On the relativistic lever paradox

Abstract

As the ‘relativistic lever paradox’ is a characteristic topic in the theory of relativity application to rotation processes, a covariant four-tensor equation is developed to describe the relativistic rigid-rotation of an extended body subjected to external torques, and its Lorentz transformation between frames S and in the standard configuration is analysed, to discuss this paradox. From the four-tensor rotation equation applied to an L-shaped body submitted to several torques it is concluded that although the system does not vary its angular momentum in frame S—in which simultaneously applied forces resultant torque is zero –, in frame , it does vary its angular momentum and exerted torque on it is non-zero. From this formalism (asynchronous formulation of relativity), in frame , angular momentum variation is related to Einstein's inertia of energy principle, and the non-zero torque is a consequence of the relativity of simultaneity, showing that this description is coherent and that there is no paradox.