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Emergence of a 4D World from Causal Quantum Gravity

J. Ambjorn, J. Jurkiewicz, R. Loll

TL;DR

Evidence is presented that a macroscopic four-dimensional world emerges from Causal Dynamical Triangulations in four dimensions dynamically, which provides a background-independent definition of the sum over geometries in nonperturbative quantum gravity.

Abstract

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.

Emergence of a 4D World from Causal Quantum Gravity

TL;DR

Evidence is presented that a macroscopic four-dimensional world emerges from Causal Dynamical Triangulations in four dimensions dynamically, which provides a background-independent definition of the sum over geometries in nonperturbative quantum gravity.

Abstract

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.

Paper Structure

This paper contains 4 sections, 7 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The emergent macroscopic 4d geometries
  3. Discussion
  4. Acknowledgment

Figures (3)

  • Figure 1: Snapshot of a "typical universe" of volume 91.1k from the Monte Carlo simulations. The total time extent (vertical direction) is $t=40$ as indicated. The circumference at integer-$t$ is the spatial three-volume $V_3(t) \times 0.02$ (in units where $a_s=1$). The surface represents an interpolation between adjacent "spatial volumes". No attempt has been made to capture the actual 4d connectivity between neighbouring spatial slices.
  • Figure 2: Measurement of spatial volume-volume correlators for spacetimes with $N_4 \approx$ 45.5, 91.1 and 184.4k, and after performing the rescaling (\ref{['5']}).
  • Figure 3: The log-log plot of the average geodesic distance $\langle r\rangle_{V_3}$ versus $V_3$. It combines data from universes where $N_4 \approx$ 45.5, 91.1, 184.4 and 371.2k.