Parallel Worlds (33 page)

Thus, we find a
beautiful and simple way of unifying all ten- dimensional and
eleven-dimensional physics into a single theory! It was a conceptual tour de
force.

I still remember
the shock generated by this explosive discovery. I was giving a talk at
Cambridge University at that time. Paul Townsend was gracious enough to
introduce me to the audience. But before my talk, he explained with great
excitement this new result,

that in the
eleventh dimension, the various string theories can be unified into a single
theory. The title of my talk mentioned the tenth dimension. He told me before I
spoke that, if this proved to be successful, then the title of my talk would
be obsolete.

I thought
silently to myself, "Uh oh." Either he was raving mad, or the physics
community was going to be turned completely upside down.

I could not
believe what I was hearing, so I fired a barrage of questions at him. I pointed
out that eleven-dimensional supermem- branes, a theory he helped to formulate,
were useless because they were mathematically intractable, and worse, they were
unstable. He admitted this was a problem, but he was confident that these questions
would be solved in the future.

I also said that
eleven-dimensional supergravity was not finite; it blew up, like all the other
theories except string theory. That was no longer a problem, he replied calmly,
because supergravity was nothing but an approximation of a larger, still
mysterious theory, M-theory, which
was
finite—it was actually string theory reformulated in the eleventh dimension in
terms of membranes.

Then I said that
supermembranes were unacceptable because no one had ever been able to explain
how membranes interact as they collide and re-form (as I had done in my own
Ph.D. thesis years ago for string theory). He admitted that was a problem, but
he was confident it, too, could be solved.

Last, I said
that M-theory was not really a theory at all, since its basic equations were
not known. Unlike string theory (which could be expressed in terms of the
simple string field equations I wrote down years ago that encapsulated the
entire theory), membranes had no field theory at all. He conceded this point as
well. But he remained confident that the equations for M-theory would
eventually be found.

My mind was sent
swimming. If he was right, string theory was once again about to undergo a
radical transformation. Membranes, which were once relegated to the dustbin of
physics history, suddenly were being resurrected.

The origin of
this revolution is that string theory is still evolving backward. Even today,
no one knows the simple physical principles that underlie the entire theory. I
like to visualize this as walking in the desert and accidentally stumbling upon
a small, beautiful pebble. When we brush away the sand, we find that the
pebble is actually the top of a gigantic pyramid buried under tons of sand.
After decades of painfully excavating the sand, we find mysterious hieroglyphics,
hidden chambers, and tunnels. One day, we will find the ground floor and
finally open up the doorway.

A ten-dimensional string can emerge from an
eleven-dimensional membrane by slicing or curling up one dimension. The equator
of a membrane becomes the string after one dimension is collapsed. There are
five ways in which this reduction can take place, giving rise to five different
superstring theories in ten dimensions.

BRANE WORLD

One of the novel
features of M-theory is that it introduces not only strings but a whole
menagerie of membranes of different dimensions. In this picture, point
particles are called "zero-branes," because they are infinitely
small and have no dimension. A string is then a "one-brane," because
it is a one-dimensional object defined by its length. A membrane is a
"two-brane," like the surface of a basketball, defined by length and
width. (A basketball can float in three dimensions, but its surface is only
two-dimensional.) Our universe might be some kind of "three-brane," a
three-dimensional object that has length, width, and breadth. (As one wit
noted, if space has
p
dimensions,
p
being an integer, then our universe is a
p
-brane, pronounced "pea-brain." A chart showing
all these pea-brains is called a "brane-scan.")

There are
several ways in which we can take a membrane and collapse it down to a string.
Instead of wrapping up the eleventh dimension, we can also slice off the
equator of an eleven-dimensional membrane, creating a circular ribbon. If we
let the thickness of the ribbon shrink, then the ribbon becomes a
ten-dimensional string. Petr Horava and Edward Witten showed that we derive the
heterotic string in this fashion.

In fact, it can
be shown that there are five ways in which to reduce eleven-dimensional
M-theory down to ten dimensions, thereby yielding the five superstring
theories. M-theory gives us a quick, intuitive answer to the mystery of why
there are five different string theories. Imagine standing on a large hilltop
and looking down on the plains. From the vantage point of the third dimension,
we can see the different parts of the plain unified into a single coherent picture.
Likewise, from the vantage point of the eleventh dimension, looking down on the
tenth dimension, we see the crazy quilt of five superstring theories as nothing
more than different patches of the eleventh dimension.

DUALITY

Although Paul
Townsend could not answer most of the questions I asked him at that time, what ultimately
convinced me of the correctness of this idea was the power of yet another
symmetry. Not only does M-theory have the largest set of symmetries known to
physics, it has yet another trick up its sleeve: duality, which gives M-theory
the uncanny ability to absorb all five superstring theories into one theory.

Consider
electricity and magnetism, which are governed by Maxwell's equations. It was
noticed long ago that if you simply interchange the electric field with the
magnetic field, the equations look almost the same. This symmetry can be made
exact if you can add monopoles (single poles of magnetism) into Maxwell's equations.
The revised Maxwell's equations remain precisely the same if we exchange the
electric field with the magnetic field and interchange the electric charge
e
with the inverse of the magnetic charge
g.
This means that electricity (if the electric charge is low)
is precisely equivalent to magnetism (if the magnetic charge is high). This
equivalence is called duality.

In the past,
this duality was considered nothing more than a scientific curiosity, a parlor
trick, since no one has ever seen a mono- pole, even today. However, physicists
found it remarkable that Maxwell's equations had a hidden symmetry that nature
apparently does not use (at least in our sector of the universe).

Similarly, the
five string theories are all dual to each other. Consider type I and the
heterotic SO(32) string theory. Normally, these two theories don't even look
alike. The type I theory is based on closed and open strings that can interact
in five different ways, with strings splitting and joining. The SO(32) string,
on the other hand, is based entirely on closed strings that have one possible
way of interacting, undergoing mitosis like a cell. The type I string is defined
entirely in ten-dimensional space, while the SO(32) string is defined with one
set of vibrations defined in twenty-six-dimensional space.

Normally, you
cannot find two theories that seem so dissimilar. However, just as in
electromagnetism, the theories possess a powerful duality: if you let the
strength of the interactions increase, type I strings change into SO(32)
heterotic strings, as if by magic. (This result is so unexpected that when I
first saw this result, I had to shake my head in amazement. In physics, we
rarely see two theories that appear totally dissimilar in all respects being
shown to be mathematically equivalent.)

LISA RANDALL

Perhaps the greatest advantage that M-theory has over string
theory is that these higher dimensions, instead of being quite small, may
actually be quite large and even observable in the laboratory. In string
theory, six of the higher dimensions must be wrapped up into a tiny ball, a
Calabi-Yau manifold, too small to be observed with today's instruments. These
six dimensions have all been compactified, so that entering a higher dimension
is impossible—more than a little disappointing to those who would one day hope
to soar into an infinite hyperspace rather than merely take brief short-cuts
through compactified hyperspace via wormholes.

However,
M-theory also features membranes; it is possible to view our entire universe as
a membrane floating in a much larger universe. As a result, not all of these
higher dimensions have to be wrapped up in a ball. Some of them, in fact, can
be huge, infinite in extent.

One physicist
who has tried to exploit this new picture of the universe is Lisa Randall of
Harvard. Resembling the actress Jodie Foster a bit, Randall seems out of place
in the fiercely competitive, testosterone-driven, intensely male profession of
theoretical physics. She is pursuing the idea that if the universe is really a
three-brane floating in higher-dimensional space, perhaps that explains why gravity
is so much weaker than the other three forces.

Randall grew up
in Queens, New York (the same borough immortalized by Archie Bunker). While
she showed no particular interest in physics as a child, she adored
mathematics. Although I believe we are all born scientists as children, not all
of us manage to continue our love of science as adults. One reason is that we
hit the brick wall of mathematics.

Whether we like
it or not, if we are to pursue a career in science, eventually we have to learn
the "language of nature": mathematics. Without mathematics, we can
only be passive observers to the dance of nature rather than active
participants. As Einstein once said, "Pure mathematics is, in its way, the
poetry of logical ideas." Let me offer an analogy. One may love French
civilization and literature, but to truly understand the French mind, one must
learn the French language and how to conjugate French verbs. The same is true
of science and mathematics. Galileo once wrote, "[The universe] cannot be
read until we have learnt the language and become familiar with the characters
in which it is written. It is written in mathematical language, and the
letters are triangles, circles, and other geometrical figures, without which
means it is humanly impossible to understand a single word."

But
mathematicians often pride themselves at being the most impractical of all
scientists. The more abstract and useless the mathematics, the better. What
set Randall off into a different direction while an undergraduate at Harvard in
the early 1980s was the fact that she loved the idea that physics can create
"models" of the universe. When we physicists first propose a new
theory, it is not simply based on a bunch of equations. New physical theories
are usually based on simplified, idealized models which approximate a phenomenon.
These models are usually graphic, pictorial, and simple to grasp. The quark
model, for example, is based on the idea that within a proton there are three
small constituents, the quarks. Randall was impressed that simple models, based
on physical pictures, could adequately explain much of the universe.

In the 1990s,
she became interested in M-theory, in the possibility that the entire universe
was a membrane. She zeroed in on perhaps the most puzzling feature of gravity,
that its strength is astronomically small. Neither Newton nor Einstein had
addressed this fundamental but mysterious question. While the other three
forces of the universe (electromagnetism, the weak nuclear force, and the
strong nuclear force) are roughly all of the same strength, gravity is wildly
different.

In particular,
the masses of the quarks are so much smaller than the mass associated with
quantum gravity. "The discrepancy is not small; the two mass scales are
separated by sixteen orders of magnitude! Only theories that explain this huge
ratio are likely candidates for theories underlying the Standard Model,"
says Randall.

The fact that
gravity is so weak explains why the stars are so big. Earth, with its oceans,
mountains, and continents, is nothing but a tiny speck when compared to the
massive size of the Sun. But because gravity is so weak, it takes the mass of
an entire star to squeeze hydrogen so that it can overcome the proton's
electrical force of repulsion. So stars are so massive because gravity is so
weak compared to the other forces.

With M-theory
generating so much excitement in physics, several groups have tried to apply
this theory to our universe. Assume the universe is a three-brane floating in a
five-dimensional world. This time, the vibrations on the surface of the
three-brane correspond to the atoms we see around us. Thus, these vibrations
never leave the three-brane and hence cannot drift off into the fifth
dimension. Even though our universe floats in the fifth dimension, our atoms
cannot leave our universe because they represent vibrations on the surface of
the three-brane. This then can answer the question Kaluza and Einstein asked in
1921: where is the fifth dimension? The answer is: we are floating in the fifth
dimension, but we cannot enter it because our bodies are stuck on the surface
of a three-brane.