JACK HIDARY: Pleasure to
welcome everyone tonight to a special session. Tonight's topic is the
Information Paradox. We have the honor of having
two very prominent physicists with us. Professor Lenny Susskind is not
only a leading physicist known throughout the
world, but he's also one of the primary interlocutors
in this debate that's gone on for more than 40 years. And it's a real pleasure
to have Lenny here tonight to share with us his
experience of this really very interesting discussion
and argument, to some extent over
many years, and where it has led us in physics. He'll be joined
tonight by Adam Brown, his longtime collaborator. And both Lenny and Adam
are here at Google at least part of the time. Lenny visiting faculty
and Adam full time now a research scientist
here with us at Google. Tonight's going to
be very illuminating, but I do encourage people
to get more information by getting a copy of Lenny's
book, "The Black Hole War." It's actually a fascinating
read and whether or not you want to get
deeper into physics, this is actually a great way to
understand the topic at hand. So with that, let's welcome
Professor Lenny Susskind-- Lenny. [APPLAUSE] LEONARD SUSSKIND:
What I like doing best in front of an audience
is explaining something-- explaining something simple in
a simple possible-- simplest possible way. Even better, I like
to explain something really hard and complicated
in a really simple way. I think there's a certain
amount of ego in doing that. You know, you get to
say, look how smart I am. But really, it's pretty
much the way I think. Everything I ever
learned about physics I learned by teaching
it or by explaining it. And so I always take
as much opportunity as I can to explain
things, partly because I learned for it. So I'm going to do one
or two simple things about black holes. And then Adam will take over
and give you the grand overview. Where's Adam? You will, will you not? Good. OK. Yeah. Oh, yes. Time, what about time? Time is important. We have some time. But it's very interesting. Different cultures perceive
time in different ways. There are some cultures in
which people think of time as being up in front
of them, or the future as being in front of you. You face the future, right? Or you don't face the future
if you're not up to it. There are other cultures who I
think it makes more sense where the-- where the future
is behind you and you're looking at the past. Why is that? Well, you can see the past. You can't see the future. So the future must be behind
you where you can see it. In the scientific world, there
are also different cultures. If I'm not mistaken, in the
computer science culture, past-- let's see, if I'm facing
this way, past is over there and future is up there. People draw circuits,
quantum circuits, or the evolution of a computer
is going from left to right. In physics, reasons
I have no idea why physics is to-- physics
always has time going upward. That's a convention. I'm not sure how
far back it goes. But I think it goes
back to Minkowski. Minkowski was the first one
to think of the world in terms of space time. Not Einstein-- Einstein
was before Minkowski. Two years before
Minkowski, Einstein invented the special
theory of relativity. But much of the way we
think about spacetime came from Hermann Minkowski,
who had this image of space and time as spacetime. There it is. There's spacetime. The lines in it are
just mathematical lines that we draw in order
to orient ourselves. Think of time as up. Space horizontal. Many of you have seen these
kind of pictures before. And one of the
diagonal lines, let's for the moment suppose that
somebody has gotten right to the center of this diagram. They didn't just pop there. They got there by traveling
through there from the past. But at some time they just are
at the center of this diagram. Then they can do two things. They have a flag. They have a laser, flashlight. They can flashlight
the light to the left, or they can flash
it to the right. How does light move? Light moves along
these 45 degree lines. 45 degrees because
we conventionally set the speed of light to one. So you move as far as
you have time to go. And those two lines are
called the light cone. One to the left, one
to the right, and they are the trajectories
of light rays. Now, where Einstein said-- this is where Minkowski said. It's probably one of the
most important observations in physics just
drawing this diagram. Einstein, a little later
yet, later than this, was starting to
think about gravity. The special theory
of relativity really had to do with
electricity and magnetism. Later came gravity. And the key insight
of Einstein-- I think it was about 1907-- was that gravity is the
same as acceleration. You all know this if you've
been in an elevator accelerating upward, you know that you feel
a sense of pushing on your feet, just like the floor does. So gravity and acceleration
are sort of the same thing. And what Einstein said is, if
you want to understand gravity, first think about
what life would be like in an
accelerating elevator-- in a uniformly
accelerating elevator. Now, the idea of acceleration--
uniform acceleration in the special
theory of relativity is a little bit
different than it is in pre relativistic physics. If you're uniformly accelerating
in pre relativistic physics, you just accelerate
more and more and more. Your velocity will increase
and increase and increase. But in relativity, you
can't accelerate faster than the speed of light. And so the blue lines are
the imaginary trajectories of people who are
uniformly accelerated. They can't get past
the black line, because the black line is
moving with the speed of light. So they move on those
hyperbolic trajectories. One next to the next, next to
the next, each accelerating off along these hyperbolic
trajectories. And if you can
understand physics as seen by those observers,
you learn something about life in an accelerated world. And according to
Einstein, you've learned something about
what gravitation is like. Let's imagine an
observer-- let's call him an observer-- moving
along one of these hyperbolas. And somebody at this point
over here throws in an object-- throws an object
toward the center. That object moves along a
straight line, for example. And it moves and
it will eventually cross the black light cone. Let's think about
that for a moment. How does somebody who is moving
along these blue trajectories, how do they see the red
particle flowing in? The answer is, they never see
the red particle falling in. The person along here-- well, let's follow this one. How does he see-- he looks back. He can't look straight across. He has to look at a light
signal coming at him. He looks and later and later
and later, he looks back. And what does he see? He sees the particle that's
falling in asympototically approach this light cone here. Never quite seeing
it go past there. That's a little bit
strange, isn't it? I mean, an ordinary observer
moving with an accelerated velocity watching a
particle fall never sees the particle fall past-- let's call it the horizon now. Why the horizon? Because he never
sees it cross there. In fact, what he sees is
a little more complicated than that. He sees the object,
whatever it is. It could be an
elementary particle. It could be a basketball. He sees it move toward
the horizon slower and slower and slower. Why slower and slower? Because it just takes an
infinite amount of time for them to get there. And at the same
time, he sees it-- [INAUDIBLE]
contract-- relativity. He sees the object get more
and more pancaked, more and more squashed. If we were to draw-- oh, here we are. If we were to draw a
picture of somebody falling into a black hole-- now
we're coming to black holes. But the point is,
we've learned something by thinking about acceleration. We're thinking
about acceleration that we've learned that
an object never quite gets past a thing that we
can call a horizon. It pancakes. It slows down. And the same thing is true-- exactly the same thing
is true of an object-- whoops-- of an object
falling toward the horizon of a black hole. As it falls in, it
pancakes, gets contracted, and asymptotically it takes
longer and longer and longer for it to get to the horizon. Again, we learned it by
thinking about acceleration. But we now apply
acceleration, and that's the way the black hole works. On the other hand,
what about somebody who is following the trajectory
of this in falling object? They don't see
anything peculiar. They don't see the
thing slow down. Why not? Well, I watch the thing. I'm falling with it. My heart is slowing down. My watch is slowing down,
at least from the outside. The particle is getting
closer and closer. My clocks are slowing down. Its clocks are slowing down. I can't tell at all that
anything peculiar is happening. And it's not, from
my point of view. And so, what do I see as I am
falling in with the object? I see it go right
past the horizon and fall into the black hole. That is the same thing
as traveling along with that red
particle and watching it fall past the light cone. OK. So that's a little bit--
it's a little peculiar. It's a funny tension in two
descriptions of the world. In one description of the
world as seen from outside, nothing ever gets
past the horizon. On the other hand, from the
other description, somebody falling in with it,
there's no obstruction to getting past the horizon. It just takes a
finite amount of time. You're outside,
then you're inside. And we understand that. This was never considered
a source of great tension in physics that the two
descriptions are so different. It was thought of
as a curiosity, but it's more than a curiosity. It is-- what we've learned is
the relativity of descriptions, descriptions of things can
be very, very different, even though they're describing
exactly the same thing. OK. So I wanted to bring that up. Adam, I'm sure, will
talk about it more. But this is the source
of the great controversy. This is part of the source of
the great controversy that's kind of occupied physics for
pretty much most of 40 years now. Now, I want to go
onto something else. I just brought this
up for your attention. I want to go onto something
else which is quite different. Again, it has to do
with black holes. But what I want
to explain to you is why black holes have entropy
and why they have temperature. I'm sure we'll
come back to this. And if not, you can
ask me about it. OK. What is entropy? First of all, what is entropy? Entropy is hidden information. Some of you are
computer scientists. All of you use computers. You know that in
your computer, there is storage of information. It's stored in bits. In a quantum computer,
it's stored in qubits. We don't have to-- I don't need to give you a
formal definition of what information is. But let me say that what entropy
is is it's hidden information. Hidden information, for
example, if I have a box and I put a number of qubits
into the box, I seal the box. I ask what-- or
bits, bits or qubits. It doesn't matter. I put a number of
them in the box. They're hidden in the box. I can't get into the box
because I don't have the key. I then say that that box has
stored hidden information. And the amount of
hidden information we call the entropy of the box. Now, sometimes
information is hidden because it's stuck in a box. But sometimes, it's
hidden because it's in the form of degrees
of freedom of objects which are just too small to see,
too numerous to keep track of. A bathtub full of hot
water has a huge amount of information in
it-- the position, velocity of every molecule. But we can't keep track of it. It's just impossible
to keep track of it. So it's hidden. That hidden information
is called entropy. And entropy is the quantity
of hidden information. So why do black
holes have entropy? Well, first of all,
it's kind of obvious. They have entropy because
stuff falls into them, or falls onto the
surface of them if you're watching
from the outside, getting closer and closer to
the surface, getting pancaked. But we can't see that stuff. It's gotten too
close to the horizon. From another point of view,
the point of view of the person falling into the black
hole, that information falls into the black
hole, but it's hidden. It's hidden from the outside. So the outside person says
that there is entropy. Now, how much entropy
can a black hole store? The answer in classical physics
is an interesting point. The first person who realized
that black holes had entropy was Bekenstein, physicist-- [INAUDIBLE] physicist--
who realized that black holes have entropy. It wasn't that he realized
that black holes have entropy. It was obvious,
although nobody said it, that black holes have
loads of entropy. In fact, the amount of entropy
that a classical black hole, before quantum mechanics
comes, how much entropy can a black hole store? An infinite amount. You can put very, very minute
bits of information stored in arbitrarily small
amounts of energy, in arbitrarily small
amounts of volume, you can drop it into the black
hole in classical physics. And you can store any
amount of information in a classical black hole
according to classical physics. So the right statement
before Bekenstein was not-- should not have
been that black holes don't have entropy. It should have been
that black holes can have infinite entropy. Stuck-- shove as
much stuff into them as you want without
putting any additional or putting negligible
amount of energy into them. That's what we're going
to talk about now. Why black holes-- not
why they have entropy, but why they have
finite entropy. OK. So let's move on. Yeah, classically,
black-- oh, S is a symbol that's always used for entropy. I do not know
where it came from. Adam, you know where S
equals entropy came from? No, I don't know. [INAUDIBLE] ADAM BROWN: Clausius. LEONARD SUSSKIND: Who? ADAM BROWN: Clausius. LEONARD SUSSKIND: Clausius. And why did he call it S? I don't, either. But S is entropy. All right. In classical physics, the
entropy of a black hole is infinite. Now, I want to come to why
black holes have finite entropy. And here's the way I'm
going to think about it. I'm going to think
about it by starting with a very tiny black hole. Where did that black
hole come from? Don't worry about it. We start with a very tiny one. It could be only
a negligible size. And now we're going to
build up our black hole until it's of whatever size
black hole we're interested in. How are we going to build it up? We're going to build it up by
dropping in bit by bit by bit information. What is the smallest amount
of information that you can drop into a black hole? And how do you drop it in? The answer is, basically,
one elementary particle. A photon dropped into a black
hole adds to its entropy, or adds to the amount of
stored information one bit. But that's not quite right. Imagine I have the
horizon of a black hole. Let's see if we have-- OK. I don't have a
good picture of it. Black hole is a big sphere. The horizon of the black
hole is a big sphere. Now, imagine I have a laser. And I use a laser to drop
in a number of photons. How much information
does every photon convey? Well, it conveys a lot
more than just one bit. Why? For example, it conveys
all of the information about what direction
it was coming in from, or where it arrived on the
horizon, from the left, from the right,
from up, from down. In fact, there are many,
many decimal points-- many, many decimals that you
could describe the direction of the incoming photon. So typically, a photon
dropped into a black hole carrying more than one bit. How can we make sure that the
photon only carries one bit? And here's the trick. You would like to drop
the photon in in a way that all you can tell is either
it got in or it didn't get in. You can't tell where it
got in from the horizon. That's all you can tell. It's either got
in or not got in. The way to do that is
to make the uncertainty in the position of the photon
bigger than the black hole-- and that's quantum mechanics--
or as big as the black hole. Now, it turns out that if you
try to make the uncertainty-- how do you do that? You make the wavelength
of a photon as big as the size of the black hole. If you make the
wavelength of the photon as big as the black
hole, then looking at the black hole-- looking at
an object with long wavelength radiation, all
you see is a blur. Same thing with a black hole. If you drop a photon in of long
wavelength, all you can tell is either it got in
or it didn't get in. Now, It turns out
that if you try to drop in light of
longer wavelength than the black whole
size, it'll just reflect off the black hole. Won't go in. True. Take it from me. Trust me, it's true. So on the other
hand, if you drop in light of smaller wavelength,
it carries more information than that single bit. So what's the trick? The trick is to drop in the
light at just the wavelength of the size of the black hole. Good. OK. So keep that in mind. And we're going to drop in
photon by photon and photon building up the size of a black
hole by adding the energy. We're going to add
energy photon by photon. Build up the black
hole, and then when it's going to build
up, when it's built up, we're going to ask
how many photons did we have to drop in to
build it up to a certain size. That will be its entropy. That will be the number of
hidden bits of information. So what do you need to
know about black holes? I originally claimed when
I first gave this lecture that I'm going to explain it to
you without any calculus-- not even calculus. If you watch carefully,
you'll notice that there's some place
where I use calculus. When I do that, jump out
of your seat and say, hey, you're using calculus, OK? All right. What do you need to know? First of all, you need
to know the radius of the horizon of a black hole. It's called the
Schwarzschild radius. And for a standard black
hole, a Schwarzschild radius is twice the mass of
the black hole, m, times the Newton constant,
Newton's gravitational constant, divided by the
speed of light squared. Incidentally, Newton's constant
is a rather small number-- in some standard units,
10 to the minus 11. Speed of light is
a large number. And so the radius
of a black hole is very small by comparison
with any other object that were given mass. Now, we're going to
drop in a photon. How much energy
do we get when we drop in a photon of
wavelength lambda. Lambda is a standard
notation for a wavelength. How much energy do we get? Well, that's quantum mechanics. So we go back to
quantum mechanics. There's a symbol called h-bar. That's a number,
Planck's constant. The speed of light
divided by the wavelength. You can check that this
has units of energy. And that's the amount of
energy that one photon of wavelength lambda has. This has nothing to
do with black holes. This is very standard. That's how much energy
you put in, h-bar C. And now we're sending
lambda equal to the radius of the black hole itself,
which h-bar C divided by r. Next, how much mass does
that give the black hole? Well, all we do is use
E equals mc squared. If we drop in a
certain energy, we divide it by C squared to
find the change in mass of the object. So we divide this
formula by C squared. That puts the C in
the denominator, and it tells us the change in
mass of the black hole as h-bar over RC. The next step, we go
back to this formula. We change the mass by this much. That tells us how much
the radius changes. And here it is. The change in R is h-bar
G-- the G comes from here-- divided by R times C cubed. You can just trace that
through and you'll find it. And that's what you find. The change in the
radius of the black hole is h-bar G over C cubed. And that's kind of interesting. Let me multiply
that formula by R. I've taken the R
in the denominator and put it up over here. Here it is. R times the change
in R is a number. That number doesn't
depend on anything except the constant
h-bar G and C. So the change on R time R is
h-bar G. Right above C cube. Now, I maintain that R
times the change in R is the change in R squared. Calculus-- calculus in a day. That's the only
calculus I've used. R delta R is one-half
the change in R squared. And R squared is proportional
to the area of the horizon. The horizon is 4 pi r squared. So the left-hand side is
proportional to the change in the area. And the right-hand
side is just a number. It doesn't matter how
big the black hole is. Every time you drop in
one bit of information, you change the area
by exactly that much. R delta R, or the same
thing, the change in the area is this universal constant. Now, this universal
constant has units of area. And it's called the Planck area. It's the square of
the Planck length. And it's about 10 to the
66 square centimeters. It's really small. 10 to the 66. So what it's telling
you is, every time you drop in a bit
of information, it changes the area of
the black hole by 10 to the minus 66 square
centimeters, the Planck unit. Well, you can turn that
around and you can say, how many units like
that do I have to put in to make a black hole of area A? That's the entropy. That's the number of hidden
pieces of information you put in. And that's proportional
to the area divided by the same universal constant. You divide it by that. So the C cube goes upstairs. The h-bar goes downstairs,
and the G goes downstairs. That is a famous formula. That formula is
Bekenstein's formula. Bekenstein-- everything
we're doing now has been sort of a
little bit fuzzy. It's a little bit
fuzzy because when I-- most of the equations
I wrote down was sort of proportionalities. They're true. I left out pies. I left out twos. I didn't really know exactly
what their longest wavelength looked-- the longest
wavelength photon I can get into a black hole is. That was a little
bit sketchy there in terms of the coefficients. Yeah. AUDIENCE: [INAUDIBLE]. LEONARD SUSSKIND: What's that? AUDIENCE: [INAUDIBLE]. LEONARD SUSSKIND:
Two-dimensional? AUDIENCE: Three. LEONARD SUSSKIND: Three. This was a
three-dimensional world. I'm sorry. I couldn't draw it
as three-dimensional. Yeah. So this is a world
of three dimensions. It would be different in four
dimensions, five dimensions, six dimensions. But very similar. Very similar, but different. The numerical
coefficients Bekenstein could not figure out. Person who figured out
the numerical coefficient with precision was Hawking. I won't go into that. That makes a more
complicated calculation. But this was the
basic calculation that stemmed from around the
time of 1975, '73, '74, '75. The calculation that
black holes have entropy, but that the entropy is finite. Oh, here's an interesting point. Notice where the h-bar goes. h-bar is a small number
that characterizes quantum units, biomechanics. If quantum mechanics were to be
replaced by classical physics, it's the same as saying
h-bar is equal to 0. To the classical world as the
world of h-bar going for zero, if you look at this
formula, you'll see indeed, as h-bar gets
smaller and smaller, what happens is the entropy
gets larger and larger. AUDIENCE: [INAUDIBLE] your
relationship [INAUDIBLE].. LEONARD SUSSKIND: Initially? AUDIENCE: Yeah. LEONARD SUSSKIND:
Goes back to Planck. It goes back to Planck. Planck knew about
the speed of light. OK. Well, I'll take a
couple of minutes and answer that question. There are three basic
units in physics-- mass, length, and time. Everybody will agree,
mass, length and time are the basic units. There are also three basic
constants in physics. When I say they're basic, let me
call them universal constants. The speed of light--
why-- in what sense is the speed of light basic? It's basic in the sense
that-- here's what it is. It's the fastest possible
speed that any object can go. Once you say that
any object can go, you're talking about
something universal. It's not a feature of photons. It's not a feature-- it's
a feature of anything. No object can move faster
than the speed of light. It's a universal constant. It's not like the speed
of sound in this room that changes from room to room. Every pair of objects
in the universe interact with a gravitational force
that's controlled by Newton's constant. So again, Newton's constant
was a very basic constant. Planck discovered yet another
constant-- his constant-- h-bar. Was it universal? Was it something that
everything in the world has to-- is controlled by? Well, I don't know
Planck knew it. I think he suspected it. I think he did suspect it. But it was Heisenberg
who said, for any object the product of the
uncertainty in position and the uncertainty
of momentum is always greater than or equal to h-bar. It's [INAUDIBLE] to be exact. Again, an element
of universality. Not for protons. Not for people,
but for anything. So those are three
basic constants. Planck asked the question, out
of those three basic constants, can we construct units of
length, mass, and time? And yes, if you have
the three constants, you can assemble them together
and construct units of space. So this C cubed over h-bar G, if
you take the square root of it, is the basic unit of length
that Planck discovered. So it was-- it was
dimensional analysis. You had these three
constants, and he said, can I make a set of
units out of them? Maybe those units are
important in some way. He didn't know in what way. Remember, this was before the
invention of quantum mechanics. Certainly, it was another
25 years or another 26 years before quantum mechanics
as we know it existed. It was before the invention
of the general theory of relativity. So he was just guessing
that these things might be important. Does that answer your question? AUDIENCE: Partly. I mean, I'm still curious how he
came up with [INAUDIBLE] value. LEONARD SUSSKIND: Oh, he just
put the constants together until he got a length. Dimensional analysis. AUDIENCE: So this was empirical. LEONARD SUSSKIND: It was--
oh, absolutely empirical. AUDIENCE: OK. LEONARD SUSSKIND: Yeah, yeah,
yeah, yeah, yeah, absolutely empirical, yes. And may have been one of
the first important, OK? OK. Well, I'm almost finished. Don't worry about it. All right. So that's where those
units came from. Now, an object like a black hole
has energy, namely, its mass, or its mass divided, E equals
mc squared, e equal-- yeah. Take the mass and multiply it
by c square, that's its energy. We say it also has entropy. If it has entropy and mass,
It has something else. Anybody know what that
something else is? Temperature, temperature. OK, so this formula over
here is called the first law of thermodynamics. What it says is
that whenever you change the entropy
of the system, you also change the energy. For example, supposing
you do change the entropy by one unit, one basic bit. Well, let's set
delta s equal to 1. The energy necessary to
change the entropy by one unit is called the temperature. That's the definition
of temperature. You're probably not
terribly familiar with that, but it is the fundamental
definition of the temperature of an object. How much energy does
it take to add one bit of hidden information to it? That's thermodynamics,
it's not quantum mechanics, it's not relativity, it's
just basic thermodynamics. All right, so if
I say every time I drop in a photon, that's one
bit, and it changes the energy. Here's the formula for
the change in energy, h bar C over R, then
this h bar C over R must be the temperature. Basic thermodynamic
argument, any person who knew thermodynamics
could have made it. Bekenstein himself
did not make it. I don't think he knew that the
black hole had temperature. Again, it was Hawking. The temperature
of the black hole is h bar C over R. Well, if
an object has temperature, it means that it radiates. An object that has
temperature is a blackbody. A blackbody is just a thing
which has temperature, but because it has
temperature, it emits photons. Any object with a
given temperature will radiate at a certain rate
controlled by the temperature. If it radiates-- this
was something new. It was always thought that
black holes were really black, meaning to say that nothing
was given off by them. But what this told Hawking-- actually, the truth is Hawking
didn't believe it at first, but he came to believe it-- that if the black hole
has entropy and energy, then according to this formula,
it must have a temperature. And if it has a temperature,
it must radiate. If it radiates, like anything
else, it will lose energy. If it loses energy, it
means it loses mass. And so eventually, the black
hole will radiate away. When the black hole radiates
away, it will just disappear. Like a lot of those-- roughly
like a droplet of water, just radiating its energy away,
either in the form of molecules of water, or even other forms,
let's say molecules of water. It'll eventually just disappear
when all of its energy is gone. This led to the big puzzle,
what happens to the stuff that fell into the black hole, all
of this hidden information, what happened to it when the
black hole evaporates? Nothing can get out of a black
hole, so it can't get out. Maybe it just disappears. Maybe it just disappears
from the world, the bits that fell into the black hole. Ah, but that's not consistent
with the laws of physics, with the most fundamental
law of physics, is that information
never disappears. It really is built deeply
into classical mechanics, it's called the
Liouville theorem. And it's really even more deeply
built into quantum mechanics, it's called unitarity. Those are just the words for it. But what it says
is that information may get lost in a
practical sense, may get lost in
a practical sense because it gets all scrambled
up and too hard to see, too hard to retrieve-- but that's a technical problem. Information itself
must never be lost. And here we now have the
situation, the black hole evaporates. Before the black hole
evaporated, you could just say, oh, it's there, it's
in the black hole. Or it's there on the
surface of the black hole. But once the black hole
completely evaporated, now you have to
answer the question, did information
really disappear? Is this something new? Do black holes
create anew, do they catalyze a new thing that
was previously unknown, namely that information can
disappear from the world? Or is there some secret way
that the information is there, in the radiation that
gets radiated away, but that's too hard to pull
apart from different photons? The argument against saying
that the information is there in the radiation is that nothing
can get out of a black hole without exceeding
the speed of light, and so it could not have
gotten out of a black hole. That was the big dilemma
that Hawking enunciated, that Hawking created. It was a big dilemma. I think he gave
the wrong answer, but it was an
extremely deep insight. And with that, I will
leave it for Adam to fill in the details. Adam? [APPLAUSE] ADAM BROWN: So what I'm
going to tell you about is trying to answer
the question, does information escape
from black holes? So this is what Lenny
just finished with. After Bekenstein and
Hawking had discovered that black holes have entropy,
and therefore eventually evaporate, that
raised a question that Hawking raised almost
immediately, in fact, after this had been-- the temperature of
a black hole had been realized, which is when
the black hole eventually disappears, the black
hole slowly gives out all its energy. When it eventually
disappears, what happens to the information that
fell into the black hole, that constituted the black hole? Does that information
make it out? Is that spewed back into the
universe along with the energy, or is it destroyed? And this has been one of
the great motivating thought experiments over the
last half century. And Lenny has played
a big part in this, the development of
this thought experiment and the implications of it. And what I'm going to
do now is just give you some understanding
of why there is a problem, what
Hawking's argument was that there should be a problem. And then maybe hint at a
few things beyond that. OK, so does information
escape from black holes? What is a black hole? You know what a black hole
is, and I just told you. It's a prediction of Einstein's
general theory of relativity, our best theory of gravity-- an object so massive and heavy
and compact that nothing, not even light, can escape. And of course, over
the last few years, the most exciting observational
things that have happened have been, we have both seen
them in the Event Horizon Telescope, and we
have heard them, or at least-- what we've seen
is the accretion disks that surround them, not
the black hole itself, because those are black, with
the exception of the Hawking radiation that's far
too faint to see. And we've also heard
them with gravity waves. OK, so here is my little
picture of a black hole. And the sophistication
of this picture is going to be everything
that we're going to need, and everything Hawking
needed to run his argument. And there are two
bits in this picture. There's the red
dot in the center, and there is the blue
circle that surrounds it. And the fact that
there's two things encodes for us the
crucial distinction that will be played between
being dead, and merely being doomed. And that's really going to be
the crucial distinction for us. So the blue is called
the event horizon, that is where you are doomed. The singularity
is at the center, and that, by the
time you get there, you are most definitely dead. And so here is a stick
figure ready to be thrown into the black hole. And in this animation,
as they pass the event horizon of the black
hole, they are, at that stage, doomed. However, they may not be dead. By contrast, once they
reach the singularity, then they are definitely dead. They have been scrunched
to a geometrical point, and generally have
an unhealthy time. And indeed, as they
approach the singularity, as they get closer and
closer to the singularity, life gets more and
more unpleasant. The tidal forces start
ripping them apart, the gravitational
field at their head is very different from
the gravitational field at their feet. Life gets increasingly
unpleasant, but they are sort of guaranteed
to be dead by the time they hit the singularity. But crucially, for a
large enough black hole, there could be nothing wrong
whatsoever with the experience of somebody who is passing
through the event horizon. So the distance between the
singularity and the event horizon is determined by
the mass of the black hole. So if you have a
black hole that weighs the same as the sun, a
solar mass black hole, that mass is about--
that distance is about one mile between
the singularity and the event horizon, which, if you're moving
at close to the speed of light, and you will indeed
be moving at very close to the speed of light by
the time you get close to it, it doesn't take
very long at all. However, if you have a much
bigger black hole, a much more massive black hole, the size
of the black hole, the distance from the singularity
to the event horizon scales linearly with the mass. So the black hole at
the center of our galaxy is a million times
the mass of the sun. Therefore, it is a million
miles between the singularity of that black hole, this
crunching point at the center where all of the
mass accumulates, and the event horizon, the
point of no return, the point at which you'd have to move
faster than the speed of light to escape. The black hole at the
center of Andromeda is, in fact, a billion
times the mass of the sun, and therefore has a
billion-mile event horizon. And if you took a black hole
that was a million times bigger again, let us say, then you
could very happily live out your entire life between
crossing the event horizon, even moving at the
speed of light, or close to the speed of light,
before you hit the singularity of the black hole. And indeed, the
tidal forces that are going to make
life unpleasant get very strong close
to the singularity, eventually becoming
formally infinite as you approach the singularity. But as you pass
the event horizon, for very large black holes,
the tidal forces are very small and life is not unpleasant. In fact, if you cross
the event horizon, you would find that there would
be no sign to you whatsoever that you have passed
the point of no return-- that to get out, you
would have to fire your rockets infinitely fast. You just glide across
completely oblivious. Now, the singularity,
of course, is where gravity gets very strong. You don't know what's
happening there. Maybe we need string theory
to describe, have any attempt to describe what's going
on at the singularity. Quantum gravity gets
extremely pronounced near the singularity. But it seems as though
nothing strange is happening at the event horizon. There's a teleologically
strange thing that's happening, which is, that's the point
at which you'd better have fired your
retrorockets, otherwise you're not getting out. But in terms of just
the local geometry, there isn't anything
strange that happens at the event horizon. You just you just pass
on through unimpeded. And therefore we think
it is well understood. OK, so the question is going to
be, when this thing evaporates, with those preliminaries
about classical black holes, the question is going to
be, does the information make it out? And maybe I should,
before explaining why there is a black
hole information paradox, explain why there isn't
a information paradox if, instead of burning up your
black hole, you burn a book, let's say. So the question is,
does the information get destroyed when
you burn a book? And in common parlance, I
think the answer would be yes. That's indeed, often the
point of people burning books, is to destroy the
information that they contained. But a physicist
would say that no, at a microscopic level, the
information in the book, when you burn it-- so what we mean by information
conservation, information escape, the information
is not destroyed. You burn the book, and you
turn all the pages of the book into a stream of
outgoing photons that have subtle
correlations between them. What that means is, you've
taken the information, and you've scrambled it up so
that it's very hard to recover. But according to our best
theories of the universe, according to quantum
mechanics, you have not destroyed
the information. The information is still
encoded in the photons. And if you were a
super-futuristic civilization that was technologically capable
of gathering all the photons and performing some
extremely complicated quantum operation on them, and
quantum measurement on them, you could discover the quantum
information that constituted the book before you burned it. So books, there is-- according to our definition of
what it means for information to be conserved, burning
books, and in fact anything non-gravitational you could ever
do, cannot destroy information. As Lenny remarked, it
is built into the sort of core of quantum mechanics,
that information can neither be created nor
destroyed, that it is conserved by all processes. And that's why when
we come and apply the same arguments
to black holes, the stakes are
going to be so high. OK, so that's if you take your
encyclopedia and you burn it. We think that
information is preserved. We assume that
you do not destroy the information [INAUDIBLE],,
a sufficiently advanced civilization could
reconstitute the information that was contained
in the encyclopedia. What if we take the
encyclopedia and throw it into the black hole? So this is going to
be the crucial thought experiment that's
going to establish that there is a problem. So you take the
encyclopedia, you throw it into the black hole. And such is your
love of learning that you jump in
after the encyclopedia and read it as you fall down
towards the singularity. Now, if you're
smart, the black hole you will select to throw
the encyclopedia into will be a very large black hole. Let's say a black hole
whose Schwarzschild radius, whose distance from
the singularity to the event horizon, is
more than 100 light years. If it it's more than
100 light years, then you're going to have
a very gentle ride, indeed. You can live out your natural
life reading the encyclopedia all the way down,
confirming that indeed, the information contained
in the encyclopedia is, through the event horizon. As you pass the event
horizon while reading your encyclopedia, nothing
particularly strange will happen to you. You will maybe have a
strange sense of foreboding, but there will be no other
sign from the universe that you have passed
the point of no return. You will be doomed, but
you will not be dead, and you will spend
the rest of your life reading the encyclopedia. And sometime before you
hit the singularity, you will perhaps finish
the encyclopedia, and that will be that. OK, so you have confirmed
that the black hole, that this encyclopedia did
indeed cross the event horizon and continue on towards
the singularity. And as I've remarked,
the event horizon is the [INAUDIBLE]
point of no return. Once you have passed
the event horizon, you can't get out
again, not-- even if you can move at the speed of light. If you take a flashlight
and shine it behind you, even that won't make it out. In fact, there is a sort
of further statement that, since you can't move fast--
if you cannot move faster than the speed of light, you can't
move to a larger radius at all. Once you've passed
the event horizon, you can't move out in
this diagram whatsoever. You are inevitably sucked
in towards the singularity. In fact, even if you move
at the speed of light out, your distance from the
singularity shrinks with time. Yeah? AUDIENCE: Is that
an observable effect of crossing the event horizon? In other words, if two people
are sitting next to each other, at some point, they
can no longer speak, because one of them is upstream? ADAM BROWN: So what would happen
is that this one can still send a message to that one,
because they send the message, and this one falls
in to collect it. The question of-- yes, so
there is something at the event horizon that happens, which
is this teleological effect, that you're definitely
going to hit the black hole. But you can't, there's
no local measurable, observable that tells you
your t-equals-infinity fate, your long-term fate. None of the curvatures--
there's none of the curvatures are getting large here. Even what the distant
stars look like to you, as you drift across the
horizon, looks, is unchanging. AUDIENCE: If I fall
in just ahead of you, close, but just ahead, could we
continue to talk to each other? ADAM BROWN: Yes, we
will be able to continue to talk to each other, depending
on how we fire our rockets. AUDIENCE: Without
firing our rockets? ADAM BROWN: Without
firing our rockets, we would continue to have a
conversation all the way down. LEONARD SUSSKIND: And
you can talk to me, and I can talk to you. ADAM BROWN: We can
talk to each other, yes, up to a certain point. Because I, even though I'm
heading toward the singularity, inevitably, I'm not moving
at the speed of light. So if you shine a
laser beam towards me, it can, up to a certain
point, catch up with me. AUDIENCE: So isn't
there a point where somebody who is just
outside of the event horizon then somebody who's just inside,
well, who is going to make it, and somebody isn't, assuming-- ADAM BROWN: Yes, if the
person who is out here decides to stay out, then
while they can continue to send messages
to the infaller, the infaller can never
send messages back. That is for sure. However, the decision of
the person who stays outside to remain outside is, they
have to know where the event horizon is to know where
to fire their retrorockets at the appropriate juncture. OK, so this is
really all Hawking required in order to establish
that there is a problem. As we said, that's far for
a large enough black hole. That could be a
hundred light years. And Hawking, in 1974,
as we just learned, decided that black holes
evaporate eventually. All of these experiments
we're describing are very theoretical,
because first of all, you need to be able to
gather all of the radiation from the black hole to decide
whether the information has made it out. And secondly, you need to
wait for your black hole to evaporate. And black holes that have-- I said a solar mass black
hole takes 10 to the 55 times the current age of the
universe to evaporate. A black hole that's
100 light years across takes
correspondingly longer. But if you could
do it, then Hawking says because there's
a temperature, eventually the black
hole will evaporate, eventually it will be gone. And you can ask
the question, what happened to the information
that fell into it? Does it evaporate
unitarity, we say. So the different ways to say
the information is conserved, is information preserved,
is the evaporation unitary? You can ask all of
those questions. All the information, at least
given the story I told you, resides in the encyclopedia,
as you live out your life reading the encyclopedia
and sailing on down to the singularity. But Hawking's
calculations showed that the Hawking
radiation, the energy that is emitted from the
black hole, is not emitted from the singularity. It's not emitted
from the singularity partly because that's what
Hawking's calculation shows. But secondly, even if there
was some radiation that was emitted from
the singularity, because the radiation can't go
faster than the speed of light, it would just fall back
into the singularity again. Does you no good. All of the Hawking radiation,
according to Hawking's formula, is emitted from the horizon. All of this Hawking
radiation, by the time the black hole is
finished evaporating, the only thing that will
be left of the black hole will be all this-- according to
Hawking's calculation, will be all of this Hawking
radiation streaming off into the night sky. Does that Hawking
radiation-- it must somehow encode the information that
made it into the singularity at the center. But there is a problem, which
is that the encyclopedia ends up at the singularity. The Hawking radiation is emitted
from the event horizon, which, as we established, can
be 100 light years away from the singularity. And the question is, how did
the information, if it escaped, how did the information
escape, given that it would have to tunnel
faster than the speed of light, 100 light years from
the singularity, out to the radiation--
out to the event horizon, in order to be admitted? So that is why Hawking
says information must be destroyed during the
evaporation of a black hole. That's what his paper says. And this has really
been one of the-- this is a big problem. As Lenny said, I think
it's ultimately incorrect. I think information does indeed
escape from a black hole. But answering and
explicating how it escapes from a black
hole, and what exactly is wrong with his
argument has been an extremely productive line
of thought, right from the word "go." Many of Lenny's
most famous ideas were developed to try
and rebut, or at least address the questions
raised by this argument. And it continues to
be a very active area of research up till today. So even in the last
few months, there have been some exciting
new developments, as people have like, figured out
another little pieces of the puzzle of quite how
the information escapes. And with that, I will-- LEONARD SUSSKIND: Let me
just interject one thing. I said earlier that there was
this tension between the two ways of seeing the black hole. From the point of
view of outside, nothing ever falls
into a black hole. So from the point of view of
outside, it's not a puzzle. It never got into
the black hole. It's only from the point
of view of somebody who's riding in
that they experience the objects as falling in. But it's this tension
between these two pictures. Well, from one picture, nothing
ever fell into the black hole. it just collected
near to the horizon, and then evaporated
from the horizon. From the other point of
view, [INAUDIBLE] puzzle. So this tension between the
two ways of seeing the world was really deeper than
was thought to be. It was not just the curiosity. ADAM BROWN: Part of the puzzle
of the information paradox is this tension
between the inside view and the outside view. I presented the inside view-- you jumping across
the black hole horizon with the encyclopedia,
reading it on the way down. As far as you're
concerned, you definitely went into the black hole, and
the information went in too. If you wisely decided not
to jump into the black hole, and to stay a long way
away from the black hole, you would actually never see
me cross the event horizon. Why? Because the light
from me would have to get to you in order
for you to see it, and nothing can escape from
the horizon of a black hole. The light cannot escape from me. So as far as somebody far
away from the black hole is concerned, they may think
that the information never even went into the black
hole to begin with. And the question, part
of the dramatic tension, I think is what
Lenny is saying, is that it's how to
reconcile this inside view with this outside view. You might just
think that they all need to tell a completely
consistent story with each other. But maybe they only need
to tell a consistent story with each other where the
observers are able to compare their stories with each other. Shall we move to a
question-answer session format now-- Lenny, do you want
to come up and-- AUDIENCE: Thank you. So thinking back of your
question, of how do you go from the singularity
to the event horizon. That information is released
at the ultimate moment the black hole
evaporates, basically? I mean, should we use
black hole to store secret for a very long time? Is that-- ADAM BROWN: It's
a great question. Should we use-- when is
the information emitted from a black hole? Actually, almost all
of the information emitted from a black
hole is emitted while it is still very large. So eventually, the black
hole will get small. As it evaporates, it starts
off very cold and big. And big means cold
for black holes, because the formula
that Lenny wrote down was that the temperature
is equal to h bar divided by the radius. So when it's big, it's cold,
evaporates really slowly. Then as it emits energy,
the radius goes down and the temperature
goes up, and it actually emits energy faster
and faster and faster. So there's a runaway
process in which it gets hotter and
hotter and hotter, and emits more and
more radiation. But you can use the formula
that Lenny wrote down to tell you when most of
the information is emitted. And most of the information
is emitted early, as in, is emitted while the
black hole is still big. Because the entropy of the black
hole is given by its radius squared. And that's tracking
how much information is left in the black hole,
and how much has already been emitted. So between the time
when the black hole is maximum size and half
the radius that it was, it's already emitted
about 3/4 of the information it will ever emit. AUDIENCE: So is there any
measurement or any way whatsoever to figure out,
at any point, that you're inside a black hole? So you said that it wasn't clear
as you crossed the boundary. But could we know
whether or not we are all hurtling towards some
ginormous black hole right now? Like everything we
know is inside some-- [INAUDIBLE] hole. LEONARD SUSSKIND: Well, if
the black hole is big enough, you can sense that you're
falling toward an object by measuring tidal forces. What are tidal forces? They're the forces
which distort you. And even if you're in free fall,
even if you're in free fall, because the gravitational
field is uniform, it's pointing toward
the center, there are forces on you
which will tend to elongate you and stretch you
along the vertical direction, and tend to compress you along
the horizontal direction. Those are forces, are
feel-able, you can sense them. But they're very, very weak, if
the black hole is big enough. So in principle, with
sufficiently good detectors, force detectors,
accelerometers, or whatever it is, if you suspected
that you were falling toward a black hole whose
mass you thought you knew, in principle, you
could measure that. But the effects of
these tidal forces would be very, very, very small. That's from the point of
view of somebody falling in. One of the things
I didn't tell you-- I told you that the black
hole has a temperature, and that temperature
is very, very low. Remember the, if you
looked at the formula that I wrote down
for the temperature, you would discover that the
mass in the denominator. So the bigger the mass
of the black hole, the lower the temperature. If you took a solar mass black
hole, the temperature, I think, would be about 10
to the minus 8? ADAM BROWN: Yeah. LEONARD SUSSKIND: Don't
ask me what [INAUDIBLE] is. ADAM BROWN: 60 nanokelvin. LEONARD SUSSKIND: 60
nanokelvin, good, all right. So the temperature is very low. You would think that
that's extremely benign. On the other hand, the-- from another point
of view, the reason the temperature is so low
is because the photons which are emitted from the
horizon lose energy as they propagate outward,
for the same reason that if I threw this up in the air-- I won't do it, don't worry. If I threw this up in the
air, as it travels upward, it loses energy,
loses kinetic energy. We talked about kinetic energy-- just to try to fight its way
out of the gravitational field. Same thing is true
of the photons that are traveling out of a,
out of the near horizon region. They lose energy,
and so from far away, as seen from far away, the
temperature of the black hole is small, because the energy
of the photons is small. But if you track it
in toward the horizon, you would say those
same photons, when they were emitted
from near the horizon, were very, very energetic. And if you do the
nominal calculation, you will find out that as
you move toward the horizon, the temperature gets bigger
and bigger and bigger until, when you get
right to the horizon, the temperature is
almost infinity, just enormously large. Nevertheless, the person who
is falling in doesn't seem-- it seems that that
person does not experience that temperature. Somehow, they're immune to it. Who does experience
the temperature, and how would you
detect that temperature? If you had a
thermometer, and you lowered it down on a
cable, fishing line, lowered it down, don't allow
it to go through the horizon, and then reel it
back in and look at what the
temperature registered, you will discover
the temperature when it was down there near the
horizon was extremely large. But the only way
to find that out is by pulling the
thermometer back up. If you were to drop the
thermometer through, and fell through with it, watching
the thermometer, nothing. So that's the curious, as I
said, the tension that's there. Do we understand that? Yeah, I think by now, we
understand it, but [INAUDIBLE].. That's for next time. You want this? ADAM BROWN: I have my own. LEONARD SUSSKIND: Oh,
you have your own. SPEAKER: Next question's here. AUDIENCE: I have two questions. My first is, so with Lenny,
we derived the radius of the black hole, right? LEONARD SUSSKIND: We
derived the entropy. AUDIENCE: Oh yes,
yes, the entropy, by starting through and working
through all the calculations. LEONARD SUSSKIND: Yeah,
what I didn't mention, incidentally, the whole
idea that the entropy was proportional to surface
area was itself a surprise. In most contexts,
if you ask what's the entropy of this room,
it would be proportional to the volume, right? Because just the number of
degrees of freedom in the room is proportional to the volume. So this in itself,
just that the entropy was proportional to
the surface area, was itself a very big surprise. But go ahead. AUDIENCE: OK. And then, in Adam's
presentation, you mentioned the
Schwarzschild radius, which is the radius from
the singularity to the event horizon. My first question is, is
the Schwarzschild radius equivalent to the radius
that we were deriving, or is the radius-- so those two are the
same, or is that-- ADAM BROWN: Yeah,
so they're the same. So the area is the
Schwarzschild radius squared, the area of the event horizon. Asking what the distance
is from the event horizon to the singularity turns out to
be a slightly tricky question, but it's about the
Schwarzschild radius. AUDIENCE: OK. And then my second
question is about the model that you showed us at the
end for the black hole. You told us that it
encoded about two pieces of information, right? But something that-- I
mean, I've noticed like, in physics in general, is
that the geometry of a model also encodes
information due to being able to use symmetry
arguments, et cetera, and things like that to tell
you things about your system. From your model, it seemed
that you had your singularity, you had your event horizon. It was circular, and it
seemed that it symmetrically radiated Hawking radiation
out of the event horizon. Was that a deliberate
choice, or was that just like an arbitrary
selection of the model? ADAM BROWN: So the question was,
when I wrote down a picture-- and Lenny also had written down
a picture of a black hole-- we drew it as circular? Spherical, as it
should have been, if it was three-dimensional--
why spherical? There turns out to be a very
good answer to that question, which is that, unless
they're spinning, unless they have
angular momentum, all black holes are circular. And if they don't start out--
er, spherical, thank you. I'm get rid of my
two-dimensional thinking. If they don't start
out spherical, they will very rapidly
"spheri-size--" LEONARD SUSSKIND:
And "spherical-ate." ADAM BROWN: And spherical-ate,
yeah, and spherical-ate. The only exception to that
is that they start off spinning, which in fact, many
astrophysical black holes do start out spinning, because
they form by two things bouncing into each other,
or they start off with a star that
is itself spinning. And even if it was only
gently spinning to begin with, by the time it's collapsed
down, conservation of angular momentum means it'll
be spinning quite rapidly. So that's really-- for
astrophysical black holes, that's typically
the only thing that stops them being
perfectly spherical, and then they bulge
out a little bit. But even then, that affects none
of the arguments that we gave. Everything would just
go through just as well, with some small changes in the
order-one factors out front, if we considered
spinning black holes. LEONARD SUSSKIND: You know
why the earth is spherical? How come the earth doesn't
look like a potato? AUDIENCE: Equilibrium? Hydrostatic equilibrium? LEONARD SUSSKIND: Well,
yes, but it's just gravity. If there was a big lump on the
earth, a mountain bigger than-- let's say twice as
big as Mount Everest-- what would happen to it? It would be
flattened by gravity. So it's all this
gravity, that's pulling in from every direction, that
tends to make it spherical, the Earth. It's much more so-- so it's the
same thing, except on steroids, the gravitational field
of the black hole. Just very quickly takes
any little bulge in it and flattens it out. Not flattens it, it
spherical-ates it. AUDIENCE: [INAUDIBLE]
minimizing the [INAUDIBLE].. And does it
[INAUDIBLE] minimize? LEONARD SUSSKIND: I
heard the word minimize, and I think that's
the right idea. SPEAKER: Actually,
sorry, the next question is here in the back. AUDIENCE: So is it right
to think of the gas giants being the
seed to a black hole, or the beginning of a black
hole being a gas giant? ADAM BROWN: So the
question is, how do actual black holes that we
actually have in our universe, how do they form? Yeah, so I mean, I
guess first of all, from the point of view
of what we're saying, how they form doesn't
really matter. But there are two-- black holes in our
actual universe tend to come in two sizes. They're either a few
times the mass of the sun, or they're of order a million
to a billion times the mass of the sun. LEONARD SUSSKIND: Most
currently, [INAUDIBLE] 30 solar masses. ADAM BROWN: Right. So the ones that we
heard with the LIGO, with the gravitational
wave detection, were 30 solar masses
each, two of those slamming into each other. The ones that we saw with the
Event Horizon Telescope, well, we saw one, and it was
a billion solar masses. It was the one at the
center of Andromeda. And those two have, from an
astrophysics point of view, have different sources. One forms the small ones
formed by starting off with very large stars, and they
undergo gravitational collapse. The sun is not big enough to
undergo gravitational collapse at the end of its life,
it'll just peter out. But if it was big enough-- of
order 30 solar masses would certainly do it-- then it would eventually
form a black hole. The ones at the
center of the galaxy, it's a little less clear. But it seems to be
just a conglomeration of a whole bunch of stuff. AUDIENCE: And so when we
observe jets, is that separate from the radiation in the model? And that information
that is being ejected is not recoverable because of
the unobservable information between the singularity
and the event horizon? ADAM BROWN: The
question was, when we see jets emerging from
astrophysical black holes, is that the same thing
as Hawking radiation? And the answer is no. And in fact, the
jets that emerge from astrophysical black
holes aren't actually coming from the
black hole, they're coming from the stuff that's
already outside the black hole. That's a classical process,
not a quantum process. And it's the part of
the magnetic field of the black hole that's already
outside the black hole that's emitting some of
its energy that way. And there's infalling
stuff as well. So that's a purely-- A, that's a purely
classical process, and B, it happens outside
the event horizon, it's not energy coming
from the black hole itself. LEONARD SUSSKIND: Yeah, the
jets are not materializing from near the horizon. The jets themselves are
stored in gas circulating around the black
hole, at maybe 2, 3, 4 times the Schwarzschild radius. Not from the singularity,
but from the Schwarzschild radius itself. So they're well outside. There's no puzzle about where
that energy is coming from. SPEAKER: Next question
is [INAUDIBLE] AUDIENCE: Hi, so in the observer
picture that you mentioned earlier, where somebody is like,
having already fallen into, past the event horizon, I'm
curious about how many degrees of freedom of motion there are. Because it seems
to me that there's probably only two degrees
of freedom of motion. Like, if you imagine like,
the concentric spheres of like, a fixed radius, you can
only move along that sphere-- and whether that has relation
to why the entropy is related, like, proportional to the
area, rather than volume. LEONARD SUSSKIND: I think the
answer to the question of why the entropy is
proportional to the area goes back to the first
picture, the picture as seen from the outside
as matter falls in, even the things that
built up the black hole in the first place, never
as seen from the outside, crosses the horizon. It just forms a sediment that
keeps getting closer and closer to the horizon. It gets pancaked into a
thin layer that gets closer and closer to the horizon. That's the classical picture. In the quantum
mechanical picture, in addition to getting
close to the horizon-- to the horizon, not
to the singularity-- it's moving into this region
of increasing temperature. And so as it falls
in, it heats up. Now, it's not the
same as these jets. These jets are formed from
well outside the horizon. It heats up as it gets closer
and closer to the horizon, and then just radiates
its energy back out. So remind me, what was
the question you asked? AUDIENCE: Oh yeah,
so from the observer is like, already past
the event horizon. How many degrees of freedom
of motion would there be? LEONARD SUSSKIND: Well, I'm not
sure what you mean by degrees of freedom in motion. For that observer, or for the
whole black hole, or for what? AUDIENCE: For that
observer inside it. Like, LEONARD SUSSKIND: No, it's
just the usual, just the usual. The observer falling through
sees nothing unusual. He says, I can go that
way, I can go that way, I can go that way, I can go
whatever direction you like. But whatever direction he
likes will, to him or her, they will feel, pretty much,
they can move in any direction. But because everything is
being swept-- because space is being swept in
toward the singularity, even if they think they're
moving outward, they're not, they're moving inward. AUDIENCE: Thank you. SPEAKER: Someone over here,
I think you've been waiting. AUDIENCE: Thank you. Hello. So to the first question,
it was mentioned that most of the information is
emitted while the black hole is still big. So that means that
information is emitted. Does that mean that? And does it mean that it somehow
persists at the event horizon? And at the same time, if we
can travel inside and read our encyclopedia, it kind
of exists inside, closer to the singularity too. And I was wondering,
what's going on there? ADAM BROWN: Well,
indeed, what is going on? So to answer the first
half of your question, what I should have said,
if I didn't want to get, if I didn't want to
prejudge whether information has escaped from a black hole
or not, what I should have said is that almost
all of the photons are emitted while the
black hole is still large. Everyone would agree on that. If you think that information
escapes from a black hole, as is now the developing
consensus, then you would say that almost
all the information escapes. You get, roughly speaking,
one bit per photon. But-- so that would be the
exact answer to that question. The second question is,
it looks like information both makes it out
from the black hole, and continues into the black
hole, with the encyclopedia. Isn't that a bit paradoxical? And indeed, that is the
information paradox. AUDIENCE: I was just wondering
if any possible resolution gets-- and how it could be so. LEONARD SUSSKIND: Oh,
absolutely, absolutely. That's for the next, that's
for the next [INAUDIBLE].. Question? ADAM BROWN: Maybe I
could ask Lenny, what is black hole complementarity? LEONARD SUSSKIND: It's
just the statement that these two
pictures can coexist, and nothing that you will ever
do will find the contradiction. But we need another
hour to do that. We need another hour. So how should we do this? SPEAKER: I think we have
another question here-- JACK HIDARY: Lenny, let
me just, on that point, let me just ask-- you know, the fact that Stephen
Hawking posed this question back in 1981, when you
and 't Hooft were there in Werner Erhard's
villa, I guess, or home, or whatever
he had at that time, and it's gone on this long--
even though now, we probably realize that Hawking
was ultimately wrong in his conclusion,
the question obviously created a huge amount of
very interesting physics. So maybe just your
contemplation on that point, that even asking a question
that ultimately perhaps, if someone answers it wrong,
still creates a huge amount of interesting physics. LEONARD SUSSKIND: Jack said it. OK, so let me tell you
what's going on here. What's going on here is
that Jack and I and Adam are engaged in a conspiracy. The conspiracy is to make
you go out and buy my book. ADAM BROWN: Shouldn't have
given away 50 copies, then? LEONARD SUSSKIND: No,
that's the way you do it. You give away 50 copies and-- we've whet your appetite,
we've caught your curiosity, at least some of you. And we have perhaps brought you
to the point where you really want to know the answer. The answer is something
that took 40 years or more, and of extremely subtle
ideas, very surprising ideas, very, very
surprising ideas. One of the key ideas is called
the holographic principle. Roughly speaking, what it says,
roughly, very roughly speaking, is that the horizon
of a black hole is kind of like a hologram. A hologram is a
two-dimensional piece of film. It encodes information of
three-dimensional character. You can reconstruct, from
the two-dimensional film, you can reconstruct full
three-dimensional, let's call it reality. Roughly speaking, the
horizon of the black hole is a two-dimensional
membrane, which is functioning as
a kind of hologram describing the three-dimensional
reality inside the black hole. So it's not a completely,
totally, completely new kind of idea. It's much more quantum
mechanical than a hologram. But this idea, which was a sort
of wild speculation when it first came out, the idea that
the information of a full three-dimensional
world, a quantum world, and a full
three-dimensional world, could be encoded in a
two-dimensional membrane like a hologram was-- well, initially, the
idea was due to myself and Gerard 't Hooft in Holland. We were both known as
pretty good physicists, and most people said, oh, these
people have lost their marbles. It took a couple of years. Primarily, the thing which
really nailed it in place was work of the physicist
Maldacena, Juan Maldacena, who found an extremely
precise and concrete version of the holographic
principle, in which-- mathematically,
extremely precise. But what it did say is
that the information in any region of
space is encoded in a number of
degrees of freedom that correspond to a
film on, on the film on the boundary of the system. The mathematics
of that is subtle. It's very interesting. It is not something that I
could not explain to you, but it's not something I can
explain to you in 10 minutes. So one answer is
to read my book. The other is, come and ask me. The third answer is, we could
do this again, and proceed toward a conclusion
in a series of steps. But it's not something
that's terribly simple. JACK HIDARY: Good,
well, on that note-- LEONARD SUSSKIND: Jack wants
me to tell stories about it, but I-- JACK HIDARY: We'll have
more sessions on this. On that note, please HELP
ME thank both Adam and Lenny for a wonderful session tonight. [APPLAUSE] LEONARD SUSSKIND:
Good, thank you, Jack. JACK HIDARY: And for those
who were not lucky enough to get the book, yes, please
do get a copy of the book. Page 22 is the story that we're
referring to, so check it out. Thank you guys.
