The Einstein Theory Of Relativity

by Lillian R. Lieber

Text extracted from opening pages of 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 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 the Remedy 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 the 19th century, which led to the creation of the revolutionary 11 Relativity Theory? Let us summarize it 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

Genres: Science, Physics, Mathematics, Nonfiction, Unfinished, Reference

336 pages, Print on Demand (Paperback)

First published March 1, 2007

Reviews

[Emma · Rating 5 out of 5]

Wonderful!

If you're looking for a layman's introduction to Einstein's theory of relativity that doesn't (completely) gloss over the mathematical aspects then this book should be your go to.

The math itself is fairly easy to understand, though perhaps not for everyone. I think that genuine interest and some patience is really all that is required! (Thought if your math skills are rusty the book may provide a challenge)

I enjoyed working through this with my younger brother, and the illustrations and word formatting were particularly enjoyable! Though often the free verse (yes I know it's not supposed to be poetry) led to me a accidentally scanning a page instead of reading it- and subsequently having to reread it.

But all in all, a great book- a bit whimsical, very fun and VERY informative!

[Cassandra Kay Silva · Rating 5 out of 5]

Fucking brilliant book! This is exactly what I was looking for. I could feel myself getting excited as I started to mentally piece together Einstein's equations and logic for myself. Then about three quarters into it the Math started blowing my mind and I felt my head exploding. Perhaps I needed more differential calculus to understand that bit. I wanted to get out graphing paper and start calculating everything for myself but then again since it was all so well laid out in the book I just carried on and marveled at the beauty and simplicity of the findings. The only thing that was kind of unnerving was the sweet kind of cartoon drawings peppered throughout the work. As the math started to get harder the drawings felt like they were taunting you. Almost like this is kiddy stuff why can't you get it. You would look over at the bunny in the picture and think, damn you rabbit what do you know about time in space...which inevitably led to thinking about the book flatland and imagining what would have happened in flatland had the bunny been introduced. An entirely circular and unnecessary point. Obviously the page with the bunny on it was absolutely grueling.

[Robert Henderson · Rating 5 out of 5]

This is a strange and wonderful exposition of relativity for the intelligent layman and a quite unique book. I don't think there is anything like it. I have a copy of the 1949 edition which is set in a curious bold sans-serif typeface on thick paper and feels almost like a book of magic spells. This modern edition is a bit easier to read and has some addition notes. The line drawings by the author's husband are very surreal and reflect the air of mystery which surrounds the subject, I suppose because curved spacetime really is weird.
The text is laid out in short lines like poetry to 'facilitate rapid reading' and this does help make the explanations clearer. Special Relativity is well covered in Part 1, but the real meat is in Part 2.

No other popular book attempts to teach you the tensor calculus needed for General Relativity in this way, and I think this book succeeds very well. Lilian Lieber makes sure you understand every step. Even I almost understand it now! Inevitably, there are one or two things introduced which you just have to take on trust, such as the Christoffel symbols but, mostly, everything is stated clearly and derived before your very eyes. It is nice to have the deflection of light near the sun and motion of the perihelion of Mercury worked out instead of just being given the results.

This is a very special book and anyone with secondary school maths should be able to follow it easily. The author encourages you at every step. Even if you don't intend to follow the mathematics you should get a good feel for what General Relativity actually is, and understand how calculations are done with it.

[Calvin Tower · Rating 5 out of 5]

I wish this book was available while I was in school. This book does an excellent job at explaining Einsteins Theory of Relativity while also providing and explaining the mathematics behind it rather than drowning you in a swamp of mathematical gibberish. The first half of the book can be followed with an understanding of high school level math (although if you are like me you might find yourself having to review more than you expected), however the second half of the book gets into non-Euclidea geometry and probably requires you to either be currently taking college calculus or in a career where you use it on a daily basis if you have any hopes of already knowing and understanding the math and concepts behind it. Fortunately the author does a superb job of laying out arguments so that you can follow the concepts even if the mathematics are beyond you.

[Alexander Pettry · Rating 4 out of 5]

I would like to begin my review by saying that I have absolutely no knowledge of mathematics, let alone Einstein's theory of relativity. I just read this book for the sake of feeling smart. Honestly, for someone who has very little knowledge on any branch of mathematics, this book is a gem. In "The Einstein Theory of Relativity: A Trip to the Fourth Dimension", Lillian R. Lieber does a great job explaining the theory while offering illustrations. This is going to be a short review for obvious reasons but all I have to say is that it's a terrific book that does a superb job articulating the very complex history of the subject as well as the final theory. I highly recommend any mathematician or scientist to have a copy on their bookshelf, or anybody who's struggling in college.

[Sacha · Rating 5 out of 5]

Who knew relativity could be made so readable? Lillian's joy is palpable through these pages and the math is real.

Also read Infinity and The Education of T.C. MITS by the same author; they are not in the GR catalog (nor as good).

[Ron Wood · Rating 5 out of 5]

An attempt at a popular treatment of relativity including tensor mathematics. Not for the lay reader but should be looked at by anyone with an interest in the subject. A very unusual book.

[Rob · Rating 5 out of 5]

When I first picked up this book it looked odd - weirdly left-aligned text and hand-drawn pictures with scatterings of equations. How on earth would this work?!

Well it does. Spectacularly.

It is gentle at first in building your intuition for special relativity and spacetime but make no mistake, this is a challenging book for those who already have some physics background. On the spectrum of difficulty it is roughly equivalent to Susskind’s new Theoretical Minimum book on GR but it is far more conversational and whimsical, whereas the TM books read a bit more like lecture notes.

If you have a basic understanding of General Relativity from popular science books and you’re craving something deeper, this could be the perfect book for you. Also in that category is Sean Caroll’s Big Ideas Vol1 (broader in scope and not quite as deep) and Geroch’s book General Relativity from A to B (more on SR than GR but builds intuition with lots of spacetime diagrams which I found really useful).

[Bob Finch · Rating 5 out of 5]

This gem is a real tour de force. A true beginner-level introduction to Einstein Relativity, both special and general theories, each taken in turn. The book builds gradually to develop an understanding of the often complex mathematics required for Einstein’s Law of Gravity (notably tensor calculus). Not a casual read but greatly rewarding to the motivated reader. After having worked through several of this book’s explanations, I found more advanced texts considerably easier to follow.

[Jim · Rating 4 out of 5]

Quirky book written in 1936 about Einstein's Theories (there are actually two) of Relativity. I've always wanted to read this book since I saw it years ago. (Lillian Lieber was a math professor who wrote other quirky books, but lived mostly in obscurity, to the point that little is known about her life).

[Timothy Morrison]

Great job at explaining this theory of nullo space

[David S. T.]

I read about the first 50 pages and this book seems like a well written, mathematically based, advanced layman's introduction to relativity; but it requires more effort than I want to give at this time. I'll revisit this later.

[Alex Carlman · Rating 4 out of 5]

wonderful