Three Roads To Quantum Gravity

40 THREE ROADS TO QUANTUM GRAVITY
to combining quantum theory and cosmology that we shall
come to.
In my opinion, conventional quantum cosmology has not
been a success. Perhaps this is too harsh a judgement. Several
of the people I most respect in the ®eld disagree with this. My
own views on the matter have been shaped by experience as
much as re¯ection. By chance I was part of the discovery of
the ®rst actual solutions to the equations that de®ne a
quantum theory of cosmology. These are called the Wheeler±
DeWitt equations or the quantum constraints equations. The
solutions to these equations de®ne quantum states that are
meant to describe the whole universe.
Working ®rst with one friend, Ted Jacobson, then with
another, Carlo Rovelli, I found an in®nite number of solutions
to these equations in the late 1980s. This was very surprising,
as very few of the equations of theoretical physics can be
solved exactly. One day in February 1986, Ted and I, working
in Santa Barbara, set out to ®nd approximate solutions to the
equations of quantum cosmology, which we had been able to
simplify thanks to some beautiful results obtained by two
friends, Amitaba Sen and Abhay Ashtekar. All of a sudden we
realized that our second or third guess, which we had written
on the blackboard in front of us, solved the equations exactly.
We tried to compute a term that would measure how much
our results were in error, but there was no error term. At ®rst
we looked for our mistake, then all of a sudden we saw that
the expression we had written on the blackboard was spot on:
an exact solution of the full equations of quantum gravity. I
still remember vividly the blackboard, and that it was sunny
and Ted was wearing a T-shirt (then again, it is always sunny
in Santa Barbara and Ted always wears a T-shirt). This was
the ®rst step of a journey that took ten years, sometimes
exhilarating and often aggravating years, before we understood
what we had really found in those few minutes.
Among the things we had to struggle with were the
implications of the fact that the observer in quantum cosmology
is inside the universe. The problem is that in all the usual
interpretations of quantum theory the observer is assumed to
be outside the system. That cannot be so in cosmology. This is