Quantum States for a Minimum-Length Spacetime

Abstract

Starting from some results regarding the form of the Ricci scalar at a point P in a (particle-like) 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.