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.
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?
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.
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.
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.
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.
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.
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.
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.
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.