On 1/15/18 1/15/18 3:30 PM, Gary Harnagel wrote:
On Sunday, January 14, 2018 at 9:42:10 AM UTC-7, Jonathan Thornburg [remove
-animal to reply] wrote:
begin analogy

Imagine an infinite static Euclidean universe (i.e., flat spacetime, no
gravity involved) filled with (stationary) fog which both emits and
scatters (visible) light, and consider a (stationary) observer in that
fog. Now suppose that at a time which we will label t=0, two things happen:
* all the fog suddenly condenses into larger water droplets, and * those
water droplets no longer emit light. Since the scattering cross-section of
large water droplets is vastly smaller than that of fog, the result is that
at t0, the sea-of-droplets is mostly transparent to light (certainly much
more transparent than the original fog was). In other words, at times t0
light basically travels in straight lines, with little scattering,
emission, or absorption.

What will our observer see at t=1 year?

Since at t0 there is minimal scattering, emission, or absorption, we see
that at t=1 year our observer will see (receive) those photons, and only
those photons, which were (a) exactly 1 light-year away from her at t=0,
and (b) travelling directly towards her at t=0. This holds in any
direction our observer looks. In other words, at t=1 year our observer
will see a uniform glow on her "sky".

At t=2 years our observer will will see those photons, and only those
photons, which were (a) exactly 2 light-years away from her at t=0, and
(b) travelling directly towards her at t=0. This holds in any direction
our observer looks. In other words, at t=2 year our observer will see a
uniform glow on her "sky". But that glow is comprised of a *different set
of photons, emitted at a different set of events* than was the glow she saw
at t=1 year.

Etc etc for any other time t0.

end analogy

As you can see, this analogy reproduces many of the features of the CMBR.
It doesn't reproduce the CMBR's temperature -- for that you need a
cosmological redshift between the last-scattering time (t=0 in the
analogy, approximately 0.5 million years after the big bang in standard
cosmology) and today. But the analogy does produce an all-sky uniform glow
seen by all observers, even at far-future times.

I like your fog analogy; however, let's consider the case where the fog
consists of photons [...]

That is not the analogy. As the first sentence says, the fog "both
emits and scatters (visible) light". The correspondence to the
cosmological model and CMBR:
fog = primordial particles
water droplets = atoms
(visible) light = CMBR

At "recombination", z ~ 1100, the cosmological expansion had reduced
the average energies of primordial particles (protons, deuterons,
alphas, electrons, ...) so much that they could form stable atoms
(mostly hydrogen and helium). Suddenly the universe became nearly
transparent to electromagnetic radiation. Today we see CMBR photons
whose time of last scatter was ~ 13 gigayears ago.

At and after recombination, the energy of the CMBR photons is far
too low for pair production (threshold = 1.022E6 eV). During
recombination the CMBR photon energy peak was a few eV; today it
is 6.624E-4 eV.

BTW there should also be a cosmic neutrino background, which decoupled
much earlier than photons. It would be very interesting if this
could be detected.

Tom Roberts