Editing M-theory (section)

===Number of dimensions===

{{main article|Extra dimensions|Compactification (physics)}}

[[File:Compactification example.svg|left|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 of space: height, width and depth. 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 [[spacetime]], three spatial dimensions and one time dimension. In this framework, the phenomenon of gravity is viewed as a consequence of the geometry of spacetime.<ref>Wald 1984, p. 4</ref>

In spite of the fact that the universe is well described by four-dimensional 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>Zee 2010, Parts V and VI</ref> Finally, there exist scenarios in which there could actually be more than four dimensions of spacetime which have nonetheless managed to escape detection.<ref>Zwiebach 2009, p. 9</ref>

One notable feature of string theory and M-theory is that these theories require [[extra dimensions]] of spacetime for their mathematical consistency. In string theory, spacetime is ''ten-dimensional'' (nine spatial dimensions, and one time dimension), {{anchor|11-dimensional spacetime}}while in M-theory it is ''eleven-dimensional'' (ten spatial dimensions, and one time dimension). In order to describe real physical phenomena using these theories, one must therefore imagine scenarios in which these extra dimensions would not be observed in experiments.<ref>Zwiebach 2009, p. 8</ref>

[[Compactification (physics)|Compactification]] is one way of modifying the number of dimensions in a physical theory.{{efn|[[Dimensional reduction]] is another way of modifying the number of dimensions.}} In compactification, some of the extra dimensions are assumed to "close up" on themselves to form circles.<ref name=autogenerated1>Yau and Nadis 2010, 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.{{efn|This analogy is used for example in Greene 2000, p. 186.}}