Date: Jan 23, 2013 12:53 AM
Author: ross.finlayson@gmail.com
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.

>

> 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 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.

http://groups.google.com/groups/search?hl=en&as_q=meso&as_uauthors=Finlayson

Regards,

Ross Finlayson