A Theory Of Everything?

Page 7

HYPERSPACE AND A THEORY OF EVERYTHING

When I was a child, I used to visit the Japanese Tea Garden in San Francisco. I would spend hours fascinated by the carp, who lived in a very shallow pond just inches beneath the lily pads, just beneath my fingers, totally oblivious to the universe above them. I would ask myself a question only a child could ask: what would it be like to be a carp?
What a strange world it would be! I imagined that the pond would be an entire universe, one that is two-dimensional in space. The carp would only be able to swim forwards and backwards, and left and right. But I imagined that the concept of "up", beyond the lily pads, would be totally alien to them. Any any carp scientist daring to talk about "hyperspace", i.e. the third dimension "above" the pond, would immediately be labelled a crank.
I wondered what would happen if I could reach down and grab a carp scientist and lift it up into hyperspace. I thought what a wondrous story the scientist would tell the others!
The carp would babble on about unbelievable new laws of physics: beings who could move without fins. Beings who could breathe without gills. Beings who could emit sounds without bub- bles.
I then wondered: how would a carp scientist know about our existence? One day it rained, and I saw the rain drops forming gentle ripples on the surface of the pond.
Then I understood.
The carp could see rippling shadows on the surface of the pond. The third dimension would be invisible to them, but vibra- tions in the third dimensions would be clearly visible. These ripples might even be felt by the carp, who would invent a silly concept to describe this, called "force." They might even give these "forces" cute names, such as light and gravity. We would laugh at them, because, of course, we know there is no "force" at all, just the rippling of the water.
Today, many physicists believe that we are the carp swimming in our tiny pond, blissfully unaware of invisible, unseen uni- verses hovering just above us in hyperspace. We spend out life in three spatial dimensions, confident that what we can see with our tele- scopes is all there is, ignorant of the possibility of 10 dimen- sional hyperspace. Although these higher dimensions are invisi- ble, their "ripples" can clearly be seen and felt. We call these ripples gravity and light.
The theory of hyperspace, however, languished for many decades for lack of any physical proof or application. But the thoery, once considered the province of eccentrics and mystics, is being revived for a simple reason: it may hold the key to the greatest theory of all time, the "theory of everything."
Einstein spent the last 30 years of his life futilely chas- ing after this theory, the Holy Grail of physics. He wanted a theory that could explain the four fundamental forces that govern the universe: gravity, electromagnetism, and the two nuclear forces (weak and strong). It was supposed to be the crowning achievement of the last 2,000 years of science, ever since the Greeks asked what the world was made of. He was searching for an equation, perhaps no more than one-inch long, that could be placed on a T-shirt, but was so powerful it could explain every- thing from the Big Bang, exploding stars, to atoms and molecules, to the lilies of the field.
He wanted to read the mind of God.
Ultimately, Einstein failed in his mission. In fact, he was shunned by many of his younger compatriots, who would taunt him with the ditty, "What God has torn asunder, no man can put to- gether."
But perhaps Einstein is now having his revenge. For the past decade, there has been furious research on merging the four fundamental forces into a single theory, especially one that can meld general relativity (which explains gravity) with the quantum theory (which can explain the two nuclear forces and electro- magnetism).
The problem is that relativity and the quantum theory are precise opposites. General relativity is a theory of the very large: galaxies, quasars, black holes, and even the Big Bang. It is based on bending the beautiful four dimensional fabric of space and time. The quantum theory, by contrast, is a theory of the very small, i.e. the world of sub-atomic particles. It is based on discrete, tiny packets of energy called quanta.
Over the past 50 years, many attempts have been tried to unite these polar opposites, and have failed. The road to the Unified Field Theory, the Theory of Everything, is littered with the corpses of failed attempts.
The key to the puzzle may be hyperspace. In 1915, when Einstein said space-time was four dimensional and was warped and rippled, he showed that this bending produced a "force" called gravity. In 1921, Theodr Kaluza wrote that ripples of the fifth dimension could be viewed as light. Like the fish seeing the ripples in hyperspace moving in their world, many physicists believe that light is created by ripples in five-dimensional space-time.
But what about dimensions higher than 5??
In principle, if we add more and more dimensions, we can ripple and bend them in different ways, thereby creating more forces. In 10 dimensions, in fact, we can accomodate all four fundamental forces!
Actually, it's not that simple. By naively going to 10 dimensions, we also introduce a host of esoteric mathematical inconsistencies (e.g. infinities and anomalies) that have killed all previous theories. The only theory which has survived every challenge posed to it is called superstring theory, in which this 10 dimensional universe is inhabited by tiny strings.
In fact, in one swoop, this 10 dimensional string theory gives us a simple, compelling unification of all forces. Like a violin string, these tiny strings can vibrate and create resonances or "notes". That explains why there are so many sub- atomic particles: they are just notes on a superstring.
(This seems so simple, but in the 1950s, physicists were drowning in an avalanche of sub-atomic particles. J.R. Oppenheim- er, who helped build the atomic bomb, even said, out of sheer frustration, that the Nobel Prize should go to the physicist who does NOT discover a new particle that year!)
Similarly, when the string moves in space and time, it warps the space around it just as Einstein predicted. Thus, in a re- markably simple picture, we can unify gravity (as the bending of space caused by moving strings) with the other quantum forces (now viewed as vibrations of the string).
Of course, any theory with this power and majesty has a problem. This theory, because it is a theory of everything, is really a theory of Creation. Thus, to fully test the theory requires re-creating Creation!
At first, this might seem hopelessly impossible. We can barely leave the earth's puny gravity, let alone create universes in the laboratory. But there is a way out to this seemingly intractable problem.
A theory of everything is also a theory of the everyday. Thus, this theory, when fully completed, will be able to explain the existence of protons, atoms, molecules, even DNA. Thus, the key is to fully solve the theory and test the theory against the known properties of the universe.
At present, no one on earth is smart enough to complete the theory. The theory is perfectly well-defined, but you see, superstring theory is 21st Century physics that fell accidentally into the 20th century. It was discovered purely by accident, when two young physicists were thumbing through a mathematics book. The theory is so elegant and powerful, we were never "destined" to see it in the 20th century. The problem is that 21st century mathematics has not yet been invented yet.
But since physicists are genetically predisposed to be opti- mists, I am confident that we will solve the theory someday soon. Perhaps a young person reading this article will be so inspired by this story that he or she will finish the theory. I can't wait!

M-THEORY: MOTHER OF ALLSUPERSTRING?

Every decade or so, a stunning breakthrough in string theory sends shock waves racing through the theoretical physics communi- ty, 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 spinoffs into my own field of mathematics ... have really been quite extraordinary. I feel I've been very privileged to witness this first hand."
And Cumrun Vafa at Harvard has said, "I may be biased on this one, but I think it is perhaps the most important develop- ment 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 nucle- ar 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 ulti- mately 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 dimen- sional space-time. Moreover, the theory easily swallows up Ein- stein'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 won- derfully diverse collection of galaxies, stars, planets, sub- atomic particles, and even people) may lie in this "non-perturba- tive region." Until this region can be probed, we don't know if string theory is a theory of everything -- or a theory of noth- ing!
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 theo- ries 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, mem- branes 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 mem- brane), 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 archi- tects of thilion, the string and various p- branes appear to be different limits of the same theory.
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 theo- ry."
To understand unfamiliar concepts such as duality, perturba- tion theory, non-perturbative solutions, it is instructive to see where these concepts first entered into physics.

Sheila Na Gig
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Copyright © 1999 Sheila Na Gig.
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