The twin paradox in compact spaces

TL;DR

This paper resolves the twin paradox in finite, compact spaces by demonstrating that twins on inertial, periodic paths agree on their ages when they meet, thanks to a preferred frame dictated by the space's topology.

Contribution

It shows how the twin paradox is resolved in compact spaces through the selection of a preferred frame, avoiding the paradox and clarifying the role of topology.

Findings

Twins on inertial, periodic orbits agree on their ages at crossings.

The topology of space singles out a preferred frame for resolving the paradox.

The apparent paradox is avoided in finite spaces with specific topologies.

Abstract

Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.