Spin-plane defects and emergence of Planck’s constant in gravity

Abstract

The possibility of building Planck’s constant into space-time geometry in presence of topological excitations is considered. This is accomplished on the ground that such space-times display a spin two-plane and spin vector which incorporate the presence of space-time torsion and dislocations via global topological defects. This, in turn, is related to the nonvanishing of specific cohomological classes labeled by an integer and carrying topological charges that can be related to a multiple of the Planck length, thus inducing quantization of the spin. Such a geometrization of ℏ could shed light on quantum gravity and be compared to the geometrization of c (the other fundamental constant) by special relativity.