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