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Journal of Applied Mathematics and Simulation
Volume 1 (1988), Issue 4, Pages 287-303
http://dx.doi.org/10.1155/S1048953388000218

Classical variational basis for Schrödinger quantum theory

School of Mathematical Sciences, Queen Mary College, Mile End Road, London E1 4NS, United Kingdom

Received 3 June 1988; Revised 3 November 1988; Accepted 3 November 1988

Copyright © 1988 Hindawi Publishing Corporation. 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.

Abstract

A two-dimensional classical hyperspace fluid theory of the vacuum which is an alternative to Schrödinger quantum theory involves a “stirring” energy density. This energy density, like entropy density, measures the local “disturbance” involved by the time evolution of a state of the system. The stirring energy density is shown to be the local source term for the rate of generation of action density with time. A classical fluid action principle is solved using the “action” of this source term without assuming quantum time evolution. Schrödinger quantum theory is recovered from this new action principle which is then discussed. Finally, the quantity made stationary by the variational principle measures disturbance in the environment as an angular change in the orientation of the whole system.