Special Relativity and Maxwell’s Equations 1 The （狭义相对论和麦克斯韦方程1）.pdfVIP

J. Broida UCSD Fall 2009 Phys 130B QM II Supplementary Notes on Special Relativity and Maxwell’s Equations 1 The Lorentz Transformation This is a derivation of the Lorentz transformation of Special Relativity. The basic idea is to derive a relationship between the spacetime coordinates x, y, z, t ′ ′ ′ ′ ′ as seen by observer O and the coordinates x , y , z , t seen by observer O moving at a velocity V with respect to O along the positive x axis. ′ y y V ′ x O′ x O These observers are assumed to be inertial. In other words, they are moving at a constant velocity with respect to each other and in the absence of any external forces or accelerations (which is somewhat redundant). In particular, there is no rotational motion or gravitational field present. Our derivation is based on two assumptions: 1. The Principle of Relativity: Physics is the same for all observers in all inertial coordinate systems. 2. The speed of light c in a vacuum is the same for all observers independently of their relative motion or the motion of the light source. We first show that this transformation must be of the form t′ = at + bx (1.1a)