Analysis of Bell's spaceships "paradox"

TL;DR

This paper examines Bell's spaceship paradox from inertial and accelerated frames, clarifying the true length of the thread and resolving the apparent paradox through detailed calculations.

Contribution

It provides a detailed analysis of Bell's paradox from multiple reference frames, clarifying misconceptions about the thread's length during acceleration.

Findings

Neither frame's measured distance reflects the actual thread length.

Calculations reveal the true length of the thread, resolving the paradox.

The analysis clarifies how relativistic effects influence measurements in accelerated systems.

Abstract

We analyse the Bell paradox from the point of view of an inertial referential frame and from the one of an accelerated frame. We calculate the distance between the two accelerated spaceships as it appears in each referential and we show that neither of the two values represent the "real" length of the thread. Calculating this latter gives a clear understanding of the so-called paradox.