By Dr. Michio Kaku
Prof. of Theoretical Physics
City College of New York
When I was a child of 8, I heard a story that will stay with me for
the rest of my life. I remember my school teachers telling us about a
great scientist who had just died. They talked about him with great
reverence, calling him one of the greatest scientists in all history.
They said that very few people could understand his ideas, but that
his discoveries changed the entire world and everything around us.
But what most intrigued me about this man was that he died before
he could complete his greatest discovery. They said he spent years on
this theory, but he died with his unfinished papers still sitting on
his desk. I was fascinated by the story. To a child, this was a great
mystery. What was his unfinished work? What problem could possibly be
that difficult and that important that such a great scientist would
dedicate years of his life in its pursuit? Curious, I decided to learn
all I could about Albert Einstein and his unfinished theory. Some of
the happiest moments of my childhood were spent quietly reading every
book I could find about this great man and his theories. When I
exhausted the books in our local library, I began to scour libraries
and bookstores across the city and state eagerly searching for more
clues. I soon learned that this story was far more exciting than any
murder mystery and more important than anything I could ever imagine.
I decided that I would try to get t o the root of this mystery, even
if I had to become a theoretical physicist to do it.
Gradually, I began to appreciate the magnitude of his unfinished
quest. I learned that Einstein had three great theories. His first two
theories, the special and the general theory of relativity, led to the
development of the atomic bomb and the present-day theory of black
holes and the Big Bang. These two theories by themselves earned him
the reputation as the greatest scientist since Isaac Newton. However,
Einstein was not satisfied. The third theory, which he called the
Unified Field Theory, was to have been his crowning achievement. It
was to be the Theory of the Universe, the Holy Grail of physics, the
theory which finally unified all physical laws into one simple
framework. It was to be the ultimate goal of all physics, the theory
to end all theories.
Sadly, it consumed Einstein for the last 30 years of his life; he
spent many lonely years in a frustrating pursuit of the greatest
theory of all time. But he wasn't alone; I also learned that some of
the greatest minds of the twentieth century, such Werner Heisenberg
and Wolfgang Pauli, also struggled with this problem and ultimately
Given the fruitless search that has stumped the world's Nobel Prize
winners for half a century, most physicists agree that the Theory of
Everything must be a radical departure from everything that has been
tried before. For example, Niels Bohr, founder of the modern atomic
theory, once listened to Pauli's explanation of his version of the
unified field theory. Bohr finally stood up and said, "We are all
agreed that your theory is absolutely crazy. But what divides us is
whether your theory is crazy enough."
Today, however, after decades of false starts and frustrating dead
ends, many of the world's leading physicists think that they have
finally found the theory "crazy enough" to be the Unified
Field Theory. Scores of physicists in the world's major research
laboratories now believe we have at last found the Theory of
The theory which has generated so much excitement is called the
superstring theory. Nearly every science publication in the world has
featured major stories on the superstring theory, interviewing some of
its pioneers, such as John Schwarz, Michael Green, and Yoichiro Nambu.
(Discover magazine even featured it twice on its cover.) My book,
Beyond Einstein: the Cosmic Search for the Theory of the Universe, was
the first attempt to explain this fabulous theory to the lay audience.
Naturally, any theory which claims to have solved the most intimate
secrets of the universe will be the center of intense controversy.
Even Nobel Prize winners have engaged in heated discussions about the
validity of the superstring theory. In fact, we are witnessing the
liveliest debate in theoretical physics in decades over this theory.
To understand the power of the superstring theory and why it is
heralded as the theory of the universe (and to understand the
delicious controversy that it has stirred up), it is necessary to
understand that there are four forces which control everything in the
known universe, and that the superstring theory gives us the first
(and only) description which can unite all four forces into a single
The Four Fundamental Forces
Over 2,000 years ago, the ancient Greeks thought that all matter in
the universe could be reduced down to four elements: air, water,
earth, and fire. Today, after centuries of research, we know that
these substances are actually composites; they, in turn, are made of
smaller atoms and sub-atomic particles, held together by just four and
only four fundamental forces.
These four forces are:
Gravity is the force which keeps our feet anchored to the spinning
earth and binds the solar system and the galaxies together. If the
force of gravity could somehow be turned off, we would be immediately
flung into outer space at l,000 miles per hour. Furthermore, without
gravity holding the sun together, it would explode in a catastrophic
burst of energy. Without gravity, the earth and the planets would spin
out into freezing deep space, and the galaxies would fly apart into
hundreds of billions of stars.
Electro-magnetism is the force which lights up our cities and
energizes our household appliances. The electronic revolution, which
has given us the light bulb, TV, the telephone, computers, radio,
radar, microwaves, light bulbs, and dishwashers, is a byproduct of the
electro-magnetic force. Without this force, our civilization would be
wrenched several hundred years into the past, into a primitive world
lit by candlelight and campfires.
The strong nuclear force is the force which powers the sun. Without
the nuclear force, the stars would flicker out and the heavens would
go dark. Without the sun, all life on earth would perish as the oceans
turned to solid ice. The nuclear force not only makes life on earth
possible, it is also the devastating force unleashed by a hydrogen
bomb, which can be compared to a piece of the sun brought down to
The weak force is the force responsible for radioactive decay. The
weak force is harnessed in modern hospitals in the form of radioactive
tracers used in nuclear medicine. For example, the dramatic color
pictures of the living brain as it thinks and experiences emotions are
made possible by the decay of radioactive sugar in the brain.
It is no exaggeration to say that the mastery of each of these four
fundamental forces has changed every aspect of human civilization. For
example, when Newton tried to solve his theory of gravitation, he was
forced to develop a new mathematics and formulate his celebrated laws
of motion. These laws of mechanics, in turn, helped to usher in the
Industrial Revolution, which has lifted humanity from uncounted
millennia of backbreaking labor and misery.
Furthermore, the mastery of the electromagnetic force by James
Maxwell in the 1860s has revolutionized our way of life. Whenever
there is a power blackout, we are forced to live our lives much like
our forebears in the last century. Today, over half of the world's
industrial wealth is now connected, in some way or other, to the
electromagnetic force. Modern civilization without the electromagnetic
force is unthinkable.
Similarly, when the nuclear force was unleashed with the atomic
bomb, human history, for the first time, faced a new and frightening
set of choices, including the total annihilation of all life on earth.
With the nuclear force, we could finally understand the enormous
engine that lies within the sun and the stars, but we could also
glimpse for the first time the end of humanity itself.
Thus, whenever scientists unraveled the secrets of one of the four
fundamental forces, it irrevocably altered the course of modern
civilization. In some sense, some of the greatest breakthroughs in the
history of the sciences can be traced back to the gradual
understanding of these four fundamental forces. Some have said that
the progress of the last 2,000 years of science can be summarized by
the mastery of these four fundamental forces.
Given the importance of these four fundamental forces, the next
question is: can they be united into one super force? Are they but the
manifestations of a deeper reality?
Two Great Theories
At present there are two physical frameworks which have partially
explained the mysterious features of these four fundamental forces.
Remarkably, these two formalisms, the quantum theory and general
relativity, allow us to explain the sum total of all physical
knowledge at the fundamental level. Without exception.
The laws of physics and chemistry, which can fill entire libraries
with technical journals and books, can in principle be derived from
these two fundamental theories, making them the most successful
physical theories of all time, withstanding the test of thousands of
experiments and challenges.
Ironically, these two fundamental frameworks are diametrically
opposite to each other. The quantum theory, for example, is the theory
of the microcosm, with unparalleled success at describing the
sub-atomic world. The theory of relativity, by contrast, is a theory
of the macrocosmic world, the world of galaxies, super clusters, black
holes, and Creation itself.
The quantum theory explains three of the four forces (the weak,
strong, and electro-magnetic forces) by postulating the exchange of
tiny packets of energy, called "quanta." When a flashlight
is turned on, for example, it emits trillions upon trillion of
photons, or the quanta of light. Everything from lasers to radar waves
can be described by postulating that they are caused by the movement
of these tiny photons of energy. Likewise, the weak force is governed
by the exchange of subatomic particles called W-bosons. The strong
nuclear force, in turn, binds the proton together by the exchange of
However, the quantum theory stands in sharp contrast to Einstein's
general relativity, which postulates an entirely different physical
picture to explain the force of gravity.
Imagine, for the moment, dropping a heavy shot put on a large bed
spread. The shot put will, of course, sink deeply into the bed spread.
Now imagine shooting a small marble across the bed. Since the bed is
warped, the marble will execute a curved path. However, for a person
viewing the marble from a great distance, it will appear that the shot
put is exerting an invisible "force" on the marble, forcing
it to move in a curved path. In other words, we can now replace the
clumsy concept of a "force" with the more elegant bending of
space itself. We now have an entirely new definition of a
"force." It is nothing but the byproduct of the warping of
In the same way that a marble moves on a curved bed sheet, the
earth moves around the sun in a curved path because space-time itself
is curved. In this new picture, gravity is not a "force" but
a byproduct of the warping of space-time. In some sense, gravity does
not exist; what moves the planets and stars is the distortion of space
However, the problem which has stubbornly resisted solution for 50
years is that these two frameworks do not resemble each other in any
way. The quantum theory reduces "forces" to the exchange of
discrete packet of energy or quanta, while Einstein's theory of
gravity, by contrast, explains the cosmic forces holding the galaxies
together by postulating the smooth deformation of the fabric of
space-time. This is the root of the problem, that the quantum theory
and general relativity have two different physical pictures (packets
of energy versus smooth space-time continuums) and different
mathematics to describe them.
All attempts by the greatest minds of the twentieth century at
merging the quantum theory with the theory of gravity have failed.
Unquestionably, the greatest problem of the century facing physicists
today is the unification of these two physical frameworks into one
This sad state of affairs can be compared to Mother Nature having
two hands, neither of which communicate with the other. Nothing could
be more awkward or pathetic than to see someone whose left hand acted
in total ignorance of the right hand.
Today, however, many physicists think that we have finally solved this
long-standing problem. This theory, which is certainly "crazy
enough" to be correct, has astounded the world's physics
community. But it has also raised a storm of controversy, with Nobel
Prize winners adamantly sitting on opposite sides of the fence.
This is the superstring theory, which postulates that all matter
and energy can be reduced to tiny strings of energy vibrating in a 10
Edward Witten of the Institute for Advanced Study at Princeton, who
some claim is the successor to Einstein, has said that superstring
theory will dominate the world of physics for the next 50 years, in
the same way that the quantum theory has dominated physics for the
last 50 years.
As Einstein once said, all great physical theories can be
represented by simple pictures. Similarly, superstring theory can be
explained visually. Imagine a violin string, for example. Everyone
knows that the notes A,B,C, etc. played on a violin string are not
fundamental. The note A is no more fundamental than the note B. What
is fundamental, of course, is the violin string itself. By studying
the vibrations or harmonics that can exist on a violin string, one can
calculate the infinite number of possible frequencies that can exist.
Similarly, the superstring can also vibrate in different
frequencies. Each frequency, in turn, corresponds to a sub-atomic
particle, or a "quanta." This explains why there appear to
be an infinite number of particles. According to this theory, our
bodies, which are made of sub-atomic particles, can be described by
the resonances of trillions upon trillions of tiny strings.
In summary, the "notes" of the superstring are the
subatomic particles, the "harmonies" of the superstring are
the laws of physics, and the "universe" can be compared to a
symphony of vibrating superstrings.
As the string vibrates, however, it causes the surrounding
space-time continuum to warp around it. Miraculously enough, a
detailed calculation shows that the superstring forces the space-time
continuum to be distorted exactly as Einstein originally predicted.
Thus, we now have a harmonious description which merges the theory of
quanta with the theory of space-time continuum.
10 Dimensional Hyperspace
The superstring theory represents perhaps the most radical departure
from ordinary physics in decades. But its most controversial
prediction is that the universe originally began in 10 dimensions. To
its supporters, the prediction of a 10 dimensional universe has been a
conceptual tour de force, introducing a startling, breath-taking
mathematics into the world of physics.
To the critics, however, the introduction of 10 dimensional
hyperspace borders on science fiction.
To understand these higher dimensions, we remember that it takes
three number to locate every object in the universe, from the tip of
your nose to the ends of the universe.
For example, if you want to meet some friends for lunch in
Manhattan, you say that you will meet them at the building at the
corner of 42nd and 5th Ave, on the 37th floor. It takes two numbers to
locate your position on a map, and one number to specify the distance
above the map. It thus takes three numbers to specify the location of
However, the existence of the fourth spatial dimension has been a
lively area of debate since the time of the Greeks, who dismissed the
possibility of a fourth dimension. Ptolemy, in fact, even gave a
"proof" that higher dimensions could not exist. Ptolemy
reasoned that only three straight lines can be drawn which are
mutually perpendicular to each other (for example, the three
perpendicular lines making up a corner of a room.) Since a fourth
straight line cannot be drawn which is mutually perpendicular to the
other three axes, Ergo!, the fourth dimension cannot exist.
What Ptolemy actually proved was that it is impossible for us
humans to visualize the fourth dimension. Although computers routinely
manipulate equations in N-dimensional space, we humans are incapable
of visualizing spatial dimensions beyond three.
The reason for this unfortunate accident has to do with biology,
rather than physics. Human evolution put a premium on being able to
visualize objects moving in three dimensions. There was a selection
pressure placed on humans who could dodge lunging saber tooth tigers
or hurl a spear at a charging mammoth.
Since tigers do not attack us in the fourth dimension, there simply
was no advantage in developing a brain with the ability to visualize
objects moving in four dimensions.
From a mathematical point of view, however, adding higher
dimensions is a distinct advantage: it allows us to describe more and
more forces. There is more "room" in higher dimensions to
insert the electromagnetic force into the gravitational force. (In
this picture, light becomes a vibration in the fourth dimension.) In
other words, adding more dimensions to a theory always allows us to
unify more laws of physics.
A simple analogy may help. The ancients were once puzzled by the
weather. Why does it get colder as we go north? Why do the winds blow
to the West? What is the origin of the seasons? To the ancients, these
were mysteries that could not be solved. From their limited
perspective, the ancients could never find the solution to these
The key to these puzzles, of course, is to leap into the third
dimension, to go up into outer space, to see that the earth is
actually a sphere rotating around a tilted axis. In one stroke, these
mysteries of the weather become transparent. The seasons, the winds,
the temperature patterns, etc. all become obvious once we leap into
the third dimension.
Likewise, the superstring is able to accommodate a large number of
forces because it has more "room" in its equations to do so.
What Happened Before the Big Bang?
One of the nagging problems of Einstein's old theory of gravity was
that it did not explain the origin of the Big Bang. It did not give us
a clue as to what happened before the Big Bang.
The 10 dimensional superstring theory, however, gives us a
compelling explanation of the origin of the Big Bang. According to the
superstring theory, the universe originally started as a perfect 10
dimensional universe with nothing in it.
However, this 10 dimensional universe was not stable. The original
10 dimensional space-time finally "cracked" into two pieces,
a four and a six dimensional universe. The universe made the
"quantum leap" to another universe in which six of the 10
dimensions curled up into a tiny ball, allowing the remaining four
dimensional universe to inflate at enormous rates.
The four dimensional universe (our world) expanded rapidly,
eventually creating the Big Bang, while the six dimensional universe
wrapped itself into a ball and collapsed down to infinitesimal size.
This explains the origin of the Big Bang, which is now viewed as a
rather minor aftershock of a more cataclysmic collapse: the breaking
of a 10 dimensional universe into a four and six dimensional universe.
In principle, it also explains why we cannot measure the six
dimensional universe, because it has shrunk down to a size smaller
than an atom. Thus, no earth-bound experiment can measure the six
Although the superstring theory has been called the most sensational
discovery in theoretical physics in the past decades, its critics have
focused on its weakest point, that it is almost impossible to test.
The energy at which the four fundamental forces merge into a single,
unified force occurs at the fabulous "Planck energy," which
is a billion billion times greater than the energy found in a proton.
Even if all the nations of the earth were to band together and
single-mindedly build the biggest atom smasher in all history, it
would still not be enough to test the theory. Because of this, some
physicists have scoffed at the idea that superstring theory can even
be considered a legitimate "theory." Nobel laureate Sheldon
Glashow, for example, has compared the superstring theory to the
former Pres. Reagan's Star Wars program (because it is untestable and
drains the best scientific talent).
The reason why the theory cannot be tested is rather simple. The
Theory of Everything is necessarily a theory of Creation, that is, it
must necessarily explain everything from the origin of the Big Bang
down to the lilies of the field. Its full power is manifested at the
instant of the Big Bang, where all its symmetries were intact. To test
this theory on the earth, therefore, means to recreate Creation on the
earth, which is impossible with present-day technology.
Although this is discouraging, a piece of the puzzle may be
supplied by the Superconducting Supercollider (SSC), which, if built,
will be the world's largest atom smasher.
The SSC - Biggest Experiment of All Time
These questions about unifying the fundamental forces are not
academic, because the largest scientific machine ever built, the SSC,
may be built to test some of these ideas about the instant of
Creation. (Although the SSC was originally approved by the Reagan
administration, the project, because of its enormous cost, is still
touch-and-go, depending every year on Congressional funding.)
The SSC is projected to accelerate protons to a staggering energy
of tens of trillions of electron volts. When these subatomic particles
slam into each other at these fantastic energies, the SSC will create
temperatures which have not been seen since the instant of Creation
(although it is still too weak to fully test the superstring theory).
That is why it is sometimes called a "window on Creation."
The SSC is projected to cost over $8 billion (which is large
compared to the science budget, but insignificant compared to the
Pentagon budget). By every measure, it will be a colossal machine. It
will consist of a ring of powerful magnets stretched out in a tube
over 50 miles in diameter. In fact, one could easily fit the
Washington Beltway, which surrounds Washington D.C., inside the SSC.
Inside this gigantic tube, protons will be accelerated to unimaginable
At present, it is scheduled to be finished near the turn of the
century in Texas, near the city of Austin. When completed, it will
employ thousands of physicists and engineers and cost millions of
dollars to operate.
At the very least, physicists hope that the SSC will find some
exotic sub-atomic particles, such as the "Higgs boson" and
the "top quark," in order to complete our present-day
understanding of the quantum theory. However, there is also the small
chance that physicists might discover "supersymmetric"
particles, which may be remnants of the original superstring theory.
In other words, although the superstring theory cannot be tested
directly by the SSC, one hopes to find resonances from the superstring
theory among the debris created by smashing protons together.
Parable of the Gemstone
To understand the intense controversy surrounding superstring theory,
think of the following parable.
Imagine that, at the beginning of time, there was once a beautiful,
glittering gemstone. Its perfect symmetries and harmonies were a sight
to behold. However, it possessed a tiny flaw and became unstable,
eventually exploding into thousands of tiny pieces. Imagine that the
fragments of the gemstone rained down on a flat, two-dimensional
world, called Flatland, where there lived a mythical race of beings
These Flatlanders were intrigued by the beauty of the fragments,
which could be found scattered all over Flatland. The scientists of
Flatland postulated that these fragments must have come from a crystal
of unimaginable beauty that shattered in a titanic Big Bang. They then
decided to embark upon a noble quest, to reassemble all these pieces
of the gemstone.
After 2,000 years of labor by the finest minds of Flatland, they
were finally able to fit many, but certainly not all, of the fragments
together into two chunks. The first chunk was called the
"quantum," and the second chunk was called
Although they Flatlanders were rightfully proud of their progress,
they were dismayed to find that these two chunks did not fit together.
For half a century, the Flatlanders maneuvered these two chunks in all
possible ways, and they still did not fit.
Finally, some of the younger, more rebellious scientists suggested
a heretical solution: perhaps these two chunks could fit together if
they were moved in the third dimension.
This immediately set off the greatest scientific controversy in
years. The older scientists scoffed at this idea, because they didn't
believe in the unseen third dimension. "What you can't measure
doesn't exist," they declared.
Furthermore, even if the third dimension existed, one could
calculate that the energy necessary to move the pieces up off Flatland
would exceed all the energy available in Flatland. Thus, it was an
untestable theory, the critics shouted.
However, the younger scientists were undaunted. Using pure
mathematics, they could show that these two chunks fit together if
they were rotated and moved in the third dimension. The younger
scientists claimed that the problem was therefore theoretical, rather
than experimental. If one could completely solve the equations of the
third dimension, then one could, in principle, fit these two chunks
completely together and resolve the problem once and for all.
We Are Not Smart Enough
That is also the conclusion of today's superstring enthusiasts,
that the fundamental problem is theoretical, not practical. The true
problem is to solve the theory completely, and then compare it with
present-day experimental data. The problem, therefore, is not in
building gigantic atom smashers; the problem is being clever enough to
solve the theory.
Edward Witten, impressed by the vast new areas of mathematics
opened up by the superstring theory, has said that the superstring
theory represents "21th century physics that fell accidentally
into the 20th century." This is because the superstring theory
was discovered almost by accident. By the normal progression of
science, we theoretical physicists might not have discovered the
theory for another century.
The superstring theory may very well be 21st century physics, but
the bottleneck has been that 21st century mathematics has not yet been
discovered. In other words, although the string equations are
perfectly well-defined, no one is smart enough to solve them.
This situation is not entirely new to the history of physics. When
Newton first discovered the universal law of gravitation at the age of
23, he was unable to solve his equation because the mathematics of the
17th century was too primitive. He then labored over the next 20 years
to develop a new mathematical formalism (calculus) which was powerful
enough to solve his universal law of gravitation.
Similarly, the fundamental problem facing the superstring theory is
theoretical. If we could only sharpen our analytical skills and
develop more powerful mathematical tools, like Newton before us,
perhaps we could solve the theory and end the controversy.
Ironically, the superstring equations stand before us in perfectly
well-defined form, yet we are too primitive to understand why they
work so well and too dim witted to solve them. The search for the
theory of the universe is perhaps finally entering its last phase,
awaiting the birth of a new mathematics powerful enough to solve it.
Imagine a child gazing at a TV set. The images and stories conveyed
on the screen are easily understood by the child, yet the electronic
wizardry inside the TV set is beyond the child's ken. We physicists
are like this child, gazing in wonder at the mathematical
sophistication and elegance of the superstring equations and awed by
its power. However, like this child, we do not understand why the
superstring theory works.
In conclusion, perhaps some of the readers will be inspired by this
story to read every book in their libraries about the superstring
theory. Perhaps some of the young readers of this article will be the
ones to complete this quest for the Theory of the Universe, begun so
many years ago by Einstein.