Аннотация:
This paper presents a study of what is sometimes regarded as the conceptual
heart of quantum theory, namely, the orthodox 'physical' interpretation of noncommuting operators as representatives of incompatible (non-simultaneouslymeasurable) observables. To provide a firm foundation for the analysis,
a definite statement of the essentials of modern quantum theory is given
briefly in the form of a mathematical axiomatization together with a review
of the two measurement constructs introduced elsewhere (Park, 1967b).
Contrary to custom in discussions on simultaneous measurability, the uncertainty principle is not dwelt upon but simply stated carefully in order to
establish its actual irrelevance to the problem at hand. It is then demonstrated
that the much quoted 'principle' of incompatibility of noncommuting observables is false. The axiomatic root of all incompatibility arguments is next
identified ; and it is shown that, with a slight modification of the basic postulates
which affects neither useful theorems nor practical calculations, quantum
physics no longer entails illogical restrictions on measurability. Among the
related topics touched upon are the problem of joint probability distributions,
the 'logical' approach to quantum mathematics (wherein noncommutativity
becomes incompatibility within a propositional calculus), and the field theoretic
attempt to unify quantal and relativistic physics through a postulated connection between incompatibility and space-like intervals.
