Variation of the Fine Structure Constant in 5d Kaluza-Klein Theory

This dissertation, "Variation of the Fine Structure Constant in 5D Kaluza-klein Theory" by Sui-chung, Ng, 吳瑞聰, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "VARIATION OF THE FINE STRUCTURE CONSTANT IN 5D KALUZA-KLEIN THEORY" Submitted by Ng Sui Chung for the degree of Master of Philosophy at The University of Hong Kong in June 2005 Theproblemofthevariabilityoffundamentalconstantsisimportantboth practically and theoretically. We surely require more and more accuracy as technologydevelopsandevenaverytinyvariationinaphysicalquantitymay cause abig difference intheexperimental outcome. Ontheotherhand, some contemporary physical theories must be modified in order to accommodate the variations of these fundamental 'constants' and that would revolutionize ourpreviousunderstanding ofthephysical world. Inthisthesis, atheoretical study on a varying fine structure constant was made. The speed of light and the Planck constant were taken as constants and therefore any variation of the fine structure constant will be owed to a varying electric charge. The theoretical framework employed was the 5D Kaluza-Klein theory. In the theory, the electric charge is proportional to the inverse of the radius of thefifth dimension. By studying a 5D cosmology, the variation of this radius and hence of the electric charge will be obtained. Previous studies related to this topic will be first reviewed. Both phe- nomenological theories and first principle theories will be included. A de- tailed review on the relation between charge and extra dimension will be given next. Following that will be the presentation of the original research. There a set of 5D cosmological equations will be derived and with certain choicesofparameters, thetraditional4DFriedmann'scosmologicalequations canbe rediscovered. Itwill also bededuced from theequations thatthe rela- tive rate of change of the fine structure constant is essentially the product of the relative energy density of the 4D cosmological constant and the Hubble constant. Using the present observed values of these constants, the rate of change of the fine structure constant will be negative and roughly equal to -12 10 per year. The 5D cosmological equations obtained will be a system of second order non-linear differential equations, of which general analytic solutions will not been obtained. For some particular cases like the radiation era, an exact solution will be found however. The evolution in this era turns out to be roughlylinearbecauseoftheverysmallnobservedcosmologicalconstant. On the other hand, for the present epoch of the universe, only an approximate solution will be inferred. It will be found that the evolution of the radius of extra dimension will include bothanexponentially increasing anddecreasing terms. And the coefficients will be given by the relative energy density of the 4D cosmological constant. By extrapolating this evolution to the next 10 billion years, it will be found that the fine structure constant will be respectively 18% and 90% less than the present value after 1 billion years and 10 billion years. DOI: 10.5353/th_b3199317 Subjects: Fine-structure constant Kaluza-Klein theories