Relativity (1931)

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Relativity: The Special and General Theory (1931)
by Albert Einstein, translated by Robert William Lawson, illustrated by Hermann Struck
Albert EinsteinRobert William Lawson1923Relativity: The Special and General Theory1931Relativity (1931), cover.jpg

RELATIVITY

THE SPECIAL AND GENERAL THEORY


RELATIVITY

THE SPECIAL AND GENERAL THEORY


BY

ALBERT EINSTEIN, Ph.D.
PROFESSOR OF PHYSICS IN THE UNIVERSITY OF BERLIN


TRANSLATED BY

ROBERT W. LAWSON, D.Sc., F. Inst. P.
UNIVERSITY OF SHEFFIELD



NEW YORK
PETER SMITH

Copyright, 1920
BY
HENRY HOLT AND COMPANY


Reprinted, September, 1931,
by permission of
Henry Holt and Company, Inc.


PRINTED IN THE U. S. A. BY
QUINN & BODEN COMPANY, INC,
RAHWAY, N. J.

PREFACE

THE present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus[1] of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist, L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having withheld from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a “step-motherly” fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for trees. May the book bring some one a few happy hours of suggestive thought!

December, 1916


NOTE TO THE THIRD EDITION

IN the present year (1918) an excellent and detailed manual on the general theory of relativity, written by H. Weyl, was published by the firm Julius Springer (Berlin). This book, entitled Raum—Zeit—Materie (Space—Time—Matter), may be warmly recommended to mathematicians and physicists.

BIOGRAPHICAL NOTE

ALBERT EINSTEIN is the son of German-Jewish parents. He was born in 1879 in the town of Ulm, Würtemberg, Germany. His schooldays were spent in Munich, where he attended the Gymnasium until his sixteenth year. After leaving school at Munich, he accompanied his parents to Milan, whence he proceeded to Switzerland six months later to continue his studies. From 1896 to 1900 Albert Einstein studied mathematics and physics at the Technical High School in Zurich, as he intended becoming a secondary school (Gymnasium) teacher. For some time afterwards he was a private tutor, and having meanwhile become naturalised, he obtained a post as engineer in the Swiss Patent Office in 1902, which position he occupied till 1909. The main ideas involved in the most important of Einstein’s theories date back to this period. Amongst these may be mentioned: The Special Theory of Relativity, Inertia of Energy, Theory of the Brownian Movement, and the Quantum-Law of the Emission and Absorption of Light (1905). These were followed some years later by the Theory of the Specific Heat of Solid Bodies, and the fundamental idea of the General Theory of Relativity.

During the interval 1909 to 1911 he occupied the post of Professor Extraordinarius at the University of Zurich, afterwards being appointed to the University of Prague, Bohemia, where he remained as Professor Ordinarius until 1912. In the latter year Professor Einstein accepted a similar chair at the Polytechnikum, Zurich, and continued his activities there until 1914, when he received a call to the Prussian Academy of Science, Berlin, as successor to Van’t Hoff. Professor Einstein is able to devote himself freely to his studies at the Berlin Academy, and it was here that he succeeded in completing his work on the General Theory of Relativity (1915–17). Professor Einstein also lectures on various special branches of physics at the University of Berlin, and, in addition, he is Director of the Institute for Physical Research of the Kaiser Wilhelm Gesellschaft.

Professor Einstein has been twice married. His first wife, whom he married at Berne in 1903, was a fellow-student from Serbia. There were two sons of this marriage, both of whom are living in Zurich, the elder being sixteen years of age. Recently Professor Einstein married a widowed cousin, with whom he is now living in Berlin.

TRANSLATOR’S NOTE

IN presenting this translation to the English reading public, it is hardly necessary for me to enlarge on the Author’s prefatory remarks, except to draw attention to those additions to the book which do not appear in the original.

At my request, Professor Einstein kindly supplied me with a portrait of himself, by one of Germany’s most celebrated artists. Appendix III, on “The Experimental Confirmation of the General Theory of Relativity,” has been written specially for this translation. Apart from these valuable additions to the book, I have included a biographical note on the Author, and, at the end of the book, an Index and a list of English references to the subject. This list, which is more suggestive than exhaustive, is intended as a guide to those readers who wish to pursue the subject farther.

I desire to tender my best thanks to my colleagues Professor S. R. Milner, D.Sc., and Mr. W. E. Curtis, A.R.C.Sc., F.R.A.S., also to my friend Dr. Arthur Holmes, A.R.C.Sc., F.G.S., of the Imperial College, for their kindness in reading through the manuscript, for helpful criticism, and for numerous suggestions. I owe an expression of thanks also to Messrs. Methuen for their ready counsel and advice, and for the care they have bestowed on the work during the course of its publication.

The Physics Laboratory
The University of Sheffield
June 12, 1920

CONTENTS


PART I
THE SPECIAL THEORY OF RELATIVITY
PAGE
I. Physical Meaning of Geometrical Propositions 1
II. The System of Co-ordinates 5
III. Space and Time in Classical Mechanics 9
IV. The Galileian System of Co-ordinates 12
V. The Principle of Relativity (in the Restricted Sense) 14
VI. The Theorem of the Addition of Velocities employed in Classical Mechanics 19
VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity 21
VIII. On the Idea of Time in Physics 25
IX. The Relativity of Simultaneity 30
X. On the Relativity of the Conception of Distance 34
XI. The Lorentz Transformation 36
XII. The Behaviour of Measuring-Rods and Clocks in Motion 42
XIII. Theorem of the Addition of Velocities. The Experiment of Fizeau 45
XIV. The Heuristic Value of the Theory of Relativity 50
XV. General Results of the Theory 52
XVI. Experience and the Special Theory of Relativity 58
XVII. Minkowski’s Four-dimensional Space 65
PART II
THE GENERAL THEORY OF RELATIVITY
XVIII. Special and General Principle of Relativity 69
XIX. The Gravitational Field 74
XX. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity 78
XXI. In what Respects are the Foundations of Classical Mechanics and of the Special Theory of Relativity unsatisfactory? 84
XXII. A Few Inferences from the General Principle of Relativity 87
XXIII. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference 93
XXIV. Euclidean and Non-Euclidean Continuum 98
XXV. Gaussian Co-ordinates 103
XXVI. The Space-time Continuum of the Special Theory of Relativity considered as a Euclidean Continuum 108
XXVII. The Space-time Continuum of the General Theory of Relativity is not a Euclidean Continuum 111
XXVIII. Exact Formulation of the General Principle of Relativity 115
XXIX. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity 119
PART III
CONSIDERATIONS ON THE UNIVERSE AS A WHOLE
XXX. Cosmological Difficulties of Newton’s Theory 125
XXXI. The Possibility of a ‘‘Finite” and yet “Unbounded” Universe 128
XXXII. The Structure of Space according to the General Theory of Relativity 135
APPENDICES
I. Simple Derivation of the Lorentz Transformation 139
II. Minkowski’s Four-dimensional Space (“World”) [Supplementary to Section XVII.] 146
III. The Experimental Confirmation of the General Theory of Relativity 148
  (a) Motion of the Perihelion of Mercury 150
  (b) Deflection of Light by a Gravitational Field 152
  (c) Displacement of Spectral Lines towards the Red 155
Bibliography 161
Index 165

Footnotes

  1. The mathematical fundaments of the special theory of relativity are to be found in the original papers of H. A. Lorentz, A. Einstein, H. Minkowski‘ published under the title Das Relativitätsprinzip (The Principle of Relativity) in B. G. Teubner’s collection of monographs Fortschritte der mathematischen Wissenschaften (Advances in the Mathematical Sciences), also in M. Laue’s exhaustive book Das Relativitäts prinzip—published by Friedr. Vieweg & Son, Braunschweig. The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity)—Joh. Ambr. Barth, 1916; this book assumes some familiarity with the special theory of relativity.


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This work is in the public domain in the United States because it was published before January 1, 1929.


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Translation:

This work is in the public domain in the United States because it was published before January 1, 1929.


The longest-living author of this work died in 1960, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 63 years or less. This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.

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