Albert Einstein at the Zürich Polytechnic: a Rare Mastery of Maxwell's Electromagnetic Theory
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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. -
Math, Physics, and Calabi–Yau Manifolds
Math, Physics, and Calabi–Yau Manifolds Shing-Tung Yau Harvard University October 2011 Introduction I’d like to talk about how mathematics and physics can come together to the benefit of both fields, particularly in the case of Calabi-Yau spaces and string theory. This happens to be the subject of the new book I coauthored, THE SHAPE OF INNER SPACE It also tells some of my own story and a bit of the history of geometry as well. 2 In that spirit, I’m going to back up and talk about my personal introduction to geometry and how I ended up spending much of my career working at the interface between math and physics. Along the way, I hope to give people a sense of how mathematicians think and approach the world. I also want people to realize that mathematics does not have to be a wholly abstract discipline, disconnected from everyday phenomena, but is instead crucial to our understanding of the physical world. 3 There are several major contributions of mathematicians to fundamental physics in 20th century: 1. Poincar´eand Minkowski contribution to special relativity. (The book of Pais on the biography of Einstein explained this clearly.) 2. Contributions of Grossmann and Hilbert to general relativity: Marcel Grossmann (1878-1936) was a classmate with Einstein from 1898 to 1900. he was professor of geometry at ETH, Switzerland at 1907. In 1912, Einstein came to ETH to be professor where they started to work together. Grossmann suggested tensor calculus, as was proposed by Elwin Bruno Christoffel in 1868 (Crelle journal) and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita (1901). -
Marcel Grossmann Awards
MG15 MARCEL GROSSMANN AWARDS ROME 2018 ICRANet and ICRA MG XV MARCEL GROSSMANN AWARDS ROME 2018 and TEST The 15th Marcel Grossmann Meeting – MG XV 2nd July 2018, Rome (Italy) Aula Magna – University “Sapienza” of Rome Institutional Awards Goes to: PLANCK SCIENTIFIC COLLABORATION (ESA) “for obtaining important constraints on the models of inflationary stage of the Universe and level of primordial non-Gaussianity; measuring with unprecedented sensitivity gravitational lensing of Cosmic Microwave Background fluctuations by large-scale structure of the Universe and corresponding B- polarization of CMB, the imprint on the CMB of hot gas in galaxy clusters; getting unique information about the time of reionization of our Universe and distribution and properties of the dust and magnetic fields in our Galaxy” - presented to Jean-Loup Puget, the Principal Investigator of the High Frequency Instrument (HFI) HANSEN EXPERIMENTAL PHYSICS LABORATORY AT STANFORD UNIVERSITY “to HEPL for having developed interdepartmental activities at Stanford University at the frontier of fundamental physics, astrophysics and technology” - presented to Research Professor Leo Hollberg, HEPL Assistant Director Individual Awards Goes to LYMAN PAGE “for his collaboration with David Wilkinson in realizing the NASA Explorer WMAP mission and as founding director of the Atacama Cosmology Telescope” Goes to RASHID ALIEVICH SUNYAEV “for the development of theoretical tools in the scrutinising, through the CMB, of the first observable electromagnetic appearance of our Universe” Goes to SHING-TUNG YAU “for the proof of the positivity of total mass in the theory of general relativity and perfecting as well the concept of quasi-local mass, for his proof of the Calabi conjecture, for his continuous inspiring role in the study of black holes physics” Each recipient is presented with a silver casting of the TEST sculpture by the artist A. -
Georg Cantor English Version
GEORG CANTOR (March 3, 1845 – January 6, 1918) by HEINZ KLAUS STRICK, Germany There is hardly another mathematician whose reputation among his contemporary colleagues reflected such a wide disparity of opinion: for some, GEORG FERDINAND LUDWIG PHILIPP CANTOR was a corruptor of youth (KRONECKER), while for others, he was an exceptionally gifted mathematical researcher (DAVID HILBERT 1925: Let no one be allowed to drive us from the paradise that CANTOR created for us.) GEORG CANTOR’s father was a successful merchant and stockbroker in St. Petersburg, where he lived with his family, which included six children, in the large German colony until he was forced by ill health to move to the milder climate of Germany. In Russia, GEORG was instructed by private tutors. He then attended secondary schools in Wiesbaden and Darmstadt. After he had completed his schooling with excellent grades, particularly in mathematics, his father acceded to his son’s request to pursue mathematical studies in Zurich. GEORG CANTOR could equally well have chosen a career as a violinist, in which case he would have continued the tradition of his two grandmothers, both of whom were active as respected professional musicians in St. Petersburg. When in 1863 his father died, CANTOR transferred to Berlin, where he attended lectures by KARL WEIERSTRASS, ERNST EDUARD KUMMER, and LEOPOLD KRONECKER. On completing his doctorate in 1867 with a dissertation on a topic in number theory, CANTOR did not obtain a permanent academic position. He taught for a while at a girls’ school and at an institution for training teachers, all the while working on his habilitation thesis, which led to a teaching position at the university in Halle. -
Zeta-Functions Associated with Quadratic Forms in Adolf Hurwitz's Estate
MATHEMATICAL PERSPECTIVES BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 3, July 2016, Pages 477–481 http://dx.doi.org/10.1090/bull/1534 Article electronically published on March 16, 2016 ABOUT THE COVER: ZETA-FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS IN ADOLF HURWITZ’S ESTATE NICOLA M. R. OSWALD AND JORN¨ STEUDING The first published proof of key analytic properties of zeta-functions associ- ated with quadratic forms is due to Paul Epstein [2] in 1903 (submitted Janu- ary 1902). The corresponding name “Epstein zeta-functions” was introduced by Edward Charles Titchmarsh in his article [15] from 1934; soon after, this terminol- ogy became common through influential articles of Max Deuring and Carl Ludwig Siegel. While examining Adolf Hurwitz’s mathematical estate at ETH Zurich, how- ever, the authors discovered that Hurwitz could have published these results already during his time in K¨onigsberg (now Kaliningrad) in the late 1880s. Unpublished notes of Hurwitz testify that he was not only aware of the analytic properties of zeta-functions associated with quadratic forms but prepared a fair copy of his notes, probably for submission to a journal. The cover of this issue shows the first page (see Figure 1). p Given a quadratic form ϕ(x1,x2,...,xp)= i,k=1 aikxixk and real parameters u1,u2,...,up; v1,v2,...,vp, Hurwitz considers the associated Dirichlet series 2πi(x v +x v +···+x v ) e 1 1 2 2 p p F(s | u, v, ϕ)= ps [ϕ(x1 + u1,x2 + u2,...,xp + up)] 2 as a function of a complex variable s, where the summation is taken over all in- tegers x1,x2,...,xp with possible exceptions of the combinations x1 = −u1,x2 = −u2,...,xp = −up (indicated by the dash). -
Chronological List of Correspondence, 1895–1920
CHRONOLOGICAL LIST OF CORRESPONDENCE, 1895–1920 In this chronological list of correspondence, the volume and document numbers follow each name. Documents abstracted in the calendars are listed in the Alphabetical List of Texts in this volume. 1895 13 or 20 Mar To Mileva Maric;;, 1, 45 29 Apr To Rosa Winteler, 1, 46 Summer To Caesar Koch, 1, 6 18 May To Rosa Winteler, 1, 47 28 Jul To Julia Niggli, 1, 48 Aug To Rosa Winteler, 5: Vol. 1, 48a 1896 early Aug To Mileva Maric;;, 1, 50 6? Aug To Julia Niggli, 1, 51 21 Apr To Marie Winteler, with a 10? Aug To Mileva Maric;;, 1, 52 postscript by Pauline Einstein, after 10 Aug–before 10 Sep 1,18 From Mileva Maric;;, 1, 53 7 Sep To the Department of Education, 10 Sep To Mileva Maric;;, 1, 54 Canton of Aargau, 1, 20 11 Sep To Julia Niggli, 1, 55 4–25 Nov From Marie Winteler, 1, 29 11 Sep To Pauline Winteler, 1, 56 30 Nov From Marie Winteler, 1, 30 28? Sep To Mileva Maric;;, 1, 57 10 Oct To Mileva Maric;;, 1, 58 1897 19 Oct To the Swiss Federal Council, 1, 60 May? To Pauline Winteler, 1, 34 1900 21 May To Pauline Winteler, 5: Vol. 1, 34a 7 Jun To Pauline Winteler, 1, 35 ? From Mileva Maric;;, 1, 61 after 20 Oct From Mileva Maric;;, 1, 36 28 Feb To the Swiss Department of Foreign Affairs, 1, 62 1898 26 Jun To the Zurich City Council, 1, 65 29? Jul To Mileva Maric;;, 1, 68 ? To Maja Einstein, 1, 38 1 Aug To Mileva Maric;;, 1, 69 2 Jan To Mileva Maric;; [envelope only], 1 6 Aug To Mileva Maric;;, 1, 70 13 Jan To Maja Einstein, 8: Vol. -
Lost in the Tensors: Einstein's Struggles with Covariance Principles 1912-1916"
JOHN EARMAN and CLARK GL YMOUR LOST IN THE TENSORS: EINSTEIN'S STRUGGLES WITH COVARIANCE PRINCIPLES 1912-1916" Introduction IN 1912 Einstein began to devote a major portion of his time and energy to an attempt to construct a relativistic theory of gravitation. A strong intimation of the struggle that lay ahead is contained in a letter to Arnold Sommerfeld dated October 29, 1912: At the moment I am working solely on the problem of gravitation and believe 1 will be able to overcome all difficulties with the help of a local, friendly mathemat- ician. But one thing is certain, that I have never worked so hard in my life, and that I have been injected with a great awe of mathematics, which in my naivet~ until now I only viewed as a pure luxury in its subtler forms! Compared to this problem the original theory of relativity is mere child's play.' Einstein's letter contained only a perfunctory reply to a query from Sommerfeld about the Debye-Born theory of specific heats. Obviously disappointed, Som- merfeld wrote to Hilbert: 'My letter to Einstein was in vain . Einstein is evidently so deeply mired in gravitation that he is deaf to everything else? Sommerfeld's words were more prophetic than he could possibly have known; the next three years were to see Einstein deeply mired in gravitation, sometimes seemingly hopelessly so. In large measure, Einstein's struggle resulted from his use and his misuse, his understanding and his misunderstanding of the nature and implications of covariance principles. In brief, considerations of general covariance were bound up with Einstein's motive for seeking a 'generalized' theory of relativity; mis- understandings about the meaning and implementation of this motivation threatened to wreck the search; and in the end, the desire for general covariance helped to bring Einstein back onto the track which led to what we now recognize *Present address c/o Department of Philosophy, University of Minnesota, Minneapolis, Minn, U.S.A. -
The Fourteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics
September 4, 2017 9:39 ws-procs961x669 MG-14 – Proceedings (Part D) D433 page 3372 3372 The renaissance of general relativity in Rome: Main actors, research programs and institutional structures Luisa Bonolis∗ Max Planck Institute for the History of Science, Berlin, Germany ∗E-mail: [email protected] Adele La Rana Sapienza University, Rome, Italy E-mail: [email protected] Roberto Lalli Max Planck Institute for the History of Science, Berlin, Germany E-mail: [email protected] We show that the revitalization of General Relativity (GR) in Rome during the 1960s was mainly shaped by the confluence of two different research programs centered around two authoritative figures: the first was the focusing of former Levi–Civita’s student Carlo Cattaneo on the mathematical problems of GR and the establishment of a research group in Rome; the second was sparked by the return in Italy of the astrophysicist Livio Gratton in 1960. We also argue that the material possibilities for a novel confluence between previously separated fields in the Roman environment was made possible by deep institutional changes and, especially, by the organizational choices and visions of Edoardo Amaldi who was leading the postwar reconstruction of Italian physics. Keywords: General relativity; relativistic astrophysics; Tullio Levi–Civita; Giuseppe Armellini; Enrico Fermi; Carlo Cattaneo; Edoardo Amaldi; Livio Gratton. The First Phase: The interwar period In the late 1960s, General Relativity (GR) definitely returned to the mainstream of physics, coming into focus in connection with major astrophysical discoveries and becoming an internationally visible, highly active field of research. In order to The Fourteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com better elucidate how this historical process — the so-called Renaissance of GR, as Clifford Will christened it — developed in Rome during the 1960s, it is necessary to put it in relation to the research and teaching of GR in the Roman institutional settings starting from the early 1920s. -
On the Occasion of the 14Th Marcel Grossmann Meeting
ICRANet on the occasion of the 14 th Marcel Grossmann Meeting – MGXIV in celebration of the International Year of Light 2015 the 100 th anniversary of the Einstein’s equations the golden jubilee of Relativistic Astrophysics The ICRANet Seats The University of Rome “La Sapienza” where the Physics Department hosts the ICRANet ICRANet Headquarters in Pescara (Italy). seat in Rome (Italy). ICRANet seat in Nice (France). National Academy of Sciences of Armenia, which hosts the ICRANet seat in Yerevan (Armenia). (Above:) CBPF, which hosts the ICRANet seat in Rio de Janeiro. (Below:) The planned seat at Cassino da Urca (Brazil). II This brochure reviews some background facts concerning the founding of ICRANet and its current structures and then turns to the 2015 celebrations of the Year of Light and the ICRANet initiated International Relativistic Astrophysics Ph.D. program (the IRAP-PhD). It then addresses the birth of relativistic astrophysics following the first fifty years of the existence of general relativity plagued mainly by the absence of observational or experimental activity. Four events marked the onset of relativistic astrophysics: the discovery by Schmidt of the first quasar in 1962, of Scorpius X1 by Riccardo Giacconi in 1963, of the cosmic background radiation by Penzias and Wilson in 1964, and of pulsars by Jocelyn-Bell and Antony Hewish in 1967. These events led to a systematic development of the understanding of the four pillars of relativistic astrophysics: supernovae where observations of the CRAB Nebula are still relevant today, white dwarfs and neutron stars, black holes and their first identification in Nature in Cygnus X1 found by Riccardo Giacconi with the UHURU satellite based on the conceptual background developed by our group in Princeton, and finally the discovery of gamma ray bursts as the largest energy source delivered in the shortest time of any astrophysical phenomenon. -
The Thirteenth Marcel Grossmann Meeting
THE THIRTEENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories by UNIVERSITY OF SZEGED on 04/12/18. For personal use only. The Thirteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com 9194_9789814612180-tpV1.indd 1 3/11/14 12:57 pm PART A THE THIRTEENTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories Proceedings of the MG13 Meeting on General Relativity Stockholm University, Stockholm, Sweden 1–7 July 2012 Editors Robert T Jantzen Villanova University, USA Kjell Rosquist Stockholm University, Sweden by UNIVERSITY OF SZEGED on 04/12/18. For personal use only. Series Editor The Thirteenth Marcel Grossmann Meeting Downloaded from www.worldscientific.com Remo Ruffini International Center for Relativistic Astrophysics Network (ICRANet), Italy University of Rome “La Sapienza”, Italy World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 9194_9789814612180-tpV1.indd 2 3/11/14 12:57 pm Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Marcel Grossmann Meeting on General Relativity (13th : 2012 : Stockholms universitet) The Thirteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories : proceedings of the MG13 Meeting on General Relativity, Stockholm University, Sweden, 1–7 July 2012 / editors Kjell Rosquist (Stockholm University, Sweden), Robert T. Jantzen (Villanova University, USA) ; series editor Remo Ruffini (International Center for Relativistic Astrophysics Network (ICRANet), Italy & University of Rome “La Sapienza”, Italy). -
Irrational Philosophy? Kronecker's Constructive Philosophy and Finding the Real Roots of a Polynomial
Rose-Hulman Undergraduate Mathematics Journal Volume 22 Issue 1 Article 1 Irrational Philosophy? Kronecker's Constructive Philosophy and Finding the Real Roots of a Polynomial Richard B. Schneider University of Missouri - Kansas City, [email protected] Follow this and additional works at: https://scholar.rose-hulman.edu/rhumj Part of the Analysis Commons, European History Commons, and the Intellectual History Commons Recommended Citation Schneider, Richard B. (2021) "Irrational Philosophy? Kronecker's Constructive Philosophy and Finding the Real Roots of a Polynomial," Rose-Hulman Undergraduate Mathematics Journal: Vol. 22 : Iss. 1 , Article 1. Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss1/1 Irrational Philosophy? Kronecker's Constructive Philosophy and Finding the Real Roots of a Polynomial Cover Page Footnote The author would like to thank Dr. Richard Delaware for his guidance and support throughout the completion of this work. This article is available in Rose-Hulman Undergraduate Mathematics Journal: https://scholar.rose-hulman.edu/rhumj/ vol22/iss1/1 Rose-Hulman Undergraduate Mathematics Journal VOLUME 22, ISSUE 1, 2021 Irrational Philosophy? Kronecker’s Constructive Philosophy and Finding the Real Roots of a Polynomial By Richard B. Schneider Abstract. The prominent mathematician Leopold Kronecker (1823 – 1891) is often rel- egated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that only the natural numbers are intuitive, thus the only basis for all mathematical objects. In fact, Kronecker developed a complete school of thought on mathematical foundations and wrote many significant algebraic works, but his enigmatic writing style led to his historical marginalization. -
Riemann Surfaces
SPECIAL TOPIC COURSE RIEMANN SURFACES VSEVOLOD SHEVCHISHIN Abstract. The course is devoted to the theory of Riemann surfaces and algebraic curves. We shall cover main results and topics such as Riemann-Hurwitz formula, elliptic curves and Weier- strass' }-function, divisors and line bundles, Jacobian variety of an algebraic curve, canonical divisor of an algebraic curve, holomorphic vector bundles, Czech- and Dolbeault-cohomology, Riemann-Roch formula. 1. Generalities This course is devoted to the theory of Riemann surfaces (RS) and algebraic curves. The foundation of the theory was made in XIX century by Bernhard Riemann, Niels Henrik Abel, Carl Gustav Jacobi, Karl Weierstrass, Adolf Hurwitz and others. Nowadays Riemann surfaces play a remarkable role in modern mathematics and appear in various parts such as algebraic geometry, number theory, topology, they also are very important in modern mathematical physics. The theory of Riemann surfaces includes and combines methods coming from three elds of mathematics: analysis, topology, and algebra (and algebraic geometry). One of the goals of the course is to show the interaction and mutual inuence of ideas and approaches. 2. Prerequisites. • Basic course in complex analysis (Theory of functions of one complex variable). • Basic facts from dierential geometry and algebraic topology. 3. Tentative syllabus (1) Riemann surfaces and holomorphic maps. Meromorphic functions. (2) Structure of holomorphic maps. Riemann-Hurwitz formula. (3) Conformal and quasiconformal maps. (4) Dierential forms on RS, Cauchy-Riemann operator, Cauchy-Green formula and solution of @¯-equation. (5) Divisors and holomorphic line bundles on RS-s. (6) Holomorphic vector bundles on RS-s and their cohomology. Serre duality.