## The proper-time Lorentz group demystified.(English)Zbl 1173.83301

Summary: 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.

### MSC:

 83A05 Special relativity 22E43 Structure and representation of the Lorentz group 81R05 Finite-dimensional groups and algebras motivated by physics and their representations