A Simple Relativity Solution to the Bell Spaceship Paradox

TL;DR

This paper offers a straightforward relativity-based explanation for the Bell Spaceship Paradox, clarifying why the string snaps and how to prevent it, while also connecting to related paradoxes like Ehrenfest's.

Contribution

It introduces a simple relativity approach to resolve the Bell Spaceship Paradox and related issues, providing clearer insights into relativistic stress and acceleration adjustments.

Findings

Clarifies why the string snaps in the paradox

Provides methods to adjust accelerations to prevent snapping

Extends the approach to rotation and orbital precession

Abstract

The Bell Spaceship Paradox has promoted confusion and numerous resolutions since its first statement in 1959, including resolutions based on relativistic stress due to Lorentz contractions. The paradox is that two ships, starting from the same reference frame and subject to the same acceleration, would snap a string that connected them, even as their separation distance would not change as measured from the original reference frame. This paper uses a Simple Relativity approach to resolve the paradox and explain both why the string snaps, and how to adjust accelerations to avoid snapping the string. In doing so, an interesting parallel understanding of the Lorentz contraction is generated. The solution is applied to rotation to address the Ehrenfest paradox and orbital precession as well.