Three Roads To Quantum Gravity

THE SOUND OF SPACE IS A STRING
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with one version of string theory or another. Thus, not only
does string theory lack experimental con®rmation, but it is
hard to imagine an experiment that could be done in the next
several decades that could de®nitively con®rm or reject it.
Nor is there anything special, from the point of view of string
theory, about having six out of nine dimensions compacti®ed
while the other three are left large. String theory can easily
describe a world in which any number of dimensions, from
nine down to none at all, are left large.
String theory thus indicates that the world we see provides
only a sparse and narrow sampling of all possible physical
phenomena, for if true it tells us that most of the dimensions
and most of the symmetry of the world are hidden. Still, many
people do believe in it. This is partly because, however
incomplete its present formulation may be, string theory
remains the one approach that uni®es gravity with the other
forces consistently at a background dependent level.
The main problem in string theory, then, is how to see
beyond it to a theory which will incorporate the successes of
string theory while avoiding its weaknesses. One approach to
this problem begins with the following question. What if there
were a single theory that uni®ed the different string theories
by interpreting each of its solutions as one of the consistent
string theories? The different string theories, together with the
spacetimes they live in, will not be put in as absolutes. Rather
they will all arise from solutions of this new theory. Note that
the new theory could not be formulated in terms of any
objects moving against a ®xed spacetime background, because
its solutions would include all the possible background
spacetimes. The different solutions of this fundamental
theory would be analogous to the different spacetimes which
are all solutions to the equations of general relativity.
Now we can argue by analogy in the following way. Let us
take any spacetime which is a solution to the Einstein
equations, and wiggle some matter within it. This will
generate gravitational waves. These waves move on the
original spacetime like ripples moving on the surface of a
pond. We can make ripples in the solution of our fundamental
theory in the same way. What if these gave rise not to waves