On the causal interpretation of quantum mechanics

Abstract

The simplest nonlinear spinor field equation admitting regular stationary solutions is considered. Following a causal interpretation of quantum mechanics, given by de Broglie in his double solution theory, these regular solutions must be regarded as describing the internal particle structure. Using this spinor field model, an attempt is made to give a statistical description of one-particle experiments by means of a Gibbsian assemblage method. It is shown that in the limiting case of pointlike nonrelativistic particles this method is equivalent to the quantum mechanical one, that is, the probability amplitude can be introduced satisfying all postulates of quantum mechanics.