Here, however, the reader may be reminded that even for those who are interested solely in trends of thought or in the evolution of ideas, no popular or semi-popular book can ever aspire to take the place of the highly technical mathematical works. The superiority of the latter lies not in the bare mathematical formulæ which they contain. Rather does it reside in the power the mathematical instrument has of giving us a deeper insight into the problems of nature, revealing unsuspected harmonies and extending our survey into regions of thought whence the human intelligence would otherwise be excluded. Thus the sole rôle a semi-popular book can hope to perform is to serve as a general introduction, to whet the appetite for further knowledge, if a craving for knowledge is within us. To presume, as the philosophers do, that a vague understanding of a highly technical subject, gleaned from semi-popular writings, or from the snatching at a sentence here and there in a technical book, should enable them to expound a theory, criticise it, and, worse still, ornament it with their own ideas, is an opinion which has done much to create a spirit of distrust towards their writings. The answer Euclid gave to King Ptolemy, “There is no royal road, no short cut to knowledge,” remains true to-day, still truer than in the days of ancient Alexandria, when science had not yet grown to the proportions of a mighty tree.
I wish to take this opportunity to express my gratitude to Prof. Leigh Page of Yale University for his kindness in looking over the manuscript and offering many valuable suggestions.
A. D’ Abro.
NEW YORK, 1927.
CONTENTS
| PAGE | ||
| FOREWORD | [ix] | |
| PART I | ||
| PRE-RELATIVITY PHYSICS | ||
| CHAPTER | ||
| I. MANIFOLDS | [23] | |
| II. THE BIRTH OF METRICAL GEOMETRY | [32] | |
| III. RIEMANN’S DISCOVERIES AND CONGRUENCE | [39] | |
| IV. THE PROBLEM OF PHYSICAL SPACE | [47] | |
| V. AN ALTERNATIVE VIEW OF NON-EUCLIDEAN GEOMETRIES | [60] | |
| VI. TIME | [71] | |
| VII. SYSTEMS OF CO-ORDINATES AND DISTANCE | [83] | |
| VIII. THE MEANING OF THE WORD RELATIVITY | [99] | |
| IX. THE PRINCIPLES OF RELATIVITY | [103] | |
| X. CLASSICAL MECHANICS AND THE NEWTONIAN PRINCIPLE OF RELATIVITY | [106] | |
| XI. THE ETHER | [116] | |
| XII. THE EQUATIONS OF ELECTROMAGNETICS AND LORENTZ’S THEORY | [125] | |
| PART II | ||
| THE SPECIAL THEORY OF RELATIVITY | ||
| XIII. EINSTEIN’S SPECIAL THEORY OF RELATIVITY | [143] | |
| XIV. RELATIVISTIC MECHANICS | [156] | |
| XV. CONSEQUENCES OF THE NEW SPACE AND TIME MEASUREMENTS—SIMULTANEITY | [161] | |
| XVI. PRACTICAL CONGRUENCE IN RELATIVITY | [187] | |
| XVII. THE MATHEMATICAL EXPRESSION OF EINSTEIN’S FUNDAMENTAL PREMISES | [193] | |
| XVIII. THE DISCOVERY OF SPACE-TIME | [195] | |
| XIX. VARIOUS POSSIBLE WORLDS | [201] | |
| XX. THE IRREVERSIBILITY OF TIME | [212] | |
| XXI. THE REALITY OF THE CONTRACTION OF LENGTHS AND OF THE LENGTHENING OF DURATIONS | [219] | |
| XXII. THE PARADOXES ASSOCIATED WITH SPACE-TIME AND THE TRIP TO THE STAR | [225] | |
| PART III | ||
| THE GENERAL THEORY OF RELATIVITY | ||
| XXIII. POTENTIALS AND FORCES | [245] | |
| XXIV. THE POSTULATE OF EQUIVALENCE | [250] | |
| XXV. THE INCLUSION OF GRAVITATION IN THE MODEL OF SPACE-TIME | [261] | |
| XXVI. TENSORS AND THE LAWS OF NATURE | [266] | |
| XXVII. THE PRINCIPLE OF GENERAL COVARIANCE, OR THE GENERAL PRINCIPLE OF RELATIVITY | [276] | |
| XXVIII. THE DISCOVERY OF THE EINSTEINIAN LAW OF GRAVITATION | [281] | |
| XXIX. THE GENERAL LAWS OF MOTION | [286] | |
| XXX. THE VERIFICATION OF EINSTEIN’S LAW | [290] | |
| XXXI. THE SEPARATION OF SPACE-TIME INTO SPACE AND TIME IN A GRAVITATIONAL FIELD | [293] | |
| XXXII. THE PRINCIPLES OF CONSERVATION | [305] | |
| XXXIII. OTHER ASPECTS OF THE GRAVITATIONAL EQUATIONS | [310] | |
| XXXIV. THE FINITENESS OF THE UNIVERSE | [313] | |
| XXXV. THE IMPORTANCE OF SPACE-TIME, AND THE PRINCIPLE OF ACTION | [347] | |
| XXXVI. THE MYSTERY OF MATTER | [356] | |
| XXXVII. THE THEORIES OF WEYL AND EDDINGTON | [360] | |
| PART IV | ||
| THE METHODOLOGY OF SCIENCE | ||
| XXXVIII. THE METHODOLOGY OF SCIENCE | [373] | |
| XXXIX. THE CO-ORDINATION OF PHYSICAL FACTS ACCOMPLISHED BY RELATIVITY | [474] | |
| XL. THE GENERAL SIGNIFICANCE OF THE THEORY OF RELATIVITY | [481] | |
| APPENDICES | ||
| I. THE SPACE AND TIME GRAPHS | [509] | |
| II. THE CURVATURES OF SPACE-TIME | [524] | |
| III. THE GRAVITATIONAL EQUATIONS | [527] | |
| IV. SPACE, GRAVITATION AND SPACE-TIME | [531] |
FOREWORD
“And now, in our time, there has been unloosed a cataclysm which has swept away space, time and matter, hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope, and entailing a deeper vision.”
H. WEYL (“Space, Time and Matter”).
THE theory of relativity represents the greatest advance in our understanding of nature that philosophy has yet witnessed.