Holography in a quantum spacetime

TL;DR

This work develops a background-independent, Planck-scale holographic framework for cosmology based on quantum causal histories and screen networks. By introducing elementary screens and a two-sided, chiral flow of information, it defines a weak holographic principle in which screen area is tied to the information capacity (via $A(s) = a\, l_{\mathrm{Pl}}^2 \ln D(s)$) rather than a bulk geometry, allowing a discrete, many-screens description without a bulk theory. It shows how such screen networks can arise from background-independent quantum gravity candidates (e.g., causal spin networks) and illustrates the construction with explicit SU_q(2) examples, while discussing the relationship to the semiclassical strong holographic principle in the continuum limit. The framework highlights how holography in cosmology may be formulated through information flow across screens, with implications for observables and the role of geometry in quantum spacetime.

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.