Minimum spacetime length and the thermodynamics of spacetime

TL;DR

This paper reviews how theories of quantum gravity suggest a minimum length scale in spacetime and explores how this discretized structure influences gravitational thermodynamics and the emergence of Einstein's field equations.

Contribution

It introduces a quantum metric framework that incorporates a minimum length scale and links microscopic spacetime entropy to macroscopic gravitational dynamics.

Findings

Minimum length of spacetime implied by quantum gravity theories

Implementation of a bi-tensorial quantum metric to ensure finite geodesic distances

Derivation of gravitational field equations from thermodynamic principles

Abstract

Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a statistical way from an effective small scale discrete structure of spacetime and its information content. In this review we begin by outlining how theories of quantum gravity imply the existence of a minimum length of spacetime as a general feature. We then describe how such a structure can be implemented in a way that is independent from the details of the quantum fluctuations of spacetime via a bi-tensorial quantum metric $q_{\alpha\beta}(x, x')$ that yields a finite geodesic distance in the coincidence limit $x\rightarrow x'$. Finally, we discuss how the entropy encoded by these microscopic degrees of freedom can give rise to the field equations for gravity through a thermodynamic variational principle.