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Arnold Sommerfeld in Einigen Zitaten Von Ihm Und Über Ihn1
K.-P. Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn Seite 1 Karl-Peter Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn1 Kurze biographische Bemerkungen Arnold Sommerfeld [* 5. Dezember 1868 in Königsberg, † 26. April 1951 in München] zählt neben Max Planck, Albert Einstein und Niels Bohr zu den Begründern der modernen theoretischen Physik. Durch die Ausarbeitung der Bohrschen Atomtheorie, als Lehrbuchautor (Atombau und Spektrallinien, Vorlesungen über theoretische Physik) und durch seine „Schule“ (zu der etwa die Nobelpreisträger Peter Debye, Wolfgang Pauli, Werner Heisenberg und Hans Bethe gehören) sorgte Sommerfeld wie kein anderer für die Verbreitung der modernen Physik.2 Je nach Auswahl könnte Sommerfeld [aber] nicht nur als theoretischer Physiker, sondern auch als Mathematiker, Techniker oder Wissenschaftsjournalist porträtiert werden.3 Als Schüler der Mathematiker Ferdinand von Lindemann, Adolf Hurwitz, David Hilbert und Felix Klein hatte sich Sommerfeld zunächst vor allem der Mathematik zugewandt (seine erste Professur: 1897 - 1900 für Mathematik an der Bergakademie Clausthal). Als Professor an der TH Aachen von 1900 - 1906 gewann er zunehmendes Interesse an der Technik. 1906 erhielt er den seit Jahren verwaisten Lehrstuhl für theoretische Physik in München, an dem er mit wenigen Unterbrechungen noch bis 1940 (und dann wieder ab 19464) unterrichtete. Im Gegensatz zur etablierten Experimen- talphysik war die theoretische Physik anfangs des 20. Jh. noch eine junge Disziplin. Sie wurde nun zu -
Ernst Zermelo Heinz-Dieter Ebbinghaus in Cooperation with Volker Peckhaus Ernst Zermelo
Ernst Zermelo Heinz-Dieter Ebbinghaus In Cooperation with Volker Peckhaus Ernst Zermelo An Approach to His Life and Work With 42 Illustrations 123 Heinz-Dieter Ebbinghaus Mathematisches Institut Abteilung für Mathematische Logik Universität Freiburg Eckerstraße 1 79104 Freiburg, Germany E-mail: [email protected] Volker Peckhaus Kulturwissenschaftliche Fakultät Fach Philosophie Universität Paderborn War burger St raße 100 33098 Paderborn, Germany E-mail: [email protected] Library of Congress Control Number: 2007921876 Mathematics Subject Classification (2000): 01A70, 03-03, 03E25, 03E30, 49-03, 76-03, 82-03, 91-03 ISBN 978-3-540-49551-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad- casting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant pro- tective laws and regulations and therefore free for general use. Typesetting by the author using a Springer TEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 46/3100/YL - 5 4 3 2 1 0 To the memory of Gertrud Zermelo (1902–2003) Preface Ernst Zermelo is best-known for the explicit statement of the axiom of choice and his axiomatization of set theory. -
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. -
Philosophia Scientiæ, 13-2 | 2009 [En Ligne], Mis En Ligne Le 01 Octobre 2009, Consulté Le 15 Janvier 2021
Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 13-2 | 2009 Varia Édition électronique URL : http://journals.openedition.org/philosophiascientiae/224 DOI : 10.4000/philosophiascientiae.224 ISSN : 1775-4283 Éditeur Éditions Kimé Édition imprimée Date de publication : 1 octobre 2009 ISBN : 978-2-84174-504-3 ISSN : 1281-2463 Référence électronique Philosophia Scientiæ, 13-2 | 2009 [En ligne], mis en ligne le 01 octobre 2009, consulté le 15 janvier 2021. URL : http://journals.openedition.org/philosophiascientiae/224 ; DOI : https://doi.org/10.4000/ philosophiascientiae.224 Ce document a été généré automatiquement le 15 janvier 2021. Tous droits réservés 1 SOMMAIRE Actes de la 17e Novembertagung d'histoire des mathématiques (2006) 3-5 novembre 2006 (University of Edinburgh, Royaume-Uni) An Examination of Counterexamples in Proofs and Refutations Samet Bağçe et Can Başkent Formalizability and Knowledge Ascriptions in Mathematical Practice Eva Müller-Hill Conceptions of Continuity: William Kingdon Clifford’s Empirical Conception of Continuity in Mathematics (1868-1879) Josipa Gordana Petrunić Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism Norman Sieroka Les journaux de mathématiques dans la première moitié du XIXe siècle en Europe Norbert Verdier Varia Le concept d’espace chez Veronese Une comparaison avec la conception de Helmholtz et Poincaré Paola Cantù Sur le statut des diagrammes de Feynman en théorie quantique des champs Alexis Rosenbaum Why Quarks Are Unobservable Tobias Fox Philosophia Scientiæ, 13-2 | 2009 2 Actes de la 17e Novembertagung d'histoire des mathématiques (2006) 3-5 novembre 2006 (University of Edinburgh, Royaume-Uni) Philosophia Scientiæ, 13-2 | 2009 3 An Examination of Counterexamples in Proofs and Refutations Samet Bağçe and Can Başkent Acknowledgements Partially based on a talk given in 17th Novembertagung in Edinburgh, Scotland in November 2006 by the second author. -
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). -
Einstein and Physics Hundred Years Ago∗
Vol. 37 (2006) ACTA PHYSICA POLONICA B No 1 EINSTEIN AND PHYSICS HUNDRED YEARS AGO∗ Andrzej K. Wróblewski Physics Department, Warsaw University Hoża 69, 00-681 Warszawa, Poland [email protected] (Received November 15, 2005) In 1905 Albert Einstein published four papers which revolutionized physics. Einstein’s ideas concerning energy quanta and electrodynamics of moving bodies were received with scepticism which only very slowly went away in spite of their solid experimental confirmation. PACS numbers: 01.65.+g 1. Physics around 1900 At the turn of the XX century most scientists regarded physics as an almost completed science which was able to explain all known physical phe- nomena. It appeared to be a magnificent structure supported by the three mighty pillars: Newton’s mechanics, Maxwell’s electrodynamics, and ther- modynamics. For the celebrated French chemist Marcellin Berthelot there were no major unsolved problems left in science and the world was without mystery. Le monde est aujourd’hui sans mystère— he confidently wrote in 1885 [1]. Albert A. Michelson was of the opinion that “The more important fundamen- tal laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote . Our future dis- coveries must be looked for in the sixth place of decimals” [2]. Physics was not only effective but also perfect and beautiful. Henri Poincaré maintained that “The theory of light based on the works of Fresnel and his successors is the most perfect of all the theories of physics” [3]. -
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 -
Hermann Minkowski Et La Mathématisation De La Théorie De La Relativité Restreinte 1905-1915
THÈSE présentée à L’UNIVERSITÉ DE PARIS VII pour obtenir le grade de DOCTEUR Spécialité : Épistémologie et Histoire des Sciences par Scott A. WALTER HERMANN MINKOWSKI ET LA MATHÉMATISATION DE LA THÉORIE DE LA RELATIVITÉ RESTREINTE 1905-1915 Thèse dirigée par M. Christian Houzel et soutenue le 20 décembre 1996 devant la Commission d’Examen composée de : Examinateur : M. Christian Houzel Professeur à l’Université de Paris VII Examinateur : M. Arthur I. Miller Professeur à UniversityCollege London Rapporteur : M. Michel Paty Directeur de recherche, CNRS Rapporteur : M. Jim Ritter Maître de conférences à l’Univ. de Paris VIII S. Walter LA MATHÉMATISATION DE LA RELATIVITÉ RESTREINTE i Résumé Au début du vingtième siècle émergeait l’un des produits les plus remarquables de la physique théorique : la théorie de la relativité. Prise dans son contexte à la fois intellectuel et institution- nel, elle est l’objet central de la dissertation. Toutefois, seul un aspect de cette histoire est abordé de façon continue, à savoir le rôle des mathématiciens dans sa découverte, sa diffusion, sa ré- ception et son développement. Les contributions d’un mathématicien en particulier, Hermann Minkowski, sont étudiées de près, car c’est lui qui trouva la forme mathématique permettant les développements les plus importants, du point de vue des théoriciens de l’époque. Le sujet de la thèse est abordé selon deux axes; l’un se fonde sur l’analyse comparative des documents, l’autre sur l’étude bibliométrique. De cette façon, les conclusions de la première démarche se trouvent encadrées par les résultats de l’analyse globale des données bibliographiques. -
1 WKB Wavefunctions for Simple Harmonics Masatsugu
WKB wavefunctions for simple harmonics Masatsugu Sei Suzuki Department of Physics, SUNY at Binmghamton (Date: November 19, 2011) _________________________________________________________________________ Gregor Wentzel (February 17, 1898, in Düsseldorf, Germany – August 12, 1978, in Ascona, Switzerland) was a German physicist known for development of quantum mechanics. Wentzel, Hendrik Kramers, and Léon Brillouin developed the Wentzel– Kramers–Brillouin approximation in 1926. In his early years, he contributed to X-ray spectroscopy, but then broadened out to make contributions to quantum mechanics, quantum electrodynamics, and meson theory. http://en.wikipedia.org/wiki/Gregor_Wentzel _________________________________________________________________________ Hendrik Anthony "Hans" Kramers (Rotterdam, February 2, 1894 – Oegstgeest, April 24, 1952) was a Dutch physicist. http://en.wikipedia.org/wiki/Hendrik_Anthony_Kramers _________________________________________________________________________ Léon Nicolas Brillouin (August 7, 1889 – October 4, 1969) was a French physicist. He made contributions to quantum mechanics, radio wave propagation in the atmosphere, solid state physics, and information theory. http://en.wikipedia.org/wiki/L%C3%A9on_Brillouin _______________________________________________________________________ 1. Determination of wave functions using the WKB Approximation 1 In order to determine the eave function of the simple harmonics, we use the connection formula of the WKB approximation. V x E III II I x b O a The potential energy is expressed by 1 V (x) m 2 x 2 . 2 0 The x-coordinates a and b (the classical turning points) are obtained as 2 2 a 2 , b 2 , m0 m0 from the equation 1 V (x) m 2 x2 , 2 0 or 1 1 m 2a 2 m 2b2 , 2 0 2 0 where is the constant total energy. Here we apply the connection formula (I, upward) at x = a. -
Chapter 6 Free Electron Fermi Gas
理学院 物理系 沈嵘 Chapter 6 Free Electron Fermi Gas 6.1 Electron Gas Model and its Ground State 6.2 Thermal Properties of Electron Gas 6.3 Free Electrons in Electric Fields 6.4 Hall Effect 6.5 Thermal Conductivity of Metals 6.6 Failures of the free electron gas model 1 6.1 Electron Gas Model and its Ground State 6.1 Electron Gas Model and its Ground State I. Basic Assumptions of Electron Gas Model Metal: valence electrons → conduction electrons (moving freely) ü The simplest metals are the alkali metals—lithium, sodium, 2 potassium, cesium, and rubidium. 6.1 Electron Gas Model and its Ground State density of electrons: Zr n = N m A A where Z is # of conduction electrons per atom, A is relative atomic mass, rm is the density of mass in the metal. The spherical volume of each electron is, 1 3 1 V 4 3 æ 3 ö = = p rs rs = ç ÷ n N 3 è 4p nø Free electron gas model: Suppose, except the confining potential near surfaces of metals, conduction electrons are completely free. The conduction electrons thus behave just like gas atoms in an ideal gas --- free electron gas. 3 6.1 Electron Gas Model and its Ground State Basic Properties: ü Ignore interactions of electron-ion type (free electron approx.) ü And electron-eletron type (independent electron approx). Total energy are of kinetic type, ignore potential energy contribution. ü The classical theory had several conspicuous successes 4 6.1 Electron Gas Model and its Ground State Long Mean Free Path: ü From many types of experiments it is clear that a conduction electron in a metal can move freely in a straight path over many atomic distances. -
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. -
Voigt Transformations in Retrospect: Missed Opportunities?
Voigt transformations in retrospect: missed opportunities? Olga Chashchina Ecole´ Polytechnique, Palaiseau, France∗ Natalya Dudisheva Novosibirsk State University, 630 090, Novosibirsk, Russia† Zurab K. Silagadze Novosibirsk State University and Budker Institute of Nuclear Physics, 630 090, Novosibirsk, Russia.‡ The teaching of modern physics often uses the history of physics as a didactic tool. However, as in this process the history of physics is not something studied but used, there is a danger that the history itself will be distorted in, as Butterfield calls it, a “Whiggish” way, when the present becomes the measure of the past. It is not surprising that reading today a paper written more than a hundred years ago, we can extract much more of it than was actually thought or dreamed by the author himself. We demonstrate this Whiggish approach on the example of Woldemar Voigt’s 1887 paper. From the modern perspective, it may appear that this paper opens a way to both the special relativity and to its anisotropic Finslerian generalization which came into the focus only recently, in relation with the Cohen and Glashow’s very special relativity proposal. With a little imagination, one can connect Voigt’s paper to the notorious Einstein-Poincar´epri- ority dispute, which we believe is a Whiggish late time artifact. We use the related historical circumstances to give a broader view on special relativity, than it is usually anticipated. PACS numbers: 03.30.+p; 1.65.+g Keywords: Special relativity, Very special relativity, Voigt transformations, Einstein-Poincar´epriority dispute I. INTRODUCTION Sometimes Woldemar Voigt, a German physicist, is considered as “Relativity’s forgotten figure” [1].