# Fearful Symmetry: The Search for Beauty in Modern Physics

This is the paperback edition of a classic from 1986 (Macmillan), later published by Princeton University Press (1999) to which a Foreword by Penrose was added in 2007 and an Afterword by the author. In the latter he briefly surveys the evolution of physics in the period 1986-2007 and some afterthoughts about the necessity of symmetry and beliefs of theoretical physicists. The Afterword has an extensive appendix with some problems, doubts, and diverging visions on supersymmetry and string theory. This edition of the book is now part of the Princeton Science Library collection.

In this book Zee is explaining how the physicists of the twentieth century have partly designed their theory on a mathematical basis and partly verified experimentally that there is the need for this whole zoo of particles and their interactions. It should be clear that the book describes the history and the situation until the moment the book was written in 1986. Clearly physics did not stop there and experimental and theoretical physics still progress, although a final solution to the problems that Zee sketches at the end of his book is still in the making: the ambition to designing the GUT (Grand Unifying Theory) and the role played by string theory, supersymmetry and the likes. Still it is most inspiring to read the book and to learn how physicists arrived at the formulation of such goals. It is written for anyone who is curious about all these fundamental particles our universe is made of and how they have evolved since this universe came into existence.

The thread throughout the book is symmetry. It is not only the title of the book, also the subtitle of the book is *The Search for Beauty in Modern Physics* which obviously refers to the well known *Tyger! Tyger!* verses by William Blake. The latter better emphasizes that it is not so much the hard mathematics that are put on the foreground but more the beauty and the mystery of this symmetry in nature. Blake's poem is often interpreted as unifying the beauty of the design and the ferocity of the animal in the mind of the creator who has put both aspects into this creature. Similarly Zee is asking *What immortal hand or eye could frame thy fearful symmetry?* by questioning the Designer of our universe why He has made it the way it is with all its complexity, and yet with all the stylistic beauty of the underlying symmetry. Zee concludes it is the task of the physicists to unravel and understand His design.

What this symmetry means has to be understood in a general mathematical sense. If something has rotational symmetry, then it means that it looks basically the same after rotation. It is rotation invariant. Therefore symmetry of a physical theory means here that it is invariant for some transformation. Symmetry seemed to govern the physics until in the 1950's it was experimentally verified that spin parity in connection with weak interaction was broken. This could be resolved by introducing antiparticles giving a kind of mirror symmetry. Next Einstein's special and general relativity is introduced which replaced Galilean invariance of Newtonian physics with Lorentzian invariance in Minkowski space for the special theory and general covariance when gravitation and fields are involved in general relativity. In the nineteenth century symmetry followed from models designed from observations, in the twentieth century it is (abstract) symmetry that defines the physical models which are verified by experiments. Conservation laws were the subject of trial and error to know what exactly was conserved. This was solved by Emmy Noether who introduced invariance under gauge symmetry. At this point Zee introduces some elements from group theory and their representations. Also quantum theory is coming into the picture and there the symmetry not only defines the underlying laws, but also the possible physical states.

Now the symmetry tornado is unleashed and the forest of subnuclear particles enter the stage. Heisenberg's isospin is a quantum construct to classify the subnuclear particles while avoiding the need of strong interaction. Then Yang and Mills came with their non-abelian gauge theory to the rescue of symmetry in the classical sense of Einstein. The Yang-Mills theory generalizes the gauge symmetry of Weyl and Noether. Here Zee's account becomes a bit personal since he was involved in developing the theory. Another phenomenon, spontaneous symmetry breaking, seemed to end the dictatorship of symmetry but physicists embarked on the construction of a GUT. The next step is supersymmetry to include all four fundamental actions: electromagnetic, strong and weak interaction, and ultimately also gravity. Unobservable curled up dimensions are loaned from the geometry of Kaluza-Klein theory and symmetry is reinstated. A last chapter is devoted to the overall role of symmetry: what was the Mind of the Creator? Is symmetry so restrictive that eventually there is only one Design possible?

Symmetry has fascinated mankind since antiquity and many books deal with the subject. The book under review is reminiscent of the book by Ian Stewart and Martin Golubitsky with the similar title *Fearful Symmetry: Is God a Geometer?* (1992) but the latter is broader reflecting on symmetry and non-symmetry appearing in nature, and not only in particle physics. That is more in the style of the book *Symmetry* by Hermann Weyl (1983), now available in the same Princeton Collection as the book under review. More confined to the realm of theoretical physics and much more recent is *A Beautiful Question* by Frank Wilczek (2015) which is close to this book. And there are of course many many more.

Zee succeeds in showing that the symmetry, a concept fully developed in mathematics, has driven the development of theoretical physics, but he does this without introducing the mathematics itself. Well, there is a brief introduction about groups and their representations, and there is the notation of SU(2), U(1), SU(5), but besides these there is no deep mathematical explanation and no further formulas. Neither do we find the technicalities of the physics equations. The book is mainly descriptive and it is easy to get lost in all the names and properties of the particles, but it should not be a problem to catch the message and the fundamental role played by symmetry.

**Submitted by Adhemar Bultheel |

**2 / Dec / 2016