So welcome everyone --
this evening we go boldly.
I think I have to say this differently,
we will boldly go where as
a professor of classics and comparative
literature I've never gone before but
as an administrator I go
very often: black holes.
[LAUGH]
Our speaker, Veronika Hubeny,
will shine what I can only imagine is a
very, very powerful light on the subject.
I'm honored to welcome you this
evening to the first inaugural talk
of the Winston Ko Frontiers
of Mathematical and
Physical Sciences Public Lecture Series.
For those of you who are not familiar with
Professor Ko and I can't imagine there
are many of those, I can tell you
that he is a legendary agent for
change in our mathematical and
physical sciences.
Winston devoted his 41 year career at
UC Davis as professor, chair and dean.
To pushing new frontiers of
discovery in everything from his own
work on subatomic particles to better
understanding the whole cosmos.
Professor Ko led the building of our
cosmology program from the ground up.
Now it's one of the top ranked
programs of its kind in the country.
UC Davis is grateful to Professor Ko and
his wife, Katie Ko, and
others who a few years ago so
generously supported the establishment
of the Winston Ko Faculty Fellowship
in Science Leadership.
This endowment supports UC Davis
faculty who are national and
international leaders in math and
physical science.
We also have the Ko family and
other generous donors to thank for
this public lecture series.
Winston, Katie, would you please stand for
a round of applause?
>> [APPLAUSE]
>> Thank you.
This evening we celebrate not
only the first Ko Lecture, but
also the first public lecture by
a member of the newly formed center for
Quantum Mathematics and Physics.
Its actually known as QMAP.
The creation of this interdisciplinary
research center is very exciting.
It's interdepartmental,
bringing together mathematicians and
theoretical physicists to explore
some of the most confounding and
mind-bending realities of
the physical universe.
The questions they explore
are as fundamental as can be.
addressing such issues such as
the origin of time in space, and
the fate of the universe.
I'm especially proud of this center
because it shows that UC Davis
can successfully transcend the boundaries
and extend the disciplinary brand
of a single department, college or school,
when the research venture calls for it.
Our Office of the Provost envisaged such
flourishing of new expertise a few years
ago when it established what we call
the hiring investment program or HIP.
The program provides funding to
hire stellar faculty in pursuit
of progressive campus goals.
Such as cultivating an emerging
field of research, strengthening
a critical aspect of graduate education or
advancing diversity in our faculty.
Thanks to this successful initiative,
we have been able to assemble at
the center a group of world class
researchers in quantum dynamics.
One of the most exciting and
provocative areas of inquiry in the field.
That is the envy of top physics
researchers at Princeton, Caltech, and
yes, even Berkeley.
We're honored to have one of those
world class researchers speaking to us
this evening.
Professor Veronica Hubeny is an expert
on quantum gravity and black holes.
After earning her PH.D.
in physics from UC Santa Barbara in 2001,
she held a post doctoral position
at Stanford's institute for
theoretical physics, and
then a research position at UC Berkeley.
She was on the faculty
at Durham University
in United Kingdom before joining
the physics department here at UC Davis.
As a core member of the new center for
the new Center for
Quantum Mathematics and Physics.
Professor Hubeny has made many
groundbreaking contributions
to our understanding of
the emergence of spacetime,
and the dynamics of black holes..
Please give a warm welcome
to Professor Hubeny.
[APPLAUSE]
>> Thank you very much.
Now, let me start by welcoming
all of you to this inaugural
QMAP and Winston Ko public talk.
It's a great pleasure and
privilege to share with you some of
the most amazing marvels of our universe.
Well, since the dawn of humanity,
people looked up in the sky and
wondered what's out there.
They wondered, what are things made of?
What led to it all and so
forth but certainly tremendous
[INAUDIBLE] but the curiosity
is still as intangible as ever.
And a quest for understanding goes on and
the deeper we probe the more
fascinating nature turns out to be.
In fact, I can't help thinking that even
the wildest imaginings of science fiction
can compare with how elegantly bizarre
nature actually is in real life.
Well, so understanding
the underlying structure of the physical
world is a subject of physics.
And fortunately for us,
it happens to be elegantly described in
the beautiful language of mathematics.
What's more, the common sensory
requirement that our mathematical
description must be self consistent
is surprisingly powerful.
So much so that even in
the extreme realms of science,
those far beyond the direct experience or
experiment we can still make
definitive predictions.
Now these are more bizarre futures yet
one of this world is its quantum nature.
And this, in fact, underlies many of
the profound questions in modern physics.
So here in Davis, a new center for
quantum mathematics and
physics has just been set up in order
to delve deeper into this unknown.
And we seek to understand them.
the underlying principles
governing our universe.
In particular we want to understand and
answer
questions such as what is the underlying
nature of space and time itself?
How did our universe get
started in the first place?
And what will be its ultimate fate?
What are the sort of
deepest manifestations,
most striking manifestations of
the quantum nature of our world?
Especially at microscopic scales?
Regarding the phonetical
structures that govern our world.
And watch new surprises do they reveal.
But the comments of others, and
I guess each one of us has their own
special fears that keep us up at night.
Now, you might think that while
these are fairly broad and
it's, you know, how do we even get
started on something like this?
But we are making good headway and
I think that we'll finally
be able to answer at least some
of these within our lifetime.
Perhaps even very soon.
One reason to be optimistic is
that these questions tentatively,
curiously, intertwined as are indeed
many diverse concepts in physics.
And this is interconnectedness that is
the most remarkable feature of our world.
And the topic of today's talk
was at least better than
anything else I could think of.
So today, I want to tell you about
my favorite object in physics,
namely black holes.
Well, most of you have probably
heard a lot about black holes,
especially in recent months.
And you probably even recognize them as
pretty spectacular objects
out there in our universe.
What's less widely appreciated
is that black holes are also
tremendously powerful
theoretical constructs,
which underline the deep relations
between desperate areas of physics.
And most people find them mind boggling,
but
black holes actually turn out to describe
much more mundane systems that we're
used to from almost every day life.
So it's this multifaceted
nature of black holes that I
want to give you some sense of today.
Now, I should probably start by
explaining what black holes are, and
that if you ask someone you can
get many different answers.
Because the simplest answer,
that they're regions
which you can never see from outside,
doesn't convey much to you yet.
The more colloquial answer — that
there are regions where gravity is so
strong that nothing, not even light,
can escape it's pull — is
perhaps easier to visualize,
though probably for the wrong reason.
But, do you know what?
Let me not shelter you from
stretching your imagination.
That's what you're here for.
So I'll try to eliminate how
I think about black holes.
But, in order to do that,
I need to tell you how we think
about our concept of space and time.
Well, according to the Aristotelian view,
space and
time were absolute and we were at
the very center of the universe with
all the heavenly bodies
orbiting around us.
Now these views started changing in
the Renaissance: When Nicolaus Copernicus
proposed a model with the Sun at the
center with the Earth orbiting around it,
that led to the first scientific
revolution, and eventually
to the Copernican Principle, which says
that our position in the Universe is
nothing special, and higher places
look pretty much like they do here.
Galileo Galilei bravely
championed Copernicus' view,
and furthermore dispensed with
the notion of absolute best.
So the laws of physics are the same for
observers,
no matter how fast they're moving.
So, you probably know
from personal experience.
For example,
if you fall asleep before your plane
takes off and you wake up mid-flight,
but for the external indicators
like the hum of the plane engine,
you will not be able to tell that you're
moving hundreds of miles per hour faster.
In fact we don't even particularly
notice right now that the Earth is
whizzing around the sun at
basically 67,000 miles per hour.
Now so far forces were into,
at instantaneously across space.
And this view was upheld by another key
figure in the scientific revolution,
Sir Isaac Newton, who noticed that
gravity affects all objects alike.
So for example, the earth orbits around
the sun because it's pulled by a force,
by a gravitation force
generated by the Sun's mass.
Just as apples on Earth fall under
the force of Earth's gravity.
That this notion of simultaneity
started shifting in
the late 1900's, sorry 1800's when.
James Clerk Maxwell noticed
that electricity and
magnetism were actually two
sides of the same coin.
Disturbances in one can
give rise to the other.
So for example if you have an oscillating
electric field that creates a magnetic
field which in turn creates
a electric field and so forth.
So you get a self-sustaining wave.
Maxwell calculated that
this wave propagates
at an astounding 186,000 miles per second!
And, recognized this as nothing but
a rule of light.
So we name that carrier of
electromagnetic force, the photon,
which you can think of as a quantum of
light, propagates at this finite speed.
And here's where we start getting
to the interesting stuff.
The so-called
Second Scientific Revolution.
[INAUDIBLE]
Had calculated that, had
observed that the speed of light is the
same no matter which direction we look in.
And so it's quite independent
of earth's velocity.
So in 1905, Albert Einstein realized,
that in order for the speed
of light to be the same for everyone,
no matter how fast they are moving.
The notion, neither space nor
time can be absolute.
This space and time join into a single
concept, so called spacetime.
Now the new theory called
special relativity.
Was quite groundbreaking and
marked a major turnover and
they still use today, especially in
situations like particle physics where
gravity is not important but
the particles are moving very fast.
But Einstein wasn't done.
There was still gravity to account for
and certainly did not fit
into the new framework.
So it took Einstein another ten years to
come up with a very theory of gravity.
But the result was one of the most
spectacular achievements of mankind.
The new theory called general
relativity poses that spacetime
can actually get warped But
presence of matter or NAG, and
it is this warpage which
manifests itself as gravity.
So, let me tell you a bit more about
general relativity since this is
the context where I can finally
start talking about black holes.
So, Einstein's key idea was that since
gravity affects all objects alive, we
should identify it with another universal
quantity, the curvature of spacetime.
You can think of this in a two
dimensional analogy of a rubber sheet.
There is nothing on the sheet It is flat,
but
if you put some heavy object,
it leaves a dimple.
And the more compact the object,
the larger the dimple.
Now if you roll a small marble
on the sheet It's not going to
look like it's going in
a straight line anymore.
It's still trying to follow
the straightest possible path, but
the sheet itself is curved, and so
it's disguised to this bending.
Now the same thing happens to spacetime.
Except that, in the case of spacetime,
it's both space and time that get warped.
So to summarize,
spacetime tells matter how to curve.
And matter, sorry how to move.
And matter, in turn,
tells spacetime how to curve.
So unlike all the previous
paradigms where spacetime
was just a passive arena on
which all the action took place.
Here spacetime is the star actor.
So unlike Newton's picture,
the earth goes around the sun not because
it's pulled by any force, but because it's
trying to follow the straightest possible
trajectory in the curved space
time produced by the sun's mass.
Now, Earth itself curves
spacetime around it.
So we, along with apples and
everything else,
follow the straightest possible path,
but we're in free fall.
But this is not just
a different description,
same physics in a fancier language.
It actually corrects Newton's gravity
where it would have gone wrong and
it predicts new effects.
Now, in daily human experience,
most of these effects are pretty
negligible, although precision instruments
can be sensitive enough to
the effects of general relativity.
So for example, the global
positioning system, in other words,
GPS units in your cell phones,
without general relativity's effects,
will get you quickly off the road,
with an error accumulating
by about 20 feet per minute.
All right.
So we have this picture
of general relativity.
But in the cosmos, the effects of general
relativity are much more striking.
So here is a picture of a starry sky,
[INAUDIBLE] a starry
sky just like our own.
But in the foreground there
are two objects which bend,
reflect the light from the distant stars.
In fact they happen to be black holes and
in this picture they do look
like holes through the stars field,
but that's misleading.
They're not holes in
the background stars field.
They're rather warpage of the foreground.
So you can see this better
when I run the movie.
All right?
So you can see that the black
holes orbit around each other, and
so the warpage changes in time.
It's like a moving lens in
front of the background.
Now you can also see here another
prediction of general relativity,
that's namely waves, ripples in
the spacetime propagating outward.
Just like Maxwell's theory of
electromagnetism predicts electromagnetic
waves, Einstein's theory of gravity
predicts gravitational waves.
And these carry away an energy, and so
the black holes as you just saw
spiral into each other and merge.
So now that you have seen
the effects of black holes,
let me tell you a bit
more about what they are.
So the more compact an object, the larger
the effect on the spacetime curvature.
And in the extreme case we can get so
much curvature that all
communication from the region
is effectively cut off.
And that is the black hole.
So in nature this might seem
very extraordinary, but
in nature this actually
occurs all the time,
typically at the end point of
a so-called gravitational collapse.
So to see what's happening,
it's nice to visualize this on
a so-called spacetime diagram.
So I have drawn here as time running
upward and space runs horizontally.
Except that, well, I have suppressed one
of the spatial dimensions because it's
hard to fit a four dimensional
spacetime on a two dimensional screen.
So if you're a observer who
stays at the origin of space,
you would follow this trajectory
of just a vertical line.
If you have some event,
like a flash of light,
that would be a point on
the spacetime diagram.
But as the light propagates outward,
everywhere in all directions,
you get this light cone.
So sometime later if you take a snapshot
of this wave front, you get a sphere
that's centered at the position
where the flash of light took place.
Now of course, we don't want to consider
real flashes of light all over the place.
But these light cones are very
useful as hypothetical objects for
telling us what is possible physically.
Why is it possible for a particle or
any physical object to go.
Its trajectory must always stay
within the local light cone.
Now, if you have a collapsing star,
at early times it's more like this,
and as time goes on it gets smaller and
smaller.
So the full evolution looks like this.
So here the star implodes to a point,
but I'll come back to that later.
But the rest of the spacetime,
what happens is very nicely
described by these light cones.
You can see that far away from the star,
the light cones look like they would
pretty much without the star at
all because they're not very sensitive
to what's happening out here.
But as you get closer,
you see the light cone starts tipping, and
at some point the sides become vertical.
At that point, it's no longer possible for
any physical trajectory,
including light, to get back out,
and that is the event hole.
That is the black hole, and
its surface is called the event horizon.
So If you were an observer who
falls into the black hole, as
you would cross this horizon, you wouldn't
see anything special happening to you.
You just merrily go on your way.
But at this point, you would have
doomed yourself on a path of no return.
And if you try to call your friends or
turn on
your emergency light beacon, your friends
would never get the light that you sent.
It wouldn't encounter any barrier.
It would simply fall in with you.
And no matter what you did subsequently,
you would be
irrevocably drawn to this central region
I have indicated by this red line.
Now that's called
the curvature singularity.
This spacetime becomes
infinitely curved and
general relativity loses
its predictive power.
So in that sense it
predicts its own downfall.
But that's good because we know
that there is more to come in
our fundamental description
of the universe.
All right.
So, of course, now I should say that this
idea might have seemed outlandish to you.
And, in fact,
it bothered Einstein a hundred years ago.
And even though Schwarzschild
wrote down the first black hole
solution only a few months
after Einstein wrote his paper.
It wasn't for
50 years that people actually started
taking the solution seriously.
Initially, it was just
sort of eccentric and
almost an embarrassment to
the otherwise beautiful theory.
It wasn't until the late
'60s that John Wheeler
actually coined the phrase black hole and
only by the '70s,
people started learning all sorts
of stuff about black holes and
what now is thought of as the golden
era of black hole research.
And it was catalyzed by sort of the
astrophysical observations catching up and
astrophysicists recognizing that black
holes are actually physical objects
out there in the universe.
So, how do they come to be?
Well, they are typically a result of
gravitational collapse of a star.
So, this is an artist's conception
of what's happening to the star.
So initially, nuclear fusion converts all
the light elements into the heavier ones.
The most stable phase is formed.
And if the star is heavy
enough to start with,
then the outward pressure
no longer sustains the star
against its own gravity and
the star collapses in the process,
releasing its enormous gravitational
potential energy in a supernova.
Now if the core is only a few
times as massive as the star,
then this object will settle down to
a neutron star, which is the densest
known regular [INAUDIBLE] object
that we know in the universe.
So its size would be scarcely
larger than the City of Davis,
that the density is so high,
that half a cup of it would
weigh as much as a mile long by mile
wide by mile tall slab of lead.
Now, that was my scenario.
If the core was heavier,
then it would undergo further
gravitational collapse and
irrevocably form a black hole.
Now it's no longer sensible to talk
about density, because the entire
star has imploded into the singularity,
but just to give you a sense.
If the entire Earth
collapsed into a black hole,
its size would be only about this big.
So in the process of this collapse,
lots of further
energy can be released in
the form of gamma ray burst.
Which in the few moments if
you would convert it to light,
all that energy, it would produce as much
power as the Sun does
in its entire lifetime.
So you see that black holes
are sort of indispensable for
some of the most energy processes
that we see in our universe,
which is good because otherwise,
it would be very hard to observe
them since no light can, of course,
escape from a black hole.
But objects in the vicinity of
a black hole get affected so
much that we see the tell-tale
signs of a black hole.
So for example, the supermassive
black hole at the center of
our own galaxy, Sagittarius,
a star, was freeze a certain by
observing sort of star's stellar
orbits around the center.
More dramatically,
if a star gets sufficiently close
to a comparable sized black hole.
It literally gets ripped apart.
More typically, as matter falls onto the
black hole and spirals in, it gets heated
up by friction and we can then
observe this corruptivistic radiation.
And pretty soon, we'll have a new
telescope, the so-called black hole
telescope that will be actually able to
resolve the angular size of a black hole.
And now on top of all that,
we have entered the exciting of
the gravitational wave detection.
So I think it's quite fitting
that the first direct detection
of gravitational waves happened
almost precisely a hundred
years after Einstein formulated general
relativity by LIGO last September.
And this was no easy task, because
the sensitivity that's required for
realistic processes to measure
the gravitational waves in
our vicinity is like measuring
the width of the human hair in
the distance to Proxima Centauri,
our nearest star.
So, it's a tremendous achievement and
sign of human ingenuity that
we were able to do it at all.
So through the signal that LIGO measures,
by comparing which predictions
of general relativity,
you can then read of a lot about
the event that took place.
In this case,
more than a billion years ago.
So you can read off what kind of objects
produced the gravitational waves,
how heavy they were and so forth.
So through all these observations,
we now learn, well,
we get some estimates of how many
black holes there are in the universe.
So already in our own
galaxy in the Milky Way,
there are 100 million approximately,
black holes,
which have mass slightly
larger than the Sun.
And so if you add up all the galaxies,
the entire universe has
some one hundred quadrillion — that's
one with 17 zeroes after it or
10 to the 17 — such black holes,
which is like greater
than the number of grains of sand
in the entire Sahara Desert.
Now in fact, each galaxy also has
a humongous super massive black hole
at its core,
which has mass of several billion
times the mass of the Sun and the size
larger than our entire solar system.
And in fact, there's a black hole produced
somewhere in our universe every second.
So by the time I finished the talk,
there will be thousands more,
[LAUGH] but the universe is so
vast that you don't have to worry
about being swallowed up
by a black hole just yet.
The newest observed black hole is in
the Sagittarius arm of our galaxy,
some comfortable 1,600
light years from Earth.
So now I have told you a little
bit about black holes, but
what I consider to be sort of the least
significant aspect of black holes.
My main purpose was to sort
of allow you to get some
intuition and to also give you a sense for
how extreme objects black holes are,
as physical objects.
So, you're probably
well-positioned now to realize how
preposterous it would be to suggest
that black holes could have any
bearing on everyday systems that
we can observed here on Earth and
yet it's precisely what we have been
learning in the last ten years And
so, to explain that, I know I have
to tell you a little bit more
about the mathematical
description of black holes.
Well, so Einstein's equation, which is
the hallmark of general relativity,
tells us how the curvature of spacetime
is related to matter distribution,
and black holes actually
are the simplest and most,
one of the simplest and
most studied solutions to this equation.
In fact we learned that black holes can
exist even without any matter at all.
So Subrahmanyan Chandrasekhar
called black holes the most
perfect macroscopic objects that there are
in the universe because the only construct
that we need for
them are our notion of spacetime.
In fact you might find it curious that
given how extreme an object black
hole is as a physical object, why is
the mathematical description so simple?
But I, in fact,
think that the two go hand in hand.
So why is it?
Why do we assume that
the solution is simple?
Let's think for a moment what
it would take to describe, say,
a star that's about to
fall in a black hole?
You would at least need to include all
the stuff that falls into the star and
all the information that that carries.
So that's a very complicated description.
However, once it collapses to a black
hole, the final state is very simple.
It's just characterized by three
numbers corresponding to its mass and
to momentum and charge.
John Wheeler characterized
this by the memorable phrase:
Black holes have no hair.
So now what is the use of that?
Well, from the pragmatic standpoint,
it's great because
it allows us to study the properties
of black holes explicitly.
And we find many surprises.
Okay, so one of the surprises is
that black holes actually behave
in some respects much more like ordinary
systems than one might have thought.
So to explain that I should tell you
how do we characterize black holes.
So the three most important
characteristics are the black hole's mass,
which I've already mentioned before,
the surface area of the event horizon, and
a weird sounding quantity called surface
gravity which you can roughly think of
as the force needed to hold
a unit mass suspended.
Just at the horizon,
you're holding it from infinity.
All right.
So those are female quantities.
Let's not compare how would
you characterize an ordinary
system like fluid or gas or some material?
Well if you don't want to bother with all
the microscopic details of the individual
particles, you can work in terms
of some grained quantities,
and the important ones are the
temperature, the energy, and the entropy.
So out of this probably the least
familiar one is the entropy, but
even that made it into popular culture.
We can think of entropy, roughly speaking,
as characterizing the amount
of disorder in the system.
So in this cartoon,
if the kid didn't have so many things,
then there wouldn't be
such a big disorder.
So we can equivalently think
of entropy as telling you
about how many distinct possible
states the system can be in.
And in fact, you can also think of
this as the amount of information that
can be stored in the system.
Now energy you are probably
much more comfortable with.
For one, we are talking about it all the
time these days, and actually we can think
of it as sort of how much work
can be produced by the system.
The temperature is probably
most intuitive for all of us.
But in many sorts of familiar
systems like Earth's oceans here,
the temperature can vary
from place to place.
But that's because the Earth's
oceans are not in equilibrium.
They're getting heated differently
in different parts, and
they have different external effects
that are changing with time.
For systems in equilibrium,
things become much simpler, as described
by the laws of thermodynamics.
So the temperature according
to the zero law thermodynamics
is the same throughout
a system equilibrium.
The first law tells us how energy
changes compared to how entropy changes,
and this is related by the temperature.
And the second law of thermodynamics tells
us that entropy must always increase.
Now these laws were already
known in the 1800s and are key
to the subjects of thermodynamics and
statistical mechanics.
Now, in the 1970s, people discovered
that the laws of black hole
mechanics actually mimic
the laws of thermodynamics.
If you replace the thermodynamical
quantities by corresponding
quantities pertaining to black holes.
So if you look at this you'll
see that you can identify black
hole mass with energy,
the black hole area with entropy.
And the surface gravity
with the temperature.
Now at this point you might just
think this is a cute analogy
built on rather tenuous
circumstantial evidence.
In fact that is initially what
people thought, but more and
more people started realizing that
it's far more than just an analogy.
So, using both experiments,
Jacob Bekenstein realized that black
hole entropy was indeed proportional to
the horizon area in order to uphold the
second law of thermodynamics in nature.
And famously,
Hawking then calculated the black hole
actually radiates or
the temperature that's
indeed given by its surface gravity
with a precise calculation.
So we learn that black holes really
are thermodynamical objects.
Now let me come to this entropy
black hole in a relation.
In a bit more detail and well I know that
one is not supposed to present
equations in public docs but
this equation is so nice and
important that I couldn't resist.
So I hope it doesn't scare you off.
So first of all what is an equation?
If I asked you to come up
with an example of one,
many of you might come up with something
like, say, one plus one is equal to two.
The equal sign means that there is
an equivalence between what is on the left
hand side and
what's on the right hand side.
But possibly one side is more
convenient to use than the other.
Now the equations that
we use in physics have
a deeper meaning in that
they tell a story and
the story that this equation
tells is particularly
intriguing So
usually if we have an equivalence.
But, it might be relating two
seemingly disparate quantities,
and the fact that it's an equation,
there's an equal sign,
means that these quantities
are actually cleared out.
In this case the equation tells
us that black hole entropy
is actually equivalent
to the horizon area.
Which is astonishing to say the least.
Now what about these other quantities,
apart from the number four you can
recognize all these other things that
are just fundamental constants of nature.
Which effectively set the scale.
In fact, most often physicists
just work in units such that
all of these are equal to one so that you
minimize the clutter in the equations.
But the presence here tells
us an important hint.
It tells us what parts
of physics are necessary
to understand the meaning of
this equation in a deeper way.
So in particular, well, you would
need almost all aspects of physics.
So you certainly need
statistical mechanics.
You need relativity, gravity,
and you need quantum mechanics.
Okay so apart from this, so
it tells us that the equation
is actually very deep and
to understand it, we need a theory
that sort of unifies all of this.
Now apart from the connection
between the subjects,
what is the actual surprise here?
Well, if you calculate how
much the entropy is for, say,
a solar mass black hole,
you get an enormous number,
something like 10 to the 77,
that's 1 with 77 zeros after it and
in fact, in statistical
mechanics the entropy is related
to the number of distinct microstates,
states in which the black hole can be,
by an exponential relation.
The number of microstates
is exponential to entropy.
So in this case it would be,
well I can't write it on the slide because
the number would be so large that even
to render it would be more than the number
of atoms in the whole universe.
It would be one followed by this
humongously large 10 to the 77th
number of zeroes after it.
So, where are all these
black hole microstates?
According to general relativity,
black holes have no air and
so we need to look further.
We need to have a theory or
framework which unifies all of this
to tell us where the microstates are.
Now string theory is one of the more
beautiful candidates that sort
of contains all of these.
And unfortunately I don't have time to
tell you anything about string theory.
But it indeed does manage to reproduce
the number of microstates precisely that
agrees with this formula
in some controlled context.
So whatever the final theory that
describes our universe happens to be,
it must at the least be such that it
upholds this equation, all right.
So, accounting from number of, or
identifying the black hole microstates
wasn't the only puzzle in town.
Perhaps the more pressing one, is the so
called black hole information paradox,
which points to a striking clash between
what general relativity tells us and
what quantum mechanics tells us.
So, according to general relativity,
anything that falls into a black
hole is lost forever,
including the information that it carries.
Now as Hawking calculated
subsequently the black hole radiates.
But, the radiation doesn't
carry away any information.
And eventually leaves the black
hole to evaporate completely.
So at the end of the day,
all the information is lost.
On the other hand, according to
quantum mechanics, that can't happen.
Quantum mechanics has an infinite
time reversibility, so
even if the information gets scrambled,
you can just turn time backwards and
recover what the information there was.
So there should be some process where we
can get all of the original stuff that
fell into the black hole.
So you can see that this process of
black hole formation and evaporation
clashes with the laws of quantum
mechanics at its fundamental level.
Now when I think that this would
be an embarrassment to us but
in fact it's a wonderful opportunity.
Because it points to a precise
place where these two
cherished theories clash with each other,
and so
we know where to look in order
to make them consistent.
All right, so let me now come
back to what we already do know.
And what's a consequence of the entropy to
area relation which is something
called the holographic principle.
So let me ask a question,
of how much information could
you maximally store,
in a given region, some box let's say.
Let's say we take it,
each edge being a foot long,
and how much information could we pack in?
Equivalently, how much entropy
would fit in that box?
Well suppose we take the box, and we
pack it with say very informative books.
And we ask what happens if
we now have more such boxes.
Well, one box would have
a volume of one cubic foot,
surface of six square feet,
because it has six sides, and
let's call the amount of
information that it has S, okay.
Two sets of boxes will then
have twice the volume and
presumably, twice as much information.
But the surface area is only
10 square feet because this
intermediate site isn't
facing out anymore.
Three boxes would have three
times as much information and
three times as much volume.
And four boxes would have four times,
eight boxes would have eight times,
and so forth.
So, this little exercise would
lead us to conclude that
the amount of information
scales with the volume, okay?
And this is indeed true when
the effects of gravity are negligible.
But when gravity comes into play,
this is no longer the case.
In fact, eventually,
no matter how little you put in a box,
eventually if you take sufficient
number of these boxes.
They will gravitationally
collapse into a black hole, and
you just learned that black hole has
an entropy that's only proportional to
the surface area, not the volume.
So the information now scales
only with the surface area.
And moreover, the black holes are the most
entropic objects that fit into
a spherical region like this.
If you try to pack any more information,
the black hole will just grow, all right.
So this observation leads to
the so-called holographic principle but
we can, in effect,
describe everything in the box just
by using information that fits on
its surface, not the entire volume.
Now, you might say, well why is it
any different than for example,
watching movies?
You see a two dimensional screen and
it's supposed to portray
a three dimensional world.
But in movies, you'll see what's
lurking behind the foreground objects,
and you don't see inside closed boxes.
Here, the assertion is that
we can describe everything.
So there will be some two-dimensional
theory that lives on the surface
of the box, that actually knows
everything that happens inside that box.
And well, unfortunately, the holographic
principle doesn't tell us what form
this theory should take, but
fortunately we have a concrete example.
The gauge gravity duality.
Before I tell you what gauge gravity
duality is let me just tell you what we
mean by duality as such.
So it's the statement that the same
physical reality can have several
different, distinct descriptions,
that are so called dual of each other.
So to illustrate the idea, that means
this convenient Escher drawing So
here you know you could be describing
things in terms of these fish.
Which get worse and worse as you go up.
But in terms of these birds, and
like many physical dualities,
this objects in terms of what you
try to describe has been going on.
Well behaved in some corner gets worse and
worse needs a good description as you go.
Away from that corner.
In physical dualities this is
typically the strength with
which those fundamental objects
interact with each other.
Now it's not just these
fundamental objects that change
from one side of the duality to another.
In fact these properties
look very different.
Much more than would be
suggested by this picture.
Okay, so let's now come back
to our gauge gravity duality.
This wonderful example of
a holographic correspondence,
this is also known as
the AdS/CFT correspondence.
It was first derived within string
theory by Juan Maldacena about almost
twenty years ago.
But we now understand that this
applies in much broader context.
So this each covered individuality
asserts that string theory which,
among others, is a theory of
gravity is exactly equivalent,
describes the same physics,
as a gauge theory.
This is a quantum string theory
without gravity that has
the special property that It looks
the same at different scales.
So it's so
called conformal field theory or CFT.
Okay so that was a lot of words but
the important point
here is that the two theories believe
in different number of dimensions.
The string theory lives in what
are called bulk in a spacetime,
which is called Anti-de Sitter
abbreviated as AdS.
This is sort of a spacetime
which is negatively curved like
an analogue of a hyperboloid.
The gauge theory lives on
the boundary of that space.
So one more dimension,
just like our surface of the box.
So in the early days, people liked to
visualize it in terms of a soup can.
So the string theory is the soup inside.
While the gauge theory is just a label
on the boundary of the soup can,
but unlike an ordinary soup can
where the label just tells you
roughly speaking what's inside,
here the label is everything.
All right so
because the two descriptions live in
different number of dimensions, we call
this correspondence holographic because
it upholds the holographic principle.
Otherwise, it has nothing
to do with real holograms.
In fact,
I think a much better analogy would have
been a stereogram like this 2-D image.
Where if you look at it in a certain way,
you see a three-dimensional
image sort of coming out at you.
In this case,
it's due to the correlations between
the different splotches that
your eyes interpret as parallax.
In other words, each of your eyes
is in slightly different position.
So it sees a slightly different image, and
your brain then interprets this very
cleverly to get the distance information.
Of course,
it can be fooled by these types of images.
So in this gauge/gravity correspondence,
the idea is
infinitely more complicated than would
have correlations between everything.
And the image that you would see
would look like a sensible lower
dimensional image that
however does give rise
to a completely different, higher
dimensional picture, the gravity side.
All right so
we see here that the space time
gets completely scrambled,
between the two sides.
But it's not random,
it's in fact, very delicate.
It's such a way that everything works out
just right on both sides
of the correspondence.
So perhaps a first question
that anyone might ask
about such a holographic correspondence
is whatever happened to this extra
dimension that now the lower
dimensional theory doesn't have?
In this case what would happen
to this radial direction.
Well fortunately part of
the answer is already suggested
by the geometry of this
entirety of spacetime.
Okay which you can think
of spacial geometry,
which is like looking on top of this.
On the lid of this soup can,
it is very nicely described by
another astral drawing, this one.
Where the size of each of these fish is
supposed to be the same
in the actual spacetime.
And so you would need to traverse
infinitely many of these fish
before you get to the boundary,
which is just here.
And moreover, any of these vertices
is just as good as any other one.
So this is symmetry in the spacetime,
where there is no real origin.
You can think of any
of these equivalently.
And so the mapping to the boundary
has to respect this symmetry.
So a given point here has
to be encoded by something.
Such that if we, for
some region on the boundary.
Such as that if we shift this,
that has to shift consistently.
So we learn that in fact
this radial bulk direction.
How close you are to the boundary must
have to to do with a scale or the size
of the corresponding object in the field
theory side on the boundary all right.
So for example points near the boundary
would be described by small arcs.
Points further in would be
described by larger arcs.
In fact, I quite like this picture for
another reason which is that it also
very nicely tells us that, well,
there are many different ways you
can describe the same bulk point.
For example, you could have taken
this arc or any of the other ones and
in fact that observation has
been used recently to relate
this mapping between the bulk and the
boundary, recast it in terms of something
that quantum information theorists
would call quantum error correction.
Now this type of relation also
gives us a very useful intuition
of what we would expect to happen in
the two theories, on the two sides.
So for example, if you have some object
in the bulk that falls, well, if you let
go of an object here, it feels the gravity
of this entire space and it will fall in.
On the boundary,
that same physical process is
described by something that's initially
localized and spreads out as time goes on.
Sort of like,
if you put a drop of ink in a cup of
water, you'll see it spreading out.
So, that's sort of
mocked up on both sides.
All right, so
I've told you just a tiny aspect of
the gauge/gravity duality but
what is it good for?
In fact, it's great for a lot of things.
So, since Maldecena's original paper,
there have been well over
10,000 research papers citing
his original work, and
it's still very much ongoing today.
So remember, that the duality relates
two theories: a theory of gravity,
meaning in high dimensions, to our main
gravitational quantum field theory,
meaning in lower dimensions.
So in the left-hand side, the systems
that we want to consider are things
that feel the gravity like black holes.
In fact, black holes are the most
prominent objects on this side,
in this space time.
Now, unlike our own expanding universe,
the cosmology of the spacetime
is different, but
everything that I have told you about
black holes still applies here.
Now what about the right-hand side?
Well, the right-hand side describes
natural familiar systems that
we're all used to.
Basically, every sort of
strongly interacting type of
systems that are described by
strongly interacting field theory.
So, a large class of these,
if you sort of look at some course level,
behaves like a fluid.
And so, but
this would be a fluid that lives
on the boundary of this
Anti-de Sitter spacetime.
And the flow of this fluid,
all the various vortices you can have and
changes in temperature and
everything like that,
is mimicked by what the black hole is
doing, by the behavior of the horizon,
and this allows us to study
even the sort of hitherto,
mysterious questions such as turbulence.
Trying to understand turbulence.
Or in quantum metaphysics,
there's still plenty of materials
which we don't really understand,
like high temperature superconductors, and
often, it happens that the best bet for
understanding resistors is to
study the dual black hole.
And so nowadays, you find many
physicists studying black holes,
even those who are not working in
general relativity for this reason.
The systems are also experimental and
accessible, and
the black hole describes things
ranging as widely as cold atoms,
which are some microkelvin temperatures,
to the hot quadron
plasma-producing colliders,
which is in trillions of Kelvin,
so spanning almost 20 orders of magnitude,
described by the same type of black hole.
All right, so this gauge/gravity
duality has been an invaluable tool,
both for
studying these strongly interacting
field theory systems, which is hard
because it's strongly interacting,
but describes many systems that we're
familiar with and want to understand
deeper by working in a higher dimensional
gravity and AdS, which is much easier.
But conversely, we can also study
quantum gravity in AdS which is very hard,
but of course,
needed to understand the fundamental
nature of spacetime and so
forth by using the field theory which for
some respect is much easier.
All right, so but
black holes have of course
formed a crucial ingredient in deriving
the gauge/gravity duality and
figure it at many stages.
But black holes also reappeared
within the duality, so
we can study black holes in eight years by
these other systems, and so you might ask,
okay, so what are the lessons that we
learn about black holes from this duality?
And while I already told you that, well,
we have seen black holes as quite
extreme objects, in some regards,
now we learn that they saturate
loads of different pounds.
And so we already saw that they're sort
of the most perfect microscopic object in
terms of the simple description.
They also happen to be jewels that
come the closest to a perfect fluid,
to ideal fluid, they happen to be most
efficient in storing information,
they also happen to be the fastest
in equilibrating things.
For example, if you have
a planet that has some mountain,
takes ages to decay, if you have a black
hole and if you deform the horizon,
the decay is faster than anything
else could possibly decay.
It's also fastest to scramble information,
and
from a quantum information
theoretic respect,
it also happens to be sort of fastest,
act like a fastest computer.
Now, with all the lessons that
we're learning from all of
this new insight about black holes,
well, an important one is,
sort of hints about the nature
of spacetime itself.
And through this correspondence,
there have been very
tantalizing hints that
the spacetime itself, well,
is certainly not a fundamental concept,
just like a fluid, for example,
is not going to be a continuum
down to arbitrarily small scales.
At some point,
you'll start seeing the particles.
Well, so too,
we now believe that spacetime has
some underlying quantum structure.
And the hints that we have been getting
is that quantum information theory,
and especially quantum concepts like
entanglement, play a crucial roll here.
So we don't yet know how spacetime, what
is spacetime at some fundamental level.
But, we have had many tantalizing
hints that it, sort of,
comes from this entanglement.
I am over time [LAUGH] so
let me end by saying that we have had,
we have seen many different
guises of black holes.
And it's amazing to know,
to think historically how they
rose in prominence over
the last century starting with
almost being an embarrassment to general
relativity to being some esoteric
objects that nobody
understood to finally being
important astrophysical objects that
we actually observe in our universe.
To being mathematically beautiful
constructs that we could then use to,
for example,
construct these profound realities
that relate many different
aspects of physics,
to finally being related
to almost ubiquitous,
being related to everyday,
ordinary systems.
So that has been quite
an impressive climb, but
we're nowhere near the summit yet
and the best is still to come.
So I think that black holes will
really hold a key to quantum gravity.
The theory that should be
a self-consistent framework that
captures both general relativity and
quantum mechanics.
And well we have had all these hints and
so far we have, I think,
there's so many different
connections that we're seeing,
that I think we have barely seen
the tip of the iceberg so far.
There's so much more yet to uncover and
to understand and to explore, and
in fact I think that in the whole
last century of general
relativity, these revelations
about black holes have brought us
to what I think is the best era
to be a theoretical physicist
exploring the mysteries of the universe
and the best is yet to come.
So, thank you.
>> [APPLAUSE]
>> Thank you, Veronika,
for a really lovely talk.
So what we have now is we
have about 15 minutes to
take questions from the audience, and
then afterwards, we can stay back for
some informal questions at the very end.
So wait for a microphone,
and we can take questions.
>> Since black holes can contain so
many particles, and so much information,
can it help us explain dark matter and
dark energy?
>> Well, I would certainly hope so.
But [LAUGH] I have no concrete ideas
to how that will do that,
that many observations in many
theories of that method and
dark energy, well, especially
we have observed dark method and
there's many models that
sort of relate that.
So there, black holes were
probably figure a little bit less.
For dark energy,
I think that's much more promising.
So it's a humongous puzzle.
If we sort of imagine from arguments
from within particle physics,
how much the natural sort of
energy we should have for
our universe, of the background
in our universe, the vacuum,
it comes out 120 orders of magnitude
off by what we actually measure.
So it's one of the biggest
problems in physics.
Now people think that
the resolution to this, but, okay,
some people hope that the resolution
to this might be some secret interplay
between things that are very, very small,
and things that are very, very large.
Something, some new modality, some new
element in our physical description.
And a very similar type of
thing is needed for, for
example, resolving this black
hole information paradox.
So black holes, this black hole
information paradox is such
a deep question that I think
understanding it will finally
lead to basically new
pseudo-scientific revolution,
completely new paradigm, and
I think that once you understand that,
we also understand dark energy as well.
>> So do we have a question on this side?
>> If black holes kind of swallow all
that energy and light around them and
nothing can escape, doesn't that
mean eventually the whole universe
will be swallowed in a giant black
hole and nothing can escape?
>> Well, not necessarily.
So it happens that our universe
is actually expanding.
It's expanding faster and faster.
So even if we have black holes
locally in our galaxy, let's say,
they will swallow up things
that are around them, but
in the meantime,
the surrounding spacetime will expand so
much that they won't have
time to swallow everything.
It's still true that,
when the universe expands so
much that there won't be much left,
you might not have things like stars and
galaxies and so forth.
But it won't all be inside a black hole.
>> Another question over here.
>> You mentioned black holes without
matter, which is kind of intriguing.
So would this happen when
entropy is very low and
consequently the event horizon's
very small or something different?
>> They can be any size.
They can be completely any size.
So it's just that, so
this equation, Einstein's equation,
that relates the curvature of
spacetime to matter distribution,
happens to be a type of equation that,
it has multiple solutions.
So one solution, if you have no matter,
is just flat spacetime.
But another solution is a black hole.
In fact, if you can sort of think of the
spacetime itself as doing the gravitating.
It starts getting curved and
that sort of gravitates,
and gravitates more and
sort of makes up a black hole.
So it has nothing to do with size.
The size, the black hole can have any
size, even without having any matter.
Now in our universe, that doesn't happen,
in the sense that typically black
holes just collapse from something,
from a star in which case,
there was some matter to create it.
But this theoretical construct or
mathematical construct, typically
people study them without bothering
with all the details of what collapsed.
Because effectively, you see,
the essence of a black hole,
as we saw in the black hole
thermodynamics, is the horizon.
Just kind of curious that nothing is
actually happening at the horizon.
There will be just empty space.
But nevertheless, the black holes
act like some physical objects where
the horizon is very important.
And for that,
it doesn't really matter whether the black
hole formed from some star that's now
squeezed into the singularity or
just is a object without any matter.
>> Can the holographic approach
help us to understand entanglement?
>> Sorry.
[LAUGH] Yes, so in fact that has been
a growing area in the recent decade or
so, or slightly less, and
it's a very fascinating development.
So entanglement for
everyone else is sort of the most
quintessential aspect
of quantum mechanics.
It's the most nonclassical manifestation
of quantum mechanics present when,
if you know everything
about a total system,
still doesn't mean that you know
everything about its individual parts.
It's what Einstein called as giving
rise to spooky action at a distance.
But, nowadays, people think of it more as
a quantum resource for tasks that can't
be performed by classical resources, like
quantum teleportation or things like that.
Now, in this gauge gravity duality,
you can ask what is entanglement,
well, a measure of entanglement,
something called
entanglement entropy of some,
say, region on the boundary and
within the fifth year,
it's a very complicated object.
It's an important one, but
it's very hard to calculate and
measure because it's so
sensitive to the environment.
And so you might think after all
this mapping between the bulk and
boundary that scramble things so
much, that on the gravity side,
in the bulk, this will be vastly more
complicated, because we use some
very non local scrambling map
to go between the two sides.
Miraculously, it turns out
to be extremely simple.
In fact this entanglement entropy,
these are to be given just
by the area of some surface.
The surface in this bulk
is like a super bubble,
it's a special type of surface
that minimizes its area and
is entanglement entropy is
given just by this area.
Basically the simplest geometric
object that you can come up with on
the gravity side, in the bulk, is actually
characterizing this entanglement entropy.
And so
there is something deep behind that,
there is some relation where this
spacetime, which tells us where
this minimal area surface is actually,
knows or arises, from entanglement.
In fact, one of the mysterious pictures,
sorry [LAUGH].
That I had in sort of creating spacetime
that looked like this, whatever,
spaghetti monster.
>> [LAUGH]
>> Is a picture of
a sort of conception of
something that people called
entanglement based bridges,
or Is equal to EPR.
Okay, those are the letters that stand for
people.
It's Einstein-Rosen and
Einstein-Podolsky-Rosen.
Einstein-Rosen refers to a wormhole,
a throat of a black hole, so
if you remember you're embedding diagrams,
discover sheet, it got default.
A black hole could be so different that it
would actually come out on the other side.
That object, this wormhole, is the Side.
The EPR side, Einstein-Podosky-Rosen,
refers to this entanglement.
And so the pictures, that somehow,
if you have entanglement
between many different things,
the fact of this entanglement actually
creates spacetime, creates this wormhole.
This is very new when people have yet
to understand it, but it's very exciting.
>> Okay, another question,
maybe on this side?
Do we have another question?
>> I'd like to ask you a question
about the mass of a black hole.
I don't even know if
it's experimentally or
observationally possible
to think of it in this way.
But are people able to measure how
much mass is going into a black hole?
And if so, does it turn out that
the observed mass of the black hole
is at the sum of all of the masses
going into it or is it something else?
>> Okay.
Already we can answer that from
the mathematical description.
It's not quite just what the masses
of those objects were at rest.
It's all this sort of energy that goes in.
So kinetic energy that's caused by
not only the mass of the object but
also the fact that it's moving.
That's the the thing that gives
rise to the black hole's mass.
By how much the black hole
actually increases its mass.
Now when it is observed,
you can certainly detect black hole
mass by looking at how things orbit it.
So for example, in the case of
the Sagittarius A star, the planetary,
sorry the stellar orbits around it narrow
it down precisely how massive it is and
how big it is, and from that people
concluded that it has to be more compact
than even anything we know of, and
therefore it has to be a black hole.
But in practice,
the amount of stuff that is falling
onto the black hole is typically
a very small fraction of
the black hole mass to start with.
So you would have to keep observing that
object, say an accreting black hole,
for a sufficiently long time to
actually see any change, but
that theoretically is certainly possible.
And I think it will be more and
more possible with this new telescope,
the black hole telescope coming online and
so forth.
So experimentally,
we live in very exciting era too.
>> So I actually just noticed the time,
I'm gonna wrap up the official
question section.
And you can come up and there will be time
for a few more questions informally with
Veronika, but let's thank Veronika
again for her fantastic talk.
[APPLAUSE]
