Exploring quantum geometry created by quantum matter

TL;DR

This paper investigates the quantum geometry generated by matter sources in 3D gravity models, revealing limitations of classical theories and emphasizing the importance of quantum effects in understanding physical reality.

Contribution

It introduces exactly soluble models to explore matter-driven quantum geometry, highlighting non-linear effects and the emergence of new scales in quantum gravity.

Findings

Quantum matter sources can significantly influence quantum geometry.

Classical and semi-classical theories have limitations in certain regimes.

Emergence of new scales leads to novel effects in quantum gravity.

Abstract

Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized. The goal of this investigation is to probe the `Coulombic' aspects of quantum geometry that are governed entirely by matter sources. Since there are no gravitational waves in 3 dimensions, 3-d gravity coupled to matter provides an ideal arena for this task. Our analysis will reveal novel aspects of quantum gravity that bring out limitations of classical and semi-classical theories in unforeseen regimes: non-linearities of general relativity can magnify small quantum fluctuations in the matter sector to large effects in the gravitational sector. Finally, this analysis leads to thought experiments that bring out rather starkly why understanding of the nature of physical reality depends sensitively on the theoretical lens with which it is probed. As theories becomes richer, new scales emerge, triggering novel effects that could not be imagined before. The model provides a concise realization of this well-known chain.