1. Extra Dimensions by Yip, Lok Hang (Vincent)&Chan, Kaitsun (John)

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

3. 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.

4. Kaluza–Klein 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.

5. 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 π 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.

6. 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

7. 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 didn’t fit the data, because it didn’t incorporate enough dimensions. • One potentially successful theory is the superstring theory which contains at least 10+ dimensions.

8. 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, 10^35 m, and as they vibrate, their resonant frequencies determine the properties, such as mass or charge, of the particles they constitute.

9. Bibliography: • http://people.cs.uchicago.edu/ • http://preposterousuniverse.blogspot.com/ • http://www.asahi-net.or.jp/~ny3k-kbys/contents/elegant_universe.html • http://www.osti.gov/

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