Fundamental Statistical Theories

Abstract

Einstein argued that since quantum mechanics is not a fundamental theory it cannot be regarded as in any sense final (See especially Einstein, 1971, and Born, 1971, on which this discussion is based.) The concept of a fundamental statistical theory may be roughly explained as follows. Let us suppose that a certain class K of physical systems may be known with complete precision. For any system of this class it is possible to completely specify its type and its state. Both pieces of information — the possible types of system, and their possible states — are theory relative. What is assumed is that for any S in K there is no extratheoretical limit on the amount of information obtainable concerning S. I shall say that a statistical theory is fundamental if it is based on a maximal amount of information concerning the systems of K. That is to say, for a fundamental theory the degree of imprecision of our knowledge may be ignored, since the theory is supposed to hold even when this is made arbitrarily small By contrast, a statistical theory which is not fundamental is explicitly designed to take account of the case where, for whatever reasons, a maximal amount of information is not available.