by Michio Kaku
What lies beyond our 4 dimensions?
Any carp scientist daring to talk about
“hyperspace”, i.e. the third dimension “above” the pond, would
immediately be labeled a crank. I wondered what would happen if I
could reach down and grab a carp scientist and lift it up into
hyperspace. I thought what a wondrous story the scientist would tell
the others! The carp would babble on about unbelievable new laws of
physics: beings who could move without fins. Beings who could
breathe without gills. Beings who could emit sounds without bubbles.
I then wondered: how would a carp scientist know about our
existence? One day it rained, and I saw the rain drops forming
gentle ripples on the surface of the pond.
The quantum theory, by contrast, is a theory of the very small, i.e. the world of sub-atomic particles. It is based on discrete, tiny packets of energy called quanta.
Over the past 50 years, many attempts have been tried to unite these polar opposites, and have failed. The road to the Unified Field Theory, the Theory of Everything, is littered with the corpses of failed attempts. The key to the puzzle may be hyperspace. In 1915, when Einstein said space-time was four dimensional and was warped and rippled, he showed that this bending produced a “force” called gravity.
In 1921, Theodr Kaluza wrote that
ripples of the fifth dimension could be viewed as light. Like the
fish seeing the ripples in hyperspace moving in their world, many
physicists believe that light is created by ripples in
(This seems so simple, but in the 1950s, physicists were drowning in an avalanche of sub-atomic particles. J.R. Oppenheimer, who helped build the atomic bomb, even said, out of sheer frustration, that the Nobel Prize should go to the physicist who does NOT discover a new particle that year!)
Similarly, when the string moves in
space and time, it warps the space around it just as Einstein
predicted. Thus, in a remarkably simple picture, we can unify
gravity -as the bending of space caused by moving strings- with the
other quantum forces (now viewed as vibrations of the string).
But there is a way out to this seemingly intractable problem. A theory of everything is also a theory of the everyday. Thus, this theory, when fully completed, will be able to explain the existence of protons, atoms, molecules, even DNA. Thus, the key is to fully solve the theory and test the theory against the known properties of the universe. At present, no one on earth is smart enough to complete the theory. The theory is perfectly well-defined, but you see, superstring theory is 21st Century physics that fell accidentally into the 20th century.
It was discovered purely by accident, when two young physicists were thumbing through a mathematics book. The theory is so elegant and powerful, we were never “destined” to see it in the 20th century. The problem is that 21st century mathematics has not yet been invented yet. But since physicists are genetically predisposed to be optimists, I am confident that we will solve the theory someday soon. Perhaps a young person reading this article will be so inspired by this story that he or she will finish the theory.
I can't wait!
A look at the higher dimensions
Spending their entire lives at the bottom of the pond, the carp would believe that their “universe” consisted of the water and the lilies; they would only be dimly aware that an alien world could exist just above the surface. My world was beyond their comprehension. I was intrigued that I could sit only a few inches from the carp, yet we were separated by an immense chasm. I concluded that if there were any “scientists” among the carp, they would scoff at any fish who proposed that a parallel world could exist just above the lilies. An unseen world beyond the pond made no scientific sense.
Once I imagined what would happen if I reached down and suddenly grabbed one of the carp “scientists” out of the pond. I wondered, how would this appear to the carp? The startled carp “scientist” would tell a truly amazing story, being somehow lifted out of the universe (the pond) and hurled into a mysterious nether world, another dimension with blinding lights and strange-shaped objects that no carp had ever seen before. The strangest of all was the massive creature responsible for this outrage, who did not resemble a fish in the slightest. Shockingly, it had no fins whatsoever, but nevertheless could move without them.
Obviously, the familiar laws of physics
no longer applied in this nether world!
The ultimate goal of physics, some believe, is to have a single equation or expression from which this colossal volume of information can be derived from first principles. Today, many physicists believe that we have found the “unified field theory” which eluded Einstein for the last thirty years of his life. Although the theory of higher dimensional space has not been verified (and, we shall see, would be prohibitively expensive to prove experimentally), almost 5,000 papers, at last count, have been published in the physics literature concerning higher dimensional theories, beginning with the pioneering papers of Theodore Kaluza and Oskar Klein in the 1920's and 30s, to the super-gravity theory of the 1970s, and finally to the superstring theory of the 1980s and 90s.
In fact, the superstring theory, which
postulates that matter consists of tiny strings vibrating in
hyperspace, predicts the precise number of dimensions of space and
(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
spatial dimension, there simply was no advantage in developing a
brain with the ability to visualize objects moving in four
If one of the Flatlanders is incarcerated in jail (which is a circle enclosing the Flatlander) we can simply peel the person off from Flatland into the third dimension and place the Flatlander back somewhere else. If we become more ambitious and stick our fingers and arms through Flatland, the Flatlanders would only see circles of flesh that hover around them, constantly changing shape and merging into other circles. And lastly, if we fling a Flatlander into our three dimensional world, the Flatlander can only see two dimensional cross sections of our world, i.e. a phantasmagoria of circles, squares, etc. which constantly change shape and merge (see fig. 1 and 2).
Now imagine that we are “three dimensional Flatlanders” being visited by a higher dimensional being. If we became lost, a higher dimensional being could scan our entire universe all at once, peering directly into the most tightly sealed hiding places. If we became sick, a higher dimensional being could reach into our insides and perform surgery without ever cutting our skin. If we were in a maximum-security, escape-proof jail, a higher dimensional being could simply “yank” us into a higher dimension and redeposit us back somewhere else. If higher dimensional beings stick their “fingers” into our universe, they would appear to us to be blobs of flesh which float above us and constantly merge and split apart.
And lastly, if we are flung into hyperspace, we would see a collection of spheres, blobs, and polyhedra which suddenly appear, constantly change shape and color, and then mysteriously disappear. Higher dimensional people, therefore, would have powers similar to a god: they could walk through walls, disappear and reappear at will, reach into the strongest steel vaults, and see through buildings. They would be omniscient and omnipotent.
Not surprisingly, speculation about
higher dimensions has sparked enormous literary and artistic
interest over the last hundred years.
Sweeping landscapes and realistic, three dimensional people were painted from the point of view of a person's eye, with the lines of perspective vanishing into the horizon. Renaissance art reflected the way the human eye viewed the world, from the singular point of view of the observer. In other words, Renaissance art discovered the third dimension. With the beginning of the machine age and capitalism, the artistic world revolted against the cold materialism that seemed to dominate industrial society. To the Cubists, positivism was a straitjacket that confined us to what could be measured in the laboratory, suppressing the fruits of our imagination.
They asked: Why must art be clinically “realistic?”
This Cubist “revolt against perspective” seized the fourth dimension because it touched the third dimension from all possible perspectives. Simply put, Cubist art embraced the fourth dimension. Picasso's paintings are a splendid example, showing a clear rejection of three dimensional perspective, with women's faces viewed simultaneously from several angles. Instead of a single point-of-view, Picasso's paintings show multiple perspectives, as if they were painted by a being from the fourth dimension, able to see all perspectives simultaneously.
As art historian Linda Henderson has written,
The weather was impossible to explain
from the limited vantage point of the ancient Egyptians, to whom the
earth appeared flat, like a two-dimensional plane.
The weak force is the force responsible for radio active decay involving electrons. The weak force is harnessed in modern hospitals in the form of radioactive tracers used in nuclear medicine. The weak force also wrecked havoc at Chernobyl.
Historically, whenever scientists unraveled the secrets of one of the four fundamental forces, this irrevocably altered the course of modern civilization, from the mastery of mechanics and Newtonian physics in the 1700s, to the harnessing of the electro-magnetism in the 1800s, and finally to the unlocking of the nuclear force in the 1900s. In some sense, some of the greatest breakthroughs in the history of science can be traced back to the gradual understanding of these four fundamental forces.
Some have even claimed that the progress of the last 2,000 years of science can be understood as the successive 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? 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 Wolf gang Pauli's explanation of his version of the unified field theory. In frustration, Bohr finally stood up and said,
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. There is widespread belief
(although certainly not unanimous by any means) in the world's major
re search laboratories that we have at last found the Theory of
James Clerk Maxwell, in the last
century, proved that the electro-magnetic force can be described by
four numbers at each point in four dimensional space-time (labeled
by A _ 1, A _ 2 , A _ 3 , A _ 4 ). These four numbers, in turn, obey
a set of equations (called Maxwell's field equations).
Kaluza then re-defined the 5th column
and row of the gravitation al field to be the electromagnetic field
of Maxwell. The truly miraculous feature of this construction is
that the five dimensional theory of gravity reduces down precisely
to Einstein's original theory of gravity plus Maxwell's theory of
light. In other words, by adding the fifth dimension, we have
trivially unified light with gravity. In other words, light is now
viewed as vibrations in the fifth dimension. In five dimensions,
there is “enough room” to unify both gravity and light.
Simply put, by adding more dimensions, we are able to describe more forces. Similarly, by adding higher dimensions and further embellishing this approach (with something called “super-symmetry), we can explain the entire particle “zoo” that has been discovered over the past thirty years, with bizarre names like quarks, neutrinos, muons, gluons, etc.
Although the mathematics required to
extend the idea of Kaluza has reached truly breathtaking heights,
startling even professional mathematicians, the basic idea behind
unification remains surprisingly simple: the forces of nature can be
viewed as vibrations in higher dimensional space.
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 collapsed and curled up into a tiny ball, allowing the remaining four dimensional universe to explode outward at an enormous rate.
The four dimensional universe (our
world) expanded rapidly, creating the Big Bang, while the six
dimensional universe wrapped itself into a tiny ball and shrunk down
to infinitesimal size. This explains the origin of the Big Bang. The
cur rent expansion of the universe, which we can measure with our
instruments, is a rather minor aftershock of a more cataclysmic
collapse: the breaking of a 10 dimensional universe into a four and
six dimensional universe.
Anyone unfortunate enough to get too
close to the funnel inexorably falls into it and is crushed to
death. One puzzle, however, is that, according to Einstein's
equations, the funnel of a black hole necessarily connects our
universe with a parallel universe. Furthermore, if the funnel
connects our universe with itself, then we have a “worm hole” (see
fig. 7). These anomalies did not bother Einstein because it was
thought that travel through the neck of the funnel, called the
“Einstein-Rosen bridge,” would be impossible (since anyone falling
into the black hole would be killed).
(Thorne is undaunted by the fact that the energy necessary to open an Einstein-Rosen bridge exceeds that of a star, and is hence beyond the reach of present-day technology. But to Thorne, this is just a small detail for the engineers of some sufficiently advanced civilization in outer space!)
Thorne even gives a crude idea of what a time machine might look like when built. (Imagine, however, the chaos that could erupt if time machines were as common as cars. History books could never be written. Thousands of meddlers would constantly be going back in time to eliminate the ancestors of their enemies, to change the outcome of World War I and II, to save John Kennedy's and Abraham Lincoln's life, etc.
“History” as we know it would become
impossible, throwing professional historians out of work. With every
turn of a time machine's dial, history would be changing like sands
being blown by the wind.) Other physicists, however, like Steven
Hawking, are dubious about time travel. They argue that quantum
effects (such as intense radiation fields at the funnel) may close
the Einstein-Rosen bridge. Hawking even advanced an experimental
“proof” that time machines are not possible (i.e. if they existed,
we would have been visited by tourists from the future).
Both sides of the controversy over time
travel acknowledge that ultimately this question will be resolved by
the Theory of Everything.
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 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, therefore, means recreating Creation on the earth, which is impossible with present-day technology.
(This criticism applies, in fact, to any
theory of Creation. The philosopher David Hume, for example,
believed that a scientific theory of Creation was philosophically
impossible. This was because the foundation of science depends on
reproducibility, and Creation is one event which can never be
reproduced in the laboratory.)
That is why it is sometimes called a “window on Creation.” Costing /8-10 billion, the SSC consists of a ring of powerful magnets stretched out in a tube over 50 miles long. In fact, one could easily fit the Washington Beltway, which surrounds Washington D.C., inside the SSC. If and when it is built, physicists hope that the SSC will find some exotic sub-atomic particles in order to complete our present-day understanding of the four forces. However, there is also the small chance that physicists might discover “super- symmetric” 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 at energies not found since the Big Bang.