DRIVEN by the faith that God must be a geometer, physicists have spent the century searching for particles -- tiny shards of mathematics -- that show we live in a symmetrical world. Many of the particles have been discovered raining from the sky, unleashed by cosmic rays bombarding the atmosphere. But many times the particles have been discovered not in the scientists' laboratories but in their equations. They were imagined into existence, conjured from thin air.
Last week, when scientists at Los Alamos National Laboratories announced that they had taken a giant step toward a goal high on physics' agenda -- showing that the neutrino has a tiny mass -- they spoke of these barely corporeal particles with all the confidence of a geologist describing rocks. How far they had come from the day more than 60 years ago when neutrinos were invented as an accounting device, a mathematical fiction to make a set of equations fly.
The fact that so airy an abstraction has become firmly cemented into our theories of the universe testifies both to human ingenuity and to what the physicist Eugene Wigner once called "the unreasonable effectiveness of mathematics" in explaining the material world.
The history of physics is filled with stories in which theorists needed a new particle to satisfy their sense of aesthetics, and nature went on to oblige.
In the early 1930's Paul Dirac, the English physicist, was staring at the equation he had divined for explaining the electron when he noticed that it could be solved two ways. The square root of 4 is either 2 or -2. Similarly, one solution of Dirac's equation yielded the negatively charged electron, just as he had intended, but the other yielded a particle no one had ever seen -- one that was exactly like the electron except with a positive charge.
Even Dirac seemed reluctant to believe that Nature took his equations quite so seriously as he did. But soon after, the track of one of these antimatter positrons (the mirror image of the signature left by an electron) was discovered in a detector called a cloud chamber. "The equation," Dirac exclaimed, "was smarter than I was."
The Little Neutrino That Could
In the case of the neutrino, nature was not so forthcoming. Since the late 1800's scientists had been enchanted by rocks like uranium that emanated invisible rays. While studying a form of this radioactivity called beta decay, in which a neutron disintegrates into a proton and an electron, scientists calculated that the energy going into the reaction did not match the energy coming out. But one of science's strongest articles of faith is that energy can neither be created nor destroyed.
This principle, the conservation of energy, had been derived in the 19th century to explain an amazing new device called the steam engine. One would like to think that the parts of atoms obey the same laws as the parts of railroad locomotives. Enrico Fermi (borrowing a notion from his colleague Wolfgang Pauli) proposed that when a neutron decays it produces not just a proton and an electron but an invisible particle called a neutrino, which carries away precisely enough energy to make the equations balance.
Why hadn't we detected these convenient little ghosts? Because, it was said, they have no charge and no mass. They fly through ourselves and our detectors -- through the whole planet Earth -- without interacting with anything.
This struck some people as a bit facile, like a certified public accountant deciding that using the Lifo inventory method (last in, first out) instead of the Fifo method (first in, first out) will make his client's books better able to withstand the scrutiny of the Internal Revenue Service. What Fermi had done was part of the accepted accounting practices of physics. Then he had to await the day that his creative arithmetic would be subjected to nature's own audit.
Two and a half decades later, in a brilliantly oblique experiment, two scientists, Frederick Reines and Clyde Cowan, detected signs of the first neutrino. Before long, these elusive particles had become so tightly woven into the standard model, science's reigning theory of matter, that no one doubted their existence. In this formulation, there are three families of particles each consisting of two quarks, a type of neutrino, and a type of electron.
While particle physicists try to simplify the standard model into a grand unified theory -- a handful of equations uniting everything from gravity to the nuclear force -- cosmologists are seeking more unity still, trying to use particle physics to explain how the universe began.
Urgently Needed: More Gravity
The big bang does a marvelous job at explaining so much about the universe -- the redshifts of distant, receding galaxies, the ratios of hydrogen and helium.
It's all the more maddening then that it has been unable to explain the one phenomenon most central to our existence: how matter congealed into enormous structures -- the galaxies and the galaxies of galaxies -- including the one in which we live. Again, the equations don't balance. There simply isn't enough gravity in all of creation for so much matter to have congealed in the billions of years since the big bang -- unless, that is, there is some unseen and perhaps unseeable substance providing the extra pull.
Now wouldn't it be convenient if this dark matter turned out to be none other than the ghostly neutrinos? But this dodge would only work if neutrinos have a tiny bit of mass. If the Los Alamos scientists are right, some of the missing mass might now be found. But neutrinos still appear too light to account for more than part of the hypothetical dark matter.
So who's really smarter -- the universe or our equations? Made from this obscure stuff called luminous matter, can we with our numbers succeed in capturing the whole? More elusive than dark matter is this phantasm called mathematics. A truly unified theory would have to explain how it is that, if Wigner was right, we live in a mathematical world, in which the complexity we see is generated by a few simple laws.
Or will the complexity turn out to be irreducible? Imagine trying to describe a Jackson Pollock painting in a single paragraph. One couldn't do it with a whole encyclopedia of words. The painting is its own shortest description.
Sitting before the vast, dizzyingly abstract canvas of the universe, scientists remain confident that they can unearth the hidden laws. But there is always the possibility that we will just keep finding puzzles embedded inside of puzzles, falling into a universe that is infinitely deep -- and not one iota simpler than it seems.
LANGUAGE: ENGLISH