I won’t be able to do justice in half an hour to all the ways in which the universe is a strange place,
but I’d like to show you a few highlights.
First of all, I’m going to talk about the ordinary world, the world, the matter we’re made out of,
the world that supports chemistry and biology as well as condensed matter and most of practical physics.
The foundations of that world are actually quite strange and wonderful, as we understand them in the deepest way today.
The picture of matter that modern physics provides is strange in many ways.
In quantum mechanics atoms appear as musical instruments, not metaphorically but almost literally.
When Bohr proposed his famous model of the hydrogen atom,
based on an analogy with planetary orbits but with only certain orbits allowed, and jumps between them,
that explained the hydrogen spectrum.
Einstein called it the highest form of musicality in the sphere of thought.
I think Einstein was referring back to ideas of Kepler and all the way back to Pythagoras about the music of the spheres,
the idea that as planets revolve around the sun, they emitted musical tones.
But here there was another additional element to that which was that the key feature of Bohr's atom was to predict
that the frequencies to be sure in light, not sound, that the atom emitted or absorbed were discrete units,
so they liked the tones of a musical instrument and were characteristic of this form of matter.
But this was only the beginning.
Shortly afterwards, when modern quantum mechanics developed, it turned out that the proper equations to describe atoms
are very much the same equations as one uses to describe the vibrations of musical instruments,
partial differential equations of the wave type.
But even that was only the beginning, as I’ll now elaborate.
With the success of quantum mechanics in the 1920s and early ‘30s,
there was a successful picture of atomic and molecular physics and the foundations of those subjects,
based on the idea that ordinary matter is made from electrons and photons,
for which there was a very good theory of quantum electrodynamics, and inside the atoms, as their centre, the nuclei,
which were made out of nucleons, protons and neutrons But the forces that held together the nuclei were quite obscure.
And it became the top of the agenda of physics to try to understand what those forces were,
what these new forces that held together the atomic nuclei were.
And in a rather complicated history, one learned that when you bashed protons and neutrons together,
they didn’t just deflect one another, but the collisions resulted in sprays of new particles
that could include many protons and many neutrons themselves together with their anti particles
and many, many new kinds of strongly interacting particles, ? mesons, ? mesons, ? mesons, ?s ...
There was a whole alphabet soup with hundreds of particles
and all of these looked more or less like protons and neutrons in their basic properties, just heavier and unstable.
So the idea came that protons and neutrons were not the most, necessarily the fundamental particles,
that they had to be understood as part of a larger picture
and so we no longer knew what were the other ingredients of ordinary matter.
In the 1960s, Gell-Mann, primarily, and Zweig introduced the idea
that you could understand a lot about all these new strongly interacting particles
by postulating that they were made out of things called quarks.
But there was no clear theory of what the forces between the quarks were, and that’s where things stood until the early ‘70s.
Now we know what the other ingredient is, it´s gluons.
What does it mean to say that, what is this operational content?
Quarks are famous for not being observable.
What about gluons?
Are they observable and how do you come to the extraordinary conclusion that protons and neutrons are made out of these more,
these particular more basic objects?
And in fact, with a particularly simple and beautiful theory,
that’s a mathematical generalisation of quantum electrodynamics, so called quantum chromodynamics or QCD.
Well, although its commonly said that you can’t see quarks or that quarks don’t exist, that’s a total lie.
Here’s a picture of quarks and gluons.
If you collide electrons and positrons at high energies, then you don’t see quarks and gluons as individual particles,
but you see the imprint of their energy and momentum on the structure of the underlying event.
That is, if you add up the energy and momentum of all these particles in a jet,
and assign it to be the energy and momentum of a quark, and add up all the energy and momentum of this jet,
and assign it to be the energy and momentum of a gluon and this one to be an anti quark, for example,
you find that you get a proper description of everything that happens at that experiment.
And the theory tells you what the relative distribution of the energy should be,
what the relative probability of different angles emerging should be,
what the relative probability of finding 2 jets versus 3 jets can be,
because 3 jets can be understood as a quark and an anti quark accompanied by radiation of a gluon.
And so you can check out the fundamental interaction between quarks and gluons in all detail
by making this identification that it’s these jets of particles that are the materialisation of the quarks and gluons,
the visible materialisation.
One aspect of this that I think is really profound and not commented on frequently, but I think is appropriate here,
is that this is a fantastic illustration of the basic principle of quantum mechanics,
that is its indeterminacy, that it only gives probabilistic results.
Because what’s done at an accelerator like LEP is collide over and over again electrons and positrons,
which are structureless pointlike objects in our equations, and seeing what comes out.
So you're doing the same thing over and over again, you spend hundreds of millions of Euros to do this,
but doing the same thing over and over again you don’t get the same result each time, you get different results.
And so it’s hard to avoid the basic implication of quantum mechanics here, that you only get probabilistic results,
you can’t predict deterministically from what you put in exactly what you're going to get out.
The theory only predicts probabilities, and it predicts the probabilities successfully.
The theory though going back to the original problem of understanding matter and understanding protons and neutrons,
seems very odd, because it tells you the basic building blocks are massless gluons, strictly massless,
they have to be massless to ensure the consistency and symmetry of the theory
for similar reasons to why physicists understand the photon to be massless or understand gravitons to be massless.
And when you fit the details of these events, you find that the quarks are almost massless.
And so we have a real challenge to build up protons and neutrons, which are famous for not being massless,
in fact, they contain all of the mass, essentially of ordinary matter from essentially massless building blocks.
It flies in the face, by the way, for chemists of Lavoisier’s discovery, that mass is conserved.
We’re starting with massless things and building up things that have mass.
Lavoisier couldn’t have been more wrong.
How is this possible?
Well, it´s possible because of Einstein’s second law.
Now, what do I mean by Einstein’s second law?
This was inspired by the first chapter of the army’s field manual, training radio engineers during World War II,
when they had to bring people who weren’t necessarily very sophisticated, up to speed rapidly.
And the first chapter of that manual is devoted to Ohm’s 3 laws, Ohm’s first law is V=IR, Ohm’s second law is I=V/R,
and there’s an Ohm’s third law which I’ll leave you to conjecture or derive.
(laughter)
In a similar vein, we have Einstein’s famous law, E=Mc2 , but then a second law, M=E/c2.
Now, that may seem a little silly, and maybe it is, but it´s not quite as silly as it seems,
because different ways or writing the same equation can suggest very different things.
E=MC2 famously suggests the possibility of deriving a lot of energy from a relatively small amount of mass
and calls to mind things like atomic bombs or nuclear reactors.
This form of writing the equation calls to mind a very different thing, it calls to mind the idea
that you can build up mass out of energy, out of pure energy.
And actually this is the form you’ll find in Einstein’s original paper, it should be called, you won’t find E=Mc2,
you’ll find this in Einstein’s original paper and the title of that paper was
“Does the Inertia of a Body Depend on its Energy Content?”.
So right from the beginning he was concerned with the idea that energy is the source, is the fundamental source of mass.
That’s because in modern physics, even in the physics of 1905, energy is a much more basic and primary quantity than mass,
it´s really, energy that’s conserved, energy that appears in the laws of thermodynamics,
energy that appears in Schrödinger’s equation and so forth and so on.
In any case, the answer we have now to Einstein’s question,
“Does the Inertia of a Body Depend on its Energy Content?” is:
Yes, exclamation point.
Double exclamation point, because the mass of the protons and neutrons, which is the bulk of the mass of ordinary matter,
derives entirely from the energy of the quarks and gluons that make them up moving around,
the quarks and the gluons themselves have no intrinsic mass, so all the mass of the protons and neutrons,
and essentially all the mass of ordinary matter, comes from that energy of motion.
That’s a very interesting story, how that works in detail,
but it’s certainly not a story I can tell in anything like half an hour.
However, let me show you that I’m not just talking through my hat by displaying the numerical calculations
that back up those assertions.
So we have a very precise, very constrained fundamental theory of how quarks and gluons interact,
a theory who’s equations are a direct generalisation of the equations of electrodynamics and are very tight,
can’t be really changed without destroying the theory.
And then we have to solve those equations to see what the masses of the particles are,
what the possible things you can build up out of quarks and gluons are.
And to solve those equations turns out to be quite challenging,
and in fact, the only workable approach that’s been successful has been to feed this problem into a gigantic computing machine,
to just put the equations in discretised form on a computing machine.
And in fact, this problem has driven the frontier of massively parallel computing.
To do a decent job, to do the job I’ve shown you here - I’m calculating the masses of different particles –
requires that you build a computer which contains roughly 10 to the 30th protons and neutrons,
run it full speed, which means a few teraFLOPS now
- teraFLOPS meaning 10 to the 12th Floating Point Multiplications Per Second - and do that for months.
And then you get accurate equations which tell you what the proton manages to do, one proton every 10 to the -24 seconds,
that is decide how much it´s going to weigh.
But the results are worth it.
So it suggests that there may be more clever ways to calculate things than we know so far.
But in any case, these are the results and I think they’re one of the greatest achievements in science ever.
From a fundamental theory that contains exactly 3 parameters here,
fixed to the mass of the light quarks, the mass of the strange quark and the one coupling constant that characterises the theory.
You use the mass of the light quark to fit the pion mass, one of the mesons,
because that’s the most sensitive to the mass of the light quark.
You fix the strange quark mass by fitting it to the ? meson, since that’s most sensitive to the strange quark mass.
You fit the coupling constant to a splitting in the heavy quark system.
The details aren’t so important but those are the diamonds.
And then everything is fixed, there’s no more wriggle room,
you have to have the calculations agree with the real world value of the masses, or else the theory is incorrect.
And as you see the theory does give the correct values within errors,
these are the errors of the numerical calculations indicated here and the boxes indicate the actual values of the masses.
One does get the masses over the particles from the fundamental theory.
And that includes as a special case here N - N stands for nucleon - these are the protons and neutrons,
and in fact, the mass of the protons and neutrons arises as claimed from the pure energy of essentially massless quarks,
that is the quarks have masses much, much smaller than the masses of the nucleon and the truly massless gluons.
So it really is Einstein’s second law in action.
So let me deconstruct this a little bit to show you what's going on under the hood inside these numerical calculations,
because it’s really quite profound.
In quantum field theory, which is the basis of everything I’m saying,
we discover that what appears to us as empty space is in reality a widely dynamical medium.
So here is a picture of what the computer is doing as it computes the mass of the proton and so forth.
What you´re seeing here is what you would see if you had eyes that could resolve distances of order 10 to the -14 centimetres
and times of order 10 to the -24 seconds.
And then you would see - according to the theory which gives so many successful predictions, we should believe it also here –
if you had eyes that were suitable, this is what you would see, you would see gluon fields coming to be and passing away.
This is what's going inside the computer, this is not an artist impression, this is an actual
- well, of course it´s false colour –
but it´s an actual picture of the gluon fluctuations.
For experts what this is is the smooth distribution of topological charge density.
And that’s what's going on in empty space, inside you and me all the time and everywhere in the universe.
And it’s really that that conditions the properties of the particles we see.
The different particles we observe correspond to the vibration-patterns that occur in this dynamical void
when it is disturbed in various ways.
So for instance, if you plunk down 3 quarks, 2 up quarks and a down quark and let them loose in this dynamical medium,
they’ll settle down into a proton.
And that’s our fundamental understanding of what a proton is.
These fluctuating fields keep the quarks together and it’s the fact
that the presence of the quarks disturbs those fields a bit and changes the energy content that generates the mass of the proton.
This is actually also not a metaphor, it´s rigorously true.
Here I show you not the proton, that’s a little complicated for technical reasons but the pion.
You plunk down a quark and an anti quark, just let them loose,
you average over those fluctuations that I showed you before and just see the net disturbance in the fields
because you want to calculate the difference between the energy in the presence of the quark and the anti quark,
that's what we call a pion, versus empty space.
So you subtract off the empty space part, just see the disturbance in the fields and this is the disturbance,
this is what a pion is.
It’s this disturbance in these fields and it’s the energy that’s made by this disturbance,
that corresponds to the mass of the pion according to Einstein’s second law.
And the proton would look very similar but it’s technically more difficult to generate.
You see, the calculations are still a little ragged, there’s statistical noise in this.
It really should be smooth and symmetrical, but even letting loose a gigantic computer to do teraFLOP operations,
teraFLOPS of operations per month, you can’t, the medium is so wildly fluctuating that there’s still noise in the output.
So let me put this altogether.
We had Einstein’s second law, m=E/c2, and then we can put this together with the Planck Einstein relationship
between energy and frequency to get m=hv /c2, E=hv and then we can rearrange this a bit to get new equals mc2/h.
This is a direct connection between the masses of the particles we observe and frequencies.
And in fact, this is the way that the masses are calculated in these numerical calculations.
You only have space and time to refer to, you don’t have a scale,
you don’t have any apparatus that directly measures energy or weight.
You need to measure something in space and time to determine the masses
and this is the relationship that’s exploited to determine the masses in those numerical calculations, quite literally.
So, instead of Kepler’s music of the sphere’s or Bohr and Einstein’s musicality in the hydrogen atom,
we now have that the masses of particles are the tones,
the frequencies of the vibration patterns of empty space, as its disturbed in different ways,
they are exactly corresponding to those frequencies, just multiplied by universal constant c2 over h.
And so, instead of the ancient music of the spheres, which was a mystical concept that never was made precise,
we put it in quarks, put it in quotations.
Now we have a very precise notion of the music of the void,
and the masses of the different particles that we observe are quite literally the tones emitted by empty space
as its disturbed in various ways.
So that’s what ordinary matter is at the deepest level and I hope you’ll agree it’s strange and beautiful.
Now, that’s the part we understand.
Now let me switch to the part that we don’t yet understand,
just as we’re celebrating our triumph in understanding how the world works, the astronomers pull some surprises on us.
Astronomers have found that ordinary matter, the stuff we’ve understood,
actually only contributes about 5% of the total mass of the universe, averaged on large scales.
Of course, it totally dominates on earth or in the solar system or even in the galaxy,
but such is the vast emptiness of space that a small amount of matter sprinkled around space,
a small density of matter sprinkled around space, can dominate averaged over the whole universe.
So the part of matter we understand, the part based on electrons, photons, quarks and gluons
is only 5% of the total mass of the universe.
That's what makes what astronomers have traditionally studied, stars, galaxies, nebulae and so forth.
But 95% is something else and in fact we’ve discovered, or astronomers have discovered that that 95% itself has 2 components.
25% is in some mysterious “dark matter”.
It clumps, but not as tightly as ordinary matter.
So around each galaxy you have a distribution of dark matter that’s more diffuse surrounding the galaxy
and even now one sees galaxies in quotes, made out entirely of dark matter with very little ordinary matter inside.
And 70% is in some mysterious “dark energy” that’s evenly spread as if it were an intrinsic property of space.
And the strangest thing about this of all is that - unlike any other form of matter we’ve encountered today –
it exerts negative pressure.
Negative pressure blows things apart and what was observed is that the expansion of the universe, instead of slowing down –
as one would expect from positive pressure and gravitational interactions - is actually,
the rate of expansion is actually increasing with time and it’s assigned to this negative pressure.
What is the dark stuff?
We don’t know.
The reason it´s called dark is that the standard probes of matter fail to reveal its existence.
It doesn’t absorb light, it doesn’t scatter light, it doesn’t cause matter to emit light.
All it does is cause gravitational deflections, that’s the way we know about it.
So how do you think about a question like this?
You’ve encountered something really strange and very difficult to study and you have no idea what it is.
Well, you can do experiments and people have done the experiments and experiments have told us that it´s dark, you know (laugh).
So what do we do then?
Well, there’s another way, we can try to improve the equations of physics.
We think we understand matter in extreme conditions,
and in fact we’ve managed to simulate the Big Bang in a laboratory
and show that to a good extent our assumptions in early universe cosmology can be proved experimentally.
I am running out of time, so I won’t.
Of course I could beautifully explain that but I don’t have time (laugh).
We can calculate, because we think we understand the early universe very well,
we can calculate the experimental and cosmological consequences of our suggested improvements of the equations.
Now what does it mean to improve the equations?
Well, for modern physicists it typically means to improve the symmetry of the equations.
And there are several concrete suggestions for how to improve the symmetries of the equations,
to make a more unified description of nature.
One is to try to take the interactions that seem separate, the strong electromagnetic and weak interactions and gravity,
and put them into a unified theory, and that requires changing the equations or adding to them.
Another is to try to unify the description of particles of different spin
that requires super symmetry which expands the equations in a different way.
And there are other examples of improving the equations, the symmetries of the equations
or understanding why the symmetries these postulated don’t manifest themselves in the world,
that lead to direct experimental testable consequences.
I don’t have time to elaborate on all of these, in fact, really I don’t have time to elaborate on any of them,
but let me just say a word about the first, because it’s particularly exciting and timely.
So I said our goal is to unify the description of the different interactions and when you try to do that
you find many things click into place.
If you make a unified gauge symmetry that extends the colour gauge symmetry of the strong interactions
and the gauge symmetry of electrodynamics and the weak interactions –
if you try to make an over-encompassing symmetry, a lot of things click into place,
but one thing doesn’t click into place immediately.
That is the intrinsic strength of those different interactions really is different.
That's why the strong interaction is strong, whereas the other interactions aren’t called strong
and that’s why a nucleus which is held together by the strong interaction is much smaller than an atom.
However, we’ve learned that empty space is a dynamical medium
and that dynamical medium changes the properties of particles that are embedded in it
and it opens the possibility that there’s a fundamental unification at short distances
which is reflected at long distances after modification by empty space as a disparity.
And you can compare what we see to an extrapolation to short distances and what we see reflects unification at short distances.
If you do that using just the particles we know about as fluctuations in empty space,
then you find that it almost but not quite works.
But if you extend, up the ante so to speak, by also including super symmetry at low energies,
then you find it works quite accurately, and as a bonus, if I put gravity in this, it would also unify with gravity.
These ideas have experimental consequences.
In order to make that unification work, the super symmetric particles that are contributing to the modification
of the coupling strengths can’t be too heavy.
They have to do that job and they can’t do that job if they’re too heavy, they won’t produce enough fluctuations.
And in fact they have to be sufficiently light that they’ll be observable at the next great accelerator,
now being constructed at Cern, the LHC, Large Hadron Collider, due to start operating in 2007.
So at that time we’ll know whether these dreams of unification really are true,
and as a consequence get profound insight into the dark matter,
because one aspect of super symmetry is that it predicts the existence of a stable particle
whose properties are just right to provide the dark matter.
So to summarise let me draw 3 great lessons from this story.
The part of the world we understand is strange and beautiful,
we’ve carried what Einstein thought was the highest form of musicality in the sphere of thought to much higher levels.
If we work to understand we can understand.
It seemed hopeless to many people that we could ever understand atomic nuclei, they’re so small,
fundamentally they’re so small and so hard to study.
And in fact Freeman Dyson in the mid ‘60s predicted that it would be 100 years before we understood the strong interactions,
but 10 years later we understood it very well.
If we work to understand, then we can understand.
And then finally, we still have a lot to learn.
Thank you.
Applause