John von Neumann and the Foundations of Quantum Physics

1. Front Matter

   Pages I-IX

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2. John von Neumann and the Foundations of Quantum Physics

   1. Introduction

      • Miklós Rédei, Michael Stöltzner

      Pages 1-4

   2. Articles

      1. J. v. Neumann’s Influence in Mathematical Physics

         • Walter Thirring

         Pages 5-10

      2. The Axiomatic Method and the Foundations of Science: Historical Roots of Mathematical Physics in Göttingen (1900–1930)

         • Ulrich Majer

         Pages 11-33

      3. Opportunistic Axiomatics — Von Neumann on the Methodology of Mathematical Physics

         • Michael Stöltzner

         Pages 35-62

      4. Von Neumann’s Theory of Quantum Measurement

         • Jeffrey Bub

         Pages 63-74

      5. Von Neumann, Gödel and Quantum Incompleteness

         • Thomas Breuer

         Pages 75-82

      6. Entropy, von Neumann and the von Neumann Entropy

         • Dénes Petz

         Pages 83-96

      7. Why von Neumann Rejected Carnap’s Dualism of Information Concepts

         • Eckehart Köhler

         Pages 97-134

      8. On the Stone — von Neumann Uniqueness Theorem and Its Ramifications

         • Stephen J. Summers

         Pages 135-152

      9. Von Neumann’s Concept of Quantum Logic and Quantum Probability

         • Miklós Rédei

         Pages 153-172

      10. The Impossible Causality: The No Hidden Variables Theorem of John von Neumann

          • Roberto Giuntini, Federico Laudisa

          Pages 173-188

      11. Quantum Mechanics Without Probabilities

          • Peter Mittelstaedt

          Pages 189-200

      12. Critical Reflections on Quantum Probability Theory

          • László E. Szabó

          Pages 201-219

   3. Unpublished Letters and Lectures by John von Neumann

      1. Editors’ Notes

         • Miklós Rédei, Michael Stöltzner

         Pages 221-224

      2. Unpublished Correspondence

         • Miklós Rédei, Michael Stöltzner

         Pages 225-229

      3. Unsolved Problems in Mathematics

         • John von Neumann

         Pages 231-246

      4. Amsterdam Talk about “Problems in Mathematics” September 2, 1954

         • Miklós Rédei, Michael Stöltzner

         Pages 247-248

      5. Quantum Mechanics of Infinite Systems

         • John von Neumann

         Pages 249-268

3. General Part

   1. Report — Documentation

      1. A New Critique of Theological Interpretations of Physical Cosmology

         • Adolf Grünbaum

         Pages 269-288

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.

• Rudolf Carnap
• Theoretical physics
• mathematical physics
• philosophy of science
• probability
• quantum mechanics
• science

• Eötvös University, Budapest, Hungary

  Miklós Rédei

• Institute Vienna Circle, Vienna, University of Salzburg, Vienna, Austria

  Michael Stöltzner

Policies and ethics