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Topic: closed universe, flat space?
Replies: 48   Last Post: May 5, 2013 2:45 PM

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 Rich Delaney Posts: 382 Registered: 12/13/04
Re: closed universe, flat space?
Posted: Apr 29, 2013 2:22 PM

On Apr 24, Dan <dan.ms.ch...@gmail.com> wrote:
> > Supposedly, our universe is closed and finite,
> > a straight line (geodesic)  traveler must return
> > to his starting poiint, yes/no?  Hence, curved space.

>
> > At the same time, astronomers claim, that
> > space is flat, to the precision of their
> > measurements.
> > So, space is closed, but also flat...  back in my
> > day, they had something called a logical
> > contradiction -

>
> Space can be 'closed' , and also, 'locally flat',
> in the sense that the Riemann tensor vanishes , or
> there exists, for any point of the space, a non-
> infinitesimal spherical section around that point
> that's indistinguishable from flat space .
>
> Consider a piece of paper: flat? Yes. Closed? No.
> You can go off the edge.

um yeah
Finally, somebody gets it -

> Now make it so that when you go trough the 'up' edge
> you end up coming from the 'down' edge , and when
> you go go trough the 'left'
> edge you end up coming from the 'right' edge .

And to do that, you have to twist the paper into a cylinder... twist,
flat... see the problem here?

> More specifically, this
> space is the factor group (R^2) / (Z^2) . The
> space is still flat, as
> far as definitions tell . However, it's closed.

wooosh! Over my head -

--
Rich