Leonard Susskind | Lecture 3: Entanglement and the Hooks that Hold Space Together

oh my god welcome you third incredibly collapsed when the sustenance three messenger lectures since not all of you were here for the earlier do lectures I recall to you that there build on the University lecture site is one of the most important of Cornell extracurricular activities and last night when he certainly fulfilled the terms of Hyrum messengers 1924 the quest for the series by raising our standard with a beautiful exposition of the interplay between quantum mechanics relativity and gravity including all of the H bars C's news there was no mistaking it we already said that he was a graduate student here at Cornell fifty years ago we learned last night that in order to mark his ascent from the South Bronx to Renaissance man were supposed to call him Leonardo we've been through the litany of his many research achievements we've talked about his extraordinary presence in communicating wheels the general public through popular box appearances on broadcast television who is many lectures available online video for this final of introduction i'll instead mention a few a couple of personal anecdotes that I've had so much contact with him is already telling he is after all a much earlier generation that made I to an earlier generation in Montesano the reason for this is at conferences and elsewhere he would always hang out with the other people because that's you know what that was his comfort level that's what he enjoyed doing and for us it was this amazing bridge you know inch through his experiences and telling an anecdote most recently what this is meant is that he's been invited to assyrians or to a series of 60th birthday commemorations we overlapped if one about a year ago and in his introduction to his talk he said hey I know why I'm invited to all of these things I'm here to make the celebrant feel younger but I have one final story that he related to me a few decades ago which is in this series of lectures since it's the fifth year anniversary of fineman's there's nominal Fineman time all of these things and Lenny told this to me as a Jew story the setup is to physicists walk in to the celebrity sandwich bar in Pasadena now in this sandwich bar they have sandwiches named after celebrities with appropriate condiments so don't know what time period this would have been maybe there was a Ronald Reagan sandwich four minutes of Clark Gable sandwich and um Leonardo uses two fine men gee I wonder what a Fineman or a sus consent which would be like and fine but replies a Susskind sandwich ha I bet it would be filled with Bologna and the Susskind allegedly in real-time retorts well at least it wouldn't be filled with ham so the last word is last night I you know asked for show of hands of people who've been here about few years ago and I'm going to pose a challenge to all of the undergraduates and graduate students here and that is which if you like Lenny will be back fifty years from now to give the hundredth anniversary of Fineman and the 50th anniversary of Susskind and remember that I said this with that if I remember correctly hello no am i turned on if I remember correctly dick gave four lectures is that right I think so hmm I don't know I think he gave four lectures but I want you to keep in mind that I'm 30 years older than he was I really I've been here for four days now yeah for four days now and this is actually I think the seventh lecture or quasi lecture that I've given I can't say that I'm sorry that this is the last one I'm over tired but I also have to say this has been an incredibly joyous experience I loved it it has been enormous fun it's been very very gratifying and I want to thank everybody who made it possible I especially want to thank Paul and I also want to thank all the people who came up to me and said I enjoyed your lectures whether you did or you didn't it made me feel good so thank you um as is my want I usually start by reading something it just reminds me of what I'm going to talk about I always forget in the beginning when I'm going to talk about and I ramble off onto something else so I always prepare myself a couple of paragraphs to begin with so here goes Einstein and Bohr had a famous debate that lasted at least 20 years it was a debate over quantum mechanics I suspect most of you if you haven't read the debate at least are very very aware of it the debate reached its climax with the idea of entanglement it's generally deemed that ball won the debate but in retrospect it's clear to me that I'm Stan's view was by far the deeper bore I think never really understood entanglement in essence he told Einstein go home and take an aspirin you'll feel better in the morning Einstein didn't want to feel better he wanted to understand it in 1935 and long after incidentally he was considered to be irrelevant Einstein wrote two papers on two entirely different subjects at the time they were widely dismissed this lecture is a tale of these two papers and the amazing connection that's being uncovered between them I should tell you that at least one of them one of them is the most highly cited of all of Einstein's papers the two papers will be known for this lecture and they are known as er that doesn't stand for emergency room and EPR can this PC EPR er stands for Einstein and Rosen he wrote the paper with Nathan Rosen I will tell you what it was all about as we go along and EPR stands for Einstein Podolsky and Rosen as I said these two papers are on entirely different subjects as far as I know neither Einstein nor anybody else have any reason to believe they were connected we will say so let me begin all right oh you know before I begin with the quantum mechanics let me begin with a classical completely ordinary experiment I need some assistance anybody want to come up and be my assistance to people oh come on to commit glom come up all right now look here's the experiment we're going to do good now I'm going to hand you something I have two things I have a chalk and a battery okay they're about the same size and shape I don't think you can tell the difference holding them in your hand you close your eyes and I'm going to hand you warning I'm not going to tell you which one okay close your eyes okay you get your not close your fists don't look alright now one of you go out of the room well you don't really have to go out of the room just go over in the corner your bed bar go over in the corner alright you're awesome you look at what you got I bet you instantly knew what he got yes how did that happen you must be magic Wow you may sit back now yes you may sit down - I'm gonna I'm gonna wander off in some other direction for a man I have a friend named Jeffrey West these are famous physicist Jeffrey well I love magic tricks okay I'm very bad at them and so my magic tricks are very very simple and usually kind of stupid so Jeffrey West had a five year old child and I said what's his name Josh Josh I'm going to show you a magic trick and he said oh yeah please show me a magic trick I love magic tricks and I said all right you see these two rings yeah I see those two rings now watch this watch this okay and he said Wow how did you do that so you can do it go ahead try it so he thought from me okay and he put his hand sorry about that that is nothing whatever to do with a lecture all right that was an illustration of something which is sort of like entanglement but it's different it's different in particular well we'll see how it's different but keep in mind that what these guys knew was less than what they could have known in classical physics you can know the exact state of a system not so you can always know the exact state of a system but knowing the state of a system in this case the system is the system of chalk and and battery knowing the exact state of a system in classical physics entails knowing exactly what's going on with each of its parts so in principle we didn't know the details of the state when we did this experiment but in principle without disturbing the system significantly we could have known more about it than we did I want you to keep in mind because that's one of the very big differences between this experiment and a real entanglement experiment all right let's begin with EPR EPR Einstein Podolsky and Rosen it also happens to stand for a term that they used in their paper elements of physical reality this was something that disturbed Einstein a lot but let me give you a very very quick quantum mechanics lesson here it goes we have a spin the spin is a little physical system for the moment let's not even worry about what it's attached to and practice it would be attached to an electron but it's a little system and it has an arrow associated with it in other words a vector it's something you can measure and when you measure it you measure its components its X component that's Y component then a Z component and so forth so let's add another system the next system is the apparatus that we use to measure it and the apparatus looks like this it's a box it's a black box well it's not black it's the box it has a little screen on it that will show an answer it has an arrow on it that says this way up in order to tell which way it's oriented and you can only enter it in any direction in three-dimensional space that you want it also has a button here the button says M for measure all right you bring the apparatus up to the spin so that it's in contact with it you press the button and you get an answer purportedly the answer is supposed to be the component of the spin along the axis of the detector you will always get in quantum mechanics either plus or minus one no intermediate answer nothing in between either plus or minus one this is a little bit peculiar that the component of a vector in an arbitrary direction should be plus or minus one do we understand this this is this is quantum mechanics is the weirdness of quantum mechanics but it's okay we did our homework and that's a consistent thing to happen now it is also true that's for any state of the spin in other words for any precise way that you set up the spin any state which means any specification complete specification of everything that you can know about the same spin everything that you can know that there is always a direction that's called the polarization direction that if you oriented the apparatus in that particular direction you would always get +1 in other words there's some direction that we would say the spin is pointing along that if you measure it along that direction you'll always get +1 by contrast if you orient the apparatus in another direction you'll get statistically somewhat random results the more orthogonal the detector is to the polarization axis the more random it is and in particular if the little this arrow here lies in the plane perpendicular to the polarization the spin you simply get random answers okay that's quantum mechanics of a single spin in a nutshell now next question can you simulate can you fool somebody into thinking the seeing quantum mechanics here's here's the here's your task you have a computer here's your computer on your computer screen you have a detector a apparatus that apparatus can be manipulated and it can be oriented in any direction you have a little M over here and you take your mouse and you click on that M and in the box here or not in the box and little circle layer appears a plus or minus one the question is can you program your computer in such a way as to fool somebody into thinking that in the computer there is a real electron and this is measuring the real electron and recording the result okay yes it's not very hard you need two things at least two things computer scientists might figure out some more stuff that you actually need but one thing you need is a random number generator because you'll have to under certain circumstances you have to generate random answers so you need a random number generator and you need a memory to record the state of the spin whatever the state of the spin means in this case it simply means a polarization direction you need to record what the state of the spin is and you need to and you need a random number generator to generate answers that's all you need and you can mimic quantum mechanics at least for the single spin now let's come to the problem let's suppose there are two spins let's suppose there are two spins and let's presume that the spins are fairly far apart so that they're not significantly interacting they're separate here's another spin and here's the detector or the apparatus that's used for measuring that spin you might expect that the state of a two spin system is simply specified by specifying two polarization vectors two polarization vectors and that they're simply two systems identical each identical to the first and in fact you can create electrons or spins in that kind of configuration you just do it by separately and independently arranging the two states of the two spins it's called a product state and a product state there's not much crosstalk no crosstalk between them no correlation between them not even any interaction between them and the two sets of experiments are completely independent each apparatus has its own random number well this is for the real spins question is can you simulate this of course you can simulate this to simulate it you simply have two random number generators two memories one over here one over here and you just do in each place the same thing that you would have done with only one spin so yes you can simulate that but there are a wider class of states available to two spins and the additional states are called entangled States for those who know quantum mechanics I will write down an example of entangled States and I will never use it again but I will not explain it I will just write it one over the square root of two times a state in which the first spin is up the second one is down - the first one down the second one up this is a quantum mechanical combination of two states in which one of the states has one spin up and the other one down and the others and vice versa and vice versa this is a proper quantum mechanical state it is a complete description of the system there is no more to know you cannot know any more quantum mechanics says there cannot be any more knowledge once you know the state of the system but it has some odd properties let me tell you what they are the odd property that I find most interesting of course there are very complicated consequences of this but I'm just going to focus on one very very simple observation if in this type of state you measure either of the two spins in any direction at all you'll get a random answer it doesn't matter which way you tilt your apparatus you'll always get a random answer in other words in this case there is no polarization vector for either of the spins and it simply doesn't look like a state of two independent spins either spin or both spins if you measure them you will get random answers I would say this is peculiar for the following reason I would say that you have absolute complete information about the composite system of two spins and you have absolutely no information about either of the parts of the system now that's weird if you think about it if you think about it I'm telling you that you have is a complete description of the composite system and yet no knowledge of either of the parts that's a feature of maximally entangled states that the entanglement has a degree of entanglement associated with it we don't need to get into the mathematics of it there can be unentangled states there can be a little bit entangled states and there can be very entangled states I'm interested in the variant angled States now okay so the question then is um if everything is random what does this thing the state tell you what it tells you about is not what happens if you make one measurement or the other one but it tells you about correlations between the two in this state the following is true pick any direction at all line up the two detectors or the two apparatuses in the same direction and measure both spins in this state here you will always although it's random what whether you get a plus or minus one if one of them gives a plus one the other one will always give a minus one in other words although the polarizations are completely undefined for the individual spins nevertheless they are found every single time to be in the opposite direction the entanglement tells you about correlations between them and tells you about relations between them but it tells you nothing about the individuals that should that shook in stein that bothered him he said what's real is the is what is real about these two spins and he came to the conclusion that the description here didn't say anything about either one of them and that bothered him somehow Bohr just was okay with it I don't even know if Bohr understood it if you read the dialogue between them you'll come to the conclusion that Bohr was mumbling in his beard and the Bohr have a beard no it was mumbling in Paul's beard um look I'm a great admirer of Bohr but in that particular one I think he was wrong anyway can you simulate this system it's kind of interesting you can simulate it alright you can simulate it on a computer or a couple of computers the situation of the entangle if they're not entangle that they're in a product state it's easy you just make two replicas of the detector and everything else if they are entangled like this in order to simulate you have to do the following you first of all have to have a kind of central processor which is going to do the computing so it sits in the middle there somewheres it has to have the usual random number generator random number generator it has to have usual random number generator the usual memory but now it's memory memorizing memorizing it's remembering the state of the two spin system not just one spin at a time it's remembering that state and the random number generator and associated pieces have to be connected by wires to the two distant computers we now remember we're now simulating it this isn't real there's no real electron there there's no real electron here we're trying to fake it in order to fake it there have to be wires there on one side let's call this Alice's side we'll use the usual Alice and Bob on Alice's side Alice is going to make a decision about what direction to measure the spin in the instant that Alice decides to measure that spin or the instant that she starts to measure that spin a message has to go to tell a random number generator in the system over here what direction Alice decided to make the measurement in what direction the her apparatus was in once that happens some things happen here and then it sends back a message with a random plus or minus one not a completely random plus or minus one but a plus or minus one that is supposed to be the answer same for Bob and Bob has to be connected to the same random number generator because of the strange entanglement or the strange correlation between them so in order to mimic in order to mimic the quantum behavior of two distant entangled systems you have to fake it with a collection of wires that connect them basically what would happen if you cut the wires and try to deal with it by two separate systems you couldn't do it this is the sense in which entanglement is non-local it's non-local in the sense that if you try to simulate it with a classical computer if you try to simulate quantum mechanics with a classical computer you have to fill space with wires those wires are would really have to genuinely be there and more than that the wires have to be able to transmit information essentially instantaneously to do this that sense in which quantum mechanics is now you may ask with all these wires around can you transmit information faster than the speed of light can you transmit from Alice to Bob a piece of information about anything you like well sure you can if you have those wires there those wires are like telephone wires and they're instantaneous so of course you can so this might seem to violate Einstein's principle that you can't send information faster than the speed of light but in fact if you restrict yourself to only those operations which make sense for quantum mechanics the thing that a quantum mechanics experiment would actually allow you to do under no circumstances will you send anything faster than the speed of light so it's a little bit strange but the strangeness has to do with simulating quantum mechanics on a classical computer that's what entanglement is about I'm sort of taking you through a tour of various various interesting things about entanglement now the next thing is entanglement a rare phenomena is it something that you have to work very very hard to arrange between systems the answer is no entanglement is extremely generic in fact it tends to spread out among systems like a like a infectious that very badly infectious disease if you have a system which is composed now of a lot of parts let's imagine we have a system that's composed of a lot of these spins here it is it's a box of spins with lots of them let's start them all in some particular state which is a product state and let's say in which they're all polarized along the z-axis I want to put some more in I want to have an even number okay we start that way that is not an entangled State each one of these things is its own private state they are not entangled you gain no information about another one by measuring one of them and that's not entangled okay now you let them interact with each other you let them just interact maybe even just a little bit some kind of forces between them maybe some interactions which tend to rearrange them a little bit and let those interactions persist for a relatively short time just a fraction of a second in a very short time this system will become maximally or very close to maximally entangled what does that mean that means if you divide the system in half in any way in fact it doesn't matter vertically divided in half diagonally divide it in half just pick out half the spins and pick out another half the spins here's what will be true the state will give you no information about either half everything that you measure about either half will be completely random but if you want to know the result of any experiment let's call this alice's share what's called as bob's share bob can predict the result of any measurement that alice will do by doing an appropriate experiment of his own which will then and it's exactly the same thing as over here these two entangled spins if you want to know what one of them is doing just look at the other one and the first one will be anti parallel with it if you were to measure it if you measure both of them they will be anti parallel the same kind of thing is true here and what's more it doesn't even matter how you divide it any way that you divide it you'll be able to predict the other half by measuring one half that means that entanglement is very pervasive things get tend to get massively entangled very quickly yo I assure you you are entangled with your neighbor in fact you're entangled with me I don't know how that feels to you but and in fact you're entangled with the Martians on Mars okay let me give you another example of entanglement in this case it's not entanglement of spins its entanglement of regions of space it also makes sense to talk about entanglement of regions of space so here's two regions of space and let's say the question that we can ask about these two regions of space is is there a particle in there or not is there a particle in here is there a particle in here okay one possible state of the system is what you would call a product state in a product state there may be a probability distribution for one particle or zero particles but they're completely independent a product state no correlation between them prepared completely independently that's called a product State but you can imagine a state a quantum state with a following property that if there's a particle in here let's call it let's call that one one particle on the left side then there will definitely be one particle on the right side but if there is no particle on the left side then there is no particle on the right side that would be a quantum state which is entangled the entanglement not now being between particles but between regions of space look and basically a physics teacher and at this point I always stop and ask are there any questions no questions then we go on there will be an exam at the end so right okay now I'm going to tell you about entanglement of the vacuum entanglement of the vacuum of space space empty space doesn't sound like it has anything so how can entanglement be relevant for empty space then well there's a whole generation of quantum theorists in particular very very active right now young people who are studying the entanglement of the vacuum are they stupid know that the actually studying something extremely interesting so to understand it again you have to go back to things that Fineman said if I am finding in others Fineman said that the vacuum is full of virtual particles it's full of virtual particles which come and go but they come and go and in fact they come and go in pairs if an electron appears in the vacuum then very nearby it or somebody nearby a positron will appear in the vacuum they come in pairs and they come and they go and they come and they go now let's imagine the vacuum empty space at some instant of time okay at some instant of time let's draw a space and I'm going to break up space into a lot of cells so let's let's first divide it in half or the divided space in half incidentally I can't draw a three-dimensional space so we'll have to stick with two-dimensional space see the same we could do for three-dimensional space but here's two dimensional space the blackboard and I'm going to divide it into cells I guess the official term is tessellated all right we're going to tessellate it and we're going to tessellate it with little cells with near the boundary here which are small these are not really separated they're supposed to fill the space but I'm just drawing them in the easiest way that I can near the edge which separates the two regions I'm going to make them small how small about the same size as their distance from the dividing line here then we're going to move out a little bit in both directions and draw slightly bigger cells how much bigger twice as big twice as far and twice as big twice as far and twice as big and of course the next step will draw big ones will be dividing space in what's called a scale and variant way or at least in a self similar kind of way and so forth and so on all right now what I tell you is what has been discovered over the years about quantum field theories about ordinary quantum thing the condom field theories are not so ordinary of course but about conventional quantum field theories is that the left-hand side is entangled with the right-hand side but which which means that you can find out things about the left-hand side by measuring making measurements on the right-hand side what is the pattern of the entanglement the pattern of entanglement and what does entanglement mean let me just say what entangle or what what's at stake here we're talking about regions of space so we're talking about exactly this question is there or isn't there a particle in this region is there it isn't there a particle in this region and they're entangled if it's always the case that a particle in here is accompanied by a particle in here an empty hole over here is Inc is goes with an empty hole over here so I'm going to draw some lines between these to indicate that they're entangled and that is the way the empty space of a quantum field theory behaves if there is a particle in one of these cells then there will be a particle in the other one if one of these cells is empty the other one will be empty so it's entangled but it goes further these are entangled if there is a particle in each one of these and now by a particle I mean a particle of wave for the technical experts I mean a particle whose wavelength is comparable to the size of the cell they're entangled these guys over here are entangled I didn't draw well but you know what I mean that's what the vacuum looks like with respect to its entanglement properties across a boundary this always has looked to me like the lacing pattern of somebody's corset I want you to keep that in mind that is important this is the vacuum in quantum field theory question can you break the entanglement what does breaking the entanglement mean it means can you create a state in which the left side and the right side or at least over some region of space in which the left side and the right side are in a product space a state in other words destroy the correlations between the left side and the right side not destroy them but just create a quantum state in which they are less correlated maybe even not correlated at all the answer is yes you can make any state you want any quantum state can be arranged somehow but it will cost you energy how do I know that the reason is because the vacuum is the lowest energy state of a quantum field theory there's nothing of lower energy than the vacuum so if I do anything to it to disrupt it in any way it will always cost energy in particular somehow disentangling some of these laces here or some of these hooks disentangling them will cost energy all right so let's draw another another view of it over here it's the same thing except I don't want to erase this nice laced up corset here and let's suppose I take some region some finite region this big and I unlace it unless it means disentangle it what does it do it creates some energy in that region let's just represent that energy by our blob here create some energy in here that's the story in quantum field theory but now let's add gravity what does the presence of energy do in gravity well energy is mass mass is the source of a gravitational field and the gravitational field is represented by curvature and the distortion of space therefore this energy density here will distort space it'll distort space in the region where it's present so when you disentangle a region like this when you unlace it what do you do you'll create some kind of distortion of the geometry of space in here and I'm going to tell you yes I'm not here the thumb just thumb I'm not here I can tell you most of the planet happy all right what does it do to space it distorts it in the following way it takes that region and it makes the distance let's say this line over here is just some line that was originally over here to the right it was over here it takes this region and increases the distance across the from one side to the other side it increases the distance from one side to the other side you know it's exactly that now that I think about it it's exactly what happens if I think was john wayne who wore a corset is that right john wayne i think was the guy who wore a corset if you were to take your scissor and cut the laces here that's what happens space can't hold itself together this is the sense in which entanglement is the hooks which hold space together and then the combination of gravity we're talking about gravity because we're talking about the distortion of space by curvature due to energy on the other hand we're also talking about entanglement so we're talking about some property of the combination of gravity and quantum mechanics and tangle mint is doing some job of holding things together now if you wait a little while if you wait a little while the disentangled system will restore its own entanglement what will happen is the extra energy that was put in here will get radiated away it will get radiated away it'll dissipate itself and the entanglement will get restored when the entanglement gets restored this is pulled back together again so I might say again that let's think about the other way let's think of it backward now instead of saying that breaking the entanglement on this connect space let's say it the other way by increasing the entanglement or turning on the entanglement between two regions of space you pull them together you pull them together and you create a seamless space in between so that's a sense in which entanglement is in some way important to the structure of space it's important to the structure to the smoothness of space we'll come back to this okay we've talked about EPR einstein-podolsky-rosen and entanglement now I want to come to ER Einstein and Rosen an entirely different subject having to do with black holes so I think the last time if you weren't here well maybe you know it maybe you don't if you don't know it I can't help it we talk about black holes and I drew a diagram representing a black hole which looks something like this this was just space of space-time this was space-time time goes up and I drew a singularity over here and what I told you is that the outside of a black hole this is representing some black hole the outside we can draw another one down here but just ignore it the outside of the black hole where Alice lives let's put Alice out here the outside of the black hole is out here the inside of the black hole beyond the horizon this line is the horizon the inside of the black hole is over here and since the rule is that light rays travel with 45-degree motion anybody who gets caught in here will eventually crash into the singularity that was a picture of what a black hole is like but you might ask what's going on on the other side somehow there seem to be two outsides of the black hole is an outside here that's Alice and there's another region of space over here that seems also to be outside the black hole let's put Bob over here what's going on here how come there are two outsides to the same black hole Bob can also fall in Bob can fall in Alice could fall in or they could both send something in and it's quite clear that the picture that should go with this two sided black holes it's called a two sided black hole the picture that goes with the two sided black holes that should really be thought of as two black holes two black holes in what space well the simplest version of it is to imagine that there are two sheets of space this is a mathematical idealization there are two sheets of space two separate spaces which are unconnected that's a little bit hard to think about if you're trying to intuit what another space which is disconnected from our space means but mathematicians have absolutely no difficulty imagining two separate independent spaces each one has its X in its Y and so forth and then what this picture is drawing is a black hole on this side you fall into the black hole on this side and a black hole on this sheet here which are connected together connected together by what is called a wormhole or an einstein-rosen bridge it's a perfectly good solution of Einstein's equations and it has some kind of connectivity between two completely disconnected sheets that's what this diagram is really illustrating here all right supposing we take a sequence of points along here starting analysis side and pass through here and we're not moving this way nobody can move that fast but just take a sequence of points what does that look like well you start analysis I'd Alice's up here Bob is down here you start up here and you pass right through and come out on Bob side can anything actually pass through from one side to another can something can Bob throw thumb to something through and it will appear at Alice's side no for Bob to throw something through he would have to exceed the speed of light you can't do that so despite the fact that this is some kind of connected structure the toussis two sheets are connected it is not possible to send information from outside one black hole to outside the other black hole this is some kind of connectivity and it shares with entanglement entanglement is also a kind of connectivity it shares with entanglement the principle that it cannot be used thus in information faster than the speed of light now you can also think a little bit differently you can imagine that these two black holes were in the same space let's take this and sort of fold it here's what I'm doing I'm taking a space which looks like this and I'm just folding it like that I'm not really doing anything to it I have not changed its geometry in any way I've just redrawn it in space so that it sort it's like this two points are far away this point and that point are far away they're about a foot away but I'm folding it so that they look a lot closer and then I'm joining them by a wormhole so this could be two black holes in the same space far apart from each other far apart means it takes a long time to go around this way you can't go from the outside of here to the outside of here altogether and it takes a long time to go around here but here's something that Alice and Bob could do they could have arranged all of this in advance but be even before the black holes were made they could have arranged in advance to somehow make this configuration we'll describe how you make it in a little while and then once it's made Bob who is 20 zillion light years away from Alice now but the wormhole connects them Bob can jump in Alice can jump in and they can meet in the interior that sounds really crazy but I believe that it's true that if you somehow were able to make one of these wormholes with two black holes at either side you could not use it to transmit information you couldn't use it to make time machines you couldn't use it to to a pass through quickly and find and exceed the speed of light but what looks like it is possible is that if everything is appropriate and picture makes sense Bob and Alice can jump in and meet in the middle of course they won't last very long this is not a good thing to do so at some point somebody I'm sure is going to ask me yes but is there an experiment associated with this yeah here's the experiment and if you meet Alice or unless you're Alice in which case you would meet Bob if you meet Bob in the inside you'll know that Susskind is right and his prediction is Right won't do you much good but if the black hole is big enough then you might last a little bit of time and you know well I don't know I really don't know what Alice and Bob do when they meet in the interior of the black hole but okay now can you have disconnected black holes disconnected I mean that they don't have wormholes between them something like that just no wormholes between them that you can't send anything in and play this little trick yes you can those are all also solutions of Einstein's equations two disconnected black holes what is it that distinguishes the connected and the disconnected black holes okay so let me redraw the connected black hole there's the connected black hole and incidentally right at the waist of a John Wayne's waist right there that's where the horizons are falling in from this side you pass the horizon here falling in from this side you pass the horizon over here if the horizons are connected if the horizons are connected and space is nice and smooth what this picture over here tells you is that there must be entanglement across the division things over here must be entangled with things over here in other words the upper black hole and the lower black hole are entangled now what am I talking about entangled black holes have nothing to do with entanglement there's simply solutions of Einstein's equations but keep in mind we're talking about quantum black holes and quantum black holes have a great deal of information at their horizon we talked about this last time that from out from the perspective of somebody outside the horizon the horizon has this pileup of zillions of degrees of freedom their quantum mechanical so analysis black hole there's a population of degrees of freedom over here on Bob's black hole is a population of degrees of freedom over here those are the things which describe everything that ever fell into the black hole and what we're saying is if the black holes are connected by an einstein-rosen bridge they must be entangled all right what about the case where they are not connected then they simply can't be entangled in fact you might think about that as the limit in which the two sides have just wandered off so far that they're really not in contact anymore in which the entanglement between the two sides has been destroyed that's the situation corresponding to the two disentangled black holes now this is extremely interesting I think it's true I don't see any way around it what determines whether there's an einstein-rosen bridge between two black holes is whether they happen to be entangled or not for the moment let's not worry about how you make entangled black holes that might be incredibly hard but let's let's a focus on that idea this idea that entanglement between two black holes is the same thing as their connectivity by an einstein-rosen bridge has a name it was named the name comes from one maldacena as almost everything in physics for the last 20 years is true it's called er equals EPR the presence of an einstein-rosen bridge is an indication that the two black holes are einstein-podolsky-rosen and tangled now I this is a which what shall I say it um it seems to me that it follows unambiguously from the principles of quantum mechanics and the principles of general relativity I don't think this idea is going to go away er equals EPR but it seems extremely far-reaching and surprising on the other hand it wouldn't mean anything if there was no way to make a pair of entangled black holes so let me tell you now in a thought experiment how you would go about making a pair of entangled black holes ah it's not something that we're going to do in the laboratory it's not something that we're going to do even in intergalactic space but it's something which in principle appears to be quite possible creating pairs of entangled particles is pretty easy well not so easy if you're an experimenter in this room you'll probably say oh come on it's not that easy but the it's on the scale of a one to ten it's pretty easy how can you do it let me give you a call one way to do it you know that um that if you collide particles electrons and they create new electron positron pairs collision how does that happen it happens by the electron and positron coming together annihilating into a photon and then the photon decays into another electron positron pea the electron-positron pair come out entangled even if the original incoming ones were not entangled new ones come out and tangled so it's not hard to make electron positron pairs that are entangled so let's think it as a given that we can make lots and lots and lots of maximally entangled pairs incidentally maximally in pears are called Bell pears be e ll Bell stands for John Bell John Stuart Bell who was one of the really great pioneers who were pioneered the study of entanglement in the 60s they called Bell pears if they're if they're maximally entangled this is a bell pair all right here's what you do you start creating Bell pears to indicate that they're entangled this one's not entangled with this one its entangled with this one to indicate it let's draw a line across here a Lisa kind of lace across there you create a lot of them in the laboratory then you give half the particles the particles on the right here you give them to Alice the ones on the left you give them to Bob and you say take them away from each other take all these ones and put them out here just drag them away capture them in a trap and displace them same with these take these far away you still have Bell pears but they're now quite far from each other now according to one of the principles of quantum mechanics once you take those Bell pairs apart they will not naturally disentangle from each other there's a theorem that if you take them apart and you only do what are called local operations you will not disentangle them they will stay entangled entanglement is very robust it's hard to get rid of it once it happens so these particles which are very very far away are nevertheless entangled the left side and the right side as quantum systems are entangled and as long as you don't bring them back together again they will stay entangled the next step is we take this cloud of particles here and we squeeze it and collapse it into a black hole it's now a black hole same on this side we collapse this into a black hole what do we have we have two entangled black holes we've succeeded in making an entangled black hole to entangle black holes and we can call it a conjecture I mean I suppose it's still a conjecture at this sort of stage but I think it's its robust conjecture that when you do that you will make a pair of black holes with an einstein-rosen bridge between them now can you use that einstein-rosen bridge is Alice outside the black hole he's Bob outside the black hole can Alice send Bob a message through the einstein-rosen bridge no you can see that from this diagram over here Bob cannot send Alice a message but again what they can do by prearrangement if everything is right and everything is nicely arranged in principle they can jump into their black holes and meet at the center how long does it take for them to meet very little time this these two may be a zillion light-years away from each other and how long does it take to for them to meet up at the center very little time um you may put you probably think I'm nuts but I think it's true this is all very interesting the question is where it's going what what's it good for where is it going nobody's going to do this this is not an experiment a feasible experiment what it has to do with it's clear that what it has to do with is it it's telling us something about the relationship between quantum mechanics and space it's telling us that the connectivity of space and the connectivity of quantum mechanics through entanglement are one in the same thing I think this is big news I think this is something that was going to catch hold and really what I think it's saying is that the deepest level quantum mechanics and gravity are not two different things which we have to synthesize together by quantizing gravity they are somehow the same thing they are somehow or at least they are so tightly joined at the hip the structure of space and the structure of entanglement or the structure of quantum mechanics they're so tightly joined at the hip that I think eventually when we get it right we will not be thinking about quantum mechanics and gravity or even quantum gravity we will just be thinking about the loof theory I don't know what it will be called but it will be one theory the two sides of which will be quantum mechanics and gravity that's my opinion I'm going to stop there and take some questions we have time for questions just make one note that finally did give seven lectures you were there seven full characters Exodia Murphy how many weeks the day he was born in 1918 how long yeah I can ask how old you Louise so that's three and a half much as a week I decide I can watch with the society physics undergraduates doesn't count over the year there was a measure which is absolutely correct um that that could well be I don't know but I think he I'll tell you my own story with entanglement my own story with entanglement is I learned about entanglement where there was a very very young undergraduate student and my reaction to it was the same as Bohr's oh this is just quantum mechanics it's not all that interesting it's just the consequence of ordinary quantum mechanics I would say I missed the boat I missed the boat and realizing just how interesting it was and the fact is that today entanglement pervades so much of physics it's hard to find an interesting article on the net that doesn't that isn't about entanglement and we're kind of living in the age of entanglement as theoretical physicists so I think I would have to say the Feinstein was very very far-reaching or his vision was very far-reaching and maybe Bohr's was not so far-reaching but you know I this is this is a matter of taste this is a matter of and the hindsight and revisionary history so I will I will yield to David that's fine still didn't understand entitlement separation okay so in inflationary cosmology or better yet in the question is how much of this is relevant to cosmology I'll phrase it that way in the sitter space which means accelerating expansion accelerating expanding universe has horizons in fact a de sitter space has the same kind of structure a very very similar structure to this two sided black hole and there is a sense in which the interior of the sitter space the space-time of a accelerated universe is a kind of einstein-rosen bridge so I think it's almost as if almost reasonable to say that we live in an einstein-rosen bridge the einstein-rosen bridge connecting to distant regions of the sitter space I'm not sure if that's what you had in mind or not but but is there is a connection yeah Lenny does this work imply that either space-time or space-time or one time I think it goes beyond that I think it see we always want the quantized gravity the same way we quantize electrodynamics I think that's ultimately going to be seen as misguided that there isn't this theory which you quantize but the two of them are so tightly joined that at some level neither of them makes sense without the other so I would say it's not a matter of quantizing gravity it's a matter of understanding them the interrelationship between quantum mechanics and gravity but yes it certainly says that space-time has quantum mechanical properties in fact that's almost completely due to quantum mechanical properties in this view but this is this is the thing which is in its infancy and people are struggling with it I told you what I think so what some of the particles between those two Alison Bob yeah what what if they what yeah if yeah that's right um entanglement has degrees of entanglement I simply talked about no entanglement which is a product state idea and the maximally entangled situation they were partially entangled the states partially entangled states have the property that you can't learn everything about one by looking at the other but you can learn some fractional information yeah you can certainly have partially entangled black holes in which case this einstein-rosen bridge tends to be longer the longer it's longer the longer it is it's very much like this well where is it we when we erase the entanglement across the boundary between two regions of space we separated them decreasing the entanglement tends to separate them and when you finally separate them completely so there's no entanglement basically there's no there's no finite and what keeps me from changing the state of one side and making nothing prevents you from making it from doing something on one side and then doing a measurement on the other side but whatever you do on one side will have no influence on the probability distribution of the second side the probability distributions for all things you can measure over here will not change if you do whatever you do at this end so you can do that and it's exactly like the penny in there or it wasn't a penny in a dime that was the chalk and the battery the instant that one person took a look at their own what they had their own share they instantly knew what the other share was but the other person who went over there didn't know so it's the same thing with entanglement when Alice does an experiment she instantly knows what Bob would get if he did the experiment but Bob doesn't know and everything about his experiment is unchanged by the probabilities so that's not a way to communicate so the way Oh howdy with hangul ranking vacuums entangled in Hangul Manhattan's because of these virtual particles the virtual particles which are created and annihilated continuously have a pattern of quanta of a quantum state which is entangled and it's a property of the lowest energy state that it likes to be entangled I don't have much more to say that we don't make the vacuum entangle the vacuum just is entangled you can what yeah it lowers its entry like that that's the word it relaxes to the entangled State yeah very good I said that it radiates away that energy and that's a form of relaxation yeah yes yes you can and this enter a confusing aspects of it you can have yes you can certainly have more than two particles entangled well the example that I gave where did I do it I said supposing you have a box of particles a boxer verb spins and you let them interact with each other they all become entangled in a very very complex pattern and the pattern is such that if you that if you divide them in half in any way you'll find one half very entangled with the other half but you can also divide them into three shares or four shares of five shares give one to Alice one to Bob on to Charlie and so forth and they still share some kind of entanglement it's a very prescient question as Charlie Bennett is emphasized this different sorry there's a notion of monogamy - tangle meant in the sense that two particles can be maximally entangled but only two you can't have three that are maximally entangled right if a is maximally entangled with B then neither one of them can meet all with angle C but if you can a partial entanglement so it as a fraction degree of entangle we can form all three of them there is a whole complex theory of the nature of boldly part-time entangled school so I can put two more questions so if contango particles in black hole is what creates the einstein-rosen green room Rosen region does that mean that if you have entangled particles outside of a black hole that they somehow distort space-time well of course they do I think what you're asking is the question if you have two entangled particles ordinary particles is there some sense in which there's an einstein-rosen bridge between them I think the answer is yes but I think it's so microscopic I mean it's not something you're going to jump into right so when you create these particles and you pull them apart for the moment you haven't collapsed them into a black hole and they're just separately individually not individually but in pairs forming these these entangled pairs is there some sense in which this entanglement that I drew there is really secretly a microscopic wormhole between them I'm not sure that's a useful concept or not but what is true is when you squeeze them together and concentrate that entanglement in small little regions as big as a black hole this entanglement will create a I'm Stein Rosen bridge so you might just think that this entanglement is already a sort of a precursor to to the presence of einstein-rosen bridges that's the way I am inclined to think about it incidentally this idea of er equals EPR it appears in the paper and it appears in number of papers with myself and one mouth it was really our primary entanglement I think they are I think they are but that would be another lecture and would the growth of complexity which is connected with the growth of entanglement is a form of clock that you internal clock to a system and yeah I think the that's right I think the tendency for entanglement to spread the antenna the tendency for entanglement the spread may well be connected with the arrow of time I think but I think that's a hard question

Channel: mrtp

Views: 40,032

Keywords: Leonard, Leonardo, Leonard susskind, stanford, stanfor university, messenger lecture, messenger, lecture, cornell, cornell university, university, physics, physicist, entanglement, space, quantum, quantum mechanics, univers, universe, modern, mechanics

Id: lH-3bFqtJjg

Length: 75min 40sec (4540 seconds)

Published: Sun Mar 20 2016