I'm going to discuss a somewhat different branch of physics,
but there are many relations.
As you may know, and this perhaps
is in the philosophical mark, all of science,
in particular all of physics, is somehow connected.
So we can talk about elementary particles.
We can talk about astrophysics, about cosmology,
about cold atoms, or whatever you name it,
all these subjects eventually are related.
And so also, the physics of gravity
eventually must be related to the physics
of the subatomic particles.
However, we do not know exactly how.
And there are many important loose ends
in our understanding of physics.
And the subject of black holes is, in particular,
a very important topic where not everything is understood.
And this I want to emphasize in today's talk.
So let me, for a moment, go to astrophysics,
and indeed, the physics of the cosmos.
This is, I don't know whether the light
could be dimmed a little bit.
This is a part of the universe as seen
by the Hubble Space Telescope.
And what you see in these pictures
is thousands of galaxies,
every galaxy being about, well, not quite as big as ours,
because these are young galaxies.
Many of them are a bit smaller.
Galaxies tend to grow after a certain amount of time.
The most surprising part of this picture
actually is not the galaxies, but the dark space in between,
because that indicates that the universe somehow is finite.
If the universe were truly infinite in size,
and would be everlasting,
there would be smaller galaxies in between,
and smaller ones, and smaller ones, and smaller ones,
and they would make the entire sky white instead of black.
But no, the sky is basically black.
So look at the black spaces in between.
Well, but today's topic is about black holes.
Now, in practically all of these galaxies,
astrophysicists suspect there are
gigantic big black holes at their center,
simply because at the center of a galaxy,
the star population is so high
that collisions can sometimes take place.
And when that happens, stars grow to above a certain size,
and then it is practically inevitable
that they'll grow things that we'll call black holes.
If you look at the center of our own galaxy,
people have registered very precisely
the positions of stars in our own galaxy
near the center of the galaxy.
And they find, when you plot carefully
the orbits of these stars,
you find that there's a spot where stars suddenly change direction,
and you see that they are strongly attracted to that particular spot.
But there's no light coming from that spot.
And this is an indication that that star there
actually is the location of a black hole.
So it's quite remarkable that itself, this object, is very dark.
You can calculate from what is being seen here,
these are just observations which have been very carefully registered.
You can deduce from those observations
that the black hole must be something like
two or three million times as heavy as the sun.
So all these stars are more or less sun-like,
but a million times more mass sits at the center
and you see practically no light.
This is a black hole.
This is with another kind of telescope in radio light
and so that you can focus on black holes from close.
And you see that a black hole actually is surrounded by a dark disk.
And that's the so-called accretion disk matter,
which is circling, orbiting around a black hole,
but very gradually sucked in.
Here the black hole doesn't really deserve its name
because it's actually the white spot at the center.
Why is it not black? Why is it white?
Well, every time something falls in, it attains tremendous velocities
and so it very quickly evaporates and becomes super hot.
And as such, it will definitely emit light.
So everything spiraling into a black hole during the process will emit light
and that's the bright spot at the center.
Now, black holes are a fundamental aspect of generativity
and generativity had been first described
and fully realized what is about Albert Einstein.
So Einstein, with his theory of generativity,
was the first to bring about a very fundamental new improvement
to Newton's old theory of gravity.
Newton's theory was not wrong,
but it had to be amended when very large velocity ions take.
Or very, very strong gravitational field.
According to Einstein, space and time are curved.
And this is just a cartoon picture.
This is not a real indication of how space and time are curved
around planet Earth.
But the idea is that it looks a bit like this
and then when you put clocks near planet Earth,
then according to the calculations and according to the theory,
you'll find that clocks will tick faster
when they are far away from the Earth.
But the closer to the Earth they come, the slower they will tick.
Again, this is very exaggerated.
In reality, you need extremely accurate atomic clocks
to even notice the difference in the clock speed.
But this has been observed and is a very important effect.
In fact, without taking this into account, your GPS would not work.
It is based on satellites which carry accurate clocks on them.
But if you wouldn't realize that these clocks are ticking at different speeds
when the satellites are further or closer to the Earth,
then the positioning procedure wouldn't work.
So this was Einstein's very important discovery.
And very soon after Einstein published his theory,
because he published it early in 1916.
His theory itself was completed late 1915.
But very soon after that, a well-known astronomer,
Kyle Schwarzschild, who was an astronomer of some reputation,
he saw Einstein's paper.
He said, well, Mr. Einstein, if you write down an equation,
even if the equation is complicated,
I can solve it in the easiest circumstance.
If you assume perfect spherical symmetry,
then most differential equations are soluble with very high accuracy.
So he took Einstein's equations and wrote down an explicit solution.
And the explicit solution, well, today I
want to show you the explicit expression
for the solution that is subject for the day after tomorrow.
But in this solution, something very strange happened.
Schwarzschild unfortunately didn't live
to see what kind of commotion his solution brought
about in the world of science, because there
was something very strange going on.
When he published it, he himself thought
that there would be an easy solution, but that wasn't right.
In fact, the solution is much more interesting
than he could himself even imagine when he wrote it down.
And the interesting thing is that you can think of the solution as,
again, a curvature of space and time.
Now, if normally space and time are curved, for instance,
because there would be a planet sitting at the center,
then this looks like a slightly curved region of space.
I draw an other universe underneath it.
These are two distinct universes.
But when you consider a Schwarzschild solution from close,
if we find something very strange, it looks like something like a wormhole.
The space and time get curved so much that beyond that spot,
basically, it curves backward to form yet another universe.
So Schwarzschild's solution of Einstein's equations
didn't describe one black hole.
It basically describes two, one sitting in the green universe
and one sitting in the brown universe.
And the black hole, in a sense, connects these two universes.
This is very strange.
And also, it's not quite true for the following reason.
This is universe one, universe two.
There's a black hole.
Well, the black hole, at first sight, looks like a wormhole.
We call this a wormhole when a worm can go through the soil to some other place.
The worm connects our universe to another.
But there's a certain number of things to be remarked before jumping to conclusions.
And that is that there is a magic line here where, essentially,
the curvature is largest.
And that's a line where time stands still.
What does it mean?
If someone would fall into this black hole solution,
his clock would go slower and slower and slower.
But when that person would be sitting on this magical spot here,
it actually is a sphere.
It's not a line.
But I couldn't draw so many dimensions on this sheet.
It's a sphere around the center of the solution.
But that's the point where time literally stands still.
So his clock stops sticking all together.
So from that point on, he can go nowhere because he has no time.
He's just standing still.
So when you actually would see from the outside someone falling to the black hole,
you'll actually see him slow down when he reaches his point.
And he would come to a standstill at that point.
So you'd say, well, that's the end.
There is no way he can go to the other side because he would have to go faster
than light to reach the other universe.
And that's the catch.
In the other universe, you would also say clocks run backwards.
That's even more awkward.
So this is a very strange wormhole.
It connects universes to other universes where time runs in the other direction.
So at this spot, time just stands still.
Well, actually, if you go into the black hole yourself,
you would not at all notice this phenomenon.
You'd notice something else.
And at that spot, you would think you would continue your way all the way in.
But when you continue all the way in, you would do so not in our time,
but in another sort of time coordinate where eternity has already passed.
Because for us, up to eternity, that observer will hang around at this line.
But the observer himself thinks that after eternity has passed by,
just a short moment for him, he will just continue inwards.
And then he'll hit what we call a singularity.
So now, physicists can argue at length, how important is it that there is a singularity?
It doesn't really lie in our universe.
It lies beyond time is infinity in our universe.
So you could say, well, it doesn't matter.
And indeed, for many applications of physics and the considerations I'll consider later,
the presence of that singularity has no direct physical consequence.
So you could also decide to ignore it.
It's just important to know that this is the way space and time gets curved
when things become too crazy.
And this is really a very crazy way in which space-time can get curved.
So you can, of course, ask, what are the consequences for physics,
all of this strange phenomenon of extremely curved space-time?
Before continuing, many physicists, actually including Einstein,
thought that all of this was far too crazy to be true.
There's something wrong.
You can't have singularities in an ordinary physical world.
So you shouldn't even believe that such a solution could ever be physically relevant.
Something probably happens to stop this from happening.
And Einstein thought that, many other physicists thought that.
But I'll now argue to you why that is false.
And actually, black holes can just form the way I just described them
in an ordinary way in order to bring down a message.
I'll tell you how you can make your own black hole.
And what I'll use for that is mobile phones.
So I'll take, like my own mobile phone, I'll take lots of mobile phones.
And the reason why I take mobile phones to make a black hole is I want to show
that they'll still work while they essentially make the transition towards
a black hole and reach the point with no return.
They'll still function as mobile phones do.
So you don't need any exotic physics to make a black hole, just ordinary physics.
And the argument goes as follows.
There's one little catch.
And this is why you shouldn't immediately run home and try to make a black hole.
Because you need a lot of mobile phones, about the mass of a galaxy.
And imagine that you take all these mobile phones and
you have them all arranged in a more or less perfect spherical configuration.
Again, I removed one dimension from this picture.
So you have to think of this three-dimensional.
They are shaped like sitting on the shell of an egg, of a spherical egg,
or an inflatable balloon.
It doesn't have to be a perfect shell.
Some people argue black holes only exist because they are a perfect
spherically symmetric solution, and nothing in the real world is perfect.
Well, okay, allow a 10% deviation on this.
It doesn't matter.
You'll still make a black hole if they are arranged only with 10% accuracy
on this sphere.
That's good enough for the argument.
So these little squares here are mobile phones.
And as I said, you need a lot of them.
Because you have the mass of a galaxy,
they're actually attracted each other gravitationally.
Now, that gravitation force at this level looks very much
like the electric force.
It also is a 1 over i squared force, just electricity.
And so it has some of the similar peculiarities as electric fields.
For instance, if you have an electric conductor,
and particularly if the conductor is spherical, but even if it were spherical,
if you put a voltage on the conductor, then inside this object,
there's no field at all.
This is why when there's lightning, you're safe if you stay inside your car.
There's no electric field inside your car
if your car is sufficiently well conducting on the outside.
So if the voltage is the same outside, there's no field inside.
Similarly here, there's no observable gravitational field,
perhaps a few stray fields, nothing much inside.
Inside, basically, nothing happens.
Space and time are also totally flat inside, no curvature.
But outside, there is.
So these blue lines, a bit difficult to see here,
indicate the gravitational field outside these mobile phones.
And they then attack each other.
So after a while, they start to travel inwards.
And nothing special happens while they travel inwards.
They're still so far away from each other.
And that's why I needed the mass of a galaxy.
I didn't want them to touch each other so they can work properly.
So you can, well, actually also need broadcast masts and so on.
But imagine that they can just communicate with each other
with some slight modification of the electronics.
Then they could still communicate with each other.
Although you have to take into account the signals don't go fast in the light.
But there's nothing special about this.
So they could interact with their neighbors the way they would normally do
without touching each other.
They move inside.
But while they move inside, they will sooner or later hit a very special point.
And that is the point we call a horizon.
That's a point with no return.
Well, they are moving.
And while they move and they're just subject to the gravitational force,
there will be absolutely nothing to stop them from going in.
And while something, if you try to stop them, that would be a problem.
If you try to stop them here, then the local observe
would think they'll have a speed of light going out.
Now, take your mobile phone, give it a speed of light.
You can't.
That would require other kinds of laws of nature, perhaps exotic ones.
So they won't stay at this horizon.
They'll just travel their way through.
So this whole cloud of mobile phones will just move in.
And while they do so, they just obey ordinary laws of nature.
Like they'll still be functioning.
In fact, after they cross the line, they still work.
So no exotic physics is needed anywhere in this argument.
However, now they come closer and closer.
And there's a problem now that I can't stop them from touching each other.
And they won't stop going in either.
So they'll continue to occupy smaller and smaller volume.
Well, that's not good for mobile phones.
So they'll squash.
And they'll stop functioning very soon.
OK, they stop functioning.
We still understand the physics.
They'll conch.
They'll melt.
They'll burn.
They'll go chemical interactions.
And we can all write down the physical laws for that.
They'll no longer function as mobile phones, never mind that.
After a while, they undergo nuclear reactions among the other.
But then, at some point, they'll hit what we call the center singularity.
There, all known laws of physics will cease to be valid and make sense.
So now we have a problem.
However, at the same time, you'd realize that it's totally physically irrelevant.
Because while they pass the horizon, for the outside observer,
that is the last thing you could ever notice of these mobile phones.
In fact, when they're here, the escape velocity
would be equal to the velocity of light.
If they are inside, the escape velocity would be bigger than light.
Impossible.
So in fact, the outside world sees them slow down.
And they stop right here, as seen by the outside observers.
And that's the whole thing.
This thing is the black hole.
And no exotic laws of nature are needed, because we didn't really
need to know what happens when they hit a singularity.
That's past eternity when that happens.
So let's not worry about it now.
So that's how a black hole works.
And at first sight, there seems to be absolutely nothing strange about it.
So I now want to discuss a topic of what black holes have to do
with elementary particles.
So far, I talked about very, very large black holes.
So again, this black hole that I talked about
would have the size of hundreds of thousands or millions of kilometers.
So it would be a very, very large black hole.
And that doesn't seem to play any direct role in elementary particle physics.
We could ask how elementary particles behave near the horizon.
But in principle, everything should be completely
calculable and straightforward.
So nothing special seems to happen at first sight.
We can ask what happens when two particles collide at LHC,
or possibly at a larger machine with more force.
Could the black hole form?
Well, I'll explain later that something like that might form,
but it will immediately decay again.
Why would a black hole decay?
Well, I'll leave that for a moment for later.
But let's discuss the branch of physics where the nature of black holes
will definitely be important.
And that is when the laws of gravity, the laws of quantum mechanics,
and the laws of relativity theory of Einstein all come together.
Now, quantum mechanics is controlled by Planck's constant,
which you usually divide by 2 pi to get this number.
It's expressed in kilograms, in meters, and in seconds.
Every constant of nature, if you will, can be expressed in terms of kilograms,
meters, and seconds.
But you need certain combinations of them to let this constant
do its job in the laws of nature.
Now, Newton's constant is a different number also expressed
in meters, kilograms, and seconds.
But you see different combinations of kilograms and meters.
And the velocity of light, of course,
is to be expressed in terms of meters per second, and is this number.
Now, we have three fundamental constants of nature.
And as soon as Max Planck discovered his fundamental radiation law,
and he realized there was a fundamental constant in his equations,
now called Planck's constant, as soon as Planck realized
there was this fundamental constant, he already knew the other two.
He said, now, we have three constants of nature, all of which
are expressed in terms of three units, the kilogram, the meter, and the second.
If I combine them in certain ways, I can remove all,
I can express all physical units in terms of these fundamental constants.
So what you get then is called the Planck units of distance, of time,
and of mass.
And if you take these particular combinations,
you get either a unit of distance, a unit of mass, or a unit of time.
Now, the unit of distance is a very, very tiny distance.
Much, much tinier than even the tiniest particles
that can be detected by the LHC.
It's just another 15 or so orders of magnitude smaller than that.
The unit for mass is very interesting, 20 micrograms.
That would be the mass of a unicellular animal,
or a tiny grain of sugar, or something like that.
So that would, in itself, sound like an interesting unit of mass
to be used in nature.
So we could ask, why do people use a standard kilogram?
Why not use this as a fundamental unit of mass in nature?
The answer to that is that of these three quantities,
neutral constants are actually very poorly known.
Only one part per 1,000 or so, a bit better than that,
but not so much better.
And that's very bad for physics.
We want to be a lot more accurate than this.
And we don't know this number sufficiently accurately.
So also, this number is not very well known.
And therefore, it's not used as a fundamental unit of nature,
but it could have been otherwise.
And the Planck time is even more crazy.
10 to the minus 44 seconds is the time a light ray needs
to cross this distance.
And this is a very, very tiny distance,
and light goes very fast.
Now, if anybody ever wants to sell you a computer
and say that the switching speed of the computer
is faster than one switch in 10 to the minus 44 seconds,
you shouldn't believe him.
Because this is probably the fastest things
that anything can do in nature.
We don't believe there are any processes in the world that
can be faster than this.
Also, there's a suspicion that maybe nothing
is smaller than this.
This mass has small and large units to cancel out.
Planck's constant is very small.
Newton's constant is very small.
So small numbers are divided by small numbers
to get something in the intermediate range.
Actually, if you want to talk about elementary particles,
this is very, very large compared
to all elementary particles.
It's very small compared to all our human mass scales.
So it's a very strange unit, indeed, for physics.
Now, this is, however, a very interesting domain of physics.
I just told you that this might be the smallest unit of distance.
And you might ask, why am I saying that?
Well, I'll try to explain.
So there's something in here that may be very important.
And this is therefore the black holes
might play a very unique and important role
in particle physics.
Now, this here is the way I like to picture the progress of science,
in physics in particular.
And what you see here is a kind of highway.
And below the highway, we see all these names
of elementary particles, some of them you've seen yesterday.
And at the left is the energies of particles, every step
of 1,000, the factor 1,000.
So this is a logarithmic scale.
I'm going up by factor 1,000 every time here.
So you see many steps of a factor of 1,000.
Eventually, we'll end up into the domain where all forces are unified,
called the grand unified theories.
And the gravitation force somehow must become important in that domain.
That's where the distance scale is 10 to the minus 35 meters,
or 10 to the minus 33 centimeters.
And just before that point, we believed all forces are unified.
Here, all particles that would have masses around that scale
would have a horizon which is bigger than the quantum wavelength
of these particles.
And therefore, those particles would no longer work as quantized particles,
but elementary particles then will be black holes, or so it may seem.
Well, to solve the picture up a little bit, today's physics is around here.
There may or may not be a Higgs in this domain.
Actually, LHC is a little bit larger.
It is roughly in this region.
And so you see that this world's most powerful accelerator
is very modest on this scale.
It already jumps from here to here.
But that's because I have factors of 1,000 on the axis here,
which is very, very fast.
So you see, physics has a long way to go before we reach that point.
But it is a very interesting point out there.
And we love to speculate about what the laws of nature
should be like at that point.
So as I said, there's a reason to suspect that physics stops at this point.
Maybe a grand unifier theory of absolutely everything
can be formulated in this domain.
And then all we have to do is calculate backwards down this highway
to calculate what things look like in the domain that we're investigating.
So imagine that you would understand everything on the top there.
Then you would understand our physics in principle.
You can imagine, and you don't have to be a very deep philosopher for this,
that that's going to be a very long journey.
And it's quite possible that you'll never achieve this.
But you can't stop theoretical physicists to speculate
about that magical domain where all forces become equal in strength,
in particular the gravitational one.
Now, I want to continue to this point where we are looking at different observers
who go with different speeds into a black hole.
Well, when we see an observer going into a black hole from some distance,
we see he goes slower and slower and slower.
And by the time he reaches the horizon, the observer will stand still.
His watch stops, his heart stops, everything stops for us.
But the guy himself will not agree with this.
He'll think that he'll go straight through.
Now, the idea is you want to apply the laws of nature
as you know them to the situation.
And it actually turns out that the fact that these two observers have
a different concept of time has very grave consequences
when you try to do physics, in particular quantum physics.
Because the time coordinate in generativity
has a very special meaning, and it does these crazy things.
But the time coordinate has another very important role in physics
in describing elementary particles.
Elementary particles have energy.
And energy corresponds to fluctuations in time, oscillations in time.
So according to quantum mechanics, energy is just a frequency of the wave packets.
Now, these two observers entirely disagree about the frequency of their wave packets.
And so they disagree about what energy is.
And eventually also disagree about what elementary particles are.
So an in-following observer has a different notion of elementary particles
than the observer that is seen from a distance.
So then we can ask, how does this square?
How can we make this whole picture in the physical world work?
So the first to ask the question correctly and give a very intriguing answer
was the guy here in the center of this image.
The others are Einstein and Newton.
And this is an episode from Star Trek.
And this episode is played by an actor playing Einstein,
another actor playing Newton, and Stephen Hawking playing Stephen Hawking.
And that occurred when Stephen was visiting Universal Studios in California.
And he was so excited that he asked, I would like to play in Star Trek.
And they said, well, OK, you played a time, does a little something,
and that Newton accidentally meets Einstein.
And here, the three smartest minds of the world, of the universe,
meet each other by some fluke of time, and so on, and then the story goes on.
But this guy at the center made a very important observation.
He discovered that because of this mismatch of what different observers
mean when they talk about particles, because of that,
the black hole actually emits particles.
It is not only a thing that is a drain or everything.
Particles, stars, galaxies can go into a black hole,
nor also things can come out.
And that was totally unexpected.
And when Hawking first reached the result, he thought, this isn't real.
I'm making a mistake.
But then he discovered he could actually compute the intensity
by which a black hole emits particles.
And he discovered it makes perfect sense.
It makes sense to suspect that the black holes cannot be completely black,
but that particles come out.
Actually, when he computed how intense is the radiation of a black hole,
he found that when black holes are smaller,
the intensity of the radiation is much bigger.
And that's because the typical wavelength of particle
is of the same size as the size of the black hole.
Now, you could argue that if a black hole emits particles,
then it loses energy, because it loses mass.
The mass is sent away in the form of particles.
So the black hole, its energy is being drained away.
Its mass is being drained away.
So because it gets lighter, it also becomes smaller.
Because it gets smaller, the intensity of the radiation will increase.
And that's a straightforward calculation.
I'll not bore you with the details.
But when you find that, then, well, if a black hole
continues to emit radiation at a faster and faster rate,
you can imagine that this whole thing might end with a gigantic explosion.
And that explosion would be a sizable one,
because the calculations show that by the time the black hole has become so tiny
that its mass is not that of a sun or a planet,
but only the mass of a mountain or so, that's still a lot of mass.
By that time, it will only take a few seconds for the black hole
to radiate all of that away in pure energy.
So the mountain, by means of the formula E is mc squared,
the whole mountain will be transformed to energy and blast away.
That is a big blast, bigger than the man-made atomic bombs of any size.
So such blasts should be recognizable for many light years away.
So when physicists realized that every now and then, perhaps in the universe,
a small black hole might radiate and give it tremendous blast,
so astrophysicists got interested in this question
and they searched the sky for a sudden blast of presumably something like gamma ray emission.
Sure enough, they found many blasts of gamma rays.
But they weren't black holes because they could be identified as coming from galactic nuclei.
That's much, much further away than light years.
There's billions of light years away.
Those are big black holes which turn a finite fraction of the mass directly into energy.
Black holes can do that because they can attract stars and other stuff.
And although the star disappears in the black hole,
before it does so, the last fraction of a second,
it might emit a size or a fraction of all its mass straight into gamma rays into the universe.
Those are big blasts.
And that's what astronomers saw and unfortunately not a decay in black hole.
I'm saying unfortunately because this would be a lovely thing to study from close
where you notice a real physically interesting phenomenon.
But that's not the way it seems.
But we can now do a very interesting Gedanken experiment.
And this might sound technical but it's basically straightforward.
And again, I'm not going to ask you to follow all the technical details here.
But I'm going to do a very simple experiment.
I'm just considering a black hole which might emit, which might absorb something.
So maybe it absorbs the clock that says that I have not so much time left.
And the clocks are safely hidden in the black hole.
And the black hole might emit objects.
It might emit particles.
But according to Hawking, it can emit anything, including keys and coins and so on.
The only thing you have to do is calculate the probability that emits that thing.
And the probability is calculable.
It is not zero.
And it is precisely given by ordinary laws of nature.
Laws of nature, he made this derivation in the 60s somewhere.
But the observation couldn't be made 20 or so years earlier or later.
Because the laws of nature that were needed for this observation are very basic ones,
which any reasonably good physicist could have derived.
But Hawking was the first to realize this.
Now what we can do is, now we have a two-way process.
We have information about a black hole plus matter going into a heavier black hole.
The black hole absorbs the alarm clock.
But it also emits things.
So now we have these two arrows.
And that is interesting.
Because now imagine a black hole to be a quantum object.
And here come the lectures in quantum field theory, which I won't bore you too much about.
But according to quantum field theory, what you have to do is,
if you want to compute a process like this, is you have to compute a quantum amplitude.
You have to compute a wave function.
And you have to square the wave function to find out what the quantum amplitude of such an emission is.
But then, and then we say, yes, according to quantum mechanics,
the amplitude in this direction is the same as the amplitude in that direction.
Because all laws of nature are reversible in time, as you know them.
Actually, there is so-called PCT invariance for the experts.
But never mind that.
There is a symmetry that relates our universe to a universe going backwards in time.
So this arrow, once you know this arrow, you can compute the other one.
So why was Hawking's calculation so interesting?
Well, there was one unknown fact in this calculation.
And just for the theoretical physicists here, I'll tell them that when you do a computation like this,
you need the amplitude of the wave function.
And you need phase space.
And phase space tells you how many different states the final thing can be in.
Well, we can compute that for keys and alarm clocks.
Because they are all known forms of matter for which we can calculate phase space.
But the one unknown animal in here is the black hole itself.
And this argument gives you phase space for a black hole.
What is phase space?
Phase space simply tells you how many different states can a black hole be in.
And this is a nice calculation you can do just by starting from Hawking's argument.
And the calculation is that the black hole has a phase space as if it's on its horizon, on its surface.
There are little squares.
The size of the square is roughly the Planck mass squared, the Planck length squared.
So 10 to the minus 65 square centimeters.
And all these little boxes here are 10 to the minus 65 square centimeters.
And on every box here, there's exactly one bit of information.
So phase space is as if you count how many bits of information can I put on the surface of a black hole.
And if you know that number, then you know how many states the black hole can be in.
And this, as physicists, we find extremely intriguing because this came out unexpectedly.
Because this is a statement about the Planck scale, this mysterious number about which we knew nothing I just said.
Now we say, yes, we know something.
We know that at that scale, there's only one bit of information on the surface area of a black hole.
Actually, the black hole itself, as I also explained on the horizon, there's empty space time.
So a pattern can go straight through this blinking thing as if nothing was happening.
So these blinking squares, to me, seem to be a property of space and time itself.
And the property is such a weird one because this is a surface.
It looks as if space and time itself, in the vicinity of the black hole, behaves as if there's a surface of which there are blinking bits and bytes of information.
We did not know that.
Now we know.
This is what the outcome of the calculation is.
So this is what we now call holography in scientific literature.
This is the statement that all of the information about particles in the universe can somehow be encoded on a surface.
Like if you made a hologram, a picture on a two-dimensional photographic plate with a laser and such, which has a limited resolution.
And then all there is to be known about the universe around us can be obtained from this surface.
So this was the crazy result that came from black hole physics.
There's actually one constant indication we don't know.
There could be some blinking things at the side, which means they are the same for all black holes.
A big black hole has many squares here.
A small black hole has only a few of them.
But they all have the same number at the side.
And we don't know how to calculate that number.
But that's just a detail that comes out of this calculation.
Now we find this very intriguing because this makes a black hole really look like ordinary matter.
Why I'm saying that?
Well, in elementary particle physics, we have gotten used to the idea that we can make a list of all particles.
And they were known at the time as the Rosenfeld table.
When I was a student, we loved to be before those tables because they were just listing all known subatomic particles.
It was not known those days.
And many of these particles actually were just exactly states of the known ones.
But anyway, they made a list of all things that exist in the universe.
Now we can add to that the list of all black hole states.
How many how many of these blinking bits and bytes do we have and what are the various of the bits and bytes that they form a complete list of all black holes.
So in principle now, black holes look very much like elementary particles.
So now it is a justified suspicion that black holes are elementary particles and elementary particles are black holes.
It's just a different way to describe the same thing.
This would be a lovely picture if true.
It would make us believe that black hole formed by mobile phones or by stars and planets contracting to make a black hole.
The black hole lived for a while and then to decay by emitting hot particles and finally explode.
This picture is time reversal symmetric.
You can also read it from right to left and it would look like a similar black hole.
So actually these are the pictures you also draw to describe interactions among elementary particles.
This black line could also be x particle or something else.
So it looks as if you can now apply the same laws of nature to black holes as you did for elementary particles.
Wouldn't that be great?
All you have to do is now calculate the details.
So we have a rough idea, but then we say, well, wait a minute, at the horizon of the black hole, we know all laws of nature exactly.
So what stops us from calculating exactly how all these black holes behave?
What are their stable states and so on?
And then you discover there is an anticlimax to the whole story.
We can't do that calculation.
We don't know how to calculate the things.
Anything better than just saying that a black hole has a very large amount of information on its horizon.
But what that information actually does is still very much in the dark.
We can't apply laws of nature to do that.
And the reason is there's something wrong with the whole picture.
And that is unfortunate.
We all believe Hawking's result is basically correct.
But they try to go into the details.
There's something wrong.
And one thing is that if you make a black hole in two different ways, you can make a collapsing star.
You can use mobile phones or you can use anything else that makes a black hole.
The final result will be the same.
At first sight, according to the basic calculations, a black hole doesn't remember how it was made.
Well, that is against the laws of quantum mechanics.
Anything you can make out of atoms remembers how it was made because that is reflected in its wave function.
And you can't make two different objects form eventually the same wave function.
That's forbidden according to the laws of quantum mechanics.
That's a statement about information.
So there was something very basically wrong about the whole idea.
And as if the black hole itself would violate the laws of quantum mechanics.
And that was what Stephen Hawking was trying to tell us.
The black hole itself is not a quantum mechanical object.
But then all particle physicists said, what?
You use quantum mechanics to derive this.
And now you're saying quantum mechanics doesn't hold.
Somewhere a mistake has been made.
So a fight started off.
And well, this is just to explain the difficulty that we had.
The difficulty that we had was this.
This is a space-time picture of a black hole.
Time runs here vertically.
Space runs horizontally.
And here is either wave of a particle.
So according to quantum physics, particles and waves are the same thing.
So now we have a wave of a particle just when the black hole is being formed.
And a part of the wave is being dragged into the black hole.
A part is allowed to escape.
But when you do that, you're doing something that's very interesting
from a quantum mechanical point of view, but also very special.
What you get is that a wave splits up in two parts.
These two parts are what we say, they are entangled.
And this is a famous phenomenon in quantum mechanics,
which has been studied very much in condensed metaphysics.
With cold atoms and such, people try to do observations of quantum entanglement.
And indeed, the particles going into the black hole are entangled
with the particles that stay out.
And this, in our case, unfortunately, is a very big problem.
Because the particles that go into the black hole cannot be observed.
They just disappear.
They don't even show up after a black hole decays.
So there's quantum entanglement between objects and other objects that disappear.
When that happens, you can no longer describe the same thing
as a single quantum wave function, and there's something basically wrong.
This is what people like Hawking kept emphasizing,
that no, you can't use quantum mechanics for a black hole,
because these things here, they disappear.
But then the particle physicists say yes,
but then the foundations of our whole concept of nature
is being attacked by this argument.
There's something wrong with it.
So the black hole doesn't seem to be allowed to be described
as a quantum object.
And here, we get into what we call a paradox.
And so now the community went into a fight,
and there were at least three different ideas.
One is that, well, too bad for that, that was what Hawking said originally.
Then some people here said, well, maybe eventually these particles
went into the black hole, finally come out after the black hole exploded.
But they're just a remnant.
The black hole explodes.
Those are Hawking particles.
And then there's a little grain left behind
that contains all those particles that went in,
and now that information is being released.
Well, the problem with that, again,
was that you can put an indefinite amount of particles into a black hole
and just wait long enough.
And that grain in the center would contain more and more information.
So that grain in the center would contain unlimited amounts of information,
very, very unphysical, nothing like we know in our physical world.
So I think that particle physics is more and more attempted to believe number three,
which is there is a very slight miscalculation in Hawking radiation.
Hawking could not be blamed for that because we all understand what he did.
And we say, well, that's technically completely correct.
But maybe it's physically wrong.
Maybe there's something we don't know yet.
And that is that these particles that come out of the black hole
actually do contain information.
They contain the information of the things that went in.
It doesn't disappear to infinity.
So that is now the argument that you all believe.
But that means you have to modify the actions of the theory.
Because at first sight, when you calculate these things, this is not what comes out.
So the question is, how can we reconcile this with the idea that laws of nature
are local, that if two objects enter through a black hole at a small distance,
they should somehow be allowed to interact with when particles come
through a black hole from a different end, they should not be allowed to interact.
Because that would be against the principle of locality of the laws of nature.
Now, many physicists don't like locality so much.
They say, well, drop it.
Who cares?
But I think that would be a big problem.
And I call this a paradox.
Now, when theoretical physicists encounter paradoxes, they'll cheer.
They'll say, hooray, this is great.
There's something wrong in our present theories.
So we have to somehow correct them.
And usually, when that happens, we'll make new discoveries.
So Max Planck himself was addressing a paradox in problems
with radiation of heated objects.
And when he found the resolution of paradox, the outcome of that
was quantum mechanics, an entire new branch of physics.
So this paradox, again, my belief is, might open up a totally new branch of physics.
So in string theory, and that is the most sophisticated approach
to try to unify all laws of nature, in string theory,
there are objects that look very much like black holes.
And yet, they behave in a physically conventional way.
So string theorists keep telling me, there's
nothing to worry about.
The black holes that we compute are just doing fine.
But for those black holes, they're not telling me
what happens when an observer goes through the horizon.
And they have no way of explaining that, because those black holes are
made of other stuff in string theory.
And they're not made of pure gravitational field.
So how to view a black hole as we made of purely gravitational field,
and yet resolve this paradox, that is a big problem that hasn't been properly answered.
So there's work to be done, and there are conflicts.
Now, one way out, and I've been studying this way out of the conflict for a long time,
myself trying to argue that if something goes into a black hole,
it will hover on the horizon, and it will never really go through the horizon.
But the Hawking particles come from the other end.
They come out of the black hole, after having hovered along the horizon
for a very long time.
So the time reverse of in-going matter is the outgoing matter.
And now, the usual argument is that you assume that these in-going things
cannot possibly transmit all the information onto the outgoing things.
But then you've forgotten something, which is that where they meet, they might interact.
And this interaction is a very strong one.
The ordinary interactions may be relatively weak,
and may be ignored in certain approximations,
particles just go through each other, basically.
But that's basically fundamentally incorrect, if you include the gravitational force.
These particles, according to a local observer here,
they would generate so much energy that it's very paradoxical.
But for a local observer, the energy of the two particles
may exceed the energy of the universe.
It becomes extremely large.
And therefore, because energy is associated to mass,
they would also gravitate.
They'll have very, very strong gravitational forces on each other.
So there will be a very strong gravitational interaction at that spot.
This is very confusing, and most physicists don't really know what to do with gravitational force.
I tried very hard myself, but didn't really make much progress here.
You can look at the horizon, and all these particles are either getting in or getting out,
as a kind of atmosphere on the horizon.
These are the candidate Hawking particles that take a long time to get out.
And the other particles that went in take an eternity to go through the horizon.
They all accumulate very near the horizon, as if they form a kind of atmosphere.
And now you can argue that if another particle goes in,
he actually does something to that atmosphere.
He drags the particles along.
That's a gravitational dragging effect.
It's very small, but it makes a lot of difference for these particles when they get out or not.
If they are only dragging a little bit, they might come out a century or so earlier or later, as the case may be.
So this dragging effect is very important and modifies the picture completely.
Yes, but how?
And how do you do the calculation correctly?
That turns out to be very, very difficult to understand.
These arguments do give you one very interesting observation,
and that is that there are not only black holes in nature,
but astrophysicists also wanted to consider white holes.
What is a white hole?
Very simple.
If you have a black hole in astrophysics, black holes always absorb things.
And astrophysicists ask, yes, what's about the time reverse?
If I take a picture of a black hole that's being formed and I turn it,
I show the picture reversed in time to you,
then you see a black hole decaying, emitting the stars that went in.
They call that a white hole.
Nobody's ever seen a white hole in a telescope.
But you will ask, what is the role of white holes in particle physics?
Well, according to the arguments I showed so far,
the white hole is related to a black hole, but the relation is a very interesting one.
It's very much like the relation between a particle which has a definite position
and a particle that has a definite velocity in quantum mechanics.
You may know that a particle can either determine the position very accurately
or its velocity, but not both.
Well, similarly here, you can either determine the in-going particles very accurately,
then you talk about the black hole,
or you can look very carefully at the outgoing particles and then you call it a white hole.
But the two are related in the same way as particles are related,
which are localized very precisely, or the velocity has been measured very precisely.
Those particles show a definite relation in the theory of quantum mechanics.
And that relation is very similar to the thing of black holes.
So that we call a quantum superposition.
One is a quantum superposition of the others and vice versa.
Now, what should this whole thing lead to?
Imagine that we could solve the problems.
I'm saying again that the problems have not been solved.
There are all sorts of interesting suggestions.
I'll say a lot more about it on Thursday in my talk about black holes in particle physics.
But that will be a more tactical talk where I'll try to explain a little bit
what kind of progress I've made myself.
But again, I'm not going to claim to have the ultimate answers here.
The picture we want to arrive at is that you have particles in nature,
maybe several particles running around.
That's particle physics, subatomic physics, the thing we study in the LHC.
And at LHC, we also study bound states of particles, like a lead nucleus,
which consists of some 200 nucleons bound together, very tightly, very gravitational force.
You can consider small black holes.
A small black hole consists of lots of particles
which basically form information on their horizon, bits and bytes on the horizon,
and unspecified unknown space time inside that basically you can't enter
because time runs backwards and all these crazy things to try to get through.
But the properties of this horizon can be understood again from empty space.
Empty space itself contains fluctuations of these particles
and a very large black hole can be understood by replacing this by empty space
as seen by an observer going inside.
Now this I call a hybrid picture.
The idea is that we have to solve a circular problem.
The problem is understand the quantum fluctuations and all the elementary particles that exist.
Well, black holes are among them, but once you have all these particles and all these black holes,
you have to consider them from the vector fluctuations
and then you can describe the surface area of a black hole.
But as you see, the problem that we are confronted with is a more or less circular one
and that's why it is so difficult to address and we don't really know how to address it properly.
All sorts of suspicions made.
Now I'll come to a point called black hole complementarity.
And that is that thing that came up when we discussed these things
and I had discussions with the particular Leonard Susskind, who also describes in his book
the idea of black holes somehow obeying some magic laws of nature.
And I call them magic because it doesn't follow from what we know of the laws of nature.
We have to modify laws of nature to make this whole picture work.
Well, the idea is that you might either consider an observer going into a black hole
and that observer will see all the particles that went in,
but that observer will not see the Hawking particles
because for that he has to modify his notion of time.
But an outside observer like Alice in Wonderland will suddenly see the Hawking particles coming out.
But that outside observer will not be able to follow what happens to the particles inside.
So either you can study the Hawking particles or you can study the particles that went into the black hole
and usually, according to if you apply the known laws of physics according to the book,
you have to consider both.
You have to consider both the Hawking particles and the objects going in.
According to black hole complementarity, we say, no, wait a minute.
You can either consider one or the other.
Both pictures of the black hole should be complete.
And that is a rather drastic modification of laws.
We have to rewrite the laws of nature at the horizon very carefully to make this work.
And you don't know how. This is a mystery.
So but this is, I think, now a step forward.
And I explained and then on Thursday how to use this to actually get a superior theory.
Now, black hole complementarity does not come automatically.
Anything containing interacting particles with gravity.
But in order to make this whole thing work, you have to modify the laws.
And amazingly, this is possible.
That is something I want to talk about then later on Thursday when how to modify models for elementary particles to make this work.
And the nice and interesting aspect of this work is that this might have an impact even on the standard model of elementary particles.
We know the standard model of elementary particles is not complete.
Many more interactions will probably have to be added.
The LHC, the Large Hadron Collider, will tell us how to add more particles to the standard model.
We don't know that yet.
But eventually, new rules have to be followed if you want to do it correctly.
And the rules are, as soon as you come close to the gravitational force, you have to take into account that black hole complementarity must hold.
Otherwise, you make a mistake.
But that gives you further new constraints on these interacting particles.
And those constraints have to be very interesting.
And they could possibly well play an important role in future versions of nature.
Unfortunately, today we don't know how particles go all the way to the highway, which I showed you in the beginning.
So most of the spots on the highway are totally unknown domains of physics.
So we have a long way to go.
But this suggests that we may have new rules that we can use to derive how particles interact.
And maybe that will help us to build new and superior theories.
We haven't gotten that yet.
But there is perhaps a way to improve that.
And this is why I think that studying black holes is so important for particle physics because we perhaps might learn new rules.
Now, I'll use the last few minutes to discuss some problems we had with the LHC not so long ago.
And that was when some people in the public started to get worried.
Uncareful theoretical physicists had been talking about black holes a little bit too much.
And so as a consequence, when people started to talk about black holes being possible to be actually produced in the LHC,
people from the public started to get worried.
But if LHC is switched on, it will make a black hole.
And if a black hole is made, that will swallow the earth because we've read so many science fiction stories.
That will probably be happening.
And then the whole universe will cease to exist.
And it's our fault.
So shouldn't we stop the LHC and their web pages?
And we got nasty emails from people who wanted us to stop the LHC because they say, well, scientists are never sure of themselves.
Maybe the LHC will make small black holes.
And then these black holes are transformed into big black holes.
And then all hell will break loose.
Well, then they draw this picture.
This artist had absolutely no idea what a black hole would look like.
It would certainly not at all do this.
I won't tell you what a large black hole would do to the earth, but it would look very, very different.
I can assure you from that.
But actually, these are the pictures that people were drawing and were shouting about.
Now, CERN had to take these noises seriously.
Let me first explain a little bit what the idea was.
Because the LHC is many, many orders of magnitude away from the Planck scale.
So nothing to worry about.
Well, except when there are new extra dimensions.
I mentioned very briefly yesterday that there could be extra dimensions which actually are curled up in a cylinder, a very tight cylinder.
According to most theories, the cylinder is so tight that LHC won't come close to revealing any of this structure.
But you could imagine a theory where the cylinder is very large and the energy scale associated with that could be in a TV domain.
Then you have new dimensions already observable for a physicist doing experiments at the LHC.
Now, you need a lot of extra dimensions before the gravitational force becomes important.
But thinking of a black hole, you would think the black hole could now distribute its horizon over all these extra dimensions.
And then the Planck scale would shift from 10 to the minus 33 centimeters to perhaps a couple of TVVs.
And so this could be our real world.
Our real world is a membrane in these extra dimensions.
And an ordinary black hole would look something like this.
The horizon of the black hole would cover all of these extra dimensions.
And then there would be an unreachable region of space-time inside.
This is a large black hole, impossible to make for any machine like LHC, because you need the mass of a mountain or something to make it.
And LHC cannot produce particles of that sort.
But what LHC might be able to do was make these very small black holes, which are black holes in all these extra dimensions.
So this would be a small black hole.
Now, this thing would be so small that its Hawking temperature would be very, very large.
And so it would immediately radiate away all its energy in terms of Hawking particles.
And that is why we said that a black hole would probably look like this.
That a black hole would be formed, but it would decay immediately into radiation, basically thermal.
But this is more or less thermal radiation. That's why it goes in all directions.
And this would be a telltale signature of something like a black hole being formed.
So it would be interesting to look at events of this sort.
But the black hole would have absolutely no time to swallow up anything. It would decay immediately.
Now, OK, then our opponent said, well, it's nice.
Your theorists are very good at making theories. But suppose that's wrong, because you just said before you didn't know.
So what's the odds, actually? So suppose the theory is wrong, could it not absorb the Earth?
Well, the only thing CERN could do is take all these anxieties seriously.
Because we don't want to pose any risk to the universe, but we also don't want to make people feel very anxious about these things.
So CERN wrote a very heavy report on the issue. We had several theoreticians and experimentalists work out what actually do we know.
And is it safe to run LHC? Will it not make a black hole gobbles off the Earth? A couple of other menaces could be imagined.
So called strangelets and other particles such as magnetic monopoles.
They could also do nasty things to our environment. So they investigated all these things.
But then they used a very simple argument in the cosmos. There are also energetic particles reaching the Earth.
And actually, these particles are much, much more energetic than anything LHC could ever produce, billions of times more energy.
In fact, the universe does LHC experiments all the time around us, except it's in a location where you can't see them.
So LHC is doing nothing that doesn't occur naturally elsewhere in the universe.
And you can actually compute that if I call one LHC laboratory working for 20 years at full capacity, that I call one LHC.
Now, according to that report, the universe takes three times ten to the 13, that's 30 billion LHCs every second.
So the universe does every second what humanity could do in 20 years or so, and then ten to the 13th of those in our region of the universe.
So that is a lot of LHC experiments, and nothing is happening.
So there's no black hole formed anywhere in our neighboring planets.
Jupiter would be much more at risk than the Earth, but neutron stars would be even more at risk.
But neutron stars are never seen to explode because a black hole is gobbling them up of that soil.
No, they do the wrong thing, and we don't see any sign of black holes taking over the game.
So this is simply not happening, and that includes also many of the other menaces of other particles that LHC might possibly make.
The universe is much, much stronger than we are.
The only thing that LHC does, it produces a collision exactly at the spot where we can study them.
So the particles come from both ends, and within one millimeter we have the collision as expected, and we can build our apparatus around it.
We cannot build an atlas detector in the stratosphere to wait and see where cosmic particles come and to find out what they are doing.
That's impossible, and that's why we have the LHC collisions, but not because anything is done that would be unique in the universe, very far from it.
So we can put these anxieties at rest.
The report, well, they went through all these islands much more carefully and explained them to you now.
And they said, well, there really is no risk with the LHC, at least not at the present energy.
But, of course, you can read between the lines.
If an LHC is being made with hundreds of thousands of times the energy, they might have to redo their homework to see whether that's safe or not.
So we're not there yet, but it doesn't seem that the LHC can possibly make anything like black holes.
So that is the end of my story.
So tomorrow and the day after, I'll have, again, other discussions of particles and gravity.
Thank you very much.
Thank you very much for this very exciting talk, and I didn't know that for some reason.
Maybe, OK, shot.
Yes.
Well, yeah, so the question is, just in case somebody there didn't hear, the question is how can matter fall to a black hole if everything stops at the horizon?
Well, it's a relative statement.
It stops at the horizon as seen by us, but actually it continues its way in, and very quickly it will be completely made invisible at the horizon, and the horizon won't change by that.
So it is ready to receive the next object falling in.
So nothing will bounce back against the horizon.
It just goes straight through.
But different observers will see different things.
So the local observer will just see the matter go straight through.
Anybody traveling with the imploding matter, with the mobile phone, will just travel straight through the horizon, and no obstacle is encountered anywhere.
But if you look at it from the outside, it looks at this whole stream that is slowing down.
It doesn't bounce back.
It's just slowing down.
And it looks from us, because we have a very distorted view on the horizon.
It looks as if all these particles going in are just accumulating on the horizon, as if they form a star.
But actually, that's only from a distance.
You know, a helicopter with a strange lens thinks there's a traffic jam, but actually there isn't any.
These things just continue their way in.
At the scene from outside, everything stops right at the horizon, but that's only a distortion of our view.
It's the same thing as looking at the horizon of planet Earth.
You could ask, you know, if all the airplanes go over the horizon, seeing from us, they'll never get beyond the horizon, because we don't see them anymore.
Will the airplanes then fall down?
Of course not.
They just go to the other side of the Earth.
So the horizon of Black Hole is a little bit like the horizon of that we see where we look far away.
That you can go over it, but you have to be there to see what it's like to go over that horizon.
I see for us, the world seems to stop at the horizon.
So it's an optical illusion rather than reality.
What do you think we should observe, like stars being reflected from the Black Hole?
I think it's not outside.
They're outside.
Yes?
This picture of the stars which were orbiting around like this, they were still very far away from the horizon.
In fact, the horizon of a Black Hole has never been explicitly observed by astronomers, because it's too small.
It's large compared to the Earth, but it's too small for a astronomer to see in his telescope explicitly the horizon of a Black Hole.
Maybe that will change with future better telescopes, but so far they have not yet been able to see explicitly the horizon.
They do see stars far away, which accelerate and decelerate again, but they stay far away from the horizon.
But I was talking about things really going in.
And you can argue that it's just an optical illusion that when we see things go again, they seem to stop.
So the local observers say they're just going straight through.
Well, this is a little problem for science fiction writers, who want to use wormholes to go to other places in the universe.
Because that would be black holes, but you mentioned tidal forces.
Now the tidal forces with the Black Hole, which has the mass of the Sun, would be tremendous.
You would be killed by the tidal force, even if the Black Hole is a couple of kilometers in size.
So a solar mass Black Hole could be about three kilometers in size.
You might think you can go through that horizon three kilometers.
Nowhere you will be killed by trying to do so because of tidal forces.
The Black Holes that will not kill you when you go through are those which are a million times heavier than the Sun.
So the Black Hole at the center of our galaxy would in principle be mild enough for you in your spaceship.
You might decide to travel in.
It won't be a very pleasant thing to do because a few seconds later you'll be killed by the singularity at the center.
So then you only have a few seconds of joy to see why I'll go through the horizon.
This is suspected to happen every now and then.
Some of the supernova explosions they see might be Black Holes merging, but it is not known for certain.
I have never heard of an astrophysicist saying for certain here we saw two Black Holes merge.
Actually, if they are just pure Black Holes we wouldn't see very much because the only thing they would do is emit gravitational radiation.
But they wouldn't give a flash of light.
Only if a star and a Black Hole merge, then a star will emit enormous amount of light and that would be a gamma ray burst.
So that would be seen with two Black Holes merging would in principle not give a gamma ray burst and that would make it very, very difficult to observe.
With one exception, they would emit gravitational waves.
Right now, gravitational wave detectors are working, but not yet with such a sensitivity that they are likely to detect anything soon.
But these gravitational wave detectors which are being used now are being upgraded.
And in a few decades, they will be certainly powerful enough to observe exactly what you say, merging Black Holes or stars merging or something.
So what will happen next? They will see gravitational peaks every now and then, radiation of something of this sort happening.
And they will be able to calculate roughly where in the universe this takes place.
So astronomers will then point the telescope to see if they see a flash of light or not.
So also, they might see absolutely nothing. In that case, there could have been two Black Holes merging.
They just escape. They are just ordinary particles, including ones that you can't detect, like neutrinos or even worse.
Pardon?
They are ordinary matter.
That is, all particles of order, electrons, neutrinos, protons, neutrons, they'll all be emitted.
They'll be dictated by the Boltzmann law or Wechsler law.
If you have heavy particles which cause lots of energy, then you need a very high temperature to create them.
The lighter particles will come more easily. So the bigger Black Holes are only emit photons and gravitons.
You won't see the gravitons. There are also even neutrinos which you won't see in general, but you will see the photons.
So they'll get a flash of light. And then when the size becomes smaller, they might emit other things, according to Boltzmann's law.
It's all statistics, all thermal radiation.
And these thermal particles, they'll behave just like ordinary particles.
There will be equal amounts of matter and antimatter. So the antimatter particles will be very visible because whatever they touch, they'll decay and annihilate and give a flash of light.
But these particles will behave like ordinary particles coming out.
About what?
All. Black Holes, I didn't mention that, but the Schwarzschild Black Hole is the easiest one to calculate, but there is a generalization solution where everything rotates.
So it carries angular momentum. And angular momentum is conserved. So they continue having that angular momentum for quite a while, and it looks slightly different from Schwarzschild.
In particular, the central singularity looks very different. And there are some other peculiarities which Schwarzschild doesn't have.
So I didn't quite understand, but rotating black holes are rather easy to find in astrophysical processes, because very often they have a cliche disk, things rotating around in one direction, and then the black holes being formed are being sped up.
So they'll make rotating black holes. There have been some speculations that the black hole at the center of our galaxy is indeed a rotating black hole, a curved black hole.
And so in the astrophysical black holes, many of them are quite likely to rotate.
There's a limit to the amount of rotation or the amount of angular momentum they can carry.
The massive black holes carry more angular momentum than the light ones, but there's an exact limit that every black hole can only carry that much angular momentum.
But I don't know what else you wanted to ask.
No, it's not possible to escape once you get past through the horizon, but there's something remarkable about rotating black holes.
There's a region, just outside the horizon, called the Ergo region, where you can send in particles, have them collide in that region, such that out comes more energy than went in.
And the reason is that the particle interacts in such a way that it cancels out the angular momentum of the black hole, and in doing so it gains some of the mass of the black hole is regained out of this process.
So you can get a little bit of the mass of the black hole, you can get out by particle interactions near a rotating black hole, but that's a technical detail that doesn't have much bearing on what I've said in this talk.
Well, as a matter of fact, we don't know. But if a black hole is as big as that, then of course we can live for billions of years before hitting the singularity.
So there have been speculations of this sort, but if we take ion consecrations as we know them today, and in relatively a few weeks' time, the Nobel Prize will be given for astrophysicist who establishes the universe, accelerates in its expansion, that's not a black hole.
So then we are relatively safe. So as far as we know, this metric around us doesn't have the black hole shape. So then we're not in a black hole, but you never know for sure. Maybe we're heading for a singularity, but that will be many, many billions of years away from us now.
How can we be sure that the language is used to formulate these problems in microservices and the language is higher than it is used to describe the relationship between the black hole and the singularity?
Well, language is extremely flexible. I understand the question, I think, because so far, language that scientists have been using has been successful, but only after a lot of effort.
So as you know very well, in the history of science, people are thinking about things in very different ways in the past and got stuck at all sorts of spots. In the old days, you had religious languages and people thought about the universe in a very different way than we think about it now.
And only after a lot of work and very slow steps, humanity discovered what the correct language is to use. And in physics in particular, we discovered that mathematics is a much more appropriate language than ordinary words.
We can translate mathematics into ordinary words, like in fact I did today and yesterday, and some of the position goes away. So I couldn't be as precise yesterday and today and tomorrow as I would like to be, but then I would have to use a blackboard and write down mathematical equations.
That is a better language than what I said today. And so today is only an approximation of what we really want to say. We've gone a lot further than that. But eventually, of course, as I've tried to emphasize today, there are things we don't understand, so the language still has to be developed to describe that correctly.
So the answer to your question is yes. When we discuss unknown or ununderstood domains of physics, we are pretty sure our language is inappropriate. We have to learn what words to use to say things better. And we are in the process of trying to learn that.
I don't think that language will be an eternal obstacle, but it certainly is a temporary obstacle, like it has been in the past, and we can learn a lot by studying the past and how science came into being. And we see what our limitations were in the past.
And I can imagine that today's limitations are of a very similar nature. We certainly haven't become so much more intelligent than people who were 100 or 1,000 years ago. So we still suffer from these limitations. So I think yes, there are limitations of this sort, but no, we can try to clear them up, and we are doing our best.
Sorry, in and out of a black hole? Oh, in and out, but not out. Unfortunately, when you try to get out, you will not get out in the same universe. The picture showed in the beginning showed two universes, but they are different universes.
And even then, the problem I mentioned with the tidal forces, you need a really big black hole if you want to survive your journey through the horizon. And when you get out, you might get out in, well, formally, mathematically, it seems you can get out. But mathematicians were ready to acknowledge that they made some simplifications in the calculations.
And physicists then tried to calculate things more precisely. They say yes, but while you try to get out, you encounter a region where things are unstable. So there's a second horizon to a black hole, which is unstable. And so if it's destabilized, then you're actually killed by your attempt to pass on your way out. So it's not a very pleasant environment. So trying to get out, you'll probably be killed.
Pardon?
Okay, a particle or something. Well, of course, this talk was about elementary particles coming out of the black hole, and about them containing the same information as the particles that went in. So that could be an affirmative answer to your question, not as a human being, but as a single particle.
The things that go in might come out with strongly disguised, disguised as a whole cloud of other particles. So the information goes in, can come out in principle. So the other answer is yes, but in a very scrambled way.
Or the cosmic rays, you mean? Well, the largest detectors one has are typically kilometers in size. For instance, you can make a radio telescope with many antennas on the ground, and they cover a domain of several kilometers in size. So then you can wait and see if a particle comes out.
Then typically, they look at particles which come there once a year or so. Then you look at one square kilometer once a year, and then you see sometimes quite dramatic things coming in with tremendous amount of energy. In fact, there's a problem there in physics, and that is particles with such enormous amount of energy will be stopped, not by the atmosphere of the Earth, but by radiation in the universe. The universe is not totally empty. There's thermal radiation coming from all directions.
That so-called cosmic background radiation will stop cosmic rays from having too much energy. They'll slow them down, and so the energy will be released. In spite of that, people still see very energetic cosmic rays hitting the Earth, and it's not quite clear where they originated.
It cannot have been too far away, because then they would have been stopped by radiation in the universe. That's a straightforward calculation. It's not quite obvious what the correct origin of these things is, but we can imagine all sorts of very violent processes in astrophysics.
For instance, magnetic fields. If magnetic fields start to sweep around, they generate electric fields as well. Then you have just a gigantic version of a particle accelerator. We do expect exploding stars to be gigantic particle accelerators.
They carry electric and magnetic fields, so they have all the ingredients of a particle accelerator in them, made by nature. Exploring stars are good generators. But these particles don't go straight, because there are magnetic fields in the cosmos, so they go through a curved trajectory.
So it's very difficult to trace back where these things came from. So it's very difficult to say what the actual origin of these cosmic ray particles is.
That is true, but they are very strongly redshifted. So now, of course, we have very good models of the universe as it started from the Big Bang, and those models do agree with the observations.
But that means that I didn't say it quite correctly. I should have said the universe is a finite lifetime. It originated from something very small that expanded. By expanding, it also slowed down all the relative motion, so that light that is emitted in the very early stage of the universe gets enormously redshifted.
And redshifted also means that the energy goes down a lot. So a very bright galaxy might look very red, very dark, when it is very, very far away from us. Now, actually, situation more complicated, those galaxies happened to be very bright also in the ultraviolet.
So now the light has shifted to the far infrared, but still they look relatively bright. So those galaxies you saw in our first picture were actually galaxies shining in a deep ultraviolet, but they look like white images on the photographic plate now.
But even further away will be galaxies which are redshifted so much that we actually don't see them anymore. So the reason why this region between the galaxies was black is perhaps not only that there are very few galaxies in between, but rather that they are very strongly redshifted.
And the region between is also so old that what you are seeing there is the universe before it made any galaxies. Because while looking far away, you also look at the past. So the most distant galaxies we see in our telescopes are actually very young galaxies, which originated shortly after the universe got started.
And they look different from the older galaxies we see closer by. But the universe has a finite moment that it got into being. So if you try to look further, you don't see any galaxies because it did not exist yet at that time.
What you had instead was a loose amount of particles of matter which were glowing in a much more general way, and that's the famous cosmic background radiation. So we don't see galaxies in stars, we just see radiation coming from everywhere with about the same intensity.
That's the famous cosmic background radiation. That's what we do see between the galaxies.
So there are many more questions. So I don't know. I can go on forever. So I can go on forever, but maybe the public gets maybe bored after a while.
Yes.
We know, yes.
Those neutrinos, which I may mention that sound, were very seriously upset much of what I said today, if true.
Well, much of what I said actually have to be modified quite considerably if that were true. So I'm just assuming that the observations were based on some strange glitch that they have overlooked.
We still believe, most of us still believe that they overlooked something. But exactly what is very difficult for, I think, in addition to put his hands on, we can try, but the idea that you have to give up relativity just for one experiment is a bit much for us.
But the experiment will have to be and will be repeated in many different ways. They repeated basically the same experiment, the same setup with different pulses, and then they found the same results.
So the result is reproducible in their experiment. And this is take for granted. But now we want other experiments where people start from scratch, do the same thing to see whether they get the same result.
And there's still much consensus among in the science community that that's unlikely, but of course not impossible. So maybe, yes, maybe we do have to revise all we know about relativity theory, which would be quite something.
We have to reintroduce the ether, which nobody of us likes very much, because it was so clean to formulate all laws of nature without an ether.
We have to ask catch our heads, how come the LHC works? Because it is very heavily based on relativity theory. If you make a microscopic change much, much smaller than the effect seen within neutrinos, the LHC will no longer work at all.
So so we have all these mysteries that have to be cleared up. And but indeed, if if there will be different velocities, the particles like neutrinos move at different velocities than than light, then what I said today will have to be revised quite considerably.
And I don't know where I would go, but even black holes would then have to be reconsidered, because at the horizon, we basically make infinite Lorentz transformations.
We go on and on and on and on. And other teams say, no, no, you have to stop at at the fraction of the speed of light, then you have to stop.
Well, this would change everything about black holes also.
Well,
well, I don't know that everybody understood the question. The question was whether we can in a lab somehow experimentally verify this this Hawking phenomenon of black holes emitting particles. Well, the thing we cannot do in the lab is make black holes.
Because those who require tremendous amounts of energy and extremely dense amount of matter that we cannot reproduce in any laboratory in any foreseeable future. So that's not going to happen.
It's the thing you can do is you can consider very large accelerations, because the difference between these two observers is a one observer is very much accelerated compared to the other.
You can consider particles being accelerated very strongly. And in fact, in particle accelerators, such as as lab, for instance, the electrons are accelerated tremendously strongly.
And so you could ask whether particles being accelerated show some jiggles in their motion, because of the thermal radiation that they emit, which would be an equivalent of Hawking radiation.
And such effects, I think, are actually known in particle physics that a very strong accelerated particle emits radiation, and this radiation is, to some extent, thermal.
And so it resembles and is somehow related to Hawking radiation. There's also in the particular Bill Unruh, who was one of the first to realize that empty space can radiate this way.
He said you can do the same thing with sound. So let's not take take light, but take sound goes a million times slower.
So now you can think of making a gas, a stream of gas and have the stream of gas go with the speed of sound and exceed the speed of sound, like having gas go through a nozzle and through the nozzle, it goes faster than the speed of sound.
And with the nozzle, it goes slower. Then that has a formly horizon. If you come too close to the nozzle, then the sound can't go back anymore. It has to be going through.
So will that thing emit Hawking radiation? And he has big theories about that. It would be why he calls it a dumbhole, because it makes no sound.
Sorry, it's not black, but dumb, because it's not visibly black, but acoustically black.
And then the question is, does that radiate phonons, the quanta of sound? Well, that's the kind of thing you can speculate about, and you could even think of doing that in a laboratory.
Yeah, unless a very urgent question, I can stop. Thank you very much for this talk.