Table of Contents
Physics Research International
Volume 2010, Article ID 808424, 18 pages
Research Article

The Statistical Origins of Quantum Mechanics

Institut für Theoretische Physik, Johannes Kepler Universität Linz, 4040 Linz, Austria

Received 26 September 2010; Revised 27 November 2010; Accepted 22 December 2010

Academic Editor: Jeremy O'Brien

Copyright © 2010 U. Klein. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is shown that Schrödinger'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.