PAUL: So quantum mechanics is seriously weird.
These things behave like waves when you're not looking,
get privacy away all by themselves.
And as soon as you look up, suddenly, it's a particle.
But how's it going to help us with white dwarfs?
Let's get back to the matter of physics now.
The idea is that quantum mechanics, it can
help us allow this white dwarf, Sirius B, to withstand this immense pressure.
How is that going to work?
BRIAN: Well, I think it really comes down
to quantum mechanics is even weirder than what we've already told you,
because there are some other rules that are very counterintuitive
So when you look at, for example, a hydrogen atom,
these are the different places, the little energy
levels that an electron can be around a hydrogen atom.
But there's a rule that chemists have figured out four atoms
heavier than hydrogen that have multiple electronics
is that the electrons do not like to be in the same state at the same time.
This is known as the Pauli exclusion principle.
And so for example, if this were for example the ground state of iron,
you might expect all of it's 26 electrons
to pile down right next-- in the lowest energy state.
But it's not allowed to do that.
Indeed, it's only one atom in each state.
And so they end up having to distribute themselves
through all the different levels.
And that turns out to give you a set of rules
that means that you can't push things together very closely.
PAUL: Yeah, so if our exclusion principle
says that particles called fermions, which includes quarks.
And hence, neutrons and protons and electrons
can only have one energy state.
It actually goes right down to some fundamental symmetry in their nature.
But other particles, it can pile up in the same energy state like protons,
for example.
But the fermions owns can't, which, as every chemist knows,
tells you start filling up the energy levels from the bottom
and so and so up.
It's interesting to think if electrons have not obeyed that rule,
then everything would be in the ground state,
and everything would be chemically like hydrogen.
And so it wouldn't be possible to have life.
Hydrogen can't do anything like carbon.
BRIAN: But it would be so much easier to calculate.
PAUL: Chemistry would be so easy.
BRIAN: Yes, that's right.
PAUL: But luckily, for the instance of life,
there is this Pauli exclusion principle, and things can't all
sit in the lowest energy state.
Then, there is a second clue.
It's called the Heisenberg Uncertainty Principle.
Now p here is momentum.
What it's telling us in x's position, what
it's telling us is if you have an uncertainty in the position
and an uncertainty when you're meant to multiply them together,
it must be more than h bar on 2.
H bar is Planck's constant divided by 2 pi.
So what this is telling you is when you confine an atom to a very small space,
cementing becomes highly uncertain.
BRIAN: Right so if I can go through and say, the uncertainty in the position
is tiny, then I'd end up not knowing much at all about it's momentum
and usually velocity, but mass.
PAUL: This is a generic thing about waves.
If you think about it, if you've got a wave
and you compress it into a small space, it must have a very short wavelength.
Or short wavelength means lots of energy,
so it's going to be moving like crazy.
In some sense, this is actually what drives diffraction
in telescopes we talked about in a previous course.
If you have a wave going through a narrow aperture in a telescope,
it bends out a lot.
It's got quite a lot of momentum.
If you have a wide aperture, it bends out less.
So these are the two clues that are going
to allow us to work out why white dwarfs like Sirius B can survive
the Heisenberg Uncertainty Principle and the Pauli exclusion principle.
So let's look at that.
