The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory

TL;DR

This paper proposes a pluralistic quantum cosmology that integrates the Bekenstein bound, holography, topological quantum field theory, and loop quantum gravity. It assigns Hilbert spaces to all timelike boundaries, with states interpreted as observer-specific information and consistency enforced by a boundary-consensus condition, thereby avoiding the need for a single universal state. A concrete realization ties the boundary Hilbert spaces to SU(2)$_q$ Chern–Simons theory, leveraging spin networks and punctured surfaces to satisfy the Bekenstein bound and realize a finite-dimensional holographic description at each boundary. The framework also offers a relational notion of time and aims to recover linearized QFT in appropriate limits, while suggesting a thermodynamic route to Einstein’s equations; overall, it provides a cohesive program for a nonperturbative quantum gravity that naturally incorporates cosmological boundary data and observer-dependent information. This approach could illuminate how classical spacetime and quantum field theory emerge from a richly structured, boundary-centric quantum cosmology.

Abstract

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.