Possible Connection between Probability, Spacetime Geometry and Quantum Mechanics

TL;DR

This paper explores a potential link between probability, spacetime geometry, and quantum mechanics, suggesting that normalized probabilities and Schwarzschild radii may be connected through nested surfaces, preserving quantum postulates across scales.

Contribution

It proposes a novel framework connecting probabilistic descriptions with spacetime geometry and quantum mechanics using nested surfaces in inhomogeneous matter distributions.

Findings

Probabilistic descriptions can be associated with Schwarzschild radii.

Quantum postulates are preserved across different geometrical scales.

Nested surfaces represent inhomogeneous matter distributions in the model.

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 micro-domain, we argue that there is a possible connection among normalized probabilities, spacetime geometry (in the form of Schwarzschild radii) and quantum mechanics (in the form of complex wave functions). We 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.