Bell's accelerating spaceships paradox and relativistic length contraction

A fifty-year old apparently paradoxical thought experiment, involving two accelerating spaceships and a thread that connects them, states that the thread breaks due to length contraction. It was revived by John Bell in a debate with colleagues at CERN in the seventies. This paradox still appears to be regarded by some physicists as a proof that (i) only physical bodies, but not space, undergo relativistic length contraction and (ii) there is a stress in the relativistically contracted body. However, a proper relativistic treatment of the paradox demonstrates that it is a manifestation of a specific relativistic acceleration phenomenon, which means that length contraction plays no role in the resolution of the paradox. It is also shown that no stress is involved in the length contraction effect.