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Re: Nonphysicist's curiosity on geometry
Posted:
Jan 23, 2013 12:53 AM


On Jan 22, 3:50 pm, "n...@bid.nes" <alien8...@gmail.com> wrote: > On Jan 20, 11:50 pm, joship...@gmail.com wrote: > > > I am not a physicist. I am not a mathematician either. > > Metoo. > > > I like to play "thinking games" around them. > > Again... > > > One of my recent wonders is the relation between scale of physics and > > geometries. In one sentence: "As scale of distance changes, does that notorious > > fifth postulate of Euclid play tricks with us?" > > "Play tricks"? No, we just notice that Euclidean geometry is only > valid in certain limited circumstances. > > > When the distance are too great in relativity, physics follows hyperbolic geometry. > > Fifth postulate is broken in one way. > > In everyday life, everything is Euclidean. Fifth postulate holds. > > No, everything is not Euclidean, the Earth's surface is curved. It > only looks flat over regions of small curvature. Gravity doesn't quite > operate inversesquare over very large distances. > > > The wonder is: > > When things become too small (in quantum physics?), does fifth postulate break > > the other way and elliptical geometry become sensible? Is there any phenomenon > > observed on that line? > > We observe the electromagnetic and gravitational forces to obey the > inversesquare law (over what you might call "medium" distances), > which clearly indicates Euclidean (or verynearlyEuclidean) geometry. > > The weak and strong nuclear forces do not obey the inversesquare > law, indicating that they do not operate in Euclidean space. > > But Elliptic space goes Euclidean (flat) at short distances rather > than large, so no. > > (crossposted to sci.math) > > Mark L. Fergerson
I call them macro, micro, and "meso" scale.
http://groups.google.com/groups/search?hl=en&as_q=meso&as_uauthors=Finlayson
Regards,
Ross Finlayson



