Relativistic dynamics in uniformly accelerated reference frames with application to the clock paradox

Abstract

Two clocks are considered, performing hyperbolic motions with oppositely directed velocities and accelerations, relative to an inertial reference frame. Five different procedures are demonstrated of how an observer following one clock can predict the time of the other clock: (1) Lagrangian description; (2) covariant generalisation of Newton's second law; (3) by means of the invariant equation for uniformly accelerated motion; (4) using the generalised Lorentz factor for time dilation, valid in the presence of a gravitational field; and (5) making use of the description of an inertial observer.