Quantum theory causal interpretation

Causal quantum theories have been developed to handle the empirical quantum evidence, and some of these theories, such as de Broglie s theory in its linear approximation, are almost as good as the usual orthodox quantum theory. A relative large number of experiments were even developed to test de Broglie s causal theory and other alternative theories as well, but only a few limited number of these proposed experiments were carried out effectively. And even so they were not carried out thoroughly. As a consequence, the results obtained were not conclusive, and no solid conclusion in favor or against the completeness of the usual orthodox interpretation of the Copenhagen School... 

J. P. Vigier and D. Bohm, Model of the causal interpretation of quantum theory in terms of a fluid with irregular fluctuations, Phys. Rev. 2(96), 208-216 (1955). 

D. Bohm and J.P. Vigier, Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations, Phys. Rev., 1954 (96) 208-217. 

The causal interpretation of quantum theory as proposed by De Broglie and Bohm is an extension of the hydrodynamic model originally proposed by Madelung and further developed by Takabayasi [36]. In Madelung s original proposal R2 was interpreted as the density p(x) of a continuous fluid with stream velocity v= VS/rri. Equation (5) then expresses conservation of fluid, while (6) determines changes of the velocity potential S in terms of the classical potential V, and the quantum potential... 

This model is not adequate in itself as it contains nothing to describe the actual location x(t) of the particle which is required for a causal interpretation of quantum theory. It is therefore necessary to postulate a particle that takes the form of a highly localized inhomogeneity that moves with the local fluid velocity v(x,t). The inhomogeneity could be of density close to that of the fluid, which is simply being carried along with the local velocity of the fluid. As in any macroscopic fluid random fluctuations are assumed [37] to occur in the Madelung fluid. It is shown that such fluctuations may lead to the statistical result, P = 2. 

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