# Proper-time measurement in accelerated relativistic systems

## TL;DR

This paper explores how proper-time measurements in accelerated relativistic systems depend on simultaneity and rigidity, providing explicit synchronization methods and discussing implications for the clock hypothesis and related paradoxes.

## Contribution

It establishes conditions for proper-time comparison in accelerated systems, explicitly computes synchronization relations, and discusses implications for the clock hypothesis and relativistic paradoxes.

## Key findings

- Proper-time measurement requires linear rigidity for simultaneity.
- Explicit synchronization relations are derived using light signals.
- Incorrect simultaneity assumptions lead to pseudo-paradoxes.

## Abstract

Separate constituents of extended systems measure proper-times on different world-lines. Relating and comparing proper-time measurements along any two such world-lines requires that common simultaneity be possible, which in turn implies that the system is linearly-rigidly moving so that momentary rest frames are identifiable at any stage of the system's journey in space-time. Once momentary rest-frames have been identified, clocks moving on separate world-lines are synchronizable by light-signal communication. The synchronization relations for two clocks are explicitly computed using light-signals exchanged between them. Implications for the clock hypothesis are included. Also, since simultaneity is frame-dependent, incorrect usage of it leads to pseudo-paradoxes. Counter-examples are discussed.