Relativistic length evolution and breakdown of rigidity: a Minkowski diagram analysis

Abstract

We analyze the length evolution of a uniformly accelerated rod from the perspective of an inertial frame moving at a constant velocity. Using Minkowski diagrams and Lorentz transformations, we show that a rod which appears rigid in one frame does not retain that rigidity in another. In the asymptotic limit, the rod's length approaches a constant proportional to the relativistic Doppler factor. These results underscore the breakdown of classical rigidity under relativistic conditions and offer a pedagogical framework for exploring relativistic kinematics in non-inertial systems.