The early axiomatizations of quantum mechanics: Jordan, von Neumann and the continuation of Hilbert's program
In the first part of his paper, the author analyses the contributions to the axiomatization of quantum mechanics by Jordan, Hilbert, and others who met the challenge that came from Hilbert's axiomatization program of physical theories. The rest of the paper is devoted to the role of John von Neumann who can be viewed as the most outstanding of Hilbert's heirs. By his proof of the impossibility of hidden variables, von Neumann pushed Hilbert's program to its very limits, blending axiomatic rigor and interpretative commitment. According to the author, von Neumann's work was a unique pivot in the history of the axiomatization of quantum theory, its most impressive achievement being the derivation of its Hilbert space features directly from physical assumptions. Thus in the field of axiomatization, von Neumann must be considered as a pupil who bettered his master. In order to substantiate his arguments, the author presents many quotations from the original publications, mostly in German.
scientific article; zbMATH DE number 1394854