My friend who counts atoms one at a time

SCIENTIST AT WORK: Abhay Ashtekar; Taste-Testing a Recipe for the Cosmos

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 Schrodinger, Paul Dirac, Werner Heisenberg, Niels
Bohr and Einstein. No recipe exists, and only a few of the ingredients are
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, whether 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 metier 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, Schrodinger 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'etat 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 Autonoma de
Mexico 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.

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