History of Lorentz Transformations

History Of Lorentz Transformations

The Lorentz transformations relate the space-time coordinates, (which specify the position x, y, z and time t of an event) relative to a particular inertial frame of reference (the "rest system"), and the coordinates of the same event relative to another coordinate system moving in the positive x-direction at a constant speed v, relative to the rest system. It was devised as a theoretical transformation which makes the velocity of light invariant between different inertial frames. The coordinates of the event in this "moving system" are denoted x′, y′, z′ and t′. Before 1905, the rest system was identified with the "aether", the supposed medium which transmitted electro-magnetic waves, and the moving system was commonly identified with the earth as it moved through this medium. Early approximations of the transformation were published by Voigt (1887) and Lorentz (1895). They were completed by Larmor (1897, 1900) and Lorentz (1899, 1904) and were brought into their modern form by Poincaré (1905), who gave the transformation the name of Lorentz. Eventually, Einstein (1905) showed in the course of his development of special relativity, that this transformation concerns the nature of space and time.

In this article the historical notations are replaced with modern notations, where

is the Lorentz factor, v is the relative velocity of the bodies, and c is the speed of light.