Date: Jan 22, 2013 6:50 PM
Subject: Re: Non-physicist's curiosity on geometry
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