An Experimental Proposal On Exploring Extra Dimensions And Some Researches On Brane World Scenarios

In this thesis, after a brief retrospection of the development of higher dimensionalspace-time theories, some researches on brane world theories, especially on the brane worldmodel proposed by Arkani-Hamed, Dimopoulous, and Dvali (ADD) are done.The exploration of extra dimensions in experiment has merely started, and it has notbeen found any clue of the existence of extra dimensions by now. Also, for the gravitationaltorsion pendulum experiment, which is thought to have some chance to find the extradimensions in ADD model, the result is not encouraging, and it is very hard to break throughits limit of capability, that is, it is not able to test the Newton's inverse-square law down toscale that is smaller than micron. Considering these and the importance of the concept of extradimensions in physics, in this thesis, an idea is proposed in spectroscopy to detect the possibledeviation from Newton's inverse-square law at small scale predicted by ADD, as well as tosearch for extra dimensions. Some illustrations are shown on hydrogen, muonic hydrogen,tauonic hydrogen, high-Z hydrogenic systems and muonic atoms. The relevant experimentsmight help to develop the test of Newton's inverse-square law down to nanometer scale, toexplore more-than-two extra dimensions scenarios in ADD model, and to set constraints forfundamental parameters such as the size of extra dimensions.Some discussions about brane world theories are also made in the area of the earlyuniverse. Special relativity is generalized to extra dimensions and quantized energy levels ofparticles are obtained. By considering the probability of particles' motion in extra dimensionsat high temperature in the very early universe, the idea of brane formation is proposed, that is,branes may have not existed since the beginning of the universe, but formed later. Beforeformation, particles of the universe may have filled the entire space which includes both extradimensions and branes (the ordinary three dimensional space). This scenario is at leastdifferent from the standard model of cosmology in four dimensional space-time in the veryearly universe. So the study of the evolution of the universe in higher dimensional space-timeis necessary. Meanwhile, a constraint for the time of brahe formation from the view ofcosmology is given. On using ADD model, such constraint is transferred to the constraint onthe number of extra dimensions. The result favors seven or more extra dimensions.