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Do Black Holes Have Hair? · Daniel and Kelly’s Extraordinary Universe

• 0:08
  Speaker 1: Hey or he have you started to go gray yet?
• 0:11
  Speaker 2: I'm not sure I ask you to answer that question.
• 0:13
  Speaker 2: You know, I want to preserve my air of mystery.
• 0:16
  Speaker 2: How about you.
• 0:17
  Speaker 1: I found a silver hair too in my beard, but
• 0:20
  Speaker 1: so far I'm still all brown up top. But you know,
• 0:23
  Speaker 1: I'm getting a little.
• 0:24
  Speaker 2: Impatient, getting impatient. What do you mean you want to
• 0:27
  Speaker 2: go gray?
• 0:28
  Speaker 1: I wouldn't mind that gravitas that comes from having a
• 0:31
  Speaker 1: little bit of gray.
• 0:32
  Speaker 2: You mean you don't have enough gravity right now?
• 0:36
  Speaker 1: My gravity has actually been increasing.
• 0:38
  Speaker 2: There you go. It sounds like your body's doing it
• 0:40
  Speaker 2: for you. But are you trying to counteract the you know,
• 0:44
  Speaker 2: whole physicist look with the shorts and the sandals.
• 0:46
  Speaker 1: Yeah, exactly, I'm trying to look a little bit more
• 0:47
  Speaker 1: grown up.
• 0:48
  Speaker 2: I'm not sure gray hair is going to help you there.
• 0:50
  Speaker 1: Maybe I should just shave my head.
• 0:52
  Speaker 2: There you go. That's one way a little older, more distinguished.
• 0:57
  Speaker 2: And after you shave it, you could paint it gray.
• 0:59
  Speaker 1: I'm not sure that's how gravitas is accumulated.
• 1:02
  Speaker 2: Sounds like physicists don't know how gravity or gravitas works.
• 1:06
  Speaker 2: Both big mysteries. Hi, I am Horehammick cartoonists and the
• 1:24
  Speaker 2: author of Oliver's Great Big Universe.
• 1:26
  Speaker 1: Hi, I'm Daniel. I'm a particle physicist and a professor
• 1:30
  Speaker 1: at UC Irvine, and I never really gone after gravitas.
• 1:34
  Speaker 2: What do you mean you just inherently have it? Can
• 1:36
  Speaker 2: you say you're a physicist?
• 1:38
  Speaker 1: People go ooh, No, exactly the opposite, trying to break
• 1:42
  Speaker 1: down those barriers, you know. That's why I wear socks
• 1:44
  Speaker 1: and sandals every day. Don't try to create any distance
• 1:48
  Speaker 1: between myself and my students.
• 1:49
  Speaker 2: Or apparently your feet and the exterior world.
• 1:53
  Speaker 1: And everyone knows that's another reason to live in southern California, right,
• 1:57
  Speaker 1: Socks optional.
• 1:59
  Speaker 2: I guess that's what physics is. It's all about, you know,
• 2:00
  Speaker 2: breaking barriers, connecting with the universe. Anyways, Welcome to our podcast,
• 2:05
  Speaker 2: Daniel and Jorge Explain the Universe, a production of our
• 2:08
  Speaker 2: Heart Radio.
• 2:09
  Speaker 1: In which we try to break down the barriers between
• 2:12
  Speaker 1: ourselves and nature, between you and a complete understanding of
• 2:16
  Speaker 1: everything we do and don't know about the universe. We
• 2:19
  Speaker 1: think the universe is the greatest mystery and we are
• 2:22
  Speaker 1: here to crack it.
• 2:23
  Speaker 2: That's right. The universe is full of barriers of things
• 2:25
  Speaker 2: we can't see things we can't understand and things that
• 2:28
  Speaker 2: we may never understand, including barriers about fashion and dress
• 2:33
  Speaker 2: codes at universities.
• 2:35
  Speaker 1: You know, people say, focus on what you're good at,
• 2:37
  Speaker 1: and so that's why I just don't pay attention to fashion.
• 2:40
  Speaker 2: So you're good at wearing sandals, it sucks.
• 2:42
  Speaker 1: I'm good at ignoring fashion. I just do my own thing.
• 2:45
  Speaker 2: Well, I am totally with you. I think the most
• 2:47
  Speaker 2: comfortable thing in the world to wear is socks and sandals.
• 2:50
  Speaker 2: If anyone does not try that out there, I highly
• 2:53
  Speaker 2: recommend it, or or socks with flip flops even better.
• 2:57
  Speaker 1: I'm so glad this is an audio only medium.
• 3:00
  Speaker 2: We don't have smell of vision, thankfully, though.
• 3:04
  Speaker 1: I'm terrified at the mental images you are creating in
• 3:07
  Speaker 1: the minds of our listeners.
• 3:08
  Speaker 2: Actually have socks that have the little notch for your
• 3:11
  Speaker 2: flip flop strap.
• 3:14
  Speaker 1: You're like one step away from those horrendous toe shoes.
• 3:17
  Speaker 2: Oh no, no, no, that's where I draw the line.
• 3:19
  Speaker 1: I see one notch is fine. Four notches two too many.
• 3:25
  Speaker 2: I don't need each of my individual toes wrapped in
• 3:28
  Speaker 2: its own little pocket.
• 3:29
  Speaker 1: Again with the troubling mental images.
• 3:31
  Speaker 2: Here, well, but toes are a big part of the
• 3:33
  Speaker 2: universe theories of everything, and so physicists have been on
• 3:37
  Speaker 2: the lookout and on the search for one SU's theory
• 3:39
  Speaker 2: that can explain everything in the universe, including all the
• 3:42
  Speaker 2: mysterious bits of it.
• 3:43
  Speaker 1: And some of the most mysterious bits of the universe
• 3:46
  Speaker 1: are those pieces that we cannot see, things hidden behind
• 3:50
  Speaker 1: the event horizon of black holes. What's going on in there?
• 3:54
  Speaker 1: Are there singularities or is there something else? How does
• 3:57
  Speaker 1: gravity work for quantum particles? All the answers are waiting
• 4:00
  Speaker 1: for us behind these barriers.
• 4:03
  Speaker 2: Yeah, black holes seem to be the sort of the
• 4:05
  Speaker 2: epitome of mystery in the universe. It's almost like a
• 4:07
  Speaker 2: little pocket that takes you out of the universe.
• 4:10
  Speaker 1: Right, Yeah, it's sort of like they are their own
• 4:12
  Speaker 1: little pocket universes because they are cut off from us.
• 4:15
  Speaker 1: And maybe the most tantalizing thing is that we can
• 4:17
  Speaker 1: only know a few things about what's gone past that barrier.
• 4:21
  Speaker 2: Yeah, they're almost like cosmic sensors, you know, they're like
• 4:25
  Speaker 2: hiding information, blacking it out for everyone to uh see
• 4:29
  Speaker 2: or a Nazi.
• 4:29
  Speaker 1: And physicists hate when they lose information. When some knowledge
• 4:34
  Speaker 1: is hidden from them, and so we spend a lot
• 4:36
  Speaker 1: of time wondering about what we can know about the
• 4:39
  Speaker 1: things that have fallen into a black hole. Is it
• 4:42
  Speaker 1: possible to show up to a black hole and know
• 4:45
  Speaker 1: what has been tossed into it?
• 4:46
  Speaker 2: Yeah, we have a lot of questions about black holes,
• 4:49
  Speaker 2: but maybe not as important as the one we're asking today.
• 4:53
  Speaker 2: So today on the podcast, we'll be asking the question
• 5:00
  Speaker 2: do black holes have hair?
• 5:03
  Speaker 1: And do black holes wear socks with their sandals?
• 5:06
  Speaker 2: I think the real question is black holes have black
• 5:09
  Speaker 2: hairs or gray hairs? Or does it depend on the
• 5:12
  Speaker 2: age of the black hole or it's gravitas exactly?
• 5:15
  Speaker 1: Maybe the really big super black holes are like the
• 5:17
  Speaker 1: silver backs of the universe.
• 5:19
  Speaker 2: I guess. Don't all black holes by definition have gravitas?
• 5:22
  Speaker 2: I mean you kind of have to take them seriously, right,
• 5:24
  Speaker 2: I guess so if gravity is the bending of space time,
• 5:27
  Speaker 2: then gravitas is like the bending of the social structure. Like,
• 5:30
  Speaker 2: are there lightweight black holes out there or you know,
• 5:33
  Speaker 2: frivolous black holes? Probably not right.
• 5:36
  Speaker 1: They probably aren't like teenage black holes that the parent
• 5:38
  Speaker 1: black holes thing should be taking their life more seriously?
• 5:42
  Speaker 2: Where did that come from?
• 5:44
  Speaker 1: Frivolous. You're like, what are these black holes doing with
• 5:47
  Speaker 1: their lives anyway? Or maybe it's just because I have
• 5:49
  Speaker 1: teenagers in high school.
• 5:51
  Speaker 2: I think you might be bringing us the home issues
• 5:55
  Speaker 2: here on the Physics podcast.
• 5:57
  Speaker 1: Well, in the end, we are trying to understand the
• 5:58
  Speaker 1: universe through the lens of our own minds, so it's
• 6:01
  Speaker 1: impossible to separate personal issues from physics issues.
• 6:05
  Speaker 2: You could be a family physicist. You know there's family physicians. Yeah,
• 6:09
  Speaker 2: there are a lot of dynamics in the household.
• 6:11
  Speaker 1: Yeah exactly. Maybe black hole therapy can solve some problems.
• 6:15
  Speaker 2: Yeah, just throw the whole family to black hole and
• 6:19
  Speaker 2: they have to get along.
• 6:21
  Speaker 1: It might get kind of hairy.
• 6:23
  Speaker 2: But Harry, apparently black holes can be, or might be
• 6:26
  Speaker 2: or could be. And so that's the question we're asking
• 6:28
  Speaker 2: here today, which is kind of a weird question. I mean,
• 6:30
  Speaker 2: who thinks of black holes having hair?
• 6:32
  Speaker 1: Physicists? Physicists use hair as a metaphor for all sorts
• 6:36
  Speaker 1: of crazy stuff.
• 6:37
  Speaker 2: Well, it's a fun question, and so as usual we
• 6:39
  Speaker 2: were wondering calming people out there, I thought about this,
• 6:42
  Speaker 2: Harry question.
• 6:43
  Speaker 1: So thanks very much to everybody who answers these questions.
• 6:46
  Speaker 1: For this really fun segment of the podcast, and we
• 6:48
  Speaker 1: are always looking for more volunteers and we want to
• 6:50
  Speaker 1: hear from you, So join the group right to me
• 6:53
  Speaker 1: to questions at Danielandjorge dot com.
• 6:56
  Speaker 2: So think about it for a second. Do you think
• 6:58
  Speaker 2: black holes have hair? Here's what people had to say.
• 7:01
  Speaker 3: I suppose you'd have to ask yourself what exactly you're
• 7:04
  Speaker 3: talking about when you mean hair. My assumption is that
• 7:07
  Speaker 3: you would be referring to a biological process, and since
• 7:09
  Speaker 3: black holes are not a biological entity, I would struggle
• 7:13
  Speaker 3: to believe that they create hair in it of themselves.
• 7:15
  Speaker 4: Well, I don't know about actual hair, but I do
• 7:18
  Speaker 4: know that when things fall into a black hole, they
• 7:20
  Speaker 4: get spaghettified. So maybe black holes are surrounded by a
• 7:23
  Speaker 4: whole bunch of spaghettified ragg doll hair.
• 7:26
  Speaker 5: I'm assuming by hair you're asking about something that I
• 7:30
  Speaker 5: have never heard of, and not asking about like hair
• 7:34
  Speaker 5: on your head.
• 7:35
  Speaker 1: But since that's the only.
• 7:36
  Speaker 5: Definition that I know, I'm going to say, no, black
• 7:38
  Speaker 5: holes do not have hair on them.
• 7:40
  Speaker 4: The only thing I can really equate hairs to would
• 7:44
  Speaker 4: be like cosmic strings of some sort. I really don't know.
• 7:49
  Speaker 4: I don't know.
• 7:50
  Speaker 1: Well, if black holes have hair, it's yet another thing
• 7:53
  Speaker 1: that tests more hair than I do.
• 7:55
  Speaker 2: All Right, some great answers here, pretty creative talking about
• 7:58
  Speaker 2: like is a cosmic a hair?
• 8:02
  Speaker 1: That's right? Cosmic strings? Are these cracks in space time
• 8:05
  Speaker 1: we talked about once, which do seem kind of hairy,
• 8:08
  Speaker 1: but are completely separate from what we mean when we
• 8:10
  Speaker 1: say black hole hair.
• 8:11
  Speaker 2: I also wonder if them you can take this question literally, like,
• 8:14
  Speaker 2: if the Earth falls into a black hole, it would
• 8:16
  Speaker 2: have a lot of hair in it literally, right, or
• 8:19
  Speaker 2: would it? I don't know.
• 8:20
  Speaker 1: Yeah, well that sort of goes to the heart of
• 8:22
  Speaker 1: the question. Really, are black holes what they eat? Or
• 8:24
  Speaker 1: does it not matter what you put into a black hole?
• 8:27
  Speaker 1: Can you not tell the history of a black hole
• 8:29
  Speaker 1: in any way?
• 8:31
  Speaker 2: I see these are internal hairs, hairs you don't really
• 8:37
  Speaker 2: want to see.
• 8:37
  Speaker 1: Maybe somehow we ended up talking about ingrown hairs on
• 8:40
  Speaker 1: the podcast.
• 8:42
  Speaker 2: Yes, do black holes have ingrown hairs?
• 8:46
  Speaker 1: Next week, the comparison between black holes and black heads?
• 8:50
  Speaker 2: Yeah, oh boy, those are very popular on the TikTok.
• 8:55
  Speaker 1: And we're back to teenage issues.
• 8:57
  Speaker 2: Here you go, black hole popping right here on the podcast,
• 9:00
  Speaker 2: it's the sound of a black hole popping. But anyways,
• 9:02
  Speaker 2: let's get down to it, Daniel, and let's maybe recap
• 9:05
  Speaker 2: for people what exactly is a black hole and what
• 9:08
  Speaker 2: do we know about them?
• 9:09
  Speaker 1: So we don't really know what a black hole is.
• 9:11
  Speaker 1: We have a theoretical concept from general relativity that tells
• 9:15
  Speaker 1: us that if you have enough matter or enough energy
• 9:18
  Speaker 1: density in a small region of space, that that space
• 9:21
  Speaker 1: will be so curved that no information can escape. No photons,
• 9:25
  Speaker 1: no particles, no gravitational waves, nothing from beyond this event
• 9:30
  Speaker 1: horizon can ever propagate out and tell you anything about
• 9:33
  Speaker 1: what's hidden behind that curtain. That's the sort of general
• 9:36
  Speaker 1: relativity idea of a black hole. And we've seen some
• 9:39
  Speaker 1: things out there in the universe that really closely resemble
• 9:43
  Speaker 1: a black hole. There's something at the center of our
• 9:44
  Speaker 1: Milky Way, there's a bunch of collapsed stars, there's something
• 9:47
  Speaker 1: at the center of other galaxies that really resembles a
• 9:50
  Speaker 1: black hole. But you know, because you can't see inside
• 9:53
  Speaker 1: the event horizon, we're not exactly sure that what we've
• 9:56
  Speaker 1: seen out there in the universe aligns with Einstein's idea
• 10:00
  Speaker 1: of what a black hole would look like.
• 10:01
  Speaker 2: Yeah, it's basically like an actual hole in space. Right, Like,
• 10:05
  Speaker 2: once you have enough mass into one spot and it's
• 10:08
  Speaker 2: tense enough, that region of space becomes a hole. Right
• 10:11
  Speaker 2: like anything you throw in there, it's going to stay
• 10:12
  Speaker 2: in there.
• 10:13
  Speaker 1: It's a hole in that sense. But a hole sort
• 10:14
  Speaker 1: of gives you an idea of like a discontinuity, like
• 10:17
  Speaker 1: there's a gap or something. But remember that space is smooth,
• 10:20
  Speaker 1: it's continuous. So what we're talking about is space being bent,
• 10:23
  Speaker 1: space being curved, you know the way that like the
• 10:25
  Speaker 1: Earth doesn't move in what looks like a straight line
• 10:27
  Speaker 1: to us because it's following the curvature of space. When
• 10:31
  Speaker 1: you put mass inside space, it bends it. It changes
• 10:34
  Speaker 1: the relative distances between things, which changes how things flow.
• 10:38
  Speaker 1: And so near a black hole, space is curved and
• 10:40
  Speaker 1: curved very very intensely, and as you get closer, that
• 10:43
  Speaker 1: curvature gets stronger and stronger. But it is continuous, right,
• 10:46
  Speaker 1: there's not like a sharp cut off. But there's a
• 10:48
  Speaker 1: point on this smooth curvature past which nothing can escape,
• 10:52
  Speaker 1: and that's the radius we call the event horizon. And
• 10:54
  Speaker 1: so you could say that's sort of like a threshold.
• 10:57
  Speaker 1: It's like a hole if you fall into you'll never escape.
• 11:00
  Speaker 2: Yeah, I think you're saying that there's no cank in space,
• 11:02
  Speaker 2: but there is sort of a point, that sort of
• 11:04
  Speaker 2: a discontinuity where light can no longer escape.
• 11:07
  Speaker 1: Yeah, there's a discontinuity sort of in your fates. Like
• 11:10
  Speaker 1: if you have photons on one side of it and
• 11:11
  Speaker 1: photons on the other side of this radius, the ones
• 11:14
  Speaker 1: past the radius can escape and fly through the universe,
• 11:17
  Speaker 1: and the ones inside the radius will never escape. So
• 11:20
  Speaker 1: there's a sort of discontinuity in the outcomes of particles.
• 11:23
  Speaker 1: But remember the event horizon. It's not a physical barrier.
• 11:26
  Speaker 1: It's just this difference in the outcomes of particles.
• 11:28
  Speaker 2: It's sort of like a real hole, right, Like there's
• 11:31
  Speaker 2: no barrier, you just follow. At some point you're on
• 11:33
  Speaker 2: the hole, and some point you're not on the hole. Yeah,
• 11:36
  Speaker 2: that's right, all right. So then what do we know
• 11:38
  Speaker 2: about black holes, if anything at all.
• 11:40
  Speaker 1: So the frustrating thing is that we have this theoretical
• 11:42
  Speaker 1: concept of what might be inside a black hole. In
• 11:45
  Speaker 1: Einstein's pictures, famelessly, this infinitely dense dot, a singularity where
• 11:50
  Speaker 1: gravity has had this runaway effect compressing and compressing and
• 11:53
  Speaker 1: compressing forever with nothing to resist it and creating this
• 11:56
  Speaker 1: infinitely dense dot at the heart of a black hole.
• 11:59
  Speaker 1: But of course we can't see inside a black hole.
• 12:01
  Speaker 1: All we can do is observe them from the outside.
• 12:04
  Speaker 1: No information escapes from the inside of a black hole,
• 12:07
  Speaker 1: according to Einstein's theory. But we can know a few
• 12:10
  Speaker 1: things about the black hole, like we're on the outside
• 12:13
  Speaker 1: of it. But we can still measure some things about
• 12:15
  Speaker 1: the black hole without going inside. For example, we can
• 12:19
  Speaker 1: know the mass of the black hole. We can measure
• 12:22
  Speaker 1: the black hole's impact on space time even past the
• 12:25
  Speaker 1: event horizon, So we can know something about the black
• 12:28
  Speaker 1: hole without even seeing past the event horizon.
• 12:31
  Speaker 2: You mean, like we can know how much gravity it
• 12:33
  Speaker 2: exerts onto the things around it.
• 12:36
  Speaker 1: Exactly. The curvature of space time continues past the event horizon, right,
• 12:40
  Speaker 1: there's no kink, Like we said, it's smooth, so past
• 12:42
  Speaker 1: the event horizon, it's still exerting an influence on space time,
• 12:47
  Speaker 1: and we can use that measurement of the curvature to
• 12:49
  Speaker 1: tell how much mass there is inside the event horizon,
• 12:53
  Speaker 1: in the same way that like you can measure the
• 12:55
  Speaker 1: mass of the Earth just by seeing its gravitational effect
• 12:58
  Speaker 1: on the Moon or on a satellite. Right, all that
• 13:00
  Speaker 1: gravity adds up and has the same effect on the point.
• 13:03
  Speaker 1: Doesn't tell you anything about like the configuration of the
• 13:06
  Speaker 1: Earth or whatever. And you could replace the Earth with
• 13:08
  Speaker 1: a point particle to have the same gravitational effect. But
• 13:11
  Speaker 1: from a distance you can measure the overall gravitational force.
• 13:15
  Speaker 1: And we can do that for a black hole obviously.
• 13:18
  Speaker 2: And the idea is that like, the more gravity of
• 13:20
  Speaker 2: black hole exerts and of the things around it, the
• 13:22
  Speaker 2: more massive it is.
• 13:24
  Speaker 1: Exactly, we can do the calculation to say how much
• 13:26
  Speaker 1: space time gets bent by black holes of a certain mass,
• 13:29
  Speaker 1: and so we can back that up and say, well,
• 13:31
  Speaker 1: we measure this amount of curvature, and so therefore black
• 13:34
  Speaker 1: hole must have this mass.
• 13:36
  Speaker 2: I wonder if like mass is the actual right term
• 13:38
  Speaker 2: for it, right, Like, we don't even know if what's
• 13:40
  Speaker 2: inside of a black hole is mass or just a
• 13:43
  Speaker 2: whole bunch of pure energy.
• 13:45
  Speaker 1: Right, that's exactly right. We use mass as a way
• 13:47
  Speaker 1: to sort of measure the energy that's inside the black hole,
• 13:50
  Speaker 1: because remember that space time is really curved by energy density,
• 13:54
  Speaker 1: not necessarily just by mass, like a proton bends space time,
• 13:58
  Speaker 1: even though it's just made of a bunch of quarks
• 14:00
  Speaker 1: which are very very low mass. But there's a lot
• 14:02
  Speaker 1: of energy stored inside the proton energy in the bonds
• 14:04
  Speaker 1: of those quarks, which contributes to its mass and contributes
• 14:08
  Speaker 1: to the curvature of space time. So on one hand
• 14:11
  Speaker 1: you could say, well, it's really just the stored energy
• 14:13
  Speaker 1: of the black hole. On the other hand, that's kind
• 14:15
  Speaker 1: of what mass is. Mass is the internal stored energy
• 14:19
  Speaker 1: of an object, and so on one hand, yeah, it's energy.
• 14:22
  Speaker 1: On the other hand, that's what we call mass.
• 14:24
  Speaker 2: Wait, so it's like it's inertial mass or gravitational mass.
• 14:28
  Speaker 2: Does that mean a black hole can have kinetic energy
• 14:30
  Speaker 2: as well well?
• 14:31
  Speaker 1: In general relativity, inertial and gravitational masses are the same thing.
• 14:35
  Speaker 1: So yes, this is its inertial mass. This is like
• 14:38
  Speaker 1: how hard it is to get it moving and how
• 14:40
  Speaker 1: hard it is to slow it down, et cetera, et cetera.
• 14:43
  Speaker 1: And yes, black holes can have kinetic energy. They can
• 14:45
  Speaker 1: move right, and you can move past a black hole,
• 14:48
  Speaker 1: and velocity is all relative. So if you're flying past
• 14:51
  Speaker 1: a black hole at half the speed of light, you
• 14:53
  Speaker 1: see it moving towards you at half the speed of light.
• 14:56
  Speaker 1: So yes, black holes can definitely move, they can have
• 14:58
  Speaker 1: kinetic energy.
• 15:00
  Speaker 2: All right. So then how would you measure the mass
• 15:02
  Speaker 2: of a black hole. You would sort of like put
• 15:04
  Speaker 2: a scale near it or throw a pebble to see
• 15:07
  Speaker 2: how it swings around it. How would you do it?
• 15:09
  Speaker 1: Unfortunately, we're not near enough any black holes to do
• 15:11
  Speaker 1: any experiments, but fortunately in astrophysics we can watch these
• 15:15
  Speaker 1: experiments happen. So the best way to measure the mass
• 15:17
  Speaker 1: with black hole is to see the motion of stuff
• 15:19
  Speaker 1: near it, like the mass of the black hole the
• 15:21
  Speaker 1: center the Milky Way. We measure by looking at stars
• 15:24
  Speaker 1: that whiz past it and seeing the gravitational force on
• 15:28
  Speaker 1: those objects and knowing how much mass has to be
• 15:31
  Speaker 1: to create that gravitational force to make the stars bend
• 15:34
  Speaker 1: the way they do. And for distant black holes and
• 15:37
  Speaker 1: other galaxies, we can see like the sort of swirl
• 15:39
  Speaker 1: of stars around the center of the galaxy and use
• 15:42
  Speaker 1: that to measure the gravitational force from the black hole.
• 15:45
  Speaker 2: Yeah, that's what I meant, you know, a pebble star.
• 15:48
  Speaker 1: Yeah, basically, yes, same thing, the pebble.
• 15:50
  Speaker 2: Method, all right, So then what else can we know
• 15:53
  Speaker 2: about a black hole?
• 15:54
  Speaker 1: Another thing we can know about a black hole is
• 15:56
  Speaker 1: it's electric charge. If you put electrons into a black hole, Well,
• 16:00
  Speaker 1: charge is concerned in the universe. So if an electron
• 16:03
  Speaker 1: falls into the black hole, the black hole now has
• 16:05
  Speaker 1: an overall negative charge. At another electron, get another negative charge.
• 16:09
  Speaker 1: So you can know the overall charge of a black hole.
• 16:13
  Speaker 2: Well, you mean like a black hole can have a voltage.
• 16:15
  Speaker 1: Yeah, a black hole can have an overall charge and
• 16:18
  Speaker 1: it can have electric fields. Right in the same way
• 16:21
  Speaker 1: that black hole has mass, and that makes for effectively
• 16:24
  Speaker 1: a gravitational field or bending of space time past the
• 16:28
  Speaker 1: event horizon. The black hole can have a charge and
• 16:30
  Speaker 1: that creates an electric field which can also be pasted
• 16:33
  Speaker 1: the event horizon.
• 16:34
  Speaker 2: Interesting, but I guess if I wonder if a black
• 16:37
  Speaker 2: hole has a negative charge, can you use it as
• 16:39
  Speaker 2: a battery? Probably not, right, Like you can't get electrons
• 16:43
  Speaker 2: to flow out of it, can you?
• 16:44
  Speaker 1: You can use a charged black hole the way you
• 16:46
  Speaker 1: can use any other kind of charged particle. Right, You
• 16:49
  Speaker 1: can use it to create electric fields. You can use
• 16:52
  Speaker 1: it to repel stuff or attract stuff. But I think
• 16:54
  Speaker 1: batteries involved like the flow of electrons through materials and
• 16:58
  Speaker 1: I don't know that's chemistry.
• 17:03
  Speaker 2: That's too hairy for you.
• 17:04
  Speaker 1: Yeah, But essentially, you can think of a black hole
• 17:06
  Speaker 1: as just like an enormous particle, right the way like
• 17:10
  Speaker 1: an electron sort of has a charge attached to it,
• 17:12
  Speaker 1: but you don't really think about like where is the charge.
• 17:15
  Speaker 1: It's just like a property of the electron. You could
• 17:17
  Speaker 1: think the black hole as just sort of like enormous particle.
• 17:20
  Speaker 1: You don't have any details about, like where is the
• 17:22
  Speaker 1: electric charge. It's just sort of like assigned to the
• 17:24
  Speaker 1: entire event horizon, the same way you assign the mass
• 17:27
  Speaker 1: to the entire event horizon. You don't really know what's
• 17:30
  Speaker 1: going on inside, how it's that mass arranged? Is it
• 17:32
  Speaker 1: still in bananas? Is it squished into something else? Is
• 17:35
  Speaker 1: it nuclear pasta? You don't know anything about the internals.
• 17:38
  Speaker 1: You just assigned it to the exterior, and then you
• 17:40
  Speaker 1: can treat it like anything else that has a charge.
• 17:42
  Speaker 2: I see, sort of like maybe the Earth. You could
• 17:44
  Speaker 2: do that with the Earth too, right, Like, I'm sure
• 17:45
  Speaker 2: the Earth has an overall.
• 17:46
  Speaker 1: Charge exactly, any extended object with an overall charge from
• 17:50
  Speaker 1: a distance, you can treat like a point particle with
• 17:52
  Speaker 1: a charge, the math is exactly the same. And the
• 17:55
  Speaker 1: case of the Earth, of course, we can know it,
• 17:57
  Speaker 1: and it's not hidden beyond an advent horizon, So we
• 17:59
  Speaker 1: could learn about this stuff in other ways. In the
• 18:01
  Speaker 1: case of a black hole, you can't. And there's something
• 18:03
  Speaker 1: sort of similar there about a black hole and a particle,
• 18:06
  Speaker 1: the way that like two electrons are identical. You know,
• 18:09
  Speaker 1: you can't tell the difference between this electron and that electron.
• 18:12
  Speaker 1: They have all the same properties. That's what defines them.
• 18:15
  Speaker 1: Two black holes with the same mass and the same charge,
• 18:17
  Speaker 1: and it'll talk about it in the same spin, are
• 18:20
  Speaker 1: really two identical objects?
• 18:22
  Speaker 2: All right? Well, talk about spin? What a spin for
• 18:24
  Speaker 2: a black hole?
• 18:25
  Speaker 1: So the same way that you can toss stuff into
• 18:27
  Speaker 1: a black hole that has charge, you can also toss
• 18:29
  Speaker 1: stuff into a black hole that makes it spin. You
• 18:32
  Speaker 1: throw something exactly towards the center of the black hole,
• 18:34
  Speaker 1: it'll make it grow and make it more massive. But
• 18:36
  Speaker 1: if you throw something into the event horizon but a
• 18:38
  Speaker 1: little bit off center, then it's sort of like you're
• 18:40
  Speaker 1: giving it a push. The way if you're like holding
• 18:42
  Speaker 1: a bicycle wheel on an axle and you hit the rim,
• 18:44
  Speaker 1: it'll start to spin. Or if you push on a
• 18:46
  Speaker 1: merry go round, it'll start to spin. If you throw
• 18:48
  Speaker 1: particles into the edge of the black hole, you can
• 18:51
  Speaker 1: get it to spin because angular momentum, like charge, doesn't
• 18:55
  Speaker 1: disappear in our universe. So that black hole then has
• 18:57
  Speaker 1: to accumulate that angular momentum, which means it has to spin.
• 19:02
  Speaker 2: But I guess the angular momentum in the universe is
• 19:04
  Speaker 2: not like a fundamental thing. Is It's not like energy
• 19:08
  Speaker 2: or regular momentum. Is it like? It's really just like
• 19:11
  Speaker 2: the difference between two points in your body and how
• 19:13
  Speaker 2: they're moving relative to each other, isn't.
• 19:15
  Speaker 1: It Now, angular momentum is just as fundamental as linear momentum,
• 19:18
  Speaker 1: and maybe even more fundamental than energy number. Energy not
• 19:22
  Speaker 1: actually conserved in our universe because conservation of energy requires
• 19:26
  Speaker 1: space to be static, and our universe space is expanding,
• 19:29
  Speaker 1: so energy is not conserved. But linear momentum and angular
• 19:32
  Speaker 1: momentum are both conserved in our universe. It comes from
• 19:36
  Speaker 1: deep symmetries. Linear momentum comes from the fact that space
• 19:39
  Speaker 1: is the same everywhere, that like translation from here to there,
• 19:42
  Speaker 1: shouldn't change your experiment, and angular momentum comes from the
• 19:45
  Speaker 1: fact that there's no preferred direction in space, that every
• 19:49
  Speaker 1: direction is equivalent, and so angular momentum has to be
• 19:51
  Speaker 1: conserved and that makes angular momentum something very fundamental to
• 19:54
  Speaker 1: the universe.
• 19:55
  Speaker 2: All right, Well, so then a black hole can have
• 19:57
  Speaker 2: angular momentum, and that is that what it's been exactly.
• 20:00
  Speaker 1: The spin of the black hole is how it stores
• 20:02
  Speaker 1: angular momentum. And there's all sorts of fascinating consequences there
• 20:05
  Speaker 1: in general relativity, because like a singularity can't spin. So
• 20:10
  Speaker 1: the idea is that inside a spinning black hole is
• 20:12
  Speaker 1: maybe not a singularity but a ringularity, like a whole
• 20:17
  Speaker 1: circle of singularities, and those singularities are all spinning together,
• 20:21
  Speaker 1: which is how they store the angular momentum. But nobody
• 20:24
  Speaker 1: really knows what's actually going on inside.
• 20:27
  Speaker 2: All right, So the things we can know about a
• 20:28
  Speaker 2: black hole are its mass, it's spin, and it's charge.
• 20:32
  Speaker 2: Now the big question is can we know how hairy
• 20:35
  Speaker 2: it is? So let's dig into that question. But first
• 20:38
  Speaker 2: let's take out a quick break. All right, we're talking
• 20:53
  Speaker 2: about the hairs of a black hole. Can a whole
• 20:56
  Speaker 2: half hairs.
• 20:58
  Speaker 1: That's exactly the question. And when physicists say hair, they
• 21:01
  Speaker 1: don't really mean hair. They're just taking a word that
• 21:05
  Speaker 1: exists that has another meaning and giving it a meaning.
• 21:08
  Speaker 1: In physics, which is, you know, has a great tradition
• 21:10
  Speaker 1: of being very confusing what.
• 21:12
  Speaker 2: You mean, like in this case it actually is like
• 21:15
  Speaker 2: a cosmic string or a particle or something, or is
• 21:18
  Speaker 2: it just a metaphor, it's.
• 21:19
  Speaker 1: A metaphor for anything else. Essentially, general relativity tells us
• 21:22
  Speaker 1: that we can know three things about a black hole.
• 21:25
  Speaker 1: Its mass, it's been its charge, and nothing else. Nothing
• 21:29
  Speaker 1: about its history, no interesting little details, no texture, no hair.
• 21:34
  Speaker 2: Is that because of the event horizon. Basically, like if
• 21:38
  Speaker 2: you wrap the Earth around an impenetrable, you know, black shield,
• 21:43
  Speaker 2: you could also not tell anything about the Earth, whether
• 21:45
  Speaker 2: it's t had hairs or not.
• 21:46
  Speaker 1: I think that's true, but maybe only because an impenetrable
• 21:50
  Speaker 1: black shield would basically have to be an event horizon
• 21:52
  Speaker 1: of a black hole. There's no other way to make
• 21:55
  Speaker 1: something truly impenetrable. If you just build something really solid
• 21:58
  Speaker 1: and black, it would like read it it's some temperature,
• 22:01
  Speaker 1: and that would tell you about what's going on inside
• 22:03
  Speaker 1: of it. The only way to really be impenetrabled to
• 22:06
  Speaker 1: give up no information would be to make a black hole.
• 22:08
  Speaker 2: I guess that's what I mean. It's like, the reason
• 22:10
  Speaker 2: we can't know anything else about a black hole is
• 22:12
  Speaker 2: because it has an event horizon which keeps all the
• 22:15
  Speaker 2: information inside. It's not something like that information is destroyed, right.
• 22:20
  Speaker 1: We don't know what's going on exactly. And that's the
• 22:22
  Speaker 1: deepest question, is like is the information destroyed? Is it
• 22:25
  Speaker 1: actually contained within black hole somehow or is it actually destroyed?
• 22:30
  Speaker 1: Like is the internal state of a black hole the same,
• 22:33
  Speaker 1: no matter what you've put into it. Make a black
• 22:35
  Speaker 1: hole out of bananas and you make another one out
• 22:37
  Speaker 1: of apples. Do you really get exactly the identical black
• 22:41
  Speaker 1: hole out of those two things if you put in
• 22:43
  Speaker 1: the same amount of mass? Or is there some history
• 22:47
  Speaker 1: there some way to tell a banana from an apple
• 22:50
  Speaker 1: black hole?
• 22:51
  Speaker 2: I guess I'm trying to, you know, relate it to
• 22:53
  Speaker 2: the earth, and like you could make an earth out
• 22:55
  Speaker 2: of bananas, and if you put it behind your impenetrable shield,
• 22:58
  Speaker 2: you could also not tell the Earth what's made out
• 23:00
  Speaker 2: of bananas or apples.
• 23:03
  Speaker 1: That's exactly right, but it conflicts with sort of other things.
• 23:06
  Speaker 1: We've seen in the universe and our quantum intuition, because
• 23:08
  Speaker 1: quantum mechanics tells us that information is not destroyed, that
• 23:12
  Speaker 1: the present is uniquely determined by the past, and that
• 23:16
  Speaker 1: therefore from the present you can always derive the past,
• 23:19
  Speaker 1: that like the past, has left a permanent imprint on
• 23:22
  Speaker 1: the present. Quantum mechanics tells us that we can run
• 23:24
  Speaker 1: the laws of physics forwards or backwards in time, so
• 23:27
  Speaker 1: we could use the present to predict the future in
• 23:29
  Speaker 1: the same way we could use the present to reveal
• 23:31
  Speaker 1: the past. And this is in conflict with that. This says, no, no, no,
• 23:34
  Speaker 1: there's no information here. Once you create a black hole,
• 23:37
  Speaker 1: you can't tell what its history is at all. There's
• 23:40
  Speaker 1: no texture to grab onto, no little details if you
• 23:43
  Speaker 1: zoom in, there are no hairs there to reveal the
• 23:46
  Speaker 1: history of the black hole.
• 23:47
  Speaker 2: I wonder if maybe the real question is not whether
• 23:50
  Speaker 2: a black hole has hair. The question seems to be
• 23:52
  Speaker 2: more like, if I toss a hair into a black hole,
• 23:54
  Speaker 2: does the hair get destroyed forever? Or is it just
• 23:58
  Speaker 2: going to stay inside the black hole and it's going
• 24:00
  Speaker 2: to be there, but we can't tell if it's there.
• 24:03
  Speaker 1: I think those are both really interesting questions, but I
• 24:05
  Speaker 1: think there are separate questions. In general relativity, we can't
• 24:08
  Speaker 1: know anything that passes the event horizon. But maybe general
• 24:11
  Speaker 1: relativity black holes are not the black holes we see
• 24:14
  Speaker 1: in our universe. Maybe there are little ripples and hairs
• 24:17
  Speaker 1: on the event horizon that we could use to learn
• 24:19
  Speaker 1: about what has fallen in. And then the second question
• 24:22
  Speaker 1: is like what happens to stuff that falls in does
• 24:24
  Speaker 1: form some new state of matter? Is that information still there?
• 24:27
  Speaker 1: Because we think that black holes eventually evaporate, that they
• 24:30
  Speaker 1: radiate away all of their energy, they lose their mass,
• 24:33
  Speaker 1: and if that information has been destroyed within them, then
• 24:36
  Speaker 1: that information is lost forever, which would be very confusing
• 24:39
  Speaker 1: from the point of view of quantum mechanics.
• 24:41
  Speaker 2: Well to the second question, I know we've talked about
• 24:43
  Speaker 2: in the podcast before, how it is possible to go
• 24:46
  Speaker 2: into a black hole and survive. Right, Like, for a
• 24:49
  Speaker 2: big enough black hole, the event horizon happens. You don't
• 24:52
  Speaker 2: have to get spaghetified or shredded apart to go into
• 24:55
  Speaker 2: technically the event horizon of a super massive black hole, right,
• 24:58
  Speaker 2: That's right.
• 24:58
  Speaker 1: And if for really large black hole holes, if they
• 25:01
  Speaker 1: do have significant charge and or spin. There are even
• 25:04
  Speaker 1: stable orbits within the event horizon of the black hole.
• 25:08
  Speaker 2: So you could like fall into a super massive black
• 25:10
  Speaker 2: hole and stay in there but still be hole, still
• 25:14
  Speaker 2: be there.
• 25:14
  Speaker 1: And still be inside. According to general relativity, yes that
• 25:17
  Speaker 1: is possible. Again, we don't really know right what is
• 25:20
  Speaker 1: going on inside there, so we don't really know the
• 25:22
  Speaker 1: fate of any of this stuff until you know, you
• 25:24
  Speaker 1: jump into a black hole and figure it out.
• 25:26
  Speaker 2: Well, not me, Maybe it should be the physinessist. I mean,
• 25:29
  Speaker 2: I think you need the cartoonist outside to draw what
• 25:32
  Speaker 2: happens and then figure out if it's a good idea.
• 25:35
  Speaker 2: But I guess what I mean is you can throw
• 25:37
  Speaker 2: a hair into a black hole and it can survive,
• 25:40
  Speaker 2: Like you can have a hair inside of a black hole.
• 25:42
  Speaker 2: It's she said, if somebody else comes by, they won't
• 25:44
  Speaker 2: be able to know whether you threw a hair in
• 25:46
  Speaker 2: there or not.
• 25:46
  Speaker 1: Exactly that's true. According to general relativity. You could build
• 25:49
  Speaker 1: a black hole out of hairs and nobody else could
• 25:52
  Speaker 1: tell the difference between that and a black hole made
• 25:54
  Speaker 1: out of toenails or something else.
• 25:56
  Speaker 2: But you would know there was a hair in there.
• 25:57
  Speaker 1: You would know because you saw it falling in.
• 25:59
  Speaker 2: You mean, yeah, or because I tossed it into the hole.
• 26:02
  Speaker 1: That's true, you would know the history, but there'd be
• 26:04
  Speaker 1: no way to measure it from the objects itself. There'll
• 26:06
  Speaker 1: be no record on the outside that would tell you. Again,
• 26:09
  Speaker 1: according to general relativity.
• 26:11
  Speaker 2: Okay, so then what does that mean? Does that mean?
• 26:14
  Speaker 2: Quantum mechanics says something differently.
• 26:16
  Speaker 1: Quantum mechanics definitely says something different, And quantum mechanics tells
• 26:19
  Speaker 1: us that this whole picture of a black hole according
• 26:22
  Speaker 1: to general relativity is very very likely wrong. Remember that
• 26:26
  Speaker 1: general relativity is not built on the foundation of quantum mechanics.
• 26:29
  Speaker 1: It makes very different assumptions about how the universe works.
• 26:32
  Speaker 1: It assumes that space and time are continuous and smooth,
• 26:36
  Speaker 1: that you can have like infinitely small distances and infinitely
• 26:39
  Speaker 1: small masses. Quantum mechanics gives us a very different picture.
• 26:42
  Speaker 1: It says everything is discreet, it's quantized, it's chunked up
• 26:46
  Speaker 1: into pieces, and there's a limited amount of information we
• 26:49
  Speaker 1: can know about the universe. General relativity says that you
• 26:52
  Speaker 1: can have tiny little objects moving in smooth paths, so
• 26:55
  Speaker 1: you can perfectly know how they move. Quantum mechanics says
• 26:57
  Speaker 1: that's not possible, and they come directly into inflict at
• 27:00
  Speaker 1: the heart of a black hole, where general relativity says
• 27:03
  Speaker 1: you have this point of infinite density and quantum mechanics says, no,
• 27:06
  Speaker 1: that's not possible. And so what we need is some
• 27:09
  Speaker 1: sort of merging of the two, a theory of quantum
• 27:11
  Speaker 1: gravity that tells us what happens when quantum objects feel
• 27:15
  Speaker 1: very strong gravity.
• 27:16
  Speaker 2: I guess maybe the question is what does quantum mechanics
• 27:19
  Speaker 2: say about the black hole hair question?
• 27:22
  Speaker 1: So quantum mechanics as we have it now doesn't know
• 27:24
  Speaker 1: how to deal with gravity for particles. Right, particles are
• 27:28
  Speaker 1: very different from things like sand, or rocks, or base
• 27:31
  Speaker 1: balls or even pieces of hair. Those things are basically
• 27:34
  Speaker 1: classical objects, so we know where they are and we
• 27:36
  Speaker 1: can talk about them as if they always have a
• 27:38
  Speaker 1: specified location. But quantum particles are different. They have like
• 27:41
  Speaker 1: probabilities of being here and probabilities of being there, So
• 27:44
  Speaker 1: we don't know how to do gravity for particles. Like
• 27:47
  Speaker 1: if a particle has a probability to be here and there,
• 27:50
  Speaker 1: does it have half the gravity here and half the
• 27:52
  Speaker 1: gravity there, or is there a gravity probability we don't know.
• 27:56
  Speaker 1: What we need is a theory of gravity for particles,
• 27:59
  Speaker 1: and nobody has one, and so until you have that theory,
• 28:02
  Speaker 1: you can't actually know what quantum mechanics even says about
• 28:06
  Speaker 1: what's going on inside a black hole, or whether there
• 28:08
  Speaker 1: are ripples in texture on the surface of the black
• 28:11
  Speaker 1: hole that you can use to figure out what's inside.
• 28:13
  Speaker 2: I see, I think this is what I'm trying to
• 28:15
  Speaker 2: get to, is like, what do you mean like quantum
• 28:18
  Speaker 2: mechanics says there are ripples on the surface that might
• 28:20
  Speaker 2: be able to tell you if a black hole is
• 28:21
  Speaker 2: made out of hairs or bananas.
• 28:23
  Speaker 1: Unfortunately, we have no perfect theory of quantum gravity, but
• 28:25
  Speaker 1: people are doing some calculations to try to figure out
• 28:28
  Speaker 1: is it possible for a quantum black hole to have hair? Wait?
• 28:31
  Speaker 2: Wait, wait, what's a quantum black hole?
• 28:33
  Speaker 1: So quantum black hole would just be a black hole
• 28:35
  Speaker 1: as described by a theory of quantum gravity, instead of
• 28:39
  Speaker 1: a classical black hole as described by general relativity. Right,
• 28:42
  Speaker 1: Einstein's classical black holes are a singularity with an event
• 28:45
  Speaker 1: horizon around them, with no hair whatsoever, a perfectly smooth surface,
• 28:48
  Speaker 1: and you can't tell anything about what's inside or what
• 28:51
  Speaker 1: was used to build it. Quantum black hole is a
• 28:53
  Speaker 1: description of a different theoretical object, one that follows rules
• 28:57
  Speaker 1: of quantum gravity.
• 28:58
  Speaker 2: All right, let's dig into that. Is a quantum black hole,
• 29:01
  Speaker 2: hole that's both black and white at the same time.
• 29:03
  Speaker 1: No, no, but that sounds awesome. I wish that were true.
• 29:08
  Speaker 1: Carlo Rovelli has this fun theory that black holes might
• 29:11
  Speaker 1: be collapsing stars that are slowed down by gravitational time dilation,
• 29:16
  Speaker 1: and eventually they turn around and become white holes. And
• 29:19
  Speaker 1: we had a fun conversation with him and some of
• 29:22
  Speaker 1: his colleagues about exactly that how a black hole can
• 29:24
  Speaker 1: be in a superposition of a state maybe being a
• 29:26
  Speaker 1: black hole, maybe being a white hole. So basically, yeah,
• 29:29
  Speaker 1: your theory is one of the contenders.
• 29:31
  Speaker 2: There you go. So, then how is a quantum black
• 29:33
  Speaker 2: hole different than a regular relativity black hole.
• 29:37
  Speaker 1: So there's a few different answers to that, because there
• 29:39
  Speaker 1: are a few different theories of quantum gravity. Right, we
• 29:41
  Speaker 1: have no perfect theory. We don't even have a theory
• 29:44
  Speaker 1: that's complete and it works on paper, not to mention
• 29:46
  Speaker 1: a theory which has been tested against what's actually happening
• 29:49
  Speaker 1: out there in the universe. So people are working in
• 29:52
  Speaker 1: different directions in quantum gravity, and some of them are
• 29:55
  Speaker 1: working specifically on this problem and have ideas for the
• 29:58
  Speaker 1: consequences of their particular quantum gravity on the hairiness of
• 30:02
  Speaker 1: a black hole. So in some theories of quantum gravity,
• 30:05
  Speaker 1: black holes have different kinds of hairs.
• 30:07
  Speaker 2: Like long hair, curly hairs, luster's hairs. What did to
• 30:11
  Speaker 2: say about what black holes could be like?
• 30:13
  Speaker 1: Yeah, so let's go through some of the options. The
• 30:14
  Speaker 1: first real progress in quantum gravity was Stephen Hawking. He said, actually,
• 30:19
  Speaker 1: let's figure out whether black holes radiate a weigh any information.
• 30:23
  Speaker 1: And he has his famous theory of Hawking radiation that
• 30:26
  Speaker 1: says that black holes generate particles. You know, if you're
• 30:30
  Speaker 1: near the surface of a black hole, it'll actually be
• 30:32
  Speaker 1: shooting off particles at you. This is Hawking radiation. The
• 30:35
  Speaker 1: thing about Hawking radiation from black holes is that it's
• 30:37
  Speaker 1: supposed to contain zero information that just depends on the
• 30:42
  Speaker 1: mass of the black hole and nothing else about the
• 30:44
  Speaker 1: internal configuration, about whether it's apples or bananas.
• 30:47
  Speaker 2: And that's because it's like generating particles out of the vacuum,
• 30:51
  Speaker 2: right out of nothingness, out of pure energy that's inside
• 30:54
  Speaker 2: the black hole. Like, it doesn't depend on what kind
• 30:58
  Speaker 2: of energy, whether it has hairs or been in it's inside.
• 31:01
  Speaker 2: It just kind of creates stuff. As I think, I
• 31:04
  Speaker 2: understand that it just creates stuff and then radiates it out.
• 31:07
  Speaker 1: That's right, that it creates stuff based just on the
• 31:09
  Speaker 1: energy the mass of the black hole. Actually it's formulated
• 31:12
  Speaker 1: fascinatingly in terms of like black hole thermodynamics. So you
• 31:15
  Speaker 1: can think about the temperature of the black hole. But
• 31:18
  Speaker 1: you have to be very careful about applying Hawking's arguments
• 31:21
  Speaker 1: to like a microscopic particle picture of what's happening about
• 31:24
  Speaker 1: creating these particles, because Hawking doesn't have again, the full
• 31:27
  Speaker 1: theory of quantum gravity. He did this sort of semi
• 31:30
  Speaker 1: classical calculation where he thought about quantum fields and near
• 31:33
  Speaker 1: event horizons, and he figured out that these quantum fields
• 31:35
  Speaker 1: have to radied. He doesn't have a microscopic picture. And
• 31:39
  Speaker 1: you'll often hear this story about Hawking radiation, about particles
• 31:42
  Speaker 1: and antip particles created near the event horizon. One falls
• 31:45
  Speaker 1: in and one escapes, et cetera, et cetera. That's all
• 31:48
  Speaker 1: hand wavy storytelling. That's not accurate it doesn't actually hold
• 31:52
  Speaker 1: together in terms of what's happening with Hawking radiation.
• 31:54
  Speaker 2: Wait, it doesn't hold together, or we don't know if
• 31:56
  Speaker 2: it's true.
• 31:57
  Speaker 1: If you start from that microscopic picture and try to
• 31:59
  Speaker 1: build up a prediction of Hawking radiation, it doesn't work.
• 32:02
  Speaker 2: What do you mean, Like, the radiation we measure from
• 32:04
  Speaker 2: a black hole doesn't match what you would predict from that.
• 32:07
  Speaker 1: Well, number one, we've never measured the radiation from a
• 32:09
  Speaker 1: black hole. This is still just theoretical.
• 32:11
  Speaker 2: So then what do you mean.
• 32:12
  Speaker 1: As soon as you make yourself this microscopic picture and
• 32:14
  Speaker 1: then you have these quantum particles, you have all sorts
• 32:16
  Speaker 1: of questions you can't answer, like about fuzziness and probability,
• 32:20
  Speaker 1: and whether the particles can fluctuate past the event horizon
• 32:23
  Speaker 1: or not. And so the quantum mechanical picture isn't really
• 32:26
  Speaker 1: complete about what's happening to these little particles. Nobody can
• 32:29
  Speaker 1: start from those particles and calculate up and predict Hawking radiation.
• 32:32
  Speaker 1: That's not what's happening. Hawking has started from sort of
• 32:34
  Speaker 1: a bigger, broader picture, just from understanding like the energy
• 32:37
  Speaker 1: flow the quantum fields near the event horizon, and predicted
• 32:41
  Speaker 1: that the emit radiation. But again there's no microscopic picture
• 32:44
  Speaker 1: that really holds together. But you want to know more
• 32:46
  Speaker 1: details about how that works. We have a whole episode
• 32:48
  Speaker 1: about Hawking radiation where we can review that in detail.
• 32:51
  Speaker 2: But I think the main picture you're saying is that
• 32:53
  Speaker 2: we do know that black holes radiate Hawking radiation. We
• 32:56
  Speaker 2: just don't know like the specific details of what's happening
• 32:59
  Speaker 2: at the border of a black hole to make that happen.
• 33:01
  Speaker 1: That's right, Hawking didn't come up with a complete theory
• 33:04
  Speaker 1: of quantum gravity, so he doesn't have a microscopic picture,
• 33:07
  Speaker 1: and he predicts this Hawking radiation, which again should contain
• 33:10
  Speaker 1: no information. So a Hawking black hole basically has no hair,
• 33:14
  Speaker 1: even though it's kind of a quantum black hole. But
• 33:16
  Speaker 1: there are other theories of quantum gravity people who've been
• 33:18
  Speaker 1: working on, and some of these do predict black hole hair.
• 33:21
  Speaker 2: All right, let's get into the hairy details of these
• 33:23
  Speaker 2: theories and whether or not black holes have hair or
• 33:26
  Speaker 2: quantum hairs or no hairs at all, and what it
• 33:29
  Speaker 2: could mean about our understanding of the laws of physics.
• 33:32
  Speaker 2: But first, let's take another quick break, all right, we
• 33:47
  Speaker 2: are braiding our knowledge of the universe here talking about
• 33:50
  Speaker 2: black hole hairs and whether they have it or not.
• 33:54
  Speaker 2: And so according to Einstein, who is famous for his hair,
• 33:56
  Speaker 2: by the way, his gray hair, even as black holes
• 33:59
  Speaker 2: don't have hair, which seems kind of mean given how
• 34:01
  Speaker 2: much hair he had. But it seems like quantum mechanics
• 34:04
  Speaker 2: at first said they didn't have hairs, but now there
• 34:06
  Speaker 2: were some theories about quantum gravity that say, maybe they
• 34:09
  Speaker 2: do have hairs.
• 34:10
  Speaker 1: That's right, And all these calculations are approximate. You know,
• 34:13
  Speaker 1: nobody has a full theory of quantum gravity that they
• 34:15
  Speaker 1: can start from and predict these things from first principles.
• 34:18
  Speaker 1: Everybody is doing sort of approximations. They're saying, well, we
• 34:21
  Speaker 1: don't have the full theory, but maybe it looks a
• 34:23
  Speaker 1: little bit like this, And if it looked like this,
• 34:25
  Speaker 1: then what would be the answer to this question? But
• 34:28
  Speaker 1: a lot of is approximate and handwavy and inconsistent with
• 34:31
  Speaker 1: other things. But you know, this is how progress is made.
• 34:34
  Speaker 1: We don't always just have a flash of insight with
• 34:36
  Speaker 1: the whole answer that we can work from. We put
• 34:38
  Speaker 1: things together and try to patch them together, and eventually
• 34:41
  Speaker 1: maybe it comes together into a bigger picture of everything, all.
• 34:44
  Speaker 2: Right, Well, so then how do these fuzzy quantum gravity
• 34:47
  Speaker 2: theories say that black holes have hair?
• 34:50
  Speaker 1: So there's a paper about ten years ago that try
• 34:52
  Speaker 1: to study the configuration of gravitons far away from a
• 34:56
  Speaker 1: black hole, so outside the event horizon. Really interesting question
• 35:01
  Speaker 1: to think about gravity as a quantum force because if
• 35:05
  Speaker 1: gravity isn't the curvature spaced time, if quantum gravity lies
• 35:08
  Speaker 1: in the direction of like figuring out how to express
• 35:11
  Speaker 1: gravity in the same kind of language that we express
• 35:14
  Speaker 1: other forces like the weak force and electricity, magnetism and
• 35:17
  Speaker 1: the strong force as forces mediated by particles the way
• 35:21
  Speaker 1: they like the photon mediates electromagnetism. Then gravity would have
• 35:25
  Speaker 1: a particle, the graviton that you use to mediate gravity.
• 35:30
  Speaker 1: And so in this picture this is like graviton based
• 35:32
  Speaker 1: quantum gravity. People thought about, like, what's happening with all
• 35:36
  Speaker 1: the gravitons in the vicinity of a black hole?
• 35:39
  Speaker 2: Like what they get sucked in too? Right?
• 35:41
  Speaker 1: Yeah? Would they get sucked in? Is there information in
• 35:44
  Speaker 1: the flow of the gravitons. People are often writing in
• 35:47
  Speaker 1: and asking me if the mass of the black hole
• 35:50
  Speaker 1: is contained within the event horizon and gravity is quantum mechanical,
• 35:54
  Speaker 1: wouldn't it need to like shoot out gravitons in order
• 35:57
  Speaker 1: to mediate gravity, and wouldn't that break the area of
• 36:00
  Speaker 1: the black hole? So you can see how it's tricky
• 36:03
  Speaker 1: to think about gravity as a quantum force. If there
• 36:06
  Speaker 1: really is an event horizon there.
• 36:08
  Speaker 2: Whoa Okay, So let me see if I got this right,
• 36:11
  Speaker 2: and a quantum theory that has gravitons in it, which
• 36:14
  Speaker 2: we don't know if they exist or not, like the
• 36:16
  Speaker 2: gravity of a black hole, you would feel it because
• 36:19
  Speaker 2: it's shooting gravitons at me or am I shooting gravitons
• 36:23
  Speaker 2: at the black hole? Couldn't both be the case?
• 36:25
  Speaker 1: Yeah, both would be the case. And one question is
• 36:27
  Speaker 1: whether those gravitons contain any information about what's inside the
• 36:32
  Speaker 1: black hole or not. On one hand, you can imagine
• 36:34
  Speaker 1: the event horizon itself just generating a gravitational field and
• 36:39
  Speaker 1: shooting off gravitons from the event horizon. No information about
• 36:42
  Speaker 1: what's going on inside, only information about the total mass. Right,
• 36:46
  Speaker 1: Like if you could change the configuration inside, if you
• 36:48
  Speaker 1: build it out of bananas instead of apples, you get
• 36:51
  Speaker 1: the same exact distribution of gravitons in the outside, or
• 36:54
  Speaker 1: is there information in the graviton ripples that tells you
• 36:58
  Speaker 1: about what's happening inside the event horizon. So there's this
• 37:01
  Speaker 1: paperback ten years ago that deduced some small changes in
• 37:05
  Speaker 1: the graviton field far away from the event horizon based
• 37:09
  Speaker 1: on the mass that was inside. Essentially like a little
• 37:12
  Speaker 1: bit of a history imprinted on the space around the
• 37:15
  Speaker 1: black hole that could tell you what had fallen in.
• 37:18
  Speaker 1: You could like show up to a black hole a
• 37:20
  Speaker 1: million years later and say, oh, there was a banana
• 37:22
  Speaker 1: and then an apple, and then three granola bars thrown
• 37:25
  Speaker 1: into this black hole.
• 37:26
  Speaker 2: What do you mean, Like, how would the banana versus
• 37:28
  Speaker 2: the apple affect the graviton that the black hole shoots out, So.
• 37:32
  Speaker 1: It affects the gravitational field outside. The gravitons themselves don't
• 37:36
  Speaker 1: pass the event horizon, but the event horizon itself has
• 37:39
  Speaker 1: some shape to it, because remember, in Einstein's general relativity,
• 37:43
  Speaker 1: a black hole is a perfectly spherical object, right like,
• 37:47
  Speaker 1: as you zoom into it, you never see any bumps,
• 37:50
  Speaker 1: any ripples, any change. It's perfectly spherical. But quantum mechanics
• 37:53
  Speaker 1: says that can't be the case, right, that there's always
• 37:56
  Speaker 1: a discritizations like a pixelization inherent to the universe, which
• 37:59
  Speaker 1: means the event horizon has to have some ripples to
• 38:02
  Speaker 1: it's some texture to it, and those tiny little deviations
• 38:05
  Speaker 1: can change the ripples of the gravitons on the outside,
• 38:09
  Speaker 1: and they're caused by the history of stuff that you've
• 38:12
  Speaker 1: thrown into the black hole. So you make a very
• 38:14
  Speaker 1: slightly different black hole if you put in bananas than
• 38:17
  Speaker 1: if you put in apples. That information is not lost,
• 38:19
  Speaker 1: it's somehow contained on the event horizon of the black hole.
• 38:23
  Speaker 2: Like if a black hole has a banana at its
• 38:25
  Speaker 2: center or an apple at its center, you're saying that
• 38:28
  Speaker 2: it might cause a different texture of the event horizon
• 38:32
  Speaker 2: at the border of it.
• 38:33
  Speaker 1: Exactly. Yeah, And you could detect this if you could
• 38:35
  Speaker 1: measure gravitons in the vicinity of the black hole.
• 38:39
  Speaker 2: How would the banana or the apple affect the texture
• 38:41
  Speaker 2: all the way at the edge of the black hole?
• 38:43
  Speaker 2: Like if I put a banana or an apple on
• 38:44
  Speaker 2: the center of the Earth, would it I guess it
• 38:46
  Speaker 2: would affect the surface of the Earth in some microscopic way.
• 38:50
  Speaker 1: You have to think about this quantum mechanically right, we're
• 38:52
  Speaker 1: talking about the quantum states of all these objects, which
• 38:55
  Speaker 1: contain the history of everything that's happened to them. Remember,
• 38:58
  Speaker 1: in a quantum world, the present is uniquely determined by
• 39:02
  Speaker 1: the past, which means that every possible past has a
• 39:06
  Speaker 1: different present, which means you can invert it. You can say, well,
• 39:09
  Speaker 1: because we're in this present, we can tell what the
• 39:11
  Speaker 1: past was. So all the tiny ripples, the details of
• 39:15
  Speaker 1: the quantum states of everything around you could be used
• 39:18
  Speaker 1: in principle to like rewind time and tell you about
• 39:20
  Speaker 1: what's happened in the past. For folks who watch that
• 39:23
  Speaker 1: show Devs, that's the whole basic principle. And so the
• 39:26
  Speaker 1: idea is that you throw a banana or an apple
• 39:29
  Speaker 1: into the black hole, it creates a slightly different black
• 39:31
  Speaker 1: hole in a way that imprints that information. I don't
• 39:34
  Speaker 1: know the details. I can't tell you, like a banana
• 39:36
  Speaker 1: black hole looks like this, or an apple black hole
• 39:39
  Speaker 1: looks like that. But in quantum mechanics, there's a lot
• 39:41
  Speaker 1: of potential information on the surface because the surface is
• 39:44
  Speaker 1: not totally smooth, it can't be whereas a gr black
• 39:48
  Speaker 1: hole has to be perfectly smooth with no information.
• 39:51
  Speaker 2: Well, I think you're saying maybe it's not specific to
• 39:54
  Speaker 2: quantum black holes. Like in a relativity black hole, you
• 39:57
  Speaker 2: could also throw a banana and everything inside of the
• 40:00
  Speaker 2: black hole could remember the banana. You just couldn't tell
• 40:02
  Speaker 2: from the outside because it's perfectly smooth. According to Einstein,
• 40:05
  Speaker 2: you're saying that in a quantum black hole, the black
• 40:08
  Speaker 2: hole is not perfectly smooth. You could maybe read from
• 40:10
  Speaker 2: its surface what you threw it.
• 40:12
  Speaker 1: Yes, exactly. That was one theory in a paper about
• 40:14
  Speaker 1: ten years ago that effectively the gravitons could tell you
• 40:17
  Speaker 1: about the texture of the surface, which would in turn
• 40:19
  Speaker 1: tell you about what's going on inside. The problem is
• 40:22
  Speaker 1: that gravitons may be impossible to ever detect. Remember, gravitons
• 40:27
  Speaker 1: are not gravitational waves. Gravitational waves are huge waves in
• 40:31
  Speaker 1: the gravitational field that we can detect. Gravitons would be
• 40:35
  Speaker 1: like drops in the ocean compared to waves in the ocean.
• 40:38
  Speaker 1: So if they exist, they're super duper tiny and it
• 40:41
  Speaker 1: may be impossible to ever see.
• 40:43
  Speaker 2: What does it have to be gravitons? I wonder if
• 40:46
  Speaker 2: there is a texture to a quantum black hole, wouldn't
• 40:49
  Speaker 2: you also maybe detect other particles coming from the Hawking
• 40:52
  Speaker 2: radiation off of it, and maybe could you could tell
• 40:55
  Speaker 2: its texture from that.
• 40:56
  Speaker 1: You could, And there was a theory a couple of
• 40:57
  Speaker 1: years ago that suggested, maybe you remember we talked about
• 41:01
  Speaker 1: on the podcast, that there might be wormholes that connect
• 41:04
  Speaker 1: the interior and exterior of the black hole, and that
• 41:07
  Speaker 1: Hawking radiation could in fact give you information about what's
• 41:11
  Speaker 1: going on inside. That it's not the way Hawking described it,
• 41:14
  Speaker 1: totally information free, but maybe actually has information about what's
• 41:18
  Speaker 1: going on inside, because these wormholes are like bridges that
• 41:21
  Speaker 1: are connecting quantum entangled particles, some of which on the
• 41:25
  Speaker 1: inside and some of which on the outside of the
• 41:27
  Speaker 1: black hole. So there are versions of quantum gravity in
• 41:29
  Speaker 1: which Hawking radiation does have information in it.
• 41:32
  Speaker 2: All right, So then what are some of the other
• 41:34
  Speaker 2: theories about quantum black holes?
• 41:35
  Speaker 1: So all these would be very very hard to detect
• 41:37
  Speaker 1: because you're talking about detecting Hawking radiation and differences in
• 41:40
  Speaker 1: it which we've never even seen, or detecting gravitons, so
• 41:43
  Speaker 1: we don't even know exist, and if they do, would
• 41:45
  Speaker 1: be very hard to see. Recently, there was an idea
• 41:48
  Speaker 1: to look for hair on extremal black holes. We've talked
• 41:51
  Speaker 1: about this on the podcast recently. Black holes have maximum
• 41:54
  Speaker 1: spin or maximum charge that they can maintain, beyond which
• 41:58
  Speaker 1: a vent horizon disappear and things go crazy. But when
• 42:01
  Speaker 1: black holes are near this extremal state, things that fall
• 42:05
  Speaker 1: into them might leave instabilities on the event horizon in
• 42:08
  Speaker 1: some theories of quantum gravity, and if so, it would
• 42:11
  Speaker 1: generate ripples in their gravitational waves, not in their gravitons,
• 42:16
  Speaker 1: and gravitational waves are things we can detect that we
• 42:19
  Speaker 1: might be able to see sometime in the future.
• 42:22
  Speaker 2: What do you mean instabilities on the event horizon? What
• 42:25
  Speaker 2: does that mean?
• 42:25
  Speaker 1: Well, think about what happens when something falls into a
• 42:27
  Speaker 1: black hole. It's going to fall into a specific spot.
• 42:30
  Speaker 1: Right you toss a banana into a black hole, You're
• 42:33
  Speaker 1: tossing it in one side of this sphere, not on
• 42:35
  Speaker 1: the other side, and so immediately what's going to happen
• 42:39
  Speaker 1: is that the event horizon is going to grow out
• 42:41
  Speaker 1: to meet you. So the event horizon is not going
• 42:43
  Speaker 1: to be spherical for a moment. Then it slurps in
• 42:45
  Speaker 1: this banana, it falls into the singularity, and the black
• 42:48
  Speaker 1: hole rings back down to a perfect sphere that's in
• 42:51
  Speaker 1: general relativity at least.
• 42:53
  Speaker 2: Wait, what do you mean if it's not perfectly spherical?
• 42:55
  Speaker 2: What shape is it? Like a blong? Does it go
• 42:58
  Speaker 2: oblong for a second?
• 43:00
  Speaker 1: Yeah, it goes oblong for a second. And if you remember,
• 43:02
  Speaker 1: we talked about merging black holes. When black holes merge,
• 43:06
  Speaker 1: their event horizons grow together, and in some moments they
• 43:09
  Speaker 1: look like a dumbbell or they look like something else.
• 43:12
  Speaker 1: And I commented on that podcast. So that's exciting because
• 43:14
  Speaker 1: it tells you something about the history of the black
• 43:17
  Speaker 1: holes in a way that you can't otherwise know. In
• 43:19
  Speaker 1: gr but there's no hair theorem applies to the stable
• 43:22
  Speaker 1: state of the black hole. Like you put a banana
• 43:23
  Speaker 1: in a black hole, you expect it it's event horizon
• 43:26
  Speaker 1: and have a little bit of a funky shape as
• 43:27
  Speaker 1: it sort of settles back down to a new stable object.
• 43:31
  Speaker 1: But in this theory of quantum gravity, it says that
• 43:33
  Speaker 1: those instabilities persist that you create like waves on the
• 43:37
  Speaker 1: surface of the black hole which ripple basically forever, they
• 43:40
  Speaker 1: don't ever.
• 43:40
  Speaker 2: Go away, sort of like a gravitational wave.
• 43:44
  Speaker 1: Almost yes, exactly, and these would generate gravitational waves, which,
• 43:48
  Speaker 1: according to this paper, we might be able to detect,
• 43:52
  Speaker 1: probably not with our current observatories like LEGO, but with
• 43:55
  Speaker 1: future gravitational wave observatories like LISA or some of the
• 43:58
  Speaker 1: other projects, we might be able to actually see these
• 44:01
  Speaker 1: gravitational waves from these hairy black holes.
• 44:04
  Speaker 2: So wait, you're saying, like, even if I drop a
• 44:06
  Speaker 2: hair or a banana into a black hole maybe a
• 44:09
  Speaker 2: billion years ago, and it happens to be one of
• 44:12
  Speaker 2: these extreme black holes even today, it might be generating
• 44:15
  Speaker 2: gravitational waves that tell me what was dropped in a
• 44:18
  Speaker 2: billion years ago.
• 44:19
  Speaker 1: That's the theory, Yes, exactly. So if you're planning to
• 44:22
  Speaker 1: commit crimes and drop your evidence into a black hole,
• 44:26
  Speaker 1: this might be a loophole.
• 44:27
  Speaker 2: Wouldn't all that information just be radiated away or it
• 44:30
  Speaker 2: would stay there for a billion years.
• 44:32
  Speaker 1: It would fade with time for sure. So if you
• 44:34
  Speaker 1: want to catch a killer using clues dropped into a
• 44:37
  Speaker 1: black hole, your best bet is to use your gravitational
• 44:39
  Speaker 1: wave observatory immediately afterwards, because it would fade away. Even
• 44:43
  Speaker 1: these ripples would eventually fade away. As you say, energy
• 44:45
  Speaker 1: is being lost, right, it's being radiated away, but in
• 44:48
  Speaker 1: principle it still persists. Forever. Technically, it just gets fainter
• 44:51
  Speaker 1: and fainter.
• 44:52
  Speaker 2: I see, like the ripple stays on the surface of
• 44:55
  Speaker 2: the black.
• 44:55
  Speaker 1: Hole somehow, mm hmm, exactly.
• 44:57
  Speaker 2: All right, Well, what does this all mean about our
• 44:59
  Speaker 2: understanding black holes? Like, there's still a big mystery. It
• 45:02
  Speaker 2: seems we don't really even understand what black holes are.
• 45:05
  Speaker 2: We've seen these things out there in space. We didn't
• 45:07
  Speaker 2: even know if they actually are black holes, if they
• 45:09
  Speaker 2: are gr black holes, if there are quantum black holes.
• 45:13
  Speaker 1: And this is really at the heart of the question,
• 45:15
  Speaker 1: what's going on out there? I suspect that what's really
• 45:19
  Speaker 1: happening in the universe is something different from any of
• 45:21
  Speaker 1: these theories. You know, it's going to be a big surprise.
• 45:24
  Speaker 1: And the exciting thing is if black holes do have hair,
• 45:27
  Speaker 1: we might be able to measure it. We might be
• 45:29
  Speaker 1: able to get these subtle signatures from the ripples on
• 45:32
  Speaker 1: the surface of the event horizon to tell us what's
• 45:35
  Speaker 1: going on inside and maybe give us some clues about
• 45:38
  Speaker 1: what kind of universe we live in.
• 45:40
  Speaker 2: Would that be the holy grail of black holes or
• 45:43
  Speaker 2: the hairy banana.
• 45:44
  Speaker 1: Exactly the way Einstein's hair is the holy grail for
• 45:47
  Speaker 1: all physicists.
• 45:49
  Speaker 2: Is it think I think like Brian Cox, is it
• 45:52
  Speaker 2: popularized and you kind of physicists here?
• 45:55
  Speaker 1: Yeah?
• 45:56
  Speaker 2: The whole like emo kind of hipster aging pop star. Yeah, yeah,
• 46:00
  Speaker 2: there you go.
• 46:01
  Speaker 1: I don't think I'm ever going to be an aging
• 46:03
  Speaker 1: pop star. But you know, there are all these really
• 46:07
  Speaker 1: deep questions about the nature of the universe we live in.
• 46:09
  Speaker 1: Is information destroyed or not? It might be the black
• 46:12
  Speaker 1: holes are like cosmic toilet, it's just flushing away this
• 46:15
  Speaker 1: information to be destroyed. Or it could be that they're
• 46:18
  Speaker 1: preserving that information. They're radiating it back out into the
• 46:21
  Speaker 1: universe somehow, and then information is not destroyed in our universe.
• 46:25
  Speaker 1: It's a pretty deep question about the nature of reality.
• 46:28
  Speaker 2: Yeah, and the nature of information itself, Like could you
• 46:31
  Speaker 2: ever destroy information? Or does the universe always remember everything?
• 46:37
  Speaker 2: Is there always a paper trail?
• 46:38
  Speaker 1: Yes, exactly. If you committed a crime a billion years ago,
• 46:41
  Speaker 1: justice might still be coming.
• 46:43
  Speaker 2: All right, Well, more deep questions about the universe and
• 46:46
  Speaker 2: a big reminder that there's still a lot for us
• 46:49
  Speaker 2: to discover and to understand and to learn about and
• 46:52
  Speaker 2: potentially to comb over as well. We hope you enjoyed that.
• 46:56
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  Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain
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• 47:17
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