Scientists are currently struggling to unify the four forces of nature into one theory, the grand unified theory, GUT. This unification must go beyond current thought, and new theories are being developed in order to connect the four forces: the electromagnetic force, the weak force, the strong force, and the force of gravity. Many theoretical physicists have turned toward superstring theories and M-theory to solve the anomalies in the standard model, and they continue to struggle and develop a "theory of everything".
THE STANDARD MODEL
The standard model is designed within the Quantum Field Theory. In order to unify the four fundamental forces, theories must be consistent with quantum mechanics and relativity. Physicists Glashow, Salam, and Weinberg successfully connected the electromagnetic and weak forces into the electroweak force. Additionally, it has been seen that at high energies, the strong and electroweak froces are the same. Therefore, a relation between these two has been seen.
Despite this type of advancement, there are certain problems with the standard model. While there has been an observed connection between electromagnetism, the strong force, and the weak force, gravity1s place in the picture is not clear. When applying Quantum Field Theory to gravity, problems arise and infinities are found. Scientists have answered this question by developing string theory.
STRING THEORY
The standard model assumes particles are zero-dimensional points. String theory takes a step in another direction and assumes strings are one-dimensional objects with no thickness and radii of 1.0 x 10^ -34 inches (the Planck length). These particles look like points, but are actually strings.
There are two types of strings: open or closed. As these strings move through space-time, they make a worldsheet. Strings are also free to vibrate. Different modes of vibrations cause different particle types because modes are seen as different masses or spins. Each vibrational mode has a set of quantum numbers that is a distinct fundamental particle. Each particle, in turn, has a different string and mode. This particular closed-string mode
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Particles in nature are classified by their spin. All particles fall into one of two categories: fermions or bosons. Fermions are particles with a 1/2 integral quantum number spin. Different fermions make up (like neutrons). Bosons are particles with an integral quantum number spin. Different bosons make up the particles which dictate forces (like photons). The original string theory, Bosonic String Theory, only took into account bosons, and completely left fermions out of the picture.
EXTRA DIMENSIONS AND KALUZA-KLEIN THEORY
The idea of extra dimension besides the three spatial we see in our universe was first introduced in Kaluza-Klein theory (or compactification) in the 1920s. In a letter written to Albert Einstein in 1919, Theodr Kaluza proposed the combination of the theories of Maxwell and Einstein by adding a fifth dimension. Kaluza showed that by examining the five-dimensional general theory of relativity, and curl up one dimension, the four-dimensional theory becomes general relativity with electromagnetism.
The idea of Kaluza-Klein theory can be applied to string theory. The mathematics of string theory requires there are ten dimensions; therefore, physicists believe the other six dimensions not observed are curled up incredibly small. String theory takes the four dimensions, and at every point in our four-dimensional world, there is a tiny six-dimensional manifold. The name of this manifold is the Calabi-Yau manifold or an orbifold.
There are thousands of different kinds of Calabi-Yau manifolds. Physicists have recently found ways to connect the many Calabi-Yau manifolds through conifold transitions with type II strings (the different types of strings are covered below). However, they are not yet able to test their predictions toward unifying the different manifolds into one cohesive string theory.
TYPES OF STRINGS
There are five consistent string theories in weak coupling perturbation theory. The sixth string theory, Bosonic String Theory (mentioned above) exists in 26 dimensions, but it did not take into account fermions and did not take into account matter. All five, however, exist in ten dimensions. They theories are the following:
The various theories are related in different ways. The two relations between theories are known as T-duality and S-duality. T-duality is the relation between two theories, one compactified with radius r, and the other compactified with radius 1/r. Type IIA and Type IIB are T-Dual; E8xE8 Heterotic and SO(32) Heterotic are T-Dual. S-Duality is the relation between the strong coupling limit of one to the weak coupling limit of the other. Type I and SO(32) Heterotic are S-Dual; Type IIB is S-Dual with itself.
Physicists hope to put together the five string theories into one monster theory, M-theory. M-theory would encompass the string theories, and theories which have yet to be discovered. M-theory can be described by a theory called 11-dimensional supergravity. By compactifying the 11th dimension, we get back to the ten dimensions we knew from above. Presently, physicists are looking for this theory which will unite 11-D supergravity with the five string theories.
TOPOLOGY OF THE STRING-FILLED UNIVERSE
String theory has a profound implication on the topology of the universe. General relativity predicts the fabric of spacetime will be smooth, even if in the presence of mass and energy. However, quantum mechanics dictates uncertainty, and predicts that everything, even fundamental particles, undergo a sort of jittering or fluctuation. The two theories are qualitatively different and are not compatible without string theory.
BLACK HOLES
If you have read my page dedicated to the physics of black holes, you will recall nothing can escape a black hole once it has crossed the event horizon, and all worldlines will go toward the singularity. However, Stephen Hawking showed black holes emit radiation from their event horizons. This appears to violate the physics of black holes because nothing should be able to escape from the black hole, so why does this occur?
Quantum mechanics says a number of collisions occur between particles and antiparticles. These collisions then result in a release of energy. It is hypothesized that particles and their antiparticle counterparts come together just outside the event horizon of a black hole. Then, one of the two (either the particle or the antiparticle) before they collide enters the black hole and is stripped from their counterpart. Thus, it appears as though the black hole appears to be decaying and to have radiation.
So where does string theory come in? Hawking radiation can also be explained as open strings interacting outside the event horizon of a black hole. One string falls into the black hole, and the other appears as emitted radiation in the form of a closed string.
The theory of black hole radiation then means that the total area of the event horizon will decrease over time, and they will decay over time. If they decay, that means black holes will have both a temperature and an entropy. Physicists were not sure how to connect quantum theory with black hole entropy.
Physicists then created the idea of a string theory black hole. A string black hole is a place where spacetime is curved infinitely and where the conditions allow a consistent string theory to occur at that point. Numerous string theory black holes have been found, and using duality symmetries from above, have been connected to other string theories. By this connection, physicists are able to count the quantum microstates and derive the equation for black hole entropy: S = A/4 (where S is the black hole entropy and A is the area of the event horizon).