The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part III. Idealizations. Hilbert space representation [Book Review]

Foundations of Physics 9 (11-12):897-928 (1979)

Abstract
We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures
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DOI 10.1007/BF00708699
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Survey of General Quantum Physics.C. Piron - 1972 - Foundations of Physics 2 (4):287-314.

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