So far, we have seen how do we measure 
the spacial scale of the universe, which 
is simply one over a Hubble constant. 
What about its temporal scale? What's the 
age of the universe? It turns out that we 
actually can't measure the age of the 
universe directly. 
However, what we can do is measure lower 
limits to the ages of all these things we 
can find. 
And, then presumably the age of the 
universe is just a little more than that. 
Several different possibilities exist. 
The first one. 
Is the globular star clusters, These are 
believed to be formed over very short 
time interval in the early universe and 
all stars in them have essentially the 
same age. 
Understanding the ages of star clusters 
or stellar populations is the basic 
fundamental thing in stellar evolution 
theory. 
So in principle we understand how the 
changes, by looking at their color 
magnitude. 
The second kind of thing that we can look 
at are white dwarfs. 
Again, these are inert, incandescent 
cores of low-mass stars that are now 
slowly cooling down. 
The cooling theory is fairly well 
understood, and by observing apparent 
luminosity function of white dwarf stars, 
you can estimate how old the, how old are 
the oldest ones. 
Another thing we can do, is estimate the 
age of the heavy elements, created in 
stars. 
Very high mass, elements, will tend to be 
radioactively unstable. 
And, if we can find long lived isotopes, 
of some of those elements, and measure 
their alter abundances, we can estimate 
the age of those elements, which 
presumably came from supernova 
explosions. 
Some of the very first stars. 
This is very similar to the carbon dating 
that's often used on planet Earth. 
That is somewhat model-dependent, because 
it depends on when the Supernova were 
exploding, but the upper limit of that 
would, again give the lower limit, the 
age of the universe. 
And finally, we could model Stellar 
populations, in a similar way that we 
model, star clusters. 
But that turns out to be much 
complicated, and, it's really not used to 
constrain the age the universe. 
The fundamental measurement here, is 
estimating the ages of globular clusters, 
which are almost as old, as our galaxy 
itself. 
This is based on a well established and 
well tested theory of stellar evolution, 
which predicts so called Isograms which 
is color magnitude diagrams and the paths 
that, main sequence and the giant branch 
will have, at any given time. 
They look like this, the main sequence 
turn-off, moves to ever lower masses. 
Lower luminosity as time goes on, and 
then stars ascend the giant branch. 
So, by measuring where the main sequence 
turnoff is, and where the giant branch 
is, we can fit the models and find out 
how old the cluster is. 
Likewise, the difference between the 
turnoff, and the position of the 
horizontal branch is another age 
indicator. 
The isograms will depend slightly, on the 
chemical composition of stars in the 
cluster. 
So there are many uncertainties, in those 
estimates but the biggest one of them 
all, is the uncertainty in the distance 
to the globular clusters. 
Stellar evolution models are pretty good 
but in detail, there's still some minor 
uncertainties that need to be resolved. 
The exact effects of the different 
abundances of chemical elements and 
diffusion from stellar course in which 
they are made towards the surface and so 
on. 
Those also contribute to the uncertainty 
and the estimate of ages of globular 
clusters. 
Nevertheless, 
measuring ages of globular clusters was 
probably one of the more reliable 
cosmological measurements for many years, 
certainly more so than any other 
cosmological parameters until the 1990s. 
The key point here was to calibrate 
exactly where the main sequences are, and 
this became possible only after Hipparcos 
satellite measured the actual paraloxes 
and distances to some metal core stars 
which defined the metal core main 
sequence that can be then applied to 
globular star clusters. 
Different groups have done that and 
typically the results they get, are the 
ages of globular clusters, on the order 
of 12 to 13 billion years. 
Which is very close to what we now know 
is the actual age of the universe of 
about 13.7 billion years. 
Here is a probability distribution of 
globular cluster ages that take into 
account all of the sources of uncertainty 
and so on. 
Clusters could have different ages and 
probably do so that will contribute to 
the spread as well. 
So the peak of this distribution is 
indeed where it should be. 
A little more than 13 giga years ago 
which allowed for a few hundred million 
years for galaxy and clusters to form. 
Of course there are no clusters older 
than the universe itself. 
The fact that the distribution has a high 
end tail is simply indicative of the 
errors in age estimates. 
The next method is estimating the ages of 
white dwarfs. 
They are fairly well understood, and they 
are cooling a very orderly fashion. 
So the faintest white dwarfs that we can 
find are probably the coolest, the ones 
that had been cooling for the longest 
period of time, and they can constrain 
the age of the cluster, or galactic disk, 
in which they are found. 
Again, theories fairly well understood. 
In over-all sense, but there's still 
details that need to be ironed out. 
Probably the best way to do this is in 
star clusters, where again, we know the 
population of white dwarfs all have the 
same age. 
And because they're really faint, and 
clusters are crowded, we need Hubble 
Space Telescope to do this. 
Here is an example of the first 
measurement of this kind in the upper 
right you see a little segment called the 
main sequence. 
In the center is the white dwarf cooling 
sequence, and you can see it stops at 
some point. 
Those are the oldest and the coolest 
white dwarfs in the cluster and their 
position determines the edge. 
So this method produced results which are 
perfectly consistent with those from. 
Main sequence, isochrome feeding, and 
that's, very different physics, so it's 
very encouraged. 
Here is the observed luminosity function, 
of y dwarfs, in this particular cluster. 
Meaning, their distribution of the 
luminosity's. 
You can see that there is a, fairly sharp 
cutoff, at the faint end, which is, 
indicative, what the h really is. 
An entirely different approach, uses ages 
of chemical elements. 
Heavy chemical elements that must have 
been produced in super nova explosions of 
say per supernovae often have unstable 
isotopes. 
And their radioactive decay can be used 
to age data the elements themselves. 
Because the age of the universe is about 
13 billion years. 
You need radioactive decays that are 
commensurate with it. 
Again, measured in billion, billions of 
years. 
There are such isotopes like thorium and 
uranium, there is also ranium and osmium, 
and a few others. 
And so you need, something that has a 
radioactive half-life, decay time of life 
time. 
But that, unfortunately, also means that 
it will be really hard to measure, in the 
laboratory, what the half-life decay time 
is. 
So doing this for variety of different 
isotopes then provides the estimate of 
the age of the oldest, supernova 
explosions, all this chemical elements in 
our galaxy. 
The abundances of these elements are done 
by very high resolution, high signal to 
noise spectroscopy of all the stars we 
can find. 
The [INAUDIBLE] are very subtle and that 
measurements are very hard. 
Nevertheless, they've been done over the 
years and results are shown. 
So for one particular star shown here. 
There are ratios of several isotopes that 
are being used to estimate the age of the 
elements that made a star. 
And the average of it is remarkably close 
to what we now know is the actual age of 
the universe. 
And it's also essentially the same as the 
age as measured for globular clusters and 
for white dwarfs. 
This is just 1 star, doing it for many 
stars improves the result. 
And so, to recap. 
We have, now, a fairly good idea of what 
the age of the universe it. 
Or at least the lower limit to it. 
Using several completely different 
methods. 
Which rely on different physics, 
different assumption, and different 
measurements. 
And they all agree. 
It's because of that we think we got it 
right. 
Moreover this is also in perfect 
agreement with age of the universe 
deduced from measurement of other 
cosmological parameters to which we'll 
come later. 
Next time we will address the question 
of, is the universe actually expanding? 
You think we would have probably figured 
this one out by now, but it's good to be 
sure.