Live Science: Michio Kaku & Dr. Charles Liu ask is time travel is possible

The Physics of Time Travel

Is it real, or is it fable?

In H.G. Wells’ novel, The Time Machine, our protagonist jumped into a special chair with blinking lights, spun a few dials, and found himself catapulted several hundred thousand years into the future, where England has long disappeared and is now inhabited by strange creatures called the Morlocks and Eloi. That may have made great fiction, but physicists have always scoffed at the idea of time travel, considering it to be the realm of cranks, mystics, and charlatans, and with good reason.

However, rather remarkable advances in quantum gravity are reviving the theory; it has now become fair game for theoretical physicists writing in the pages of Physical Review magazine. One stubborn problem with time travel is that it is riddled with several types of paradoxes. For example, there is the paradox of the man with no parents, i.e. what happens when you go back in time and kill your parents before you are born? Question: if your parents died before you were born, then how could you have been born to kill them in the first place?

There is also the paradox of the man with no past. For example, let’s say that a young inventor is trying futilely to build a time machine in his garage. Suddenly, an elderly man appears from nowhere and gives the youth the secret of building a time machine. The young man then becomes enormously rich playing the stock market, race tracks, and sporting events because he knows the future. Then, as an old man, he decides to make his final trip back to the past and give the secret of time travel to his youthful self. Question: where did the idea of the time machine come from?

There is also the paradox of the man who is own mother (my apologies to Heinlein.) “Jane” is left at an orphanage as a foundling. When “Jane” is a teenager, she falls in love with a drifter, who abandons her but leaves her pregnant. Then disaster strikes. She almost dies giving birth to a baby girl, who is then mysteriously kidnapped. The doctors find that Jane is bleeding badly, but, oddly enough, has both sex organs. So, to save her life, the doctors convert “Jane” to “Jim.”

“Jim” subsequently becomes a roaring drunk, until he meets a friendly bartender (actually a time traveler in disguise) who wisks “Jim” back way into the past. “Jim” meets a beautiful teenage girl, accidentally gets her pregnant with a baby girl. Out of guilt, he kidnaps the baby girl and drops her off at the orphanage. Later, “Jim” joins the time travelers corps, leads a distinguished life, and has one last dream: to disguise himself as a bartender to meet a certain drunk named “Jim” in the past. Question: who is “Jane’s” mother, father, brother, sister, grand- father, grandmother, and grandchild?

Not surprisingly, time travel has always been considered impossible. After all, Newton believed that time was like an arrow; once fired, it soared in a straight, undeviating line. One second on the earth was one second on Mars. Clocks scattered throughout the universe beat at the same rate. Einstein gave us a much more radical picture. According to Einstein, time was more like a river, which meandered around stars and galaxies, speeding up and slowing down as it passed around massive bodies. One second on the earth was Not one second on Mars. Clocks scattered throughout the universe beat to their own distant drummer.

However, before Einstein died, he was faced with an embarrassing problem. Einstein’s neighbor at Princeton, Kurt Goedel, perhaps the greatest mathematical logician of the past 500 years, found a new solution to Einstein’s own equations which allowed for time travel! The “river of time” now had whirlpools in which time could wrap itself into a circle. Goedel’s solution was quite ingenious: it postulated a universe filled with a rotating fluid. Anyone walking along the direction of rotation would find themselves back at the starting point, but backwards in time!

In his memoirs, Einstein wrote that he was disturbed that his equations contained solutions that allowed for time travel. But he finally concluded: the universe does not rotate, it ex- pands (i.e. as in the Big Bang theory) and hence Goedel’s solution could be thrown out for “physical reasons.” (Apparently, if the Big Bang was rotating, then time travel would be possible throughout the universe!)

Then in 1963, Roy Kerr, a New Zealand mathematician, found a solution of Einstein’s equations for a rotating black hole, which had bizarre properties. The black hole would not collapse to a point (as previously thought) but into a spinning ring (of neutrons). The ring would be circulating so rapidly that centrifugal force would keep the ring from collapsing under gravity. The ring, in turn, acts like the Looking Glass of Alice. Anyone walking through the ring would not die, but could pass through the ring into an alternate universe. Since then, hundreds of other “wormhole” solutions have been found to Einstein’s equations. These wormholes connect not only two regions of space (hence the name) but also two regions of time as well. In principle, they can be used as time machines.

Recently, attempts to add the quantum theory to gravity (and hence create a “theory of everything”) have given us some insight into the paradox problem. In the quantum theory, we can have multiple states of any object. For example, an electron can exist simultaneously in different orbits (a fact which is responsible for giving us the laws of chemistry). Similarly, Schrodinger’s famous cat can exist simultaneously in two possible states: dead and alive. So by going back in time and altering the past, we merely create a parallel universe. So we are changing someone ELSE’s past by saving, say, Abraham Lincoln from being assassinated at the Ford Theater, but our Lincoln is still dead. In this way, the river of time forks into two separate rivers. But does this mean that we will be able to jump into H.G. Wells’ machine, spin a dial, and soar several hundred thousand years into England’s future? No. There are a number of difficult hurdles to overcome.

First, the main problem is one of energy. In the same way that a car needs gasoline, a time machine needs to have fabulous amounts of energy. One either has to harness the power of a star, or to find something called “exotic” matter (which falls up, rather than down) or find a source of negative energy. (Physicists once thought that negative energy was impossible. But tiny amounts of negative energy have been experimentally verified for something called the Casimir effect, i.e. the energy created by two parallel plates). All of these are exceedingly difficult to obtain in large quantities, at least for several more centuries!

Then there is the problem of stability. The Kerr black hole, for example, may be unstable if one falls through it. Similarly, quantum effects may build up and destroy the wormhole before you enter it. Unfortunately, our mathematics is not powerful enough to answer the question of stability because you need a “theory of everything” which combines both quantum forces and gravity. At present, superstring theory is the leading candidate for such a theory (in fact, it is the ONLY candidate; it really has no rivals at all). But superstring theory, which happens to be my specialty, is still too difficult to solve completely. The theory is well-defined, but no one on earth is smart enough to solve it.

Interestingly enough, Stephen Hawking once opposed the idea of time travel. He even claimed he had “empirical” evidence against it. If time travel existed, he said, then we would have been visited by tourists from the future. Since we see no tourists from the future, ergo: time travel is not possible. Because of the enormous amount of work done by theoretical physicists within the last 5 years or so, Hawking has since changed his mind, and now believes that time travel is possible (although not necessarily practical). (Furthermore, perhaps we are simply not very interesting to these tourists from the future. Anyone who can harness the power of a star would consider us to be very primitive. Imagine your friends coming across an ant hill. Would they bend down to the ants and give them trinkets, books, medicine, and power? Or would some of your friends have the strange urge to step on a few of them?)

In conclusion, don’t turn someone away who knocks at your door one day and claims to be your future great-great-great grandchild. They may be right.

The Physics of Interstellar Travel

To one day, reach the stars.

When discussing the possibility of interstellar travel, there is something called “the giggle factor.” Some scientists tend to scoff at the idea of interstellar travel because of the enormous distances that separate the stars. According to Special Relativity (1905), no usable information can travel faster than light locally, and hence it would take centuries to millennia for an extra-terrestrial civilization to travel between the stars. Even the familiar stars we see at night are about 50 to 100 light years from us, and our galaxy is 100,000 light years across. The nearest galaxy is 2 million light years from us. The critics say that the universe is simply too big for interstellar travel to be practical.

Similarly, investigations into UFO’s that may originate from another planet are sometimes the “third rail” of someone’s scientific career. There is no funding for anyone seriously looking at unidentified objects in space, and one’s reputation may suffer if one pursues an interest in these unorthodox matters. In addition, perhaps 99% of all sightings of UFO’s can be dismissed as being caused by familiar phenomena, such as the planet Venus, swamp gas (which can glow in the dark under certain conditions), meteors, satellites, weather balloons, even radar echoes that bounce off mountains. (What is disturbing, to a physicist however, is the remaining 1% of these sightings, which are multiple sightings made by multiple methods of observations. Some of the most intriguing sightings have been made by seasoned pilots and passengers aboard air line flights which have also been tracked by radar and have been videotaped. Sightings like this are harder to dismiss.)

But to an astronomer, the existence of intelligent life in the universe is a compelling idea by itself, in which extra-terrestrial beings may exist on other stars who are centuries to millennia more advanced than ours. Within the Milky Way galaxy alone, there are over 100 billion stars, and there are an uncountable number of galaxies in the universe. About half of the stars we see in the heavens are double stars, probably making them unsuitable for intelligent life, but the remaining half probably have solar systems somewhat similar to ours. Although none of the over 100 extra-solar planets so far discovered in deep space resemble ours, it is inevitable, many scientists believe, that one day we will discover small, earth-like planets which have liquid water (the “universal solvent” which made possible the first DNA perhaps 3.5 billion years ago in the oceans). The discovery of earth-like planets may take place within 20 years, when NASA intends to launch the space interferometry satellite into orbit which may be sensitive enough to detect small planets orbiting other stars.

So far, we see no hard evidence of signals from extra-terrestrial civilizations from any earth-like planet. The SETI project (the search for extra-terrestrial intelligence) has yet to produce any reproducible evidence of intelligent life in the universe from such earth-like planets, but the matter still deserves serious scientific analysis. The key is to reanalyze the objection to faster-than-light travel.

A critical look at this issue must necessary embrace two new observations. First, Special Relativity itself was superceded by Einstein’s own more powerful General Relativity (1915), in which faster than light travel is possible under certain rare conditions. The principal difficulty is amassing enough energy of a certain type to break the light barrier. Second, one must therefore analyze extra-terrestrial civilizations on the basis of their total energy output and the laws of thermodynamics. In this respect, one must analyze civilizations which are perhaps thousands to millions of years ahead of ours.

The first realistic attempt to analyze extra-terrestrial civilizations from the point of view of the laws of physics and the laws of thermodynamics was by Russian astrophysicist Nicolai Kardashev. He based his ranking of possible civilizations on the basis of total energy output which could be quantified and used as a guide to explore the dynamics of advanced civilizations:

Type I: this civilization harnesses the energy output of an entire planet.

Type II: this civilization harnesses the energy output of a star, and generates about 10 billion times the energy output of a Type I civilization.

Type III: this civilization harnesses the energy output of a galaxy, or about 10 billion time the energy output of a Type II civilization.

A Type I civilization would be able to manipulate truly planetary energies. They might, for example, control or modify their weather. They would have the power to manipulate planetary phenomena, such as hurricanes, which can release the energy of hundreds of hydrogen bombs. Perhaps volcanoes or even earthquakes may be altered by such a civilization.

A Type II civilization may resemble the Federation of Planets seen on the TV program Star Trek (which is capable of igniting stars and has colonized a tiny fraction of the near-by stars in the galaxy). A Type II civilization might be able to manipulate the power of solar flares.

A Type III civilization may resemble the Borg, or perhaps the Empire found in the Star Wars saga. They have colonized the galaxy itself, extracting energy from hundreds of billions of stars.

By contrast, we are a Type 0 civilization, which extracts its energy from dead plants (oil and coal). Growing at the average rate of about 3% per year, however, one may calculate that our own civilization may attain Type I status in about 100-200 years, Type II status in a few thousand years, and Type III status in about 100,000 to a million years. These time scales are insignificant when compared with the universe itself.

On this scale, one may now rank the different propulsion systems available to different types of civilizations:

Type 0

• Chemical rockets
• Ionic engines
• Fission power
• EM propulsion (rail guns)

Type I

• Ram-jet fusion engines
• Photonic drive

Type II

• Antimatter drive
• Von Neumann nano probes

Type III

• Planck energy propulsion

Propulsion systems may be ranked by two quantities: their specific impulse, and final velocity of travel. Specific impulse equals thrust multiplied by the time over which the thrust acts. At present, almost all our rockets are based on chemical reactions. We see that chemical rockets have the smallest specific impulse, since they only operate for a few minutes. Their thrust may be measured in millions of pounds, but they operate for such a small duration that their specific impulse is quite small.

NASA is experimenting today with ion engines, which have a much larger specific impulse, since they can operate for months, but have an extremely low thrust. For example, an ion engine which ejects cesium ions may have the thrust of a few ounces, but in deep space they may reach great velocities over a period of time since they can operate continuously. They make up in time what they lose in thrust. Eventually, long-haul missions between planets may be conducted by ion engines.

For a Type I civilization, one can envision newer types of technologies emerging. Ram-jet fusion engines have an even larger specific impulse, operating for years by consuming the free hydrogen found in deep space. However, it may take decades before fusion power is harnessed commercially on earth, and the proton-proton fusion process of a ram-jet fusion engine may take even more time to develop, perhaps a century or more. Laser or photonic engines, because they might be propelled by laser beams inflating a gigantic sail, may have even larger specific impulses. One can envision huge laser batteries placed on the moon which generate large laser beams which then push a laser sail in outer space. This technology, which depends on operating large bases on the moon, is probably many centuries away.

For a Type II civilization, a new form of propulsion is possible: anti-matter drive. Matter-anti-matter collisions provide a 100% efficient way in which to extract energy from mater. However, anti-matter is an exotic form of matter which is extremely expensive to produce. The atom smasher at CERN, outside Geneva, is barely able to make tiny samples of anti-hydrogen gas (anti-electrons circling around anti-protons). It may take many centuries to millennia to bring down the cost so that it can be used for space flight.

Given the astronomical number of possible planets in the galaxy, a Type II civilization may try a more realistic approach than conventional rockets and use nano technology to build tiny, self-replicating robot probes which can proliferate through the galaxy in much the same way that a microscopic virus can self-replicate and colonize a human body within a week. Such a civilization might send tiny robot von Neumann probes to distant moons, where they will create large factories to reproduce millions of copies of themselves. Such a von Neumann probe need only be the size of bread-box, using sophisticated nano technology to make atomic-sized circuitry and computers. Then these copies take off to land on other distant moons and start the process all over again. Such probes may then wait on distant moons, waiting for a primitive Type 0 civilization to mature into a Type I civilization, which would then be interesting to them. (There is the small but distinct possibility that one such probe landed on our own moon billions of years ago by a passing space-faring civilization. This, in fact, is the basis of the movie 2001, perhaps the most realistic portrayal of contact with extra-terrrestrial intelligence.)

The problem, as one can see, is that none of these engines can exceed the speed of light. Hence, Type 0,I, and II civilizations probably can send probes or colonies only to within a few hundred light years of their home planet. Even with von Neumann probes, the best that a Type II civilization can achieve is to create a large sphere of billions of self-replicating probes expanding just below the speed of light. To break the light barrier, one must utilize General Relativity and the quantum theory. This requires energies which are available for very advanced Type II civilization or, more likely, a Type III civilization.

Special Relativity states that no usable information can travel locally faster than light. One may go faster than light, therefore, if one uses the possibility of globally warping space and time, i.e. General Relativity. In other words, in such a rocket, a passenger who is watching the motion of passing stars would say he is going slower than light. But once the rocket arrives at its destination and clocks are compared, it appears as if the rocket went faster than light because it warped space and time globally, either by taking a shortcut, or by stretching and contracting space.

There are at least two ways in which General Relativity may yield faster than light travel. The first is via wormholes, or multiply connected Riemann surfaces, which may give us a shortcut across space and time. One possible geometry for such a wormhole is to assemble stellar amounts of energy in a spinning ring (creating a Kerr black hole). Centrifugal force prevents the spinning ring from collapsing. Anyone passing through the ring would not be ripped apart, but would wind up on an entirely different part of the universe. This resembles the Looking Glass of Alice, with the rim of the Looking Glass being the black hole, and the mirror being the wormhole. Another method might be to tease apart a wormhole from the “quantum foam” which physicists believe makes up the fabric of space and time at the Planck length (10 to the minus 33 centimeters).

The problems with wormholes are many:

a) one version requires enormous amounts of positive energy, e.g. a black hole. Positive energy wormholes have an event horizon(s) and hence only give us a one way trip. One would need two black holes (one for the original trip, and one for the return trip) to make interstellar travel practical. Most likely only a Type III civilization would be able harness this power.

b) wormholes may be unstable, both classically or quantum mechanically. They may close up as soon as you try to enter them. Or radiation effects may soar as you entered them, killing you.

c) one version requires vast amounts of negative energy. Negative energy does exist (in the form of the Casimir effect) but huge quantities of negative energy will be beyond our technology, perhaps for millennia. The advantage of negative energy wormholes is that they do not have event horizons and hence are more easily transversable.

d) another version requires large amounts of negative matter. Unfortunately, negative matter has never been seen in nature (it would fall up, rather than down). Any negative matter on the earth would have fallen up billions of years ago, making the earth devoid of any negative matter.

The second possibility is to use large amounts of energy to continuously stretch space and time (i.e. contracting the space in front of you, and expanding the space behind you). Since only empty space is contracting or expanding, one may exceed the speed of light in this fashion. (Empty space can warp space faster than light. For example, the Big Bang expanded much faster than the speed of light.) The problem with this approach, again, is that vast amounts of energy are required, making it feasible for only a Type III civilization. Energy scales for all these proposals are on the order of the Planck energy (10 to the 19 billion electron volts, which is a quadrillion times larger than our most powerful atom smasher).

Lastly, there is the fundamental physics problem of whether “topology change” is possible within General Relativity (which would also make possible time machines, or closed time-like curves). General Relativity allows for closed time-like curves and wormholes (often called Einstein-Rosen bridges), but it unfortunately breaks down at the large energies found at the center of black holes or the instant of Creation. For these extreme energy domains, quantum effects will dominate over classical gravitational effects, and one must go to a “unified field theory” of quantum gravity.

At present, the most promising (and only) candidate for a “theory of everything”, including quantum gravity, is superstring theory or M-theory. It is the only theory in which quantum forces may be combined with gravity to yield finite results. No other theory can make this claim. With only mild assumptions, one may show that the theory allows for quarks arranged in much like the configuration found in the current Standard Model of sub-atomic physics. Because the theory is defined in 10 or 11 dimensional hyperspace, it introduces a new cosmological picture: that our universe is a bubble or membrane floating in a much larger multiverse or megaverse of bubble-universes.

Unfortunately, although black hole solutions have been found in string theory, the theory is not yet developed to answer basic questions about wormholes and their stability. Within the next few years or perhaps within a decade, many physicists believe that string theory will mature to the point where it can answer these fundamental questions about space and time. The problem is well-defined. Unfortunately, even though the leading scientists on the planet are working on the theory, no one on earth is smart enough to solve the superstring equations.

Conclusion

Most scientists doubt interstellar travel because the light barrier is so difficult to break. However, to go faster than light, one must go beyond Special Relativity to General Relativity and the quantum theory. Therefore, one cannot rule out interstellar travel if an advanced civilization can attain enough energy to destabilize space and time. Perhaps only a Type III civilization can harness the Planck energy, the energy at which space and time become unstable. Various proposals have been given to exceed the light barrier (including wormholes and stretched or warped space) but all of them require energies found only in Type III galactic civilizations. On a mathematical level, ultimately, we must wait for a fully quantum mechanical theory of gravity (such as superstring theory) to answer these fundamental questions, such as whether wormholes can be created and whether they are stable enough to allow for interstellar travel.

Physics of the Impossible hits the NY Times Best Seller List

Physics of the Impossible by Michio Kaku hit the NY Times Bestseller list at #12 in an upcoming edition of the Times.

From Seattle Times: Invisibility? Time travel? “Physics of the Impossible” says it may not be far-fetched: “Kaku encourages us to take seriously ideas the world’s great intellects consider crazy, reminding us that these same powerful minds sometimes wonder whether such way-out theories and models of the universe are crazy enough to be true.”

BBC Time Series (5 Clips) COSMIC TIME

Throughout history, one thing has never changed – time. It is something we rely on to plan our lives, and it is consistent, regular and ceaseless. But is it? High in the Alps, Michio encounters a mystery – tiny particles called muons which shouldn’t exist. They don’t last long enough to be detected on Earth – and yet here they are. The answer to this mystery lies in one of the greatest discoveries of all time – Einstein’s theory of relativity. The faster you travel, the slower time ticks. So time is not fixed at all.

BBC Time Series (5 Clips) LIFETIME

Why is our time limited? And does it have to be? Could our age-old dream of immortality ever be possible? In episode two, Michio Kaku explores these questions and meets some of the key people involved in the cutting-edge research into ageing. He travels to the amazing Methuselah tree, which is almost 5000 years old and still producing new pine cones. He discovers that time does get faster as you get older and, under hypnosis, he goes in search of his lost time, stored as memories. But it only proves that lost time is really gone forever.

THE PHYSICS OF SCIENCE FICTION 2023

Starships. Time Travel. Black holes. Wormholes. Alien civilizations. Hyperspace. Anti-matter drive. Parallel universes.

Physics of Science Fiction (Physics 332) is a course Professor Michio Kaku will be teaching this Spring Semester EXCLUSIVELY for students at The City College of New York (CCNY). It applies physics to explain some of most sensational themes found in science fiction.

This exciting and popular course is taught online by Dr. Kaku, professor of theoretical physics, New York Times best-selling author, TV and radio personality, and co-founder of string field theory. The course uses lectures, slideshows and planetarium shows to explain the cutting edge of science.

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 PHYSICS OF SCIENCE FICTION

Star Ships. Time Travel. Black holes. Wormholes. Alien civilizations. Hyperspace. Anti-matter drive. Parallel universes.

Physics of Science Fiction (Physics 332) is a new course which Professor Michio Kaku will be teaching this Fall Semester exclusively for students at The City College of New York (CCNY). It applies physics to explain some of most sensational themes found in science fiction.

This exciting new course is taught online by Dr. Kaku, professor of theoretical physics, NY Times best-selling author, TV and radio personality, and co-founder of string field theory. The course uses lectures, slideshows and planetarium shows to explain the cutting edge of science. MAY THE FORCE BE WITH YOU! Sorry, this course is for registered CCNY students only.

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.

• The Physics Behind Ball Design
• The Multiverse Has 11 Dimensions
• Advances in Holographic Technology Could Have Far-Reaching Implications
• What Travels Faster Than the Speed of Light?
• NASA Sending First Humanoid Robot Into Space
• Humans Have Lived in Space for a Decade (And Counting)!
• Intergalactic “G” Mail?
• China Creates the Worlds Fastest Supercomputer, Operating at 2.507 Petaflops
• Time Travel in a 1928 Chaplin Film?
• The 1000 Genomes Project Will Help Us Understand Genetic Variations

Opportunity to have Dr. Kaku answer some of your Science Questions on Camera in a BigThink.com Interview

My new television show “Sci-Fi Science” on The Science Channel is inspired by my book “Physics of the Impossible.” The first season of the show takes viewers through the wildest frontiers of science with a real-world look into the world of phasers, teleportation, light-sabers, invisibility, time travel and more. Filming for the second season is nearing an end, and will be launched on The Science Channel on Sept. 1 at 9 pm. I’ve decided to try something new with my Big Think blog—offering you the opportunity to have me answer some of your questions on camera. The basis of the topics are “shows” from the first season of “Sci-Fi Science.”

All you have to do is post your questions in the comments section on my Big Think Blog (Links Bleow). Some time in the near future, I will choose questions from each topic in the series and answer them on camera in another Big Think interview. The final product will prominently be displayed on my Big Think Blog (Dr. Kaku’s Universe). 

Please find the links to the 3-Part series below (each with different topics):

PART 1) Video Blog Series– How to Explore the Universe & Travel to a Parallel Universe

PART 2) Video Blog Series– How to Become a Superhero & How to Build a Sci-Fi Robot

PART 3) Video Blog Series– How to Teleport & Become Invisible

SCI-FI SCIENCE: Physics of the Impossible – Series Premieres on the Science Channel – Tuesday, December 1 at 10 PM

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.

Radio Programs

Dr. Kaku hosts a weekly science radio program that airs on over 100 commercial radio stations nationwide and also online worldwide.

Topics covered include black holes, time travel, higher dimensions, string theory, wormholes, search for extra-terrestrial 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.

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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.
	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 Purchase from Amazon.
	Beyond Einstein: The Cosmic Quest for the Theory of the Universe Publisher: Anchor Books; September 1, 1995 Purchase from Amazon.

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