Speaker
Description
John von Neumann’s path towards the construction of a logic for quantum mechanics is historically retraced, starting from the analysis of his seminal contributions on the mathematical foundations of quantum mechanics in the 1920s and 1930s, up to his joint work with G. Birkhoff on quantum logic in 1936, and his first paper on operator algebras with F. J. Murray in the same year. The main emerging feature is his growing dissatisfaction with the Hilbert space formalism because of the ensuing infinite and not a priori normalizable quantum probability, that led him to look for a new mathematical structure for quantum logic, later identified with the modular projection lattice of the so-called type II1 factor. The subsequent debate on von Neumann’s proposal is also retraced, including K. R. Popper’s criticism. In particular, we deal with the crucial issue of how to relate von Neumann’s more general structure to the conventional Hilbert space based quantum mechanics by critically analysing later contributions by a number of scholars, such as G. Mackey, G. Piron, J. M. Jauch, G. Ludwig and J. C. T. Pool.
