Extra Dimensions

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Extra Dimensions

• by Yip, Lok Hang (Vincent)Chan, Kaitsun (John)

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What are dimensions?

• dimensions are the parameters required to
  describe the position and relevant
  characteristics of any object within a conceptual
  space.

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What is the fourth dimension?

• Einstein's General Theory of Relativity confronts
  our notions of dimension by describing the
  universe in four dimensions three familiar
  spatial dimensions, plus the dimension Time.
• This makes sense if one thinks of an event
  happening at not only a certain location in the
  universe, but also at a specific time in history.
  This concept led to the term space-time to
  describe the universe

                                                
                Two-dimensional analogy of
space-time distortion.
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KaluzaKlein theory

• As elegant as Einstein's theory was in explaining
  the gravitational force and the large-scale
  geometric structure of the universe, it could not
  fully explain any forces, gravitational or
  otherwise, at very small scales.
• The Kaluza-Klein Theory is a model that seeks to
  unify the two fundamental forces of gravitation
  and electromagnetism.
• This theory was first published in 1921 and was
  discovered by the mathematician Theodor Kaluza
  who extended general relativity to a
  five-dimensional space-time.

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What are extra dimensions?

• Kaluza might mean that the universe contain an
  extra, curled up spatial dimension.
• Although it is hard to visualize fourth dimension
  or higher, we can make analogies to help us
  understand this concept.
• 
  On a sphere, a circle's
  circumference is less
• 
  than p times the length of a
  diameter.  A two-
• 
  dimensional surveyor could
  thus detect the
• 
  curvature of his world even
  if he couldn't see the
• 
  third dimension.

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2 dimensions 2 curl up dimensions 4
dimensions
                                                                                                                                                                                                                   
6-dimensional Calabi-Yau space
2 normal dimensions with 6 extra dimensions
curled up in Calabi-Yau spaces
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Why are extra dimensions important?

• The whole point in hypothesizing the existence of
  extra dimensions is to unify the fundamental
  physical forces -gravity, electromagnetism, and
  the strong and weak nuclear forces- under one
  single theory.
• Kaluza's and Klein's 5-dimensional version
  general relativity that contains both
  electromagnetism and 4-dimensional general
  relativity, however, It didnt fit the data,
  because it didnt incorporate enough dimensions.
• One potentially successful theory is the
  superstring theory which contains at least 10
  dimensions.

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Basics of superstring theory

• The basic of this theory is that all matters are
  not particles, but tiny, one-dimensional loops of
  vibrating string.
• These loops are as small as the Plank length,
  1035 m, and as they vibrate, their resonant
  frequencies determine the properties, such as
  mass or charge, of the particles they constitute.
  

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Bibliography

• http//people.cs.uchicago.edu/
• http//preposterousuniverse.blogspot.com/
• http//www.asahi-net.or.jp/ny3k-kbys/contents/ele
  gant_universe.html
• http//www.osti.gov/

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