The early axiomatizations of quantum mechanics: Jordan, von Neumann and the continuation of Hilbert's program
type: Item
instance of: scholarly article
title: The early axiomatizations of quantum mechanics: Jordan, von Neumann and the continuation of Hilbert's program
zbMATH Open document ID: 0942.01014
DOI: 10.1007/PL00007551
author: Jan Lacki
published in: Archive for History of Exact Sciences
publication date: 2000-08-21T00:00:00Z
review text: 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.
reviewed by: Andreas Kleinert
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 1394854
zbMATH Keywords: quantum mechanics
zbMATH Keywords: axiomatization
zbMATH Keywords: hidden variables
zbMATH Keywords: Hilbert
zbMATH Keywords: von Neumann
MaRDI profile type: Publication
full work available at URL: pl00007551
OpenAlex ID: W2090558596
description: scientific article; zbMATH DE number 1394854