Anthony Zee: Einstein Gravity in a Nutshell

Škoda is not just a carmaker; it is producing happy drivers. And you may see that even the engines in the factory are having a great time.

In the same way, Anthony Zee – as Zvi Bern noticed – decided to make many readers fall in love with the physics of general relativity by having written this wonderful tome, Einstein Gravity in a Nutshell. Bern said that the goal wasn't to create new experts but Zee corrected him that he wanted to make the readers fall in love so deeply that they may dream about becoming experts, too. And the clearly enthusiastic Anthony had to enjoy the writing of the book, too.

I received this large, almost 900-page scripture on Einstein's theory yesterday. Obviously, I haven't read the whole book yet but I may have spent more time with it than most readers (more than zero) so that I can tell you why you should buy it and what philosophy, style, and content you may expect.




It's a book addressed to a wide variety of readers, including very young ones (perhaps college freshmen and bright high school students) and amateur physicists. Experienced physicists and professionals may find some gems or at least entertainment in the book, too. Because of this goal, the book starts with elementary things such as the units including \(G,c,\hbar\) and Planck units, relativity even in classical physics, as well as basics of curved spaces, differential geometry, and so on.




The style is witty and somewhat dominated by words – and amusing titles. You may find lots of philosophical and historical remarks and stories from Anthony's professional life but the physics is always primary. And I mean physics, not rigorous mathematics. Tony is focusing on objects, phenomena, and their measurable and calculable quantities and the purpose of physics is to understand them and calculate them. So he spends almost no time with various picky issues – whether a function has to be smooth; whether one should use one fancy word from abstract mathematics or another. In fact, he considers the suppressed role of rigorous maths to be a part of the "shut up and calculate" paradigm that he subscribes to.

In some sense, you could say that the approach resembles the Feynman Lectures on Physics. It is very playful and the author is always careful to tell you think that are still fun and stop elaborating on details when he could start to bore you. So the book (probably) keeps its fun status at every place (it's true for the portions I have read). But Anthony Zee manages to penetrate much more deeply into general relativity with this strategy.

Once he goes through all the basics – which allow a beginner to start with the subject almost from scratch but which seem very entertaining for a reader who doesn't really need such introductions anymore – and he answers all the FAQs on tensors and lots of other things, he offers some of the simplest derivations of Einstein's equations and is ready to apply them.

It's useful to know what concepts are considered primary starting points by the author. I would say that Zee is elevating the concept of symmetries and the action – the latter allows us to formulate most dynamical laws in classical and quantum physics really concisely (although we know perfectly consistent quantum systems that don't seem to have any nice action; and the action always assumes that we prefer a particular classical limit of a quantum theory – and the classical limit isn't necessarily unique).

Concerning the applications, some of the historically important applications that were designed to verify the theory are suppressed. But you get very close to the cutting edge, including the general-relativistic aspects of topics that are hot in the contemporary high-energy theoretical physics and the cosmological/particle-physics interface. So you may actually learn advanced topics about black holes including some Hawking radiation (including the numerical prefactors of the temperature; but the author doesn't go extremely far here; note that amusingly enough, the Hawking radiation is even discussed in an introductory chapter); large and warped extra dimensions; de Sitter and anti de Sitter space including a discussion of conformal transformations (although it doesn't seem like a full-fledged textbook on AdS/CFT); topological field theories; Kaluza-Klein theory (with extra spatial dimensions) and braneworlds; Yang-Mills theory (there's lots of electromagnetism in the earlier chapters); even twistor theory; discussions on the cosmic inflation and the cosmological constant problem; and heuristic thoughts on quantum gravity (some of them are more heuristic than the state-of-the-art allows us; but Zee's philosophy is that textbook shouldn't be composed exclusively of the totally established stuff ready to be carved in stone).

Using lots of witticisms and clever analogies, Zee also proves some things you wouldn't expect – e.g. that Hades isn't inside the Earth. The equivalence principle is compared to the decision of all airlines, regardless of the size (and the size of their aircraft), to fly between two distant cities along the same path on the map. Witty and apt.

Anthony is convinced that most authors are explaining things in unnecessarily complicated ways – in some cases, perhaps, they want to look smart by looking incomprehensible. That's not Zee's cup of tea. He enjoys to simplify things as much as possible (but not more than that). And he loves to formulate things so that the reader is led to the conclusion that things are simple and make sense, after all. For example, there is a fun introduction to the least action principle (light isn't stupid enough not to know the best path) and we learn that "after Lagrange invented the Lagrangian, Hamilton invented the Hamiltonian". It makes sense, doesn't it?

There's a lot to find in the book. Some readers say that the book is less elementary than Hartle's book but more elementary than Carroll's. Maybe. Anthony is more playful and less formal but there are aspects in which he gets further than any other introductory textbook of GR.

The book is full of notes, a long index, and simply clever exercises. The illustrations are pretty and professional. If you are buying books to see photographs of attractive blonde women with toys, you won't be disappointed, either.

Because the book is really extensive and even the impressions it has made on your humble correspondent in the single day are numerous, I have to resist the temptation to offer you examples, excerpts etc. because that could make this blog entry really long by itself. Instead, I recommend you once again to try the book.