Editing String theory (section)

=== Extra dimensions <span class="anchor" id="Number of dimensions"></span> ===

[[File:Compactification example.svg|right|thumb|alt=A tubular surface and corresponding one-dimensional curve.|An example of [[compactification (physics)|compactification]]: At large distances, a two dimensional surface with one circular dimension looks one-dimensional.]]

In everyday life, there are three familiar dimensions (3D) of space: height, width and length. Einstein's general theory of relativity treats time as a dimension on par with the three spatial dimensions; in general relativity, space and time are not modeled as separate entities but are instead unified to a four-dimensional (4D) [[spacetime]]. In this framework, the phenomenon of gravity is viewed as a consequence of the geometry of spacetime.<ref>[[#Wald|Wald]], p. 4</ref>

In spite of the fact that the Universe is well described by 4D spacetime, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily.{{efn|For example, in the context of the [[AdS/CFT correspondence]], theorists often formulate and study theories of gravity in unphysical numbers of spacetime dimensions.}} There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics.<ref name="Zee 2010"/> Finally, there exist scenarios in which there could actually be more than 4D of spacetime which have nonetheless managed to escape detection.<ref>[[#Zwiebach|Zwiebach]], p. 9</ref>

String theories require [[extra dimensions]] of spacetime for their mathematical consistency. In bosonic string theory, spacetime is 26-dimensional, while in superstring theory it is 10-dimensional, and in [[M-theory]] it is 11-dimensional. In order to describe real physical phenomena using string theory, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments.<ref>[[#Zwiebach|Zwiebach]], p. 8</ref>

[[Image:Calabi yau.jpg|left|thumb|alt=Visualization of a complex mathematical surface with many convolutions and self intersections.|A cross section of a quintic [[Calabi–Yau manifold]] ]]

[[Compactification (physics)|Compactification]] is one way of modifying the number of dimensions in a physical theory. In compactification, some of the extra dimensions are assumed to "close up" on themselves to form circles.<ref name="Yau and Nadis 2010, Ch. 6">[[#Yau|Yau and Nadis]], Ch. 6</ref> In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions.

Compactification can be used to construct models in which spacetime is effectively four-dimensional. However, not every way of compactifying the extra dimensions produces a model with the right properties to describe nature. In a viable model of particle physics, the compact extra dimensions must be shaped like a [[Calabi–Yau manifold]].<ref name="Yau and Nadis 2010, Ch. 6"/> A Calabi–Yau manifold is a special [[topological space|space]] which is typically taken to be six-dimensional in applications to string theory. It is named after mathematicians [[Eugenio Calabi]] and [[Shing-Tung Yau]].<ref>[[#Yau|Yau and Nadis]], p. ix</ref>

Another approach to reducing the number of dimensions is the so-called [[brane cosmology|brane-world]] scenario. In this approach, physicists assume that the observable universe is a four-dimensional subspace of a higher dimensional space. In such models, the force-carrying bosons of particle physics arise from open strings with endpoints attached to the four-dimensional subspace, while gravity arises from closed strings propagating through the larger ambient space. This idea plays an important role in attempts to develop models of real-world physics based on string theory, and it provides a natural explanation for the weakness of gravity compared to the other fundamental forces.<ref name=Randall/>