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
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