Quantum mechanics and the geometry of spacetime: Juan Maldacena

thank you very much our final speaker this afternoon is Professor Juan maldacena from the Institute for Advanced Study in Princeton professor maldacena discovered something called gauge gravity duality or the a DSC F T correspondence which really revolutionized our understanding of string theory it has dominated work in this field for approximately the past 20 years presser maldacena is a member of the world Academy of Science as well as the United States National Academy of Science and he's going to talk today about quantum mechanics and space-time oh thank you thank you very much so it's a great honor and pleasure to be here in yeah I'm not it's a great pleasure to be here and I hope let's see okay very good so I'll be talking about quantum mechanics and the geometry of space-time so we've heard many times that general relativity produced two stunning predictions the first one is black holes and the second is the expanding universe and these predictions were so surprising that I think himself was surprised by them and refused to believe them in some ways so I love this phrase that Einstein is supposed to have told the Metra he said your math is great but your physics is dismal when la Mettrie was trying to explain the expanding universe to Einstein and I love it because that's often what physicists tell string theories now now in both cases the both cases these predictions are surprising because they we a drastic stretch in your space and time or time are involved now if you want to incorporate quantum mechanics into general relativity there is a very simple approach which is to say you have general relativity general relativity is a classical field theory and then we ought to quantize this theory now it is hard to change the shape of space-time so here the whole earth is babe barely changing the shape of space-time around it and so for most situations we can think of quantum fields in a fixed geometry and that's usually a good approximation and we can consider it even gravitons on that fixed geometry and this leads essentially to the to thinking about what the quantum version of general relativity as an effective field theory and this is a good systematic Logan approximation and it's good for low low energy questions but it's not valid for all questions I mean it certainly fails for the beginning of the Big Bang for example or the interior of the black holes but it can answer some this simple approach can give also surprising predictions and there are two surprising predictions of this approach and the first one is that black holes have a temperature so the temperature is proportional to one over the size of the black hole so if we start with some big black hole and we make it smaller and it looks he could look red and if we make it even smaller could look white so we can really have white black holes so we have if you so in this sense they are surprising even the name is wrong okay so if you have a black hole whose size is of the order of the wavelength of light you would see it white now the second surprising prediction closely connected to the previous one is that an accelerating universe also has a temperature so formula is very similar so that preacher is proportional to one over the size of the apparent horizon in this universe and both effects are proportional to H bar so they are quantum mechanical effects and this and they basically have the same origin as we'll see in a moment in a moment and this second effect so the first effect is predicted theoretically but hasn't been observed experimentally because the black hole's that are producing nature are very big and have very tiny temperatures which are not experimentally detectable however the second effect as we'll see is very relevant for us and what makes it relevant is the theory of inflation so this is the idea that there is a period of almost constant acceleration in the very early universe when the universe is expanding with constant acceleration and in the classical theory this produces a very large and homogeneous universe so we had just classical general relativity coupled to the scalar field that produces inflation we would produce perfectly homogeneous universe however quantum fluctuations lead to the give rise to those damp to the temperature or the temperature which is the same effect give rise to small fluctuations and these small fluctuations are the fluctuations we see in the CMB and are the fluctuations that are the seeds for cosmic structures like galaxies and so on so we see that quantum mechanics seems to be crucial for understanding the large-scale geometry of the universe and certainly the theory of inflation including this mountain effects is the best theory we have today to describe this logical structure so we often think that quantum mechanics is important for understanding the geometry at very small distances but even if we ask the question of why the geometry of the universe a long distance is it is what it is we see that we come back to understanding the interaction between quantum mechanics and geometry okay now since this effect of the the temperature the hope in temperature or the temperature in the sitter space is so important I thought that I would just give a short description of how it arises so it's useful to consider first another problem slightly different problem so we consider just Minkowski space with a simply flat space and we try to look at flat space from the perspective of an accelerating observer to imagine you are an observer following a trajectory with constant acceleration right so we are there with a rocket let's say moving with constant acceleration and this constant acceleration measures some time and the operator that generates these time translations is the boost so in order to go from this point here on the trajectory to a later point on the trajectory that simply corresponds to a boost around the origin so a Lorentz transformation around the origin and if we if we take this time translation generator and we continue it to Euclidean time as we often do in order to think about the preparation of the quantum state and so on then we find that the boost becomes a rotation so if we take the same picture and we go to we make this time coordinate the time as seen by the accelerated observer we continue it to Euclidean time then we see that that time translation corresponds to translation around the origin but the interesting feature about this is that this this rotation is periodic so up so we start rotating around direction and we come back to the same situation and we know that if we take a quantum system and we consider it in Euclidean time with periodic Euclidean time that's equivalent to considering the thermal and sampler we consider in a thermal state and then we get a temperature which is proportional to what the inverse temperature is proportional to 2pi arts so the physical size of this circle and this is an effect that was first discovered was found in this terms by V Sonja and Whitman but who really realized independently that it meant that an observer who's accelerating would actually see this temperature measure this temperature if we had a thermometer so that's a physical effect and this this effect has one surprising aspect which is that we started in quantum mechanics on a state that was just a unique state the vacuum but the accelerated also accelerating observer sees the state as a mixed state so as a thermal state and so on this arises because the accelerating observer has access only to the right wedge so he can only receive signals from this well he cannot certainly not receive signals from this side of the space-time and so there are parts of the space-time that he cannot see and and the fact that he sees the temperature is related to the fact that the vacuum is a very highly entangled state so if you there if you start with the vacuum state so that's a pure state but if there are some degrees of freedom some quantum degrees of freedom that you cannot see and you only see parts of the degrees of freedom then if you have an entangled state then that part of the degrees of freedom could look thermal could look like a mixtape now going back to the black hole case so we can imagine a black hole that forms from collapse for example we often in order to describe black holes and their associated geometry we use these diagrams which are called Penrose Carter diagrams and they basically represent their little map of the space-time geometry the vertical Direction corresponds to the time direction and the horizontal Direction is the radial direction for example and then we have some spheres that I'm not drawing explicitly and here in these diagrams the metric of trace time has been rescaled but we preserve the fact that light rays move at 45 degrees so any time like trajectory will be a line moving vertically at not more than 45 degrees so when we have a black hole there are some regions of the space-time that cannot send signals to the outside so for example if we have an event here in the interior we will send the concent signals but those signals will end up at the singularity and will not make it to the outside so if we stay outside the horizon so let's say we're an observer who states outside the horizon at the fixed distance from the horizon we'll have to accelerate in order not to fall into the black hole more or less very much the same way that we are accelerating here but not to fall into the earth then will be somewhat similar to that sorry the geometry near this region is very similar to the geometry we had in Minkowski space and for that reason this observer will see a temperature and that's basically the physical origin of the Hawking temperature now the fact that there is a temperature for black holes which came from special relativity near the black hole horizon together with quantum mechanics plus the relationship plus Einstein's equations which imply a relationship between the size and the mass of the black hole and then we can use the first law of thermodynamics to define an entropy so this is just the the equation we use to define the entropy we can then calculate by integrating this we can calculate the entropy and it turns out that is given by a very simple formula given by the area of the horizon divided by H bar G Newton so here we see that as we send H bar to 0 we get the huge entropy so the entropy is infinite in the classical limit in addition the entropy defined in this way obeys the area obeys a second law so the area of the horizon increases so this had been proven before by Hawking before the temperature was discovered and so we see that that fact that comes from classical Einstein's equations translates into a Kazan interpretation as the increase of the entropy so this gives an interesting relationship between Einstein's equations and thermodynamics so we see that in some regimes Einstein's equations have the same implications of thermodynamics and reduce the thermodynamics so it all this formulas suggest that if we view the black hole from outside then relativity is giving us a thermodynamic or approximate description of the system if we say outside quantum mechanics suggests that there should be an exact description where the entropy the fine-grained entropy does not increase as seen from the outside and where hawking radiation is pure so it's not it's not mixed that it would be mixed only if we make some approximation now also if we think about the black hole that forms and then it evaporates by emitting Hawking radiation then we would start with a situation where we form a black hole and then we end up with radiation and that looks similar to a scattering process where we send something in and something comes out and the general rules of quantum mechanics implies that this transformation should be a unitary transformation there should be no information loss so that also suggests that there should be such a description now I would suggest that the fact that general relativity implies that there is the second law such as that information is not lost I mean if it were true that the interior of the black hole should be thought as a second asymptotic vision then there is no reason why the second law should hold if you stay outside the horizon so suddenly that would not be true if we just keep part of the system so we only consider this room and then some air comes out of this room you can carry entropy and the second Oh doesn't have to hold inside the room but that's not the case when we remain outside black holes so the second law continues to hold if we include this gravitational contribution to the entropy so one wonders whether there is some way of describing this in a way that respects unitarity from the outside and that we need to one we need to identify the degrees of freedom that give rise to that black hole entropy since the black hole entropy depends on gravity so it came it's given just simply by this term a nice geometrical formula Pakistani Hawking then it implies that if we manage to identify this degrees of freedom this will be the degrees of freedom of quantum gravity and so they should remain somehow something about the structure of space-time and then in order to find the unitary description we should also understand the dynamics of this degrees of freedom now doing this is something that quire's going beyond perturbation theory certainly be definitely beyond gravity as an effective field theory and so for that purpose we turn to string theory and so string theory started out defined in terms of a perturbative expansion as ed explained and that perturbative expansion doesn't have they would travel eight problems that the perturbative expansion in quantum field theory has and however for the black hole problem we really need to go beyond perturbation theory and it turns out that string theory contains some interesting solitons which are called d-branes and the solitons thinking about the solitons led to inspire some non perturbative definitions of the theories in some cases so first it was through something called matrix theory and then also the gate gravity duality so I'll describe in more detail the second example the gate gravity duality so the gauge gravity Drollet is a kind of bridge that relates to theories of physics one is the kind of theories we are discussing theories with a dynamical space-time a quantum mechanical space-time for example string theory or quantum gravity theories and on the other hand we have a quantum field theory or theory of quantum interacting particle so conventional quantum field theory and the simplest examples use consider gravity in an asymptotically anti-de sitter space space which has constant negative curvature and the sitter spaces is essentially like hyperbolic space so hyperbolic space is the simplest negatively curved space it was the inspiration for developing non-euclidean geometries the first one of the first examples of non-euclidean geometries and we call anti-de sitter the version of hyperbolic space that has one time like direction and so in this duality in this relationship what happens is that in the interior of this space we have quantum gravity so we have the quantum mechanical version of hyperbolic space or the simply you can view it as a simplest example of quantum gravity in the same way the hyperbolic space was the simplest example Oh third space curves a curved space and so here in the here we have one like dynamical gravity and on the boundary we have quantum field theory theory of quantum interacting particles and this is a valid in the sense that we could either think of the theory defining to deteriorate or in terms of the boundary and the battery lives just purely the Valerii theory the punter particles in fewer in the boundary and so then from that point of view the radial Direction is an emergent direction and the whole space-time in interior emerges from this dynamics is available some features of which we'll discuss later now the argument for which the argument that these two things should be related it was based on this difference that conscious we can discover the Zebras are some solid solid objects that carry some have some tension that you could think of them as membranes stretched in space-time they carry some tension and some charges and if you put a large collection of this price you they will curve the space-time around and you can calculate how the curve the space-time around using Einstein equations that leads to certain black brain geometries so these are generalizations of black hole geometries and the geometry to get a very similar black holes now for since it had to give in a very precise description of how to think about this difference in string theory I want to take the low energy limit of that description and we get certain super symmetric version of quantum chromodynamics and four dimensions it comes from the excitations on this disgrace and the near horizon geometry of this reference is a certain context interspace and since we certain in ten dimensions we also have a cart sphere and so we get stripped here in a very specific space now here I've given the name specific names of these theories very precisely but there are relationships like this many other cases now this gives a relationship between large n gauge theories and strength and this relationship has been anticipated by but though and it's based on the idea that it blew on carries a color and an anti color and you could consider an alternative theory where instead of having three colors that we have in ordinary fans of quantum chromodynamics we have n colors so more mathematical is the gauge group would be su n step and then we take the Guardian limit we find that the interactions between the effective interactions between a particle so we can consider states where the colors of one moon tangled or same as anti color of the next and he substrates the interaction between such correlated colors on at the colors is very strong while the interaction between colors that are not related to each other is relatively weak and in this way we by taking the large n limit even the effective interaction between correlated plus strong then we form this change so the elementary skeptics will be changed in this space of colors and that should behave essentially like strings in some in some space that was the arena and so this cloth strengths are what you CD will be called glucose objects made through a fury of the floor and the string coupling is proportional to 1 over the number of colors I have to mention that this ideas are based on an experimental observation which is just that we find these trains we find some hand strains in chromodynamics and the best evidence for funding credible evidence for this trains coming looking at the spectrum of Messrs in promoting events so we find this linear relationship between the mass square of the mesons and their spins so these are some elementary chronic particles from interacting particles and this linear relation can be explained very simply in terms of a rotating spring model where that rotating spring one predicts indeed that there is great the mass square of the particle and spin by over ha the constant which is the tension of the strength so I only search has to note that these strengths that are made of clothes are certainly observed in nature and the there are at least explain I similar to the strengths we think about in in string theory we think that this frame should correspond to the particular strength of chromodynamics should correspond to strings which are very similar to elementary strings with having implemented string theory except the living on a curved space a space that has one more dimension and in the particular case of n equal to 4 super-yang-mills which is a particular super symmetric theory of quantum chromodynamics then we can find precisely which strings those are and they are basically the strength of 10 dimensional spring theory now as we can explain T when the we consider space which is weakly curved then with the curved means that the radius of curvature is much bigger than the typical size of the string of an oscillating straight the typical size of a graviton viewed as an oscillating strain then straight here reduces to gravity so when this is much bigger than 1 the strength irritability strategy now that's how that in this type of wallet is the size of the Rays of curvature in terms of the size of the strain is proportional to the effective interior coupling so the coupling between this gluons that are for a correlated and so straight to some positive power so if we want to have a radius of curvature much bigger than the size of the string so that Einstein gravity is a good approximation then we are talking about the quantum field theories which are very strongly coupled in addition the Newton constant related to the straight coupling goes like one over N squared we also need a large their hand so large number of fields and also stronger so we need these two conditions you know north to get Einstein gravity in the interior now one interesting aspect of this relationship is the emergence of this extra bulk direction with its dynamical gravity in the interior and one simple cartoon picture for how this extra dimension emerges is the following so you can think of the boundary excitations as little drops so that this the feet here and the batter is typically scale invariant theory and so you can have blocks of different size so in order to specify the an excitation on the boundary theory we not only have to give the position in space but also the size of that excitation and since the theories scale-invariant has those sacral clocks can have different sizes and the blocks with different sizes are related by symmetry in the fields so they should have intrinsically same characteristics and we realize this in developing not by saying that the Red Rock here is some particular some strange involved and the blue one is exactly the same one but displaced along the extra dimension so we get the picture where okay so it's not working oh it's not working sorry okay given that I could be effort to do this so we have some objects here in the vault which can be doing their own thing and they are represented by very strong interacting particles here on the boundary here this picture doesn't represent the fact properly that we mean the last number of particles and very strong interactions so we can describe drag holes in the interior which corresponds to again a large fluid or very strongly graphene particles here the blue dots to completely fill the boundary in a very unison way I just ran out of patience going well this is the gamma carton picture how we use the black hole from the Vander thermal thermal because particles were through the proper cost-savings a gasifier is not a good idea because it really doesn't reflect the fact that they are very strong interact she's a very strong injecting fluid of particles in the batter and we can calculate the entropy as well in two ways one is the area of the horizon using the Hawking that Einstein formula and also we can calculate it as the number of states of this fluid in the boundary theories for the fluid and the boundary here is the thermal state that has many different microstates and by counting those microstates we can reproduce in cases where we can count them in the strongly capital Theory we can reproduce the host and formally and here the picture is that an ultra volume to the black hole would be a perturbation of the boundary Theory does eventually thermolysis with the rest of the crew now one this relationship has also met one interesting relationship to hydrodynamics so we said that the filter at finite temperature should correspond to a black ring in this curve hunter de sitter space so we can consider venturi the same flat space and the black hole is a black hole which has an extended direction sometimes called the black frame and we can consider long-distance ripples on this black brain so small deviations from the just straight black brain and this higher this represent this correspond to the tidal dynamic mode from this Floyd just correspond to small deformations on this proof since this fluid is exist in a theory which is translation and boosting barium we can make we can give it a small velocity of the fluid in one region and a different velocity far away and this creates a perturbation that eventually will dissipate and will form again a uniform flow ISM and so what is dissipation in the boundary theory and formalization corresponds to absorption of this way to use this way outside the Rice's that falls into the black hole and this way we can calculate transfer coefficients such as the viscosity using wave equations on this background so complicated problem in strong and rapid 150 relating these transfer coefficients translates into a simple problem of solving wave equations from this geometric pattern and what can one control is people have shown that Einstein's equations in this limit reduce to the equations of hydrodynamics first relativistic hydrodynamics where you can also take the the number of used equipment and find that really also reduces to navier-stokes equations when the velocity fluid is much less than 1 and this picture has been useful to discover the for the discoverer of the role of anomalies in hydrodynamics it was found that when one prior to compare the Aston equations to the questions you get in hydrodynamics they didn't match so there wasn't a match and it was in the match because the the equations of callable dynamics were not the correct ones when we have anomalous global anomalies in the theory and then then after understanding what goes on in this examples of how gravity was then the this anomalous hydrodynamics could be understood in conditionally even in cases which did not have a gravity do so this is an application of using Einstein gravity events answer questions to learn something about the different field of physics say like the field of physics of hydrodynamics so using this you can form a black hole and predict what comes out using the boundary theory so assume the duality you get evolution from the outside observer and no information loss I said here consume the duality so one can ask how well-established is a geography presently so there is a lot of evidence in the simplest examples and also a lot of complicated examples and further evidence and in the simplest examples the four large and one can use the techniques of integrated and one can do computations at any value of the effective coupling and one can see how this change of clothes which are going to the description of wit coupling get transformed into the strength moving in ten dimensions this has been shown in an enlarged series of papers by many authors but we still don't have explicit change of variables between the four description and the boundary description the one I think a complete understanding of the this relationship would be to find an explicit change of variables between the description and the battery theory in the description interior much in the same way that we have a let's say put a transform that allows us to change the wave function of position space to momentum space for example so we are not there yet however the meantime one can use these qualities and one can turn black holes into a source of information so because and these words because strongly coupled 50 problems translate into simple gravity problem as we have seen for the case of dynamics before and this has been used for heavy iron polish for modeling heavy on collisions for trying to understand high-temperature superconductors etc has led to an application of geometry in the techniques of geometry and relativity to other connections to other areas of business so rather than describing this application support ticket one would ask the question of why should strong coupling simplify the problem is there any other example in physics where having a strongly coupled system actually leads to a simplification so an example is imagine you had a gas of particles and you want to describe the dynamics of discussing progress in terms of hydrodynamics you know for that to be successful you need some you need strong interact strong enough interactions to locally thermalize discuss so if you can see R interactions for very weak interactions then you will need to use the Boltzmann equation which is more complicated than tell dynamics now what we think is going on in gravity or something very similar so there is a gravity should somehow be the dynamics of entanglement now I have no idea what this means this is a team that is currently being explored and which since we have something something of true food now the next business crisis I press explain why I'm saying this so and so these are more completely understood in context so first point is the following so the local the basket founder experience is a local point of injury local means that there that really at the very top of the theory you have local qubits that defined locally at this point in space we have some set of qubits and another pump in theory the bathroom is as we to the Hawking radiation or even the case of rinder radiation for an excellent view of server is a highly entangled stay and so if we have all the qubits in the boundary theory so here I've drawn just a few of these qubits so they're all in some quantum state highly correlated between the different ones this motion is just trying to represent the fact that if we restrict attention to let's say the prohibition then we'll see these qubits has been in a mistake so they've not been a pure conquered step that they will be in a mixed day and one can calculate we can quantify the degree of mixture of how many might be from microspace we have by calculating the entropy so associated to the density matrix with which we will describe that mixtape so that roughly speaking is the amount of this entropy the amount of disorder that we'll see in this set of qubits if we only restricted the attention to these qubits starting with the vacuum state and we could do this not only for the working but for any state and if there is a gravity the world that entropy can be computed in a simple way by calculating the area of a minimal surface which ends on the boundaries of this vision at the boundary so this is the formula which is very similar to the Hawking bekenstein formula and it's a substantial general session of the Pope in Pakistan formula for situations where we don't have clean infected so we see this connection between entanglement and geometry so the entanglement pattern in the state of the boundary Theory can translate into geometrical pinches in the interior so what I described in the previous transparency was the particular case of the vacuum where we have the perfect hyperbolic space in the interior and this is just one of the hyperbolic space logistic surfaces but if we were to change the topic to another state that would be at stake with a different geometry in the interior then the shape of this curve will change and the amount of entanglement will depend on the geometric features of that statement interior so we see that space-time is closely connected to the entanglement property to the fundamental degrees of freedom so there is a slogan which I also don't understand somehow the determinant is the glue the whole space and together and just to illustrate this and try to describe perhaps the most extreme personal taste and this would take us first the description of a certain space time which is the two sided partial solution so this space-time which essentially the space-time that's right well um just months after the discovery of general relativity except that he founded in coordinates which got some coordinates which are goes outside in this region so this we should represent so here far away we have flat face flat Minkowski space and this surface here are the horizon of the black hole so R equal to zero in the shorter well are equal to the are but is the place in the interaction solution where the time time component of the metric Washington to zero in the first original Russia coordinates it was later understood that you can continue that metric reverse the interior Eddington I guess was the first one to write the coordinate system though he apparently didn't realize to subscribe in the interior the matter was the first one to say that you could go to the horizon and Canon gross and realize that this if you take just this surface you can continue this surface and through the horizon and into a second side where you have a second asymptotic region a second asymptotically flat space station and then eventually crew Scott gave us this cool picture of extending that original solution in the maximum possible way so that we get this solution so we have vacuum everywhere that's the simplest spherically symmetric solution of Einstein gravity so we have Einstein gravity is our theory of general relativity relativity and this is the simplest straight Ally symmetric solution if we have a black hole that prompts for matter as we saw in the bank of diagram we had the core we only get the right part of the distribution so only a portion of this diagram however we can still ask what is the interpretation of this solution was interpretation of this simplest we have nothing right now that simpler solution in asymptotically class space as I complete a level in anti-de sitter space so in this curved spaces that were discussing so again is a classhole' to this part of the solution corresponds to a black hole in anti-surface face similar black picture that we saw before of the anti center space with a black object in the center and this again has a second side and a second family a second distribution in this case we can make a little more precise statement of what in how how we should describe this so recall that before we said that the black hole is at a mistake in the context of under theory that's a black hole seen from the outside and that looks like a thermos take here but the idea is that if we have this food geometry now we have two boundaries we have the left boundary and the right angle so we have to separate the filthiest two separate non-interactive in series and it is a determination correspond to a nintendo state in these two years so we have set of plates on the right here in a set of states in the left theory and we form this particular entangle state called the thermal fin double it was considered for different reasons when thinking about thermal filters and this then it should be the state is the pure state in the new school in the keeper spacer which is the product in your faces pictures and that's what described this geometry but there's a good argument that this should be the case that is disputed by somebody's so here we see that we have a geometric connection between the left hand right hand side that doesn't derive from the dynamical connection of the phenomena the you freedo but it's a rising purely because of the antenna so so here similarly the short resolution should give you this entangled some kind of and the black hole to dilute the space-time this isn't hard to think about so still taking all that to think about the closely related situation where we have two black holes but not living in the same space-time where we have two black holes and they're identified for interior so these are two black holes that are shared share in the interior now become two black holes in nature they will not be inscribed at this geometry was going on an interior but this is a geometry which we could consider and this geometry looks like a wormhole so if you are you can have this tool across very important rather than this galaxy the other in another galaxy if you are one meter outside this black hole and they said your friend is one meter outside a black hole the distance from the outside could be millions of light years but the distance truly a special distance could be just two meters now if you plan to enter the horizon and go and visit your friend then you would start you start out from the outside and you would try to visit your friend but you find that this crisis starts moving away from you and you let that end up at the singularity and you will not be able to go to the other side which is a good thing so these solutions which are natural solutions to general relativity and do not lead to a violation of the principle of general relativity which is that know that no signal stenographer likes the ambient our West will have some confusing situation so the equations of relativity themselves do not allow us to construct the professor with wormholes which i think is an important physical principle so these are not the wormholes of science fiction well this this market however can be arranged to produce a forbidden meeting so imagine there are two people whose families want to keep apart they somehow they're sent to different galaxies in the first chamber but they somehow manage to arrange to produce a blast with a pair of black holes in this particular and understate so they can do is the two black hole share interior they can both jump into the respective black holes and actually meet in design but this the people from the outside we shall see them committing suicide because he should drop into the respective drug laws and then but they actually met inside but they cannot tell anyone outside so this suggests a correspondence between these I can cross and bridges of wormholes and entangled entangle States and so in this particular case of the wormhole we want to interpret them as an EP a pair of two classes in a very particular entangle state so we see that large amounts of entanglement in this particular case can give back to genetic connection but we think that this might be a more Jeannette marginal property of quantum gravity and which one can hold is erep our correspondence relating to papers that - and Rosen wrote one below scheme but they both actually these two papers in the same year and one can complicate and a movement pattern of the two sided back hold and get a salad or from the raw code used in salad by several people now the black hole interior is not completely understood in the central Dakota's how to describe the black interior from the point of view of the boundary theory even whether we can do this so general relativity assembly tells us that black holes should have an interior but channel activity doesn't tell us why the exterior here is unitary their hand is bothering descriptions tell us why the exterior is unitary but nonetheless whether this is actually an interior there are some paradoxes that arrives in some night constructions as pointed out by Matthew and Mary Mary for instance over and this is really an active area it's been explored and there are many ideas for what to do with it so there are many ideas that people are cut suggested and some maybe some of them are wrong maybe the correct picture is to combine all of these ideas in an internet or current fashion so we think that quantum mechanics in curved space-time gave rise to interesting effects Hawking radiation and the emergence of primordial inflationary fluctuations live effects are crucial for explaining features of our universe and Garko thermodynamics poses very interesting problems so understanding the entropy the unitary Eocene from the outside understanding information problem understanding the interior and we hope that exploration of this program will lead to well expression this Roman Catholic - connections between strongly Captain Planet and fin theories and gravity and it also has led the practical applications of general relativity to other fields of physics so people who are interested in superconductors for example sometimes write down Einstein's equations analyze models and so on we've seen that patterns of entanglement seem to be closely connected to geometry and the swinging of the work in this direction which I haven't been able to review but this one of the very actively explored areas and I would say that the Blackwell interior continues to be a fastening problem whose resolution with draaga give us new insights into the structure of space-time and not only that but probably understanding fully this problem will also lead to understanding of cosmology because after all the interior of a black hole looks like a collapsing cosmology so probably understanding properly would also lead to understand as much well thank you very much thank you very much well that concludes this special session I want to thank all the speakers for their excellent talks unfortunately one event Penta whadya and the other organizers for arranging this wonderful celebration of the Einstein Sentinel

Channel: International Centre for Theoretical Sciences

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Id: vB5_GYobc8g

Length: 48min 25sec (2905 seconds)

Published: Wed Jul 01 2015