On Radar Time and the Twin `Paradox'

In this paper we apply the concept of radar time (popularised by Bondi in his work on k-calculus) to the well-known relativistic twin paradox'. Radar time is used to define hypersurfaces of simultaneity for a class of travelling twins, from the Immediate Turn-around’ case, through the Gradual Turn-around' case, to the Uniformly Accelerating’ case. We show that this definition of simultaneity is independent of choice of coordinates, and assigns a unique time to any event (with which the travelling twin can send and receive signals), resolving some common misconceptions.