The statistical origins of quantum mechanics

TL;DR

This paper derives Schrödinger's equation from three statistical postulates, linking quantum mechanics to classical statistical concepts and supporting a statistical interpretation of quantum theory.

Contribution

It introduces a derivation of quantum mechanics from statistical principles, emphasizing the statistical origins of its fundamental equations.

Findings

Schrödinger's equation derived from statistical postulates

Quantum and classical statistical theories are compared

Fundamental differences between quantum and classical statistics identified

Abstract

It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.