A synchronous formulation of relativistic statics

Abstract

A form-invariant synchronous formulation of relativistic statics is proposed in which one does not deal with a hidden momentum such as the one associated with the von Laue flux. This momentum is unphysical. It is also shown that the line of reasoning that has been used in the theory of the additional momentum always yields a compensating result for the net moment of the external forces. The new synchronous formulation is established after specifying the concept of equilibrium of an extended body. It describes the equilibrium in the inertial frame in which the equilibrium conditions are written in contradistinction to the asynchronous formulation of Cavalleri and Salgarelli, in which the equilibrium described is always the one relative to the proper frame of the body. The present formulation requires the relevant 4-torque to be constant, and further establishes the relationships that the components of the 4-torque must fulfil if equilibrium is given.