The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part II. Idealizations. “Perfect measurements”

Abstract

The application of the conceptual analysis (CA) method outlined in Part I is illustrated on the example of quantum mechanics. In Part II, we deduce the complete-lattice structure in quantum mechanics from postulates specifying the idealizations that are accepted in the theory. The idealized abstract concepts are introduced by means of a topological extension of the basic structure (obtained in Part I) in accord with the “approximation principle”; the relevant topologies are not arbitrarily chosen; they are fixed by the choice of the idealizations. There is a typical topological asymmetry in the mathematical scheme. Convexity or linear structures do not play any role in the mathematical methods of this approach. The essential concept in Part II is the idealization of “perfect measurement” suggested by our conceptual analysis in Part I. The Hilbert-space representation will be deduced in Part III. In our papers, we keep to the tenet: The mathematical scheme of a physical theory must be rigorously formulated. However, for physics, mathematics is only a nice and useful tool; it is not purpose.