When Entanglement Met Black Hole / Quantum Information Theory & Low Energy Problem of Quantum Gravity

0:00 The following is an academic lecture on mathematics. Now, let's do something more interesting. Now, we'll talk a bit about geometric entropy. Antropy in quantum field theory, where I try to define here and there, which are spatial or space-time regions. Probably the easiest way to think about it is time slice, the separation of the space, three dimensions that we call here, everything else is there, or we can have some denser splittings. Then, what we try to do is to produce a reduced density matrix that corresponds to this grid here, and actually mathematically it's ill-defined object, so a lot of renormal regularization and renormalization will be required in the process. And typically, this reduced state is mixed. So we have non-zero entropy even for your state. Then, a number of years ago already, quite ingenious arguments show that you can argue that entropy is a function of the area. Then, pretty often you may need a cutoff. More clever arguments show that entropy is even proportional to the area. and then it's very tempting to say that they cut off with the size of the Planck scheme. What I want to show now is, let's take seriously this splitting. Let's write the entire state as an entangled combination of states here and states there, and see whether this density matrix, something that we try to sell as density matrix, has a definite transformation law. And the answer is no, exactly as in the case of per single product. So, in fact, can I possibly try to ask you to describe more precisely what we'd like here and there specifically? Which operators are you going to use to define meeting here and which operators do you need to define there? Right, there's a set of meeting operators to define stuff here. Yeah, one of the examples would take local operators on the time slice. here to use this operator. Right. Okay. So you find that that tensor, if I go to a different reference frame, and I look at the transformed version of those operators, then I will get a different

2:30 entanglement? Well, you may have different entanglement, and again, to perform the transformation, you need to know not only operators here, but also operators there. So you exactly like with the spin and momentum part of the description of the single particle, I cannot give you just partial information and Lorentz transformation, and then you will be able to figure out how this region of space moves on different torches. I'm only confused by that, because my understanding of the resolution of this, which you just described, is that if I have my REST brain, I have a pre-operator that I use to describe sin. Now, if I go in a Lorentz-transformed brain, there is a large-transformed version of that operator, but now it describes something that fixes the spin at a moment. Now the entanglement defined between the operator I call spin and the rest of the world, the entanglement somebody in a different barrette being described as the entanglement between this mixed spin and operator and reservoirs. That entanglement is the same, so I'm wondering if there's... Since I'm not sure that I followed you exactly, I may say that depending on exactly what you call your operators, and depending also on whether you say you have a wave packet, so each moment of one time a difference happens, we may have the same entanglement, or we may have different entanglement, we may have maximal validation of element abilities for certain types of operators, or less than maximal if you define them different. So, just what I want to say is that it will depend very strongly on your definitions, on the records that perform, on the records that are available. So, essentially this is the same case here. So you're saying it depends on what you call here, what you call there? Yeah, what you call here, what you call there, and even on the style specification of this here. So, if you want to have a transformation law for other density metrics, our unitary transformation should also split up into here and there. And the question is whether it's possible. The answer is not. Because if, for example, we have a vacuum state, well, it's trivial on dimensional representation, it could have one particle state. Again, it's irreducible representation. Now, a tensor product of two reducible representations generally is not irreducible unless we are willing to take the state, Our state exactly splits into the direct product of two vectors. But for these two vectors we cannot have a space like correlations.

5:00 No bell type violations. So there is a nice contradiction. Transformations do not split into here and there spaces. And then cause their implications for the end. Now from non covariance, let's go to non invariance. We have to do it in different settings, ways and without boundary conditions, these cutoffs, and basically it's given tape. We get something, we have to paste it. And one of the given tapes is different versions of attributes of the graphic bound. Going back to Beckenstein 1702 and all the way down here. How to import them, how to get them out of the usual field theory. For example, one particular case where you can do it wasn't led by Uxuber. You can do it. You can have your holographic bound. And very naive, probably very naive space like for that amount. You have a box. You analyze a metalous boson field in that box, box of the size L. you impose two cutoffs and one cutoff on the maximum available quant of energy so it restricts the number of modes. Then you impose energy cutoff. You want this thing to be stable. You don't want your box to collapse containers that will blacken. This is energy bound for the entire system. So we have ultraviolet and infrared cutoffs. than some quite, whatever, combinatorics, and we can show that, indeed, for the bosonic field, maximal entropy is bounded by area and some free factors. Very nice. Now let's use this form of the users in different ways. First of all, if you say that this thing is maximal entropy, is observer-dependent, pretty often we define effective number of the views of freedom in the inverse procedure. We take an exponent of entropy and this is our entropy. Now, if one changes to other changes, it's pretty trivial. But what's interesting is that this presumably bad thing changes dependently may be useful. And it's useful for saving the space-like holographic bound from a very simple effect.

7:30 Now, I try to be clear. I'm not stating that the native form of holographic bound is stated. You have a system, you have possible maximal entropy of the system, and it's bounded by one-quarter of the space-like area, the surface of the boundary. I don't know whether it's really true or not. What I'm going to show is that the simplest and most direct attack fails, just because entropy is non-invariable. So, the story runs as follows. OK, I have my rest frame, very nice, entropy is bounded by this principle. Now I go to another frame, length frames, area shrinks, entropy is invariant. going to violate the bound. But we have a defense. Both area and entropy change, and area change, okay? Obviously, if we look at how the bound has been derived, we need to insert Doppler factors in various places, And following the chain of derivation, we actually see that entropy gets down faster than the area. So if you plot this entropy-to-area ratio, it goes down fast if we just boost the zoom parallel to one side of the cross. Now, again, this is just a defense against a symbol of X. I don't know whether the boundary is safe or apparently not. But this is one of the examples of what happens if you have to take the track of your entropy as well. All right. Well, in non-invariant, non-invariant, now let's look at something invariant. And we have very nice, invariant examples in blank holes. Here again, have to be careful. We look like two observers, both of them, observers and barrage. None of them is falling into the blank hole. So we have, let's say, one observer at rest, one which has Lorentz boosted with respect to it somewhere at infinity.

10:00 They have different Lorentz frames in nature. they introduce different time-slices objects. The different time-slices cut the horizon of the black hole differently. But thanks to the Hawking-area theorem, and adding in the quantum-consuming polygraphic corrections to black hole entropy as in the functions of the area, these two entropies, these observers should ascribe to the black hole, are the same. And on the other hand, again, grossly amusing, and saying it in one not very precise statement, there are model calculations, 1 plus 1 space-time, where we have two different observers, that time slicing has the same crossing point of the horizon, and the entropy has been calculated explicitly, and they did the same. Now, I think that when you usually expect something to be non-invariant and it turns to be invariant, it may give us stronger hints, or at least criteria to test against when we try to find a microscopic structure. So that's probably something to remember. After that, okay, non-invariants, invariants, let's go for a bit of more non-invariants again. So, one of the interesting cases is axillary cavity. In this case, unlike the standard under effect, we cannot argue that part of the world is inaccessible to one of the observers. We have a Minkowski observer, we have an accelerated observer to get as a cavity. And if we read carefully the analysis that exists in several papers, we can consider to get the following situations. We have an accelerated observer that has a vacuum state in his cavity. And we can have a Minkowski detector, something really falling inside the cavity. The detector detects thermal radiation, nearly as like a standard under radiation. If we try to analyze how the picture looks in Minkowski's quantization, it's not very easy. but we see that what is your state for this accelerated observer is a mixed state for the lingotsky observer.

12:30 Entropy goes like that. Another nice example. This is the state inside the cabin? Why is it a mixed state? For anyone? It goes like that. For example, very simple, not very simple, but the calculation of Paris and company, you throw inertial detector. Of course, it's pure zero, it's pure vacuum state where it's very clear. But you throw the detector in, its detection rate, its station It looks thermal with a temperature which is what you expect in the usual honor effect times some factor. You can just do a long and boring calculation of whitening functions. We can have your interest in a slightly different example. Just normal. Accelerated absorber. He or she accelerates. Minkowski vacuum outside. Well, not Minkowski vacuum outside. Beyond the absorber's horizon, we can put method. In this case, we don't have boundary conditions. And, however, if we have two such accelerated observers, with the same acceleration, but with different velocities, and the matter is essentially beyond the horizon of any one of them, we can do several renewableization procedures, defining energy, defining entropy in each of these observers, and these entropies will be different. I think I skipped the details, but if you are interested, I can discuss it. So, going through this invariance, non-invariance stuff, very nice. But now, let us see what our conventional quantum information theory may do for us, if it is applied to unconventional situations. And one of these unconventional situations is a black hole in certain loop quantum gravity models.

15:00 Now, I'm definitely not arrogant enough to try to explain loop quantum gravity in five minutes and half a slide. So, I'll try to pick up some features that are relevant for our monthly information. So, we're trying to deal with static black hole. Given a moment of time, we describe it by a certain spin network. Now, spin network is basically a language to represent states in loop-running gravity. And there are prescriptions on how to represent different geometric operators, like area operator, volume operator, lens operator, in terms of space. What's important for us is it's really a graph with edges labeled by representations of SU, so qubits or something bigger. One of the features that emerges, and you do careful analysis, is that the states should be, as you told, invariant. Now, our description of the black hole, our model, is that part of the spin network, which lies beyond what is classical in the horizon, is unaccessible to us. So, in this case, states that describe the surface and leave on the links that cut the surface should be as you can compare. Now, in my talk, I'm going to do further simplification. I will take cubic length over, because, so, labelling each such link just by basic representation of this . But the results can be generalized for whatever link it needs to be viewed. So, humifly. And then we have a standard counting story. Entirely simple. Assuming the most possible currently operator ordering in full quantum gravity, we have elementary area which which is connected, which is related to each link cutting the surface, given by a square root formula. We will work with three halves. And in our model, again, to make life simpler, we have a given number of spins, two-end spins.

17:30 Area, then, is elementary area times the number of units. and all states, or all legal microscopic states, that give us the same area. Okay, all states that just satisfy the total speed is the zero. Then the counting goes extremely easily. The total number of such states, if you have two n states, given the bicathlon number, very nice symposium expression, logarithm of this nice symposium expression, and, well, it's not a miracle because basically it looks more like what you could get out We have a term which is proportional to the area and we have a logarithm correction, a logarithm correction if we try to make our model more involved What's interesting is that this thing is 3 over 2, 3 halves So what now? Now we take the same thing and write it in a more complicated form. So we do offensive counters, offensive counters. We introduce the density matrix, which is an equally weighted mixture of all the liquid of your things. Of course we define it for Neumann entropy, and surprise surprise we get the same number. Why? Because now we can more naturally, we can more naturally address the question of entanglement. And here I have to stop for a second and talk about what measure we're going to take. So, of course, entanglement, first of all, it was only bipartite entanglement. Then, if you have pure bipartite state, then the light is extremely simple. I already mentioned, reduced density matrix. The entropy of the reduced density matrix are a degree of entanglement. For mixed state, the light is more complicated. We can measure which is appropriate for us in entanglement of formation. It means we pick up, we go through all possible, with bipartite decompositions of our state, our weak state, with all possible weights, with decomposing pure state, so for each pure state to take its degree of entanglement, make weighted average, and take minimum over all possible decompositions.

20:00 The minimum is our entanglement of prohibition. Usually this problem is intractable, we know we have an exact result for that information for the students. But since our state having a very special structure, it's possible to get the exact result. I'm not going to show the entire proof, but let me just present the optimal baseline. look at different splittings of this and start from the easiest one, sum two qubits versus the rest. Basically, this is a good idea for that, is angular momentum basis. So, we label this aggregate two spaces to n minus two spins by the angular momentum, the whole spin and projection. And we need the degeneracy. Of course, if we have only two spins on one side, then we have only one in each case. But in general, there are many. Again, we can have them. Here we see the already typical picture. We have total spin zero. we can have either unentangled states or direct products on both sides, or maximally entangled states for a respective value of unentangled momentum change. And this picture proceeds through all kinds of bipartisanship. Now, think to zero external spin constraint. All alternative decompositions of our row, So all viewer states in these different positions should be linear combinations for that basis state. Then it's possible to show that the reduced density matrices have especially nice form that allow to use concavity arguments and we indeed can prove that this basis is minimal average attempt. Then what is left is counting and asymptotics. And we have that for an untangled state in the limit of a large number of spins an untangled fraction is one quarter. so very easily the entanglement in this case is 3.25. Not very inspiring, even if we can...

22:30 it's very tempting to connect unentangled fraction to potentially any kind of model of operation. But that's... we're different. What happens if we go higher? We can go higher. We can end up splitting into two pieces of halves. and estimates the entanglement of distance. And it is full of n. Now we are sort of facing the old story that entropy of this pole versus entropy of this part. And, well, we know that entropy of the pole is less equal to entropy of the parts. we can take reduced density matrices on our same basis. What we find is that the entropy of these reduced density matrices is just proportional to n. So the entropy of the black hole is the sum of the entropy of the species and three times, unfortunately, but we are not going to change the model in the process. the entanglement between these pieces. So, even if our cubic black hole is not really made up of independent cubits, this is what we call cubits, just area hole, they are, well, in some sense nearly independent, and their logarithmic corrections, we can trace them to the end. Now, I hope that this paper will be finally finished this month. Then it will be 0, 5, 0, 1. Otherwise I'm going to kill my co-author. What's the point of having one? 0. And now let me finish with... I have to admit a bit of PR. I'd like to connect attainment and hope in creation and the so-called information was heard. We attempt this several times during the workshop. Here's the story. We have some matter that collapses to the black pole.

25:00 horizon, black hole radiates, eventually nearly fully evaporates, for the observer that ends up somewhere outside of the infinity, radiation is thermal or nearly thermal, so for example if you put in a viewer state, we get thermal radiation is the output, the process is definitely non-unitary, information is lost. And there are different methods to explain the results. There are different implications proposed to multi-mechanical gravity, or different ingenious explanations, or just attempts to explain the way this information lost by ignoring the opening theory of our results. But actually, we try to see that this entropy is actually a good thing. So, ideal scenario will run like that. We start from matter. It's like a very high-rated shell. And let's for simplicity describe it as a pure state. The state over space-time, classically, is nearly Minkowski, so the appropriate state of one gravity, if you believe in it, corresponds to this classical picture and approximately in its direct form of space. Then, at least in the case of particularly less space-time, where we can speak about Hamiltonians and not only Hamiltonian constraints, we can hope to get unitary evolution for everything, both gravity and matter. And then, obviously, if we trace out states of gravity, and I mean not in some late times, and again, Okay, obviously the state of gravity is such that the space-time moves Neurodmin-Kofsky. But one thing is just to say Neurodmin-Kofsky and one other is actually a trace-out appropriate state. We get entropy. We get mixed density matrix, we get entropy. But, if we release, here at the base of the start, from the newer state, then the output is straight. We start from the newer state, we can hold it unitarily, we can reduce density matrix, which is mixed.

27:30 Entropy of the reduced density matrix is the entanglement entropy. So, if, as we call, we are able to show the existence of such meter operator, the entropy of interdiction is the entanglement entropy between space, time, state, and memory states. And here I'd like to finish. So thank you very much for your attention. And let's run for some of the items. Reduced density matrices are not covariant. Entropy and the number of degrees of freedom are observer dependent. We can see in entanglement the culprit which is responsible for logarithmic corrections for black hole entropy. And we hope that we can see entropy in the black hole radiation as an entanglement entropy between gravity and matter. And I have to thank also all these people who might discuss the different pieces of this work. Thank you. So, I think this is a great talk and I really enjoyed it. However, I actually think that you and Edith Prentiss-Schuller and the talk, too bad from this, are maybe creating a misleading impression by claiming that entropy is not covarian. You know, back in 1934, when Tobin wrote his book on quantum system mechanics and gravitation to look at quantum mechanics in gravitational setting, he thinks very clearly that entropy is a scalar quantity. And you're saying it's not a scalar quantity. Now, I think I understand the difference from having heard these two talks. You are just saying something that is quite different from the last 70 years, right? And I think that you were both right, okay? But I think there's something misleading about this. So, now, if one defines entropy according to some operators, if there's an operator like Alice's, let's say Alice of the Academy,

30:00 And he has a number operator, right, a number operator called N. Now, that defines an operator and there's this operator in all the rest of the world which consists of all the operators that commute with N. Now, so there's an entanglement between the reduced Hilbert space, the reduced density matrix, one of the potentially plotting Hilbert space, defined by Bob's operator N. Right? And you've been typewriting, Robert's operator N. You've been typewriting this. Now, Alice, in her own reference frame, her own coordinate system, which may be wildly different from Robert's, also has an operator N', which is her description of this operator N'. And she actually agrees with Bob, here's this operator, and she describes it differently. Here's all the rest of the world who commutes with this operator N'. Now, the operator, the entropy of entanglement that corresponds to Alice's operator N', which is basically the same as Robert's operator N', is the same for Alice and for Robert. is scalar quantity, the operator defined entropy. I just wanted to make sure that that's not, because when you talk about... I would say, yeah, first I have to, yeah, I... You're absolutely right, and that's correct. What may be an additional level of complication is that entropy is going to reduce states. usually diverges and they have to renormalize. So if by this renormalization procedure is not explicitly covariant, the resulting entropy will not be covariant. And this is one of the examples that I briefly mentioned. When you have two oscillated observers which have different velocities, some matter beyond their horizons, their state is different from Minkowski vacuum seen by direct observer, and they can ascribe different and their normalize entities at different. So I think it's an additional level of implication. But if you transform properly, then the transformation is unitary, and if you see unitary, then everything is unitary.

32:30 So that entity, the operator defined entity, is a scalar, do you agree with that? Okay, good. Then I don't know. That defined entity is a scalar. So probably... It's very dangerous to say entropy. Oh, I completely agree with that. That's why I think that if one says... That's why I would perform, you know, what's an idea of this paper called, you know, tensor product structures are observable to mine. So if you take the observables that define your tensor product structure, And then you compare the entity that's given by those observables, and you transform from the different coordinate, correct that entity to that scalar form. But, like, really, if we get to do the spin, a spin is not perfect. Again, if you try to define very clever operators, then you can, in particular situations, fight it. But, again, it's a big room. Yes, please. So you're saying that the state of the gravitation of the field, initially and finally, is this before? Just way before the Giacola formed, and way after the Giacola operated, you said that they... Well, you see, I expect that in the process, we'll have some gravitational waves. For example, at the very least, it's in the classic location. Since this also should be accommodated somehow in my description, then I expect that my gravitational state in the beginning and the end are different. What is gravitational waves? For example, what we try to do is to take a spherically symmetric case and we just model what's anything they're working on for a small change and now for black hole. Now we try to add the material matter, go again to the quantization procedure and see what happens. That's sort of the optimal program. If there is, we can say, another way. If we hope to restore unity at hand, again, I'm not sure that I will sit in bed at night if there is no unity there. If I want to see a clear answer, then we should look at gravity and method together. And then either we get it or not.

35:00 So actually it looks like we have time for a 15 minute break before the next talk, which is at 5.30 for a teeny or a couple of them. It's very powerful and you should go beyond constructivity, and in particular, I hope that it will be very useful in common gravity, and I do have such an example. So the low energy problem in common gravity is a very difficult problem, but I've tried to say a few things, I've tried to sketch what it is, and I've been like others, it's background independent approaches to quantum gravity and so we've all been looking for tools on how to address that and in fact the most promising one I've found comes from quantum error correction. So here is roughly what I want to talk about today. So I'll try to describe what a low energy problem in quantum gravity is which basically needs to find propagating modes in a background independent quantum theory of gravity and you have to do that in order to make contact with physics and change that your theory is correct and the thing that in principle you would think that the tool to address this with would be statistical physics I'll show you why but it doesn't work in a straight manner however in quantum information theory you can see this problem as an analogous error correction and think of the propagating modes that you're looking for as basically noise-like subsystems. At least that's the tooling quantum error correction that I've been looking at. And I have an example where that works very nicely and that's the Svarchal black hole in loop quantum gravity which I'm going to derive as a noise-like subsystem. And then I want to discuss certain around dependence and locality and also related to this work is work on the relation between error correction and the renormalization group that I'm probably, you know, but I don't really plan to say much about, but I could do it so in private if you want. So this, this is all that's being talked about today is

37:30 done with an assortment of people. The first idea of using those subsystems in gravity is things that we have been doing with David Kudlen, who is at the Institute for quantum computing and PI. And someday that paper will appear. In the meantime, so we were looking for a nice example, but that came out in a collaboration with Olaf Dreyer and Liv Smolin, that is out. And the related work on the relationship to their normalization group and other issues I'll discuss at the end is in progress with this particular sort of the goal. So background independence and background independent quantum gravity. So the standard law of course is that quantum gravity should be some sort of unification of GR and quantum theory and it should contain both. Now in GR, the basic lesson of GR is that all events and their relations are physical. And the coordinates that you might use to describe them have no physical meaning. And therefore coordinate distances are not physical quantities. So in general relativity, the metric is a dynamical variable. That is, there is no background space and time. That is what, this is what you need when you say background-independence. Now there is, there are of course technical ways to describe this in the continuum case in GR in terms of diffeomorphism invariants but we tend to use the term background-independence because that you can take beyond a case where you have differentiable manifolds. So since quantum gravity should contain GR you would expect that it ought to contain this principle too. So you're looking for a quantum theory of gravity that is background independent. It's actually not very hard to make one. It sounds fancy, but it's easy to make. So instead of discussing something based on standard geometrical ideas and space and so on that would get into trouble, you could easily guess that a nice structure to base a background independent theory on can be a network. And in fact, as Danny mentioned before, the networks that we use are spin networks.

40:00 They were invented in the late 60s by Roger Penrose as a way to derive space out of a discrete quantity and rediscovered in the 80s in the context of low-pound gravity. And so what a spin network is, is simply a graph And the edges of the graph are labeled by representations of n2, and the nodes of the graph are intertwiners. So if I give you the tensor product of the representations, there is several ways to extract the trivial one out, and that is a label that I put on the map. Now, they are very beautiful, and they have a very rich structure, even though they are such simple objects. So, as I said, the original result of Rogers from a very long time ago is that in the large spin limit, these abstract graphs reproduce directions in Euclidean 3-spin. When they were rediscovered in quantum gravity, they were found to be the basis states for background independent spatial geometry. And these are the type of things I will actually be using here mostly. And for those spin networks, you have, you can find the quantum operators that measure and volumes have discrete spectrum. And since I'm going to use that, I'm going to say something about what that is. So the idea is that there is a network describing space. So if I take this sheet of paper, I should be able to ask what the area of that is, and you should be able to derive it in terms of the network. And you do the calculation by straightforward quantization of the classical area operator and you find that the area depends on the representations of the edges that puncture your sheet. So in this case up here the area of this guy there is only one edge of representation i going through it, so the area of potem is this particular combination plant-with-plant area. And the statement is that there is discreteness, because in order to make the area

42:30 bigger, I have to make it big enough so that I have a new edge puncture in that area, in which case I'm going to get a discrete increment of the area. So the increment is not necessarily the plank length, it will be bigger than the plank length? Yes. It's of the order of the plank length. But it's not continuous, that's the increment of the plank length. Now that represents space, these are states for space. Presumably if you want to evolve a network, you will not do so continuously, that would rather flash with what I was just discussing before. So the way that we evolve a network is by local moves. So what a local move is, is basically I select a subgraph in my network, I cut it out, and I replace it with a new subgraph with exactly the same boundary. And such a is basically a unitary, a microscopic unitary operator in my theory and you can show that I can go between any two networks using a very small number of generating moves. So I'm allowed to choose a valence that I prefer, usually four, for the networks and then for example for four network, four valent networks, then And there's only four moves that can take me between any two networks. So if I give you the operators that give you the transition between these types of local moves, I give you the dynamics of the theory. Why is it four? Because trivalent ones do not have trivial inter-etwiners on the nodes, and the inter-etwiners is related to the volume operator, so it will be zero volume for three. And five and more, you can expand in terms of four values, which is the basis states you're about to do that. So one has a more convenient way to keep track of the dynamics, instead of just giving you the local evolution moves. So as the network evolves, I can, instead of considering a sequence of evolving networks, I can equivalently think of these objects that are called spin forms.

45:00 And what they are, they're two-dimensional complexes, two-dimensional networks if you like. And now the faces of these are sheets that are labeled by the reducible representation usually as U2, and the edges are labeled by the intertwiners. And you can check that space-like cuts through these poles are spin vectors. Now, you should note also here that there is no sense in which there is some preferred foliation. It doesn't mean that this is before that before that. The only thing that you have to respect is the order in which you change the graph, but I can make space light cuts in a number of different ways. So, I can give you a model, a background independent model for a quantum theory of gravity, by giving you a spin phone. And so what I have to do is choose the type of two-complex I allow, so there might be conditions on what the networks are, for example four-valent, simple, complicated, whatever you want there, the group, it might be SU2, it might be some other group, and there might be no representations, like for example the photodynamical triangulations Renata was talking about, the very particular two-complexes and no labels on that. the amplitude for a given move. And then what do I do? I take the product of the amplitude for every move or event. I have to sum over all the labels of the network and I have to sum over histories. So if I give you an initial and a final state, I should, this is a path in the graph, the formalism for quantum gravity, I should be able to go between these two in all possible ways. So, I give you the theory as an amplitude from my initial state to a final state, some are related to some are related to product. I read a lot of notes. That's nice. So now I have a background-redependent probability. Now what do I do with it? Well, so the idea is that somehow from this, you're So these are, this is supposed to be the universe at plump scale, with plump scale events, plump scale puzzle structure and you want to get low energy ordinary space time.

47:30 So clearly it's easier said than done. On that side there are stars and photons and I have to find stars and photons on the left. And it's not really surprising that at this point I have a problem. Basically, so I said this thing that background events means that it should only have the events and the relationship between the events. Okay, but how do you get an event? So you can say an event is when a photo from that projector hits the screen. But to have that event, I have to first have the photo that actually gets from the projector the screen. So I have to be able to identify something before and something after as being the same thing. Here I just have a big soup of stuff. I can talk about a Planck scale event. It's hard to find anything that takes a long time in there. And having a sum over histories doesn't help. So what I need to do is from my my favorite spin form model, identify effective propagating degrees of freedom. So you might think that the fact that you basically have a theory that is given as a partition function is a promising step. After all, this type of partition function is not terribly unlikely, unlike what you have in a spin model. And if you do condensed matter theory, I can give you a horizontal string chain and you can rewrite it so that you can see that there are string waves. So, I'll do the same thing here. And basically that's what we focused on for quite a while. It's not that straightforward. One of the things, apart from the fact of course that they are complicated and everything, let's leave aside the practical matter of how to solve a complicated model. You have no lattice spacing, since you're obviously background independent. And even more, you have a quantum sum over lattices. So, it's actually, it's your stuff. And, to also get a sense of what the task here is, what you call low energy limit in

50:00 quantum gravity is what everybody else calls high energy physics. So, what you want to do is to recover things like photons and protons out of the spin pole. That means that you want a coarse grain, 10 to the 20 orders of magnitude, and be left with what is described by QFT, which is a unitary theory. So you want to extract a unitary theory out of a Planck scale, too. Now, if you don't do that, then you really have nothing. So in particular, I said something about discreteness of area, but you have to check that that is the case. How do you check it? So there are, there have been several papers in the last few years about possible experiments testing these treatments. But to go from your background-independent quantum theory of gravity genuinely to the lab, which is particles on a fixed background, I have to solve this problem. And so that's the main open problem. Of course, it's not just background events, there are serious complications here in particular. As you might guess, any low energy problem, any low energy limit would depend on the dynamics. And the dynamics is, of course, ugly. GR is bad enough that one taxation of GR is worse. So, so what's the idea? This handle idea will get more precise later. But the idea is, well, maybe what we see around us is what nature encoded must have survived the Planck scale theory. And what we see, since obviously we're not seeing part-of-the-art defects, should be almost noiseless with respect to the Planck scale fluctuations. I'm gonna drop the the rest of the talk. I'm happy enough if I could get a proton out and worry about the proton interacting later. So in the standard setup of the evolution of an open quantum system where my combined state space is that of the system times the environment, I have Hamiltonian with an interaction term. And the organ evolution is as usually given by a

52:30 completely positive map that takes the state space of my system to whatever I can extract later that I can still call the same system. So the idea is that the propagating mode should in some sense be a subsystem that is conserved under the the noise evolution that is evolved unitarily. And I'm going to use the theory of noise-based subsystems for that. And the nice thing is that does depend on the dynamics, which is something I don't want to think about because, as I said, dynamics is ugly or I don't even know what the dynamics is. But it only depends on the symmetries of it. And that makes my life infinitely easier. So I'll have, I first have an example of a noiseless subsystem, a basic example of a noiseless subsystem in error correction for the three quantum gravity people in the audience. And then I'll have the quantum gravity example of a noiseless subsystem for everybody's benefit. Okay, so the standard example is three qubits in a bath that could be an electromagnetic field or something like that with an interaction Hamiltonian of this form where this acts on the state space of the system and that part acts on the state space of the environment and the essays are combination of the Carley matrices and they generate the SU2e algebra so they are global rotations of the three spins. So what this Hamiltonian does is it conflicts the spins but it cannot distinguish between them. So the symmetry here is permutations of the three spins. Now I can do the usual decomposition of that state space in terms of its irreducible representations. And then I know the following. I know that this part appears twice and therefore on this

55:00 part of the state space I have to choose the following basis where lambda is 0 and 1 and it picks which one of the two parts I'm in, and as z is plus or minus a half. And clearly, since my noise cannot tell on which part I am, that should be protected, why that can be flipped freely, and it is the noisy part. So that's all I really need to do. I'm going to now consider this label as my degree of freedom that is noiseless and the rest gets all the noise. So I have now decomposed this part of the system in this form where this is So, by the way, this spans a two-dimensional space space, and this is why the subsystem finds something that is noisy. So, what do I have? I have my three qubits, in which I have a protected qubit, which is, however, none of the three. and not even a subspace of one of the three but if that's the job that I'm interested in it behaves as a free party according to a degree of freedom so note that it is not a subspace of the original state system because there is still the direct sum with the three half representation part so this is not I cannot extract the qubit as a subspace The formal construction, doing the same job, was provided by these guys with some inspiration, I guess, so especially in cases of computer-free subspace, which is, in fact, the one I'm going to use for example I'm going to work on here, however, I'm going to go through this construction. So, what do you do? You have an interacting system with a given state space and environment.

57:30 So, in the case of my example, I just described a state space for the three qubits. The interaction algebra is clearly a club algebra of all the operators that connect on your state space. So it was the SU algebra in the previous example and in general that will decompose in the following way. I would have a direct sum of irreducible representations of the interaction algebra and for each irreducible representation I'm going to have this formula decomposition where I'm going to have this split into, I'm just using B of C here, this is just dj by dj dimensional matrix algebras and they will appear with a certain multiplicity. So that's nu j is the multiplicity of that component in this situation. Now, in general, I'm going to have an interaction commutant, which is all the operators in the algebra operators of my state space that commute with everything in the interaction algebra. Now, anonymously, if the interaction algebra splits this way, the commutant splits the other way. So, for the dj by dj dimensional matrix algebra there, I'm just going to get a dj multiplicity of this new j by new j matrices there. So, the notation is a bit hard to actually read out. And here is the interesting part, that any symmetries interaction algebra means that you will have a non-tradial commuted. And while discussing symmetries might be enough, for example, it wasn't an example I showed, going into the computation structure is more powerful than actually a way to become positive So, in that light, my state space of the system decompose in this form and as you can see this part here is left unchanged by the interactions and that is the normal subsistence. So that's what I'm looking for and that's what I'm hoping is going to be capturing propagating degrees of freedom in a plan-scale quantum value model.

1:00:00 And I have an example of such a thing but first the general idea is as I said the noiseless subsystems should be useful for describing the long term behavior of the system because they are conserved and what you would like to do is to be able to divide the quantum gravitational field into subsystems and those properties that are conserved under interactions systems, will be those that characterize the low energy limit. So in particular, you would want the commutant, the symmetries that are either preserved or emerging, include the symmetries of classical spacetime, such as Poincaré or the Sittre. And after all, you want the Poincaré symmetry to get Fock particles, which is then out-of-been business. Now, these symmetries are a little hard to deal with for now. So, I have the easy example that everybody always starts with, which is the search of black hole in uniform gravity. I'm sorry, before you comment that. So, my understanding about gravity is, you know, that the normal sense of gravity are different forms of endurance in local Lorentz transformation. So, those are automatically in there already. Okay so that's an interesting point and I have to say I don't really know how exactly to answer your question. At a certain level the diffeomorphism invariance, you can say the analog of diffeomorphism is building to background independent. Now the Poincare somehow different because if I want to have three particles, I have to get it somehow out of the system. Maybe the next example is actually not so bad. Maybe I can answer this a little bit better afterwards because I think it's a little hard to say to give an answer to the abstract. No, it wasn't a very good question. It wasn't a very funny question. I can tell you what the analog of an answer in this case. I do not know the full answer. So here, you can use the spinet works to count the state of a black hole, as Danny already did an hour ago.

1:02:30 So if I give you a black hole, there is really a spinet work describing a state of that black hole. So, in a little more detail, it's going to be needed here. And so, in fact, how that works is, so what I want to do is to consider the system being the surface of the black hole and the environment being the spinetwork outside the black hole, or what's often called the bulk. Now, according to these people who have done this analysis, the conditions that a surface this is a black hole, amounts to a state space that is given, spanned by the invariant states of a u-monitor entitlement on the puncture sphere. Now what that means for all practical purposes is that you have a sphere with some number of punctures, each of which is labeled by an MA label where these are the usual M's Clearly, I have a constraint on what my punctures are, because they should add up to give me the right area. So if I fix the area, I'm not allowed to put quite anything here. And the other thing is that there's an old JPL braiding. So if I move one puncture around another one in this state space, I pick up a page. And the environment is the red, is the spin and the horizon. So you can write this state space as your system, which is a black hole of area A times the red. Now, the question is the following, this just knows that you have a black hole of area A. Now, which part, which states in this guide correspond to the quantum analog of a Svarchal black hole? So clearly not every black hole of area A is a Svarchal black hole. So which ones are the Svarchal black holes? Now, what I'm going to use is use the symmetries in the system environment interaction that just described.

1:05:00 So the classical Svartier black hole has an SO3 symmetry. So if there is a microscopic analogue of a Svartier black hole, which you're trying to construct here, there must be a microscopic analogue, some group GQ, of SO3 in the dynamics that will become SO3 in the classical limit. That's the main assumption. Now, if there is such a thing, that would correspond to a non-trivial commutative dynamics. I'm sorry, I'm sorry, you were saying that's a, that might happen, but that's not a necessary condition for the SOP in the classroom, right? You could have nodes in something like that and you might discover that you might have some mechanism for big black holes. There could be a more complicated way for this to handle than what I'm describing. or there might be a non-microscopic analog of a Schwarzschild blood hole and there's some mysterious mechanism. But I'm going for the conservative assumption, which is you have a classical continuum symmetry here. There should be some underlying discrete one in the fundamental theory. And I'm looking for a simple way that the underlying one will map to the continuum SO3 in the way that I just constructed. So, I mean, it's not really a very strong assumption, if it's not like that, I have no idea what it would be, but it's a very reasonable assumption. But, I don't know, the heat refers to how do I know this is the right theory in the first place. So, but if I have this symmetry, then I'll have a non-trivial commutant. And, so my symmetry should be part of the commutant. Of course, there would be other things in the community, not just the microscopic analogue of the HL3 symmetry, right? So, the point is, of course, that should be a symmetry in the system-environment interaction, which, of course, we don't really know, for sure, not explicitly in the theory. So, even though one knows that you should go through the dynamics to answer any kind of such questions, nobody in this field actually has particularly wanted to do it. So, things are actually leading up because even though I do not know the interaction algebra, it is possible to restrict it sufficiently to find the noise-based subsystem that corresponds to GQ. So, here I am going to construct GQ so that it has what you expect are the reasonable

1:07:30 properties that are analogous plus for 3. So, the first thing, GQ should be a discrete group. I have a discrete field. Then, of course, the interaction algebra should add simultaneously and locally on the state space of the system and that would be mine. Now, a state, my state space is simple enough that I'm going to give you a set of generators for an interaction. But not a lot of things can happen to a puncture sphere with little labels on them. So what can you do? You can add or remove punctures or you can braid them. So if you braid them, as I said before, you will pick up a phase that is of that form, so it's a sum of the labels on the two punctures divided. That's the level of the Transom theory, and it's a function of the area and the parameter. Of course, a lot of trouble in the theory was partly behind this work in its parameter, but you don't care about it. So anyhow, that's, you care about that part. And I want to have symmetric actions, symmetric ratings. So I'm going to be paralyzed braiding all the functions. Now, although that's generators for anything that could happen on the surface, not anything can happen because I'm constrained to keep the area fixed. So adding or removing functions will change the area. So that's how. So I'm left with braiding something. Now, you can know that because of the structure of the phase that you pick up, if you fix the j on, you take two edges with the same stick on them, but they can be different ends. So if I braid and then permute, that's the same as permuting and then braiding, because the phase depends on the other side. So what do I have? I have that my

1:10:00 interaction algorithm should commute, or at least the part that is restricted to a fixed area, should commute with the permutations. So I have that gq should be in the product of permutations of k things where kj is a number of punctures with the same j. I'm almost done. The last condition I need is SO3 is a transitive group. And I need the analog for that in GQ. So for every given two punctures, there should be an element of GQ that connects them. In order to be able to do that for any two punctures, then I can only do it if Kj is all the punches that I have. So I'm basically done. This, um, for a GQ to be the quantum analog, microscopic analog of SO3, all J's have to be the same in a quantum smash of black hole. So there's two big knowledge you can do, one is to get the cosmic energy and apply it to them, to say that my anatomians have the same, but I'm not going to have the same solution. But here it seems that you're applying the solution to each one, which one would say is what should I have to do? Any solution? No. Why am I not to say? What are you saying that the source of the quantum black hole, the cosmic structure, the same symmetry as the classical particular state of the cosmic structure? I guess I would expect... If I ask that the black hole, which somebody did before this and got an answer, if I ask that a black hole should be rotational in vain, What I would get is that all M's should be the same, not all J's should be the same. Why would I even ask for you, I guess I might say the expectation value of an average has a solution, but if any particular unconductable, why should any particular solution, I should just expect that the classical limits, why should it, why should it, why should it. Right, so one way to slightly rephrase your question, I think the same question, if I detail of what I should be taking is expectation value, say of the area, so for example the

1:12:30 area does not have to stay the same, it should be within some bounds that are appropriate, and also take expectation values of everything, right? And then ask, like this thing goes to lesson three. So that's true, that would be a proper calculation and basically that is the next thing to do if you want to do it in more detail somehow. Okay, so my attitude to that was that there are other things about blood holes in glucone and gravity that have enough problems. I didn't really want to commit more work than that. That is, as an example of what could happen. But you're basically right. Why are you looking at it like that? Yes, yes. Probably, I wouldn't want what you're saying. I'll find somebody to do it in the future. Is the braiding's representation just multiplication by phases, that's all it does? Is the? The representation of braiding is just multiplication by phases, it doesn't have any other complexity. So just for Jonathan, just to justify things, that's how all calculations are done on these black holes. Nobody ever does the calculations like what you were saying. it's not so clear right so you would not get it as clean as that but then you would be averaging more things right and you would have to throw out more things it's not clear that you would get a different answer Okay, so the state space of the quantum's virtual black hole is the noise-lessed system corresponding to this GQ symmetry of the dynamics. So in the state space of quantum's virtual black holes in the open-graded fixed area, the ones for fixed J are the analog of a quantum's virtual black hole in the way I define it. whether that's a true swatch-up at all, as Jonathan says, you can see.

1:15:00 Now, some of the context of what we did that for, that you don't care to know about very much, had to do with entropy counting. In particular, I should say j here. Once you have fixed all j's to be the same, then you can show that the entropy is dominated by the minimum j's. And then entropy and enter a large, complicated argument with everybody else in the field. And another thing that was interesting here... What sort of example does that give the normal entropy for a black hole? In the sense that it's area over something. Yeah, yeah. The something is a problem. So it's not really area over four because there is a parameter in front of the area, that everybody's arguing about in that field. So, yeah, it's not surprising it would be there because I'm only counting things on the surface anyway. So, in a certain sense, that's the easy part. The core is the difficult part. Yeah. I mean, I can tell you something more about the background of that if you want over dinner, but it's not really worth discussing the part of this. But what's nice here is that there are some opportunities Some further things to do, other than what Jonathan said, in particular, there are things like the quasi-normal nodes, which are the limiting nodes of a black hole, so I can kick a black hole and then it drinks down, emitting quasi-normal node frequencies, and in this context, there would be the excited states of the nodes of the subsystem. You could also discuss, you can see discussing rotating black holes in a similar way, you wouldn't ask for transitivity anymore, because not everything goes to everybody else. You have a different kind of symmetry where you're rotating around an axis. And the thing is that this is pretty because in this context, unlike the way that as much as black hole is usually identified in group conogravity, all of these are different states in the same state space you're starting with, which is what you would expect. And the way it's usually done, it's very hard to go between things. Okay, so a couple of lessons at this point for us. One is the noiseless subsystem is a dynamical construction. Now, I feel very stupid saying that to you.

1:17:30 Of course, if I'm doing a low-energy problem, it had better be a dynamical construction. If I take a spin system and I'm post-graining it to derive its low-energy behavior, of course, what I'm looking at is a plutonium. But as I said again, in this field, because of difficulties with the dynamics, a lot of things are done at the so-called panematic level, where in particular, what people do is just take one graph and try to derive semi-classical properties of one graph, which is clearly wrong. I mean, you would not really try to derive semi-classical properties of a spin chain without a hematonia. So here, you have a dynamical construction. And again, as I was mentioning before, if you try to do symmetries at the dynamical level, you would get stupid answers. So if I try to say that I have SO3 symmetry of a state, I would end up having all the m's being the same, and so I would have an entropy of one state. Now, although that's somebody that a person working back around independence, quantum gravity would get scared about, the relief is that we only need the interaction dynamics, not the dynamics of the theory. And from the interaction dynamics, we only need the symmetries. Now, of course, the interaction algebra should depend on the energy level or approximation you're interested in. And that brings us to a different subject, which is that, strictly speaking, to do what I want to do, one would want an approximate or emergent notion of a neutral subsystem, which is not something that you guys currently have as far as I know, but one could imagine doing that. Now, conversely, in both model building, that is, making my favorite spin form, I should be able to use, in this sense, the low energy symmetries to constrain the microscopic dynamics. So I'm telling myself that I know, in a way not unlike what I just did before, I should be able to give you the fundamental moves so that, at a certain appropriate level, I have the synergies. Now a couple of comments. One is propagating nodes versus background independence. So it's true that this method is background independent in the sense that it does not rely on a particular graph or state and is defined by the dynamics.

1:20:00 On the other hand, the noise of the subsystem is a subsystem of a subsystem. So in the black hole, I have to give you the state space of black holes of a given area. Then it's background independent. You can go inside and find the ones that have the barriers you care about. But I have to give you the proofs. So that was something that troubled us for quite a while. or rather control has confused us to just say exactly what the situation is, but basically that's how it is. So I have to, at some level, give you the interaction dynamics so that you can start working. Therefore, I have to give you a split. I have to give you a boundary somewhere. I have to start with a boundary in my ear. So if you like, in local gravity, when I do these cultivations with a black hole, you could or should object is that the black hole boundary I started with is not derived somehow from the underlying theory. What you would like to do is that I give you this big complicated spin-tong and you say here, in some sense, is a black hole surface. The way it's done is that it's putting the hat. Once somebody did that for you, then you can do other things. And that's really what that means too. Now, that's, so if you give me a boundary, then I can do a lot of background things inside. So, of course, there are many interesting situations in quantum gravity where you have a boundary. There is gravity with a boundary and quantum gravity with a boundary. And then you can deal with those cases. But there's another thing as well that I think is interesting, is that the boundary does not have to be a physical boundary. So in the case of extracting a qubit from three qubits, I can think of it as coarse grainy, where I go from a high energy mode to a low energy mode, or at least that's the analog I would like to get. And I can think of the high energy modes as the environment. And the boundary is somehow in the tracing out of those nodes. So, I'm not really going to say anything more because it's not very easy to say something to here on this level.

1:22:30 These sort of thoughts have made us trying to relate the noiseless subsystem method to renormalization group for common systems and thus we're currently in progress with these people. But the point is the boundary does not have to be a physical one, in which case I have many, many more situations where I can use this method to learn what we would have thought. Another common is most of the systems in locality, or microscopic versus macroscopic locality. So one can try to assign geometric or causal or locality properties to the sub-forms or the sub-rads. So I can look at this part of the sub-form, of the spin-form, and see that that's a different part than this one here, which is very tempting. And you might, for example, try to say that this line here corresponds to the word line of something, conceivable in a particle. And people actually try to do that, but you're not really allowed to do that. A given form is not an ideal side of the dynamics. You have to take into account the sum over forms. In which case, if I'm not at this proposition of this, I don't really know who is where. Now, so the question is, which locality here corresponds to the locality of the low energy derived. In the nodular subsystem construction, the degree of freedom you extract is not anywhere in particular with respect to the underlying 1,0.3 dot. So, in fact, this method suggests that you should start with your Planck scale theory, extract the nodular subsystems, that's a big word, I know that's a complicated thing to do, but if I did that, then it's those that I should be assigning locality or geometric or causal properties to, and it is from them, from these properties that I should try to extract the continuum effective spacetime. Okay, this is some list of what I'm doing or intend to do. So in the black hole case, it's sort of funny because we were actually looking for an example

1:25:00 for months, somehow we were just looking at things the wrong way, and then that came up and it's actually a rich example. So some things is, as I said, cross-normal nodes or rotating black holes from the same state space. Then it's another thing to do is try to get the actual black hole state space in a string form. And that one here refers to what Jonathan was talking about, do the calculation properly. Propagating modes in phonograph into the boundary, that says I can find other cases where I have a phonograph into the boundary and I'm given an interaction in algebra on the boundary, it's not the stats, so there's a number of other cases to look at. I would really love to understand noiseless subsystems as separating scales where the environment is the small scale fluctuations and the system is the coarse grade fluctuations and finally these two are related to really be able to use what I'm talking about I need interactions at some point so I need approximate noiseless subsystems even more I need emergence symmetries And so that requires certain extensions of the theory of noiseless subsystems. And symmetries like Poincaré-Symmetry that are quite different from the perspective form. Thank you. Do you know if these noiseless subsystems have been used to describe in some other example which does not involve gravity successfully, the transition between quantum mechanics into classical physics? I mean, because you want to do that for gravity, right? So I wonder if you've seen it somewhere else. Here, what I want to do is go quantum to quantum. So I want to get subatomic particles out of Planck's scale here, so they're quantum to quantum. The classical part, I don't know, I haven't really thought about, That's not really what I try to do, I don't know, maybe you guys, and you shouldn't ask me, has somebody tried to do that? I don't know. I guess you're not error-correcting to get that classical bit out of qubits, that's

1:27:30 not really what... Well, any time you have the explicit symmetry of this source, you have some noiseless subsystem where you go to a few subsystem interfaces for the same thing. And so, there are many very familiar examples that are known that are long before quantum of information and plot of gravity, right? So the fact that the Schroeder equation is correct, if you have a Schroeder equation that's translation dependent, then momenta is a good idea. It's a good idea, right? Because momenta, a momenta plot where it disputes the material. That's what I'm doing. Yeah, so it's explicitly, you know, creating the particles that are spanning a who is a substance in a system in this case. So, you know, a lot of these ideas of this but they're not written in this language and the general physics is of course not new but this I mean I don't think that I've never seen a number of subsystem instead of what you're saying. No, no, but this decomposition, if you have an algebra and it's commutant, and then you can decompose the representations of some of the algebraics of what's a mutant, the algebraic axon is 100 years old, and it has been used by explicit wood and by Peter and other people starting in the 1923, so, yeah, but I, yeah, I think that's not the kind of example that you want. so I actually am kind of wondering why you're trying to go quantum to quantum in that it is kind of a pure gravity theory and you don't necessarily know that black holes became quantum mechanics right no I'm actually not particularly interested in the black hole example for example what I would like test is for example the distribution statement in terms of cosmic ray experiment. In that case... Well, no, I mean, you do want... I do want to find a photon somewhere in there. It's a quantum system. Where would matter appear? I thought the degrees of freedom here were kind of just describing... Yeah, I glossed over that. So if you... the standard understanding is if you use SU2 as your

1:30:00 representations, then it's supposed to be pure gravity. I could have added other representations, say U1, et cetera, and that's supposed to be matter. It might also not be really like that. That comes from a certain quantization, right? So I can write another model and presume that all sorts of degrees of freedom can come out. It's not obvious that that's a certain and prejudice that the SC2 should give you gravity and the U1 should give you the electromagnetic field, et cetera, but that's something. But for sure, at a basic level, the models I was talking about can have degrees of freedom that are not just gravitational, or classical gravitational. Where does classical general relativity come in from the spin point? Well, it depends who you're talking about. My idea is that where it should come in is, it sounds like a messy construction, but that's the only one I can see working, if any, is that if you extract particles, then from the way they behave, you should be able to infer the space time. That's the understanding here, or at least that's the motivation behind that. So I first have to extract the propagating introduce freedom, one way or another. I mean, after all, you do know that space time is there because you sense something through it, right? That's what you're doing for sure. But have you set yourself up in such a way that you would approximate the metric of the classical metric in some way? No, which way? Has the model been set up in such a way that something like the classical metric would appear? Well, quite the opposite. So a lot of these models, like, for example, what Renata was talking about yesterday, orchestradizations of classical geometries. So regi-calculus has been along those lines, that you have a classical, you have a orchestradization of a classical geometry. Here, that's not the idea. I mean, that's, it's a, it's a limited viewpoint, let's say, that you would have that. have a system that is not unlike a condensed matter system out of which you should be able

1:32:30 to extract matter at a certain level which should behave as if there is a gradation of the others. It's a long shot, but that's kind of... So it's quite distinct from these other kind of state-sum systems, where you're actually approximating the method discreetly, right in the outset. Yes, it is distinctly, yes. I mean I can also imagine having said that I can use the same method in those systems so for example in what Renata was talking about you have state sums of geometries discreetly and then the calculation involves finding a typical history in a computer simulation and then extracting certain geometrical properties from that but there's still a question of what propagates through this and for example where is the gravity of what she was discussing so I mean I can still use in that context, but they are not limited to that. What Renaud was discussing is an example of the situation that at least what she seemed to be planning is that you do get the process of quantifier symmetry and the solutions that dominated or impacted the rules. Is it because they were flat? They were flat, I mean they were basically... They were basically flat, but that information is extracted from a typical history. Right, that's right. So you don't know... Yeah, so for the typical, do you seem to consider the function of one very similar thing? Yes, so, okay, so, I mean, the background here is the following. You can do, you can basically do two things when you're given a partition function. One is to try to solve it, which, more or less, what she's doing is that. The other is to extract the low-energy physics, and that's what this applies for, because, I mean, you can hardly go beyond what she's done, but that's not I mean in standard statistical physics you don't stop to what you can solve I can't say anything specific to this question. Yes, of course, that's the interesting question. I would guess that I would guess that the ground state let me not guess

1:35:00 maybe I'll talk to some other point in the future. I'd like to say something coherent but yes, that's the question. Can you kind of black hole? Okay, I'll and count the number of holes through it, piercings, and only then sort of apply the symmetry so that you get basically everything you want. What is it that makes this thing a black hole rather than just a sphere? Where is that coming to do? Well, the conditions that, the black hole conditions are those that give you the, you want your sign on the sphere and the boundary. So you start, the way that this is done is that you start with a sphere and you put conditions on it for that to be a black hole, classical conditions. And in the quantization of that equilibrium gravity, that gives you the U1 transatlantic states. I can give you a reference for that if you want. Yeah. I mean, so, at a certain level, just a surface of area A would not be given by U1-chern-Samos theory, right? It would be given more by what Danny was discussing, which is spins on your surface. That's a somewhat different theory than what I'm here. Okay, well, if there's no more questions, let's thank Ritini again. And I guess it's worth a reminder that people going to the banquet will be leaving here at 7.30.