The strong philosophical opposition of many physicists of the 1900's to the subjectivistic tendencies, which found scientific support by the interpretation of Quantum Mechanics given from the Copenhagen School, demanded a theoretical engagement and experiences, in the aim to overgo Quantum Mechanics, judged an incomplete theory, by the construction of a new complete theory, more general than Quantum Mechanics. Quantum Mechanics, whose scientific validity was incontrovertible, would be a statistical approximation of this new theory.
Einstein and others had the purpose to think a theoretical operation analogous to that one with which Boltzmann and Maxwell had explained the laws of the Thermodynamics: the macroscopic quantities of the Thermodynamics, as, for example, the pressure and the absolute temperature, are only the macroscopical manifestation of the mean values of the dynamic properties of the molecules. Such properties (position, speed, momentum, kinetic energy...) in principle are perfectly conceivable and describable by Newton's laws and therefore are realistic and causal. The renunciation to the mechanical description of a system, as, for example, a gas, through the analysis of the motion of the single molecules that compose it, is a necessity of fact, due to the great number of molecules contained also in a small fraction of mole.
The mechanical parameters relative to the state of the molecules do not appear directly to the level of exposition used by the classical Thermodynamics and can therefore be considered as hidden variables with respect to this level.
Another interesting analogy for the relationship that would exist between Quantum Mechanics and an its generalization which could recover the causality, shown by D. Bohm in 1952 (see also David Z. Albert, Bohm's Alternative to Quantum Mechanics, Scientific American, Volume 270, Number 5, pp. 32-39, May 1994.), comes from the analysis of the brownian motion, that is the typical motion of spores or particles of smoke in the air or of droplets in a colloidal suspensions, that moves following irregular trajectories, describable only in a statistic way .
Such motion, as explained by Einstein himself, is caused by the hits of the molecules of the medium against a particle. So it is causal, but cannot be determined only by the knowledge of parameters inherent to the particle. But its determination would be possible if we could know the motion parameters of every molecule with which the particle interacts in the course of the time.
Practically, we can only give a probabilistic description of the brownian motion of a particle, but this description enjoys remarkable property: a particle in a time interval Δt endures fluctuations of size Δx around its mean position and of size Δp around its mean moment so that
where C is a constant which depends on several parameters of medium as, e.g., temperature, viscosity, etc.
We have therefore an expression analogous to Heisenberg uncertainty principle. The big difference is that the Plank's constant h is universal, irreducible, while C depends, in last analysis, on accidental whirling of molecules, that is on the mean values of their parameters. Consequently the value of C can be reduced arbitrarily acting on the molecular parameters (for example, diminishing the temperature of the medium).
However, starting from such analogies, Bohm developed various models of hidden variables and his job has been continued in the last fifty years by many theoretical and experimental researchers.