This week, we have a challenge episode for you.
We've been talking about the Big Bang theory a lot recently,
and the most important piece of evidence for this theory
is the cosmic microwave background radiation.
It tells us that the universe was once
most certainly much smaller, hotter, and denser
than it is today.
The photons of the cosmic background radiation
were released when the universe was around 380,000 years
old, and had just cooled down enough for the hydrogen
plasma that filled the universe to become hydrogen gas.
Free electrons were captured by protons
to form the very first atoms.
In the process, the distance that the average photon
could travel went from not very far
to greater than the length of the entire observable universe.
When we look at the CMB today, we really
are looking at the universe from 13.7 billion years ago.
We're looking at an ocean of orangey, red-hot plasma that
would later collapse into galaxies, and people,
and stuff.
OK, here are some episodes on the CMB of you.
Today, I have two questions for you
about how far those CMB photons actually traveled.
The first one is purely conceptual
and requires no math, while the second most definitely
requires math.
Choose only one to answer.
The advantage of trying the harder one
is that you'll be competing against fewer people,
but that won't help you if you get it wrong.
So here we go.
The universe was much smaller when the CMB light was emitted.
In fact, all of those blobs of plasma were a mere 43 million
light years away from the patch of space that would later
contain the Milky Way.
Back then, this patch of space just
contained a slight over-density of plasma
that looked pretty much the same as the rest of those blobs.
However, the light from the CMB had
to travel a lot further than those 43 million light years
to reach this patch of space because it was traveling
through an expanding universe.
By the time it reaches us, right now, the universe
has expanded so that the galaxies and clusters
that those blobs evolve into are now 1,100 times further away,
giving us an observable universe that's
93 billion light years across.
So first question-- what physical distance
did that light from the CMB travel
through an expanding universe to reach us today?
Seriously, no math required.
OK, and the math-y question-- just before the CMB was
created, the universe was filled with this plasma
that consisted mostly of protons, electrons, and helium
nuclei.
That plasma was effectively opaque
because photons couldn't travel far without bouncing off
all those free electrons.
The universe became transparent when
it cooled enough for those electrons
to be captured by protons to form the first hydrogen
atoms in an event called recombination.
The question is what average distance could a photon travel
before being scattered by an electron
just before recombination?
The only hint I'll give you is to tell you
some of the numbers you will need to look up or figure out.
You'll need an estimate of the baryonic mass and volume
of the observable universe, you'll
need the redshift of the CMB, and the Thomson Scattering
Cross-section.
Your answer doesn't have to be too accurate.
Within a factor of two or so is fine.
You should be able to get a good estimate with some pretty
simple calculations, but you must
show me those calculations.
E-mail your answers to pbsspacetime@gmail.com
within two weeks for a chance to win a PBS Space Time t-shirt.
We'll randomly select three correct answers
for each of the two questions.
Your submission should use the subject line CMB Challenge.
We filter by subject line, so make sure
you use exactly that phrase.
You should just submit one answer,
and please don't discuss the problem
in the comments or anywhere else online, let alone
give your answers there.
If you do, you're disqualified.
I also have a quick announcement.
This coming Monday, March, 14th, I'll
be participating in a public seminar on the new LIGO
discovery of gravitational waves.
It's at my own Lehman College in New York City.
If you're in the area and would like to attend,
please RSVP to pbsspacetime@gmail.com
with the subject line NYC Gravitational Waves.
And as long as we still have space,
you'll receive full details.
You'll learn way more about gravitational waves
than on any YouTube show.
Happy physic-ing, and see you next week
for a full new episode of Space Time.
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