Reading Help Relativity: The Special and General Theory
Clickable text below...
Prev
Next Page #
`
` RELATIVITY: THE SPECIAL AND GENERAL THEORY `
` `
` BY ALBERT EINSTEIN `
` `
` `
` `
` `
` CONTENTS `
` `
` Preface `
` `
` Part I: The Special Theory of Relativity `
` `
` 01. Physical Meaning of Geometrical Propositions `
` 02. The System of Co-ordinates `
` 03. Space and Time in Classical Mechanics `
` 04. The Galileian System of Co-ordinates `
` 05. The Principle of Relativity (in the Restricted Sense) `
` 06. The Theorem of the Addition of Velocities employed in `
` Classical Mechanics `
` 07. The Apparent Incompatability of the Law of Propagation of `
` Light with the Principle of Relativity `
` 08. On the Idea of Time in Physics `
` 09. The Relativity of Simultaneity `
` 10. On the Relativity of the Conception of Distance `
` 11. The Lorentz Transformation `
` 12. The Behaviour of Measuring-Rods and Clocks in Motion `
` 13. Theorem of the Addition of Velocities. The Experiment of Fizeau `
` 14. The Hueristic Value of the Theory of Relativity `
` 15. General Results of the Theory `
` 16. Expereince and the Special Theory of Relativity `
` 17. Minkowski's Four-dimensial 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 `
` 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 `
` 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 Speical Theory of Relativity `
` Considered as a Euclidean Continuum `
` 27. The Space-Time Continuum of the General Theory of Relativity `
` is Not a Eculidean Continuum `
` 28. Exact Formulation of the General Principle of Relativity `
` 29. 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 `
` `
` 30. Cosmological Difficulties of Netwon's Theory `
` 31. The Possibility of a "Finite" and yet "Unbounded" Universe `
` 32. The Structure of Space According to the General Theory of `
` Relativity `
` `
` `
` Appendices: `
` `
` 01. Simple Derivation of the Lorentz Transformation (sup. ch. 11) `
` 02. Minkowski's Four-Dimensional Space ("World") (sup. ch 17) `
` 03. The Experimental Confirmation of the General Theory of Relativity `
` 04. The Structure of Space According to the General Theory of `
` Relativity (sup. ch 32) `
` 05. Relativity and the Problem of Space `
` `
` Note: The fifth Appendix was added by Einstein at the time of the `
` fifteenth re-printing of this book; and as a result is still under `
` copyright restrictions so cannot be added without the permission of `
` the publisher. `
` `
` `
` `
` PREFACE `
` `
` (December, 1916) `
` `
` 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 `
` `
` 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 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 "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 practice, for `
` example, of seeing in a "distance" two marked positions on a `
` practically rigid body is something which is lodged deeply in our `
` habit of thought. We are accustomed further to regard three points as `
` being situated on a straight line, if their apparent positions can be `
` made to coincide for observation with one eye, under suitable choice `
` of our place of observation. `
` `
` If, in pursuance of our habit of thought, we now supplement the `
` propositions of Euclidean geometry by the single proposition that two `
` points on a practically rigid body always correspond to the same `
` distance (line-interval), independently of any changes in position to `
` which we may subject the body, the propositions of Euclidean geometry `
` then resolve themselves into propositions on the possible relative `
` position of practically rigid bodies.* Geometry which has been `
` supplemented in this way is then to be treated as a branch of physics. `
` We can now legitimately ask as to the "truth" of geometrical `
` propositions interpreted in this way, since we are justified in asking `
` whether these propositions are satisfied for those real things we have `
` associated with the geometrical ideas. In less exact terms we can `
` express this by saying that by the "truth" of a geometrical `
` proposition in this sense we understand its validity for a `
` construction with rule and compasses. `
` `
` Of course the conviction of the "truth" of geometrical propositions in `
` this sense is founded exclusively on rather incomplete experience. For `
` the present we shall assume the "truth" of the geometrical `
` propositions, then at a later stage (in the general theory of `
` relativity) we shall see that this "truth" is limited, and we shall `
` consider the extent of its limitation. `
` `
` `
` Notes `
` `
` *) It follows that a natural object is associated also with a `
` straight line. Three points A, B and C on a rigid body thus lie in a `
` straight line when the points A and C being given, B is chosen such `
` that the sum of the distances AB and BC is as short as possible. This `
` incomplete suggestion will suffice for the present purpose. `
` `
`
` RELATIVITY: THE SPECIAL AND GENERAL THEORY `
` `
` BY ALBERT EINSTEIN `
` `
` `
` `
` `
` CONTENTS `
` `
` Preface `
` `
` Part I: The Special Theory of Relativity `
` `
` 01. Physical Meaning of Geometrical Propositions `
` 02. The System of Co-ordinates `
` 03. Space and Time in Classical Mechanics `
` 04. The Galileian System of Co-ordinates `
` 05. The Principle of Relativity (in the Restricted Sense) `
` 06. The Theorem of the Addition of Velocities employed in `
` Classical Mechanics `
` 07. The Apparent Incompatability of the Law of Propagation of `
` Light with the Principle of Relativity `
` 08. On the Idea of Time in Physics `
` 09. The Relativity of Simultaneity `
` 10. On the Relativity of the Conception of Distance `
` 11. The Lorentz Transformation `
` 12. The Behaviour of Measuring-Rods and Clocks in Motion `
` 13. Theorem of the Addition of Velocities. The Experiment of Fizeau `
` 14. The Hueristic Value of the Theory of Relativity `
` 15. General Results of the Theory `
` 16. Expereince and the Special Theory of Relativity `
` 17. Minkowski's Four-dimensial 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 `
` 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 `
` 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 Speical Theory of Relativity `
` Considered as a Euclidean Continuum `
` 27. The Space-Time Continuum of the General Theory of Relativity `
` is Not a Eculidean Continuum `
` 28. Exact Formulation of the General Principle of Relativity `
` 29. 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 `
` `
` 30. Cosmological Difficulties of Netwon's Theory `
` 31. The Possibility of a "Finite" and yet "Unbounded" Universe `
` 32. The Structure of Space According to the General Theory of `
` Relativity `
` `
` `
` Appendices: `
` `
` 01. Simple Derivation of the Lorentz Transformation (sup. ch. 11) `
` 02. Minkowski's Four-Dimensional Space ("World") (sup. ch 17) `
` 03. The Experimental Confirmation of the General Theory of Relativity `
` 04. The Structure of Space According to the General Theory of `
` Relativity (sup. ch 32) `
` 05. Relativity and the Problem of Space `
` `
` Note: The fifth Appendix was added by Einstein at the time of the `
` fifteenth re-printing of this book; and as a result is still under `
` copyright restrictions so cannot be added without the permission of `
` the publisher. `
` `
` `
` `
` PREFACE `
` `
` (December, 1916) `
` `
` 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 `
` `
` 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 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 "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 practice, for `
` example, of seeing in a "distance" two marked positions on a `
` practically rigid body is something which is lodged deeply in our `
` habit of thought. We are accustomed further to regard three points as `
` being situated on a straight line, if their apparent positions can be `
` made to coincide for observation with one eye, under suitable choice `
` of our place of observation. `
` `
` If, in pursuance of our habit of thought, we now supplement the `
` propositions of Euclidean geometry by the single proposition that two `
` points on a practically rigid body always correspond to the same `
` distance (line-interval), independently of any changes in position to `
` which we may subject the body, the propositions of Euclidean geometry `
` then resolve themselves into propositions on the possible relative `
` position of practically rigid bodies.* Geometry which has been `
` supplemented in this way is then to be treated as a branch of physics. `
` We can now legitimately ask as to the "truth" of geometrical `
` propositions interpreted in this way, since we are justified in asking `
` whether these propositions are satisfied for those real things we have `
` associated with the geometrical ideas. In less exact terms we can `
` express this by saying that by the "truth" of a geometrical `
` proposition in this sense we understand its validity for a `
` construction with rule and compasses. `
` `
` Of course the conviction of the "truth" of geometrical propositions in `
` this sense is founded exclusively on rather incomplete experience. For `
` the present we shall assume the "truth" of the geometrical `
` propositions, then at a later stage (in the general theory of `
` relativity) we shall see that this "truth" is limited, and we shall `
` consider the extent of its limitation. `
` `
` `
` Notes `
` `
` *) It follows that a natural object is associated also with a `
` straight line. Three points A, B and C on a rigid body thus lie in a `
` straight line when the points A and C being given, B is chosen such `
` that the sum of the distances AB and BC is as short as possible. This `
` incomplete suggestion will suffice for the present purpose. `
` `
`