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Re: Old Stars/Olber's Paradox



Jim G. wrote:
David Bowman has this wonderful bent of giving vivid and compact overviews
of the issue ...

This is a joke, right? I don't know about vividness, but compactness does not
characterize my posts. (I do wish I could find better ways to say what I have
to say with far fewer words.)

Indeed, I find myself wondering what measurement can distinguish between a
distant galaxy's fleeing ours (*into* space) with some Doppler velocity and
a "stationary" distant galaxy with the space expanding between us and it.
Is there any more than the Hubble Red Shift? And why can't a distant galaxy
have a velocity within the Universe *and* the space of the Universe expand?
How can I tell the difference? I wonder if this is a meaningful question. (:-)

This is indeed a difficult observational problem to contend with. Ordinary
Doppler shifts and the cosmological red-shift of the Hubble expansion of space
are observationally the same. This problem is the single biggest source of
uncertainty in the measured values of the Hubble constant H_0. In practice
the galaxies and galactic clusters are not exactly at rest in comoving
coordinates, but have their own local haphazard and orbital motions with
respect to each other. This means that the ordinary Doppler shifts of the
galaxies are on top of the cosmological red-shift. For the nearby galaxies
the cosmological red-shift (being proportional to distance) is tiny compared
to the Doppler effect due to the local galactic motions. This means that in
order to accurately measure the cosmological expansion rate the cosmological
red-shift of the galaxies must dominate over the local motions the galaxies,
which, thus, must be very distant. The trouble is that it is very difficult
to independently measure the distance to these distant galaxies apart from
their red-shifts. The distance to the close by galaxies can be measured by
looking at the individual bright Cepheid variable stars in them (since they
have a known absolute luminosity). The distant galaxies are too far to see
even the brightest separate stars in them. Thus estimating their distance
requires indirect statistical extrapolation techniques which are calibrated
with the supposedly known distances to the nearby galaxies. Such techniques
tend to be fraught with uncertainty.

4) The luminous matter of the universe is hierarchically
arranged in a fractal arrangement whose Hausdorff dimension
is less than 3 so that the sources of light are a set of
measure zero in space (yielding an average density of zero)
allowing there to be not enough light sources to light up
the sky in most directions.

Now this is new thinking to me. Is this commonly discussed? A bit of a
tutorial would help here -- at least for me -- others??.

Try looking in Mandlebrot's books on Fractals. Also, I think I remember that
this possibility was first discussed by Fournier.

Well yes, David, that is why the background is at 3K, but why can we *see*
it?. I think the answer is that, if we assume that c has been constant since
the BB (we don't have much of a choice but to assume this), that space has
been expanding with the Universe (an unnerving thought), and that the
expansion of space has been <c (but what if it hasn't?), then the photons
have had more than enough time to fill the Universe no matter what the
mechanism of the BB.

I would change the last sentence above so that the phrase "fill the Universe"
reads "fill the *observable* Universe". It is only the photons from the part
of the universe which is within the light-travel-time horizon of us which have
had more than sufficient time to reach us. Light from the more distant
reaches of the universe hasn't got here yet. This is essentially because the
farther away the source, the faster its separation in space is growing between
the source and us. The most distant sources have been receding from us faster
than c, but because the overall cosmic expansion is slowing down with time,
their recession rate is also slowing down, thus allowing the light from them
to eventually reach us.

BUT this doesn't answer for me why I can see quasars (or Q's flashlight) --
which is where we were in the Old Star thread. ...

Try re-reading my previous (probably much too obscure) posts on this thread.
I believe the answer *is* in them somewhere.

David Bowman
dbowman@gtc.georgetown.ky.us