DOCSLIB.ORG

A Helping Hand

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Helping Hand thesis A helping hand One hundred years ago last month, a the rudiments of quantum field theory research paper appeared in the journal “Grossmann, you have learns to write down Lagrangian functions Zeitschrift für Mathematik und Physik, in manifestly covariant form, thereby co-authored by a Swiss mathematician to help me, or else I’ll ensuring the relativistic invariance of the from ETH Zürich. Written with a physicist go crazy!” resulting theory. colleague, the paper presented the results of It may be, of course, that someone in the a two-year collaborative effort, which had role of Grossmann would have existed, even flowered from a friendship formed when if Grossmann himself had not. Gravity is the two men were students some years intimately linked with spacetime curvature before. Their paper of January 1914 stands derivative and more. This mathematical and differential geometry. Even if Einstein as a historical monument to the power of machinery and language, Sauer argues, was had failed to see precisely how, someone timely collaboration. originally brought into the theory largely by else presumably would have eventually The physicist lacked the mathematical Grossmann. He not only pointed Einstein succeeded, learning the right mathematical knowledge to give his deepest insights to crucial mathematical papers — such as language on their own, or meeting someone, concrete form. The mathematician helped to a 1901 article on the absolute differential like Grossmann, who could help. This kind of show him how, bringing recent mathematical calculus by Gregorio Ricci-Curbastro and mathematics — a step up in abstraction from theories to bear. The result was a paper Tullio Levi-Civita — but took real steps in the mathematics of classical mechanics — entitled ‘Outline of a general theory of forging the emerging theory into these terms. was increasingly in the air. relativity and a theory of gravitation’. Indeed, it seems it was Grossmann At the time of Grossman and Einstein, Most physicists will have guessed by who kicked off the use in physics of the Emmy Noether was making major advances now that the physicist in question was now ubiquitous term ‘tensor’, favouring in abstract algebra and group theory, and Albert Einstein. The mathematician was the idea that equations written in terms of bringing these into the foundations of field one Marcel Grossmann. History records tensors would be manifestly of the same theory. Following general relativity came that Einstein discovered general relativity form in all coordinate systems. Sauer notes the Hilbert-space formulation of quantum in complete form in 1915, yet what many that Ricci-Curbastro and Levi-Civita had theory, Paul Dirac’s relativistic quantum physicists might not know is just how never used ‘tensor’ in this context, instead theory, field theories with broken symmetries significant a role Grossmann played in calling these objects “systèmes covariants ou and the rise of mathematical physics as the giving that theory its final form. Indeed, contrevariants”. Grossmann, Sauer’s study guiding light of physics. Grossmann’s imprint the Einstein–Grossmann paper of 1914 of the notebooks suggests, “actually helped is all over today’s theories of cosmology and came within a hair’s breadth of describing clarify the very mathematical status of the string theory. the correct equations of general relativity. objects that were entering the centre stage of After his work with Einstein, “We had come at that time already very their theoretical efforts.” Marcel Grossmann did further research in close to the solution,” Einstein later wrote. Einstein’s notebooks make pointed synthetic and non-Euclidean geometry, but “At the time we lacked only a few relations reference to Grossmann’s contributions to the also became very active outside of research. of a formal nature, without which the link development of the mathematical formalism. In the years following the First World War, between the formulas and already known On one page, where an expression appears he helped found and run a twice-weekly laws cannot be attained.” for the Riemann–Christoffel tensor — an magazine promoting open debate on Swiss Even today, however, no one has written object with four indices capturing the national affairs and spent considerable energy a biography of Marcel Grossmann. He local curvature of a manifold — Einstein in efforts to reform the Swiss education never claimed to be a co-inventor of the has written “Grossmann tensor of fourth system. Beneficial education, in his view, theory, merely a helper. He and Einstein manifold”. It was Grossmann who showed would not only instil specific knowledge but remained friends for two decades until how to reduce this tensor to an object with should “create a frame of mind that enables Grossmann’s death in 1936. The historical only two indices that would be suitable for a the young person at the end of his studies to evidence — as historian Tim Sauer points gravitational field equation, pointing the way swim about without swimming coach and out in a new examination of Einstein’s to the correct mathematical objects needed without swimming rings, even when the notebooks and other documents of the period to develop fully covariant field equations. current would flow in unexpected directions.” (http://arXiv.org/abs/1312.4068) — clearly I’m sure none of this is news to physicists He remained all the time a staunch believer shows that Grossmann played a hugely working with general relativity, who have in broad education, perhaps instructed from influential role in pushing Einstein towards long known of Grossmann’s contributions. A his own experience with Einstein of the vast his final theory. prominent series of international conferences potential for a little knowledge from other Open almost any modern textbook on even bears his name. Yet it might also be fields to make a big difference. general relativity and you’ll encounter several said that Grossmann not only helped forge When Einstein first approached his friend, chapters of mathematical preliminaries. general relativity, but was instrumental in seeking help in 1912, he did so with the For example, a popular undergraduate changing the mathematical language of following words: “Grossmann, you have to textbook by Bernard Schutz starts out physics. His tensor notation left a mark help me, or else I’ll go crazy!” It is fortunate covering topics such as covariant and not only on the form of general relativity, for physics that Grossman helped. ❐ contravariant tensors, measures of curvature but indeed on all fundamental theories on differentiable manifolds, the covariant developed since. Every physicist studying MARK BUCHANAN 84 NATURE PHYSICS | VOL 10 | FEBRUARY 2014 | www.nature.com/naturephysics © 2014 Macmillan Publishers Limited. All rights reserved.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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).
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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).
    [Show full text]
  • Marcel Grossmann for the Love of Mathematics
    springer.com Popular Science : Popular Science in Physics Graf-Grossmann, Claudia Marcel Grossmann For the Love of Mathematics Gives fascinating new insights into Einsteins friendship and collaboration with Grossmann Accessible and gripping reading for the layman and science historian alike Thoroughly researched and written by Marcel Grossmann's granddaughter Includes detailed scientific-historical appreciation by GR expert Tilman Sauer Zurich, summer 1912. Albert Einstein has just returned from Prague to the city on the Limmat. He sends a plea for help to his former fellow student, the mathematician Marcel Grossmann (1878-1936), for he is in need of assistance with the mathematical calculations of his general theory of relativity. What then follows is one of the most fascinating chapters of science history, with far-reaching consequences for the lives of the two friends. Marcel Grossmann’s granddaughter paints here a picture of a fiery and many-talented scientist and patriot. She Springer traces the influence of an entrepreneurial family during Germany’s rapid industrial expansion in 1st ed. 2018, XVIII, 263 p. the late 19th century. The family’s fluctuating fortunes take the story to the vibrant city of 1st 91 illus., 1 illus. in color. Budapest on the Danube; they enable readers to sense the pioneering spirit at Zurich’s young edition Polytechnic Institute (now ETH Zurich) – but also reflect the worries and hardships of the First World War and interwar years. The Foreword is written by Prof. Remo Ruffini, founder and president of the International Center for Relativistic Astrophysics and the Marcel Grossmann Printed book Meetings. Last but not least, an extensive contribution by Dr.
    [Show full text]
  • The Fourteenth Marcel Grossmann Meeting on Recent
    September 4, 2017 9:33 ws-procs961x669 MG-14 – Proceedings (Part D) D429 page 3348 3348 A brief history of the energy-momentum tensor 1912-1915: Einstein physicist’s logic in compromising gravitation with relativity Jean-Pierre Provost∗ Universit´e de Nice Sophia Antipolis, Nice, 06108/France ∗E-mail: [email protected] In MG13 (Stockholm 2012) we discussed how the history (1900-1911) of relativistic dy- namics was intimately linked to issues concerning energy momentum tensors, in particu- lar the electromagnetic one. Here we examine how, for Einstein, the expected properties of the matter and gravitational field tensors have been sources of inspiration strongly conditioning his quest for a relativistic description of gravitation. It is in this physical framework already present in 1912 that in competition with Hilbert at the fall of 1915, he thinks to have justified general covariance. Keywords: Einstein; General Relativity; Energy-momentum tensor. 1. Introduction: The point of view of energy momentum tensors (E.M.T) The history of general relativity (G.R) has been extensively studied by historians and philosophers and has become a ‘well written subject’ as T. Sauer said in his MG13’s talk 1 referring to Ref. 2. But in our opinion Einstein’s path to G.R has too often been written from the mathematical perspective of the final result, with Einstein ‘stumbling’ (J.D. Norton) or following a ‘bumpy road’ (M. Janssen) before touching the destination of general covariance. As we shall emphasize, the physical point of view of the role played by the energy momentum tensor (E.M.T) in Ein- stein’s quest for conciliating relativity with gravitation is unavoidable because it is at the basis of his logic from 1912 to 1915.
    [Show full text]
  • General Relativity Conflict and Rivalries
    General Relativity Conflict and Rivalries General Relativity Conflict and Rivalries: Einstein's Polemics with Physicists By Galina Weinstein General Relativity Conflict and Rivalries: Einstein's Polemics with Physicists By Galina Weinstein This book first published 2015 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2015 by Galina Weinstein All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-8362-X ISBN (13): 978-1-4438-8362-7 “When I accompanied him [Einstein] home the first day we met, he told me something that I heard from him many times later: ‘In Princeton they regard me as an old fool.’ (‘Hier in Princeton betrachten sie mich als einen alten Trottel’.) […] Before he was thirty-five, Einstein had made the four great discoveries of his life. In order of increasing importance they are: the theory of Brownian motion; the theory of the photoelectric effect; the special theory of relativity; the general theory of relativity. Very few people in the history of science have done half as much. […] For years he looked for a theory which would embrace gravitational, electromagnetic, and quantum phenomena. […] Einstein pursued it relentlessly through ideas which he changed repeatedly and down avenues that led nowhere. The very distinguished professors in Princeton did not understand that Einstein’s mistakes were more important than their correct results.
    [Show full text]
  • Albert Einstein's Methodology
    Albert Einstein's Methodology Galina Weinstein This paper discusses Einstein's methodology. The first topic is: Einstein characterized his work as a theory of principle and reasoned that beyond kinematics, the 1905 heuristic relativity principle could offer new connections between non-kinematical concepts. The second topic is: Einstein's creativity and inventiveness and process of thinking; invention or discovery. The third topic is: Einstein considered his best friend Michele Besso as a sounding board and his class-mate from the Polytechnic Marcel Grossman – as his active partner. Yet, Einstein wrote to Arnold Sommerfeld that Grossman will never claim to be considered a co-discoverer of the Einstein- Grossmann theory. He only helped in guiding Einstein through the mathematical literature, but contributed nothing of substance to the results of the theory. Hence, Einstein neither considered Besso or Grossmann as co-discoverers of the relativity theory which he himself invented. 1 The Principles of Relativity as Heuristic Principles 1.1 Einstein's reply to Ehrenfest Einstein had a friend, Paul Ehrenfest a Jewish physicist from Vienna. In 1907 Ehrenfest wrote a paper.1 There were the known problems in the 19th century electrodynamics of moving bodies. Einstein's 1905 solution appeared to Ehrenfest very similar to Hendryk Antoon Lorentz's solution to these problems, the celebrated theory of the electron. Ehrenfest thought that Einstein's deformed electron (from his 1905 relativity paper) could have been obtained from the good old theory of Lorentz, if we only used the method of deduction. If this was so, Ehrenfest understood that Einstein's theory was nothing but a reformulation of the electrodynamics of Lorentz.
    [Show full text]