Relativity: The Special and General Theory — Albert Einstein
You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org . If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title : Relativity : the Special and General Theory Author : Albert Einstein Translator : Robert W. Lawson Release date : February 1, 2004 [eBook #5001] Most recently updated: January 7, 2022 Language : English Original publication : Methuen & Co Ltd,, 1920 Other information and formats : www.gutenberg.org/ebooks/5001 Credits : Brian Basgen and Jeroen Hellingman Revised by Richard Tonsing. *** START OF Relativity The Special and General Theory A Popular Exposition By Albert Einstein, Ph.D. Professor of Physics in the University of Berlin Authorised Translation by Robert W. Lawson, D.Sc. University of Sheffield 1916 Table of Contents Preface I. The Special Theory of Relativity I. Physical Meaning of Geometrical Propositions II. The System of Co-ordinates III. Space and Time in Classical Mechanics IV. The Galileian System of Co-ordinates V. The Principle of Relativity in the Restricted Sense VI. The Theorem of the Addition of Velocities Employed in Classical Mechanics VII. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity VIII. On the Idea of Time in Physics IX. The Relativity of Simultaneity X. On the Relativity of the Conception of Distance XI. The Lorentz Transformation XII. The Behaviour of Measuring-Rods and Clocks in Motion XIII. Theorem of the Addition of Velocities. The Experiment of Fizeau XIV. The Heuristic Value of the Theory of Relativity XV. General Results of the Theory XVI. Experience and the Special Theory of Relativity XVII. Minkowski’s Four-Dimensional Space II. The General Theory of Relativity XVIII. Special and General Principle of Relativity XIX. The Gravitational Field XX. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity XXI. In What Respects Are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory? XXII. A Few Inferences from the General Principle of Relativity XXIII. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference XXIV. Euclidean and Non-Euclidean Continuum XXV. Gaussian Co-Ordinates XXVI. The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum XXVII. The Space-Time Continuum of the General Theory of Relativity is Not a Euclidean Continuum XXVIII. Exact Formulation of the General Principle of Relativity XXIX. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity III. Considerations on the Universe as a Whole XXX. Cosmological Difficulties of Newton’s Theory XXXI. The Possibility of a “Finite” and yet “Unbounded” Universe XXXII. The Structure of Space According to the General Theory of Relativity I. Simple Derivation of the Lorentz Transformation [Supplementary to Section XI] II. Minkowski’s Four-Dimensional Space (“World”) [Supplementary to Section XVII] III. The Experimental Confirmation of the General Theory of Relativity ( a ). Motion of the Perihelion of Mercury ( b ). Deflection of Light by a Gravitational Field ( c ). Displacement of Spectral Lines Towards the Red IV. The Structure of Space According to the General Theory of Relativity [Supplementary to Section XXXII] 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 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 the trees. May the book bring some one a few happy hours of suggestive thought! December, 1916 A. EINSTEIN PART I The Special Theory of Relativity I Physical Meaning of Geometrical Propositions In your schooldays most of you who read this book made acquaintance with the noble building of Euclid’s geometry, and you remember—perhaps with more respect than love—the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. By reason of our past experience, you would certainly regard everyone with disdain who should pronounce even the most out-of-the-way proposition of this science to be untrue. But perhaps this feeling of proud certainty would leave you immediately if some one were to ask you: “What, then, do you mean by the assertion that these propositions are true?” Let us proceed to give this question a little consideration. Geometry sets out form certain conceptions such as “plane,” “point,” and “straight line,” with which we are able to associate more or less definite ideas, and from certain simple propositi