Three Roads To Quantum Gravity

204 THREE ROADS TO QUANTUM GRAVITY
description of such a space. Such a spin network must then be
something like a metal. A metal looks smooth because the
atoms in it have a regular arrangement, consisting of almost
perfect crystals that contain huge numbers of atoms. So the
question we are asking is analogous to asking how probable it
is that all the atoms in the universe would arrange themselves
in a crystalline structure like the atoms in a metal, stretching
from one end of the universe to another. This is, of course,
exceedingly improbable. But there are about 10 75 spin network
nodes inside every atom, so the probability that all of them are
arranged regularly is less than 1 part in 10 75 ± smaller still.
It may be that this is an underestimate and the probability is
not quite so small. There is one way of ensuring that all the
atoms in the universe arrange themselves in a perfect crystal,
which is to freeze the universe down to a temperature of
absolute zero, and compacted so as to give it a density high
enough for hydrogen gas to form a solid. So perhaps the spin
network representing the geometry of the world is arranged
regularly because it is frozen.
We can ask how probable this is. We can reason that if the
universe were formed completely by chance it would have a
temperature which is some reasonable fraction of the maximum
possible temperature. The maximum possible temperature
is the temperature that a gas would have if each atom was
as massive as the Planck mass and moved at a fair fraction of
the speed of light. The reason is that if the temperature were
raised beyond point, the Planck temperature, the molecules
would all collapse into black holes. Now, for the atoms of
space to have a regular arrangement the temperature must be
much, much less than this maximum temperature. In fact, the
temperature of the universe is less than 10 732 times the
Planck temperature. So the probability that a universe, chosen
randomly, would have this temperature is less than 1 part in
10 32 . So we conclude that it is at least this improbable that the
universe is as cold as it is.
Whichever way we make the estimate, we conclude that if
space really has a discrete atomic structure, then it is
extraordinarily improbable that it would have the completely
smooth and regular arrangement we observe it to have. So this