# Relativity: The Special and General Theory

Albert Einstein

## 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

# Contents

## Part 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

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

## Part II. The General Theory of Relativity

XVIII. Special and General Principle of Relativity

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

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

## Part 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

## Appendices

Appendix I. Simple Derivation of the Lorentz Transformation [Supplementary to Section XI]

Appendix II. Minkowski’s Four-Dimensional Space (“World”) [Supplementary to Section XVII]

Appendix III. The Experimental Confirmation of the General Theory of Relativity

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