M Theory
Because the dimensionality exceeds the dimensionality of five superstring theories in 10 dimensions, it was originally believed that the 11-dimensional theory is more fundamental and unifies all string theories (and supersedes them). However, in a more modern understanding, it is another, sixth possible description of physics of the full theory that is still called "string theory." Though a full description of the theory is not yet known, the low-entropy dynamics are known to be supergravity interacting with 2- and 5-dimensional membranes.
This theory is the unique supersymmetric theory in eleven dimensions, with its low-entropy matter content and interactions fully determined, and can be obtained as the strong coupling limit of type IIA string theory because a new dimension of space emerges as the coupling constant increases.
Drawing on the work of a number of string theorists (including Ashoke Sen, Chris Hull, Paul Townsend, Michael Duff and John Schwarz), Edward Witten of the Institute for Advanced Study suggested its existence at a conference at USC in 1995, and used M-theory to explain a number of previously observed dualities, sparking a flurry of new research in string theory called the second superstring revolution.
According to Witten and others, the M in M-theory could stand for master, mathematical, mother, mystery, membrane, magic, or matrix.
Witten reluctantly admits the M in M-theory can also stand for murky because the level of understanding of the theory is so primitive. However, originally the letter was taken from membrane, but since Witten was more skeptical to membranes than his colleagues, he just kept the "M".
Later, he let the meaning be a matter of taste for the user of the word "M-theory".
In the early 1990s, it was shown that the various superstring theories were related by dualities, which allow physicists to relate the description of an object in one super string theory to the description of a different object in another super string theory. These relationships imply that each of the super string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".
M-theory is not yet complete; however it can be applied in many situations (usually by exploiting string theoretic dualities).
The theory of electromagnetism was also in such a state in the mid-19th century; there were separate theories for electricity and magnetism and, although they were known to be related, the exact relationship was not clear until James Clerk Maxwell published his equations, in his 1864 paper A Dynamical Theory of the Electromagnetic Field. Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language.
However, some scientists have questioned the tangible successes of M-theory given its current incompleteness, and limited predictive power, even after so many years of intense research.
In late 2007, Bagger, Lambert and Gustavsson set off renewed interest in M-theory with the discovery of a candidate Lagrangian description of coincident M2-branes, based on a non-associative generalization of Lie Algebra, Nambu 3-algebra or Filippov 3-algebra. Practitioners hope the Bagger-Lambert-Gustavsson action (BLG action) will provide the long-sought microscopic description of M-theory.
History and Development
Prior to May 1995
Prior to 1995 there were five (known) consistent superstring theories (here on referred to as string theories), which were given the names Type I string theory, Type IIA string theory, Type IIB string theory, heterotic SO(32) (the HO string) theory, and heterotic E8×E8 (the HE string) theory.
The five theories all share essential features that relate them to the name of string theory. Each theory is fundamentally comprised of vibrating, one dimensional strings at approximately the length of the Planck length.
Calculations have also shown that each theory requires more than the normal four spacetime dimensions (although all extra dimensions are in fact spatial.) However, when the theories are analyzed in detail, significant differences appear.
Type I string theory and others
The Type I string theory has vibrating strings like the rest of the string theories. These strings vibrate both in closed loops, so that the strings have no ends, and as open strings with two loose ends.
The open loose strings are what separates the Type I string theory from the other four string theories. This was a feature that the other string theories did not contain (The Type IIA and Type IIB string theories also contain open strings, however these strings are bound to D-branes, that is to say, they are tight).
String vibrational patterns
The calculations of the String Vibrational Patterns show that the list of string vibrational patterns and the way each pattern interacts and influences others vary from one theory to another.
These and other differences hindered the development of the string theory as being the theory that united quantum mechanics and general relativity successfully. Thus each of the five string theories becomes a special case of M-theory.
As the names suggest, some of these string theories were thought to be related to each other.
In the early 1990s, string theorists discovered that some relations were so strong that they could be thought of as an identification.
Type IIA and Type IIB
The Type IIA string theory and the Type IIB string theory were known to be connected by T-duality; this essentially meant that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R, where distances are measured in units of the Planck length.
This was a profound result. Second, because it is possible to build up any space by gluing circles together in various ways, it would seem that any space described by the IIA string theory can also be seen as a different space described by the IIB theory.
The heterotic SO(32) and the heterotic E8×E8 theories are also related by T-duality; the heterotic SO(32) description of a circle of radius R is exactly the same as the heterotic E8×E8 description of a circle of radius 1/R. This implies that there are really only three superstring theories, which might be called (for discussion) the Type I theory, the Type II theory, and the heterotic theory.
There are still more dualities, however.
The Type I string theory is related to the heterotic SO(32) theory by S-duality; this means that the Type I description of weakly interacting particles can also be seen as the heterotic SO(32) description of very strongly interacting particles. This identification is somewhat more subtle, in that it identifies only extreme limits of the respective theories.
However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.
Only two string theories
Given the above commonalities there appear to be only two string theories: the heterotic string theory (which is also the type I string theory) and the type II theory. In order to describe our world, strings must be extremely tiny objects.
So when one studies string theory at low energies, it becomes difficult to see that strings are extended objects — they become effectively zero-dimensional (pointlike). However, since string theory also describes gravitational interactions, one expects the low-energy theory to describe particles moving in gravitational backgrounds.
Finally, since superstring string theories are supersymmetric, one expects to see supersymmetry appearing in the low-energy approximation. These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory.
Supergravity theories
The possible supergravity theories were classified by Werner Nahm in the 1970s.
This similar denomination is not a coincidence; the Type IIA string theory has the Type IIA supergravity theory as its low-energy limit and the Type IIB string theory gives rise to Type IIB supergravity. The heterotic SO(32) and heterotic E8×E8 string theories also reduce to Type IIA and Type IIB supergravity in the low-energy limit.
This suggests that there may indeed be a relation between the heterotic/Type I theories and the Type II theories.
In 1994, Edward Witten outlined the following relationship: The Type IIA supergravity (corresponding to the heterotic SO(32) and Type IIA string theories) can be obtained by dimensional reduction from the single unique eleven-dimensional supergravity theory. This means that if one studied supergravity on an eleven-dimensional spacetime that looks like the product of a ten-dimensional spacetime with another very small one-dimensional manifold, one gets the Type IIA supergravity theory.
It seems plausible, then, that there is some quantum theory — which Witten dubbed M-theory — in eleven-dimensions which gives rise at low energies to eleven-dimensional supergravity, and is related to ten-dimensional string theory by dimensional reduction. Dimensional reduction to a circle yields the Type IIA string theory, and dimensional reduction to a line segment yields the heterotic SO(32) string theory.
Same underlying theory
M-theory would implement the notion that all of the different string theories are different special cases and/or different presentations of the same underlying theory (M-theory).
It may be some time before the full implications of these theories are known.
The promise of M-theory is that all of the different string theories would become different limits of a single underlying theory.
Nomenclature
There are two issues to be dealt with here:
When Witten named M-theory, he did not specify what the "M" stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe. Other suggestions by people such as Michio Kaku, Michael Duff and Neil Turok in that documentary are "mother" (as in "mother of all theories"), and "master" theory.
Cynics have noted that the M might be an upside down "W", standing for Witten.
Others have suggested that for now, the "M" in M-theory should stand for Missing or Murky. The various speculations as to what "M" in "M-theory" stands for are explored in the PBS documentary based on Brian Greene's book The Elegant Universe.
The name M-theory is slightly ambiguous.
(It might also stand for U-duality, which is both a reference to Sen's own work and a kind of particle physics pun.)
M-theory in the following descriptions refers to the more general theory, and will be specified when used in its more limited sense.
M-theory and membranes
In the standard string theories, strings are assumed to be the single fundamental constituent of the universe. Like the tenth spatial dimension, the approximate equations in the original five superstring models proved too weak to reveal membranes.
P-branes
A membrane, or brane, is a multidimensional object, usually called a P-brane, with P referring to the number of dimensions in which it exists.
The inclusion of p-branes does not render previous work in string theory wrong on account of not taking note of these P-branes. Strings with closed loops, like the graviton, are completely free to move from membrane to membrane.
Of the four force carrier particles, the graviton is unique in this way. For example once you get to 3 dimensional surfaces you have to deal with solid objects with knot shaped holes, and then you need the whole of knot theory just to classify them.
Orientable 2-branes are tori with multiple holes cut out of them.
Matrix theory
The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Supergravity.