*Special Relativity and Classical Field Theory: The Theoretical Minimum* by Leonard Susskind and Art Friedman

The third book in Susskind’s Theoretical Minimum series (based off the video lectures here) covers special relativity and classical field theory, specifically electromagnetism (general relativity is the next planned book). It’s assumed the reader has read the first book in the series where things like the action, Lagrangian, and Hamiltonian are developed, but there’s still lots of review and hand-holding. Appendix B is a review of some vector calculus operations.

I thought this book was great, and is filled with a bunch of great nuggets even for somebody with a degree in physics. For example, one longstanding question I’ve had is why the Lagrangian only goes up to the first derivative of position (aside from the “It’s equivalent to Newton’s Second Law” cop-out). Susskind’s satisfying answer: it’s because of locality [1]. And just for fun, Appendix A is all about magnetic monopoles.

Speaking of locality, Susskind lists four fundamental principles that underlie all of physics, and then uses them directly in producing results in electromagnetism. That is he doesn’t just have an interesting philosophical discussion, but translates them into meat-and-potatoes mathematics and then uses them to solve problems. These principles are: the action principle, locality, Lorentz invariance, and gauge invariance.

This is my favorite so far of the Theoretical Minimum series. People who have only seen Maxwell’s equations developed to their vector calculus form that appears on T-shirts (for example, most engineers) will be guided to their “higher” formulation in terms of tensors. The connection between special relativity and electromagnetism is deep, and it’s with that connection that Einstein began (paragraph one!) his famous special relativity paper. With this book the reader will clearly see how once you observe that a current-carrying wire generates a magnetic field, special relativity necessarily follows.

Also, “GROUCHO!” 😄 (see p. 392)

[1] And from Coopersmith I got a satisfying answer to why the Lagrangian depends explicitly on the first derivative: it serves as an infinite set of “internal boundary conditions” to enforce continuity.