Newton's gravitational coupling constant from a quantum of area

TL;DR

This paper generalizes a previous calculation of Newton's gravitational constant G by relating it to a quantum of area and an integer dimension of microscopic space, proposing a modified energy law and potential long-range interactions.

Contribution

It introduces a generalized formula for G based on quantum area and internal space dimension, extending previous models and suggesting new interactions among microscopic degrees of freedom.

Findings

G is inversely proportional to the logarithm of the internal space dimension d_{atom}

The model excludes the case d_{atom}=1

Proposes a modified energy equipartition law for gravity

Abstract

A previous calculation of Newton's gravitational coupling constant G is generalized. This generalization makes it possible to have "atoms of two-dimensional space" with an integer dimension d_{atom} of the internal space, where the case d_{atom}=1 is excluded. Given the quantum of area l^2, the final formula for G is inversely proportional to the logarithm of the integer d_{atom}. The generalization used may be interpreted as a modification of the energy equipartition law of the microscopic degrees of freedom responsible for gravity, suggesting some form of long-range interaction between these degrees of freedom themselves.