Three Roads To Quantum Gravity

102 THREE ROADS TO QUANTUM GRAVITY
the idea that matter is made out of atoms; it has to do with
missing information. The entropy of the black hole itself
seems to have nothing to do with either atoms or with
information. It is a measure of a quantity which has to do
with the geometry of space and time: it is proportional to the
area of the black hole's event horizon.
There is something incomplete about a law which asserts a
balance or an exchange between two very dissimilar things. It
is as though we had two kinds of currency, the ®rst of which
was exchangeable into a concrete entity such as gold, while
the other had no worth in terms other than paper. Suppose we
were allowed to freely mix the two kinds of money in our
bank accounts. Such an economy would be based on a
contradiction, and could not survive for long. (In fact,
communist governments experimented with two kinds of
currency, one convertible into other currencies and one not,
and discovered that the system is unstable in the absence of
all sorts of complicated and arti®cial restrictions on the use of
the two kinds of money.) Similarly, a law of physics that
allows information to be converted into geometry, and vice
versa, but gives no account of why, should not survive for
long. There must be something deeper and simpler at the root
of the equivalence.
This raises two profound questions:
. Is there an atomic structure to the geometry of space and
time, so that the entropy of the black hole could be
understood in exactly the same way that the entropy of
matter is understood: as a measure of information about the
motion of the atoms?
. When we understand the atomic structure of geometry will
it be obvious why the area of a horizon is proportional to the
amount of information it hides?
These questions have motivated a great deal of research since
the mid-1970s. In the next few chapters I shall explain why
there is a growing consensus among physicists that the
answer to both questions must be `yes'.