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

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 transportproduce 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.