🚀 go-pugleaf

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>Actually it was the explanation of Olber's paradox in your FAQ that
>prompted my question.  You account for the paradox in terms of
>redshifting starlight downwards (4) and the age of the universe (5).
>So it occurred to me that if indeed the bulk of the 6000K starlight
>that *has* reached us so far has been redshifted down so far as to
>appear to have vanished "into obscurity," maybe it hadn't completely
>vanished but had become the 3K background radiation.

In a way your original thought was on track.  At one point, when
the universe was much hotter (and the observable part much smaller)
the blackbody radiation was a uniform blaze of light.  It has since
redshifted away into microwaves.  (The energy density of stellar luminosity 
*now* is much greater than the CMBR energy density now.)  On the other hand 
the finite age of the universe means that not every line of sight can hit a 
star.

>Meanwhile Ben Zellner sent me email to the effect that the *shape* of
>the 3K radiation was the clue.  It is the right shape for blackbody
>radiation from a *fixed* temperature, and is presumed to be that
>temperature at which atoms formed and the plasma became transparent
>(the "big flash"?).  Black-body radiation summed over the distribution
>of temperatures of stars yields a different shape from what one gets
>with a fixed temperature.

>I found this somewhat convincing but not completely so since it left
>open the possibility of some combination of temperature and distance
>distributions that could fake single-temperature radiation.  Too big a
>coincidence?  Nowhere near as big a coincidence as required for the
>FAQ's (3), stars lined up to hide behind each other.  ...

This is why nobody believes explanation number 3 in the FAQ.  It is
in there for historical reasons and as a straw man.

>In addition it raised a question in my mind as to why all the radiation
>from the "big flash" *was* characteristic of a single temperature, i.e.
>why has it all been downshifted the same amount.  Shouldn't the parts
>of the flash that appear further away from us reach us at a lower
>temperature?  Or was the universe so small back then that all parts of
>it would now appear equidistant to any modern observer?

Uh, I'm not sure what you're thinking here.  In the standard hot
big bang, there is a hot sea of photons and other particles in
thermal equilibrium.  As the universe expands, the gas cools; as it
cools through certain temperatures, interesting things happen:
quarks combine into nucleons, nucleons combine into the light nuclei.
Then at a certain temperature the photons do not have the energy
to keep the protons et al ionized.  The protons and electrons
combine into neutral hydrogen, which couples much more weakly to
the photons, so that the hydrogen and radiation no longer are in thermal
equilibrium.  From this point on the radiation cools away independently
of the matter.

We see the CMBR as a cooled version of the "last scattering surface,"
which is when the decoupling occurred.  The CMBR photons being 
detected now were emitted ~10 Gyr ago from a 3-sphere around us, of
radius such that they get here now.  There isn't really a "flash,"
but such as it was, we don't see any "further" parts of it.  It's
all at the same radius.  As time goes by, obviously, we are seeing a 
3-sphere of larger radius.

>Furthermore as the plasma continued to cool, presumably it continued to
>radiate.  Why doesn't that contribution skew the shape away from a
>single-temperature shape?  Is it because the amount of radiation
>decreases with the 4th power of the temperature, and hence the skew
>must be negligible?

Remember, we're "seeing" the photon gas at one single cosmic time, the
time of decoupling.  But the photons in it have come a long way and gotten 
redshifted in the process.

>Vaughan Pratt				There's no truth in logic, son.

"Die Logik muss f\"ur sich selber sorgen."