SOME ASYMPTOTIC CONDITIONS OF WORLDLINES IN MINKOWSKI SPACE

This paper presents four asymptotic conditions of smooth worldlines in Minkowski space that are often used in special relativistic particle dynamics. (A) Permanency with respect to an observer's time. (B) Perma nency with respect to the proper time. (C) Finiteness of the gamma fac tor. (D) Intersection with the light cone of any apex. The conditions (B) and (D) are free from observers and it is verified that (A) and (C ) are invariant conditions for all inertial observers. To examine the inclusion relations between (A), (B), (C) and (D), some inclusion rela tions are proved and some are denied by counter examples. Then the con cluding Venn diagram is obtained. Such researches must interest theore tical physicists who unintentionally use one or plural number of these conditions.