Journal Article

Homotopy symmetry in the multiply connected twin paradox of special relativity

Boudewijn F. Roukema and Stanislaw Bajtlik

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 390, issue 2, pages 655-664
Published in print October 2008 | ISSN: 0035-8711
Published online October 2008 | e-ISSN: 1365-2966 | DOI:
Homotopy symmetry in the multiply connected twin paradox of special relativity

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In a multiply connected space, the two twins of the special relativity twin paradox move with constant relative speed and meet second time without acceleration. The twins' situations appear to be symmetrical despite the need for one to be younger due to time dilation. Here, the suggestion that the apparent symmetry is broken by homotopy classes of the twins' worldlines is re-examined using space–time diagrams. It is found that each twin finds her own spatial path to have zero winding index and that of the other twin to have unity-winding index, i.e. the twins' worldlines' relative homotopy classes are symmetrical. Although the twins' apparent symmetry is in fact broken by the need for the non-favoured twin to non-simultaneously identify spatial domain boundaries, the non-favoured twin cannot detect her disfavoured state if she only measures the homotopy classes of the two twins' projected worldlines, contrary to what was previously suggested. We also note that for the non-favoured twin, the fundamental domain can be chosen by identifying time boundaries (with a spatial offset) instead of space boundaries (with a temporal offset).

Keywords: reference systems; time; cosmology: theory

Journal Article.  7689 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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