The Burgers equations and the Born rule

TL;DR

This paper explores the deep mathematical connections between Burgers, diffusion, and Schrödinger equations within stochastic mechanics, deriving the Born rule from complex stochastic processes and Fokker-Planck formalism.

Contribution

It provides a novel derivation of the Born rule from complex stochastic processes using a Fokker-Planck approach, linking stochastic mechanics with quantum probability.

Findings

Derivation of the Born rule from complex stochastic processes

Connection established between Burgers equation and quantum mechanics

Demonstration of the Burgers equation as a stochastic geodesic equation

Abstract

The present work demonstrates the connections between the Burgers, diffusion, and Schroedinger's equations. The starting point is a formulation of the stochastic mechanics, which is modeled along the lines of the scale relativity theory. The resulting statistical description obeys the Fokker-Planck equation. This paper further demonstrates the connection between the two approaches, embodied by the study of the Burgers equation, which from this perspective appears as a stochastic geodesic equation. The main result of the article is the transparent derivation of the Born rule from the starting point of a complex stochastic process, based on a complex Fokker-Planck formalism.