The Universe in the Rearview Mirror: How Hidden Symmetries Shape Reality - Hardcover

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Introduction

In which I set everything up, so it’s probably best not to skip ahead

Why is there something rather than nothing?

Why is the future different from the past?

Why are these questions a serious person should even ask?

There is a gleeful skepticism of the orthodox in popular discussion of science. Reading some of the twittering, blogging chatter out there, you might suppose that relativity is nothing more than the ramblings of some dude at a party instead of one of the most successful physical theories ever, and one that has passed every observational and experimental test thrown at it for a century.

To the uninitiated, physics can seem littered with a ridiculous number of rules and equations. Does it have to be so complicated?

Physicists themselves sometimes bask in the aloof complexity of it all. A century ago when asked if it was true that only three people in the world understood Einstein’s Theory of General Relativity, Sir Arthur Eddington thought for a few moments and casually replied, “I’m trying to think who the third person is.” These days, relativity is considered part of the standard physicist toolkit, the sort of thing taught every day to students barely out of short pants. So let’s put aside the highfalutin idea that you have to be a genius to understand the mysteries of the universe.

The deep insights into our world have almost never been the result of simply coming up with a new equation, whether you are Eddington or Einstein. Instead, breakthroughs almost always come in realizing that things that appear different are, in fact, the same. To understand how things work, we need to understand symmetry.

The great twentieth century Nobel laureate Richard Feynman likened the physical world as a game of chess. Chess is a game filled with symmetries. The board can be rotated half a turn and it will look just as it did before you started. The pieces on one side are (except for the color) a nearly perfect mirror reflection of the pieces on the other. Even the rules of the game have symmetries in them. As Feynman put it:

The rule on the move of a bishop on a chessboard is that it moves only on the diagonal. One can deduce, no matter how many moves may be made, that a certain bishop will always be on a red square. . . . Of course, it will be, for a long time, until all of a sudden, we find that it is on a black square (what happened of course, is that in the meantime it was captured, another pawn crossed for queening, and it turned into a bishop on the black square). That is the way it works in physics. For a long time we will have a rule that works excellently in an over all way, even when we cannot follow the details, and then some time we may discover a new rule.

Watch a few more games, and you might be struck by the insight that the reason a bishop always stays on the same color is that it always goes along a diagonal. The rule about conservation of color usually works, but the deeper law gives a deeper explanation.

Symmetries show up just about everywhere in nature, even though they may seem unremarkable or even obvious. The wings of a butterfly are perfect reflections of one another. Their function is identical, but I would feel extremely sad for a butterfly with two right wings or two left ones as he pathetically flew around in circles. In nature, symmetry, and asymmetry generally need to play off one another. Symmetry, ultimately, is a tool that lets us not only figure out the rules but figure out why those rules work.

Space and time, for instance, aren’t as different from one another as you might suppose. They are a bit like the left and right wings of a butterfly. The similarity between the two forms the basis of Special Relativity and gives rise to the most famous equation in all of physics. The laws of physics seem to be unchanging over time—a symmetry that gives rise to conservation of energy. It’s a good thing too; it’s thanks to the conservation of energy that the giant battery that is the sun manages to power all life here on earth.

To some people’s (okay, physicists’) minds, the symmetries that have emerged from our study of the physical universe are as beautiful as that of diamonds or snowflakes or the idealized aesthetic of a perfectly symmetric human face.

The mathematician Marcus Du Sautoy put it nicely:

Only the fittest and healthiest individual plants have enough energy to spare to create a shape with balance. The superiority of the symmetrical flower is reflected in a greater production of nectar, and that nectar has a higher sugar content. Symmetry tastes sweet.

Our minds enjoy the challenge of symmetries. In American style crosswords, typically the pattern of white and black squares look identical whether you rotate the entire puzzle a half a turn or view it in a mirror. Great works of art and architecture: the pyramids, the Eiffel tower, the Taj Mahal, are all built around symmetries.

Search the deepest recesses of your brain, and you may be able to summon the five Platonic solids. The only regular three dimensional figures with identical sides are the tetrahedron (four sides), cube (six), octahedron (eight), dodecahedron (twelve), and the icosahedron (twenty). A nerd (e.g., me) will think back fondly to his early years and recognize these as the shapes of the main dice in a Dungeons & Dragons set.

Symmetry can simply refer to the way things “match” or “reflect” themselves in our daily casual chitchat, but of course it has a much more precise definition. The mathematician Hermann Weyl gave a definition that’s going to serve us well throughout this book:

A thing is symmetrical if there is something you can do to it so

that after you have finished doing it, it looks the same as before.

Consider an equilateral triangle. There are all sorts of things that you do to a triangle to keep it exactly the same. You can rotate a third of a turn, and it will look as it did before. Or you could look at it in a mirror, and the reflection will look the same as the original.

The circle is a symmetric object par excellence. Unlike triangles, which look the same only if you turn them a specific amount, you can rotate a circle by any amount and it looks the same. Not to belabor the obvious, but this is how wheels work.

Long before we understood the motions of the planets, Aristotle assumed that orbits must be circular because of the “perfection” of the circle as a symmetric form. He was wrong, as it happens, as he was about most everything he said about the physical world.

It’s tempting to fall into the sense of sweet, smug satisfaction that comes from mocking the ancients, but Aristotle was right in a very important sense. Although planets actually travel in ellipses around the sun, the gravitational force toward the sun is the same in all directions. Gravity is symmetric. From this assumption, and a smart guess about how gravity weakens with distance, Newton correctly deduced the motions of planets. This is one of the many reasons you know his name. Something that doesn’t look nearly as perfect as a circle—the elliptical orbits of the planets—is a consequence of a much deeper symmetry.

Symmetries reveal important truths throughout nature. An understanding of how genetics really worked had to wait until Rosalind Franklin’s x ray imaging of DNA allowed James Watson and Francis Crick to unravel the double helix structure. This structure of two complementary spiral strands allowed us to understand the method of replication and inheritance.

If you run in particularly geeky circles, you may have heard a scientist refer to a theory as natural or elegant. What this normally means...