DESPITE
HIS thick glasses, rumpled jacket, a tie that barely reaches past his
sternum and the obligatory chalk-covered pants of a professor, he cuts a
handsome figure. Striding across the room in long, sure steps, he
conducts his lecture like a maestro, the rat-a-tat-tat of the chalk on
the board providing a counterpoint to his high, breathy, sometimes
inaudible voice. He talks of ''vector bundles,'' ''spin groups,''
''Dirac operators,'' ''connected Lie groups,'' ''trivial modules,''
''free loop spaces.'' At one point he pauses: ''We've been living in a
finite dimensional world. Now I'm inviting you to jump into a world of
infinite dimension.''
He
is Edward Witten of the Institute for Advanced Study in Princeton, N.J.
At the age of 36, he is among the foremost physicists of his day, and
he is in New York lecturing the Columbia University mathematics
department on, of all things, the applications of physics to
mathematics. Math - which has to do with abstract, intangible
relationships - has always been an important tool in physics - which has
to do with concrete forces and objects in the actual world. Witten has
turned things upside down, attempting to show how physics can provide
new insights into math. Turning things upside down is something he seems
to do as a matter of course.
''We
shouldn't toss comparisons with Einstein around too freely,'' says Sam
B. Treiman, a member of the physics department at Princeton, ''but when
it comes to Witten. . . .'' His hands open in a gesture of helplessness.
''He's head and shoulders above the rest. He's started whole groups of
people on new paths. He's started whole new fields. He produces elegant,
breathtaking proofs which people gasp at, which leave them in awe.''
Harvard
physicist Sidney Coleman calls Witten, simply, ''smarter than anyone
else. He's brought light where there was darkness. Everything he does is
golden. If you go to any theoretical physics department in the world,
you can see that people are touched, and touched deeply, by Ed's work.''
Witten
is everywhere at once, publishing papers and lecturing on cosmology,
mathematics and many different aspects of physics. When Witten talks,
physicists listen. In particular, they perked up their ears several
years ago when he began to pay serious attention to a seemingly bizarre
and long-forgotten theory that turns our current picture of the physical
universe on its head. Although it is nearly impossible to put a finger
on the single contribution that has made Witten such a force in physics,
his passion for this controversial theory makes him a leading proponent
of what may be the most revolutionary idea in physics in more than half
a century - as revolutionary, claims Witten, as relativity; as
revolutionary as quantum theory.
If
the theory is right, as Witten believes it may ultimately prove to be,
it could provide entirely new answers to fundamental questions asked by
philosophers, poets and theologians since the beginning of human time:
Why is the universe the way it is and what is the origin of matter?
(Box, page 24.) Although the term makes Witten uncomfortable, some
people call it a ''theory of everything.''
''String
theory,'' as it is commonly known (some scientists call it
''superstring theory''), does away with the familiar image of a universe
composed of billiard-ball-like particles pushed and pulled by familiar
forces like gravity and electricity. Quantum theory had already revealed
in the 1920's that the billiard balls have curious wave-like
properties: they are more like vibrations than well-defined points in
space. Now string theory is proposing that these points, in fact, are
tiny loops, or closed ''strings,'' that the universe is built not of
Grape-Nuts but of Cheerios. The strings, too, vibrate invisibly in
subtle resonances. These vibrations, so the theory goes, make up
everything in the universe - from light to lightning bugs, from gravity
to gold.
These
strings are not, of course, visible, nor are they like rubber bands or
pieces of twine. Impossible to detect by any means known to science
today, they are mathematical curves. Talking about strings, like talking
about billiard balls or waves, is a crude way of trying to comprehend
the unfamiliar in familiar terms. But then, physics has always had to
resort to metaphor. As the late Niels Bohr, the father of quantum
theory, once put it, ''When it comes to atoms, language can be used only
as in poetry. The poet, too, is not nearly so concerned with describing
facts as with creating images.''
Previous
scientific theories describing the universe have not yet been able to
create an image that fits all the pieces of the universe together within
a single conceptual framework. Physicists have opened the atom, like a
series of Russian dolls, to reveal, first, electrons, protons and
neutrons - then, more exotic entities like neutrinos and quarks. They
have learned how nuclear, gravitational and electromagnetic forces mold
these particles into molecules and galaxies. But nobody knows why, among
other things, there should be electrons at all, or why particles are
affected by gravity. String theory, according to its adherents, has the
potential of offering a single consistent explanation for everything
from the inner workings of the atom to the structure of the cosmos.
Unfortunately,
string theory contains what some scientists consider to be a major
flaw. The mathematical consistency that makes it so compelling is
revealed only if we are willing to suspend our belief in a world
fashioned from the familiar four dimensions of height, breadth, width
and time, and instead suppose the existence of six additional hidden
dimensions - a total of 10 in all.
Imagine
a closed string - a loop -of some kind of fundamental stuff. Now
imagine that the loop rotates, twists and vibrates not only in the three
familiar spatial dimensions (plus one dimension of time) but also in
six other dimensions we can't perceive. As the loop wriggles, it
resonates in many different modes, like a 10-dimensional violin string
sending out cosmic versions of A or E flat. These vibrations, if string
theory is correct, determine all the possible particles and forces of
the universe.
Pressed
for further explanation, Witten smiles and shrugs. ''Nobody understands
this much better than I just explained it to you,'' he says.
Ten
dimensions don't bother Witten in the least: ''These extra dimensions
aren't stranger than a lot of other things physicists think about.''
Still, the notion of a 10-dimensional universe and the absence of any
experimental data that could offer proof of it have caused many
physicists to be highly skeptical. ''It's not obvious how string theory
explains certain striking facts about the universe,'' says Frank A.
Wilczek, of the Institute of Theoretical Physics at the University of
California, Santa Barbara.
To
be sure, string theory has a great deal to explain. For example, it
will have to show just how it is that six extra dimensions remain
invisible to us. String theorists imagine these dimensions to be
''rolled up'' tightly around themselves on scales billions of times
smaller than the nucleus of an atom. But they do not yet know how, why
or when the six hidden dimensions rolled up. Perhaps, some theorists
say, they simply failed to expand billions of years ago when the rest of
the universe began doing so.
Such
doubts do not in any way diminish Witten's conviction. ''It is very
possible that a proper understanding of string theory will make the
space-time continuum melt away,'' Witten says. ''String theory is a
miracle through and through.''
WITTEN
STARTED GETTING OFFERS of professorships within a few years of
completing graduate school at Princeton, where he became a full
professor at 28. He's received a plethora of prizes from all over the
world, including a MacArthur Fellowship and, most recently, the National
Science Foundation's Alan T. Waterman Award for best young researcher.
That
medal, along with other prestigious awards, is piled ingloriously in
the corner of a bookcase in a spare bedroom Witten uses as a study,
sharing it with his wife, Chiara Nappi, also a Princeton physicist.
Their house could be anybody's suburban ranch. The few pictures on the
walls are mostly children's crayon drawings (they have two daughters).
There is an Exercycle in the kitchen and a pool in the backyard where,
on a recent sunny Wednesday, the Wittens gave a party for 40 first
graders. While children in wet bathing suits ran in and out of the
living room, Witten discussed the status of string theory.
In
physics, the yearning for an ultimate explanation has always been
evident. Time and time again, physics has advanced when seemingly
diverse phenomena have turned out to be different aspects of the same
thing. Newton's great discovery, for instance, was that the same force
that pulled the apple to the ground also held the moon in its orbit
around the earth and the earth in its orbit around the sun. Magnetism,
electricity and light were long thought to be completely unconnected -
until Maxwell and Faraday found that all were manifestations of
electromagnetism. Einstein's theory of relativity grew out of his
efforts to reconcile electromagnetism with classical mechanics.
Most
recently, physicists have been obsessed with trying to unify, or find
connections among, the known fundamental forces of nature: gravity,
electromagnetism, the ''strong'' force that holds particles together
within the nucleus of an atom and the ''weak'' force that accounts for,
among other things, radioactivity, the spontaneous disintegration of the
nucleus that results in the emission of energy. (Recent research has
raised the question of whether there is another force in the universe
that somehow counteracts gravity.) Electromagnetism, the strong and the
weak forces, and all the known particles in the universe can be
described in terms of quantum theory, a fact Witten considers ''magic.''
The theory has given rise to an entire field of scientific inquiry to
which Witten himself has made several important contributions. According
to quantum theory, everything results from the interactions of fields
of energy. The fields vibrate, but only in certain patterns or
resonances that correspond to specific quantities (hence the term
''quantum'') of energy. These resonances are the familiar particles and
forces of the everyday world. In fact, physicists who use giant
accelerators to smash atoms and search for exotic particles have been
known to call their work ''resonance hunting.''
Quantum
theory managed to clear up a host of questions and led to an
understanding of subatomic processes that has since produced everything
from lasers to semiconductors. Nevertheless, quantum theory cannot
account for gravity. Mathematical calculations that try to fit gravity
within that framework yield unworkable results.
''If
it weren't for gravity,'' says Witten, ''we'd probably think we already
knew everything fundamental about nature. But gravity doesn't fit. It's
a clue that something is wrong with our understanding. Why gravity
doesn't fit is the big mystery of mysteries.'' Yet gravity interacts
with every kind of energy in the universe - even a light beam falls
under its influence. So gravity has to obey the same laws of nature. The
question is, what are they?
FOR
MUCH OF HIS CAREER, EINSTEIN struggled to unite gravity with
electromagnetism to explain all of nature in terms of one ''unified
field.'' He never succeeded. But in 1919, he got a letter from an
obscure German-born physicist named Theodor F.E. Kaluza suggesting that
electromagnetism could be understood as a fifth-dimensional
manifestation of gravity. Kaluza didn't explain why the fifth dimension
remained unperceived. But in 1926, a Swedish mathematician, Oskar Klein,
suggested this was so because the fifth dimension was rolled up so
tightly - existed on such a tiny scale - that it did not affect anything
as large as even a subatomic particle.
String
theory is a resurrected form of the Kaluza-Klein theory, although
vastly more sophisticated. Just as Klein's fifth dimension shriveled up
into invisibility, so the extra six dimensions in string theory somehow
''compacted.'' If we accept the idea of those six hidden dimensions,
string theory proposes, mathematical inconsistencies that have plagued
previous attempts to reconcile quantum theory and gravity wondrously
disappear.
But
it's not clear that string theory accurately represents reality. No
evidence apart from mathematical consistency supports the existence of
six extra dimensions. Still, mathematical consistency, Witten says, has
been ''one of the most reliable guides to physicists in the last
century.''
Even
if it has mathematical consistency, what string theory is still missing
are underlying concepts. ''Vibrating strings in 10 dimensions is just a
weird fact,'' says Witten. ''An explanation of that weird fact would
tell you why there are 10 dimensions in the first place.''
''I
wish I had a bigger role in all this,'' says Witten, somewhat puzzled
by all the attention he's been getting lately. ''To be honest, it's not
clear that I'm newsworthy.''
Formal,
quiet, withdrawn, Witten is hesitant to talk about his accomplishments.
At times, he seems so other-worldly that one can easily understand why
his graduate students call him (with great respect and admiration) ''the
Martian.''
Sidney
Coleman, the Harvard physicist, remembers visiting Witten in Princeton
just after Witten had moved there from Cambridge. (Witten was a member
of the Harvard Society of Fellows for several years before taking his
first job as professor.) Coleman asked him how he compared living in
quiet, suburban Princeton with his previous existence in the bustling
Boston area. Witten responded: ''In Princeton, I sit at my kitchen table
at night doing physics instead of going down to Nassau Street. At
Harvard, I sat at my kitchen table at night doing physics instead of
going to Harvard Square.''
To
some extent, the world of the theorist is by definition a private one.
The work requires no lab, no test tubes, no cyclotrons, no
supercomputers, no equipment of any sort apart from a pencil and paper,
and sometimes not even that. Although Witten has graduate students, he
is reluctant to involve them in his more speculative projects. ''It
would be gambling their futures,'' he says.
He
rarely even sits down at a desk to write, according to his wife. ''He
thinks. He lies down on the bed. He sits like this,'' she says, resting
her chin on her wrist. ''He never does calculations except in his mind. I
will fill pages with calculations before I understand what I'm doing.
But Edward will sit down only to calculate a minus sign, or a factor of
two.''
If
you listen to Witten, becoming a physicist was almost a casual thing.
Although his father, Louis Witten, is a gravitational physicist (now at
the University of Cincinnati), he says he wasn't all that influenced by
his family. ''I came within a whisker of doing other things.''
Witten
grew up in Baltimore and got his undergraduate degree in history at
Brandeis, where his real interest, however, was linguistics. Before he
entered graduate school at Princeton, he wrote articles for The Nation,
The New Republic and other publications. For a six-month period during
1972, he worked on George McGovern's Presidential campaign as aide to
one of the candidate's legislative assistants. McGovern wrote him a
recommendation for graduate school. Still, Witten feels, he lacked the
qualities necessary for a career in writing or politics, foremost among
them, ''common sense.'' When he entered graduate school at Princeton, he
came very close to choosing mathematics before settling on physics.
WITTEN'S
COLLEAGUES TEND to give him far more credit than he gives himself,
especially when it comes to his role in bringing string theory out of
the closet.
Physicists
didn't set out to look for string theory, nor did they seriously follow
up Kaluza-Klein. Rather, they tripped over string theory in the dark
and have been trying to figure out exactly what it is ever since. ''I
don't think that any physicist would have been clever enough to have
invented string theory on purpose,'' says Witten. ''Luckily, it was
invented by accident.''
In
1968, an Italian physicist named Gabriele Veneziano was investigating
the strong force (the glue that holds particles together within the
nucleus) when he stumbled upon what Witten describes as ''a formula that
had a few curious properties.'' It was a few years later, through the
work of Yoichiro Nambu of the University of Chicago and others, that
people ''realized that silly formula described vibrating strings.''
For
a few years, string theory generated a great deal of interest. By the
mid-1970's, however, it had been largely abandoned, partly because other
lines of thought seemed more promising, and partly because it required
the unacceptable idea of extra dimensions.
''When
people found out that it only made sense in 10 dimensions,'' says
Witten, ''most people left the field.'' His own interest in it was
sparked primarily by the work of the physicists John H. Schwarz of the
California Institute of Technology, and Michael B. Green of Queen Mary
College in London. Witten remembers going through a ''few rough months
to learn about it. It was unlike anything anyone had seen before. There
was no encouragment from anybody.''
By
all accounts, it was a series of papers written by Schwarz and Green in
the early 1980's that resuscitated the theory. In 1984, they published
an important paper that, according to Nobel Prize-winning physicist
Steven Weinberg of the University of Texas, answered a question that had
also been posed by Witten.
The
question had to do with anomalies that appeared in theories that tried
to put gravity together with quantum field theory. Anomalies are defects
in a theory that yield absurd results and make the theory meaningless.
Witten, along with Luis Alvarez-Gaume of Harvard, discovered a new class
of anomalies. Even more important, he showed that the origin of the
anomalies was topological - that is, related to geometric properties
that do not arise in four dimensions but do arise in 10.
Topology,
the study of the properites of geometric figures as they are distorted
or deformed in various dimensions, is, for Witten, ''basic.'' The
thought that lay people might not be familiar with topology strikes him
as funny. ''That's like saying they don't know how to speak in prose,''
he says. A cup with one handle, for instance, is topologically
equivalent to a doughnut. If the cup were made of malleable clay, it
could be reshaped into the doughnut without tearing the material. ''It's
so obvious,'' Witten says. ''There are properties of things that change
when you break them, but not when you bend them.'' He sighs:
''Physicists didn't use to take topology seriously either.''
Topology
is critical to Witten because the question of whether the real world
can be explained by string theory depends not only on whether the extra
dimensions exist, but also on the forms they take in space - whether
they are, say, rolled up like tubes or have holes like doughnuts or are
spheres.
Appealing
to extra dimensions actually makes some problems simpler. Consider a
riddle: A pair of explorers walks due south for one mile, then due east
for one mile, then due north for one mile, only to find themselves back
at the starting point. Question: What color are the bears?
This
riddle makes no sense as long as the explorers are walking on a flat,
two-dimensional surface, as on a conventional map. But the earth is a
three-dimensional sphere. Its surface curves. Taking this into account,
the answer to the riddle becomes obvious: The explorers' starting point
was the North Pole. The bears are white. In his Victorian science
fiction classic ''Flatland,'' Edwin Abbott demonstrated eloquently that
what seems puzzling and obscure in one dimension can become crystal
clear in another. In his hypothetical world of two-dimensional triangles
and squares, a three-dimensional sphere was an incomprehensible object.
As it passed through this flattened space, it would first appear as a
point, then as a widening circle that finally shrank back to a point and
faded away. A two-dimensional creature can see only one two-dimensional
slice of a sphere at a time. It takes a three-dimensional onlooker to
see a sphere in its entirety.
And
if we could see the universe in its 10-dimensional entirety, string
theory presumes, a new symmetry would appear and the puzzling array of
forces and particles would be revealed as different facets of one
cohesive whole.
Unfortunately,
this tantalizing symmetry inherent in 10-dimensional space is not easy
to translate into four-dimensional particles and forces. To be
comprehended, it requires incredibly subtle mathematical tools, ones
that probably haven't even been invented.
SEVERAL
YEARS ago, Witten had a conversation with a colleague that struck him
deeply. ''He was talking about a very talented physicist who wasn't as
productive as he might have been. And he said it was because he never
worked on the kinds of problems for which he was really suited.''
Witten
has been serious about taking his colleague's implied advice. What he's
suited for, he says, is ''taking a physics problem and finding a
solution based on bizarre mathematics. String theory is going to require
a lot of new mathematics -and applying bizarre mathematics to physics
is what I'm good at.''
During
the past several years, Witten has been one of the leaders in a new
liaison that string theory has forged between physicists and
mathematicians. ''In my book, he's the leader,'' says I.M. Singer, a
mathematics professor at the Massachusetts Institute of Technology.
''He's one of two people I call if I get stuck. His intuition is
fantastic.'' Of his most important contributions, Witten describes
several as contributions not to physics, but to mathematics. ''He's got
more mathematical muscles in his head than I like to think about,'' says
Weinberg of the University of Texas.
Close
liaisons between physics and mathematics have marked most of the major
advances in our understanding of the universe. Newton needed to invent a
new kind of mathematics -calculus - to complete his theory of gravity.
Einstein's general relativity relied on a geometry of curved space
invented by Georg F.B. Riemann in the mid-1800's. Quantum theory
required a tool called ''functional analysis.''
String
theory, Witten says, ''brings us to the frontiers of mathematics.'' But
that doesn't deter him: ''I realized I could actually turn it around,
and get some surprising insights about mathematics from physics.''
The
new marriage between physics and mathematics has made physics truly
difficult for the first time for Witten. That's one reason he has
accepted an invitation to join the prestigious Institute for Advanced
Study next door to Princeton, where he'll be free from teaching
obligations. ''I want to work in a more ambitious way on half as many
things.'' All of them are aspects of string theory.
Witten's
work cannot now, nor for the foreseeable future, be tested in a lab. In
fact, it is so far removed from observable reality that a lifetime or
more may be required before its value - or any possible application - is
known. Theoretical physics is a risky business. ''It's extremely
important to believe in what you're doing,'' Witten says. ''But it's
difficult to have faith when things are so speculative. I remember when
my smallest daughter was learning to crawl. It was clear that she could
do it, but she didn't seem to realize that it was a worthwhile thing to
pursue. It reminds me of my own efforts.''
''One
lesson you can learn,'' he continues, ''is don't make mistakes. But
that's not very useful. Another lesson is, don't give up on right ideas.
But how do you know they're right?''
Because
string theory is so speculative, a good many physicists regard it with
suspicion and even disdain. Harvard Nobel laureate Sheldon L. Glashow
co-authored an article in Physics Today with his colleague Paul Ginsparg
- entitled ''Desperately Seeking Superstrings?'' - in which they wrote:
''A naive comparison suggests that to calculate the electron mass from
superstrings would be a trillion times more difficult than to explain
human behavior in terms of atomic physics.''
Witten
describes such criticism as ''manifest silliness. It's not always so
easy,'' he says, ''to tell which are the easy questions and which are
the hard ones. In the 19th century, the question of why water boils at
100 degrees centigrade was hopelessly inaccessible. If you told a
19th-century physicist that by the 20th century you would be able to
calculate this, it would have seemed like a fairy tale. . . . Quantum
field theory is so difficult that nobody fully believed it for 25
years.''
Witten
points out that neutron stars and gravitational lenses - large
concentrations of matter in outer space that produce, for earthly
observers, double images of stars - were considered science fiction,
pure speculation, until they were suddenly found in the skies. ''The
history of science is littered with predictions that such and such an
idea wasn't practical and would never be tested. The history of physics
shows that good ideas get tested.''
String
theory, for Witten, is too good not to be true. If it seems difficult
and complicated, that only means it's not well understood. For now,
string theory remains ''a piece of 21st-century physics that fell by
chance into the 20th century,'' he says. What physicists are working
with today is but ''a few crumbs from the table compared to the feast
which awaits us.''
Still,
he worries at times that it might be too difficult. ''There are long
odds against its leading anywhere in the next few years, but I feel I
would be missing the point if I didn't try.''
John
Ellis, a theoretical physicist at the European Center for Nuclear
Research, the international laboratory in Geneva, recently wrote,
''Superstring phenomenology is still a very young subject. There are
many open questions and technical problems, and it is easy to ridicule
superstring advocates for their totalitarian fervor. However, in the
words of a candy wrapper I opened a few years ago: 'It is only the
optimists who achieve anything in this world.' ''
Or, as Witten says, ''To test string theory, we will probably have to be lucky. But in physics, there are many ways of being lucky.''
