Tell me in brief about the M-theory.?

Answer 1

M-theory is a cutting-edge theory of physics that deals with the extension of superstring theory. It is somewhat contentious in the physics community, in the absence of experimental backup. If ever experimentally verified, M-theory and string theory would represent remarkable advances in science.

In 1995, Edward Witten initiated what has been called the Second Superstring Revolution by introducing M-theory to the world. This theory combines the 5 different string theories (along with a previously abandoned attempt to unify General Relativity and Quantum Mechanics called eleven-dimensional Supergravity) into one theory. This is accomplished by knitting together a web of relationships between each of the theories called dualities (specifically, S-duality, T-duality, and U-duality). Each of these dualities provides a way of converting one of the string theories into another.

T-duality is probably the most easily explained of the dualities. It has to do with the size, denoted by R, of the curled up dimensions of the string theories. It was discovered that if you take a Type IIA string theory that has a size R and change the radius to 1/R then you will end up getting what is equivalent to a Type IIB theory of size R. This duality, along with the others, creates connections between all 5 (or 6, if you count supergravity) theories.

Factually, these dualities' existence had been known before Witten came up with the idea of M-theory. What Witten did was to predict that the fact that all of these different theories were connected was as a result of there being some underlying theory to which they were all approximations. Additionally, it was found that the equations that required string theory to exist in 10 dimensions were also approximations. The proposed (and somewhat nebulous) M-theory would instead be a theory that took place in 11 dimensions, although the details have not been pinned down.

M-Theory is a variation of String Theory, taking into account all of the 5 String Theories and showing they are basically the same (in a general sense). M-Theory is the most current version of SuperString Theory that uses 11 dimensions, Superstring Theory uses between 8 and 22.

According to its creator, Ed Witten, as quoted in the PBS documentary based on Brian Greene's book "The Elegant Universe", the "M" in M-theory "stands for magic, mystery, or matrix, according to taste." He also added, "Some cynics have occasionally suggested that M also stands for 'murky,' because our level of understanding of the theory is in fact so primitive." Then, jokingly, he said, "Maybe I shouldn't have told you that!"

Skeptics of M-theory have joked that the "M" means "Moronic" or "Moron!"

Answer 2

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.