The Pursuit of Quantum Gravity

Cécile DeWitt-Morette

Memoirs of Bryce DeWitt from 1946 to 2004

123 Cécile DeWitt-Morette Department of Physics Center for Relativity University of Texas at Austin Austin Texas USA [email protected]

ISBN 978-3-642-14269-7 e-ISBN 978-3-642-14270-3 DOI 10.1007/978-3-642-14270-3 Springer Heidelberg Dordrecht London New York

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Preface

This book is written for the curious reader. I hope it will also be a good read for the professional physicist. It develops and supplements the biographical memoir (16 pages) prepared by Steven Weinberg for the National Academy of Sciences.1 It is also a companion to Bryce DeWitt’s last book [BD 103]2 The Global Approach to Quantum Field Theory (1042 pages, first published in 2003, reprinted with corrections in 2004). Bryce’s book is an excellent physicist’s record of his pursuit of quantum gravity. As an introduction to the theme of the book, two pieces from Bryce DeWitt are reproduced in extenso: “Why Physics?” consists of a few hand-written pages addressed to his grandson, and A posthumously published article “Quantum Gravity: Yesterday and To- day” addressing the questions: “Why Quantum Gravity?” and “Why Link Quantum Gravity and Bryce DeWitt’s Memoirs?” The structures of quantum physics and gravitation physics do not constitute a single logical system. Digging deeper into their respective structures may reveal a common root. Therefore the pursuit of quantum gravity requires a profound understanding of both quantum physics and gravitation physics. As G.A. Vilkovisky wrote to me, “Quantum Gravity is a combination of two words, and one should know both. Bryce understood this as nobody else, and this wisdom is completely unknown to many authors of the flux of papers that we see nowadays.”3 Sections I and II deal with the status of quantum physics and gravitation physics in the late forties. A couple of major topics are then selected in each 1 Steven Weinberg, “Bryce Seligman DeWitt, 1923–2004: A Biographical Memoir”, National Academy of Sciences (2008). This memoir incorporates materials given to Weinberg by DeWitt before his death and is reproduced in Sect. V.1. 2 References to DeWitt’s own list of publicationsare indicated in the text in square brack- ets prepended BD. 3 E-mail correspondence dated Dec. 28, 2007. vii field because they were of special interest to Bryce. Quantum gravity itself is the focus of Sect. III. It captures Bryce’s work from 1946 to 2004 and places it in its scientific, historical, and human context. I have been blessed and burdened by an enormous amount of material for the preparation of this book; in addition to, I believe, a complete set of published material, I have most of Bryce’s reports to institutions and referee reports to journals, letters of recommendation, correspondence, research proposals, unpublished documents, and my memories (les souvenirs que la mémoire invente!4). I have included extensive quotes from Bryce. They are printed in blue. Bryce’s writings were carefully crafted, and he could not stand any editing (except by his fourth daughter Abigail, who edited his last writing “God’s Rays”). Therefore I could not summarize his quotes, paraphrase them, or select brief quotes out of context. I have added introductions, motivations, and historical comments that place his technical progress in a larger context and make his research papers easier to read.5 Ihaveincludedafewtechni- cal notes when necessary to justify some statements. The reader not inter- ested in technical details can gloss over them without losing the thread of the topic. The material in blue (Bryce’s quotes) and the material in black (Cécile’s contributions and others’) are meaningful by themselves; together they make a whole. Including extensive quotes occasionally creates a few duplications, but they are not verbatim duplications; a later quote shows the maturation of an earlier one. My task has been made manageable thanks to the help of Brandon DiN- unno, John Stachel, and Lawrence Shepley, and to the offer from The Uni- versity of Texas Center for American History to be the repository of Bryce’s documents.6 The support that The University of Texas provides to its Professors Emer- iti is gratefully acknowledged. Without an office, and all the facilities of the Physics Department, I could not have completed this task in a timely fash- ion. In addition, my office is close to Austin Gleeson’s and whenever I needed something, I only had to poke my head in his always open door. I have enjoyed many visits to the InstitutdesHautesEtudesScientifiques at Bures-sur-Yvette, France, an oasis in the fast moving, crowded schedule of modern times – an oasis where one finds the peace necessary for concen- tration and the stimulation of other travellers following their own pursuits.

4 Recollections that memory invents. 5 For instance, in Bryce’s condensed notation, an index may refer to coordinates both in the domain and in the range of the function. Occasionally he used mathematical terms heuristically; I have often been frustrated by his use of the word “measure” in functional integrals. Like many physicists he talks of gauge fields as connections. In reality gauge potentials are pull-backs of connections on a principal bundle. 6 see Sect. V.4. viii These pages are memoirs around the theme “Quantum Gravity”.7 Once a neglected problem in the backwaters of the flow of physics research, quantum gravity has now become a major challenge in fundamental physics.8 The pursuit of quantum gravity goes on. This book began as a scrapbook of its beginnings and matured into its present form, though it is not, and was not meant to be, a scholarly piece of Science History in the strict sense. Some colleagues have suggested pertinent additions, in particular Thibault Damour, Jürg Fröhlich, Phillip Morrison, and Larry Smarr, but I have kept in mind the size of the book and its scientific level – and hope to have achieved a nicely readable balance. There are some who seem to question the rôle of publishers in the age of the internet; but a great publisher eliminates the gangue from the mineral ore by addition or by subtraction. My manuscript has been made into a book thanks to the care and expertise of Dr. Christian Caron, Executive Publishing Editor at Springer-Verlag, Theodor C.H. Cole, Copy and Language Editor, andBirgitMünch,DeskEditor.

Cécile Morette, épouse DeWitt9

7 For a balanced non-technical review on the development of the field as a whole, see e.g. C. Rovelli, Notes for a brief history of quantum gravity, arXiv: gr-qc/0006061v3 (23 Jan 2001). 8 It is also mentioned outside physics. For instance, when Alan Sokal wanted to play a hoax on a cultural studies journal, he sent a parody of postmodern academic prose titled “Transgressing the Boundaries Towards a Transformative Hermeneutics of Quan- tum Gravity” to Social Text. The article was published in 1996, and the hoax became an often-quoted anecdote (Alan D. Sokal, “Transgressing the Boundaries Towards a Trans- formative Hermeneutics of Quantum Gravity”, Social Text 46/47, 217–252 (1996)). 9 I use my French legal name to indicate that my work as a physicist and as a spouse are independent of each other. The concept of a person, or an object, assuming different functions in different contexts is not unusual. In mathematics an operator is defined only together with the space on which it operates. The same is true in human relation- ships. As a mother and as a wife a person’s behavior may be different. The label “spouse” was inappropriately attached to my qualifications as physicist, and antinepotism regulations were invoked to deny me a position in the same department as my husband. The concept “conflict of interest” is sometimes used inappropriately. My French name, as recorded on my birth certificate is “Cécile, Andrée, Paulette Morette-Payen, veuve DeWitt” I prefer “épouse” to “veuve”. French birth certificates are updated to reflect an individual’s État Civil. ix

Contents

Introduction ...... 1 Why Physics? ...... 1 Why Quantum Gravity? Why Link Quantum Gravity and Bryce DeWitt’s Memoirs? ...... 5

I Progress in Quantum Physics Since the Late Forties ...... 13 I.1 Functional Integration as a Major Technique in Quantum Physics ...... 13 I.2 The Geometry of Gauge Fields ...... 17 I.2.1 Classical Gauge Fields ...... 17 I.2.2 Quantum Gauge Fields ...... 19

II Progress in Gravitation Since the Late Forties ...... 25 II.1 Numerical Relativity ...... 25 II.1.1 Classical Relativity ...... 25 II.1.2 Toy Models for Quantum Gravity ...... 31 II.2 Bryce DeWitt’s Lectures on Relativity ...... 36 II.3 The 1973 Eclipse Expedition ...... 43

III Quantum Gravity ...... 51 III.1 Ph.D. Thesis (Harvard 1950) ...... 51 III.2 Covariant Quantization vs. Canonical Quantization ...... 56 III.2.1 Dirac’s Constrained Hamiltonian Dynamics ...... 56 III.2.2 The Wheeler-DeWitt Equation ...... 57 III.2.3 The “Trilogy” ...... 60 III.3 The Gravity Research Foundation Essay (1953) ...... 61 III.4 The Institute of Field Physics (1955–1964) ...... 69 III.4.1 Original Documents ...... 69 III.4.2 A Stone Thrown Into a Pool and Its Ripples ...... 79

xi III.5 The 1957 Chapel Hill Conference ...... 87 III.6 Everett’s Theory and the “Many Worlds” Interpretation ...... 91 III.6.1 Everett’s Theory Viewed by Bryce DeWitt ...... 94 III.6.2 Everett’s Theory Viewed by John Wheeler ...... 97 III.7 Relativity, Groups, and Topology...... 100 III.8 Quantum Field Theory in Curved Spacetime ...... 104 III.9 Supermanifolds ...... 107 III.10 The Global Approach to Quantum Field Theory ...... 110 III.11 The Pursuit Goes On ...... 114

IV A Few Comments from Bryce DeWitt ...... 119 IV.1 Amateurs, Crackpots, Professionals, and Gravitation ...... 119 IV.2 Research Centers ...... 121

VBibliography...... 123 V.1 A Biographical Memoir by Steven Weinberg ...... 123 V.2 Publications ...... 131 V.3 Curriculum Vitae ...... 140 V.4 Archives Storedat the Centerfor AmericanHistory ...... 145

About the Author ...... 147

Name Index ...... 149

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