Thanks to Brilliant dot org for sponsoring
this episode.
Hey Crazies.
There’s a number that gets thrown around
a lot for the age of the universe.
Even I’ve used it a few times:
13.8 billion years ago.
13.8 billion years ago.
13.8 billion years ago.
13.8 billion years ago.
13.8 billion years.
13.8 billion years ago.
Of course, Dave S has to show up and ask where
that number comes from.
How dare you make me work!
Ha! Just kidding. I love this stuff.
Anyway, the age of the universe isn’t something
we can measure directly.
We need data.
We need models.
And we need to make some assumptions,
but we’ll make sure those assumptions are
reasonable.
After we have all that, we can calculate the
universe’s age.
Well, kind of. I’ll come back to that.
First, Data!
No no, not Data the person, scientific data.
There we go.
These numbers are all from the Planck space
telescope.
Well, technically speaking, that’s not data.
That’s results.
All Planck could really measure was light
frequency data.
I took everything pedantic about myself and
I put it into you.
What was I thinking?
So he’s right as usual.
The Planck telescope only measures light frequencies
in the microwave range.
This is Cosmic Microwave Background or CMB.
It’s a map of the distant sky in every direction.
Different colors represent slightly different
peak frequencies or temperatures.
Emphasis on the word “slightly.”
The detectors on the telescope are very sensitive.
If they had the same sensitivity as your eyes,
it would look like this,
which isn’t much to look at.
But it does support two basic assumptions
we need to make:
One.
The universe is homogeneous,
which means it looks the same no matter where
you are inside it.
And two.
The universe is isotropic, which means
it looks the same in every direction from where you are.
Basically, on the grand scale, there’s nothing
special anywhere.
The CMB is not the only data we have that
supports these assumptions,
but it’s pretty clear cut evidence.
When we take the sensitive details into account
though, we can actually infer quite a bit
more about the universe.
Like these things, many of which have been
backed up by other evidence.
Astrophysicists keep themselves very busy
with this stuff.
In fact, here’s the age of the universe
right here,
which was calculated using this information
here.
Emphasis on calculated.
So how was it calculated?
That’s where the model comes in!
Ok, let’s get all our ducks in a row.
We need to know how events in space-time are
separated,
How the energy inside that space-time behaves,
and how those two things are related to each other.
Event separation is described by something
called a space-time metric.
In this case, the Flower Metric.
If you were to divide the universe up into
infinitely small points,
this tells us their size and shape.
The “k” tells us how space is curved.
You can see direction is independent of that,
which makes sense, since we already assumed it was isotropic.
We happen to know from the Planck data
Results!
We happen to know from the Planck results
that we have the exact amount of energy
to smooth out all the curvature.
Space is not curved on the cosmological scale.
So our metric looks a little simpler, but
we’ve got one more part to worry about.
This “a” is called the “Scale Factor”
because it tells us the scale of universe.
For simplicity, we define the current value
of that to be one.
But that changes over time, so we need it
to keep it in the model.
Next, we want to know a little bit more about the
stuff inside that space-time.
That’s where the stress-energy tensor comes
in.
It tells us how much energy there is at any
particular event
and all the different ways that energy could
affect its surroundings.
Gravity isn’t about mass.
It’s about energy.
And there is a lot of energy in the universe,
but, on the grand scale, it’s not doing
anything particularly complex,
so we’ll say there’s a little pressure
and that’s about it.
Then, we relate these two things through Einstein’s
equations
and we get something called the Friedmann
equations.
This is their true form, but it makes more
sense to write them like this.
These tell us how fast space is expanding
and how much that rate is changing.
You can see they each depend on a few things.
We have some of that information from the
Planck space telescope,
everything except the pressure.
Right now, there really isn’t any pressure.
But if you plug in zero,
the age of the universe comes out to be
9.7 billion years,
which doesn’t make sense.
There are globular star clusters in our own
galaxy older than that.
Just because I did some math, that doesn't 
mean anything.
We need to make sure it actually applies to
our universe.
While there isn’t any overall pressure in
the universe now,
there certainly was in the distant past.
Hmm, we need an equation of state.
We need some way to relate the pressure to
the energy content.
That’s tricky at best and impossibly
complex at worst.
The main problem we run into is that our timeline
of the universe is split in two,
right here at the formation of the CMB.
Most of the events that happened after that,
we can see with telescopes.
Everything before that, we need data and models
from particle accelerators.
The further back in time we go, the higher
the energies are.
So far, in the Large Hadron Collider, we’ve
gotten up to 13 tera electron volts,
which only puts us back to the Electro-weak
Epoch.
Anything before that would be highly speculative.
With all this in mind, let’s at least try
to get a number that makes sense.
The purpose of the Friedmann equations is
to solve for the scale factor.
By definition, the scale factor currently
equals 1.
If we project into the future, we see the
inevitable heat death.
That’s the death of heat.
Projecting into the past, we can see the age
of the universe.
It’s just measured horizontally from the
beginning of the graph to now.
All current knowledge considered, that comes
to 13.8 billion years old.
But don’t forget the equation of state problem.
We don’t really know much about the universe
during this period.
It might have only lasted a tiny fraction
of a second.
But it’s entirely possible that it lasted
a billion years or an infinite amount of time.
Our concept of time might not even make sense
back then.
Without an equation of state, we simply can’t
know for sure.
So, the 13.8 billion years isn’t really
the age of the universe.
It’s just how far back our current knowledge
of the universe goes.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like
to keep up with us.
And if you want to see more of the math I
kind of glazed over,
check out this great blog post by Robert Low.
It’s actually what inspired this video in
the first place.
Link in the doobly doo.
And, until next time, remember, it’s
OK to be a little crazy.
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Several of you commented about how the GPS
unit doesn’t have its own atomic clock.
Yes, that’s true.
It would make it impractically expensive.
It uses the satellite clocks instead to find
out the exact time before finding your location.
It gets atomic clock accuracy for free.
Sorry I forgot to mention it and thanks for
watching!
