Three Roads To Quantum Gravity

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p in the formula for the radiation emitted by these black
holes.
A second idea about a black hole's entropy is that it is a
count, not of the ways to make a black hole, but of the
information present in an exact description of the horizon
itself. This is suggested by the fact that the entropy is
proportional to the area of the horizon. So the horizon is
something like a memory chip, with one bit of information
coded in every little pixel, each pixel taking up a region 2
Planck lengths on a side. This picture turns out to be
con®rmed by calculations in loop quantum gravity.
A detailed picture of the horizon of a black hole has been
developed using the methods of loop quantum gravity. This
work started in 1995 when, inspired by the ideas of Crane,
't Hooft, and Susskind, I decided to try to test the holographic
principle in loop quantum gravity. I developed a method for
studying the quantum geometry of a boundary or a screen. As
I mentioned earlier, the result was that the Bekenstein bound
was always satis®ed, so that the information coded into the
geometry on the boundary was always less than a certain
number times its total area.
Meanwhile, Carlo Rovelli was developing a rough picture
of the geometry of a black hole horizon. A graduate student of
ours, Kirill Krasnov, showed me how the method I had
discovered could be used to make Carlo's ideas more precise.
I was quite surprised because I had thought that this would be
impossible. I worried that the uncertainty principle would
make it impossible to locate the horizon exactly in a quantum
theory. Kirill ignored my worries and developed a beautiful
description of the horizon of a black hole which explained
both its entropy and its temperature. (Only much later did
Jerzy Lewandowksi, a Polish physicist who has added much
to our understanding of loop quantum gravity, work out how
the uncertainty principle is circumvented in this case.)
Kirill's work was brilliant, but a bit rough. He was subsequently
joined by Abhay Ashtekar, John Baez, Alejandro
Corichi and other more mathematically minded people who
developed his insights into a very beautiful and powerful
description of the quantum geometry of horizons. The results