On Friday, September 13, 2024 at 4:06:49 AM UTC-6 Alan
Grayson wrote:
On Thursday, September 12, 2024 at 11:07:49 PM UTC-6
Alan Grayson wrote:
On Thursday, September 12, 2024 at 11:00:21 PM UTC-6
Brent Meeker wrote:
On 9/12/2024 9:21 PM, Alan Grayson wrote:
On Thursday, September 12, 2024 at 3:55:45 AM
UTC-6 Quentin Anciaux wrote:
Le jeu. 12 sept. 2024, 11:53, Alan Grayson
<[email protected]> a écrit :
On Thursday, September 12, 2024 at
2:40:56 AM UTC-6 Quentin Anciaux wrote:
I just gave you a full proof that
as long as the expansion is uniform
and expansion rate > 0, then it
follows objects will sooner or
later recess from each other at
speed > c.
What was the justification for the
geometric progression? I made no such
assumption in my "proof".
As explained multiple times and in the
quote you made, expansion is uniform and
happens at every point in space.
What bothers me about your method is that
you*assume* a geometric increase in the
separation distance, when, IMO, that's the
variable that must be calculated (which I did).
So no matter how many times you affirm your
proof as valid, I can't agree. AG
You didn't calculate the expansion parameter,
which is the Hubble constant. It's an observed
value.
Brent
Why must I do that, when I just want to show that
eventually the recessional velocity exceeds c? Also,
I don't see why theta is fixed, when the end of the
arc defines the position of the receding galaxy. AG
Now I am not sure I proved the recessional velocity is
greater than c, after some time has passed. If the
sphere is expanding, then the distance between any two
fixed points on the sphere will increase as time passes.
But that was obvious due to the expansion. What's wrong,
if anything? AG
Now I see the light. We've been struggling to prove that a
receding galaxy will fall out of view if the universe is
expanding, but all the so-called "proofs" fail, but for
different reasons. What Quentin offers is not a proof. He's
just repeating a result done by someone else,*using
mathematics*, which he believes (and might be true). Brent
is mistaken in his apparent belief that the proof of concept
requires appeal to Hubble's law. This is also mistaken IMO
since the result to be proven depends *exclusively* on the
*geometry *of an expanding sphere. Finally, my proof also
fails, since it's obvious that the arclength, s, between
two galaxies on an expanding sphere, will obviously
increase as the sphere expands. That is, ds/dt will
obviously be positive since the arclength is increasing.
IOW, a constantly increasing arclength s, assuming a
uniformly expanding sphere, necessarily yields ds/dt > 0,
but it does NOT demonstrate that the velocity of the
receding galaxy eventually increases to be greater than c.
When I have the energy, I will calculate the *second time
derivative* of the arclength, s, hopefully to demonstrate,
that for a uniformly expanding sphere, the *four* terms of
the second derivative of s, imply a*positive acceleration*.
This will establish that eventually the receding galaxy will
pass out of view for the observer on the assumed stationary
galaxy. Comments welcome. AG
