## Mansoulié: All of Physics

June 25, 2020

All of Physics (Almost) in 15 Equations
Bruno Mansoulié
(World Scientific, 2017)
138 p.

The usual rule in popular science writing is “No Equations!” Sometimes additional exclamation marks are added. But Bruno Mansoulié has taken the opposite tack and structured his little book around a curated set of basic equations that summarize many of the principal ideas of physics. He presents each equation and then, in the space of 5 or 8 pages, describes what it means, explains how it came about or what deep ideas it is connected to, or tells us a story about how the equation has affected his own life.

A good exercise, before opening the book, is to try to guess which 15 equations he chose, or to write down which 15 you would choose were you the author. Some of his are natural choices: Newton’s second law, the law of universal gravitation, the mass-energy equivalence, the Schrodinger equation, the Heisenberg Uncertainty Principle, and Maxwell’s equations. They are either pillars of the discipline or famous in their own right for the insights they encapsulate.

But the non-obvious choices are also interesting. We get one equation for thermodynamics (the ideal gas law) and one for fluid mechanics (Navier-Stokes equation [ugh!]). He opens the book with the laws of reflection and refraction, the former allowing him to reflect on the relationship between heuristics (like the law of reflection) and thorough understanding of the underlying physics (which in this case requires an advanced course in electromagnetism), and the latter providing a springboard to introduce the principle of least action, one of the deepest ideas in all of physics. He also spends time on the Einstein field equations of General Relativity (blessed be they), Feynman diagrams (which are pictorial representations of equations), and, at the end, the “Theory of Everything equation” that is, as yet, undiscovered, and may not exist.

Although the book is pitched at a general readership, and is gentle in a soft-vowel, French-professor way, there are nooks and crannies the full charm of which can, I am convinced, be appreciated only by a fellow physicist. A chapter on Maxwell’s equations contains a sweetly affectionate tribute to Jackson’s famous textbook on the subject, which many graduate students (yours truly included) have wrestled with, and the chapter on the Dirac equation (“the most beautiful, the purest of all”) won my heart as it swooned over the equation’s very typography:

the harmonious roundness of the $\gamma$, the gentleness of the $\partial$, the sharpness of the first $i$, the delicateness of the $\mu$ indices set like appoggiaturas, and the deep mystery of the $\psi$.

It’s that kind of book: appreciative, open to wonder, musing, personal, occasionally philosophical, and sometimes digressive, and it’s a pleasant read too.