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, fr om the `Immediate Turn-around’ case, through the `Gradual Turn-around’ case, to th e `Uniformly Accelerating’ case. We show that this definition of simultaneity is i ndependent 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.
C.E. Dolby and S.F. Gull, On radar time and the twin `paradox’, Am. J. Phys. 69, 1257-1261 (2001)