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32: Gaze into the Abyss (Part Three; Black Holes)
422 Plays6 years ago
A lot of the information in this episode of Breaking Math depends on episodes 30 and 31 entitled "The Abyss" and "Into the Abyss" respectively. If you have not listened to those episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.
Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?
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Transcript
Introduction & References to Previous Episodes
00:00:00
Speaker
A lot of the information in this episode of Breaking Math depends on episodes 30 and 31, entitled The Abyss and Into the Abyss respectively. If you have not listened to those episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way, because otherwise we'd waste most of your time re-explaining concepts we've already covered.
00:00:21
Speaker
Black holes are so bizarre when we're measured against the yardstick of the mundanity of our day-to-day lives that they inspire fear, awe, and controversy.
Exploring Black Hole Paradoxes & Entanglement
00:00:30
Speaker
In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes? All this and more on this episode of Breaking Math, and part three on a series of black holes.
Hosts Introduction & Support Promotion
00:00:47
Speaker
Episode 32, Gaze into the Abyss.
00:00:56
Speaker
I'm Jonathan. And I'm Gabriel. And you're listening to Breaking Math. You can find us on BreakingMathPodcast.com, Facebook.com slash Breaking Math Podcast. And if you'd like to support us, we have a Patreon. We're selling a poster from there that costs what? $35. Yeah, that's right. $35. And that's Patreon.com slash Breaking Math, not Patreon.com slash Breaking Math Podcast, as we've said before on the show.
00:01:20
Speaker
Yes. And what's exciting is our first shipment of posters has officially been shipped. I'm so excited. I can't wait to hear from anybody who has bought a poster. Jonathan spent a very long time on them and it has painstaking detail about tensor mathematics, which is used in Einstein's theory of general relativity. Which of course is the most current version of gravitational theory that's widely accepted and developed in 1916. So it's been holding on for a very long time.
Meeting The Credible Hulk
00:01:50
Speaker
What's also exciting is there's a Facebook page called The Credible Hulk. I don't know if any of you guys follow this page. He is generally affiliated with the skeptics community. He's also into science. He spreads a lot of information about science and critical thinking. And we found out that, well, first of all, I'll mention his Facebook page has over 200,000 likes. I thought that was pretty darn impressive.
00:02:17
Speaker
I messaged him because I read one of his blogs about mathematics. He's you know, he's really into math So I thought hey, maybe he would really enjoy one of these tensor posters. So I messaged him and Guess what? It turns out he lives right here in our home state of Albuquerque, New Mexico Yeah, he goes to the University of New Mexico and
00:02:37
Speaker
So I literally just drove down to UNM and I met him in the library and we hung out. This was a couple of days ago. By the time you heard this podcast, it was probably a week ago. You can go to our Facebook page at facebook.com slash breaking math podcast. And you can see a picture of me hanging out with a guy from the credible Hulk Facebook page. I'm pretty proud of that. That's pretty cool.
00:02:58
Speaker
Yeah. And so, um, what are we going to be talking about on this episode? What type of things? So this episode is a very interesting one. Jonathan had mentioned that it's a pretty deep one. That's true. That's true.
Theoretical Black Hole Phenomena
00:03:10
Speaker
We're going to be talking about solutions to the Hawking information paradox, which we went over in our last episode. Yeah. And we're also just going to be talking about some of the weirder, like less proven, more esoteric versions of black hole theory.
00:03:28
Speaker
That's right. That's right. In fact, I think we're even, I think if I'm reading the outline, you know, correctly, we're even going to start off with some of the strange ideas about black holes. Yeah. And we'll come back to this idea later too. Um, it's the idea of Holium black Holium. What on earth is that? So what that is, is like, if you have a black hole that is managed to get itself less than the Planck mass, which is 21.8 or so micrograms.
00:03:54
Speaker
which is about as much energy as there is about a really big tank of gas in a car. So you could imagine that being like something like less than that being just the tiniest little black hole that has no way of evaporating because it's too small, forming a stable type of matter. Some people even think it's part of dark matter, holium, because it has all the properties of dark matter.
00:04:16
Speaker
All it emits is gravitational radiation, the same way that excited phase transitions in normal matter are electromagnetic radiation. This is amazing. So, so this is, again, I realize this is entirely in theory, but as you said earlier, in theory, you can have black holes that are just not big enough to evaporate. Can you clarify why the, their size or even their initial size would have anything to do with their ability to evaporate?
00:04:44
Speaker
Yeah, there's a maximum size that, I mean, a maximum amount of energy that a photon can have. And that's 21.8 milligrams worth of energy. Remember E equals MC squared. So energy and mass can be related. And that's how you get the amount of energy for this photon. And that's a photon with a wavelength.
00:05:01
Speaker
equal to the Planck length, which is the smallest you could get in the universe.
Mechanics of Black Holes & Hawking Radiation
00:05:06
Speaker
So if you have a black hole that's small enough, there might be no way for it to radiate energy because it's so small that its temperature would be too high to radiate out energy. There's debates on whether or not this is even physically
00:05:20
Speaker
thing this is only this is only about six years old this stuff Wow I had no idea Wow so so this this stuff that they're calling black hole sorry it's holy um yeah just holy okay and what was the the resource that put this idea into your head
00:05:37
Speaker
Um, well I got it from Wikipedia, but the people who designed it, um, were K chavda and a Pete's chavda in 2002. Okay. So it's 16 years old. I miss red 2002. That's when I graduated high school.
00:05:53
Speaker
So this is interesting. So you mentioned earlier that a photon can have a maximum energy that makes any sense in our physical universe. And that is a wavelength. Sorry, is it a wavelength? The size of the Planck length. Now you had mentioned earlier that, prior to us recording this, that there is no minimum energy a photon can have.
00:06:14
Speaker
Well, some people say that. Other people say it's probably the radius of the observable universe or the diameter. I can't remember which one. But so it might change over time, which might make sense because the universe is expanding and the expansion is by our own measurements accelerating. Wow. Wow. How interesting. Interesting. OK. So now is there any reason why this black holium would not exist?
00:06:39
Speaker
Like there might be a way for, like it might, for example, if a black hole is very, very small, it might just have a very small probability of radiating out small photons and things like that. So it might not be an absolute limit. Um, there's, we don't know much about the mechanics of black holes, especially when they intersect with the plank length and things like that. That's where we go into a lot of confusion is where the giant world and the tiny world intersect because we have different theories governing both of them.
00:07:09
Speaker
Now, you may have mentioned this earlier, but I'm still just very, very curious. For the sake of our discussion on this theoretical thing called blackholium, what did you say was the size of a black hole that would not be able to evaporate?
00:07:27
Speaker
21.8 micrograms, which is a very, very small amount. That's like, um, a 50th of a grain of sand. Wow. And then what would, do you know what the radius of this kind of black hole would be when it first becomes a black hole? It would be, I think the plank length. Oh, wow. Oh man. That's crazy. Okay. Wow. So yeah, as you can see there, there's a whole lot of, uh, strange ideas and that's not in black. Holium is not the only, you know, theoretical idea that comes out of black holes. There's, there's all kinds.
00:07:57
Speaker
Yeah. And we're going to be discussing a few of those on this episode. Yeah. Although we are not going to do a full recap of the previous two episodes, she would do a very, very, very small recap just for our listeners who may not have listened to the episode in a while.
00:08:11
Speaker
Yeah, sure. Um, information is stored on the edge of black holes. One bit of information is one square plank length. So all, and we'll be talking about that when we talk about the holographic principle, we're also going to be talking a little bit about, um, Oh, we're also going to be talking about the event horizon a lot. And the event horizon is a, uh, it describes a sphere. The radius of the event horizon, uh, is how big the sphere is. And, um,
00:08:38
Speaker
The property of the event horizon is that any event that happens within the event horizon could not, in theory, go out of the event horizon. So it's the point at which light cannot escape. So you can't send signals out of a black hole.
00:08:51
Speaker
Yeah, and also I'll talk a little bit about Hawking radiation, which we got into deeply in the last episode. Stephen Hawking was aware of some properties of quantum mechanics, specifically virtual particles. And I think it was Richard Feynman who first introduced virtual particles. Is that right?
00:09:09
Speaker
I think that he had a lot to do with it. Yeah. Okay. When I first read about virtual particles, how, how should I put this? There wasn't a lot of, of context given to them. I, you know, that, that term stuck with me and I tried very hard to read more about them. But frankly speaking, when you're in high school and you're learning about physics and chemistry, virtual particles are never really mentioned.
00:09:28
Speaker
Yeah. Virtual particles are a lot like potential energy. They're not real, but they have very measurable effects. Like if you hold a ball up, it has a certain amount of potential energy with respect to like, it is different. Like on the surface of the earth, it has a certain amount of potential energy, which is how much energy you will have when it falls to the surface of the earth. Um, like a spring, when you press it down, has a certain amount of potential energy, which is the amount of energy that happens when you release it. And in the same way, virtual particles, a good model for them is that.
00:09:57
Speaker
they pop in and out of existence in pairs. And if you take this to be literally true and ignore quantum physics for half a second, then this is a good description. They just pop it out of existence. If stuff blocks them joining together because they pop out, two different types of particles, an antiparticle and a particle, but a different type of antiparticle, like literally one with negative energy,
00:10:22
Speaker
Emit from a point and then they suck each other back into each other and then they never exist It's like though they never existed and and I think that with respect to virtual particles They're called virtual because the average of their energy is zero, but that doesn't mean that they're at any given instant in time The energy is zero
00:10:42
Speaker
In free space, in a solution where you don't have complexity at all, there's no detail to the universe, like just a blank space of the universe, then their existence sums up to zero, which means that they will not be detected from outside. Like if we have a sphere and inside of the sphere, space time is flat.
00:11:01
Speaker
which never happens, by the way, but it's the ideal situation. You will never detect a virtual particle from inside that sphere. That's fascinating. One of the great descriptions I heard, and again, I heard, I mentioned this on a previous podcast, the Ask Science Mike podcast. I think on one of them, he was talking about a lake, you know, in the early hours of the morning before anybody is playing in it at all, you know, it looks like glass. It's almost perfectly flat.
00:11:27
Speaker
But then when you have people playing in it, you get all kinds of wakes, and you get waves, and you get ripples, and all kinds of things. And with virtual particles, the fact is that in our universe, according to the laws of quantum mechanics, you've got fields that permeate all of space. And these fields are not static. They do fluctuate. And virtual particles can also be described as the fluctuations in the field. Is that a good roundabout description of these?
00:11:56
Speaker
Yeah. And to tag on to that, let's, let's say that we had a, um, a book and we put it on the surface of this pond and we took it off, you would see the edges of the book. It would look like a square kind of like rippling out, right? Yes. Yes. And, um, you can imagine like, if we took a book, the exact same shape and size of the pond and pressed into the pond and then took it off, there'd be no.
00:12:19
Speaker
If you were perfectly flat there'd be no place where a ripple would start or ripple would end It would have all the ripples would happen at the same time and thus no ripples would happen that is essentially how virtual particles interact because like if for example we took we
00:12:35
Speaker
change the surface of the water at a certain place, it would change the way that it interacts with the flat thing, and it would not be flat at that place. So that's how virtual particles work. And to listen to more about virtual particles, listen to episode 31, Into the Abyss of Breaking Math.
00:12:50
Speaker
Right, right, yeah. And then again, just for the sake of our recap, you had mentioned earlier that virtual particles can also be described as existing in pairs. Hawking radiation is the description of the event where you have virtual particles pop into existence right at the event horizon of a black hole, and that means that one of them will go into the black hole, and one of them will go out of the black hole, and it will never annihilate. Therefore, it becomes a real particle.
00:13:18
Speaker
Yeah. But here's the funny thing. You're not really creating matter. We know that there is the law of conservation of matter and the law of conservation of energy, which means both matter and energy cannot be created nor destroyed. They can only be transferred.
00:13:34
Speaker
So when you have these particles pop into existence and not annihilate, well, according to the mathematics, a little bit of the black hole that is the same size as the virtual particle that now exists as a real particle, that part of the black hole evaporates.
00:13:51
Speaker
Yeah. And to go a little bit more into that, I think that it's like, I have a personal theory. It's not a very widely accepted theory that the interior, like the event horizon, I don't think anything really exists. I think talking about what exists inside of a black hole is essentially silly. And I think that this points to that because the longer a virtual particle exists, the more it becomes like a real particle. So it can't have negative energy anymore. For example, it takes on positive energy.
00:14:18
Speaker
The whole idea that a virtual particle can have negative energy. I hear the words that are coming out of your mouth and they make sense in terms of like, you know, a sentence with proper syntax and grammar, but what on earth is negative energy? I mean, what the definition of energy is the ability to do work. So is negative energy that
00:14:39
Speaker
What does that even mean? That's a work debt. So it's like a work request. It's like billing somebody for work. The universe is really a big accountant. That's insane. That is absolutely insane. So if you think about it, like if this virtual particle turned into two particles, the one in the middle would be observed differently than the one on the outside.
00:14:59
Speaker
So either black hole complementarity exists in a way different than we think it does to me, or just the inside of a black hole is a silly thing to talk about. And I think it's a silly thing to talk about because quantum physics tells us that if we can't measure something, then it's silly to talk about it. And honestly, I think that we just need to apply that to space-time singular, like not just singularities, but event horizons.
00:15:22
Speaker
So is this Jonathan just, you know, lifting up that rug and sweeping the whole question? I'm just kidding. I'm just kidding, man. Yeah. So I destroy things on principle, not because of shame. Very good. Now the idea of Hawking radiation and the eventual evaporation of black holes brought up what we discussed in our previous podcast, and that is
00:15:43
Speaker
Stephen Hawking's information paradox and the whole idea is is information ultimately scrambled or is it ultimately completely destroyed such that it never you know it's as though it never existed to begin with now the latter has some very very scary consequences but we've already discussed that so I'm not going to go into great detail here yeah the biggest one meaning that if you'd run a black hole in reverse it's as likely for radiation to come out as a kitten
00:16:09
Speaker
Yeah. Yeah. It's, it's in other words, it's essentially nonsensical and that's, you know, physicists like causality, physicists like things being able to describe, being able to be described and predictable. So destroying information is a big no-no. It's almost, it's almost like the ultimate practical joke that our universe is. Cause that makes no sense at the end, you know?
00:16:30
Speaker
Yeah. Under our current definitions. So now what's worth mentioning, you know, in our research for this episode, oh, this was an amazing episode to research for. It's, it's the, all the thought that has gone into this is just mind boggling. So what's fascinating is right now, uh, you know, if you ask any physicist who's working on this problem, the information paradox is considered solved.
Information Paradox and Quantum Mechanics
00:16:55
Speaker
It is, I'd say, widely accepted that information is not, in fact, destroyed. However, what's very interesting is although that's accepted, you could say, thank God for that, what's not accepted is entirely why. As we have prepared in this episode, a few things to talk about and a few possible solutions to the information paradox, and some of them, I don't mind saying, are a little out there.
00:17:25
Speaker
But, you know, it's certainly considered a fact that information is not destroyed. So in this episode, this final episode in the series, we're going to talk about the three or four or more models that try to explain why the information is not in fact destroyed. Yeah. And without further ado, here's the rest of the episode.
00:17:48
Speaker
So we're going to talk about right now is complementarity, the no cloning theorem and the no communication theorem. Yeah. Um, so I think that the first thing we'll talk about is, is the, the origins of this. So almost immediately after finding out about the, about the information paradox, the physicist Leonard Susskind, as well as Gerald, how do you say his last name?
00:18:09
Speaker
I think toft i'm i'm sorry sorry i'm not editing that out you have to live with that okay t apostrophe h o o f i'm sorry his last name he's just digging a hole i know i know
00:18:24
Speaker
So almost immediately they came up with something called complementarity. Now, well, they didn't come up with that. It's a quantum physics thing. Okay. So I'm going to give you my definition of complementarity. And then Jonathan, I think you should give your definition. Complementarity is when you have two models that can describe something like
00:18:44
Speaker
You can have two mathematical models that describe a phenomenon. And they seem to contradict one another, but they both accurately describe something. And the thing is, they can both be found to be true depending on how a phenomenon is observed. Now this actually exists. You want to add anything to that?
00:19:05
Speaker
Yeah, like what we could talk about is position and momentum because it's easiest to understand using just a simple model. So let's say we're at a shooting range and we don't have our glasses on. So we can't see anything down the range, but we know that there is a ball moving around and it's moving. We know that it's moving and we receive this information very quickly and we start shooting bullets as fast as we can at this ball that's moving down the shooting range.
00:19:34
Speaker
If we look at how the stuff scatters off of the ball, we'd know exactly where the ball was, but because the bullets are so powerful, I mean, they put a hole in a man's chest, they're probably gonna move the ball so much that we don't know what its momentum was to start with. However, if we just shoot very light bullets at it, we could look at their deflection, measure the momentum, but because the position is being measured so inaccurately because we have to fire a lot of tiny bullets over a lot of time,
00:20:03
Speaker
we don't know its original position. So position and momentum are considered complementary because you either know a ton about the position or a ton about the momentum or a little about both. If we know that we can know x amount about the position and then y about the momentum, we can't know both at the same time.
00:20:22
Speaker
Yeah, and actually, I know exactly what you're talking about, Jonathan, because in the case of photons, let's replace the bullets in your example with photons. The thing about measuring things, the only way that we can have information about something is to measure it.
00:20:39
Speaker
But when you measure it, you know, it requires seeing it or, or detecting it somehow interacting with it requires interview. Thank you interacting with it. So, you know, if you look at it, you have to have light bounce off something and then, and then reflect and go back to your eye. Well, frankly speaking, you've changed it by, by a photon touching it. So, so, you know, it's no longer in the same state that it was before the photon touched it.
00:21:06
Speaker
Yeah, it's related to the Heisenberg uncertainty principle. And a lot of that can be thought of from a macroscopic point of view, like.
00:21:12
Speaker
If we have a beaker of water and want to know what temperature it is, we could put a thermometer in there, but the thermometer is probably going to be a different temperature than the water, so we're going to change the temperature of the water by measuring it. Same thing with measuring something's length. You might think that a ruler is a perfect way to measure something, but even the presence of the ruler, like the temperature of the ruler, is going to cause expansion or contraction.
00:21:36
Speaker
of the thing that's measuring, it's going to change the geometry of space time around it. There's no way of measuring anything without changing it. You know, and so that's one aspect of complementarity, you know, so you might say, okay, fine. So you don't know exactly what temperature something is when you measure it. The thing about it is, though, it gets really, really weird.
00:22:01
Speaker
And I'm specifically referring to the double slit experiment. When we're talking about complementarity, we can talk about light, light or even other other parts of the matter. Electron beams. Yeah, electron beams or even, you know, DNA itself. Although you'd require an incredibly high energy beam for DNA.
00:22:20
Speaker
That's true, that's true, that's true. All of these things can be described as being either a wave or a particle. And before the double slit experiment, and before it was done properly, by the way, that experiment I think was described as the most beautiful experiment in all the physics of all of time, because it clearly illustrates this principle.
00:22:44
Speaker
This double slit experiment, and again that's a pretty popular experiment, essentially showed that light is either a wave or a particle depending on how you measure it.
00:22:55
Speaker
Yeah, and the double slit experiment, just real quick, let's imagine you have a very still bathtub. And let's imagine you have two pencils about a foot away from each other, and you start bobbing the pencils up and down, creating waves. They're going to kind of crisscross and create kind of a trellis type pattern, right? Yeah, you're going to have the ripples that are going to spread out. And cross with each other. Yeah, interference. Yeah, yeah, yeah. Yeah, and so if we had a board at the end of the waves, we could measure how high the waves are, and it would be
00:23:24
Speaker
It would be something that would be kind of a ripple. It would start like if you do if you do frequency equals amount basically. Yeah. So it would be you'd you'd have an interference pattern. It wouldn't be the same as if you just did one of them or the other one.
00:23:42
Speaker
Yeah, exactly. You know, so and you've got you've got constructive interference and that's when you've got two waves that come together and their amplitudes are added together. You get a giant wave. Yeah. So that's like if on the left pencil, there's a certain place where the wave is high and the right pencil without the left pencil in the same place of the wave or high, both pencils together, the wave will be twice as high.
00:24:02
Speaker
Yeah, or twice as low if you've got two with the troughs that come together. And of course, if one would be high and the other would be exactly as low, then the level is the same as the level of the water. They cancel out to zero. So yeah, that's clearly unambiguously a wave. Yeah. And so if we start with the wave kind of further back, so let's take the two pencils and let's go way far back so that we have both pencils about the same far backness as a point pretty far back in the bathtub.
00:24:31
Speaker
at the start of the bathtub and the two things are next to the drain, basically, the whole thing that we had set up. Now, if we replace the two points where we were making the ripples with a wall, but to put two spaces where the ripples were being generated, then when we generate ripples from our point really far back, it will ripple out through the spaces and create little tiny ripples and they'll interact the same way. So you'll have the same pattern on the end of the bathtub, right? Yeah, yeah, yeah, exactly, exactly.
00:25:00
Speaker
And so the rule is for quantum physics is that the height of the wave, no matter if it's positive or negative, gets squared.
00:25:09
Speaker
And the square of the height of the wave is the probability that a particle will exist there. And so the double slit experiment is really simple. You just take a black piece of cardboard or something, or something thinner than cardboard, and then you take two razor blades, put a little thin piece of something between them, and you cut the fabric and you shine a light beam through it from far away. And you'll see a ripple pattern at the thing that it projects onto.
00:25:35
Speaker
Yeah, pretty much, pretty much. Yeah. But if you even send one, if you, and they've done this with, uh, if you replace the holes in, um, the sheets with two reflective little strips of nickel and you fire electrons at it, then the electrons will cause the interference pattern. But if you slow it down, so they have just one electron going through at a time, it'll have the same pattern.
00:25:57
Speaker
Yeah. So, so it's, you know, you would think that that would be unambiguous proof that light travels as, as a wave and not as a particle, but it's just weird because you can't describe everything that goes on with light as only a wave. I mean, I, you know, Einstein talked about little packets, you know, like he specifically talked about packets of light when he was talking about the photoelectric. Yeah, exactly. That requires packets of light.
00:26:24
Speaker
Yeah, and the photoelectric effect just real quick is if you take two sheets of gold leaf that are charged with the same amount of charge, if you shine all the red light you want, you could turn the sun into red light and shine it at this and they will never come together. But you're showing a little bit of ultraviolet light, just a tiny bit and they'll come together. And it has to do with the way that the particles interact, but it shows that stuff travels in quantum. There's a minimum amount of, there's a package of energy.
00:26:49
Speaker
Yeah, yeah, that's crazy. So the thing is, you have these physicists who designed these experiments who basically said, now I know that light travels in packets. I know we see it as a wave, so I'm very curious. What happens if I put a little sensor, any kind of a light sensor by one of these two slits? I want to see if I can measure the light as it goes through one or the other.
00:27:13
Speaker
The wild thing is, and the point we're trying to make with this entire section of this podcast on complementarity, is that as soon as the scientists designing the experiment try to measure what goes on at the slit, it no longer behaves as a wave. It behaves as a single particle only going through one of the slits or the other.
00:27:36
Speaker
Yeah, and you could do that by, light can be polarized. I mean, when you go to the movie theaters and you watch a 3D movie, the light from the left eye is polarized, let's say left, left and right, and the right one is up and down. So if you have a polarizer that's left and right in your left eye, it'll only let the stuff that's left and right into your eye, and it'll block everything else. But if you have an up and down polarizer in the right one, nothing will go through.
00:27:58
Speaker
If you did it at 45 degrees, you know, like a diagonal angle, then it would let half of both go through. That's why you can't turn your head when you go to the theaters. That's why it causes a lot of neck strain. Yeah. But so let's say we had the two slits and we put a vertical polarizer in front of one and a horizontal in front of the other one so that when we so when it hits the wall, what we could do is have another vertical polarizer and then just measure whether or not it went to the left or the right one. Giving it that information means that it no longer looks like a ripple. It just looks like two fuzzy dots next to each other.
00:28:27
Speaker
Yeah. And so I think that in the history of science, this was a moment that almost like sanity just went out the window, or rather the sense of familiarity. You know what I mean? Oh, yeah. And here's the bizarre part, though. If we put a diagonal polarizer after the two polarizers that were like the experiment that we just did, we put a diagonal polarizer in front of both of them, thereby erasing the information.
00:28:54
Speaker
It's a double slit pattern again. That's just weird. So things don't behave the way that we would expect them to. Now that is the namesake of this section. It's describing things in our universe in a complementarity. That's the term.
00:29:12
Speaker
Yeah, complimentary way, complimentary based way in a complimentary way where, where you have two different ways of describing something and the, the key descript, the, the T sorry, the key description here is that they're both true. So what does this have to do with the Hawking information paradox and, and, and how information might be conserved?
00:29:37
Speaker
Well, we got to talk about the no cloning theorem, uh, to talk about that. Okay. Okay. So, so just so that our listeners are keeping up. So we're going to talk about, about how information might be conserved with this whole idea. It definitely is conserved. Okay. How it definitely is conserved with this whole idea of complementarity and what it has to do with something else called the no cloning theorem. So, so hang on tight.
00:29:59
Speaker
Yeah. So then basically we got to talk really quickly about entanglement. If two particles that are entangled, like let's say I take a photon and entangle it, that means I create two lower energy photons that they both, no matter how far away from it, so I could send one to Alpha Centauri and keep one on earth. And as soon as I measure any property of my particle,
00:30:23
Speaker
I will know if I was very careful about my accounting and what I did to that particle, I would know the state of the one that was in Alpha Centauri immediately. Meaning that if I sent entangled particles to Alpha Centauri every year, then we could do something like, let's say they needed a certain type of supply.
00:30:43
Speaker
and they measured the particle, thus letting me know that they needed that supply. I think it might be the case that we could increase the efficiency by twice, but I would have to double check that. Interesting. I know that entanglement is a fairly popular idea. It's another very, very, very weird idea.
00:31:06
Speaker
So you said earlier that for entanglement to happen, you have to have two particles in close proximity. Do you know at what point they become entangled?
00:31:16
Speaker
I think they become entangled in as much as the other properties are shared. I mean, our, um, coherence because entanglement and coherence are complimentary themselves. Oh, wow. Interesting. Now I know that that entanglement, this is just a quick sidebar. I know that entanglement with electrons can happen as soon as they share a shell. I almost had a ton closer there.
00:31:38
Speaker
Yeah. And what's interesting though, is that entangled electrons are different than entailed photons. Really? Because entangled photons will have the same property as we talked about in our bell episode, but entangled electrons will have opposite properties. Wow. Okay. So, so, so really this shows that entanglement is, is not just something with one, like it's not related exclusively to the, like, you know, the, um, poly exclusion principle, you know, like it's just, if two particles interact in any way, they can become entangled.
00:32:05
Speaker
Yeah. And real quick, the reason why we can't send a signal faster than light is let's say we entangle a particle here and one on Alpha Centauri and the one on, and then we wanted to, let's say we wanted to send a signal at the exact same time here in Alpha Centauri. And so we measure our particle. They.
00:32:21
Speaker
they cannot, if they measure their particle at any time, then they are the ones who make the particle one thing. So this leads us into no cloning theorem, because if they could clone the state of their particle, then they could just keep firing off clones of it and then see what their states are. And if they're random, then that means we haven't measured our particle, but as soon as we measure ours, it would become the same one every time.
00:32:45
Speaker
Which means that we'd be able to send a signal faster than light and thus violate causality. So let me let me slow down Real quick here. So so we're talking about two things here and there's a nuanced there's a small difference here We're talking about sending or rather having information Faster than light and then we're talking about signals now There's a difference as Jonathan said earlier you can get two particles and you can entangle them and not not measure them at all not measure either one of them and
00:33:14
Speaker
And as Jonathan said earlier, you can send one off arbitrarily far light years and light years away. If you measure one, then automatically you've got information about the other one. So you may know something about it, which is interesting because, you know, if you haven't measured it, how do you know if an electron is spin up or spin down? Well, if it's entangled with your electron and you measure your electron and it's spin down,
00:33:38
Speaker
then you know for a fact that there's an electron far, far, far away that's been up. But as you said, you can't send a signal. And not only that, it's very hard to send time information because let's say I sent one particle to Alpha Centauri, which is four light years away, saying that if five years in the future or some event happens, like let's say,
00:33:58
Speaker
is less than a dollar per pound, then I measure my photon or whatever particle I have. And so when I measure mine, they know theirs. So what they could do is they could agree that that happens, but the way that it works out, they would have to confer with us. So there's no way of knowing whether or not they, basically we can't go into the math and we'll go into another episode,
00:34:25
Speaker
You have to confer with the other particle, so you cannot send information faster than light, no matter what. Yeah, and then, so essentially, the no cloning theorem can be said another way, the no communication theorem. You know, you're not going to be able to send any kind of like a Morse code signal via entangled particles at all.
00:34:48
Speaker
Yeah, and just real quick about the entanglement thing, if two particles are entangled, you could think of them as having instant communication, quote unquote, communication with each other. So you can almost think about it like, let's say we have ours and the one in Alpha Centauri, let's say the one in Alpha Centauri gets measured. This is the way that I think about it personally, and it helps me a lot.
00:35:07
Speaker
All of a sudden, time reverses from Alpha Centauri because it's measured there. All of time starts reversing and then in the light cone, which is the sphere expanding at the speed of light from the center of Alpha Centauri, time starts reversing. So it sends an anti-time signal until the origin of when the two particles were entangled and wherein it goes forward in time again and
00:35:35
Speaker
You don't have to think about it that way, but it helps me. Did you guys catch all that? You all caught all that, right? You're following? Okay, okay, great. Maybe it wasn't very coherent. Unlike entanglement. Can you just go back in time and listen to it again? You know what I mean? Like, if you're entangled with this podcast? I don't know.
00:35:54
Speaker
Okay, so the question is then, you know, if you're Leonard Susskind, the physicist Leonard Susskind, who is a professor at Princeton, and you're trying to explain why information is not destroyed in black holes, how can you use this idea of the no cloning theorem to, and also this whole idea of complementarity to prove that information is conserved when black holes evaporate? Well, the no cloning theorem actually presents a problem for black hole complementarity.
00:36:24
Speaker
But black hole complementarity basically states that there seems to be two things that happens to information when it hits a black hole. Either it gets kind of like scrambled up and put on the surface, or it goes through the black hole and nothing seems to happen at first. Like if it's a supermassive black hole, the equations say that you wouldn't even be able to tell once you pass through the event horizon. Okay, so let's just go through these one at a time. I'm gonna slow down real quick.
00:36:47
Speaker
So let's pretend, as you said earlier, in the example of a supermassive black hole, if you are driving a spaceship and you or whatever, if you're just by yourself and you're going toward a black hole, you're not even going to notice when you cross the point of no return. All right.
00:37:04
Speaker
Yeah, because, and here's the thing, because it's a point of no return, once I'm past it, I can never send a signal out. But once I'm out of it, I can, basically once you're in, you can never become out again. And once you're out, you either become in or you stay out. So they seem to be separated.
00:37:22
Speaker
Complementarity is, because of a complicated reason, something that you could look at. And spaghettification happens in the middle of black holes and near the singularity, which is the point at the center. And that's where gravitational forces, like let's say you fall in like feet first. The gravitational force near your feet when you get close to the center of a black hole with the current equations would be so much greater than the force at your head that you'd be stretched, as Stephen Hawking says, like a piece of spaghetti.
00:37:51
Speaker
Interesting, interesting. Now, real quickly, as we're talking about complementarity, when you talked about once you're out, now, I don't mean once you're out as though you can be in a black hole and then suddenly you're out, that's not possible. Rather, let's talk about what happens if you are an observer who watches something go into a black hole. It's entirely different, and this is just weird. Yeah, it's almost like, let's say you had a book with, like, that it was just written in watercolor,
00:38:19
Speaker
And you take a page out of it and you dip it in the sink. And as soon as you dip it in the sink, all the information spreads across the surface. That's what we predict would happen. If you see something falling into a black hole, it would just scramble. Okay. So, so again, we've got two perspectives here and these two perspectives are complementary, are complementary. One perspective where if you are the person going into the black hole, what you'd experience. And then one perspective is if you are far outside of the black hole and you see somebody else go inside.
00:38:49
Speaker
Well, possibly complementary, because if they violate the no-cloning theorem, they cannot by definition be complementary. Okay, you're right. Leonard Susskind proposed this idea that information is conserved because of complementarity.
00:39:07
Speaker
Now, did he think that the information is conserved because as you're watching something go into a black hole, the information is, well, obviously whatever it is, is like burned up. I don't want to say burned up, but destroyed and all the information. Well, that's not to be very clear. It's not destroying information. Okay. Scrambling information is just increasing the entropy and that's perfectly legal in physics.
00:39:28
Speaker
Cool. So he basically says that information is conserved with black holes because of complementarity. And as long as you're the person who's watching it happen, whatever went into it, that information is now scrambled on the outside of a black hole. So is that the conservation of information? Yeah. The reason why that's a potential solution
00:39:49
Speaker
is because the whole thing with Stephen Hawking's information paradox is once it crosses the event horizon, there's no way of retrieving the event. Because you can think of causality as being strings that are connected by light. Light is the fastest this stuff can go. So everything's connected by this light or virtual light or pseudo light, whatever you want to call
Holographic Principle and Black Holes
00:40:07
Speaker
it. So once something falls into a black hole, because light cannot escape, information cannot escape. Because remember, information, the things that relate cause and effect, that is information.
00:40:17
Speaker
So if black hole complementarity exists, then the surface of the black hole, or the exterior surface, which is proposed to be one plank length above the surface of the black hole, contains all the information. But once you pass that, you still retain all of your information. So it lets every reference point retain its information.
00:40:40
Speaker
It lets every reference point, uh, retain its, um, mass and where the mass goes. And the two points cannot be, well, they can kind of, we'll talk about in a second communicate together. So they are complimentary. Okay. Now for our listeners, just so that we're, we're tracking here. Yeah, this is weird. This is very weird. This is really weird. This is a breaking edge. This is like, if you could solve most of the stuff we were talking about in this problem, then you could write a paper.
00:41:10
Speaker
Okay, so for the sake of our listeners, I just want to point out that complementarity is really, really weird. And it involves, you know, when you can describe something two different ways, like, like waves or particles. And Leonard Susskind had the whole idea of
00:41:27
Speaker
applying that to black holes and saying, well, as long as you're seeing an object that goes into a black hole, as long as you're seeing it get evaporated on the surface of a black hole, the information is conserved. So I don't know. Well, the reason why black hole complementarity is probably proposed is because of the no communication theorem and no cloning theorem,
00:41:52
Speaker
Essentially, they modeled a black hole as a quantum interaction, which involves a thing called an S matrix. You look up more on that. It's too complicated to go into. Yeah. In fact, I think Leonard Susskind talks a lot about the S matrix in his book, The Black Hole War, just to give him another plug. It's a good book. You know, it's wordy at points, but he's got so many diagrams and it's really not terribly hard to understand.
00:42:18
Speaker
No, it really isn't. And, um, so basically he just looked at, there's a prediction about what happens to stuff falling into a black hole. When you look outside of the black hole, there's a different prediction for when you're inside of a black hole. And also there's a difference between the inside and outside of a black hole that involves information.
00:42:35
Speaker
So therefore they must be complimentary. And that's really not that weird of an assumption to make. It goes off of a lot of philosophical reasons for quantum physics. Yeah. It's just, um, still, you know, whether, whether it's the double slit experiment or black holes or anything else, complimentary is just weird.
00:42:53
Speaker
Yeah, but one thing that the Monty Hall problem, which we covered in which episode was that? Monty Hall, it wasn't QED, was it episode seven? I don't think it was QED. We covered the Monty Hall problem, which you can look up online. It's an incredibly unintuitive, but very, very, very simple problem. And if that can be unintuitive, then black holes have all the rights in the world to be unintuitive.
00:43:16
Speaker
The next thing seems unrelated at first and to a lot of you and even to us, we'll see him a little unrelated still after we go over everything, but it's called the holographic principle.
00:43:28
Speaker
Yeah, this is an interesting one. I actually first heard about this, I think it was from the documentary, although there's numerous documentaries I've seen that go into the holographic principle. One of them is the one on the BBC on the Hawking Information Paradox. You can Google it and probably find it. I've also seen it on the Science Channel, in fact. There was a, I think it was called Through the Wormhole narrated by Morgan Freeman. They talk a lot about the holographic principle in that show too.
00:43:57
Speaker
So how how would we describe the holographic principle? Well, first, let's imagine we have a library. Let's say it's a Smithsonian or a museum, whatever, something with information in it. And we could draw a sphere with a radius of a certain radius around that museum, right? Yes, yes.
00:44:17
Speaker
And that museum would not have enough mass to create a black hole, right? Because it exists. Definitely. Yeah. Yeah. Meaning that if we kept making that library more and more dense, there'd be a point at which it forms a black hole with that radius. Okay. I'm definitely following you so far.
00:44:34
Speaker
Now because a black hole has a certain amount of entropy that is defined by its surface area, and remember the surface area of a sphere is equal to the square of its radius times 4 pi, whereas the volume is the cubed of the radius. Now to give you a difference between the square and the cubed, 2 squared is 4 while 2 cubed is 8.
00:44:55
Speaker
3 cubed is 27 while 3 squared is 9. So it gets bigger way faster. Yes. So this is the interesting thing is the whole idea of a holographic principle, I think essentially emerged first with black holes. If it weren't for black holes, we would never have the holographic principle.
00:45:14
Speaker
Yeah, and we've talked about zeros before on this show. I think we talked about it in QED episode seven or so. Yes, that's correct. We talked about how zeros and infinities usually tell us new things. Even with quantum physics, it was the calculation that it often had infinite energy that led to the discovery of quantum physics. Yeah. Now, as you're talking... Which is also obviously false, but...
00:45:37
Speaker
As we're talking about the black hole holographic principle, this was, I believe first introduced at least one of the two physicists was Leonard Susskind. In conjunction with Beckenstein. Yeah. And again, what this has to do with it may even be smart or maybe wise for us first to talk about what a hologram is and why it applies.
00:45:57
Speaker
Yeah, a hologram would people think of it as a two-dimensional object that has three-dimensional data. So your driver's license probably has a little thing on it where you rotate it and it changes color. That's a very simple hologram. And it has technically three-dimensional data because you could imagine a surface that it reflects light based on the angle that it comes in. But a more complicated hologram could be one of those that shows a 3D object.
00:46:25
Speaker
The holographic holography in mathematically just says that you have one dimension representing another dimension in a certain way entirely. Yeah. And the reason why you can arrive at the holographic principle with black holes is because with a black hole, it's impossible to get any more dense than a black hole. You can't pack any more information in a black hole. So when you put more stuff in it, the black hole inevitably grows because you're not going to get any more packed.
00:46:55
Speaker
Yeah, meaning that if you made a black hole out of the highest entropy stuff that it could be made out of, it would not change entropy when it turned into a black hole. All the stuff that was already scrambled enough.
00:47:06
Speaker
Yes. So specifically with a black hole, because you can't pack any more entropy and you can't pack any more information in the volume of it, it can be said that all of the possible information that describes the stuff in a black hole can fit on the surface area of a black hole.
00:47:27
Speaker
Yeah. And the thing is that because a sphere for a certain amount of surface area has the least amount of volume and because a Schwarzschild black hole is spherical, it means that no matter what bounding. So let's say we had a, I don't know.
00:47:44
Speaker
a duck-shaped volume of space. The surface area of that duck would be more than is needed to encapsulate everything in there, and a sphere would be the least amount. So basically it's a lowest upper bound on the information of the stuff inside. And remember we talked about how information is encoded in plank units, almost like pixels on the surface of things.
00:48:12
Speaker
Yeah. And what I love about the, the, um, holographic principle is how I don't want to say easy it is to, to arrive at, but it's not intuitive. Like you, I wouldn't have thought of it, you know.
00:48:25
Speaker
Yeah, and it depends completely on the fact that black holes have entropy. But here's the weird thing about it, is that we have a thing called natural units. Natural units basically set a bunch of fundamental constants, which we've talked about a lot on this show, to one. So the gravitational constant, instead of being like six times 10 to the negative 23rd or whatever it is, it's equal to one. The Boltzmann constant is one. Speed of light is one. The Coulomb constant is one, and the Boltzmann constant is one.
00:48:53
Speaker
Now you always have to have other constants like the other, the two remaining based on the fine structure constant and the gravitational fine structure constant. But you could set a lot of this stuff to one, which means that in this set of natural units, instead of the radius of the black hole being G, the gravitational constant times M divided by C squared, it would just be equal to M because everything is just turns out to be one.
00:49:17
Speaker
Yeah, that's interesting. I'm not, I'm not sure I'm entirely following. Yeah. So like, let's say like G instead of, instead of a C being like meters per second. What we do is we define a meter in a second in the, in such a way that instead of having 300 million to one meters to seconds, we just have one to one distance to time. Okay.
00:49:40
Speaker
And you could define up to four of these constants of the six or so that are the universal constants make them equal to one. Interesting. Now, let me ask you real quick. One thing that I'm still not quite clear on is although I certainly understand the holographic principle, and I understand that information that goes into a black hole can be stored on the surface of the black hole, what does that mean for when a black hole evaporates?
00:50:09
Speaker
Well, what that means is that because one of black hole evaporates, its entropy goes down and it gets the entropy. The entropy doesn't go down in the whole universe. It's evaporated away. Um, so the entropy goes elsewhere. So that's all that's that saying. Okay. Okay.
00:50:24
Speaker
So then, so, so I guess my question is, um, you know, I know that in documentaries I've seen about Leonard Susskind and, and, and his solutions to the, the information paradox. Does this holographic principle actually serve as a viable solution to the information paradox?
00:50:40
Speaker
No, it's just a property of space time, really. So that's just some gee whiz fun information for you guys. Not just gee whiz fun. It tells us something very fundamental about the way that mass is structured in the universe. Like we've talked about neutron stars and how incredibly dense they are, right? Yeah. And that's a star made out of neutrons. And if you remember, a neutron is like an atom is made out of neutrons and protons in the middle have some electrons spinning around it, which are much, much lighter than the protons. Yep. Yep.
00:51:09
Speaker
Those protons are obviously very dense. Yes, if we had a mass dense as protons that was about I think it what is it is the Chundeskar limit? I think it's like three point four solar masses. It would turn into a black hole meaning that density. You can't have that density.
00:51:25
Speaker
everywhere, and we'll go into the math real quick. So if the radius of a black hole is the mass, let's just call that m, what's the area of the surface area of the black hole? I'm sorry, say that again. If the radius of our sphere that defines our black hole is m, what is the area of the, what is the surface area of that black hole? Okay, so that's just the surface area of a sphere in this case. Yeah, which is four pi m squared, which means that the volume of the, and the volume of the black hole is four thirds pi m cubed.
00:51:56
Speaker
If we divide the mass of the black hole by the volume of the black hole, we get 3 divided by 4 pi times m squared, so m squared is on the bottom of the fraction.
00:52:07
Speaker
No, what does that all mean? If you work it out, it means that the bigger you draw, let's say we have a random universe, you draw a sphere that has a certain radius, the amount of stuff that you could put in that is actually inversely related to the radius squared, meaning that we could actually draw a fractal that has some of the same properties as the universe. It would be very, very dense at small scales, but the more you go out, the more stuff is spaced apart.
00:52:34
Speaker
And that's the holographic principle. It's pretty amazing. Yeah. And also there, there's some practical consideration for, you know, like even us, like our information could be on some hypothetical surface of the universe too. Yeah. And actually just talking about the universe, the observable universe, the radius of our universe from our measurements and calculations and science and everything we've been doing in the last hundred years is about 8.8 times 10 to the 26 meters. Now a black hole.
00:53:04
Speaker
that would be able to contain all that mass that we've been able to measure in the universe would have a radius of about 7.4 times 10 to the 25 meters, meaning that there is about 11 times as much radius as we need in the universe to not violate this. So even the universe itself obeys the holographic principle, meaning the universe is very, very not dense, because some black holes, if you measure their density, if you created an object of the same density on Earth, it could float in water.
00:53:32
Speaker
Some could even float in air. Wow. Interesting. In the end, that'd be like on the super massive scale.
00:53:40
Speaker
So when we brought up the no cloning theorem, the reason why we brought up this as well as the description of entanglement is that this has to do with something called the firewall paradox with black holes. And the firewall paradox basically says that, you know, when stuff enters a black hole, it seems like the information is very, very highly scrambled and stored on its surface because, you know, black holes,
00:54:08
Speaker
have a certain amount of entropy. Now, here's a weird thing, and we've talked about this before, is that in general relativity, black holes have no entropy whatsoever. So entropy has to be a quantum property, which led, after a lot of work, Leonard Susskind and Ta-Hooft and friends, to say that a black hole's event horizon has a horizon right above it, one plank length above it,
00:54:32
Speaker
which has the property that scrambles information that goes into the black hole, but black hole complementarity might exist at the same time. So you can imagine going through like a magic mirror. Like when it, when somebody jumps into this magic mirror, we see them, we see, we see the magic mirror just go crazy and start showing static and scrambling around them. But the person jumping into the magic mirror feels himself going to Elson Wonderland.
00:54:56
Speaker
Yeah, something, it's something quite wild. Here's a weird thing about the firewall paradox though, is that because we talked about entanglement before and how particles that are entangled share properties forever until one is measured. And I want to mention something else as well. We had mentioned specifically that in order for two particles to be entangled, they have to be in very, very close proximity. Now we deliberately didn't talk about exactly what happens that causes those entanglements. I believe they just have to interact.
00:55:26
Speaker
Well, they have to have other properties which are kind of shoehorned in. So like, for example, two electrons in the shell of an atom, which they're entangled because everything else that they share is exactly the same. So it's almost like the pigeonhole principle. They just are pigeonholed into sharing a lot of things and the longer they're in that state, the more likely they are to be entangled from my understanding.
00:55:51
Speaker
You know, one of the things I want to mention is radical paradigm shifts as soon as new information is considered. And this information is sitting right under our nose. I don't mean information like a pun, like information paradox. So, you know, in previous episodes, we talked about the fact that, you know, black holes have high entropy. And we just talked about this whole idea of entanglement. Now, entanglement was known about when Stephen Hawking introduced his information paradox that's based on virtual particles.
00:56:21
Speaker
But something that was completely overlooked at that time, at least the way I read about it, is the whole idea that virtual particles themselves, when they pop into existence, they pop in from the same point. Therefore, virtual particles are entangled. That's very, very important, because if they are entangled, they share something in common. They share some information in common, at least, you know, if you measure one of them, then you have information about the other one.
00:56:50
Speaker
Now here's the thing though, once you measure one, the other one is irrelevant because they're entangled, but that is very true technically.
00:56:56
Speaker
Yeah. So, so, you know, the fact that this is not brought up until, gosh, you know, as late as 2012, that's when the firewall paradox was first published and first discussed. Fact is when you have one virtual protocol go into the black hole and you have one go into the rest of the universe, that entanglement, uh, is, is, is what's responsible for this firewall.
00:57:21
Speaker
Yeah, and essentially you can think about it this way. Like if we send a photon into a black hole, that photon has a certain amount of momentum. So the black hole is going to move a little once we fired the thing into it because the black hole is like anything else. It could still be affected by forces. We can move a black hole around. We can use it as a battery if we want to.
00:57:39
Speaker
And so really what we can say is the information that goes into a black hole. Now, this is different from the holographic principle, which we also talk about in this episode. But when you consider entanglement, the information from the contents of the black hole is, well, at least in terms of the virtual particles, that information is entangled into the horizon of the black hole.
00:58:04
Speaker
Yeah, so we could think about, and here's the weird part, and here's the firewall paradox. Let's say we sent a particle across the event horizon. So now that particle, let's name it Alice, is entangled with the black hole whose name is Bob. And Bob is entangled with, Alice is now inside the black hole, still entangled with Bob.
00:58:27
Speaker
Now Bob, now via Hawking radiation, which we talked about, emits Charlie, which means that since they're entangled and since the original two are entangled, that means Alice has some properties in common with Charlie. Now, if we take Charlie and send it back into the black hole,
00:58:44
Speaker
then we could communicate between Alice and Charlie because the thing is that since they're entangled and now they're going to the same place, Alice and Charlie contain the same amount of information, which means that at any point that we reflect Charlie from the outside of the black hole, our decision to reflect or not the particle into the black hole is communicating information into the black hole, which means that we could tell somebody inside the black hole
00:59:13
Speaker
stuff that's going on outside of the black hole and have it violate causality. We violate space-time. We talk about this. This is in violation of the no cloning theorem, essentially. And I will say that my solution that the inside of a black hole doesn't exist because it's a space-time being a knit actually does seem to solve this. Is this, sorry, for the sake of our listeners, is this the first time we, I don't remember if we discussed this before the podcast or actually on the podcast.
00:59:40
Speaker
Uh, I think we discussed it right before the podcast. So, so, so, you know, as we're planning this episode, Jonathan talks about his solution for, for, for the buckle work where, as you said earlier, it's not even worth it to discuss anything at all with respect to what happens inside the black hole. Like it doesn't exist.
00:59:55
Speaker
Yeah. And just to talk about that, there's another paradox where let's say we have a shell that has enough mass to become a black hole when it's one light year in radius, but we make it one light year and one year in radio and one mile in radius. So it's a little bit bigger than it's supposed to be. Now we, um, what we do is that we make sure that at the, that at a certain pre given time, it all fuses together at a small enough radius to create a black hole.
01:00:24
Speaker
General relativity tells us that at that instant that that happens, event horizon will start forming where the singularity is and start expanding at the speed of light.
01:00:34
Speaker
meaning that if we measure some event that happens at time T in the future with respect to creating the, like let's say we have some reference time and we say like, okay, if Central Park is 30 degrees Celsius or more than we send a photon, then we make sure that the black hole collapses. And we could do that using a complex wiring, making sure that all the black hole goes at the same time.
01:01:00
Speaker
Now with the general relativity equations, we've just sent information a year in the future into the center of the black hole, because as soon as they measure light coming out of the center of the black hole, which happens right before they die from the, or at least get trapped by the event horizon, then they, they know something that happens about the future. They can never tell us about it, but they know it, but it still violates causality in the quantum sense.
01:01:28
Speaker
So essentially, we've exchanged the information paradox for a new one called the firewall paradox. And there's not really agreement about how you solve this firewall paradox. Again, as Jonathan said, his idea that something no longer exists when it crosses the event horizon.
01:01:48
Speaker
That's just, oh, that still causes a knot in my stomach. You know, I gotta be honest, I don't like thinking about non-existence and the fact that you have a spherical, roughly, you got an approximate sphere that doesn't exist. But you know what I mean? Like, isn't that weird?
01:02:03
Speaker
Yeah, I mean, my view is that if you can't measure it, then talking about whether it exists or if it exists or the shape of its existence is perverse in a way.
Nature of Black Hole Interiors
01:02:14
Speaker
Wow. Yeah. So it's sort of like, what's that scene in The Lion King when Mufasa is showing Simba. See, all of this is going to be your land. And he's like, well, dad, what about that shadowy area over there? He's like, we don't talk about that.
01:02:30
Speaker
So it's like that, but that's the inside of a black hole. We don't talk about that. That doesn't exist. Not necessarily that we don't talk about it. It's that we know what exists. In my view, a black hole is the edge of a black hole. And talking about stuff, we just fetishize Euclidean geometry.
01:02:48
Speaker
we think, oh, just because something, like if something has a hole in it, there must be something in it. So it's like, no, a hole can just exist as a whole. So when we're talking about things like the, the, what was that limit you said earlier? The Chud Discard limit. Yes. Yes. So, so is there a limit with the knowledge that our listeners can have about black holes? Have they reached that limit? Um, Oh no, you, you could Google for gears. No, no, no, no. Here's the way that I'm thinking about it though is that if we have a mug,
01:03:13
Speaker
Let's say we painted a design on the mug. What design do we paint on the space between the handle and the mug? We can't paint anything on it. In the same way, to me, black holes don't exist. Of course they exist because they have a boundary, just like the mug handle has a boundary. But talking about what can be painted, it's like how many angels can dance on the head of a pin, that old medieval question.
01:03:36
Speaker
Yep. Okay. So you need that hole in the handle to pick up the mug. So, so we, we need black holes. It's like, man, that's just weird. And you could probably disregard some of that stuff, but like, you know, I, like I said, that's my personal theory and it might not hold up to scrutiny, but I am.
01:03:57
Speaker
i don't know i'm letting you guys know what i think yeah yeah i mean i guess my my point earlier is you know if we had if we had much more of this podcast it would be like my brain is all full so my brain would just like get bigger because of the pressure of my skull that would just explode and of course the radius of his brain would equal the amount of mass energy that created that information because it's a black hole i don't know yeah something like that
01:04:21
Speaker
Whoo, okay, so is that it? Should we bring our discussions on a black hole, at least in terms of talking about the current models to a close and just say something hokey like, well, don't take my words for it. I said words, so not to be confused with a certain show on channel, on PBS.
01:04:43
Speaker
Oh, the one is LeVar Burton. That's not the one you're talking about. No, no, no, it's not. So reading butterfly or something. Yeah. Reading butterfly. Exactly. So with respect to black holes, we're going to end this, you know, but I say after, after three long episodes, I'm talking about, you know, whether information is conserved. I like it. I'm just going to say, don't take my words for it. You know, Google it yourself. You guys are smart with the cell phones and the Google and all that. Yeah.
01:05:14
Speaker
Now we're gonna just talk about some fun things about black holes real quick. Yeah, I agree. Fun, fun things with black holes. Jonathan, I can't wait to hear what you have to say about this. I wish you guys could see the expression on Gabriel's face because it's one of utter exhaustion. Oh my gosh. Yeah, I feel like Rick and Morty. What was that one clip from Rick and Morty? What episode was it? Oh, you mean this clip?
01:05:45
Speaker
Yeah, where they were, yeah, they were just like, he couldn't handle it, you know, all the pressure. That's how I feel after trying, you know, like there's so many weird concepts with black holes. I just feel like it turns your brain inside out and then like grinds it to a pulp, you know? It's a lot to take in, man. It's a lot to take in.
01:06:08
Speaker
Yeah, we're just going to talk real quick about some fun. I keep calling them fun things. Maybe I should stop. But one thing, like black holes we've talked about before, they radiate a lot of Hawking radiation at small scales. So it's possible to use a one ton or like a 1 million. I don't know how big it would have to be.
01:06:25
Speaker
But a black hole as energy storage, just move it around using particles and like beams and stuff. Maybe if it's charged black hole, use virtual particle interactions using electromagnetism to move it around, something like that. And you could create a spaceship that turns all of a certain amount of mass into energy.
01:06:44
Speaker
Because remember, a black hole turns all of its mass into energy. So as it goes through the universe, it could just pick up energy and throw it into the black hole, like the furnace. The way you're talking, Jonathan, you're reminding me of sci-fi. I'm thinking of two things. The first thing I'm thinking about is all the instances in sci-fi, in popular sci-fi, where black holes are mentioned. Now I can name a few. I can name Star Trek episodes. Is it Star Trek where they've got red matter that turns things into a black hole?
01:07:09
Speaker
Oh, no. Okay. I think it is. I think I don't know. But it sounds like one of those Star Trek things that I wish didn't exist. I love Star Trek. They just fudge it. The other one is it's mentioned in Rick and Morty as well. Rick is bragging about his intellectual prowess and he says, Morty, I can turn a black hole inside out or something like that.
01:07:27
Speaker
Which is called a white hole, which is a region of space in which nothing can enter, not nothing can exit. So the first thing I'm thinking about is when black holes are mentioned, but as you're talking about these hypothetical scenarios with black holes, I'm wondering about some black hole fiction. Have you ever wondered about what it would be like to write some science fiction about black holes, Jonathan?
01:07:52
Speaker
I have not, but if you have, as a listener of Breaking Math, we'd love to hear from you. Send your Black Hole stories to breakingmathpodcast.gmail.com. And if you send a really good one, we'll read it on air and we'll just make it a special addition to our podcast. We'll credit you and everything. Man, I want to read some Black Hole stories, like some film noir about Black Holes, or like a murder mystery with Black Holes.
01:08:17
Speaker
Like, you know, they say don't stare into the abyss because the abyss will stare back into you. So like, you know, the way I interpret that is don't don't go sitting next to the to a black hole on the on on a bus. You know what I mean? Like, that'd be weird. Yeah. And of course, we we ourselves as breaking math would create fiction of black about black holes. But we're far too dignified for that. And you will never see any production of black hole heist coming out soon in about a week.
01:08:45
Speaker
Yeah, that's right. It wouldn't be us who does that. I mean, I don't imagine who it would be. But here's another weird thing. Because any mass energy, mass energy meaning mass or energy or energy stress, if you look at the tensor in general relativity, creates gravitation, meaning that light itself creates gravitation.
01:09:06
Speaker
a meaning that if you send a photon out with the wavelength of the Planck length, and remember the shorter the wavelength, the higher the energy, and the Planck length is the shortest you could possibly be in this universe, no matter what kind of yardstick you have, you'd create a bike hole going the speed of light, or almost the speed of light, I'm not totally sure, with a Planck mass, which is about 21.8 micrograms, which would have as much energy as a large tank of gasoline.
01:09:32
Speaker
Hmm. Wow. This whole idea that you can create a block hole with nothing but light, that is just insane. Again, I guess it makes sense because light and mass are, you know, different versions of the same thing as proven by Einstein's theory. Wow. It's nuts.
01:09:47
Speaker
Yeah. And of course we already talked about holium, uh, and how it would be like normal matter, but made out of black holes. Yeah. And, um, yeah, there's just so many potential because in the primordial universe, when stuff was really, really high energy, small black holes probably were created all the time. So it's very possible that in that froth, all the dark matter, which account dark matter and dark energy together account for like 90 some percent of the mass energy in the universe.
Speculation on Dark Matter Composition
01:10:15
Speaker
Yeah, so you're saying one of the theories is that dark matter is in fact Holium or rather black holes that just will never ever evaporate. That's nuts. Yeah, and of course all that is very theoretical and I mean, I guess we still there's so many experiments to be done on things like the LHC.
01:10:34
Speaker
which can tell us about high energy conditions. There's new experiments to be devised, maybe an entirely new type of thing that could be scaled like an accelerator. Maybe in 40 years we'll know about a black hole-erator or something like that.
01:10:52
Speaker
Physics is honestly just talking about sci-fi but then doing it in the lab at the same time and flying by the seat of your pants and going to conferences and arguing with people and it's all very, very colorful. Awesome, awesome.
01:11:07
Speaker
Black holes seem bizarre, but not as bizarre as the fact that out in the uncharted backwaters of the unfashionable end of the western spiral arm of the galaxy lies a small, unregarded yellow sun, and orbiting this at a distance of roughly 92 million miles is an utterly insignificant little blue-green planet whose ape-descended lifeforms are so amazingly primitive that they still think digital watches are a pretty neat idea, but have ascertained the existence of a so-called exotic object which exists at scales far outside of their experience.
01:11:37
Speaker
And as we consider what we've learned, let us marvel at the fact that we're living in a world where new mathematical zeros and infinities, such as those found in and around black holes, are found, and that we've already harvested undruptive bounties from this nearly god-forbidden information. I'm Jonathan. And I'm Gabriel. And this has been Breaking Math.
01:11:58
Speaker
Gabriel, do you have anything to plug? So actually a few things. I think I plugged last time the fact that I'm still working my way through a great fan fiction book called Harry Potter and the methods of rationality. I'd love to do a podcast on this. I don't know that I can. I need to look into the legality of that aspect. We probably can.
01:12:16
Speaker
I'd also like to plug some ideas for future podcasts. I really want to get into economics. I had a discussion on Facebook that was on, somebody had posted a video, the essence of the video was on socialism. And it said, in essence, socialism is not all that bad. It's been misunderstood. It's been misrepresented, et cetera, et cetera. The comments in this video were pure vitriol, like so much hatred.
01:12:44
Speaker
Now, the reason why I want to bring this up as a discussion is I'd like to talk about models of economic stability. And I'd like to talk about how not only different nations do it, you know, in terms of their economics, how much of it is influenced by the state and how much of it is influenced by, you know, privatization, but also within the United States, I'd like to talk about how different states and their economies are diversified.
01:13:09
Speaker
how they relate to the federal government as well as just the state government. All of that stuff fascinates me.
01:13:17
Speaker
And at the heart of economics lies game theory, which is so simple that it wasn't discovered until like the 20th century and even John von Neumann was confused by it. Yeah. And what I love about this topic is, you know, I had mentioned earlier the whole, the vitriolic exchange. Is that a term vitriolic? The vitriolic exchange where people were, you know, like using horrible terms to talk about other human beings.
01:13:44
Speaker
Well, I want to break things down as much as we can into mathematical models. I'm very familiar with, let's say, fiscally conservative arguments for economic stability and individual rights and liberties. I'm also aware of ideas that sometimes things are more efficient if they're done at a federal level.
01:14:07
Speaker
So without even going one way or the other, to be frank, I'm very interested in just discussing and then tearing apart different ideas about economics. And I am, you know, obviously this will come down to math, but then what, you know, the other question is what assumptions do you make in your mathematical models?
01:14:29
Speaker
Yeah. And of course, if we're being mathematicians, we have to be able to accept conclusions. So even though we might not swing one way or the other, we might make some statements that would seem to some people as controversial. So we're not maybe doing that next episode, but we might be. So keep on look, look out for that because we're definitely going to do it at some point in the future. Yeah, it'll be a, you know, after doing this, this three part on black holes, my brain feels like it's scrambled across the edge of this, of the event. My, my brain is,
01:14:59
Speaker
We definitely need a palate cleanser. So I just thought talking about economics would at least be invigorating and interesting. You know what I mean? Oh yeah, definitely. And the way that I've wanted to do it with my friends across the political spectrum is I'd love to talk about any model and talk about it as though I'm trying to sell you on it, but then also talk about the critiques. Like Karl Marx, even for those who are very opposed to communism,
01:15:26
Speaker
They say, well, he certainly addresses some concerns with human behavior and critiques, you know, even though somebody might not be a communist, they can still acknowledge what he said and why it may be appealing to some people. And then, you know, the opposite is true as well.
01:15:44
Speaker
So, yeah. And in my opinion, one of them is more true than the other, but we won't go into that. We also have the $35 breaking math tensor poster now shipping from breaking math. Just go to patreon.com slash breaking math and order yours today. And we're sorry. We've been, I think we're like five episodes. We've said breaking patreon.com slash breaking math podcast.
01:16:06
Speaker
Yeah. Yeah. We, it is breaking math. Is it breaking? No, it's a patreon.com slash breaking now. Oh, that's right. We had some people actually send in a message and say, Hey, you gave me the 404 error. There's no website there. Oh,
Patreon Correction & Mobile Game Introduction
01:16:18
Speaker
I'm sorry. It's patreon.com slash breaking math. My bad.
01:16:22
Speaker
We're professional people recording professional things with professional equipment, professionally. Okay, so there's actually one other thing that I want to plug. I want to have my roommate actually, who's my wife's cousin called Josh. He introduced me to a game on his Android, on his cell phone called HolyO in a game where essentially what you play as a black hole.
01:16:45
Speaker
Basically you just basically you just play as a black hole against four other people you eat you start off small the more you eat the larger you get until basic you're basically you're devouring the entire city block by block including other black holes if they're smaller than you are.
01:17:05
Speaker
Wow. And I even saw you playing it the other day and you as a black hole, I caught on fire. So that's kind of the firewall sort of not really, but, you know, awesome. Awesome. Well, well, thanks for bringing that enjoyment to this, you know, not a problem.
Closing Remarks & Series Conclusion
01:17:17
Speaker
Thank you. Awesome. Josh, we'll talk to you later, man. But thank you for listening to our first successful three parter on breaking math. You're very appreciated as a listener. And until next time. Uh, break some math. Is that a new motto? No.