Holography in a quantum spacetime

TL;DR

This paper introduces a background independent holographic framework for quantum cosmology, relating quantum information flow to the causal structure of quantum spacetime without relying on a bulk theory.

Contribution

It formulates a holographic principle based on quantum information flow and causal networks, suitable for background independent quantum cosmological models.

Findings

Defines screens as measurement sets with bidirectional information flow

Introduces geometry via screen capacity as quantum information channel

Proposes a discrete, background independent holographic theory

Abstract

We propose a formulation of the holographic principle, suitable for a background independent quantum theory of cosmology. It is stated as a relationship between the flow of quantum information and the causal structure of a quantum spacetime. Screens are defined as sets of events at which the observables of a holographic cosmological theory may be measured, and such that information may flow across them in two directions. A discrete background independent holographic theory may be formulated in terms of information flowing in a causal network of such screens. Geometry is introduced by defining the area of a screen to be a measure of its capacity as a channel of quantum information from its null past to its null future. We call this a ``weak'' form of the holographic principle, as no use is made of a bulk theory.