Reality Conditions

Monday, September 18, 2006

On Price (and Penrose) on Time Asymmetry in Quantum Mechanics

The latter chapters of Huw Price's book Time's Arrow and Archimedes' Point contain much of interest for the philosopher, including an account of the notion of causation which distinguishes clearly and convincingly its subjective, "anthropocentric" aspects from its objective ones. For the physicist, however, the most interesting thing is bound to be Price's original attempt to provide an interpretation of quantum mechanics which is realistic in Einstein's sense, involves local hidden variables, and gets around Bell's theorem by accepting a form of "advanced causation" in which the future affects the past. According to Price physicists ought to consider seriously the possibility of such advanced causation, because the ordinary interpretation of quantum mechanics is time-asymmetric, and his interpretation restores time-symmetry and makes QM fall in the line with the rest of physics in this respect.

Such strong claims need a strong defense, of course. Price starts by considering the proposition: "Two systems have typically their properties uncorrelated before interacting but often have them correlated after interacting". This time-asymmetric proposition is uncontroversially true for macroscopic systems (think of meeting a guy and talking with him; after the talk you will both remember things about the other so there will be a correlation between your brains which did not exist previous to the meeting) but this asymmetry is just a consequence of the lower entropy if the initial state, and can be explained statistically in the same way as the Second Law of Thermodynamics. (The temporally reversed process of you two knowing of each other before the meeting and not afterwards is physically possible, just reversing the trajectories of each particle, but is extremely unlikely in the same way that a gas going spontaneously all to the corner of its container is.) Price claims, however, that we accept implicitly the same asymmetry for microsystems (in this case he calls it "micro-innocence"), and that the statistical explanation is not available for them.

His thought experiment is a photon that passes succesively through two polarizers aligned in different directions. We expect the state of the photon between the polarizers to be correlated with the state (i.e. the direction) of the first polarizer but not with that of the second. In other words, the state of a photon after going though a polarizer is correlated with it, but the state of a photon before going through a polarizer is not. Price views this asymmetry as "suspicious" because according to him it is a) not related to the statistical asymmetry of macroscopical systems, and b) not based on any asymmetry in the dynamical laws of physics, which are (with an unimportant tiny exception) time-symmetric. He therefore suggests that we should consider abandoning the assumption of micro-innocence and allowing correlations between microscopic systems before they interact. And, lo and behold, he finds that this assumption is just what we need to get a "local hidden variables" interpretation of quantum mechanics work, despite Bell's theorem; because if the probability distribution of hidden variables can depend on the future measurements we will make on them, then the correlations in the Aspect experiments and their like are easily explained without any superluminal influences.

The argument has therefore two steps, which look like a sort of bait-and-switch: first comes the claim that micro- innocence is an independent principle used currently in physics without good justification, and then the proposal to reject it and allow "incoming correlations". But the first step can and should be contested, in my opinion. Micro-innocence does not seem to me to exist as a principle independent of "macro-innocence", which has a harmless statistical explanation.

It is telling that Price's example involves a photon interacting with polarizers, which are macroscopical objects. If we consider instead a completely microscopical process, like two electrons repelling by exchange of a photon, we don't expect the outcoming properties to be any more correlated than the incoming ones -conservation of momentum allows to calculate any of the four momenta from knowledge of the other three, without regard to whether they are in- or outcoming; the process is completely time-symmetric. So the suspicion arises that an apparent asymmetry appears only when we consider the interaction of a microsystem with a macrosystem, and in particular, when we view the interaction as a measurement.

It is in fact true that in the naive "measurements collapse the wave function" interpretation of QM measurements are irreduciblely time-asymmetrical. Knowing that there has been a measurement at time t allows us to infer that at time t' close to t in the future the state is close to an eigenstate of the measured quantity, but does not allow a similar inference for times t' close to t in the past. Roger Penrose has made much of this asymmetry with a purpose diametrically opposite to Price's; while Price tries to restore lost time symmetry by allowing incoming correlations in a hidden-variables theory, Penrose tries to posit the collapse of the wave function as an objective, robustly time-asymmetric process with an ultimate explanation in a speculative quantum gravity theory. Both seem to be making too much of the time asymmetry of measurements, in my opinion. It is a more plausible and conservative suggestion that measurements (involving as they do macroscopic systems) are time-asymmetrical for the familiar statistical reasons of increase of entropy. As John Baez pointed out in person to Penrose, if the measured quantum system and the measuring macroscopic apparatus were in thermal equilibrium measurements wouldn't have any asymmetry. Penrose responds to this objection in his more recent book, The Road to Reality, but his answer seems unconvincing. (If I remember correctly not having the book with me, he says that making inferences to the future we apply quantum mechanics confidently and it is only when we try to use it to the past we need to specify whether there is thermal equilibrium or not, etc. It seems to me that this is just because we normally take the macroscopic time-asymmetry by granted.) The decoherence approach to the measurement problem gives my contention that any asymmetry has familiar statistical roots a strong support, it seems to me.

However, this only undercuts partially Price's argument. He may not be able to make the "bait-and-switch" argument for his interpretation of QM if ordinary QM has no fundamental asymmetry in need of purging; but his proposal that local hidden variables theories with incoming correlations may account for the Bell inequalities survives intact. He skillfully and in my opinion successfully defends the idea against many intuitive but philosophically dubious objections (such as the one that these correlations would render free will impossible as the coming particle would "know" already which measurement we decide to perform on it) and makes it worth for any physicist working in the area to consider it seriously. And this, for a philosophical outsider to the physics communtiy, is no mean feat at all.

2 Comments:

  • Hi Alejandro,

    Thanks for the interesting post, it touches a topic I am currently working on. I find myself agreeing with may things you write from Price, except the last. I would have thought indeed that the existance of correlations before interaction (which I think exist, but wait for my next paper) would remove free will. What is Price's argument against it?

    Best regards,

    B.

    By Blogger Bee, at 6:54 PM, September 18, 2006  

  • Hi Bee, I will be very interested to see your paper indeed. I can't reproduce exactly Price's argument because I haven't got his book with me here. But the main point is that "causation" is partially an anthropocentric notion, and the temporal asymmetry of causation (the idea that a future event cannot be the cause of a past one) is rooted in the time asymmetry of our situation in the world as agents -we act "to produce results" in the future. Normally, at least. But if advanced causation in Price's sense existed, we could say that our (free-willed) choice of the experimental setup caused the incoming particle to be in a given state, even if the particle was in this state prior to our decision. It would be a case in which the normal time orientation of agency was reversed, but there is no reason to say that this reduces our free will.

    Bell seems to have considered and rejected the psosibility of advanced causation because he thought that correlations between our decision and the state of the photon "pre-determined from the beginning of time" would make our free will nonexistent. But it is not determinism by itself that imperils free will -most philosophers nowadays are compatibilists and accept that free will can coexist with determinism. What could imperil free will is if the correlations came from a common past cause, and knowledge of it could make someone predict our actions (or create paradoxes by telling us to decide in an opposite way). But nothing of this is true in our model: there is no common cause in the past from which the correlations come (they come only "backwards" from the future interaction) and nobody could measure the state of the photon to predict our decision, because by the fact of measuring it, it would be true in fact that it was correlated with him and not with us! So there is no reason to deny we have free will because of the incoming correlation.

    By Blogger Alejandro, at 4:23 AM, September 19, 2006  

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