Editing M-theory (section)

===Quantum gravity and strings===

{{main article|Quantum gravity|String theory}}

[[Image:Open and closed strings.svg|right|thumb|alt=A wavy open segment and closed loop of string.|The fundamental objects of string theory are open and closed [[string (physics)|strings]]. ]]

One of the deepest problems in modern physics is the problem of [[quantum gravity]]. The current understanding of [[gravity]] is based on [[Albert Einstein]]'s [[general theory of relativity]], which is formulated within the framework of [[classical physics]]. However, [[fundamental interaction|nongravitational forces]] are described within the framework of [[quantum mechanics]], a radically different formalism for describing physical phenomena based on [[probability]].{{efn|For a standard introduction to quantum mechanics, see Griffiths 2004.}} A quantum theory of gravity is needed in order to reconcile general relativity with the principles of quantum mechanics,{{efn|The necessity of a quantum mechanical description of gravity follows from the fact that one cannot consistently [[coupling (physics)|couple]] a classical system to a quantum one. See Wald 1984, p. 382.}} but difficulties arise when one attempts to apply the usual prescriptions of quantum theory to the force of gravity.{{efn|From a technical point of view, the problem is that the theory one gets in this way is not [[renormalizable]] and therefore cannot be used to make meaningful physical predictions. See Zee 2010, p. 72 for a discussion of this issue.}}

[[String theory]] is a [[mathematical theory|theoretical framework]] that attempts to reconcile gravity and quantum mechanics. In string theory, the [[point particle|point-like particles]] of [[particle physics]] are replaced by [[one-dimensional]] objects called [[string (physics)|strings]]. String theory describes how strings propagate through space and interact with each other. In a given version of string theory, there is only one kind of string, which may look like a small loop or segment of ordinary string, and it can vibrate in different ways. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the vibrational state of the string. In this way, all of the different elementary particles may be viewed as vibrating strings. One of the vibrational states of a string gives rise to the [[graviton]], a quantum mechanical particle that carries gravitational force.{{efn|For an accessible introduction to string theory, see Greene 2000.}}

There are several versions of string theory: [[type I string|type I]], [[type IIA string|type IIA]], [[type IIB string|type IIB]], and two flavors of [[heterotic string]] theory ({{math|[[special orthogonal group|''SO''(32)]]}} and {{math|[[E8 (mathematics)|''E''<sub>8</sub>×''E''<sub>8</sub>]]}}). The different theories allow different types of strings, and the particles that arise at low energies exhibit different [[symmetry (physics)|symmetries]]. For example, the type I theory includes both open strings (which are segments with endpoints) and closed strings (which form closed loops), while types IIA and IIB include only closed strings.<ref>Zwiebach 2009, p. 324</ref> Each of these five string theories arises as a special limiting case of M-theory. This theory, like its string theory predecessors, is an example of a quantum theory of gravity. It describes a [[force (physics)|force]] just like the familiar gravitational force subject to the rules of quantum mechanics.<ref name="Becker, Becker, and Schwarz 2007, p. 12">Becker, Becker, and Schwarz 2007, p. 12</ref>