The Gravitational Bohr Radius

TL;DR

This paper explores a hypothetical gravitational atom and proposes that, under a fractal cosmological paradigm, its size is comparable to the standard atomic scale, challenging conventional gravitational assumptions.

Contribution

It introduces a revised calculation of the gravitational Bohr radius using a fractal paradigm, suggesting a much smaller size than traditionally predicted.

Findings

Revised GBR is approximately 2π times the standard Bohr radius.

Traditional calculations predict an astronomically large GBR.

Fractal paradigm implies a significantly stronger gravitational coupling at atomic scales.

Abstract

The gravitational Bohr radius (GBR) characterizes the size of a hypothetical ground state hydrogen atom wherein the binding interaction between its nucleus and its electronic structure is purely gravitational. The conventional calculation of the GBR, based on the standard Newtonian gravitational coupling constant, yields an astronomical size for the "gravitational atom". On the other hand, a discrete fractal cosmological paradigm asserts that the gravitational coupling constant that applies within Atomic Scale systems is roughly 38 orders of magnitude larger than the conventional gravitational constant. According to calculations based on predictions of this discrete fractal paradigm, the value of the GBR is actually on the order of 2 pi times the standard Bohr radius. Implications of this revised gravitational Bohr radius are discussed.