# The 'twin paradox' in relativistic rigid motion

## TL;DR

This paper revises the 'twin paradox' within relativistic rigid motion, analyzing age differences between astronauts at different spaceship locations and exploring implications for relativistic systems and light signal synchronization.

## Contribution

It introduces a new perspective on the twin paradox in rigid relativistic motion, considering spatially extended systems and light signal synchronization.

## Key findings

- Age difference depends on distance and rapidity change.
- Proper-time varies along the spaceship's length during acceleration.
- Conditions for simultaneous light signal arrival are established.

## Abstract

Relativistic rigid motion suggests a new version for the so-called `twin paradox', comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being rigid, is simultaneously at rest, the twins' ages, measured as the proper-times along their individual world lines, are different when they are located at remote parts of the spaceship. The age, or proper-time, difference depends on the distance at rest between the astronauts and the rapidity difference between start to end. The relation of the age difference with the relative Doppler shift of light signals transmitted between the astronauts, and implications for the possibility to assign common age (proper-time) to complex, spatially extended, relativistic systems, are also discussed. The condition for simultaneous arrival of light signals emitted simultaneously from the opposite ends of a rigidly accelerating spaceship is resolved.