Editing M-theory (section)

==History and development==

{{Main article|History of string theory}}

===Kaluza–Klein theory===

{{main article|Kaluza–Klein theory}}

In the early 20th century, physicists and mathematicians including Albert Einstein and [[Hermann Minkowski]] pioneered the use of four-dimensional geometry for describing the physical world.<ref>Yau and Nadis 2010, p. 9</ref> These efforts culminated in the formulation of Einstein's general theory of relativity, which relates gravity to the geometry of four-dimensional spacetime.<ref name="Yau and Nadis 2010, p. 10">Yau and Nadis 2010, p. 10</ref>

The success of general relativity led to efforts to apply higher dimensional geometry to explain other forces. In 1919, work by [[Theodor Kaluza]] showed that by passing to five-dimensional spacetime, one can unify gravity and [[electromagnetism]] into a single force.<ref name="Yau and Nadis 2010, p. 10"/> This idea was improved by physicist [[Oskar Klein]], who suggested that the additional dimension proposed by Kaluza could take the form of a circle with radius around {{nowrap|10<sup>−30</sup>}} cm.<ref>Yau and Nadis 2010, p. 12</ref>

The [[Kaluza–Klein theory]] and subsequent attempts by Einstein to develop [[unified field theory]] were never completely successful. In part this was because Kaluza–Klein theory predicted a particle (the [[Graviscalar|radion]]), that has never been shown to exist, and in part because it was unable to correctly predict the ratio of an electron's mass to its charge. In addition, these theories were being developed just as other physicists were beginning to discover quantum mechanics, which would ultimately prove successful in describing known forces such as electromagnetism, as well as new [[nuclear force]]s that were being discovered throughout the middle part of the century. Thus it would take almost fifty years for the idea of new dimensions to be taken seriously again.<ref>Yau and Nadis 2010, p. 13</ref>

===Early work on supergravity===

{{main article|Supergravity}}

[[File:Edward Witten.jpg|left|thumb|upright=0.8|alt=A portrait of Edward Witten.|In the 1980s, [[Edward Witten]] contributed to the understanding of [[supergravity]] theories. In 1995, he introduced M-theory, sparking the [[second superstring revolution]].]]

New concepts and mathematical tools provided fresh insights into general relativity, giving rise to a period in the 1960s–1970s now known as the [[history of general relativity|golden age of general relativity]].<ref>Wald 1984, p. 3</ref> In the mid-1970s, physicists began studying higher-dimensional theories combining general relativity with supersymmetry, the so-called supergravity theories.<ref>van Nieuwenhuizen 1981</ref>

General relativity does not place any limits on the possible dimensions of spacetime. Although the theory is typically formulated in four dimensions, one can write down the same equations for the gravitational field in any number of dimensions. Supergravity is more restrictive because it places an upper limit on the number of dimensions.<ref name="Duff 1998, p. 64"/> In 1978, work by [[Werner Nahm]] showed that the maximum spacetime dimension in which one can formulate a consistent supersymmetric theory is eleven.<ref>Nahm 1978</ref> In the same year, [[Eugène Cremmer]], [[Bernard Julia]], and [[Joël Scherk]] of the [[École Normale Supérieure]] showed that supergravity not only permits up to eleven dimensions but is in fact most elegant in this maximal number of dimensions.<ref>Cremmer, Julia, and Scherk 1978</ref><ref name="Duff 1998, p. 65">Duff 1998, p. 65</ref>

Initially, many physicists hoped that by compactifying eleven-dimensional supergravity, it might be possible to construct realistic models of our four-dimensional world. The hope was that such models would provide a unified description of the four fundamental forces of nature: electromagnetism, the [[strong nuclear force|strong]] and [[weak nuclear force]]s, and gravity. Interest in eleven-dimensional supergravity soon waned as various flaws in this scheme were discovered. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as [[chirality (physics)|chirality]]. [[Edward Witten]] and others observed this chirality property cannot be readily derived by compactifying from eleven dimensions.<ref name="Duff 1998, p. 65"/>

In the [[first superstring revolution]] in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. Unlike supergravity theory, string theory was able to accommodate the chirality of the standard model, and it provided a theory of gravity consistent with quantum effects.<ref name="Duff 1998, p. 65"/> Another feature of string theory that many physicists were drawn to in the 1980s and 1990s was its high degree of uniqueness. In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an arbitrary [[Lagrangian (field theory)|Lagrangian]]. In string theory, the possibilities are much more constrained: by the 1990s, physicists had argued that there were only five consistent supersymmetric versions of the theory.<ref name="Duff 1998, p. 65"/>

===Relationships between string theories===

Although there were only a handful of consistent superstring theories, it remained a mystery why there was not just one consistent formulation.<ref name="Duff 1998, p. 65"/> However, as physicists began to examine string theory more closely, they realized that these theories are related in intricate and nontrivial ways.<ref>Duff 1998</ref>

In the late 1970s, Claus Montonen and [[David Olive]] had conjectured a special property of certain physical theories.<ref>Montonen and Olive 1977</ref> A sharpened version of their conjecture concerns a theory called [[N = 4 supersymmetric Yang–Mills theory|{{math|''N'' {{=}} 4}} supersymmetric Yang–Mills theory]], which describes theoretical particles formally similar to the [[quark]]s and [[gluon]]s that make up [[atomic nucleus|atomic nuclei]]. The strength with which the particles of this theory interact is measured by a number called the [[coupling constant]]. The result of Montonen and Olive, now known as [[Montonen–Olive duality]], states that {{math|''N'' {{=}} 4}} supersymmetric Yang–Mills theory with coupling constant {{math|''g''}} is equivalent to the same theory with coupling constant {{math|1/''g''}}. In other words, a system of strongly interacting particles (large coupling constant) has an equivalent description as a system of weakly interacting particles (small coupling constant) and vice versa<ref name="Duff 1998, p. 66">Duff 1998, p. 66</ref> by spin-moment.

In the 1990s, several theorists generalized Montonen–Olive duality to the S-duality relationship, which connects different string theories. [[Ashoke Sen]] studied S-duality in the context of heterotic strings in four dimensions.<ref>Sen 1994a</ref><ref>Sen 1994b</ref> [[Chris Hull]] and [[Paul Townsend]] showed that type IIB string theory with a large coupling constant is equivalent via S-duality to the same theory with small coupling constant.<ref>Hull and Townsend 1995</ref> Theorists also found that different string theories may be related by T-duality. This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent.<ref name="Duff 1998, p. 67">Duff 1998, p. 67</ref>

===Membranes and fivebranes===

String theory extends ordinary particle physics by replacing zero-dimensional point particles by one-dimensional objects called strings. In the late 1980s, it was natural for theorists to attempt to formulate other extensions in which particles are replaced by two-dimensional [[supermembranes]] or by higher-dimensional objects called branes. Such objects had been considered as early as 1962 by [[Paul Dirac]],<ref>Dirac 1962</ref> and they were reconsidered by a small but enthusiastic group of physicists in the 1980s.<ref name="Duff 1998, p. 65"/>

Supersymmetry severely restricts the possible number of dimensions of a brane. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.<ref>Bergshoeff, Sezgin, and Townsend 1987</ref> Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime. Shortly after this discovery, [[Michael Duff (physicist)|Michael Duff]], Paul Howe, Takeo Inami, and Kellogg Stelle considered a particular compactification of eleven-dimensional supergravity with one of the dimensions curled up into a circle.<ref>Duff et al. 1987</ref> In this setting, one can imagine the membrane wrapping around the circular dimension. If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. In fact, Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory.<ref name="Duff 1998, p. 66"/>

In 1990, [[Andrew Strominger]] published a similar result which suggested that strongly interacting strings in ten dimensions might have an equivalent description in terms of weakly interacting five-dimensional branes.<ref>Strominger 1990</ref> Initially, physicists were unable to prove this relationship for two important reasons. On the one hand, the Montonen–Olive duality was still unproven, and so Strominger's conjecture was even more tenuous. On the other hand, there were many technical issues related to the quantum properties of five-dimensional branes.<ref>Duff 1998, pp. 66–67</ref> The first of these problems was solved in 1993 when [[Ashoke Sen]] established that certain physical theories require the existence of objects with both [[electric charge|electric]] and [[magnetic monopole|magnetic]] charge which were predicted by the work of Montonen and Olive.<ref>Sen 1993</ref>

In spite of this progress, the relationship between strings and five-dimensional branes remained conjectural because theorists were unable to quantize the branes. Starting in 1991, a team of researchers including Michael Duff, Ramzi Khuri, Jianxin Lu, and Ruben Minasian considered a special compactification of string theory in which four of the ten dimensions curl up. If one considers a five-dimensional brane wrapped around these extra dimensions, then the brane looks just like a one-dimensional string. In this way, the conjectured relationship between strings and branes was reduced to a relationship between strings and strings, and the latter could be tested using already established theoretical techniques.<ref name="Duff 1998, p. 67"/>

===Second superstring revolution===

[[File:Limits of M-theory.svg|upright=1.6|thumb|alt=A star-shaped diagram with the various limits of M-theory labeled at its six vertices.|A schematic illustration of the relationship between M-theory, the five [[superstring theory|superstring theories]], and eleven-dimensional [[supergravity]]. The shaded region represents a family of different physical scenarios that are possible in M-theory. In certain limiting cases corresponding to the cusps, it is natural to describe the physics using one of the six theories labeled there.]]

{{main article|Second superstring revolution}}

Speaking at [[Strings (conference)|Strings]] '95 at the [[University of Southern California]] in 1995, Edward Witten of the [[Institute for Advanced Study]] made the surprising suggestion that all five superstring theories were in fact just different limiting cases of a single theory in eleven spacetime dimensions. Witten's announcement drew together all of the previous results on S- and T-duality and the appearance of two- and five-dimensional branes in string theory.<ref>Witten 1995</ref> In the months following Witten's announcement, hundreds of new papers appeared on the Internet confirming that the new theory involved membranes in an important way.<ref>Duff 1998, pp. 67–68</ref> Today this flurry of work is known as the [[second superstring revolution]].<ref>Becker, Becker, and Schwarz 2007, p. 296</ref>

One of the important developments following Witten's announcement was Witten's work in 1996 with string theorist [[Petr Hořava (theorist)|Petr Hořava]].<ref name="Hořava and Witten 1996a">Hořava and Witten 1996a</ref><ref>Hořava and Witten 1996b</ref> Witten and Hořava studied M-theory on a special spacetime geometry with two ten-dimensional boundary components. Their work shed light on the mathematical structure of M-theory and suggested possible ways of connecting M-theory to real world physics.<ref>Duff 1998, p. 68</ref>

===Origin of the term===

Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten was skeptical of the role of membranes in the theory. In a paper from 1996, Hořava and Witten wrote

{{Blockquote|As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes.<ref name="Hořava and Witten 1996a"/>|sign=|source= }}

In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that the ''M'' should stand for "magic", "mystery", or "membrane" according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known.<ref name="Duff 1996, sec. 1" /> Years later, he would state, "I thought my colleagues would understand that it really stood for membrane. Unfortunately, it got people confused."<ref>{{cite book |last=Gefter |first=Amanda |date=2014 |title=Trespassing on Einstein's Lawn: A Father, a Daughter, the Meaning of Nothing and the Beginning of Everything |publisher=Random House |isbn=978-0-345-531438}} at 345</ref>