Book Review: Fearful Symmetry

Book Review: Fearful Symmetry: The Search for Beauty in Modern Physics by Anthony Zee.

Anthony Zee is a prominent physicist who has written a well-regarded, if somewhat idiosyncratic text (Quantum Field Theory in a Nutshell) as well as several popular books on physics. Fearful Symmetry is his look at the central role symmetry has come to play in modern physics, and it is aimed at the general reader. The roots of the word symmetry mean something like “proportioned together,” and we use it to describe things we regard as harmoniously proportioned. We each have some sense of symmetry, and it plays a key role in our perception of beauty.

The decorative art of even rather low-tech cultures often makes use of symmetrical patterns – patterns that repeat with translation or rotation. A circle looks the same, seen from any direction, a square looks the same if you rotate it by 90 degrees, and one stretch of railroad track looks a lot like any other. Most animals are bilaterally symmetric, and faces that depart too far from this ideal are typically considered unattractive.

The key notion that underlies symmetry is that which is unchanged when something else changes. It is no accident that this notion has a large sway over us. It’s the thing that makes the world comprehensible. We sort the world into things that are the same and note their differences. Each tiger is no doubt different from every other, but they are all scary – but bunny rabbits rarely are. It’s easier to build with bricks that come in only one (or a few) types than with stones of random size and shape.

The symmetries that interest Zee, though, are symmetries of the laws of fundamental physics. Of course any law (of physics or man) is a sort of symmetry in itself. When Galileo noted that all objects (in the absence of friction) fell at the same rate, he was recognizing a symmetry of nature – that the acceleration due to gravity applied to all falling objects. When Newton noted that the motion of the moon could be explained by the same gravitational law that explained the fall of the apple, he was generalizing that symmetry to the cosmos.

The symmetries in the mathematical form of the physical laws themselves are slightly more abstract, and require making an intellectual separation between the laws themselves and the particulars of a given physical situation. In Galileo’s form of the law of gravity, the accelerations of the individual falling masses are the same, but there is a special direction picked out – down. Newton’s form frees us from that restriction by noting that the thing that is special about down is not the direction but the incidental circumstance that down happens to be the direction in which the center of a whole bunch of mass happens to lie. This generalization to a more symmetrical form turns gravity from something special about the Earth to a cosmic universal. The recognition universal gravitation was one of the most profound intellectual transformations in the history of the human race – it was the end of Earth as the center of the universe.

Zee's favorite symmetries, local symmetries, don’t really enter the picture until the start of the twentieth century. Two profoundly revolutionary concepts, relativity and the quantum, turn out to be intimately connected to symmetry, and symmetry proves crucial to understanding their consequences. The mathematical language of symmetry is the theory of groups and group representations. This represents a pretty deep challenge to the author who doesn’t want to use any actual mathematics. My impression is that he succeeds pretty well, but it’s hard to be confident because I’m actually supposed to know a little bit about these things. I should mention that my point of view is that of someone who has studied this subject but has forgotten a lot of what little I once knew. When a physicist, even an old and none too bright one like your frequently humbled correspondent, reads a popularization it’s never quite clear that his appreciation of the work has much relevance to that of the general reader, so will the intended audience feel the same?

Zee’s book was first published in 1986, well after the triumph of symmetry in particle physics, and not long after the first string theory “revolution.” The present edition dates from 1999, and he has updated with an afterword on string theory since, but the story of strings in not central to his book – but the concept of symmetry is pretty central to string theory. His story takes us to the so called Grand Unified Theories (GUTs) of the day, SU(5) and SO(10), which aimed to integrate strong, weak and electromagnetic interactions without gravity. Strings, of course, include gravity as well.

The predicted signature of GUTs (proton decay) has not been observed, and with strings the experimental evidence is so far absent as well. Zee doesn’t want to commit on the subject of strings, but he is a bit skeptical. His prejudice, he says, is that the concepts are too conservative – basically just the same old relativity and quantum mechanics. Perhaps he is right, but its probably worth mentioning that quantum field theory was left for dead a couple of times before its great triumph in the 70’s – first by Oppenheimer and others in the early 1940’s and again in the 1960’s, for the same reason – the old guys thought it was too conservative an approach. Well, the future is still out there, waiting to happen.

Zee, I should mention, takes Einstein’s point of view – not interested in “this or that phenomenon” but trying to understand whether “God had any choice in how he made the Universe.” If the multiverse idea is correct, the answer is clearly the one Einstein and Zee didn’t like – our laws of physics are an essentially accidental consequences of how some moduli happened to settle. It’s not a prospect I find appetizing, but then God didn’t actually ask for my opinion.

I recommend Fearful Symmetry to anyone with an interest in physics. If non-physicists happen to read or have read it, I would be interested in your opinions as to how you found his explanations – physicists too, of course.