Bell's Spaceships Problem and the Foundations of Special Relativity

Abstract

Recent ‘dynamical’ approaches to relativity by Harvey Brown and his colleagues have used John Bell's own solution to a problem in relativity which has in the past sometimes been called ‘Bell's spaceships paradox’, in a central way. This paper examines solutions to this problem in greater detail and from a broader philosophical perspective than Brown et al. offer. It also analyses the well-known analogy between special relativity and classical thermodynamics. This analysis leads to the sceptical conclusion that Bell's solution yields neither new philosophical insights concerning the foundations of relativity nor differential support for a specific view concerning the existence of space-time.

Acknowledgements

I would like to thank the two anonymous referees of this journal for their careful and constructive criticisms and Rachel Fernflores for her insightful comments on an earlier draft of this article.

Notes

If the ships A and B execute BRM, then they do not execute ‘identical acceleration programmes’. Instead, A and B move with very specific but different constant proper accelerations. Consequently the ships have to accelerate for different amounts of proper time before shutting off their engines to ensure the two ends of the string ‘arrive’ at the same inertial frame F′.

We created Figures 1 and 3 using Maple 13.

This assumes, of course, that A and B set their clocks to read the same value of proper time, e.g. when they received the light signal from C and began accelerating.

The relationship between D _AB , D _BA , and λ as a function of the elapsed proper time τ for either A or B is somewhat subtle. We explore this relationship and other relationships assumed in this paper analytically, and display the relevant plots, in Fernflores (forthcoming).

Additional information

Notes on contributors

Francisco Fernflores

Francisco Fernflores is at the Philosophy Department, California Polytechnic State University. Correspondence to: Philosophy Department, California Polytechnic State University, 1 Grand Ave., San Luis Obispo, CA 93407-0327, USA.