Ted Jacobson, « What can Black Holes teach us about Quantum Gravity ? »

thank you very much for inviting me and thank you to the organizers for a very interesting meeting I always like to not a philosopher as some people I said but I like philosophy I took a class in philosophy of science in college and it almost made me quit physics because of the philosophy not because I preferred philosophy because the philosophy convinced me that I didn't know what the hell I was talking about in physics which I guess was a good thing but by the end of the class I finally like things came back into focus in a new way yeah I had to write a term paper and it was about Einstein's view of reality but anyway we can talk about that afterwards also I wanted to say like Steve Karl if I had a connection with Cecile do it in fact she was my supervisor at University of Texas and I feel a connection with her coming here because of a count of all she was would-be Institute and so I just want to remark on that my talk today is a subject that I was asked to speak about so what can black holes teach us about come on and gravity I don't mean to imply that I will answer this in any definitive way at all but I share some thoughts about it oh here this thing so that's the magic 8-ball when I was a kid I had a magic 8-ball does anybody know what that is no in France well you know an 8-ball and pool table it's the black ball with a hate on it but this one was a little bigger and you asked a question you held it in your hand and you ask it questions and then to find the answer you turn it over upside down and there was a kind of tetrahedral piece that floated inside a fluid inside would float up to the top and you'd see it through an obscure window so anyway that's it brought back to mind when I was thinking about what can black holes teach us about quantum gravity here's the plan of the talk I hope I get to it there are two things at a certain coarse-grained level I'll talk about black hole entropy and the main well one of the main messages it's not really about black holes and then that part is all on a computer and hopefully I'll get through that in a suitable time and then I'll talk about the second point which is a black hole information paradox and I also would say it's also not really about about black holes however black holes point our noses in fruitful directions and that's why we're talking about black holes oops so I'll start with a famous thought experiment that got bekenstein started on defining black hole entropy if a cup of tea is dropped into a black hole the entropy in the cup disappears from the outside world bekenstein realized well something changes though the black hole grows in particular the area of the black hole grows and this was shortly after Hawking had proved the area theorem in classical general relativity the area of an event horizon can never decrease which was striking to everybody in his analogy with the second law of thermodynamics so for that reason and others bekenstein proposed that the black hole actually has an entropy which compensates the loss of entropy from the outside and that was in 1972 in particularly propose the entropy is proportional to the area since entropy is dimensionless if we don't use Boltzmann's constant we need to divide that area by something with dimensions of length squared in four dimensions spacetime and so presumably I mean you could simply by dimensional analysis guess that that must be the Planck length squared however he did much more as I'll tell you in a moment I mean his reasoning was much deeper than that it's in any case for those that might not be familiar the Planck length squared is h-bar times Newton's constant divided by the speed of light cubed it's a very tiny length squared and so this is an enormous amount of entropy far more than could have been for instance in the star that collapsed to form the black hole by the way this black hole is elliptical from up you know oblate because it's spinning he also proposed the generalized second law so that was the key idea so even though the entropy outside maybe I even have a pointer here the outside entropy goes down because the cup of tea fell inside something went up in fact by enough so that the total the sum of the outside entropy in this black hole entropy in fact went up people he proposed that law as he called it the generalized second law and he tested it in his paper from 1972 and well let me first before I talk about the test just talk a little bit about the reasoning he used to justify this they went far beyond dimensional analysis ok the argument I'm going to give it is the argument he gave but it's using it's like with the benefit of hindsight version of the argument so first of all he really wanted to consider something that was like thermodynamics and he needed to relate the entropy change of the black hole to some energy change to apply the first law of thermodynamics so he derived the first law of thermodynamics he was actually the first person to do that I think and that's a relationship between if you have whoops if you have a black hole of mass M angular momentum J and charge Q with a electrostatic potential Phi at infinity or the difference between infinity and the horizon angular velocity of the horizon Omega H and an area of the horizon a and a surface gravity of the horizon this is not what he had so but some some other function here there's a relationship between the differentials of these quantities which he just extracted by looking at the ker solution occurred neumann solution from general relativity which is the rotating charge black hole you could just vary those parameters and infer this formula a much deeper version our derivation of this came shortly thereafter by Bardeen Carter and Hawking in which it was realized that you know how general it was and how it was really coming from diffeomorphism invariance and how the coefficient of the area term the surface gravity is an intensive quantity so for a bekenstein it was just a function of these parameters but it's a it's a locally defined quantity on the horizon and we're over on a on an oblate horizon like that it's not necessarily constant because it's not a spherically symmetric object nevertheless the surface gravity is a constant on the horizon of a black hole and that's analogous to the zeroth law of thermodynamics which was realized after bekenstein stare evasion okay so bekenstein have this relation but he didn't know that was surface gravity it was just some parameter and his reasoning was to interpret the left-hand side as the entropy change times the temperature and then the right-hand side according to the Clausius relation of thermodynamics would be the heat flux into the black hole so he's interpreting this combination as heat flux into the black hole and fusion you cute oh that's a different cue yes thank you whoops okay so here's the that's true so his the most interesting thing about his entire derivation was the next step he said from an information theory point of view an entropy his account of the logarithm of distinguishable states or something like that or information missing information so the smallest change that entropy could make not in statistically speaking on average but with a definite change of information a certain change in information would be logarithm of two so he said there must therefore be a minimum amount of heat that could be added to the black hole and if he could figure out what that minimum amount of heat was then he could figure out what unit to measure area and to get entropy so just forgetting the area term for a minute just look at this equation the minimum heat that can be added is just T sorry I read it wrote the other way T is the minimum heat divided by it log two so what is that minimum heat that can be added so he reasoned that if you try to lower you know you can make why is there any minimum that's the key question you can just take an arbitrarily small Madison and just put it into the black hole but an arbitrarily small mass has a large wavelength and so if it's you know the wavelength is huge compared to the black hole it wouldn't necessarily go in and then you realize well actually I don't even need a small mass I could take any mass but just lower it extremely close to the event horizon because of the gravitational redshift its energy measured at infinity or it's killing energy would be arbitrarily small the closer it is to the horizon this is not falling in it's a static mass being held above the horizon the mass can be made arbitrarily small so it looks like there is no minimum until we take into account quantum mechanics oops this was not oh I'm pushing around thing until we take into account quantum mechanics so here's the minimum heat we can put in mu is just the mass of some particle we're going to try to put in as a little a killing energy as possible the size of the particle is be some finite B and the killing energy is the norm of the killing field Chi at whatever location the mass is at times the mass and so we're looking for the minimum that this product can be now the norm of the killing field is zero on the horizon and near the horizon it grows linearly with proper distance and the coefficient of that linear growth is the surface gravity so Chi is just Kappa and the distance from the horizon the minimum is the size of the particle B so this just becomes Kappa B mu min but now B mu min is an energy as a length times an energy that's how small can I possibly make be for a given mass the uncertainty relation tells me that could be no smaller than h-bar and therefore the minimum value of that product is h-bar so the minimum heat that can be added is H bar Kappa and going back to here that means that the temperature is of order H bar Kappa the surface gravity and that was beckons teens argument although like I said he didn't know Kappa was the surface gravity that means that the minimum area change is actually H bar G if you just follow this equation and that's the pipe length squared and therefore finally that the entropy is the area divided by H bar G just read out of this equation so he didn't just you know he derived that the unit of entropy H bar T is independent of the black hole mass charge and spin it really is a property it really is a justification that the area can be considered well it's a good candidate for the role of entropy welcome back to that now his generalized second law he tested it with thought experiments and he had a problematic experiment actually where it seemed to not satisfy the second law and he that was an experiment where the black hole is placed in a bath of radiation where the radiation temperature is actually lower than this effective temperature of the black hole h-bar Kappa and if that happens still though because it's a black hole radiation will go into the black hole but nothing will come out so heat will be flowing from a colder reservoir to a hotter one violating the generalized second law so it's strange that he managed to fool himself at this point that that was okay he did note that at that very except a low temperature the wavelength of the radiation is very long in fact as much longer than the black hole size by something like a factor of 100 and he said therefore this process of radiation going into the black hole is dominated by quantum fluctuations in the radiation bath and so what you know but he concluded so therefore it's okay somehow the second law doesn't have to hold it was really a strange lapse of reason given how clear the rest of the reasoning in the paper is in any case he fooled himself and really the fact of the matter is there's no way the generalized second law can hold unless the black hole actually radiates at this temperature so he could have in that paper inferred the existence of Hawking radiation without calculating anything in quantum field theory so the hulking temperature actually it's not just h-bar Kappa roughly it has a very specific coefficient which is one over two pi if they would be in the generalized second look harden the input being the generalized second look yes no convention sees wonders yes at this point it wasn't a little bit of loud ok and that means that the coefficient in the entropy is also very precise it's one fourth of the area divided by Planck length squared we heard about this earlier in fact I should say the talks that have come so far in the conference set up my talk perfectly because all the ingredients have been explained so what's going on here what is Hawking radiation the thing that jacob bekenstein didn't consider is even though he was thinking about fluctuations is that a black hole sitting in vacuum is is actually immersed in the vacuum of quantum fields so it's never actually isolated and in fact the quantum vacuum is unstable in the presence of a black hole and the radiation the paradox of having something come out of a black hole which is what was making him not introduced Hawking radiation is solved by the fact that the Hawking radiation doesn't come out of the black hole it's filling a vacuum instability around the horizon and the radiation we see you could say came from outside the horizon and it's partnered with its correlated with quantum field fluctuations inside the horizon which fall in actually they're trying to come out but they fall backwards in they're dragged in so that's the nature of Hawking radiation and the whole story fits together beautifully ok so what is this black hole entropy what is it counting and what is the source of this thermodynamic behavior of what started out as a theory of partial differential equations and supremely classical physics the key I claim or believe or assert or argue is that is to remember the key fact about general relativity which is that are about black holes in general relativity is that a horizon is not a special place in space-time it's like any other place if you fall across the horizon you can't tell you are following across it might be a small enough black hole that the curvature is fairly large there but it wouldn't be qualitatively different on the horizon and you know a Schwarzschild radius away so therefore we may as well look for the answers to this deep question in flat space-time forget about black holes so here's the story of black hole thermodynamics in flat space-time I'm going to just state a few facts and then I'll explain them in the following so first of all bekenstein is derivation actually applies not just to black hole entropy but to acceleration horizon entropy the origin of the Hawking radiation actually exists in flat space already and it's known as the Unruh effect just that the vacuum of flat space-time looks thermal when viewed in a restricted region the Minkowski vacuum has an entanglement entropy the quantum fluctuations in the vacuum which scale with the area and therefore provide a candidate for the states that the black hole entropy is counting and now it gets further what about this classical partial differential equation well just from thermodynamic principles applied to this restricted vacuum it implies the necessity that the causal structure of space-time is actually dynamical it is not rigid and in fact that the Einstein equation holds and I'll just mention a little bit how that reasoning goes and finally all of this were getting out of basically flat space-time reason Newton's constant which is going to appear in this Einstein equation that's derived this way it depends on the matter content in the universe and it runs with energy in fact it becomes large at short distances though all of that is coming out of flat space-time so to understand that the key is this picture it's to think about the symmetry of flat space-time and put that together with the quantum field theory so in Euclidean this is just the including plane over here it has translational and rotational symmetry about any Center so we can choose Cartesian coordinates to make the translation symmetry manifest or rotational or polar coordinates to make rotation symmetry manifest and that's the flow of the rotational symmetry around a particular origin in Minkowski space also as we heard about I guess yesterday there are similar symmetries as translation and time and space and there is hyperbolic rotation about any point here I'm just talking about two dimensions of Minkowski space but orthogonal to those two dimensions we can have any number of space like dimensions that don't play a role in what I'm saying we can choose Cartesian like coordinates or bankowski coordinates to make the translation symmetries manifest or we can choose polar coordinates as type of molecule or coordinates to make the hyperbolic rotation symmetry manifest and the just like here R is the radius from the fixed point here L is the proper length from the fixed point over here and this coordinate patch these coordinates cover just this triangle here I think I'm going to add the triangle yeah there we go ADA is analogous to theta it's the hyperbolic angle and the flow of this symmetry is hyperbolas whereas here we have circles so the difference is that here the flow sends the entire space into itself whereas here each of these four wedges flows into itself under this hyperbolic symmetry now here's about when we add quantum field theory in it turns out that Lorentz invariants and stability of the vacuum actually imply that the the vacuum of a quantum field theory of Minkowski space is a thermal state I mean it's actually the zero energy eigen state of the Hamiltonian but that's the Hamiltonian that generates time translations in space time but if we restrict to observations inside this right hand wedge region is called a Rindler wedge then the vacuum state which is pure appears as a mixed state because of those correlations in vacuum fluctuations on either side of this point or really of this plane because we have other dimensions orthogonal to that so we take the vacuum the ground state of the handle translation Hamiltonian zero form the projector trace over the field degrees of freedom on the left hand side we get a density matrix and that density matrix in fact has the form of a thermal state where the Hamiltonian is just the generator of this hyperbolic rotation symmetry which is called the boost Hamiltonian and the temperature is h-bar divided by 2 pi which you might remember seeing in the Hawking temperature formula there was h-bar over 2 pi times the surface gravity this was actually derived by algebra by axiomatic quantum field theory people Abyssinia know and Vickerman in the same year basically as Davies and also Unruh came upon it from a very different physics viewpoint and this so this is once again saying that the vacuum looks thermal at this temperature I should say that temperature doesn't h-bar over 2 pi has dimensions of action energy so how can it be temperature but temperature in the sense that it's conjugate to this Hamiltonian and this Hamiltonian doesn't have dimensions of energy either it has dimensions of action because it's like an angular momentum generating this hyperbolic rotation rather than being an energy nevertheless if we pick a particular observer in this wedge say following this hyper hyperbola and if that observer makes observations localize that there worldline well then they wouldn't want to use the hyperbolic angle as their time chord that they use their proper time and if I scale to the proper time of this observer that depends on the acceleration of that observer which actually is the reciprocal of the of the distance the proper distance of that observer to the horizon so that local observer measures the temperature h-bar times the acceleration over 2 pi that's the Unruh temperature which is also h-bar over 2 pi L L being that radial distance so note that the acceleration of that hyperbola diverges as as L goes to 0 is the hyperbola gets closer to the light cone and that means that you know there's a lot of you can think about that as quantifying the amount of entropy in this thermal State it's like if you're in a thermal bath this temperature is infinite that's an awful lot of entropy and we can estimate actually how much entropy in the following way the entered the von Neumann entropy in the right hand wedge is minus trace of the right hand density matrix times its log now let's just treat that roughly like a thermal bath with a temperature T local where T local as the temperature I just mentioned here oops sorry the key thing is its dependence on 1 over L so I'm going to integrate the inter density cubed over volume the volume has a transverse area and a proper distance from the origin there T depends reciprocally on L so we have 1 over L cubed Y L and if we integrate that we get 1 over l squared and at the lower limit of integration L is 0 so 1 over l squared is infinite but if we cut it off at some finite epsilon we'll get 1 over epsilon squared so this tells us that the entanglement entropy and the vacuum bills like the area divided by some cutoff epsilon which I'm just putting in my hand at this stage and this is what I was claiming it as a candidate for the origin of black hole entropy any questions so far actually so the hypothesis that this really is that black hole entropy is entanglement entropy has actually been supported by all kinds of calculations for example involving free fields with various types of regulators you know playing the role of that epsilon also what was mentioned earlier the real takahagi formula in a DSC ft context which has nothing to do with black holes but it equates the entanglement entropy in a conformal field theory in the in the boundary at the thermo quantum field theory to the area of the minimal surface that hangs down from that into the bulk divided by 4g it's not a hundred percent clear I mean this is a that this is correct because of course it's really infinite in the theory that we have in our hands and it the actual precise result depends on the cutoff and the way we make it and also in fact it depends on unresolved issues on how to precisely define an entanglement entropy when you have fields with a gauge symmetry or diffeomorphism especially with diffeomorphism symmetry i just mentioned here also that in order to fully agree with black hole entropy you have to include corrections beyond the area term but I shouldn't get into that right now so this reminds me of the article of t-bo's that I read just before coming here about clunk RA and Lorenson Einstein the origin of special relativity back in those days Lorentz and punk RA were all concerned with constructing a physical model of a divergent thing which was an electron which they would have liked I guess to be a point except that would have infinite self energy so it had to have a size but then because it had to have a size a head tongue mechanical properties that held it together and then they tried to calculate how it deforms under boosts and all of that and it was a difficult program and I mean from Perez model that Tebow talked about in there that was the grand success I guess the best formulation of the problem was after all just some artificial model that he invented and into in the end what have we learned it's all irrelevant Einstein made the right move to just cut through the whole thing and just say forget about that model just clearly this symmetry has to be there this symmetry being Lorentz symmetry in fact let's make it a fundamental principle and build physics anew on top of it and we'll deal with that electron structure you know down the road get on the hike slope it solved it in a way but it still has infinite some energy it still has something itself energy I mean so certain problems you shouldn't solve at certain times in physics and I guess I feel like the reason I brought it up is I sort of feel like this is an example of that it's obvious I would claim that black hole entropy is entanglement every way but in precisely in what sense in terms of what quantities and how to resolve these ambiguities we are not in a position really to answer today you're aware of the work of survey solo Dylan who showed what you're going to discuss next that actually this infinite part computed Li is equal to the minimization of G due to the fields to include so from this point of view it's precisely not the part of the answer what is just the consistency check yeah I don't see it that way okay to acknowledge that it was not sorry it was not what that's so right so I'll make exactly the opposite argument right now so are you also gonna comment on this drum interval accounting it yeah went down the road everything is done the world - thank you - no no I with in this talk yes okay so how how so if there's this entanglement entropy out there and bekenstein told us remember we should the generalized entropy is black hole entropy plus the entropy outside now this entanglement entropy is entropy outside so I should include it I guess in the outside term and yet if I take the cutoff to the epsilon down to the Planck length the outside entropy is now just as big as the black hole entropy is so and moreover so how could I deal with that so here's what I what I believe is how we should think about it and deal with it the entanglement the question is how is this entanglement entropy apportioned between in the generalized entropy between the outside entropy term and the black hole entropy term so here's the total entropy if I impose a cutoff epsilon I get an outside entropy and then I have the remaining the black hole entropy but now in order for the story to be consistent that is I should be able to move that cutoff and count more or less of the entanglement entropy as outside entropy then that must mean that Newton's constant because that's the only thing that can vary on this side of the equation is also epsilon dependent and varies in just the right way that the sum of those two is invariant under a shift of Epsilon or in other words in renormalization group invariant some but not separate terms and that's actually been shown again in in certain contexts where the ambiguities can be dodged and things seem well-defined there are quite a number of what I find very can arguments that this is the right way to interpret this if it is then of course we can think about two limits we can take epsilon going to infinity that means that the short distance cutoff is very long basically so there's virtually no entanglement entropy to talk about all of the entropy is in this term and that's the limit epsilon to infinity that corresponds to Jean being equal to Nu this constant what we mean by Newton's constant and it's all intact it's all black all entropy it's all bekenstein Hawking entropy if we take the other limit where epsilon goes to 0 the entropy shifts from this term to this term and I would say it becomes all entanglement entropy but in one case we have a microscopic explanation of what it is and why it's there and the other case it's a total mystery so I personally draw the conclusion from this that black hole entropy is entanglement entropy of the vacuum it's just that we don't have a complete handle on what that means today by the way infinity is it plus infinity for bosons minus infinity forever so it's always present it's always plus infinity but there is a sign issue like for gauge fields which there's an interesting story that's been I would say largely resolved recently by Donnelly involved but we should that's a very technical thing ok but but is this vacuum entanglement entropy how could this possibly be true because the amount of entanglement entropy depends on how many quantum fields are in the theory right if I have three families in the standard model I have more entropy than if I have one but the only way that could be true as if Newton's constant also depends on the number of fields in the theory and why should Newton's constant always be matching perfectly what it has to be for this formula to be true so here's my proposed understanding of the answer that just to basically infer that the Einstein equation and the equality of Newton's constant was kind of the reciprocal of with the entropy divided by the area is that the unsent equation is the equation of state of the vacuum fluctuations so again the vacuum is a pure state there's nothing thermodynamic to think about but if we restrict our view of it to a wedge it becomes a subsystem and it's got lots of degrees of freedom and it's all mixed up and so that's a context where thermodynamic should apply and I applied it this is from wave a paper a long time ago so just thinking about and I don't want to get deep into the argument I'll just state the ingredient pieces of the conclusion defining a local causal horizons analogous to black hole horizons considering the local Minkowski space structure defining heat flux as the amount of boost energy flowing across the horizon and demanding the Clausius relation holds assuming also that the horizon area a with some coefficient I don't know gives the entropy and demanding the Clausius relation D s is DQ over T what is that going to imply well first of all it implies that the area must change if there's a non zero heat flux but how can the area of a causal horizon change when a causal horizon is just defined by the trajectories of null geodesics so it means there must be focusing of null geodesics is face time which is which is the statement that there's curvature in space-time so space-time must be curved the causal structure must change in a respond in a way that responds to the flux of boost energy boost energy can be constructed from the energy momentum tensor so this is going to give a relation between the area change and the energy momentum tensor and in fact using the Rachael during equation of geodesic deviation it actually implies that the ice if I assume that it holds on all possible horizons pointing in all different directions at every point in space-time this this set of assumptions implies the Einstein equation with some value of Newton's constant and that value is determined by this coefficient alpha whatever it is you get a Newton's constant that's 1 over 4 H bar alpha oh I should say and I'm assuming the temperature here is the temperature I just mentioned the Unruh temperature of the vacuum possible what weight weighs a key boot and I just want to make one point the first equation is equal alpha a with some alpha seems very not rusyn because one is tempted to say well it's 2 in most entangled entropy that fall sooner but if you look for you know potential matter physics you have something like that but alpha depend on the state so the the strong input is the no dependence of how from the state Theory say I think that's what we because we try to to see why doesn't happen for other systems so we try to go through and and any other system has a mouth on the people of this state so this is a strong entity yeah yeah the reasoning that I was so the justifications such as it is would be that the vacuum at short distances is universal in any state it has the same structure of course that's not really true because you could have phase transitions in the vacuum or something and actually you could have BRE normalizations of doing this constant that feed into the formula but putting that aside it's the universality of the structure of the vacuum independent of the state that motivates this to do this to be a constant okay so that so let's see what conclusions we draw from this whole story or we could draw or might draw so it seems to follow that black hole entropy includes and maybe a hundred percent vacuum entanglement entropy secondly if we if the entanglement entropy had been infinite so if I have no cut off then Newton's constant would be zero that is I wouldn't have any gravity because the going back to the equation oops the variation so in order to match a finite DQ if area if F alpha is infinite the area variation has to be zero or putting it differently I solve for G and it goes like one over alpha F alpha or infinite G would be zero and this is crucial because otherwise we'd be convincing ourselves that it's impossible to write down a quantum field theory that has no gravity in it it's just obviously not true it's just that it's the finiteness of the entropy that forces gravity on us okay conversely what is it that's making this cutoff since gravity is a consequence of the entropy being finite it stands to reason that gravity should be responsible for making the entropy finite somehow there should be a link between the finiteness and the existence of gravity going in the other direction and there is an argument you can make from the gravitational dressing of the vacuum fluctuations that they would be cut off when the when the separation of the fluctuation on the other side of the horizon of that pair is shorter than the Planck length and I made that argument in this paper it's a it's a very hand wavy argument but I think it has a nugget of truth in it the Newton's constant the number and species of matter fields and there's no species problem that is problem with this story coming from the the fact that the entanglement entropy depends on the number of species also actually this I gave it a thermodynamic derivation here the Einstein equation but recently I approached this a different way and gave a statistical derivation not based on the Clausius relation but based on a principle that the vacuum entanglement is maximal because the vacuum is somehow an equilibrium state of entanglement and this applies in a small gym music balls at fixed spatial volume so it's not a story about involving horizons it's just a story about comparing the entanglement entropy in a small ball in the vacuum state to the entanglement entropy in a small ball in some other state and let me just say one word about this you might think ok this this is nuts how can I mean here's a ball in the vacuum okay clearly I can just take a an entangled pair of qubits and put one inside the ball and you know increase the entropy by log 2 but the thing is if I do that that bit has some energy and that energy sources gravity and the gravity makes the area of the ball shrink at fixed volume and it shrinks by enough that actually the total entropy goes down not up so that's the principle of that argument that is a good question and I buy recently talking to by email with Mattie Ross akka I don't know if you know that guy's a Finnish young Finnish physicist had an interesting thought about the possible answer to that which is that if you look at the so if you imagine there's some screen structure underlying this you might think that the size of the algebra of quantum fields inside the ball is determined by the spatial volume because the ball because of the ball because extensivity of the quantum field algebra or something like that and so I mean obviously if you enlarge the algebra then you could have more entropy it's like you know the entropy of a gas in a box is not maximal in equilibrium if you allow yourself to make the Box bigger so somehow you should fix the number of possible states you're even talking about it before you compare the entropy that's the best I can do it's very hand waiting yeah just in the argument I just assumed it because I noticed that if I assumed it it worked okay and then yeah I just want to emphasize also what what should we conclude from this is the Einstein equation thermodynamics is gravity you know different from all other quantum fields should we not quantize gravity all that kind of question arises I think the answer is no it's not really different we know that we can apply in fact this hasn't been said yet in this meaning but it really should be emphasized you know quantum gravity is a big mystery in many ways but in one way it's not a mystery at all we can simply apply quantization to it as an effective field theory like we would with any quantum field theory it won't be well-defined in energy scales up at the Planck scale and it's predictions will only be precise up to ambiguities of order the reciprocal of energy scale you're probing to the Planck scale but still it's a perfect other than that which is actually the case for many quantum field theories we use it's a perfectly well-defined 1 and field there and I don't think any of this implies that that doesn't hold for gravity on the other hand it does seem that if we were to this is saying that if we were to probe the dynamics of space-time at the Planck scale we shouldn't expect necessarily a conservative theory like a field theory would be maybe it should be more like a dissipative phenomenon because after all that's the this regularity of the causal structure is emerging from some statistical property of the vacuum so I would say it seems to it seems that dissipative effects should be expected at the Planck scale by the way think as people like motels like Keanu EPA did you use he has a Moto e II understand equation he called entanglement entropy no entanglement a query will be could he eat again thank you very much right now another question species problem in string theory there is an infinite spectrum of particles yeah is it a problem for this that's why I thought there are signs for hands behind there are signs with high spin circuits the the contribution to the legalization of Jesus events on the spin families but yeah - life safety cage pills have minor signs but like I said there's a story behind that where you have to get into the edge mode entropy of gauge fields that hadn't been accounted for in the heath kernel method and positive jealousy with an infinite number of particles yeah oh yeah I haven't studied closely but people looked at like the the entangled the entangled entropy in string theory and I don't think there's a committee it's them the fact that the masses of the component fields are getting its Planckian takes care of it I I don't know it should be yeah I agree that it's a question but I don't agree that it's a problem necessarily can I ask about the dissipative yeah I mean if we agree that general relativity is an effective theory then I would seem like the conclusion at the Planck scale is that that theory breaks down and we're just going to need some other more fundamental description of physics at the Planck scale right so so why are you claiming that physics at the Planck scale you know will be dissipative rather than just physics so some other degrees of freedom well see I feel like big a bit I would be ignoring the lesson that I've learned from the story I told so far if I just said well at the point scale breaks down so something takes over so what should take over base if I hadn't learned what I've just described I guess I would have thought you know some unified field theory of it I don't know string theory or something but the thing is it seems like what we're being shown is that there's something there is something statistical about the vacuum and it's really the dynamics of this complicated vacuum that is giving rise to gravity as we know it so in past experience when we had large-scale regularities that came from an underlying complex statistical phenomenon there is dissipation you know it's not it's not another theory of the kind we know at the large scale it's a very different thing at the small scale that's the only that's the reasoning I'm thinking of anyway now I get to the question Gary asked about before what about microstate counting and I'll talk about just very briefly in string theory and in loop quantum gravity to decide how much depth to go into here I guess I'd like a time reading if that's possible party okay great cause I think this is my last slide on this part and before I get to the information which I can make in a very contracted way my point I want to make on the Meishan paradox that can be made briefly okay so we have this fantastic counting of blackhole microstates in string theory which we already heard a little bit about just what I would say and some of the question you could say is what where do I come from proposing that black hole entropy really corresponds to these disadvantage angleman we have a very different story that accounts for it in string theory in what is that story so it doesn't count black hole space that's the first statement the string theory story is account string States on deep brains at weak string coupling so there's no black hole it's a flat space configuration of a stack of deep rings with strings on so how is that a calculation of black hole microstates well it's a trick it uses supersymmetry to link this calculation that I just described to a different number which is the number of states you would have had a strong coupling so supersymmetry apparently is this magic symmetry that has the property that you can change a coupling constant from weak to strong so much so much change that a stack of deep brains in flat space becomes a black hole at strong coupling but you know based on the principle of the supersymmetry that the number of states at a fixed values of the charges doesn't change therefore the number is calculated where it's easy to calculate it relatively easy to calculate it as string States on D branes but that's also one knows equal to the number at strong coupling where you have a black hole note that in this calculation Newton's constant is not renormalized so Newton's constant in string theory comes out of as gary told us the string coupling constant and the string length and under this supersymmetry setting the the long distance low energy sin is the same in the strong coupling theory as in the weak coupling so one can actually calculate the actual numerical coefficient of the bekenstein Hawking entropy in terms of four times Newton's constant in the denominator and be you know precise about the coefficient so the result of this ultraviolet microstate counting can match the bekenstein Hawking entropy perfectly this doesn't logically mean of course that string theory is the Right theory of quantum gravity what it means is something like first of all this argument using supersymmetry that sounds very slick really seems to be correct it also means that the effective field theory we extract at low energy from the string theory you know will be it's consistent with you with the fact that we could have calculated the black hole entropy from it from the low energy side and it better match so this shows that string theory is not in a word but it doesn't show that string theory is quantum gravity in our world okay now another extinct counting that exists is in loop quantum gravity in this case it's I would say it does count black hole states identified to the extent that we know how to identify them so far plausibly in loop quantum gravity what they are is actually a kind of spin network this is a discrete model of space and loop quantum gravity and in fact the result of this counting is directly related to a kind of entanglement entropy and it scales with the area but unlike the string calculation it's not it doesn't give a sharp answer for the coefficient because first of all it depends on a free parameter in the theory it's not known yet how to pin down call the emergency parameter and because Newton's constant unlike in this super symmetric case the Newton's constant that's used in the calculation is the microscopic one at the at the cutoff scale of the theory that's not the low-energy effective Newton constant so that's a second reason why it can't be compared actually I think there may be a problem with this I argued in this paper which has gotten incredibly little attention but if the result of this calculation gives the same answer for a black hole in this in pure gravity as a dozen black hole couple two Maxwell fuel gravity couple two Maxwell field and that's usually described as a great success of this but I actually think it's a problem because the running of Newton's constant is different if you have a Maxwell field and if you don't and therefore in order for this calculation to actually be agreeing quantitatively with the bekenstein Hawking entropy in both theories it seems in both both with and without a Mexico field seems incompatible so I'm not strongly arguing that there's a problem but it it looks like a problem to me okay so that's it for that part and if you want me to stop I can but I could also okay great so what we want to do is turn this off and use the boards now actually just close and I have some notes it's done by hand thank you let me just catch my breath first everybody I feel like I'm unloading on you all my strong opinion in of believes okay so that was a story of how black hole entropy isn't really about black holes it's about the vacuum in any space-time and now I want to make the case that the black hole information paradox is not about black holes either and what do I mean by that so first I should say that I believe for about three decades that there was no information paradox because inside a black hole there's a piece of space-time cut off from the outside there's a singularity where curvature becomes Infinite and we're not sure what happens so so what if information falls in there and becomes lost to the outside maybe there's a baby universe where the information goes but in a DSC ft has been mentioned several times so far in the meeting there's a very strong argument that at least in that setting and I'm very happy to just consider that setting as a test case the conformal field theory is unitary and it is dual to at least a lot of what's going on in the space-time including the possibility of forming and evaporating a black hole so it looks like black hole formation and evaporation must be unitary at least in that setting and so that was when I began to change my mind and there's another argument that connects this to just general relativity's fundamental principle which is general covariance this argument came from Don Merrill and it introduces the notion of boundary unitarity he made a pain argument that on account of diffeomorphism invariance the hamiltonian for gravity plus any matter in the theory is strictly a boundary term in fact the Hamiltonian is a combination of constraints and a boundary term but the constraints are zero by the constraint equation in order to satisfy diffeomorphism invariance if we're acting on a quantum state the fact that the constraint is zero is the statement of the Willard with equation holds so to evolve a quantum state we would apply the hamiltonian whose only nonzero action is at infinity at the boundary and then Meryl says okay let me consider all besides so one thing I could measure at the boundary is the total energy of the space-time that's the value of the Hamiltonian let's say I could imagine I could measure other things there as well and in the anti-de sitter setting what's nice about the boundary is its it seems like there are more observables that you can get your hands on at the boundary of space-time and carried through the picture of this cylindrical space-time so this is the bulk boundary and we should just think about observers who live at the boundary and observe whatever can be observed from the boundary and what Meryl pointed out is that those observable any observable and quantum mechanics evolves by Heisenberg equation of motion by commutator with the Hamiltonian the observables you can observe at the boundary define an algebra and one element of that algebra is the Hamiltonian and therefore that algebra evolves into itself under time evolution and therefore any information you could have by measuring elements of that algebra at one time involves unitarily into information you could have it any other time in the boundary so in a nutshell that's his argument it's very slick why should be a single time slice of the binary yeah what she said fiscal illusion illusion to come from anything can tell me the Hamiltonian over general relativity is boundary term at infinity yeah based on you know the set of data and philosopher which it is it is think about the classical theory yeah I think it's different courts are clear in quantum mechanically why the question is what what is different here I mean because in the classical theory also you can do funk you can set up initial data yeah but you cannot do just somebody you need to you you feed out on the bottom right which is the painless human news function they're not determining a later tiny bound mr. Fixit everything about this is exactly the argument that so I had a meeting last year Steve and Bob Wald and Aaron wall and I started a quadrille log I guess you could so trying to resolve this question yes so definitely the classical theory doesn't have this property because there is initial data which doesn't register let's say and the boundary on this slice but could come affect the boundary layer yeah so I think Steve can probably help me explain this first of all imagine that the spectrum just for a moment and I don't think the result really depends on this but suppose the spectrum of the Hamiltonian were non degenerate quantum mechanically then you could measure the state from the boundary uniquely no no but that's actually it's that short but this shows you couldn't make the same statement in classical mechanics so what's different is the role the Hamiltonian plays in the theory and the information it contains is different in the two theories but let's not get hung up on this now we could discuss it later otherwise I'd never get to my basic I just reported to you the way that Meryl made the case I found it to be striking because it just uses diffeomorphism ignorance it doesn't invoke string theory or radius EFT and at the same time it both kind of explains to me partly why ats CFT something like that should even be possible and at the same time it gives an independent argument why black hole that formation and evaporation might be unitary and he called this property boundary unitarity just to emphasize that it's a statement about the boundary observables only there might be observables in the bulk as i think gary mentioned in his talk like we might have a spacetime without a boundary and surely that has some observable somehow if we understand quantum gravity and probably then also in general you could have a situation like this with a bulk observables that are not in the boundary algebra but that's also irrelevant to the discussion at the moment because all we're talking about is whether information is lost at the boundary because that seems to be the only sharp statement that I have a strong reason to believe in unitarity wise and and it's traceable directly to diffeomorphism in very okay so that's the starting point now we get a paradox why so easily to snitch or two idiots in this picture justice has nothing about me because it looks like this piece of news I play into any space language yeah maril did argue that it applied in Minkowski space also but it's a trickier argument and it actually is more of an S matrix light argument because the boundary isn't time like there we have to null pieces scry - inscribe + so he made an argument that the evolution from scribe - described + is unitary but here we since it's time like we actually have a story that we have an argument that is that unitarity holds continuously as a function of boundary time so as and as I mentioned earlier we have more because of a BSc of T we see that there's all these boundary observables that we could get a handle on here that we wouldn't know how to deal with an asymptotic Li flat space-time at least yet ok so what about the paradox then so the paradox comes because we might form a black hole by say sending a pulse of start with the vacuum inject energy into the space-time have it collapsed and form a black hole the horizon comes out like this there's a singularity whatever that is how it's resolved Hawking radiation starts to happen and some of that Hawking radiation reaches the boundary and on the other hand this pair of a hockey quantum minutes correlated partner remember that came from vacuum just the structure of the vacuum locally here near the Verizon so this hulking quantum state is entangled with its partners state by the way what's never talked about is what degree of freedom is entangled with is involved in this entanglement and the answer is the occupation number of the mode basically so a given pair corresponds to some given frequency in say spherical harmonic labels or whatever it's a mode and that mode could be occupied at different levels and the state is a superposition of a product of this and a certain occupation number and this at the same occupation number okay so it's entangled and that means that when it reaches the boundary let's say here a moment you ought to look at the first one so this quantum arrives at the boundary my boundary observer can observe it sees it to be in a mixed state is it because it's entangled with this partner behind the horizon so it looks like the quantum state measured at the boundary would now no longer be a pure state even though we may have started initially with a pure state and this is basically the problem we can't you can't be in a qubit cannot be entangled at the same time with two different qubits look yet because so far we don't need a bra code for that just a creation what goes here was yeah this is a point I'm about to make okay no well here I'm talking about black hole evaporation now so this qubit is entangled with that one so it can't also be entangled with something else out here the argument would go and therefore the state out here must have gone from a pure state to a mixed state but that's incompatible with boundary unitarity so there's a paradox the firewall proposal was basically saying okay that conclude it must not be true after all that this qubit is entangled with this qubit and therefore but that means the state here is not really the vacuum state because if it's the vacuum they are entangled that the firewall people didn't require the firewall right away with the first particle they'll right we're gonna get to that yeah later and they should have required it right away this is one of my key points in fact let me make it right now the firewall people so I think the argument is being made completely incorrectly they're trying to solve the wrong problem so a problem they were trying to solve is trying to show that the relation between the initial state before the black hole forms and the final state after it's completely evaporated are related by unitary transformation so in particular all the Hawking radiation is now in a pure state finally at the end what I would like to emphasize is that the first talk in quantum comes out we already have a problem with boundary unitarity we shouldn't be trying to just show and this is where anti-de sitter space is very useful as opposed to considering flat space-time because it's much more than the statement that the in state is related to the out state by unitary it's continuously the boundary algebra is continuously evolving unitarily that's true in the CFT and it's true according to Merrill's argument so we should be worried from the time the first talking quantum reaches the boundary we should be worried we have a paradox already and therefore in any case you're right what they they weren't worried about that but they said once it's halfway evaporated if you still haven't if the Hawking quanta has still haven't become purified by their correlations with each other you had better interrupt this process in time for the Hawking quanta that come out to purify the early ones as you can't cure a 5 million things with 10 things ten cubits you can't purify a million maximally mixed cubits with ten other cubits so halfway through it the so-called page time they said it had better be that there's no more of this entanglement at the horizon but if there's no entanglement that means the state is not the vacuum state there and so what is it it's some very singular state of quantum fields called the firewall but like I just said a moment ago I think they should have been worried at the first step and so let's worry about the first step now I still haven't made the case although I did Carla just anticipated a second ago that the real problem here has nothing to do with black holes let me make another diagram where I don't make a black hole I send something in from the boundary and I just arrange for the following process to happen it is some kind of collision happens and and a pulse comes out to the boundary but that's not all it also has a some kind of a resonance part of the energy goes on like this and it lives for some amount of time I don't know how much doesn't really matter and then it finishes decaying and the pulse goes out to the boundary and it's easy to you know we always have this could be like what's it called parametric down-conversion of an atom where you get correlated photons coming out of it this is like the first one this is the second one so these two can be entangled with each other you start with a pure state of this shell coming in and it goes through this process and this outgoing shell or quantum or whatever it is is entangled with that one now let's look at that from the viewpoint of the boundary server so when the first shell reaches the boundary at this time slice it's in a mixed state because it's entangled with this resonance or it's entangled with this if I had made this shorter therefore just like here I had a problem with boundary unitarity it seems like I have a problem here with it of course if I wait long enough the entangled partner gets there and finally it's no problem in this case maybe unlike in the black hole case it's clear that from the in state to the out state I would have a unitary evolution but that's not all we should be worrying about what happens at this time slice this is entangled with this but somehow the boundary algebra is still evolving unitarily so I believe that if we solve this problem we have solved this problem and it's not really a problem about black holes so how could we possibly solve this problem what are we missing because it's clearly a huge problem it's you know I don't know if I should wait for you to finish her but I do object I don't think this is a problem the example on the right at least in the context of gauge gravity duality because the gauge theory is supposed to be equivalent to everything in the bulk a particle sitting at the center of AES is described by some operator in the dual gauge there it doesn't have to doesn't describe only things which make it out to infinity if the particle comes out to infinity its described by a local operator locally so Gary everything you're saying but also apply to this picture yes but here you have the added complication of having a horizon and describing things inside the horizon which we don't know as well how to do but that doesn't mean in your logic should become at this point I you know the question is not whether it's unitary at each stage I think everybody would agree that black hole formation and evaporation corresponds to a state on the boundary which is a pure state at every moment of time what we're trying to understand is how in detail that you know happen but I'm telling you I think you're trying to understand the wrong thing you're missing the right way to formulate this problem you see I don't see a problem on the right you have exactly the same problem that you have here let me explain it so what was the problem here it was the monogamy of entanglement so here an observer could have fallen into this space-time observed that this pair is entangled with each other and yet we believe that the observer at the boundary all their observables evolve unitarily despite the fact that this quantum arrives in a mixed state no the particle that falls in is also described on the boundary well but if that's the solution then there's no problem you see the problem is the problem is to reconcile local quantum field theory from the viewpoint of a bulk observer with boundary unitarity of course we know especially if we believe in a DSC F T which I'm willing to to do at least provisionally of course we know that boundary evolution is exactly unitary the paradox is to is to reconcile that with the fact that the bulk observer can apply local quantum field theory at large distance scales and sees entanglement now that paradox applies exactly the same way here as it applies here so I believe that you are you and then the entire community is focusing on the wrong question if you want to answer it but if you believe that the boundary state is not just aware of what makes it out to infinity but it also knows about the particle inside then there is no problem but then you can see exactly the same thing here yes and and we do I mean but then what's the paradox you're trying to resolve our dots is to understand not from the boundary standpoint but from the ball standpoint exactly information comes out yes this is what I said the paradox is to reconcile local quantum field theory being applicable in the bulk and yet that seeming to contradict the fact that the boundary is evolving unitarily that applies here exactly the same way as it applies here well maybe you should finish and we can talk about that break break okay so I I have so the only remaining thing I have to say is a proposal of where to look for the resolution to this paradox I don't have the resolution so the place we should look for the resolution is we should remember why was there a problem in the first place it was only because we believed in boundary unitarity which is only true because of diffeomorphism invariance now usually when people discuss this black hole information paradox and the firewall and all of that they never discuss almost never except occasionally a little lip service the role of diffeomorphism invariance and I think therefore they're basically missing the point it must be that dip feel morphism invariance which is that once responsible for boundary unitarity is also responsible for resolving this apparent contradiction now what is diffeomorphism tell us embarrass tell us about bulk physics remember the reason I had boundary unitarity is that Hamiltonian was an integral over a slice of some constraints [Applause] plus a boundary term and these are zero so it's just a boundary term and the statement that these are zero in the quantum theory is the wheel are doing equation let's call it the wheeler do it operator acting on the quantum state equals zero so the whole story wouldn't get off the ground unless we have this condition holding otherwise what this term would not be zero in the Hamiltonian so the resolution of this puzzle must begin with this equation it's not an afterthought it's a new thought okay and this equation tells us something that there's something extremely non-local about the structure of hilbert space and quantum gravity because what is size size a it's a functional of say the three metric on our slice Sigma and other fields and what is this operator it's a second order or functional differential operator and it's like Annalee classically it would be an elliptic equation elliptic equations are non local equations deep that kind of to satisfy an elliptic equation need every part of the space communicates with every other part of the space to establish it a boundary condition an elliptic equation over here you change the boundary condition you change the solution over there so what this means is that if we imagine that the hilbert space of quantum gravity starts out as some kind of a tensor product of local factors like in local quantum field theory so let's call it h i local so i'm thinking of this part i'm going to fix this like a lattice quantum field theory or something i have local factors in space each one has a children space i tensor them all together i get the hilbert space of a point theory that's not what we have we might start with that kinematically but then we have to say we're only interested in the Subspace of the hilbert space that satisfies this equation so now let me project out of that the wheeler de Wit projector if that's actually the structure of the hilbert space of quantum gravity and since it's now no longer just a tensor product the whole language I was using when I was describing this problem is strictly speaking not correct like what language was I using over here well I was thinking at a local Hilbert space for this quantum and a local one for that and it's a tensor product of the two and I define the von Neumann entropy of there are these density matrix in the usual way etcetera what this is telling us is that we can't talk about that Hilbert space by itself it's actually correlated with the rest of the Hilbert space outside and I don't mean correlated in the sense of the corner it's it's a putting it differently visit there's no observable in quantum gravity that talks about just this entanglement of this Parekh the way the firewall paper poses it what you really have to do is form a diffeomorphism invariant observable that describes what you're talking about but to do that you know then you're doing something completely different you might be jumping in from the boundary integrating the geodesic equation locating this by the time on some clock all the stuff in that observable involves the gravitational field everywhere and so I'm not saying I know how to start calculating this but what I'm pointing out is that once you change your viewpoint and say I'm going to if you're going to worry about this problem based on diffeomorphism in there Dondre unitarity then you better worry about what is the true context of that theory which is this diffeomorphism invariant over space so that's basically my thought about it the the non factorize ability of the hilbert space it's not a little bit of nonlocality it's massively non-local and yet at the same time somehow for certain purposes we can forget about all that and just use local quantum field theory at large scales and so I think what's so interesting about the black hole information paradox now that I've just you know accepted that there is a paradox is to resolve this incredible discrepancy of viewpoints and it's a discrepancy because there are two very different theories and here's almost where I think Margit closest to the full up full philosophical issue in it in all of this it's like we have two extremely different theory paradigms local quantum field theory and quantum gravity which has a hilbert space structure that's totally different and we need to learn how to integrate those two to resolve this paradox that's it oh you think that they say normal modes could play a role in calculating entanglement entropy because they are like the fingerprint off the black hole they are there and they are not arbitrarily given so they're entangled if it's outside inside maybe also with the point moves later yeah I guess I would think of them as the you know part of the gravitational contribution to that entanglement entropy Jim York had an old paper that was proposing exactly that we should look to me spectrum of quasi normal modes to account for the black line Rafi and I it seems definitely that it must be part of it but I don't see why we should imagine the whole thing he got it to within a couple of percent numerically you mean the aerial oh yeah with the right coefficient I should look at that again actually the paper when was it to get this paper eighty-five I think he had a term the quantum Virgo sphere no she was using to describe those that contribution is very anything between the idea that the black holes could be maximally scumbling and the fact that you were talking about I don't know something like a dissipative in a minute oh I don't think so because I think that scrambling property somehow holds over at the semi-classical level whereas this dissipation I was thinking that would be something quite beyond semi-classical I felt very good to this final discussion that you gave me they want to see whether you can where they can be pushed further in the following sense you pointed out the nonlocality of the the deep nonlocality what does not answer could be yes news for we know limits in which the boundary theory gives the the perturbative theory inside of a given geometry so it's an issue of how far we are from that limited boundary theory has n going to infinity as the physical theories for finding n but I know what window and said I'm going to finish each one to zero in some sense I can reconstruct the geometry inside pretty well all the way to me although it where all the way to the similarity or all the way to the religion when someone to stop happen so between the the sort of common picture that we find maybe a person it is manly see egg if if it's FaceTime inside with a given causal structure which is what you say come on I mean that's doesn't say together and the oh my god is the sum of all possible geometries whatsoever I mean the total darkness going to grab unite there is a the two things can come together by by building the semi-classical geometry as much as possible until the single a meter into the pump to reach over something happens so in other words I think that your picture can still spell in maybe some mobs we're weird it goes wrong with the house instruction cannot be trusted the word day the the quantum reality becomes important breaking the maybe the background geometry seriously wait were you saying that that's um a necessary component of resolving it because in the picture with the resonance that can be perfect that could look quite semi-classical and weakly curved everywhere I can think of it the solution of the puzzle in quotes can be exactly like your right picture with the only difference that somewhere the background geometry I mean the the nonlocality should come in in the file what is this more mechanically the nonlocality the elliptic equation you're talking about is not only efficient space telling these in the space of the geometries so it's a superposition of geometries that matter yeah no people can say well superposition of Jones even Jordan with fluctuations is the same thing what I'm pointing out is that not know is not the same thing having it a single gentleman to be small fluctuation which is a quantum story and some superposition of geologists and the question is where is this superposition which is going to matter and I expect that is gonna matter where the black hole story why do we have two black hole shouldn't we simplify this as I'm suggesting and consider that the question without a block oh yeah so then where are you pointing to I think that they would agree event on the right hand side and I can have both things I can have a geometry inside they they you need to guru from outside that yeah you don't say anything what really is a problem it's so the question make it say the same thing in the black hole I had become so what are you doing but you have to finish up the story where is the thing that adds up you see this why do you keep pointing me back to the black hole side I just explained that we should first resolve the question without the black hole because it contains the essential question what is the problem if you want to understand from the Balch standpoint the right hand side you do quantum field theory and you see the quantum field theory see the part on the center you see the particles going out everything's in a pure state at every time everything's in a pure state everything's consistent using ordinary know if a problem is we can't it appears to contradict Nomar unitarity not if you allow four operators on the boundary corresponding to one again you could say precisely the same thing about the black hole problem you never see you compete the never cheat between the two beaches so you don't see any quantum gravity problem in the second so you say there is only the third one gravity problem there's no sort of automatically problem no ok I'm saying sort of the opposite today's those I think the puzzle raised by reconciling the applicability of local quantum field theory in the bulk with boundary unitarity which is deep puzzle of black hole information is as far as I'm concerned also occurs in without a black hole and so it makes a lot of sense to consider it without of what go and solve it there first is no solution there's no known solution so far there definitely there's no known solution you think there's no there's not there's not I have one paper suggesting a rough idea of a solution I guess I can I can tell you that I think I have one more thought about the solution that might be worth mentioning so I what's the the biggest consequence of the we learn to it equation so maybe the question they're closing is this easily to mediate state the state of the boundary pure or not that's a question you're asking I'm not asking it I'm assuming it is because I believe the evidence Romania CFT and also from Merrill's boundary unitarity argument so it's UNITA you all the way through if you consider all the observables and I'm not claiming I know what those all are all the observables accessible at the boundary they evolve unitarily into themselves I'm taking down as an assumption based on those arguments that I find pretty compelling at least a provisional assumption the paradox arises from the apparent contradiction between that assumption and the applicability of local quantum field theory bulk but did they write that some local facilities up a couple right it also is here around the horizon which is why we have to introduce a firewall the horizon is just like any region over here it's it's not quantum gravity originally I I don't think anyone would have proposed a firewall if you had an object with one pair created and one goes in and one goes out I think the right that's the amazing ability of black holes to turn otherwise intelligent people's minds too much there's no contradiction with local quantum field theory I just explained over here and there is no there's a contradiction with local quantum field theory in that picture that's the process that happens all the time in quantum field theory like you described it in terms of something about atoms the contradiction is that this quantum has to be entangled with something at the boundary and at the same time entangled with this that violates the monogamy of entanglement you can see why I haven't convinced anybody yet the one comment I thought I should add about what might underlie was a resolution to fully appreciate like you might think I think Carla was getting out a little bit this could be a very semi-classical picture a small perturbation of the MP yes but I think I'll okay but that I really think there is no we should resolve the problem here there has to be something subtle here as well what subtle thing is to remember the vacuum that was the thing bekenstein for God to think about let's think about it again once we turn on gravity and implement fully diffeomorphism invariance the vacuum is a very different thing even if the space-time looks very semi-classical every vacuum fluctuation that we have quantum field theory is now dressed by its gravitational interactions and so and it's done in a way somehow described by this wheeler de Wit equation so there's something extremely non-local time together vacuum fluctuations everywhere in the space-time of the gravitational degrees of freedom as well as the matter that I'm drawing a picture of here and I think there's some kind of redundancy of encoding of the information so that it is somehow true that we can violate quote-unquote the monogamy of entanglement of course we're not going to violate a mathematical theorem about tensor products and so forth but once we phrase the question in a physically meaningful way I eat a few morphism in variant way it will be possible to reconcile the two statements because the information is in more than one place in the state if I will argument can be phrased without any reference to T V by talking about the entanglement between literally talking quanta and they move like that and something inside yeah you can just think of the Hawking point of kind of like far away but not an infinity yeah yeah I would say that's not the version I accept exactly so exactly so USA so you're saying to do that you have to assume that the three in two spaces and Fuli the spaces it takes some of these three and they will you either glacier to tell us that this nowadays good yes and also it's only the boundary unitarity that I believe that I don't believe that the Hawking radiation collected somewhere in the space-time have to be pure that's not what boundary unitarity tells me exactly look Gary let me just point out something sociological that might motivate you to consider doubting your conviction a lot of people and extremely smart people much smarter than me have worked on it very hard trying to reconcile this and gotten absolutely nowhere and it's clear that they're missing something really basic and what I'm proposing is what they're missing the problem is being formulated incorrectly let me just leave you agree with you that I think your comment about the wheeler do it constraint and and what it implies about the vacuum of quantum gravity I think is very important and it's not being taken into account and the fact that things are more non-local than people counting I think that could very well be a key to understanding the puzzle I just am still not agreeing that you can capture everything with the diagram on the right that people are worried about but I think you know what you're proposing as a solution could well be important for solving the problem that everyone agrees is a problem right I think in the end the solution would speak for itself [Applause]

Channel: ERC PhiloQuantumGravity

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Length: 101min 0sec (6060 seconds)

Published: Thu Dec 14 2017