Three Roads To Quantum Gravity

138 THREE ROADS TO QUANTUM GRAVITY
us that the spin network picture of quantum geometry is not
just a product of someone's imagination ± rather, it follows
directly from combining the basic principles of quantum
theory with those of relativity.
The loop approach to quantum gravity is now a thriving
®eld of research. Many of the older ideas, such as supergravity
and the study of quantum black holes, have been incorporated
into it. Connections have been discovered to other approaches
to quantum gravity, such as Alain Connes's non-commutative
approach to geometry, Roger Penrose's twistor theory and
string theory.
One lesson we have learned from this experience is the
extent to which science progresses quickly when people with
different backgrounds and educations join forces to push back
the frontiers. The relationship between theoretical physicists
and mathematical physicists is not always smooth. It is rather
like the relationship between the scouts who ®rst explore the
frontier, and the farmers who come after them and fence the
land and make it productive. The mathematical farmers need
to tie everything down, and determine the exact boundaries of
an idea or a result, while we physicist scouts like our ideas
when they are still a bit wild and untamed. Each has a
tendency to think that they did the essential part of the work.
But something we and the string theorists have both learned is
that in spite of their different ways of working and thinking, it
is essential that mathematicians and physicists learn to
communicate and work with one another. As happened with
general relativity, quantum gravity requires new mathematics
as much as it requires new concepts, ideas and ways of doing
calculations. If we have made real progress it is because we
have discovered that people can work together to invent
something that no one person could have come up with alone.
In the end, what is most satisfying about the picture of
space given by loop quantum gravity is that it is completely
relational. The spin networks do not live in space; their
structure generates space. And they are nothing but a
structure of relations, governed by how the edges are tied
together at the nodes. Also coded in are rules about how the
edges may knot and link with one another. It is also very