The Universe of General Relativity, Springer 2005.Pdf

Total Page:16

File Type:pdf, Size:1020Kb

The Universe of General Relativity, Springer 2005.Pdf Einstein Studies Editors: Don Howard John Stachel Published under the sponsorship of the Center for Einstein Studies, Boston University Volume 1: Einstein and the History of General Relativity Don Howard and John Stachel, editors Volume 2: Conceptual Problems of Quantum Gravity Abhay Ashtekar and John Stachel, editors Volume 3: Studies in the History of General Relativity Jean Eisenstaedt and A.J. Kox, editors Volume 4: Recent Advances in General Relativity Allen I. Janis and John R. Porter, editors Volume 5: The Attraction of Gravitation: New Studies in the History of General Relativity John Earman, Michel Janssen and John D. Norton, editors Volume 6: Mach’s Principle: From Newton’s Bucket to Quantum Gravity Julian B. Barbour and Herbert Pfister, editors Volume 7: The Expanding Worlds of General Relativity Hubert Goenner, Jürgen Renn, Jim Ritter, and Tilman Sauer, editors Volume 8: Einstein: The Formative Years, 1879–1909 Don Howard and John Stachel, editors Volume 9: Einstein from ‘B’ to ‘Z’ John Stachel Volume 10: Einstein Studies in Russia Yuri Balashov and Vladimir Vizgin, editors Volume 11: The Universe of General Relativity A.J. Kox and Jean Eisenstaedt, editors A.J. Kox Jean Eisenstaedt Editors The Universe of General Relativity Birkhauser¨ Boston • Basel • Berlin A.J. Kox Jean Eisenstaedt Universiteit van Amsterdam Observatoire de Paris Instituut voor Theoretische Fysica SYRTE/UMR8630–CNRS Valckenierstraat 65 F-75014 Paris Cedex 1018 XE Amsterdam France The Netherlands AMS Subject Classification (2000): 01A60, 83-03, 83-06 Library of Congress Cataloging-in-Publication Data The universe of general relativity / A.J. Kox, editors, Jean Eisenstaedt. p. cm. – (Einstein studies ; v. 11) Includes bibliographical references. ISBN-13 978-0-8176-4380-5 (alk. paper) ISBN-10: 0-8176-4380-X (alk. paper) 1. Relativity (Physics)–History–Congresses. 2. General relativity (Physics)–History–Congresses. 3. Gravitation–History–Congresses. 4. Cosmology–History–Congresses. 5. Unified field theories–History–Congresses. 6. Einstein, Albert, 1879-1955. I. Kox, Anne J., 1948- II. Eisenstaedt, Jean III. Series. QC173.5.U55 2005 530.11–dc22 2005047817 ISBN-10 0-8176-4380-X e-IBSN 0-8176-4454-7 Printed on acid-free paper. ISBN-13 978-0-8176-4380-5 c 2005 The Center for Einstein Studies The Einstein Studies series is published under the sponsorship of the Center for Einstein Studies, Boston University. All rights reserved. This work may not be translated or copied in whole or in part without the writ- ten permission of the publisher (Birkhauser¨ Boston, c/o Springer Science+Business Media Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de- veloped is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. (TXQ/EB) 987654321 www.birkhauser.com This volume is dedicated to the memory of Peter Havas Contents PREFACE ......................................................... ix 1 Fresnel’s (Dragging) Coefficient as a Challenge to 19th Century Optics of Moving Bodies JOHN STACHEL ................................................... 1 2 Poincare’s´ Relativistic Theory of Gravitation SHAUL KATZIR ................................................... 15 3 Standing on the Shoulders of a Dwarf: General Relativity—A Triumph of Einstein and Grossmann’s Erroneous Entwurf Theory JURGEN¨ RENN .................................................... 39 4 Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy JURGEN¨ RENN .................................................... 53 5 A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913 JOHN D. NORTON ................................................. 67 6 Einstein and the Principle of General Relativity, 1916–1921 CHRISTOPH LEHNER ............................................... 103 7 Einstein and the Problem of Motion: A Small Clue DANIEL KENNEFICK ............................................... 109 8 A Note on General Relativity, Energy Conservation, and Noether’s Theorems KATHERINE BRADING ............................................. 125 9 Weyl vs. Reichenbach on Lichtgeometrie ROBERT RYNASIEWICZ ............................................. 137 viii Contents 10 Dingle and de Sitter Against the Metaphysicians, or Two Ways to Keep Modern Cosmology Physical GEORGE GALE .................................................... 157 11 George Gamow and the ‘Factual Approach’ to Relativistic Cosmology HELGE KRAGH ................................................... 175 12 George McVittie, The Uncompromising Empiricist JOSE´ M. SANCHEZ´ -RON ............................................ 189 13 False Vacuum: Early Universe Cosmology and the Development of Inflation CHRIS SMEENK ................................................... 223 14 Hilbert’s “World Equations” and His Vision of a Unified Science U. MAJER AND T. SAUER ........................................... 259 15 Einstein, Kaluza, and the Fifth Dimension DANIELA WUNSCH¨ ................................................ 277 16 Unified Field Theory: Early History and Interplay Between Mathematics and Physics HUBERT F. M. GOENNER ........................................... 303 17 Is Quantum Gravity Necessary? JAMES MATTINGLY ................................................ 327 18 Einstein in the Daily Press: A Glimpse into the Gehrcke Papers MILENA WAZECK ................................................. 339 19 Syracuse: 1949–1952 JOSHUA GOLDBERG ............................................... 357 20 A Biased and Personal Description of GR at Syracuse University, 1951–1961 E. T. NEWMAN ................................................... 373 Preface A century ago, in 1905, Albert Einstein published, “On the Electrodynamics of Mov- ing Bodies,” in which the foundations were laid for the Special Theory of Relativity. Ten years later his relativistic theory of gravitation and the General Theory of Relativ- ity appeared. Fifty years ago, Einstein passed away in Princeton. In the 1980s, John Stachel, then Editor of the Collected Papers of Albert Einstein, brought together a group of historians, philosophers, physicists, and mathematicians who had one thing in common: a lively interest in the history and foundations of the theories of relativity. At a meeting in 1986 at Osgood Hill, this group met for the first time to discuss the prehistory, development, reception, and other aspects of relativity. It was the beginning of a valuable tradition. Since then every three or four years a meeting has been organized during which historical and foundational issues in general (and special) relativity have been discussed. Osgood Hill was followed by Luminy in 1988. Then came Johnstown (1991), Berlin (1995), Notre Dame (1999), and finally Amsterdam (2002), the proceedings of which are presented in this volume (supplemented with some papers from the preceding meeting). Once again these articles clearly show that an historical approach can lead to new insights into the development and elaboration of relativity. The prehistory of special relativity and an early attempt at a relativistic theory of gravitation are covered in pa- pers by John Stachel and Shaul Katzir, respectively. The birth and early history of gen- eral relativity are the topics of the papers by Jurgen¨ Renn, John Norton, and Christoph Lehner. They are followed by Daniel Kennefick’s contribution, which focuses on one of the major problems in general relativity: the problem of motion. That general rela- tivity has close ties to mathematics becomes clear from Katherine Brading’s paper on the conservation laws and Robert Rynasiewicz’s article on the axiomatization of the theory. Five papers then follow on cosmology, a topic of research that owes much of its existence to General Relativity. George Gale, Helge Kragh, and JoseS´ anchez-Ron´ take a closer look at the work of Herbert Dingle and Willem de Sitter, George Gamov, and George McVittie, respectively, while Chris Smeenk discusses an aspect of more contemporary cosmology. x Preface As is well known, during the second part of his active life Einstein pursued the goal of creating a unified field theory to unify gravitation and electromagnetism. That he was not the only one searching for a unified theory becomes clear from the contri- butions of Ulrich Majer and Tilman Sauer on the work of David Hilbert and of Hubert Goenner on the early history of unified field theory. Next, Daniela Wunsch¨ studies the work of Einstein and Theodor Kaluza, which is not just of historical value but in recent years has provoked much interest. Finally, James Mattingly presents some considerations on the necessity of quantum gravity. The volume concludes with three contributions on a more “personal” level. First, Milena Wazeck uses the recently-discovered papers of the physicist Ernst Gehrcke to provide a view of the reception of relativity by the general public. Next, the two renowned relativists Josh Goldberg and Ted Newman share with us their recollections of the time when they were both actively contributing to the further development of the General Theory of Relativity. A.J.
Recommended publications
  • Frame Covariance and Fine Tuning in Inflationary Cosmology
    FRAME COVARIANCE AND FINE TUNING IN INFLATIONARY COSMOLOGY A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2019 By Sotirios Karamitsos School of Physics and Astronomy Contents Abstract 8 Declaration 9 Copyright Statement 10 Acknowledgements 11 1 Introduction 13 1.1 Frames in Cosmology: A Historical Overview . 13 1.2 Modern Cosmology: Frames and Fine Tuning . 15 1.3 Outline . 17 2 Standard Cosmology and the Inflationary Paradigm 20 2.1 General Relativity . 20 2.2 The Hot Big Bang Model . 25 2.2.1 The Expanding Universe . 26 2.2.2 The Friedmann Equations . 29 2.2.3 Horizons and Distances in Cosmology . 33 2.3 Problems in Standard Cosmology . 34 2.3.1 The Flatness Problem . 35 2.3.2 The Horizon Problem . 36 2 2.4 An Accelerating Universe . 37 2.5 Inflation: More Questions Than Answers? . 40 2.5.1 The Frame Problem . 41 2.5.2 Fine Tuning and Initial Conditions . 45 3 Classical Frame Covariance 48 3.1 Conformal and Weyl Transformations . 48 3.2 Conformal Transformations and Unit Changes . 51 3.3 Frames in Multifield Scalar-Tensor Theories . 55 3.4 Dynamics of Multifield Inflation . 63 4 Quantum Perturbations in Field Space 70 4.1 Gauge Invariant Perturbations . 71 4.2 The Field Space in Multifield Inflation . 74 4.3 Frame-Covariant Observable Quantities . 78 4.3.1 The Potential Slow-Roll Hierarchy . 81 4.3.2 Isocurvature Effects in Two-Field Models . 83 5 Fine Tuning in Inflation 88 5.1 Initial Conditions Fine Tuning .
    [Show full text]
  • PDF Solutions
    Solutions to exercises Solutions to exercises Exercise 1.1 A‘stationary’ particle in anylaboratory on theEarth is actually subject to gravitationalforcesdue to theEarth andthe Sun. Thesehelp to ensure that theparticle moveswith thelaboratory.Ifstepsweretaken to counterbalance theseforcessothatthe particle wasreally not subject to anynet force, then the rotation of theEarth andthe Earth’sorbital motionaround theSun would carry thelaboratory away from theparticle, causing theforce-free particle to followacurving path through thelaboratory.Thiswouldclearly show that the particle didnot have constantvelocity in the laboratory (i.e.constantspeed in a fixed direction) andhence that aframe fixed in the laboratory is not an inertial frame.More realistically,anexperimentperformed usingthe kind of long, freely suspendedpendulum known as a Foucaultpendulum couldreveal the fact that a frame fixed on theEarth is rotating andthereforecannot be an inertial frame of reference. An even more practical demonstrationisprovidedbythe winds,which do not flowdirectly from areas of high pressure to areas of lowpressure because of theEarth’srotation. - Exercise 1.2 TheLorentzfactor is γ(V )=1/ 1−V2/c2. (a) If V =0.1c,then 1 γ = - =1.01 (to 3s.f.). 1 − (0.1c)2/c2 (b) If V =0.9c,then 1 γ = - =2.29 (to 3s.f.). 1 − (0.9c)2/c2 Notethatitisoften convenient to write speedsinterms of c instead of writingthe values in ms−1,because of thecancellation between factorsofc. ? @ AB Exercise 1.3 2 × 2 M = Theinverse of a matrix CDis ? @ 1 D −B M −1 = AD − BC −CA. Taking A = γ(V ), B = −γ(V )V/c, C = −γ(V)V/c and D = γ(V ),and noting that AD − BC =[γ(V)]2(1 − V 2/c2)=1,wehave ? @ γ(V )+γ(V)V/c [Λ]−1 = .
    [Show full text]
  • Annual Report to Industry Canada Covering The
    Annual Report to Industry Canada Covering the Objectives, Activities and Finances for the period August 1, 2008 to July 31, 2009 and Statement of Objectives for Next Year and the Future Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo, Ontario N2L 2Y5 Table of Contents Pages Period A. August 1, 2008 to July 31, 2009 Objectives, Activities and Finances 2-52 Statement of Objectives, Introduction Objectives 1-12 with Related Activities and Achievements Financial Statements, Expenditures, Criteria and Investment Strategy Period B. August 1, 2009 and Beyond Statement of Objectives for Next Year and Future 53-54 1 Statement of Objectives Introduction In 2008-9, the Institute achieved many important objectives of its mandate, which is to advance pure research in specific areas of theoretical physics, and to provide high quality outreach programs that educate and inspire the Canadian public, particularly young people, about the importance of basic research, discovery and innovation. Full details are provided in the body of the report below, but it is worth highlighting several major milestones. These include: In October 2008, Prof. Neil Turok officially became Director of Perimeter Institute. Dr. Turok brings outstanding credentials both as a scientist and as a visionary leader, with the ability and ambition to position PI among the best theoretical physics research institutes in the world. Throughout the last year, Perimeter Institute‘s growing reputation and targeted recruitment activities led to an increased number of scientific visitors, and rapid growth of its research community. Chart 1. Growth of PI scientific staff and associated researchers since inception, 2001-2009.
    [Show full text]
  • Harmonic and Complex Analysis and Its Applications
    Trends in Mathematics Alexander Vasil’ev Editor Harmonic and Complex Analysis and its Applications Trends in Mathematics Trends in Mathematics is a series devoted to the publication of volumes arising from conferences and lecture series focusing on a particular topic from any area of mathematics. Its aim is to make current developments available to the community as rapidly as possible without compromise to quality and to archive these for reference. Proposals for volumes can be submitted using the Online Book Project Submission Form at our website www.birkhauser-science.com. Material submitted for publication must be screened and prepared as follows: All contributions should undergo a reviewing process similar to that carried out by journals and be checked for correct use of language which, as a rule, is English. Articles without proofs, or which do not contain any significantly new results, should be rejected. High quality survey papers, however, are welcome. We expect the organizers to deliver manuscripts in a form that is essentially ready for direct reproduction. Any version of TEX is acceptable, but the entire collection of files must be in one particular dialect of TEX and unified according to simple instructions available from Birkhäuser. Furthermore, in order to guarantee the timely appearance of the proceedings it is essential that the final version of the entire material be submitted no later than one year after the conference. For further volumes: http://www.springer.com/series/4961 Harmonic and Complex Analysis and its Applications Alexander Vasil’ev Editor Editor Alexander Vasil’ev Department of Mathematics University of Bergen Bergen Norway ISBN 978-3-319-01805-8 ISBN 978-3-319-01806-5 (eBook) DOI 10.1007/978-3-319-01806-5 Springer Cham Heidelberg New York Dordrecht London Mathematics Subject Classification (2010): 13P15, 17B68, 17B80, 30C35, 30E05, 31A05, 31B05, 42C40, 46E15, 70H06, 76D27, 81R10 c Springer International Publishing Switzerland 2014 This work is subject to copyright.
    [Show full text]
  • Hubble's Evidence for the Big Bang
    Hubble’s Evidence for the Big Bang | Instructor Guide Students will explore data from real galaxies to assemble evidence for the expansion of the Universe. Prerequisites ● Light spectra, including graphs of intensity vs. wavelength. ● Linear (y vs x) graphs and slope. ● Basic measurement statistics, like mean and standard deviation. Resources for Review ● Doppler Shift Overview ● Students will consider what the velocity vs. distance graph should look like for 3 different types of universes - a static universe, a universe with random motion, and an expanding universe. ● In an online interactive environment, students will collect evidence by: ○ using actual spectral data to calculate the recession velocities of the galaxies ○ using a “standard ruler” approach to estimate distances to the galaxies ● After they have collected the data, students will plot the galaxy velocities and distances to determine what type of model Universe is supported by their data. Grade Level: 9-12 Suggested Time One or two 50-minute class periods Multimedia Resources ● Hubble and the Big Bang WorldWide Telescope Interactive ​ Materials ● Activity sheet - Hubble’s Evidence for the Big Bang Lesson Plan The following represents one manner in which the materials could be organized into a lesson: Focus Question: ● How does characterizing how galaxies move today tell us about the history of our Universe? Learning Objective: ● SWBAT collect and graph velocity and distance data for a set of galaxies, and argue that their data set provides evidence for the Big Bang theory of an expanding Universe. Activity Outline: 1. Engage a. Invite students to share their ideas about these questions: i. Where did the Universe come from? ii.
    [Show full text]
  • Lemaître and Hoyle: Contrasting Characters in Science and Religion
    S & CB (2012), 24, 111–127 0954–4194 RODNEY HOLDER Lemaître and Hoyle: Contrasting Characters in Science and Religion Georges Lemaître was a jocular Roman Catholic priest and Fred Hoyle a bluff Yorkshireman who despised organised religion. Both were giants of twentieth century cosmology but espoused diametrically opposed cosmological models. This paper explores the extent to which ideology, and particularly religion, played a part in the controversies over the Big Bang and steady-state theories. A significant problem for many cosmologists, including Hoyle, was posed by the idea that the universe had a temporal beginning: an eternal, unchanging universe seemed metaphysically preferable. And Hoyle was highly polemical about religion in his popular writings. In contrast, Lemaître saw no theological import from the Big Bang, and never entered a debate about its theological implications until, perhaps unexpectedly, he took issue with an address given by the Pope. Hoyle’s seminal work on stellar nucleosynthesis led him to speak of a ‘superintellect monkeying with physics’ though this was never identified with the God of classical theism. The work of both Lemaître and Hoyle resonates with more recent debates concerning cosmology. Key words: Lemaître, Hoyle, Big Bang, steady-state theory, cosmology, creation Introduction In Georges Lemaître and Fred Hoyle we have two characters who are so utterly different in many ways, yet who shared one very significant attrib- ute: they were giants in twentieth century cosmology and astrophysics. In short, here we have a Belgian Roman Catholic priest who can rightly be described as the Father of the Big Bang, and in Hoyle an atheist York- shireman who pioneered the alternative of a steady-state universe with neither beginning nor end.
    [Show full text]
  • The Rebirth of Cosmology: from the Static to the Expanding Universe
    Physics Before and After Einstein 129 M. Mamone Capria (Ed.) IOS Press, 2005 © 2005 The authors Chapter 6 The Rebirth of Cosmology: From the Static to the Expanding Universe Marco Mamone Capria Among the reasons for the entrance of Einstein’s relativity into the scientific folklore of his and our age one of the most important has been his fresh and bold approach to the cosmological problem, and the mysterious, if not paradoxical concept of the universe as a three-dimensional sphere. Einstein is often credited with having led cosmology from philosophy to science: according to this view, he made it possible to discuss in the pro- gressive way typical of science what had been up to his time not less “a field of endless struggles” than metaphysics in Kant’s phrase. It is interesting to remember in this connection that the German philosopher, in his Critique of Pure Reason, had famously argued that cosmology was beyond the scope of science (in the widest sense), being fraught with unsolvable contradictions, inherent in the very way our reason functions. Of course not everybody had been impressed by this argument, and several nineteenth-century scientists had tried to work out a viable image of the universe and its ultimate destiny, using Newtonian mechanics and the principles of thermodynamics. However, this approach did not give unambiguous answers either; for instance, the first principle of thermodynamics was invoked to deny that the universe could have been born at a certain moment in the past, and the second principle to deny that its past could be infinite.
    [Show full text]
  • The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 4, October 2016, Pages 513–554 http://dx.doi.org/10.1090/bull/1544 Article electronically published on August 2, 2016 THE EMERGENCE OF GRAVITATIONAL WAVE SCIENCE: 100 YEARS OF DEVELOPMENT OF MATHEMATICAL THEORY, DETECTORS, NUMERICAL ALGORITHMS, AND DATA ANALYSIS TOOLS MICHAEL HOLST, OLIVIER SARBACH, MANUEL TIGLIO, AND MICHELE VALLISNERI In memory of Sergio Dain Abstract. On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein’s prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detec- tion of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole bina- ries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science.
    [Show full text]
  • 1 Clifford Algebraic Computational Fluid Dynamics
    Clifford Algebraic Computational Fluid Dynamics: A New Class of Experiments. Dr. William Michael Kallfelz 1 Lecturer, Department of Philosophy & Religion, Mississippi State University The Philosophy of Scientific Experimentation: A Challenge to Philosophy of Science-Center for Philosophy of Science, University of Pittsburgh October 15-16, 2010. October 24, 2010 Abstract Though some influentially critical objections have been raised during the ‘classical’ pre- computational simulation philosophy of science (PCSPS) tradition, suggesting a more nuanced methodological category for experiments 2, it safe to say such critical objections have greatly proliferated in philosophical studies dedicated to the role played by computational simulations in science. For instance, Eric Winsberg (1999-2003) suggests that computer simulations are methodologically unique in the development of a theory’s models 3 suggesting new epistemic notions of application. This is also echoed in Jeffrey Ramsey’s (1995) notions of “transformation reduction,”—i.e., a notion of reduction of a more highly constructive variety. 4 Computer simulations create a broadly continuous arena spanned by normative and descriptive aspects of theory-articulation, as entailed by the notion of transformation reductions occupying a continuous region demarcated by Ernest Nagel’s (1974) logical-explanatory “domain-combining reduction” on the one hand, and Thomas Nickels’ (1973) heuristic “domain- preserving reduction,” on the other. I extend Winsberg’s and Ramsey’s points here, by arguing that in the field of computational fluid dynamics (CFD) as well as in other branches of applied physics, the computer plays a constitutively experimental role—supplanting in many cases the more traditional experimental methods such as flow- visualization, etc. In this case, however CFD algorithms act as substitutes, not supplements (as the notions “simulation” suggests) when it comes to experimental practices.
    [Show full text]
  • Catoni F., Et Al. the Mathematics of Minkowski Space-Time.. With
    Frontiers in Mathematics Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta, USA) Benoît Perthame (Ecole Normale Supérieure, Paris, France) Laurent Saloff-Coste (Cornell University, Rhodes Hall, USA) Igor Shparlinski (Macquarie University, New South Wales, Australia) Wolfgang Sprössig (TU Bergakademie, Freiberg, Germany) Cédric Villani (Ecole Normale Supérieure, Lyon, France) Francesco Catoni Dino Boccaletti Roberto Cannata Vincenzo Catoni Enrico Nichelatti Paolo Zampetti The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers Birkhäuser Verlag Basel . Boston . Berlin $XWKRUV )UDQFHVFR&DWRQL LQFHQ]R&DWRQL LDHJOLD LDHJOLD 5RPD 5RPD Italy Italy HPDLOYMQFHQ]R#\DKRRLW Dino Boccaletti 'LSDUWLPHQWRGL0DWHPDWLFD (QULFR1LFKHODWWL QLYHUVLWjGL5RPD²/D6DSLHQ]D³ (1($&5&DVDFFLD 3LD]]DOH$OGR0RUR LD$QJXLOODUHVH 5RPD 5RPD Italy Italy HPDLOERFFDOHWWL#XQLURPDLW HPDLOQLFKHODWWL#FDVDFFLDHQHDLW 5REHUWR&DQQDWD 3DROR=DPSHWWL (1($&5&DVDFFLD (1($&5&DVDFFLD LD$QJXLOODUHVH LD$QJXLOODUHVH 5RPD 5RPD Italy Italy HPDLOFDQQDWD#FDVDFFLDHQHDLW HPDLO]DPSHWWL#FDVDFFLDHQHDLW 0DWKHPDWLFDO6XEMHFW&ODVVL½FDWLRQ*(*4$$ % /LEUDU\RI&RQJUHVV&RQWURO1XPEHU Bibliographic information published by Die Deutsche Bibliothek 'LH'HXWVFKH%LEOLRWKHNOLVWVWKLVSXEOLFDWLRQLQWKH'HXWVFKH1DWLRQDOELEOLRJUD½H GHWDLOHGELEOLRJUDSKLFGDWDLVDYDLODEOHLQWKH,QWHUQHWDWKWWSGQEGGEGH! ,6%1%LUNKlXVHUHUODJ$*%DVHOÀ%RVWRQÀ% HUOLQ 7KLVZRUNLVVXEMHFWWRFRS\ULJKW$OOULJKWVDUHUHVHUYHGZKHWKHUWKHZKROHRUSDUWRIWKH PDWHULDOLVFRQFHUQHGVSHFL½FDOO\WKHULJKWVRIWUDQVODWLRQUHSULQWLQJUHXVHRILOOXVWUD
    [Show full text]
  • Mathematicians Fleeing from Nazi Germany
    Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D.
    [Show full text]
  • The Principle of Equivalence As a Criterion of Identity Ryan Samaroo
    Forthcoming in Synthese The Principle of Equivalence as a Criterion of Identity Ryan Samaroo Somerville College, Woodstock Road, Oxford, OX2 6HD, United Kingdom [email protected] Dedicated to the memory of William (Bill) Demopoulos Abstract In 1907 Einstein had the insight that bodies in free fall do not “feel” their own weight. This has been formalized in what is called “the principle of equivalence.” The principle motivated a critical analysis of the Newtonian and special-relativistic concepts of inertia, and it was indispensable to Einstein’s development of his theory of gravitation. A great deal has been written about the principle. Nearly all of this work has focused on the content of the principle and whether it has any content in Einsteinian gravitation, but more remains to be said about its methodological role in the development of the theory. I argue that the principle should be understood as a kind of foundational principle known as a criterion of identity. This work extends and substantiates a recent account of the notion of a criterion of identity by William Demopoulos. Demopoulos argues that the notion can be employed more widely than in the foundations of arithmetic and that we see this in the development of physical theories, in particular space-time theories. This new account forms the basis of a general framework for applying a number of mathematical theories and for distinguishing between applied mathematical theories that are and are not empirically constrained. 1. Introduction “The principle of equivalence,” which Einstein originally used to refer to one particular statement, has come to refer to a number of interrelated principles in the theory of gravitation.1 1 Einstein’s first formulation of the principle can be found in his article “On the Relativity Principle and the Conclusions Drawn from It” (1907, p.
    [Show full text]