The Proper-Time Lorentz Group Demystified

Abstract

Proper velocities are measured by proper time as opposed to coordinate velocities, which are measured by coordinate time. The standard Lorentz transformation group, in which each transformation is expressed by a coordinate velocity and an orientation between two inertial frames, is well known. In contrast, the equivalent proper-time Lorentz transformation group, in which each transformation is expressed by a proper velocity and an orientation between two inertial frames is unknown. The dignity of special relativity theory requires that every possible means be explored for the solution of a problem so elegant and so celebrated. Fortunately, a so called gyro-formalism approach to special relativity enables the elusive proper-time Lorentz transformation group to be uncovered.