On the Geometrization of Quantum Mechanics

TL;DR

This paper proposes a geometric reformulation of quantum mechanics where particles follow geodesics in a curved space influenced by quantum potential, unifying quantum effects with space-time geometry similar to gravity in general relativity.

Contribution

It introduces a novel geometrization approach to quantum mechanics, representing quantum evolution as geodesic motion in a curved space induced by quantum potential.

Findings

Quantum effects incorporated into space-time geometry.

Particles follow geodesics determined by quantum potential.

Unifies quantum mechanics with geometric space-time concepts.

Abstract

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.