Three Roads To Quantum Gravity

202 THREE ROADS TO QUANTUM GRAVITY
values of the masses of the elementary particles and the
strengths of the fundamental forces. One can estimate the
probability that the constants in our standard theories of the
elementary particles and cosmology would, were they chosen
randomly, lead to a world with carbon chemistry. That
probability is less than one part in 10 220 . But without carbon
chemistry the universe would be much less likely to form
large numbers of stars massive enough to become black holes,
and life would be very unlikely to exist. This is evidence for
some mechanism of self-organization, because what we mean
by self-organization is a system that evolves from a more
probable to a less probable con®guration. So the best argument
we can give that such a mechanism has operated in the
past must have two parts: ®rst, that the system be structured
in some way that is enormously improbable; and second, that
nothing acting from the outside could have imposed that
organization on the system. In the case of our universe we are
taking this second part as a principle. We then satisfy both
parts of the argument, and are justi®ed in seeking mechanisms
of self-organization to explain why the constants in the
laws of nature have been chosen so improbably.
But there is an even better piece of evidence for the same
conclusion. It is right in front of us, and so familiar that it is
dif®cult at ®rst to understand that it also is a structure of
enormous improbability. This is space itself. The simple fact
that the world consists of a three-dimensional space, which is
almost Euclidean in its geometry, and which extends for huge
distances on all sides, is itself an extraordinarily improbable
circumstance. This may seem absurd, but this is only because
we have become so mentally dependent on the Newtonian
view of the world. For how probable the arrangement of the
universe is cannot be answered a priori. Rather, it depends on
the theory we have about what space is. In Newton's theory
we posit that the world lives in an in®nite three-dimensional
space. On this assumption, the probability of us perceiving a
three-dimensional space around us, stretching in®nitely in all
directions, is 1. But of course we know that space is not
exactly Euclidean, only approximately so. On large scales
space is curved because gravity bends light rays. Since this