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

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What are dimensions? ddddimensions 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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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.

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What are extra dimensions? KKKKaluza might mean that the universe contain an extra, curled up spatial dimension. AAAAlthough 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.

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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 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.

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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, 10^35 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: kbys/contents/elegant_universe.html kbys/contents/elegant_universe.html kbys/contents/elegant_universe.html

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