Inside Black Holes | Leonard Susskind

all right first of all I honestly don't have much idea what I'm doing here Joe asked me Friday afternoon to do this and I said no I'm going home for the weekends you're going to spend the pleasant weekend with my wife we're going to go to the theater I'll have absolutely no time to prepare he said it doesn't matter for these people don't worry about it a little matter so number one I'm unprepared number two I don't know who I'm speaking to I see in the audience a bunch of my my black holy friends but I assume I'm going to I'm going to ignore them completely I was told this maybe a biologist or two here is that right and an astrophysicist I don't know okay so it's a it's a mixed group which is fine that's good and the last thing is quite frankly I thought we would be sitting around the table is a lunch thing you know food sitting around a table like we do in Stanford in a civilized way and one person who stands up in talks while the others eat lunch I did not expect to be in an auditorium or giving a lecture so let's start and it would be very helpful if you ask questions because I'm like a wind-up doll you I wind up with questions and then I like to answer them but I'm going to begin trying to tell you why my friends and I are joined together here to explore a set of questions which has come up I would say about black holes but to say it's about black holes is much too narrow it's much too narrow what we're addressing is a problem which has been around for close to 100 years a problem of how to synthesize or how to put together quantum mechanics and gravity it's been a for a good number of years there was very little the subject kind of exploded with the advent of Hawking's and beckon Stein's discovery of black hole thermodynamics and I'm going to tell you a little about that but I'm also going to try to tell you exactly why we're here to explore a certain paradox um paradoxes are very interesting in fact it's generally the way forward when you simply don't have anything else when you have no experiments when you have no empirical data but you'll have a set of concepts and the set of concepts clash when the set of concepts clash then you may have something to learn light traveling at the speed of light and every frame of reference Adam's not decaying down to the point where the electron falls into the nucleus quarks not getting out of the out of the proton and neutron the cosmological constant being a hundred and twenty three orders of magnitude smaller than the start of life our life forms all these are paradoxes sometimes they're really clashes of principle and that's when we stand to learn something really new and really exciting that's hopefully what's going on now now whether we'll be smart enough to crack it I don't know ah whether we'll all discover perhaps that we were making a foolish error no no whether we would discover that joke polchinski was making a foolish error I don't know I don't think so no I don't think so I think there's a big paradox the big paradox will get solved my guess is the solution will be that we were going on the right track before the paradox but we were missing something enormous some big huge piece of the story and that we have a good chance to learn it now so what is it all about well it's about quantum gravity and the first I want to say is that you should not think of quantum gravity as being quantizing gravity quantizing is a an operation that we do are known classical theories we take a known classical theory we invent some hocus-pocus called plus own brackets and possum bread the formula there's a rule is a set of rules they're act invented them that has gotten us nowhere with quantum gravity it's gotten us almost nowhere almost nowhere at all and it's probably because quantum mechanics and gravity are linked in a much much tighter way joined-at-the-hip as they say in a way that doesn't allow us to separate them of course we can study classical gravity there's no doubt about that but some of us are beginning to feel I think probably everybody here that quantum mechanics and gravity are joined in a much much deeper way in an inseparable kind of way and that it doesn't really make sense to take the classical theory and just apply to at the standard rules well if the standard rules aren't helpful and if and if there's no experimental data all we can do is explore these paradoxes which come up now and then most of the paradoxes have been about black holes why black holes what does a black hole have to do with quantum mechanics anyway my friend who I hardly know in fact there are I don't think I really know him anymore eastern Alma 1976 or a Freeman Dyson thinks that it's a complete waste of time to think about quantum mechanics and gravity in the same breath quantum mechanics is of course applica folk applicable for very tiny things gravity is apical for very big things why mix the two all together and of course the answer is it's just intolerable to have two theories which seem to clash and simply don't want to fit together it's intolerable for for curious people for people with the kind of itch that want to put the together into a into a neat framework a neat universal framework and so you know we're just obsessed with the question because we're curious about it that's the only reason as far as I can tell I don't think quantum gravity is going to solve the the climate change problem or the cancer problem or anything else we do it because because we're curious about it okay now why black holes black holes happen to be the place where quantum mechanics and gravity come together despite the fact that black holes are very big and very heavy the structure of the way that they contain information the way that they that they interact with the west rest of the world through radiation and other things is highly quantum mechanical and so black holes seem to be the natural doorway the place where we get really surprising really surprising paradoxes from that we can explore in hopes to learn more about the connection between quantum mechanics and gravity that's the point all right so let's let me begin about black holes with some tension that was already there in the classical theory of black holes it's not a real paradox but it's a bit of tension so let me show you what the tension is the tension has to do with the difference of descriptions from outside the black hole and from somebody falling into a black hole here's a black hole what I've drawn is the horizon of the black hole and the horizon of the black hole is a place from which on the outside somebody can shoot radiation or something else can shoot things out which which will escape and the inside is the place that gravity is so strong that anything you shoot either in or out will wind up at some nasty singularity at the center we don't need to be more precise about it than that it's a dividing line it's a point of no return anything that falls through is trapped anything that is outside has a chance to escape now the property of clocks and measuring-rods get very distorted near a horizon in the following way you probably all know this but let me just remind you that if an object is falling into a black hole from the perspective of the outside from the point of view of coordinates which are built to describe the outside of the black hole what happens is the object asymptotically slowly approaches the horizon now this is because clocks slow down in a funny way near the horizon nothing is observable about that slowing down of the observer flowing in the reason is his clock slowed down his heartbeat slows down every internal clock that he has slows down so this is nothing but his comparison with outside clocks far away watching him is such that first of all he asymptotically slower and slower and slower and slower approaches the horizon and at the same time Lorentz contraction takes place so after a long time this blob over here this is all classical metal becomes a thin little blob asymptotically approaching closer and closer to the horizon in fact not only will that observer be I was I was going to say stretched out stretched out it's not quite the right word classically just plastered against the horizon like this but everything that ever fell in to make the black hole has exactly the same property it's all contained in infinitely thin while not infinitely thin but progressively thinner and thinner shells that approach the horizon asymptotically livor quite getting there takes an infinite amount of time from the perspective of the outside observer for anything to get to the horizon so in a sense nothing ever gets there and our description of the black hole from the outside should be then a shell called the horizon inside of which there is nothing that will ever be important to us because from our perspective nothing ever fell through and all the matter that ever fell onto the horizon is in this progressively thinner way the filler that's a kind of sediment sedimentary structure that just Falls toward the horizon never quite getting there now there are two things which are infinite first for a classical black hole the first is the time that it takes for anything to get to the black hole surface and the second is the amount of information that you can hide in this thin sedimentary level in this thin sedimentary structure that just approaches the horizon there is no limit classically on how much structure of this kind you can have at the horizon of a black hole structure I mean information bits of information bits of information and classical physics can be encoded in arbitrarily weak signals of arbitrarily low frequency or energy of sorry of lob arbitrarily low energy and so these weak signals can carry any amount any number of bits any number of bits of information and so the hidden information at the horizon of a black hole can be infinite in classical physics hidden information has another word the word is entropy so in classical physics some people sometimes think that bekenstein discovered that black holes have entropy not at all what he discovered is that they don't have too much entropy that the amount of entropy that they have is in fact finite so we'll come to that a moment so those two things that are infinite the time that it takes to fall through the horizon from the outside and the amount of information that can be stored on the horizon all for those people look for those people who know about black holes is a familiar and a standard story for those people who don't know anything about relativity what I'm about to say next will be useless but for those people who are somewhere in between let me draw you a diagram to show you how it is consistent that it can take a finite amount of time to fall through the horizon for the infalling observer and yet an infinite amount of time as seen from the outside that I neglect to say I don't remember if I said that the amount of proper time that it takes something to fall through is quite finite that's the pension a finite amount of time that the infalling observer experiences falling through the horizon and an infinite amount of time as seen from the outside all right so it's a simple picture that will help that's Minkowski space why am i interested in Minkowski space because Einstein caught us the first thing you want to do when you want to understand gravity is understand acceleration understand physics in flat space in the accelerated coordinate system an accelerated coordinate system in Minkowski space looks like this these are the lines of constant position and the lines of constant time look like this it's a kind of hyperbolic structure this is an in falling reference frame time goes this way space goes this way and those are the formally accelerated a frame of reference now imagine oh this is T equals 0 this is T equals 1 this is T equals 2 T equals 3 that's not that I thought that until you get up to this line and that's T equals infinity a little bit odd now somebody falls through unless somebody moves along this turret direction here there's no horizon here there's no black hole here this is just flat space-time but how long does it take for this blue observer here to pass the light cone over well from the point of view of his own internal clocks it's clear it's a finite amount of proper time the length of this line is finite nothing special this observer falling through doesn't care about this odd set of coordinates on the other hand somebody's standing outside and staying outside involves accelerating you cannot stay to the left of this light cone without accelerating in the same way that I cannot stand on the floor of this room without accelerating accelerating means experience an exam acceleration I think Stein said if you want to understand gravity understand acceleration here we're trying to understand acceleration we have a funny situation if you stay outside this light cone and watch somebody falling through it takes an infinite amount of time on the other hand there's nothing infinite about the perceptions of a person flowing through so both are true both are true classically it was never regarded as a tremendous paradox it was just regarded as a curiosity this is the structure of a black hole geometry very near the horizon you don't have to know very much all you have to know is that the region back here maps to the region behind the horizon and notice that somebody who's out here can never send a signal to this side of this light cone that's equivalent to saying that something that falls through the horizon can never send the signal out any signal winds up going in and not out all right so that's that's the set up infinite time finite time infinite amount of infinite amount of information can be stored arbitrarily close to the horizon all right now as I said information hidden information is called entropy well he was in 1972 that Jacob I asked a very fundamental question somehow nobody had asked it before if a black hole can store an incident amount of information it just keeps collecting and collecting and collecting either think of it that way or falling into the black hole either way you'll have a situation which is somewhat like early quantum mechanics or before pre quantum mechanics in pre quantum mechanics the radiation field of a given amount of energy could contain an infinite amount of information it was called the ultraviolet disaster because each mode of the radiation field no matter what its frequency is can store arbitrary amounts of entropy what will happen classically is if you have some energy contained in radiation it will just migrate more and more and more into the ultraviolet modes whether it's simply an infinite phase space to absorb the entropy to contain the entropy same thing would happen here any amount of entropy that's in space here will just get sucked more and more and more into the black hole and if you didn't account for the fact that the black hole itself had entropy you would conclude that entropy was lost to the world it's not lost to the world it's absorbed into this infinitely thin layers here and it can't get out not without getting very close to the speed of light but bekenstein didn't like that it didn't feel right he suspected that somehow black holes are like anything else and have a finite entropy I'm going to take you through beckham Stein's argument because if I don't teach you anything else this is really one of the most beautiful Gedanken pieces of physics that I know of and it can be taught easily thought to to a physicist who doesn't know about black holes in fact it can be taught to a high school student that doesn't know calculus so I don't see any high school students that don't know calculus but you might take this home and explain it to your teenager why do black holes have a finite entropy and how much is the entropy and here's the way the argument goes let's what we're going to do is we're going to build up a black hole from scratch by dropping in particle by particle by particle and asking after we've built up the black hole to a certain size what's the amount what's the number of particles that we need to send in why particles in a simple situation a single particle contains one bit of information it's either there or it's not there well that's not right wait a minute that's not right if I want to build up a black hole by sending in bit by bit and a bit means one piece of information I cannot do it with high frequency or localized photons the reason is a localized photon has more information in it than just the fact that it's either there or not there namely it has information about where it might fall into the horizon so what you want to do to send in one bit of information into a black hole is to send it in in the form of a photon whose wavelength is so long that you can't distinguish where it passed through the horizon okay so let me write some simple formulas on the blackboard and you get the idea because it's very simple the first formula is the formula for the radius of the black hole in terms of its mass that's equal to the Schwarzschild radius and many of you have seen it twice the mass times Newton's constant divided by C squared that's why black holes are so small G is small C is big a black hole for a given mass the mass of a black hole of the massive sorry the size of a black hole and mass the earth would be about as big as a peanut that's what they see is that doing here in a small G okay so that's one formula next formula I'm going to start I'm going to imagine building up the black hole from a small tiny little thing by throwing in one particle one photon at a time one massless photon at a time but a mass a photon whose wavelength is about equal to R at that time why because I don't want that photon to have any information about it other than the fact that it fell into the black hole okay so the wavelength is equal to R how much energy does that add to the black hole well the energy of a photon is let's call it Delta e the change in the energy that's H Bar C over lambda now notice I'm doing quantum mechanics now H bar has come into it the change in the energy of the black hole due to sending one bit of information in is H bar C over lambda where lambda is equal to R what about the change in the mass of a black hole well we use e equals mc-squared so the change in the mass of the black hole will have two additional powers of C downstairs and the change in the mass is H bar over RC okay next step let's compute the change in the radius of the black hole we know the change in the mass so the change in the radius due to dropping in one photon the change in the radius is going to be two G over C squared times H bar over RC haven't even used any calculus yet and I'm not going through that's the change in the radius of the black hole adding one bit of information to it namely a photon was either there or not there okay let me clean it up there's a C cube downstairs and there's an R downstairs I want to get the are out of the right hand side that's easy to do you just multiply by our but R times Delta R is a familiar thing it's the change in R squared which is the change in the area of the horizon what's that oh you're right somebody's very quick yes indeed you need some calculus to know that R Delta R is Delta of the area now I have set everything under the Sun equal to 1 except the important point that I said 2 pi 4 PI I don't know the change in the area other thoughts have the change in the area of the black hole due to one bit of information is a universal constant it does not depend on the radius of the black hole doesn't depend on its mass each time you add one bit you add another unit of area to the size of the black hole to the horizon area you can write this a different way you can say the number of bits that it took to make a black hole of radius R and I'm going to call that the entropy of the black hole it's the number of hidden bits of information that s for entropy I don't know how I said we've got to be entropy but they're the entropy of the black hole the number of bits of formation is equal to the area the final area since each bit increases the area by this much then by this much then the entropy of the black hole is the area measured in this unit the 2 is not important here actually the 2 is important that it's not 2 but H bar G C cubed this trickles into the four downstairs are not coming from this argument coming from Hawking's a very sophisticated argument but this is the basic idea the entropy of a black hole the number of the maximum number of bits of information that you can hide in it and sending in photon by photon this way does maximize the information that you can get in there the maximum amount of information or the entropy of the black hole is the area in a unit which is the plunk unit ten to the minus sixty six square centimeters a very small unit event of area that was the discovery of second Stein and later Hawking put some some additional substance into it in fact what Hawking III I wasn't around I left I was certainly around at that time I was almost an old man at that time but uh but I wasn't around Cambridge when this was done or Princeton so I don't know exactly who figured out what and when and where but once a thing has both entropy and energy energy is its mass MC squared it has both entropy and mass it's going to have temperature I'll just remind you de equals temperature D s and if you know how the energy changes as a function of entropy or how the entropy changes as a function of energy then you know the temperature and what you find from a little bit of thermodynamics there's another equation the Hawking temperature T is equal to 1 over 8 pi and now I'm actually putting in numbers eight PI H bar and now I've forgotten where the C's go I don't remember anybody remember it's just dimensional analysis so if you're like me the speed of light is equal to 1 1 over H bars you have mass mass of the black hole the temperature goes down with mass down with energy that's negative specific heat hmm I usually do Thank You G the important thing to note well o all of it is important but the H bar is in the denominator in other words in the classical limit the entropy or the amount of the storage capacity of the black hole to hide information becomes infinite but quantum mechanics as in many other contexts makes things which classically are infinite makes them finite notice also that the temperature is a quantum effect the temperature would be zero in classical physics and the entropy infinite that is the description of a black hole from the outside from the outside a black hole is just an object with a certain energy a certain entropy and because it has a temperature it radiates it radiates blackbody radiation unlike the Sun which radiates with wavelengths vastly smaller than the Sun so you could use sunlight to resolve the Sun in the sky the black hole radiates with wavelengths comparable to the whole size of a black hole so if you try to look at a black hole with its own radiation it looks pretty fuzzy that's not why this thing is called fuzzify or is it it's not I don't think okay that's the description from outside just an ordinary thing a warm cooling thing just for some numbers incidentally the the entropy of a solar mass black hole I think if someone's up there 10 to the 70 if I don't remember exactly 10 to the 68th so it's that's that's big you can't think of anything else in nature that's the size of a black hole that would have anything comparable its temperature is very small or ten to the minus eight degrees or something like that and it's an odd object has some other amazing properties thermal eise's faster than anything else but that's okay the central question is if this is what well let's think about it for a moment what it's telling us is that this infinitely thin sediment and it's infinite capacity to hold information was not right somehow there's a finite capacity to hold information and one way of thinking about it is to say that you cannot store anything on a vertical scale here smaller than the Planck length that's basically what it comes down to there's a fundamental length on the horizon or just adjacent to the horizon and information cannot be squeezed smaller than that that's what this says of course another very odd thing is in almost every context where we think about entropy entropy in this room is proportional to the volume of the room not the area of the room that's kind of telling us somehow that there's nothing inside the black hole that there's just nothing inside the black hole because the entropy is proportional to its area on the other hand classical black hole physics also tells us that it's meaningful for somebody to fall through the horizon it takes a finite proper time and so now we are getting into paradox land the exterior of the black hole has a brick wall or a shell that nothing can penetrate through it on the way everything gets stuck at this this is called the stretched horizon incidentally stretched because it's a little bit bigger than the horizon it's called the stretched arisin and the picture is that a black hole is just a hollow sphere with absolutely nothing in it because it's entropy is proportional with surface area with some kind of microscopic degrees of freedom it could be strain theory it could be fuzzballs it could be who knows what it is but some kind of microscopic structure it's hot it has temperature incidentally you might think that is low temperature it doesn't the photons which come out here become red shifted as they go out that's why the temperature is so low is seen from far away but the temperature close by that same temperatures blue shifted and its enormous ly hot so that's our picture of the black hole from the exterior it took a long time to develop it it took a long time to develop it and get the ideas what I think is correct but in all of the studies of black holes in the land of black hole information so forth in the last 25 years or 20 years or so forth the emphasis was on this picture from the outside and people forgot to ask wait a minute how do we describe the infalling observer in this same picture the infalling observer one possibility is that the black hole really is just a hollow thing with nothing in it most not even any space-time in it in which case nothing could penetrate it that's why man but that's not very satisfying for the simple reason that Einstein's theory of gravity and this picture here certainly suggests that a freely falling observer would take a finite time to go through so the puzzle arose of how to reconcile the idea that things can be on the inside of the black hole planets stars whatever if the black hole is big enough things can be in there from the point of view of an observer falling through the horizon with the picture from outside that it's just this whole thing with micro physics on the outer boundaries that led to an idea which I think most of the people who work in the subject accept is correct an idea called the holographic principle I'm just going to state it very very briefly the basic idea is that this boundary structure out here functions as something like a hologram I'm not going to try to do better than that for this audience now with Juan is one well to say to here no he he knows all this he put this in a very very sharp context the idea had been around for a few years before he got his hands on it but he really nailed it and got a very clear idea of it but the idea is yes there are things on the inside but their relationship to this structure which is holding all the information that ever fell onto the black hole is roughly speaking this is a metaphor it's not a theory the metaphor of the hologram the information can either be thought of as being stored on the film or the film can just be thought of as a representation of the three-dimensional reality and I'm not going to go into that any deeper than that because that would take us all day ok so that's the picture as it was roughly a year and a half ago not quite the whole story in addition this material or whatever it is being hot can also radiate and in the process of radiating it loses energy and the whole thing gets smaller and smaller until it evaporates that's the you know amazing evaporating black hole okay so let's come to the quantum mechanics of this and what we think we owe what what the dilemma is what the what the conflict of principle is the first thing is to put yourself in an in falling frame of reference that's just passing through the horizon there's one thing that quantum mechanics requires of the of the description of empty space the infalling observer according to this theory just experiences empty space nothing more falls through experiences an empty space an empty space has a property it's called entanglement it's quantum entanglement if you don't know about quantum entanglement well you can read you can read them Venice / bees description of it it's as good as anything else but what other quantum entanglement is it's a relationship between pairs of systems it's not a relationship that has to be there but it's a relationship between pairs of systems that can be realized a pair of electrons just a pair of regions of space which says that those regions are highly correlated but in a deeply quantum mechanical sense I won't try to explain tangle meant except to say that it's what Einstein called spooky action of the distance it's not action at a distance but it is spooky and here's what vacuum quantum field theory the theory of empty space tells us it tells us if somebody passes through they should see the interior regions of space let's call them a the center barbarians have some notation which involves any number of twiddles and primes and stars and it's very bad and B B of course is the obvious notation for zone that's supposed to be a joke a is the interior so a for interior B for zone and why B is called the zone doesn't doesn't matter at all the interior just beyond the horizon and the exterior two regions of space are highly entangled I will represent that by drawing a line between them there is no line between them but they enjoy this property of entanglement between them when entanglement means is that if you measured B you could find out what you want to know about a if you measure a you can find out what you want to know about be there entangled oh that's fine no problem there until the black hole starts evaporating and as it evaporates what happens is the entanglement between a and B between the interior of black hole and the near horizon region the region just outside the horizon gets replaced basically these degrees of freedom go flying off they go flying off into the radiation and after the radiation has emitted in particular after about half of it has been emitted half the radiation that will ever be emitted instead of a being entangled with be a the interior of the black hole and B are entangled instead with the very very distant talking radiation the Hawking radiation is impossibly far from the black hole by the time the black hole was radiated and so one is left in a dilemma it looks like something awful has hello sorry one more step a has become entangled with the radiation far away but now there's a famous quantum mechanical theorem it's called the monogamy of entanglement two things if you have three things and two of them are entangled with each other the third cannot be entangled with either so now we have a puzzle if in order to make sense out of this holographic picture of the interior of a black hole we require from the point of view of the infalling observer that a and B be entangled but at the same time we discover that these degrees of freedom become entangled with very distant radiation then the result is that the entanglement between B and a must be destroyed that sounds like a disaster because the destruction of the of the entanglement between these two linear regions here would really perturb the nature of the vacuum between the interior and the exterior very seriously would make it hot would make it very dangerous it would imply that any somebody falling through the horizon here would not see sensible physics there they will see something awful yes both I'm simplifying a little bit I'm simplifying it now yeah B becomes entangled with the radiation and can no longer be entangled with a which really means it can't be entangled with a stretched horizon but but you know let's let's keep it simple so instead of this bond being there entanglement to be with AE we have D with this thing out here the Hawking radiation far away as I said that's a that sounds like a terrible perturbation on the horizon of the black hole unless there's one possibility that information theoretically and Counting where and bits of information are stored unless the interior of the black hole is really encoded in the distant talking radiation then we'll simply say B is entangled the Hawking radiation but the Hawking radiation is just another way of speaking about the stuff behind the horizon that's called an A equals RB theory and it stands for the interior being constructed somehow out of the radiation far away which is entangled with B now I won't try to explain that except to indicate to you how absurd it is what it's saying is that somehow the interior of the black hole is really being represented nearby black hole you know a black hole at the in this room that its interior would be represented in terms of degrees of freedom which could be I don't know how many times bigger than the universe far away that doesn't sound reasonable nevertheless I think it's true I think as well were being driven that a degree of D localization first of all let me say this even the holographic principle was a D localization and aware information was one thing which we all accept the idea that the interior of a region is described by degrees of freedom on its boundary that already is a degree of the localization but this is an extreme degree of D localization that the information describing Alice falling through the horizon over here is contained not on Alpha Centauri not at the you know much much further away seems absurd what's the resolution of this after the black hole has become entangled with a very very distant radiation well one possible answer to my mind a clumsy heavy-handed brutal dumbbell idea there's a firewall idea now the firewall idea is a misnomer I don't think you should think there's some terrible fire just outside the horizon I think the firewall idea really should be phrased by saying once you disrupt the entanglement between B and a then the right picture according to the firewall enthusiasts is that there just is no interior the interior has been scooped up and put out here in the radiation information theoretically there is no interior somebody falling in just hits a blank wall not a firewall but a dead end a you're not going to terminated okay but that doesn't matter I mean this the idea that's that's one resolution i don marloth seems to be the only person who truly believes this with any real intensity Joe Joe says things like well I don't really believe it but all the evidence seems to point be pointing in that direction but I don't really believe it and other people myself want all the saint of the Berlinda brothers I mean these are really substantial people very real heavyweights they think the firewall is a crock and I think the firewall is a crock but damn it we can't figure out what's wrong with Joe's arguing many people I excuse me I that was a bad thing to say right it has been many people's argument we think it's a crock but we can't figure out exactly what's wrong with it I myself suspect if there's something something truth and others think there's something correct about the idea that the distant talking radiation is information theoretically and holographically a description of the inferior of the black hole but there are other paradoxes I only I didn't I've I have not explained the full ammunition that the firewall people have to bring to bear on this they have a number of arguments I think those Fineman who said if you have more than one argument there probably you're bad because one argument but but in this case I think the more arguments or the stronger the case is and we don't know what's going on there are different theories I could tell you one of them has to do with wormholes some you know really nutcase people who believe in wormholes other people think that quantum error correction is important they're also crazy I belong to both groups but my own guess is whether or not it's wormholes and quantum error correction I don't I don't really think it's a it's um it's these firewalls that just seems a little bit too simple to me my guess is we're going to learn something truly deep about the connection between quantum mechanics and gravity from this exercise and I can't tell you what it is with any certainty right now but it's exciting it's exciting it's interesting one has the feeling that at anytime some young person can come along put his finger on it and that it will really be some new perspective into the quantum mechanics of gravity that I think is unexpected um I mean I talk longer than I expected to actually I was expecting to stop and field questions so I can do that now for a little while until thank you question what does it take for two quantities to know what have you to be entangled what is the condition well uh or not I'm not your biologist that's the food so you learn a little bit of karmic cash right okay that's that they have come out not the way so systems have wave functions wave functions depend on the degrees of freedom of the system and if you have a pair of systems in the wave function depends on both variables so it's a sigh of let's call them X and y but these don't have to be coordinates they're just two variables an unentangled state is one which is a product sigh of X and Phi of Y this is a state in which there were no correlations statistical independence but quantum statistical independence between the two systems any state which is not of a product form is called entangled now there are degrees of entanglement how strongly are they entangle just a mild deviation from product would have a little bit of entanglement there are situations which are extremely entangled I will write one down but in which there's an enormous degree of correlation so much so that anything you want might want to know about one of them you can look at something in the other one now this classical correlation is similar but the difference is something like this if I tell you that I have a probability distribution a probability distribution you know what a probability district distribution means but you also I think most people would say the following is true if I know everything that can be known about a composite system then I know everything that can be known about either of its parts that's logic I mean how can either you're not mean right quantum entanglement is exactly the opposite you can know everything that can be known about a composite system when it's a highly entangled state and still have no knowledge whatever about the individual components where you have a lot of knowledge about is the relationship in the correlation between the individual components so quantum entanglement everybody know who invented quantum entangled right to me it was Einstein who was very very he was extremely troubled by this idea that you could know everything about a system and um nothing about its parts that I think if I had to guess what really bothered him and made him feel very uncomfortable on mechanics he called it he called it that quantum mechanics could not identify elements of physical reality I think what he meant was exactly this you could know everything about a composite system and are nothing about its parts so that's what entanglement means and entanglement is entangling itself in the theoretical physics now really major way statistical mechanics of condensed matter physics it's a black hole physics all over the place that will probably get into into cosmology at some point it's it's an infection infection and here is entanglement disease that's intact yes sir Matthew I was trying personally make any set but could AMD disentangle that's very bad for the vacuum for that it's question of energy if the Hamiltonian of the system favors entanglement for example singlet state of a pair of electrons then to break that entanglement cost energy right to break the entanglement between a and B would necessarily HEPA vacuum but would necessarily increase the energy of the vacuum in between if every single mode near the horizon if the entanglements were all broken by this radiation then you can call it a firewall you can call it complete destruction of the nature of the horizon but it would be brutal it would be like taking gum a pair of electrons which like to be in a singlet state like means that lowers their energy and forcibly disentangle them would raise the energy you raise the energy of every one of these and that's a that's a serious perturbation does that assume you know the Hamiltonian arbitrary short scales right on that well we're not talking about arbitrarily small scales if we're let's suppose we don't want to know whether there's a true plunky and firewall we just want to know when we pay to the horizon we scalded by hot water hot water is very close to the VAT or the temperature of hot water is practically the vacuum but nevertheless it would burn you then we can be talking in are things that are pretty well separated here separated by a Compton wavelength associated with boiling water so you can't get around this by saying oh look this is all plunky and physics very close to the horizon I won't do it for you I don't know if that answered your question or not when bits of piece of information fall into the black hole the black extends in certain center area expands radius and so when the black expands the information already at the surface what happened to them they get swallowed into a black hole or they yeah we thought horizon well okay from the outside point of view what happens when something falls into a black hole is an almost a causal way I don't think it really is a causal but the horizon expands a little bit this stuff comes out to meet it that falls in and mixes up mixes up with the with the stuff in the stress horizon that's the picture that is common these days ah that falls in it is absorbed into this hot stretched horizon it's bits absorbed into here but through this holographic mapping it's equivalent to something falling through the horizon it and I think we understand that a little bit we don't understand that a lot or we understand it reasonably well it's what happens when all of the correlations and in you transfer to the radiation going out on the stand I have a question trying to understand the entangle bit again this specific entanglement or entanglement in general well the case that you've drawn there so you have an beyond Peyser yeah are you starting in that state or yeah yeah yeah yeah that's that's not holding it because that's the state that you expect the black hole to settle down to who after it's good for let's consider a case where you have an antenna called nd just outside the horizon outside and I think I'm done 8 volts in huh as far as B is concerned the entanglement with a never ceases right that's right and so in that case well okay they could remain entangled if you have an entangled pair and you throw one even you can think of it two ways both are equivalent one way is to say the other member of the entangled pair gets smooth or whatever you love the right word is scrambled is the technical term no it is did you not scramble that bit gets scrambled into the stretched horizon here and gets absorbed into the black hole but then what you say is that the this particle over here has become entangled with the black hole become entangled with the stress riser another picture of the same thing is that it's entangled with a particle which falls inside incidentally there's a neat analogy for this which is building one now the saner almost everything do the 1 now the singer imagine you have a mirror it's a spherical mirror and you have a charge out here thinking quite mechanics but the quantum mechanical charge then the charge develops an image charge on the inside now there's no real charge on the inside what is really going on what's really going on is the charges in the mirror get readjusted they get readjusted and simulated charged in the period you can think about the quantum mechanics of this particle here again I was thinking of course of the other pair of particles one entangled with each other you throw one in you get your choice to think about this particle being entangled with the charge distribution on the horizon or more accustomed the huge charge of the Interior and there's some similarity here that you can think of this particle as it certainly remains entangled with something you can't destroy an angle which this particle either be thought of as being entangled with the degrees of freedom of the stretched horizon analogously to the to the charges of the mirror or you can think of as being entangled with a holographic image on the inside black shirt when we are talking about the interior of the black pen we ignored the presence of the severe the promise of reality there's a security director yeah and we ignore it it's not yes we ignore it but sufficiently big black hole okay that's a very good question so let me tell you what the usual answer would be they take a very very big black hole that the singularity is deep in the interior somewheres of course this is a misleading picture but that's good enough our purpose right now but if the black hole is sufficiently big there's a region way out here far from the singularity where the singularity is just not important so you could ask your questions about what happens to somebody who falls in and restrict yourself to this region here which has not been where space is more or less flat where the presence of the singularity is not a serious issue when you get near the singularity of course everything bright everything to be no breaks down so for a sufficiently big black hole let's say a black hole a black hole like get the center of the biggest galaxies a billion solar masses a billion solar masses somebody falling in would have about 20 minutes after passing the horizon during which they were far enough from the singularity that they would not feel huge tidal forces they would not feel anything serious and you can frame all the questions about this region here so there's not to say the singularity is not important or not interesting but the paradox can be formulated independently of the properties of the singularity question so the Hawking radiation is in the form of electron positron pairs product but don't mostly pop mandra gravitons okay so and if that somehow carries the information from the interior of the black hole can you do funny things by throwing the Hawking radiation into other black holes even worse you can do really funny things by throwing the Hawking radiation back into the original opera and this is what a lot of our debates are about good lankan experiments and infinite confusion about what happens in a tree to your friend a pianist a game you're trying to say that there's a be the horizon degrees of freedom and the radiation his mind here's my terminology I call the horizon these things here I called H and then B and H this is the near horizon stuff near the black hole formed black hole now B is entangled with something what on earth could be be entangled with a he'll be a rectangle Alice and Bob so I called as Allison's Bob this horizon and this are the maniacs the the center barbarians call this thing they do close be but what do you call this thing detail better than this one here see okay but they're all the same is there any way to think about a possible severe a and B are information information this is same the rear-ended by a put you are bees they're some kind of depend upon where a and B are no no no I'm not saying it's wrong I'm just saying they no such proposal yeah a isn't angle would be that's different than saying a is good right but I think if I point if you'd do this would be the same if this is a great event probability Hong zero because sa totally absolutely DMV in avoiding you calculator is a and B word almost because for example SOP a B if it's up your sleep yesterday has to be equal this would be alright no so then that doesn't say a is big some are more intensity say well and some I'm a moment I don't think this is a question of morality what is a question of morality yeah he must have a monogamous but uh in any other moral sense the sake of things is entangle is a very deep relationship it's not quite the same as saying they're the same it does say that anything you want to know about a any measurement that you would like to make on a you can find out the answer by doing an appropriate measurement on B it makes eight and be awfully closely related but it's not quite the same as saying though this information theoretically that's one that's one possible way to think about it the other possible way is to say that a is are in either case you come up you do come up against you cannot have you really can't have eight and bb-8 sorry eight and our or for that matter a and B being two identical copies of the same thing that's the no pony so I neglected to say that you might have said okay there's just another copy of a out here no you can't make copies of things that's a theory yes would their view on dense matter and that all something could be more convinced to the black hole tomorrow that's that is it that's a good question and it would be lovely if we have some convinced matter analog for this that we could appeal to and look at and I don't know any it seems to me that these issues really do have to do with the combination of gravity auto mechanics I don't know anybody who has a good condensed matter the neurology for happens but that could be wrong there is a condensed matter analogy to what happens or four black holes for the dumb hole don't like death that's because sound is replacing white you made some of you may know it if you take a lake a lake of water flat you put a drain hole into the bottom of it so that the water or whatever the fluid happens to be drains out in such a way so fast that at some place the water exceeds the speed of sound then you have something which is in some ways similar to a black hole if you pass that point sound cannot get out it creates Hawking radiation and you could ask can you manufacture the same kind of paradox well not really because if you ask what happens to the information that falls into substrate it simply doesn't get radiated back out in all radiation it just goes down the drain you find it on the floor the floor of your room cave underneath there so there's no there's no good analogy for this kind of holographic behavior so I don't know if it had one more but this is mother biologists I don't know visit so you're from there you know that tangle three-way yeah but at the same time you said earlier that you can entanglement is a graded quantity yes yes yes yes to share you good good you can you can you can have you can have a you can have a state in which B is partially entangled with a and partially in kind or that won't do it it just won't do it for practical purposes of practical purposes for the purposes of the discussion it's very useful to think of the empty space as having essentially maximal entanglement between DNA but that's not exact but it does and that's of course one of the first things people think about when they hear this paradox you see oh well this is these are not maximally entangled and these are not going to be maximally entangled maybe we can squeeze through there's a not be the case there's a more refined version of this called video multiple the inequalities drug that is normal so variability that doesn't what we find job of it before we thank Marty is ready give me an essence of the group here very things afternoon wine cheese yes there's egg one cheese there's a my ears holders we're not deploying we promote okay so that'll j5 okay all right you you

Channel: aoflex

Views: 525,764

Rating: 4.8295679 out of 5

Keywords: lecture, seminar, ucsb, UC Santa Barbara, KITP, Math, Mathematics, physics, particle physics, qft, quantum field theory, String Theory, quantum gravity, black holes, quantum black holes, firewall, relativity, space, time, spacetime, Susskind, Lenny Susskind, general relativity, EPR, Stanford, Stanford University (College/University), Complementarity, Workshop, Entanglement, Leonard Susskind (Author), GR, event horizon, Cosmology, Leonard Susskind, Universe, interstellar, quantum mechanics, gravitation

Id: yMRYZMv0jRE

Length: 70min 32sec (4232 seconds)

Published: Sun Nov 24 2013

Reddit Comments

[u/bushwakko]

Leonard.

[u/[deleted]]

Is this general audience or maths heavy lecture? Most of Susskind's lectures are extremely advanced.