Three Roads To Quantum Gravity

THE HOLOGRAPHIC PRINCIPLE
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the geometry of space, which determines the area of The
Screen, must change in response to the ¯ow of energy.
Jacobson shows that this actually implies the equations of
Einstein's theory.
Another reason to believe the Bekenstein bound is that it
can be derived directly from loop quantum gravity. To do this
one only has to study the problem of how a screen is
described by the quantum theory. As shown in Figure 40, in
loop quantum gravity a screen will be pierced by edges of a
spin network. Each edge that intersects the screen contributes
to the total area of the screen. It turns out that each edge that is
added also increases the amount of information that can be
stored in a quantum theoretic description of the screen. We
can add more edges, but the information a screen can store
cannot increase faster than its area. This is just what is
required by the Bekenstein bound.
Perhaps the ®rst person to realize the radical implications
of the Bekenstein bound was Louis Crane. He deduced from it
that quantum cosmology must be a theory of the information
exchanged between subsystems of the universe, rather than a
theory of how the universe would look to an outside observer.
This was the ®rst step towards the relational theories of
quantum cosmologies later developed by Carlo Rovelli, Fotini
Markopoulou and myself. Gerard 't Hooft later began to think
about the horizon of a black hole as something like a
computer, along the lines I have described. He proposed the
®rst version of the holographic principle and gave it its name.
It was then quickly championed by Leonard Susskind, who
showed how it could be applied to string theory. Since then at
least two other versions of the holographic principle have
been proposed. So far there is no consensus on which is right.
I shall explain two of the versions, which are called the strong
and weak holographic principles.
The idea of the strong holographic principle is very simple.
Since the observer is restricted to examining The Thing by
making observations through The Screen, all of what is
observed could be accounted for if one imagined that, instead
of The Thing, there was some physical system de®ned on the
screen itself (Figure 41). This system would be described by a