On 12/25/2018 4:42 PM, [email protected] wrote:
On Tuesday, December 25, 2018 at 11:26:14 PM UTC, Brent wrote: On 12/25/2018 8:01 AM, [email protected] <javascript:> wrote:On Tuesday, December 25, 2018 at 1:16:53 PM UTC, John Clark wrote: On Mon, Dec 24, 2018 at 3:21 PM <[email protected]> wrote: >> You can never prove that any physical quantity is exactly zero, but we do know from observations of the cosmic microwave background radiation that if the universe is curved at all it is by less than one part in 100,000. /> Agreed. However, IMO the observed universe cannot be flat with exactly zero curvature (which I refer to as "mathematically flat) since that would imply infinite volume / If information can't travel faster than light then by definition the radius of the spherical volume of the universe you can observe can't be larger than the age of the universe in years times a light year. *> */which contradicts its finite age./ There is no reason spacetime couldn't extend a finite distance into the past but an infinite distance into the future. *The observable universe could continue to expand forever, but it always has a finite radius. We have no information about the unobserved part, so it could be any size, maybe even tiny. AG*All of those inferences are based on the universe obeying Friedman's equations, i.e. Einstein's equations for a homogeneous, isotropic universe. So they are inconsistent with the unobserved part of the universe obeying some other conditions. Whether there is a solution with the observable patch being different from the unobservable part is an open question. If you find one, publish it. But you can't just assume that because there's an unobserved part that it could be anything.*If we don't know anything about the unobservable part of the universe, it could obey any conditions; maybe consistent with the Friedman's equations, maybe not. I was just saying we can't assume anything. AG*
And I'm saying you can't say the observable part of the universe satisfies the Friedman equations and the rest of can be anything. That the rest of the universe is constrained by what the observable part is like is a consequence of Einstein's equations. Could Einstein's equations be wrong? Sure they could, but they've passed every test, so applying them is not an assumption.
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