Fundamental statistical theories

Einstein argued that since quantum mechanics is not a fundamental theory it cannot be regarded as in any sense final. The pure statistical states of the quantum theory are not dispersion-free. In this sense, the theory is significantly statistical. The problem investigated in this paper is to determine under what conditions is a significalty statistical theory correctly regarded as fundamental. The solution developed in this paper is that a statistical theory is fundamental only if it is complete; moreover the quantum theory is complete. (B.R.H.)