Fly by Night Physics is a delightful romp through a remarkable range of fascinating physics topics, using straightforward tools and intuition to understand problems without deriving or relying on complicated equations.” I wrote that for a back-cover blurb after reading pre-publication excerpts and I still feel that way after reading the entire book.

The book is written in a fun conversational style, with frequent asides and endnotes, ranging from the tongue-in-cheek to the historic or bibliographic. In fact, my harshest complaint is that the endnotes were not footnotes, as I had to keep flipping back and forth to read them. It is aimed at the advanced undergraduate, and the math is relatively simple (some calculus, a LOT of symmetry arguments, and many references to the “dull function hypothesis”). However, the physics ranges from the simple to the utterly profound and even senior faculty will learn a lot.

Zee aims to show us how to determine (not derive!) equations from fundamental principles and then how to extract maximum knowledge from those equations without solving them analytically. This is similar in spirit to Sanjoy Mahajan's The Art of Insight in Physics and Engineering.1 However, while Mahajan focuses on presenting and categorizing the many different techniques (Guesstimation, dimensional analysis, lumping, etc.), Zee focuses on the physics.

The first chapter discusses dimensional analysis (without getting into the details of the Buckingham Pi theorem) and shows the power of the technique. He starts with the internet meme “Welcome to Dum Dum Town, home of the Angry Ducks, founded 1869, population 12, elevation 233 feet, total 2114” to show the importance of units, quickly derives the period of a pendulum $T∝l/g$, and then argues for using the angular frequency $ω$ (rather than T or f) as being more natural (and thereby avoiding large factors such as $2π$). He introduces the “dull function hypothesis” to argue that while dimensional analysis tells us that $ω=f(θ)$ (since $θ$ is dimensionless, dimensional analysis tells us nothing about $f(θ))$, $f(θ)$ should be a dull function and that we can expect it to be of order unity. The rest of the chapter is a lightning tour applying dimensional analysis to Kepler's law, black holes, the hydrogen atom and the uncertainty principle, diffusion, and the energy released by the first atomic bomb test. He then uses the dull function hypothesis and symmetry to show how to plausibly interpolate between known endpoints of an unknown function.

He presents very deep arguments in a disarmingly straightforward (but neither “obvious” nor “simple”) manner. For example, when discussing electromagnetism, he shows how to guess the Lagrangian density by invoking symmetries (rotational, time reversal, and parity) to argue that it must be a linear combination of E2 and B2 (using c =1) and since the sum (E2 + B2) is already taken (it's the energy density), it must be the difference $L∝(E2−B2)$. He also shows how electromagnetic waves can propagate. The Coulomb field drops off as $1/r2$ because of $∇→ϕ$ and $ϕ∝1/r$. If the electromagnetic wave also dropped off as $1/r2$, then the energy per unit time passing through a sphere would vanish rapidly with increasing r, which must be wrong. The resolution comes from $∇→$ operating on the $eikr$ term which gives the factor of $k∝1/λ$ so that the electric field decreases as 1/r, not 1/r2. Similarly, the extra factor of 1/r is replaced by c2/a in the Larmor radiation formula.

Later chapters show the range of problems that can be attacked. He discusses natural units in Chapter 4, where we can define all three basic units (length, time, and mass) in terms of the three fundamental constants (G, c, and $ℏ$), freeing us from artificial human creations. (There is also an amusing diatribe against the Boltzmann constant kB, on the grounds that temperature is just an energy scale and kB exists solely to relate this energy scale to “quaint markings on a tube of mercury.”) The Cube of Physics then shows the interrelationship among various fields, starting with Newtonian mechanics and “turning on” G, 1/c, and $ℏ$ in turn, to get Newtonian gravity, Einsteinian mechanics, and quantum mechanics, ending up with quantum gravity when all are turned on. As a callow sophomore, a similar cube (using relativity, quantization, and finite vs infinite degrees of freedom—the last distinguishing between particle theories and field theories) showed me the beautiful unity of physics and helped convince me to become a physicist.

There is something here for everyone [except people wedded to rigorous derivations (but they stopped reading this review long ago)]. Those of us who love gee-whiz topics will appreciate his discussions of black-hole entropy, Hawking radiation, and quantum gravity. Those of us who love the physics of the mundane world will appreciate his discussions of water waves, from gravity waves to surface-tension waves (aka ripples), and other applications of surface tension, from dripping faucets to the optimal size of alveoli in our lungs.

I tell students in my Guesstimation class to “dare to be imprecise.” He writes “In physics as in life, it pays to know when one can afford to be sloppy.” This book should help all of us improve our physics intuition and to better appreciate when and where to be sloppy.

1.
Sanjoy
Mahajan
,
The Art of Insight in Physics and Engineering
(
MIT Press
,
Cambridge, MA
,
2014
).

Lawrence Weinstein is a professor of physics at Old Dominion University, and the author of Guesstimation: Solving the World's Problems on the Back of an Envelope (with John Adam), Guesstimation 2.0, and The Great Courses video course Nuclear Physics Explained. In his spare time, he smashes atoms at the Thomas Jefferson National Accelerator Facility, for which he was named an APS Fellow.