is an attempt to explain all of the particles
and fundamental forces
of nature in one theory by modelling them as vibrations of tiny supersymmetric
strings. It is considered one of the most promising candidate theories of quantum gravity
. Superstring theory is a shorthand for supersymmetric string theory
because unlike bosonic string theory
, it is the version of string theory
that incorporates fermions
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 atomic 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 three of the four fundamental forces – electromagnetic, strong nuclear and weak nuclear forces - but not for gravity. The development of a quantum theory of gravity must therefore come about by different means than those used for the other forces.
The basic idea is that the fundamental constituents of reality are strings of the Planck length (about 10−33 cm) which vibrate at resonant frequencies. Every string in theory has a unique resonance, or harmonic. Different harmonics determine different fundamental forces. The tension in a string is on the order of the Planck force (1044 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.
- See also: Why does consistency require 10 dimensions?
Our physical space
is observed to have only three large dimensions
and—taken together with time as the fourth dimension—a physical theory must take this into account. However, nothing prevents a theory from including more than 4 dimensions, per se. In the case of string theory
to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions compactified
Our minds have difficulty visualizing higher dimensions because we can only move in three spatial dimensions. 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. Six-dimensional Calabi-Yau shapes can account for the additional dimensions required by superstring theory. The theory states that every point in space (or whatever we had previously considered a point) is in fact a very small manifold where each extra dimension has a size on the order of the Planck length.
Superstring theory is not the first theory to propose extra spatial dimensions; the Kaluza-Klein theory had done so previously. Modern string theory relies on the mathematics of folds, knots, and topology, which were largely developed after Kaluza and Klein, and has made physical theories relying on extra dimensions much more credible.
Number of superstring theories
Theoretical physicists were troubled by the existence of five separate string theories. This has been solved by the second superstring revolution in the 1990s during which the five string theories were discovered to be different limits of a single underlying theory: M-theory.
| String Theories
|| Spacetime dimensions|
|| 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
|| Supersymmetry between forces and matter, with both open and closed strings, no tachyon, group symmetry is SO(32)
|| Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions spin both ways (nonchiral)
|| Supersymmetry between forces and matter, with closed strings only, no tachyon, massless fermions only spin one way (chiral)
|| 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)
|| 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).)
Chiral gauge theories can be inconsistent due to anomalies. This happens when certain one-loop Feynman diagrams cause a quantum mechanical breakdown of the gauge symmetry. The anomalies were canceled out via the Green-Schwarz mechanism.
Integrating general relativity and quantum mechanics
typically deals with situations involving large mass objects in fairly large regions of spacetime
whereas quantum mechanics
is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case in which they are combined is in the study of black holes
. Having "peak density", or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony in order to predict conditions in such places; yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.
The major problem with their congruence is that, at sub-Planck (an extremely small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with loops. These loops have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of sub-Planck length dimensional warping, there being no matter that is of sub-Planck length.
The Five Superstring Interactions
There are five ways open and closed strings can interact. An interaction in superstring theory is a topology changing event. Since superstring theory has to be a local theory to obey causality the topology change must only occur at a single point. If C represents a closed string and O an open string, then the five interactions are, symbollically:
OOO + CCC + OOOO + CO + COO
All open superstring theories also contain closed superstrings since closed superstrings can be seen from the fifth interaction, they are unavoidable. Although all these interactions are possible, in practice the most used superstring model is the closed heterotic E8xE8 superstring which only has closed strings and so only the second interaction (CCC) is needed.
The single most important equation in (first quantisized bosonic) string theory is the N-point scattering amplitude. This treats the incoming and outgoing strings as points, which in string theory are tachyons
, with momentum
which connect to a string world surface at the surface points
. It is given by the following functional integral
which integrates (sums) over all possible embeddings of this 2D surface in 26 dimensions.
The functional integral can be done because it is a Gaussian to become: