PAUL: OK, now onto our second clue, the second fundamental principle
of cosmology.
This comes, like so much of astronomy, from the study of spectra.
BRIAN: Ah, a spectrum.
So if we remember, a spectrum is what happens
when you spread the colors of light out into the colors the rainbow
and we assign each color a wavelength.
Remembering blue light and ultraviolet has short wavelengths,
and infrared-- so we're going to have green, yellow, orange, red, infrared,
as you get in the longer and longer wavelengths.
And that's the wavelength of light that you're going to measure.
And we measured it in angstroms, which is
10 to the minus 10 meters per angstrom.
So they're very, very short wavelengths.
PAUL: Well, we've plotted the amount of energy at each wavelength,
and so you can see, these wavelengths have a lot of energy,
and for these wavelengths down there don't have very much energy coming out
of that particular wavelength.
BRIAN: And so when you see a spectrum like this,
it's actually a mixture of two things.
Part of it is because we're looking at a galaxy, in this case, full of stars
and the stars are hot.
And hot things glow, just like if you really
turn, for example, your stove top up really, really hot,
it'll start glowing red.
That's because it's hot.
But then there are these little narrow lines, absorption lines, and sometimes
there's emission lines, and that's due to the atomic transitions
of each element.
They have these places of energy motion between the electrons,
they're different levels, and those show up at places of color.
And so for example, hydrogen has very specific lines, for example,
at 6,563 angstroms as one of the big lines of hydrogen, H-alpha.
But then things like sodium, magnesium, various molecules, calcium, all
have different things.
PAUL: Yeah.
So this is very familiar to any astronomer,
and we would look at a spectrum like this
and read off which elements are there.
Now, that's all well and good.
But the strange thing is-- this is a key observation--
is that when you look at a faraway galaxy,
you see a different spectrum from a nearby one.
So here's a spectrum of a nearby galaxy.
And now let's look at the far away one, and you can see the change.
BRIAN: OK, the red one is the distant one.
OK.
PAUL: And it looks the same, but shifted-- red-shifted.
Moved to a longer wavelength.
What you find is that every dip, or peak, or bump
in the spectrum, every emission or absorption line,
has had its wavelength increased by a constant ratio.
And that ratio is called the red shift and written
for some unknown reason as Z rather than R,
and it's given by the shift in wavelength divided
by the wavelength you'd expect in a nearby galaxy or in a laboratory.
So what's going on here?
BRIAN: Well, we know that waves get shifted by the Doppler shift.
So we hear that in sound when a police car goes by you.
The sound waves get shifted, and compressed, and stretched,
and the pitch changes.
Light's a wave, so that same effect's going to happen.
So one can use the red shift to measure velocity.
So when we see a red shift, it's like the objects are moving away from us.
And the first order, that velocity can be calculated
as the ratio of the shift of light is equal to the ratio
to the speed of light.
PAUL: Yes.
There's an approximation valid for speeds much less
than the speed of light, but the galaxies we are talking about
are like that.
So what it's telling you is, if the lines been shifted
by a 1% longer wavelength, means whatever
has produced them has been moving away from us at 1% of the speed of light.
That's a red shift of 0.01.
BRIAN: And so a galaxy that's been shifted by this much
though, that's a big shift.
So that means it's moving, apparently, at a good fraction
of the speed of light.
Now we're going to see that maybe it's not actual motion,
but it's sort of apparently moving.
PAUL: Yeah.
Now it turns out that almost every galaxy is moving away from us.
There are one or two very nearby galaxies that aren't, but almost
every galaxy is moving away from us.
And if you plot how fast they're moving away from us against distance,
you get this plot.
What we're plotting here is how fast they're moving away from us.
You can see that's 10,000 kilometers per second, 30,000 kilometers per second.
BRIAN: That's like 10% of the speed of light, if it's a velocity.
PAUL: Yes.
BRIAN: And then we measure distance.
And we can see there's a one-to-one correspondence.
The further away you go, the faster the motion.
PAUL: And this is known as the Hubble law,
and its parameterised as a velocity is proportional to a constant, Hubble's
constant, which is about 70 kilometers per second per megaparsec,
times the distance.
BRIAN: So 70 kilometers per second per megaparsec means
if I'm a megaparsec away, I expect to be moving
with a velocity of 70 kilometers per second.
PAUL: Away from us.
BRIAN: Yes.
But away from us.
Now everything is moving away from us.
This is something that Edwin Hubble discovered in 1929.
Now if everything's moving away from us, Paul,
that seems to violate the Copernican principle, e.g.
we're no place special.
It seems like we are a special place.
We're this place that everything's going away from.
We're a very unpopular place in the universe.
PAUL: Yeah.
Let's say you're living on some distant galaxy a billion light years away.
The universe, as we've just said, may look uniform--
BRIAN: Yeah.
PAUL: But they'd be able to tell, hey, everything's
moving away from that point.
That point must be the worst place in the universe or something,
but anyway, special.
But it turns out that, actually, that's not quite the case.
I'm going to show you a little calculation here.
Now this is using vectors.
If you're unfamiliar with vectors we'll put in a link for you.
You can go and remind yourself about this a bit.
But this is the vector form of the Hubble law equation.
What it's telling us, this is us.
We're in the outskirts of this galaxy over here.
We got two other galaxies I call galaxy A and galaxy B over here.
And what we've said is the velocity is equal to a constant times the distance.
But these got a little arrow over the top,
which means they're vectors, which means that the velocity is
in the same direction as the distance, and proportional to it.
BRIAN: Right.
So the vectors, remember, are how far and the direction, typically,
is how we can think of them.
PAUL: Yeah.
So this galaxy is relatively near, so it's
got a relatively small velocity, and the velocity's in the same direction
as the displacement vector.
BRIAN: Right.
PAUL: This one's further away, so it's got a bigger velocity,
and once again, it's in the same direction.
And that's simply writing down in mathematical form,
everything's moving away from us.
The further away they are, the faster they're moving.
BRIAN: And so what you've stated here is Hubble's law is saying the direction
and the distance is the same.
So that all makes sense to me.
It just says that direction, we have one answer.
That direction, we have another answer.
So it's just like we just saw, with direction added, OK?
PAUL: Yeah.
But where this vector thing comes in very useful is if you now ask,
OK, let's say you've got aliens living on this galaxy here.
What would they see?
Now if they look back at us, we would appear
to moving away from them at equal but opposite speed.
But how about this one over here?
What would they see for this other galaxy over here?
BRIAN: OK.
PAUL: So the first thing they can ask is,
what's the distance, the vector displacement,
from galaxy A to galaxy B?
So that's, what's the vector from there to there?
And that's simply xb minus xa, the vector sum.
BRIAN: So that's vector arithmetic.
PAUL: You go minus xa plus xb, and that gets you from there to there.
BRIAN: So that would be that arrow.
Yes.
OK.
So good.
PAUL: So that's how far away galaxy B looks from galaxy A.
But then we look at the velocity.
The velocity of galaxy B with respect to velocity A.
And once again, the same thing applies.
You've got the change in relative velocity
is equal to velocity B minus velocity A. So if you go back,
it's got this velocity minus this velocity
is going to tell how that thing appears to be moving from its point of view.
BRIAN: OK.
PAUL: So if you do that calculation, we know that the relative velocity is
velocity B vector minus velocity A. But we also know, from the last slide
that velocity B is H0xb, and velocity A is H0xa.
BRIAN: Ah.
PAUL: And so if we take the H0s outside, it's just H0 times xb minus xa,
which we just said up here is delta x.
BRIAN: Ah, so it's the distance times the Hubble constant.
PAUL: Yes.
So the aliens on galaxy A are seeing that the velocity
of galaxy B, and relative to them, is just
equal to the Hubble constant times the distance, relative to them.
Just what we see on Earth.
BRIAN: So that means what we've just shown, using mathematics,
and we've literally proved, is that if we see this Hubble law,
everyone sees exactly the same Hubble law.
They see the same thing to us and to this other galaxy.
We all see the same thing.
PAUL: Yeah.
So in fact, this is perfectly consistent with our homogeneous uniform universe,
the Copernican principle.
Because not only do we see galaxies uniformly, but wherever you are,
you see everything moving away.
So how can you work out where the real center is?
BRIAN: Ah.
Well, I guess we're going to have to think about general relativity, this.
But it strikes me that if we think of the universe, it literally seems to be,
the further away, the faster the motion.
So that means the universe is expanding.
So let's do a balloon analogy.
So let's just think of the universe as being the surface of the balloon.
I'm going to put little dots on it, and as I blow the balloon up,
every dot, which is a galaxy, is moving away from every other dot.
So the galaxies are expanding away from each other.
And the further away you are, the faster the motion
will be as I blow the balloon up.
So I sort of get Hubble's law.
But where is the center?
It's the center of the balloon.
And what was that?
That was when I started blowing the balloon up.
So the center would be like the moral equivalent to the Big Bang,
when you started blowing the universe up.
PAUL: Yeah.
Because we can't really tell where the center
is, because you can never actually measure if you're moving,
or you can measure something relative to something else.
BRIAN: Yeah.
PAUL: Another analogy would be like baking up bread.
Let's say you'd had a sultana load and you bake it in the oven.
And we'll have sultanas as galaxies, and the dough is transparent.
As it gets bigger--
BRIAN: For people not from Australia, a sultana is a raisin.
So it's raisin bread or sultana bread.
Yes.
PAUL: OK.
So anyway, small, black things inside your bread.
It doesn't really matter what they are.
And as the bread gets bigger and bigger, it carries them all apart.
And so every sultana will think, hey, every other sultana's
moving away from us.
Unless they actually look outside the loaf into of oven,
they can't really tell which one's moving.
BRIAN: Yes.
PAUL: It's like with your balloon.
If they look outside their sheet of balloon,
they can see where the center of the balloon is.
BRIAN: Yeah.
PAUL: But we're talking about a three-dimensional universe.
We can't see outside it.
BRIAN: Hm.
PAUL: This here is my attempt to simulate this.
So these tastefully colored spheres are galaxies,
and they're all moving away from each other.
BRIAN: They're all moving away from us, and they're getting smaller,
because they're getting further and further away.
So we're literally embedded in this universe.
And if we ask ourself, well, where's the common center,
the common center is right at the beginning
of when we started when we are all crammed into the same spot.
PAUL: So from where we're sitting here, looks
like everything's moving away from us.
But if we were actually on that dot, or any dot,
they would see exactly the same thing.
So they can't really tell.
So those are our two clues.
We seem to have a universe that looks the same from any point of view.
BRIAN: Yeah.
PAUL: And it's one that's, everything's moving away from every point.