Hyperspace (4 page)

For decades, physicists have wondered why the four forces of nature appear to be so fragmented—why the “cheetah” looks so pitiful and broken in his cage. The fundamental reason why these four forces seem so dissimilar, notes Freund, is that we have been observing the “caged cheetah.” Our three-dimensional laboratories are sterile zoo cages for the laws of physics. But when we formulate the laws in higher-dimensional space-time, their natural habitat, we see their true brilliance and power; the laws become simple and powerful. The revolution now sweeping over physics is the realization that the natural home for the cheetah may be hyperspace.

To illustrate how adding a higher dimension can make things simpler, imagine how major wars were fought by ancient Rome. The great Roman wars, often involving many smaller battlefields, were invariably fought with great confusion, with rumors and misinformation pouring in on both sides from many different directions. With battles raging on several fronts, Roman generals were often operating blind. Rome won its battles more from brute strength than from the elegance of its strategies. That is why one of the first principles of warfare is to seize the high ground—that is, to go
up
into the third dimension, above the two-dimensional battlefield. From the vantage point of a large hill with a panoramic view of the battlefield, the chaos of war suddenly becomes vastly reduced. In other words, viewed from the third dimension (that is, from the top of the hill), the confusion of the smaller battlefields becomes integrated into a coherent single picture.

Another application of this principle—that nature becomes simpler when expressed in higher dimensions—is the central idea behind Einstein’s special theory of relativity. Einstein revealed time to be the fourth dimension, and he showed that space and time could conveniently be unified in a four-dimensional theory. This, in turn, inevitably led to the unification of all physical quantities measured by space and time, such as matter and energy. He then found the precise mathematical expression for this unity between matter and energy:
E
=
mc
²
, perhaps the most celebrated of all scientific equations.
^*

To appreciate the enormous power of this unification, let us now describe the four fundamental forces, emphasizing how different they are, and how higher dimensions may give us a unifying formalism. Over the past 2,000 years, scientists have discovered that all phenomena in our universe can be reduced to four forces, which at first bear no resemblance to one another.

The electromagnetic force takes a variety of forms, including electricity, magnetism, and light itself. The electromagnetic force lights our cities, fills the air with music from radios and stereos, entertains us with television, reduces housework with electrical appliances, heats our food with
microwaves, tracks our planes and space probes with radar, and electrifies our power plants. More recently, the power of the electromagnetic force has been used in electronic computers (which have revolutionized the office, home, school, and military) and in lasers (which have introduced new vistas in communications, surgery, compact disks, advanced Pentagon weaponry, and even the check-out stands in groceries). More than half the gross national product of the earth, representing the accumulated wealth of our planet, depends in some way on the electromagnetic force.

The strong nuclear force provides the energy that fuels the stars; it makes the stars shine and creates the brilliant, life-giving rays of the sun. If the strong force suddenly vanished, the sun would darken, ending all life on earth. In fact, some scientists believe that the dinosaurs were driven to extinction 65 million years ago when debris from a comet impact was blown high into the atmosphere, darkening the earth and causing the temperature around the planet to plummet. Ironically, it is also the strong nuclear force that may one day take back the gift of life. Unleashed in the hydrogen bomb, the strong nuclear force could one day end all life on earth.

The weak nuclear force governs certain forms of radioactive decay. Because radioactive materials emit heat when they decay or break apart, the weak nuclear force contributes to heating the radioactive rock deep within the earth’s interior. This heat, in turn, contributes to the heat that drives the volcanoes, the rare but powerful eruptions of molten rock that reach the earth’s surface. The weak and electromagnetic forces are also exploited to treat serious diseases: Radioactive iodine is used to kill tumors of the thyroid gland and fight certain forms of cancer. The force of radioactive decay can also be deadly: It wreaked havoc at Three Mile Island and Chernobyl; it also creates radioactive waste, the inevitable by-product of nuclear weapons production and commercial nuclear power plants, which may remain harmful for millions of years.

The gravitational force keeps the earth and the planets in their orbits and binds the galaxy. Without the gravitational force of the earth, we
would be flung into space like rag dolls by the spin of the earth. The air we breathe would be quickly diffused into space, causing us to asphyxiate and making life on earth impossible. Without the gravitational force of the sun, all the planets, including the earth, would be flung from the solar system into the cold reaches of deep space, where sunlight is too dim to support life. In fact, without the gravitational force, the sun itself would explode. The sun is the result of a delicate balancing act between the force of gravity, which tends to crush the star, and the nuclear force, which tends to blast the sun apart. Without gravity, the sun would detonate like trillions upon trillions of hydrogen bombs.

The central challenge of theoretical physics today is to unify these four forces into a single force. Beginning with Einstein, the giants of twentieth-century physics have tried and failed to find such a unifying scheme. However, the answer that eluded Einstein for the last 30 years of his life may lie in hyperspace.

Einstein once said, “Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.”
³
If Einstein is correct, then perhaps these four forces are the “tail of the lion,” and the “lion” itself is higher-dimensional space-time. This idea has fueled the hope that the physical laws of the universe, whose consequences fill entire library walls with books densely packed with tables and graphs, may one day be explained by a single equation.

Central to this revolutionary perspective on the universe is the realization that higher-dimensional
geometry
may be the ultimate source of unity in the universe. Simply put, the matter in the universe and the forces that hold it together, which appear in a bewildering, infinite variety of complex forms, may be nothing but different vibrations of hyperspace. This concept, however, goes against the traditional thinking among scientists, who have viewed space and time as a passive stage on which the stars and the atoms play the leading role. To scientists, the visible universe of matter seemed infinitely richer and more diverse than the empty, unmoving arena of the invisible universe of space-time. Almost all the intense scientific effort and massive government funding in particle physics has historically gone to cataloging the properties of subatomic particles, such as “quarks” and “gluons,” rather than fathoming
the nature of geometry. Now, scientists are realizing that the “useless” concepts of space and time may be the ultimate source of beauty and simplicity in nature.

The first theory of higher dimensions was called
Kaluza-Klein theory
, after two scientists who proposed a new theory of gravity in which light could be explained as vibrations in the fifth dimension. When extended to
N
-dimensional space (where
N
can stand for any whole number), the clumsy-looking theories of subatomic particles dramatically take on a startling symmetry. The old Kaluza-Klein theory, however, could not determine the correct value of
N
, and there were technical problems in describing all the subatomic particles. A more advanced version of this theory, called
supergravity theory
, also had problems. The recent interest in the theory was sparked in 1984 by physicists Michael Green and John Schwarz, who proved the consistency of the most advanced version of Kaluza-Klein theory, called
superstring theory
, which postulates that all matter consists of tiny vibrating strings. Surprisingly, the superstring theory predicts a precise number of dimensions for space and time: ten.
^*

The advantage of ten-dimensional space is that we have “enough room” in which to accommodate all four fundamental forces. Furthermore, we have a simple physical picture in which to explain the confusing jumble of subatomic particles produced by our powerful atom smashers. Over the past 30 years, hundreds of subatomic particles have been carefully cataloged and studied by physicists among the debris created by smashing together protons and electrons with atoms. Like bug collectors patiently giving names to a vast collection of insects, physicists have at times been overwhelmed by the diversity and complexity of these subatomic particles. Today, this bewildering collection of subatomic particles can be explained as mere vibrations of the hyperspace theory.

The hyperspace theory has also reopened the question of whether hyperspace can be used to travel through space and time. To understand this
concept, imagine a race of tiny flatworms living on the surface of a large apple. It’s obvious to these worms that their world, which they call Apple-world, is flat and two dimensional, like themselves. One worm, however, named Columbus, is obsessed by the notion that Appleworld is somehow finite and curved in something he calls the third dimension. He even invents two new words,
up
and
down
, to describe motion in this invisible third dimension. His friends, however, call him a fool for believing that Appleworld could be bent in some unseen dimension that no one can see or feel. One day, Columbus sets out on a long and arduous journey and disappears over the horizon. Eventually he returns to his starting point, proving that the world is actually curved in the unseen third dimension. His journey proves that Appleworld is curved in a higher unseen dimension, the third dimension. Although weary from his travels, Columbus discovers that there is yet another way to travel between distant points on the apple: By burrowing into the apple, he can carve a tunnel, creating a convenient shortcut to distant lands. These tunnels, which considerably reduce the time and discomfort of a long journey, he calls
wormholes
. They demonstrate that the shortest path between two points is not necessarily a straight line, as he’s been taught, but a worm-hole.

One strange effect discovered by Columbus is that when he enters one of these tunnels and exits at the other end, he finds himself back in the past. Apparently, these wormholes connect parts of the apple where time beats at different rates. Some of the worms even claim that these wormholes can be molded into a workable time machine.

Later, Columbus makes an even more momentous discovery—his Appleworld is actually not the only one in the universe. It is but one apple in a large apple orchard. His apple, he finds out, coexists with hundreds of others, some with worms like themselves, and some without worms. Under certain rare circumstances, he conjectures, it may even be possible to journey between the different apples in the orchard.

We human beings are like the flatworms. Common sense tells us that our world, like their apple, is flat and three dimensional. No matter where we go with our rocket ships, the universe seems flat. However, the fact that our universe, like Appleworld, is curved in an unseen dimension beyond our spatial comprehension has been experimentally verified by a number of rigorous experiments. These experiments, performed on the path of light beams, show that starlight is bent as it moves across the universe.

When we wake up in the morning and open the window to let in some fresh air, we expect to see the front yard. We do
not
expect to face the towering pyramids of Egypt. Similarly, when we open the front door, we expect to see the cars on the street, not the craters and dead volcanoes of a bleak, lunar landscape. Without even thinking about it, we assume that we can safely open windows or doors without being scared out of our wits. Our world, fortunately, is not a Steven Spielberg movie. We act on a deeply ingrained prejudice (which is invariably correct) that our world is
simply connected
, that our windows and doorways are not entrances to wormholes connecting our home to a far-away universe. (In ordinary space, a lasso of rope can always be shrunk to a point. If this is possible, then the space is called simply connected. However, if the lasso is placed around the entrance of the wormhole, then it cannot be shrunk to a point. The lasso, in fact, enters the wormhole. Such spaces, where lassos are not contractible, are called
multiply connected
. Although the bending of our universe in an unseen dimension has been experimentally measured, the existence of wormholes and whether our universe is multiply connected or not is still a topic of scientific controversy.)

Mathematicians dating back to Georg Bernhard Riemann have studied the properties of multiply connected spaces in which different regions of space and time are spliced together. And physicists, who once thought this was merely an intellectual exercise, are now seriously studying multiply connected worlds as a practical model of our universe. These models are the scientific analogue of Alice’s looking glass. When Lewis Carroll’s White Rabbit falls down the rabbit hole to enter Wonderland, he actually falls down a wormhole.