What is membrane theory?plz help me?

Question

plz give me as detailed as possible.

Answer 1

In physics, M-theory (sometimes also called U-theory) is put forward as the master theory that unifies the five superstring theories. Drawing on the work from a number of string theorists (including Chris Hull, Paul Townsend, Ashoke Sen, Michael Duff, and John Schwarz) Edward Witten of the Institute for Advanced Study proposed the existence of this physical model at a conference at USC in 1995, explaining a number of previously observed dualities and sparking a flurry of new research in string theory, called the second superstring revolution.

In the early 1990s, it was shown that the various superstring theories were related by dualities, which allows physicists to relate the description of an object in one string theory to the description of a different object in another theory. These relationships imply that each of the string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".

M-theory is not complete as of yet [Greene-TFOTC-chapter 13], 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. Witten has suggested that a general formulation of M-theory will probably require the development of new mathematical language.

Contents
* 1 Basics
* 2 Naming conventions, or What does M stand for?
* 3 M-theory in various backgrounds
* 4 M-Theory and Membranes
o 4.1 Matrix Theory
* 5 Big Bang
* 6 Spiritual Implications of M-Theory
* 7 The Anti-deSitter/Conformal Field Theory Correspondence
* 8 Further reading
* 9 External links
* 10 Papers

Basics

It was believed before 1995 that there were exactly five consistent superstring theories, which are called, respectively, the Type I string theory, the Type IIA string theory, the Type IIB string theory, the heterotic SO(32) (the HO string) theory, and the heterotic E8×E8 (the HE string) theory.

As the names suggest, some of these string theories are 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. The Type IIA string theory and the Type IIB string theory are connected by T-duality; this means, essentially, 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.

This is a profound result. First, it is an intrinsically quantum mechanical result; the identification is not true classically. Second, because we can 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. This means that we can actually identify the IIA string theory with the IIB string theory: any object which can be described with the IIA theory has an equivalent, although seemingly different, description in terms of the IIB theory. This means that the IIA theory and the IIB theory are really aspects of the same underlying theory.

There are other dualities between the other string theories. 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. There are then 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. String theorists have found strong evidence that the two theories are really the same, even away from the extremely strong and extremely weak limits, but they do not yet have a proof strong enough to satisfy mathematicians. However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.

At this point, there are only two string theories: the heterotic string theory (which is also the type I string theory) and the type II theory. There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.

This last step, however, is the most difficult and most mysterious. It is best explained first in a certain limit. 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). Consequently, the quantum theory describing the low energy limit is a theory which describes the dynamics of particles moving in spacetime, rather than strings. Such theories are called quantum field theories. 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.

The possible supergravity theories were classified by Werner Nahm in the 1970s. In 10 dimensions, there are only two supergravity theories, which are denoted Type IIA and Type IIB. This 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 1995, 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. (And the Type IIB supergravity theory can be obtained by using T-duality.) However, eleven-dimensional supergravity is not consistent on its own — it does not make sense at extremely high energy, and likely requires some form of completion. 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.

Taking seriously the notion that all of the different string theories should be different limits and/or different presentations of the same underlying theory, the concept of string theory must be expanded. But little is known about this underlying theory. The bonus is that all of the different string theories may now be thought of as different limits of a single underlying theory.
Edward Witten, founder of M-Theory
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Edward Witten, founder of M-Theory
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Naming conventions, or What does M stand for?

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. According to Witten himself, "'M' stands for 'magic,' 'mystery' or 'membrane,' depending on your taste." Also suggested, has been 'matrix' (see below) and 'mother of all theories'. 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 [citation needed]. The various speculations as to what "M" in "M-theory" stand for are explored in the PBS documentary based on Brian Greene's book "The Elegant Universe."

* The name M-theory is slightly ambiguous. It can be used to refer to both the particular eleven-dimensional theory which Witten first proposed, or it can be used to refer to a kind of theory which looks in various limits like the various string theories. Ashoke Sen has suggested that more general theory could go by the name U-theory, which might stand for Ur, Uber, Ultimate, Underlying, or perhaps Unified. (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 in various backgrounds
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Although no complete description of M-theory (in the more general sense) exists, it can be formulated in certain limits.


M-Theory and Membranes

Prior to M-theory, strings were thought to be the single fundamental constituent of the universe, according to string theory. When M-theory unified the five superstring theories, another fundamental ingredient was added to the makeup of the universe - membranes. Like the tenth spacial dimension, the approximate equations in the original five superstring models proved too weak to reveal membranes. A membrane, or brane, is a multidimensional object, usually called a p-brane, with p referring to its spacial dimensional makeup. The p-branes range from any number of spacial dimensions from zero to nine.

The inclusion of p-branes does not render previous work in string theory wrong on account of not taking note of these p-branes. P-branes are much more massive ("heavier") than strings, and when all higher dimensional p-branes are much more massive than strings, they can be ignored, as researchers had done unknowingly in the 1970s.

Shortly after Witten's breakthrough in 1995, Joseph Polchinski of the university of California at Santa Barbara discovered a fairly obscure feature of string theory. He found that in certain situations the endpoints of strings (strings with "loose ends") would not be able to move with complete freedom as they were attached, or stuck within certain regions of space. Polchinski then reasoned that if the endpoints of open strings are restricted to move within some p-dimensional region of space, then that region of space must be occupied by a p-brane. These type of "sticky" branes are called Dirichlet-p-branes, or D-p-branes. His calculations showed that the newly discovered D-p-branes had exactly the right properties to be the objects that exert a tight grip on the open string endpoints, thus holding down these strings within the p-dimensional region of space they fill.

Not all strings are confined to 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. Researchers speculate that this is the reason why investigation through the weak force, the strong force, and the electromagnetic force have not hinted at the possibility of extra dimensions. These force carrier particles are strings with endpoints that confine them to their p-branes. Further testing is needed in order to show that extra spacial dimensions indeed exist through experimentation with gravity.

Matrix Theory

The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Supergravity. Though this formulation provided a key link to the low-energy limits of string theories, it was recognized that a full high-energy formulation (or "UV-completion") of M-theory was needed. For an analogy, the Supergravity description is like treating water as a continuous, incompressible fluid. This is great for describing long-distance effects such as waves and currents, but inadequate to understand short-distance/high-energy phenomena such as evaporation, for which a description of the underlying molecules is needed. What, then, are the underlying degrees of freedom of M-theory?

Banks, Fischler, Shenker and Susskind (BFSS) conjectured that Matrix theory could provide the answer. They demonstrated that a theory of 9 very large matrices, evolving in time, could reproduce the Supergravity description at low energy, but take over for it as it breaks down at high energy. While the Supergravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, what is known as "non-commutative geometry" takes over, somewhat similar to the way the continuum of water breaks down at short distances in favor of the graininess of molecules.
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Big Bang

Unlike more conventional views of creation in modern physics, that are Ex nihilo, the M-Theory vision, although not yet complete, is of the whole observable universe being one of many super expanded 4 dimensional branes of an 11 dimensional existence. While branes of alternative universes exist "near us" their formulation of physical laws may differ from our own, as their number of dimensions. It is currently believed that a collision of "universe branes" somehow compacted enough energy to form what established physicists called the Big Bang.
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Spiritual Implications of M-Theory

Since a very basic underlying assumption of M-theory is the co-existence of many unconceivable dimensions and parallel universes, some schools of spirituality consider it to be a scientific "proof" to their own metaphysical claims about God, the heavens and so on. M-theory for itself, however has made no such claims.

Answer 2

I purely have one cat yet she craves interest. we don't enable her out anymore yet she'll claw on the door and meow for hours. And in the journey that your on the pc and not paying interest to her she'll leap on the table step all over the keyboard and claw at your hand each and every time you progression the mouse around.

Answer 3

M-theory, the theory formerly known as Strings
The Standard Model
In the standard model of particle physics, particles are considered to be points moving through space, tracing out a line called the World Line. To take into account the different interactions observed in Nature one has to provide particles with more degrees of freedom than only their position and velocity, such as mass, electric charge, color (which is the "charge" associated with the strong interaction) or spin.
The standard model was designed within a framework known as Quantum Field Theory (QFT), which gives us the tools to build theories consistent both with quantum mechanics and the special theory of relativity. With these tools, theories were built which describe with great success three of the four known interactions in Nature: Electromagnetism, and the Strong and Weak nuclear forces. Furthermore, a very successful unification between Electromagnetism and the Weak force was achieved (Electroweak Theory), and promising ideas put forward to try to include the Strong force. But unfortunately the fourth interaction, gravity, beautifully described by Einstein's General Relativity (GR), does not seem to fit into this scheme. Whenever one tries to apply the rules of QFT to GR one gets results which make no sense. For instance, the force between two gravitons (the particles that mediate gravitational interactions), becomes infinite and we do not know how to get rid of these infinities to get physically sensible results.


String Theory
In String Theory, the myriad of particle types is replaced by a single fundamental building block, a `string'. These strings can be closed, like loops, or open, like a hair. As the string moves through time it traces out a tube or a sheet, according to whether it is closed or open. Furthermore, the string is free to vibrate, and different vibrational modes of the string represent the different particle types, since different modes are seen as different masses or spins.
One mode of vibration, or `note', makes the string appear as an electron, another as a photon. There is even a mode describing the graviton, the particle carrying the force of gravity, which is an important reason why String Theory has received so much attention. The point is that we can make sense of the interaction of two gravitons in String theory in a way we could not in QFT. There are no infinities! And gravity is not something we put in by hand. It has to be there in a theory of strings. So, the first great achievement of String Theory was to give a consistent theory of quantum gravity, which resembles GR at macroscopic distances. Moreover String Theory also possesses the necessary degrees of freedom to describe the other interactions! At this point a great hope was created that String Theory would be able to unify all the known forces and particles together into a single `Theory of Everything'.


From Strings to Superstrings
The particles known in nature are classified according to their spin into bosons (integer spin) or fermions (odd half integer spin). The former are the ones that carry forces, for example, the photon, which carries electromagnetic force, the gluon, which carries the strong nuclear force, and the graviton, which carries gravitational force. The latter make up the matter we are made of, like the electron or the quark. The original String Theory only described particles that were bosons, hence Bosonic String Theory. It did not describe Fermions. So quarks and electrons, for instance, were not included in Bosonic String Theory.
By introducing Supersymmetry to Bosonic String Theory, we can obtain a new theory that describes both the forces and the matter which make up the Universe. This is the theory of superstrings. There are three different superstring theories which make sense, i.e. display no mathematical inconsistencies. In two of them the fundamental object is a closed string, while in the third, open strings are the building blocks. Furthermore, mixing the best features of the bosonic string and the superstring, we can create two other consistent theories of strings, Heterotic String Theories.

However, this abundance of theories of strings was a puzzle: If we are searching for the theory of everything, to have five of them is an embarrassment of riches! Fortunately, M-theory came to save us.


Extra dimensions...
One of the most remarkable predictions of String Theory is that space-time has ten dimensions! At first sight, this may be seen as a reason to dismiss the theory altogether, as we obviously have only three dimensions of space and one of time. However, if we assume that six of these dimensions are curled up very tightly, then we may never be aware of their existence. Furthermore, having these so-called compact dimensions is very beneficial if String Theory is to describe a Theory of Everything. The idea is that degrees of freedom like the electric charge of an electron will then arise simply as motion in the extra compact directions! The principle that compact dimensions may lead to unifying theories is not new, but dates from the 1920's, since the theory of Kaluza and Klein. In a sense, String Theory is the ultimate Kaluza-Klein theory.
For simplicity, it is usually assumed that the extra dimensions are wrapped up on six circles. For realistic results they are treated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.


M-theory
Apart from the fact that instead of one there are five different, healthy theories of strings (three superstrings and two heterotic strings) there was another difficulty in studying these theories: we did not have tools to explore the theory over all possible values of the parameters in the theory. Each theory was like a large planet of which we only knew a small island somewhere on the planet. But over the last four years, techniques were developed to explore the theories more thoroughly, in other words, to travel around the seas in each of those planets and find new islands. And only then it was realized that those five string theories are actually islands on the same planet, not different ones! Thus there is an underlying theory of which all string theories are only different aspects. This was called M-theory. The M might stand for Mother of all theories or Mystery, because the planet we call M-theory is still largely unexplored.


There is still a third possibility for the M in M-theory. One of the islands that was found on the M-theory planet corresponds to a theory that lives not in 10 but in 11 dimensions. This seems to be telling us that M-theory should be viewed as an 11 dimensional theory that looks 10 dimensional at some points in its space of parameters. Such a theory could have as a fundamental object a Membrane, as opposed to a string. Like a drinking straw seen at a distance, the membranes would look like strings when we curl the 11th dimension into a small circle.


Black Holes in M-theory
Black Holes have been studied for many years as configurations of spacetime in General Relativity, corresponding to very strong gravitational fields. But since we cannot build a consistent quantum theory from GR, several puzzles were raised concerning the microscopic physics of black holes. One of the most intriguing was related to the entropy of Black Holes. In thermodynamics, entropy is the quantity that measures the number of states of a system that look the same. A very untidy room has a large entropy, since one can move something on the floor from one side of the room to the other and no one will notice because of the mess - they are equivalent states. In a very tidy room, if you change anything it will be noticeable, since everything has its own place. So we associate entropy to disorder. Black Holes have a huge disorder. However, no one knew what the states associated to the entropy of the black hole were. The last four years brought great excitement in this area. Similar techniques to the ones used to find the islands of M-theory, allowed us to explain exactly what states correspond to the disorder of some black holes, and to explain using fundamental theory the thermodynamic properties that had been deduced previously using less direct arguments.
Many other problems are still open, but the application of string theory to the study of Black Holes promises to be one of the most interesting topics for the next few years.

Answer 4

Sorry, I don't know..