Parallel Worlds (29 page)

In 1946, Erwin
Schrodinger also caught the bug and discovered what he thought was the fabled
unified field theory. Hurriedly, he did something rather unusual for his time (but
which is not so unusual today): he called a press conference. Even Ireland's
prime minister, Eamon De Valera, showed up to listen to Schrodinger. When
asked how certain he was that he had finally bagged the unified field theory,
he replied, "I believe I am right. I shall look like an awful fool if I am
wrong." (The
New York Times
eventually
found out about this press conference and mailed the manuscript to Einstein and
others for comment. Sadly, Einstein realized that Schrodinger had rediscovered
an old theory that he had proposed years earlier and had rejected. Einstein was
polite in his response, but Schrodinger was humiliated.)

In 1958,
physicist Jeremy Bernstein attended a talk at Columbia

University where
Wolfgang Pauli presented his version of the unified field theory, which he
developed with Werner Heisenberg. Niels Bohr, who was in the audience, was not
impressed. Finally, Bohr rose up and said, "We in the back are convinced
that your theory is crazy. But what divides us is whether your theory is crazy
enough."

Pauli
immediately knew what Bohr meant—that the Heisenberg- Pauli theory was too
conventional, too ordinary to be the unified field theory. To "read the
Mind of God" would mean introducing radically different mathematics and
ideas.

Many physicists
are convinced that there is a simple, elegant, and compelling theory behind
everything that nonetheless is crazy and absurd enough to be true. John Wheeler
of Princeton points out that, in the nineteenth century, explaining the immense
diversity of life found on Earth seemed hopeless. But then Charles Darwin introduced
the theory of natural selection, and a single theory provided the architecture
to explain the origin and diversity of all life on Earth.

Nobel laureate
Steven Weinberg uses a different analogy. After Columbus, the maps detailing
the daring exploits of the early European explorers strongly indicated that
there must exist a "north pole," but there was no direct proof of its
existence. Because every map of Earth showed a huge gap where the north pole
should be located, the early explorers simply assumed that a north pole should
exist, although none of them had ever visited it. Similarly, the physicists of
today, like the early explorers, find ample indirect evidence pointing to the existence
of a theory of everything, although at present there is no universal consensus
on what that theory is.

HISTORY OF STRING THEORY

One theory that
clearly is "crazy enough" to be the unified field theory is string
theory, or M-theory. String theory has perhaps the most bizarre history in the
annals of physics. It was discovered quite by accident, applied to the wrong
problem, relegated to obscurity, and suddenly resurrected as a theory of
everything. And in the final analysis, because it is impossible to make small
adjustments without destroying the theory, it will either be a "theory of
everything" or a "theory of nothing."

The reason for
this strange history is that string theory has been evolving backward.
Normally, in a theory like relativity, one starts with fundamental physical
principles. Later, these principles are honed down to a set of basic classical
equations. Last, one calculates quantum fluctuations to these equations. String
theory evolved backward, starting with the accidental discovery of its quantum
theory; physicists are still puzzling over what physical principles may guide
the theory.

The origin of
string theory dates back to 1968, when two young physicists at the nuclear
laboratory at CERN, Geneva, Gabriele Veneziano and Mahiko Suzuki, were
independently flipping through a math book and stumbled across the Euler Beta
function, an obscure eighteenth-century mathematical expression discovered by
Leonard Euler, which strangely seemed to describe the subatomic world. They
were astonished that this abstract mathematical formula seemed to describe the
collision of two n meson particles at enormous energies. The Veneziano model
soon created quite a sensation in physics, with literally hundreds of papers
attempting to generalize it to describe the nuclear forces.

In other words,
the theory was discovered by pure accident. Edward Witten of the Institute for
Advanced Study (whom many believe to be the creative engine behind many of the
stunning breakthroughs in the theory) has said, "By rights,
twentieth-century physicists shouldn't have had the privilege of studying this
theory. By rights, string theory shouldn't have been invented."

I vividly
remember the stir string theory created. I was still a graduate student in
physics at the University of California at Berkeley at that time, and I recall
seeing physicists shaking their heads and stating that physics was not supposed
to be this way. In the past, physics was usually based on making painfully
detailed observations of nature, formulating some partial hypothesis,
carefully testing the idea against the data, and then tediously repeating the
process, over and over again. String theory was a seat-of-your-pants method
based on simply guessing the answer. Such breathtaking shortcuts were not
supposed to be possible.

Because
subatomic particles cannot be seen even with our most powerful instruments,
physicists have resorted to a brutal but effective way to analyze them, by
smashing them together at enormous energies. Billions of dollars have been
spent building huge "atom smashers," or particle accelerators, which
are many miles across, creating beams of subatomic particles that collide into
each other. Physicists then meticulously analyze the debris from the collision.
The goal of this painful and arduous process is to construct a series of
numbers, called the scattering matrix, or S-matrix. This collection of numbers
is crucial because it encodes within it all the information of subatomic
physics—that is, if one knows the S-matrix, one can deduce all the properties
of the elementary particles.

One of the goals
of elementary particle physics is to predict the mathematical structure of the
S-matrix for the strong interactions, a goal so difficult that some physicists
believed it was beyond any known physics. One can then imagine the sensation
caused by Veneziano and Suzuki when they simply guessed the S-matrix by
flipping through a math book.

The model was a
completely different kind of animal from anything we had ever seen before.
Usually, when someone proposes a new theory (such as quarks), physicists try to
tinker with the theory, changing simple parameters (like the particles' masses
or coupling strengths). But the Veneziano model was so finely crafted that even
the slightest disturbance in its basic symmetries ruined the entire formula. As
with a delicately crafted piece of crystal, any attempt to alter its shape
would shatter it.

Of the hundreds
of papers that trivially modified its parameters, thereby destroying its
beauty, none have survived today. The only ones that are still remembered are
those that sought to understand why the theory worked at all—that is, those
that tried to reveal its symmetries. Eventually, physicists learned that the
theory had no adjustable parameters whatsoever.

The Veneziano
model, as remarkable as it was, still had several problems. First, physicists
realized that it was just a first approximation to the final S-matrix and not
the whole picture. Bunji Sakita, Miguel Virasoro, and Keiji Kikkawa, then at
the University of Wisconsin, realized that the S-matrix could be viewed as an
infinite series of terms, and that the Veneziano model was just the first and
most important term in the series. (Crudely speaking, each term in the series
represents the number of ways in which particles can bump into each other. They
postulated some of the rules by which one could construct the higher terms in
their approximation. For my Ph.D. thesis, I decided to rigorously complete this
program and construct all possible corrections to the Veneziano model. Along
with my colleague L. P. Yu, I calculated the infinite set of correction terms
to the model.)

Finally,
Yoichiro Nambu of the University of Chicago and Tetsuo Goto of Nihon University
identified the key feature that made the model work—a vibrating string. (Work
along these lines was also done by Leonard Susskind and Holger Nielsen.) When a
string collided with another string, it created an S-matrix described by the
Veneziano model. In this picture, each particle is nothing but a vibration or
note on the string. (I discuss this concept in detail later.)

Progress was
very rapid. In 1971, John Schwarz, Andre Neveu, and Pierre Ramond generalized
the string model so that it included a new quantity called spin, making it a
realistic candidate for particle interactions. (All subatomic particles, as we
shall see, appear to be spinning like a miniature top. The amount of spin of
each subatomic particle, in quantum units, is either an integer like 0, 1, 2 or
a half integer like 1/2, 3/2. Remarkably, the Neveu-Schwarz-Ramond string gave
precisely this pattern of spins.)

I was, however,
still unsatisfied. The dual resonance model, as it was called back then, was a
loose collection of odd formulas and rules of thumb. All physics for the
previous 150 years had been based on "fields," since they were first
introduced by British physicist Michael Faraday. Think of the magnetic field
lines created by a bar magnet. Like a spiderweb, the lines of force permeate
all space. At every point in space, you can measure the strength and direction
of the magnetic lines of force. Similarly, a field is a mathematical object
that assumes different values at every point in space. Thus, the field measures
the strength of the magnetic, electrical, or the nuclear force at any point in
the universe. Because of this, the fundamental description of electricity,
magnetism, the nuclear force, and gravity is based on fields. Why should
strings be different? What was required was a "field theory of
strings" that would allow one to summarize the entire content of the
theory into a single equation.

In 1974, I
decided to tackle this problem. With my colleague Keiji Kikkawa of Osaka
University, I successfully extracted the field theory of strings. In an
equation barely an inch and a half long, we could summarize all the information
contained within string theory. Once the field theory of strings was
formulated, I had to convince the larger physics community of its power and
beauty. I attended a conference in theoretical physics at the Aspen Center in
Colorado that summer and gave a seminar to a small but select group of
physicists. I was quite nervous: in the audience were two Nobel laureates,
Murray Gell-Mann and Richard Feynman, who were notorious for asking sharp,
penetrating questions that often left the speaker flustered. (Once, when Steven
Weinberg was giving a talk, he wrote down on the blackboard an angle, labeled
by the letter W, which is called the Weinberg angle in his honor. Feynman then
asked what the W on the blackboard represented. As Weinberg began to answer,
Feynman shouted "Wrong!" which broke up the audience. Feynman may
have amused the audience, but Weinberg got the last laugh. This angle
represented a crucial part of Weinberg's theory which united the
electromagnetic and weak interactions, and which would eventually win him the
Nobel Prize.)

In my talk, I
emphasized that string field theory would produce the simplest, most
comprehensive approach to string theory, which was largely a motley collection
of disjointed formulas. With string field theory, the entire theory could be
summarized in a single equation about an inch and a half long—all the
properties of the Veneziano model, all the terms of the infinite perturbation
approximation, and all the properties of spinning strings could be derived
from an equation that would fit onto a fortune cookie. I emphasized the
symmetries of string theory that gave it its beauty and power. When strings
move in space-time, they sweep out two-dimensional surfaces, resembling a
strip. The theory remains the same no matter what coordinates we use to
describe this two-dimensional surface. I will never forget that, afterward,
Feynman came up to me and said, "I may not agree totally with string
theory, but the talk you gave is one of the most beautiful I have ever
heard."

TEN DIMENSIONS

But just as
string theory was taking off, it quickly unraveled. Claude Lovelace of Rutgers
discovered that the original Veneziano model had a tiny mathematical flaw that
could only be eliminated if space- time had twenty-six dimensions. Similarly,
the superstring model of Neveu, Schwarz, and Ramond could only exist in ten
dimensions. This shocked physicists. This had never been seen before in the entire
history of science. Nowhere else do we find a theory that selects out its own
dimensionality. Newton's and Einstein's theories, for example, can be formulated
in any dimension. The famed inverse- square law of gravity, for example, can be
generalized to an inverse- cube law in four dimensions. String theory, however,
could only exist in specific dimensions.

From a practical
point of view, this was a disaster. Our world, it was universally believed,
existed in three dimensions of space (length, width, and breadth) and one of
time. To admit a ten- dimensional universe meant that the theory bordered on
science fiction. String theorists became the butt of jokes. (John Schwarz
remembers riding in the elevator with Richard Feynman, who jokingly said to
him, "Well, John, and how many dimensions do you live in today?") But
no matter how string physicists tried to salvage the model, it quickly died.
Only the die-hards continued to work on the theory. It was a lonely effort
during this period.