Why string theory?

Why did physicists create string theory? The answer is because neither Einstein's relativity theories nor quantum physics can explain quantum gravity. The problem is that when you get down to the tiny realm of quantum particles, the equations that describe gravity don't work. In other words, gravity doesn't involve both space and time as a unit like Einstein predicted. This is one of the reasons that Einstein's equations break down and involve infinity when applied to the Big Bang or a black hole singularity. Basically, it means that space and time are not linked.

String theory tries to deal with this dilemma by making one-dimensional particles into two-dimensional strings that propagate through space and interact with each other. Strings can be open or closed in a loop and can vibrate at different frequencies. One of the consequences of string theory is the proposal of higher dimensions. Einstein only proposed 4 dimensions, the fourth being time. String theory predicts at least 10 and in some theories 11. Bosonic string theory predicts 26.

Another aspect of string theory is that one of the vibrational states of a string corresponds to a graviton, the particle that carries the force of gravity. This is an attempt to get around Einstein's dilemma and create a unified theory of everything.

When we talk about string theory we have to bring in M-theory, which is the theory of branes or membranes. Branes are two-dimensional sheets to which strings are attached. Strings can be either open or closed. Closed strings are important because they could explain gravity. Closed strings are when two strings are attached at both ends, and they are associated with the graviton, the theoretical particle of gravity. The proposed reason why gravitons have not been detected is because it takes a huge amount of energy to set them free.
String theory predicts parallel universes, wormholes that extend to distant parts of our universe and also from one parallel universe to another, the fact that the universe is a hologram on the surface of space or in a black hole, time travel, and multiple big bangs created by branes colliding.

Bosonic string theory was one of the first but it was discarded because the math didn't work correctly to predict newly discovered particles.
However, there are five types of string theory that are accepted:

Type I has both open and closed strings and has a form of mathematical symmetry.

Type IIA uses closed strings with symmetrical vibrations regardless if they travel left or right along the closed string. The open strings are attached to D-branes with an odd number of dimensions. D-branes exist in 10 dimensions, and they can be finite or infinite in size. What's even crazier is that D-branes in different dimensions can interact. Open strings can attach to these D-branes.

Type IIB uses closed strings with asymmetrical vibrations depending on if they travel left or right along the closed string. The open strings are attached to D-branes with an even number of dimensions.

Type HO is a Heterotic (distinct vibrations depending on vibrational direction) string theory that only uses closed strings whose right-moving vibrations resemble type II strings and whose left-moving vibrations resemble bosonic strings.

Type HE is a Heterotic string theory is similar to type HO with a different symmetry group.
One of the crazy things about string theory is the idea of extra dimensions. Where are these extra dimensions? The answer is that they are in Calabi-Yau manifolds. This is a very strange mathematical approach to understanding extra dimensions in a branch of string theory known as super string theory that incorporates fermions and supersymmetry. Calabi-Yau space involves tiny dimensional space that's curled and folded tightly to a point that they are impossible to see. The more energy that a particle has the more tightly it's folded. It turns out that Calabi-Yau manifold math predicts all sorts of particles that have not been detected yet.

M-theory introduces branes or membranes, the two dimensional sheets to which strings are attached. M-theory takes the 10 dimensions of string theory and adds one more, time. M-theory also takes the five different string theories concerning dualities and makes them equivalent. Duality means that you can look at the same phenomenon with two different theories. This is the cornerstone of M-theory. However, there are two kinds of duality: T-duality and S-duality. T-duality stands for topological or toroidal. Basically, it deals with how you fold space. Let's say you're working in a dimension that's compacted down to a circle of radius R. The space becomes a cylinder. If you wrap your closed sting around the cylinder, both the dimension and the string have radius R. The number of times the closed string is wound around the cylinder is the winding number and you also have the momentum number of the string. If you also wind a closed string around a cylinder with radius 1/R then the two strings have the same momentum number. Thus, two different dimension spaces can be the same. T-duality relates Type IIA and Type IIB for example in this fashion.

S-duality is also called strong-weak duality. This involves a coupling constant, which indicates how probable the string will break apart and join other strings. Sounds like a divorce to me! Basically, a strong coupling constant in one theory relates to a weak-coupling constant in another theory. S-duality relates Type 1 and type HO string theories and type IIB and S-duality to itself.

Getting back to branes, p-branes are needed to make a particle. When you wrap a p-brane around a tiny space you get a particle. If you wrap it around a very tiny space you get a massless particle. The fact that a p-brane can be infinite in some directions and limited in other directions is needed to describe a black hole. This idea was introduced to get around the idea that strings cannot describe all particles.

That's enough for now. My head hurts!

Thanks for reading.