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Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E
BOOK REVIEW Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E. Rowe Einstein’s Italian modern Italy. Nor does the author shy away from topics Mathematicians: like how Ricci developed his absolute differential calculus Ricci, Levi-Civita, and the as a generalization of E. B. Christoffel’s (1829–1900) work Birth of General Relativity on quadratic differential forms or why it served as a key By Judith R. Goodstein tool for Einstein in his efforts to generalize the special theory of relativity in order to incorporate gravitation. In This delightful little book re- like manner, she describes how Levi-Civita was able to sulted from the author’s long- give a clear geometric interpretation of curvature effects standing enchantment with Tul- in Einstein’s theory by appealing to his concept of parallel lio Levi-Civita (1873–1941), his displacement of vectors (see below). For these and other mentor Gregorio Ricci Curbastro topics, Goodstein draws on and cites a great deal of the (1853–1925), and the special AMS, 2018, 211 pp. 211 AMS, 2018, vast secondary literature produced in recent decades by the world that these and other Ital- “Einstein industry,” in particular the ongoing project that ian mathematicians occupied and helped to shape. The has produced the first 15 volumes of The Collected Papers importance of their work for Einstein’s general theory of of Albert Einstein [CPAE 1–15, 1987–2018]. relativity is one of the more celebrated topics in the history Her account proceeds in three parts spread out over of modern mathematical physics; this is told, for example, twelve chapters, the first seven of which cover episodes in [Pais 1982], the standard biography of Einstein. -
Philosophical Rhetoric in Early Quantum Mechanics, 1925-1927
b1043_Chapter-2.4.qxd 1/27/2011 7:30 PM Page 319 b1043 Quantum Mechanics and Weimar Culture FA 319 Philosophical Rhetoric in Early Quantum Mechanics 1925–27: High Principles, Cultural Values and Professional Anxieties Alexei Kojevnikov* ‘I look on most general reasoning in science as [an] opportunistic (success- or unsuccessful) relationship between conceptions more or less defined by other conception[s] and helping us to overlook [danicism for “survey”] things.’ Niels Bohr (1919)1 This paper considers the role played by philosophical conceptions in the process of the development of quantum mechanics, 1925–1927, and analyses stances taken by key participants on four main issues of the controversy (Anschaulichkeit, quantum discontinuity, the wave-particle dilemma and causality). Social and cultural values and anxieties at the time of general crisis, as identified by Paul Forman, strongly affected the language of the debate. At the same time, individual philosophical positions presented as strongly-held principles were in fact flexible and sometimes reversible to almost their opposites. One can understand the dynamics of rhetorical shifts and changing strategies, if one considers interpretational debates as a way * Department of History, University of British Columbia, 1873 East Mall, Vancouver, British Columbia, Canada V6T 1Z1; [email protected]. The following abbreviations are used: AHQP, Archive for History of Quantum Physics, NBA, Copenhagen; AP, Annalen der Physik; HSPS, Historical Studies in the Physical Sciences; NBA, Niels Bohr Archive, Niels Bohr Institute, Copenhagen; NW, Die Naturwissenschaften; PWB, Wolfgang Pauli, Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg a.o., Band I: 1919–1929, ed. A. Hermann, K.V. -
Lecture Notes for Felix Klein Lectures
Preprint typeset in JHEP style - HYPER VERSION Lecture Notes for Felix Klein Lectures Gregory W. Moore Abstract: These are lecture notes for a series of talks at the Hausdorff Mathematical Institute, Bonn, Oct. 1-11, 2012 December 5, 2012 Contents 1. Prologue 7 2. Lecture 1, Monday Oct. 1: Introduction: (2,0) Theory and Physical Mathematics 7 2.1 Quantum Field Theory 8 2.1.1 Extended QFT, defects, and bordism categories 9 2.1.2 Traditional Wilsonian Viewpoint 12 2.2 Compactification, Low Energy Limit, and Reduction 13 2.3 Relations between theories 15 3. Background material on superconformal and super-Poincar´ealgebras 18 3.1 Why study these? 18 3.2 Poincar´eand conformal symmetry 18 3.3 Super-Poincar´ealgebras 19 3.4 Superconformal algebras 20 3.5 Six-dimensional superconformal algebras 21 3.5.1 Some group theory 21 3.5.2 The (2, 0) superconformal algebra SC(M1,5|32) 23 3.6 d = 6 (2, 0) super-Poincar´e SP(M1,5|16) and the central charge extensions 24 3.7 Compactification and preserved supersymmetries 25 3.7.1 Emergent symmetries 26 3.7.2 Partial Topological Twisting 26 3.7.3 Embedded Four-dimensional = 2 algebras and defects 28 N 3.8 Unitary Representations of the (2, 0) algebra 29 3.9 List of topological twists of the (2, 0) algebra 29 4. Four-dimensional BPS States and (primitive) Wall-Crossing 30 4.1 The d = 4, = 2 super-Poincar´ealgebra SP(M1,3|8). 30 N 4.2 BPS particle representations of four-dimensional = 2 superpoincar´eal- N gebras 31 4.2.1 Particle representations 31 4.2.2 The half-hypermultiplet 33 4.2.3 Long representations 34 -
Albert Einstein
THE COLLECTED PAPERS OF Albert Einstein VOLUME 15 THE BERLIN YEARS: WRITINGS & CORRESPONDENCE JUNE 1925–MAY 1927 Diana Kormos Buchwald, József Illy, A. J. Kox, Dennis Lehmkuhl, Ze’ev Rosenkranz, and Jennifer Nollar James EDITORS Anthony Duncan, Marco Giovanelli, Michel Janssen, Daniel J. Kennefick, and Issachar Unna ASSOCIATE & CONTRIBUTING EDITORS Emily de Araújo, Rudy Hirschmann, Nurit Lifshitz, and Barbara Wolff ASSISTANT EDITORS Princeton University Press 2018 Copyright © 2018 by The Hebrew University of Jerusalem 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 press.princeton.edu All Rights Reserved LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA (Revised for volume 15) Einstein, Albert, 1879–1955. The collected papers of Albert Einstein. German, English, and French. Includes bibliographies and indexes. Contents: v. 1. The early years, 1879–1902 / John Stachel, editor — v. 2. The Swiss years, writings, 1900–1909 — — v. 15. The Berlin years, writings and correspondence, June 1925–May 1927 / Diana Kormos Buchwald... [et al.], editors. QC16.E5A2 1987 530 86-43132 ISBN 0-691-08407-6 (v.1) ISBN 978-0-691-17881-3 (v. 15) This book has been composed in Times. The publisher would like to acknowledge the editors of this volume for providing the camera-ready copy from which this book was printed. Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources. Printed in the United States of America 13579108642 INTRODUCTION TO VOLUME 15 The present volume covers a thrilling two-year period in twentieth-century physics, for during this time matrix mechanics—developed by Werner Heisenberg, Max Born, and Pascual Jordan—and wave mechanics, developed by Erwin Schrödinger, supplanted the earlier quantum theory. -
Einstein's Physical Strategy, Energy Conservation, Symmetries, And
Einstein’s Physical Strategy, Energy Conservation, Symmetries, and Stability: “but Grossmann & I believed that the conservation laws were not satisfied” April 12, 2016 J. Brian Pitts Faculty of Philosophy, University of Cambridge [email protected] Abstract Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein’s physical strategy and the particle physics deriva- tions compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work relate to emerging knowledge (1911-14) of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equa- ′ µ µ ν tions, Einstein used an identity from his assumed linear coordinate covariance x = Mν x to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor’s asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell’s theory (which avoids negative-energies but gets an asymmetric canonical tensor as a result) as on a scalar theory (the Newtonian limit). -
Rapport Van De Stuurgroep Asscher-Vonk Ii
PROEVEN VAN 150 PARTNER- SCHAP RAPPORT VAN DE STUURGROEP ASSCHER-VONK II VOORBEELDEN van museale samenwerking en initiatieven gericht op kwaliteit, publieksbereik, kostenbesparing en efficiency 4 oktober 2013 PROEVEN VAN 150 PARTNER- SCHAP RAPPORT VAN DE STUURGROEP ASSCHER-VONK II VOORBEELDEN van museale samenwerking en initiatieven gericht op kwaliteit, publieksbereik, kostenbesparing en efficiency INHOUD DEEL I MUSEA OP WEG NAAR MORGEN: WAARNEMINGEN VAN DE STUURGROEP ASSCHER-VONK II 5 h 1 INLEIDING 9 h 2 DOEL VAN HET RAPPORT 11 h 3 VOORBEELDEN UIT DE MUSEALE PRAKTIJK: 13 3.1 VORMEN VAN SAMENWERKING 14 3.2 MINDER KOSTEN, MEER INKOMSTEN, MEER EFFICIENCY 17 3.3 KENNIS DELEN, KRACHTEN BUNDELEN 27 3.4 MEER EN NIEUW PUBLIEK 32 3.5 GROTERE ZICHTBAARHEID VAN COLLECTIES 39 h 4 MUSEA OVER SAMENWERKING 43 h 5 HOE VERDER 46 BIJLAGEN: b1 DE OPDRACHT VAN DE STUURGROEP ASSCHER-VONK II 48 b2 EEN OVERZICHT VAN DE GESPREKSPARTNERS 49 DEEL II 50 150 VOORBEELDEN van museale samenwerking en initiatieven gericht op kwaliteit, publieksbereik, kostenbesparing en efficiency COLOFON 92 DEEL I PROEVEN VAN PARTNERSCHAP RAPPORT VAN DE STUURGROEP ASSCHER-VONK II MUSEA OP WEG NAAR MORGEN: WAARNEMINGEN VAN DE STUURGROEP ASSCHER-VONK II In Musea voor Morgen stond het al: “Er is meer oog voor samen- werking en synergie nodig, in het belang van het publiek en de samenleving.”1 Met het vervolg op dat rapport, Proeven van Partnerschap, brengt de stuurgroep Asscher-Vonk II bestaande voorbeelden van samenwerking en initiatieven in de museumsector in kaart die zijn ontplooid om in veran- derende tijden kunst en cultuur van topkwaliteit te kunnen blijven bieden. -
Felix Klein and His Erlanger Programm D
WDS'07 Proceedings of Contributed Papers, Part I, 251–256, 2007. ISBN 978-80-7378-023-4 © MATFYZPRESS Felix Klein and his Erlanger Programm D. Trkovsk´a Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. The present paper is dedicated to Felix Klein (1849–1925), one of the leading German mathematicians in the second half of the 19th century. It gives a brief account of his professional life. Some of his activities connected with the reform of mathematics teaching at German schools are mentioned as well. In the following text, we describe fundamental ideas of his Erlanger Programm in more detail. References containing selected papers relevant to this theme are attached. Introduction The Erlanger Programm plays an important role in the development of mathematics in the 19th century. It is the title of Klein’s famous lecture Vergleichende Betrachtungen ¨uber neuere geometrische Forschungen [A Comparative Review of Recent Researches in Geometry] which was presented on the occasion of his admission as a professor at the Philosophical Faculty of the University of Erlangen in October 1872. In this lecture, Felix Klein elucidated the importance of the term group for the classification of various geometries and presented his unified way of looking at various geometries. Klein’s basic idea is that each geometry can be characterized by a group of transformations which preserve elementary properties of the given geometry. Professional Life of Felix Klein Felix Klein was born on April 25, 1849 in D¨usseldorf,Prussia. Having finished his study at the grammar school in D¨usseldorf,he entered the University of Bonn in 1865 to study natural sciences. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
Mathematical Genealogy of the Union College Department of Mathematics
Gemma (Jemme Reinerszoon) Frisius Mathematical Genealogy of the Union College Department of Mathematics Université Catholique de Louvain 1529, 1536 The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. Johannes (Jan van Ostaeyen) Stadius http://www.genealogy.math.ndsu.nodak.edu/ Université Paris IX - Dauphine / Université Catholique de Louvain Justus (Joost Lips) Lipsius Martinus Antonius del Rio Adam Haslmayr Université Catholique de Louvain 1569 Collège de France / Université Catholique de Louvain / Universidad de Salamanca 1572, 1574 Erycius (Henrick van den Putte) Puteanus Jean Baptiste Van Helmont Jacobus Stupaeus Primary Advisor Secondary Advisor Universität zu Köln / Université Catholique de Louvain 1595 Université Catholique de Louvain Erhard Weigel Arnold Geulincx Franciscus de le Boë Sylvius Universität Leipzig 1650 Université Catholique de Louvain / Universiteit Leiden 1646, 1658 Universität Basel 1637 Union College Faculty in Mathematics Otto Mencke Gottfried Wilhelm Leibniz Ehrenfried Walter von Tschirnhaus Key Universität Leipzig 1665, 1666 Universität Altdorf 1666 Universiteit Leiden 1669, 1674 Johann Christoph Wichmannshausen Jacob Bernoulli Christian M. von Wolff Universität Leipzig 1685 Universität Basel 1684 Universität Leipzig 1704 Christian August Hausen Johann Bernoulli Martin Knutzen Marcus Herz Martin-Luther-Universität Halle-Wittenberg 1713 Universität Basel 1694 Leonhard Euler Abraham Gotthelf Kästner Franz Josef Ritter von Gerstner Immanuel Kant -
University Museums and Collections Journal 7, 2014
VOLUME 7 2014 UNIVERSITY MUSEUMS AND COLLECTIONS JOURNAL 2 — VOLUME 7 2014 UNIVERSITY MUSEUMS AND COLLECTIONS JOURNAL VOLUME 7 20162014 UNIVERSITY MUSEUMS AND COLLECTIONS JOURNAL 3 — VOLUME 7 2014 UNIVERSITY MUSEUMS AND COLLECTIONS JOURNAL The University Museums and Collections Journal (UMACJ) is a peer-reviewed, on-line journal for the proceedings of the International Committee for University Museums and Collections (UMAC), a Committee of the International Council of Museums (ICOM). Editors Nathalie Nyst Réseau des Musées de l’ULB Université Libre de Bruxelles – CP 103 Avenue F.D. Roosevelt, 50 1050 Brussels Belgium Barbara Rothermel Daura Gallery - Lynchburg College 1501 Lakeside Dr., Lynchburg, VA 24501 - USA Peter Stanbury Australian Society of Anaesthetis Suite 603, Eastpoint Tower 180 Ocean Street Edgecliff, NSW 2027 Australia Copyright © International ICOM Committee for University Museums and Collections http://umac.icom.museum ISSN 2071-7229 Each paper reflects the author’s view. 4 — VOLUME 7 2014 UNIVERSITY MUSEUMS AND COLLECTIONS JOURNAL Basket porcelain with truss imitating natural fibers, belonged to a family in São Paulo, c. 1960 - Photograph José Rosael – Collection of the Museu Paulista da Universidade de São Paulo/Brazil Napkin holder in the shape of typical women from Bahia, painted wood, 1950 – Photograph José Rosael Collection of the Museu Paulista da Universidade de São Paulo/Brazil Since 1990, the Paulista Museum of the University of São Paulo has strived to form collections from the research lines derived from the history of material culture of the Brazilian society. This focus seeks to understand the material dimension of social life to define the particularities of objects in the viability of social and symbolic practices. -
Shs-17-2018-14.Pdf
Science beyond borders Nobukata Nagasawa ORCID 0000-0002-9658-7680 Emeritus Professor of University of Tokyo [email protected] On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics Abstract Possible reasons are studied why Ladislas (Władysław) Natanson’s paper on the statistical theory of radiation, published in 1911 both in English and in the German translation, was not cited properly in the early history of quantum statistics by outstanding scientists, such as Arnold Sommerfeld, Paul Ehrenfest, Satyendra Nath Bose and Albert Einstein. The social and psychological aspects are discussed as back- ground to many so far discussions on the academic evaluation of his theory. In order to avoid in the future such Natansonian cases of very limited reception of valuable scientific works, it is pro- posed to introduce a digital tag in which all the information of PUBLICATION e-ISSN 2543-702X INFO ISSN 2451-3202 DIAMOND OPEN ACCESS CITATION Nagasawa, Nobukata 2018: On social and psychological aspects of a negligible reception of Natanson’s article of 1911 in the early history of quantum statistics. Studia Historiae Scientiarum 17, pp. 391–419. Available online: https://doi.org/10.4467/2543702XSHS.18.014.9334. ARCHIVE RECEIVED: 13.06.2017 LICENSE POLICY ACCEPTED: 12.09.2018 Green SHERPA / PUBLISHED ONLINE: 12.12.2018 RoMEO Colour WWW http://www.ejournals.eu/sj/index.php/SHS/; http://pau.krakow.pl/Studia-Historiae-Scientiarum/ Nobukata Nagasawa On social and psychological aspects of a negligible reception... relevant papers published so far should be automatically accu- mulated and updated. -
The “Geometrical Equations:” Forgotten Premises of Felix Klein's
The “Geometrical Equations:” Forgotten Premises of Felix Klein’s Erlanger Programm François Lê October 2013 Abstract Felix Klein’s Erlanger Programm (1872) has been extensively studied by historians. If the early geometrical works in Klein’s career are now well-known, his links to the theory of algebraic equations before 1872 remain only evoked in the historiography. The aim of this paper is precisely to study this algebraic background, centered around particular equations arising from geometry, and participating on the elaboration of the Erlanger Programm. An- other result of the investigation is to complete the historiography of the theory of general algebraic equations, in which those “geometrical equations” do not appear. 1 Introduction Felix Klein’s Erlanger Programm1 is one of those famous mathematical works that are often invoked by current mathematicians, most of the time in a condensed and modernized form: doing geometry comes down to studying (transformation) group actions on various sets, while taking particular care of invariant objects.2 As rough and anachronistic this description may be, it does represent Klein’s motto to praise the importance of transformation groups and their invariants to unify and classify geometries. The Erlanger Programm has been abundantly studied by historians.3 In particular, [Hawkins 1984] questioned the commonly believed revolutionary character of the Programm, giving evi- dence of both a relative ignorance of it by mathematicians from its date of publication (1872) to 1890 and the importance of Sophus Lie’s ideas4 about continuous transformations for its elabora- tion. These ideas are only a part of the many facets of the Programm’s geometrical background of which other parts (non-Euclidean geometries, line geometry) have been studied in detail in [Rowe 1989b].