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**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.