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 > > 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. Moreover, it seems contradictory that a universe which has expanded for a finite duration, could be infinite in spatial extent. TIA. > > > On Thu, Nov 9, 2017 at 4:42 PM, Brent Meeker <[email protected] > <javascript:>> wrote: > >> Cosmologist think the universe is spatially flat. That just means >> triangles have interior angles summing to 180deg. It doesn't have anything >> to do with extent. But the universe is not flat in spacetime; it's >> expanding and at an increasing rate. >> >> Brent >> >> On 11/9/2017 3:10 PM, [email protected] <javascript:> wrote: >> >> IIUC, the difference is huge. In the former case, the universe is open, >> spatially infinite with infinite mass (assuming a nonzero mass distribution >> on large scale everywhere), whereas the latter is closed, finite in spatial >> extent and mass. But I notice that most cosmologists claim the universe is >> *flat*, as in mathematically flat. Are they just speaking loosely and >> really mean the universe is ASYMPTOTICALLY flat? I find it contradictory >> for a universe which is finite in age, to be truly mathematically FLAT. TIA. >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "Everything List" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/everything-list/0XZFBcBdqYU/unsubscribe >> . >> To unsubscribe from this group and all its topics, send an email to >> [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
