Newton's constant from a minimal length: Additional models

TL;DR

This paper develops two models of holographic screens linking Newton's constant to a minimal length scale, demonstrating the generic nature of Klinkhamer's proposed new length scale in quantum gravity.

Contribution

It introduces two microscopic models of holographic screens that derive Newton's law with a minimal length scale, connecting quantum surface structures to gravity.

Findings

The models reproduce Newton's law thermodynamically.

The new length scale's significance appears robust across models.

Connections to loop quantum gravity surface structures.

Abstract

We follow arguments of Verlinde and Klinkhamer, and construct two models of the microscopic theory of a holographic screen that allow for the thermodynamical derivation of Newton's law, with Newton's constant expressed in terms of a minimal length scale contained in the area spectrum of the microscopic theory. One of the models is loosely related to the quantum structure of surfaces and isolated horizons in loop quantum gravity. Our investigation shows that the conclusions reached by Klinkhamer regarding the new length scale seem to be generic in all their qualitative aspects.