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Dr. Kaku’s latest book is officially released and available in stores and online at your bookseller of choice. This also marks the start of Dr. Kaku’s multi-city national book tour. Check this website, and visit Dr. Kaku’s Facebook Fan Page for more details and updates about the tour and other appearances.

“THE FUTURE OF THE MIND: The scientific quest to understand, enhance, and empower the mind.”

The Future of the Mind

Telepathy. Telekinesis. Mind reading. Photographing a dream. Uploading memories. Mentally controlled robots. A Brain Net to replace the internet.

These feats, once considered science fiction, have now been achieved in the laboratory, as documented in THE FUTURE OF THE MIND.

But the book goes even further, analyzing when one day we might have a complete map of the brain, or a back up Brain 2.0, which may allow scientists to send consciousness throughout the universe. AVAILABLE NOW!


Houdini believed that telepathy was impossible. But science is proving Houdini wrong. Telepathy is now the subject of intense research at universities around the world, where scientists have already been able to use advanced sensors to read individual words, images, and thoughts in a person’s brain. This could alter the way we communicate with stroke and accident victims who are “locked in” their bodies, unable to articulate their thoughts except through blinks. But that’s just the start. Telepathy might also radically change the way we interact with computers and the outside world.

Indeed, in a recent “Next 5 in 5 Forecast,” which predicts five revolutionary developments in the next five years, IBM scientists claimed that we will be able to mentally communicate with computers, perhaps replacing the mouse and voice commands. This means using the power of the mind to call people on the phone, pay credit card bills, drive cars, make appointments, create beautiful symphonies and works of art, etc. The possibilities are endless, and it seems that everyone— from computer giants, educators, video game companies, and music studios to the Pentagon— is converging on this technology.

True telepathy, found in science-fiction and fantasy novels, is not possible without outside assistance. As we know, the brain is electrical. In general, anytime an electron is accelerated, it gives off electromagnetic radiation. The same holds true for electrons oscillating inside the brain, which broadcasts radio waves. But these signals are too faint to be detected by others, and even if we could perceive these radio waves, it would be difficult to make sense of them. Evolution has not given us the ability to decipher this collection of random radio signals, but computers can. Scientists have been able to get crude approximations of a person’s thoughts using EEG scans. Subjects would put on a helmet with EEG sensors and concentrate on certain pictures— say, the image of a car. The EEG signals were then recorded for each image and eventually a rudimentary dictionary of thought was created, with a one- to- one correspondence between a person’s thoughts and the EEG image. Then, when a person was shown a picture of another car, the computer would recognize the EEG pattern as being from a car.

The advantage of EEG sensors is that they are noninvasive and quick. You simply put a helmet containing many electrodes onto the surface of the brain and the EEG can rapidly identify signals that change every millisecond. But the problem with EEG sensors, as we have seen, is that electromagnetic waves deteriorate as they pass through the skull, and it is difficult to locate their precise source. This method can tell if you are thinking of a car or a house, but it cannot re- create an image of the car.

That is where Dr. Jack Gallant’s work comes in…


The epicenter for much of this research is the University of California at Berkeley, where I received my own Ph.D. in theoretical physics years ago. I had the pleasure of touring the laboratory of Dr. Gallant, whose group has accomplished a feat once considered to be impossible: videotaping people’s thoughts. “This is a major leap forward reconstructing internal imagery. We are opening a window into the movies in our mind,” says Gallant.

When I visited his laboratory, the first thing I noticed was the team of young, eager postdoctoral and graduate students huddled in front of their computer screens, looking intently at video images that were reconstructed from someone’s brain scan. Talking to Gallant’s team, you feel as though you are witnessing scientific history in the making.

Gallant explained to me that first the subject lies flat on a stretcher, which is slowly inserted headfirst into a huge, state- of- the- art MRI machine, costing upward of $3 million. The subject is then shown several movie clips (such as movie trailers readily available on YouTube). To accumulate enough data, the subject has to sit motionless for hours watching these clips, a truly arduous task. I asked one of the postdocs, Dr. Shinji Nishimoto, how they found volunteers who were willing to lie still for hours on end with only fragments of video footage to occupy the time. He said the people in the room, the grad students and postdocs, volunteered to be guinea pigs for their own research.

As the subject watches the movies, the MRI machine creates a 3-D image of the blood flow within the brain. The MRI image looks like a vast collection of thirty thousand dots, or voxels. Each voxel represents a pinpoint of neural energy, and the color of the dot corresponds to the intensity of the signal and blood flow. Red dots represent points of large neural activity, while blue dots represent points of less activity. (The final image looks very much like thousands of Christmas lights in the shape of the brain. Immediately you can see that the brain is concentrating most of its mental energy in the visual cortex, which is located at the back of the brain, while watching these videos.)

Gallant’s MRI machine is so powerful it can identify two to three hundred distinct regions of the brain and, on average, can take snapshots that have one hundred dots per region of the brain. (One goal for future generations of MRI technology is to provide an even sharper resolution by increasing the number of dots per region of the brain.)

At first, this 3-D collection of colored dots looks like gibberish. But after years of research, Dr. Gallant and his colleagues have developed a mathematical formula that begins to find relationships between certain features of a picture (edges, textures, intensity, etc.) and the MRI voxels. For example, if you look at a boundary, you’ll notice it’s a region separating lighter and darker areas, and hence the edge generates a certain pattern of voxels. By having subject after subject view such a large library of movie clips, this mathematical formula is refined, allowing the computer to analyze how all sorts of images are converted into MRI voxels. Eventually the scientists were able to ascertain a direct correlation between certain MRI patterns of voxels and features within each picture.

At this point, the subject is then shown another movie trailer. The computer analyzes the voxels generated during this viewing and re- creates a rough approximation of the original image. (The computer selects images from one hundred movie clips that most closely resemble the one that the subject just saw and then merges images to create a close approximation.) In this way, the computer is able to create a fuzzy video of the visual imagery going through your mind. Dr. Gallant’s mathematical formula is so versatile that it can take a collection of MRI voxels and convert it into a picture, or it can do the reverse, taking a picture and then converting it to MRI voxels.

I had a chance to view the video created by Dr. Gallant’s group, and it was very impressive. Watching it was like viewing a movie with faces, animals, street scenes, and buildings through dark glasses. Although you could not see the details within each face or animal, you could clearly identify the kind of object you were seeing.

Not only can this program decode what you are looking at, it can also decode imaginary images circulating in your head. Let’s say you are asked to think of the Mona Lisa. We know from MRI scans that even though you’re not viewing the painting with your eyes, the visual cortex of your brain will light up. Dr. Gallant’s program then scans your brain while you are thinking of the Mona Lisa and flips through its data files of pictures, trying to find the closest match. In one experiment I saw, the computer selected a picture of the actress Salma Hayek as the closest approximation to the Mona Lisa. Of course, the average person can easily recognize hundreds of faces, but the fact that the computer analyzed an image within a person’s brain and then picked out this picture from millions of random pictures at its disposal is still impressive.

The goal of this whole process is to create an accurate dictionary that allows you to rapidly match an object in the real world with the MRI pattern in your brain. In general, a detailed match is very difficult and will take years, but some categories are actually easy to read just by flipping through some photographs. Dr. Stanislas Dehaene of the Collège de France in Paris was examining MRI scans of the parietal lobe, where numbers are recognized, when one of his postdocs casually mentioned that just by quickly scanning the MRI pattern, he could tell what number the subject was looking at. In fact, certain numbers created distinctive patterns on the MRI scan. He notes, “If you take 200 voxels in this area, and look at which of them are active and which are inactive, you can construct a machine-learning device that decodes which number is being held in memory.”

This leaves open the question of when we might be able to have picture quality videos of our thoughts. Unfortunately, information is lost when a person is visualizing an image. Brain scans corroborate this. When you compare the MRI scan of the brain as it is looking at a flower to an MRI scan as the brain is thinking about a flower, you immediately see that the second image has far fewer dots than the first.

So although this technology will vastly improve in the coming years, it will never be perfect. (I once read a short story in which a man meets a genie who offers to create anything that the person can imagine. The man immediately asks for a luxury car, a jet plane, and a million dollars. At first, the man is ecstatic. But when he looks at these items in detail, he sees that the car and the plane have no engines, and the image on the cash is all blurred. Everything is useless. This is because our memories are only approximations of the real thing.) But given the rapidity with which scientists are beginning to decode the MRI patterns in the brain, will we soon be able to actually read words and thoughts circulating in the mind?


In fact, in a building next to Gallant’s laboratory, Dr. Brian Pasley and his colleagues are literally reading thoughts— at least in principle. One of the postdocs there, Dr. Sara Szczepanski, explained to me how they are able to identify words inside the mind.

The scientists used what is called ECOG (electrocorticogram) technology, which is a vast improvement over the jumble of signals that EEG scans produce. ECOG scans are unprecedented in accuracy and resolution, since signals are directly recorded from the brain and do not pass through the skull. The flipside is that one has to remove a portion of the skull to place a mesh, containing sixty-four electrodes in an eight-by-eight grid, directly on top of the exposed brain.

Luckily they were able to get permission to conduct experiments with ECOG scans on epileptic patients, who were suffering from debilitating seizures. The ECOG mesh was placed on the patients’ brains while open- brain surgery was being performed by doctors at the nearby University of California at San Francisco.

As the patients hear various words, signals from their brains pass through the electrodes and are then recorded. Eventually a dictionary is formed, matching the word with the signals emanating from the electrodes in the brain. Later, when a word is uttered, one can see the same electrical pattern. This correspondence also means that if one is thinking of a certain word, the computer can pick up the characteristic signals and identify it. With this technology, it might be possible to have a conversation that takes place entirely telepathically. Also, stroke victims who are totally paralyzed may be able to “talk” through a voice synthesizer that recognizes the brain patterns of individual words.

Not surprisingly, BMI (brain-machine interface) has become a hot field, with groups around the country making significant breakthroughs. Similar results were obtained by scientists at the University of Utah in 2011. They placed grids, each containing sixteen electrodes, over the facial motor cortex (which controls movements of the mouth, lips, tongue, and face) and Wernicke’s area, which processes information about language. The person was then asked to say ten common words, such as “yes” and “no,” “hot” and “cold,” “hungry” and “thirsty,” “hello” and “good-bye,” and “more” and “less.” Using a computer to record the brain signals when these words were uttered, the scientists were able to create a rough one- to- one correspondence between spoken words and computer signals from the brain.

Later, when the patient voiced certain words, they were able to correctly identify each one with an accuracy ranging from 76 percent to 90 percent. The next step is to use grids with 121 electrodes to get better resolution. In the future, this procedure may prove useful for individuals suffering from strokes or paralyzing illnesses such as Lou Gehrig’s disease, who would be able to speak using the brain-to-computer technique.


At the Mayo Clinic in Minnesota, Dr. Jerry Shih has hooked up epileptic patients via ECOG sensors so they can learn how to type with the mind. The calibration of this device is simple. The patient is first shown a series of letters and is told to focus mentally on each symbol. A computer records the signals emanating from the brain as it scans each letter. As with the other experiments, once this one- to- one dictionary is created, it is then a simple matter for the person to merely think of the letter and for the letter to be typed on a screen, using only the power of the mind.

Dr. Shih, the leader of this project, says that the accuracy of his machine is nearly 100 percent. Dr. Shih believes that he can next create a machine to record images, not just words, that patients conceive in their minds. This could have applications for artists and architects, but the big drawback of ECOG technology, as we have mentioned, is that it requires opening up patients’ brains.

Meanwhile, EEG typewriters, because they are noninvasive, are entering the marketplace. They are not as accurate or precise as ECOG typewriters, but they have the advantage that they can be sold over the counter. Guger Technologies, based in Austria, recently demonstrated an EEG typewriter at a trade show. According to their officials, it takes only ten minutes or so for people to learn how to use this machine, and they can then type at the rate of five to ten words per minute.


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THE FUTURE OF THE MIND: The Scientific Quest to Understand, Enhance, and Empower the Mind

Kaku's Vulcan Mind Meld



MICHIO KAKU tackles the most fascinating and complex object in the known universe: the human brain.

THE FUTURE OF THE MIND brings a topic that once belonged solely to the province of science fiction into a startling new reality.

This scientific tour de force unveils the astonishing research being done in top laboratories around the world — all based on the latest advancements in neuroscience and physics — including recent experiments in telepathy, mind control, avatars, telekinesis, and recording memories and dreams.

THE FUTURE OF THE MIND is an extraordinary, mind-boggling exploration of the frontiers of neuroscience.

Dr. Kaku looks toward the day when we may achieve the ability to upload the human brain to a computer, neuron for neuron; project thoughts and emotions around the world on a brain-net; take a “smart pill” to enhance cognition; send our consciousness across the universe; and push the very limits of immortality.

For an excerpt from ‘THE FUTURE OF THE MIND’, click here.

Available in Paperback, Hardcover, Kindle, Audio CD, & Audible.

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


Visit Dr. Kaku’s Facebook Fan Page for your connection to the online community of over 3 million fans of THE FUTURE OF THE MIND featuring interviews, exclusive events, and fan-only content.


– You can call 866-323-2538 and record a question or comment, anytime day or night, directly to Dr. Kaku.
The best questions will appear on Science Fantastic, which airs in 130 cities across the US, Siriius XM satellite radio, and the internet. It airs weekly, on Saturdays and Sundays, for 3 hours. Check this website for dates, times, cities, call letters of the stations, etc.
It is by far the largest nationally syndicated science radio show on commercial radio.
Scores of Nobel Laureates have appeared on the show, and now is your turn!
– For the month of August, we will interview top scientists about the latest research on the brain.

Physics of the Future: How Science Will Change Daily Life by 2100 by Michio Kaku (To be Released on March 22, 2011)

Physics of the Future: How Science will Change Daily Life by 2100 by Michio Kaku – To Be Released on March 22, 2011

Based on interviews with over three hundred of the world’s top scientists, who are already inventing the future in their labs, Kaku—in a lucid and engaging fashion—presents the revolutionary developments in medi cine, computers, quantum physics, and space travel that will forever change our way of life and alter the course of civilization itself.

Pre-Order Your Copy of Physics of the Future by clicking on one of the vendors below:

Dr. Kaku’s astonishing revelations include:

  • The Internet will be in your contact lens. It will recog nize people’s faces, display their biographies, and even translate their words into subtitles.
  • You will control computers and appliances via tiny sen sors that pick up your brain scans. You will be able to rearrange the shape of objects.
  • Sensors in your clothing, bathroom, and appliances will monitor your vitals, and nanobots will scan your DNA and cells for signs of danger, allowing life expectancy to increase dramatically.
  • Radically new spaceships, using laser propulsion, may replace the expensive chemical rockets of today. You may be able to take an elevator hundreds of miles into space by simply pushing the “up” button.

Like Physics of the Impossible and Visions before it, Physics of the Future is an exhilarating, wondrous ride through the next one hundred years of breathtaking scientific revolution.

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.


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.