An Analysis of the Proper Time Variation of Rigid Bodies Extending Along Inertial Motion in Space

Yiduo Zhang

doi:10.54254/2753-8818/2025.DL25453

Theoretical and Natural ScienceOpen access

An Analysis of the Proper Time Variation of Rigid Bodies Extending Along Inertial Motion in Space

Research Article

Open Access

An Analysis of the Proper Time Variation of Rigid Bodies Extending Along Inertial Motion in Space

Yiduo Zhang ^1*

¹ Harrow International School Hong Kong, 38 Tsing Ying Road, Tuen Mun, New Territories, Hong Kong, 999077

^*Corresponding author: yiduozhang79@gmail.com

Published on 24 July 2025

TNS Vol.132

ISSN (Print): 2753-8826

ISSN (Online): 2753-8818

ISBN (Print): 978-1-80590-305-5

ISBN (Online): 978-1-80590-306-2

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Abstract

Proper time and time dilation, though well-established in special relativity, are predominantly analysed for point particles. Much less attention has been given to how proper time behaves across spatially extended rigid bodies in inertial motion. Existing studies have explored differential aging effects under relativistic rigid motion, but primarily in scenarios involving acceleration. Therefore, this paper aims to investigate how proper time varies across different points of an extended object experiencing purely inertial motion, focusing on how the different clock synchronisation conventions affect the overall desynchronisation in proper time. This paper uses classical formulations of special relativity in order to contribute to a new perspective on the role of simultaneity in distributed time frames. This paper discovered that the two primary clock synchronization conventions— the Einstein convention and slow clock transport—produce comparable desynchronization in proper time; however, each method presents distinct advantages and disadvantages in practical contexts, necessitating a complementary approach to effectively address desynchronization in applications like satellite communication.

Keywords:

Proper Time, Clock Synchronisation, Spatially Extended Bodies, Inertial Frames, Relativity of Simultaneity

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References

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References

[1]. Ben-Ya’acov, U. (2016). The ‘twin paradox’ in relativistic rigid motion. European Journal of Physics, 37(5), 055601. https: //doi.org/10.1088/0143-0807/37/5/055601

[2]. Einstein, A. (1905). On the electrodynamics of moving bodies (W. Perrett & G. B. Jeffery, Trans.). The principle of relativity (pp. 37–65). Dover Publications. (Original work published 1905).

[3]. Rao, A. V. G., Mallesh, K. S., & Rao, K. N. S. (2015). On time-interval transformations in special relativity. arXiv. https: //doi.org/10.48550/arXiv.1105.4085

[4]. Born, M. (1909). The theory of the rigid electron in the kinematics of the principle of relativity. Annalen der Physik, 29(3), 571–584. https: //doi.org/10.1002/andp.19093230306

[7]. Rothenstein, B., & Popescu, S. (2007). Lorentz transformations: Einstein’s derivation simplified. arXiv. https: //doi.org/10.48550/arXiv.physics/0702157

[8]. Mitaroff, W. A. (2023). Aspects of clock synchronisation in relativistic kinematics—A tutorial. arXiv. https: //doi.org/10.48550/arXiv.2306.09582

Cite this article

Zhang,Y. (2025). An Analysis of the Proper Time Variation of Rigid Bodies Extending Along Inertial Motion in Space. Theoretical and Natural Science,132,1-8.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

About volume

Volume title: Proceedings of CONF-APMM 2025 Symposium: Simulation and Theory of Differential-Integral Equation in Applied Physics

ISBN: 978-1-80590-305-5(Print) / 978-1-80590-306-2(Online)

Editor: Marwan Omar, Shuxia Zhao

Conference website: https://www.confapmm.org/dalian.html

Conference date: 27 September 2025

Series: Theoretical and Natural Science

Volume number: Vol.132

ISSN: 2753-8818(Print) / 2753-8826(Online)

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