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

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 ${\left|\psi \right|}^2$, and local stream velocity, $\frac{d\xi }{\mathrm{dt}}=\frac{\nabla S}{m}$, 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 ${\left|\psi \right|}^2$. 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.