The Einstein Theory of Relativity

Text extracted from opening pages of book: THE EINSTEIN THEORY OF RELATIVITY Text By LILLIAN R. LIEBER Drawings By HUGH GRAY LIEBER HOLT, RINEHART AND WINSTON New York / Chicago / San Francisco To FRANKLIN DELANO ROOSEVELT who saved the world from those forces of evil which sought to destroy Art and Science and the very Dignity of Man. PREFACE In this book on the Einstein Theory of Relativity the attempt is made to introduce just enough mathematics to HELP and NOT to HINDER the lay reader/ lay can of course apply to various domains of knowledge perhaps then we should say: the layman in Relativity. Many popular discussions of Relativity, without any mathematics at all, have been written. But we doubt whether even the best of these can possibly give to a novice an adequate idea of what it is all about. What is very clear when expressed in mathematical language sounds mystical in ordinary language. On the other hand, there are many discussions, including Einstein's own papers, which are accessible to the experts only. vii We believe that there is a class of readers who can get very little out of either of these two kinds of discussion readers who know enough about mathematics to follow a simple mathematical presentation of a domain new to them, built from the ground up, with sufficient details to bridge the gaps that exist FOR THEM in both the popular and the expert presentations. This book is an attempt to satisfy the needs of this kind of reader. viii CONTENTS PREFACE Part I - THE SPECIAL THEORY I. INTRODUCTION 3 II. The Michelson-Morley Experiment 8 III. Re-Examination of the Fundamental Ideas 20 IV. The Remedy 31 V. The Solution of the Difficulty 39 VI. The Result of Applying theRemedy 44 VII. The Four-Dimensional Space-Time Con tinuum 57 VIII. Some Consequences of the Theory of Relativity 69 IX. A Point of Logic and a Summary 83 The Moral 87 Part II - THE GENERAL THEORY A GUIDE TO PART II 91 X. Introduction 95 XI. The Principle of Equivalence 101 XII. A Non-Euclidean World! 107 XIII. The Study of Spaces 113 XIV. What Is a Tensor? 127 XV. The Effect on Tensors of a Change in the Coordinate System 1 41 XVI. A Very Helpful Simplification 150 ix XVII. Operations with Tense-160 XVIII. A Physical Illustration 167 XIX. Mixed Tensors 173 XX. Contraction and Differentiation 1 78 XXI. The Little g's 187 XXII. Our Last Detour 191 XXIII. The Curvature Tensor at Last 200 XXIV. Of What Use Is the Curvature Tensor? 206 XXV. The Big G's or Einstein's Law of Gravitation 21 3 XXVI. Comparison of Einstein's Law of Gravitation with Newton's 219 XXVII. How Can the Einstein Law of Gravitation Be Tested? 227 XXVIII. Surmounting the Difficulties 237 XXIX. The Proof of the Pudding 255 XXX. More About the Path of a Planet 266 XXXI. The Perihelion of Mercury 272 XXXII. Deflection of a Ray of Light 276 XXXIII. Deflection of a Ray of Light, cont. 283 XXXIV. The Third of the Crucial Phenomena 289 XXXV. Summary 299 The Moral 303 Would You Like to Know? 310 THE ATOMIC BOMB 318 Parti THE SPECIAL THEORY I. INTRODUCTION. In order to appreciate the fundamental importance of Relativity, it is necessary to know how it arose. Whenever a revolution 11 takes place, in any domain, it is always preceded by some maladjustment producing a tension, which ultimately causes a break, followed by a greater stability at least for the time being. What was the maladjustment in Physics in the latter part of the19th century, which led to the creation of the revolutionary 11 Relativity Theory? Let us summarize it briefly: It has been assumed that all space is filled with ether, * through which radio waves and light waves are transmitted any modern child talks quite glibly * This ether is of course NOT the chemical ether which surgeons use! ft is not a liquid, solid, or gas, it has never been seen by anybody, its presence is only conjectured because of the need for some medium to transmit radio and light waves. 3