Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

• URL: http://arxiv.org/abs/2301.05467v3
• Date: Sat, 3 Jun 2023 08:55:26 GMT
• Title: Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion
• Authors: Folkert Kuipers
• Abstract summary: We show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a process that is rotated in the complex plane. We then extend this theory to relativistic theories on integrals using the framework of second order geometry.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Ito deformation of the Poincare (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.

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