Basics of Special Theory of Relativity - Mahatme , Upendra B. (Basics of Special Theory of Relativity, 2023)
The book starts with an introduction to motion, relative motion, observer and frame of reference, state of absolute rest and state of absolute motion. The difference between the inertial frame of reference and non-inertial frame of reference has been discussed. The Galilean transformation equations are derived for the space-time observations taken from inertial frames moving with nonrelativistic relative speed. Consequently, the invariance in acceleration, length invariance and time interval invariance (space and time invariance) on the basis of Galilean transformation equations are proved. The concept of luminiferous ether medium as an absolute frame has been discussed only in which the observations for the state of absolute motion and state of absolute rest can be taken. The assumptions for the ether medium have been mentioned. Then the famous Michelson-Morley experiment was studied in detail to prove the ether medium and ether drag. The negative result of this experiment and conclusions from it are given. Principles and postulates of the special theory of relativity are discussed. Lorentz transformation equations are derived for the space-time observations taken from inertial frames moving with relativistic relative speed. The equations for time dilation and length contraction are derived using the Lorentz transformations and the simultaneity of event also has been discussed using these transformations. The variation of mass with velocity (relativistic mass) has been derived using the velocity addition theorem. At the end of this book, the study on Einstein’s famous mass-energy relation, the relation between relativistic energy and relativistic momentum, and the particle of zero rest mass has been given.