On Mon, Jan 20, 2020 at 7:49 AM Alan Grayson <[email protected] > <javascript:>> wrote: > > *> What I HAVE established is that flatness is incompatible with a >> universe which had a beginning. So if it's flat, it never had a beginning; >> or else it did, and is closed, hyper-spherical in shape. AG* > > > Are you talking about spatial curvature or spacetime curvature? >
I think the former, but I am unclear about the difference between the cases. There might not be a difference. AG > By "curvature" do you mean the angles of a triangle add up to something > other than 180 degrees, or do you mean if you keep going in one direction > you will eventually end up where you started? They are not necessarily the > same thing. > One would eventually end up where one started IF the universe were perfectly homogeneous, but since it isn't this is an idealization for discussion purposes. And since the curvature is slightly positive, if the expansion were frozen, the sum of angles of a triangle would be larger than 180 deg. AG > > If the universe once expanded faster than the speed of light (as inflation > hypothesizes) then it's conceivable the angles of a triangle could add up > to be more than 180 degrees, so the universe would have a positive spatial > curvature like a sphere does, > This is what I imagine, but I don't see the necessity of expansion faster than light. AG > and yet you'd be going further and further from your starting point into > infinity and never return. > You might never return due to the rate of expansion being temporarily faster than light, but I think the universe would still be closed. AG > And as long as there had been a faster than light expansion at some point > in the universe's history if the angles of a triangle added up to less than > 180 degrees then the universe would have negative spatial curvature, like > the shape of a saddle does, and you'd still never return to your starting > place. > > John K Clark > -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/4855bfc1-f2d1-4a09-b9ac-aede60209e13%40googlegroups.com.
