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The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. ...each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. ~ Michio Kaku

String theory is a theoretical framework of physics in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity.

Quotes

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  • Is string theory a futile exercise as physics, as I believe it to be? It is an interesting mathematical specialty and has produced and will produce mathematics useful in other contexts, but it seems no more vital as mathematics than other areas of very abstract or specialized math, and doesn't on that basis justify the incredible amount of effort expended on it.
  • ... within particle theory, string theory is a big subject. There are few large particle theory groups within major universities that do not have at least one person doing string theory. In total, there are probably a couple of thousand people at universities around the world whose mortgage is paid either by doing string theory, using string theory, working with tools made within string theory, solving problems using methods developed in string theory, or simply having their mental map of the world at the smallest possible scales set by string theory.
  • ... one of the main beefs with the string theory is that it is so flexible you can get almost anything out of it. ... String theorists themselves are not too happy about it.
  • String theory... resolves the central dilemma confronting contemporary physics—the incompatibility between quantum mechanics and general relativity—and that unifies our understanding of all of nature's fundamental material constituents and forces. But to accomplish these feats, ...string theory requires that the universe have extra space dimensions. ...
    Physicists have found that a key signal that a quantum mechanical theory has gone haywire is that particular calculations yield "probabilities" that are not within... acceptable range. For instance... infinite probabilities. ...string theory cures these infinities. ...a residual ...problem remains. In the early days ...calculations yielded negative probabilities ...so string theory appeared to be awash in its own quantum-mechanical hot water. ...
    Physicists found that the troublesome calculations were highly sensitive to the number of independent directions to which a string can vibrate. ...if strings could vibrate in nine independent spatial directions, all of the negative probabilities would cancel out. ...
    Kaluza and Klein provide a loophole... in addition to our familiar three... there are six other curled-up... rather than just postulating the existence of extra dimensions, as had been done by Kaluza, Klein, and their followers, string theory requires them.
    • Brian Greene, The Elegant Universe (1999) Ch. 8 More Dimensions Than Meet the Eye.
  • Currently, string theorists are in a position analogous to an Einstein bereft of the equivalence principle. ...[A] central organizing principle that embraces ...all ...features of the theory within one overarching and systematic framework ...is still missing.
    • Brian Greene, The Elegant Universe (1999, 2003) Ch. 15 "Prospects."
  • Now, this change from point-particles to strings that are so small they look like points might not sound like it would accomplish much. But it does. Superstring theory successfully merges general relativity and quantum mechanics.
  • To build matter itself from geometry — that in a sense is what string theory does. It can be thought of that way, especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. … He would have liked the fact that there is an underlying geometrical principle — which, unfortunately, we don’t really yet understand.
    • David Gross, in his interview in Superstrings: A Theory of Everything? (1988) edited by P.C.W. Davies and Julian Brown
  • The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. ...each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. ...The string vibrates in ten dimensions because it requires... generalized Ramanujan functions in order to remain self-consistent.
    • Michio Kaku, in Hyperspace : A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995) Ch.7 Superstrings
  • I have no idea whether the properties of the universe as we know it are fundamental or emergent, but I believe that the mere possibility of the latter should give the string theorists pause, for it would imply that more than one set of microscopic equations is consistent with experiment — so that we are blind to these equations until better experiments are designed — and also that the true nature of the microscopic equations is irrelevant to our world.
  • One can ask whether the situation today in string theory is really as favorable as it was for field theory in the early 60's. It is difficult to know. Then, of course we had many more experiments to tell us how quantum field theories actually behave. To offset that, we have today more experience and greater mathematical sophistication.
  • Consistent, relativistic string theories had already been written down in two, ten or twenty-six dimensions (the last being relevant only to bosonic strings) in the 1970s. A closed string is a loop which replaces a spacetime point. Its quantum oscillations correspond to particles of higher spins and higher masses, which may be arranged in a linear trajectory in a spin-versus-mass ... (Regge) plot. If the slope parameter of this trajectory — the only parameter in the theory — is adjusted to equal the Newtonian constant, one can show, quite miraculously, that in the zeroth order of the closed bosonic string there emerges from the string theory Einstein's gravity in its fullness! (The higher orders give modifications to Einstein's theory, with corrections which have a range of length = 10–33 cm.)
  • The most recent chapter in our new understanding of nonperturbative effects in string theory has been the incorporation of unstable branes and open string tachyons into the overall framework of the theory. It has turned out that an understanding of unstable D-branes is necessary to properly describe all D-branes. This is natural from the point of view of K-theory, where brane configurations which are equivalent under the annihilation of unstable branes are identified ... The long-mysterious tachyon instability of open string theory has finally been given a physical interpretation: it is the instability of the D-brane that supports the existence of open strings. The instability disappears in the tachyon vacuum, in which the D-brane decays. Moreover, the belief that D-branes are solitonic solutions of string theory has been confirmed: starting with the appropriate tachyonic field theory of unstable space-filling branes, one can describe lower dimensional D-branes as solitonic solutions. Lower dimensional D-branes are thereby essentially obtained as solitons of the tachyon field theory, so, in some sense, lower-dimensional D-branes can be thought of as being made of tachyons! It has also been shown that the physics of unstable D-branes is captured by string field theory, thus making it a candidate for a non-perturbative formulation of string theory capable of describing changes of the string background.
  • ... all of these caveats really work only against the idea that the final theory of nature is a quantum field theory. They leave open the view, which is in fact the point of view of my book, that although you can not argue that relativity plus quantum mechanics plus cluster decomposition necessarily leads only to quantum field theory, it is very likely that any quantum theory that at sufficiently low energy and large distances looks Lorentz invariant and satisfies the cluster decomposition principle will also at sufficiently low energy look like a quantum field theory. Picking up a phrase from Arthur Wightman, I’ll call this a folk theorem. At any rate, this folk theorem is satisfied by string theory, and we don’t know of any counterexamples.
  • From the beginning it was clear that, despite its successes, the Standard Model of elementary particles would have to be embedded in a broader theory that would incorporate gravitation as well as the strong and electroweak interactions. There is at present only one plausible candidate for such a theory: it is the theory of strings, which started in the 1960s as a not-very-successful model of hadrons, and only later emerged as a possible theory of all forces.
  • It's possible that the true structures in the underlying theory are something quite different — and the obvious candidate is strings. That direction, I think, is certainly worth working on. We don't whether that's the correct direction.
  • String theory at its finest is, or should be, a new branch of geometry. ...I, myself, believe rather strongly that the proper setting for string theory will prove to be a suitable elaboration of the geometrical ideas upon which Einstein based general relativity.
    • "Edward Witten" interview, Superstrings: A Theory of Everything? (1992) ed. P.C.W. Davies, Julian Brown
  • I would expect that a proper elucidation of what string theory really is all about would involve a revolution in our concepts of the basic laws of physics - similar in scope to any that occurred in the past.
    • "Edward Witten" interview, Superstrings: A Theory of Everything? (1992) ed. P.C.W. Davies, Julian Brown
  • It's been said that string theory is part of the physics of the twenty-first century that fell by chance into the twentieth century. That's a remark that was made by a leading physicist about fifteen years ago. ...String theory was invented essentially by accident in a long series of events, starting with the Veneziano model... No one invented it on purpose, it was invented in a lucky accident. ...By rights, string theory shouldn't have been invented until our knowledge of some of the areas that are prerequisite... had developed to the point that it was possible for us to have the right concept of what it is all about.
    • "Edward Witten" interview, Superstrings: A Theory of Everything? (1992) ed. P.C.W. Davies, Julian Brown
  • Generally speaking, all the really great ideas of physics are really spin-offs of string theory... Some of them were discovered first, but I consider that a mere accident of the development on planet earth. On planet earth, they were discovered in this order [general relativity, quantum field theory, superstrings, and supersymmetry]... But I don't believe, if there are many civilizations in the universe, that those four ideas were discovered in that order in each civilization.
    • Edward Witten, as quoted by John Horgan, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age (1996)
  • I feel that we are so close with string theory that—in my moments of greatest optimism—I imagine that any day, the final form of the theory may drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before and that well into the twenty-first century, when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory.
  • Unlike a Feynman graph, which is divided into different lines, which can represent particles of different types with different masses and spins, any part of a string world sheet is equivalent to any other so "there is only one string." Whatever particles there are going to be represent different states of vibration of one basic string. Also there are not any vertices in the string world sheet so we do not have the freedom to tell the string how to interact.

See also

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Superstring theory

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