Three Roads To Quantum Gravity

160 THREE ROADS TO QUANTUM GRAVITY
dependence. Each string theory moves against a different
background spacetime, so to de®ne a string theory one must
®rst ®x the dimension of space and the geometry of spacetime.
In many cases space has more dimensions than the three we
observe. This is explained by the hypothesis that in our
universe the extra dimensions are curled up too tightly for
us to perceive directly. We say that the extra six dimensions
have been compacti®ed. Since string theory is simplest if the
world has nine spatial dimensions, this leads to a picture in
which many of the different consistent string theories in three
dimensions can be understood as arising from different ways
of choosing the structure of a hidden six-dimensional space.
There are at least hundreds of thousands of ways in which
the six extra dimensions may be compacti®ed. Each way
corresponds to a different geometry and topology for the extra
six dimensions. As a result there are at least that many
different string theories that are consistent with the basic
observation that the world has three large spatial dimensions.
Furthermore, each of these theories has a set of parameters
that describe the size and other geometric properties of the six
compacti®ed dimensions. These turn out to in¯uence the
physics that we see in the three-dimensional world. For
example, the geometry of the extra dimensions in¯uences
the masses and the strengths of the interactions of the
elementary particles we observe.
It is most likely irrelevant whether these extra dimensions
exist in any literal sense. If one is drawn to a picture of our
three-dimensional `reality' embedded in some higher-dimensional
realm, then one can believe in the extra dimensions, at
least as long as one is working in this background dependent
picture. But these extra dimensions can also be seen as purely
theoretical devices which are useful for understanding the list
of consistent string theories in three dimensions. As long as
we stay on the background dependent level, it does not really
matter.
As a result, although it is a uni®ed theory, string theory in
its present form makes few predictions about the physics we
actually observe. Many different scenarios for what the new,
more powerful particle accelerators will ®nd are consistent