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July 19, 2015 at 7:41 am #2894David MillerParticipant
Hi 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
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 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 12, 2015 at 1:57 am #2653David MillerParticipantHi Pete
Thanks for your interesting paper. For what it’s worth I vote for Fig. 4 of your paper.
I got a bit stuck on Sect. 4.2. How do we choose the values of $ \alpha_2$ and $\beta_2$? Do we have to anticipate what angles we are going to choose in other repetitions of the experiment?
On a more general note, is there any mileage in thinking about the SEPRB approach or more formal methods of mapping a bipartite system (i.e. with a causal fork) onto a single quantum system? As you explain on p. 2, the idea is to discover causal structure from observed statistical correlations. The statistical correlations are the same in the two case just referred to so does that mean the causal structure should be the same? If so, maybe that can be used to support Fig.4, even, with more maybe’s, with backward pointing arrows!?
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 11, 2015 at 1:12 am #2623David MillerParticipantHi Daniel Rohrlich
Firstly and with respect, I am very enthusiastic about your idea of using “the existence of a classical limit” as an axiom. Apart from the fact that you have shown it to be fruitful, I think it strengthens physicists’ “grip on reality” which seems to be being progressively loosened.
I have a few questions/comments about your retrocausality argument which I hope you might consider responding to.
(1) In your GHZ example, Jim steers a bipartite system into a mixture of either product or entangled states. In an EPRB experiment, Jim can steer a single quantum system into a mixture of polarization states of his choice. Does the involvement of entangled states in the GHZ case add anything to the argument? It “feels” like it does (the paper of Timpson and Brown may be relevant here).
(2) In the DCES case, Jim steers into states which span the Hilbert space while in the GHZ case, Jim steers into a subspace. Is there a material difference?
(3) In our submission to this forum, Matt Farr and I try to draw a distinction between “correlation” and “causation”. In our terms, “correlation” applies when joint probabilities are changed but marginals are not. “Causation” is reserved for changes in the marginal probabilities. Relativistic causality means we are talking about “correlation” in this sense in the relevant cases. Perhaps your suggestion about retrocausality in A reasonable thing that just might work attracted criticism because the term unconsciously implies in the minds of readers that a (retro)change in marginal probabilities is involved. Perhaps a better and less alarming term is “retrocorrelation”. But if the marginal probabilities are not changed can there be a distinction between “correlation” and “retrocorrelation” (except by bringing in the direction of causation when the marginals are changed)?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”).

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