Extra Dimensions &Extra Dimensions &The String TheoryThe String Theory

By: Justin Calame-MarsBy: Justin Calame-Mars

Alex KornfeldAlex Kornfeld

Grand UnificationGrand Unification

General Relativity explains relationships between General Relativity explains relationships between matter (gravity)matter (gravity)

Quantum Theory explains relationships between Quantum Theory explains relationships between forces (electro-magnetism) forces (electro-magnetism)

Neither Theory works if the other is also applied Neither Theory works if the other is also applied to the systemto the system

This sparked the search for the Grand Unification. This sparked the search for the Grand Unification.

How it Comes TogetherHow it Comes Together

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Extra Dimensions?Extra Dimensions?

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

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Kaluza-Klein SolutionKaluza-Klein Solution

Kaluza created a curled up Kaluza created a curled up dimension to attempt to dimension to attempt to unify the theories. unify the theories.

Later on, Klein posited Later on, Klein posited that those dimensions that those dimensions existed at every point in existed at every point in space. space.

Due to extreme faults, the Due to extreme faults, the idea was abandoned until idea was abandoned until the string theory was the string theory was proposed. proposed.

What is the String Theory?What is the String Theory?

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

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Why Strings?Why Strings?

Quantum theory’s building blocks are Quantum theory’s building blocks are zero-dimensional point charges. zero-dimensional point charges.

By replacing them with one-dimensional By replacing them with one-dimensional strings, it can become the quantum theory strings, it can become the quantum theory of gravity. of gravity.

This effectively unifies the four natural This effectively unifies the four natural forces by describing them with the same forces by describing them with the same set of equations.set of equations.

How it WorksHow it Works

The strings are of size The strings are of size 1010-35-35 m. m.

By vibrating at By vibrating at different frequencies, different frequencies, they become different they become different particles. particles.

The strings themselves The strings themselves are lines of energy. are lines of energy.

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Calabi-Yau ManifoldCalabi-Yau Manifold

A manifold is an abstract A manifold is an abstract mathematical space for mathematical space for which every point has its which every point has its own neighborhood where it own neighborhood where it can move. can move.

A Calabi-Yau manifold is A Calabi-Yau manifold is one in which every one in which every neighborhood has a complex neighborhood has a complex neighborhood of neighborhood of nn-space. -space.

The 6D manifolds allow for The 6D manifolds allow for the extra dimensional the extra dimensional vibration of superstringsvibration of superstrings

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SupersymmetrySupersymmetry

In order to include every kind of particle in the In order to include every kind of particle in the string theory, there must be a correlation between string theory, there must be a correlation between all kinds. all kinds.

Supersymmetry relates the particles that transmit Supersymmetry relates the particles that transmit forces to the particles that transmit matter. forces to the particles that transmit matter.

When one electron exerts electromagnetic force on When one electron exerts electromagnetic force on another, it does so by emitting a photon which is another, it does so by emitting a photon which is later absorbed by the other electron.later absorbed by the other electron.

SupersymmetrySupersymmetry

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

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Why can’t we see other Why can’t we see other dimensions?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.

The Future of String TheoryThe Future of String Theory

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

SourcesSources

http://en.wikipedia.org/wiki/String_theorhttp://en.wikipedia.org/wiki/String_theoryy

http://theory.tifr.res.in/strings/dmw.htmlhttp://theory.tifr.res.in/strings/dmw.html http://tena4.vub.ac.be/beyondstringtheohttp://tena4.vub.ac.be/beyondstringtheo

ry/index2.htmlry/index2.html http://www.superstringtheory.com/index.http://www.superstringtheory.com/index.

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