My name is Hermann, I'm a bit of a fan of you,
because in the end I'm very happy to be here in Germany.
I'm very happy to be here with you today,
and I'm very happy to be here with you in English.
So, ladies and gentlemen, it is a great honor for me to be invited
to give a series of lectures here dedicated to a great scientist
and philosopher from Weizsäcker.
Although I will not really speak too much about philosophy in these lectures,
I think philosophy is far too difficult for me to talk about.
I'd rather stick to physics, but I think these branches of physics
that I'm talking about have ample connections with philosophy
and they give continuously, they inspire people to philosophize
about what science really is about and how we should think about things
and how we should continue doing our field of science.
So, let me begin by bringing you to high up in the atmosphere
in a region between France and Switzerland, right above the border.
The border is here somewhere, and this is the town of Geneva in the background.
Lake Geneva here, a famous fountain right at the spot.
On the background, you see the Alps and the Mont Blanc,
so it is a beautiful scenery here.
If you are sitting in an airplane, high above all this,
the thing you will not see is this circle because the circle is underground.
It is a practically perfectly circular tunnel at some places,
something like 100 meters under the ground.
What you definitely won't see when you are sitting in the airplane
is that in these circles, two beams of particles are going in opposite directions
and at various spots, these little circles here, they are made to collide
and physicists then investigate what happens when these particles collide.
What you are looking at here is actually to be considered a microscope.
It is the world's biggest microscope, not only big in size,
but also big in magnifying power.
Actually, at this moment, Europe is far ahead of any other spot on the Earth,
including the United States.
For once, we can be proud of Europe to have here a superior machine
where we can search about the scientific features of matter
at the very tiniest conceivable distance scales.
The machine which was first built in this tunnel was called LEP,
Large Electron-Positon Collider.
Electrons and positrons are very light subatomic particles
and they are relatively easy to collide,
and when you collide, you have them collide,
you can draw very important conclusions from that.
But the magnifying power of the machine was still limited
if you actually managed to collide hadrons together in this machine.
You reach even bigger magnification.
This is called Large Hadron Collider.
Hadron is just a word that was used in this abbreviation.
We are really talking about protons
and we are talking about heavier nuclei of heavy elements, in particular lead.
Lead is one of the heaviest species of atoms,
so the lead nucleus is heavier and larger and has a higher charge than most others.
So when you have them collide, you generate even bigger energies.
Not really bigger magnification, but you are studying another domain of physics.
I'll explain more about that.
Now let's go into the tunnel inside it.
This is actually a picture made by a Taylor lens
because you can actually see the curvature of the tunnel,
but it is 26 kilometers in circumference,
so it's a very large tunnel indeed.
And it is completely filled at first sight with these monstrous cylindrical tubes.
These blue cylinders you see here are magnets.
They are very, very powerful magnets,
as powerful as we can make them.
I'll later explain why you need those magnets.
But right now let's remind you that these magnets are each 15 meters long
and each of them carry a weight of 35 tons.
So these are quite big machines.
Everything is big in this accelerator.
But to tell you a little bit about the kind of physics that we are doing there,
I go back to the year 1969.
And the reason for that is twofold.
1969 was a nice period in physics when lots of bits and pieces had come to places,
but there were still many, many mysteries which were totally unsolved.
I also chose the year because that was the year
when I started to study the subject as a student at Utrecht University.
And in 1969, a summary of the subatomic science of those days,
it was quite easy to give.
We had just a couple, a bunch of different kinds of very fundamental subatomic particles.
They had been investigated in great detail and the properties had been registered.
And what we did with the particles is very similar to what biologists do
when they study plants and animals.
They put them in categories, in families, in genera, in species, in races, and so on.
So we do the same thing with particles.
So we have, the photon is one of the first fundamental particles to be discovered.
Then the so-called leptons, of which there were two species,
E minus and mu minus, but they both had a companion lepton called neutrino,
neutrinos of the electron type, neutrino of the muon type.
And drawing a box around these two particles means that they seem to be very closely related.
So the closest cousins of particles we put in families and then we draw boxes around them,
just like biologists do.
The particles are given Greek names, Greek or Latin letters,
and the minus here means that these particles are electrically charged.
It has nothing on top of them. They are usually electrically neutral.
Then the hadrons is another set of particles,
and the hadrons fall into two subclasses, the mesons and the baryons.
And I won't really need, in what I say, I won't really need you to remember all these details.
I'll just very briefly flash them on the screen.
The photon, which is the most elementary particle inside the atomic nucleus,
together with a neutron, again, for closely related species.
So we put a box around them, and then there were other things that you could put together,
and they have also larger boxes around them,
indicating that these, in turn, are relatively closely related.
These particles carry spin zero. These carry spin one-half.
Spin is a property which I'll refer to more frequently.
It simply means that particles, when they move, they also rotate around the axis.
So just like a soccer ball or a tennis ball with effect, with spin, these particles also spin.
But they spin in a very special way, which we indicate by numbers.
Either zero, one-half, three-half, or spin one for the photon, and so on.
So particles may spin with different rates.
And this is a thing that you might want to remember.
Now, this was roughly the list of the subatomic particles in those days.
The list is not quite complete, because you could also add the antiparticles.
And associated to the leptons, e-minus and mu-minus,
there were the anti-leptons, which always have the opposite electric charge, so e-plus and mu-plus.
E-plus is also called positron, so the large electron-positon collider
would be a machine where e-minus collides against its own antiparticle.
That was what that machine was doing.
And also, the barons have antiparticles, the anti-barons,
and this thing has been three-half, it has an antiparticle, and so on.
There were more particles than these in the subatomic arena,
but they usually could be considered as excited states.
Sometimes a particle, when it is hit very high by other particles,
it goes into some higher vibration mode,
or it starts to spin faster than these minimal values.
Those we call excited states, and they were clearly recognized
as the excited states of these primary objects.
So you could list all those excited states, because, you know,
these are these particles basically in their most stable configuration.
And this was pretty much it, but it was also quite clear
that there were very many mysteries about these particles,
which are much less well understood.
What was understood in the 1960s was that these particles have two features.
One is dynamics, how do particles move around once you give them a kick?
And the other is, when particles come close to each other,
they might exert forces on each other.
And we wanted to categorize and become familiar with the forces
that are active in the subatomic world.
And it was realized that there seemed to be something like
four different kinds of forces.
So a force can be viewed as some effect that particles have on each other,
and the effect could be due to the exchange of further particles.
I'll explain that in more detail.
There were four types of forces recognized in those days.
There's electromagnetism, perhaps the best understood of all,
because electromagnetism also occurs in the ordinary world around us,
in a television set, in a mobile phone, in a radio, in lightning,
also ordinary light.
All these are electromagnetic phenomena,
and those were already understood since the mid of the 19th century
when Maxwell wrote down the basic equations for this force.
Then, besides that, there were two forces
which are special to the atomic nucleus,
and that's the strong force and the weak force.
And then there was something very strange, gravitation,
the simple fact that when I drop something, it falls on the ground.
To the ground, that's the gravitational force acting.
Gravity is a very special force,
but when you consider the gravitational force
between two elementary particles, it is extremely weak.
Gravity is much, much weaker than any of the other forces,
and in a particle accelerator,
the effects of gravity are practically impossible to detect.
So gravity is a kind of odd thing in here,
and we leave it out for most of the time.
But then, what are the strong forces and the weak force?
Are there many different kinds of strong forces?
Are there many different kinds of weak forces?
This we did not know in the 1960s,
but the mystery was soon going to be lifted,
and in fact, in the early 70s, everything fell in place.
Let me first concentrate on the weak force,
and this is what was understood during the 1960s or even earlier.
It was understood that most weak phenomena take place
at one point in space and time, just an event, a flash,
and then a weak force has it that if two particles come close,
like the electron and what I'll later explain
to be a subatomic particle, the U quark,
if these two particles come together, they might both transmute.
So the E might transmute into a neutrino of the electron type.
The U might transmute into a B.
And there are other phenomena that can take place
when the weak force is active.
So the weak force must be seen as a force
which causes particles to change into other particles when they collide.
And, well, actually, when the electron collides against the U,
it goes into an electron neutrino,
but if you take a mu, it will go into a mu neutrino.
And these will go the same way.
You could also put something else there.
You could put a D and go into a U there as well.
Then, at first sight, nothing happens.
Nothing much seems to happen here.
But if you look more carefully,
you find that other properties of the particles change
so that the weak interaction takes place here,
can still be recognized.
Also, downstairs you could make substitutions like this.
So the weak force, well, this was just what I'm saying now,
is a bookkeeping statement about the weak force.
What kind of weak forces are there?
And physicists made a full list of all possible transitions
that could take place.
And they noted that transitions typically take place in two ways.
Here's a particle that transmutes,
and here's a particle that transmutes.
So looking at this, it wasn't too difficult to imagine
that the weak force takes place in two steps.
So when the E goes over into new E,
or a mu goes over to new mu,
or a D goes over to U, then something happens here.
A new particle might either be created or captured.
That new particle would then be created or captured
at this spot as well.
So it would fly from here to here or in the other direction.
And then a similar transportation takes place at this end.
This W was given a name.
That's the easy part of our field.
We can give names for everything.
So it's called W for the particle which intermediates in the weak force.
This W turned out to be a particle that is electrically charged.
You can see that because this thing is electrically charged.
This is neutral.
So electric charge had to travel from here to here to here.
So it's a charged thing.
And with a little bit more, or considerably more effort,
it was realized that this particle has spin.
It spins with quantity one around its axis.
That's not easy to derive,
but the measurements and observations are made very carefully.
And it's found that this must be a spinning object.
So this was the weak interaction,
but then there were still many mysteries about it.
But there was something that was quite striking about the weak force
and quite beautiful and which gave us the impression
that there was exactly one kind of weak force.
And that was that when you look at these transitions,
it could take place.
E could go over a new E.
Mu could go over a new mu.
Protons could make transmitted the neutrons.
Protons could also transmit into lambda particles.
All these transformations would take place at the same rate
with the same strength you could say that.
Again, you measure very carefully the strength of the force
and you find that all these transitions have the same strength.
Well, they have the same strength, but not quite.
When you measure more accurately,
you find that this transition was a little bit weaker than those two
and this one was a lot weaker.
So this one was about 95% weaker than this.
So just one part out of 20 weaker than that.
And this only 5%.
So this was much weaker than the other forces.
And that was quite mysterious.
And this was a topic of hot debate,
what was going on with the weak force.
And my then advisor, Martinez Feldman,
was working at CERN in Geneva.
There's a big theory group there,
so their theoreticians also come together
and they discuss these topics.
And one day a colleague of his came rushing into his office,
the colleague by the name of Nicola Cabibor.
Cabibor came rushing in his office at his shop.
Tini.
That's the name.
Martinez was also a teeny.
It's an angle.
And what did he mean by saying it's an angle?
He said it's an angle because you have to look at these fields
as being vectors pointing in some direction.
And when the electron makes transition to an electron neutrino,
you will say it goes from here to here.
It goes in some direction.
And this you have to remember.
But then when you look at the proton and the lobda particle,
the proton could be sitting here,
the lobda could be sitting there.
Or sorry, the lobda and the neutron.
The lobda could be sitting here, the neutron could be sitting there.
If the proton makes transition to the neutron,
it goes in this direction.
If the proton makes transition to a lobda,
it goes in that direction.
And all you have to say now is that this angle is a little bit tilted.
It doesn't go straight.
It goes with the angle.
And the value of the angle is easy to compute.
It's about 13 degrees.
If the angle is 13 degrees,
then the cosine squared, the angle is 0.95.
The sine squared angle of the angle is 0.05.
Together they are one.
And so that's why this only goes in 95% of the strength.
And this is 5% of the strength.
So if you now say there's a rotation here,
then the length of this vector is the same as the length of D2
within the experimental accuracy that was known in those days.
So that is a great idea.
And this idea turned out to be precisely correct.
This is the correct way in which we now think about the weak force.
And so Weltmann, from that moment on,
knew that they were onto something very, very basic.
And he thought, well, this will mean that the weak force
must be as fundamental as electromagnetism.
Because in both cases,
you could say that there's a particle being exchanged.
In the case of electromagnetism, if you have two charged particles,
the strength of the force on which they attract or repel each other
is determined by the way they are coupled to the photon.
And the quantity that's relevant there is called electric charge.
All particles have essentially the same electric charge.
Sometimes they have electric charge, 0.
But when they have electric charge, the quantity is always the same.
Or in some rare cases, 2 or 3 or more times that quantity.
But always a multiple or fundamental unit of charge,
the charge of the electron.
And that makes electromagnetism a very universal force, a unique force.
Now Weltmann realized the same had to be true for the weak force.
Here and here, the charge, whatever you could call it, is the same,
except that particles transmute into other particles
when they exchange a particle.
But then the particle exchange here, the weak particle,
looks very much like the photon.
I showed you in the beginning, the photon has been 1.
Well, the weak particle also has been 1.
So it looks exactly the same.
Isn't that nice?
Well, there had been a theory about this
that had been proposed in the beginning of the 1950s.
So long ago, Yang and Mills made a very fundamental observation.
Through lots of trial and error, it wasn't easy.
The mathematics was unfamiliar in those days.
But Yang and Mills figured out
that there is a way to rewrite Maxwell's old theory about electromagnetism.
Maxwell had written a beautiful set of equations
saying how electric and magnetic fields evolve when you switch them on,
how they affect each other, and how they can give rise to waves,
like radio waves and so on.
He had all these equations figured out.
But Yang and Mills discovered you can generalize those equations.
You can write very similar-looking equations,
but they are more complicated.
When you have a Yang-Mills field instead of an electromagnetic field here,
and if a charged particle like a proton goes through the Yang-Mills field,
actually the proton will transmute into a neutron.
Or if you have a neutron, say, it might go back into a proton.
I drew two particles here because they start being identical,
and when they go through the field, they are different.
So particles can make a transportation into different particles
when they go through a field.
And they could write down the equations for such fields,
and they look very much like Maxwell's equations, but they are more general.
However, they also have the feature that there is a uniqueness of the force.
So the charge that you put in this theory had to be
a multiple of one particular unit of charge.
And that, Weltman realized, that could be the explanation
as to why the weak force has this universal character.
Well, you can ask, what happened to the charge of the proton and the neutron?
When a proton goes through a neutron, the proton is charged, the neutron is neutral.
What happened to the charge?
Well, Yang and Mills realized that the electromagnetic field
has quanta of energy, called the photons.
Well, their Yang-Mills fields also have quanta of energy,
called the Yang-Mills bosons.
But this time, these quanta are electrically charged.
So if a proton makes a transportation to a neutron,
the charge goes away into the energy quanta of the field.
So once you realize that, you realize that the energy quanta
of the Yang-Mills fields themselves are electrically charged.
Well, the photon is electrically neutral.
So the photon doesn't transmit any charge from here to here.
It leaves the charged particles as they are.
But in the Yang-Mills case, the charge might continue,
but the charge might also travel to the other side.
That means that the Yang-Mills particles themselves are charged,
and so they can also transmit themselves, so to speak.
Now, that was something new.
So this is a new phenomenon in the Yang-Mills theory
that had not been realized before.
And that made the theory a lot more complicated to study.
So, well, this was a beautiful theory to be used for the weak force,
felt the thought.
But then there was something wrong.
And what was wrong?
There were two things wrong about the theory.
One was that electromagnetism has a long range.
You could take two magnets and have them very far apart,
and they still feed each other.
The magnetic field of the Earth spreads all way back into the cosmos.
And even between stars, you can detect magnetic fields
that go from one star to another star.
So they range enormously far, these magnetic fields.
And that is directly related to the fact that the particle being exchanged,
the photon itself, has no intrinsic mass.
If you say the mass of the photon is zero.
Now, in the weak case, the situation is totally different.
The weak force had to have a very short range
because the two points where the transportation takes place
basically coincide.
So the force even, the range is even so small
that in the machines of those days you couldn't even detect
that the force has any range at all.
So the weak fields would only go for a very short distance and then stop.
So this is something totally different.
And unfortunately, in Yang and Mills, in their equations,
the fields also would have an infinite range.
So there was something that did not work well
in the case of the weak force.
But what can you do about this if you have a field
where the particles have a different mass
and where the fields have a different range?
Well, you notice that you're using the wrong equations.
So Weltman and Feynman and some other people like Shelley Glashow,
they all realize that you have to modify the equations.
So what they did is they just add a term to the equations.
Just add a mass term.
I won't bore you with the details of the equations themselves.
Just say that by a little modification of the equations
you would simply postulate that the particle has a mass after all.
It automatically reduces the range of the force to a very short range.
So all seem to be just working fine if you do that.
And just calculate what happens.
Well, you calculate what happens.
Now, in the simplest case, a single particle is exchanged.
But some people like Weltman and Feynman realized
that these things might also happen.
If you exchange a particle at the same time,
another particle might be exchanged from here to here.
This is among the rules of doing field theory with elementary particles.
The rules are very strict.
The rules require that there's a good order in cause and effect.
The photon actually doesn't know whether it's going to meet the same particle
or a different particle.
How can it tell?
So there must be an occasion where the photon is being emitted from here
and from here, and that photon could be captured by this line
as well as captured by that one.
So there are many different kinds of diagrams you can draw.
And the question is, if you know how to compute this,
then how do you compute these diagrams?
As it turned out, this was quite difficult.
And it was actually a big discovery,
and people were very proud, like Weltman and Feynman,
when they found that, well, it works.
You can do this.
And when you compute diagrams of this sort,
where basically you have one extra link,
things go in one closed loop basically,
then if you compute diagrams of this sort, it works.
The theory gives meaningful and sensible answers.
So Weltman, my advisor at that point,
thought that he was well on his way to become famous
and to make a good theory for the week four.
So the next thing he did was,
what happens if you have exchange of two particles?
Now, this is one page of a long paper that he wrote,
and the paper was completely full of diagrams,
and it all went terribly out of hand.
So very often he found that not only you have particles,
but you had to write additional lines,
which are not really particles, but auxiliary expressions
and to make things work.
He called them ghost particles,
discovered that one ghost particle is not enough.
He needed different ghost particles
and they interact in very complicated ways,
and he ended up writing expressions of this sort
and basically discovered that it didn't work
in the case that there are two or more loops.
When you have more particles exchanged at the same time,
everything goes wrong.
So somehow the theory isn't right.
The two loop diagrams of this sort simply didn't lead
to any useful result at all.
So something was wrong and what is it?
Something had been overlooked.
Now, the thing that had been overlooked could later be realized
and be the following.
When you have a spin one particle such as a photon
or the weak intermediate boson,
well, they can spin in different directions.
But now, if you add a mass to the equations,
then the spin one object must be able to rotate
in three distinct ways.
That is a peculiar feature of quantum mechanics
that I can't explain in a short time,
because if you play tennis,
the ball can spin in very many different ways,
but electric particles can only spin in a few ways.
But the spin one particle with pass
can spin in three directions.
If it has no intrinsic mass,
the particle will always go with the speed of light.
And then one spin direction becomes impossible.
It can only spin in two ways.
So the photon spins in two ways,
but the weak and the immediate boson that was needed
for the weak force spins in three different ways.
And a spin mode was missing,
and Weltman and Feynman didn't care about that spin mode at all.
Now, there was apparently other,
but later we discovered this difficulty was related.
There was a problem with the symmetry
of the Yang-Mills system as well.
When the electron transmutes into a neutrino,
you can say the electron is here, the neutrino is there,
this vector rotates,
it only works if the neutrino is identical to the electron.
So the original Yang-Mills system
that Yang-Mills so partly wrote down because it was so beautiful
and the scheme seemed to work perfectly,
that system required that particles transmute to each other, yes,
but they had to be identical particles.
They shouldn't be different.
Well, the neutrino is different from the electron.
Neutrinos are neutral, they are much lighter,
and electrons carry electric charge.
So somehow the symmetry wasn't perfect
and you had to do something else.
And the particles had to be somehow indistinguishable.
The symmetry had to be broken.
That was the very important message.
How do you break a symmetry?
And this is where Mr. Higgs comes in.
Mr. Higgs noticed that there had been many ideas
and theories about symmetry and nature
and how symmetry could be broken.
But the ideas hadn't been done,
investigated very carefully in the Yang-Mills case
or in the case of electromagnetism,
where you could also have symmetry breaking.
And Peter Higgs discovered that if you do that,
you have to introduce an extra particle.
Now, basically the same mechanism
had also been investigated by two other people,
Francois Englert and Robert Brauch,
who were working together in Brussels,
on very much the same idea,
but they concentrated on what this symmetry breaking did
to the Yang-Mills particles, the weak intermediate boson.
So Englert and Brauch discovered
that this gives you a much more natural way
to add a mass to the vector boson
without ruining the number of ways things can spin,
and Higgs concentrated on this extra particle
that the whole phenomenon also creates.
So these people had already proposed the idea,
but mostly their ideas were not taken very seriously
because there were very many powerful mathematicians
who had also worked on symmetry breaking,
and they basically hadn't quite understood
what the full consequence of spontaneous symmetry breaking is.
Now, let me introduce what spontaneous symmetry breaking is
by taking a comparison that was displayed in a beautiful way
when Nambu received his Nobel Prize,
a Japanese physicist, a few years ago.
He said he was too old to give his lecture himself,
so he had his lecture given by a younger collaborator,
a Polish physicist by the name of Bieronicki Bierola.
And Bieronicki Bierola gave a beautiful talk
explaining spontaneous symmetry breaking.
Nambu actually had been one of the first to say that symmetry
and symmetry breaking are important in the subatomic particles.
So Bieronicki Bierola said,
take a perfectly straight cylindrical rod,
and now you push on the rod, and when you push very hard,
you find that the rod becomes a little bit shorter
if you squeeze it like that.
Now, if you push harder still, it will not only become shorter,
it will start to buckle.
And this simply means that you press too hard
and it's taking no longer straight,
but the question is, in what direction will it buckle?
Will it go left? Will it go right, forward or backward?
Well, the answer is you don't know, and it doesn't matter much.
But the fact is that the perfectly symmetric shape,
we call this symmetric because you can rotate it
and it doesn't change its appearance.
If you rotate this thing, it does change its appearance.
So this is an example of symmetry breaking,
but it happens spontaneously.
You don't have to create an asymmetry in the equations.
You just have to create a situation that the most stable configuration
is one where the symmetry is broken.
We can say it in different ways.
We can think of a particle that sits in a potential well.
And the potential well takes the shape of a Mexican hat.
Now, if you take a Mexican hat and have a particle right on top of that,
this would be the symmetric configuration.
And this would be a solution of the equations,
because if the particle sits right in the middle,
it has nowhere to go if you stay there.
But you can imagine very well that this is not the most stable configuration.
The most stable configuration would be
that the particle will sit somewhere in the rim of the Mexican hat.
If it sits there, you find, first of all, that now the particle can move around.
Originally, it had only one place to sit.
Now it can run around in the rim of the hat.
That is an extra degree of freedom.
And this is how spontaneous symmetry breaking
could add a degree of freedom to the young mill's particles,
allowing them to rotate in a third direction.
So this one is the sort of comparison you can make.
Now, this would also make the counting work,
and it would also allow you to understand
how particles can be transmitted to different particles.
All you have to say is that this field called Higgs field
is oriented in a certain way,
but now you can distinguish the other particles
whether they are parallel or orthogonal to the Higgs field.
If they are parallel, you call them neutrino.
If they are orthogonal, you call them electron.
So the Higgs field gives a kind of reference frame
in the fields of particles,
such that now with this reference frame,
you can distinguish the electron from the neutrino.
So having one extra field in the system
would allow you to describe young mill's forces
acting among different particles,
as long as they also act on the Higgs,
and the Higgs couples interact with the other particles as well,
and at the same time, it gives the extra degree of freedom.
So it will do these two jobs at once.
And this was a much more superior way to introduce symmetry breaking
and to have a theory that makes the weak force work.
So you not just add a mass term to the equations,
but you attribute the mass term to a phenomenon called spontaneous symmetry breaking.
The effect was the same.
The effect was that you get now equations
where effectively the Higgs generates a mass,
both for the electron and it generates a mass for the young mill's particle.
So you could say, well, what did Feynman and Wehrman do wrong then?
Well, what did it wrong was that if you do this,
there's one mode of movement that you might forget,
and that is a vector can rotate,
but the vector can also get a variable length.
Now, if you say that the length of the vector of this reference field is just fixed,
then it serves no other purpose than distinguishing electrons from neutrinos and such.
But now, if also its length can vary,
the length remains the same when you rotate that.
So that length remains, implies yet another degree of freedom.
So now what you find is that you get one other degree of freedom,
and that is roughly this.
If we go back to this picture I had before,
that I had this degree of freedom,
now you have another degree of freedom, which is this one.
The particle can also wiggle in this direction in the rim of the Mexican hat,
and that movement is yet another degree of freedom,
which costs energy, therefore it costs mass,
and that corresponds to an extra particle called Higgs particle.
When you calculate its properties, you find that Higgs can have any mass,
but it cannot have any spin, it has no spin,
and it is a single neutral particle that you then obtain.
Actually, the hat should be considered to be in four dimensions.
It's a four-dimensional, not a two-dimensional hat,
but rather a four-dimensional hat, but that's a detail.
These are the people who are later going to collect their Nobel Prize in Stockholm
for rather than the first model, exactly along these lines.
And Weinberg was the most explicit in writing down the model.
So it's called the Weinberg model, or sometimes Weinberg's salam,
but salam was not so precise in identifying what the particles are.
Weinberg had this picture, the electron, and the muon can spin to the right,
and then they cannot transmit to anything else.
When they spin to the left, they can transmit to a neutrino.
And then there were three carriers of the weak force.
They needed a neutral one as well.
This was a new thing in Weinberg's theory that the neutral component
was not realized to exist before, but it had to be so,
because the photon couples to the left and the right particles
were more likely than the weak particles.
So you needed two neutral things here.
One of them plays the role of the ordinary photon,
but the other is a member of the weak intermediate bosons.
And then you had this extra animal,
the totally neutral spin zero particle called Higgs particle.
So that now was the model, and this model was the beginning
of a new development in nature that in physics and science
resulted to the standard model of elementary particles.
Weinberg was a very wise person, because he said this is a model for leptons.
So he only applied it to parts of all particles.
But there are many strongly interacting particles, halons,
which also are sensitive to the strong force.
But Weinberg didn't write that down.
Why did he not write it down?
He said, well, there's something I don't understand here,
so I'll leave him out.
That is a wise thing to do, because there was something
that Weinberg did not know.
And that was a property in the hadronic sector of the quarks
that was not understood in those days.
And because of that, Weinberg realized that if you make any prediction there,
you'll make false predictions, which are not corroborated
by experiment already in those days.
So he knew he would be generating a theory that predicts wrong things
if he would try to include the hadrons.
But fact was, he didn't know that there were hadrons around
that had been discovered in those days.
So that was an important thing to do.
Now the counting works, because now we have at very short distances,
you don't notice much of the symmetry breaking,
and you have three Yang-Mills gauge fields,
each having only two elicities.
And there are four real scalar fields, which are the Higgs field components.
So you have three times two ways in which the gauge fields can rotate,
and four ways in which the scalar fields can behave,
because there are four components of the scalar field.
All together, 10 degrees of freedom.
And now, if you go to much larger distance scales,
you find that the weak force at short range disappears,
and the gauge particles behave as massive fields.
Now they can each spin in three directions.
So you have three massive vector fields, each spinning in three ways,
but of the Higgs field, only the radial component survives.
The transverse components only serve to identify different particles
and to allow those things to rotate in three ways.
But now you have only one Higgs left.
And then you have three times three plus one is again,
sorry, 10 degrees of freedom to rotate.
And now you see that the counting works.
And without this number 10 being the same as this number 10,
the theory would kill itself.
It would not give useful predictions.
For this theory to work, it was essential that this acceleration of freedom,
this Higgs field was there.
So that is how the physicists came to predict the Higgs particle.
Now let me go back a little bit to the experiment.
How do you accelerate particles and how do they work as a microscope?
Well, we take a particle and you can actually generate charged particles relatively easily.
For instance, in the old television sets where televisions were still big boxes,
then you had a little hot fiber which sends out electrons and ions in a vacuum.
And then they are accelerated by the electric field.
So what you do is you take two electrodes.
You take a charged particle and say two electrodes,
and if the charged particle has positive electric charge,
then it will be accelerated by the electric field between the electrodes.
If it highly moves here, it gets accelerated so much
that the kinetic energy corresponds to the amount of energy that it can gain
if this electric charge moves from this electrode to that electrode.
Imagine that you put the largest amount of voltage on the electrode
that is experimentally possible, something around a million volts.
If you try to put more than a million volts in the electrode,
you always get discharges all over the place.
So it is very hard to keep such electrodes isolated experimentally
if you raise the voltage to much more than a million volts.
And if you have a particle with charge E, the fundamental unit of charge,
its energy will be one mega electron volt.
That is just a unit of energy that you use for particles.
Now, however, in the LAC, we don't give particles one million electron volts,
but seven billion electron volts.
That is seven million times as much.
How do you give particles seven million times the energy that you see here?
We can't put a voltage of seven billion volts on electrodes
because then they discharge immediately.
I can't even generate such a high voltage at all.
But what you can do instead is you just take very many electrodes
and while the particle moves from here to here,
you switch the charges of the electrodes very fast.
So you have a million volts here when the particle sits here.
As soon as the particle sits between these two electrodes,
again, it gives a million volts and so on and so forth.
So the particle gets a kick of a million volts every time it passes through electrodes.
So the kinetic energy just builds up.
Now, the next thing you want to do is have this particle go into circles
because then it can pass through the same electrodes many, many times.
And that way you can accelerate particles to fantastic energies.
How do you make particles go into circles?
If you don't do anything about it, the particles will travel straight lines.
But they will travel in circles if you take a strong magnet.
So you have a magnetic field and then in a magnetic field,
a particle will deviate orthogonal to the field and its direction of motion.
So the particle will go in that direction.
So you take very many strong magnets which force particles to go full circle
and you put the electrodes there to accelerate those particles.
And that is what a particle accelerator really does, just this.
Here you see one of these gigantic magnets being tossed down inside a tunnel.
This is also 100 meters vertically.
It has to go down and then you have to have 1800s of these large magnets
filling the entire tunnel and then very many other kinds of magnets
which are needed not only to bend the beam of particles
but to focus and to manipulate the beam of the particles in as many ways as possible.
Because we needed really very very narrow beams of particles
so that they are very narrow so that when they hit each other head on
there is a chance at all that particles collide.
Only if you focus them very very well you will get a significant number of collisions.
LHC is built to have the largest possible number of collisions
that can be reached technically, about 100 million per second.
So that is what you try to do.
Now here is the result of the large electron-positron collider,
the previous accelerator we are in Geneva.
And what you see here, all these names are other laboratories,
a few of them actually here in Hamburg and others in other places.
And they had measured, what did they measure? We call it cross-section.
Well, if you collide electrons and positrons, E plus and E minus,
they might either give two muons, two photons might come out
or hydraulic particles might come out.
And while they do that, sometimes the collisions are very frequent,
sometimes the collisions are very rare.
When they are frequent it looks as if the electron blows itself up,
it makes itself much bigger so that the probability of colliding becomes much bigger.
So that is why we express the frequency of the collisions
as if the size of the electron varies while they move around each other.
So we call that a total cross-section.
And the total cross-section is divided into different kinds of cross-sections
for different events that can take place.
The hadrons are the most likely events.
You can see that it is about three or four times ten to the fourth.
But here you can see this is a logarithmic plot.
So you can see that the cross-section of the electrons
suddenly increases by a factor of nearly a thousand at this spot.
What does this peak, if you go down, that peak is about at 95 giga electron volts.
And that is the mass of the neutral component of the weak force,
the weak intermediate vector boson.
It's neutral because the electrons didn't give away their charges here.
The charge funds could also be measured.
And you see now here you see a beautiful curve.
And here this curve is a theoretical calculation.
And the dots here are the measurements.
Well, they had to adapt the curve across to the measurements.
But there were only very few parameters people could play with.
The width of the curve was not yet very well known.
So that could be played with.
And the location was not very well known.
So that could be played with.
But otherwise, there was not much room for manipulation.
So we just had to wait and see whether the theory agrees to the experiment.
As you see, the curves go right through the experimental data without any error.
In fact, the error of the data was too small to be visible on this plot here.
Now, the first version of lab stopped at around this point.
So when I first showed this plot, I stopped right here.
I said, look at the beautiful agreement between theory and experiment.
But then after that, before shutting it down,
the lab was being upgraded into a machine that could reach twice the amount of energy.
In particular, the French members of CERN
insisted that they should not put more money in the machine
so that it could reach not further than 200.
So anyway, they started to measure the same curves.
And these red dots were the results that were seen then.
That was a new set of data.
And for this picture, I just glued the two together
so that actually the agreement between theory and experiment was just perfect.
And much to people's disappointment, there was no deviations in theory and experiment anywhere here.
So the curve just continues like this, and there's nothing seen in here.
In particular, what you don't see is a little peak that would have been caused by the Higgs particle.
No Higgs in this plot anywhere.
And, well, actually, the Higgs should not be directly produced this way,
because the electron is far too light.
But there would be other effects visible due to the Higgs in these data.
But nothing was seen.
So actually, it went a little beyond 200.
The lab was designed to go until 200.
But just before shutting the lab off,
they did what you might do when you send your car to the...
Well, your car is a lost case, and it has to be demolished.
But just before having your car demolished, you try how fast could it actually go?
So that's what they did with the lab.
How fast could it actually go?
You know, it has to be brought down anyway.
So let's see how far it goes.
It went a little bit further than 200, but then they could perhaps have gone to 220
if they had been given a year more of running time.
But they decided to do something better to make the LHC, which goes to much higher energies.
And that for sure, the LHC, who could not only detect the Higgs particle,
could also find all its properties.
This is a map of CERN not to scale.
But at the same time, in this map, you see a little bit of CERN history.
Everything started in this corner here with small accelerators.
And then, when I was there, they had just built the Portland Cincotone accelerator,
and they were about constructing this monster here, which is 300 meters in size,
already quite a considerable, beautiful machine.
They also had another accelerator here, the electron storage,
the circuit storage rings, which had been dismantled again.
But now they use all these historical accelerators as pre-accelerators for the big machine.
So the first accelerate particles here, then they are energetic enough to be put in this big circle,
accelerated further in SPS, and then from SPS they go in this direction in the big machine
or in that direction in the big machine, so they can go in two different directions
and be made to collide.
These are the four principal experimental areas.
There are a few smaller places where they also look at what happens when they collide.
In Holland, they are basically involved with the Atlas machine,
but there are four others by these different names.
So actually, the machine builds such that you have four groups of experimenters
who actually compete against each other.
There is no other competition in the world than this.
So in order to have some healthy competition anyway in this science,
we have four rather than one detector sites, and have them fight,
see who can detect new things earlier than the others.
And if one of them detects something, the other is going to check whether it actually works.
This is the Atlas machine, and actually what the machine has is it contains
gigantic big coils. These spidery legs here are very big superconducting coils
which generate very strong magnetic fields going in circles around.
You are looking right from the direction where the beam is going,
so the beam goes from where you are into this and then continues and into directions.
In the middle here, some of the collisions take place.
And then particles will be detected when the collisions have taken place.
To show to you how big the machine is, there is someone standing here.
You might not have noticed, but this is a person,
and this is the size of the machine, several stories high.
Actually, the machine was still being built here. It is still mostly empty.
When it is filled, it looks more like this, where all the electronics are in place.
Of course, you cannot see the interior anymore.
Then there is another machine, the Alice.
Alice is a machine where people in particular concentrate on what happens when heavy nuclei collide.
Not protons themselves. Well, they can also study that in this machine.
But in particular, they want to study what happens when two lead nuclei collide.
The lead nuclei have been stripped of all the 82 electrons each.
They have an electric charge of 82 times one, instead of one.
Which means that the energy of the lead nuclei is 82 times as much as the energy of the protons.
But that energy is divided over more than 200 nucleons.
The average energy of the nuclei is a little bit less than what the single protons have.
As a microscope, it does not work that well. It is also a very ugly microscope.
Feynman would have compared this with what you do in an accelerator if you collide two grand pianos.
You cannot actually detect what happens when you collide grand pianos.
All you can do is just listen to what happens.
That is what they do here also.
It is a very hard experiment, but they try to learn a lot about what happens when you do that.
This is another machine, and this is the fourth machine I just flashed them through.
This will be a simulated Higgs event.
Now, when I planned to come and give this talk, I still did not know whether or perhaps LHC would already have reported events that indicate the Higgs particle.
They still have not done so.
Instead, there are still simulations, so they are searching for events of this sort and still searching very hard.
The machine works extremely well, but you see how difficult it is to detect the Higgs particle.
You get thousands of particles in one single collision.
Actually, not only that, the beams are so narrow that they collide at different spots within a few centimeters away from each other.
In a region of about 20 centimeters, there could be four or five collisions of this sort taking place.
One of them could be the Higgs if you are very lucky, but how to see that there is a Higgs in here?
Well, the Higgs does not travel any observable distance.
It immediately decays into other particles.
All you can try to do is to see if you can recognize decay products from decaying Higgs in this whole mess here.
That is what computers are for today.
Also, hundreds of millions of collisions of this sort take place every second.
The computer investigates them in real time to figure out which are the interesting collisions.
In most cases, particles are like sponges and they just go through each other without really hitting each other very hard.
They just go through each other causing a big mess with nothing particularly interesting.
Those collisions are different from these.
Most of the debris in that case just go in a forward direction, so they do not cause any signal that is worth investigating, according to the experts.
But if many particles go in sideways directions such as here and many charged particles are forming these circles, then something interesting happens and then you want to investigate this.
When they did simulation experiments, they said this was a Higgs particle, but it is our job to figure out how to do it.
This is a diagram that people set up before the experiment.
They had done very accurate calculations to compare the theory with experiments.
It is very important that you do the calculations accurately and they accumulated all data that could be found in different particle accelerators, in particular in the left accelerator.
They checked how well do theory and experiment agree, allowing the mass of Higgs, which is one unknown parameter, to vary.
Horizontally, you have to have mass of the Higgs particle on a logarithmic scale vertically to the extent to which theory and experiment agree.
Actually, the extent to which they disagree, I should say.
Chi-squared says that the error is twice the expected error, four times six times and so on.
Twice the expected error is nothing to be worried about. It could be a statistical fluctuation.
Below two, you see that the mass of the Higgs can vary from this value to somewhere like 200 or perhaps 300 GeV.
That is the allowed value.
If you have an error six times the expected error, there is something to worry about.
Something is wrong in either calculations or analysis or theory.
Some things have been missing. Some things have not been done very carefully.
Something is wrong, but that happens very often in our field of science.
In particular, when you try to measure the velocity of neutrinos, you might get errors of six units.
Perhaps six is not too much to worry about. Then the Higgs could be something like 400 or so GeV.
The yellow region has already been excluded because LEP would have seen the Higgs in different ways directly.
It would have been detected if it had been lighter than about 100 or more precisely 114.
This was some time ago, this plot. Now the yellow region would be a little bit more to the right.
The Higgs has to be in the right domain.
You see, the preferred value is a relatively light value of the Higgs mass.
Somewhat disturbing for theories such as me, I would have much more preferred a heavier Higgs because something is strange.
Now, LHC was taken into surface in the beginning of September of 2008 and it worked beautifully, but only for a week or so.
Because then something rather nasty happened. An explosion took place.
Remember I told you that the magnets each weigh 35 tons.
Well, an explosion took place. Fortunately, nobody was there, so no personal casualties.
But very personal casualties among the magnets.
Because one magnet just jumped up with its 35 tons and came down again at a different location.
So the connection was a bit fumbled after that.
So, a whole mass of scars were this explosion.
Of course, the vacuum was broken, so the whole beam pipe filled with rubbish.
The explosion was a nasty explosion. The question was what happened.
Of course, this was totally unexpected. Otherwise, they wouldn't have turned on the machine so easily.
So the question was what happened. What happened was later rather quickly identified.
It was suspected rather early on and was confirmed somewhat later when the machine was put back to ordinary temperatures.
The machine would normally be at 1.9 degrees Kelvin above absolute zero.
They had to wait a month for a thing to heat up to room temperature.
Then they could open things up and see what happened.
Well, they knew that the weak spot was an electric link between the wires that feed the magnets at room temperature
and the wires of the magnet itself, which are 1.9 Kelvin above absolute zero.
So very, very low temperature.
So a very special way of soldering these connections had to be carried out.
A very special kind of solder to make sure that the resistance of the joint would be less than a few nano ohms.
Now, when I make a lamp on my bicycle and I solder the lamp to its generator,
if that resistance would be less than one ohm, I would be very proud of myself.
But it usually isn't.
Now, this should be less than a couple of nano ohms, a billionth of an ohm.
So the suspicion was it heated up too much. The resistance was a little bit too big.
It heated up and then some of the material melted and then it evaporated.
Why did it evaporate?
Well, you have to remember that in a magnet magnetic fields generate cost energy.
If you make the most powerful magnet of the world, you can count that the energy of the magnetic field inside the magnet is mega joules of energy.
The enormous amount of energy sits in the magnet.
All that sits in the electric current that goes through the magnet.
If you interrupt that current, that energy has to go somewhere.
It does not go into stopping that current.
Even if you have no connection at all, the current will continue, but it will form a spark.
The spark will go from one end to the other end, even if there's no connection.
The connection actually evaporated.
The spark continues and then a spark does something like in a bad science fiction movie.
The spark starts to do this and then it was reconstructed.
What the spark had done was something that they hadn't counted on.
It had hit one of those pipes carrying liquid helium.
Now, liquid helium at very low temperature takes about one thousandth of the volume of the gaseous helium.
When helium evaporates, its volume expands by a factor of thousands.
It has a pipe full of liquid helium, a big pipe, sending helium all around all these magnets.
If that suddenly gets heated up and helium decides to evaporate, the volume expands by a factor of thousands.
That was the explosion.
It caused a big mess.
It took a few months for the engineers to clear up the mess and to repair the magnets.
They had spare magnets.
They could put it in their place and everything would be back to normal again.
Except they had not realized that this could happen.
So now the question was, how can we avoid this happening again?
They opened up all the magnets, all the 1800s of them.
They found one magnet where the mistake, the error, had been made.
Exactly that we suspected here.
The connection was sold incorrectly.
So this is a human mistake.
If you have to solder two thousand magnets, you make one little mistake and that causes this effect.
So now we have to make sure that such a mistake doesn't happen again.
And the only thing to make sure that you are under control of things is to put many new detectors on these magnets.
So they put many new detectors on the magnets and they still aren't sure.
So until today, the machine still works at half its full capacity.
The magnetic field is half of the full magnetic field.
It means that the energy of the particles is only half of the design energy.
The magnetic field has energy in the magnets, which is only one quarter of the design value.
And that is considered safe up until today.
But they're still down there to put the full power on those magnets before they have put more detectors on the whole thing.
The whole machine will be again opened up after the end of next year.
And then there will be a full year of servicing of the machine.
And then they'll know for sure that you can run at full design energy and they'll go all the way to 15 TeV.
Right now it goes only to seven TeV for the full energy.
So the magnifying power of the microscope will increase by a factor of two after that.
So here are some of the superlatives and the statistics here.
All together some 10,000 superlative magnets. Many of them are focusing devices.
They have been cooled to 1.9 Kelvin. Helium itself is 4.2 Kelvin.
About half the total world reserve of liquid helium is in this machine, 130 tons.
And all the magnets together carry 15,000 megajoules of magnetic energy.
So imagine that you have to interrupt that in a fraction of a second.
That is a lot of energy.
Superconducting wires are feeding the magnets all together from 1,200 tons.
And the fields have to be specified very, very accurately.
It's not allowed to have more than 0.01% of variation in the magnetic field strength.
Otherwise the machine simply doesn't work.
The competitor, for a long time in the United States there was a similar machine,
which did not go to seven or to 15 TeV, but only to two TeV or so.
The machine near Fermilab, near Chicago, called Fermilab.
The American machine, which is a beautiful principle building.
And if you look at the airplane, you see two circles.
This machine collides protons against anti-protons.
So it's a different setup.
And for a long time it was a competitor of CERN.
But since the configuration is again different,
and physicists like to work with different configurations
so that you can do different experiments.
You compete in a different way.
One machine will be better than this.
The other machine will be better than that.
And this is a situation already some time ago in March.
I couldn't find a more recent plot because today it's already different.
A lab could go all the way to 114.
If the Higgs mass would be less than 114 GeV,
so much less than 200, the actual lab gave to the electrons,
but this is the energy it would give to the Higgs particle,
then it could be excluded.
So the Higgs cannot be lighter than 114 GeV,
otherwise lab would have seen it.
The Higgs could not have been heavier than 185,
otherwise it would already have been seen also by the LHC by now.
So they could already exclude this domain.
The machine in the United States could investigate this intermediate domain
and could exclude the Higgs mass between 157 and 173.
In those days this was still a gray area,
but also that machine has been improving its data a lot.
It has accumulated more and it is widening this bit.
We all hope to discover the Higgs,
but there's still a wide region in between here
and a very small wide domain here existed in March.
I think this domain had now been filled.
But here is still a possibility for the Higgs particle.
The LHC is rapidly improving,
it's a luminosity that is the intensity of the beams is rapidly increasing,
which means that they find more and more collisions,
they can accumulate the statistics,
and they hope that very soon statistics will be good enough for sound
to be able to fill the entire gap in here.
This region is the most difficult one
because you have to wait for the Higgs to decay to other particles.
They decay into W plus W minus, the weak bosons,
and those are relatively easy to detect.
So that means that this region has already been ruled out.
Here the Higgs is too light to decay into two Ws,
it has to decay into two kinds of quarks, B and B by,
and those are also relatively easy to detect in particular for Fermilab.
So they managed to exclude also this domain.
Here the best signal will be the Higgs can decay into two photons,
that's a more difficult process,
because many other animals decay into photons as well,
so you have a very big background.
And that's why lots of statistics is needed
to be sure that there is no signal from the Higgs as well.
And that's why it takes so long,
it takes hundreds of millions of collisions
before it can exclude this domain also.
So as of today it's still not yet certain
whether there is a Higgs at all,
they have not yet quite close to gap, but nearly did so,
and so far I've heard it is going to be very, very quiet.
What if the Higgs particle is not found?
Well, then it could be that there are many Higgses,
because if there are many Higgses,
then they could all do part of the job and so hide each other.
So if you take one single thing it's easy to detect,
if the single thing is broken to pieces
and all the bits are spread all over the axis,
then it's much higher to detect.
So maybe there are more than one Higgses, or many more.
The Higgs would also be very, very heavy,
way to the right of that previous plot.
Then you would have some things that have to be explained,
the precision experiments are then off by more than six standard deviations,
so something is wrong there.
And okay, there will be work to be done, but it's not impossible.
It just means that the theory will have to be adapted
and the calculation has to be reconsidered.
Strictly no Higgs will be more mysterious.
If there's no Higgs at all, then the whole theory itself is wrong,
but the theory has worked extremely well in the past.
The precision experiments have given tremendously accurate results.
So physicists are very reluctant to say
that the whole Higgs theory is altogether wrong.
It's not totally impossible, of course,
but there would be a lot to worry about.
In any case, there would always be contradictions.
If or if not the Higgs is found, in any case,
something interestingly discovered.
If no Higgs is found, it means that nature is quite different
from what we think it is at those distance scales.
If it is so different, then we also predict that in that case,
there will be many, many new particles just around the corner.
If we switch on the machine to a higher energy,
they'll probe the even shorter distance range,
and then there will be many particles there
because they all have to play the role of a Higgs particle
in some way or other, and then the world will be very, very exciting again
for physicists, in particular for theoreticians.
But so far, nothing of this has yet showed up,
so we're still very puzzled about what the true situation will be.
I think I don't want to continue very much longer,
but also the strong force.
The strong force is very different from the weak force.
If you consider the strong fields in two quarks,
the field lines take a totally different shape.
This was something you had to realize also in the 1970s
that the strong force is also a Yang-Mills theory,
but not like the weak electromagnetism, but again very different.
The field lines in the case of the strong force take this shape,
like a pipe which runs from quark to antiquark.
No matter how far you pull them apart, you can't get them loose,
you can't shake this pipe off.
This is easy to shake off because the field lines widen
and so it becomes very weak.
So the field becomes weak if you separate the charges far,
but here the field does not become any weaker if you try to separate the quarks,
and that means that no matter how far you try to separate them,
the force between them will be constant.
And actually that's the constant of nature, the force between two quarks,
about 14 tons.
So imagine half the LHC magnet just pulling two single quarks together.
That's a very strong force.
So no wonder that the quarks could not be separated.
So this is typically the Alice experiment.
You have two lead nuclei, each containing over 200 nucleons,
82 of which are protons.
When they collide, they might hit each other in this way,
and then where they hit each other, they might generate a new form of matter.
This is called a quark-gluon plasma,
and it's a totally different but equally interesting field of study
that the LHC will also try to do.
Or then very briefly, some of the more outrageous theories,
the more beautiful theories about spin.
Normally, a particle is a boson or a fermion.
Bosons are particles where the spin is an integer number.
Fermions are particles where the spin is half of an integer,
miles and a half, a plus one and a half,
depending on whether it spins to the right or spins to the left.
Non-spinning particles are also bosons.
Now according to some theories,
you actually have to arrange particles into what is called super multiplets.
A super multiplet is a particle that can spin both in integer
and in half-odd integer values of the spin.
That would be fantastic if true,
because this would be a new property of space and time itself.
When we study the theories here,
we need to modify our picture of space-time
to make particles spin in both integer and half-odd integer ways.
The only thing is that none of the observed particles can do that.
All the particles have either this or this,
and the particles which would be one-half a spin apart
are not visible in the standard model.
So nothing of this has been seen,
but you still theorize that maybe at very tiny distance scales
or at very high energies, these new patterns will show up.
And that would mean that new supersymmetry particles would be observed.
So the LHC is not a single-purpose machine.
Just like a big telescope,
when astrophysicists build a new telescope,
the new telescope is not going to study only one thing.
You're not going to make a new telescope just look only at one planet or one star,
nor use it for very many different things.
Similarly, LHC will look at many different things.
It will look not only for the Higgs particle,
which is one of its primary tasks,
it will also start to require gluon plasma.
It will see if there are supersymmetry.
Actually, there are strange forms of matter
which have been discovered by astrophysicists in the universe,
very far away from us.
Forms of matter which do not fit in our standard picture of our forces.
Well, and then the unexpected things,
objects with strange quantum numbers, sort of lepto quarks,
perhaps extra space dimensions.
Maybe supersymmetry is not the whole story.
Maybe there's much more happening with space time.
Extra dimensions.
That will be revealed itself by having many series of new particles
and then the most outrageous things like black holes,
or even less expected things.
We don't really expect that LHC can make anything like a black hole,
but something very resembling a black hole could come out in principle.
That would require the extra dimensions also to occur.
In that case, there will be fantastic miracles coming out of LHC.
Unfortunately, LHC today has not yet brought any of these miracles.
Supersymmetry seems to be hidden better than expected.
The Higgs particle is hiring itself very well.
So we still have work to do.
Perhaps we have to wait for the machine working at full power.
Only from 2014 or so, it will start working at full power,
and maybe only then we'll find all these fantastic new things.
But there's a lot of work to be done for the machine
and it will run for several decades before we have really tried everything.
Hopefully, LHC will give us a new view of nature.
You're certainly opening up a whole new domain of the physical world
which so far has been hidden for us.
I want to say something about the grand unification, but I'll stop there.
You can think of more beautiful patterns of elementary particles,
but all that is for the future.
I would love to continue this lecture with actually a discussion.
So if you have questions or remarks or criticism,
then this could be the moment.
I don't know how to organize this.
I can't allow this, but thank you very much.
Thank you very much for talking for this.
And we have time for some questions.
There's a question.
Well, nothing would be bad.
I mean, both of these features would require us to redo our calculations, give us lots of work.
Now, if you don't like to work, then it would be bad.
But most theoreticians love to see unexpected things happen.
So if there's no Higgs, that would be certainly unexpected.
I would certainly have expected the Higgs.
I would have expected it had to be already found by now.
That hasn't happened.
So now that heterogram faster light is not only unexpected,
it would overthrow much of the existing theory,
in particular theory that makes LHC work.
So we would have been working with the machine that we wouldn't understand.
How come that we switch the button in a particle full circle in this tunnel,
exactly as predicted by relativity theory, not an inch faster or slower.
And that would be totally impossible without relativity theory.
So something is definitely right about relativity.
And if neutrinos say otherwise, well, we'll have to sketch our heads very hard about what they are really saying.
And still a vast majority of scientists think that there's some fluke here.
This is a detective story.
There's something hidden somewhere, some crazy phenomenon that we didn't think about.
I don't think personally that it will be any violation of special relativity.
But if a modification would be needed in special relativity,
of course we would like to be the first to know.
And we would love to see a new twist in our picture of the world.
So it wouldn't be bad, but it would be totally unexpected.
It's a very important and relevant question because you may know in the 1980s
a new theory came up which was shedding so much different light on our field
that people thought perhaps this is the end, perhaps this is the final theory.
It's called string theory or super string theory.
Super string theory seemed to be so promising that it might give an answer to all questions
that you could ever ask, and that would be the end of it.
Now that has not materialized, and I've always warned those two enthusiastic colleagues of mine,
wait a minute, you are not there yet, even approximately, so don't be too optimistic here.
I think that was right.
In the meantime, however, string theory did generate very, very interesting new mathematical structures
which are very suggestive, but they are not going to give the final answer, at least not very soon.
So my guess is that many, many more generations of physicists will be needed to come even close
to a more complete picture, and quite possibly the ultimate truth will never be found.
I mean, that's, of course, who are we to be able to find the ultimate truth?
On the other hand, there are reasons to suspect that there is an ultimate equation,
because if you now include the gravitational force, I have not mentioned much gravity,
but if you do include gravity, it seems that there is a smallest distance in physics.
Gravity upsets everything about space time at a very special length scale of 10 to the minus 33 centimeters.
That's a ridiculously small length, even compared to the particles that we're looking at now.
LHC doesn't even come close to that.
But it does seem there's a fundamental limit to how small things can get into nature.
There's nothing smaller than 10 to the minus 33 centimeters.
If true, it seems to many of us that then the ultimate equation of nature must lie somewhere up there.
And if it lies there, maybe you'll be able to find it.
If you find the ultimate equation, that would still not be the end of physics.
It would be the end of a search for mysteries in the physical world.
But we would still have to try to solve the equations.
They're probably infinitely complex.
So we would always be busy trying to explain the things you actually see,
or to work out the consequences of these equations.
And not only in physics, but physics, as you know,
branches into chemistry, into biology, into medicine, into psychology, and so on.
All these different branches of science, I think,
can still be deduced to the fundamental equations at the Planck scale.
But to find the proper connections to identify how things work
and to work out the equations, that would probably require an infinite amount of work,
because nature is extremely complex there.
And I don't think we'll ever find the ultimate truth of how the equations work.
We can always try to add decimal places to our calculations
or add more ingenuity in addressing the problems and so on.
I don't think that will ever end.
One peculiar thing that the lab machine gave
was that probably there are not more than three neutrinos.
And the reason is, if the neutrinos are very light,
and so far we haven't been able to measure the mass in absolute terms,
only some mass differences between neutrinos.
It's very, very small, all of them.
Such very light neutrinos cannot exist, and that has been excluded by lab,
because if there will be many more light neutrinos,
the W and Z bosons would also decay into other neutrinos.
You can calculate that.
And that doesn't happen.
That has been excluded by the observations.
So a good reason to believe there are no more than three generations of neutrinos.
Now, there could be very heavy neutrinos,
but that would require the Higgs field to be coupled very strongly to those neutrinos.
And that doesn't seem to be the case either.
The Higgs doesn't couple so strongly to other objects as well.
So this gives us practically close arguments
that probably there are no more neutrinos.
We can't be totally sure.
There might be some loopholes there.
For instance, there are other kinds of neutrinos,
which are still possible if they don't interact weakly themselves,
but they couple to the existing neutrinos.
They are called Majorana neutrinos,
and they couple to observe neutrinos in such a way that you can explain
why neutrinos are so much lighter than the other particles, yet not zero mass.
So those are also called neutrinos, but they're actually something else,
but they look a little bit like neutrinos.
And there could be several more of those.
So there's no airtight answer to the question,
but the easiest extensions of the theory,
such as just another generation of quarks and leptons, that's impossible.
But other strange things we never know for sure.
Yes, you mentioned dark energy and dark matter.
Now, there are actually two totally different concepts,
although for some strange reason, in astrophysical settings,
they act in a very similar way.
So dark energy is basically a property of empty space itself.
There's energy in empty space that is not directly observable,
but has a gravitational effect.
And the gravitational effect is that while the universe expands,
that energy increases.
And that means that the universe expands faster and faster and faster.
And that's a property of some relic energy in the vacuum.
So that's the way how to square the observations
for which actually the Nobel Prize will be given to investigators
who found the acceleration in the expansion of the universe.
That's due to dark energy.
It's very unlikely that LHC can say anything about that,
because dark energy in any small region of space
is extremely tiny and immutable.
So we can't measure anything there.
Dark matter is something else.
A kind of particle, that's the most popular theory,
is a kind of particles which form a gas of matter
that sits between galaxies doing nothing except for gravitation.
So it acts gravitationally on the galaxies,
and that's how it's seen by astrophysicists.
Otherwise, it's a kind of matter which does not fit in a standard model.
However, maybe it links to the particles we know at very high energies.
So it could be the LHC can generate processes
where dark matter is being produced.
That will be observed.
It will be difficult, but they will be able to observe it.
But basically what happens is the particles collide and nothing comes out,
or not quite the full amount of energy comes out.
There's missing energy in the collision.
That missing energy goes into matter that's somehow neutral
and doesn't reveal itself in any of the detectors,
just like dark matter in the universe.
So that could be then you have a strong candidate for dark matter.
What you then have to do next is study the property
of that missing cloud of particles.
Now, you can imagine it's high because you look at something that isn't there,
but you look at how much of it isn't there,
and in which direction does the isn't there go,
because all that you can measure.
And so with lots of patience, you can find the property of that dark matter.
And that is something the LHC will be prepared to do
if the phenomenon shows up, they'll try to investigate it.
Thank you.