Relativity

The Special & The General Theory

By Albert Einstein

PRINCETON UNIVERSITY PRESS

Copyright © 2019 Princeton University Press and The Hebrew University of Jerusalem
All rights reserved.
ISBN: 978-0-691-19181-2

Contents

Preface to the Paperback Edition, xiii,
Introduction, xvii,
Einstein as a Missionary of Science, 1,
Einstein's Booklet: Relativity: The Special and the General Theory, 7,
PART I: The Special Theory of Relativity,
1. Physical Meaning of Geometrical Propositions, 11,
2. The System of Co-ordinates, 14,
3. Space and Time in Classical Mechanics, 18,
4. The Galileian System of Co-ordinates, 21,
5. The Principle of Relativity (in the Restricted Sense), 23,
6. The Theorem of the Addition of Velocities Employed in Classical Mechanics, 27,
7. The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity, 28,
8. On the Idea of Time in Physics, 32,
9. The Relativity of Simultaneity, 36,
10. On the Relativity of the Conception of Distance, 39,
11. The Lorentz Transformation, 41,
12. The Behaviour of Measuring-Rods and Clocks in Motion, 47,
13. Theorem of the Addition of the Velocities. The Experiment of Fizeau, 50,
14. The Heuristic Value of the Theory of Relativity, 54,
15. General Results of the Theory, 56,
16. Experience and the Special Theory of Relativity, 62,
17. Minkowski's Four-Dimensional Space, 68,
PART II: The General Theory of Relativity,
18. Special and General Principle of Relativity, 72,
19. The Gravitational Field, 76,
20. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity, 80,
21. In What Respects Are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory?, 85,
22. A Few Inferences from the General Principle of Relativity, 88,
23. Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference, 93,
24. Euclidean and Non-Euclidean Continuum, 97,
25. Gaussian Co-ordinates, 101,
26. The Space-Time Continuum of the Special Theory of Relativity Considered as a Euclidean Continuum, 106,
27. The Space-Time Continuum of the General Theory of Relativity Is Not a Euclidean Continuum, 109,
28. Exact Formulation of the General Principle of Relativity, 113,
29. The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity, 117,
PART III: Considerations on the Universe as a Whole,
30. Cosmological Difficulties of Newton's Theory, 122,
31. The Possibility of a "Finite" and Yet "Unbounded" Universe, 125,
32. The Structure of Space According to the General Theory of Relativity, 131,
Appendixes,
1. Simple Derivation of the Lorentz Transformation (Supplementary to Section 11) (1918), 133,
2. Minkowski's Four-Dimensional Space ("World") (Supplementary to Section 17) (1918), 140,
3. The Experimental Confirmation of the General Theory of Relativity (1920), 142,
4. The Structure of Space According to the General Theory of Relativity (Supplementary to Section 32) (1946), 153,
5. Relativity and the Problem of Space (1953), 155,
A Reading Companion: Thirteen Commentaries,
Physics and Geometry (§§ 1–2), 180,
Mechanics and Space (§§ 3–6), 182,
Light Propagation and Time (§§ 7– 9), 187,
Light Propagation and Space (§§ 10– 12 and Appendix 1), 191,
Physics in Relativistic Space and Time (§§ 13– 16), 193,
The World of Four Dimensions (§ 17 and Appendix 2), 201,
From Special to General Relativity, 204,
Gravitation and Inertia (§§ 18–21), 205,
Acceleration, Clocks, and Rods (§§ 22–23), 209,
Gravitation and Geometry (§§ 24–27), 213,
Gravitation and General Relativity (§§ 28–29), 218,
The Challenge of Cosmology (§§ 30–32 and Appendix 4), 222,
The Relation between Theory and Experiment (Appendix 3), 226,
The Changing Concept of Space (Appendix 5), 230,
A History and Survey of Foreign-Language Editions,
The English Translation, 244,
The French Translation, 247,
The Italian Translation, 252,
The Spanish Translation, 256,
The Russian Translation, 259,
The Chinese Translation, 262,
The Japanese Translation, 266,
The Polish Translation, 270,
The Czech Translation, 273,
The Hebrew Translation, 276,
Concluding Remarks, 279,
Appended Documents,
A Letter from Walther Rathenau to Einstein, 281,
A Sample Page of Einstein's Handwriting, 284,
Manuscript of Appendix 3 of the Booklet, 286,
Further Reading, 293,
Index, 297,

CHAPTER 1

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 your 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 from 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 propositions (axioms) which, in virtue of these ideas, we are inclined to accept as "true." Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, i.e. they are proven. A proposition is then correct ("true") when it has been derived in the recognised manner from the axioms. The question of the "truth" of the individual geometrical propositions is thus reduced to one of the "truth" of the axioms. Now it has long been known that the last question is not only unanswerable by the methods of geometry, but that it is in itself entirely without meaning. We cannot ask whether it is true that only one straight line goes through two points. We can only say that Euclidean geometry deals with things called "straight lines," to each of which is ascribed the property of being uniquely determined by two points situated on it. The concept "true" does not tally with the assertions of pure geometry, because by the word "true" we are eventually in the habit of designating always the correspondence with a "real" object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

It is not difficult to understand why, in spite of this, we feel constrained to call the propositions of geometry "true." Geometrical ideas correspond to more or less exact objects in nature, and these last are undoubtedly the exclusive cause of the genesis of those ideas. Geometry ought to refrain from such a course, in order to give to its structure the largest possible logical unity. The...