Date: Jan 23, 2013 12:53 AM
Subject: Re: Non-physicist's curiosity on geometry
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.
> > I like to play "thinking games" around them.
> > 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 inverse-square 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
> inverse-square law (over what you might call "medium" distances),
> which clearly indicates Euclidean (or very-nearly-Euclidean) geometry.
> The weak and strong nuclear forces do not obey the inverse-square
> 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.