On the Bell's spaceships paradox and proper length for accelerated bodies

TL;DR

This paper analyzes the Bell's spaceships paradox using Born's definition of proper length to understand the behavior of the thread connecting accelerating spaceships.

Contribution

It applies Born's proper length concept to the Bell's paradox, providing new insights into the proper length of accelerated bodies.

Findings

Proper length varies with acceleration according to Born's definition

The thread's tension depends on the acceleration profile

Clarifies the relativistic effects on extended bodies under acceleration

Abstract

We study the Dewan-Beran-Bell thought experiment of two spaceships connected by a thread that start accelerated motion and discuss the proper length of the thread by means of Born's definition of proper length for arbitrary motion.