Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

On the Emergence of Spacetime and Matter from Model Sets

Version 1 : Received: 18 November 2021 / Approved: 19 November 2021 / Online: 19 November 2021 (14:32:22 CET)
Version 2 : Received: 22 March 2022 / Approved: 23 March 2022 / Online: 23 March 2022 (09:26:42 CET)

How to cite: Amaral, M.; Fang, F.; Aschheim, R.; Irwin, K. On the Emergence of Spacetime and Matter from Model Sets. Preprints 2021, 2021110359 (doi: 10.20944/preprints202111.0359.v2). Amaral, M.; Fang, F.; Aschheim, R.; Irwin, K. On the Emergence of Spacetime and Matter from Model Sets. Preprints 2021, 2021110359 (doi: 10.20944/preprints202111.0359.v2).

Abstract

We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.

Keywords

Quantum Gravity; Problem of Time; Particle Physics; Emergence; Holographic Principle; Model Sets

Subject

PHYSICAL SCIENCES, Particle & Field Physics

Comments (1)

Comment 1
Received: 23 March 2022
Commenter: Marcelo Amaral
Commenter's Conflict of Interests: Author
Comment: We improved the introduction and abstract to better motivate and contextualize the results. We have included the conclusions and generally improved the presentation of the results.
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