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SANTA BARBARA, Calif. — Dr. Abhay Ashtekar, the leader of a worldwide effort to unify the two most profound, abstract and mathematically baroque theories of physics discovered in this century, is sprinkling frozen mango cubes on scoops of vanilla ice cream.

After a meal of fish and tamales during which he puttered about his kitchen in a green apron emblazoned with bright flowers and the words "golden poppies," Dr. Ashtekar serves the dessert to his wife, Christine Clarke, and two visitors while needlessly apologizing for his cooking skills.

"I have never been able to follow a recipe," he says ruefully. "I just add what seems right."

The irony in this bit of self-criticism is lost on no one at the sun-splashed kitchen table. A flair for working without a recipe is a necessity for pursuing the central scientific passion of Dr. Ashtekar, who heads the Center for Gravitational Physics and Geometry at Pennsylvania State University and is in town to help organize a six-month workshop.

His passion boils down to this: An attempt at creating a sort of cosmic nouvelle cuisine by merging Albert Einstein's theory of general relativity with the laws of quantum mechanics, which were first worked out in the 1920's by a number of physicists including Erwin Schrödinger, Paul Dirac, Werner Heisenberg, Niels Bohr and Einstein. No recipe exists, and only a few of the ingredients are known.

Between them, these theories seem to explain the observed universe, but they express profoundly different conceptions of matter, time and space. That philosophical schism also leaves physicists in deep doubt over how to deal with phenomena in which both theories should be valid -- in the realms of the very small and the very energetic, like the Big Bang in which the universe was allegedly born.

"We have two wildly successful theories that have defined 20th-century physics," said Dr. Gary Horowitz, a physicist at the University of California at Santa Barbara, where the workshop is being held through July. "These theories are fundamentally incomplete and inconsistent with each other, and we just can't go on like that."

Relativity theory describes how the gravity of everything from subatomic particles to massive stars distorts and curves the four dimensions of space-time, like coconuts rolling on a rubber sheet. That changing curvature, in turn, determines exactly how the objects orbit about one another or fall together. A large enough congregation of matter can collapse to a point of infinite density, called a singularity, and shroud itself in a sphere of darkness -- a black hole, whose gravity is so powerful that nothing can escape from it, not even light.

On the other hand, standard quantum mechanics tells the tale of a "flat" space in which particles refuse to orbit smoothly; instead, they can hop suddenly from one spot to another, carrying with them only specific, sharply defined amounts of energy called quanta, like tourists holding no bills smaller than a 20. And far from respecting the crisp determinism of classical relativity, these particles sometimes exist not at definite positions but rather as fuzzy clouds of probability.

In culinary terms, these two kinds of physics have remained as distinct as a Tex-Mex barbecue and a New Age vegetarian picnic taking place in the same park. But most physicists, like Dr. Ashtekar, believe that since there is just one universe, there should be just one fundamental way of describing it.

Dr. Roger Penrose of the University of Oxford said that both theories also had internal problems, like the strange singularities that form in general relativity and the unmanageable infinities that also crop up in quantum mechanics. "The expectation is that to resolve these issues, we need the correct union between general relativity and quantum mechanics," Dr. Penrose said. "In my view," he added, Dr. Ashtekar's approach "is the most important of all the attempts at 'quantizing' general relativity."

That approach has led to a daring conception of space-time that shares characteristics with both the quantum world and general relativity. On incredibly tiny scales -- 10-33 centimeters, or smaller than a trillionth of a trillionth of the diameter of an atom -- space-time becomes jagged and discontinuous. At those scales, Dr. Ashtekar said, space dissolves into a sort of polymer network, "like your shirt," which looks continuous from a distance but is actually made of one-dimensional threads.

These developments had their start in the 1980's with a mathematical reformulation of Einstein's theory by Dr. Ashtekar, which allowed it to be molded into something that looked like a modified quantum theory. The equations that resulted were later shown to predict the polymers by Dr. Ashtekar, Dr. Carlo Rovelli of the Center for Theoretical Physics at the University of Marseilles in France and Dr. Lee Smolin of Pennsylvania State University.

Dr. Ashtekar freely points out that no one yet knows if this conception is right and that nature has actually chosen to fricassee space at the smallest scales. His approach to unification is not even the most popular one; many elementary particle physicists, including Dr. Horowitz, the Santa Barbara physicist, think that vibrations of 10-dimensional entities called strings might hold the key to all the forces of nature, including gravity.

But because it uses relativity theory as its jumping-off point, the approach dreamed up by Dr. Ashtekar and his colleagues is "the most in the spirit of Einstein," said Dr. Thomas Thiemann, a physicist at the Albert Einstein Institute, a part of the Max Planck Society in Potsdam, Germany.

Though known as a researcher of intimidating mathematical prowess, Dr. Ashtekar, 49, seems to approach his métier without much solemnity about its cosmic implications. After lunch, he sat outside in brilliant sunlight near an orange tree, sipping tea, shuffling through visual depictions of what the fabric of space might be. On his mug, a Gary Larson cartoon showed a schoolboy raising his hand in class and asking: "Mr. Osborne, may I be excused? My brain is full."

Dr. Ashtekar's light touch is more than a matter of style. Later, when pressed, he shrugged off the almost religious significance that some cosmologists have suggested a final theory will have.

"That arrogance is somewhat misplaced," he said. "I personally feel this is a great intellectual challenge; it's very difficult and all that." But physics, he said, "is only a part of the whole mystery of nature, of existence and ourselves."

Abhay Ashtekar grew up in small cities in the Indian state of Maharastra, which contains Bombay. At 15, while living in Kolhapur, a town surrounded by lush green sugar cane fields, he came across the popular book "One, Two, Three . . . Infinity" (last printed in 1988 by Dover) by the physicist George Gamow and decided that he liked mathematics and cosmology. Two years later (after the first year of college in India), a math professor explained to him that it was actually possible to make a living doing research on such topics.

"Coming from a middle-class family, you either became a doctor or an engineer or you entered civil service," Dr. Ashtekar said. The notion of a career fiddling with ideas "was a total revelation," he said. "And my mind was set. I wanted to try to do pure research."

He began showing a flair for not following scientific recipes almost immediately, discovering a small but significant error in the answer to a problem given in "The Feynman Lectures on Physics," a set of introductory volumes written by the late Dr. Richard P. Feynman, a Nobel Prize winner. Dr. Ashtekar wrote to Feynman -- and still has the treasured reply conceding that the textbook was wrong.

Sometime later he walked into the United States consulate in Bombay and searched university catalogues for graduate programs in gravitation. He eventually landed, a very uncertain 20 years old, at the University of Texas, Austin. On his first day on campus, he had to work up his courage just to enter the physics building. Eventually he entered, climbed a set a stairs, looked both ways down a corridor and hurried out again.

His confidence returned quickly. He went on to complete his Ph.D. at the University of Chicago, and then to appointments in Oxford, Paris and Syracuse, N.Y., before settling at Penn State.

Dr. Ashtekar gradually became interested in a field that many theorists before him had entered at their peril. "The history of quantum gravity," wrote Dr. Rovelli of Marseilles in a recent review, "is a sequence of moments of great excitement followed by great disappointments."

In an early attempt, Schrödinger announced in 1947 that he had managed to unify Einstein's equations with the theory of electromagnetic fields. But Einstein dismissed the work and condemned the worldwide news coverage it had scored.

From such episodes, wrote Einstein, "the reader gets the impression that every five minutes there is a revolution in science, somewhat like the coups d'état in some of the smaller unstable republics."

Later, Feynman and others tried to slip gravity into the quantum version of electromagnetism that had been developed, but the hybrid theory exploded with mathematical infinities when all the interactions it permitted were added up. And in the heyday of a unified theory called supergravity, Dr. Stephen W. Hawking, the physicist at the University of Cambridge, gave a talk titled "Is the End of Physics in Sight?"

It was not, yet, and when infinities reared their head in supergravity, some of its ideas were salvaged and woven into string theory.

Dr. Ashtekar's approach, which drew in part on work in the 1960's by Dr. John Wheeler of Princeton University, began with Einstein's equations directly. Following his mathematical taste buds rather than accepted formalisms, Dr. Ashtekar searched for some way to transmute the theory's geometric spirit into the fuzzy quantum world.

His first step was to express Einstein's equations in terms of variables with a chirality, or "handedness," in which a circle drawn in the clockwise sense would look different from one drawn in the opposite sense. Against all intuition, Einstein's equations, which show no preference for direction, broke into simpler pieces in the Ashtekar variables. From that vantage, first achieved in 1986, he was able to use straightforward tricks developed in the 1920's for creating a quantum theory from a deterministic one.

"It's rather curious," said Dr. Chris Isham, a theorist at Imperial College in London. "At one level, it was simply a redefinition of variables, which one might think was a fairly minor thing to do. But it really rejuvenated the whole field and caused quite an explosion of activity," Dr. Isham said. Soon there followed the solutions showing the polymerlike structure of space. The interlocking polymers "quantize" space in a particularly odd way, since each strand is somehow loaded with a definite amount of cross-sectional area. So to figure out the area inside a circle in this weird space, one would count up the strands that puncture its surface and multiply by the quantum of area carried by each of them. In this way, area is not smooth but comes in bundles.

The same rule holds for the area of a black hole's event horizon, the place beyond which anything is drawn into the black hole. Last year Dr. Ashtekar, Dr. John Baez of the University of California at Riverside, Dr. Kirill Krasnov of Penn State and Dr. Alejandro Corichi of the Universidad Nacional Autónoma de México showed that the polymers running into a black hole in a sense hold it "still" at the puncture points, like a water balloon supported on blunt pins. The rest of the horizon is free to jiggle about quantum mechanically.

Like the bouncing and jiggling of atoms in an ordinary gas, such motion has a definite entropy (or randomness) and therefore a temperature. Drawing on earlier formulas obtained with Dr. Jerzy Lewandowski of the University of Warsaw, Dr. Ashtekar and his colleagues were able to calculate the entropy for a black hole, matching a legendary 1974 prediction by Dr. Hawking.

The theory has other bizarre consequences, such as a bending of space that could be caused by immensely energetic photons of light. But the theory still faces challenges, particularly in the treatment of the "time" part of space-time. Until better observational tests turn up, the furious bake-off whose prize is unifying physics will remain a theoretical one. The entrants are not limited to strings and quantum geometry, which are beginning to look almost conservative. Dr. Penrose of Oxford believes that quantum mechanics itself will have to be modified before a fully successful merger with relativity can be made. Dr. Rafael Sorkin of Syracuse University is starting from scratch, postulating bits of existence he calls "the atoms of space-time" and working upward toward the macroscopic laws of physics.

In his side yard, Dr. Ashtekar, after a brief disappearance, brings a late afternoon snack for his visitors. It is a reminder that no matter what package of formulas emerges, he is likely to be kneading and rolling them in his mathematical kitchen, so to speak, with results that could not be predicted by looking at the picture on the box.

Submitted: Tuesday, April 20, 1999 - 12:00am