 OK. Thank you very much. Why do we care black holes so much? One of the reasons is that it provides testing ground for theories of quantum gravity. In fact, here, even the basic questions still remain debatable. For example, do black holes evolve with unitarity consistent with the quantum mechanics? Or does an informed observer pass the event horizon smoothly, as suggested by general relativity? Or are dynamics local outside the quantum least stretched horizon, as you could usually postulate in quantum theory? And these questions started, of course, by the famous paper by Stephen Hawking in 70s. But we are still not reaching consensus, as exemplified by recent work in Amp's Armory Maroll Porczynski, I'm sorry. And an important thing here is that this issue involves all three pillars of modern physics, quantum mechanics, general relativity, and statistical mechanics. So we hope that understanding this issue will lead to some way or maybe long way towards the understanding of microscopic theory of quantum gravity, which is elusive so far. And in this talk today, I want to present a picture that aims to give some answers to these questions. And I will argue that a key to address these issues is to understand how semi-classical space time emerges from the microscopic or fundamental theory of quantum gravity. In particular, I argue that degrees of freedom described by semi-classical theory is really, really only a tiny subset of the whole degrees of freedom in the microscopic theory, and that the physics of black hole information concerns these vast degrees of freedom, which is totally not describable in semi-classical theory, but which you can view as the localized in certain specific, with certain specific configuration around the black hole. The talk is mostly based on the work with my students, Fabio Sanchez and Sean Weinberg. And this picture has been developed gradually, but the latest one with all the element in it was written in last December in these two papers and also based on some other papers as well. So let's start from reminding what we have been thinking or what we've been learning about the quantum mechanics of black hole so far. As is well known, it started from information loss paradox by Hawking. Let's think about some big black hole, classical black hole, and think about sending in or dropping some, say, book A into this black hole. What happens? What happens is that because of a time delay, this book will be absorbed into the horizon, slow down, slow down, slow down, absorbed into the horizon, and then this black hole will later evaporate in the form of Hawking radiation. That's what the semi-classical analysis will suggest. Now let's do another experiment. Instead of book A, let's send the book B with, say, same mass. And because it's the same mass, this book B will be absorbed into the horizon, and then, no hair theorem will say that this black hole is the same. And therefore, the later evolution is also the same, so the final Hawking radiation is also the same. I'm too much simplifying this, but essentially that's the picture of this information loss. Namely, final state is exactly the same, even if initial states are different. This kind of situation we never hit in the history of physics, because if you have complete knowledge about the current state of the system, then usually you can put that in an equation motion and solve backwards in time. You must be able to solve the initial condition in Newtonian equation and Schrodinger equation as well. But in this case, the final state is exactly same. If that's the case, you completely lose information, namely, unitarity is lost. It's not impossible, okay? But now, we don't think that this is a situation. Based on many theoretical progress, but one suggestion come from, okay, let's put this entire system in the ADS and map to the CFT, okay, ADS CFT, and then we know conformal field theory is unitary, so all these processes is unitary, or we believe our belief on quantum mechanics that increased by many experiments and so on. We now think that's not the case. If you drop the different book A or B, then the final state Hawking radiation is slightly different to quantum state. That does not mean that spectrum is different necessarily. It could be spectrum, it could be black body, but quantum state could be different, right? It's entanglement structure could be different. Left-right plus right-left, or left-right minus right-left states are different, but the spectrum could be same and so on, okay? But a quantum state is different. So if you have a complete quantum state, put back into Schrodinger equation so backwards in time, we now think that the initial state can be recovered by inversely solving time evolution, okay? At this point, the black hole is not nothing special. Of course, information become invisible because it's become time, it's detailed information. It's like burning book A, B, the final state looks same, just dirty airs and ashes and so on, but information is there only in the sense that if you know entire location of molecules and velocities, then you can send sort of back, back was Newtonian equation to recover initial state. So this looks like conventional object, okay? But interesting thing about gravity come when we view the same experiment from folding observer's point of view, okay? Let's imagine that you're folding with the book and we, again, drop the book A, okay? So you're folding with the book but because of equivalency principle, because you're folding, 3D folding, you essentially don't feel gravity, except for, I mean, weak tire force which is completely weak in a large graph battle. So entire information of the book, whether the book is A or similarly, B would be inside the horizon at late time, really, because you're folding with the book and the book itself is inside. So later time, the book is inside. But we just argue that if you, that really, as viewed from exterior point of view is right, then entire information about the initial state must be outside horizon at late time. You must be able to recover what was A or B from holding radiation. But now the information is inside, if you describe from the same experiment from different to different strength, which is right. You may think that, okay, the information could be inside and both outside, that's fine, that's what's wrong with it. But that contradicts the basic theorem of quantum mechanics, which is no Croning theorem. Whole quantum information cannot be copied. So the argument is simple. If you have a copy machine of copying spin up to spin up up and spin down to down down, if such a copy machine exists, you can send the superposition up plus down to that copy machine. And any operation in quantum mechanics is linear. So what you would expect is up plus down down. But if you wanna copy these states, then what you want is up plus down whole square and you lose interference down. That's why by the way our world classicalizes. You can, the classical world, you can compare information, you have experiment, I tell you, and you tell somebody and you can compare these copying of the information cannot include all interference down, it violates the quantum mechanics. So it can't be like who informations both inside and outside, in a sense, is violating quantum mechanics. And this is, I did not use any string theory or loop corner, whatever, no explicit model. This is unitary equivalence principle and linearity of quantum mechanics. Those are in crash and that people confuse, pretty much. But one genius suggestion was made, which is known as the name of complementarity in 90s by Sasuke and Tov and companies. And here we can ask, is it nearly contradiction? Can you observe this experiment to be, you are both an exterior observer and inforing observer. Can it be at the same time? If you describe system from exterior, then the picture is that book will be absorbing to horizon and then later come back the whole information coming back as a Hawking radiation. That's it. If you have a horizon, you cannot access interior. So you should regard this interior space time absent. You cannot, even in principle, at this level. Similarly, if you're affording it, the book will be interior, true. Okay, no, interior space time now is there. But can you access Hawking radiation? No, you're already inside. You can never access Hawking radiation. You should not include all these things in your description of the physics. So if you focus on something you can operationally do, you don't have a real contradiction. That was the suggestion. That's it, great. And so the reason here is that including both lake Hawking radiation, which contains information about the initial state and interior space time inside the horizon is just double counting. So it's either, in a case that you're waiting at the exterior and then jumping later, then of course you have to do carefully. Some part of it from exterior, some part of the interior, but it's not all, clearly not all. Something you can access is the only thing you should include. And that correspond to equal time hypersurface must be chosen carefully. Because if you choose this kind of equal time hypersurface, then this equal time hypersurface goes through both lake Hawking radiation and the inforing object. Then you have a copy of the two things. And the point is that this equal time hypersurface which is nothing wrong at the level of semi-classical gravity. You can choose the equal time hypersurface on which the curvature is much, much smaller than prime scale. And we usually think the semi-classical field theory is completely applicable in that kind of situation. But then this leads to exactly this paradox. Of course this is not something single observer can see. This is a Penrose-Tapis diagram. What single observer can see is this, within this triangle. But usually quantum field theory doesn't care. You just have some equal time hypersurface and then you can do quantum field theory. But that is over counting. So this is hypothesis or a proposal beyond a usual quantum field theory in space time. At long distances. But the hope here was that now by taking carefully this equal time hypersurface only within the region, single observer can access. Then you can still use quantum field theory and then address all these questions in the semi-classical picture. That was a hope. But now there was a famous Amps argument. Or that may not be the case. That may not be enough. But here's the argument. It's called five-word argument. It must have hard. The point is that you can still formulate the problem within the single causal patch. Namely in the space time region where a single observer can, in principle, access. You can have still a problem in that space time region. You can't use this type of argument. OK, you cannot access this part. And the other person can access this part but not that part. No, within a single patch, you still can formulate the problem. That was the point of Amps. Let's look at this. Suppose you're just falling from in the field past and then enter the grapple and then hit the singularity. So this region between 45 degrees line inside this is what you can get the signal from. Now you have Hawking emission earlier. The black hole have Hawking emission. And then later Hawking emission. If the theory is unitary, that means that these two Hawking radiation, which is emitted earlier and emitted later, must be entangled. Because you start from pure state. It must recover pure state. So pure state, some part is in black hole. Some part is black hole. Some part is coming earlier. Some part coming later. These must be correlated in such a way that it go back to the pure state. So the unitary is there in this picture. And then, of course, late Hawking quantum and early Hawking quantum must be entangled. Entangled means up, down, plus, down, up, or something. So it just has to be entangled, correlated, quantum correlated. On the other hand, if this horizon region is smooth, it's like mostly Minkowski if you fall in, then any mold just outside the black hole horizon and just inside must be correlated. Because Minkowski vacuum is whole of the correlation. If you put some hypothetical surface in any Minkowski region and they look at the mold in both sides, then it's a maximum entanglement. That's just the P-puree. According to P-puree analysis, that's the case. But the problem is that these two are not possible to happen simultaneously. Because if one is entangled with some other, Bob is entangled with Alice, that's it. Bob cannot be entangled with other Charlie. This is called monogamy of entanglement. This is just mathematical statement. You can easily prove it. So unitary really requires these B and C to be entangled. And smooth horizon requires A and B to be entangled. And those requirement happens within a single coser patch, namely a single person can access. You cannot use complementary. That was the basic argument. And they said the simplest possibility may be, OK, unitary is so sacred in quantum mechanics. So maybe horizon may be not. So generally, that would be totally wrong if you just jump in the black hole. Something stupid happens. Even though this horizon could be 10 kilometer, 100 kilometer, big thing. We're not talking about Planck scale or quantum gravity. It's a long distance thing. It's a drastic conclusion. So it's good to remember, because this is just, it may be confused, so this is just not, that you may think the Hawking quantum, the wave length is of all the m in unit of Planck mass. Planck length to be 1 from now on. So Hawking wave length is a big m. And Schwarzschild radius is 2m. So Hawking quantum wave length is of all the Schwarzschild radius. So this near black hole region is just OK. If you send in a Hawking area, only Hawking, one Hawking wave length, that is not correct. If the semi-classical theory is correct, if you send in, for example, Hawking type soft photon, and then because of blue shift, a wave length becomes shorter and shorter and shorter and shorter and shorter. And you can change, to do that, you can change the coordinates from Schwarzschild radius r to essentially log of r. It's called total coordinate r star. And then in that coordinate r star, then Hawking wave length stays the same, if you solve the propagation in that coordinate. And then you can see near black hole region, the Schwarzschild horizon is 2m, and the black hole thermal atmosphere end at 3m, because that's the way the black hole gravitational potential has a barrier. And those regions are big regions. The semi-classically big region. And if any information is stored in black hole, which is a quantum stress horizon, and then if that information have to go out, then those information, whatever that is, whatever that is, this is entangled with early Hawking radiation, and then you're tossed. And whatever that is, it's entangled with early radiation, which is needed to recover unitarity. And then the smooth horizon required that mode is entangled with the other partner mode in the other side of the horizon, and just, OK? You can't do that. So here is, again, basic crash of principles, which was not solved by complementary only apparently. At least that's the arms of claim, that I use unitarity and physics to localize just, OK? So whatever that is, you don't need detail outside the stress horizon, and then equivalence principle. All these three cannot simultaneously be true. And clearly, this is a big issue, a very annoying issue. So many people studied various aspects of it. Here I want to tell you about our own picture, how this can be avoided, and how we can get the quantum evolution of black holes without firewall. At least we can avoid the argument. We cannot compute everything like it's actually horizontally smooth from fundamental theory. Current technology does not allow that. If it is allowed, somebody must have computed it already. And it's a very natural picture from our point of view. So we start from the question, what is actually the semi-classical theory? The semi-classical theory is the theory of quantum matter and radiation. It's a quantum on classical exact space time background. That's how we treat the system in semi-classical theory, or semi-classical picture. Whatever, even semi-classical string theory on semi-classical background, we're still doing that. But uncertainty, in principle, says that there is no such exact space time. You must have uncertainty, clearly, because you have a time scale for the evolution of the space time, and you have energy uncertainty. For example, think about dynamically evolving, dynamically formed black hole. Then the time scale for the evolution of the quantum state is of order n in unit of prime scale, prime things to be 1, because that's a time scale of 1 emission of the Hawking photon. The state becomes an orthogonally different state after time scale of order n. So you have the characteristics time scale of order n. That means that the characteristic energy uncertainty must be the inverse of that, and because the system is non-nearativistic, that means that the characteristic uncertainty of black hole mass m is of order 1 over m. So whatever we're calling the black hole of mass m must be actually something between m and m plus 1 over m. The superposition of these things, because if it's an exact energy eigenstate, it must not be evolving. It must be stationary state. But we're talking about the black hole formed in the specific time and evolving with the time scale of order m. So how many possible ways to superpose an energy eigenstate within this energy interval of 1 over m from m to m plus 1 over m? You have a lot of states. How many states you are there between m and m plus 1 over m? Classically, continuously infinity, of course. You can have m plus 0.1 m, m plus 0.2 m, plus 0.001 m. It's continuously infinity. But quantum mechanically, this number become finite and discrete. Like how many cosilators? So amplitude is not now continuous. You can have discrete. And logarithm of that number correspond to bacon-style Hawking entropy. So it's not like exponentially new degrees of freedom show up when you go into quantum mechanics. It's not, of course, reduction. Quantum mechanics is the reduction of the states. And it becomes discrete. Continuous things became discrete. So that means all these things without exciting anything around the black hole. All these things, because it's just a slightly different m in some sense. All these are vacuum states. So what semi-classical theory describes as a vacuum state, black hole vacuum, correspond to many, many, many different microstates. Of course, it's parameterized by k, index k, from 1 to e3s. Bacon-style Hawking entropy after reading all that. So the general states, general microstates for black hole is parameterized by this index, which is a microscopic of the spacetime. You can even imagine that this is a slightly different m. Of course, it's not the exact m, because then it would be energy eigenstate. So it's a slightly different superposition. But the number of independent states between m and m plus 1 over m, that index k, and the semi-classical excitation on top of it. Suppose you have a matter, or detector, or u in the near black hole region. So these are microstates. Of course, these two index are really not separable, as I will argue later. But you can imagine this is the case. And in fact, this index a is a tiny, tiny perturbation on the Bacon-style Hawking entropy. This was first estimated at 1293. And if you think about the most entropic configuration of a usual matter, you can put in a certain region, the entropy is much smaller than the area, the area to 3 quarter naivety. So this is an area of a macroscopic quantity. So this semi-classical perturbation is tiny perturbation. Most of the degrees of freedom you can store in certain region in spacetime is vacuum degrees of freedom. And that corresponds to slightly different m. You can think that way. And then semi-classical, what is a semi-classical theory? That is, semi-classical picture is a one which you obtain by coarse-graining. You're just not looking at this index k. Technically, you're just taking a maximal mixture of this k index. That's what the semi-class theory is. So what you're calling black hole vacuum state is already maximal mixture state of the different k. So it's clear, Hawking get the non-unitary result. You're talking about mixture state already. That is what the semi-classical theory is from the beginning. So this leads to the picture that what is described by the semi-classical theory, like really matter is falling in. That's like this index a. That is a tiny, tiny, tiny subset of entire degrees of freedom you can have in the fundamental theory, which is counted by Beckenstein-Hawking entropy and the possible configuration of vacuum from semi-classical point of view. It's excitation from fundamental theory point of view, of course. Black hole is excitation. And the physics of black hole information concerns this major part of the degrees of freedom. So if you're looking at degrees of freedom in a semi-classical picture, what is a mode and so on in semi-classical spacetime, you certainly won't be able to get anything. So imagine that this spacetime picture going to spacetime picture, you're already close grain. And then talking about the mode or something you're tossed. You'll never be able to understand in a correct way. That's the misconception, I would say. And how this guy, this k degrees of freedom, interacts with the exterior system, like you put the detector, you can have information back. And this k can be viewed as distributed in a fixed frame, can be distributed according to thermodynamic entropy. You can calculate in semi-classical theory, which is strongly picked towards the horizon. Because entropy can be visible even in the theory after coarse-graining microscopy degrees of freedom. You can calculate entropy of this desk even without knowing. You're actually counting microscopic atoms. You can calculate by thermodynamics and then where the degrees of freedom is. So it's completely delocalized. And because it's completely delocalized, because you can calculate the thermodynamic, the thermo-atmosphere of the semi-classical black hole, and that entropy also is in the edge of the zone, of this black hole zone. So at the semi-classical level, you don't need to bring the information from there to this. No mode which is propagating in this big region, thermo-atmosphere from here, if there is any more, in any sense, you're tossed. This must be entangled with already radiation, this must be entangled with this, amps, firewall. But you don't need to, because this information is in slightly different M, or slightly different configuration of space time. It's slightly different M. And depending on what's slightly different M, the Hawking quantum shows up at the edge of the zone. That's around three times M, which is a macroscopic way away from the horizon. And then it goes up. And because this extract the energy from black hole, of course, you excite the negative energy excitation, it's ingoing, and later a negative energy excitation hit the horizon, and black hole dissipate into smaller mass. The negative energy excitation is totally fine, right? Because negative energy with respect to background, of course, this is not negative energy on top of Minkowski, but this is standard. So this is the right picture. The semi-classical level, you should not think that the entropy is there at Schwarzschild horizon, and then horizon, and then comes out, no. Then you're done, okay? You're tossed. And that's fine because information is, like this information is space time, delocalized. Because state, information on state is always delocalized, EPR, and so on, yeah? That has nothing to do with Hamiltonian being no local. So now, at the microscope area, what's happening? I can give you the even toy, a bit more. Suppose initially the black hole microstate is one, two, three, four to the two end, and how this state evolved. You may think, okay, you extract one bit of information to Hawking quantum. You may be like Hawking quantum, state is R1 if it's odd microstate, and Hawking state is R2 if it's even, okay? That's a model of one bit of extraction. And then now you excite negative energy, excitation to conserve energy, and then one, two, three, four. You may think this is the most naive way of extracting, but it's happening here, not there, okay? But this doesn't work. By the way, this issue was also discussed in amps. Because if that's the case, this state, because the black hole mass M, on top of that you have negative energy excitation to compensate Hawking quantum energy, this state has energy M minus delta M, later have to be dissipated or relaxing into the black hole of mass M minus delta M, whose entropy is smaller than two N, or log two N. It must be N, it must be reducing, it must be relaxing into N state, because the entropy is given by the energy, or mass, which is vacant state Hawking formula. You don't have two N states to relax into. So you can't unitary do it. You can't have inverse, two N different states relaxing into N possible states, is of course violating inversibility, reversibility. So it must be like this, and that avoids everything. So if you extract here the one bit of information to Hawking state, if the microstate is odd, then Hawking state is R1, if microstate is even, Hawking state is R2, R1, R2, R1, R2, but the black hole state can be one, one, two, two, three, three, and dot, dot, dot, two, N, N. And this evolution as a whole is unitary, it's clearly invertible. But you cannot separate the black hole state and the Hawking state, because then black hole psi one goes to psi star one, and psi two also goes to psi star one, you may think it's unitary, but now Hawking state is different. So as a whole revolution it's still unitary. But this black hole state only has N, not two N, so later you can be relaxing to smaller number of states represented by smaller black or Wittgenstein entropy because mass is smaller, okay? So this must be what's going on. And so this is saying that if you have a negative energy excitation, actually entropy is not one to two N, but it's one to N, so that means that entropy is a negative, okay? But negative entropy is okay because negative entropy with respect to background value. So it's completely consistent, negative energy carries negative entropy, usually entropy is controlled by energy, okay? So the black hole information extraction actually occur in a semi-classical level of picture through in going negative information, okay? So not really information like coming through and so on. That is the key. Then you don't have any of the amps actually in consistency. So you can see at this point what was wrong with a conventional Hawking pair creation picture, right? You have a positive and negative thing at the horizon. One of the things is falling into the horizon then they have Hawking. Of course, nobody literally believed this like a heuristic pair creation picture, but let me just highlight that what's really wrong with that picture. First of all, usually you think it's at the horizon this pair creation is happening. Therefore one quantum is entering into black hole. It's not. Really the creation is happening at the edge of the zone which is a macroscopically away from the horizon, okay? So far away it is a 20 kilometer black hole then it's a 30, I mean it's in R so it's not a proper distance but it's anyway it's like far away and of course it's a quantum. Wave range is also big. So it's not like specific location at 3M. The wave range is pretty big there. But that's where this is happening. The other thing is that if it's a pair creation created particle is entangled, right? If you have electron and positron it's been left and it's been right, right? It's always completely maximally entangled but that's not the case, okay? The emitted quantum is R1, R2 and the state is one and one. And actually this lack of entanglement between the created pair is a source of information extraction, okay? Because of that you can extract the information from there consistently with the unitary and locality. So this means that you cannot describe this K index or something in semi-classical in semi-classical phi theory. So some breakdown of semi-classical picture being complete at a large distance scale. But that breaking is subtle because you can always ask, oh now I'm saying that this information Hawking information extraction process is Hawking quantum M coming in, negative energy delta M minus delta M going in. That's the information extraction process. Let's think about the time reversal process. In a time reversal process Hawking quantum of all the delta M coming in and negative energy delta M comes out and then it's just pair annihilating in some sense, right? It's not really entangled but it's pair annihilating and so that means that you may think if you send in soft quantum before, far before reaching to the horizon it may be annihilated, okay? That's a huge violation of semi-classical phi theory if that were the case. But that is not true because this usual Hawking emission process is a thermal entropy increasing process, usual process. So this time reversal process must be analogous to something like ink in the water is very specific configuration and you evolve, evolve, it goes to the corner, okay? That's the time reversal of, okay? You have a very fine-tuned initial state it can happen but usually that's not the case. Usual processes of sending in soft quantum is just go through. Then a semi-classical theory is really, really good way to describe. So the violation of semi-classical picture is pretty sour. So it's not something like you can parameterize in a very simple manner, simple way, okay? So with this, we just, successful reference frame change is really possible because you now don't have any obstacle of having informing frame. For example, if you have some frame which is falling from far from the horizon and just falling and then it just has a huge velocity when it passes the horizon. So therefore, it's something like extracting suppose you have some detector hovering across to the horizon and just clicking, clicking, clicking and then extracting information and click, click, click because it's a blue shift, click, click, click, very fast. But now this very fast clicking this is the time, this is the time, this is the time from a short shift of time click, click, click, click, click, click, click but from falling guys, this clicking happens at the space time scale of order m, okay? The next clicking is over m. It's huge time scale, okay? So it's a mostly Minko scale. So that's consistent with the equivalence principle. And this is the last slide before conclusion. So, and one implication of that is actually the Hawking effect is not the Oogoo effect as you might have heard many times. But I claim it's not, okay? Because in Hawking effect, if you hover it, if detector is hovering very close to near the horizon if you're falling in, then it looks like this clicking is like long distance because one click because of the flash boost it could click here and then distance m away the next click. So the clicking time scale is over m in Hawking case. And at all the m, you have a curvature, okay? You have complete curvature. So you can have, you can have a deviation from Minko scale. You can have actually information to be extracted that way. On the other hand, in Oogoo effect, in Minko scale space, the curvature is exactly zero. So the clicking will not extract any information. That's not consistent, the inconsistent with the equivalence principle. You may think it's inconsistent, right? Hawking effect is gravity. Oogoo effect is acceleration. Equival principle says that both are same but equivalence principle says that if they are same at the single point. On the other hand, quantum state is a configuration of equal time hyposynthesis, global information. The globally it's different. Globally it's a different effect. That's consistent with the equivalence principle. So quantum mechanics and equivalence principle is very subtle, but they're consistent. So I've only one word, given this, this, more or most all, you think is a thermal radiation, a thermal matter, thermal radiation is actually spacetime degrees of freedom. It's K, it's some stupid thing, which is not obeying usual semi-classical equation motion. It is not describable in semi-classical PQE. So that looks like sometimes spacetime, it's slightly different. And sometimes it looks like a matter, thermal, thermal radiation. It's some strange object. And that means that actually Boltzmann-Brenn problem is not there. Because Boltzmann-Brenn problem, if you know it, I was just kidding. If you know it. Boltzmann-Brenn problem assume that the dosito-entropy, dosito-summer radiation obeys usual semi-classical equation motion. Okay, so summarizing. So thinking about information of IO problem in a graph called quantum physics, we led to some specific picture for the emergence of semi-classic spacetime to the extent you can do in this semi-classical level. So I'm not claiming, of course, microscopic or all these dynamics of Hamiltonian was known. But now this is a picture. So you have in the fundamental theory of quantum gravity, you have vast degrees of freedom. It's counted by Beckenstein-Holking entropy. This is way beyond something you can do at the level of packing semi-classical matter. And you coarse-grain, you just coarse-grain, like coarse-grain in atomic configuration of the desk. And you coarse-grain leaving high enough energy matter which clearly has identity as a matter in spacetime. And the coarse-grain, the rest. That is what the semi-classical theory was, quantum theory on curved spacetime. And this coarse-grain is very subtle, that it's not like this region you coarse-grain. No, it's just much more subtle thing as I explained in the time reversal picture of the Hawking emission. And then, of course, if you coarse-grain also the quantum matter in quantum theory, you can go to completely classical theory. So in that sense, quantum theory is, of course, partial classicalization. You also classicalize only spacetime, keeping the quantum nature of matter on radiation. But that's a vast degrees of freedom, of course, graining. And black hole information concerns exactly these degrees of freedom. That's why, of course, minute use, commit to semi-classical picture, you toss. You have arms parallel. From the beginning, that's not the right thing to discuss these things. And these degrees of freedom, we don't really know what that is. Sometimes it looks like spacetime, a slightly different M. It's a K index. Sometimes it looks like a thermal radiation, because you can count the thermal radiation. What that is, that's really the key understanding this would be a really, really key step towards full understanding quantum theory. Thanks. OK. So I think it's rather late. And most of the time, question time has been used by the talk. I think we're having lunch next. And so you're certainly welcome to talk to Professor Yasunori during lunch. Thank you. If there's one quick question and a quick answer, we will do that. OK. If it's not quick, you can do it at lunch. So in the 90s, when people were thinking about this, so one attitude was that any reasonable quantum theory of gravity in a asymptotically Minkowski space should be unitary in the sense that you have some initial state, which is pure. And then it evolves unitary. And you have a final state, which is pure. And the black hole could be viewed as some kind of resonance. So if the initial state is pure, of course, the von Neumann entropy is 0. And under unitary evolution, it remains 0. So the black hole, therefore, is necessarily a mixed state. And so you could think of the black hole as a resonance, which is entangled with its continuum. Are you giving a microscopic description? Yeah, the description. The statement that, OK, has to be very quick. And the statement of that, if you think semi-classically, that statement. And that means that this mode B must be entangled with a C. That's exactly the same statement. You have to go back to pure state. But I am saying that that B mode is not there in semi-classical picture. Rather, the C is entangled with the index K, which is what the exact value of M you can imagine that way. So Paolo, huh? So before clapping, just one information about logistic for the meal. So there will be two ways of getting food. So people that basically register for PASCOs and paid the registration fee, the food will be distributed on the terrace outside. While local people or people that are financed by ICDP will get the food to the standard cafeteria. Anyway, just the two lines eventually will be in the same place, which is on the terrace. But just these should avoid the lines. OK, thanks. Let's thank Jacinori Nomura again.