### Abstract

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 language | English |
---|---|

Pages (from-to) | 1495-1499 |

Number of pages | 5 |

Journal | Journal of the Physical Society of Japan |

Volume | 62 |

Issue number | 5 |

Publication status | Published - 1993 May |

### Fingerprint

### Keywords

- Asymptotic condition
- Special relativity
- Worldline

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*62*(5), 1495-1499.

**Some asymptotic conditions of worldlines in Minkowski space.** / Yoneda, Gen; Ishigami, Yoshiyasu; Arima, Satoshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 62, no. 5, pp. 1495-1499.

}

TY - JOUR

T1 - Some asymptotic conditions of worldlines in Minkowski space

AU - Yoneda, Gen

AU - Ishigami, Yoshiyasu

AU - Arima, Satoshi

PY - 1993/5

Y1 - 1993/5

N2 - 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.

AB - 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.

KW - Asymptotic condition

KW - Special relativity

KW - Worldline

UR - http://www.scopus.com/inward/record.url?scp=21144478363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144478363&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21144478363

VL - 62

SP - 1495

EP - 1499

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 5

ER -