but I don’t think it’s unresolvable. Large conductors are treated as constraints in electrostatics, in a way that individual charges are not. So long as there’s some *ultimate* constraint (i.e. a cosmological boundary condition), I think there’s a path to making it all work.
The most detailed hand-waving explanation I’ve written was a FQXi essay from a while back: see pages 5 and 6. The question that standard QM has trouble with is basically whether a single atom interacting with a photon should be viewed as a “measurement/constraint” on the photon or not. The nice thing about retrocausal accounts is that the answer to this question can depend on the bigger-picture, and what happens later.
That said, I also think it’s fair to put these questions aside for now, and simply assume that macroscopic measurements work as boundary constraints on microscopic systems (as you’re basically doing!). So I think it’s fine to treat a non-invasive/intermediate Stern-Gerlach apparatus as an external boundary condition — just one that shouldn’t need to introduce any discontinuity at that point, at least in the models I most prefer.
Cheers! -KenJuly 16, 2015 at 5:33 pm #2802
Thanks Ken. Maybe I should clarify my clarification: What I had in mind was something like the ontology I sketch in here:
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?July 17, 2015 at 12:32 am #2816
Yes, I agree with that last bit. It’s been ages since I’ve read that paper of yours, and I still have a few here I’d like to get to first, but thanks for reminding me about it; I’ll check it out soon with all this in mind!
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