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08-13-2006, 10:41 PM

Hyperspace: A Scientific Odyssey

A look at = the=20 higher dimensions

By Michio Kaku

Do higher dimensions exist? = Are there=20 unseen worlds just beyond our reach, beyond the normal laws of physics? = Although=20 higher dimensions have historically been the exclusive realm of = charlatans,=20 mystics, and science fiction writers, many serious theoretical = physicists now=20 believe that higher dimensions not only exist, but may also explain some = of the=20 deepest secrets of nature. Although we stress that there is at present = no=20 experimental evidence for higher dimensions, in principle they may solve = the=20 ultimate problem in physics: the final unification of all physical = knowledge at=20 the fundamental level.

My own fascination with higher dimensions = began=20 early in childhood. One of my happiest childhood memories was crouching = next to=20 the pond at the famed Japanese Tea Garden in San Francisco, mesmerized = by the=20 brilliantly colored carp swimming slowly beneath the water lilies. In = these=20 quiet moments, I would ask myself a silly question that a only child = might ask:=20 how would the carp in that pond view the world around them? Spending = their=20 entire lives at the bottom of the pond, the carp would believe that = their=20 =93universe=94 consisted of the water and the lilies; they would only be = dimly aware=20 that an alien world could exist just above the surface. My world was = beyond=20 their comprehension. I was intrigued that I could sit only a few inches = from the=20 carp, yet we were separated by an immense chasm. I concluded that if = there were=20 any =93scientists=94 among the carp, they would scoff at any fish who = proposed that=20 a parallel world could exist just above the lilies. An unseen world = beyond the=20 pond made no scientific sense. Once I imagined what would happen if I = reached=20 down and suddenly grabbed one of the carp =93scientists=94 out of the = pond. I=20 wondered, how would this appear to the carp? The startled carp = =93scientist=94 would=20 tell a truly amazing story, being somehow lifted out of the universe = (the pond)=20 and hurled into a mysterious nether world, another dimension with = blinding=20 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=20 not resemble a fish in the slightest. Shockingly, it had no fins = whatsoever, but=20 nevertheless could move without them. Obviously, the familiar laws of = physics no=20 longer applied in this nether world!

The Theory of=20 Everything

Sometimes I believe that we are like the carp living = contently=20 on the bottom of that pond; we live our lives blissfully ignorant of = other=20 worlds that might co-exist with us, laughing at any suggestion of = parallel=20 universes.

All this has changed rather dramatically in the past = few=20 years. The theory of higher dimensional space may now become the central = piece=20 in unlocking the origin of the universe. At the center of this = conceptual=20 revolution is the idea that our familiar three dimensional universe is = =93too=20 small=94 to describe the myriad forces governing our universe. To = describe our=20 physical world, with its almost infinite variety of forms, requires = entire=20 libraries overflowing with mountains of technical journals and stacks of = obscure, learned books. The ultimate goal of physics, some believe, is = to have a=20 single equation or expression from which this colossal volume of = information can=20 be derived from first principles. Today, many physicists believe that we = have=20 found the =93unified field theory=94 which eluded Einstein for the last = thirty years=20 of his life. Although the theory of higher dimensional space has not = been=20 verified (and, we shall see, would be prohibitively expensive to prove=20 experimentally), almost 5,000 papers, at last count, have been published = in the=20 physics literature concerning higher dimensional theories, beginning = with the=20 pioneering papers of Theodore Kaluza and Oskar Klein in the 1920's and = 30s, to=20 the supergravity theory of the 1970s, and finally to the superstring = theory of=20 the 1980s and 90s. In fact, the superstring theory, which postulates = that matter=20 consists of tiny strings vibrating in hyperspace, predicts the precise = number of=20 dimensions of space and time: 10.

Why Can't we See the Fourth = Dimension?=20

To understand these higher dimensions, we remember that it takes = three=20 numbers to locate every object in the universe, from the tip of your = nose to the=20 ends of the world. For example, if you want to meet some friends in = Manhattan,=20 you tell them to meet you at the building at the corner of 42nd street = and 5th=20 avenue, on the 37th floor. It takes two numbers to locate your position = on a=20 map, and one number to specify the distance above the map. It thus takes = three=20 numbers to specify the location of your lunch. (If we meet our friends = at noon,=20 then it takes four numbers to specify the space and time of the=20 meeting.)

However, try as we may, it is impossible for our brains = to=20 visualize the fourth spatial dimension. Computers, of course, have no = problem=20 working in N dimensional space, but spatial dimensions beyond three = simply=20 cannot be conceptualized by our feeble brains. (The reason for this = unfortunate=20 accident has to do with biology, rather than physics. Human evolution = put a=20 premium on being able to visualize objects moving in three dimensions.=20

There was a selection pressure placed on humans who could dodge = lunging=20 saber tooth tigers or hurl a spear at a charging mammoth. Since tigers = do not=20 attack us in the fourth spatial dimension, there simply was no advantage = in=20 developing a brain with the ability to visualize objects moving in four=20 dimensions.)

Meeting a Higher Dimensional Being

To understand = some of=20 the mind-bending features of higher dimensions, imagine a = two-dimensional world,=20 called Flat land (after Edwin A. Abbott's celebrated novel) that = resembles a=20 world existing on a flat table-top. If one of the Flatlanders becomes = lost, we=20 can quickly scan all of Flatland, peering directly inside houses, = buildings, and=20 even concealed places. If one of the Flatlanders becomes sick, we can = reach=20 directly into their insides and per form surgery, without ever cutting = their=20 skin. If one of the Flatlanders is incarcerated in jail (which is a = circle=20 enclosing the Flatlander) we can simply peel the person off from = Flatland into=20 the third dimension and place the Flatlander back somewhere else. If we = become=20 more ambitious and stick our fingers and arms through Flatland, the = Flatlanders=20 would only see circles of flesh that hover around them, constantly = changing=20 shape and merging into other circles. And lastly, if we fling a = Flatlander into=20 our three dimensional world, the Flatlander can only see two dimensional = cross=20 sections of our world, i.e. a phantasmagoria of circles, squares, etc. = which=20 constantly change shape and merge (see fig. 1 and 2). Now imagine that = we are=20 =93three dimensional Flatlanders=94 being visited by a higher = dimensional being. If=20 we became lost, a higher dimensional being could scan our entire = universe all at=20 once, peering directly into the most tightly sealed hiding places. If we = became=20 sick, a higher dimensional being could reach into our insides and = perform=20 surgery without ever cutting our skin. If we were in a maximum-security, = escape-proof jail, a higher dimensional being could simply =93yank=94 us = into a=20 higher dimension and redeposit us back somewhere else. If higher = dimensional=20 beings stick their =93fingers=94 into our universe, they would appear to = us to be=20 blobs of flesh which float above us and constantly merge and split = apart. And=20 lastly, if we are flung into hyperspace, we would see a collection of = spheres,=20 blobs, and polyhedra which suddenly appear, constantly change shape and = color,=20 and then mysteriously disappear. Higher dimensional people, therefore, = would=20 have powers similar to a god: they could walk through walls, disappear = and=20 reappear at will, reach into the strongest steel vaults, and see through = buildings. They would be omniscient and omnipotent. Not surprisingly,=20 speculation about higher dimensions has sparked enormous literary and = artistic=20 interest over the last hundred years.

Mystics and = Mathematics

Fyodor=20 Dostoyevsky, in The Brothers Karamazov, had his protagonist Ivan = Karamazov=20 speculate on the existence of higher dimensions and non-Euclidean = geometries=20 during a discussion on the existence of God. In H. G. Wells' The = Invisible Man,=20 the source of invisibility was his ability to manipulate the fourth = dimension.=20 Oscar Wilde even refers to the fourth dimension in his play The = Canterville=20 Ghost as the homeworld for ghosts.

The fourth dimension also appears = in the=20 literary works of Marcel Proust and Joseph Conrad; it inspired some of = the=20 musical works of Alexander Scriabin, Edgar Varege, and George Antheil. = It=20 fascinated such diverse personalities as the psychologist William James, = literary figure Gertrude Stein, and revolutionary socialist Vladimir = Lenin.=20 Lenin even waged a polemic on the N-th dimension with philosopher Ernst = Mach in=20 his Materialism and Empirio-Criticism. Lenin praised Mach, who =93has = raised the=20 very important and useful question of a space of n-dimensions as a = conceivable=20 space,=94 but then took him to task by insisting that the Tsar could = only be=20 overthrown in the third dimension.

Artists have been particularly = interested in the fourth dimension because of the possibilities of = discovering=20 new laws of perspective. In the Middle Ages, religious art was = distinctive for=20 its deliberate lack of perspective. Serfs, peasants, and kings were = depicted as=20 if they were flat, much the way children draw people. Since God was = omnipotent=20 and could therefore see all parts of our world equally, art had to = reflect His=20 point of view, so the world was painted two-dimensionally. Renaissance = art was a=20 revolt against this flat God- centered perspective. Sweeping landscapes = and=20 realistic, three dimensional people were painted from the point of view = of a=20 person's eye, with the lines of perspective vanishing into the horizon.=20 Renaissance art reflected the way the human eye viewed the world, from = the=20 singular point of view of the observer. In other words, Renaissance art=20 discovered the third dimension. With the beginning of the machine age = and=20 capitalism, the artistic world revolted against the cold materialism = that seemed=20 to dominate industrial society. To the Cubists, positivism was a = straitjacket=20 that confined us to what could be measured in the laboratory, = suppressing the=20 fruits of our imagination. They asked: Why must art be clinically = =93realistic?=94=20 This Cubist =93revolt against perspective=94 seized the fourth dimension = because it=20 touched the third dimension from all possible perspectives. Simply put, = Cubist=20 art embraced the fourth dimension. Picasso's paintings are a splendid = example,=20 showing a clear rejection of three dimensional perspective, with women's = faces=20 viewed simultaneously from several angles. Instead of a single = point-of-view,=20 Picasso's paintings show multiple perspectives, as if they were painted = by a=20 being from the fourth dimension, able to see all perspectives = simultaneously. As=20 art historian Linda Henderson has written, =93the fourth dimension and=20 non-Euclidean geometry emerge as among the most important themes = unifying much=20 of modern art and theory.=94

Unifying the Four = Forces

Historically,=20 physicists dismissed the theory of higher dimensions because they could = never be=20 measured, nor did they have any particular use. But to understand how = adding=20 higher dimensions can, in fact, simplify physical problems, consider the = following example. To the ancient Egyptians, the weather was a complete = mystery.=20 What caused the seasons? Why did it get warmer as they traveled south? = The=20 weather was impossible to explain from the limited vantage point of the = ancient=20 Egyptians, to whom the earth appeared flat, like a two-dimensional=20 plane.

But now imagine sending the Egyptians in a rocket into = outer=20 space, where they can see the earth as simple and whole in its orbit = around the=20 sun. Suddenly, the answers to these questions become obvious. From outer = space,=20 it is clear that the earth tilts about 23 degrees on its axis in its = orbit=20 around the sun. Because of this tilt, the northern hemisphere receives = much less=20 sunlight during one part of its orbit than during another part. Hence we = have=20 winter and summer. And since the equator receives more sunlight on the = average=20 than the northern or southern polar regions,

it becomes warmer as we = approach the equator.

In summary, the rather obscure laws of the = weather=20 are easy to understand once we view the earth from space. Thus, the = solution to=20 the problem is to go up into space, into the third dimension. Facts that = were=20 impossible to understand in a flat world suddenly become obvious when = viewing a=20 unified picture of a three dimensional earth.

The Four Fundemental=20 Forces

Similarly, the current excitement over higher dimensions = is that=20 they may hold the key to the unification of all known forces. The = culmination of=20 2,000 years of painstaking observation is the realization that that our = universe=20 is governed by four fundamental forces. These four forces, in turn, may = be=20 unified in higher dimensional space. Light, for example, may be viewed = simply as=20 vibrations in the fifth dimension. The other forces of nature may be = viewed as=20 vibrations in increasingly higher dimensions. At first glance, however, = the four=20 fundamental forces seem to bear no resemblance to each other. They are:=20

Gravity is the force which keeps our feet anchored to the spinning = earth and=20 binds the solar system and the galaxies together. Without gravity, we = would be=20 immediately flung into outer space at l,000 miles per hour. Furthermore, = without=20 gravity holding the sun together, it would explode in a catastrophic = burst of=20 energy. Electro-magnetism is the force which lights up our cities and = energizes=20 our household appliances. The electronic revolution, which has given us = the=20 light bulb, TV, the telephone, computers, radio, radar, microwaves, = light bulbs,=20 and dishwashers, is a byproduct of the electro-magnetic = force.

The strong=20 nuclear force is the force which powers the sun. Without the nuclear = force, the=20 stars would flicker out and the heavens would go dark. The nuclear force = not=20 only makes life on earth possible, it is also the devastating force = unleashed by=20 a hydrogen bomb, which can be compared to a piece of the sun brought = down to=20 earth. The weak force is the force responsible for radio active decay = involving=20 electrons. The weak force is harnessed in modern hospitals in the form = of=20 radioactive tracers used in nuclear medicine. The weak force also = wrecked havoc=20 at Chernobyl. Historically, whenever scientists unraveled the secrets of = one of=20 the four fundamental forces, this irrevocably altered the course of = modern=20 civilization, from the mastery of mechanics and Newtonian physics in the = 1700s,=20 to the harnessing of the electro-magnetism in the 1800s, and finally to = the=20 unlocking of the nuclear force in the 1900s. In some sense, some of the = greatest=20 breakthroughs in the history of science can be traced back to the = gradual=20 understanding of these four fundamental forces. Some have even claimed = that the=20 progress of the last 2,000 years of science can be understood as the = successive=20 mastery of these four fundamental forces. Given the importance of these = four=20 fundamental forces, the next question is: can they be united into one = super=20 force? Are they but the manifestations of a deeper reality? Given the = fruitless=20 search that has stumped the world's Nobel Prize winners for half a = century, most=20 physicists agree that the Theory of Everything must be a radical = departure from=20 everything that has been tried before. For example, Niels Bohr, founder = of the=20 modern atomic theory, once listened to Wolf gang Pauli's explanation of = his=20 version of the unified field theory. In frustration, Bohr finally stood = up and=20 said, =93We are all agreed that your theory is absolutely crazy. But = what divides=20 us is whether your theory is crazy enough.=94

Today, however, = after decades=20 of false starts and frustrating dead ends, many of the world's leading=20 physicists think that they have finally found the theory =93crazy = enough=94 to be=20 the unified field theory. There is widespread belief (although certainly = not=20 unanimous by any means) in the world's major re search laboratories that = we have=20 at last found the Theory of Everything.

Field Theory in Higher=20 Dimension

To see how higher dimensions helps to unify the laws of = nature,=20 physicists use the mathematical device called =93field theory.=94 For = example, the=20 magnetic field of a bar magnet resembles a spider's web which fills up = all of=20 space. To describe the magnetic field, we introduce the field, a series = of=20 numbers defined at each point in space which describes the intensity and = direction of the force at that point. James Clerk Maxwell, in the last = century,=20 proved that the electro-magnetic force can be described by four numbers = at each=20 point in four dimensional space-time (labeled by A _ 1, A _ 2 , A _ 3 , = A _ 4 ).=20 These four numbers, in turn, obey a set of equations (called Maxwell's = field=20 equations).

For the gravitational force, Einstein showed that the = field=20 requires a total of 10 numbers at each point in four dimensions. These = 10=20 numbers can be assembled into the array shown in fig. 3. (Since g _ 12 = =3D g _ 21=20 , only 10 of the 16 numbers contained within the array are independent.) = The=20 gravitational field, in turn, obey Einstein's field equations. The key = idea of=20 Theodore Kaluza in the 1920s was to write down a five dimensional theory = of=20 gravity. In five dimensions, the gravitational field has 15 independent = numbers,=20 which can be arranged in a five dimensional array (see fig.4). Kaluza = then=20 re-defined the 5th column and row of the gravitation al field to be the=20 electromagnetic field of Maxwell. The truly miraculous feature of this=20 construction is that the five dimensional theory of gravity reduces down = precisely to Einstein's original theory of gravity plus Maxwell's theory = of=20 light. In other words, by adding the fifth dimension, we have trivially = unified=20 light with gravity. In other words, light is now viewed as vibrations in = the=20 fifth dimension. In five dimensions, there is =93enough room=94 to unify = both=20 gravity and light.

This trick is easily extended. For example, if = we=20 generalize the theory to N dimensions, then the N dimensional = gravitational=20 field can be split-up into the following pieces (see fig. 5). Now, out = pops a=20 generalization of the electromagnetic field, called the =93Yang-Mills = field,=94=20 which is known to describe the nuclear forces. The nuclear forces, = therefore,=20 may be viewed as vibrations of higher dimensional space. Simply put, by = adding=20 more dimensions, we are able to describe more forces. Similarly, by = adding=20 higher dimensions and further embellishing this approach (with something = called=20 =93supersymmetry), we can explain the entire particle =93zoo=94 that has = been=20 discovered over the past thirty years, with bizarre names like quarks,=20 neutrinos, muons, gluons, etc. Although the mathematics required to = extend the=20 idea of Kaluza has reached truly breathtaking heights, startling even=20 professional mathematicians, the basic idea behind unification remains=20 surprisingly simple: the forces of nature can be viewed as vibrations in = higher=20 dimensional space.

What Happened Before the Big Bang?

One = advantage=20 to having a theory of all forces is that we may be able to resolve some = of the=20 thorniest, long-standing questions in physics, such as the origin of the = universe, and the existence of =93wormholes=94 and even time machines. = The 10=20 dimensional superstring theory, for example, gives us a compelling = explanation=20 of the origin of the Big Bang, the cosmic explosion which took place 15 = to 20=20 billion years ago, which sent the stars and galaxies hurling in all = directions.=20 In this theory, the universe originally started as a perfect 10 = dimensional=20 universe with nothing in it. In the beginning, the universe was = completely=20 empty. However, this 10 dimensional universe was not stable. The = original 10=20 dimensional space-time finally =93cracked=94 into two pieces, a four and = a six=20 dimensional universe. The universe made the =93quantum leap=94 to = another universe=20 in which six of the 10 dimensions collapsed and curled up into a tiny = ball,=20 allowing the remaining four dimensional universe to explode outward at = an=20 enormous rate. The four dimensional universe (our world) expanded = rapidly,=20 creating the Big Bang, while the six dimensional universe wrapped itself = into a=20 tiny ball and shrunk down to infinitesimal size. This explains the = origin of the=20 Big Bang. The cur rent expansion of the universe, which we can measure = with our=20 instruments, is a rather minor aftershock of a more cataclysmic = collapse: the=20 breaking of a 10 dimensional universe into a four and six dimensional=20 universe.

In principle, this also explains why we cannot measure = the six=20 dimensional universe, because it has shrunk down to a size much smaller = than an=20 atom. Thus, no earth-bound experiment can measure the six dimensional = universe=20 because it has curled up into a ball too small to be analyzed by even = our most=20 powerful instruments. (This will be disappointing to those who would = like to=20 visit these higher dimensions in their lifetimes. These higher = dimensions are=20 much too small to enter.)

Time Machines?

Another longstanding = puzzle=20 concerns parallel universes and time travel. According to Einstein's = theory of=20 gravity, space-time can be visualized as a fabric which is stretched and = distorted by the presence of matter and energy. The gravitational field = of a=20 black hole, for example, can be visualized as a funnel, with a dead, = collapsed=20 star at the very center (see fig. 6). Anyone unfortunate enough to get = too close=20 to the funnel inexorably falls into it and is crushed to death. One = puzzle,=20 however, is that, according to Einstein's equations, the funnel of a = black hole=20 necessarily connects our universe with a parallel universe. Furthermore, = if the=20 funnel connects our universe with itself, then we have a =93worm hole=94 = (see fig.=20 7). These anomalies did not bother Einstein because it was thought that = travel=20 through the neck of the funnel, called the =93Einstein-Rosen bridge,=94 = would be=20 impossible (since anyone falling into the black hole would be=20 killed).

However, over the years physicists like Roy Kerr as well = as Kip=20 Thorne at the Calif. Institute of Technology have found new solutions of = Einstein's equations in which the gravitational field does not become = infinite=20 at the center, i.e. in principle, a rocket ship could travel through the = Einstein- Rosen bridge to an alternate universe (or a distant part of = our own=20 universe) without being ripped apart by intense gravitational fields. = (This=20 wormhole is, in fact, the mathematical representation of Alice's Looking = Glass.)

Even more intriguing, these wormholes can be viewed as = time=20 machines. Since the two ends of the wormhole can connect two time eras, = Thorne=20 and his colleagues have calculated the conditions necessary to enter the = wormhole in one time era and exit the other side at another time era. = (Thorne is=20 undaunted by the fact that the energy necessary to open an = Einstein-Rosen bridge=20 exceeds that of a star, and is hence beyond the reach of present-day = technology.=20 But to Thorne, this is just a small detail for the engineers of some=20 sufficiently advanced civilization in outer space!) Thorne even gives a = crude=20 idea of what a time machine might look like when built. (Imagine, = however, the=20 chaos that could erupt if time machines were as common as cars. History = books=20 could never be written. Thousands of meddlers would constantly be going = back in=20 time to eliminate the ancestors of their enemies, to change the outcome = of World=20 War I and II, to save John Kennedy's and Abraham Lincoln's life, etc. = =93History=94=20 as we know it would become impossible, throwing professional historians = out of=20 work. With every turn of a time machine's dial, history would be = changing like=20 sands being blown by the wind.) Other physicists, however, like Steven = Hawking,=20 are dubious about time travel. They argue that quantum effects (such as = intense=20 radiation fields at the funnel) may close the Einstein-Rosen bridge. = Hawking=20 even advanced an experimental =93proof=94 that time machines are not = possible (i.e.=20 if they existed, we would have been visited by tourists from the=20 future).

This controversy has recently generated a flurry of = papers in=20 the physics literature. The essential problem is that although = Einstein's=20 equations for gravity allow for time travel, they also break down when=20 approaching the black hole, and quantum effects, such as radiation, take = over.=20 But to calculate if these quantum corrections are intense enough to = close the=20 Einstein-Rosen bridge, one necessarily needs a unified field theory = which=20 includes both Einstein's theory of gravity as well as the quantum theory = of=20 radiation. So there is hope that soon these questions may be answered = once and=20 for all by a unified field theory. Both sides of the controversy over = time=20 travel acknowledge that ultimately this question will be resolved by the = Theory=20 of Everything.

Recreating Creation

Although the 10 dimensional = superstring theory has been called the most fascinating discovery in = theoretical=20 physics in the past decades, its critics have focused on its weakest = point, that=20 it is almost impossible to test. The energy at which the four = fundamental forces=20 merge into a single, unified force occurs at the fabulous =93Planck = energy,=94 which=20 is a billion billion times greater than the energy found in a proton. = Even if=20 all the nations of the earth were to band together and single-mindedly = build the=20 biggest atom smasher in all history, it would still not be enough to = test the=20 theory. Because of this, some physicists have scoffed at the idea that=20 superstring theory can even be considered a legitimate =93theory.=94 = Nobel laureate=20 Sheldon Glashow, for example, has compared the superstring theory to the = former=20 Pres. Reagan's Star Wars program (because it is untestable and drains = the best=20 scientific talent).The reason why the theory cannot be tested is rather = simple.=20 The Theory of Everything is necessarily a theory of Creation, that is, = it must=20 explain everything from the origin of the Big Bang down to the lilies of = the=20 field. Its full power is manifested at the instant of the Big Bang, = where all=20 its symmetries were intact. To test this theory, therefore, means = recreating=20 Creation on the earth, which is impossible with present-day technology. = (This=20 criticism applies, in fact, to any theory of Creation. The philosopher = David=20 Hume, for example, believed that a scientific theory of Creation was=20 philosophically impossible. This was because the foundation of science = depends=20 on reproducibility, and Creation is one event which can never be = reproduced in=20 the laboratory.)

Although this is discouraging, a piece of the = puzzle may=20 be supplied by the Superconducting Supercollider (SSC), which, if built, = will be=20 the world's largest atom smasher. The SSC (which is likely to be = cancelled by=20 Congress) is designed to accelerate protons to a staggering energy of = tens of=20 trillions of electron volts. When these sub-atomic particles slam into = each=20 other at these fantastic energies within the SSC, temperatures which = have not=20 been seen since the instant of Creation will be generated. That is why = it is=20 sometimes called a =93window on Creation.=94 Costing /8-10 billion, the = SSC consists=20 of a ring of powerful magnets stretched out in a tube over 50 miles = long. In=20 fact, one could easily fit the Washington Beltway, which surrounds = Washington=20 D.C., inside the SSC. If and when it is built, physicists hope that the = SSC will=20 find some exotic sub-atomic particles in order to complete our = present-day=20 understanding of the four forces. However, there is also the small = chance that=20 physicists might discover =93super- symmetric=94 particles, which may be = remnants of=20 the original superstring theory. In other words, although the = superstring theory=20 cannot be tested directly by the SSC, one hopes to find resonances from = the=20 superstring theory among the debris created by smashing protons together = at=20 energies not found since the Big Bang.

A look at = the=20 higher dimensions

By Michio Kaku

Do higher dimensions exist? = Are there=20 unseen worlds just beyond our reach, beyond the normal laws of physics? = Although=20 higher dimensions have historically been the exclusive realm of = charlatans,=20 mystics, and science fiction writers, many serious theoretical = physicists now=20 believe that higher dimensions not only exist, but may also explain some = of the=20 deepest secrets of nature. Although we stress that there is at present = no=20 experimental evidence for higher dimensions, in principle they may solve = the=20 ultimate problem in physics: the final unification of all physical = knowledge at=20 the fundamental level.

My own fascination with higher dimensions = began=20 early in childhood. One of my happiest childhood memories was crouching = next to=20 the pond at the famed Japanese Tea Garden in San Francisco, mesmerized = by the=20 brilliantly colored carp swimming slowly beneath the water lilies. In = these=20 quiet moments, I would ask myself a silly question that a only child = might ask:=20 how would the carp in that pond view the world around them? Spending = their=20 entire lives at the bottom of the pond, the carp would believe that = their=20 =93universe=94 consisted of the water and the lilies; they would only be = dimly aware=20 that an alien world could exist just above the surface. My world was = beyond=20 their comprehension. I was intrigued that I could sit only a few inches = from the=20 carp, yet we were separated by an immense chasm. I concluded that if = there were=20 any =93scientists=94 among the carp, they would scoff at any fish who = proposed that=20 a parallel world could exist just above the lilies. An unseen world = beyond the=20 pond made no scientific sense. Once I imagined what would happen if I = reached=20 down and suddenly grabbed one of the carp =93scientists=94 out of the = pond. I=20 wondered, how would this appear to the carp? The startled carp = =93scientist=94 would=20 tell a truly amazing story, being somehow lifted out of the universe = (the pond)=20 and hurled into a mysterious nether world, another dimension with = blinding=20 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=20 not resemble a fish in the slightest. Shockingly, it had no fins = whatsoever, but=20 nevertheless could move without them. Obviously, the familiar laws of = physics no=20 longer applied in this nether world!

The Theory of=20 Everything

Sometimes I believe that we are like the carp living = contently=20 on the bottom of that pond; we live our lives blissfully ignorant of = other=20 worlds that might co-exist with us, laughing at any suggestion of = parallel=20 universes.

All this has changed rather dramatically in the past = few=20 years. The theory of higher dimensional space may now become the central = piece=20 in unlocking the origin of the universe. At the center of this = conceptual=20 revolution is the idea that our familiar three dimensional universe is = =93too=20 small=94 to describe the myriad forces governing our universe. To = describe our=20 physical world, with its almost infinite variety of forms, requires = entire=20 libraries overflowing with mountains of technical journals and stacks of = obscure, learned books. The ultimate goal of physics, some believe, is = to have a=20 single equation or expression from which this colossal volume of = information can=20 be derived from first principles. Today, many physicists believe that we = have=20 found the =93unified field theory=94 which eluded Einstein for the last = thirty years=20 of his life. Although the theory of higher dimensional space has not = been=20 verified (and, we shall see, would be prohibitively expensive to prove=20 experimentally), almost 5,000 papers, at last count, have been published = in the=20 physics literature concerning higher dimensional theories, beginning = with the=20 pioneering papers of Theodore Kaluza and Oskar Klein in the 1920's and = 30s, to=20 the supergravity theory of the 1970s, and finally to the superstring = theory of=20 the 1980s and 90s. In fact, the superstring theory, which postulates = that matter=20 consists of tiny strings vibrating in hyperspace, predicts the precise = number of=20 dimensions of space and time: 10.

Why Can't we See the Fourth = Dimension?=20

To understand these higher dimensions, we remember that it takes = three=20 numbers to locate every object in the universe, from the tip of your = nose to the=20 ends of the world. For example, if you want to meet some friends in = Manhattan,=20 you tell them to meet you at the building at the corner of 42nd street = and 5th=20 avenue, on the 37th floor. It takes two numbers to locate your position = on a=20 map, and one number to specify the distance above the map. It thus takes = three=20 numbers to specify the location of your lunch. (If we meet our friends = at noon,=20 then it takes four numbers to specify the space and time of the=20 meeting.)

However, try as we may, it is impossible for our brains = to=20 visualize the fourth spatial dimension. Computers, of course, have no = problem=20 working in N dimensional space, but spatial dimensions beyond three = simply=20 cannot be conceptualized by our feeble brains. (The reason for this = unfortunate=20 accident has to do with biology, rather than physics. Human evolution = put a=20 premium on being able to visualize objects moving in three dimensions.=20

There was a selection pressure placed on humans who could dodge = lunging=20 saber tooth tigers or hurl a spear at a charging mammoth. Since tigers = do not=20 attack us in the fourth spatial dimension, there simply was no advantage = in=20 developing a brain with the ability to visualize objects moving in four=20 dimensions.)

Meeting a Higher Dimensional Being

To understand = some of=20 the mind-bending features of higher dimensions, imagine a = two-dimensional world,=20 called Flat land (after Edwin A. Abbott's celebrated novel) that = resembles a=20 world existing on a flat table-top. If one of the Flatlanders becomes = lost, we=20 can quickly scan all of Flatland, peering directly inside houses, = buildings, and=20 even concealed places. If one of the Flatlanders becomes sick, we can = reach=20 directly into their insides and per form surgery, without ever cutting = their=20 skin. If one of the Flatlanders is incarcerated in jail (which is a = circle=20 enclosing the Flatlander) we can simply peel the person off from = Flatland into=20 the third dimension and place the Flatlander back somewhere else. If we = become=20 more ambitious and stick our fingers and arms through Flatland, the = Flatlanders=20 would only see circles of flesh that hover around them, constantly = changing=20 shape and merging into other circles. And lastly, if we fling a = Flatlander into=20 our three dimensional world, the Flatlander can only see two dimensional = cross=20 sections of our world, i.e. a phantasmagoria of circles, squares, etc. = which=20 constantly change shape and merge (see fig. 1 and 2). Now imagine that = we are=20 =93three dimensional Flatlanders=94 being visited by a higher = dimensional being. If=20 we became lost, a higher dimensional being could scan our entire = universe all at=20 once, peering directly into the most tightly sealed hiding places. If we = became=20 sick, a higher dimensional being could reach into our insides and = perform=20 surgery without ever cutting our skin. If we were in a maximum-security, = escape-proof jail, a higher dimensional being could simply =93yank=94 us = into a=20 higher dimension and redeposit us back somewhere else. If higher = dimensional=20 beings stick their =93fingers=94 into our universe, they would appear to = us to be=20 blobs of flesh which float above us and constantly merge and split = apart. And=20 lastly, if we are flung into hyperspace, we would see a collection of = spheres,=20 blobs, and polyhedra which suddenly appear, constantly change shape and = color,=20 and then mysteriously disappear. Higher dimensional people, therefore, = would=20 have powers similar to a god: they could walk through walls, disappear = and=20 reappear at will, reach into the strongest steel vaults, and see through = buildings. They would be omniscient and omnipotent. Not surprisingly,=20 speculation about higher dimensions has sparked enormous literary and = artistic=20 interest over the last hundred years.

Mystics and = Mathematics

Fyodor=20 Dostoyevsky, in The Brothers Karamazov, had his protagonist Ivan = Karamazov=20 speculate on the existence of higher dimensions and non-Euclidean = geometries=20 during a discussion on the existence of God. In H. G. Wells' The = Invisible Man,=20 the source of invisibility was his ability to manipulate the fourth = dimension.=20 Oscar Wilde even refers to the fourth dimension in his play The = Canterville=20 Ghost as the homeworld for ghosts.

The fourth dimension also appears = in the=20 literary works of Marcel Proust and Joseph Conrad; it inspired some of = the=20 musical works of Alexander Scriabin, Edgar Varege, and George Antheil. = It=20 fascinated such diverse personalities as the psychologist William James, = literary figure Gertrude Stein, and revolutionary socialist Vladimir = Lenin.=20 Lenin even waged a polemic on the N-th dimension with philosopher Ernst = Mach in=20 his Materialism and Empirio-Criticism. Lenin praised Mach, who =93has = raised the=20 very important and useful question of a space of n-dimensions as a = conceivable=20 space,=94 but then took him to task by insisting that the Tsar could = only be=20 overthrown in the third dimension.

Artists have been particularly = interested in the fourth dimension because of the possibilities of = discovering=20 new laws of perspective. In the Middle Ages, religious art was = distinctive for=20 its deliberate lack of perspective. Serfs, peasants, and kings were = depicted as=20 if they were flat, much the way children draw people. Since God was = omnipotent=20 and could therefore see all parts of our world equally, art had to = reflect His=20 point of view, so the world was painted two-dimensionally. Renaissance = art was a=20 revolt against this flat God- centered perspective. Sweeping landscapes = and=20 realistic, three dimensional people were painted from the point of view = of a=20 person's eye, with the lines of perspective vanishing into the horizon.=20 Renaissance art reflected the way the human eye viewed the world, from = the=20 singular point of view of the observer. In other words, Renaissance art=20 discovered the third dimension. With the beginning of the machine age = and=20 capitalism, the artistic world revolted against the cold materialism = that seemed=20 to dominate industrial society. To the Cubists, positivism was a = straitjacket=20 that confined us to what could be measured in the laboratory, = suppressing the=20 fruits of our imagination. They asked: Why must art be clinically = =93realistic?=94=20 This Cubist =93revolt against perspective=94 seized the fourth dimension = because it=20 touched the third dimension from all possible perspectives. Simply put, = Cubist=20 art embraced the fourth dimension. Picasso's paintings are a splendid = example,=20 showing a clear rejection of three dimensional perspective, with women's = faces=20 viewed simultaneously from several angles. Instead of a single = point-of-view,=20 Picasso's paintings show multiple perspectives, as if they were painted = by a=20 being from the fourth dimension, able to see all perspectives = simultaneously. As=20 art historian Linda Henderson has written, =93the fourth dimension and=20 non-Euclidean geometry emerge as among the most important themes = unifying much=20 of modern art and theory.=94

Unifying the Four = Forces

Historically,=20 physicists dismissed the theory of higher dimensions because they could = never be=20 measured, nor did they have any particular use. But to understand how = adding=20 higher dimensions can, in fact, simplify physical problems, consider the = following example. To the ancient Egyptians, the weather was a complete = mystery.=20 What caused the seasons? Why did it get warmer as they traveled south? = The=20 weather was impossible to explain from the limited vantage point of the = ancient=20 Egyptians, to whom the earth appeared flat, like a two-dimensional=20 plane.

But now imagine sending the Egyptians in a rocket into = outer=20 space, where they can see the earth as simple and whole in its orbit = around the=20 sun. Suddenly, the answers to these questions become obvious. From outer = space,=20 it is clear that the earth tilts about 23 degrees on its axis in its = orbit=20 around the sun. Because of this tilt, the northern hemisphere receives = much less=20 sunlight during one part of its orbit than during another part. Hence we = have=20 winter and summer. And since the equator receives more sunlight on the = average=20 than the northern or southern polar regions,

it becomes warmer as we = approach the equator.

In summary, the rather obscure laws of the = weather=20 are easy to understand once we view the earth from space. Thus, the = solution to=20 the problem is to go up into space, into the third dimension. Facts that = were=20 impossible to understand in a flat world suddenly become obvious when = viewing a=20 unified picture of a three dimensional earth.

The Four Fundemental=20 Forces

Similarly, the current excitement over higher dimensions = is that=20 they may hold the key to the unification of all known forces. The = culmination of=20 2,000 years of painstaking observation is the realization that that our = universe=20 is governed by four fundamental forces. These four forces, in turn, may = be=20 unified in higher dimensional space. Light, for example, may be viewed = simply as=20 vibrations in the fifth dimension. The other forces of nature may be = viewed as=20 vibrations in increasingly higher dimensions. At first glance, however, = the four=20 fundamental forces seem to bear no resemblance to each other. They are:=20

Gravity is the force which keeps our feet anchored to the spinning = earth and=20 binds the solar system and the galaxies together. Without gravity, we = would be=20 immediately flung into outer space at l,000 miles per hour. Furthermore, = without=20 gravity holding the sun together, it would explode in a catastrophic = burst of=20 energy. Electro-magnetism is the force which lights up our cities and = energizes=20 our household appliances. The electronic revolution, which has given us = the=20 light bulb, TV, the telephone, computers, radio, radar, microwaves, = light bulbs,=20 and dishwashers, is a byproduct of the electro-magnetic = force.

The strong=20 nuclear force is the force which powers the sun. Without the nuclear = force, the=20 stars would flicker out and the heavens would go dark. The nuclear force = not=20 only makes life on earth possible, it is also the devastating force = unleashed by=20 a hydrogen bomb, which can be compared to a piece of the sun brought = down to=20 earth. The weak force is the force responsible for radio active decay = involving=20 electrons. The weak force is harnessed in modern hospitals in the form = of=20 radioactive tracers used in nuclear medicine. The weak force also = wrecked havoc=20 at Chernobyl. Historically, whenever scientists unraveled the secrets of = one of=20 the four fundamental forces, this irrevocably altered the course of = modern=20 civilization, from the mastery of mechanics and Newtonian physics in the = 1700s,=20 to the harnessing of the electro-magnetism in the 1800s, and finally to = the=20 unlocking of the nuclear force in the 1900s. In some sense, some of the = greatest=20 breakthroughs in the history of science can be traced back to the = gradual=20 understanding of these four fundamental forces. Some have even claimed = that the=20 progress of the last 2,000 years of science can be understood as the = successive=20 mastery of these four fundamental forces. Given the importance of these = four=20 fundamental forces, the next question is: can they be united into one = super=20 force? Are they but the manifestations of a deeper reality? Given the = fruitless=20 search that has stumped the world's Nobel Prize winners for half a = century, most=20 physicists agree that the Theory of Everything must be a radical = departure from=20 everything that has been tried before. For example, Niels Bohr, founder = of the=20 modern atomic theory, once listened to Wolf gang Pauli's explanation of = his=20 version of the unified field theory. In frustration, Bohr finally stood = up and=20 said, =93We are all agreed that your theory is absolutely crazy. But = what divides=20 us is whether your theory is crazy enough.=94

Today, however, = after decades=20 of false starts and frustrating dead ends, many of the world's leading=20 physicists think that they have finally found the theory =93crazy = enough=94 to be=20 the unified field theory. There is widespread belief (although certainly = not=20 unanimous by any means) in the world's major re search laboratories that = we have=20 at last found the Theory of Everything.

Field Theory in Higher=20 Dimension

To see how higher dimensions helps to unify the laws of = nature,=20 physicists use the mathematical device called =93field theory.=94 For = example, the=20 magnetic field of a bar magnet resembles a spider's web which fills up = all of=20 space. To describe the magnetic field, we introduce the field, a series = of=20 numbers defined at each point in space which describes the intensity and = direction of the force at that point. James Clerk Maxwell, in the last = century,=20 proved that the electro-magnetic force can be described by four numbers = at each=20 point in four dimensional space-time (labeled by A _ 1, A _ 2 , A _ 3 , = A _ 4 ).=20 These four numbers, in turn, obey a set of equations (called Maxwell's = field=20 equations).

For the gravitational force, Einstein showed that the = field=20 requires a total of 10 numbers at each point in four dimensions. These = 10=20 numbers can be assembled into the array shown in fig. 3. (Since g _ 12 = =3D g _ 21=20 , only 10 of the 16 numbers contained within the array are independent.) = The=20 gravitational field, in turn, obey Einstein's field equations. The key = idea of=20 Theodore Kaluza in the 1920s was to write down a five dimensional theory = of=20 gravity. In five dimensions, the gravitational field has 15 independent = numbers,=20 which can be arranged in a five dimensional array (see fig.4). Kaluza = then=20 re-defined the 5th column and row of the gravitation al field to be the=20 electromagnetic field of Maxwell. The truly miraculous feature of this=20 construction is that the five dimensional theory of gravity reduces down = precisely to Einstein's original theory of gravity plus Maxwell's theory = of=20 light. In other words, by adding the fifth dimension, we have trivially = unified=20 light with gravity. In other words, light is now viewed as vibrations in = the=20 fifth dimension. In five dimensions, there is =93enough room=94 to unify = both=20 gravity and light.

This trick is easily extended. For example, if = we=20 generalize the theory to N dimensions, then the N dimensional = gravitational=20 field can be split-up into the following pieces (see fig. 5). Now, out = pops a=20 generalization of the electromagnetic field, called the =93Yang-Mills = field,=94=20 which is known to describe the nuclear forces. The nuclear forces, = therefore,=20 may be viewed as vibrations of higher dimensional space. Simply put, by = adding=20 more dimensions, we are able to describe more forces. Similarly, by = adding=20 higher dimensions and further embellishing this approach (with something = called=20 =93supersymmetry), we can explain the entire particle =93zoo=94 that has = been=20 discovered over the past thirty years, with bizarre names like quarks,=20 neutrinos, muons, gluons, etc. Although the mathematics required to = extend the=20 idea of Kaluza has reached truly breathtaking heights, startling even=20 professional mathematicians, the basic idea behind unification remains=20 surprisingly simple: the forces of nature can be viewed as vibrations in = higher=20 dimensional space.

What Happened Before the Big Bang?

One = advantage=20 to having a theory of all forces is that we may be able to resolve some = of the=20 thorniest, long-standing questions in physics, such as the origin of the = universe, and the existence of =93wormholes=94 and even time machines. = The 10=20 dimensional superstring theory, for example, gives us a compelling = explanation=20 of the origin of the Big Bang, the cosmic explosion which took place 15 = to 20=20 billion years ago, which sent the stars and galaxies hurling in all = directions.=20 In this theory, the universe originally started as a perfect 10 = dimensional=20 universe with nothing in it. In the beginning, the universe was = completely=20 empty. However, this 10 dimensional universe was not stable. The = original 10=20 dimensional space-time finally =93cracked=94 into two pieces, a four and = a six=20 dimensional universe. The universe made the =93quantum leap=94 to = another universe=20 in which six of the 10 dimensions collapsed and curled up into a tiny = ball,=20 allowing the remaining four dimensional universe to explode outward at = an=20 enormous rate. The four dimensional universe (our world) expanded = rapidly,=20 creating the Big Bang, while the six dimensional universe wrapped itself = into a=20 tiny ball and shrunk down to infinitesimal size. This explains the = origin of the=20 Big Bang. The cur rent expansion of the universe, which we can measure = with our=20 instruments, is a rather minor aftershock of a more cataclysmic = collapse: the=20 breaking of a 10 dimensional universe into a four and six dimensional=20 universe.

In principle, this also explains why we cannot measure = the six=20 dimensional universe, because it has shrunk down to a size much smaller = than an=20 atom. Thus, no earth-bound experiment can measure the six dimensional = universe=20 because it has curled up into a ball too small to be analyzed by even = our most=20 powerful instruments. (This will be disappointing to those who would = like to=20 visit these higher dimensions in their lifetimes. These higher = dimensions are=20 much too small to enter.)

Time Machines?

Another longstanding = puzzle=20 concerns parallel universes and time travel. According to Einstein's = theory of=20 gravity, space-time can be visualized as a fabric which is stretched and = distorted by the presence of matter and energy. The gravitational field = of a=20 black hole, for example, can be visualized as a funnel, with a dead, = collapsed=20 star at the very center (see fig. 6). Anyone unfortunate enough to get = too close=20 to the funnel inexorably falls into it and is crushed to death. One = puzzle,=20 however, is that, according to Einstein's equations, the funnel of a = black hole=20 necessarily connects our universe with a parallel universe. Furthermore, = if the=20 funnel connects our universe with itself, then we have a =93worm hole=94 = (see fig.=20 7). These anomalies did not bother Einstein because it was thought that = travel=20 through the neck of the funnel, called the =93Einstein-Rosen bridge,=94 = would be=20 impossible (since anyone falling into the black hole would be=20 killed).

However, over the years physicists like Roy Kerr as well = as Kip=20 Thorne at the Calif. Institute of Technology have found new solutions of = Einstein's equations in which the gravitational field does not become = infinite=20 at the center, i.e. in principle, a rocket ship could travel through the = Einstein- Rosen bridge to an alternate universe (or a distant part of = our own=20 universe) without being ripped apart by intense gravitational fields. = (This=20 wormhole is, in fact, the mathematical representation of Alice's Looking = Glass.)

Even more intriguing, these wormholes can be viewed as = time=20 machines. Since the two ends of the wormhole can connect two time eras, = Thorne=20 and his colleagues have calculated the conditions necessary to enter the = wormhole in one time era and exit the other side at another time era. = (Thorne is=20 undaunted by the fact that the energy necessary to open an = Einstein-Rosen bridge=20 exceeds that of a star, and is hence beyond the reach of present-day = technology.=20 But to Thorne, this is just a small detail for the engineers of some=20 sufficiently advanced civilization in outer space!) Thorne even gives a = crude=20 idea of what a time machine might look like when built. (Imagine, = however, the=20 chaos that could erupt if time machines were as common as cars. History = books=20 could never be written. Thousands of meddlers would constantly be going = back in=20 time to eliminate the ancestors of their enemies, to change the outcome = of World=20 War I and II, to save John Kennedy's and Abraham Lincoln's life, etc. = =93History=94=20 as we know it would become impossible, throwing professional historians = out of=20 work. With every turn of a time machine's dial, history would be = changing like=20 sands being blown by the wind.) Other physicists, however, like Steven = Hawking,=20 are dubious about time travel. They argue that quantum effects (such as = intense=20 radiation fields at the funnel) may close the Einstein-Rosen bridge. = Hawking=20 even advanced an experimental =93proof=94 that time machines are not = possible (i.e.=20 if they existed, we would have been visited by tourists from the=20 future).

This controversy has recently generated a flurry of = papers in=20 the physics literature. The essential problem is that although = Einstein's=20 equations for gravity allow for time travel, they also break down when=20 approaching the black hole, and quantum effects, such as radiation, take = over.=20 But to calculate if these quantum corrections are intense enough to = close the=20 Einstein-Rosen bridge, one necessarily needs a unified field theory = which=20 includes both Einstein's theory of gravity as well as the quantum theory = of=20 radiation. So there is hope that soon these questions may be answered = once and=20 for all by a unified field theory. Both sides of the controversy over = time=20 travel acknowledge that ultimately this question will be resolved by the = Theory=20 of Everything.

Recreating Creation

Although the 10 dimensional = superstring theory has been called the most fascinating discovery in = theoretical=20 physics in the past decades, its critics have focused on its weakest = point, that=20 it is almost impossible to test. The energy at which the four = fundamental forces=20 merge into a single, unified force occurs at the fabulous =93Planck = energy,=94 which=20 is a billion billion times greater than the energy found in a proton. = Even if=20 all the nations of the earth were to band together and single-mindedly = build the=20 biggest atom smasher in all history, it would still not be enough to = test the=20 theory. Because of this, some physicists have scoffed at the idea that=20 superstring theory can even be considered a legitimate =93theory.=94 = Nobel laureate=20 Sheldon Glashow, for example, has compared the superstring theory to the = former=20 Pres. Reagan's Star Wars program (because it is untestable and drains = the best=20 scientific talent).The reason why the theory cannot be tested is rather = simple.=20 The Theory of Everything is necessarily a theory of Creation, that is, = it must=20 explain everything from the origin of the Big Bang down to the lilies of = the=20 field. Its full power is manifested at the instant of the Big Bang, = where all=20 its symmetries were intact. To test this theory, therefore, means = recreating=20 Creation on the earth, which is impossible with present-day technology. = (This=20 criticism applies, in fact, to any theory of Creation. The philosopher = David=20 Hume, for example, believed that a scientific theory of Creation was=20 philosophically impossible. This was because the foundation of science = depends=20 on reproducibility, and Creation is one event which can never be = reproduced in=20 the laboratory.)

Although this is discouraging, a piece of the = puzzle may=20 be supplied by the Superconducting Supercollider (SSC), which, if built, = will be=20 the world's largest atom smasher. The SSC (which is likely to be = cancelled by=20 Congress) is designed to accelerate protons to a staggering energy of = tens of=20 trillions of electron volts. When these sub-atomic particles slam into = each=20 other at these fantastic energies within the SSC, temperatures which = have not=20 been seen since the instant of Creation will be generated. That is why = it is=20 sometimes called a =93window on Creation.=94 Costing /8-10 billion, the = SSC consists=20 of a ring of powerful magnets stretched out in a tube over 50 miles = long. In=20 fact, one could easily fit the Washington Beltway, which surrounds = Washington=20 D.C., inside the SSC. If and when it is built, physicists hope that the = SSC will=20 find some exotic sub-atomic particles in order to complete our = present-day=20 understanding of the four forces. However, there is also the small = chance that=20 physicists might discover =93super- symmetric=94 particles, which may be = remnants of=20 the original superstring theory. In other words, although the = superstring theory=20 cannot be tested directly by the SSC, one hopes to find resonances from = the=20 superstring theory among the debris created by smashing protons together = at=20 energies not found since the Big Bang.

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