The Equivalence Principle, Special Relativity, and Newton’s Gravitational Law

Abstract

Special relativity dictates that, for the laboratory observer, the inertial mass, m _i, of a particle with rest mass m _o performing a linear motion is γ³ m _o, where γ is the Lorentz factor. Using instantaneous inertial frames one shows that this result is valid also for arbitrary particle motion, including circular orbits. In view of the equivalence principle, however, this implies that the gravitational particle mass, m _g, also equals γ³ m _o. Therefore the combination of special relativity and of the equivalence principle introduces a γ⁶ correction term to Newton’s gravitational law under relativistic conditions. The gravitational force becomes unbound and can exceed the magnitude of any other force as { v} approaches the speed of light c. How can one explain that this amazing result has not been discussed before? Could it be that we do not pay sufficient attention to special relativity and to the equivalence principle?