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.

© 1996 John Baez

baez@math.removethis.ucr.andthis.edu