我们的脸不可能长得对称?

MELISSA BLOCK, host:

You're listening to ALL THINGS CONSIDERED from NPR News.

We talk about beauty in people, in nature, in art. How about beauty in condensed matter physics?

NPR's Joe Palca reports now on a physicist who found some.

JOE PALCA: This is a story about matter and the beautiful properties it can display. But to understand what kind of properties and what sort of beauty, you have to dig deep. So, let's get started. The stuff the world is made of comes in a variety of phases. There's the gas phase, the liquid phase, the solid phase, and each of these phases has different characteristics.

Dr. ALAN TENNANT (Physicist, Helmholtz Center Berlin): Liquid flows. Solids are stuck there.

PALCA: That's Alan Tennant. He's a condensed matter physicist at the Helmholtz Center Berlin in Germany. Condensed matter physicists are concerned with transitions.

Dr. TENNANT: When you change from liquid to gas, you get a transition.

PALCA: Transitions are interesting because matter takes on some unusual properties as it makes transitions. To get a transition from ice to liquid water, you add heat. But Tennant isn't working something as everyday as the phase transitions of water. He's interested in the exotic transitions of the element cobalt, and that requires exotic tools.

Dr. TENNANT: Instead of using heat, we use high magnetic fields in very low temperatures.

PALCA: Really, really low temperatures, like close to absolute zero, as low as you can go. This is where quantum physics kicks in. In the quantum world, it's all about how single atoms of matter behave. And in the quantum world, the states of matter are not at all like the ones we know, and their transitions aren't either.

Dr. TENNANT: At the exact point where you change from one state to another, that's where you get the really important stuff.

PALCA: Some transitions are complicated and messy, but not the ones Tennant finds in his cold cobalt.

Dr. TENNANT: The quantum aspect of the system provides a kind of simplification, a kind of extra layer of order in the system that you wouldn't expect.

PALCA: In fact, the order Tennant and his colleagues found has a kind of beautiful, complicated symmetry.

Mr. ROBERT KONIK (Physicist, Brookhaven National Laboratory): They found this E8 symmetry.

PALCA: That's Robert Konik, a physicist at the Brookhaven National Laboratory. Now, here's where the story gets kind of tricky. Explaining transitions in quantum states of matter is easy compared to trying to explain E8 symmetry, but it's part of where the beauty lies, so let's try.

PALCA: E8 is one of a group of symmetries known as Lie symmetries, first studied by a 19th-century Norwegian mathematician named Lie. Konik took a crack at explaining them.

Mr. KONIK: If you had a ball, something that was perfectly spherical, the ball can be rotated about any of its axes, and the ball looks the same.

PALCA: So Lie symmetries are things that stay symmetrical when you rotate them, like spheres.

Mr. KONIK: That would be the very simplest, you know, it's more sort of generalized notions of rotations. For example, you can go to - think about symmetries involving rotations in higher dimensional spaces.

PALCA: I think I'd rather not just now. But the point here, as Alan Tennant says, is that in this weird quantum world, under certain precise conditions, a new kind of order emerges that was previously unknown.

Dr. TENNANT: When I started out, I really expected that quantum systems would be somehow more complicated and, you know, somehow more confusing than the everyday world that we're familiar with, but every system basically that we've looked at has turned out to be elegant. It's turned out to be truly beautiful.

PALCA: So beauty lies at the heart of matter. But then English poet John Keats knew that when he wrote the last lines of "Ode on a Grecian Urn," beauty is truth, truth beauty that is all ye know on earth and all ye need to know.

Joe Palca, NPR News, Washington.