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.Comment: slightly modified version, 24 pages, no figure
