Three Roads To Quantum Gravity

AREA AND INFORMATION
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system which is very carefully prepared, or which incorporates
structures that preserve a memory of what has happened
to it ± such as a complex molecule such as DNA ± can be seen
to evolve from a less ordered to a more ordered state.
The argument here is rather subtle, and it took several
decades for most physicists to be convinced. The originator of
the idea that entropy had to do with information and
probability, Ludwig Boltzmann, committed suicide in 1906,
which was before most physicists had accepted his arguments.
(Whether his depression had anything to do with the
failure of his colleagues to appreciate his reasoning, Boltzmann's
suicide had at least one far-reaching consequence:
it convinced a young physics student named Ludwig Wittgenstein
to give up physics and go to England to study
engineering and philosophy.) In fact, the arguments that
®nally convinced most physicists of the existence of atoms
had just been published the year before by the then patent
of®ce clerk Albert Einstein (`Same Einstein', as my physics
teacher used to say.) This argument had to do with fact that
the statistical point of view allowed the laws of thermodynamics
to be violated from time to time. What Boltzmann
had found was that the laws of thermodynamics would be
exactly true for systems that contained an in®nite number of
atoms. Of course, the number of atoms in a given system, such
as the water in a glass, is very large, but it is not in®nite.
Einstein realized that for systems containing a ®nite number
of atoms the laws of thermodynamics would be violated from
time to time. Since the number of atoms in the glass is large,
these effects are small, but they still may in some circumstances
be observed. By making use of this fact Einstein was
able to discover manifestations of the motions of atoms that
could be observed. Some of these had to do with the fact that a
grain of pollen, observed in a microscope, will dance around
randomly because it is being jiggled by atoms colliding with
it. As each atom has a ®nite size, and carries a ®nite amount of
energy, the jiggles that result when they collide with the grain
of pollen can be seen, even if the atoms themselves are far too
small to be seen.
The success of these arguments persuaded Einstein and a