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RELATIVITY: THE SPECIAL AND GENERAL THEORY `
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BY ALBERT EINSTEIN `
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CONTENTS `
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Preface `
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Part I: The Special Theory of Relativity `
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01. Physical Meaning of Geometrical Propositions `
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02. The System of Co-ordinates `
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03. Space and Time in Classical Mechanics `
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04. The Galileian System of Co-ordinates `
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05. The Principle of Relativity (in the Restricted Sense) `
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06. The Theorem of the Addition of Velocities employed in `
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Classical Mechanics `
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07. The Apparent Incompatability of the Law of Propagation of `
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Light with the Principle of Relativity `
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08. On the Idea of Time in Physics `
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09. The Relativity of Simultaneity `
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10. On the Relativity of the Conception of Distance `
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11. The Lorentz Transformation `
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12. The Behaviour of Measuring-Rods and Clocks in Motion `
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13. Theorem of the Addition of Velocities. The Experiment of Fizeau `
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14. The Hueristic Value of the Theory of Relativity `
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15. General Results of the Theory `
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16. Expereince and the Special Theory of Relativity `
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17. Minkowski's Four-dimensial Space `
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Part II: The General Theory of Relativity `
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18. Special and General Principle of Relativity `
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19. The Gravitational Field `
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20. The Equality of Inertial and Gravitational Mass as an Argument `
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for the General Postulate of Relativity `
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21. In What Respects are the Foundations of Classical Mechanics `
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and of the Special Theory of Relativity Unsatisfactory? `
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22. A Few Inferences from the General Principle of Relativity `
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23. Behaviour of Clocks and Measuring-Rods on a Rotating Body of `
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Reference `
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24. Euclidean and non-Euclidean Continuum `
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25. Gaussian Co-ordinates `
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26. The Space-Time Continuum of the Speical Theory of Relativity `
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Considered as a Euclidean Continuum `
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27. The Space-Time Continuum of the General Theory of Relativity `
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is Not a Eculidean Continuum `
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28. Exact Formulation of the General Principle of Relativity `
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29. The Solution of the Problem of Gravitation on the Basis of the `
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General Principle of Relativity `
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Part III: Considerations on the Universe as a Whole `
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30. Cosmological Difficulties of Netwon's Theory `
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31. The Possibility of a "Finite" and yet "Unbounded" Universe `
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32. The Structure of Space According to the General Theory of `
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Relativity `
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Appendices: `
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01. Simple Derivation of the Lorentz Transformation (sup. ch. 11) `
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02. Minkowski's Four-Dimensional Space ("World") (sup. ch 17) `
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03. The Experimental Confirmation of the General Theory of Relativity `
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04. The Structure of Space According to the General Theory of `
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Relativity (sup. ch 32) `
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05. Relativity and the Problem of Space `
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Note: The fifth Appendix was added by Einstein at the time of the `
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fifteenth re-printing of this book; and as a result is still under `
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copyright restrictions so cannot be added without the permission of `
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the publisher. `
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PREFACE `
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(December, 1916) `
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The present book is intended, as far as possible, to give an exact `
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insight into the theory of Relativity to those readers who, from a `
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general scientific and philosophical point of view, are interested in `
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the theory, but who are not conversant with the mathematical apparatus `
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of theoretical physics. The work presumes a standard of education `
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corresponding to that of a university matriculation examination, and, `
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despite the shortness of the book, a fair amount of patience and force `
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of will on the part of the reader. The author has spared himself no `
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pains in his endeavour to present the main ideas in the simplest and `
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most intelligible form, and on the whole, in the sequence and `
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connection in which they actually originated. In the interest of `
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clearness, it appeared to me inevitable that I should repeat myself `
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frequently, without paying the slightest attention to the elegance of `
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the presentation. I adhered scrupulously to the precept of that `
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brilliant theoretical physicist L. Boltzmann, according to whom `
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matters of elegance ought to be left to the tailor and to the cobbler. `
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I make no pretence of having withheld from the reader difficulties `
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which are inherent to the subject. On the other hand, I have purposely `
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treated the empirical physical foundations of the theory in a `
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"step-motherly" fashion, so that readers unfamiliar with physics may `
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not feel like the wanderer who was unable to see the forest for the `
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trees. May the book bring some one a few happy hours of suggestive `
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thought! `
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December, 1916 `
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A. EINSTEIN `
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PART I `
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THE SPECIAL THEORY OF RELATIVITY `
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PHYSICAL MEANING OF GEOMETRICAL PROPOSITIONS `
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In your schooldays most of you who read this book made acquaintance `
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with the noble building of Euclid's geometry, and you remember -- `
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perhaps with more respect than love -- the magnificent structure, on `
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the lofty staircase of which you were chased about for uncounted hours `
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by conscientious teachers. By reason of our past experience, you would `
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certainly regard everyone with disdain who should pronounce even the `
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most out-of-the-way proposition of this science to be untrue. But `
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perhaps this feeling of proud certainty would leave you immediately if `
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some one were to ask you: "What, then, do you mean by the assertion `
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that these propositions are true?" Let us proceed to give this `
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question a little consideration. `
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Geometry sets out form certain conceptions such as "plane," "point," `
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and "straight line," with which we are able to associate more or less `
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definite ideas, and from certain simple propositions (axioms) which, `
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in virtue of these ideas, we are inclined to accept as "true." Then, `
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on the basis of a logical process, the justification of which we feel `
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ourselves compelled to admit, all remaining propositions are shown to `
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follow from those axioms, i.e. they are proven. A proposition is then `
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correct ("true") when it has been derived in the recognised manner `
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from the axioms. The question of "truth" of the individual geometrical `
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propositions is thus reduced to one of the "truth" of the axioms. Now `
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it has long been known that the last question is not only unanswerable `
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by the methods of geometry, but that it is in itself entirely without `
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meaning. We cannot ask whether it is true that only one straight line `
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goes through two points. We can only say that Euclidean geometry deals `
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with things called "straight lines," to each of which is ascribed the `
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property of being uniquely determined by two points situated on it. `
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The concept "true" does not tally with the assertions of pure `
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geometry, because by the word "true" we are eventually in the habit of `
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designating always the correspondence with a "real" object; geometry, `
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however, is not concerned with the relation of the ideas involved in `
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it to objects of experience, but only with the logical connection of `
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these ideas among themselves. `
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It is not difficult to understand why, in spite of this, we feel `
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constrained to call the propositions of geometry "true." Geometrical `
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ideas correspond to more or less exact objects in nature, and these `
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last are undoubtedly the exclusive cause of the genesis of those `
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ideas. Geometry ought to refrain from such a course, in order to give `
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to its structure the largest possible logical unity. The practice, for `
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example, of seeing in a "distance" two marked positions on a `
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practically rigid body is something which is lodged deeply in our `
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habit of thought. We are accustomed further to regard three points as `
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being situated on a straight line, if their apparent positions can be `
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made to coincide for observation with one eye, under suitable choice `
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of our place of observation. `
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If, in pursuance of our habit of thought, we now supplement the `
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propositions of Euclidean geometry by the single proposition that two `
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points on a practically rigid body always correspond to the same `
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distance (line-interval), independently of any changes in position to `
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which we may subject the body, the propositions of Euclidean geometry `
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then resolve themselves into propositions on the possible relative `
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position of practically rigid bodies.* Geometry which has been `
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supplemented in this way is then to be treated as a branch of physics. `
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We can now legitimately ask as to the "truth" of geometrical `
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propositions interpreted in this way, since we are justified in asking `
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whether these propositions are satisfied for those real things we have `
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associated with the geometrical ideas. In less exact terms we can `
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express this by saying that by the "truth" of a geometrical `
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proposition in this sense we understand its validity for a `
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construction with rule and compasses. `
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Of course the conviction of the "truth" of geometrical propositions in `
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this sense is founded exclusively on rather incomplete experience. For `
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the present we shall assume the "truth" of the geometrical `
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propositions, then at a later stage (in the general theory of `
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relativity) we shall see that this "truth" is limited, and we shall `
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consider the extent of its limitation. `
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Notes `
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*) It follows that a natural object is associated also with a `
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straight line. Three points A, B and C on a rigid body thus lie in a `
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straight line when the points A and C being given, B is chosen such `
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that the sum of the distances AB and BC is as short as possible. This `
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incomplete suggestion will suffice for the present purpose. `
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