[MUSIC PLAYING] Black holes are one of
the strangest objects in our universe. To make one, we need
both general relativity and quantum mechanics. Today, I'm gonna show you how. [MUSIC PLAYING] In a previous episode, we
discussed the true nature of black holes. We talked about them as
general relativistic entities, as space time regions whose
boundary curvature effectively removes the interior from
our observable universe. Now, it'd be a great idea
to watch this video first, if you haven't already. Now, these are some
abstract ideas. And really, black holes
were, at first, just a strange construction
of general relativity. And just because something
exists in the mathematics does not mean it has
to exist in reality. So are black holes real? The answer is yes. Black holes are
astrophysical realities that we have ample evidence for. Yet, to actually
form a black hole, Einstein's descriptions of
mass energy and space time are not enough. We need quantum mechanics. If you're up for it,
let's build a black hole. First step-- find a very
massive star, and wait. Let it cook-- not for long
because these guys have very short lives. Just wait a few million
years for the supernova. If you get impatient, you can
turn up the core temperature by bombarding it with
gravitational waves. It'll be done quicker. The details of the
deaths of massive stars are pretty awesome. But they can be found
in lots of places. So we'll just gloss
over them here. In the last throes of a
very massive star's life, increasingly frantic
fusion in the interior produces one periodic
table element after another, in
Russian doll shells of increasingly
heavy nuclei that finally surround an iron core. The formation of
that core represents the end of exothermic fusion. Fusing two iron nuclei
absorbs energy. It doesn't release it. So starved of an energy
source, the stellar core collapses on itself. Electrons are slammed into
protons in the iron nuclei, forging a neutron star. The collapsing outer
shells ricochet off this impossibly dense nugget
in a supernova explosion, enriching the galaxy
with juicy new elements. The leftover core,
the neutron star, is a very weird beast-- a ball
of neutrons the size of a city, with a mass of at least
1.4 suns and the density of an atomic nucleus. We see them, when we
see them, as pulsars. Now, beneath the thin
atmosphere of iron plasma, a neutron star is a
quantum mechanical entity. And it's a quantum phenomenon
that saves it, for the moment, from final collapse. It's also a different
quantum phenomenon that will let us push
it over the edge, creating a black hole. To understand how space works
for a quantum object like this, we need to think not in regular
3D space or even 4D space time but, rather, in six dimensional
quantum phase space. For a neutron star,
this is the space of both 3D position
and 3D momentum. And it defines the
volume that can be occupied by the strange
matter in a neutron star. Now, the exact way that the
matter of a neutron star fills this 6D
quantum phase space depends on two
important principles of quantum theory,
the Pauli exclusion principle and the Heisenberg
uncertainty principle. These govern the
delicate balance between stability and collapse. The Pauli exclusion
principle basically just says that two things can't
occupy the same place at the same time. And by thing, I mean
fermion, the particle type comprising all regular matter. For example, electrons,
protons, and neutrons. Now, by place, I mean location
in quantum phase space. So two fermions can occupy
the same physical location just fine, as long as their
momenta or any other quantum property is different. Now, this rule is
what keeps electrons in their separate stable
orbits and, in turn, is part of what allows solid
matter to have its structure. In the case of a neutron star,
position momentum phase space is completely full of neutrons. Every spatial location and
every momentum location connected to those spatial
locations contains a neutron. OK. Jargon alert. This weird state of
matter where phase space is completely full-- we
call it degenerate matter. And the degeneracy pressure,
resulting from particles not having anywhere
else to collapse into, is incredibly
strong-- strong enough to initially resist the
insane gravitational crush of a neutron star. As far as we know,
there's no way to overcome Pauli exclusion--
at least, not directly. See, it's not a matter of force. Two fermions just can't ever
occupy the same quantum state. And that's that. So the neutron star is safe. But come on. We want to build a black hole. Fortunately, there's
another quantum phenomenon that lets us get around the
Pauli exclusion principle. The Heisenberg
uncertainty principle tells us that the properties
of a quantum entity are fundamentally uncertain. The details may be a
topic for another episode, but in short, quantum
mechanics describes matter as a distribution
of possibilities. Certain numerical
properties that you can assign to a
particle exist in a wave of varying degrees of maybe. Location is one such property. A neutron, for instance,
is not in any one place but exists as a cloud
of possible locations that might be
tightly constrained or may be very spread out. Location remains a
possibility cloud until the neutron interacts
with another particle, at which point, its
location is resolved. This is the weirdest, coolest
aspect of quantum mechanics. And we'll try to get back
to it in another episode. But for now, we have
a black hole to make. The Heisenberg
uncertainty principle tells us that particular
pairs of quantities, position and momentum
or time and energy, must, when taken together,
contain a minimum degree of uncertainty. If one is tightly
constrained, then the other must be uncertain and span a
wide range of potential values. So a neutron star is comprised
of the densest matter in the universe. Its constituent neutrons
are about as constrained in position as you can get. Therefore, the Heisenberg
uncertainty principle tells us that they must have
highly undefined momenta. Very, very large
neutron velocities become part of the
possibility space. To put it another
way, the neutrons are packed so close
together in position space that their momentum
space becomes gigantic. Phase space expands. And here's the
thing-- the denser the neutron star becomes, the
more momentum space you get. So Heisenberg lets us circumvent
that pesky degeneracy pressure. If we can somehow add more
matter to a neutron star-- throw another star
at it, maybe-- it won't get spatially larger. The extra matter certainly
needs somewhere to go. The star must expand. But it doesn't expand
in position space. The star expands
in momentum space. In position space, it
actually gets smaller. The more massive of the neutron
star, the smaller its radius. This is a quantum effect,
even though it's happening on the scale of a star. Until now, the neutron star has
hovered above a critical size. The space time curvature at
the neutron star's surface is pretty extreme. Clocks run noticeably slower. And the densities
inside the star produce some very
strange states of matter. However, despite this, the
star is still very much a thing in this universe. And yet, below the
star's surface, there lurks the potential
event horizon, the surface of infinite time dilation. Now, the event horizon
doesn't actually exist as long as the
neutron star stays larger than the would-be horizon. However, if we can increase
the mass of the neutron star, the actual star shrinks, and
the event horizon expands. You can see where
I'm going with this. There's a mass where the
radius of the neutron star and the event horizon overlap. It's three times
the mass of the sun. At this point, the event horizon
actually comes into being. And the neutron star
submerges beneath it. We've finally created
our black hole. But what happens
to the star when it slips below its event horizon? Everything inside is
lost from this universe. Space time is radically
altered inside the star with all geodesics, space
time paths, turning inward, towards the center. When the black hole
first forms, the material inside must resemble the stuff
of the original neutron star. But there's no stopping
ultimate collapse. All paths lead to the central
point of infinite curvature, the singularity. From the point of view
of the star itself, the inward cascade happens. All position space collapses
towards the singularity. While momentum space
expands accordingly, with the corresponding enormous
velocities all inward-pointing. Neutrons are certainly
shredded into component quarks and gluons. But what happens to these
as the star approaches an infinitesimal point,
the Planck scale? Physics cannot yet tell us. From the point of view of
an outside observer-- so, us-- this never happens. The black hole forms. The stellar core goes dark. But on our timeline,
nothing ever happens beyond the
event horizon again. We can't meaningfully think
about what's happening now; beneath the event horizon
there is no corresponding now. The material of the star and all
events that happen to it are no longer a part
of the timeline of the external universe. On our clock, the singularity
forms infinitely far in the future. To us, there is only
the event horizon. So this is how a real
astrophysical black hole is made. The mass of the stellar core
becomes the apparent mass of the black hole. And very few other properties
of the collapsed material are remembered. The black hole retains mass,
electric charge, and spin. And these continue to influence
the outside universe, sometimes in very important ways. Of course, a real black hole
is not the static creature that we sometimes
describe in theory. They grow. They leak. They change. We'll get to what this
means, for black holes and for the universe, in
another episode of "Space Time." In a previous episode, we talked
about the Alcubierre drive. Well, our friends over
at "The Good Stuff" just made a video
about a man who's attempting to build his own
Alcubierre drive in his garage. You should check this out. They interview some
Australian astrophysicist about the drive's plausibility. Now, "The Good
Stuff" guys talk some smack about the lack of
beards here on "Space Time." And sure, they have some
pretty luxuriant flavor savers. But I challenge you guys to
grow this much handsome stubble in between single frames. Now, in the last
full episode, we talked about how to
stop a killer asteroid from hitting the earth. You guys had some
great questions. Jonathan Sny and others
wonder whether, instead of the gravitational
tractor, you could just land a spacecraft
on the asteroid and push it with its rockets. Well, actually, it's going to
take the same amount of fuel to pull by a
gravitational tractor as it would to push
an asteroid by landing a rocket on it, assuming
that the rocket can push with perfect efficiency. Now, that's tricky because
the asteroid will certainly be rotating. And you can only push when
the rocket is pointing in the right direction. Also, as we've
discovered recently, when we landed Philae
probe on a comet, landing on irregularly shaped bodies,
with very weak gravity, is extremely tricky. The gravitational tractor
gets around these issues. moxshyfter asked about the
plausibility of directing a killer asteroid into the sun. So even the largest
asteroid hitting the sun would barely make a splash. The problem is that changing its
velocity enough to hit the sun, or even to fall into
Earth's orbit-- which was another suggestion--
would take vastly more energy than just nudging it off course. Sam Gilfellan wants
know how large an object we'd need to destroy
in order to form a ring system around the earth. So if we want a ring system like
Sam's, that has the same ratio of planet mass to ring mass--
of about 1 to 50 billion, then we'd need an
object the same size as the one that killed the
dinosaurs, so more than 100 trillion tons. We'd also need to nudge it off
direct impact and explode it. But totally worth it. A ring system around the
earth would be awesome. A lot of people point out that
One-Punch Man could easily destroy a killer asteroid. I agree. NASA, this is "Space Time." Tell Mr. Willis to stand down. Yeah. We have a new guy. [MUSIC PLAYING]
Watch the whole episode here: https://youtu.be/xx4562gesw0
This show delves into the physics of our universe, and answers some pretty awesome questions like: Could you fart your way around in space?