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Black Holes: Relativity & Quantum · Acedra
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Black Holes: Relativity & Quantum
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0:00
[MUSIC PLAYING]
0:03
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]
0:17
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
0:45
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.
1:18
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
1:43
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.
2:17
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.
2:51
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
3:23
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.
3:52
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.
4:26
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.
4:58
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
5:27
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.
6:01
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.
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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.
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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.
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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
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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.
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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.
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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.
9:42
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.
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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.
10:43
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."
11:11
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
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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.
12:05
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
12:33
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.
13:05
NASA, this is "Space Time." Tell Mr. Willis to stand down. Yeah. We have a new guy. [MUSIC PLAYING]
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