Possible Connection between Probability, Spacetime Geometry and Quantum Mechanics

Abstract

Following our discussion [Physica A 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro-to the microdomain, we argue that there is a possible connection among normalized probabilities P, spacetime geometry (in the form of Schwarzschild radii r s ) and quantum mechanics (in the form of complex wave functions ψ), namely PWe show how this association along different (n)-nested surfaces -representing curve space due to an inhomogeneous density of matter-preserves the postulates of quantum mechanics at different geometrical scales.