The Theoretical Minimum: What You Need To Know To Start Doing Physics, by Leonard Susskind and Geoge Hrabovsky

When I first looked at this book, I thought that this book was about the theoretical minimum relating to physics that people needed to know to be a well-rounded or scientifically literate person. Thankfully, this is not the case, as this book is pretty tough sledding, and likely will be for the vast majority of readers. It is testament to the way in which physicists are out of touch with the general mathematics knowledge (and interest) of the general population that they consider this book to be a minimum rather than as being closer to a maximum of the level of physics that anyone who did not study it intensively in college/at university could ever dare to remember. I took plenty of statics and mechanics and a couple of classes of physics myself, and this math was at the border of my own ability to recognize what the authors were doing and why, and if that is the case, then those whose mathematics skills are much lower than my own are not even going to understand what is going on here. This is not auspicious for being a minimum of any kind, even of the modest kind the authors intend–for how many people want to do physics anyway? What does it even mean to do physics and why would anyone want to, at least as the authors envision it?

This book is a bit more than 200 pages in length, but it feels far longer when your eyes strain at the mathematics of the book trying to understand it. The authors organize this book in the form of lectures, of which there are eleven lectures and interludes after the first 3 lectures that give additional math for the reader to wrap their heads around. The lectures all begin with some sort of joke, often involving bars or drinking (which one will likely need to do a lot of to get through this book). After a short preface the book begins with a lecture on the nature of classical physics and an interlude on spacers, trigonometry, and vectors (1). The second lecture, on motion, is followed by a discussion on integral calculus, which makes sense since the velocity of an object is the first derivative of the position and the acceleration is the first derivative of the velocity (2). The third lecture deals with dynamics (3), followed by an interlude on partial differentials, which again makes sense in light of the contents. This is followed by a discussion of systems of more than one particle (4) and energy (5). After this point the lectures get increasingly more difficult to understand, starting with the principle of least action (6), various symmetries and conservation laws (including a negative -1st conservation law) (7), Hamiltonian mechanics and time-transition invariance (8), the phase space fluid and the Gibbs-Lionville theorem (9), Poisson brackets, angular momentum, and more about symmetries (10), and electric and magnetic forces (11), which gets the reader to the state of classical physics just before the rise of quantum mechanics. There is an appendix on central forces and planetary orbits and then an index.

This book is the first book of a series of books, and this became obvious to me as I read the book and was increasingly concerned when the authors stated that some point would be discussed in a future volume, indicating that while this book is a very ambitious achievement on its own for anyone to attain, it is the first of at least four books or more in a series that are theoretical minimums of other types of physics. Indeed, this book is as hard as it is and as demanding and ambitious as it is not because the material here is necessary in order to do classical mechanics, which requires far less knowledge, but because the authors are setting up the mathematics necessary to do quantum mechanics, which is far beyond the level most people would want to go. For the authors, it appears that doing physics means being scientifically aware of the complexities of quantum mechanics and able to understand the mathematics of phase space that make it possible to make some sort of conclusions about matters that are on the edge of scientific understanding, and well beyond the imagination or worst nightmares of the vast majority of the public. Given the sort of mathematics that is included here, this book is a theoretical minimum only to a theoretical physicist who dreams, as these authors comment in their introduction, that one could write a book that included all of what a physicist would want others to know about physics, which would then be a far more massive book than this one. What physicists call dreams is what the rest of the people of the world call their worst nightmares, alas.