Three Roads To Quantum Gravity

126 THREE ROADS TO QUANTUM GRAVITY
yielded de®nite predictions about the structure of space and
time on the Planck scale.
I invited Abhay to give a talk about this at Yale, where I had
just become an assistant professor. At the talk was a graduate
student named Paul Renteln, from Harvard, who had also
been studying Sen's papers. It was clear to us that Ashtekar's
formulation would be the key to further progress. Afterwards,
I drove Abhay to the airport in Hartford. On the hour's drive
between New Haven and Hartford my car had not one but two
¯at tyres ± and Abhay still just caught his ¯ight. He had to
hitch a ride for the last few miles, while I waited on the side of
the road for help.
When I ®nally got home I sat down immediately and began
to apply to the new formalism of Sen and Ashtekar the
methods Louis Crane and I had developed during our unsuccessful
attempts to re-invent string theory. A few weeks
later there began a semester-long workshop in quantum
gravity at the Institute for Theoretical Physics in Santa
Barbara. By another piece of luck, I had convinced the
authorities at Yale to let me spend a semester there, just after
they had hired me. As soon as I got there I recruited two
friends, Ted Jacobson and Paul Renteln. We found right away
that a very simple picture of the quantum structure of space
emerged if we used something very like the electric superconductor
picture for the ¯ux lines of the gravitational ®eld.
At ®rst I worked with Paul. Fearful of the in®nities that come
with continuous space, we used a lattice, much like Wilson's
lattice. We found that the new form of the Einstein equations
implied very simple rules for how the loops interact on the
lattice. But we ran into the same problem as I had ten years
before: how to get rid of the background imposed by the use of
a ®xed lattice.
Ted Jacobson suggested that we try to follow Polyakov and
work without a lattice. I have already described the result,
in Chapter 3. The next day we were standing in front of a
blackboard, staring at something which it had never occurred
to us, nor anyone else, to even look for. These were exact
solutions to the full equations of the quantum theory of
gravity.