Fulfilling Einstein's dream

Einstein considered that quantum mechanics must only be an approximate theory which was derivable from a "classical" theory which did not have the same philosophical problems. In a 1949 essay, Reply to Criticisms published in response to the essays in Albert Einstein: Philosopher-Scientist he wrote

...Within the framework of statistical quantum theory there is no such thing as a complete description of the individual system. ....The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. .... For if the statistical quantum theory does not pretend to describe the individual system (and its development in time) completely, it appears unavoidable to look elsewhere for a complete description of the individual system; in doing so it would be clear from the very beginning that the elements of such a description are not contained within the conceptual scheme of the statistical quantum theory....this scheme could not serve as the basis of theoretical physics. Assuming the success of efforts to accomplish a complete physical description, the statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. I am rather firmly convinced that the development of theoretical physics will be of this type; but the path will be lengthy and difficult.

Stephen Adler has attempted to fulfill this mission in his book,  Quantum Theory as an Emergent Phenomena: Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory
A review of the book by Philip Pearle gives a very helpful summary.  More comments on that later...