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PAUL GINSPARG: I welcome you to the third and incredibly last Lenny Susskind's three Messenger Lectures. Since not all of you were here for the earlier two lecture, I recall to you that they're billing on the university lecture site as one of the most important of Cornell extracurricular activities. And last night, Lenny certainly fulfilled the terms of Hiram Messenger's 1924 request for this series by raising our model standard with a beautiful exposition of the interplay between quantum mechanics, relativity, and gravity, including all of the H-bars, [? Cs, ?] and [INAUDIBLE].
[LAUGHTER]
There was no mistaking it. We've already said that he was a graduate student here at Cornell 50 years ago. We heard last night that in order to launch his ascent from the South Bronx to Renaissance man, we're supposed to call him Leonardo.
[LAUGHTER]
But we've been through the litany of his many research achievements. We've talked about his extraordinary presence in communicating real science to the general public through popular books, appearances on broadcast television, through his many lectures available online in video. For this final introduction, I'll instead mention a couple of personal anecdotes. That I've had so much contact with him, it's already telling. He is, after all, a much earlier generation than me.
[LAUGHTER]
Although, I too am earlier generation than Maldacena.
[LAUGHTER]
The reason for this is at conferences and elsewhere, he would always hang out with the younger people because that was his comfort level. That's what he enjoyed doing. And for us, it was this amazing bridge through his experiences and telling of anecdotes. Most recently, what this has meant is that he's been invited to a series of 60th birthday commemorations.
We overlapped at 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.
[LAUGHTER]
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 50 year anniversary of Feynman's, there's been a nominal Feynman tie-in to all of these things. And Lenny told this to me as a true story.
The set-up is, two physicists walk into the celebrity sandwich bar in Pasadena. Now, in this sandwich bar, they have sandwiches named after celebrities with appropriate condiments. So I don't know what time period this would have been. Maybe there was a Ronald Reagan sandwich or maybe it was a Clark Gable sandwich. And Leonardo muses to Feynman, "gee, I wonder what a Feynman or a Susskind sandwich would be like?" And Feynman replies, "a Susskind sandwich? Ha! I bet it would be filled with bologna."
[LAUGHTER]
And Susskind, allegedly in real time, retorts, "well, at least it wouldn't be filled with ham."
[LAUGHTER]
So the last word is last night I asked for a show of hands of people who had been here 50 years ago. And I'm going to pose a challenge to all of the undergraduates and graduate students here. And that is which of you, like Lenny, will be back 50 years from now to give the 100th anniversary of Feynman and the 50th anniversary of Susskind, and will remember that I said this. With that, let's welcome Leonard.
[APPLAUSE]
LEONARD SUSSKIND: If I remember correctly-- ah. Hello? Nope. Am I turned on? If I remember correctly, Dick gave four lectures, is that right? I think so. 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. 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 a little bit 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. 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 what 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 it 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 Bohr won the debate.
But in retrospect, it's clear to me that Einstein's view was by far the deeper. Bohr, 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 is being uncovered between them.
I should tell you that at least 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. 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 were on entirely different subjects. As far as I know, neither Einstein nor anybody else had any reason to believe they were connected.
We will see. So let me begin. Oh, 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 assistants? Two people.
Oh, come on. Two-- come here. Come on. Come up. All right. Now. 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. 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 one. I'm not going to tell you which one.
OK, close your eyes. OK, you get-- you get this one. Now closes your fists. Don't look.
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. You're a bad boy. Go over in the corner. All right, you don't listen.
You look at what you've got. I bet you instantly knew what he got.
SPEAKER 1: Yes, I did.
LEONARD SUSSKIND: How did that happen?
[LAUGHTER]
You must be magic. You may sit down now.
[LAUGHTER]
AUDIENCE: You have to release the other guy.
LEONARD SUSSKIND: Yes, you may sit down too.
[LAUGHTER]
I'm going to wander off in some other direction for a minute. I have a friend named Geoffrey West. He's a famous physicist. I love magic tricks. I'm very bad at them, and so my magic tricks are very, very simple and usually kind of stupid.
So Geoffrey West had a five-year-old child and I said-- what was 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. And he said, wow, how did you do that? I said you can do it. Go ahead, try it.
So he thought for a minute, OK. And he put his hand. Sorry about that. That has nothing whatever to do with the 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. 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 battery. Knowing the exact state of the 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. 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. A spin is a little physical system.
For the moment, let's not even worry about what it's attached to. In 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, its y component, and 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 just a 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 orient it in any direction in three dimensional space that you want.
It also has a button here. The button says M for measure. 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 1. No intermediate answer. Nothing in between. Either plus or minus 1.
This is a little bit peculiar that the component of a vector in an arbitrary direction should be plus or minus 1, but we understand this. This is quantum mechanics. It's the weirdness of quantum mechanics, but it's OK. We did our homework and that's a consistent thing to happen.
Now, it is also true that 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 could know about the spin, everything that you can know-- that there's always a direction-- it's called a polarization direction-- that if you oriented the apparatus in that particular direction, you would always get plus 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 plus 1. By contrast, if you orient the apparatus in another direction, you will get statistically somewhat random results. The more orthogonal the detector is to the polarization axis, the more random it is.
And in particular, if this arrow here lies in the plane perpendicular to the polarization of the spin, you simply get random answers. That's quantum mechanics of a single spin in a nutshell. Now, next question.
Can you simulate-- can you fool somebody into thinking they're seeing quantum mechanics? Here's your task. You have a computer. Here's your computer. On your computer screen, you have a detector, an 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 down in the box in a little circle there appears a plus or minus 1. 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?
Yes, it's not very hard. You need two things, at least two things. A computer scientist might figure out some more stuff that you actually need. But one thing you need is a random number generator because under certain circumstances, you'll 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 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, 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. In 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 numbers. 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.
1 over the square root of 2 times a state in which the first spin is up, the second one is down, minus 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 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 anymore. 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 the odd property that I find most interesting. Of course, there are detailed mathematical 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 spins 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 a complete description of the composite system, and yet no knowledge of either of the parts.
That's a feature of maximally entangled states. 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 very entangled states now.
OK. So the question then is, 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 whether you get a plus or minus 1, if one of them gives a plus 1, the other one will always give a minus 1. 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 it tells you about relations between them, but it tells you nothing about the individuals. That shook Einstein. That bothered him. He said, what's real? 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 OK 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. Did Bohr have a beard? No. He was mumbling in Paul's beard.
[LAUGHTER]
Look, I'm a great admirer of Bohr, but on that particular one, I think he was wrong. Anyway, can you simulate this system? It's kind of interesting. You can simulate it, all right. You can simulate it on a computer or a couple of computers, the situation of the entangles.
They're not entangled. If 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 it, 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's just in the middle there somewhere.
It has to have the usual random number generator, random number generator. It has to have the usual random number generator, the usual memory. But now its memory, 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 distinct computers. Remember, we're now simulating it. This isn't real. There's no real electron. 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 her apparatus was in. Once that happens, some things happen here and then it sends back a message with a random plus or minus 1, not a completely random plus or minus 1, but a plus or minus 1 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 the quantum behavior of two distant entangled systems, you have to fake it with a collection of wires that connect them basically. What will 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 tried to simulate quantum mechanics with a classical computer, you will have to fill space with wires. Those wires 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 with 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. 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 makes 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 interesting things about entanglement. Now, the next thing is, 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 an infectious, a very badly infectious disease. If you have a system which is composed now 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 polarize along the z-axis. I want to put some more in. I want to have an even number.
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.
Now you let them interact with each other. You let them just interact, maybe even just a little bit. Some kind of force is between then, 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, 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 divided in half. Just pick out half the spins and pick out another half of 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. Let's call this 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. Anyway 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 tend to get massively entangled very quickly.
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. And in fact, you're entangled with the Martians on Mars.
Let me give you another example of entanglement. In this case, it's not entanglement of spins. It's 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?
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 the following property. That if there's a particle in here-- let's call that 1, 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, I'm 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.
OK, now I'm going to tell you about entanglement of the vacuum, entanglement of the vacuum of space. 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? No. They're actually studying something extremely interesting. So to understand it, again, you have to go back to things that Feynman said, Feynman and others. Feynman said that the vacuum was full of virtual particles.
It's full of virtual particles which come and go, bip, bip, bip bip. 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 somewhere 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. 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 first divide it in half. We're going to divide space in half.
Incidentally, I can't draw a three dimensional space, so we'll have to stick with two dimensional space. Let's say that 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 tessellate it.
We're going to tessellate it and we're going to tessellate it with little cells which 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. And 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, we'll draw bigger ones. We'll be dividing space in what's called a scale invariant way or at least in a self similar kind of way and so forth and so on. Now, what I tell you is what has been discovered over the years about quantum field theories, about ordinary quantum-- quantum field theories are not so ordinary, of course-- but about the conventional quantum field theories is that the left hand side is entangled with the right hand side, which means that you can find out things about the left hand side by making measurements in the right hand side.
What is the pattern of entanglement? The pattern of entanglement-- and what does entanglement mean? Let me just say what entangle-- or 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 or 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 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 state, in other words, destroy the correlations between the left side or the right side-- not destroy them, but just create a quantum state in which they're less correlated, maybe even not correlated at all.
The answer is yes, you could 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. OK, so let's draw 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. Unlace it means disentangle it. What does it do? It creates some energy in that region.
Let's just represent that energy by a 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 the gravitational field and the gravitational field is represented by curvature and the distortion of space. Therefore, this energy density here will distort space. It will 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 create some kind of distortion of the geometry of space in here.
[PHONE RINGS]
I'm going to tell you-- yes? I'm not here. Just tell them I'm not here. I could tell you-- ah, OK. What does it do to space? It distorts it in the following way.
It takes that region and it makes the distance-- let's see. 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 from one side to the other side. It increases the distance from one side to the other side.
Now that I think about it, it's exactly what happens if-- I think it was John Wayne who wore a corset? Is that right? John Wayne, I think was the guy who wore the corset. If you were to take your scissors and cut the laces here, blip. 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.
Entanglement is doing some job of holding things together. Now, 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'll 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 one 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 disconnects 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.
OK. 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 talked about black holes and I drew a diagram representing a black hole which looks something like this. This was just 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 the 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 on 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 of 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 a black hole. There's 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 hole-- this is called a two-sided black hole-- the picture that goes with a two-sided black hole is that it 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 and 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 the 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. Supposing we take a sequence of points along here starting on Alice's side and pass through here. 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 on Alice's side. Alice is up here. Bob is down here. You start up here and you pass right through and come out on Bob's side. Can anything actually pass through from one side to another?
Can Bob throw something through and it will appear 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 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 to send 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'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 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 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 pass through quickly 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. 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-- 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. I really don't know what Alice and Bob do when they meet in the interior of the black hole.
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 also solutions of Einstein's equations. Two disconnected black holes. What is it that distinguishes the connected and the disconnected black holes? OK, so let me redraw the connected black hole.
There's the connected black hole. And incidentally, right at the waist of 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 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. They're 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 the perspective of somebody outside the horizon, the horizon has this pileup of zillions of degrees of freedom. They're quantum mechanical.
So on Alice's black hole, there's a population of degrees of freedom over here. On Bob's black hole, there's 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.
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 they're wandered off so far that they're really not 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 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.
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-entangled.
Now, this is a-- what shall I say? 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. 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'd probably say, oh, come on. It's not that easy. But on the scale of 1 to 10, it's pretty easy. How can you do it?
Let me give you one way to do it. You know that if you collide particles, electrons and they create new electron-positron pairs in a 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 pair.
The electron-positron pair come out entangled. Even if the original incoming ones were not entangled, the new ones come out entangled. So it's not hard to make electron-positron pairs that are entangled. So let's take it as a given that we can make lots and lots and lots of maximally entangled pairs.
Incidentally, maximally entangled pairs are called Bell pairs, B-E-L-L. Bell stands for John Bell, John Stewart Bell, who was one of the really great pioneers who pioneered the study of entanglement in the '60s. They're called Bell pairs if they're maximally entangled.
This is a Bell pair. All right, here's what you do. You start creating Bell pairs. To indicate that they're entangled-- this one's not entangled with this one. It's entangled with this one. To indicate it, let's draw a line across here, a lace, a 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 pairs, 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 succeeded in making an entangled black hole, two entangled black holes. And we can call it a conjecture.
I mean, I suppose it's still a conjecture at this stage, but I think it's a robust conjecture. Now 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?
Here's Alice outside the black hole. Here'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.
These two may be a zillion light years away from each other and how long does it take for them to meet up at the center? Very little time. 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'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'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 at 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. Or at least they're 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 "Ruff" 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.
[APPLAUSE]
PAUL GINSPARG: We have lots of time for questions. I'll just make one note that Feynman did give seven lectures. You were there. Maybe you only went to four.
[LAUGHTER]
LEONARD SUSSKIND: It was seven full-scale lectures? Well, he was 30 years younger than me. How many weeks did it take?
PAUL GINSPARG: He was born in 1918, so he would have been on the order of 46 years old.
LEONARD SUSSKIND: No, how long-- I didn't ask how old he was. I asked how long did it take to do the seven lectures?
PAUL GINSPARG: Two weeks.
LEONARD SUSSKIND: Two weeks. So that's 3 and 1/2 lectures a week. I did seven this week.
PAUL GINSPARG: You know, I think lunch with the [? soggy ?] physicists undergraduates doesn't count as a lecture.
[LAUGHTER]
Are there any questions? Yes.
AUDIENCE: Do you know that Bohr wrote a reply to EPR?
LEONARD SUSSKIND: In which-- yes, and John Stewart Bell read it and said it was completely incomprehensible.
AUDIENCE: Many people had that reaction.
LEONARD SUSSKIND: Yes, did you?
AUDIENCE: But in fact, well, I struggled with it many times over the years. But I think that reply demonstrates that Bohr understood perfectly well what entanglement was. In particular, he says there was nothing new about this. When you do a measurement, the apparatus becomes entangled with the microscopic system that you are measuring, which is absolutely correct. He then goes on to analyze what EPR was saying in terms of such an experiment.
LEONARD SUSSKIND: That could well be. I don't know. I'll tell you my own story with entanglement. My own story with entanglement is I learned about entanglement when I was a very, very young undergraduate student. And my reaction to it was the same as Bohr's. Huh, 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 in 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 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 Einstein was very, very far reaching, or his vision was very far reaching, and maybe Bohr's was not so far reaching. But you know, this is a matter of taste. This is a matter of hindsight and revisionary history. So I will yield to David. That's fine. Still, he didn't understand entanglement.
[LAUGHTER]
AUDIENCE: The question is, can you [? demonstrate ?] the [? usefulness ?] [INAUDIBLE]?
LEONARD SUSSKIND: So in the [INAUDIBLE] cosmology, or better yet in--
AUDIENCE: Repeat the question please.
LEONARD SUSSKIND: The question is, how much of this is relevant to cosmology? I'll phrase it that way. In de 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 de Sitter space, the space-time of a accelerated universe is a kind of Einstein-Rosen Bridge. So I think it's almost reasonable to say that we live in an Einstein-Rosen Bridge, the Einstein-Rosen Bridge connecting two distant regions of de Sitter space. I'm not sure if that's what you had in mind or not, but there's certainly a connection. Yeah.
AUDIENCE: Well, Lenny, does this work imply that either space, time, or space-time are quantized?
LEONARD SUSSKIND: I think it goes beyond that. We always want to quantize 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 make sense without the other.
So I would say it's not a matter of quantizing gravity. It's a matter of understanding 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 a thing which is in its infancy and people are struggling with it. I told you what I think.
AUDIENCE: So what if some of the particles between those two, Alice and Bob's black holes--
LEONARD SUSSKIND: Yeah, what if they what?
AUDIENCE: What if some of them are entangled?
LEONARD SUSSKIND: Yeah, that's right. Entanglement has degrees of entanglement. I simply talked about no entanglement, which is a product state idea, and the maximally entangled situation. There are partially entangled states.
Partially entangled states have the property, but you can't learn everything about one by looking at the other, but you can learn some factional information. Yeah, you can certainly have partially entangled black holes, in which case, this Einstein-Rosen Bridge tends to be longer.
It's longer. The longer it is-- it's very much like this. Well, where is it? When we erased 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 finite wormhole left anymore.
AUDIENCE: [INAUDIBLE].
LEONARD SUSSKIND: What's that?
AUDIENCE: Perhaps the entangled particle's [INAUDIBLE]. What keeps me from changing the state of a particle on one side and making a measurement of the other side? Does that make [INAUDIBLE]?
LEONARD SUSSKIND: Nothing prevents you from doing something on one side and then doing the 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 distribution 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 and the-- or it wasn't the penny and the dime. It 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 there's not a way to communicate. It's not a good way to communicate.
AUDIENCE: How do you [INAUDIBLE].
LEONARD SUSSKIND: How do you entangle a vacuum? Vacuum is entangled.
AUDIENCE: But you say that [INAUDIBLE]?
LEONARD SUSSKIND: The entanglement happens because of these virtual particles. The virtual particles which are created and annihilated continuously have a pattern of a quantum state which is entangled. And it's a property of the lowest energy state that elects to be entangled.
I don't have much more to say on that. We don't make the vacuum entangled. The vacuum just is entangled.
AUDIENCE: [INAUDIBLE]?
LEONARD SUSSKIND: You can what?
AUDIENCE: [INAUDIBLE].
PAUL GINSPARG: Yeah, the space zips up because it's lower energy, so it's relaxed.
LEONARD SUSSKIND: Yeah. It lowers its energy. 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.
AUDIENCE: Is there any way to have more than two particles entangled?
LEONARD SUSSKIND: Yes. Yes, you can. And there are confusing aspects of it. 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 box of 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 divide them in half in any way, you will find one half very entangled with the other half. But you can also divide them into three shares or four shares or five shares. Give one to Alice, one to Bob, one to Charlie, and so forth, and they still share some kind of entanglement.
PAUL GINSPARG: It's a very [? pressing ?] question because as Charlie Bennett is emphasizing, there's a notion of monogamy in entanglement in the sense that two particles can be maximally entangled, but only two. You can't have three that are maximally entangled.
LEONARD SUSSKIND: That's right. If A is maximally entangled with B, then neither of them can be at all entangled with C. But you can have partial entangled in there, so there's a fractional degree of entanglement we can put on all three of them. And there's a whole complex theory of the nature of multipartite entanglement, it's called.
PAUL GINSPARG: So I think we'll try to get two more questions.
AUDIENCE: So if entangled particles and black holes is what creates the Einstein-Rosen Bridge, does that mean that if you have entangled particles outside of a black hole that they somehow distort space-time?
LEONARD SUSSKIND: Well, of course they do.
AUDIENCE: More so than [INAUDIBLE]?
LEONARD SUSSKIND: 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.
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 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 an Einstein-Rosen Bridge. So you might just think that this entanglement is already a sort of a precursor to the presence of Einstein-Rosen Bridges. That's the way I'm inclined to think about it.
Incidentally, this idea of ER equals EPR, it appears in a paper-- and it appears in a number of papers-- myself and Juan Maldacena. But the idea was really Maldacena's idea.
PAUL GINSPARG: OK, one more.
AUDIENCE: There's [INAUDIBLE].
LEONARD SUSSKIND: I'm sorry. I heard [INAUDIBLE] and I heard entanglement.
PAUL GINSPARG: Are they moving?
LEONARD SUSSKIND: I think they are. I think they are, but that would be another lecture and it would-- the growth of complexity which is connected with the growth of entanglement is a form of clock, internal clock to a system. Yeah, that's right. I think the tendency for entanglement to spread, the tendency for entanglement to spread may well be connected with the arrow of time, I think. But I think that's a hard question.
PAUL GINSPARG: Another lecture, so tomorrow [INAUDIBLE].
Theoretical physicist Leonard Susskind delivered the last of his three Messenger Lectures on "The Birth of the Universe and the Origin of Laws of Physics," May 1, 2014. Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University, and Director of the Stanford Institute for Theoretical Physics.
