How old are you, Tach? Seriously. You are artificially hiding events from the \(S''\) observer, and pretending it means something. True. The Lorentz transforms from \(S'\) tell us what the \(S''\) observer would directly measure. They tell us that the \(S''\) observer would directly measure this: Please Register or Log in to view the hidden image! Good questions, for which a relativistic theory of elasticity would be needed to thoroughly answer, but Janus's post in the original thread gives big clues. I think that the Lorentz transforms prove that the rod bends in \(S''\). Because that would be a physical contradiction. Breaking is an absolute physical effect. The rod doesn't break in \(S'\), therefore it doesn't break in \(S''\). Prove it.