Some Asymptotic Conditions of Worldlines in Minkowski Space

Gen Yoneda, Yoshiyasu Ishigami, Satoshi Arima

Research output: Contribution to journalArticlepeer-review


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) Permanency with respect to the proper time. (C) Finiteness of the gamma factor. (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 relations are proved and some are denied by counter examples. Then the concluding Venn diagram is obtained. Such researches must interest theoretical physicists who unintentionally use one or plural number of these conditions.

Original languageEnglish
Pages (from-to)1495-1499
Number of pages5
Journaljournal of the physical society of japan
Issue number5
Publication statusPublished - 1993 Jan 1


  • asymptotic condition
  • special relativity
  • worldline

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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