Superstring theory
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The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics which describes the other three fundamental forces acting on the microscopic scale.
The development of a quantum field theory of a force invariably results in infinite (and therefore useless) probabilities. Physicists have developed mathematical techniques (renormalization) to eliminate these infinities which work for the electromagnetic, strong nuclear and weak nuclear forces, but not gravity. Thus the development of a quantum theory of gravity must come about by different means than were used for the other forces.
The basic idea is that the fundamental constituents of reality are strings of the Planck length (about 10−35 m) which vibrate at resonant frequencies. The tension of a string (8.9×1042 newtons) is about 1041 times the tension of an average piano string (735 newtons). The graviton (the proposed messenger particle of the gravitational force), for example, is predicted by the theory to be a string with wave amplitude zero. Another key insight provided by the theory is that no measurable differences can be detected between strings that wrap around dimensions smaller than themselves and those that move along larger dimensions (i.e., effects in a dimension of size R equal those whose size is 1/R). Singularities are avoided because the observed consequences of "big crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of a string, at which point it would actually begin expanding.
Extra dimensions
Our physical space is observed to have only four large dimensions, and a physical theory must take this into account, but nothing prevents a theory from involving more than 4 dimensions, per se. In the case of string theory, consistency requires spacetime to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compact dimensions.
Our minds have difficulty visualizing higher dimensions because we can only move in three spatial dimensions. Even then, we only see in 2+1 dimensions; vision in 3 dimensions would allow one to see all sides (including the inside) of an object simultaneously. One way of dealing with this limitation is not to try to visualize higher dimensions at all, but just to think of them as extra numbers in the equations that describe the way the world works. This opens the question of whether these 'extra numbers' can be investigated directly in any experiment (which must show different results in 1, 2, or 2+1 dimensions to a human scientist). This, in turn, raises the question of whether models that rely on such abstract modelling (and potentially impossibly huge experimental apparatus) can be considered 'scientific'. 6-dimensional Calabi-Yau shapes can account for the additional dimensions required by superstring theory.
Superstring theory is not the first theory to propose extra spatial dimensions; see Kaluza-Klein theory. Modern string theory relies on the mathematics of folds, knots, and topology, which was largely developed after Kaluza and Klein, and has made physical theories relying on extra dimensions much more credible.
See also: Why does consistency require 10 dimensions?
Number of superstring theories
Theoretical physicists were troubled by the existence of five separate superstring theories. This has been solved by the second superstring revolution in the 1990s during which the five superstring theories were discovered to be different limits of a single underlying theory: M-theory.
| String Theories | ||
|---|---|---|
| Type | Spacetime dimensions | Details |
| Bosonic | 26 | Only bosons, no fermions means only forces, no matter, with both open and closed strings; major flaw: a particle with imaginary mass, called the tachyon |
| I | 10 | Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32) |
| IIA | 10 | Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral) |
| IIB | 10 | Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral) |
| HO | 10 | Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is SO(32) |
| HE | 10 | Supersymmetry between forces and matter, with closed strings only, no tachyon, heterotic, meaning right moving and left moving strings differ, group symmetry is E8×E8 |
The five consistent superstring theories are:
- The type I string has one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special in the sense that it is based on unoriented open and closed strings, while the rest are based on oriented closed strings.
- The type II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-chiral (parity conserving) while the IIB theory is chiral (parity violating).
- The heterotic string theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensional gauge groups: the heterotic E8×E8 string and the heterotic SO(32) string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) Lie groups, string theory singles out a quotient Spin(32)/Z2 that is not equivalent to SO(32).)
See also
References
- For further reference see the list at string theory.
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