Three Roads To Quantum Gravity

132 THREE ROADS TO QUANTUM GRAVITY
discrete had come to me in a ¯ash as I was trying to calculate
the volume of some quantum geometry, while I was sitting for
an hour in a noisy room in a garage waiting for my car to be
®xed. The page of my notebook was ®lled with many messy
integrals, but all of a sudden I saw emerge a formula for
counting. I had begun to calculate a quantity on the assumption
that the result was a real number, but found instead that,
in certain units, all the possible answers would be integers.
This meant that areas and volumes cannot take any value, but
come in multiples of ®xed units. These units correspond to
the smallest areas and volumes that can exist. I showed these
calculations to Carlo, and a few months later, during a period
we spent working together at the University of Trento, in the
mountains of north-east Italy, he invented an argument that
showed that the basic unit of area could not be taken to zero.
This meant there was no way to avoid the conclusion that if
our theory were true, space had an `atomic' structure.
I well remember our work in Trento for another reason. In
the previous year one of our students, Bernd Bruegmann, had
come to my of®ce with a very disturbed look on his face. His
thesis problem was to apply the new methods from loop
quantum gravity to QCD on a lattice, and see whether the
properties of protons and neutrons would emerge. While
doing so he did what good scientists should do, but which
we had not, which was to check the literature thoroughly. He
had found a paper in which methods very similar to ours had
already been applied to QCD by two people we had never
heard of, Rodolfo Gambini and Anthony Trias, who were
working in Montevideo and Barcelona.
Scientists are human, and we all suffer from the need to feel
that what we do is important. Pretty much the worst thing that
can happen to a scientist is to ®nd that someone has made the
same discovery before you. The only thing worse is when
someone publishes the same discovery you made, after you've
published it yourself, and does not give you adequate credit.
It was true that we had discovered the method of working
with loops in the realm of quantum gravity rather than in
QCD, but there was no avoiding the fact that the method we
had developed was quite close to the one that Gambini and