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THE GOD EQUATION: The Quest for a Theory of Everything

Michio Kaku, renowned theoretical physicist and #1 New York Times bestselling author of THE FUTURE OF THE MIND and THE FUTURE OF HUMANITY tells the story of the greatest quest in all of science.

The God Equation

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When Newton discovered the law of gravity, he unified the rules governing the heavens and the Earth. Since then, physicists have been placing new forces into ever-grander theories. But perhaps the ultimate challenge is achieving a monumental synthesis of the two remaining theories—relativity and the quantum theory.

This would be the crowning achievement of science, a profound merging of all the forces of nature into one beautiful, magnificent equation to unlock the deepest mysteries in science: What happened before the Big Bang? What lies on the other side of a black hole? Are there other universes and dimensions? Is time travel possible? Why are we here?

Kaku also explains the intense controversy swirling around this theory, with Nobel laureates taking opposite sides on this vital question. It is a captivating, gripping story; what’s at stake is nothing less than our conception of the universe.

Written with Kaku’s trademark enthusiasm and clarity, this epic and engaging journey is the story of The God Equation.

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KAKU ON THE SCIENCE AND FANTASY OF THE NEW FANTASTIC FOUR MOVIE

Click to Visit the Fantastic Four Movie WebsiteFantastic Four, a contemporary re-imagining of Marvel’s original and longest-running superhero team, centers on four young outsiders who teleport to an alternate and dangerous universe, which alters their physical form in shocking ways. In a series of four special featurettes released by 20th Century FOX, legendary physicist Dr. Michio Kaku tells us why there’s more to the science of Fantastic Four than you may expect. The videos feature a healthy amount of new Fantastic Four footage that should whet your appetite for the movie, which hits theaters on August 7th. The first is entitled ‘Alternate Dimensions.’ WATCH NOW!

Fantastic Four - In Theaters August 7

The Last Ten Blog Entries from Dr. Kaku’s Blog; Dr. Kaku’s Universe (Hosted by BigThink.com) 10/28 – 11/11

Take a look at the last ten blog entries on Dr. Kaku’s BigThink.com blog; Dr. Kaku’s Universe. Don’t forget to register on the Big Think website so you can make comments on the blog entries where Dr. Kaku will be answering questions.

Blackholes, Wormholes and the Tenth Dimension

Will these concepts be proven by a theory of everything?

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.

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!

For the complete library of books by Dr. Michio Kaku, click here.

Hyperspace – A Scientific Odyssey

A look at the higher dimensions

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.

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 Mathematics

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 Fundemental 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 Dimension

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.

For the complete library of books by Dr. Michio Kaku, click here.

M-Theory: The Mother of all SuperStrings

An introduction to M-Theory

Every decade or so, a stunning breakthrough in string theory sends shock waves racing through the theoretical physics community, generating a feverish outpouring of papers and activity. This time, the Internet lines are burning up as papers keep pouring into the Los Alamos National Laboratory’s computer bulletin board, the official clearing house for superstring papers. John Schwarz of Caltech, for example, has been speaking to conferences around the world proclaiming the “second superstring revolution.” Edward Witten of the Institute for Advanced Study in Prince- ton gave a spell-binding 3 hour lecture describing it. The after- shocks of the breakthrough are even shaking other disciplines, like mathematics. The director of the Institute, mathematician Phillip Griffiths, says, “The excitement I sense in the people in the field and the spin-offs into my own field of mathematics … have really been quite extraordinary. I feel I’ve been very privileged to witness this first hand.”

Cumrun Vafa at Harvard has said, “I may be biased on this one, but I think it is perhaps the most important development not only in string theory, but also in theoretical physics at least in the past two decades.” What is triggering all this excitement is the discovery of something called “M-theory,” a theory which may explain the origin of strings. In one dazzling stroke, this new M-theory has solved a series of long-standing puzzling mysteries about string theory which have dogged it from the beginning, leaving many theoretical physicists (myself included!) gasping for breath. M-theory, moreover, may even force string theory to change its name. Although many features of M-theory are still unknown, it does not seem to be a theory purely of strings. Michael Duff of Texas A & M is already giving speeches with the title “The theory formerly known as strings!” String theorists are careful to point out that this does not prove the final correctness of the theory. Not by any means. That may make years or decades more. But it marks a most significant breakthrough that is already reshaping the entire field.

Parable of the Lion

Einstein once said, “Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.” Einstein spent the last 30 years of his life searching for the “tail” that would lead him to the “lion,” the fabled unified field theory or the “theory of everything,” which would unite all the forces of the universe into a single equation. The four forces (gravity, electromagnetism, and the strong and weak nuclear forces) would be unified by an equation perhaps one inch long. Capturing the “lion” would be the greatest scientific achievement in all of physics, the crowning achievement of 2,000 years of scientific investigation, ever since the Greeks first asked themselves what the world was made of. But although Einstein was the first one to set off on this noble hunt and track the footprints left by the lion, he ultimately lost the trail and wandered off into the wilderness. Other giants of 20th century physics, like Werner Heisenberg and Wolfgang Pauli, also joined in the hunt. But all the easy ideas were tried and shown to be wrong. When Niels Bohr once heard a lecture by Pauli explaining his version of the unified field theory, Bohr stood up and said, “We in the back are all agreed that your theory is crazy. But what divides us is whether your theory is crazy enough!”

The trail leading to the unified field theory, in fact, is littered with the wreckage of failed expeditions and dreams. Today, however, physicists are following a different trail which might be “crazy enough” to lead to the lion. This new trail leads to superstring theory, which is the best (and in fact only) candidate for a theory of everything. Unlike its rivals, it has survived every blistering mathematical challenge ever hurled at it. Not surprisingly, the theory is a radical, “crazy” departure from the past, being based on tiny strings vibrating in 10 dimensional space-time. Moreover, the theory easily swallows up Einstein’s theory of gravity. Witten has said, “Unlike conventional quantum field theory, string theory requires gravity. I regard this fact as one of the greatest in- sights in science ever made.” But until recently, there has been a glaring weak spot: string theorists have been unable to probe all solutions of the model, failing miserably to examine what is called the “non-perturbative region,” which I will describe shortly. This is vitally important, since ultimately our universe (with its wonderfully diverse collection of galaxies, stars, planets, sub- atomic particles, and even people) may lie in this “non-perturbative region.” Until this region can be probed, we don’t know if string theory is a theory of everything — or a theory of nothing! That’s what today’s excitement is all about. For the first time, using a powerful tool called “duality,” physicists are now probing beyond just the tail, and finally seeing the outlines of a huge, unexpectedly beautiful lion at the other end. Not knowing what to call it, Witten has dubbed it “M-theory.” In one stroke, M-theory has solved many of the embarrassing features of the theory, such as why we have 5 superstring theories. Ultimately, it may solve the nagging question of where strings come from.

“Pea Brains” and the Mother of all Strings

Einstein once asked himself if God had any choice in making the universe. Perhaps not, so it was embarrassing for string theorists to have five different self-consistent strings, all of which can unite the two fundamental theories in physics, the theory of gravity and the quantum theory.

Each of these string theories looks completely different from the others. They are based on different symmetries, with exotic names like E(8)xE(8) and O(32).

Not only this, but superstrings are in some sense not unique: there are other non-string theories which contain “super- symmetry,” the key mathematical symmetry underlying superstrings. (Changing light into electrons and then into gravity is one of the rather astonishing tricks performed by supersymmetry, which is the symmetry which can exchange particles with half-integral spin, like electrons and quarks, with particles of integral spin, like photons, gravitons, and W-particles.

In 11 dimensions, in fact, there are alternate super theories based on membranes as well as point particles (called super- gravity). In lower dimensions, there is moreover a whole zoo of super theories based on membranes in different dimensions. (For example, point particles are 0-branes, strings are 1-branes, membranes are 2-branes, and so on.) For the p-dimensional case, some wag dubbed them p-branes (pronounced “pea brains”). But because p-branes are horribly difficult to work with, they were long considered just a historical curiosity, a trail that led to a dead-end. (Michael Duff, in fact, has collected a whole list of unflattering comments made by referees to his National Science Foundation grant concerning his work on p- branes. One of the more charitable comments from a referee was: “He has a skewed view of the relative importance of various concepts in modern theoretical physics.”) So that was the mystery. Why should supersymmetry allow for 5 superstrings and this peculiar, motley collection of p-branes? Now we realize that strings, supergravity, and p-branes are just different aspects of the same theory. M-theory (M for “membrane” or the “mother of all strings,” take your pick) unites the 5 superstrings into one theory and includes the p-branes as well. To see how this all fits together, let us update the famous parable of the blind wise men and the elephant. Think of the blind men on the trail of the lion. Hearing it race by, they chase after it and desperately grab onto its tail (a one-brane). Hanging onto the tail for dear life, they feel its one- dimensional form and loudly proclaim “It’s a string! It’s a string!”

But then one blind man goes beyond the tail and grabs onto the ear of the lion. Feeling a two-dimensional surface (a membrane), the blind man proclaims, “No, it’s really a two-brane!” Then another blind man is able to grab onto the leg of the lion. Sensing a three-dimensional solid, he shouts, “No, you’re both wrong. It’s really a three-brane!” Actually, they are all right. Just as the tail, ear, and leg are different parts of the same lion, the string and various p- branes appear to be different limits of the same theory: M- theory. Paul Townsend of Cambridge University, one of the architects of this idea, calls it “p-brane democracy,” i.e. all p- branes (including strings) are created equal. Schwarz puts a slightly different spin on this. He says, “we are in an Orwellian situation: all p-branes are equal, but some (namely strings) are more equal than others. The point is that they are the only ones on which we can base a perturbation theory.” To understand unfamiliar concepts such as duality, perturbation theory, non-perturbative solutions, it is instructive to see where these concepts first entered into physics.

Dualty

The key tool to understanding this breakthrough is something “duality.” Loosely speaking, two theories are “dual” to each other if they can be shown to be equivalent under a certain interchange. The simplest example of duality is reversing the role of electricity and magnetism in the equations discovered by James Clerk Maxwell of Cambridge University 130 years ago. These are the equations which govern light, TV, X-rays, radar, dynamos, motors, transformers, even the Internet and computers. The remarkable feature about these equations is that they remain the same if we interchange the magnetic B and electric fields E and also switch the electric charge e with the magnetic charge g of a magnetic “monopole”: E <–> B and e <–> g (In fact, the product eg is a constant.) This has important implications. Often, when a theory cannot be solved exactly, we use an approximation scheme. In first year calculus, for example, we recall that we can approximate certain functions by Taylor’s expansion. Similarly, since e^2 = 1/137 in certain units and is hence a small number, we can always approximate the theory by power expanding in e^2. So we add contributions of order e^2 + e^4 + e^6 etc. in solving for, say, the collision of two particles. Notice that each contribution is getting smaller and smaller, so we can in principle add them all up. This generalization of Taylor’s expansion is called “perturbation theory,” where we perturb the system with terms containing e^2. For example, in archery, perturbation theory is how we aim our arrows. With every motion of our arms, our bow gets closer and closer to aligning with the bull’s eye.) But now try expanding in g^2. This is much tougher; in fact, if we expand in g^2, which is large, then the sum g^2 + g^4 + g^6 etc. blows up and becomes meaningless. This is the reason why the “non-perturbative” region is so difficult to probe, since the theory simply blows up if we try to naively use perturbation theory for large coupling constant g. So at first it appears hopeless that we could ever penetrate into the non-perturbative region. (For example, if every motion of our arms got bigger and bigger, we would never be able to zero in and hit the target with the arrow.) But notice that because of duality, a theory of small e (which is easily solved) is identical to a theory of large g (which is difficult to solve). But since they are the same theory, we can use duality to solve for the non-perturbative region.

S, T, and U Dualty

The first inkling that duality might apply in string theory was discovered by K. Kikkawa and M. Yamasaki of Osaka Univ. in 1984. They showed that if you “curled up” one of the extra dimensions into a circle with radius R, the theory was the same if we curled up this dimension with radius 1/R. This is now called T- duality: R <–> 1/R When applied to various superstrings, one could reduce 5 of the string theories down to 3 (see figure). In 9 dimensions (with one dimension curled up) the Type IIa and IIb strings were identical, as were the E(8)xE(8) and O(32) strings.

Unfortunately, T duality was still a perturbative duality. The next breakthrough came when it was shown that there was a second class of dualities, called S duality, which provided a duality between the perturbative and non-perturbative regions of string theory. Another duality, called U duality, was even more powerful.

Then Nathan Seiberg and Witten brilliantly showed how another form of duality could solve for the non-perturbative region in four dimensional supersymmetric theories. However, what finally convinced many physicists of the power of this technique was the work of Paul Townsend and Edward Wit- ten. They caught everyone by surprise by showing that there was a duality between 10 dimensional Type IIa strings and 11 dimension- al supergravity! The non-perturbative region of Type IIa strings, which was previously a forbidden region, was revealed to be governed by 11 dimensional supergravity theory, with one dimension curled up. At this point, I remember that many physicists (myself included) were rubbing our eyes, not believing what we were seeing. I remember saying to myself, “But that’s impossible!”

All of a sudden, we realized that perhaps the real “home” of string theory was not 10 dimensions, but possibly 11, and that the theory wasn’t fundamentally a string theory at all! This revived tremendous interest in 11 dimensional theories and p- branes. Lurking in the 11th dimension was an entirely new theory which could reduce down to 11 dimensional supergravity as well as 10 dimensional string theory and p-brane theory.

Detractors of String Theories

To the critics, however, these mathematical developments still don’t answer the nagging question: how do you test it? Since string theory is really a theory of Creation, when all its beautiful symmetries were in their full glory, the only way to test it, the critics wail, is to re-create the Big Bang itself, which is impossible. Nobel Laureate Sheldon Glashow likes to ridicule superstring theory by comparing it with former Pres. Reagan’s Star Wars plan, i.e. they are both untestable, soak up resources, and both siphon off the best scientific brains.

Actually, most string theorists think these criticisms are silly. They believe that the critics have missed the point. The key point is this: if the theory can be solved non- perturbatively using pure mathematics, then it should reduce down at low energies to a theory of ordinary protons, electrons, atoms, and molecules, for which there is ample experimental data. If we could completely solve the theory, we should be able to extract its low energy spectrum, which should match the familiar particles we see today in the Standard Model. Thus, the problem is not building atom smashers l,000 light years in diameter; the real problem is raw brain power: of only we were clever enough, we could write down M-theory, solve it, and settle everything.

Evolving Backwards

So what would it take to actually solve the theory once and for all and end all the speculation and back-biting? There are several approaches. The first is the most direct: try to derive the Standard Model of particle interactions, with its bizarre collection of quarks, gluons, electrons, neutrinos, Higgs bosons, etc. etc. etc. (I must admit that although the Standard Model is the most successful physical theory ever proposed, it is also one of the ugliest.) This might be done by curling up 6 of the 10 dimensions, leaving us with a 4 dimensional theory that might resemble the Standard Model a bit. Then try to use duality and M- theory to probe its non-perturbative region, seeing if the symmetries break in the correct fashion, giving us the correct masses of the quarks and other particles in the Standard Model. Witten’s philosophy, however, is a bit different. He feels that the key to solving string theory is to understand the under- lying principle behind the theory.

Let me explain. Einstein’s theory of general relativity, for example, started from first principles. Einstein had the “happiest thought in his life” when he leaned back in his chair at the Bern patent office and realized that a person in a falling elevator would feel no gravity. Although physicists since Galileo knew this, Einstein was able to extract from this the Equivalence Principle. This deceptively simple statement (that the laws of physics are indistinguishable locally in an accelerating or a gravitating frame) led Einstein to introduce a new symmetry to physics, general co-ordinate transformations. This in turn gave birth to the action principle behind general relativity, the most beautiful and compelling theory of gravity. Only now are we trying to quantize the theory to make it compatible with the other forces. So the evolution of this theory can be summarized as: Principle -> Symmetry -> Action -> Quantum Theory According to Witten, we need to discover the analog of the Equivalence Principle for string theory. The fundamental problem has been that string theory has been evolving “backwards.” As Witten says, “string theory is 21st century physics which fell into the 20th century by accident.” We were never “meant” to see this theory until the next century.

Is the End in Sight?

Vafa recently added a strange twist to this when he introduced yet another mega-theory, this time a 12 dimensional theory called F-theory (F for “father”) which explains the self-duality of the IIb string. (Unfortunately, this 12 dimensional theory is rather strange: it has two time co-ordinates, not one, and actually violates 12 dimensional relativity. Imagine trying to live in a world with two times! It would put an episode of Twilight Zone to shame.) So is the final theory 10, 11, or 12 dimensional?

Schwarz, for one, feels that the final version of M-theory may not even have any fixed dimension. He feels that the true theory may be independent of any dimensionality of space-time, and that 11 dimensions only emerges once one tries to solve it. Townsend seems to agree, saying “the whole notion of dimensionality is an approximate one that only emerges in some semiclassical context.” So does this means that the end is in sight, that we will someday soon derive the Standard Model from first principles? I asked some of the leaders in this field to respond to this question. Although they are all enthusiastic supporters of this revolution, they are still cautious about predicting the future. Townsend believes that we are in a stage similar to the old quantum era of the Bohr atom, just before the full elucidation of quantum mechanics. He says, “We have some fruitful pictures and some rules analogous to the Bohr-Sommerfeld quantization rules, but it’s also clear that we don’t have a complete theory.”

Duff says, “Is M-theory merely a theory of supermembranes and super 5-branes requiring some (as yet unknown) non- perturbative quantization, or (as Witten believes) are the under- lying degrees of freedom of M-theory yet to be discovered? I am personally agnostic on this point.” Witten certainly believes we are on the right track, but we need a few more “revolutions” like this to finally solve the theory. “I think there are still a couple more superstring revolutions in our future, at least. If we can manage one more superstring revolution a decade, I think that we will do all right,” he says. Vafa says, “I hope this is the ‘light at the end of the tunnel’ but who knows how long the tunnel is!” Schwarz, moreover, has written about M-theory: “Whether it is based on something geometrical (like supermembranes) or some- thing completely different is still not known. In any case, finding it would be a landmark in human intellectual history.” Personally, I am optimistic. For the first time, we can see the outline of the lion, and it is magnificent. One day, we will hear it roar.

For the complete library of books by Dr. Michio Kaku, click here.

Hyperspace and a Theory of Everything

What lies beyond our 4 dimensions?

When I was a child, I used to visit the Japanese Tea Garden in San Francisco. I would spend hours fascinated by the carp, who lived in a very shallow pond just inches beneath the lily pads, just beneath my fingers, totally oblivious to the universe above them.

I would ask myself a question only a child could ask: what would it be like to be a carp? What a strange world it would be! I imagined that the pond would be an entire universe, one that is two-dimensional in space. The carp would only be able to swim forwards and backwards, and left and right. But I imagined that the concept of “up”, beyond the lily pads, would be totally alien to them. Any carp scientist daring to talk about “hyperspace”, i.e. the third dimension “above” the pond, would immediately be labelled a crank. I wondered what would happen if I could reach down and grab a carp scientist and lift it up into hyperspace. I thought what a wondrous story the scientist would tell the others! The carp would babble on about unbelievable new laws of physics: beings who could move without fins. Beings who could breathe without gills. Beings who could emit sounds without bubbles. I then wondered: how would a carp scientist know about our existence? One day it rained, and I saw the rain drops forming gentle ripples on the surface of the pond.

Then I understood.

The carp could see rippling shadows on the surface of the pond. The third dimension would be invisible to them, but vibrations in the third dimensions would be clearly visible. These ripples might even be felt by the carp, who would invent a silly concept to describe this, called “force.” They might even give these “forces” cute names, such as light and gravity. We would laugh at them, because, of course, we know there is no “force” at all, just the rippling of the water.

Today, many physicists believe that we are the carp swimming in our tiny pond, blissfully unaware of invisible, unseen uni- verses hovering just above us in hyperspace. We spend our life in three spatial dimensions, confident that what we can see with our telescopes is all there is, ignorant of the possibility of 10 dimensional hyperspace. Although these higher dimensions are invisible, their “ripples” can clearly be seen and felt. We call these ripples gravity and light. The theory of hyperspace, however, languished for many decades for lack of any physical proof or application. But the theory, once considered the province of eccentrics and mystics, is being revived for a simple reason: it may hold the key to the greatest theory of all time, the “theory of everything.”

Einstein spent the last 30 years of his life futilely chasing after this theory, the Holy Grail of physics. He wanted a theory that could explain the four fundamental forces that govern the universe: gravity, electromagnetism, and the two nuclear forces (weak and strong). It was supposed to be the crowning achievement of the last 2,000 years of science, ever since the Greeks asked what the world was made of. He was searching for an equation, perhaps no more than one-inch long, that could be placed on a T-shirt, but was so powerful it could explain every- thing from the Big Bang, exploding stars, to atoms and molecules, to the lilies of the field.

He wanted to read the mind of God. Ultimately, Einstein failed in his mission. In fact, he was shunned by many of his younger compatriots, who would taunt him with the ditty, “What God has torn asunder, no man can put together.” But perhaps Einstein is now having his revenge. For the past decade, there has been furious research on merging the four fundamental forces into a single theory, especially one that can meld general relativity (which explains gravity) with the quantum theory (which can explain the two nuclear forces and electro- magnetism).

The problem is that relativity and the quantum theory are precise opposites. General relativity is a theory of the very large: galaxies, quasars, black holes, and even the Big Bang. It is based on bending the beautiful four dimensional fabric of space and time. The quantum theory, by contrast, is a theory of the very small, i.e. the world of sub-atomic particles. It is based on discrete, tiny packets of energy called quanta. Over the past 50 years, many attempts have been tried to unite these polar opposites, and have failed. The road to the Unified Field Theory, the Theory of Everything, is littered with the corpses of failed attempts. The key to the puzzle may be hyperspace. In 1915, when Einstein said space-time was four dimensional and was warped and rippled, he showed that this bending produced a “force” called gravity. In 1921, Theodr Kaluza wrote that ripples of the fifth dimension could be viewed as light. Like the fish seeing the ripples in hyperspace moving in their world, many physicists believe that light is created by ripples in five-dimensional space-time.

But what about dimensions higher than 5?

In principle, if we add more and more dimensions, we can ripple and bend them in different ways, thereby creating more forces. In 10 dimensions, in fact, we can accomodate all four fundamental forces! Actually, it’s not that simple. By naively going to 10 dimensions, we also introduce a host of esoteric mathematical inconsistencies (e.g. infinities and anomalies) that have killed all previous theories. The only theory which has survived every challenge posed to it is called superstring theory, in which this 10 dimensional universe is inhabited by tiny strings.

In fact, in one swoop, this 10 dimensional string theory gives us a simple, compelling unification of all forces. Like a violin string, these tiny strings can vibrate and create resonances or “notes”. That explains why there are so many sub- atomic particles: they are just notes on a superstring. (This seems so simple, but in the 1950s, physicists were drowning in an avalanche of sub-atomic particles. J.R. Oppenheim- er, who helped build the atomic bomb, even said, out of sheer frustration, that the Nobel Prize should go to the physicist who does NOT discover a new particle that year!) Similarly, when the string moves in space and time, it warps the space around it just as Einstein predicted. Thus, in a remarkably simple picture, we can unify gravity (as the bending of space caused by moving strings) with the other quantum forces (now viewed as vibrations of the string).

Of course, any theory with this power and majesty has a problem. This theory, because it is a theory of everything, is really a theory of Creation. Thus, to fully test the theory requires re-creating Creation! At first, this might seem hopelessly impossible. We can barely leave the earth’s puny gravity, let alone create universes in the laboratory. But there is a way out to this seemingly intractable problem. A theory of everything is also a theory of the everyday. Thus, this theory, when fully completed, will be able to explain the existence of protons, atoms, molecules, even DNA. Thus, the key is to fully solve the theory and test the theory against the known properties of the universe. At present, no one on earth is smart enough to complete the theory. The theory is perfectly well-defined, but you see, superstring theory is 21st Century physics that fell accidentally into the 20th century. It was discovered purely by accident, when two young physicists were thumbing through a mathematics book. The theory is so elegant and powerful, we were never “destined” to see it in the 20th century. The problem is that 21st century mathematics has not yet been invented yet. But since physicists are genetically predisposed to be opti- mists, I am confident that we will solve the theory someday soon. Perhaps a young person reading this article will be so inspired by this story that he or she will finish the theory. I can’t wait!

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(All airtimes are on Saturday unless otherwise noted.)

 
Tell your local radio station that you want SCIENCE FANTASTIC.

 


Exploration

 

 

 

Exploration with Michio Kaku, is an hour long radio program on science, technology, politics, and the environment. It is broadcast each week on WBAI New York City (99.5 FM), and re-aired on stations across the country via the Ku National Radio Satellite. Exploration can also be heard worldwide as a live streaming simulcast by various national terrestrial radio stations and online archive curated by KPFA Berkeley (94.1 FM) and Pacifica Foundation Radio.

LISTEN NOW LISTEN NOW to any broadcast from the KPFA Online Archive.


Topics covered include black holes, time travel, higher dimensions, string theory, wormholes, search for extra-terrestial life, dark matter and dark energy, the future of space travel, genetic engineering, the aging process, the future of medicine, the human body shop, artificial intelligence, the future of computers and robots, as well as topics from science fiction.

Publications

Quantum Supremacy: How The Quantum Computer Revolution Will Change Everything

Publisher: Doubleday; May 2, 2023

Go to Book Detail Page.

The God Equation: The Quest for a Theory of Everything

Publisher: Doubleday; April 6, 2021

Go to Book Detail Page.

The Future of Humanity: Terraforming Mars, Interstellar Travel, Immortality, and Our Destiny Beyond Earth

Publisher: Doubleday; February 20, 2018
Publisher: Anchor (Paperback); April 2, 2019

Go to Book Detail Page.

Go to Book Detail Page The Future of the Mind: The Scientific Quest to Understand, Enhance, and Empower the Mind (Paperback Edition)

Publisher: Anchor Books; February 17, 2015

Go to Book Detail Page.

Purchase from Amazon.
Purchase from Apple iBooks.

Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100 (Paperback Edition)

Publisher: Anchor Books; February 21, 2012

Purchase from Amazon.

Physics of the Impossible: A Scientific Explorations into the World of Phasers, Force Fields, Teleportation, and Time Travel

Publisher: Doubleday; March 11, 2008

Purchase from Amazon.

Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos

Publisher: Anchor Books; February 14, 2006

 

Purchase from Amazon.

Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension

Publisher: Oxford University Press; October 1995

Purchase from Amazon.

Visions: How Science Will Revolutionize the 21st Century and Beyond

Publisher: Oxford Paperbacks; March 4, 1999

Purchase from Amazon.

Einstein’s Cosmos: How Albert Einstein’s Vision Transformed Our Understanding of Space and Time (Great Discoveries)

Publisher: W. W. Norton & Company; May 16, 2005

Beyond Einstein: The Cosmic Quest for the Theory of the Universe

Publisher: Anchor Books; September 1, 1995

 

READY FOR MORE?

CLICK FOR MORE BY MICHIO KAKU

Articles

The Physics of Extraterrestrial Civilizations

Sure, we have our technology: airplanes, the internet, satellites. But what would an advanced civilization millions of years old look like? Learn about the different types, and why our civilization ranks a measly Type-0.


The Physics of Interstellar Travel

What would it take to reach the stars? Explore the real physics behind interstellar travel.


The Physics of Time Travel

It looks easy in the movies, but time travel is still theory. Learn about the physics behind navigating time travel.


What to Do If You Have a Proposal for the Unified Field Theory?

Looking for a way to present your theory of everything? Let Dr. Kaku guide you on your path towards submitting a well formed proposal on the Unified Field Theory


So You Want to Become a Physicist?

Becoming a physicist in 3 exciting steps! What more could you want?


Hyperspace and a Theory of Everything

How would a ‘carp scientist’ explain the 3rd dimension, to his 2 dimensional pond inhabitants? Learn about higher dimensions from Dr. Kaku’s well known childhood story – the Japanese Tea Garden.


Black Holes, Wormholes and the Tenth Dimension

What lies on the other side of a black hole? Discover the quest to find a ‘theory of everything’, which could finally explain some of the strangest objects in the cosmos and beyond.


M-Theory: The Mother of all Superstrings

What makes M-Theory a mother of all theories, and when will scientists be able to verify it? Learn about the people and concepts behind the M-Theory.


Hyperspace: A Scientific Odyssey

A vivid and exciting look at higher dimensions and their role in a ‘theory of everything’.


Excerpt from ‘THE FUTURE OF THE MIND’

An excerpt from Dr. Kaku’s New York Times bestseller for your review.


 

ACADEMIC PAPERS

Brush up on your mathematics and delve into the world of Theoretical Physics. Note: These papers are in PDF format, requires Adobe Acrobat to view.

Symmetries and String Field Theory in D=2

How Unstable are Fundamental Quantum Super Membranes?

Sub Critical Closed String Field Theory (Less then 26)

Ultra-Violet Behavior of Bosonic Quantum Membranes

A Note on the Stability of Quantum Super Membranes

 

Smaller is stronger — now scientists know why

As structures made of metal get smaller — as their dimensions approach the micrometer scale (millionths of a meter) or less — they get stronger. Scientists discovered this phenomenon 50 years ago while measuring the strength of tin “whiskers” a few micrometers in diameter and a few millimeters in length.

About

Michio Kaku at the Chalkboard

Dr. Michio Kaku — theoretical physicist, bestselling author, acclaimed public speaker, renowned futurist, and popularizer of science. As co-founder of String Field Theory, Dr. Kaku carries on Einstein’s quest to unite the four fundamental forces of nature into a single grand unified theory of everything.

 

NEW YORK TIMES BESTSELLING AUTHOR

Kaku’s newest book, THE FUTURE OF THE MIND was released on February 25, 2014 and is now available. To see more, click here.

Dr. Kaku is the author of numerous New York Times Bestselling Books:

To search this website for book-related updates, click here.

 


 

MEDIA FIGURE AND POPULARIZER OF SCIENCE

Kaku has starred in a myriad of science programming for television including Discovery, Science Channel, BBC, ABC, and History Channel. Beyond his numerous bestselling books, he has also been a featured columnist for top popular science publications such as Popular Mechanics, Discover, COSMOS, WIRED, New Scientist, Newsweek, and many others. Dr. Kaku was also one of the subjects of the award-winning documentary, ME & ISAAC NEWTON by Michael Apted.

He is a news contributor to CBS:This Morning and is a regular guest on news programs around the world including CBS, Fox News, CNBC, MSNBC, CNN, RT. He has also made guest appearances on all major talk shows including The Daily Show with Jon Stewart, The Colbert Report with Stephen Colbert, The Late Show with David Letterman, The Tonight Show with Jay Leno, Conan on TBS, and others.

BBC Series: Time — Michio Kaku goes on an extraordinary exploration of the world in search of time.

BBC Four series: Visions of the Future — 3 part series exploring the cutting edge science of today, tomorrow, and beyond.

History Channel’s The Universe — Interviews with the world’s leading physicists and historians are woven together with animated recreations and first-person accounts to explain concepts such as the formation of galaxies, the creation of elements and the formation of Earth itself.

COSMOS Magazine — He stretches his mind to 11 dimensions, understands what Einstein failed to grasp, and he plans for the death of our Sun, five billion years from now. Michio Kaku is a superhero of the incomprehensible.

 


 

RADIO ON-AIR PERSONALITY

Michio Kaku hosts two weekly radio programs heard on stations around the country and podcast around the world.

Science Fantastic — a live science radio talk show which airs every Saturday.

Explorations in Science — airing every first, third, and fifth Fridays of each month and podcast every Tuesday.

For the full details of Dr. Kaku’s radio shows, visit Dr. Kaku’s Radio Page.

 


 

ACADEMIA

Theoretical Physicist — Dr. Michio Kaku is the co-creator of string field theory, a branch of string theory. He received a B.S. (summa cum laude) from Harvard University in 1968 where he came first in his physics class. He went on to the Berkeley Radiation Laboratory at the University of California, Berkeley and received a Ph.D. in 1972. In 1973, he held a lectureship at Princeton University.

Michio continues Einstein’s search for a “Theory of Everything,” seeking to unify the four fundamental forces of the universe—the strong force, the weak force, gravity and electromagnetism.

He is the author of several scholarly, Ph.D. level textbooks and has had more than 70 articles published in physics journals, covering topics such as superstring theory, supergravity, supersymmetry, and hadronic physics.

Professor of Physics — He holds the Henry Semat Chair and Professorship in theoretical physics at the City College of New York (CUNY), where he has taught for over 25 years. He has also been a visiting professor at the Institute for Advanced Study at Princeton, as well as New York University (NYU).

 

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