States, effects, and operations: fundamental notions of quantum theory. Lectures in mathematical physics at the University of Texas at Austin; ed. by A. Bohm, J.D. Dollard and W.H. Wootters

## §i States and Effects Almost all treatments of quantum mechanics agree in ascribing fundamental importance to the notions of "state" and "observable". The physical interpretation of these notions, however, differs considerably from one author to another. The discussion of as many as possible of these different points of view is not the subject of the present investigation, in view of both the limited space available and the insufficient familiarity of the author with most of them. We prefer instead to follow here as closely as possible one particular interpretation of quantum mechanics, which has been elaborated by Ludwig and his school [2], and which the present author considers to be particularly satisfactory. A detailed exposition of Ludwig's theory would still go far beyond the limits of space available here. We shall try to sketch some of the main ideas only, and to encourage any reader who is interested in more details to consult the original literature quoted above. Another reason for not entering a detailed discussion of various interpretations of quantum mechanics is our conviction that the more technical parts of the present work, if suitably reformulated, are compatible with most or even all of them. We thus believe that even a reader who disagrees completely with the interpretation proposed here many profit from the following investigations, even if the burden of reinterpreting our results in terms of his preferred interpretation of quantum mechanics is entirely left to himself. According to Ludwig, any physical theory is in some sense to be interpreted "from outside", i.e., in terms of "pretheories" not belonging to the theory in question itself. For quantum mechanics in particular, these "pretheories" belong to the realm of classical physics, and describe the construction and application of macroscopic prepa- States and effects....Pages 1-12 Operations....Pages 13-41 The first Representation theorem....Pages 42-61 Composite systems....Pages 62-80 The second representation theorem....Pages 81-102 6 Coexistent effects and observables....Pages 103-149 References....Pages 150-152