Three Roads To Quantum Gravity

HOW TO COUNT SPACE
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Since then, Julian Barbour has become known to most
people working in relativity, and recently he has become
even more widely known and appreciated as a result of the
publication of his radical theories on the nature of time. But
in the early 1980s few people knew of his work, and I was
very fortunate to meet him shortly after I had realized that my
lattice gravity theory was in trouble. During this meeting he
explained to me the meaning of space and time in general
relativity, and the role of the relational concept in it. This
gave me the conceptual language to understand why my
calculations were showing that gravity was nowhere to be
found in the theory I had constructed. What I needed to do
was invent something like Wilson's lattice theory, but in
which there was no ®xed lattice, so that all the structures
were dynamical and relational. A set of points connected by
edges ± in other words a graph ± is a good example of a system
de®ned by relationships. But what I had done wrong was to
base the theory on a ®xed graph. Instead, the theory should
produce the graph, and it should not mirror any pre-existing
geometry or structure. It should rather evolve according to
rules as simple as those that Wilson had given for the motion
of loops on his lattice. It was to be ten years before a way
appeared which made this possible.
During those ten years I spent my time on a variety of
unsuccessful attempts to apply techniques from particle
physics to the problem. These techniques were all background
dependent, in that they assumed that you could ®x a
single classical spacetime geometry and study how quantized
gravitational waves, called gravitons, move and interact on
the background. We tried lots of different approaches, but
they all failed. Besides this I wrote a few papers on supergravity,
the new theory of gravity which had been invented by
one of my advisors, Stanley Deser, and others. Those attempts
also came to nothing. Then I wrote a few papers about the
implications of the entropy of black holes, making various
speculations about their connection with problems in the
foundations of quantum mechanics. Looking at them now, it
seems to me that these papers were the only interesting things
I did during those years, but I have no evidence that very