Interpretation of quantum theory

Abstract

The interpretation of quantum theory presented here is based on a concept of probability density which was first introduced in 1944 for the purpose of revealing unsuspected connections between quantum and classical theories but which was not previously applied to the interpretation of quantum theory. From classical Hamilton-Jacobi theory a definition oforbital density can be set up and this, divided by velocity or momentum, yields a very natural kinetic concept of probability densityP, viz. P=const × orbital density/momentum. A proof is repeated here which was given in earlier papers and which shows that, on the basis of a reasonable assumption, this definiton of probability density leads straight to Schrödinger’s time-independent equation. The resulting interpretation refers to individual systems, not ensembles, but is otherwise to some extent like Margenau’s;i.e measurement consists of a random selection of one possible eigenstate and eigenvalue, weighted by the square of the coefficient in an appropriate expansion; measurement either destroys the measured object or knocks it into some unknown state, hence there is no Einstein-Podolsky-Rosen paradox; measurement is a matter of observation, not prediction, hence measurement is outside the scope of quantum theory; there is no «collapse of the wave function»; the projection postulate is not admitted.