A THEORY OF EVERYTHING?
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 gave up.
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 Everything.
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 framework.
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 earth.
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 "gluons."
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 space.
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 and time.
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 theory.
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.
Superstrings
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 dimensional universe.
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 your lunch.
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 mysteries.
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 dimensional universe.
Recreating Creation
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 energies.
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 called Flatlanders.
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 "relativity."
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.
------------------------------------------------------------------
Dr. Kaku is author of Beyond Einstein (Bantam) and the forthcoming book, Hyperspace, upon which this article is based.
Back to List of Articles, or Home page
BLACK HOLES, WORMHOLES, AND THE 10Th DIMENSION
Dr. Kaku is professor of theoretical physics at the City Univ. of New York and author of Hyperspace: A Scientific Odyssey Through Parallel Universe, Time Warps, and the 10th Dimension (Oxford Univ. Press).
Last June, astronomers were toasting each other with champagne glasses in laboratories around the world, savoring their latest discovery. The repaired $2 billion Hubble Space Telescope, once the laughing stock of the scientific community, had snared its most elusive prize: a black hole.
But the discovery of the Holy Grail of astrophysics may also rekindle a long simmering debate within the physics community. What lies on the other side of a black hole? If someone foolishly fell into a black hole, will they be crushed by its immense gravity, as most physicists believe, or will they be propelled into a parallel universe or emerge in another time era?
To solve this complex question, physicists are opening up one of the most bizarre and tantalizing chapters in modern physics. They have to navigate a minefield of potentially explosive theories, such as the possibility of "wormholes," "white holes," time machines, and even the 10th dimension!
This controversy may well validate J.B.S. Haldane's wry observation that the universe is "not only queerer than we sup- pose, it is queerer than we can suppose."
This delicious controversy, which delights theoretical physicists but boggles the mind of mere mortals, is the subject of my recent book, Hyperspace.
BLACK HOLES: COLLAPSED STARS
A black hole, simply put, is a massive, dead star whose gravity is so intense than even light cannot escape, hence its name. By definition, it can't be seen, so NASA scientists focused instead on the tiny core of the galaxy M87, a super massive "cosmic engine" 50 million light years from earth.
Astronomers then showed that the core of M87 consisted of a ferocious, swirling maelstrom of superhot hydrogen gas spinning at l.2 million miles per hour. To keep this spinning disk of gas from violently flying apart in all directions, there had to be a colossal mass concentrated at its center, weighing as much as 2 to 3 billion suns! An object with that staggering mass would be massive enough to prevent light from escaping.
Ergo, a black hole.
THE EINSTEIN-ROSEN BRIDGE
But this also revives an ongoing controversy surrounding black holes. The best description of a spinning black hole was given in 1963 by the New Zealand mathematician Roy Kerr, using Einstein's equations of gravity. But there is a quirky feature to his solution. It predicts that if one fell into a black hole, one might be sucked down a tunnel (called the "Einstein-Rosen bridge") and shot out a "white hole" in a parallel universe!
Kerr showed that a spinning black hole would collapse not into a point, but to a "ring of fire." Because the ring was spinning rapidly, centrifugal forces would keep it from collapsing. Remarkably, a space probe fired directly through the ring would not be crushed into oblivion, but might actually emerge unscratched on the other side of the Einstein-Rosen bridge, in a parallel universe. This "wormhole" may connect two parallel universes, or even distant parts of the same universe. (See diagram.)
THROUGH THE LOOKING GLASS
The simplest way to visualize a Kerr wormhole is to think of Alice's Looking Glass. Anyone walking through the Looking Glass would be transported instantly into Wonderland, a world where animals talked in riddles and common sense wasn't so common.
The rim of the Looking Glass corresponds to the Kerr ring. Anyone walking through the Kerr ring might be transported to the other side of the universe or even the past. Like two Siamese twins joined at the hip, we now have two universes joined via the Looking Glass.
Some physicists have wondered whether black holes or worm- holes might someday be used as shortcuts to another sector of our universe, or even as a time machine to the distant past (making possible the swashbuckling exploits in Star Wars). However, we caution that there are skeptics. The critics concede that hundreds of wormhole solutions have now been found to Einstein's equations, and hence they cannot be lightly dismissed as the ravings of crack pots. But they point out that wormholes might be unstable, or that intense radiation and sub-atomic forces surrounding the entrance to the wormhole would kill anyone who dared to enter.
Spirited debates have erupted between physicists concerning these wormholes. Unfortunately, this controversy cannot be re- solved, because Einstein's equations break down at the center of black holes or wormholes, where radiation and sub-atomic forces might be ferocious enough to collapse the entrance. The problem is Einstein's theory only works for gravity, not the quantum forces which govern radiation and sub-atomic particles. What is needed is a theory which embraces both the quantum theory of radiation and gravity simultaneously. In a word, to solve the problem of quantum black holes, we need a "theory of everything!"
A THEORY OF EVERYTHING?
One of the crowning achievements of 20th century science is that all the laws of physics, at a fundamental level, can be summarized by just two formalisms: (1) Einstein's theory of gravity, which gives us a cosmic description of the very large, i.e. galaxies, black holes and the Big Bang, and (2) the quantum theory, which gives us a microscopic description of the very small, i.e. the microcosm of sub-atomic particles and radiation.
But the supreme irony, and surely one of Nature's cosmic jokes, is that they look bewilderingly different; even the world's greatest physicists, including Einstein and Heisenberg, have failed to unify these into one. The two theories use different mathematics and different physical principles to describe the universe in their respective domains, the cosmic and the microscopic.
Fortunately, we now have a candidate for this theory. (In fact, it is the only candidate. Scores of rival proposals have all been shown to be inconsistent.) It's called "superstring theory," and almost effortlessly unites gravity with a theory of radiation, which is required to solve the problem of quantum wormholes.
The superstring theory can explain the mysterious quantum laws of sub-atomic physics by postulating that sub-atomic particles are really just resonances or vibrations of a tiny string. The vibrations of a violin string correspond to musical notes; likewise the vibrations of a superstring correspond to the particles found in nature. The universe is then a symphony of vibrating strings.
An added bonus is that, as a string moves in time, it warps the fabric of space around it, producing black holes, wormholes, and other exotic solutions of Einstein's equations. Thus, in one stroke, the superstring theory unites both the theory of Einstein and quantum physics into one coherent, compelling picture.
A 10 DIMENSIONAL UNIVERSE
The curious feature of superstrings, however, is that they can only vibrate in 10 dimensions. This is, in fact, one of the reasons why it can unify the known forces of the universe: in 10 dimensions there is "more room" to accommodate both Einstein's theory of gravity as well as sub-atomic physics. In some sense, previous attempts at unifying the forces of nature failed because a standard four dimensional theory is "too small" to jam all the forces into one mathematical framework.
To visualize higher dimensions, consider a Japanese tea garden, where carp spend their entire lives swimming on the bottom of a shallow pond. The carp are only vaguely aware of a world beyond the surface. To a carp "scientist," the universe only consists of two dimensions, length and width. There is no such thing as "height." In fact, they are incapable of imagining a third dimension beyond the pond. The word "up" has no meaning for them. (Imagine their distress if we were to suddenly lift them out of their two dimensional universe into "hyperspace," i.e. our world!)
However, if it rains, then the surface of their pond becomes rippled. Although the third dimension is beyond their comprehension, they can clearly see the waves traveling on the pond's surface. Likewise, although we earthlings cannot "see" these higher dimensions, we can see their ripples when they vibrate. According to this theory, "light" is nothing but vibrations rippling along the 5th dimension. By adding higher dimensions, we can easily accommodate more and more forces, including the nuclear forces. In a nutshell: the more dimensions we have, the more forces we can accommodate.
One persistent criticism of this theory, however, is that we do not see these higher dimensions in the laboratory. At present, every event in the universe, from the tiniest sub-atomic decay to exploding galaxies, can be described by 4 numbers (length, width, depth, and time), not 10 numbers. To answer this criticism, many physicists believe (but cannot yet prove) that the universe at the instant of the Big Bang was in fact fully 10 dimensional. Only after the instant of creation did 6 of the 10 dimensions "curled up" into a ball too tiny to observe. In a real sense, this theory is really a theory of creation, when the full power of 10 dimensional space-time was manifest.
21St CENTURY PHYSICS
Not surprisingly, the mathematics of the 10th dimensional superstring is breathtakingly beautiful as well as brutally complex, and has sent shock waves through the mathematics community. Entirely new areas of mathematics have been opened up by this theory. Unfortunately, at present no one is smart enough to solve the problem of a quantum black hole. As Edward Witten of the Institute for Advanced Study at Princeton has claimed, "String theory is 21st century physics that fell accidentally into the 20th century." However, 21st century mathematics necessary to solve quantum black holes has not yet been discovered!
However, since the stakes are so high, that hasn't stopped teams of enterprising physicists from trying to solve superstring theory. Already, over 5,000 papers have been written on the subject. As Nobel laureate Steve Weinberg said, "how can anyone expect that many of the brightest young theorists would not work on it?"
Progress has been slow but steady. Last year, a significant breakthrough was announced. Several groups of physicists independently announced that string theory can completely solve the problem of a quantum black hole. (However, the calculation was so fiendishly difficult it could only be performed in two, not 10, dimensions.)
So that's where we stand today. Many physicists now feel that it's only a matter of time before some enterprising physicist completely cracks this ticklish problem. The equations, although difficult, are well-defined. So until then, it's still a bit premature to buy tickets to the nearest wormhole to visit the next galaxy or hunt dinosaurs!
Back to List of Articles, or Home page
WHAT HAPPENED BEFORE THE BIG BANG?
Einstein's theory of gravity, which gives us the Big Bang theory and black holes, was subjected to the most stringent test yet and passed with flying colors. In the latest (Oct.) issue of Physics Today, astronomers from Harvard, MIT, and the Haystack Observatory proudly announced that they had confirmed Einstein's theory to within an astonishing .04% accuracy by measuring the bending of radio waves from the quasar 3C279 near the edge of the visible universe.
But there is some irony in this announcement. Each success only highlights a yawning gap. Even as scientists hail ever more accurate tests of Einstein's theory of warped space, Einstein himself knew that his theory broke down at the instant of the Big Bang. The theory had feet of clay.
Relativity was worthless, he realized, when it came to answering the most embarrassing cosmic question in all of science: What happened before the Big Bang? Ask any cosmologist this question, and they will throw up their hands, roll their eyes, and lament, "This may be forever beyond the reach of science. We just don't know."
Until now, that is.
A remarkable consensus has been developing recently around what is called "quantum cosmology," where scientists believe that a merger of the quantum theory and Einstein's relativity may resolve these sticky theological questions. Theoretical physicists are rushing in where the angels fear to tread!
In particular, an appealing but starting new picture is emerging in quantum cosmology which may be able to synthesize some of the great mythologies of creation.
There are two dominant religious mythologies. According to Judeo-Christian belief, the universe had a definite beginning. This is the Genesis hypothesis, where the universe was hatched from a Cosmic Egg. However, according to the Hindu-Buddhist belief in Nirvana, the universe is timeless; it never had a beginning, nor will it have an end.
Quantum cosmology proposes a beautiful synthesis of these seemingly hostile viewpoints. In the beginning was Nothing. No space, no matter or energy. But according to the quantum principle, even Nothing was unstable. Nothing began to decay; i.e. it began to "boil," with billions of tiny bubbles forming and expanding rapidly. Each bubble became an expanding universe.
If this is true, then our universe is actually part of a much larger "multiverse" of parallel universes, which is truly timeless, like Nirvana.
As Nobel laureate Steve Weinberg has said, "An important implication is that there wasn't a beginning; that there were increasingly large Big Bangs, so that the [multiverse] goes on forever - one doesn't have to grapple with the question of it before the Bang. The [multiverse] has just been here all along. I find that a very satisfying picture."
Universes can literally spring into existence as a quantum fluctuation of Nothing. (This is because the positive energy found in matter is balanced against the negative energy of gravity, so the total energy of a bubble is zero. Thus, it takes no net energy to create a new universe.)
As Alan Guth, originator of the inflationary theory, once said, "It's often said there is no such thing as a free lunch. But the universe itself may be a free lunch."
Andre Linde of Stanford has said, "If my colleagues and I are right, we may soon be saying good-bye to the idea that our universe was a single fireball created in the Big Bang."
Although this picture is appealing, it also raises more questions. Can life exist on these parallel universes? Stephen Hawking is doubtful; he believes that our universe may co-exist with other universes, but our universe is special. The probability of forming these other bubbles is vanishingly small.
On the other hand, Weinberg believes most of these parallel universes are probably dead. To have stable DNA molecules, the proton must be stable for at least 3 billion years. In these dead universes, the protons might have decayed into a sea of electrons and neutrinos.
Our universe may be one of the few compatible with life. This would, in fact, answer the age-old question of why the physical constants of the universe fall in a narrow band compatible with the formation of life. If the charge of the electron, the gravitational constant, etc. were changed slightly, then life would have been impossible. This is called the Anthropic Principle. As Freeman Dyson of Princeton said, "It's as if the universe knew we were coming." The strong version of this states that this proves the existence of God or an all-powerful deity.
But according to quantum cosmology, perhaps there are millions of dead universes. It was an accident, therefore, that our universe had conditions compatible with the formation of stable DNA molecules.
This leaves open the possibility, however, that there are parallel universes out there which are almost identical to ours, except for some fateful incident. Perhaps King George III did not lose the Colonies in one such universe.
However, I can calculate the probability that one day you might be walking down the street, only to fall into hole in space and enter a parallel universe. You would have to wait longer than the lifetime of the universe for such a cosmic event to happen. So I guess the United States is safe for the present!
As J.B.S. Haldane once said, "the universe is not only queerer than we suppose, it is queerer than we can suppose."
Dr. Michio Kaku is Prof. of theoretical physics at the City Univ. of New York and author of Hyperspace: a Scientific Odyssey through the 10th Dimension (Oxford Univ. Press).
Back to List of Articles, or Home page
HYPERSPACE: A SCIENTIFIC ODYSSEY THROUGH THE TENTH DIMENSION
Dr. Michio Kaku is professor of theoretical physics at the CUNY Graduate Center and CCNY. This article is adapted from his next book, Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10th Dimension (Oxford). He is the author of Introduction to Superstrings (Springer-Verlag).
Do higher dimensions exist? Are there unseen worlds just beyond our reach, beyond the normal laws of physics?
Although higher dimensions have historically been the exclusive realm of charlatans, mystics, and science fiction writers, many serious theoretical physicists now believe that higher dimensions not only exist, but may also explain some of the deepest secrets of nature. Although we stress that there is at present no experimental evidence for higher dimensions, in principle they may solve the ultimate problem in physics: the final unification of all physical knowledge at the fundamental level.
My own fascination with higher dimensions began early in childhood. One of my happiest childhood memories was crouching next to the pond at the famed Japanese Tea Garden in San Francisco, mesmerized by the brilliantly colored carp swimming slowly beneath the water lilies. In these quiet moments, I would ask myself a silly question that a only child might ask: how would the carp in that pond view the world around them?
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 THEORY OF EVERYTHING
Sometimes I believe that we are like the carp living contently on the bottom of that pond; we live our lives blissfully ignorant of other worlds that might co-exist with us, laughing at any suggestion of parallel universes.
All this has changed rather dramatically in the past few years. The theory of higher dimensional space may now become the central piece in unlocking the origin of the universe. At the center of this conceptual revolution is the idea that our familiar three dimensional universe is "too small" to describe the myriad forces governing our universe.
To describe our physical world, with its almost infinite variety of forms, requires entire libraries overflowing with mountains of technical journals and stacks of obscure, learned books. 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 supergravity 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 time: 10. (See xxxx issue of Thesis.)
WHY CAN'T WE SEE THE FOURTH DIMENSION?
To understand these higher dimensions, we remember that it takes three numbers to locate every object in the universe, from the tip of your nose to the ends of the world.
For example, if you want to meet some friends in Manhattan, you tell them to meet you at the building at the corner of 42nd street and 5th avenue, 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 your lunch. (If we meet our friends at noon, then it takes four numbers to specify the space and time of the meeting.)
However, try as we may, it is impossible for our brains to visualize the fourth spatial dimension. Computers, of course, have no problem working in N dimensional space, but spatial dimensions beyond three simply cannot be conceptualized by our feeble brains. (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 dimensions.)
MEETING A HIGHER DIMENSIONAL BEING
To understand some of the mind-bending features of higher dimensions, imagine a two-dimensional world, called Flat land (after Edwin A. Abbott's celebrated novel) that resembles a world existing on a flat table-top.
If one of the Flatlanders becomes lost, we can quickly scan all of Flatland, peering directly inside houses, buildings, and even concealed places. If one of the Flatlanders becomes sick, we can reach directly into their insides and per form surgery, without ever cutting their skin. 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.
MYSTICS AND MATHEMATICIANS
Fyodor Dostoyevsky, in The Brothers Karamazov, had his protagonist Ivan Karamazov speculate on the existence of higher dimensions and non-Euclidean geometries during a discussion on the existence of God. In H. G. Wells' The Invisible Man, the source of invisibility was his ability to manipulate the fourth dimension. Oscar Wilde even refers to the fourth dimension in his play The Canterville Ghost as the homeworld for ghosts.
The fourth dimension also appears in the literary works of Marcel Proust and Joseph Conrad; it inspired some of the musical works of Alexander Scriabin, Edgar Varege, and George Antheil. It fascinated such diverse personalities as the psychologist William James, literary figure Gertrude Stein, and revolutionary socialist Vladimir Lenin.
Lenin even waged a polemic on the N-th dimension with philosopher Ernst Mach in his Materialism and Empirio-Criticism. Lenin praised Mach, who "has raised the very important and useful question of a space of n-dimensions as a conceivable space," but then took him to task by insisting that the Tsar could only be overthrown in the third dimension.
Artists have been particularly interested in the fourth dimension because of the possibilities of discovering new laws of perspective. In the Middle Ages, religious art was distinctive for its deliberate lack of perspective. Serfs, peasants, and kings were depicted as if they were flat, much the way children draw people. Since God was omnipotent and could therefore see all parts of our world equally, art had to reflect His point of view, so the world was painted two-dimensionally.
Renaissance art was a revolt against this flat God- centered perspective. 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 fourth dimension and non-Euclidean geometry emerge as among the most important themes unifying much of modern art and theory."
UNIFYING THE FOUR FORCES
Historically, physicists dismissed the theory of higher dimensions because they could never be measured, nor did they have any particular use. But to understand how adding higher dimensions can, in fact, simplify physical problems, consider the following example. To the ancient Egyptians, the weather was a complete mystery. What caused the seasons? Why did it get warmer as they traveled south? 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.
But now imagine sending the Egyptians in a rocket into outer space, where they can see the earth as simple and whole in its orbit around the sun. Suddenly, the answers to these questions become obvious. From outer space, it is clear that the earth tilts about 23 degrees on its axis in its orbit around the sun. Because of this tilt, the northern hemisphere receives much less sunlight during one part of its orbit than during another part. Hence we have winter and summer. And since the equator receives more sunlight on the average than the northern or southern polar regions, it becomes warmer as we approach the equator.
In summary, the rather obscure laws of the weather are easy to understand once we view the earth from space. Thus, the solution to the problem is to go up into space, into the third dimension. Facts that were impossible to understand in a flat world suddenly become obvious when viewing a unified picture of a three dimensional earth.
THE FOUR FUNDAMENTAL FORCES
Similarly, the current excitement over higher dimensions is that they may hold the key to the unification of all known forces. The culmination of 2,000 years of painstaking observation is the realization that that our universe is governed by four fundamental forces. These four forces, in turn, may be unified in higher dimensional space. Light, for example, may be viewed simply as vibrations in the fifth dimension. The other forces of nature may be viewed as vibrations in increasingly higher dimensions.
At first glance, however, the four fundamental forces seem to bear no resemblance to each other. They are:
Gravity is the force which keeps our feet anchored to the spinning earth and binds the solar system and the galaxies together. Without gravity, 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.
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.
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. 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 earth.
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, "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. 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 Everything.
FIELD THEORY IN HIGHER DIMENSIONS
To see how higher dimensions helps to unify the laws of nature, physicists use the mathematical device called "field theory." For example, the magnetic field of a bar magnet resembles a spider's web which fills up all of space. To describe the magnetic field, we introduce the field, a series of 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, 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).
For the gravitational force, Einstein showed that the field requires a total of 10 numbers at each point in four dimensions. These 10 numbers can be assembled into the array shown in fig. 3. (Since g _ 12 = g _ 21 , only 10 of the 16 numbers contained within the array are independent.) The gravitational field, in turn, obey Einstein's field equations.
The key idea of Theodore Kaluza in the 1920s was to write down a five dimensional theory of gravity. In five dimensions, the gravitational field has 15 independent numbers, which can be arranged in a five dimensional array (see fig.4). 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.
This trick is easily extended. For example, if we generalize the theory to N dimensions, then the N dimensional gravitational field can be split-up into the following pieces (see fig. 5). Now, out pops a generalization of the electromagnetic field, called the "Yang-Mills field," which is known to describe the nuclear forces. The nuclear forces, therefore, may be viewed as vibrations of higher dimensional space. 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 "supersymmetry), 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.
WHAT HAPPENED BEFORE THE BIG BANG?
One advantage to having a theory of all forces is that we may be able to resolve some of the thorniest, long-standing questions in physics, such as the origin of the universe, and the existence of "wormholes" and even time machines.
The 10 dimensional superstring theory, for example, gives us a compelling explanation of the origin of the Big Bang, the cosmic explosion which took place 15 to 20 billion years ago, which sent the stars and galaxies hurling in all directions. In this theory, the universe originally started as a perfect 10 dimensional universe with nothing in it. In the beginning, the universe was completely empty. 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.
In principle, this also explains why we cannot measure the six dimensional universe, because it has shrunk down to a size much smaller than an atom. Thus, no earth-bound experiment can measure the six dimensional universe because it has curled up into a ball too small to be analyzed by even our most powerful instruments. (This will be disappointing to those who would like to visit these higher dimensions in their lifetimes. These higher dimensions are much too small to enter.)
TIME MACHINES?
Another longstanding puzzle concerns parallel universes and time travel. According to Einstein's theory of 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 black hole, for example, can be visualized as a funnel, with a dead, collapsed star at the very center (see fig. 6). 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).
However, over the years physicists like Roy Kerr as well as Kip Thorne at the Calif. Institute of Technology have found new solutions of Einstein's equations in which the gravitational field does not become infinite 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 universe) without being ripped apart by intense gravitational fields. (This wormhole is, in fact, the mathematical representation of Alice's Looking Glass.)
Even more intriguing, these wormholes can be viewed as time machines. Since the two ends of the wormhole can connect two time eras, Thorne 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 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).
This controversy has recently generated a flurry of papers in the physics literature. The essential problem is that although Einstein's equations for gravity allow for time travel, they also break down when approaching the black hole, and quantum effects, such as radiation, take over. But to calculate if these quantum corrections are intense enough to close the Einstein-Rosen bridge, one necessarily needs a unified field theory which includes both Einstein's theory of gravity as well as the quantum theory of radiation. So there is hope that soon these questions may be answered once and for all by a unified field theory. Both sides of the controversy over time travel acknowledge that ultimately this question will be resolved by the Theory of Everything.
RECREATING CREATION
Although the 10 dimensional superstring theory has been called the most fascinating 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 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.)
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 (which is likely to be cancelled by Congress) is designed to accelerate protons to a staggering energy of tens of trillions of electron volts. When these sub-atomic particles slam into each other at these fantastic energies within the SSC, temperatures which have not been seen since the instant of Creation will be generated. 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.
WE ARE NOT SMART ENOUGH
Superstring physicists, however, are not bothered by these criticisms. To them, 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 ever larger atom smashers; the problem is being clever enough to solve the theory.
Edward Witten of the Institute for Advanced Study, 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 theory was discovered 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 is that 21st century mathematics has not yet been discovered. That is the fundamental problem: at present, millions of solutions to these equations have been discovered, but no one is smart enough to determine how to select the correct one. In other words, although the string equations are perfectly well-defined and have millions of solutions, no one is capable at present of determining which is the unique solution. If we could only sharpen our analytical skills and develop even more powerful mathematical tools, perhaps we could solve for the unique solution and settle 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 determine its unique solution.
Imagine a child gazing at a TV set. The images and stories conveyed on the screen are easily understood by the child, who can easily change the channels and manipulate the settings on the TV 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 theory works.
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 then rained down on Flatland.
These Flatlanders were intrigued by the beauty of the fragments, which could be found scattered all over their world. The scientists of Flatland concluded that these fragments must have come from a single 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 only a few of the fragments together. Many Flatlanders began to think that these pieces could never be reassembled. Finally, some of the younger, more rebellious scientists suggested a heretical solution: perhaps these chunks could fit together if they were moved "up" in the third dimension.
This immediately set off the greatest scientific controversy in years. The older scientists scorned 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, and hence not a theory at all.
However, the younger scientists were undaunted. Using pure mathematics, they could show that every one of these pieces fit together perfectly if they were assembled in the unseen third dimension. The younger scientists claimed that the problem was therefore theoretical, rather than experimental, even if it can never be tested.
And so the controversy rages, both in Flatland as well as in our own three dimensional world.
"THE MIND OF GOD"
In conclusion, the theory of higher dimensions has set off perhaps the most delicious, lively debate in theoretical physics in generations. Although the existence of these higher dimensions cannot be verified by any experiment on this planet, it has already sparked an avalanche of papers in the leading research institutes around the world. Although the mathematics required to find the unique solution has soared to dizzying heights, physicists around the world are confident that the unique solution will eventually be found.
Nobel laureate Steven Weinberg, in his book Dreams of a Final Theory, holds out for the exciting possibility of attaining the Final Theory. He writes, "How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century."
Cosmologist Steven Hawking, who closes his book A Brief History of Time on this theory, has written, "...if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we would know the mind of God."
Perhaps one day one of the readers of this article may gaze into a pond and notice the carp swimming on the bottom, beneath the lilies. Perhaps the reader will be inspired to investigate the theory of higher dimensions and complete the quest for the Theory of the Universe.