Re: Old Stars

[Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us]

This is a repost of a post of mine which was originally sent 07/08/96,
14:05 EDT and which seems to have been lost and/or mangled in cyberspace.  If
you receive both this post and the original one please delete at least one of
them and accept my apology for cluttering up your mailbox.

On Fri, 5 Jul 1996 19:04:53 -0400 David Abineri asked the following:      
> ...
> When we look at the oldest stars we can see, we are looking back to
> a time just after the big bang. How is it that we (planet earth) have
> arrived 'here' before the light that left those stars?
> ...

After getting some responses that did not satisfy him he later wrote:
> ...
> We are in a particular place in space relative to where the big bang took
> place (or where early stars were first formed). Light from an early star
> traveled that distance at the speed of light (of course) during the
> lifetime of that star, say 5 billion years just as an example. Now, 5
> billion years later, the Earth and solar system are formed. and 5 billion
> years after that, intelligent life appears. (this is a *very* rough
> chronology)
>
> Now, my question is, how can that life form ever hope to capture any of the
> light from that early star. If it is able to, then that must mean that the
> materials from which earth is formed, which also originated with the big
> bang (although were parts of other stars and planets before coming together
> as our solar system) must have traveled faster than light in order to have
> arrived HERE before the light that we now observe from that early star
> which is only just arriving now!
>
> This seems to be like the thought experiment where one leaves the earth
> and travels faster than light in order to look back at the earth and see
> its history unfolding.
>
> What am I and my students missing here?? Thanks for your collective help.

To this Jim Green responded:

> Let me try to clarify the question a bit -- maybe we can get a better response
> . ...
> But let's talk about quasars, light sources older than stars.  These formed
> 15\9yrs ago -- give or take a year or two.  These objects no longer exist
> presumably having decayed to galaxies or such. So the light we see left them
> some 15\9yrs ago and so it has traveled a distance of 15\9ltyrs.  But the
> interstellar matter Sol was made from can't travel at anything like c, so if
> Sol formed 5\9yrs ago and we some time after that, it must have formed well
> less than 5\9ltyrs distant from the bang.  
>
> Hence, the relative flash of the quasars of 15\9yrs ago must have passed
> this spot in the Universe long ago.  By some watches at least 10\9yrs ago --
> when even the interstellar matter hadn't arrived here.  Even the large star
> which went super nova to nucleate Sol hadn't even formed yet!  So how can we
> see the quasars now?  
>
> Is that your question?
>
>
> At this point we might be regaled with stories of curved space-time and how
> the quasar flash has made several orbits around the circumference of the
> Universe as the Universe AND space have been expanding.  But don't believe a
> word of it.

I think that the main problem here is a confusion as to the nature of the
Hubble expansion of the universe.  It seems from David A.'s posts that he and/
or his students think of the big bang as an outward (in space) explosion of
matter from a particular point in a pre-existent space(time).  For instance,
he asks "How is it that we (planet earth) have arrived 'here' before the light
that left those stars?".  The matter that the earth is made of is NOT thought
to have been blasted out to 'here' from a center-of-explosion somewhere else.
There is no race between the outward moving matter (which later formed the
earth) and the light of distant ancient stars [actually galaxies and quasars]
which left them much earlier, near the center of the blast when the "fireball"
had a much smaller size, such that the matter had to outrun that light for
about 15 billions of years so that the light is just now overtaking the matter
out where we are.  The Big Bang is NOT thought of as having happened at a
particular point in space and in time.  Rather, it happened at ALL points in
space at a particular point in time (actually, at the beginning of time).  The
BB happened 'here' just as much as it happened anywhere/everywhere else.  This
is because *all places* were *very* close together then.  Since the BB the
"fabric" of space has been stretching (more or less) uniformly (not counting
local perturbations and not counting the "inflationary era" between 10^-35 to
10^-32 sec after the BB).  It is space itself which is expanding.  The matter
has been, for the most part, just "hitching a ride" on the expanding space.
On a large enough length scale the matter is everywhere locally "at rest" with
respect to the local reference frames in which the expansion is viewed as
isotropic.  Thus the particles of matter (i.e. galaxies) are not moving away
from each other through a preexistent, previously empty, space, but are, in a
sense (in comoving coordinates), actually at rest w.r.t. each other.  The
distance between the galaxies is only growing because the "fabric of space" is
stretching and "new space" is continuously being created between the galaxies.
(Remember the analogy of the continuously inflating balloon or of the
stretching infinite rubber sheet with spots (galaxies) painted on it.)

Now suppose (as is the case is the inflationary cosmologies) that the universe
is infinite in spatial extent and "flat" on a large enough length scale.
(This is a 3-d version of the uniformly stretching rubber sheet model.)  When
light is emitted from one galaxy and travels toward another one its wavelength
is stretched "en route" as the space through which it is propagating is
stretched.  This causes the receiving galaxy to receive red-shifted light.
The amount of the red-shift is a direct measure of the distance and time over
which the light ray has been propagating to get there.  When we look at light
from a distant young galaxy or quasar which left the source shortly after the
BB, it just means that for most of the time since the BB the light beam has
been travelling toward us and just now has finally reached us.  There is,
presumably, a "horizon" at a radius of about 15 billion ly or so beyond which
the light from those sources hasn't had time to reach us yet since the BB.
There is also another further "horizon", beyond which light from those regions
beyond it can never reach us in the future (if the Hubble expansion rate
settled down to a finite non-zero value in the asymptotically distant future)
since those sources are so far away that the stretching of space is causing
them to move away from us faster than c.  We are literally outrunning the
light from them.  This would always be the case in an open hyperbolic space
with not enough "dark matter" to close the universe.  In the borderline flat
space case which just barely has enough matter to halt the Hubble expansion, I
believe I recall, the expansion rate will slow down more and more allowing the
light from regions which would have been forever beyond the second horizon to
eventually catch up with us.  This is because a place in a region which is
receding from us faster than c now will eventually be receding from us slower
than c in the distant future, allowing the light from that place to eventually
reach us.  Whether or not all places, no matter how distant, will eventually
become causally connected in the flat space borderline universe is something
that I am not sure about right now.  I would have to consult a GR book, and
none of mine are handy right now as I am posting from home and am not in my
office at the moment.

Note to Jim G., I did not mention the phrase "curved space-time" in the above 
explanation (although I did say "stretching of space") and I certainly don't
advocate that light from a quasar "has made several orbits around the
circumference of the Universe as the Universe AND space have been expanding".

David Bowman
dbowman@gtc.georgetown.ky.us

P.S.  My apologies to Alex Burr for mistakenly thinking he anonymously sent
the garbled/merged message.  My mail reader doesn't show the ARPA header on
my mail so any post without a signature at the bottom appears to me as
anonymous.  I hope Dick has fixed whatever problem there was with the server.