Plain Background    Criticism of String Theory    Pictorial Calabi-yau

Many Thanks to James I Digol (Nickname from TOE Quest) for this Term Paper

An Intro to what Supertrings are - 01-29-2006, 12:39 AM

We have reached an extraordinary point in the history of science, for some physicists believe they are now on the verge of having a single theory that will unite all of what we have learned in science under one mathematical "umbrella." This quixotic quest on unification oftentimes considered as the holy grail of modern physics has led physicists to have a framework with the capacity to explain every fundamental feature upon which the universe is constructed and is called the Superstring Theory. This theory attempts to unite all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny strings. For this reason, it is sometimes described as possibly being the "theory of everything" or the "final" theory. These grandiose descriptive terms are meant to signify the deepest possible theory of physics - a theory that underlies all other, one that does not require or even allow for a deeper explanatory base.

The purpose of this term paper is fivefold. First, it gives an overview of the fundamental interactions which are to be unified, together with all the particles, by superstring theory. Second, it discusses how superstring theory resolves the conflict between Einstein’s general theory of relativity and quantum mechanics. Third, it also describes the nature of strings and the properties they possess which are crucial on unification. Fourth, it presents the current problems of the theory and the possible resolutions needed for its full mastery. Finally, it concludes that superstring theory may possibly unify all the forces and particle but certainly it does not end all sciences. Superstring theory only purports that the universe we are living is fundamentally made up of strings and everything that we see, feel, or experience are merely the vibrations of these strings.

The culmination of more than 2000 years of painstaking observation is the realization that all physical phenomena in our universe can be reduced to four fundamental forces, which at first bear no resemblance to one another. They are called the strong and weak nuclear forces, the electromagnetic force, and the gravitational force, or simply, gravity.

Stephen Hawking (1996) points out that gravity is the most familiar of the forces being responsible for keeping earth in orbit around the sun as well as keeping our feet anchored on it. The mass of an object measures how much gravitational force it can exert as well as feel. The electromagnetic force is the next most recognized. It is the force driving all of the convenience of modern life - lights, computers, TVs, cellphones, etc. - and underlies the awesome might of lightning storms and the gentle touch of human hand. Microscopically, the electric charge of a particle plays the same role for the electromagnetic force as mass does for gravity: it determines how strongly the particle can exert as well as respond electromagnetically.

He also states that the strong and weak forces are less familiar because theory strength rapidly diminishes over a distance except on subatomic distance scales; they are the nuclear forces. This is why these two forces were discovered only much more recently. The strong force is responsible for keeping quarks "glued" together inside protons and neutrons and keeping protons and neutrons tightly crammed together inside atomic nuclei. Thus it is vital in the stability of all matter. On the other hand, the weak force is best known as the force responsible for the radioactive decay of substances such as uranium and cobalt.

And dazzled with the dissimilarity of these forces, physicists have faced the central challenge of theoretical physics today as on how to unify these four forces into a single force so that we can be able to understand the wonderful variety of nature in a unified way. Steven Weinberg (1999) affirms that the greatest advances of the past have been the steps toward this goal: beginning with the unification of terrestrial and celestial mechanics by Isaac Newton in the 17th century; of optics with electricity and magnetism by James Clerk Maxwell in the 19th century; of space-time geometry and the theory of gravitation by Albert Einstein in the years 1905 and 1916; and of chemistry and atomic physics through the advent of quantum mechanics in the 1920s.

Time Magazine chose him as the "Person of the 20th Century," Albert Einstein has made a remarkable turning point on the course of scientific journey which began in the past. He was acclaimed a genius by many for the formulation of his three great theories. His first theory of Special Relativity led to the development of atomic bombs used in Japan that ended WWII and unlocked the secrets of stars. Then a few years after, he extended this theory to encompass gravity to have a General Theory of Relativity, which gave us space warps, the Big Bang, and Black Holes. But many didn’t realize that his greatest theory was never finished: a "theory of everything." Einstein’s crowning achievement was to have been done his dream of a unified field theory, one that would interweave all of nature’s forces and material constituents within a single theoretical tapestry.

Thereafter, the quest on unification continued but rather on a different track. The development of quantum mechanics in 1925 has given the physicists the first comprehensive formulation with which to pry opens the secrets of the atom. If Einstein extended his Special Relativity to the cosmos, quantum mechanics, by contrast, is a theory of the microcosm, where subatomic particles are held together by particle-like forces dancing on the sterile stage of space-time. Fairly rapidly, quantum theory began to give us an inclusive framework in which to describe the visible universe: the material universe consists of atoms and its constituents. And after decades of wandering in the wilderness, physicists have unified three fundamental forces, excluding gravity, into what is called the Standard Model, based on a zoo of bizarre particles called quarks, leptons, Higgs boson, gluons and more.

However, Michio Kaku (2000) insists that the details of the Standard Model are actually boring and unimportant. But the most interesting feature of this model is that it is based on symmetry. What has propelled this investigation into matter is that we can see the unmistakable sign of symmetry within each of nature’s fundamental interactions. Haber and Kane (1999) also explain that the interactions among the various particles are symmetric, that is, unchanged in the face of a number of subtle interchanges.

Promoters of the Standard Model can say truthfully that it fits all known experimental data. They can correctly point out that there are no experimental results that contradict the Standard Model. Nonetheless, nobody, not even its most fervent advocates, believes it is the final theory. First, the Standard Model does not describe gravity so it is necessarily incomplete. Kaku (2000) also explicates that when attempts are made to splice Einstein’s theory with the model, the resulting theory gives nonsensical answers. Physicists then declared that a quantum theory of gravity is nonrenormalizable, meaning that it cannot yield sensible, finite numbers to describe simple processes. Second, and perhaps the most important, it is mathematically very ugly, as many believe, because it crudely splices three very different interactions together. It is as if the Standard Model is like to cross three entirely different animals, such as an ant, a chicken, and a whale. Weinberg (1999) apologizes for the theory’s shortcomings and admits that it cannot be the final theory.

And so, by the 1980s, physics was reaching an impasse. It has been described as the greatest scientific problem of all time. Some have even dubbed it as the "Holy Grail of Modern Physics," the quest to unite quantum theory with gravity, thereby creating a "Theory of Everything." This is the problem that has frustrated the finest minds of the 20the century like Einstein (Mukerjee, 1996). At the time when certain pundits are predicting the end of science on the grounds that all important discoveries have already been made, it is worth emphasizing that the two main pillars of twentieth-century physics, quantum mechanics and Einstein’s general relativity, are mutually incompatible. Davies and Brown (1980) stresses that quantum mechanics sought to explain why atoms are stable and do not instantly fall apart. It also accounts for many of the observed properties of matter and radiation on the scale of molecules and smaller. In contrast, they also add that general relativity is a theory of space, gravity and cosmology. However, general relativity seems to break down when it is confronted by the behavior of atoms and molecules. Equally, quantum theory has faced with the challenge on the dynamics of exotic celestial objects called black holes. Thus, Duff (1990) infers that one cannot simply bring the two together to construct a single theory that would hold true from the atoms up to the solar system and beyond to the whole universe.

Until recently, the best hope for a theory that would resolve this dilemma was based on strings in a theory called Superstring Theory. Intense research over the past decades by physicists and mathematicians around the world has revealed that this new approach to describe matter at its most fundamental level resolves the tension between the aforementioned theories. In fact, Brian Greene (2000: pp. 81), a string theorist, affirms that the theory shows more: within the framework, general relativity and quantum mechanics "require one another for the theory to make sense." According to superstring theory, the marriage of the laws of the large and the small is not only a happy but inevitable as well.

Before embarking the basics of the theory, it is worthy to note that the particles making up the Standard Model are the "letters" of all matter. Just like their linguistic counterparts, they appear to have no further internal substructure. Superstring theory proclaims otherwise. According to which, if one could examine these particles with greater precision - a precision many orders of magnitude (about 10-33 cm) far beyond our present technological capacity - one finds that each is not point-like, but instead consists of a tiny one-dimensional loop. Like an infinitely thin rubber band, each particle contain vibrating, oscillating, dancing filament that has named a string. The undulations of such strings create everything: the electrons, quarks, including space, time, and even us. The way this is done is extremely mathematical and detailed but Edward Witten of Princeton University used an analogy to elucidate how strings work. He says that if we listen to a tuning fork, it seems harsh to our ear and that’s because we hear a pure tone rather than the higher overtones that you get from a piano or violin that give its richness and beauty. So in the case of one of these strings, it oscillates in many different forms - similarly to the overtones of a piano string. And these forms of vibrations are interpreted as different elementary particles and forces. All are different forms of vibration of the same basic string.

Moreover, the vibrations of the strings result primarily on their unusual characteristics they acquire, namely, its multidimensionality and supersymmetry. Multidimensionality, one of the deepest secrets of string theory and is still not well understood, implies that strings vibrate, not in our common space-time dimensions, but rather in 10 spatial dimensions. This may sounds fictional but Edward Witten explains that the theory technically requires extra dimensions (Kaku, 2000). The big zoo of elementary particles that we have implies more dimensions so that in many ways the strings can vibrate in many different directions. But the question arises as to why we perceive only space (length, width and height) and time dimensions. Stephen Hawking (1996) suggests that the other dimensions are curled up into space of enormously small size, something like a million million million million millionth of an inch! This is so small that we just don’t notice it. It is like the surface of an orange: if one looks at it close up, it is all curved and wrinkled, but if of one looks at it from a distance, one can’t see the bumps and it appears to smooth. So it is with space-time, on a very small scale, which 10-dimensional and highly curved, but on bigger scales you don’t see the curvature of the extra dimensions.

Another very important property of superstring theory is embodied in a separate physical theory called supersymmetry. Though it was explored prior to the formulation of the string theory, supersymmetry maintains that there is a constant underlying symmetry between everything in the universe, that everything is alike underneath its appearance to humankind. Like the string theory, this theory includes more than the normal four dimensions that have been accepted by physicists. It is known to them that symmetry helps unify theories, and more dimensions means more symmetry, so there is a greater chance with Supersymmetry that fundamental force can be linked together.

The marriage of string theory and Supersymmetry is the major reason why we have superstring theory. According to David Freedman, string theory is a natural foundation for superstrings, which are strings having the properties of Supersymmetry (Davies & Brown, 198. They are the same underneath, but depending on the frequencies at which the superstrings vibrate forming particles and the forces. And Haber and Kane (1999) prove that this unification also predicts new forms of matter and energy called "superparticles" - particles that are posited to be the "superpartners" of the particles in Standard Model. So if a laboratory experiment reveals the presence of these particles, then it will be a signpost pointing to the correctness of superstring theory. This possible confirmation of supersymmetry would help particle physicists to solve many problems they’ve encountered in the Standard Model. It will also explain why gravity is so weak and possible give us the missing matter of the universe, the so-called "dark matter" (e.g. superparticles) which constitutes thirty percent of it. For all these reasons, Weinberg (1993) believes that finding evidence of supersymmetry would be one of the most important discoveries of all time (Weinberg, 1993).

Before, the incorporation of supersymmetry with string theory has afflicted string theorists a quandary of having five different versions of it which differ primarily on what kind of strings they allow (either open or closed) and how they implement supersymmetry. These results are something of an embarrassment to the proponents of the theory. Because superstring theory claims to be a theory of everything, there should be really only one consistent formulation of it, but instead there were five. Here is where M-Theory steps into the rescue.

M-Theory was introduced by Edward Witten in 1995 after he initiated what has been called the Second Superstring Revolution which successfully combined the five superstring theories and as well as the long-been abandoned 11-dimensional Supergravity theory. This is accomplished by knitting together a web of relationships between each of the theories called dualities (specifically S-, T- and U-duality). Each of these dualities provides a way of converting one of the string theories into one another. Through this, M-Theory may explain the origin of strings.

Unfortunately, Witten’s remark and those of the others indicate that it could be decades or centuries before M-Theory is fully developed and understood. They considered it as a piece of 21st-century physics brought down to 20th-century. Weinberg (1999) also stresses out that we have not discovered any fundamental principle that governs the new theory. In fact, even the mathematics of the M-theory is so abstract and complicated that, to date, no one even knows the exact equations of the new theory. Instead, Kaku (2000) says that they know only approximations to these equations, and even approximations to these approximations are so difficult that they as yet have been partially solved.

Another problem concerns with the experimental evidences that it failed to comply. Physicists have agreed that no matter how elegant or beautiful a theory may be, it is doomed if it disagrees with reality. But in the case of superstring theory, it is still on the level of making predictions and there is still no observation today that contravenes the theory. And besides, proving the existence of superparticles requires machines powerful enough to accelerate particles to energy still far beyond the capacity of current particle accelerators. On top of that, Kaku (2000) imagines that discovering the curled extra dimensions are such an extreme condition that require machines as big as the solar system and would be unlikely to be funded by the present economic climate.

In order to resolve such issues, Kaku (2000) also believes that the theory is theoretical, not experimental, at the moment and it is presumably necessary to understand the deep principles in which the theory is based. In a sense, the development of superstring theory is in sharp contrast to general relativity: in general relativity, the detailed structure of the theory follows form Einstein’s penetrating insights into the logic of the laws of physics. However in superstring theory, Mukerjee (1996) opines that certain details have come first; string theorists are still groping for a unifying insight into the logic of the theory. And they also believe that for the logic to be discovered, the principles of general relativity must be a special case of the more general principles of superstring theory, and so in a sense general relativity can serves as a guide (Weinberg, 1993). Brian Greene (2000) also adds that the resolution of these possibilities may be developing a deep understanding of the logical status of the theory will undoubtedly lead to profound mathematical and physical problems. It should also lead to a better understanding of the predictions of the superstring theory. Consequently, the prospect is for a period of intellectual ferment and rapid advance.

And so, all the information presented in this term paper substantially purport that superstring theory would possibly resolves the tension between general relativity and quantum mechanics, there by unifying all the fundamental forces and the material constituents of our universe by modeling them as vibrations of strings. Nonetheless, almost everyone agrees that claiming superstring theory as a theory of everything would in no way mean that psychology, biology, geology, chemistry and even physics had been solved, in some sense, subsumed. The universe is such a wonderfully rich and complex place that the discovery of the final theory would not spell he end of science. Quite the contrary, the discovery of a TOE - the ultimate explanation of the universe at its most fundamental level, a theory that does not rely on anything else - would provide the firmest foundation on which to build our understanding of the world. Its discovery would certainly mark a beginning, not an end. It would also provide an unshakable pillar of coherence forever assuring us that the universe is a comprehensible place.

In conclusion, superstring theory is indeed a valuable one which realizes the above ideals: to further the understanding of all humankind and as well as the vastness of the universe where we live. Nevertheless, superstring theory will only end a certain kind of science - the science that proceeds by endlessly asking why. You may be asked such as why the moon goes around the earth. Well, gravity holds it. And why does gravity behave that way? Well, there is curvature of space and time. And why is that true? Well, who knows, it may be superstring theory of some sort. That series of why, why, why questions, like an unpleasant child, will come to an end in a final theory and then we will know. We will know the book of rules that govern everything.