On Sunday, January 14, 2018 at 9:42:10 AM UTC-7, Jonathan Thornburg [remove -animal to reply] wrote:
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Gary Harnagel wrote:
I'm having trouble picturing why we should see the CMBR at all. Since it's
traveling at the speed of light but we're moving somewhat slower, shouldn't
it have passed us long ago? I know, the FLWR metric must have something to
do with it, but ...

To try to answer Gary Harnagel's question:

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 hope this makes things a bit clearer (no pun intended).

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
currently visiting Max-Plack-Institute fuer Gravitationsphysik
(Albert-Einstein-Institut), Potsdam-Golm, Germany

Thanks, JT.

I like your fog analogy; however, let's consider the case where the fog
consists of photons which begin in some finite volume of space. They
would be moving in random directions at c and, presumably, would
interact in some process to create particles with mass, conserving
energy and momentum. But pair production can't satisfy both energy and
momentum conservation unless there is some other mass that can absorb
the excess of one or the other, yes? Of course, the big bang has the
same problem, as well as the problem of having equal parts matter and
antimatter.

Anyway, the created particles will still have kinetic energy and will
disperse, but at lower speeds than the unconverted photons. So my
original question is still unanswered by the fog analogy.