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.
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
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.
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.
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.
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