BERKELEY, CALIF. -- When David Pines thinks about superconductors, he imagines Cinderella.

"I keep seeing these wonderful new superconductors in the shape of her magic slipper," said Pines, a theoretical physicist from the University of Illinois. "Every one of us has a different way to try and make that shoe fit. We have some nice feet here, but nothing we can walk on."

It has been more than a year since two IBM physicists discovered ceramics that carry electric current without energy-wasting resistance at higher temperatures than anyone thought possible. And still nobody understands how they work.

Theories are advanced each week, and each week they are rejected. For experimental physicists -- the tinkerers of the trade -- it has been a year of intense joy. Labs bubble with excitement, as people mix elements in the seemingly random search for better materials.

But for theorists, who pursue their contemplative livelihood with a pencil and a pad, the revolution has been tough to find. The field's leaders gathered here last week at the first major conference dedicated to figuring out the theoretical basis of these new materials. But after they spent a week exchanging ideas, their confusion has not ended.

"This is the beginning of an entirely new physics," said Vladimir Kresin of the Lawrence Berkeley Lab, which sponsored the conference. "It took almost 50 years to explain superconductivity after it was discovered. We all know how much is at stake, but miracles are hard to produce."

Many scientists now feel that in order to perfect the new superconductors it will first be essential to grasp the exotic way in which they work. And if they are perfected, warm superconductors promise to revolutionize almost all uses of electricity.

Last month, experimental physicists proved that the standard theory of superconductivity, elucidated in 1957 for metals cooled to 400 degrees below zero, no longer applies at high temperatures. So it has fallen to theoretical physics to provide answers to a set of questions that only a few months ago did not exist.

Theorists always play a crucial role in physics. Using mathematical models, Albert Einstein changed beliefs about the universe by devising a new way to think about time and space. Often, theorists are sophisticated dreamers, while experimentalists are the ones who get their hands dirty. In the end, decisions in physics are made by experiment.

While experimental physicists are busy studying the electronic properties of the new ceramic materials being used as superconductors -- heating them, cooling them and probing them with electronic scalpels -- theorists are calculating the relationships of the smallest subatomic particles.

Using computer projections, or their heads, they try to predict how electrons will act under specific conditions. Much of their work relies on mathematics, for they will take the atomic weight of a certain element and manipulate different variables associated with it. With the bond between copper and oxygen, for instance, a theorist might add the atomic weight, multiply it by the strength of the bond between them and try to deduce how much energy is needed to force electrons to pair up. There are as many ways to add spin, weight and the motion of particles as there are theorists or computer programs.

The two branches of physics cooperate, but there is a healthy dose of tension between the groups.

"We are stuck all our lives with these guys who are out there with big saws whenever we get on a limb," Pines said. "Sometimes it can be pretty rough."

Marvin Cohen of the University of California at Berkeley, for years a leader in the field, puts the tentative nature of their work another way.

"We need a Fawn Hall with a shredder," he said at last week's meeting, attended by 500 physicists from around the world. "Because a month from now we are going to be sorry about some of the theories we are pushing."

In order to create superconductivity, electrons must bind in pairs. This permits them to flow effortlessly through a vibrating three-dimensional lattice of atoms without bumping into other particles and having their energy turn into wasteful heat. In normal conductors, impurities in the material trap wandering electrons, making them less efficient.

The old theory had an elaborate explanation for how -- and why -- electrons join in pairs. Basically, it held that the electrons get hooked by a wave, called a phonon. As one electron zips though the structure of a material, it creates a powerful wake that drags along a partner.

The wake, or phonon, is a complicated glue that holds the pair of electrons together in an intimate dance that allows them to overcome resistance. As the temperatures rise in the material, its atoms vibrate more violently until the pairs of electrons are broken and superconductivity is lost. In the high-temperature materials recently discovered, phonons appear unable to keep electrons together.

Many theorists still agree that electrons pair up in the new materials, they just don't agree how they do it.

Phonons are not the only things that can bind electrons and most of the current theoretical work centers on what other pairing mechanisms might exist.

Among the theories put forth at the conference are suggestions that an exciton, or strong electronic excitation, occurs in the new materials that forces the electrons to join. Excitons can be thought of as much stronger glue than phonons, and much more likely to keep working when temperatures start to climb and atoms get active.

Being wrong, Pines said, is something expected of good theorists.

"If a person isn't wrong at least 50 to 75 percent of the time they are not pushing hard enough," he said. "You have to be wrong a lot or you are doing safe science, which is boring."

Science has been anything but boring lately for those working on superconductors. Disagreements are lively and theories can be far-fetched. But everyone has sights set on the same finish line.

"About five of us went out last night and I conducted what I'll call the first annual Chez Panisse Poll," said Pines, referring to a popular local restaurant.

He said that after they covered a tablecloth with competing equations, he asked his colleagues how long it would be before somebody found what everybody was looking for, a stable room-temperature superconductor.

"Everyone agreed it will come and it will come soon," Pines said. "We just hope we have something to do with it."