When I was a child, I used to visit the Japanese tea garden in San Francisco and gaze for hours at the carp swimming in the shallow pond.
I was fascinated by the strange world that these carp inhabited, a flat, two-dimensional world just beneath the lily pads.
The carp could move forward-backward, left-right, but the concept of "up" was totally alien and made no sense to them. I imagined any carp "scientist" living in the pond would scoff at the idea of higher dimensions and unseen worlds. Then one day I imagined grabbing one of the carp "scientists" and thrusting it into the world of "up". What an amazing world the carp would see: beings moving without fins and breathing without water - a whole new law of physics emerging just above the carp universe.
Today, many physicists believe that we are the fish. We live our entire lives scoffing at the idea of unseen worlds, worlds beyond our comfortable "pond" of three dimensions. Yet physicists are confronting the existence of dimensions beyond human ken, dimensions that have endlessly fascinated mystics, mathematicians, and charlatans.
What is driving this fascination with higher dimensions is something called "superstring theory", which has revolutionised the scientific landscape, overturning centuries of cherished ideas. Although it has not yet been experimentally verified, superstring theory postulates that our universe may be 10 or even 11-dimensional, perhaps co-existing with an infinite number of parallel universes.
Superstring theory may be the fabled "theory of everything", a single theory (perhaps an equation that, when written, is no more than one inch long) which can explain all physical phenomena, from the Big Bang to the expanding universe, the formation of atoms, the evolution of the Earth and even life itself.
This is the Holy Grail of physics. Eventually, this theory of everything may explain some of the deepest secrets of the cosmos, such as what happened before the Big Bang, whether the flow of time can be reversed, whether gateways can exist through space-time, and the ultimate fate of the universe.
Four forces rule the universe
Today, we realise that there are just four forces which rule the entire universe.
* First is gravity, which guides the planets in their orbits. Without gravity, the Sun would explode and the Solar System would fly apart. It was Isaac Newton who gave us the first theory of gravity, which today still guides our deep-space probes with unerring accuracy.
* Second is the electromagnetic force, which lights our cities, energises our power plants, and has unleashed the internet and the information revolution. Everytime there is a blackout, we are thrown several hundred years into the past.
* Third - the weak nuclear force is the force of radioactive decay. The weak force is not powerful enough to hold the nucleus of the atom together, so an atom of uranium or plutonium can decay. Hospitals today use radioactive substances to identify and cure diseases. This force also helps heat the centre of the Earth, resulting in volcanoes, earthquakes, and continental drift.
* Last, the strong nuclear force is sufficiently powerful enough to bind the nucleus of the atom together. It was Ernest Rutherford who first demonstrated the existence of a tiny nucleus at the centre of the atom and speculated that a new nuclear force must be necessary to hold it together.
Einstein and relativity
Today, we know that these four forces can be explained in two larger frameworks (see figure one, page 10). The first is Einstein's theory of general relativity, which explains the gravitational physics of very large objects (for instance, black holes, the Big Bang, the expanding universe).
Einstein showed that Newton's theory of gravity could be explained by assuming that space is curved. Imagine placing a bowling ball on a taut sheet, so it sinks a little into the fabric. Now imagine shooting a marble across the sheet. Naturally, the marble swings in a curved path around the ball. At first, it looks as though the bowling ball exerts a "force" which pulls the marble into orbit around the ball. But to a relativist, it is obvious that there is no "force", there is only the shape of the fabric which alters the marble's course. Hence, the "force" of gravity is only the curvature of space directing the marble.
The quantum theory
The second great theory is the quantum theory, which can explain the phenomenon of the very small sub-atomic world. It can describe the electromagnetic, weak, and strong nuclear forces, but not gravity. It assumes that all forces of the universe come in packets called "quanta".
The quanta of the electromagnetic force is called the photon, a particle of light. (In the Star Trek series, they use "photon torpedoes" to fight off enemy space ships. I chuckle at this, since a photon torpedo is nothing more than a flashlight.) Quantum theory is the exact opposite of general relativity. Instead of smooth surfaces, we have discrete packets of energy for the three other forces. This is a mystery: why should nature, at the most fundamental level, obey two different sets of laws, with different mathematics, different assumptions, and different physical pictures?
It was Einstein who first made the first valiant attempt to unify these forces into a single theory, which he called the "unified field theory". He spent 30 years trying to "read the mind of God". However, he failed.
Physicist Freeman Dyson has written that the "road to the unified field theory is littered with the corpses of failed attempts".
Nobel laureate Wolfgang Pauli, who was a severe critic of Einstein's work, once quipped: "What God has torn asunder, let no man put together." But even Pauli eventually caught the bug. With another Nobel laureate, Werner Heisenberg, Pauli put forth his version of the unified field theory in 1958 when Pauli visited Columbia University. Niels Bohr, who was in the audience, was sceptical and finally stood up and said: "We in the back are convinced your theory is crazy. But what divides us is whether your theory is crazy enough."
Too many particles
Any "theory of everything" has to be "crazy enough" to solve a host of potentially fatal problems. The first is the problem of "infinities".
Whenever someone naively combines gravity theory with the other quantum forces, the theory produces nonsensical answers in the form of infinite results. So far, the only known theory which can eliminate these infinities is string theory. Also, any unified field theory has to explain why there are so many sub-atomic particles. In the 1950s, our atom smashers would break apart atoms, only to find scores of new sub-atomic particles spewing out of the debris. Physicists were drowning in new sub-atomic particles, each given a Greek name. The situation was getting so desperate that J Robert Oppenheimer, father of the atomic bomb, said that the next Nobel prize should go to the physicist who did not discover a new particle.
Today, after decades of failed attempts, many physicists think that superstring theory is "crazy enough" to explain the flood of sub-atomic particles and unify all four forces into a single theory.
String theory postulates that the sub-atomic particles we see in nature are not point particles, but actually tiny vibrating strings. If we could, for example, take a super-microscope and view an electron, we would see that it is not a dot, but a tiny closed vibrating string (see figure two). If we change the vibration of this string, then it might turn into a new type of particle, such as a graviton, a quantum of gravity. If we change the vibration of the string enough, we should be able to turn it into any particle or force in the universe, thereby unifying gravity with the other forces. (When I got my PhD in physics from the University of California at Berkeley in 1972, I had to memorise all the names of the sub-atomic particles, numbering several hundred at that time - a hellish ordeal. In the future, I hope that graduate students will only have to say: "string".) But the most astonishing claim of superstring theory is that the universe was 10-dimensional at its beginning. (When this was first claimed in the 1970s, it nearly killed string theory for a decade. String theorists became the butt of jokes. String pioneer John Schwarz remembers being in the elevator with Nobel laureate Richard Feynman, who said to him, "and how many dimensions are you in today, John?"). If we allow for membranes, then the theory can even be defined in 11 dimensions (see box, page 12).
But string theorists now have the last laugh. Their theory has enjoyed a remarkable renaissance, partly because it is the only game in town. No other theory can claim to unify the four forces.
Mind of God
If string theory is correct, then we have a simple, elegant way of understanding the universe. The hundreds of sub-atomic particles that physicists have carefully catalogued for 50 years are nothing but the various notes that can be played on the superstring. The "melodies" that one can play on these interacting strings correspond to the laws of chemistry. The "harmonies" of the vibrating string correspond to the laws of physics. The universe corresponds to a symphony of strings. And finally, the "mind of god" is cosmic music resonating through 10-dimensional hyperspace. This leaves open the tantalising question of if there is a conductor guiding these strings.
Although a theory of everything would be the crowning achievement of modern science, the cynic may still ask: what practical applications does the theory have? Unfortunately, the theory predicts that the energy at which this unification takes place is beyond human comprehension (a quadrillion times more powerful than our most powerful machine). The theory has no immediate application. But one day, we expect that this will answer some of our deepest questions concerning space and time.
For example, Einstein's equations allow for the possibility of "wormholes" which may give us shortcuts to the stars and even time machines. (The first mention of a wormhole in popular literature was by mathematician Charles Dodgson who, as Lewis Carroll, wrote Through the Looking Glass. The "looking glass" is a wormhole, a portal or gateway which connects the countryside of Oxford with Wonderland).
A real "looking glass" is a spinning black hole. It probably collapses not into a dot, but into a spinning ring (the centrifugal force of the spinning ring prevents the ring from collapsing into a single point). If one travels through the ring, then one leaves our universe and enters another parallel universe (see figure three). Although Einstein's equations allow for the existence of these wormholes, it is not known how stable they are. Some believe that quantum radiation will kill you as you enter the wormhole.
Others disagree. Ultimately, it will take a theory of everything to settle the question of whether we can enter a parallel universe (see box, page 12).
Also, a number of peculiar solutions of Einstein's equations have been found which allow for time travel, so that you can journey into the past and perhaps even kill your parents before you are born. For example, if the universe were rotating (which it is not), one could travel around the universe and go back in time.
Similarly, if you travelled around a rotating, infinitely long cylinder, like dancing around a Maypole, you might find yourself in the distant past.
According to physicist Kip Thorne, a more "realistic" time machine might be built if one had something called "negative matter"; then one might be able to transverse across such a wormhole to the past. Although different designs for time machines have been made by physicists, only a theory of everything can state whether such a machine is possible.
Last, a unified field theory should take us back before the Big Bang itself. It is conceivable that our universe is an expanding bubble, coexisting in an ocean of other bubbles. We may, in fact, live in an infinite "multiverse" of bubble universes. Even as you started reading this paragraph, scores of universes might have undergone genesis. In superstring theory, we have millions upon millions of solutions, each one corresponding to a possible realistic universe within the multiverse. The goal of string theory, which is so far unfinished, is to find a universe among the multiverse which precisely predicts all the physical features of our universe. Physicists around the world are feverishly trying to achieve this. If someone can find a perfect match between our universe and one of these universes in the multiverse, it would be the greatest modern scientific achievement.
The unified field theory may also determine the death of the universe. The latest report from the WMAP satellite (which studies cosmic background radiation) in February last year paints a bleak picture of our demise. The universe is not only expanding, it is accelerating, propelled by a mysterious "dark energy" or "anti-gravity" which makes up 73 per cent of the matter and energy content of the universe. Trillions of years from now, temperatures may approach absolute zero. Stars may eventually burn up their nuclear fuel, and any intelligent species may have to huddle around the dying embers of black holes.
At this point, there may be only one way to escape. In my forthcoming book, Parallel Worlds, I speculate that perhaps the unified field theory may give us a way to evade the Big Freeze, by leaving the universe entirely. With enough energy, one might conceivably leave our dying universe and transverse through hyperspace to a younger, warmer universe and start all over again.
Einstein once said that if one stumbles upon the tail of a lion, one can assume that there is a great beast attached. I think that after decades of careful work, we are now in the final stages of revealing the true dimensions of the lion. No one knows when the theory will be completed.
Maybe tomorrow. Maybe in a few decades. But when that day dawns, then we will hear the lion roar, and it will be magnificent.
Dr Michio Kaku is professor of physics at the City University of New York and is the co-founder of string field theory (a branch of string theory).
He is also author of Hyperspace (OUP pound;9.99), Visions (OUP pound;8.99) and the forthcoming Einstein's Cosmos and Parallel Worlds
The weakest point of string theory is that it cannot be tested directly. It would take an atom smasher the size of a galaxy to test this theory.
Since string is really a theory of the universe, to test it would require creating a "baby universe" in our laboratory, which is impossible, although physicists such as Stephen Hawking have written about baby universes. But indirect experiments might find the following: * Dark matter. In addition to dark energy, we realise, much to our surprise, that 23 per cent of the universe is made of a new type of substance that is invisible but fills up the universe, keeping the galaxies from flying apart. By contrast, the familiar heavy elements that make up our world comprise only 0.5 per cent of the universe.
The leading candidate for dark matter is the "photino", a higher vibration or note of the superstring. There are scores of international teams of scientists trying to capture dark matter particles in their labs. Any day now, physicists may announce that they have captured dark matter, possibly winning them a Nobel prize. If dark matter turns out to be made of the photino, it would give an enormous boost to string theory.
* In 2007, the largest atom smasher in the world will be turned on outside Geneva, Switzerland. The LHC (Large Hadron Collider) will smash protons at tens of trillions of electron volts, re-creating conditions not seen since the Big Bang itself. Out of these titanic collisions, scientists hope to find "sparticles," or super particles predicted by string theory.
* Last year, the first gravity wave detector went online. LIGO (Laser Interferometer Gravitational Wave Observatory) comprises two laser laboratories which can detect faint gravitational disturbances from colliding neutron stars and black holes. By 2020, gravity wave detectors such as LISA (Laser Interferometry Space Antenna) will be put into outer space. LISA will consist of three satellites orbiting the sun, connected by three laser beams. The gravitational waves left-over from the Big Bang itself can be measured by analysing the slight jiggling of these three satellites. This "echo of creation" may be sufficient to test some of the predictions of string theory.
* Many laboratories around the world are searching for evidence of higher dimensions. String theory says that these dimensions are extremely tiny, so they may have eluded scientists for centuries. Gravity, for example, might "leak" into these other dimensions, and small deviations may be found to Newton's famous inverse square law which are measurable.