The Genesis of General Relativity BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE Editors ROBERT S. COHEN, Boston University JÜRGEN RENN, Max Planck Institute for the History of Science KOSTAS GAVROGLU, University of Athens Editorial Advisory Board THOMAS F. GLICK, Boston University ADOLF GRÜNBAUM, University of Pittsburgh SYLVAN S. SCHWEBER, Brandeis University JOHN J. STACHEL, Boston University MARX W. WARTOFSKY†, (Editor 1960--1997) VOLUME 250 The Genesis of General Relativity Edited by Jürgen Renn Volume 4 GRAVITATION IN THE TWILIGHT OF CLASSICAL PHYSICS: THE PROMISE OF MATHEMATICS Editors Jürgen Renn and Matthias Schemmel Max Planck Institute for the History of Science, Germany Associate Editors Christopher Smeenk UCLA, U.S.A. Christopher Martin Indiana University, U.S.A. Assistant Editor Lindy Divarci Max Planck Institute for the History of Science, Germany A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-3999-9 (HB) ISBN-13 978-1-4020-3999-7 (HB) ISBN-10 1-4020-4000-8 (e-book) ISBN-13 978-1-4020-4000-9 (e-book) As a complete set for the 4 volumes Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2007 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. TABLE OF CONTENTS Volume 4 From an Electromagnetic Theory of Matter to a New Theory of Gravitation Mie’s Theories of Matter and Gravitation. 623 Christopher Smeenk and Christopher Martin Source text 1912–1913: Foundations of a Theory of Matter (Excerpts). 633 Gustav Mie Source text 1914: Remarks Concerning Einstein’s Theory of Gravitation . 699 Gustav Mie Source text 1915: The Principle of the Relativity of the Gravitational Potential. 729 Gustav Mie Source text 1913: The Momentum-Energy Law in the Electrodynamics of Gustav Mie . 745 Max Born Including Gravitation in a Unified Theory of Physics The Origin of Hilbert’s Axiomatic Method . 759 Leo Corry Hilbert’s Foundation of Physics: From a Theory of Everything to a Constituent of General Relativity. 857 Jürgen Renn and John Stachel Einstein Equations and Hilbert Action: What is Missing on Page 8 of the Proofs for Hilbert’s First Communication on the Foundations of Physics?. 975 Tilman Sauer Source text 1915: The Foundations of Physics (Proofs of First Communication) . 989 David Hilbert Source text 1916: The Foundations of Physics (First Communication) . 1003 David Hilbert Source text 1917: The Foundations of Physics (Second Communication) . 1017 David Hilbert From Peripheral Mathematics to a New Theory of Gravitation The Story of Newstein or: Is Gravity just another Pretty Force? . 1041 John Stachel Source text 1877: On the Relation of Non-Euclidean Geometry to Extension Theory . 1079 Hermann Grassmann Source text 1916: Notion of Parallelism on a General Manifold and Consequent Geometrical Specification of the Riemannian Curvature (Excerpts) . 1081 Tullio Levi-Civita Source text 1918: Purely Infinitesimal Geometry (Excerpt). 1089 Hermann Weyl Source text 1923: The Dynamics of Continuous Media and the Notion of an Affine Connection on Space-Time . 1107 Elie Cartan Index: Volumes 3 and 4 . .1131 Volume 3 (parallel volume) Gravitation in the Twilight of Classical Physics: An Introduction . 1 Jürgen Renn and Matthias Schemmel The Gravitational Force between Mechanics and Electrodynamics The Third Way to General Relativity: Einstein and Mach in Context . 21 Jürgen Renn Source text 1901: Gravitation . 77 Jonathan Zenneck Source text 1900: Considerations on Gravitation . 113 Hendrik A. Lorentz Source text 1896: Absolute or Relative Motion? . 127 Benedict and Immanuel Friedlaender Source text 1904: On Absolute and Relative Motion . 145 August Föppl An Astronomical Road to a New Theory of Gravitation The Continuity between Classical and Relativistic Cosmology in the Work of Karl Schwarzschild . 155 Matthias Schemmel Source text 1897: Things at Rest in the Universe . 183 Karl Schwarzschild A New Law of Gravitation Enforced by Special Relativity Breaking in the 4-Vectors: the Four-Dimensional Movement in Gravitation, 1905–1910. 193 Scott Walter Source text 1906: On the Dynamics of the Electron (Excerpts) . 253 Henri Poincaré Source text 1908: Mechanics and the Relativity Postulate . 273 Hermann Minkowski Source text 1910: Old and New Questions in Physics (Excerpt) . 287 Hendrik A. Lorentz The Problem of Gravitation as a Challenge for the Minkowski Formalism The Summit Almost Scaled: Max Abraham as a Pioneer of a Relativistic Theory of Gravitation . 305 Jürgen Renn Source text 1912: On the Theory of Gravitation . 331 Max Abraham Source text 1912: The Free Fall . 341 Max Abraham Source text 1913: A New Theory of Gravitation . 347 Max Abraham Source text 1915: Recent Theories of Gravitation . 363 Max Abraham A Field Theory of Gravitation in the Framework of Special Relativity Einstein, Nordström, and the Early Demise of Scalar, Lorentz Covariant Theories of Gravitation . 413 John D. Norton Source text 1912: The Principle of Relativity and Gravitation . 489 Gunnar Nordström Source text 1913: Inertial and Gravitational Mass in Relativistic Mechanics . 499 Gunnar Nordström Source text 1913: On the Theory of Gravitation from the Standpoint of the Principle of Relativity . 523 Gunnar Nordström Source text 1913: On the Present State of the Problem of Gravitation . 543 Albert Einstein From Heretical Mechanics to a New Theory of Relativity Einstein and Mach’s Principle. 569 Julian B. Barbour Source text 1914: On the Relativity Problem . 605 Albert Einstein Source text 1920: Ether and the Theory of Relativity. 613 Albert Einstein FROM AN ELECTROMAGNETIC THEORY OF MATTER TO A NEW THEORY OF GRAVITATION CHRISTOPHER SMEENK AND CHRISTOPHER MARTIN MIE’S THEORIES OF MATTER AND GRAVITATION Unifying physics by describing a variety of interactions—or even all interactions— within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen world function (Hamilto- nian). Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called solitons); furthermore he clarified the use of variational principles in the context of special relativity. The following brief introduc- tion to Mie’s work has three main objectives.1 The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic worldview. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in partic- ular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. In September 1913 Einstein presented a lecture on the current status of the prob- lem of gravitation at the 85th Naturforscherversammlung in Vienna. Einstein’s lec- ture and the ensuing heated discussion, both published later that year in the Physikalische Zeitschrift, reflect the options available for those who took on the task of developing a new theory of gravitation. The conflict between Newtonian gravita- tional theory and special relativity provided a strong motivation for developing a new gravitational theory, but it was not clear whether a fairly straightforward modification of Newton’s theory based on classical field theory would lead to a successful replace- ment. Einstein clearly aimed to convince his audience that success would require the more radical step of extending the principle of relativity. For Einstein the develop- ment of a new gravitational theory was intricately connected with foundational prob- 1 There are several recent, more comprehensive discussions of Mie’s work, which we draw on here: (Kohl 2002; Vizgin 1994; 26–38; Corry 1999, 2004, chaps. 6 and 7). Born (1914) gives an insightful, influential reformulation of Mie’s framework, and (Pauli 1921, §64, 188–192 in the English transla- tion) and (Weyl 1918, §25, 206–217 (§26) in the English translation of the fourth edition) both give clear contemporary reviews. Jürgen Renn (ed.). The Genesis of General Relativity, Vol. 4 Gravitation in the Twilight of Classical Physics: The Promise of Mathematics. © 2007 Springer. 624 CHRISTOPHER SMEENK AND CHRISTOPHER MARTIN lems in classical mechanics, and in the Vienna lecture he motivated the need to extend the principle of relativity with an appeal to Mach’s analysis of inertia. Accord- ing to Einstein Mach had accurately identified an “epistemological defect” in classi- cal mechanics, namely the introduction of a distinction between inertial and non- inertial reference frames without an appropriate observational basis.2 The special the- ory of relativity had replaced Galilean transformations between reference frames with Lorentz transformations, but the principle of relativity still did not apply to accelerated motion. Extending the principle of relativity to accelerated motion depended on an idea Einstein later called “the most fortunate thought of my life,” the principle of equivalence. This idea received many different formulations over the years, but in 1913 Einstein gave one version of this principle as a postulate: his sec- ond postulate requires the exact equality of inertial and gravitational mass. He further argued that this equality undermines the ability to observationally distinguish between a state of uniform acceleration and the presence of a gravitational field.