Black hole thermodynamics suggests that the maximum entropy that can be
contained in a region of space is proportional to the area enclosing it rather
than its volume. I argue that this follows naturally from loop quantum gravity
and a result of Kolmogorov and Bardzin' on the the realizability of networks in
three dimensions. This represents an alternative to other approaches in which
some sort of correlation between field configurations helps limit the degrees
of freedom within a region. It also provides an approach to thinking about
black hole entropy in terms of states inside rather than on its surface.
Intuitively, a spin network complicated enough to imbue a region with volume
only lets that volume grow as quickly as the area bounding it.Comment: 7 pages, this essay received an Honourable Mention in the Gravity
Research Foundation Essay Competition 2005; reformatted for IJMP (accepted
for publication) with minor typographical corrections and some extended
discussio
