Twin paradox and space topology

Details Twin paradox and space topology Twin paradox and space topology

2000-06-16

arxiv.org/abs/physics/0006039v1

Eur.J.Phys.23:277,2002

Physics

Classical Physics

6 pages, latex, 3 figures

Scientific paper

10.1088/0143-0807/23/3/306

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.

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