Archimedes Volume 10 Archimedes NEW STUDIES in the HISTORY and PHILOSOPHY of SCIENCE and TECHNOLOGY

Archimedes Volume 10 Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY

VOLUME 10

EDITOR

JED Z. BUCHWALD, Dreyfuss Professor of History, California Institute of Technology, Pasadena, CA, USA.

ADVISORY BOARD

HENK BOS, University of Utrecht MORDECHAI FEINGOLD, Virginia Polytechnic Institute ALLAN D. FRANKLIN, University of Colorado at Boulder KOSTAS GAVROGLU, National Technical University of Athens ANTHONY GRAFTON, Princeton University FREDERIC L. HOLMES, Yale University PAUL HOYNINGEN-HUENE, University of Hannover EVELYN FOX KELLER, MIT TREVOR LEVERE, University of Toronto JESPER LÜTZEN, Copenhagen University WILLIAM NEWMAN, Harvard University JÜRGEN RENN, Max-Planck-Institut für Wissenschaftsgeschichte ALEX ROLAND, Duke University ALAN SHAPIRO, University of Minnesota NANCY SIRAISI, Hunter College of the City University of New York NOEL SWERDLOW, University of Chicago

Archimedes has three fundamental goals; to further the integration of the histories of science and technology with one another: to investigate the technical, social and prac- tical histories of specific developments in science and technology; and finally, where possible and desirable, to bring the histories of science and technology into closer contact with the philosophy of science. To these ends, each volume will have its own theme and title and will be planned by one or more members of the Advisory Board in consultation with the editor. Although the volumes have specific themes, the series it- self will not be limited to one or even to a few particular areas. Its subjects include any of the sciences, ranging from biology through physics, all aspects of technology, bro- adly construed, as well as historically-engaged philosophy of science or technology. Taken as a whole, Archimedes will be of interest to historians, philosophers, and scien- tists, as well as to those in business and industry who seek to understand how science and industry have come to be so strongly linked. David Hilbert and the Axiomatization of Physics (1898-1918) From Grundlagen der Geometrie to Grundlagen der Physik

LEO CORRY Cohn Institute for History and Philosophy of Science, Tel Aviv University, Israel

Springer-Science+Business Media, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-6719-7 ISBN 978-1-4020-2778-9 (eBook)

DOI 10.1007/978-1-4020-2778-9

Printed on acid-free paper

All Rights Reserved © 2004 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2004. Softcover reprint of the hardcover 1st edition 2004 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

To my mother, Nora T. de Corry

CONTENTS

Preface ...... xi Acknowledgements and Credits ...... xv

Introduction...... 1

Chapter 1: Late Nineteenth Century Background...... 11 1.1. Hilbert’s Early Career...... 11 1.1.1 Algebraic Invariants...... 17 1.1.2 Algebraic Number Fields...... 20 1.1.3 Deep Roots in Tradition ...... 23 1.2. Foundations of Geometry ...... 25 1.2.1 Riemann...... 25 1.2.2 Projective Geometry...... 30 1.2.3 Nineteenth-Century Axiomatics...... 35 1.2.4 Pasch and the Italian School...... 40 1.3. Foundations of Physics...... 45 1.3.1 Kinetic Theory, Mechanistic Foundations...... 46 1.3.2 Carl Neumann ...... 51 1.3.3 Heinrich Hertz...... 54 1.3.4 Paul Volkmann ...... 61 1.3.5 Ludwig Boltzmann...... 63 1.3.6 Aurel Voss...... 66 1.4. Mathematics and Physics in Göttingen at the Turn of the Century .....71 1.4.1 Felix Klein ...... 72 1.4.2 The Physicists ...... 78 viii CONTENTS

Chapter 2: Axiomatization in Hilbert’s Early Career...... 83 2.1. Axiomatics, Geometry and Physics in Hilbert’s Early Lectures...... 83 2.1.1 Geometry in Königsberg...... 83 2.1.2 Geometry in Göttingen ...... 89 2.1.3 Mechanics in Göttingen...... 91 2.2. Grundlagen der Geometrie...... 93 2.2.1 Independence, Simplicity, Completeness...... 95 2.2.2 Fundamental Theorems of Projective Geometry ...... 97 2.2.3 On the Concept of Number ...... 99 2.3. The 1900 List of Problems ...... 101 2.3.1 Foundational Problems ...... 104 2.3.2 A Context for the Sixth Problem ...... 109 2.4. Early Reactions to the Grundlagen...... 110

Chapter 3: The Axiomatic Method in Action: 1900-1905...... 119 3.1. Foundational Concerns – Empiricist Standpoint...... 120 3.2. Hilbert and Physics in Göttingen circa 1905...... 127 3.3. Axioms for Physical Theories: Hilbert’s 1905 Lectures ...... 138 3.3.1 Mechanics...... 138 3.3.2 Thermodynamics...... 154 3.3.3 Probability Calculus...... 164 3.3.4 Kinetic Theory of Gases ...... 168 3.3.5 Insurance Mathematics...... 171 3.3.6 Electrodynamics ...... 172 3.3.7 Psychophysics...... 175 3.3.8 A post-1909 addendum ...... 178 3.4. The Axiomatization Program by 1905 – Partial Summary ...... 179

Chapter 4: Minkowski and Relativity: 1907-1909 ...... 185 4.1. The Principle of Relativity ...... 189 4.2. The Basic Equations of Electromagnetic Processes in Moving Bodies ...... 193 4.2.1 Three Meanings of “Relativity” ...... 193 4.2.2 Axioms of Electrodynamics ...... 195 4.2.3 Relativity and Mechanics...... 197 4.2.4 Relativity and Gravitation ...... 200 4.3. Space and Time...... 206 4.3.1 Groups of Transformations ...... 208 4.3.2 Empirical Considerations...... 210 4.3.3 Relativity and Existing Physical Theories ...... 212 4.4. Max Born, Relativity, and the Theories of the Electron...... 213 4.4.1 Rigid Bodies...... 217 4.5. Minkowski, Axiomatics and Relativity – Summary ...... 219 CONTENTS ix

Chapter 5: From Mechanical to Electromagnetic Reductionism: 1910-1914 ...... 227 5.1. Lectures on Mechanics and Continuum Mechanics...... 234 5.2. Kinetic Theory...... 236 5.3. Radiation Theory ...... 242 5.3.1 Hilbert and Kirchhoff’s Law: 1912 ...... 247 5.3.2 Reactions and Sequels: Early 1913 ...... 253 5.3.3 Pringsheim’s Criticism: 1913...... 259 5.3.4 Hilbert’s Final Version: 1914 ...... 263 5.3.5 Kinetic and Radiation Theory: General Remarks .....265 5.4. Structure of Matter and Relativity: 1912-1914...... 267 5.4.1 Molecular Theory of Matter - 1912-13...... 267 5.4.2 Electron Theory: 1913...... 271 5.4.3 Axiomatization of Physics: 1913 ...... 274 5.4.4 Electromagnetic Oscillations: 1913-14...... 279 5.5. Broadening Physical Horizons - Concluding Remarks...... 284

Chapter 6: Einstein and Mie: Two Pillars of Hilbert’s Unified Theory.....287 6.1. Einstein’s Way to General Relativity ...... 287 6.2. Mie’s Electromagnetic Theory of Matter...... 298 6.2.1 First and Second Installment: Early 1912...... 299 6.2.2 Third Installment: November 1912...... 304 6.3. Contemporary Debates on Gravitation...... 306 6.4. Born’s Formulation of Mie’s Theory...... 309 6.5. The Background to Hilbert’s Unified Theory – Summary ...... 315

Chapter 7: Foundations of Physics: 1915-1916 ...... 317 7.1. Einstein in Göttingen – Summer of 1915 ...... 320 7.2. Hilbert’s Unified Theory – General Considerations...... 330 7.3. Hilbert’s Communication to the GWG – November 1915 ...... 334 7.3.1 Axioms and Basic Assumptions ...... 334 7.3.2 The Hamiltonian Function and the Field Equations .340 7.3.3 Summary and Additional Considerations...... 343 7.4. The Hilbert-Einstein Correspondence and Einstein’s Four Communications – November 1915 ...... 345 7.5. Hilbert’s Unified Theory: First Printed Version – March 1916...... 355 7.6. Foundations of Physics – Summary...... 360

x CONTENTS

Chapter 8: Hilbert and GTR: 1916-1918...... 363 8.1. Mie’s Reaction ...... 370 8.2. Einstein’s Reaction ...... 373 8.3. Hilbert Teaches GTR – 1916-1917 ...... 376 8.4. Hilbert’s Second Communication – December 1916...... 384 8.5. Göttingen Debates on Energy Conservation in GTR – 1918 ...... 388 8.6. Later Talks and Writings on GTR...... 392 8.7. Last Versions of Hilbert’s Theory...... 399 8.8. Hilbert´s Way to GTR – Summary and Concluding Remarks...... 403

Chapter 9: Epilogue...... 409 9.1. Foundations of Quantum Theory ...... 414 9.2. The Culture of “Nostrification” in Göttingen...... 419 9.3. General Relativity and Geometry ...... 423 9.4. Hilbert and Participant Histories of GTR...... 431 9.5. Hilbert and Physics – Concluding Remarks ...... 437

Appendix 1: General Chronology of Events Mentioned in the Text ...... 445 Appendix 2: Hilbert’s Göttingen Courses on Physics...... 450 Appendix 3: Seminars, Miscellaneous Lectures...... 453 3.A. Advanced Seminars Taught by Hilbert ...... 453 3.B. Public Lectures by Hilbert...... 453 3.C. Physical lectures at the GMG and GWG by Hilbert...... 454 3.D. Lectures on Physical Issues at the GMG by Others...... 454

Appendix 4: Hilbert’s Physics Assistants and Doctoral Students...... 458 4.A. Assistants for Physics...... 458 4.B. Doctoral Students on Physical Topics ...... 458

Apendix 5: Letters Quoted in the Book...... 459 Appendix 6: Items from the Hilbert Nachlass referred to in the Book ...... 462 Appendix 7: Hilbert’s Axioms for Radiation Theory ...... 465

References...... 467 Commonly Used Abbreviations...... 467 Published and Unpublished Sources...... 469

INDEX ...... 497

PREFACE

The present book is the outcome of several years of research on the history of early twentieth-century exact sciences, particularly the work of David Hilbert on physical topics. This more focused research started during the academic year 1994- 95, which I spent at the Max-Planck-Institut für Wissenschaftsgeschichte, Berlin, and continued intensely during the following year, at the Dibner Institute for History of Science and Technology at MIT. Later on, it has continued as part of my regular academic activities at the Cohn Institute for the History and Philosophy of Science and Ideas, Tel-Aviv University. The first, partial results of my research appeared in 1997 as a lengthy article in Archive for History of Exact Sciences: “David Hilbert and the Axiomatization of Physics (1895-1905)” (Corry 1997a). Over the next few years many works dealing with topics directly and indirectly related to my own focus of interest have been published by several colleagues. Together with some additional articles written by myself, these publications have helped create a very comprehensive picture of the themes that I consider in this book. The recent publication of Vols. 6-8 of the Collected Papers of Albert Einstein (CPAE) has added an invaluable tool for all scholars working in this area. With the publication of this book I have tried to bring a balanced and inclusive synthesis of recent, related work, as I see it from my own point of view and from the point of view of my main topic of interest here: Hilbert and the Axiomatization of Physics. I have tried my best to indicate throughout the text those secondary sources on which I have directly relied when dealing with specific issues in the various chapters. Still, in a book of this kind there are many intellectual debts that cannot be acknowledged by means of footnotes, and which I’d like to point out here, while sincerely thanking to all those persons who have helped me in one way or another. Of great significance in the preparation of my work has been the continued cooperation and critical reading I have received from David Rowe at various stages. Likewise, his many publications on the Göttingen mathematical culture continually provided me with a highly reliable source of help and scholarly reference. During xii PREFACE my year at the MPIWG-Berlin, and thereafter, I benefited very much from illuminating discussions on the history of modern physics with Jürgen Renn, Tilman Sauer and John Stachel. On different occasions, many other friends and colleagues have read and criticized diverse parts of my manuscript, provided useful hints and information, or simply answered specific queries I directed at them. Their remarks and suggestions led to many additions, changes and improvements for which I am very thankful: Klaus Bärwinkel, Jed Buchwald, Juan B. Climent, Olivier Darrigol, Michael Eckert, Moritz Epple, José Ferreirós, Albrecht Fölsing, Helene Gispert, Jeremy Gray, Ulf Hashagen, Erwin Hiebert, Tom Hawkins, Michel Janssen, Shaul Katzir, Ole Knudsen, Daniel Levy, Jesper Lützen, Ulrich Majer, Paolo Mancosu, John Norton, Don Osterbrock, Walter Purkert, Jim Ritter, Laura Rodriguez, Richard Staley, Hans-Jürgen Schmidt, George Smith, Arne Schirrmacher, Erhard Scholz, Hans-Joachim Vollrath, Scott Walter. I also acknowledge the significant input received from an anonymous referee in the form of critical remarks to an earlier manuscript of this book. If, in spite of the great help provided by all these learned persons and good friends, my book still contains errors or shortcomings, these should be attributed, as usual, only to me. I have also received invaluable help from several institutions and organizations with which I have been in contact over these years. The Cohn Institute, through the congenial and sustained support of Barbara and Bert Cohn, has always provided a warm academic home from which to pursue my own scholarly interests without losing sight of a broader intellectual picture. I thank all my colleagues at the institute for their continued encouragement and interest, and especially Naomi Diamant for her always efficient and gracious handling of the institute’s office matters, without which we could not even start to function. During my stay at the MPIWG-Berlin and thereafter, the library staff, headed by Urs Schoepfflin, and especially with the help of Urte Brauckmann and Matthias Schwerdt, spared no effort in helping me gather published and unpublished material that proved essential for conducting my work. Lindy Divarci, also at the MPIWG- Berlin, has provided me sustained support on editorial matters. The difficult task of inspecting the manuscripts of Hilbert’s courses and the letters in his Nachlass at Göttingen was much alleviated by the kind help of Helmut Rohlfing (Staats- und Universitätsbibliothek Göttingen - Handschriftenabteilung) and Jürgen Matthes (Bibliothek des Mathematisches Institut). Klaus and Friedrich Mie kindly put at my disposition the Nachlass of their granduncle Gustav Mie, which I was able to track with the help of Professor Helmut Spehl, at Freiburg. Although I do not quote directly from any specific document of that interesting collection, the possibility of examining its contents was very helpful for understanding the spirit of Mie’s work. They also provided me with a portrait of Gustav Mie in their possession, and allowed its publication. I thank them very much for their help and openness. In collecting the pictures that appear in this book and in preparing their electronic versions, I received the important assistance of Barbara Wolff (Albert Einstein Archives, Jewish National and University Library, Jerusalem), Helmut Rohlfing and Martin Liebetruth (Staats- und Universitätsbibliothek Göttingen), PREFACE xiii

Heather Lindsay (American Institue of Physics), and Margrit Prussat (Deutsches Museum, Munich). This book is published in the ARCHIMEDES series mainly due to the active interest taken in it by the editor of the series, Jed Z. Buchwald, an interest for which I am sincerely thankful. I acknowledge the administrative and editorial support provided by Ingrid Krabbenbos and Charles Erkelens at Kluwer, as well as the technical advise of the author support team for preparing the camera ready copy. The English prose of my text has been considerably improved through the sympathetic, and always professional, services of Miriam Greenfield. Difficulties encountered while reading and translating certain, intricate German manuscript passages were alleviated at various occasions through the friendly help of Alexandre Métraux and of Moritz Epple. Of the various primary sources quoted in the book, many have never appeared in print at the time of writing these lines, to the best of my knowledge. Such sources are fully quoted in the German original in the footnotes and in English translation in the main text. Unless otherwise stated in the text, all translations into English (of either published or unpublished texts) are mine. In the case of Einstein’s published works and correspondence I have used translations now available in the English version of the Collected Papers, which I cite accordingly.

My final and warmest thanks go to my most faithful fan-club: my dear wife, Efrat, my children Daniel and Avigail, and the other members of the family - mother, brother, sister, and their cohorts. I hope to have stood up to their very high, and perhaps somewhat unfounded, expectations.

Tel-Aviv, April 2004

ACKNOWLEDGEMENTS AND CREDITS

Original manuscripts are quoted in the book by permission of the following institutions: Nachlass David Hilbert: Niedersaechsische Staats- und Universitätsbibliothek Goettingen, Abteilung Handschriften und Seltene Drucke. Lecture Notes, David Hilbert: Bibliothek des Mathematisches Institut, Universität Göttingen. Nachlass Max Born, Nachlass Erich Hückel, Nachlass Ruge – DuBois- Reymond, Nachlass Johannes Stark: Staatsbibliothek zu Berlin, Preußischer Kulturbesitz. Special thanks I owe to Peter Damerow for allowing me to quote from the manuscript of Hilbert’s lectures on axiomatization (Hilbert 1913c), belonging to his private collection. Some of the important letters quoted in the book were recovered only recently for the Hilbert Nachlass in Göttingen, through the important efforts of Klaus Sommer (cf. Sommer 2002).

Some of the material published throughout the book had appeared earlier in scattered publications, and it has been brought here with varying degrees of modification, ranging from slight editorial or language changes to total reformulation. In all cases I have asked for permissions with the original publishers, as follows: Studies in History and Philosophy of Science Part B, Vol. 30, No 2, 1999, Pages 159-183, Leo Corry, “From Mie’s Electromagnetic Theory of Matter to Hilbert's Unified Foundations of Physics”, with permission of Elsevier. Archives for History of Exact Sciences, Springer Verlag: Vol. 51, pp. 83-198, Leo Corry, “David Hilbert and the Axiomatization of Physics (1895-1905)”; Vol. 51, pp. 273-314, Leo Corry, “Hermann Minkowski and the Postulate of xvi ACKNOWLEDGEMENTS AND CREDITS

Relativity”; Vol. 53, pp. 489-527. “David Hilbert between Mechanical and Electromagnetic Reductionism (1910-1915)”. Mathematical Intelligencer, Springer Verlag: Vol. 20 (3), pp. 52-58, “Hilbert on Kinetic Theory and Radiation Theory”.

For the photographs reproduced in this book I acknowledge the following permissions:

Fig. 1 (p. 5) David Hilbert: Niedersächsische Staats- und Universitäts- bibliothek Göttingen (NSUB). Fig. 2 (p. 14) Minkowski in 1883: NSUB. Fig. 3 (p. 16) Hilbert in 1885: NSUB. Fig. 4 (p. 31) Felix Klein: NSUB. Fig. 5 (p. 67) Aurel Voss: NSUB. Fig 6 (p. 77) Arnold Sommerfeld: Photo Deutsches Museum, Munich. Fig. 7 (p. 80) Woldemar Voigt: NSUB. Fig. 8 (p. 108) The Göttingen Mathematische Gesellschaft in 1902: NSUB. Fig. 9 (p. 120) Felix Klein in 1904: NSUB. Fig. 10 (p. 131) Ludwig Prandtl: AIP Emilio Segrè Visual Archives, Landé Collection. Fig. 11 (p. 135) Max Abraham circa 1905: NSUB. Fig. 12 (p. 137) Walter Kaufmann circa 1908: NSUB. Fig. 13 (p. 157) Original manuscript drawing appearing in Hilbert 1905, p. 163: NSUB. Fig. 14 (p. 159) Original manuscript drawing appearing in Hilbert 1905, p. 166: NSUB. Fig. 15 (p. 180) Tatyana and Paul Ehrenfest: Ia. Frenkel, Leningrad Physico- Technical Institute, courtesy AIP Emilio Segrè Visual Archives. Fig. 16 (p. 187) Minkowski during his Göttingen Years: NSUB. Fig. 17 (p. 192) Henri Poincaré: Cliché Henri Manuel, courtesy AIP Emilio Segrè Visual Archives, Physics Today Collection. Fig. 18 (p. 202) Diagram for Minkowski’s theory of gravitation. Fig. 19 (p. 203) Diagram for Minkowski’s theory of gravitation. Fig. 20 (p. 208) Original Diagram of Minkowski's “Space and Time” Talk. Fig. 21 (p. 230) Hilbert circa 1910: NSUB. Fig. 22 (p. 233) Alfred Landé: NSUB. Fig. 23 (p. 245) The Fisrt Solvay Conference in Brussels, 1911: Photo courtesy of the Albert Einstein Archive, Jewish National and University Library, Jerusalem. Published with the permission of the Solvay Institutes. Fig. 24 (p. 258) Max Planck: ©Lotte Meitner-Graf, London, courtesy AIP Emilio Segrè Visual Archives, Landé Collection. Fig. 25 (p. 260) Ernst Pringsheim: Photograph by Alfens Baschkov, courtesy AIP Emilio Segrè Visual Archives, Kohn Photo Collection. ACKNOWLEDGEMENTS AND CREDITS xvii

Fig. 26 (p. 275) Original manuscript frontispiece of Hilbert 1913c: Peter Damerow, Berlin, personal collection. Fig. 27 (p. 288) Albert Einstein circa 1916: Photo courtesy of the Albert Einstein Archive, Jewish National and University Library, Jerusalem. Published with the permission of the Museum Boerhaave, Leiden. Fig. 28 (p. 298) Gustav Mie (from the Gustav Mie Nachlass): Published with the permission of the Mie Family (Kiel and Berlin). Fig. 29 (p. 318) Peter Debye: NSUB. Fig. 30 (p. 327) Paul Hertz: NSUB. Fig. 31 (p. 331) Galley proofs of Hilbert’s 1915 article: NSUB. Fig. 32 (p. 346) Arnold Sommerfeld: Copyright Transocean Berlin, G.m.b.H., courtesy AIP Emilio Segrè Visual Archives, Physics Today Collection. Fig. 33 (p. 365) Einstein in Leiden, with Ehrenfest, de Sitter, Eddington, and Lorentz AIP Emilio Segrè Visual Archives. Fig. 34 (p. 367) Max Born as a soldier: AIP Emilio Segrè Visual Archives, Landé Collection. Fig. 35 (p. 381) Karl Schwarzschild: NSUB. Fig. 36 (p. 389) Felix Klein: NSUB. Fig. 37 (p. 392) Emmy Noether in 1925: NSUB. Fig. 38 (p. 395) Hermann Weyl: AIP Emilio Segrè Visual Archives, Nina Courant Collection. Fig. 39 (p. 410) Richard Courant: AIP Emilio Segrè Visual Archives, Nina Courant Collection. Fig. 40 (p. 412) Max Born as a mature scientist: NSUB. Fig. 41 (p. 439) Geheimrat David Hilbert: NSUB.