Three Roads To Quantum Gravity

184 THREE ROADS TO QUANTUM GRAVITY
make string theory truly a quantum theory of gravity. Loop
quantum gravity is faced with the problem of how to show
that a quantum spacetime described by an evolving spin
network will grow into a large classical universe, which to a
good approximation can be described in terms of ordinary
geometry and Einstein's theory of general relativity. This
problem arose in 1995 when Thomas Thiemann, a young
German physicist then working at Harvard, presented for the
®rst time a complete formulation of loop quantum gravity
which resolved all the problems then known to exist.
Thiemann's formulation built on all the previous work, to
which he added some brilliant innovations of his own. The
result was a complete theory which in principle should be
able to answer any question. Furthermore, the theory could be
derived directly from Einstein's general theory of relativity by
following a well de®ned and mathematically rigorous procedure.
As soon as we had the theory, we began calculating with it.
The ®rst thing to calculate was how a graviton might appear
as a description of a small wave or disturbance passing
through a spin network. Before this could be done, however,
we had to solve a more basic problem, which was to understand
how the geometry of space and time, which seems so
smooth and regular on the scales we can see, emerges from the
atomic description in terms of spin networks. Until this was
done we would not be able to make sense of what a graviton
is, as gravitons should be related to waves in classical
spacetime.
This kind of problem, new to us, is very familiar to
physicists who study materials. If I cup my hands together
and dip them into a stream I can carry away only as much
water as will ®ll the `cup'. But I can lift a block of ice just by
holding it at its two sides. What is it about the different
arrangements of the atoms in water and ice that accounts for
the difference? Similarly, the spin networks that form the
atomic structure of space can organize themselves in many
different ways. Only a few of these ways will have a regular
enough structure to reproduce the properties of space and
time in our world.