John Von Neumann and the Foundations of Quantum Physics

by Redei, Miklos; Stoltzner, Michael

• ISBN13: 9780792368120
• ISBN10: 0792368126
• Format: Hardcover
• Copyright: 2001-02-01
• Publisher: Kluwer Academic Pub

Summary

John von Neumann (1903-1957) was undoubtedly one of the scientific geniuses of the 20th century. The main fields to which he contributed include various disciplines of pure and applied mathematics, mathematical and theoretical physics, logic, theoretical computer science, and computer architecture. Von Neumann was also actively involved in politics and science management and he had a major impact on US government decisions during, and especially after, the Second World War. There exist several popular books on his personality and various collections focusing on his achievements in mathematics, computer science, and economy. Strangely enough, to date no detailed appraisal of his seminal contributions to the mathematical foundations of quantum physics has appeared. Von Neumann's theory of measurement and his critique of hidden variables became the touchstone of most debates in the foundations of quantum mechanics. Today, his name also figures most prominently in the mathematically rigorous branches of contemporary quantum mechanics of large systems and quantum field theory. And finally - as one of his last lectures, published in this volume for the first time, shows - he considered the relation of quantum logic and quantum mechanical probability as his most important problem for the second half of the twentieth century. The present volume embraces both historical and systematic analyses of his methodology of mathematical physics, and of the various aspects of his work in the foundations of quantum physics, such as theory of measurement, quantum logic, and quantum mechanical entropy. The volume is rounded off by previously unpublished letters and lectures documenting von Neumann's thinking about quantum theory after his 1932 Mathematical Foundations of Quantum Mechanics . The general part of the Yearbook contains papers emerging from the Institute's annual lecture series and reviews of important publications of philosophy of science and its history.

Table of Contents

A. JOHN VON NEUMANN AND THE FOUNDATIONS OF QUANTUM PHYSICS
Introduction	1	(4)
Articles
J. v. Neumann's Influence in Mathematical Physics	5	(6)
Walter Thirring
The Axiomatic Method and the Foundations of Science: Historical Roots of Mathematical Physics in Gottingen (1900-1930)	11	(24)
Ulrich Majer
Opportunistic Axiomatics - von Neumann on the Methodology of Mathematical Physics	35	(28)
Michael Stoltzner
Von Neumann's Theory of Quantum Measurement	63	(12)
Jeffrey Bub
Von Neumann, Godel and Quantum Incompleteness	75	(8)
Thomas Breuer
Entropy, von Neumann and the von Neumann Entropy	83	(14)
Denes Petz
Why von Neumann Rejected Carnap's Dualism of Information Concepts	97	(38)
Eckehart Kohler
On the Stone - von Neumann Uniquness Theorem and Its Ramifications	135	(18)
Stephen J. Summers
Von Neumann's Concept of Quantum Logic and Quantum Probability	153	(20)
Miklos Redei
The Impossible Causality: the No Hidden Variables Theorem of John von Neumann	173	(16)
Roberto Giuntini
Federico Laudisa
Quantum Mechanics without Probabilities	189	(12)
Peter Mittelstaedt
Critical Reflections on Quantum Probability Theory	201	(68)
Laszlo E. Szabo
Unpublished Letters and Lectures
John von Neumann
Editors' Notes	221	(4)
Unpublished Correspondence	225	(6)
Unsolved Problems in Mathematics (1954)	231	(16)
Amsterdam Talk about ``Problems in Mathematics'' (1954)	247	(2)
Quantum Mechanics of Infinite Systems (1935/6)	249	(20)
B. GENERAL PART
Report - Documentation
A New Critique of Theological Interpretations of Physical Cosmology (7th Vienna Circle Lecture)	269	(20)
Adolf Grunbaum
Scientific Understanding in the Twentieth Century	289	(16)
Wesley C. Salmon
From Russell's Logical Atomism to Carnap's Aufbau: Reinterpreting the Classic and Modern Theories on the Subject	305	(14)
Henrique Jales Ribeiro
Review Essay
Recent Works on Otto Neurath	319	(10)
Massimo Ferrari
Reviews
Reconsidering Logical Positivism. Cambridge: Cambridge University Press, 1999 (Thomas Mormann)	329	(4)
Michael Friedman
Causality and Explanation. New York-Oxford: Oxford University Press, 1998 (Maria Carla Galavotti)	333	(4)
Wesley C. Salmon
Hans Reichenbach - sein Leben und Wirken. Osnabruck: Phoebe-Autorenpress 1997 (Reinhard Siegmund-Schultze)	337	(3)
Karin Gerner
Herbert Hochberg (Eds.), Austrian Realism: From Aristotelian Roots to the Vienna Circle (Monist 83, no. 1, 2000) (Maria E. Reicher)	340	(4)
Barry Smith
From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in 1920s. New York-Oxford: Oxford University Press, 1998
Paolo Mancosu
Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. London-New York: Routledge, 1999 (Ulrich Majer)	344	(5)
James Robert Brown
Ludwig Boltzmann: Troubled Genius as Philosopher. Dordrecht: Kluwer 1999 (Synthese 119) (Torsten Wilholt)	349	(4)
John Blackmore
Unterwegs zur Musiksoziologie. Auf der Suche nach Heimat und Standort, annotated by Reinhard Muller. Graz-Wien: Nausner & Nausner, 1998 (Andrea Lindmayr-Brandl and Johannes L. Brandl)	353	(4)
Kurt Blaukopf
Handbuch der deutschsprachigen Emigration 1933-1945. Darmstadt: Wissenschaftliche Buchgesellschaft, 1998 (Hans-Joachim Dahms)	357	(10)
Claus-Dieter Krohn
Patrik von zur Muhlen
Gerhard Paul
Lutz Winckler
Activities of the IVC
Activities 2000	361	(1)
Preview 2000/2001	362	(2)
Research Projects / Workshops	364	(1)
Publications	364	(1)
Library and Documentation	365	(2)
Index of Names	367