Development of special and general theories of relativity and their applications

Abstract

This project gives the thorough development of the two theories of relativity namely special and general theories. Since the birth of general relativity (GR) came after special relativity (SR), soon after comprehensive introduction which enlighten on properties of light and failure of experiments to prove existence of ether which was a hypothesized medium for carrying light, chapter two deals with special relativity. In chapter two, inertial frames of reference as environment for SR to work properly are explained. Also included in this chapter are Galilean and Lorentz transformation equations, showing how the coordinates of space and time of two different inertial reference frames are related. Whereas the Galilean transformation denies the idea of time and distance being defmed differently in different inertial frames, the Lorentz transformation proves otherwise. The Lorentz transformation plays an essential part in the consequences of SR which are listed in this project with elaborative discussion on them. Chapter two closes by showing how SR leads us to the attaining of very vital relation, viz. mass-energy relation and, gives experimental proofs of the time dilation and relativistic velocity addition rule. The chapter three of this project engaged fully discourses the introduction of gravitation to the relativity theory where the heuristic derivation of Einstein's fields equations is carried out systematically. The engine of the GR is the two fundamental principles; the equivalence and covariant principles which are clearly shown in this work how their application is indispensable to the arrival at Einstein's field equations. The applications of these two theories (SR and GR) were not left without being given serious attention in chapter four. The last page of this project contains discussion and recommendations for further research. iv