Quantum Mechanics of Geometry

TL;DR

This paper reviews a six-year development of a quantum framework for Riemannian geometry, exploring its implications for black hole thermodynamics and future research directions.

Contribution

It introduces a detailed quantum geometric framework and demonstrates how it can be tested through black hole thermodynamics.

Findings

Quantum geometry framework developed over six years

Testable predictions for black hole thermodynamics

Discussion of future research directions

Abstract

Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate students in physics. As an illustrative application, I indicate how some of the detailed features of the micro-structure of geometry can be tested using black hole thermodynamics. Current and future directions of research in this area are discussed.