On Sunday, September 15, 2024 at 1:26:44 AM UTC-6 Alan Grayson wrote:
On Saturday, September 14, 2024 at 11:40:13 PM UTC-6 Brent Meeker wrote: On 9/14/2024 8:50 PM, Alan Grayson wrote: On Saturday, September 14, 2024 at 2:53:08 PM UTC-6 Alan Grayson wrote: On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker wrote: On 9/14/2024 12:30 AM, Alan Grayson wrote: But it's not a property of an expanding sphere without the condition that the expansion has a constant proportional rate; so the relative distances keep the same proportions. The further away something is the faster it is moving away. That's why your first assumption ds/dt=const gives a result inconsistent with Hubble's law, it doesn't keep theta constant for every point. Brent I never assumed ds/dt = const. Rather I calculated ds/dt and found it not surprisingly positive, which I concluded was insufficient to show ds/dt would eventually be > c. AG Hubble's law or something equivalent is necessary to give more definition to the problem. The balloon model does the same as Hubble's law; it posits that the expansion preserves proportions, i.e. if s=>s+ds then n*s=>n*s +n*ds. Brent I recall from years ago the proportion issue we discussed. Obviously, if r, the radius of sphere, increases by x%, so will any great circle on the sphere since its circumference also increases by x%, given the formula for circumference 2*pi*r. So, Hubble's measurements indirectly imply that the global geometry of the universe is spherical. AG Let's face it; Hubble's measurements strongly confirm an unexpected result; namely, that the global geometry of the universe is spherical, not flat, as I have previously articulated. AG Actually it appears to be flat, which means distances obey Pythagoras theorem, and infinite. It's the same in all directions, and so has rotational symmetry, which isn't exactly the same as spherical. Brent I should have written "approximately spherical" since the universe is not perfectly isotropic. But I prefer approximately spherical compared to flat because as we go backward in time, we can enclose the universe in a sphere, implying it is *finite *in spatial extent (not infinite). A physicist I was in contact with, objected to this model on the grounds that I hadn't taken into account the *Unobservable* universe, which could be infinite. It then occurred to me that the Unobservable universe was plausibly created during Inflation, when in a mind-boggling short time interval, the universe underwent a *HUGE* expansion in space, much much faster than the speed of light. I pointed out this possibility to the physicist I was in brief contact with, but he never replied. Very recently I posed this conjecture (which I have no possible experiment for testing it) to Alan Guth. I also asked him, when he assumes the universe was around the size of a proton when Inflation began, was he referring only to the Observable universe, or both hypothetic parts, Observable and Unobservable. Did he make any distinction among the possible choices? I am hoping he will reply. AG One other thing; if the universe is approximately spherical and expands forever, it will become *asymptotically* flat, but never actually, mathematically flat. Moreover, it's likely to be so large now, that our measurements cannot distinguish between actually, mathematically flat, and extremely small but positive curvature. AG -- 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/b64202aa-f3e2-4f23-a636-2e3b78043f69n%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/b64202aa-f3e2-4f23-a636-2e3b78043f69n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- 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/98667022-f509-4c84-9ec4-dc3adfc1847fn%40googlegroups.com.
