Extra Dimensions & The String Theory

1. Extra Dimensions &The String Theory By: Justin Calame-Mars Alex Kornfeld

2. Grand Unification • General Relativity explains relationships between matter (gravity) • Quantum Theory explains relationships between forces (electro-magnetism) • Neither Theory works if the other is also applied to the system • This sparked the search for the Grand Unification.

3. How it Comes Together

4. Extra Dimensions? • Before the string theory, Theodor Kaluza and Oskar Klein attempted to unify electromagnetism and gravity, finding that the mathematics they used proved to match reality more closely if another dimension was added.

5. Kaluza-Klein Solution • Kaluza created a curled up dimension to attempt to unify the theories. • Later on, Klein posited that those dimensions existed at every point in space. • Due to extreme faults, the idea was abandoned until the string theory was proposed.

6. What is the String Theory? • The String Theory is the solution, positing that particles we see are really strings oscillating at a certain frequency. These strings are connected to some n-dimensional compact space.

7. Why Strings? • Quantum theory’s building blocks are zero-dimensional point charges. • By replacing them with one-dimensional strings, it can become the quantum theory of gravity. • This effectively unifies the four natural forces by describing them with the same set of equations.

8. How it Works • The strings are of size 10-35 m. • By vibrating at different frequencies, they become different particles. • The strings themselves are lines of energy.

9. Calabi-Yau Manifold • A manifold is an abstract mathematical space for which every point has its own neighborhood where it can move. • A Calabi-Yau manifold is one in which every neighborhood has a complex neighborhood of n-space. • The 6D manifolds allow for the extra dimensional vibration of superstrings

10. Supersymmetry • In order to include every kind of particle in the string theory, there must be a correlation between all kinds. • Supersymmetry relates the particles that transmit forces to the particles that transmit matter. • When one electron exerts electromagnetic force on another, it does so by emitting a photon which is later absorbed by the other electron.

11. Supersymmetry • Since both the photon and the electron are simply the same string vibrating in different modes, the emission of a photon from an electron appears as splitting of a string into two strings. Conversely, the absorption of a photon by an electron appears as joining of two strings into one.

12. Why can’t we see other dimensions? • The extra dimensions posited by Kaluza and Klein are so small that they are imperceptible to even our finest equipment. • Conversely, if you consider a 3D space like our own, a photon would only live on our 3D space so all the other six dimensions would be literally dark. No photons, or light, would come from these other dimensions, and no light would leak into these dimensions, since the photons can only exist on our 3D space.

13. The Future of String Theory • We are still far from understanding the full import of the theory. At present, we do not even know the full equations of the theory. Ultimately, the fate of the theory will be determined by its experimentally testable predictions. If these ideas turn out to be true and string theory is eventually verified in experiments, we will have found the Theory of Everything.

14. Sources • http://en.wikipedia.org/wiki/String_theory • http://theory.tifr.res.in/strings/dmw.html • http://tena4.vub.ac.be/beyondstringtheory/index2.html • http://www.superstringtheory.com/index.html