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I THE WHITE DWARF AFFAIR: Chandrasekhar, Eddington and the Limiting Mass •>y Sakura Gooneratne University College London University of London A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the History of Science 2005 UMI Number: U592031 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U592031 Published by ProQuest LLC 2013. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 2 ABSTRACT The White Dwarf Affair: Chandrasekhar, Eddington and the Limiting Mass by Sakura Gooneratne A thesis describing and analysing the controversy between Subrahmanyan Chandrasekhar and Arthur Stanley Eddington over the limiting mass of white dwarf stars. The aim of the thesis is to discover why the controversy occurred and to analyse the reasons behind Eddington's rejection of relativistic degeneracy and the limiting mass. The ultimate reason behind Eddington's attack on relativistic degeneracy was found to be Eddington’s severe objection to singularities which was apparent long before Chandrasekhar's discovery of the limiting mass and occurred in three separate areas of research undertaken by Eddington during this period: astrophysics, cosmology, general relativity and Dirac’s relativistic equation of the electron which led to Eddington's fundamental theory. The thesis will focus on the problem of the limiting mass of white dwarfs between 1929 and 1935 but will use the problem to analyse Eddington's view of singularities within the three different research areas spanning two decades from 1916 to 1936. The Chandrasekhar-Eddington controversy is set within Eddington's earlier controversies with James Jeans and Edward Arthur Milne who together with Eddington founded theoretical astrophysics during the 1920s. The thesis will examine the problem of white dwarfs within the context of the earlier controversies on stellar structure. As well as the technical analysis of the controversy, the thesis will also analyse the social dynamics and interactions within the astronomical community and their impact on the controversies. The aim of this thesis is to create a more complete picture of the Chandrasekhar- Eddington controversy by analysing Eddington's arguments for rejecting relativistic degeneracy, the limiting mass of white dwarfs and singularities not just within the context of astrophysics, but also cosmology, general relativity and quantum mechanics and to provide some new explanations as to why Eddington opposed relativistic degeneracy. 3 Acknowledgements I would like to thank my supervisors Andrew Gregory, Arthur I. Miller and Steve Miller for their invaluable help and support in guiding me through the preparation and completion of my thesis. Special thanks go to Hasok Chang who has been an inspirational mentor and gave me the courage to finish. I would like to thank the UCL Graduate School who gave me a travel grant which enabled me to research the Chandrasekhar Archive at the University of Chicago and the Oral History Archive at the Institute of Physics in Washington DC. I would like to thank my friends Helen Wickham, Jesse Schust, and Gaitee Hussain and her family who continued to encourage and push me; and Lalitha Chandrasekhar, Takeshi Oka, Clive Kilmister and Meg Weston-Smith for their help in painting a balanced picture of the controversy. And finally, I would like to dedicate this thesis to my sister Yuki and my parents Hiroko and Wilbert whose love and encouragement have meant more to me than they will ever know. 4 TABLE OF CONTENTS INTRODUCTION 6 CHAPTERS 1 Early Astrophysical Controversies 35 1.1 Eddington-Jeans Controversy: 1916 - 1928 38 1.1.1 Radiative Equilibrium and Cepheid Variability 42 1.1.2 The Mass-Luminosity Relation 52 1.1.3 Stellar Structure 57 1.2 The Eddington-Milne Controversy: 1929 - 1931 61 1.2.1 Boundary Conditions and Energy Liberation 64 1.2.2 The Problem of Opacity 66 1.2.3 Nuclear Model of a Star 68 1.3 Interpreting the Eddington-Jeans-Milne Controversy 71 1.3.1 The Effect of Controversies on Friendship 77 1.3.2 On the Credibility of Astrophysics 81 2 White Dwarfs and Collapsed Stellar Configurations 89 2.1 Early Research 95 2.1.1 The Discovery of White Dwarf Stars 95 2.1.2 Milne and his Degenerate Stellar Cores 101 2.1.3 The Milne Brigade: Degeneracy Research amongst Milne's Students 106 2.1.4 Opposition to Milne's Centrally Condensed and Collapsed Configurations 110 2.2 The Stoner-Anderson Formula 113 2.2.1 Stoner: A Small Diversion into Astrophysics 113 2.2.2 The Stoner-Anderson Formula for Relativistic Degeneracy 118 2.2.3 The Reception of the Stoner-Anderson Formula by Astronomers 124 2.3 Lev Landau and the Limiting Mass 131 3 The Controversy 138 3.1 Chandrasekhar and the Case of the Badly Behaved Stars 138 3.1.1 The Discovery of the Limiting Mass 138 3.1.2 Collaboration and Disagreement regarding Milne's Degenerate Core Theory 150 3.1.3 Rethinking the Limiting Mass and Establishing an Exact Theory 160 3.2 The Exact Theory of the Limiting Mass of White Dwarfs 165 3.2.1 The Papers 167 3.3 Eddington's Attack: On ‘Relativistic Degeneracy’ 171 4 After the Controversy 181 4.1 The Reluctant Astronomers 181 5 4.1.1 Eddington's Unexpected Attack 181 4.1.2 Lack of Peer Support for Chandrasekhar 188 4.1.3 Eddington's Authority 193 4.1.4 Racial Prejudice 198 4.2 Chandrasekhar's Correspondence with Dirac, McCrea and Rosenfeld 199 4.2.1 Dirac 200 4.2.2 McCrea 204 4.2.3 Rosenfeld 206 4.3 Final Encounters with Eddington 221 4.3.1 IAU Conference in Paris 1935 221 4.3.2 International Conference on White Dwarfs in Paris 1939 223 4.4 Social Interactions and Group Dynamics 231 4.4.1 Group Dynamics within the Chandrasekhar-Eddington Controversy 231 4.4.2 Aftermath of the Controversy 234 5 Eddington's Arguments 240 5.1 Cosmology 244 5.1.1 The Static Universe and the Einstein and de Sitter Models 244 5.1.2 The Expanding Universe and the Lemaitre-Friedmann Model 254 5.2 Bridging General Relativity and Quantum Mechanics 262 5.2.1 Dirac’s Relativistic Equation of the Electron 263 5.2.2 The Fine Structure Constant and Gravitational Collapse 274 5.3 Singularities 278 5.3.1 A Brief History of Singularities 278 5.3.2 The Problem with Singularities 284 5.4 Relativistic Degeneracy and Singularities 290 5.5 Eddington the Quaker 299 CONCLUSION 305 Appendix I: The Stoner-Anderson Formula 317 Appendix II: Chandrasekhar's Theory of the Limiting Mass 322 BIBLIOGRAPHY 327 Introduction 6 INTRODUCTION Aim The aim of this thesis is to describe and clarify the controversy over the limiting mass of white dwarf stars between the astrophysicists Subrahmanyan Chandrasekhar and Arthur Stanley Eddington which occurred in 1935, but whose repercussions were felt for the next thirty years. I will try to show that Eddington's rejection of the Chandrasekhar Limit is due to his absolute instinctive rejection of singularities. The reasons behind the controversy range from purely mathematical to conceptual, and perhaps even psychological, and although the thesis will not give a definitive explanation for Eddington's behaviour, an attempt will be made to assess the events leading up to the controversy and to follow the astrophysicists through and beyond it. The thesis will cover the birth of theoretical astrophysics, the early astrophysical controversies between Eddington, Jeans and Milne, research on white dwarfs and the limiting mass, the controversy between Chandrasekhar and Eddington, its aftermath and, finally, an analysis of the reasons why the controversy occurred with respect to Eddington's stance against relativistic degeneracy and his views on singularities.