To go along with the astronaut/twin "paradox" there is a less well known
paradox involving length contraction. It is known as the rocket-rope
paradox and as Bell's spaceship paradox. If interested see this website:
http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
There are two versions. In one version the rockets have a constant
proper acceleration. In the other version the rocket engines are turned
off after some prearranged time so only SR is needed. The question is
whether a rope (or spring) connected between the rockets will physically
stretch (or break) or not. There are three interpretations: SR1 - rope
will stretch or break, SR2- rope will not stretch or break, and Physical
Effect- rope will stretch or break. If interested after reading above
reference, I would recommend reading the following references in order
followed by other references: original article by Dewan & Beran,
objection by Nawrocki, & response by Dewan.