Twin paradox and space topology
Classical Physics
2008-11-26 v1 General Physics
Abstract
If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than along any other one.
Cite
@article{arxiv.physics/0006039,
title = {Twin paradox and space topology},
author = {Jean-Philippe Uzan and Jean-Pierre Luminet and Roland Lehoucq and Patrick Peter},
journal= {arXiv preprint arXiv:physics/0006039},
year = {2008}
}
Comments
6 pages, latex, 3 figures