The case for the Universe to be a quantum black hole

Abstract

We present a necessary and sufficient condition for an object of any mass m to be a quantum black hole (q.b.h.): The product of the cosmological constant lambda and the Planck constant h, lambda and h corresponding to the scale defined by this q.b.h., must be of order one in a certain universal system of units. In this system the numerical values known for lambda are of order one in cosmology and about 10^122 for Planck scale. Proving that in this system the value of the cosmological h is of order one, while the value of h for the Planck scale is about 10^(-122), both scales satisfy the condition to be a q.b.h., i.e. lambda x h of order 1. In this sense the Universe is a q.b.h..We suggest that these objects, being q.b.h., give us the linkage between thermodynamics, quantum mechanics, electromagnetism and general relativity, at least for the scale of a closed Universe and for the Planck scale. A mathematical transformation may refer these scales as corresponding to infinity (our universe) and zero (Planck universe), in a scale relativity sense.