Frank Wilczek, "The Universe is a Strange Place" - Ford/MIT Nobel Laureate Lecture Series 3/7/2005

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GRAY: Good afternoon. I'm Paul Gray, and it's my pleasure to welcome you to this, the seventh and final Ford/MIT Nobel Laureate Lecture. On behalf of the Institute, I would like to express our gratitude to the Ford Motor Corporation for its sponsorship of this program over the last five years. Frank Wilczek received the Nobel Prize in Physics in October 2004, and I quote from the citation, "for the discovery of asymptotic freedom and the theory of the strong interaction," end quote.

Professor Wilczek, who is the Herman Feshbach Professor of Physics, came to MIT five years ago in 2000 following appointments at UCSB-- University California Santa Barbara-- at Princeton, and at the Institute for Advanced Study. He received his bachelor's degree from the University of Chicago and his PhD from Princeton University. And I should note that the work that is principally recognized by the Nobel Committee in this award was work that Professor Wilczek did while a graduate student at Princeton. No one would ever accuse the Swedish Academy of Sciences of rushing to judgment.

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Professor Wilczek is one of the world's most eminent theoretical physicists. He has received numerous honors, fellowships, and prizes, and he is beyond all that a very distinguished science writer. Before I ask him to come up, let me remind you that there will be a reception in the lobby of the auditorium following the end of this presentation. Professor Wilczek will take questions at the end of his presentation.

I had the opportunity last Friday to hear Professor Wilczek when he addressed the Institute's governing board, and I know that you're in for a treat as he speaks today on "The Universe is a Strange Place." Please join me in welcoming Professor Wilczek.

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WILCZEK: The universe is stranger than I had thought. So my theme today is "The Universe is a Strange Place," and I'd like to start by justifying that with reference to the part of the universe we do understand so we can be sure it's a strange place by describing the theory of our part of the universe-- that is, the part that consists of us, among other things, the material we're made out of, the material in our immediate environment, the stuff that chemists and biologists deal with. Then we'll get on to the really strange stuff later in the lecture.

So the picture that modern physics provides of ordinary matter is strange in many ways. In quantum mechanics, atoms appear as musical instruments not in a metaphorical way, but in a very precise way. When Bohr introduced his model of the hydrogen atom based on quantized planetary orbits, the primary formula of that model-- the Bohr model of the atom-- was a formula for the frequencies of light that's emitted in terms of various physical constants and pure whole numbers, these 1/n1 squared minus 1/n2 squared.

So it was an appearance of formulas for frequencies very reminiscent of the formulas you would get for determining the frequencies that musical instruments can emit, but here, it's the frequencies of light. And because of that, when Einstein learned of this model and of some of its successes, he called it the highest form of musicality in the sphere of thought. Ironically, quantum mechanics later became much more musical, and Einstein didn't accept it. Let me show you in a way that's more eloquent than equations. You can ignore this thing streaming by.

[CHUCKLING]

This is a wonderful piece of software by Dean Dowager called Adam in a Box that in real time computes the wave function of the hydrogen atom of electrons circling a nucleus in a hydrogen atom and allows you to see how the stable wave patterns of electrons change as you emit different kinds of light. You can also look at more elaborate wave patterns by super-posing. It's a wonderful program, and you really ought to look into it and even pay for it if you're--

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It allows you to play microcosmic God-- spin the atom around. And the point is, for those of you who've seen things like [? Kolodny ?] patterns or sprinkled filings on a drum and watch it be hit, these are the kinds of things you see. These are wave patterns. In fact, the equations of musical instruments are exactly the equations one encounters in describing what happens inside hydrogen atoms according to the modern quantum theory.

So that's the physics of the 1920s. As things have developed through the 20th century, we've succeeded in understanding much more about matter, not only about the structure of the outer parts of atoms, the electron wave patterns around a central nucleus, but also what the nuclei themselves are made out of. And so we have a pretty complete picture of ordinary matter, and according to this picture, which has been rigorously tested in many ways, matter is made from electrons and photons, or really, fields named the electron field and the photon field that create and destroy photons and electrons. The photon field is also called the electromagnetic field. And as we saw, it's really fields in the description of electrons. The electrons are not to be thought of as particles but as spread-out objects, as wave patterns.

And then, you learn in high school or even maybe in grammar school that the other fact about ordinary matter, the other constituent of ordinary matter, the atomic nuclei, is made out of protons and neutrons. And that represents the physics of the 1930s, when Chadwick discovered the neutron in the early 1930s-- in 1932-- and people thought that that was an elementary particle, as was a proton, and you can build up the description of matter by getting an accurate picture of how protons and neutrons interacted. But when they looked into it in more detail, they found that protons and neutrons are actually very complicated objects. It's very hard to read the message they described.

Then, thanks to work by Jerry Friedman, among others, and theoretical work by Murray Gell-Mann and others, it became clear that there were simpler objects inside protons and neutrons inside what are called nucleons that are quarks. And there had to be something else to hold the quarks together, but that was unclear what it was. And it was my fate to figure out that besides the quarks, there was something very precise that we can describe-- gluons-- that make up the protons and neutrons and nothing else. That's a complete description.

And furthermore, it will become important later to know that the theory of electrons and photons is very, very much parallel to the theory of quarks and gluons. The theory of quarks and gluons is a more elaborate, mathematically complex version, but a recognizable version of electrodynamics called the non-Abelian gauge theory where the quarks play a similar role to electrons, and the gluons are a generalization of the photons.

How do we know something like that? How do we come up with a proof that those are the constituents of matter? And that's what I'd like to describe in the next few minutes.

This is a tremendously beautiful picture, also due largely to MIT'S physicists. I give a different version of this talk elsewhere.

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This is a picture of an event taking place at the CERN accelerator near Geneva at the so-called large electron positron collider. This red stuff is all equipment. This is the beam pipe. These are different magnets and detectors. The physical part are these tracks of particles emerging, and what you're seeing here are a quark, an antiquark, and a gluon.

What's done at this accelerator is that over and over again, electrons and positrons are collided with one another, and what comes out is studied. It's a very profound point, although not often remarked in this context, that the fact that you don't get the same thing coming out every time even though you've put the same thing in is a direct manifestation of the quantum behavior of quantum mechanics-- that there's a probability of different things happening. You don't get a determinant result from the same input.

And one thing that happens fairly frequently is that you get bunches of particles coming out like this, so-called jets. Most often when you get jets, you get two jets in equal and-- in two opposite directions 180 degrees apart. We interpret that as a quark and an antiquark. When you get three just like this, we interpret it as a quark, an antiquark, and a gluon. What does that mean interpreted? They're not particles. They're not single particles. They are these conglomerates of particles.

What gives us the right to make that interpretation, much less think of it as evidence for the idea that matter is made out of quarks and gluons? And that's really where asymptotic freedom comes in. Asymptotic freedom is the property of our theory of quarks and gluons, a very difficult property to realize consistently in quantum mechanics and special relativity.

In our particular theory of how quarks and gluons interact with each other, radiation events that significantly change the overall flow of energy and momentum at high energy are very rare, whereas radiation events that don't change the overall flow of energy and momentum are quite common. That immediately gives you the interpretation that what we're seeing here is a single, rare radiation event where the quark and antiquark receding from the initial evolution-- initial annihilation event-- emit a gluon that significantly perturbs the overall flow of energy and momentum. But then, all the other radiation events are of the common variety that produce particles, produce radiation of quarks and antiquarks and gluons, but don't change the overall flow.

So the initial direction and the amount of energy in these different jets is set by the underlying quarks and gluons and the hard radiation events, but then they get dressed up by the common soft radiation events. So you don't see the single particles literally, but only as jets. However, if you do a soft focus and instead of following the particles individually just sum up all the energy and momentum in these things and these jets, then they should have the predictable properties of individual quarks and gluons.

And we have the precise theory that describes that basic interaction, and that enables you to-- and comparing with the experiment, comparing the probability of having two jets versus three jets versus four jets, the different angles at which they might emerge with different relative energies, with different-- and how all that changes as a function of the energy of the initial annihilation allows you to test in great and rigorous detail the basic assumptions of the theory and make sure that it's correct. So we can be pretty sure that what we're viewing here is a quark, an antiquark, and a gluon. We can't tell which is which because that's obscured by the dressing process that goes from the individual particles to the jets.

But if anyone tells you that you can't see quarks, you can tell them that it's a lie, that you do see quarks and antiquarks and gluons quite literally, just not as individual particles-- only as the imprint of energy and momentum and jets. So that's a little strange. Pretty-- but enables us to be sure that we have a fruitful theory that's actually predicting results of experiments and can be falsified-- could have been falsified.

But in fact, by comparing results of measurements this experiment and others like it, what you find is that you can fit them all done at different energies here that-- this indicates the overall energy-- different energies-- that the basic principle of asymptotic freedom that enables the whole machine to run-- that is, that radiation events that take a lot of energy are rare and so correspond to a small coupling-- small value of this coupling. So high-energy radiation events are rare, whereas the energy radiation events that only involves small changes in the flow, small transfers of energy and momentum we say are quite common.

So that's a gift from heaven which enables us both to see the basic interactions and to understand why they were obscure before at lower energies and why things get complicated. So that, I think, is to the educated eye, a convincing demonstration that there are quarks and gluons and that they interact in the way that this elegant mathematical theory predicts. But it leaves a question both of intellectual closure and of credibility or the need for clarity. That is, we're claiming that the things that make protons and neutrons and you and me and ordinary matter, things that have mass, are these strictly massless gluons that are like photons and quarks that are almost massless, that have masses much, much smaller than the protons and neutrons themselves. And we're claiming that's all there is, or at least that's the simplest form of the theory.

How can we convince ourselves of something like that? How can we rise to the challenge of computing not only what happens at high energies, but how these soft radiation events, these low-energy radiation events, orchestrate themselves into the particles, including protons and neutrons and you and me that we see? How is it possible to construct heavy objects out of objects that don't weigh anything?

And the answer to that challenge comes from Einstein's second law. Einstein's first law, Einstein's famous law, is e equals mc squared. Before telling you what Einstein's second law is, I'd like to relate a story.

During the Second World War, the army had to train a lot of radio engineers rapidly from people who didn't necessarily know much about radio engineering or even basic electricity, and it's a job that they managed to do very, very well and successfully. And we can look at the textbooks they used at the time as models of teaching. And in the army's training manual for electrical engineers, in the first chapter, you will find a description of Ohm's three laws. Now, Ohm's first law is v equals ir. Ohm's second law is i equals v divided by r.

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And I'll leave it to you as an exercise to figure out Ohm's third law. In a similar spirit, together with Einstein's famous first law-- e equals mc squared-- we have Einstein's second law, m equals e divided by c squared. Now, that may seem silly to just rearrange things algebraically and consider that as a different law, but it's not completely silly. It's a primitive version of what the great physicist Paul Dirac called playing with the equations, because writing essentially the same equation in different ways can suggest different things.

In this case, it's very true. If you think about e equals mc squared, famously, what it suggests is the possibility of getting large amounts of energy from small amounts of mass, and so it suggests things like the possibility of making nuclear weapons or nuclear reactors that get a lot of energy out of doing strange things to mass. But if you write it this way, it suggests something different. It suggests the possibility of explaining mass purely in terms of energy. In fact, really, this should be called Einstein's first law, or maybe his zeroth law, because this is the form that he actually had in his original paper.

In the original paper, you will not find the equation e equals mc squared, but rather, this equation-- m equals e divided by c squared. And the title of the paper was a question. "Can the Inertia of a Body"-- or "Does the Inertia of a Body Depend on its Energy Content?" So right from the beginning, Einstein was thinking of the possibility of creating mass out of pure energy. And remarkably enough, that's what actually happens in our modern theory of quarks and gluons and the strong interactions.

I won't try to describe that in technical detail, but I'll show you some pictures that suggest some of the mechanisms that come into play, which are really very, very beautiful, very, very unexpected, and very, very different from what you learn in elementary physics. In quantum field theory, we discover that what appears to us as empty space is in reality a wildly dynamical medium, as well as the famous uncertainty in position and momentum that is encoded in Heisenberg's uncertainty relation.

In relativity, there's a related form of the uncertainty relation that relates energy and time. That is, if you study things for short enough times, you'll find that the energy fluctuates. And in particular, that means that you can borrow energy for very short amounts of time to create particles and antiparticles, so-called virtual particles. And so if you look even at empty space with a very high resolution in time, we find that it's full of all kinds of particles and antiparticles and forms a dynamical medium because these particles and antiparticles, while they exist, can interact with each other and affect also the properties of other particle-- real particles-- that happen to be around.

These virtual particles are so important that I wrote a sonnet about them, and with very little prompting, I'll recite it. Okay. Virtual particles-- beware of thinking nothing's there. Remove what you can. Despite your care, behind remains a mindless seething of mindless clones beyond conceiving. You'll get the right version if you buy the book, actually. They come in a wink and dance about. Whatever they touch is moved by doubt. What am I doing here? What should I weigh? These thoughts can induce rapid decay.

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Fear not. The terminology is misleading. Decay is virtual particle breeding, and seething, though mindless, can serve noble ends. This clone stuff exchanged is a bond between friends. To be or not? The choice seems clear enough, but Hamlet vacillated, and so does this stuff.

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So that's the poetic version, and here's--

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Oh, thanks. And here's the even more poetic version due to Derek Leinweber. This is actual calculation of virtual particles-- that is, fluctuations actually taking the equations of this basic theory-- quantum chromodynamics-- discretizing them, putting them on a lattice, and just solving for these quantum mechanical fluctuations.

And this is what you find. This is not an artist impression. This is data, and well, the data is somewhat massaged, of course. They don't really come in colors. They're not really this big. They're not really this smooth, most important. But for experts, what this is is the smooth topological charge density. And this QCD lava lamp is what's going on in empty space all the time within you and me, according to our correct theory of the strong interactions, QCD.

And this dynamical vacuum has many consequences. One of the consequences is asymptotic freedom, which I mentioned. This is the kind of dynamics that underlies that phenomenon. But it very much relates to this problem of calculating the masses of particles and accounting for the mass of the proton and neutron, and ultimately, ordinary matter because I told you that mass corresponds directly to energy. Einstein told you that, actually, and I agreed.

So the different particles we observe, therefore, correspond-- well, they correspond to different vibration patterns, very different, stable vibration patterns in space. Remember, the description of particles, even for electrons, was waves. So they're all vibration patterns moving in different ways. And stable particles that we identify as particles and can reproduce are just vibration patterns that have a particularly long lifetime that we can identify over and over again. And so in that language, the different particles we observe correspond to vibration patterns that occur in this dynamical void when it's disturbed in various ways.

This language is extravagant if you're just doing ordinary quantum mechanics, but if you're doing quantum field theory and doing QCD, it really is the right language. You have to use it, and here's an example. This is how one produces in-- again, in these numerical experiments, and again, this is data-- a particle. We notionally plunked down a quark and an antiquark here. You can do that very conveniently numerically, even though it would be quite a challenge to do it cleanly in a laboratory.

So then, they run free. They settle down. They create disturbances in those fluctuating fields. Their presence-- they have influence, and they create disturbances in those fluctuating fields. If we average over the fluctuations and just keep the net disturbance created by having an extra quark and an antiquark around, this is the extra disturbance in the fields. This is much smaller than the fluctuations, by the way, but you average over the fluctuations because that's empty space.

We measure energies relative to that, and this tells you what the particle is. The particle is this particular excitation in otherwise empty space. It's this pattern that persists over time. This is actually the pion. There would be similar pictures if you looked at protons and neutrons. So this is our deepest understanding of what protons and neutrons are. They're these stable vibration patterns in the dynamical void.

Now let's play with equations a little bit because it leads to a very beautiful realization. So we had this-- m equals e divided by c squared. If we actually want to use this numerical experiment to calculate the mass, well, we don't get to weigh those things, those numerical patterns. It would be complicated to build in a gravitational field and see the response.

What's much easier to do is to exploit the Planck relation between energy and frequency. So you see the frequency of vibrations of the fields and relate that to the energy they're carrying according to e equals Planck's constant times the frequency. And so when we actually want to measure the masses, what we actually look at numerically is these frequencies and use this equation.

Now, if we call that the first law of determining masses, then the second law would be this one, which expresses that every mass is associated uniquely with the corresponding frequency, and that suggests something different. That suggests something very beautiful and poetic, actually. The masses of particles are-- not are like, not are similar to, not are metaphorically suggested by-- they are the tones, the frequencies of these vibration patterns in the dynamical voice.

Here's what comes out of the calculations numerically. And these calculations, by the way, are very hard work, mostly hard work by computers, but also some hard work by the people who program them. And it's a very important activity in which MIT plays a leading role with John Negele and Andrew Pochinsky, especially.

What comes out of these kinds of calculations is convincing evidence that this theory of quarks and gluons, really, and nothing else, really does account for the vast bulk of the mass of ordinary matter. Here, and in terms of very, very few parameters-- I haven't emphasized it, and it would be hard to do justice to it in a talk like this.

But the theory is so symmetrical, so tight, so on the verge of being inconsistent that it's difficult to change in any way. It has very few adjustable parameters. If we fix the adjustable parameters, the mass of the up and down quarks from the pion mass, the mass of the strange quark from the kaon mass, then nothing else remains to be fixed, and you get unique predictions for the masses of a lot of other particles-- strongly interacting particles that have been measured-- including n here. n is the nucleon. Those are the proton and neutron. And so we really have accounted quantitatively using this mathematically simple but profound theory of quarks and gluons for the mass of protons, neutrons, and ultimately, you and me and everything around us in our immediate vicinity.

So the ancient dream that there was a music of the spheres emitted by planets circling around the sun, or even earlier, I guess, planets circling around the Earth-- that ancient dream, which always was nothing but a dream-- it didn't have any rigorous content and so has quotation marks-- has become something quite rigorous, quite literal, and even true, that there's a music of the void, and to read it, to hear it, what you have to do is look at the table of particle masses. That's it. Those are the tones emitted by the void.

So from this little survey of our strange understanding of the part of the universe we do understand in a profound way, I think we can draw two great lessons. First of all, if we work to understand, then we can understand. In the late-- even as late as the late 1960s and early 1970s, physicists despaired-- some physicists, the faint of heart-- despaired of ever understanding this mess of the strong interactions. Freeman Dyson, who is probably the most brilliant person I ever met and a very distinguished physicist, predicted famously in 1969 that it would be 100 years before we began to understand the strong interaction.

But four years later, we had the theory, and it came about because there was freewheeling research along many, many lines, some of which seemed unpromising, some of which was hard to assess, and much of which did turn out to be unfruitful. But by a vast effort involving many, many physicists, experimentalists, and theorists over an international community sharing values of openness and honesty so that they could correct each other and learn from each other, we humans did manage to understand and find this world which is so remote from our everyday experience.

And then secondly, that the part of the world we understand is by any standard strange, and also, I think, quite beautiful. It's even more beautiful if you study the equations and understand it properly, but I hope even these pictures and rough indications have indicated some of it.

So that's the part we do understand. Now, I'd like to-- and that's ordinary matter, things around us we really understand quite profoundly. In the reductionist sense, I think, we're close to closing on that. We really do understand the behavior of ordinary matter and its basic properties in principle under ordinary conditions with a very, very wide definition of what ordinary means. That would include everything relevant to chemistry, biology, astrophysics.

But in cosmology, we meet our match. And in cosmology, we don't know what's going on. Astronomers recently have found that ordinary matter, the stuff I've been talking about so rhapsodically, contributes only about 5% of the total mass in the universe. So that makes stars, galaxies, nebulae, planets, people, frogs, things like that. But it's only 5% of the universe as a whole if you count by mass.

25% is in some mysterious dark matter. Well, we don't know what it is. It's not really dark. It's transparent. If it were dark, then by studying how it absorbed light, we could determine its properties. But in fact, it's impervious to light. It's been impervious so far to all the normal methods of astronomy-- optical astronomy, radio astronomy, even neutrino astronomy.

The dark matter has only been detected through its gravitational influence on ordinary matter, which we can see. From that, we learn how much there is and that it clumps and that it exerts very little pressure. And then, of course, we learn from what it doesn't do that it Interacts very, very weakly with ordinary matter.

There are some ideas about what that might be, some very good and exciting ideas which I'll come to momentarily. 70% of the matter in the universe-- 70% of the mass, I should say-- when you average over the universe as a whole on very large scales is in something called dark energy, which is even more weird. This is evenly spaced, as if it's not clumping at all, as if it were-- in other words, it were an intrinsic property of space and time that space weighs a little bit. Every little volume has a little bit of weight-- a very little bit of weight, but it adds up over enormous volumes. And even stranger, this stuff exerts negative pressure. It pushes things apart and makes the universe actually have an accelerated expansion instead of a slowing down expansion, which is what you'd expect from ordinary gravity on very large scales.

The challenge is, what is it? We don't know. How do you go about answering a question like that or coming to terms with it? Well, one way is to do experiments, and that's very important. But if you have no idea what it is and your attempts to do experiments to find out have been frustrating-- you find that you're measuring 0 over and over again-- you search for an alternative. Or if you're a theorist who doesn't know how to do experiments, also, you have to consider a different strategy.

So another strategy is to try to improve the equations of the part of physics we know. What does that mean, to improve them? Well, it's-- well, before I get to that, we're in a fortunate situation that way because we think we understand the behavior of matter in extreme conditions. That's another aspect of asymptotic freedom. Things simplify at very, very high energies or at short distances. So our description, which simplifies in those regimes, is perfectly tailored to the needs of big bang cosmology where in the early moments of the universe you had a lot of stuff which was very hot, very energetic, and very stuffed together.

So that's what we really understand well. Geology is hard. Cosmology is very easy, and here's the proof. That's how simple the early universe looks.

Here's an experiment at the so-called RHIC accelerator, where people collide heavy nuclei together at extreme energies and over very limited volumes for very limited times-- produce the sorts of temperatures and conditions that haven't been seen in the universe for the last 10 to the 10 or 11 seconds-- years, rather. And it looks complicated, but if you follow that strategy I mentioned of looking at the flows of energy and momentum rather than trying to resolve every single particle, then you can reconstruct, even from such a complicated typology of events with thousands of different tracks emerging, that there was in that initial collision down there a hot fireball that had the kind of properties when described in terms of quarks and gluons that we use in our description of the early universe, that they're weakly interacting, that they form a kind of quark-gluon plasma.

So the early universe is user-friendly to us, which means that if you have some guess for how to improve the equations that has consequences producing new kinds of particles, we can trace through the evolution of the universe to see how those particles would have been produced during the big bang, and then we can go out and look for them. We can go out and look for exotic properties.

For instance, if you have a theory that predicts a new kind of particle that interacts very, very weakly with ordinary matter and is produced roughly enough to make the dark matter, well, maybe it is the dark matter. So that's how the aesthetic quest for improving the equations can tie up with the physical quest for understanding the universe.

Now, the main strategy that physicists have employed very successfully over the course of the 20th century in trying to improve their equations is to try to extend the amount of symmetry that they have. Special relativity was an example of this, where you try to make the laws look the same to observers moving at different speeds.

Electrodynamics is a more intricate example, where there's something called gauge invariance which, very roughly speaking, is the possibility of adjusting the zero of the electric potential independently at different places, which has a profound implementation in quantum mechanics. QCD was an extension of electrodynamics to have an even more extensive symmetry and so forth. General relativity was a postulate that even more extensive motions than uniform motions at a constant velocity leave the equations the same.

I'll go through this quickly. There are many exciting and interesting attempts now, or suggestions, for how to improve the equations. One is based on the similarity I mentioned between the strong interaction and the electrodynamic interaction, where quarks are similar to electrons and gluons are a generalization of photons. That suggests since they are described in the same way that there could be a more profound theory that had those as sub-theories, where they would be manifestations like different sides of one die, different ways of looking at one richer, overlying reality. They could be combined or unified into an encompassing theory.

Doing that in detail suggests new kinds of experiments, proton decay because-- well, I won't go into why-- and supersymmetry. Supersymmetry is another kind of symmetry which postulates the possibility of extra dimensions of a different character than the ordinary dimensions of space and time that we deal with in familiar experience or even in special relativity. These extra dimensions are quantum dimensions. They're very small.

If you move into the extra dimensions, what happens is that your spin changes. You change from a spin 0 particle into a spin 1/2 particle, for example. And if supersymmetry is an approximate property of the world, that's very exciting because it means that there have to be many more particles corresponding to the particles we know boosted into those extra dimensions. So when they peek out into the extra dimensions, they have to look different.

And also, implementing supersymmetry gives you a candidate for what the dark matter is. Improving the equations of QCD and improving the spelling here-- should be QCD protection-- gives you another suggestion for a new kind of particle, which remarkably enough also is a candidate to form dark matter. Beautifying the equations of the electric and weak-- the electroweak interactions suggests the existence of new kinds of particles called the Higgs particles, which are a big target of future accelerators. So this theme of extending the symmetries of the equation is a very rich one and suggests the way to make progress in the future of physics.

But physics is ultimately an empirical science, and these beautification of the equations wouldn't be fertile if they didn't lead to definite predictions. Now, each of the things I mentioned does lead to definite predictions, but it would take me four more colloquia of this size to explain them properly. I just want to give you the merest hint of one of the most compelling ideas and, I think, one of the most exciting ones as a way of climaxing.

So I mentioned the idea that the different kinds of interactions are described by mathematically similar theories. So we have the electromagnetic interaction-- actually, this is not quite that. It's the so-called hypercharge interaction, but let's just say it's the electromagnetic interaction for simplicity-- the strong interaction, which is mathematically similar and described just by a different coupling constant and a different symmetry, and the weak interaction, which is also described by similar mathematics.

And we would like to think that they're all aspects of one unified theory, but there's a big barrier to that at first sight. If they were really all aspects of the same thing, they should have a similar strength. That would be part of implementing an extended symmetry that includes all these symmetries of the separate interactions as sub-symmetries.

However, when you study the strength of the different interactions at accelerators here, you find that they don't have the same strength. There's a reason that the strong interaction is called the strong interaction and the electromagnetic interaction isn't and the weak interaction is even called the weak interaction. The reason is that the strong interaction is stronger. So its inverse coupling, which is pictured here, is smaller than the inverse of the electromagnetic coupling. And so the unification does this possible-- unification of these doesn't seems to be a nonstarter.

However, the great lesson from asymptotic freedom was that the power of these interactions changes with energy, or equivalently, changes with distance. And we would expect the most basic interactions to be the ones that occur at the highest energies or the shortest distances.

So what we need to do to see if this hypothesis of unification really works, whether it can be made to work, is to extend this calculation for the strong interaction, which is experimentally verified and shows how the interaction gets weaker at higher energies or [INAUDIBLE] shorter distances, to extend this to the other interactions and to extend the whole calculation to much higher energies. And we can do that with the stroke of a pen. It's the same sort of calculation.

And when we do that using the kinds of dynamical vacuum we know about for sure, the kinds of virtual particles we know about for sure, it almost-- but not quite-- works. But if we do it including that hypothesis of supersymmetry I mentioned, then it seems to work quite accurately, and we get an unexpected bonus that not only do the different interactions of the standard model that we study ordinarily at accelerators-- the weak, strong, and electromagnetic interactions unify. But if we plotted on this same graph also gravity, which acting as a force between elementary particles is ridiculously small compared to the other interactions-- so its inverse coupling would start out way up here somewhere, maybe over there. It also changes with distance in a way we can calculate, and it turns out that it unifies very nearly with these other ones, too.

So we're encouraged in our speculations in beautifying the equations leads to not ugly consequences but still more beautiful consequences, to beautiful surprises. It works better than it should have worked, more than we had a right to anticipate. But is it true?

Ultimately, experiment is the arbiter, and in this case, we'll find out soon because these ideas of supersymmetry require that there be a new world of particles that are not too heavy, and in fact, their masses are such that they should be accessible at the next great accelerator, the Large Hadron Collider being built again at CERN near Geneva. The US has shirked its responsibilities in recent years here, but that's due to start operating in 2007, and within a few years after that, we'll see if these beautiful ideas about improving the equations by improving their symmetry, unifying the different interactions, including the possibility of extra quantum dimensions in supersymmetry, whether all those which seem to come together and form a beautiful package really govern the world or not. It's a very exciting situation.

So I had two great lessons before. Now I'm prepared to add one more in conclusion. I stick by this one. If we work to understand, we can understand. We learn that even more difficult and seemingly inaccessible problems like what is the dark matter can start yielding to theoretical insight.

By demanding more beautiful equations, we get candidates, we get possibilities for understanding what the dark matter is. The part of the world we understand is strange and beautiful. That hasn't changed. We're only trying to make it more beautiful. But the third lesson is-- I hope you'll agree-- we still have a lot to learn. Thank you.

[APPLAUSE]

OK, so now I'll take questions, either about the subject of this talk or anything else. I may not answer them, but I'll take the questions. I can't see very well, so you'll have to-- we have a-- okay, someone who has a question, just come to the mic and [INAUDIBLE]. All right. This lady would like to [INAUDIBLE]. Yes?

AUDIENCE: I understand there as interesting work done on the theory of space and time [INAUDIBLE] and I wondered if you could [INAUDIBLE] a demonstration.

WILCZEK: Yeah. Strange things happen in Stockholm at the time of the Nobel Prize, including some strange events in space and time. I'd like to show you that here is the banquet hall-- let me expand this a bit-- where the great banquet is held. This is basically a town square covered up so that you can have town events in the winter.

And the Nobel Banquet, which is a banquet for 1,400 people, including the Swedish royal family down to third cousins, the prize winners and their guests, and a lot of the government and members of the Royal Academy, people like that-- it's a difficult ticket to get. But 1,400 means there are elaborate preparations, and because these are such August people, they don't like to wait around for their food, so there have to be a lot of waiters prepared to serve everybody simultaneously. The king goes first, but then everybody else gets the same-- at the same time.

So the logistics are quite daunting. Preparations go on for a long time. To do justice to this whole event would take quite a lot of patience. But to aid us, what they've done is make a photo by taking pictures every 15 seconds and then running it as a movie. So here are the preparations and the occasion of the Nobel Banquet.

[BEGIN VIDEO PLAYBACK]

[MUSIC PLAYING]

That middle table is the table where the King and Nobel Prize winners sit. You can see lights going on and off. That's rehearsals of the opera that comes together with the banquet. The whole banquet is accompanied by scenes from "The Magic Flute" this year. And now you'll see the waiting staff rehearsing. There's the opera. There's the opera. The places are set. The wait staff-- it's a dress rehearsal. Candles are lit, and now people start arriving.

[CHUCKLING]

People eat very fast. "Magic Flute." It's something.

[END PLAYBACK]

So I hope you'll agree that--

[APPLAUSE]

You see, the universe really is a very strange place.

[CHUCKLING]

Okay. Yes?

AUDIENCE: Does string theory answer some of these question?

WILCZEK: Okay, the question is, does string theory answer some of these questions? I think in its present form, it doesn't really answer any questions. It poses a lot of questions and gives some hints about what the answers might be, but it doesn't really supply algorithms or definite predictions. So it's a very interesting and promising thing to work on, but at present, it's more questions than answers.

AUDIENCE: I was wondering, what does it actually mean, the energy at a particular point to be oscillating? What is the energy of a point in space? Can you describe that any more than that?

WILCZEK: Well, yeah. In principle, what you're supposed to do is surround the point by a scale. Well, scale is a little-- in principle, the right way to do it is you look at the neighborhood of your point, see how much it's curved by throwing gravitons at it and scattering and seeing how much it's curved, and that gives you a measurement of the curvature of space time, which is directly proportional to the energy momentum density. And then you look at smaller and smaller volumes, and that gives you the energy momentum density.

Of course, you don't actually have energy at a point. You have a certain density at a point. That's a highly idealized description of how operationally you would do it. I'm afraid in this context, I think that's as deep as I want to go into it. We could discuss it privately. There's much more to say about it. Yes?

AUDIENCE: Thank you for this great lecture, and I was really intrigued by the point you made that the mass is the frequency itself. And I was wondering, could you comment on how that relates to-- how does the internal state of mind and thoughts relate to the external state of matter? Because the internal state is more frequencies of different vibrations and external [INAUDIBLE].

WILCZEK: Yes, this suggests-- what I've told you about is hard scientific facts until the very end, where things were labeled speculative and are speculative. Certainly, the first part of the lecture I was talking about ordinary matter. These are very hard, rigorously tested, battle-worn consequences. So scientific facts is as hard as they get, I think.

So there really is that rigorous sense in which mass is frequency. The masses of particles really do correspond to frequencies of stable vibrations in the void, and we really are, in a sense, children of light-- that is, we, made out of protons and neutrons, primarily, which see, we seem to be very heavy and weighed down. We're actually produced out of very light particles and gluons and almost massless quarks. Then it's up to you how poetic you find it.

It does not in itself, I think, lead to metaphysical or theological consequences. So when we discovered that we're children of light, I wouldn't want to put a theological spin on it. But having said that, what does emerge clearly, as I've said, is that the world is very strange and very beautiful. And then, we can admire it and be happy to live in it and happy that we can learn about it, too. Oh, yes?

AUDIENCE: I don't think this is on. Is it?

WILCZEK: Yeah, I can hear you. I'll repeat the question.

AUDIENCE: My question is-- you talked about gravitons earlier.

WILCZEK: Yes.

AUDIENCE: What do you think would be the implications if we were to actually experimentally detect gravitons? How much of an impact would it have on the questions you discussed?

WILCZEK: Okay, so the question is if we actually detected gravitons, what implications would that have for questions that I discussed? So let me put that in a broader context. One of the exciting frontiers, one of the main frontiers, including here at MIT, of experimental astrophysical research is the quest to detect gravitational waves.

Now, gravitational waves are not individual gravitons. They consist of many, many gravitons acting together in a sort of Bose-Einstein condensate, if you like, or just a coherent wave. And there are firm theoretical predictions that gravitational waves really do exist. There are estimates of the strength that they have. They're very weakly interacting with matter, as I sort of alluded to, so they're very difficult to detect, but people are optimistic. They've worked very hard to make very sensitive detectors. They're optimistic that they'll start detecting gravitational waves before too many more decades are out, and that would be very exciting.

It would teach you-- it would be like a whole new form of telescope that's especially attuned to the most violent events in the universe, because it's only violent events that produce enough of these very, very weakly interacting waves to be detectable. And furthermore, since the waves are so weakly interacting, they penetrate. So you can indirectly see what's going on deep inside exploding stars, for instance, or maybe from the early universe.

So that would be very exciting, but that wouldn't be the detection of single gravitons. The detection of really quantum effects in gravity-- so you have to worry about small numbers of gravitons-- would be a real surprise because, well, it would mean that gravity is behaving very differently than conventional extrapolation of what we know because if you start estimating based on what we know, the interaction of individual gravitons with any detector that we're likely to have not just for decades but for many centuries is too feeble to be practical.