|Chapter 1: The History of Relativity
|Chapter 2: The Speed of Light
|Chapter 3: The Invariant Interval and the Lorentz Transform
|Chapter 4: Applications of Derivatives
|Appendix 1: The Greek Alphabet
|Appendix 2: Physical Units
Although there are many books available on the topic of special relativity, I find them all disappointing. There are books for the general public, but without math one cannot really understand this theory at any but the most rudimentary levels. The books written at the undergraduate level are unstatisfying to me because they do not teach you how to work problems. At the graduate level most of this information is available, but it's scattered over a dozen different books, each seemingly with a unique notation. I wrote this book so that there would be one book that covered all of special relativity.
Physics was developed by people, and therefore is permeated with the personalities of the greatest of the physicists, if you know how to look. Ernst Mach taught us that we should speak only of things that are measurable, and that effects in our universe have causes which are within our universe. Einstein was not confortable with abstract mathematics, and therefore avoided topics like group theory and differential forms ("Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.") He taught that things should be as simple as possible, but no simpler. Another important influence in modern physics is Hans Bethe, who taught firmly that unless you can solve problems and predict numbers, you're not doing physics. Bethe's influence comes to us not only through his own work, but through his collegues at Cornell and through Richard Feynman. This book is written very much in the spirit of these men.
This book is divided into sections. Not all readers will be interested in all sections.
Chapters 1, 2, and 3 are a simple introduction to relativity at an advanced high school or lower division college level. Only basic algebra is presumed.
Chapters 4, 5, and 6 work in vector and tensor notation. This is written at an advanced upper-division or graduate level.
Chapters 7, 8, and 9 are kinematics, useful at the graduate level for people who will be working problems.
Chapters 10, 11, and 12 are the relativistic theory of the electromagnetic field. This is important for anyone moving on in quantum field theory or general relativity.
Chapters 13 and 14 explore relativity in alternative spaces, useful at the graduate level for people going on to quantum field theory.
This book is based on notes I took in classes taught by William Wagner and John Nodvik at USC; Mark Wise at Caltech; Steven Carlip at UC Davis; and Graciela Gelmini at UCLA.