Parallel Worlds (32 page)

Recall the
analogy of designing a sleek rocket, in which vibrations in the wings may
eventually grow and tear the wings off. One solution is to exploit the power of
symmetry, to redesign the wings so that vibrations in one wing cancel against
vibrations in another. When one wing vibrates clockwise, the other wing
vibrates counterclockwise, canceling the first vibration. Thus the symmetry of
the rocket, instead of being just an artificial, artistic device, is crucial to
canceling and balancing the stresses on the wings. Similarly, super- symmetry
cancels divergences by having the bosonic and fermionic parts cancel out
against each other.

(Supersymmetry
also solves a series of highly technical problems that are actually fatal to
GUT theory. Intricate mathematical inconsistencies in GUT theory require
supersymmetry to eliminate them.)

Although supersymmetry represents a powerful idea, at present
there is absolutely no experimental evidence to support it. This may be because
the superpartners of the familiar electrons and protons are simply too massive
to be produced in today's particle accelerators. However, there is one
tantalizing piece of evidence that points the way to supersymmetry. We know now
that the strengths of the three quantum forces are quite different. In fact, at
low energies, the strong force is thirty times stronger than the weak force,
and a hundred times more powerful than the electromagnetic force. However,
this was not always so. At the instant of the big bang, we suspect that all
three forces were equal in strength. Working backward, physicists can calculate
what the strengths of the three forces would have been at the beginning of
time. By analyzing the Standard Model, physicists find that the three forces
seem to converge in strength near the big bang. But they are not precisely
equal. When one adds super- symmetry, however, all three forces fit perfectly
and are of equal strength, precisely what a unified field theory would suggest.
Although this is not direct proof of supersymmetry, it shows at least that
supersymmetry is consistent with known physics.

The strengths of the weak, strong, and electromagnetic forces
are quite different in our everyday world. However, at energies found near the
big bang, the strengths of these forces should converge perfectly. This
convergence takes place if we have a supersymmetric theory. Thus, supersymmetry
may be a key element in any unified field theory.

DERIVING THE STANDARD MODEL

Although
superstrings have no adjustable parameters at all, string theory can offer
solutions that are astonishingly close to the Standard Model, with its motley
collections of bizarre subatomic particles and nineteen free parameters (such
as the masses of the particles and their coupling strengths). In addition, the
Standard Model has three identical and redundant copies of all the quarks and
leptons, which seems totally unnecessary. Fortunately, string theory can derive
many of the qualitative features of the Standard Model effortlessly. It's
almost like getting something for nothing. In 1984, Philip Candelas of the
University of Texas, Gary Horowitz and Andrew Strominger of the University of
California at Santa Barbara, and Edward Witten showed that if you wrapped up
six of the ten dimensions of string theory and still preserved supersymmetry
in the remaining four dimensions, the tiny, six-dimensional world could be
described by what mathematicians called a Calabi-Yau manifold. By making a few
simple choices of the Calabi-Yau spaces, they showed that the symmetry of the
string could be broken down to a theory remarkably close to the Standard
Model.

In this way,
string theory gives us a simple answer as to why the Standard Model has three
redundant generations. In string theory, the number of generations or
redundancies in the quark model is related to the number of "holes"
we have in the Calabi-Yau manifold. (For example, a doughnut, an inner tube,
and a coffee cup are all surfaces with one hole. Eyeglass frames have two
holes. Calabi-Yau surfaces can have an arbitrary number of holes.) Thus, by
simply choosing the Calabi-Yau manifold that has a certain number of holes, we
can construct a Standard Model with different generations of redundant quarks.
(Since we never see the Calabi-Yau space because it is so small, we also never
see the fact that this space has doughnut holes in it.) Over the years, teams
of physicists have arduously tried to catalog all the possible Calabi-Yau
spaces, realizing that the topology of this six-dimensional space determines
the quarks and leptons of our four-dimensional universe.

M-THEORY

The excitement surrounding
string theory unleashed back in 1984 could not last forever. By the mid-1990s,
the superstring bandwagon was gradually losing steam among physicists. The easy
problems the theory posed were picked off, leaving the hard ones behind. One
such problem was that billions of solutions of the string equations were being
discovered. By compactifying or curling up space-time in different ways, string
solutions could be written down in any dimension, not just four. Each of the
billions of string solutions corresponded to a mathematically self-consistent
universe.

Physicists were
suddenly drowning in string solutions. Remarkably, many of them looked very
similar to our universe. With a suitable choice of a Calabi-Yau space, it was
relatively easy to reproduce many of the gross features of the Standard Model,
with its strange collection of quarks and leptons, even with its curious set of
redundant copies. However, it was exceedingly difficult (and remains a
challenge even today) to find precisely the Standard Model, with the specific
values of its nineteen parameters and three redundant generations. (The
bewildering number of string solutions was actually welcomed by physicists who
believe in the multiverse idea, since each solution represents a totally self-consistent
parallel universe. But it was distressing that physicists had trouble finding
precisely our own universe among this jungle of universes.)

One reason that
this is so difficult is that one must eventually break supersymmetry, since we
do not see supersymmetry in our low-energy world. In nature, for example, we do
not see the selec- tron, the superpartner of the electron. If supersymmetry is
unbroken, then the mass of each particle should equal the mass of its
superparticle. Physicists believe that supersymmetry is broken, with the result
that the masses of the superparticles are huge, beyond the range of current
particle accelerators. But at present no one has come up with a credible
mechanism to break supersymmetry.

David Gross of
the Kavli Institute for Theoretical Physics in Santa Barbara has remarked that
there are millions upon millions of solutions to string theory in three
spatial dimensions, which is slightly embarrassing since there is no good way
of choosing among them.

There were other
nagging questions. One of the most embarrassing was the fact that there were
five self-consistent string theories. It was hard to imagine that the universe
could tolerate five distinct unified field theories. Einstein believed that God
had no choice in creating the universe, so why should God create five of them?

The original
theory based on the Veneziano formula describes what is called type I
superstring theory. Type I theory is based on both open strings (strings with
two ends) as well as closed strings (circular strings). This is the theory that
was most intensely studied in the early 1970s. (Using string field theory,
Kikkawa and I were able to catalog the complete set of type I string
interactions. We showed that type I strings require five interactions; for
closed strings, we showed that only one interaction term is necessary.)

Kikkawa and I
also showed that it is possible to construct fully self-consistent theories
with only closed strings (those resembling a loop). Today, these are called
type II string theories, where strings interact via pinching a circular string
into two smaller strings (resembling the mitosis of a cell).

The most
realistic string theory is called the heterotic string, formulated by the
Princeton group (including David Gross, Emil Martinec, Ryan Rohm, and Jeffrey
Harvey). Heterotic strings can accommodate symmetry groups called E(8)
X
E(8) or O(32), which are large enough to swallow up GUT
theories. The heterotic string is based entirely on closed strings. In the
1980s and 1990s, when scientists referred to the superstring, they tacitly were
referring to the heterotic string, because it was rich enough to allow one to
analyze the Standard Model and GUT theories. The symmetry group E(8)
X
E(8), for example, can be broken down to E(8), then E(6),
which in turn is large enough to include the SU(3)
X
SU(2)
X
U(i) symmetry
of the Standard Model.

Type I strings undergo five
possible interactions, in which strings can break, join, and fission. For
closed strings, only the last interaction is necessary (resembling the mitosis
of cells).

MYSTERY OF SUPERGRAVITY

In addition to
the five superstring theories, there was another nagging question that had
been forgotten in the rush to solve string theory. Back in 1976, three
physicists, Peter Van Nieuwenhuizen, Sergio Ferrara, and Daniel Freedman, then
working at the State University of New York at Stony Brook, discovered that
Einstein's original theory of gravity could become supersymmetric if one
introduced just one new field, a superpartner to the original gravity field
(called the gravitino, meaning "little graviton," with spin 3/2).
This new theory was called supergravity, and it was based on point particles,
not strings. Unlike the superstring, with its infinite sequence of notes and
resonances, supergravity had just two particles. In i978, it was shown by
Eugene Cremmer, Joel Scherk, and Bernard Julia of the Ecole Normale Superieure
that the most general supergravity could be written down in eleven dimensions.
(If we tried to write down su- pergravity theory in twelve or thirteen
dimensions, mathematical inconsistencies would arise.) In the late 1970s and
early 1980s, it was thought that supergravity might be the fabled unified field
theory. The theory even inspired Stephen Hawking to speak of "the end of
theoretical physics" being in sight when he gave his inaugural lecture
upon taking the Lucasian Chair of Mathematics at Cambridge University, the same
chair once held by Isaac Newton. But super- gravity soon ran into the same
difficult problems that had killed previous theories. Although it had fewer
infinities than ordinary field theory, in the final analysis supergravity was
not finite and was potentially riddled with anomalies. Like all other field
theories (except for string theory), it blew up in scientists' faces.

Another
supersymmetric theory that can exist in eleven dimensions is supermembrane
theory. Although the string has just one dimension that defines its length,
the supermembrane can have two or more dimensions because it represents a
surface. Remarkably, it was shown that two types of membranes (a two-brane and
five-brane) are self-consistent in eleven dimensions, as well.

However,
supermembranes also had problems; they are notoriously difficult to work with,
and their quantum theories actually diverge. While violin strings are so
simple that the Greek Pythagoreans worked out their laws of harmony two
thousand years ago, membranes are so difficult that even today no one has a
satisfactory theory of the music based on them. Plus, it was shown that these
membranes are unstable and eventually decay into point particles.

So, by the mid
1990s, physicists had several mysteries. Why were there five string theories in
ten dimensions? And why were there two theories in eleven dimensions,
supergravity and supermem- branes? Moreover, all of them possessed
supersymmetry.

ELEVENTH DIMENSION

In 1994, a bombshell was dropped. Another breakthrough took
place that once again changed the entire landscape. Edward Witten and

Paul Townsend of
Cambridge University mathematically found that ten-dimensional string theory
was actually an approximation to a higher, mysterious, eleven-dimensional
theory of unknown origin. Witten, for example, showed that if we take a
membranelike theory in eleven dimensions and curl up one dimension, then it
becomes ten-dimensional type IIa string theory!

Soon afterward,
it was found that all five string theories could be shown to be the same—just
different approximations of the same mysterious eleven-dimensional theory.
Since membranes of different sorts can exist in eleven dimensions, Witten
called this new theory M-theory. But not only did it unify the five different
string theories, as a bonus it also explained the mystery of supergravity.

Supergravity, if
you'll recall, was an eleven-dimensional theory that contained just two
particles with zero mass, the original Einstein graviton, plus its
supersymmetric partner (called the grav- itino). M-theory, however, has an
infinite number of particles with different masses (corresponding to the
infinite vibrations that can ripple on some sort of eleven-dimensional
membrane). But M-theory can explain the existence of supergravity if we assume
that a tiny portion of M-theory (just the massless particles) is the old super-
gravity theory. In other words, supergravity theory is a tiny subset of
M-theory. Similarly, if we take this mysterious eleven-dimensional membranelike
theory and curl up one dimension, the membrane turns into a string. In fact, it
turns into precisely type II string theory! For example, if we look at a
sphere in eleven dimensions and then curl up one dimension, the sphere
collapses, and its equator becomes a closed string. We see that string theory can
be viewed as a slice of a membrane in eleven dimensions if we curl up the
eleventh dimension into a small circle.