Relativistic Coordinate Transformation

Abstract

Lorentz coordinate transformations explore change of measurement of events by different inertial observers; the body is still in the same state of motion as before; it is the observer who is changing her frame of reference. However, we can also ‘boost’ material bodies using a simple modification of the Lorentz coordinate transformation. We show how three physics inputs: i) the isotropy and homogeneity of space; ii) the principle of relativity; and iii) the universality of the speed of light; allow us to determine the form of Lorentz coordinate transformation. Exercises show invariance of speed of light. We discuss atmospheric muon motion. Properties of the transformation such as the Galilean limit, and the Larmor form of Lorentz transformations are presented. The concept of inverse transformation is introduced.