The Large Numbers Hypothesis and Quantum Mechanics

TL;DR

This paper proposes a hypothesis that quantum mechanics and gravitational phenomena are invariant under discrete scale transformations, leading to large-scale quantization effects that could explain cosmic and planetary structures.

Contribution

It introduces a novel large-scale scale invariance hypothesis linking quantum mechanics with cosmological phenomena, extending the scale invariance concept to the universe.

Findings

Large scale quantization of angular momentum consistent with universe and galaxy properties.

Derived relations matching galaxy cluster and star mass-spin data.

Calculated planetary orbit radii using scaled quantum principles.

Abstract

In this paper, the suggested similarity between micro and macro-cosmos is extended to quantum behavior, postulating that quantum mechanics, like general relativity and classical electrodynamics, is invariant under discrete scale transformations. This hypothesis leads to a large scale quantization of angular momenta. Using the scale factor $\Lambda \sim 10^{38}$, the corresponding quantum of action, obtained by scaling the Planck constant, is close to the Kerr limit for the spin of the universe -- when this is considered as a huge rotating black-hole -- and to the spin of Godel's universe, solution of Einstein equations of gravitation. Besides, we suggest the existence of another, intermediate, scale invariance, with scale factor $\lambda \sim 10^{19}$. With this factor we obtain, from Fermi's scale, the values for the gravitational radius and for the collapse proper-time of a typical black-hole, besides the Kerr limit value for its spin. It is shown that the mass-spin relations implied by the two referred scale transformations are in accordance with Muradian's Regge-like relations for galaxy clusters and stars. Impressive results are derived when we use a $\lambda$-scaled quantum approach to calculate the mean radii of planetary orbits in solar system. Finally, a possible explanation for the observed quantization of galactic redshifts is suggested, based on the large scale quantization conjecture.