STRING THEORY LINKS
| "The Second Superstring Revolution" by John Schwarz |
| "Superstring Theory" by Brian Greene |
| "Superstrings!", online introduction by John Pierre |
| "A
World of Strings" at www.hypermind.com
(where other related talks and articles are available) |
| "A Layman's Guide to M-theory" by Mike Duff |
| Related articles in Scientific American:
"The theory formerly known as strings" by Mike Duff, Sci.Am. 278 (1998) 54-59 "The Nature of Space and Time" by S. Hawking and R. Penrose "The Evolution of the Universe" by P.J.E. Peebles et al. |
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10 dimensional
heterotic superstring models
8 dimensional
heterotic superstring models
6 dimensional
heterotic superstring models
4 dimensional
heterotic superstring models
Davies, P.C.W. and Brown, Julian Russell (Eds.). Superstrings: A Theory of Everything? Cambridge, England: Cambridge University Press, 1988.
de Wit, B.; Fayet, Pierre.; and van Nieuwenhuizen, Peter. (Eds.). Supersymmetry and Supergravity `84: Proceedings of the Trieste Spring School, 4-14 April, 1984. Singapore: World Scientific, 1984.
Ferrara, Sergio (Ed.). Supersymmetry, 2 vols. Amsterdam, Netherlands: North-Holland, 1987.
Freund, Peter George Oliver. Introduction to Supersymmetry. Cambridge, England: Cambridge University Press, 1988.
Freund, Peter George Oliver and Mahanthappa, K.T. (Eds.) Superstrings. New York: Plenum Press, 1988. $85.
Green, Michael B.; Schwarz, John H.; and Witten, Edward. Superstring Theory, Vol. 1: Introduction. Cambridge, England: Cambridge University Press, 1987. $?.
Green, Michael B.; Schwarz, John H.; and Witten, Edward. Superstring Theory, Vol. 1. Cambridge, England: Cambridge University Press, 1987.
Hatfield, Brian. Quantum Field Theory of Point Particles and Strings. 1992. $45.
Kaku, Michio. Introduction to Superstrings. New York: Springer-Verlag, 1988. 568 p. $?.
Lee, H. C. (Ed.). An Introduction to Kaluza-Klein Theories: Workshop on Kaluza-Klein Theories, Chalk River/Deep River, Ontario, 11-16 August 1983. Singapore: World Scientific, 1984. 313 p.
Misra, S.P. Introduction to Supersymmetry and Supergravity. New York: Wiley, 1992. 240 p. $98.
Mohapatra, Rabindra Nath. Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics, 2nd ed. New York: Springer-Verlag, 1992. 405 p. $49.95.
Procesi. String Theory.
Ross, Graham G. Grand Unified Theories. Menlo Park, CA: Benjamin/Cummings, 1985. 497 p. $?.
Schwartz, John H. (Ed.). Superstrings: The First 15 Years of Superstring Theory, 2 vols. Singapore: World Scientific, 1985.
Siegel, Warren. Introduction to String Field Theory. Singapore: World Scientific, 1988. 244 p. $22.
Srivastava, Prem P. Supersymmetry, Superfields and Supergravity: An Introduction. Bristol: A. Hilger, 1986. 162 p.
Wess, Julius and Bagger, Jonathan. Supersymmetry and Supergravity, 2nd ed., rev. and expanded. Princeton, NJ: Princeton University Press, 1992. 259 p. $29.95.
West, Peter C. Introduction to Supersymmetry and Supergravity. Singapore: World Scientific, 1986. 289 p. $28.
West, Peter C. (Ed.). Supersymmetry: A Decade of Development. Bristol: A. Hilger, 1986. 483 p..
Yau, Shing-Tung (Ed.). Mathematical Aspects of String Theory. Singapore: World Scientific, 1987. 654 p. $93.
In the euphoria following the
first superstring revolution in 1985, some of the less experienced participants
in the enterprise thought that we were on the verge of constructing a complete
fundamental theory of the physical world. To put it mildly, I found this naive.
In this setting, the phrase "Theory of Everything" was introduced and propagated
by the public media. This was very unfortunate for several reasons.
The TOE phrase is very misleading
on several counts. First of all, the theory is not yet fully formulated, and
when it is (which might still take decades) it is not entirely clear that it
will be the last word in fundamental physics.
Furthermore, even if the theory
is a complete description of quantum dynamics, it seems unlikely that it will
also provide a theory of initial conditions, which is another key ingredient
required to explain why we observe the particular universe that we do.
But even if a theory of initial
conditions is also obtained, there will still be much about this universe that
cannot be explained. Many things, such as our very existence, are a consequence
of the inherent quantum indeterminacy of nature. I believe that cannot be overcome.
Maybe that is just as well, because if we had old-fashioned classical determinism,
the future would be fully determined, which would undermine our humanity.
There is also a more mundane
sort of unpredictability that is also to be expected. Many of the things that
the theory predicts unambiguously in principle could require intractable calculations.
Part of the art of physics is to identify those things that can be calculated.
The other reason the TOE phrase
upset me is that it alienated many of our physics colleagues, some of whom had
serious doubts about the subject anyway.
Quite understandably, it gave
them the impression that people who work in this field are a very arrogant bunch.
Actually, we are all very charming and delightful.
Previous |Next
| Contents | Resolving Contradictions | Supersymmetry | A Brief History of Superstings |
| Basic Ideas of Superstring Theory | Superstring Revolution, part deux |
The urge to discover a fundamental theory underlying all natural phenomena has been expressed since the beginning of civilization. From the reduction of all matter to ``earth, air, fire, water'', we have progressed considerably, and can now reduce all matter to a large collection of elementary particles and all forces to another set of elementary particles.
The most fundamental theory of this sort that is substantially confirmed by experiment is the ``Standard Model'' of three interactions: electro-magnetic, weak nuclear and strong nuclear. In this model, particles like electrons, muons, neutrinos and quarks (which make up matter) experience some or all of these forces, and particles like photons, W and Z bosons and gluons are responsible for the forces themselves. Exchange of force carriers between matter particles is the mechanism which we believe underlies the interaction process.
The best thing about the Standard Model is that we can calculate the rates at which interactions take place, then go out and measure the same rates in an accelerator or other laboratory, and compare. The very successful result of this comparison leads us to believe that the model is right, though (like all scientific theories) it may be approximate or incomplete.
The worst thing about the Standard Model is that it does not incorporate the fourth and best-known force in nature: gravity. This is believed to be mediated by the exchange of gravitons, and due to problems of mathematical consistency, no one has ever been able to incorporate gravity into the Standard Model. So it is surely incomplete. Another problem with this model is that one has to assume the existence of distinct forces and their carriers. Einstein hoped that there would be a ``unified'' theory in which all known forces would emerge out of a single one in some way. Electricity and magnetism used to be thought of as two forces, but now we know they are different aspects of the same (electro-magnetic) force. Could the same type of unification hold for the four forces that are today viewed as distinct?
A unified theory of this sort must be an essentially unique framework in which all the different kinds of forces and particles occur naturally. We should not have to fix the masses and charges of particles from experiment; rather the theory should fix them automatically to be the right values. Clearly this is an ambitious goal. Even more clearly, this means the theory should possess a great degree of inner beauty and mathematical consistency. To discover the unified theory, we must look among those physical models which broadly resemble nature and in addition satisfy the above criteria. Only at a later stage -- after the detailed structure of the theory is understood -- can we check whether it describes our world.
String theory is currently the most promising example of a candidate unified theory. We do not yet know whether it correctly describes nature, but it seems to be a theory which broadly describes a world similar to ours, and is endowed with beauty and consistency to an astonishing degree.
The physical idea is utterly simple. Instead of many types of elementary point-like particles, we postulate that in nature there is a single variety of string-like object. The string is not ``made up of anything'', rather, it is basic and other things are made up of it. As with musical strings, this basic string can vibrate, and each vibrational mode can be viewed as a point-like elementary particle, just as the modes of a musical string are perceived as distinct notes!
Thus string theory certainly is a model of elementary particles. The great surprise is that mathematical equations describing strings are highly constrained by consistency. In some sense, most of the equations we would think of writing down turn out to be inconsistent, only a few appear to be allowed. Indeed, it looks most likely that (unlike particle theories) there is only one string theory! If so, what does it predict, and is it the promised unified theory?
Researchers studying the equations of string theory soon discovered a wealth of surprises. First of all, among the particles arising as vibrations of the string, we find some which are very similar to electrons, muons, neutrinos and quarks -- known matter particles. There are others similar to photons, W and Z bosons and gluons -- known force carriers. And there is one particle similar to the graviton, the elusive fourth force carrier.
Now since the structure of the theory is unique, we can work out (not postulate) what are the types of interaction between these particles. Astonishingly, at low energies the interactions are precisely of the type appearing in the Standard Model, and as a welcome bonus, we also get the gravitational interaction that Einstein originally discovered. So string theory predicts, roughly speaking, the right types of particles and the right types of interactions among them. The famous mathematical inconsistency which for decades made it impossible to incorporate quantum gravity with the other interactions, is conspicuous by its absence in string theory. It is almost as if gravity needs strings in order to exist!
Besides these surprises, there are many others that we have stumbled upon in the last decade. In string theory, the fact that there are three space dimensions in our world might also be predicted rather than assumed. The dimension of ``space-time'' is variable in string theory, in the sense that we have to understand and solve string equations to determine it. This has not been done yet, because of the great complexity of the theory. But we may get there in the next few years. If the answer comes out to be four (three space and one time) then we would have ``explained'' one of the most deep and abiding mysteries since the dawn of civilization: why does our world have the dimensionality that it has? If the answer is something else then string theory may be the wrong theory of nature, though we may still learn something about the right theory. Only comparison with experiment can give us convincing answers.
Some properties of string theory are rather hard to accept at first sight. For example, in this theory very small distances are equivalent to very large ones, and very feeble interactions are equivalent to very strong ones. These properties run counter to our everyday experience, and yet it is not ruled out that they could be true in nature. Qualitative predictions like this could have an impact on our picture of the early universe, and with luck we might even get encouraging signs from the cosmos that string theory is on the right track.
8 November 1995.