Non-coordinate time/velocity pairs in special relativity

Motions with respect to one inertial (or “map”) frame are often described in terms of the coordinate time/velocity pair (or “kinematic”) of the map frame itself. Since not all observers experience time in the same way, other time/velocity pairs describe map-frame trajectories as well. Such coexisting kinematics provide alternate variables to describe acceleration. We outline a general strategy to examine these. For example, Galileo’s acceleration equations describe unidirectional relativistic motion exactly if one uses V = dx dT , where x is map-frame position and T is clock time in a chase plane moving such that γ′ = γ √ 2 γ+1 . Velocity in the traveler’s kinematic, on the other hand, has dynamical and transformational properties which were lost by coordinatevelocity in the transition to Minkowski space-time. Its repeated appearance with coordinate time, when expressing relationships in simplest form, suggests complementarity between traveler and coordinate kinematic views. 03.30.+p, 01.40.Gm, 01.55.+b Typeset using REVTEX 1