On Radar Time and the Twin `Paradox'

TL;DR

This paper uses radar time to analyze the relativistic twin paradox, providing a coordinate-independent way to define simultaneity and clarify misconceptions about the scenario.

Contribution

It applies radar time to the twin paradox, offering a novel, coordinate-independent approach to defining simultaneity for accelerating twins.

Findings

Radar time defines unique simultaneity hypersurfaces.

The approach is coordinate-independent.

It clarifies misconceptions about the twin paradox.

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.