Einstein Theory of Relativity

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Einstein Theory of Relativity

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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. 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.
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 the Remedy 44
VII. The Four-Dimensional Space-Time Continuum 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
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