Hello!
In this lecture we'll learn how Hubble's law
tells us the age of the universe, how expansion
of the universe affects distance measurements,
and why the observable universe has a horizon.
We left off with Hubble measuring the distances
to galaxies, and the finding that the farther
the galaxy, the faster its velocity away from
us.
We also learned that Hubble's law says the
velocity of a galaxy is proportional to the
Hubble constant times the distance to the
galaxy.
But what does all this mean for our universe?
The fact that distant galaxies are moving
away the fastest implies something fundamental.
Our universe is expanding.
When I was a young sprout and first learned
about expansion of the universe, I thought
everything was expanding- me, coffee cups,
rulers, everything.
But this isn't what's going on.
It's the space between galaxies that is expanding,
not the stuff inside the galaxies.
Within galaxies and galaxy clusters, there
is enough gravity to hold things together.
We observe that galaxies across the universe
are moving away from one another.
This implies that galaxies must have been
closer together in the past.
Tracing this convergence back in time, we
reason that all the matter in the observable
universe started very close together.
The entire universe came into being at a single
moment.
But the universe isn't expanding into anything.
There's the universe, and that's it.
Worse yet for our brains to think about is
that the universe doesn't appear to have a
center or an edge.
The distribution of galaxies appears to be
relatively smooth, meaning that no matter
where you look or where you live in the universe,
the overall appearance of the universe is
the same.
The idea that matter in the universe is evenly
distributed, without a center or an edge,
is often called the cosmological principle.
The cosmological principle has not been proven
beyond a doubt, but it is consistent with
all observations to date.
We can use Hubble's constant to determine
how long the universe has been expanding,
which is essentially the age of the universe.
The velocity of anything is the distance it
travels over the time it takes to travel that
distance.
To see how long it takes to get somewhere,
you divide the distance you traveled by your
velocity.
For example you drive for 100 miles at 50
miles per hour, it takes you 2 hours.
We can calculate how long galaxies have been
speeding through the universe in the same
way.
We know their velocities from observing the
Doppler redshift.
The distance we can obtain via Hubble's Law.
The time since that the universe has been
expanding is equal to one over the Hubble
constant.
The age of the universe is, then the inverse
of the Hubble constant.
A larger Hubble constant will give us a younger
universe, and a smaller Hubble constant will
give us an older universe.
For a Hubble constant of 22 kilometers per
second per million light-years, we calculate
the age of the universe to be about 13.6 billion
years.
We've been assuming a constant rate of expansion.
But what if the universe was expanding more
quickly in the past?
If that were the case, then the universe would
have reached its current size faster than
we think.
The universe would actually be younger.
If the expansion rate of the universe is increasing-
and we think it is, more on that later- then
the age of the universe would be greater.
You may have been wondering- if the universe
is expanding and galaxies are flying away
from us, then how do we ever really know how
far away something is?
Well, we can't.
For stuff that's nearby, universal expansion
isn't a problem, but for way distant galaxies,
distances can get confusing.
We therefore define the "lookback time".
This is the time it takes the light from a
distant object to reach us.
Lookback time is unambiguous.
If the lookback time is 600 million years,
the light really traveled through space for
a period of 600 million years to reach us.
To get an idea of how this works, imagine
our Milky Way and a distant galaxy 400 million
years ago.
A supernova explosion occurs in the distant
galaxy.
Photons of light travel in all directions
away from the supernova.
Because space is expanding, the distance between
the Milky Way and the galaxy gets larger.
The photons of light that reach us from the
supernova took 400 million years.
Therefore we say the galaxy has a lookback
time of 400 million years.
An object's lookback time is directly related
to its redshift.
The expansion of the universe stretch out
all the photons within it, shifting them to
longer, redder wavelengths.
We call this effect a cosmological redshift.
We can think of the redshift as being caused
by either the Doppler effect as the galaxy
moves away from us, or from the expansion
of space stretching the photons out.
For very distant galaxies it's preferable
to interpret the redshift as coming from the
expansion of space because as space expands
galaxies are being carried along with it rather
than flying through it.
I mentioned earlier that the universe doesn't
appear to have an edge.
But the universe does have a horizon beyond
which we cannot see.
The cosmological horizon marks the limit of
the observable universe.
It's a boundary in time, not space.
It exists because we cannot see back to a
time before the universe began.
The universe is about 14 billion years old,
so therefore the lookback time of the cosmological
horizon is about 14 billion years.
The distance to this horizon is in fact much
greater because of the expansion of space.
It's actually around 47 billion light-years.
I'll leave you here to ponder the enormity
of our universe.
Take care, and I'll talk to you soon.
