Three Roads To Quantum Gravity

170 THREE ROADS TO QUANTUM GRAVITY
for were it continuous any region could contain an in®nite
amount of information.
It is remarkable that all three roads lead to the general
conclusion that space becomes discrete on the Planck scale.
However, the three different pictures of quantum spacetime
that emerge seem rather different. So it remains to join these
pictures together to make a single picture which, when we
understand it, will become the one ®nal road to quantum
gravity.
At ®rst it may not be obvious how to do this. The three
different approaches investigate different aspects of the
world. Even if there is one ultimate theory of quantum
gravity, there will be different physical regimes, in which
the basic principles may manifest themselves differently.
This seems to be what is happening here. The different
versions of discreteness arise from asking different questions.
We would ®nd an actual contradiction only if, when we asked
the same question in two different theories, we got two
different answers. So far this has not happened, because the
different approaches ask different kinds of question. It is
possible that the different approaches represent different
windows onto the same quantum world ± and if this is so,
there must be a way of unifying them all into a single theory.
If the different approaches are to be uni®ed, there must be a
principle which expresses the discreteness of quantum
geometry in a way that is consistent with all three approaches
If such a principle can be found, then it will serve as a guide
to combining them into one theory. In fact, just such a
principle has been proposed in recent years. It is called the
holographic principle.
Several different versions of this principle have been
proposed by different people. After a lot of discussion over
the last few years there is still no agreement about exactly
what the holographic principle means, but there is a strong
feeling among those of us in the ®eld that some version of the
holographic principle is true. And if it is true, it will be the
®rst principle which makes sense only in the context of a
quantum theory of gravity. This means that even if it is
presently understood as a consequence of the principles of