The Gravitational Bohr Radius
When theoretical physicists want to tell us that gravitation is exceedingly weak in the microcosm, they use the Gravitational Bohr Radius as the archetypal example. The GRB is the radius of a hydrogen atom if the binding interaction of the atom was gravitational instead of electromagnetic. When calculated under the assumption that the Newtonian gravitational coupling factor (G) is an absolute constant that applies anywhere in the cosmos, the GRB equals roughly 1.2 x 10^31 cm. This is bigger than the whole observable universe.
On the other hand, Discrete Scale Relativity asserts that the reason we are having so much trouble in theoretical physics these days (no strings, no supersymmetry, no WIMP dark matter, no marriage of General Relativity and Quantum Mechanics, etc.) is our insistence on absolute scale, and an absolute value of G on all cosmological Scales.
Discrete Scale Relativity shows how the scaling for nature’s actual discrete self-similar (i.e., discrete conformal) geometry is radically different. When DSR’s scaling is used to calculate the GBR the result about 2pi times the conventional Bohr radius for the ground state of hydrogen.
The same DSR scaling gives a Planck radius, mass and time that are strongly related to hydrogen’s nucleus — the proton.
Here is a paper that elaborates on the above issues.
With Discrete Scale Relativity we do not lose the any good and well-tested physics. We gain answers to many enigmas and a far more unified physics than we have ever had.