On Tuesday, January 14, 2020 at 3:37:22 PM UTC-7, Alan Grayson wrote: > > > > On Tuesday, January 14, 2020 at 11:56:51 AM UTC-7, Alan Grayson wrote: >> >> >> >> On Tuesday, January 14, 2020 at 10:27:27 AM UTC-7, John Clark wrote: >>> >>> >>> >>> On Tue, Jan 14, 2020 at 6:47 AM Alan Grayson <agrays...@gmail.com> >>> wrote: >>> >>> >>> >>>> > >It is true for a de Sitter universe as a solution of the Einstein >>>>> equations. If the universe is spherical, it will eventually recontract, >>>>> and >>>>> light cannot get right round and back to its starting point before the >>>>> universe recontracts to a point. If the universe is expanding via dark >>>>> energy, even if spherical, light still cannot get round because of the >>>>> expansion. In other words, you can never see the back of your own head no >>>>> matter what the geometry of the universe!!!!! >>>>> Bruce >>>>> >>>>>> >>>> > *Since it's not a perfect sphere* [...] >>>> >>> >>> Because we're talking about curved Spacetime and not curved space and >>> because non-Euclidean geometry must be used (due to that minus sign that >>> sneaks into Pythagoras formula if time is one of the dimensions) it's >>> misleading to call it a "sphere", it's even misleading to call it the >>> surface of a 4D sphere. What we really want to know is it the geometry of >>> the universe is open or closed. >>> >> >> *Hypersphere; closed; if you believe it's age is finite. AG * >> >>> >>> >>>> *> light never exactly returns to its starting point. That's just an >>>> approximation * >>>> >>> >>> That's what happens in a de Sitter universe, its flat and open and you >>> get a de Sitter universe if the universe is not dominated by matter but by >>> the Cosmological Constant, which is probably Dark Energy. >>> >> >> *Since it's not perfectly homogeneous, a beam of light can be bent, this >> way and that way, so it's unlikely to return exactly to its point of >> origin. You know, what we OBSERVE and MEASURE is an expanding universe, so >> an ad hoc insertion of an infinite spatial extent is suspect. AG* >> > > *It's like a leaf on a tree. The leaf is our universe, closed and finite > in spatial extent. It's attached to what I've called "the substratum", > analogous to a tree, possibly infinite in spatial extent and having an > infinite past. Let's call it "the Tree of Life". Our universe is connected > to it, has been since the BB, which is why it's expanding, like a leaf > growing. AG* >

*A fruit tree is a better analogy, since most fruits are approximately spherical, as is our universe (hyper-spherical); observable and non-observable regions. It must be somehow connected to its source or origin, but how that connection manifests is currently above my pay grade. The problem with current models of a flat universe is that the infinity of spatial extent implied, seems like an ad hoc hypothesis, not organically connected with the rest of the theory. AG * > >> Already about 74% of the matter/energy in our universe is in the form of >>> Dark Energy, and as time progresses that percentage can only increase and >>> we'll get closer and closer to a pure de Sitter universe. That's because >>> the Cosmological Constant is a property of empty space, so as the >>> accelerating universe creates more space it also creates more Dark Energy, >>> however the total amount of matter (both regular and dark) remains fixed. >>> And in a de Sitter universe the distance between any 2 non-accelerating >>> points will, given enough time, eventually be moving apart faster than the >>> speed of light. >>> >>> >>>> *> **Let's forget it. These discussions are worthless.* >>>> >>> >>> It appears you are not following your own advice. >>> >>> 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e5052199-9914-4a56-bcb1-a78bd7441095%40googlegroups.com.