  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.
