Quantum states for a minimum-length spacetime

TL;DR

This paper explores a quantum framework for spacetime with a minimum length, proposing an operator for the Ricci scalar and linking horizon entropy to area, independent of field equations.

Contribution

It introduces a quantum operator for the Ricci scalar at a point in a minimal-length spacetime and supports the area-entropy relation through quantum informational arguments.

Findings

Proposes an explicit form for the Ricci scalar operator as a quantum observable.

Provides quantum-informational support for horizon entropy proportional to area.

Analyzes null separations within a minimal-length quantum spacetime framework.

Abstract

Starting from some results regarding the form of the Ricci scalar at a point $P$ in a spacetime endowed with a minimum distance, we investigate how they might be accommodated, specifically for the case of null separations, in a as-simple-as-possible quantum structure for spacetime at $P$, and we try to accomplish this in terms of potentially operationally-defined concepts. In so doing, we provide a possible explicit form for the operator expressing the Ricci scalar as a quantum observable, and give quantum-informational support, thus regardless of or before field equations, to associating with a patch of horizon an entropy proportional to its area.