©William O. Straub, 2014


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Who Was Hermann Weyl?
Wheeler's Tribute to Weyl (PDF)

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Weyl's Spinor and Dirac's Equation
Weyl's Conformal Tensor
Weyl Conformal Gravity
Weyl's 1918 Theory
Weyl's 1918 Theory Revisited
Weyl v. Schroedinger
Why Did Weyl's Theory Fail?
Weyl and the Aharonov-Bohm Effect
Weyl's Scale Factor
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Weyl and Higgs Theory
Lorentz Transformation of Weyl Spinors
Riemannian Vectors in Weyl Space
Introduction to Quantum Field Theory
Electron Spin
Clebsch-Gordan Calculator
Bell's Inequality
The Four-Frequency of Light
There Must Be a Magnetic Field!
Kaluza-Klein Theory
A Brief Look at Gaussian Integrals

Kets, Bras and All That
General Relativity
God and Physics
God and Light

Particle Chart (Courtesy CPEP)

Einstein's 1931 Pasadena Home Today


Uncommon Valor

Sophie did not forget Jesus
Long live freedom!

Gravitation
Charles W. Misner, Kip S. Thorne, John A. Wheeler
W. H. Freeman and Company, 1973


I found this book in a public library in the little town of Lone Pine, California, in 1975. The book had absolutely no business being there, wedged as it was among ancient Readers Digest book abridgments, crumbling National Geographics, and the usual assortment of old donated tomes that inevitably end their lives in rural libraries such as this. But however it got there, I'm not complaining. The book really changed my life. 

At first glance, Gravitation is daunting reading. Your first impression will probably be colored by the fact that it weighs about six pounds and takes up almost 1,300 pages. If you have no mathematical training beyond algebra, then forget about it. But if you've ever wanted to learn general relativity, this is it -- the official version, the Bible of gravity, spacetime and cosmology. It's all there, and in modern mathematical notation. Like the real Bible, books like this are good for the soul. No doubt, Riemann and Einstein would have been proud.

The book's chapters appear to cover the minimum of what one would expect from a text such as this: flat and curved spacetime physics, Einstein's gravitational equations, relativistic star formation, the evolution of the universe, gravitational collapse, gravity waves, and experimental tests of general relativity. However, the book's depth of coverage on these topics is impressive to say the least.

The book's subjects are developed along two tracks: Track 1 is focused on key physical ideas, while Track 2 is intended as an enriched and expanded version of the Track 1 material. The authors state that the entire book is suitable for a rigorous, one-year course at the graduate level, but for the life of me I can't see anyone getting through the book's 1,300 pages of rigorous mathematics in that short period of time. 

An interesting approach to learning is the authors' description of the mathematics and notation of differential geometry and general relativity. They present various mathematical objects almost as machines or engines, which provides a unique view as to how these quantities actually function. Another pleasant aspect of the book is its wonderful graphics which, unfortunately for me, were rather hard to grasp at times. The book also provides many biographical sketches of those scientists who were most responsible for the development of general relativity and its mathematics. The book is also replete with many tables, boxes and other sidebar material containing data that you'll not likely see anywhere else (one box actually made me cheer: "Farewell to
x4 = ict"). Finally, the book's authors write with clarity and ingenuity, with much cleverness and wit thrown in, and there's also the occasional use of prose and poetry, all very appropriate for a book whose main subject is as much philosophy as it is physics. 

As far as gauge invariance is concerned, you'll have to do some digging. There's some material on geometric gauge transformations and the invariance of Einstein's equations in the weak-field limit, but nothing specific to Weyl's 1918 work. While the book's index is comprehensive, I still found it hard to track down specific topics. 

If you're new to general relativity, I would suggest you find another less demanding book in order to prepare for this one. By far the best one I've found to date is Adler-Bazin-Schiffer's Introduction to General Relativity. The book's mathematical notation is not as modern as Gravitation, but it's far easier to understand for the novice.