Three Roads To Quantum Gravity

CHAPTER 12
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THE HOLOGRAPHIC PRINCIPLE
In Part II we looked at three different approaches to quantum
gravity: black hole thermodynamics, loop quantum gravity
and string theory. While each takes a different starting point,
they all agree that when viewed on the Planck scale, space
and time cannot be continuous. For seemingly different
reasons, at the end of each of these roads one reaches the
conclusion that the old picture according to which space and
time are continuous must be abandoned. On the Planck
scale, space appears to be composed of fundamental discrete
units.
Loop quantum gravity gives us a detailed picture of these
units, in terms of spin networks. It tells us that areas and
volumes are quantized and come only in discrete units. String
theory at ®rst appears to describe a continuous string moving
in a continuous space. But a closer look reveals that a string is
actually made of discrete pieces, called string bits, each of
which carries a discrete amount of momentum and energy.
This is expressed in a simple and beautiful way as an
extension of the uncertainty principle, which tells us that
there is a smallest possible length.
Black hole thermodynamics leads to an even more extreme
conclusion, the Bekenstein bound. According to this principle
the amount of information that can be contained in any
region is not only ®nite, it is proportional to the area of the
boundary of the region, measured in Planck units. This
implies that the world must be discrete on the Planck scale,