Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations

Abstract

In this paper, we propose a physical model leading to the causal interpretation of the quantum theory. In this model, a set of fields which are equivalent in many ways to a conserved fluid, with density ${|\ensuremath{\psi}|}^{2}$, and local stream velocity, $\frac{d\ensuremath{\xi}}{\mathrm{dt}}=\frac{\ensuremath{\nabla}S}{m}$, act on a particle-like inhomogeneity which moves with the local stream velocity of the equivalent fluid. By introducing the hypothesis of a very irregular and effectively random fluctuation in the motions of the fluid, we are able to prove that an arbitrary probability density ultimately decays into ${|\ensuremath{\psi}|}^{2}$. Thus, we answer an important objection to the causal interpretation, made by Pauli and others. This result is extended to the Dirac equation and to the many-particle problem.