Three Roads To Quantum Gravity

150 THREE ROADS TO QUANTUM GRAVITY
twenty-®rst-century mathematics that had fallen by luck into
our hands in the twentieth century. This does not sound quite
as good now as it used to.) The problem is that we do not yet
have string theory expressed in any form that could be that of
a fundamental theory. What we have on paper cannot be
considered to be the theory itself. What we have is no more
than a long list of examples of solutions to the theory; what
we do not yet have is the theory they are solutions of. It is as if
we had a long list of solutions to the Einstein equations,
without knowing the basic principles of general relativity or
having any way to write down the actual equation that de®nes
the theory.
Or, to take a simpler example, string theory in its present
form most likely has the same relationship to its ultimate form
as Kepler's astronomy had to Newton's physics. Johannes
Kepler discovered that the planets travel along elliptical
orbits, and he was able to use this principle together with
two other rules he discovered to write down an in®nite
number of possible orbits. But it took Newton to discover the
reason why the planetary orbits are ellipses. This allowed him
to unify the explanation of the motions of the planets with
many other observed motions, such as the parabolic trajectories
that Galileo had discovered are followed by projectiles
on the Earth. Many more examples of solutions to string
theory have recently been discovered, and the virtuosity
required to construct these solutions in the absence of a
fundamental principle is truly humbling. This has made it
possible to learn a lot about the theory, but so far, at least, it
does not suf®ce to tell us what the theory is. No one has yet
had that vital insight that will make it possible to jump from
the list of solutions to the principles of the theory.
Let us begin, then, with what we do know about string
theory, for these are reasons enough to take it seriously.
Quantum theory says that for every wave there is an
associated particle. For electromagnetic waves there is the
photon. For electrons there is the electron wave (the wavefunction).
The wave doesn't even have to be something
fundamental. When I strike a tuning fork I set up waves that
travel up and down it: these are sound waves travelling in