Bronis Vidugiris wrote:
The arrow of time problem does seem closely related with the quantum measurement problem.I'll get around to some remarks on this in a while.
A few days back I recall someone posting to sci.physics, saying that Penrose thought that consciousness was what collapsed the wavefunction. Someone else replied that no, Penrose believed that it took the emission of one graviton to collapse the wavefunction (roughly speaking). Right now I'm visiting the new Center for Gravitational Physics and Geometry at Penn State, and Penrose is a visiting member, so walking to lunch yesterday I mentioned this and asked him what he thought he believed. He'd never heard of sci.physics but knew about bulletin boards in general, and smilingly said "I might as well be dead" not reading sci.physics, since people are arguing about what he thinks without him having a chance to say anything. He cringed at the notion of consciousness collapsing the wavefunction, saying that a lot of people seemed to think that, and that they must not have read his book. I ventured that perhaps it was because he discussed both consciousness and quantum mechanics.
He said that he had come up with a better idea than the "one graviton" notion. It goes roughly like this. Consider a superposition of 2 quantum states, and consider the difference of mass density functions in these two states. Calculate the gravitational self-energy of this difference (after taking absolute values, presumably - though he didn't say this); the reciprocal of this energy gives a time, and this time should represent the lifetime after which collapse should occur, leaving the system in one or the other state.
I should emphasize a number of qualifications he added. First, it was very clear from everything he said that all this was very tentative and just an order-of-magnitude sort of thing, not a precise theory. (He suggested a slight refinement of it that I forget, too.) Also, he said that most wavefunction collapse was due to quantum entanglement (correlation with the environment), and that this new mechanism would only supplement that method, hence only matter when the superposed system was quite isolated from the environment.
Somehow everything he said came across much more clearly as a tentative exploration than when I read his book, The Emperor's New Mind. Perhaps this is just a matter of how the printed word works.
At lunch, by the way, he said a bit about the movie about Hawking. He said it made him and all the physicists besides Hawking look quite silly. (I hadn't thought so myself, actually.) They didn't interview him in his office. Instead, the director had a set built in London based on what he thought the office of an Oxford professor should look like. It had a large chestnut desk with no papers on it at all, and a plush chair. There was a statue near the window, and the window looked out onto a fake Oxford building with gargoyles. The chair, unfortunately, was nailed to the floor at an uncomfortable distance from the desk. He complained, so they pried it off the floor and re-nailed it closer to the desk. (He said he never knew why they didn't move the desk closer to the chair. I suspect it too was nailed down.) Only Hawking had his actual office used in the movie. Penrose said he might mention this in his next book.
Anyway, after lunch he said he thought that quantum gravity might require nonlinear corrections to existing quantum theory. I asked him why he thought so - was it mainly for cosmological reasons? I was referring to his Weyl curvature hypothesis but he didn't understand I meant this, and said no, it was mainly because if virtual black holes were constantly generating entropy (turning pure states to mixed ones) there should be some complementary process that "purified" mixed states, and this should be wavefunction collapse. This completely confused me since I could only think of the von Neumann description of wavefunction collapse as the process of turning a pure (but superposed) state into a mixed state! It took quite a while for us to understand each other, but it hinged upon the conceptual difficulties with the notion of a mixed state: does it merely describe the observer's "subjective" ignorance of the state, or should it be taken as the ultimate "objective" description of the state in some cases. He said Hawking (who originated the problem of pure states becoming mixed due to information falling down virtual black holes, one of the hot topics in quantum gravity research right now) held the latter view, that the mixed state was "objective". He also noted that a density matrix is strictly speaking not quite the same as a mixture of states because a given density matrix can be expressed as different mixtures of different pure states. In any event, he gave a scenario where first correlation information fell into a virtual black hole, which then disappeared, leaving a mixed state, and then wavefunction collapse reduced the resulting mixed state into one of the pure states it was a mixture of. This made his views a little clearer to me - though only a little, now that I think about it.
In any event, I then mentioned that by "cosmological considerations" I'd meant his hypothesis that the Weyl curvature was low near initial singularities and high near final ones. He said yes, this too hinted at modifications of quantum theory in the presence of gravity that gave rise to some sort of irreversibility. He mentioned a thought experiment that I'd seen somewhere else, perhaps in his book. It goes as follows.
4 \ 1* ------- \ --------- >2 \ 3Here a light bulb at 1 emits photons which hit a half-mirrored surface and either go through to 2 or bounce off to 3. If a single photon is emitted, it should wind up in a superposition of 1/√2 being at 2 and 1/√2 being at 3, and we confidently predict that it has a 50-50 chance of getting to 2 or 3. If, however, we observe a photon at 2 and "retrodict" where it came from, quantum mechanics (supposedly) gives that it must have been a superposition of 1/√2 being at 1 and 1/√2 being at 4. This would seem to mean it had at 50-50 chance of coming from the lightbulb or from somewhere else! Blatant nonsense. Ergo, there is some inherent time-reversal asymmetry about how we apply quantum theory.
I told him I'd seen this argument and found it very annoying. He said that everyone said so, but nobody had refuted it. Unfortunately I had never gotten around to organizing my thoughts about it, so I had to wing it. After some hemming and hawing, I said that the real irreversibility was simply due to the fact that we use retarded rather than advanced solutions of Maxwell's equations, which in turn was due to the thermodynamical arrow of time. (My review of Zeh's book The Physical Basis of the Direction of Time explains this point, though rather briefly, and the book itself goes into more detail.) In other words, if the whole system were in a box and had reached thermodynamic equilibrium, so the walls were just as hot as the lightbulb, we would be justified in concluding, upon seeing a photon at 2, that there was a 50-50 chance of it originating from 1 or 4. It is only that our world is in a condition of generally increasing entropy that allows for the steup with a hot lightbulb and cool walls to occur, and we can't blame quantum mechanics for that time asymmetry.
He thought a while and said that well, a condition of thermal disequilibrium was necessary for a measurement to be made at all, but the real mystery was why we feel confident in using quantum mechanics to predict and not retrodict. This mystery can be traced back to gravity, in that gravity is the root of the arrow of time. (Again, see Zeh's book for more on this.) I was a bit disappointed that he didn't think my remarks dealt a crushing blow to this thought experiment , but I had to agree that if this was all he thought the moral of the experiment was, he was right.
Today he gave a talk on computability and consciouness, and suggested that the the key to consciousness might be quantum correlations in the microtubules comprising the neural cytoskeletons, but I think this is enough for now - I'm sure it'll appear in his book.