On Radar Time and the Twin `Paradox'

2001/04/24 by Carl E. Dolby, Stephen F. Gull · 1 voice · 8 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Mathematics and Applications #Relativity and Gravitational Theory #gr-qc #hep-th

paper · pdf · doi:10.1119/1.1407254

published as Am.J.Phys. 69 (2001) 1257-1261 · 9 pages, 10 figures. Minor changes (includes minor corrections not in published version)

arxiv created 2002/03/06 · arxiv updated 2009/11/30

Abstract

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.

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Discussions

• There is no frame with any jumps back in time. That would violate the definition of a coordinate chart. A coordinate chart is a smooth and invertible mapping between events in spacetime and points in [stackexchange, 11 points]

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