John Bell Workshop 2014

What Retrocausal Explanations Look Like (Online Tues. 1/13, 11:30am PST)

This topic contains 18 replies, has 4 voices, and was last updated by Quantum Speculations Quantum Speculations 5 years, 6 months ago.

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  • #1627
    Ken Wharton
    Ken Wharton
    Member

    While it is generally known that retrocausal models can provide an account of Bell-inequality violations in terms of spacetime-local beables, new models can now explicitly show how this comes about. By analyzing a simple local-beable model that precisely recovers the quantum joint probabilities for measurements on a Bell state, general concerns about retrocausal models can be analyzed at a much deeper level than previously possible. (Including questions of locality, fine-tuning, free-settings, etc.) With this framework it is possible to assess whether various general concerns apply to this specific model, instead of mere straw-man alternatives. In this workshop, I am particularly interested to see whether surviving concerns are better classified as outstanding physics questions or philosophical objections.

    • This topic was modified 5 years, 6 months ago by Ken Wharton Ken Wharton.
    #1779
    Ken Wharton
    Ken Wharton
    Member

    I’ve been having an email conversation about this paper with Daniel Rorhlich, the most relevant parts of which might be useful for others; with his permission I’m including these parts here. (I also have slightly edited the paper, based on his feedback and comments.)

    (DR): I don’t understand your statement, in Sect. IIB, that “The joint probability W(α)W(β), then, will be dominated by cases where either α or β is zero.” I understand that two particles emerge from a common source, with one particle going to Bob and the other to Alice; the particles have opposite spin vectors. Alice and Bob then measure the particles’ spin components along any axes they want. Why should either of those axes correspond to the original spin vector of one of the particles?

    (KW): Because of retrocausality. From a causal-order perspective, it’s the original (hidden) spin vector that corresponds to one of the future settings, not the other way around.

    (DR): I grant that W(α) and W(β) are dominated by small arguments α and β, but if the orientation of Alice’s spin-component measurement does not correspond to the original orientation of the particle that comes her way (or to an orthogonal orientation), that small argument is irrelevant; and likewise for Bob.

    (KW): Okay, let’s work it out in detail. Suppose that the original spin orientation is halfway between Alice’s and Bob’s setting, so both particles need at *least* a θ/2 anomalous rotation to match the future boundary condition. Then (since gamma is much smaller than theta), the biggest possible value of W(α) is about 4/θ^2, and W(β) is also maximum at 4/θ^2, so W(α)W(β)=16/θ^4. There are less likely cases as well, including anomalous rotations of (pi – θ/2), etc.

    (KW): But if the original spin orientation is exactly aligned with Alice’s future setting, then W(α) is 1/gamma^2, and W(β) is 1/θ^2 (all the anomaly is on Bob’s particle), so the joint probability of this scenario is W(α)W(β)=1/(θ*gamma)^2. In the limit that gamma<<θ, this joint probability is overwhelmingly more probable than the case in the previous paragraph. So it’s overwhelmingly more probable that the original spin orientation will happen to be aligned with one of the future settings.

    #1811

    Hi Ken,

    This is a very interesting paper. I would like to know whether a retrocausal explanation has the ability to derive the Born rule. I think this question is closely related to the missing account of how a future measurement setting influences the measured system physically (which has been referred to by you). It seems that only after we know the underlying mechanism, can we answer similar questions. Here I am also curious about the underlying mechanism. Is there some particle or wave which transfers the retrocausal influence? What equation of motion does it obey? Can we test its existence by experiments? etc.

    Best,
    Shan

    #1813
    Ken Wharton
    Ken Wharton
    Member

    Dear Shan,

    Thanks for the great question. On “deriving” the Born rule (or Schulman’s anzatz that does the needed work in this paper), you could try wading through my derivation in http://arxiv.org/abs/1301.7012 , but I’m still not totally happy with this account (and indeed I’ve never even submitted it for publication).

    More importantly, that paper lays out a mechanism for how this can work (although a simpler version of even that has now been published: http://www.mdpi.com/2078-2489/5/1/190 ) . Probably this is the one most worth reading if you’re interested in what follows. Crucially, the retrocausal mechanism is *not* something that solves an equation of motion, or can be thought of as “transferring information” back in time. Instead, it’s the same mechanism used in 3D stat. mech., as applied to 4D systems.

    One analogy I sometimes use is ‘finite edge effects’ in stat. mech. This is where the size of a (3D) lattice has an effect on the probabilities inside the lattice, and is well understood. This is a “mechanism” in which learning about a boundary (the edge of the lattice) will change the probabilities one assigns to the interior without requiring a physical flow of information. Say there’s an experimenter who has the ability to set the lattice boundary (say, increasing or decreasing the size of the full lattice). When I find out her choice of setting, I would update the probabilities I assigned to the interior. This is all perfectly standard 3D stat mech; you solve these problems “all at once”, looking at the possibility space (given the boundary) and assigning each microstate an equal a priori probability. If I learn something about the boundary, I update my probabilities accordingly.

    Now, it’s hard for some people to mentally extend this analogy to 4D, and it can’t be done at all without going into a block universe mindset (see my (regrettably too-harsh) rant in Rorhlich’s topic). But try to picture a “static” 4D lattice. The logic in the previous paragraph means that when one learns about the boundary at the end of the 4th dimension, one updates the probabilities one assigns to the *bulk* of the lattice. If this 4th dimension is time, that’s exactly the sort of retrocausality we need: learning about the future boundary setting (i.e. a measurement setting) allows me to change the probabilities I assign to the past.

    Okay; that’s the subjective perspective (the only perspective in which one can talk about information or probabilities, imho). What’s “really” going on in such a scenario? The objective story in 3D is that there *is really one microstate* of the system, we just don’t know which one it is. So that’s my objective story in 4D as well; there’s really one “microshistory”, we just don’t know which one it is. And how can that one true microshistory conform to the future measurement setting? Because it’s *not* the solution to some Cauchy-problem/equation of motion. It’s the solution to a 4D boundary problem, which the universe has resolved “all at once”. Just because we learn about the universe one time-slice at a time doesn’t mean that the universe need be so limited; indeed, in Lagrangian GR similar “all-at-once” approaches are regularly used.

    Hope that was somewhat intelligible… Thanks again!

    Best, K

    #1814
    Richard Healey
    Richard Healey
    Participant

    Ken,

    Thanks, this is very interesting.

    Here is a small (corrected!) question. In part of your answer to your own question “Is this model local?” you say “Alice’s measurement settings are certainly a contributing causal factor to the probabilities at Bob’s apparatus”. Suppose in one instance Alice’s vector underwent an anomalous rotation but Bob’s didn’t. Would you still say that in this instance Alice’s measurement setting was a contributing factor to the chance of Bob’s getting one outcome rather than the other? Or do you take causal factors to be general conditions rather than particular events, so that even though the local beable influence chain here went from Bob to Alice and not vice versa, in other instances it went the other way around?

    #1816
    Ken Wharton
    Ken Wharton
    Member

    Hmmm… Interesting. My first reaction is that Alice’s measurement setting is still a causal factor, but of course here I’m heavily influenced by Huw Price and the interventionist account of causality that he advocates.

    What makes me pause a bit here is by focusing on *one particular history*, it’s unclear whether I’m still allowed to imagine counterfactual cases in which Alice could have made a different setting. (Or, more relevantly, Alice believing that she could have made a different setting.) Without this (real or apparent) freedom in the settings, Huw would say that you can’t define causation in the first place. So if Alice doesn’t consider counterfactual settings, she wouldn’t take her choice to be a choice at all, which means that it’s not a “cause” by Huw’s account.

    But if Alice still imagines that it could have been different, then yes, her choice is a “cause” by Huw’s account – even if there’s no rotation on Bob’s particle. Really, her choice determines the probabilities of spin orientation at preparation, which is precisely what Bob measures (given no rotation on his particle), so I think it’s a pretty clear causal link (and local, in a certain sense).

    One analog to your question that occurs to me is the probability that you’re dealt 3 aces, given my choice of whether or not to take an ace out of the deck of cards before the hand is dealt. Surely most people would say that my choice is a causal factor of the probabilities. But how would you answer the question of whether I had a causal impact, given only the one special case that I chose to take an ace out of the deck, and you’re dealt 3 aces anyway? Kind of a tricky causality question, retro- or not-.

    #1817
    Richard Healey
    Richard Healey
    Participant

    Suppose Alice does imagine it could have been different (as I think she should).
    My thought was that in the case I described Bob has a case that Alice’s choice had no influence on the chance of his outcome, since (as it happened) he was the one who fixed the joint spin axis in this instance with the result that his outcome had a 50-50 chance of either result.

    #1818
    Ken Wharton
    Ken Wharton
    Member

    Ah, I see the issue. The question is whether the “causal influence” sweeps from Alice to Bob (via the past) or vice-versa. My answer is neither. Together, both of their choices join to causally influence the past and each other’s outcomes.

    Here’s a spatial analogy: What causes the exact pattern of normal modes in a laser cavity; does the causation sweep from the left-mirror, or the right-mirror? The obvious answer is “neither”; both mirrors together cause the normal modes. (An imagined change in either mirror would change the modes; picture Alice controlling one mirror and Bob controlling the other.)

    Does that help?

    #1819
    Richard Healey
    Richard Healey
    Participant

    Thanks, that’s the clarification I was looking for.
    Now I’ll have to think more about whether I agree with your answer!

    Here’s a more substantial issue.
    In your introduction you lay out “the options on the table”, but don’t include the option of a past-common-cause explanation with no superluminal influences but with no beables continuously linking this non-factorizable common cause to its joint effects. I think this is the best take on how quantum theory explains violations of Bell inequalities—and therefore the best explanation we currently have.

    If that’s right, then the “options” you list are research programs in search of new theories seeking to go beyond quantum theory in search of a deeper, or more complete, explanation. Is that how you see them?

    #1820
    Ken Wharton
    Ken Wharton
    Member

    Ah yes… I agree, once you allow a non-factorizable ontology, one gets a lot more options. But I was only talking about explanations with *all* of the “beables localized in spacetime”.

    And yes, I’m looking for something deeper; the analogy I like to use is that quantum theory is like thermodynamics without knowledge of statistical mechanics. I’m looking for the analog to stat. mech. that explains QM, in the same way that thermodynamics has an underlying explanation.

    #1821
    Richard Healey
    Richard Healey
    Participant

    The nonfactorizablity I was talking about is a property of joint probability distributions (by contrast with the factorizability needed to derive CHSH inequalities in conjunction with the probabilistic independence of the “hidden states” from the choice of subsequent measurement settings—the assumption you reject). If (as I believe) the probabilities that figure in such distributions aren’t elements of the (physical) ontology—if they aren’t beables—then failure of factorizability does not entail a nonfactorizable ontology.

    #1822
    Ken Wharton
    Ken Wharton
    Member

    If I understand you properly, I think I’d put that in the category of “giving up on causal explanations entirely” (which I admit is also an option, but I’d argue that the entire scientific method hinges on not taking it).

    The question I’m asking is how to *explain* those very joint probabilities in terms of a spacetime-local-beable ontology.

    Still, we’re in perfect agreement that probabilities shouldn’t be part of an ontology! 🙂

    #1823
    Richard Healey
    Richard Healey
    Participant

    I understand quantum theory as a theory that enables us to explain experimental violations of Bell inequalities in a way that appeals to localized conditions whose obtaining causes the localized events recorded in those experiments. So I think it’s appropriate to say quantum theory helps us explain their violation causally. (See my paper posted in the previous IJQF forum on the meaning of the wave function).
    But this explanation does not mention any beables (local or nonlocal) continuously connecting those events to their cause(s). Is that giving up on causal explanations, or giving a causal explanation of a kind some (e.g. Einstein) would not like?

    #1824
    Richard Healey
    Richard Healey
    Participant

    I understand quantum theory as a theory that enables us to explain experimental violations of Bell inequalities in a way that appeals to localized conditions whose obtaining causes the localized events recorded in those experiments. So I think it’s appropriate to say quantum theory helps us explain their violation causally. (See my paper posted in the previous IJQF forum on the meaning of the wave function).
    But this explanation does not mention any beables (local or nonlocal) continuously connecting those events to their cause(s). Is that giving up on causal explanations, or giving a causal explanation of a kind some (e.g. Einstein) would not like?

    #1825
    Ken Wharton
    Ken Wharton
    Member

    I’m probably too close to Einstein’s perspective to be able to objectively answer that last question… But I have a counter question for you: Given that there is just one tiny change you need to make to your story to regain a causal explanation (in my sense), why resist taking it?

    Two months ago, in the last iWorkshop, you quoted me saying the following (and said you generally agreed with it…):

    ” For me, this just adds to the evidence that \psi is best viewed as a collection of classical probability distributions, most of which are wrong. The correct distribution one should use is conditional on the future measurement geometry (i.e. the choice of the next strong measurement.) So \psi is isomorphic to something like P(m(x,t)|G), where m(x,t) are some spacetime-localized microstates, and G is the future measurement geometry-choice. For any given G, P is just a classical probability distribution, but you can’t use it until you know G.”

    My question to you is: why *not* go back and update your P(m) upon learning G, if doing so could avail you a causal explanation of the strangest quantum phenomena? (A space-time-based explanation of P for any particular G is clearly available; the only problem is a space-time-based explanation of P for all possible G’s.) If P’s aren’t part of your ontology anyway, why not simply jettison all the ones that are never used, and search for an explanation of the one that is?

    #1826
    Richard Healey
    Richard Healey
    Participant

    Let me make it clear that I see no philosophical problems with your favored program for going beyond quantum theory, and I encourage you to pursue it. I’d help you if I were a (better) physicist, and the payoff could be great if it proves successful! I do have an epistemic worry about the extra local beables required by the program: they remind me of Bohmian trajectories and the Everettian universal quantum state in their inherent experimental inaccessibility. But that worry should not derail pursuit of the program.

    Meanwhile, what are we to make of quantum theory, the best physical theory we have and arguably the best physical theory we have ever had? My present interest as a philosopher is in showing why that theory is free of any conceptual problems and metaphysical extravagances like superluminal influences, “flashes”, many worlds or a physical role for consciousness; and seeing what philosophers and others can learn from its novel non-representational strategy for informing us about the world and how to understand it. I think too many “Interpretations” of quantum theory misunderstand quantum theory and so fail to learn the right lessons—about probability, causation, explanation, laws, and (most importantly) about different uses of physical models to achieve the goals of science—description, prediction and explanation of physical phenomena.

    #1827
    Ken Wharton
    Ken Wharton
    Member

    Fair enough! 🙂

    And many thanks for all the interesting questions, too.

    -K

    #1828
    Ruth Kastner
    Ruth Kastner
    Participant

    I would say that we should be renouncing local (light-like or subluminal) causation as the explanation of quantum correlations–which Einstein would not like, of course. I think this is part of moving beyond classical thinking, and into a different ‘paradigm’, to use Kuhnian language.

    #1829

    Hi Ken,

    Many thanks for your reply and explanation! I would like to learn more details about your retrocausal theory by reading these two papers.

    Best,
    Shan

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