PAUL: So, we've seen that the amount of energy you can get out of a collapsing
star is a staggering 10 to the 47 joules, or thereabouts.
Bu there's a problem.
Our idea was that the center of the star collapses
to form a neutron star-- tastefully shown in purple there.
And then you've got the rest of the star which collapses down.
And this generates huge amounts of energy.
And this then causes it to bounce back out again.
But there's the trouble.
If something drops in and bounces back out,
it usually bounces back to at most the same height as where it came from.
You see that here.
When I drop the ball, it never bounces back higher than where it started from.
In fact, with each bounce, it loses a bit of energy,
and gets to a lower and lower height.
So that wouldn't be a very impressive supernova.
If you have the rest of the stuff in the star fall down, bounce out, fall
down, bounce out, fall down, bounce out-- there'd be a lot of energy
sure as it falls in.
But energy's use up as it comes back out again.
And then perhaps back as it goes in.
And each time you lose more and more of it.
You would get any blast wave thrown out.
But we know that these supernovae produce things like the Crab Nebula.
So how can get stuff blown out from something
like this, a falling situation?
Well, there is a way.
Let me demonstrate.
Instead of dropping one ball, let me drop two--
a small one on top of a big one.
Look what happens.
It goes much higher.
What's going on here?
Well, the basic idea is, let's say you've got something big.
And you're bouncing something much smaller off it.
And it comes in with some velocity, v. Then
if it's an elastic collision, one in which energy
is conserved-- so energy isn't wasted and you're making a noise
or deforming the ball or heat or something
like that-- that would also come out with the same velocity
relative to the big thing.
So that's all the physics we need.
Let's see how it applies in this two-ball drop.
So here we have a surface.
Initial situation, let's separate the balls out to make it a bit clearer.
I've got a big ball and a small ball.
And they're both about to hit the surface
Since they're both moving about the same speed, let's call it v.
Now the first thing that's going to happen
is the big ball will hit the surface.
The big ball is much smaller than the earth it's hitting.
So if it's an elastic collision, it will leave the earth
at an upward speed of v. So secondly, we're
going to get the small ball, still moving downwards at speed v.
And now we've got the big ball going upwards at speed v.
So the next step is going to be the small ball hitting the big ball.
So once again, the same rule applies.
Let's assume the big ball is much bigger than the small ball.
What is the speed with which the small ball approaches the big ball?
Well, from the big ball's point of view-- it's moving up at speed v,
the one's moving down at speed v-- so the relative speed is actually 2v.
So from the big ball's point of view, the small ball
is approaching it at speed 2v.
And so afterwards, will leave it at speed 2v.
So after this, the big ball is moving up at speed v. We're
assuming it's much bigger than the small ball,
so isn't much affected by the impact.
Small ball came in at 2v, and it goes out at 2v.
But that's 2v relative to 1v upwards.
So that means relative to the ground, it's
actually moving up at speed of 2 plus 1 equals 3v.
So that's how you can get the ball to bounce very, very high.
In the case of the small ball, infinitely smaller than the big one,
and everything's perfectly elastic, it'll go up at about 3 times the speed.
In principle, you could do even more complicated situations,
like having an even smaller ball up here on top-- in that case,
to have a third collision.
So this one is now going down, still with speed
v. It's now going to hit something with speed 3v upwards.
So the rotor speed is going to be 4v, so it will then head up at 7v upwards.
And in principles, have even small dots.
So that's a possible explanation of how supernova can blow stuff out.
The idea would be that you have your neutron star,
and you have the heavy lower levels of the star come in and bounce out.
And they're not going particularly fast.
But then, a lighter higher level comes in.
And it now, instead of bouncing off the stationary neutron star,
bounces off the matter that's already moving out.
So that means it'll go even faster.
And then you might get an even lighter, further out layer of the star come in.
And it's now bouncing off the extremely fast-moving stuff.
And so it can go out at an enormous speed.
So in principle, this could work it.
It could give us extremely high output speed, which could produce something
like the Crab Nebula we see.
There's only one trouble.
To get these very high speeds, you need ever-smaller balls, i.e.,
ever smaller amounts of mass.
Most of the mass can't do this.
Only a very tiny fraction-- like the highest ball-- can go out.
So the amount of energy we're getting out
has got to be much less than the total energy.
So roughly speaking, it might only be a 0.1% or something like this.
So instead of the 10 to the 47 joules we're
talking about for the entire energy of collapse,
we might only get a pathetic 10 to the 44 joules, or something like this.
