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science, medicine and the environment | MIND OVER MATTER

To Tell the Simple Truth, Symmetry Is Stunning


Even in sunny Los Angeles, it's probably fair to say that everybody loves a snowflake. But beyond the sheer pleasure of catching one on the tip of one's tongue, snowflakes teach lessons about truth and beauty--two of the strangest bedfellows ever to share a bunk in the house of science.

What does truth have to do with beauty, and how can snowflakes enlighten their relationship?

Snowflakes are beautiful because they embody just the right amount of symmetry. For whatever reason, people find symmetry beautiful--whether in the mathematically perfect spirals of snail shells, the harmonies in music, the well-ordered arrangements of diamond crystals or the multifaceted reflections in kaleidoscopes or decorative tiles.

In physics, symmetry has an uncanny ability to lead scientists to the truth. Recently summing up 50 years of progress in fundamental physics, the director of UC Santa Barbara's Institute for Theoretical Physics, David Gross, concluded: "The secret of nature is symmetry."

He advised his colleagues: "When searching for new and more fundamental laws of nature, we should search for new symmetries."

If you don't think physicists take symmetry seriously, consider that they are spending billions of dollars to track it down. The most conspicuous consumer is the Large Hadron Collider, a collaboration of dozens of nations at the world's foremost physics lab, the European Center for Particle Physics.

When completed sometime in the early 2000s, the collider will accelerate protons to near the speed of light, then smash them together in miniature versions of the big bang. What researchers hope to find is symmetry.

Symmetry has a slightly different meaning to physicists and mathematicians than it does to lay people. Something is symmetrical in the "technical sense" to the extent that you can change it and the change doesn't make a difference. It doesn't make a difference if you make something bigger or smaller, turn it upside down or inside out, or put it on backward.

Snowflakes are somewhat symmetrical in that you can't tell the difference between a snowflake and its mirror image, or a snowflake turned upside down. But if you rotate it slightly, it looks different; so the snowflake isn't perfectly symmetrical. A circle is far more symmetrical: It doesn't change no matter how you rotate it.

You also can't melt a snowflake and expect it to look the same. In fact, although no two snowflakes look exactly alike, melted snowflakes always do, because two drops of water always look alike. From the physicist's standpoint, the water that snow melts into is far more symmetrical than (though perhaps not as beautiful as) the snowflakes it came from.


In effect, the physicists at the Large Hadron Collider will be melting matter to find the perfect symmetry hidden underneath. At the extremely high temperatures they hope to achieve, the various particles of nature will "melt" into a more homogenous state, just as distinctive snowflakes melt into indistinguishable puddles of water.

Why would they want to do that? To find out what fundamental features of the universe do not change--which hidden symmetries lie behind the apparent diversity they see.

They would like to know, for example, why protons have a lot more mass than electrons. Why is there a difference--a lack of symmetry--between the two? At very high temperatures, they hope to re-create the symmetry that existed before particles acquired different masses, "breaking," or destroying, the symmetry.

At the same time, they hope to find out why the particle world as we know it contains two very different species: particles you can put your hand through (such as light particles or photons), and particles you can't (such as those that make up atoms). Call them apples and oranges.

At the super-high energies of the Large Hadron Collider, however, physicists believe they will find a hidden symmetry--a supersymmetry, or "SUSY," as it's affectionately called. According to SUSY theory, each particle teams up with a counterpart in the other particle family to make a perfectly symmetric team. Quarks, which are matter particles, are paired with light-like particles known as squarks. The supersymmetrical "spartner" of the photon is the photino.

Supersymmetry should reveal how the apples and oranges that seem so different on the surface fell off the same primordial tree.

Meanwhile, Stanford University has just announced the first successful collision between particles in a new accelerator designed to explore the absence of symmetry. If anything, this is more important (to us, at least) than symmetry.

Without symmetry breaking, we wouldn't be here.

The newborn universe gave birth to matter and antimatter in equal--that is to say, symmetrical--amounts. Now, we have only matter. Somehow, when the universe "froze" into its current state, it lost some of its symmetry.

The universe, in other words, is a lot like a drop of water that froze into a snowflake.

What a lovely thought.

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