On 11/9/2017 9:15 PM, Alan Grayson wrote:
On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker <[email protected] <mailto:[email protected]>> wrote:On 11/9/2017 8:55 PM, [email protected] <mailto:[email protected]> wrote:On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: On 11/9/2017 6:23 PM, Alan Grayson wrote:The difference between spatially flat and asymptotically flat for a huge universe would be virtually impossible to distinguish by measuring the sum of angles in a triangle. Moreover, I don't see how spatially flat can have nothing to do with extent, since in applying Euclidean geometry we surely seem to be dealing with an infinitely extended plane. TIA.Not necessarily. You could have periodic boundary conditions. But most cosmologists do assume the universe is infinite in spatial extent. Of course the flatness isn't measured by triangulation. It's measured by comparing the spatial spectrum of the CMB variations to model predictions with different mass densities. https://arxiv.org/pdf/astro-ph/0004404 <https://arxiv.org/pdf/astro-ph/0004404> Brent However flatness is measured, the criterion still seems Euclidean and hence infinite in extent if one believes the triangle measured has combined angles of 180 degrees. And I don't see how this is distinguishable from asymptotically flat for a huge but finite universe.It's not.That's my point. No way of distinguishing flat from asymptotically flat for a huge universe, so the assumption of infinite spatial extent by cosmologists seems unwarranted. But as you note below, the universe could have begun with infinite spatial extent. But ours didn't AFAIK. It began as astronomically tiny and expanded via inflation.
But you don't know that. According to Einstein's equations the visible part of the universe started at /*zero*/ size. Of course no one takes that entirely seriously since at very small distances quantum mechanics must invalidate Einstein's equations.
Brent
Moreover, it seems contradictory that a universe which has expanded for a finite duration, could be infinite in spatial extent. TIA.It can if it starts off infinite. Remember the expansion in Einstein's equation is just a /*factor*/, not an absolute value. Brent
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