On Monday, December 24, 2018 at 5:22:34 AM UTC, Bruce wrote: > > On Mon, Dec 24, 2018 at 4:02 PM <[email protected] <javascript:>> wrote: > >> On Monday, December 24, 2018 at 4:47:02 AM UTC, Bruce wrote: >>> >>> On Mon, Dec 24, 2018 at 3:33 PM <[email protected]> wrote: >>> >>>> On Monday, December 24, 2018 at 4:22:24 AM UTC, [email protected] >>>> wrote: >>>>> >>>>> On Monday, December 24, 2018 at 3:50:33 AM UTC, Brent wrote: >>>>>> >>>>>> On 12/23/2018 4:47 PM, [email protected] wrote: >>>>>> >>>>>> *If by "flat", you mean mathematically flat, like a plane extending >>>>>> infinitely in all directions, as opposed to asymptotically flat like a >>>>>> huge >>>>>> and expanding sphere, you have to reconcile an infinitesimally tiny >>>>>> universe at the time of the BB, and simultaneously an infinitely large >>>>>> universe extending infinitely in all directions. AG* >>>>>> >>>>>> >>>>>> All that's "infinitesimally tiny" is the visible universe. You must >>>>>> know that the Friedmann equation just defines the dynamics of a scale >>>>>> factor, not a size. >>>>>> >>>>> >>>>> *Are you claiming the visible universe at the BB was infinitesimally >>>>> tiny, but the non visible part was infinitely large (mathematically >>>>> flat), >>>>> or huge (asymptotically flat)? AG * >>>>> >>>> >>>> *Bruce says the universe is always flat if k=1. How can it be >>>> everywhere flat if there's a region which is infinitely tiny; hence not >>>> flat in the visible region? How are we to imagine this? TIA, AG * >>>> >>> >>> That's a bit confused. k=0 corresponds to a universe that is everywhere >>> flat (in space, but not necessarily in the time dimension - i.e., it might >>> be expanding. Our current visible universe originated in a small (tiny) >>> region of the total structure, which might be infinite in extent, but flat >>> everywhere, even in our tiny region. >>> >> >> *Not to split hairs, but how can the tiny visible region also be flat and >> infinite in extent, if its age is finite? I can imagine the visible region >> to be asymptotically (but not mathematically) flat, and therefore finite in >> extent. AG * >> > > I said that the total structure might be infinite in extent, not the > region that became our visible universe. Flatness is a mathematical > property -- imagination readily fails to visualise these things. >
*I can visualize it. The total structure might be infinite in extent (flat, possibly like a mathematical plane) or just very large, but the visible universe, being of finite age, can be no larger than asymptotically flat (like the surface of a huge expanding sphere) and thus finite in spatial extent. I've noticed that some cosmologists are sloppy in claiming the visible part is "flat" and infinite, which is impossible, failing to qualify "flat" to mean "asymptotically flat", finite in spatial extent because it has finite age. I think this answers Brent's issue with my comments as well. AG* > Bruce > -- 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.
