  An approach to quantum gravity and cosmology is proposed based on a synthesis
of four elements: 1) the Bekenstein bound and the related holographic
hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a
new approach to the interpretational issues of quantum cosmology and 4) the
loop representation formulation of non-perturbative quantum gravity. A set of
postulates are described, which define a (\it pluralistic quantum cosmological
theory.) These incorporates a statistical and relational approach to the
interpretation problem, following proposals of Crane and Rovelli, in which
there is a Hilbert space associated to each timelike boundary, dividing the
universe into two parts. A quantum state of the universe is an assignment of a
statistical state into each of these Hilbert spaces, subject to certain
conditions of consistency which come from an analysis of the measurement
problem. A proposal for a concrete realization of these postulates is
described, which is based on certain results in the loop representation and
topological quantum field theory, and in particular on the fact that spin
networks and punctured surfaces appear in both contexts. The
Capovilla-Dell-Jacobson solution of the constraints of quantum gravity are
expressed quantum mechanically in the language of Chern-Simons theory, in a way
that leads also to the satisfaction of the Bekenstein bound.
