On 8/7/2025 10:17 PM, Alan Grayson wrote:
I finally was able to identify and resolve my confusion about Hubble's
Law. First, let's use a geometric model to establish that the
recessional velocity of distant galaxies increases as the universe
expands. For convenience, assume the universe is spherically shaped
and uniformly expanding, and consider two galaxies at distances of one
and ten billion light years removed from our own. As r, the radius of
the universe increases linearly, so will the separation distances of
these remote galaxies, since the arc distances to these galaxies, if
they placed e.g, on the equator, will also increase linearly. So in
some unit of time, if say the rate of increase is 10%, the closer
galaxy will recede by 10% of 1 billion light years, or 100 milllion
light years, whereas the most distant galaxy will recede 1 billion
light years in *the same time duration*. So clearly, in an expanding
universe, more distant galaxies will recede faster than nearer galaxies.
Let's now consider the light emitted from these galaxies. The light
reaching us left those galaxies 1 and 10 billion years ago
respectively. If their red shifts represent their recessional
velocities when the light was emitted, it would imply that in the
early universe those galalaxies were receding very rapidly, the
farther away *in time* they are, that is the more distant they are,
the more rapidly they must be receding.
Why not phrase this as the equally true statement, "The more distant
they are the more rapidly /*we */must be receding.", which is then
consistent with your first paragraph?
Anyway, I'm glad you resolved it to your own satisfaction.
Brent
But this contradicts the geometric model, wherein we have
inferentially proven the opposite; that in early times, those galaxies
were receding with *decreasing *velocity as their separation distances
from us was decreasing. So what the hell is going on?
The answer is that although the light emitted from those galaxies was
emitted in the distant past, the expansion of the universe distorted
those emissions as they propagated in our direction. That is, the red
shifts observed were caused by the expansion of the universe, and
therefore represents the current red shifts of those receding galaxies.
AG
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