Anthony Zee, a theoretical physicist at UC Santa Barbara and the Kavli Institute, likes to put things in nutshells: we have his well-known Quantum Field Theory in a Nutshell as well as the book under review, Einstein Gravity in a Nutshell. It is of course arguable that these things, as so many others, should not be put into nutshells at all — indeed, all too often, when some one says something like, “let me put it in a nutshell,” he is either dissembling and performs a contradiction immediately following (by going on and on and on), or his attempt at making things pithily clear by means of concision ends up in a catastrophe of confusion: where are the details? But there are nutshells and there are nutshells, and Zee is a believer in very big nutshells: Quantum Theory in a Nutshell comes in at over 500 pages, and now Einstein Gravity in a Nutshell goes its predecessor some 300-plus pages better. I guess the idea is that these big subjects deserve to be presented in a coherent manner, with a unifying principle in place, as it were. And this is certainly descriptive of what we are dealing with in Zee’s books.
The present book is accordingly concerned with what Einstein provided to science in the form of his general theory of relativity (i.e., Einstein gravity — as Zee points out, the terms are synonymous). Its approach is perhaps somewhat idiosyncratic: Zee’s writing reads very much like the transcription of a lecture, modulo the printed mathematics of course. There is an undeniable element of purposed informality in the prose, meant to facilitate a more holistic learning experience.
Indeed, both of Zee’s books “in a nutshell” are extremely reader-friendly. UCLA’s Zvi Bern’s review of QFT in a Nutshell in Physics Today states that in his opinion “it is the ideal book for a graduate student to curl up with after having completed a course in quantum mechanics,” and the same youngster might curl up with a copy of the book under review after, presumably, a course in special relativity.
Zee is a bit more careful about the prerequisites for his audience. He describes it as consisting of “students enrolled in a course on general relativity, students and others indulging in the admirable practice of self-study, professional physicists in other research specialties who want to brush up, and readers of popular books on Einstein gravity who want to fly beyond the superficial discussions these books … offer.” It should be noted that mathematicians with interest in this business would probably be counted as admirable self-studiers and readers of popularizations now desiring to fly higher.
But this really masks a warning: Zee is not writing for us, he’s writing for our somewhat distant cousins, the physicists. And it shows, of course, on nearly every page of the book. To illustrate this reality, here is something, verbatim, from p. 36: “… we have introduced the Kronecker delta δkj, defined by δkj = 1 if k = j, δkj = 0 if k ≠ j (which we can think of as an ancestor of the Dirac delta function) …” and the Dirac delta function, already introduced on p. 27 as “an infinitely sharp spike” is then sterilized with the phrase “the precise form … does not matter.” I can’t resist a variation of a theme of George Bernard Shaw: mathematicians and physicists are truly separated by a common language.
Fine, then. With these caveats and kvetches in place, I must admit that, as its nutshell predecessor, Einstein Gravity in a Nutshell is very appealing to me, and I am certainly won over by Zee’s chatty but on-the-money style (bearing in mind that I am no one’s idea of a physicist). There is an awful lot in the book, or rather the books: the nutshell has three compartments, and it adds up to quite a ramified course. Book One is devoted to going “From Newton to Riemann: Coordinates to Curvature,” Book Two takes us “From the Happiest Thought to the Universe,” and finally Book Three deals with “Gravity at Work and at Play.” A propos, regarding this happiest thought, we read the following on p. 265
I was sitting in a chair in the patent office in Bern when all of a sudden a thought occurred to me: “If a person falls freely he will not feel his own weight.” I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation. (A. Einstein)
And there you have it. Be forewarned that it’s physics, not mathematics, all the differential geometry notwithstanding — the Einstein summation convention’s ubiquity is a tell-tale sign, and for me a somewhat painful one. But, as Feynman used to put it the book is full of “some [actually a lot!] of the good stuff.”
Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.