PAUL: So those are the two fundamental principles behind modern cosmology.
One is that every place in the universe is the same.
Once you're on a big enough scale-- which means in
practice more than about 100 megaparsecs or so.
And the second principle is that everything
is moving away from everything else.
And the further apart two things are, the faster they're moving apart.
Now, this gives us a rather strange universe, Brian,
a universe where everything is moving away.
And no matter where you are, even 10 billion light years away,
you'd see the same sort of thing.
Galaxies out to as far as you can see, in endless procession--
all moving away from you.
BRIAN: Right.
And we can think about the logical extension of that.
You have this universe which is seemingly expanding.
But that means in the past it was different than it is in the future.
Things are closer together in the past.
And so that distance is related in some sense to time.
The distance things are is dependent on time.
So in some weird way, time and distance, or space,
are sort of related to each other.
PAUL: And that sounds a lot like relativity.
In particular, the whole nature of space and time
relies on Einstein's theory of general relativity.
We dealt with special relativity in the violent universe course.
But now we're going to talk about general relativity, which
is in some sense the most fundamental theory of space and time and gravity.
Now Einstein came to this by pondering something
that most people didn't think was an issue.
BRIAN: Right.
So in 1907 he was thinking-- as Einstein obviously did a lot of--
and he was thinking about the two types of matter that
existed within the physical theory of the time.
PAUL: Yes, so, if you remember your high school physics-- well, what is mass?
Brian, how would you define mass?
BRIAN: Well, in my daily job I think of mass
as being the thing that gravity affects.
So I have the force of m, and an m, big G,
and then a distance between the masses.
And there's a force between that.
PAUL: that's one equation that uses mass.
It's Newton's equation of gravity-- force equals GMm over r squared.
And that's actually very similar to other force equations in physics--
for example, the force between electric charges.
Once again, you're going to get 1 over r squared.
And you get a constant that tells you how strongly a particular particle
interacts with something.
Which in the case of electromagnetism is its charge.
And in the case of gravity, is its mass.
BRIAN: Yep.
PAUL:So that's sort of saying that mass is a gravitational charge.
It tells you how strongly something pulls and is pulled by gravity.
That's all well and good, but there's another quite different place
where mass comes in.
BRIAN: OK, well, that is true.
So for example, if I was going to measure the force,
I'd also have to worry about ma-- F equals ma.
That's Newton's other-- one of his other big hits.
So that one, that a doesn't necessarily have to be gravity,
it could be something also.
PAUL: Yeah, so I could imagine you're sitting by the harbor in Sydney,
and you have an oil tanker.
And you push it.
You're applying a force, but it doesn't accelerate very much.
But if you have a small speedboat and you push it, it'll move.
So this is telling you how much something resists being pushed around.
Some big bruiser doesn't like being pushed around very much.
Some small wimpy thing gets pushed around very easily.
BRIAN: Yeah.
So I can use this, for example, to figure out
how I'm going to be accelerated by Earth's gravity.
I take the force of gravity and the F equal ma, and I equate them.
And I could say a is equal to this thing from Newton's law of gravity.
And that's a very useful little way to figure out
what gravity is going to do to me.
PAUL: Yeah, so normally most people just said, OK.
We've got one equation with mass, another equation with mass.
Learn them.
Repeat them in the exam.
End of story.
But where it took the genius of Einstein was to think, hold on a minute.
You've got mass in F equals ma.
And that's kind of like inertial mass.
It's telling you how much inertia something has.
And you have gravitational mass, which is telling you
how strongly things gravitate.
Why do they have anything to do with each other?
BRIAN: Right.
And so, not only do they seem to have something to do with each other,
I think his big thought was, he thought they must always have something
to do with each other.
And they must always be equivalent.
But that turns out to be kind of a complicated thing
to think through, as Einstein found out.
PAUL: Yeah, I mean, for other forces-- like electromagnetism--
it's not the case.
You could have something with a very strong charge and not much mass,
or something with very large mass and not much charge.
So if you have an electric field, things will all accelerate at different rates.
But if you have a gravitational field, the force is proportional to the mass,
and the inertia is proportional to the mass.
So it cancels out.
Which is why at least in a vacuum, when there's no air resistance,
everything falls at the same rate.
So that's telling us that these two things--
which really have quite different concepts.
One's about resisting motion, and one's about a force--
that they're proportional to each other.
They are the same thing.
Why?
BRIAN: So I don't think we know why, even to this day.
But it's certainly, if you think that logical consistency-- OK.
Here on earth, makes things work.
But what happens if you want to throw in getting close to the speed of light.
And then we know we have all those relativistic effects.
Well how do you make those things then always be the same?
PAUL: Yeah.
So it's a real puzzle.
And this is what Einstein's great thought
was, why these two things-- which apparently
have not much to do with each other-- why are they related?