Albert Einstein [Einstein - Relativity: The Special and the General Theory

Relativity.indd 1

4/20/2017 1:30:12 PM

Relativity.indd 2

4/20/2017 1:30:12 PM

Relativity.indd 3

4/20/2017 1:30:12 PM

Published by

Rupa Publications India Pvt. Ltd 2017

7/16, Ansari Road, Daryaganj

New Delhi 110002

Sales centres:

Allahabad Bengaluru Chennai

Hyderabad Jaipur Kathmandu

Kolkata Mumbai

Edition Copyright Rupa Publications India Pvt. Ltd 2017

The views and opinions expressed in this book are the authors own and the facts are as reported by him which have been verified to the extent possible, and the publishers are not in any way liable for the same.

All rights reserved.

No part of this publication may be reproduced, transmitted, or stored in a retrieval system, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher.

ISBN: 978-81-291-4743-1

First impression 2017

10 9 8 7 6 5 4 3 2 1

This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated, without the publishers prior consent, in any form of binding or cover other than that in which it is published.

Relativity.indd 4

4/20/2017 1:30:12 PM

Contents

Preface ix

Note to the Fifteenth Edition

xi

Part I

The Special Theory of Relativity

1. Physical Meaning of Geometrical Propositions

2. The System of Co-ordinates

3. Space and Time in Classical Mechanics

4. The Galileian System of Co-ordinates

5. The Principle of Relativity (in the Restricted Sense) 13

6. The Theorem of the Addition of Velocities Employed in Classical Mechanics

7. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity

8. On the Idea of Time in Physics

9. The Relativity of Simultaneity

10. On the Relativity of the Conception of Distance 27

11. The Lorentz Transformation

Relativity.indd 5

4/20/2017 1:30:12 PM

12. The Behaviour of Measuring-Rods and Clocks in Motion 34

13. Theorem of the Addition of the Velocities.

The Experiment of Fizeau

14. The Heuristic Value of the Theory of Relativity 41

15. General Results of the Theory

16. Experience and the Special Theory of Relativity 48

17. Minkowskis Four-Dimensional Space

Part II

The General Theory of Relativity

18. Special and General Principle of Relativity

19. The Gravitational Field

20. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity 66

21. In What Respects Are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory?

22. A Few Inferences from the General Principle of Relativity 72

23. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference

24. Euclidean and Non-Euclidean Continuum

25. Gaussian Co-ordinates

26. The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum

27. The Space-Time Continuum of the General Theory of Relativity Is Not a Euclidean Continuum

28. Exact Formulation of the General Principle of Relativity 93

29. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity

Relativity.indd 6

4/20/2017 1:30:12 PM

Part III

Considerations on the Universe as a Whole

30. Cosmological Difficulties of Newtons Theory

31. The Possibility of a Finite and Yet Unbounded Universe 105

32 The Structure of Space According to the General Theory of Relativity

Appendices

1. Simple Derivation of the Lorentz Transformation 113

2. Minkowskis Four-Dimensional Space (World)

3. 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

4. The Structure of Space According to the General Theory of Relativity

5. Relativity and the Problem of Space

Bibliography 151

Relativity.indd 7

4/20/2017 1:30:12 PM

Relativity.indd 8

4/20/2017 1:30:13 PM

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 short ness 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 with held from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the em pirical 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

A. EINSTEIN

Relativity.indd 9

4/20/2017 1:30:13 PM

Relativity.indd 10

4/20/2017 1:30:13 PM

Note to the

Fifteenth Edition

In this edition I have added, as a fifth appendix, a presentation of my views on the problem of space in general and on the gradual modifications of our ideas on space result ing from the influence of the relativistic view-point. I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning.

A. EINSTEIN

June9th, 1952

Relativity.indd 11

4/20/2017 1:30:13 PM

Plates

The Author, 1949

Frontispiece

( Photo: Camera Press, London)

The Author, 1920

Facing page 1

( Drawing by Hermann Struck)