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July 10, 2015 at 12:34 am #2591David MillerParticipant
This is joint work with Matt Farr.
We are interested in the intrinsic causal structure of quantum mechanics. For instance: Is it possible for a cause to arise in a closed quantum system? Is the structure of quantum mechanics compatible with retrocausality, i.e. causal influence of “earlier” events by “later” events as indexed by the direction of time on a clock in the laboratory in which the experiments are performed?
Our “cause” is an operation C performed on the quantum systems and the “effects” are measurements A and B performed before and after C. We eliminate preparation or preselection as a source of causal structure by requiring the initial state(s) be maximally mixed. We also do not allow postselection of subensembles because that could be a source of artificial causation.
We conclude retrocausation could occur in a generalised form of quantum mechanics but there is no practical means of achieving that at present.
We also suggest that the concepts of causation and correlation should be more clearly distinguished. We consider correlation as a change in the joint probabilities of events without a change in the marginal probabilities. On that basis, a maximally entangled bipartite system is an example of pure correlation and not causation. Therefore analysis in terms normally used to deal with causation should not be applied to maximally entangled bipartite systems without reconsideration. In particular it seems appropriate to reconsider the application of Reichenbach’s principle of common cause to that case.
Since correlation is a symmetric relation between variables, it should be regarded as bidirectional in time. While causation and retrocausation are distinguishable, could it ever be meaningful to say there is a difference between correlation and retrocorrelation?
July 10, 2015 at 5:14 am #2603Michael B. HeaneyParticipantHi David,
I’m reading your paper, and would like to get an intuitive, physical understanding of what you mean by the words causal, retrocausal, bicausal, acausal, and a correlator. Could you please help?
Thanks,
Michael
July 11, 2015 at 12:35 am #2621David MillerParticipantHi Michael
Thanks for your question – it’s good to have a chance to try to explain in informal language.
We’re trying to see what QM per se can tell us about causality. For example, where in the algebra is retrocausality ruled out (if it is)? We know the joke about a physicist being asked to come up with a theory about horses in a paddock, the natural starting point is to assume the horses are spheres and the paddock is a frictionless plane. So we begin by specifying a simple scenario – the “neutral causal background” (NCB).
First of all in classical terms. The rules are Alice flips a fair coin and sends the result (H or T) to Bob. Alice can’t send a message this way. She could if she used an unfair coin – we rule out that sort of strategy by requiring the initial state to be maximally mixed. Alice could message by not always sending on the result (eg retaining some or all H results) – we deal with that strategy by ruling out subensemble selection – all runs must be used. There is a correlation between Alice’s and Bob’s results – when Alice gets H, so does Bob. For the NCB we stop this by introducing C which randomises Alice’s result (eg toss a different coin and send it to Bob or change Alice’s result in 50% of cases, etc). Now Alice and Bob just get H or T half the time and there is no correlation between them. This is the NCB.
In the QM case Alice and Bob don’t have to measure in the same basis but otherwise the scenario is the same.
Now let C be any operation. Can C change the probabilities of Alice’s and Bob’s measurements? If so, are there any restrictions imposed on the effects of C by QM?
If there is a C which can change Bob’s probabilities, we say C is a cause.
If there is a C which can change Alice’s probabilities, we say C is a retrocause.
If C changes the joint probabilities of Alice and Bob without changing the probabilities of Alice or Bob, we say it is a correlator.
If C changes the joint probabilities of Alice and Bob and changes the probabilities of Alice or Bob, we would say it is a correlator and cause (Bob’s) or correlator and retrocause (Alice’s).
Note in the above, I have used “message” here and then morphed to “cause”. This bears further discussion elsewhere. In the NCB scenario, the two ideas are the same?/similar?. Given the restriction to a maximally mixed preparation state and no subensemble selection, Bob can never “feel” a cause from Alice (without C). Therefore the link between them is better thought of as a correlation. [Obviously, in the back of our minds is the EPRB experiment.] By the way, Matt Farr calls subensemble selection “artificial” causation which I think is an excellent term.
It turns out that C as a cause or a correlator is easy, even unitary operations (in a larger Hilbert space) do the trick.
The surprising thing is that C as a retrocause does not appear to be logically impossible according to QM. It’s certainly technically impossible. It seems that starting from the postulates of Barnett et al and Pegg et al, the algebra of QM is flexible enough to accommodate retrocausation proper (as distinct from correlation where the “retro” issue doesn’t arise – there is no basis for saying (pure) correlation acts ‘forwards” rather then “backwards”).
July 11, 2015 at 6:32 pm #2639Michael B. HeaneyParticipantHi David,
Thank you, that is very helpful.
Suppose Alice has an excited atom that can emit a photon, and Charlie (C) has a ground state atom that can absorb the photon. Alice measures the state of her atom every minute. She finds it in the excited state (H) for the first 3 minutes, then she finds it in the ground state (T) for the next 3 minutes. Charlie finds his atom in the ground state for the first 4 minutes, then in the excited state for the next 2 minutes. So Alice measures HHHTTT and Charlie measures TTTTHH. Now repeat the experiment, but just before minute 5 Charlie puts his atom in the excited state. Now Alice measures HHHHHH and Charlie measures TTTTHH. It seems like Charlie’s action has changed the probabilities of Alice’s earlier measurements. Would you say that C is a retrocause? Or am I still misunderstanding something?
Thanks,
Michael
July 12, 2015 at 1:36 am #2651David MillerParticipantHi Michael
Fortunately the case we consider avoids the situation you refer to. For example, your example does not begin with a maximally mixed state and it is implicit in our case that each member of the ensemble is available for A, B and C to be performed on them.
When considering transitions, as your example does, the role of final states is a thorny question. There is a brief discussion of this in Feynman’s thesis p.4 where, comparing his (and Wheeler’s) theory of action at a distance (= advanced and retarded potentials) with conventional theory, he says “It is here that the theory of action at a distance gives us a different viewpoint. It says that an atom alone in empty space would, in fact, not radiate.” (emphasis in the original) There have been interesting discussions about this and related matters over the years but it seems minds still differ. Certainly in condensed matter systems an electron can’t tunnel out of a quantum well unless there are empty states nearby but normal quantum mechanics seems to handle that OK without requiring anything retro.
July 12, 2015 at 3:06 am #2655Michael B. HeaneyParticipantThank you for your explanation!
July 13, 2015 at 3:20 pm #2688Robert GriffithsParticipantDear David,
I took a careful look at your attachment (Miller & Farr). Here are my thoughts.
I think you have taken up an interesting but subtle topic; causality in general, not just in quantum mechanics, has given rise to a lot of discussion. As opposed to statistical correlation, causes are supposed to precede their effects, so seem to be connected with thermodynamic irreversibility, which in turn is, typically, introduced in classical statistical mechanics and in quantum theory using a temporal boundary condition. You, obviously, want to get around this, so you chose intial and final states to be completely noisy. So far so good.
But then you introduce measurements of A and B. This seems to me dangerous, because measurements are inherently irreversible processes, both in classical and quantum physics, and whatever conclusions you come to are in danger of being “polluted” due to measurement processes. Of course one can in principle get around this issue in the classical case by including the measurement apparatuses within the larger system. And that is in principle possible in quantum theory if you adopt an interpretation in which the dynamics is intrinsically time symmetrical: Bohm, Everett, consistent histories (CH). Standard (textbook) quantum mechanics will not do, unless you have a textbook superior to any I have ever seen.
My book explains how this can be done using CH. But I think a better approach would be to get rid of A and B measurements entirely by instead using A and B properties (represented by projectors belonging to some projective decompositions of the identity, in general different for A and B); at least that is simpler, and may be worth exploring before you tackle measurements. That leaves the intermediate operation C. If C is unitary it is not a source of irreversibility; unitaries do not single out a sense of time. However, in Sec. III you employ Kraus operators, and at this point irreversibility has slipped back in, as is evident if you obtain the Kraus operators by the usual approach of modeling a system and its environment as uncorrelated (a product state) at the initial time, but not (in general) at the final time. In the case of a unital channel it is true that the closure condition also holds if each C_k is replaced by its adjoint, but I don’t see why this, by itself, removes temporal irreversibility.
In summary, I think you have an interesting project and your approach may yield interesting insights. But are you not in danger of removing visible sources of irreversibility by concealing them in some other place?
Bob Griffiths
July 14, 2015 at 6:39 am #2720David MillerParticipantDear Bob
Thanks very much for your interest and comments. I agree with your reasoning entirely. You have raised valid points about temporal (ir)reversibility which is perfectly understandable because our submission is under the Topic “Timesymmetric theories”. But our submission, and I think some other of the submissions here, aren’t really purporting to be “timesymmetric” and we should have made that clear.
I think the term “timesymmetric” is being interpreted rather loosely in this Topic. Probably to most physicists, certainly those without an interest in foundations, it means time(better motion)reversal symmetry which is usually learnt in connection with Kramers theorem. I don’t think anybody means that here. Probably the next stage is something to do with time’s arrow(s). But I think ““Timesymmetric theories” has come to mean anything involving things like retrocausality, or states propagating backwards in time.
Anyway, to get back to your points, measurements A and B (and C involving Kraus operators) certainly remove any possibility of “timesymmetry”. A and B are there to record the “effects” of the “cause”. The aim is to see what it is in the algebra (rather than ideas about “causality”, etc) which prevents C changing A when it is able to change B. Also, at first at least, it seems surprising that C could change B when C was unitary and the initial state was maximally mixed (this is not dealt with explicitly in the short version in our submission – it’s rather obvious on reflection but it does need a larger Hilbert space where the initial state becomes not maximally mixed).
Finally, I agree that if one wants to talk about properties not directly the result of measurement, so timesymmetry can be properly talked about, then CH is the most thoroughly thoughtout and justified way to go.
David
July 17, 2015 at 1:13 pm #2830Ken WhartonMemberHi David and Matt,
Apologies for taking so long to get to this very interesting piece! Some notes:
– This is probably my own personal bias showing, but at the end of the first column, I thought at first that you were talking about running the experiment in two different timedirections. So you might help people like me here if you just note that you’re talking about switching A and B.
– How much of this analysis requires “maximally mixed” states to be ontic, rather than epistemic? It seemed to me that it didn’t matter in this analysis; do you agree?
– While I appreciate the distinction you’re making between causation and correlation, I’m not sure you want to claim that your “correlator” is “weaker than being a cause”. The language you use implies there’s no causation for a correlatorC, but that’s like telling me I can’t have a causal influence on a random unknown bit if I’m giving a choice of flipping it or not. In Huw’s interventionist account of causation, I’d still “have a causal influence” on the outcome, while in your language it would be “weaker than a cause”.
– Even though your *definitions* of different C’s depend on starting with a maximallymixed state, wouldn’t those C’s “maintain” their status (as causal, correlator, etc.) whether or not they were part of this particular measurementchain that started with I? I would think that they would, but this raises the same issue as above. Any given correlatorC can clearly become an ordinary cause if the initial preparation is no longer maximally mixed, and can become known to the Ccontroller. Since nothing has changed about C itself in this scenario, I would think this would be more evidence that your “correlation” *includes* (ordinary) causation, and is not mutually exclusive of it.
– David, I can’t believe you didn’t cite your own paper (our “action duality” piece) along with [6] and [7]! 🙂
– Any explicit insight you have as to nonmaximally entangled states in this framework would be much appreciated; that’s what I’m working on myself these days.
Best, Ken
July 18, 2015 at 2:57 am #2849David MillerParticipantHi Ken
Thanks for your comments. We will clarify the “switching” of A and B is not different time directions and include more references!
Yes, I think our paper is neutral with respect to ontic/epistemic.
I agree the distinction (if any!?) between “cause” and “correlator” needs further thought and elaboration. If Alice reflips a fair coin she knows she has done that but nobody else (who hasn’t watched her, etc) can find out whether she has or not. Under those circumstances, is it correct to say the coin carries a “causal influence” due to the reflip? More generally, if p^B(j) is not changed, B cannot tell whether C was performed or not so there can be no evidence of a causal influence from B’s results alone. On the other hand p^{AB}(i\&j) can be changed by C – evidence of correlation.
Of course Alice carries a record of the reflip but she didn’t start out in a maximally mixed state. It is true that C is independent of the state it acts on but isn’t it possible even classically that the same operation can be a cause under some circumstances but not others?
Finally, the bipartite states in Sect. IV are general – can be product, partitally entangled or maximally entangled.
Cheers
David
July 18, 2015 at 11:25 am #2865Ken WhartonMemberAll good questions about the cause/correlation issues… Do you have a classical example in mind as an answer to your last question?
Still, you can’t carefully address these questions without comparing your definition of causation to some *other* definition of causation. Even if you don’t want to bring in other causation accounts, where your definition yields conclusions that seem at odds with our commonsense notion of causation, you probably should address that mismatch. Certainly under Huw’s interventionist account you couldn’t claim that reflipping a fair coin is not a cause, and this account matches better with my common sense on this issue, at least.
And I think you’re always going to have some mismatch if your definition doesn’t delve in below the level of observable probabilities. Our causal instincts have to do with ontology, and if it’s possible that you’re working at an epistemic level, your definition won’t match common sense. Specifically, taking your coin example, I can’t imagine there are many people who would think the status of a “cause” could be dependent on what other external observers can *know*. (That said, I do think there is almost always going to be some subjective aspect to causation, but that should be the subjectivity of the agent doing the causing, not other external agents.)
Best, Ken
July 19, 2015 at 7:41 am #2894David MillerParticipantHi Ken
As a classical example of something sometimes being a cause and sometimes not, I think of the proverbial butterfly in the Amazon jungle causing a hurricane – sometimes it does but mainly it doesn’t.
I think you can only go so far with classical intuitions about quantum causes because as we have found out from nonlocality, etc “commonsense” is not always a good guide, that is why it is good to just calculate the quantum answer. Take the EPRB case and let Alice rotate her spin about the zaxis before she measures. That doesn’t change anything that either Alice or Bob alone can possibly get as a measurement outcome so if it is a “cause” of anything, that thing or effect can’t be Alice’s or Bob’s results alone. (I’m assuming a “cause” must at least under some circumstances be capable of producing an “effect”.) However Alice rotating her spin can change the correlations between Alice’s and Bob’s results. The “effect” is a change in the correlations (joint probabilities) but not the individual probabilities. This doesn’t necessarily involve entanglement because the same thing happens in the corresponding SEPRB cases. Unlike a cause, it is at least arguable there is no way of determining which direction the correlation takes place, ie Alice to Bob and vice versa is the same “effect” (joint probability), including in the two possible SEPB cases. So it still seems to me, for the time being at least, that there is a difference between a cause and a correlator.
To remove any doubt, I don’t think ‘a “cause” could be dependent on what other external observers can *know*’.
Thanks for your interest.
David

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