THE LARGE NUMBERS HYPOTHESIS AND QUANTUM-MECHANICS

In this paper, the suggested similarity between micro and macrocosmos is extended to quantum behavior, postulating that quantum mechanics, l ike general relativity and classical electrodynamics, is invariant und er discrete scale transformations. This hypothesis leads to a large sc ale quantization of angular momenta. Using the scale factor Lambda sim ilar to 10(38), the corresponding quantum of action, obtained by scali ng 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 - an d to the spin of Godel's universe, solution of Einstein equations of g ravitation. Besides, we suggest the existence of another, intermediate , scale invariance, with scale factor lambda similar to 10(19). With t his factor we obtain, from Fermi's scale, the values for the gravitati onal 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-s pin relations implied by the two referred scale transformations are in accordance with Muradian's Regge-like relations for galaxy clusters a nd stars. Impressive results are derived when we use a lambda-scaled q uantum approach to calculate the mean radii of planetary orbits in sol ar system. Finally, a possible explanation for the observed quantizati on of galactic redshifts is suggested, based on the large scale quanti zation conjecture.