The Special Theory of Relativity, proposed by Albert Einstein in 1905, fundamentally changed how we understand space and time. It arose from the failure of classical mechanics to explain the behavior of light and the null result of the Michelson-Morley experiment. This post covers the detailed mathematical derivations of the theory, including the Michelson-Morley experiment, Lorentz transformations, length contraction, time dilation, relativistic velocity addition, and the energy-momentum relations. Comprehensive Notes: Special Theory of Relativity 1. Michelson-Morley Experiment Objective: To detect the existence of the "aether" (a hypothetical medium thought necessary for light waves to travel) and calculate the speed of the Earth with respect to it. Apparatus: A Michelson Interferometer was used to compare optical path lengths for light moving in two mutually perpendicular directions. Deriva...