On 7/19/2025 7:36 PM, Alan Grayson wrote:
On Saturday, July 19, 2025 at 6:48:18 PM UTC-6 Brent Meeker wrote:
On 7/19/2025 10:54 AM, Alan Grayson wrote:
On Friday, July 18, 2025 at 11:34:17 PM UTC-6 Brent Meeker wrote:
On 7/18/2025 6:49 PM, Alan Grayson wrote:
*And the farther away it is, the greater is its red shift
and recessional velocity. So the recessional velocity seems
to be DECREASING with time as the universe expands. *
The second does not follow from the first. Further away means
later in time. Further away is receding faster.
Brent
*Let me rephase that; first, consider the model of the universe
as an expanding sphere and two separated galaxies on that sphere,
say on the equator. As we discussed, it's an effect of geometry
that the rate of the separation distance increases depending on
the initial separation distance, and the red shift increases as
well as the separation velocity. *
Why do you write "as well as"? The red shift /is due to/ the
separation velocity.
*OK, no problem. AG*
*That's as time moves forward. Now we get the same result when we
consider time moving backward, as we look backward in time and
see the red shift and recessional velocity increasing. *
First you write "consider time moving backward" and then you write
"as we look backward"?? Are you considering time reversed
motion; bodies moving closer together? Or are you just thinking
of how things must have been ten or so billion years ago? Or are
you saying you're going to look at some distant galaxies, which
are implicitly far back in time from the "now" defined by distance
from the CMB? What are you measuring the recessional velocity
from? From some specific galaxy? Or from galaxies at some
specific distance? If you mean a specific galaxy then in the past
we were closer to it and therefore our recession from it was
slower. If you mean galaxies at a specific distance then the
Hubble parameter being constant means that recession velocity was
the same in the past.
*I'm considering galaxies in varying distances from our galaxy, so I'm
looking at recessional velocities in the past, and they are all
increasing. *
So you're considering recessional velocities from specific galaxies, all
of which are increasing and that implies that in the past all those
velocities were smaller.
*So, even though a now distant galaxy was close to the point in
spacetime which was where our galaxy came into existence, wasn't it
still receding rapidly from that location? *
No. Recession velocity is De. So if our galaxy came into existence
near another galaxy, D was small and our recession velocity */from that
galaxy/* was small.
Brent
*How then can anyone conclude that the separation velocity was small? AG*
Try thinking in terms of the Hubble parameter as constant. That
means space has been expanding by a constant multiplier, e>1, per
unit time. So our recessional velocity relative to galaxies at a
given distance D, is and always has been De. Once you've got that
straight you can consider models in with e changes with time from
the Big Bang, which is modeled by all those nice colored curves I
posted.
*There's my dilemma. Whether we go backward or forward in time,
two separated galaxies exhibit increasing red shift and
increasing recessional velocity. AG*
No, e is a constant. So if you consider two specific galaxies
their separation in the past was less and a smaller D means a
lesser recessional velocity De.
Brent
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