Talk:Orientable manifold

I think it should go in orientability Tosha 05:13, 22 Aug 2004 (UTC)

Out of curiosity, can someone point out a reference for why the space-time manifold is believed to be orientable? Is this a matter of practicality, or is there experimental evidence for this? Am I being obtuse in asking whether there's experimental evidence for a global property of the universe? forgive me. Wilgamesh 01:22, 13 Sep 2004 (UTC)

On the small scale, one believes it for obvious reasons (handedness in biological molecules is another good reason). An unorientable space-time would have an orientable double cover. Wouldn't that be the 'real' underlying space-time, anyway? Charles Matthews 07:42, 13 Sep 2004 (UTC)

I thought that handedness of biological molecules was considered to be mostly a matter of which type of molecule got "adopted" first? They do say that some particle physics reactions are supposed to be asymmetrical for matter and antimatter, but I suppose that its conceivable that this might be a local "democratic" effect - one could hypothesise that in a region dominated by "normal" matter, reactions may be "pushed" in favour of more "normal" matter, but in a region where antimatter dominated, antimatter might be favoured. A chirality field, perhaps? Perhaps when we start using our particle accelerators to assemble clusters of antimatter atoms, it might be useful to look for a weakening or reversal of these rules in the vicinity.ErkDemon 22:54, 30 July 2005 (UTC)[reply]

If I understand correctly, the point is that there aren't small paths for molecules to take that will reverse their orientation. Ie, we don't observe molecules switching their handedness so that implies that local orient reversing maps at best require a high energy to traverse. Second, orientation reversing paths haven't been observed (including phenomena that would imply their existence) on any scale in the universe. The double cover mentioned above would have an identification of pairs of points (since there would then be a 2-1 map to the observed space-time). For that reason, I'd be reluctant to call it the "real" space-time.

Another matter is the claim that it is generally believed that the universe is closed. My understanding here is that there is no concensus on this point and plenty of evidence to indicate that we're in an open space-time manifold. For example, the models of expanding universes are inherently open. -- KarlHallowell 19:45, 15 February 2006 (UTC)[reply]