What is “information” in physics? Why do we think it’s preserved, and what happens to information when it falls into a black hole? Why is this a problem? I discuss these questions and more in today’s Ask a Spaceman!
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EPISODE TRANSCRIPTION (AUTO-GENERATED)
What if I told you that I could tell you your future? That I could stare at you long enough and tell you exactly where you're gonna be, what you're gonna be doing, who you'll fall in love with, what kind of job you'll have, how you'll die, and even more. I could tell you what your carbon and oxygen atoms will end up doing billions of years from now. You probably wonder if you're listening to the right show, and the answer is you are listening to the right show because I can tell you your future. I can stare at you long enough and tell you your entire future history.
It's true. Why? Because this is physics and physics can predict the future. If I'm studying a system, which system here is just a generic vaguely physics y jargon word for a bunch of stuff doing their own things, anything from a particle in a box to, you know, you, congratulations. When it comes to physics, you are just a system.
If I'm studying a system and I know its state, and state here is just a generic physics jargon word for the current status of the system where all the particles right now in this slice of time, what they're doing with their speeds and spins and momenta and positions, everything, just all the the contents of that system. If I know the system and its state, then I can predict the future of that system. Why? Because this system evolves in time according to the laws of physics. And the laws of physics tell us how one state evolves into another state, evolves into another state, evolves into another state, evolves into another state, evolves into another, etcetera.
I think you get the picture. So if you are a system, and you are, and you're made of a bunch of physical stuff, and if the laws of physics are correct, then I can simply crunch the numbers and tell you how your state evolves with time. In other words, I can predict your future. This is called determinism, and it's kind of a big deal. And what's really cool about determinism is that it can be run-in reverse.
Time here, when it comes to physical systems and their states, in their evolution with time, time is just a parameter. It's just a number that steadily increases, and you see how the state changes as this thing called time changes. But the thing called time in principle, not in reality, but, you you know, that's another episode which I've already talked about. The time can run backwards. In inside the equations of physics, time can run forwards or backwards equally.
Now it doesn't happen in real life, like I said, but in the equations themselves, time can run forwards and backwards. So you can take this state of you at the present at the now, and you can run it forward in the future. You could also run it forward back into the past because the laws of physics allow you to go in both directions. So we can evolve systems and their states from past to future and also future to past. In other words, the laws of physics are reversible, and in, like, five minutes that's gonna come up again.
So I want you to remember that word reversible. Now before I get too far, you may start to get a little bit annoyed. I am sitting here telling you that you're just a physical system, and you have a state, and I can predict your future because I know the laws of physics. I know every little atom and molecule inside of you. If I can record perfectly your state, then I can apply the laws of physics and chemistry and all the other stuff, and I can know exactly what you're gonna do in the future.
You might be a little bit annoyed about this whole free will stuff and all that. Well, too bad that is a different kind of show, and, not my problem. But what about quantum mechanics? You know, quantum mechanics throws, apparently a monkey wrench in this whole determinism thing, where you can if I know precisely your state and I can evolve this state with time, and I know what you will do in the future. Quantum mechanics sits back and says, no.
Everything's probabilities, man. You don't know what you're gonna get. You can't measure me precisely. You can't know both my position and my momentum simultaneously to perfect accuracy. I mean, come on.
You're just not allowed to do that in the quantum mechanical world. So you might be tempted to think that, quantum mechanics gets rid of determinism. This whole idea of taking states and evolving them with time and knowing them perfectly, that is so nineteen hundreds. That is so steam engine age. Like, this train whistles and top hats.
No. No. No. Quantum mechanics is the new hotness. New hotness says no more determinism.
Well, quantum mechanics is still physics. Right? And physics is still deterministic, but just deterministic about a different thing. Instead of states in quantum mechanics, you have quantum states. Instead of knowing precisely the position and momentum and spin and everything else about a system, you have a set of probabilities.
Next time you go looking for the particle, you might find it over here with really good chance and maybe over here with slightly less chance, and then way out there with almost no chance at all, but not zero. Yeah. You you might get lucky. It might be out there. Same thing for the momentum.
Same thing for the spin. Same thing for everything in the state. Instead of perfectly well defined positions and momenta and everything else, you just have clouds of probability. And in quantum mechanics, the way the laws of physics are applied, they don't take the positions and the momenta and the spins and evolve them with time. No.
They take the quantum state and evolve it with time. They take the entire cloud of probabilities and move it with time. So if you look at right now, like now, here's my cloud of where the particle might be. I can apply the laws of physics, and I can wait a while. And then I can ask, where has that cloud moved?
Oh, it's not gonna be over here, and we're now it's gonna be over there. There's a better chance of finding the particle over there than there was before. So determinism still holds, but it's determining a different thing. It's determining the quantum state, not the state state. And this idea of reversibility still holds.
I can take a quantum state and I can evolve it forward in time and see where it'll be in the future. And I can also evolve it backwards in time and see where it was in the past. The laws of physics don't care about the arrow of time. So determinism still holds in a quantum universe and reversibility still holds in a quantum universe. The quantum mechanics doesn't change the overall picture.
It just changes what we're determining and what we're reversing. And the big picture is that information is preserved. Wait. Wait. Wait.
Hold on. Hold on. Hold on. How was I made able to make a big where where why did I just start tossing out this word information? And preserved and is.
Like, these these are very, very important words that just apparently came out of nowhere. Information, which is the subject of today's episode thanks to a question from Peter j, is the combination. This word information has meaning in physics, and it's the combination of your state plus determinism plus reversibility. When you put that together, you find that information is preserved. If I look at your state, this is everything about you right now, and I know for sure the the laws of physics allow me to figure out how your state will change both in the future and the past, and I can go in either direction equally, that means your information content is preserved.
It means everything I know about you will change. It might mix up. It might be in a different place, but the raw information content of you is still preserved. Your identity is still preserved in our universe, either a classical universe or a quantum universe. Now you might get mixed up.
Let's say you die. I'm sorry to go very morbid and dramatic off the bat, but, you know, let's I wanna go extreme. I wanna provoke an emotional response so this really sinks in. Let's say you die, and your carbon and oxygen atoms start leaking out into the the ground and the air, but it's all governed by the laws of physics. Right?
So I could fast forward a million years from now, and I could keep track of all your little carbon and oxygen atoms, and where they've gone, and who breathed them, and where they went, everything. But since the laws of physics carried me through all those millions of years, now it might be complicated, but that's a different problem. We're talking about stuff in principle. I could pluck out all those carbon and oxygen atoms, rewind the clock by a million years reversing the laws of physics, put them back into your body and reanimate you like Frankenstein's monster. The laws of physics allow me to do that, and even the quantum laws of physics allow me to do it.
It just gets a little bit fuzzier, but the principle is still there. Your information content is preserved. It might become very, very mixed, but it is not destroyed. It's just out there in a different form. Okay.
If you want a slightly less dramatic example, let's take your a book, your favorite book. Maybe your favorite book is your place in the universe. It doesn't have to be. I'm just not gonna be your friend if it's not. I mean, it's you can live your life.
I'm not gonna judge you. And if you're not gonna buy my book, you can at least contribute to Patreon. That's patreon.com/pmstarter, which is how you keep this show going. Thank you to all your generous contributions every single month that feed me and clothe me and house me so that I can keep sharing science. What if I took your favorite book, which might or not be your place in the universe, and I burned it?
Very cruel thing of me to do, but I'm not technically destroying any information. I'm not destroying the information content of the book. I am scrambling it. I'm making it nearly unrecognizable, but the content is still there. I could take the pile of ashes and the smoke collected in a big chamber, and since it's all governed by the laws of physics, I could reverse that state of ashes and smoke.
I can reverse it back in time, and I could re in principle, reconstitute your favorite book. That seems weird that when you burn a book, you're not destroying its fundamental information. But it's right there in physics. It's right there. You're scrambling it like crazy But if I took two books if I took one book in another book, that's totally different and I burn them the ashes are a little bit different.
The smoke is a little bit different because the information content in the first book and the second book are a little little tiny bit different. And it gets imprinted even subtly in the ashes and the smoke, and I can bring them back and I can reconstitute the two books because I've only scrambled, not destroyed. So information is preserved across the universe as far as we can tell, so let's just run with it for now. What about black holes? Black holes swallow things and they never come out.
Where does the information go? When information, when, you know, stuff falls into a black hole, where does the information go? Well, we have to ask what happens when anything falls into a black hole, and of course there's a split perspective. If you're the one doing the falling into the black hole, then you just sink down below the event horizon. You don't even know the event horizon is there, and then eventually you swirl down into the singularity, and you're encounter oblivion.
But from the outside perspective, remember, if I'm watching something else fall into a black hole, it never quite crosses the event horizon. It gets slower and slower and slower, more and more and more redshifted, but it appears, for all intents and purposes, for the purposes of this discussion at least, stuck to the surface. And we have those split perspectives and you're like, how in the world can we have split perspectives? Welcome to the wonderful world of relativity where nobody agrees on anything. You just have to live with it.
So we can ask, what happens to the information? Well, maybe the information sinks down to the center of the singularity, and we'll get to that later. But from our point of view watching from the outside universe, nothing really sinks into the black hole, it gets stuck on the surface. The information gets stuck on the surface. And when a black hole eats something, it grows more massive, which means it has more surface area, so there's more room on the surface to accommodate that extra information.
So as black holes feed, more and more information gets piled onto the surface. Already there's some issues with this statement about what happens to the information that falls into a black hole. Because there's something about black holes called and I'm sorry. I'm not in charge of naming things. This is called the no hair theorem.
Impure general I'm I'm I know. I swear. I'm not I promise you I didn't just make this up just for a funny joke. It's just it's just a thing, folks. In pure general relativity, which is how we understand the existence of black holes, black holes have three and only three properties, mass, charge, and spin.
If you have two black holes with identical masses, identical spins, and identical mix them around and and and then lift up the cup and ask you which one was black hole a and which was black hole b, you wouldn't be able to tell. You said, I don't know. They have the same mass, same charge, same spin. Black holes don't care what they eat. Black holes don't care what they eat.
But already, we're sensing that there might be a little bit of an issue here because different stuff falls into different black holes. That information gets pasted on the surface, and yet, all a black hole cares about when it comes to general relativity is its mass spin in charge. So already we're getting a sense that, oh, yeah. Yeah. Information matters.
What falls into a black hole matters, and yet maybe it doesn't? I'm not exactly sure, and no one else is exactly sure, but let's keep going. The big issue when it comes to the so called black hole information paradox is Hawking radiation. Stephen Hawking, back in the seventies, along with some other collaborators, realized that black holes aren't exactly black. They're just kind of mostly black.
They're a little bit gray. They emit radiation through a very complicated quantum mechanical process, which I devoted an entire episode on. You should go back and listen to that because it took a half hour to untangle that. So for today, we'll just accept as fact that black holes glow a little bit. They emit Hawking radiation.
They lose energy, which means they lose mass, and, eventually, black holes go away. Black holes evaporate by emitting this radiation, by glowing a little bit. And they glow in a very, very, very specific way. The the radiation that emit they emit, it's not just any old radiation. No.
It's black body radiation. AKA and again, the horrible name, thermal radiation. It's a good thing I already did an episode on thermal radiation, so you can listen to that. But I'll recap. Thermal radiation is the radiation given off by hot glowing things.
You are giving off thermal, aka, black body radiation. It's in the infrared, so it's hard to see with your eyeballs. The sun is giving off radiation, thermal radiation, black body radiation, mostly in the visible, which makes it very easy to see. If you're made of stuff, then your stuff is emitting thermal radiation. Turns out black holes also emit thermal radiation.
And thermal radiation is random. It has no memory. It doesn't care what's making, especially in the case of black holes. If you have a black hole with a certain mass, a certain charge, a certain spin, it will emit a certain kind of thermal radiation. If you have a different black hole with a different mass, a different spin, a different charge, it will emit a different thermal radiation.
You can tell them apart by five two black holes with identical masses, identical spins, identical charges. Their Hawking radiation will be exactly identical. Exactly identical. Regardless of what fell into the black holes, their radiation will be the same. And then eventually, both black holes will disappear, and that's the big problem.
Here's our full paradox. Information is preserved across the universe. Information, when stuff falls into a black hole, the information gets stuck to the surface. The black hole emits totally random radiation that doesn't care about what fell in, and then the black hole goes away. Where did all the information go?
Where'd it go? It's gone. It's gone. You can put information inside of a black hole, and then the the black hole dies, and with it, apparently, so does the information. But I thought information cannot be destroyed, and then right here in our faces is a place where information is destroyed in our universe.
What is going on? If I throw myself into a black hole and I throw you into another black hole, and then the black holes disappear, what happened to our memories? I can't trace that back. I can't trace the carbon and oxygen atoms and rewind the laws of physics to reconstitute you because in this case, the black holes have eaten the information and then the black holes died and went away themselves. There are no more carbon and oxygen atoms.
There is no more information. It's not like scrambling information it's not like burning a book the information is just poof gone what's going on Well, we don't know. Sorry. We don't have a solution to this paradox. We don't.
We don't know the answer. It it is a standing paradox, and it has been for a few decades. But people are very, very interested in this paradox because this question of what happens to information inside of black holes or outside of black holes or on black holes or within or around black holes sits at the boundary of gravity and quantum mechanics. Because Hawking radiation itself is a quantum mechanical process. Black holes are a general relativity gravity thing, and we're so interested in this paradox because we feel like the resolution of the paradox could lead to new physics, and new physics is always awesome.
We feel like if we can crack this paradox, there'll be something new to learn about the universe, especially in this very, very tricky, thorny, difficult area of the intersection of general relativity and quantum mechanics where gravity meets small. So what are some possible solutions that people are tossing around? Maybe information really does get destroyed. Man, we'd have to do a lot of rewriting, but, you know, hey. That's life.
We've had to do it before, but we're very reluctant to do it because, like, everything we know about physics, everything we know about quantum mechanics and relativity are all screaming at us that information is preserved in the universe. And so if you're gonna make an exception here for quantum mechanics, man, you got a lot of rewriting rewriting to do. Like like so like, all of physics needs rewritten to accommodate the fact that information really can be destroyed. And that's, man, that's that's a headache. Alright?
I mean, we'll do it if we have to. Trust me. We're scientists, but we won't do it, like, just because we feel like it. We're gonna do it if we're forced to do it. But maybe that's the answer.
That information really does get destroyed in our universe, that physics is not fully reversible, that states aren't fully capture everything, you know, etcetera. It's all the whole deal. But maybe when we finally crack a combination of gravity and quantum mechanics, that's exactly what it will tell us. It'll be like, hey, folks. By the way, information can't get destroyed.
Who knows? Maybe information somehow gets imprinted on the Hawking radiation, where the Hawking radiation is in quite thermal, is in quite black body, where if you stared at the radiation emitted by a black hole for long enough, you could write down the information, and you could very slowly and painstakingly unscramble it and get back to your original state, just like your carbon and oxygen atoms floating around in rivers and trees and rocks, you know, millions of years from now. Difficult thing, but, you know, with enough patience and enough grad students, we could probably figure it out. That seems like the most appealing answer because then we don't have to rewrite the laws of physics, and it just pushes on the boundary a little bit, like, oh, yeah. You know, Hawking's original idea in the seventies wasn't exactly right, and we gotta add this little modification.
The trouble here, and and even though that's the most appealing answer, the trouble is we have no idea how that actually goes down. Try as we might, we can't figure out the path of information getting into Hawking radiation. Like, we can't figure out how Hawking radiation gets modified to reflect the information that got stuck to the surface. Like, just we can't figure out the math. We can't do it.
And so even though that's the answer we really, really, really want and we've been wanting for a few decades, is we can't we can't have it. Because even if it's out there, we can't figure it out. But it'd be exciting if we could figure it out because, again, new physics. It would teach us something about Hawking radiation. Maybe information doesn't get stuck to the surface.
Maybe it sinks down into, like, a tiny nugget at the center. Now as far as we can tell, in general relativity, the center of a black hole is an infinitely dense point, the singularity. We know that's wrong, but we don't know what's right. So maybe there's something down there, a little nugget. Could be very tiny.
Could be kind of big. It doesn't matter. There could be a nugget. We don't know if that nugget exists. Well, we know something has to give when we look at singularities inside of black holes.
If we don't know what we'd get out at the end of the day is a nugget, and the nugget that can store all the information, and then the black hole evaporates, but leaves behind the nugget, and all the information that got locked in the black hole is a is eventually released back into the universe. Good luck trying to find that nugget. Or maybe I mean, people have been working on this for decades, and theorists are theorists, and sometimes they get a little bit bored and a little bit lonely because they don't show up at social events or department parties. Maybe something super funky crazy is going on, like information is getting funneled into other universes or looping back in time, but we're not even gonna go there. Yes.
It'd be exciting if one of those are true because of new physics, but, like, let's we're not even gonna go down that road. What's the ultimate resolution of black hole information paradox? Who knows? Honestly, who knows? This is kind of why paradoxes are so dang fun.
Thank you so much for listening, and especially big thanks to my top Patreon contributors this month, Robert r, John, Matthew k, Helga b, Justin z, Matt w, Justin g, Kevin o, Duncan m, Corey, d, Kirk b, Bara Kay, Nooter Dude, Chrissy and Eric m. It is your contributions and everyone else's that keep this show running patreon.com/pm sir. And, of course, hey. Hey. Hey.
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You can't believe how much that helps. And follow me on social media. I'm at Paul Matzler. You know the deal, and I will see you next time for more potentially incomplete. But we're gonna hope for complete knowledge of time and space.