Revision 147178452 of "Supersymmetrische Stringtheorie" on dewiki

{{Unreferenced|date=December 2007}}

{{string-theory}}
{{see|string theory}}

'''Superstring theory''' is an attempt to explain all of the [[Elementary particle|particles]] and [[fundamental force]]s of nature in one theory by modeling them as vibrations of tiny [[supersymmetry|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]] and [[supersymmetry]].

== Background ==

The deepest problem in [[theoretical physics]] is harmonizing the theory of [[general relativity]], which describes gravitation and applies to large-scale structures ([[star]]s, [[galaxies]], [[super cluster]]s), 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 force|electromagnetic]], [[Strong interaction|strong nuclear]] and [[Weak interaction|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.

=== Basic idea ===

The basic idea is that the fundamental constituents of reality are strings of the [[Planck units|Planck length]] (about 10<sup>&minus;35</sup> m) which vibrate at [[resonance|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]] (10<sup>44</sup> [[newton]]s). 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 Crunch]]es" 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==
:''See also: Why does consistency require [[Why 10 dimensions|10 dimensions]]?''
Our [[physical space]] is observed to have only three large [[dimension]]s &mdash; and taken together with time as the fourth dimension &mdash; 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]], [[consistency]] requires [[spacetime]] to have 10, 11 or 26 dimensions. The conflict between observation and theory is resolved by making the unobserved dimensions [[Compactification (physics)|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 modeling (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.

Superstring theory is not the first theory to propose extra spatial dimensions, the [[Kaluza-Klein theory]] did already. 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.  

{{unsolved|physics|Is [[string theory]], superstring theory, or [[M-theory]], or some other variant on this theme, a step on the road to a "[[theory of everything]]," or just a blind alley?}}

== 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]].
{| border="1" cellpadding="1" cellspacing="1" bordercolorlight="#666699" bordercolordark="#666699" bgcolor="#CCFFCC" mm_noconvert="TRUE"
|- bgcolor="#FFFFFF"
! colspan="3" class="dark" | String Theories
|-
! class="dark" | Type
! class="dark" | Spacetime dimensions<br>
! class="dark" | Details
|-
! bgcolor="#FFCCCC" class="dark" | Bosonic
| align="CENTER" class="dark" | 26
| bgcolor="#FFFFCC" class="dark" | Only [[boson]]s, no [[fermion]]s means only forces, no matter, with both open and closed strings; major flaw: a [[Particle physics|particle]] with imaginary [[mass]], called the [[tachyon]]
|-
! bgcolor="#FFCCCC" class="dark" | I
| align="CENTER" class="dark" | 10
| bgcolor="#FFFFCC" class="dark" | [[Supersymmetry]] between forces and matter, with both open and closed strings, no [[tachyon]], group symmetry is [[special orthogonal group|SO(32)]]
|-
! bgcolor="#FFCCCC" class="dark" | IIA
| align="CENTER" class="dark" | 10
| bgcolor="#FFFFCC" class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only, no [[tachyon]], massless [[fermion]]s spin both ways (nonchiral)
|-
! bgcolor="#FFCCCC" class="dark" | IIB
| align="CENTER" class="dark" | 10
| bgcolor="#FFFFCC" class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only, no [[tachyon]], massless [[fermion]]s only spin one way (chiral)
|-
! bgcolor="#FFCCCC" class="dark" | HO
| align="CENTER" class="dark" | 10
| bgcolor="#FFFFCC" class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only, no [[tachyon]], [[heterotic]], meaning right moving and left moving strings differ, group symmetry is [[special orthogonal group|SO(32)]]
|-
! bgcolor="#FFCCCC" class="dark" | HE
| align="CENTER" class="dark" | 10
| bgcolor="#FFFFCC" class="dark" | [[Supersymmetry]] between forces and matter, with closed strings only, no [[tachyon]], [[heterotic]], meaning right moving and left moving strings differ, group symmetry is [[E8 (mathematics)|''E''<sub>8</sub>×''E''<sub>8</sub>]] 
|}

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 string|open]] and [[closed string]]s, 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-[[chirality (physics)|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 group]]s:  the heterotic [[E8 (mathematics)|''E''<sub>8</sub>×''E''<sub>8</sub>]] string and the heterotic [[special orthogonal group|SO(32)]] string. (The name heterotic SO(32) is slightly inaccurate since among the SO(32) [[Lie group]]s, string theory singles out a quotient Spin(32)/Z<sub>2</sub> that is not equivalent to SO(32).)

Chiral [[gauge theory|gauge theories]] can be inconsistent due to [[anomaly (physics)|anomalies]]. This happens when certain one-loop [[Feynman diagram]]s cause a quantum mechanical breakdown of the gauge symmetry. Having anomalies cancel puts a severe constraint on possible superstring theories.

==Integrating general relativity and quantum mechanics==
	
[[General relativity]] 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 hole]]s. 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.

== See also ==

* [[AdS/CFT]]
* [[Grand unification theory]]
* [[List of string theory topics]]
* [[M-theory]]
* [[Quantum gravity]]
* [[String theory]]

== References ==

<references/>
[[Category:String theory]]
[[Category:Supersymmetry]]

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