On the Bell's spaceships paradox and the proper length of an accelerated body

摘要

We draw upon the Dewan-Beran-Bell thought experiment of two spaceships connected by a thread that begin to accelerate to discuss the difficulties in extending the notion of proper length to bodies in arbitrary motion. We propose a relativistic extension of proper length by combining Born's definition of infinitesimal distance and the notion of local simultaneity. Finally we examine how the length of the thread between the ships evolves and compare it with other relativistic extensions.