Time and Chance by David Albert, Harvard University Press, $20.50,
ISBN 0674003179
IF YOU see a half-melted ice cube sitting in a puddle of water, it鈥檚 a safe
bet that it will be more melted in a few minutes鈥� time. You can also be fairly
sure that the ice cube was frozen solid not so long ago. One of the triumphs of
19th-century physics, mainly due to Ludwig Boltzmann and J. Willard Gibbs, was
linking elementary, macroscopic observations such as these to the microscopic
point of view, the behaviour of atoms and molecules. It鈥檚 impossible to know the
exact disposition of every molecule in a partly melted ice cube. But Boltzmann
and Gibbs showed how to obtain a statistical description of the most likely
microscopic arrangements for a given macroscopic system. Newtonian mechanics
then gives a probabilistic prediction of what happens next.
From these simple beginnings arose the second law of thermodynamics, in the
version according to statistical mechanics. It states that with overwhelming
likelihood鈥攖hough not absolute certainty鈥攅ntropy increases with
time, and ice cubes tend to melt.
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But there鈥檚 a problem. If you try to 鈥渞etrodict鈥� what has happened, will you
discover that the ice cube should have been more frozen in the past? Sadly, no.
There鈥檚 a catch. Statistical mechanics predicts that there is an equal
probability that the ice cube melts whether you go forwards or backwards in
time. The underlying physical laws are symmetric with respect to the direction
of time, and the statistical description makes no distinction between past and
future.
This argument gained prominence in the 1890s, leading many scientists to
doubt the worth of statistical mechanics. In Time and Chance,
philosopher David Albert tells this tale in an intense and generally lucid
way鈥攚ith some hair-splitting digressions鈥攑ointing out subtleties
that physicists, lax creatures that they are, tend to gloss over or ignore.
He then tries to resolve the matter. It seems to me that Albert very much
underestimates what Boltzmann, Gibbs and others have said on the subject. He
makes some errors in physics that mislead him before, at length, he reaches the
right answer.
If I am reading him correctly, Albert thinks that a full statistical
mechanical description of any system ought to contain, implicitly, an objective
record of its past, thus obviating the retrodiction problem. But this misses the
point of statistical mechanics, which is to provide a sort of minimal guess
about the system, based on its present condition alone. We use it to predict the
future because we don鈥檛 have anything better to go on.
As Albert observes, we know what happened in the past. Statistical mechanics
allows the possibility that our melting ice was frozen at earlier time, and the
fact that this possibility is apparently highly unlikely is of no consequence,
because the statistical description of the ice cube is supplanted by actual
knowledge of past events. This is roughly the conclusion that Albert
reaches.
But Albert also cherishes his 鈥減ast hypothesis鈥�, that the Universe must have
begun in a state of low entropy in spite of the fact that Max Planck first
pointed this out as a criticism of statistical mechanics. Boltzmann alluded to
the question in an 1895 Nature paper, and it has been emphasised again
by Oxford鈥檚 Roger Penrose.
Albert tries to tie quantum mechanical uncertainty into the picture. Here he
relies on a speculative modification of quantum mechanics that I, for one, find
unappealing. In the end, this book sheds no light on the empirically obvious but
still mysterious fact that the past and the future are different.
Having said all that, I will somewhat perversely conclude by recommending
that anyone with a deep interest in this subject should take a look at Albert鈥檚
book. He writes in an idiosyncratic style, saying the same thing in
more than one way, in several (as it were) different ways,
frequently italicising. But he wrestles ferociously with the issues,
and while many physicists will find his answers opaque and unsatisfactory, his
presentation of the questions is provocative.