- Superstring theory
Superstring theory 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 theorythat incorporates fermionsand supersymmetry.
The deepest problem in
theoretical physicsis 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 forcesacting on the atomic scale.
The development of a
quantum field theoryof 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 gravitymust 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 spaceis 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, consistencyrequires spacetimeto 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-Yaushapes 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 manifoldwhere 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 theoryhad 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 revolutionin the 1990s during which the five string theories were discovered to be different limits of a single underlying theory: M-theory.
The five consistent superstring theories are:
type I stringhas 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.
type II stringtheories 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).
heterotic stringtheories 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 "E"8×"E"8 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
General relativitytypically deals with situations involving large mass objects in fairly large regions of spacetimewhereas quantum mechanicsis 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 changingevent. Since superstring theory has to be a local theoryto obey causalitythe 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 integralwhich 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:
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