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
