Quantum Fields: The Real Building Blocks of the Universe - with David Tong

Tonight I would like to talk to you about one of the great questions in science. It's a question that goes back at least two and a half thousand years, to the ancient Greeks. And it is an issue that has been debated in this room many, many times over the last 200 years, but it is an important issue. And I think it's important that we review it. And the question is simply this. It's, what are we made of? What are the fundamental elements of nature from which you, I, and everything else in the

universe

are built? That is the story I would like to tell you.

So what I would like to do is try to give you an overview of our current knowledge. I would also like to try to give you an overview of where we hope to go in the future, what progress we can expect to make in the coming years and decades. And we're going to cover a lot of ground in this talk. I have to warn you now, especially since I'm going to talk about literally every single thing in the

universe

. We are going to talk, among other things, about what is happening in the most powerful particle collider in the world.

This is a machine called the Large Hadron Collider, or LHC for short. A lot will come up in this talk. And it's a machine that is located underground in a place called CERN which is on the outskirts of Geneva. We'll also talk about experiments from recent years that look back in time to the Big Bang, giving us insight into what was happening in the first fractions of a second after time came into existence. And on top of all this, I also want to give you an idea about the abstract theoretical ideas, and even a little idea about the mathematics that underlies our current understanding of the universe.

Because I am a theoretical physicist. What I do is study the equations, try to understand the equations that govern the world we live in. Therefore, I would like to give you an idea of ​​what it is about. At some point... I should warn you now. At some point, I'll even show you an equation. You know, they can send you to training courses for this kind of thing. There is rule number one. Rule number one is never show them any equations. If you show them equations, you will simply terrify them. At some point in this conference, everyone will be terrified, so prepare yourselves.

OK? OK. You know, there's a traditional way to start conversations like this. The traditional way is to be very cultured and talk about what Democritus and Lucretius said two thousand five hundred years ago and the ideas that the ancient Greeks had about atoms. But you know, I don't want to start like that. We've come a long way in two and a half thousand years and, you know, there are better places to start a scientific talk. So the first modern image we had of what the universe is made of, everything we are made of, is this. I hope this is familiar to most people here.

This is the periodic table of elements. OK? It is one of the most iconic images in all of science. What we have here is about 120 different elements. I should point out, no less than 10 of which were discovered in this very

building

, and which constitute, or at least in the 19th century were thought to constitute, everything that existed in nature. So it's true that whatever material you get, you can distill it into its components and you will find that all of those components are made from one of these 120 elements. So it's a great time for science. It is truly one of the triumphs of science.

It is also, I might add, the reason I stopped studying chemistry in school. Because if you're a chemist, this is basically the best there is. You know, if we're honest, it's kind of a disaster. Everything in the universe is categorized into left-wing things that explode if you put them in water and right-wing things that don't actually do much, if we're honest. You organize everything in these stupid ways. And it looks a bit like Australia. There's a big depression at the top, and then there are these two strips of elements that you have to place at the bottom, because there's no room for them in the middle, where they belong.

You know, I don't know about you, if you asked me to make a fundamental classification of everything in the universe, this is not what I would have chosen. Are there chemists in the public? I'm sorry for you. OK. But you know, I'm not alone in this. It's not just me who thinks this is a silly way to organize nature. Nature itself thinks that this is a foolish way of organizing nature. Of course, we know that this is not the bottom line: this is not the end of the story. These are not the fundamental pillars. And the first person to

real

ize that there is something deeper than this was a Cambridge physicist called JJ Thomson.

Then, in the late 19th century, JJ Thomson discovered a particle that was smaller than an atom and which we now call an electron. And in 1897, he announced this in this room (in fact, in this very series of lectures) before an astonished audience, an audience that was so astonished that at least half of them did not believe what he was saying. There was a very distinguished scientist who later told JJ Thomson that he thought it was all a hoax, that JJ Thomson had been pulling their leg. But of course, it's not a hoax. These are not the fundamental elements of nature.

And fifteen years after JJ Thomson's discovery, his successor at Cambridge, a man called Ernest Rutherford, had discovered exactly what these atoms are made of. And this is the image that Rutherford came up with. We now know that each of these elements consists of a nucleus, which is tiny. The metaphor that Rutherford himself used was like a fly in the center of the cathedral. And then, orbiting this nucleus, I might add, in rather fuzzy orbits, are the electrons, which in some ways very sparsely fill the rest of the space. That's a picture of these atoms. We later learned that the core itself is not fundamental.

The nucleus contains smaller particles. They are particles that we call protons and neutrons. And in the 1970s we learned that protons and neutrons are not fundamental either. Then, in the 1970s, we learned that inside each proton and neutron are three smaller particles that we call quarks. There are two different types of quarks. I guess in the 1970s physicists didn't have a classical Greek education and had run out of classy names. That's why we call these quarks up quark and down quark. OK? Without a good reason. It's not that the up quark is higher than the down quark.

It's not that he points. There is simply no good reason. The up quark and the down quark. So the proton consists of two up quarks and one down quark. And the neutron consists of two down quarks and one up quark. These, as far as we know, are the fundamental components of nature. We have never discovered anything smaller than the electron and we have never discovered anything smaller than quarks. So we have three particles that everything we know is made of. And it is worth emphasizing that it is something surprising. Know? In some ways we take it for granted.

We learn this in school. We didn't

real

ly think about it deeply. Everything we see in the world, all the diversity of the natural world, you, me, everything around us, are the same three particles with slightly different rearrangements that repeat themselves over and over again. It's an incredible lesson to learn about how the world is set up. So that's what we have. We have one electron and two quarks. And you know, these are not the fundamental pillars that the Greeks had thought about, and they certainly are not the fundamental pillars that the Victorians had thought about. But you know, the spirit of the thing hasn't really changed.

The spirit is exactly what Democritus said 2,500 years ago, that they are like LEGO bricks with which everything in the world is built. These LEGO bricks are particles, and the particles are the electron and two quarks. It is a very nice photo. It is a very comforting image. It is the image we teach children in school. It's the image we even teach students in college. And there is a problem with that. The problem is that it is a lie. It's a white lie. It's a white lie that we tell our children because we don't want to expose them to the difficult and horrible truth too soon.

It is easier to learn if you believe that these particles are the fundamental components of the universe. But it's simply not true. The best theories we have of physics are not based on the quark particle and the two quark particles; sorry, the electron particle and the two quark particles. In fact, the best theories we have of physics are not based on particles at all. The best theories we have tell us that the fundamental components of nature are not particles, but something much more nebulous and abstract. The fundamental components of nature are fluid substances that extend throughout the universe and undulate in strange and interesting ways.

That is the fundamental reality in which we live. We have a name for these fluid-like substances. We call them

fields

. This is an image of a field. This is not the kind of field that physicists have in mind. You know, this is what you think a field is if you're a farmer or a normal person. If you are a physicist, you have a very different image in your mind when you think of

fields

. And I'll tell you the general definition of a field and then we'll look at some examples to get you familiar with this. The physical definition of field is as follows.

It is something that, as I said, is spread throughout the universe. It is something that takes on a particular value at each point in space. And what's more, that value can change over time. So a good image to have in your mind is the fluid one, undulating and swaying throughout the universe. Now, it is not a new idea. It is not an idea that just occurred to us. It's an idea that dates back almost 200 years. And like so many things in science, it's an idea that originated in this very room. Because, as I'm sure many of you know, this is Michael Faraday's home.

And Michael Faraday started this series of lectures in 1825. He gave over a hundred of these Friday night speeches, and the vast majority of them were about his own discoveries about experiments that he performed on electricity and magnetism. So he did a lot of things in electricity and magnetism over many decades. And in doing so, he developed an intuition about how electrical and magnetic phenomena work. And intuition is what we today call electric and magnetic field. So what he imagined was that everywhere in space were these invisible objects called electric and magnetic fields. Now, we learned this in school.

Again, it's something we take for granted because we learned it at a young age, and we don't appreciate how big a radical step this Faraday idea is. I want to emphasize that it is one of the most revolutionary abstract ideas in the history of science that these electric and magnetic fields exist. So let me... there's supposed to be demonstrations on this. I'm not just a theoretical physicist. I am a very theoretical physicist. It's very difficult for me to do any kind of experiment that works. But I'm just going to show you something that everyone has seen.

They are magnets. OK? And we all played these games when we were kids or when we were in school. You take these magnets and you move them together. And as they get closer and closer, there's a force that you can feel

building

up and pushing, the pressure pushing against these two magnets. And it doesn't matter how often you do it, or how many degrees you have in physics. It's a little magical. Know? And you all know this. There is something special about this strange feeling you get between magnets. And this was the genius of Faraday. It was to appreciate that even though you can't see anything in the middle, even though no matter how closely you look, the space between these magnets will appear to be empty, he said, yet there is something real there.

There is something real and physical, which is invisible, but it is accumulating, and that is what is responsible for the force. That's why he called them lines of force. Now we call it a magnetic field. This, of course, is a photo of Michael Faraday. This is a photo of Michael Faraday giving a lecture behind this very table. Here is a drawing from one of Michael Faraday's articles. It was pointed out to me before. When you leave, there's a rug right here. The rug has this pattern, this image repeats over and over again. And down here is one of the most famous demonstrations that Michael Faraday did here.

So I will explain to you what Faraday did. On the right, there is a small coil with a hand on top. This is a battery and the battery passes a current around this coil. And by doing so, a magnetic field is induced in this. This is what is called a solenoid. And then Faraday did the following. He just moved this little coil A through this big coil B like this. And something miraculous happened. When you do that, there is a moving magnetic field. Faraday's great discovery was induction. It gives rise to a current in B, which then, at this end of the table, causes a needle to flash like this.

So extremely simple. You move a magnetic field and a current is generated, causing a needle to flash on the other side of the table. This amazed the public in the 19th century. Because you were doing something and affecting the needle on the other end of the table, but you never touched the needle. It was incredible. You could make something move without evenGet close to him, without even touching him. We're a little jaded these days. You can do the same experiment. You can pick up your cell phone. You can press some buttons. You can call someone on the other side of the earth in a matter of seconds.

But it's the same principle. But this was the first time the field was shown to be real. You can communicate using the field. You can affect distant things using the field without even touching it. This is the legacy of Michael Faraday. There are not only particles in the world. There are other objects that are a little more subtle that are called fields and are distributed throughout space. By the way, if you ever want to really appreciate the genius of Michael Faraday, he gave this lecture in 1846. He gave many lectures in 1846. But there was one in particular that he finished 20 minutes early.

He ran out of things to say, so he engaged in idle speculation for 20 minutes. And Faraday suggested that these invisible electric and magnetic fields that he had postulated were literally the only thing we had seen. He suggested that these are electric and magnetic field waves, which is what we call light. So, it took a course of 50 years for people like Maxwell and Hertz to confirm that this is really what light is made of, but it was the genius of Faraday who appreciated this, that there were waves in the electric magnetic field, and those waves are light. that we see around us.

OK. This, then, is Faraday's legacy. But it turns out that this idea of ​​the fields was much more important than Faraday had thought. And it took us more than 150 years to appreciate the importance of these fields. So what happened in these 150 years was that there was a small revolution in science. In the 1920s, we realized that the world is very, very different from the common sense ideas that Newton and Galileo had conveyed to us centuries before. Then, in the 1920s, people like Heisenberg and Schrodinger realized that on the smallest scales, on the microscopic scales, the world is much more mysterious and counterintuitive than we ever imagined it could be.

This, of course, is the theory we now know as

quantum

mechanics. So there's a lot I could say about

quantum

mechanics. Let me tell you one of the jokes of quantum mechanics: one of the jokes is that energy is not continuous. Energy in the world is always divided into a small discrete lump. Actually, that's what the word quantum means. Quantum means discrete or global. So the real fun begins when you try to take the ideas of quantum mechanics, which say that things must be discrete, and try to combine them with Faraday's ideas about fields, which are largely smooth, continuous objects that undulate. and they oscillate. in the space.

So the idea of ​​trying to combine these two theories is what we call quantum field theory. And here is the implication of quantum field theory. The first implication is what happens with the electric and magnetic field. Thus, Faraday taught us, and Maxwell later, that the waves of the electromagnetic field are what we call light. But when you apply quantum mechanics to this, you discover that these light waves are not as smooth and continuous as they seemed. So if you look closely at light waves, you will find that they are made of particles. They are small particles of light, and they are particles that we call photons.

The magic of this idea is that that same principle applies to all the other particles in the universe. So everywhere in this room is something we call an electron field. It is like a fluid that fills this room and, in fact, fills the entire universe. And the waves of this fluid of electrons, the waves of the waves of this fluid, are linked into small bundles of energy by the rules of quantum mechanics, and those bundles of energy are what we call the particle, the electron. All the electrons in your body are not fundamental. All the electrons that exist in your body are waves of the same underlying field.

And we are all connected to each other. Just as all ocean waves belong to the same underlying ocean, the electrons in your body are waves of the same field as the electrons in my body. There is more than this. There are also two quark fields in this room. And the waves of these two quark fields give rise to what we call up quark and down quark. And the same goes for any other type of particle in the universe. There are fields that underlie everything. And what we think of as particles are actually not particles at all, they are waves of these fields linked together into small beams of energy.

This is Faraday's legacy. The vision of Faraday's fields has taken us this far. There are no particles in the world. The basic components of our universe are these fluid substances we call fields. Alright. OK. So what I want to do in the rest of this talk is tell you where that vision takes us. I want to tell you what it means that we are not made of particles. We are made of fields. And I want to tell you what we can do with that and how we can better understand the universe around us. OK? So here's the first thing.

Take a box and take everything that exists out of it. Take all the particles out of the box, all the atoms out of the box. What remains is pure emptiness. And this is what the vacuum cleaner looks like. So what you're seeing here is a computer simulation that uses our best theory of physics from something called the standard model, which I'll introduce later. But it's a computer simulation of absolutely nothing. This is an empty space. Literally empty space with nothing inside. This is the simplest thing you can imagine in the universe. And you can see, it's an interesting place to be, an empty space.

It's not dull or boring. What you are seeing here is that even when the particles are removed, the field still exists. The field is there. But, in addition, the field is governed by the rules of quantum mechanics. And there's a principle in quantum mechanics, called the Heisenberg Uncertainty Principle, that says you can't sit still. And the field has to obey this. So even when there's nothing else there, the field is constantly bubbling and fluctuating in what is, honestly, a very complicated way. These are things we call vacuum quantum fluctuations. But this is what nothingness looks like from the perspective of our current physical theories.

It is worth saying that this is a computer simulation. It looks a bit like a cartoon, but it's actually a pretty powerful computer simulation and took a long time to make. But these are not just theoretical. These quantum fluctuations that exist in pure vacuum are things we can measure. There is something called Casimir force. The Casimir force is a force between two metal plates that are pushed together basically because there is more of it on the outside than on the inside. And you know, these are real. These are things we can measure and they behave just as we would predict from our theories.

So this is nothing. And this brings me to the more mathematical side of the conversation. Because there is a challenge in this. This is the simplest thing we can imagine in the entire universe and it is complicated. It's amazingly complicated. It doesn't get any easier than this. You know, if now you don't want to understand anything more than a single particle, well, that's a lot more complicated than this. And if you want to understand that 10 to 23 particles do something interesting, that's actually a lot more complicated than this. So there is a problem... it's my problem, not yours... in approaching this fundamental description of the universe, and that is that it is simply difficult.

The mathematics that we use to describe quantum fields, to describe everything that constitutes us in terms of quantum fields, is substantially more difficult than the mathematics that arises in any other area of ​​physics or science. It is really difficult. I can put this into some perspective. There is a list of six open problems in mathematics. The six most difficult problems in mathematics are considered. There used to be seven, but a crazy Russian solved one of them. So there are six left. You will win a million dollars if you can solve any of these problems. If you know a little math, it's things like the Riemann hypothesis or P versus MP.

They are notoriously difficult problems. This is one of those six problems. You will make a million dollars if you can understand this. So what does it mean? It doesn't mean you can build a big computer and just show that they are there. It means that can you understand from first principles by solving the equations the patterns that emerge within these quantum fluctuations? It is an extraordinarily difficult problem. You know, writing is the kind of thing I do. I don't know a single person in the world who is actually working on this problem. That's how difficult it is.

We don't really even know how to begin to understand these kinds of ideas in quantum field theory. OK. This topic of math being challenging is something that will be addressed later in the talk. So I'd like to just digress a little bit for a few minutes and give you an idea of ​​what we can do mathematically and what we can't do mathematically, just to tell you what the situation is. in terms of understanding these theories called quantum field theories that underlie our universe. So there are times when we understand very well what happens with quantum fields.

And that basically happens when these fluctuations are very calm and tame, when they are not wild and strong. These are big. But when they are much calmer, when the emptiness is more like a mill pond than a raging storm, in those cases, we really believe we understand what we are doing. And to illustrate this, I just want to give you this example. So this number g is a particular property of the electronic particle. And I will quickly explain to you what it is. The electron is a particle and it turns out that the electron spins. It orbits much like the Earth's orbit.

And it has a rotating axis. And you can change the axis of that turn. And the way you change it is by taking a magnetic field like this. And in the presence of a magnetic field, the electron will spin. The electron will stay in one place, but it will rotate. And then the spin axis will rotate slowly like this. This is what is called a procession. And the speed at which the axis of that spin is processed is dictated by this number here. OK? So it's not the most important thing in the big picture. However, historically, this has been extremely important in the history of physics, because it turns out that it is a number that can be measured very, very precisely through experiments.

And so this issue has acted as a testing ground for us to see how well we understand the theories underlying nature and, in particular, quantum field theory. So let me tell you what you're seeing here. The first number is the result of many, many decades of arduous experiments that measure this characteristic of the electron very, very precisely. It's called a magnetic moment, for what it's worth. And the second number is the result of many, many decades of very tortuous calculations sitting with pencil and paper and trying to predict from the first principles of quantum field theory what the magnetic moment of the electrons should be.

And as you can see, it is simply spectacular. And there is nothing like it anywhere else in science where there is agreement between theoretical calculation and experimental measurements. I think it's 12 or 13 significant figures. It's really amazing. In any other area of ​​science, you will jump for joy if you get the first two numbers right. Economy, not even that. Only this is where we are in particle physics on a good day when we really understand what we are doing with them. It is substantially better than any other area of ​​science. 12 significant figures. But this, of course, I have shown you because it is our best result.

There are many other results that are not as good. And the difficulty arises when those quantum vacuum fluctuations begin to become wilder and stronger. So let me give you an example. It should be possible to sit down and calculate from first principles the mass of the proton. We have the equations. Everything should be there. We just need to work hard and find out what the mass of the proton is by simply doing calculations. We've been trying to do this for about 40 years. We can achieve this with an accuracy of around 3%. Which is not bad. We are at 3% there.

But we should be much, much better. We should push these levels of precision. And the reason is very simple. We have the correct equation. We're pretty sure we're solving the right equation. It's just that we're not smart enough to figure it out. In 40 years, the most powerful computers in the world, a lot of smart people. But we have not been able to resolve this. OK. There are other situations that I won't tell you about and in which we don't even get off the ground. There are some situations where, for quite subtle reasons, we cannot use computers to help us and we simply have no idea what we are doing.

So it's a bit of a strange situation. We have these theories of physics. They are the best theories we have ever developed, as you can see from this. But at the same time, they are also the theories that we understand the least and to progresswe have this strange balancing act between increasing our theoretical understanding and figuring out how to apply it to the experiments we're doing. . And again, it is a topic I will return to at the end of the conference. Alright. So far, I've been talking a bit generally about what we're made of. And this is the joke in the middle of the talk.

You are all made of quantum fields and I don't understand them. At least I don't understand them as well as I think I should. So what I want to do now is get into a little more specific details. I want to tell you exactly what quantum fields are made of. In fact, I will tell you exactly what quantum fields exist in the universe. And the good news is that not many of them. So I'll just tell you all of them. So we start with the periodic table. This is the new periodic table. And it's much simpler.

You know, it's much better. There are the three particles of which we are all made. There is the electron and the two quarks, the up quark and the down quark. And as I have stressed, particles are not fundamental. What is really fundamental is the field that underlies them. And then it turns out that there is a fourth particle that I haven't talked about until now. It's called a neutrino. It is not important as to what we are made of, but it does play another important role in other parts of the universe. These neutrinos are everywhere. You have never noticed them, but since I started this talk, between 10 and 14 of them have circulated through the body of each and every one of you, both coming from above in outer space and from below, because they flow through the earth and then they continue.

They are not very sociable. They don't interact. So this is what everything is made of. These are the four particles that form the basis of our universe. Except then something pretty strange happened. For a reason we don't understand at all, nature has decided to take these four particles and reproduce them twice. This is actually the list of all the fields that make up the particles in our universe. So what are we seeing here? This is the electron. It turns out that there are two other particles that behave exactly the same as the electron in every way, except that they are heavier.

We call them the muon, which has a mass approximately 200 times that of the electron, and the tau particle, which is 3,000 times heavier than the electron. Why are they there? We have no idea at all. It is one of the mysteries of the universe. There are also two more neutrinos. So there are three neutrinos in total. And the two quarks that we met for the first time are now joined by four others that we call strange quark and charm quark. And then when we got here, we really ran out of inspiration to name them. We call them bottom quark and top quark.

So I should emphasize. We understand very, very well that things are going this way. We understand why they come in a group of four. We understand why they have the properties they have. We do not understand at all that he is going down this path. We don't know why there are three of these instead of two or 17. That's a mystery. But this is all. This is all in the universe. All you're made of is these three at the top. And only when we move on to more exotic situations, like particle colliders, do we need others in the background.

But everything we have seen can be done from these 12 particles, 12 fields. These 12 fields interact with each other and interact through four different forces. Two of them are extremely familiar. They are the force of gravity and the force of electromagnetism. But there are also two other forces that operate only on small scales of a nucleus. So there is something called the strong nuclear force, which holds the quarks together inside the protons and neutrons. And there is something called the weak nuclear force, which is responsible for radioactive decay and, among other things, making the sun shine. Again, each of these forces is associated with a field.

So Faraday taught us about the electromagnetic field, but there is a field associated with it, which is called the gluon field, and a field associated with it, which is called the W and Z boson field. There is also a field associated with gravity. And this was really Einstein's great vision of the world. The field associated with gravity turns out to be space and time itself. So if you've never heard that before, that was the world's shortest introduction to general relativity. And I'm not going to say anything more about it. I'll let you find out for yourself.

OK. So this is the universe we live in. There are 12 fields that give matter, I will call it the matter field, and another four fields that are the forces. And the world we live in is this combination of all 16 fields that interact with each other in interesting ways. So that's what you should think the universe is like. It's full of these fields, fluid-like substances. 12 matter, four forces. One of the matter fields begins to oscillate and undulate. Let's say the electron field starts oscillating up and down, because there are electrons there. That will start one of the other fields.

It will activate, say, the electromagnetic field, which, in turn, will also oscillate and ripple. There will be light that will be emitted. So that will swing a little bit. At some point, it will begin to interact with the quark field, which in turn will oscillate and ripple. And the image we get is this harmonious dance between all these fields, intertwined, swaying, moving from one side to the other. That is the image we have of the fundamental laws of physics. We have a theory underlying all of this. It is, in short, the pinnacle of science. It's the greatest theory we've ever come up with.

We gave it the most shockingly trashy name you've ever heard. We call it standard model. When you hear the name of the standard model, it sounds tedious and mundane. It really should be replaced by The Greatest Theory in the History of Human Civilization. OK? That's what we're seeing. OK. So that's it, except it's not quite. I actually missed that field. There is something else we know that has become quite famous in recent years. It was a field that was first suggested in the 1960s by a Scottish physicist named Peter Higgs. And by the 1970s, it had become an integral part of the way we thought about the universe.

But for a long time, we had no direct experimental evidence that this existed, where direct experimental evidence means that we make this Higgs field ripple so that we see a particle associated with it. And this changed. This changed markedly four years ago at the LHC. These are the two LHC experiments that discovered it. They are the size of cathedrals and filled with electronic devices. They are amazing things. This is called Atlas. This is called CMS. That Higgs particle doesn't last long. The Higgs particle lasts between 10 and 22 seconds. So it's not like you see it and can take a photo of it and upload it to Instagram.

It's a little more subtle. This is the data, and this little bump here is how we know this Higgs particle existed. This is an image of Peter Higgs' find. So this was the last pillar. You know, it was important. It was something really important. And it was important for two reasons. The first is that this is what is responsible for what we call mass in the universe. So the properties of all particles, things like electric charge and mass, are actually a statement about how their fields interact with other fields. So the property we call the electric charge of an electron is a statement about how the electron's field interacts with the electromagnetic field.

And the property of its mass is the statement about how it interacts with the Higgs field. So understanding this was really necessary to understand the meaning of mass in the universe. So it was a big problem. The other reason it was so important is that this was the last piece of our puzzle. We had this theory we called the standard model. We've had it since the 1970s. This was the last thing we needed to find out to be sure this theory is correct. And the surprising thing is that this particle was predicted in the 1960s. We have been waiting for 50 years.

We finally created it at CERN. It behaves exactly as we thought. It behaves absolutely perfectly as we predicted using these theories. OK. This will be the scary part of the talk. I've been telling you about this theory. And I've been waving my hands pretending I'm a field. Let me tell you what the theory really is. Let me show you what we do. This is the equation of the standard model of physics. I don't expect you to understand it, especially since there are parts of this equation that no one on the planet understands. But still, I want to show it to you for the following reason.

This equation correctly predicts the outcome of every experiment we have performed in science. Everything is contained in this equation. This is really the pinnacle of the reductionist approach to science. It's all here. So I admit it. It's not the simplest equation in the world. But it's not the most complicated either. You can put it on a t-shirt if you want. In fact, if you go to CERN, you can buy a t-shirt with this equation on it. Let me give you an idea of ​​what we are seeing. The first term here was written by Albert Einstein and describes gravity.

What that means is that if you could solve this small part of the equation, just this R, you can, for example, predict how fast an apple falls from a tree, or the fact that the planet's orbits around the sun are formed ellipses. Or you can predict what happens when two huge black holes collide with each other and form a new black hole, sending gravitational waves throughout the universe. Or, in fact, you can predict how the entire universe expands. This all comes from solving this small part of the equation. The next term in the equation was written by James Clerk Maxwell and says everything about electromagnetism.

So all the experiments that Faraday spent his entire life doing in this building... in fact, all the experiments over many centuries, from Coulomb to Faraday, from Hertz to modern laser developments, everything... in this small part of the equation. So there is some power in these equations. This is the equation that governs the strong nuclear force, the weak nuclear force. This is an equation that was first written down by a British physicist named Paul Dirac. He describes the matter. He describes those 12 particles that make up matter. Surprisingly, each of them obeys exactly the same equation. These are Peter Higgs' equations.

And this is an equation that tells you how matter interacts with the Higgs particle. So everything is here. It is truly an amazing achievement: this is our current limit of knowledge. We have never done an experiment that couldn't be explained by this equation. And we have never found a way for this equation to stop working. So this is the best we currently have. OK. It's the best we currently have. However, we want to do better, because we know for sure that there are things that cannot be explained by this. And the reason we know this is that, although this explains all the experiments we have done here on Earth, if we look up in the sky, there are additional things that are still a mystery.

So if we look into space, there are, for example, invisible particles out there. In fact, there are many more invisible particles than visible ones. We call them dark matter. Obviously we can't see them because they are invisible. But we can see its effects. We can see their effects in the way galaxies rotate or in the way they bend light around galaxies. They are out there. We don't know what they are. There are even more mysterious things. There is something called dark energy, which spreads throughout space. It is also a kind of field, although we do not understand it, that makes everything in the universe repel everything else.

Other things. We know that early in the first seconds, before that, the first fractions of a second after the Big Bang, the universe experienced a very rapid phase of expansion that we call inflation. We know it happened, but it's not explained by that equation I just showed you. So these are the kinds of things that we're going to have to understand if we're going to move forward and decide what are the next laws of physics that go beyond the standard model. I could spend hours talking about any of these. I'm going to focus only on the last one.

I'm going to tell you a little about inflation. So the universe is 13.8 billion years old. And we understand pretty well... well, we don't understand at all how it started. We don't understand what started everything at time t equal to 0, but we understand pretty well what happened after it started. And we know in particular that for the first 380,000 years the universe was filled with a fireball. And we know this for sure because we have seen the fireball. In fact, we have seen it and photographed it. This is called cosmic microwave background radiation, but a much better name is the Fireball that filled the universe when it was much younger.

The fireball cools down. Its light has been flowing through the universe for 13.8 billion years. But we can see it. We can take this photograph. And we can understand very well what was happening in these first moments of the universe. And as you can see, it literally looks like a fireball. There are red parts that are hotter. There are blue parts that are colder.And by studying this flicker that can be seen in this image, we get a lot of information about what was happening 13.8 billion years ago, when the universe was a baby. One of the main question we want to ask is what caused the fireball to flicker?

And we have an answer to this. We have an answer, which I think is one of the most surprising things in all of science. It turns out that although the fireball lasted 380,000 years, what caused this flicker could not have occurred for the vast majority of that time. Whatever the cause of this fireball's flickering, it actually took place in the first fractions of a second after the Big Bang. And what it was was the following. So when the universe was very, very young, shortly after the Big Bang, there were no particles, but there were quantum fields, because quantum fields were everywhere.

And there were these quantum fluctuations of the vacuum. And what happened was that the universe expanded very, very quickly, and it caught these quantum fluctuations on the spot. Thus, quantum fluctuations spread throughout the sky, where they froze. And it is these void fluctuations here that are the waves that are seen in the fireball. So it's an amazing story that vacuum quantum fluctuations took place 10 to minus 30 seconds after the Big Bang. They were absolutely microscopic. And now we see them spread throughout the universe, stretched 20 billion light years across the sky. That's what you're seeing here. And yet, you do the math for this and it matches perfectly with what you see here.

This is, then, another of the great triumphs of quantum field theory. But it leaves many questions. The most important one is, what field are we looking at here? What field is this that is imprinted on the background radiation? And the answer is that we don't know. The only one of the standard model fields that has any hope of being is the Higgs. But most of us think it's not the Higgs, but probably something new. But what we would like to do in the future is get a much better image of this fireball, in particular get the polarization of the light.

And by having an idea of ​​this, we can understand much better the properties of this field that fluctuated in the early universe. OK. This look into the future is one of the best hopes we have for moving beyond the standard model and understanding new physics. In the last 10 minutes, however, I'd like to bring you back to Earth, more or less. We have a lot of experiments here on Earth that we're also trying to do better, where we're also trying to go beyond the standard model of physics, beyond that equation, to understand what's new. And there are many of them, but the most notable is the one I have already mentioned.

It's the LHC. So what happened was that the LHC discovered the Higgs boson in 2012. And shortly after that, it shut down for two years. Had an update. And last year, in 2015, the LHC was turned on again with twice the energy it had when it discovered the Higgs. And the objective was twofold. The goal was, first, to better understand the Higgs, which has been achieved fantastically, and, second, to discover new physics beyond the Higgs, new physics beyond the Standard Model. So before I tell you what has been seen, let me tell you some of the ideas we have had, some of our expectations and hopes about what would happen in the future.

So this is again our favorite equation. The idea has always been the following. You know, if you were a Victorian scientist and you went back and looked at the periodic table of elements, then it's true that there are patterns there that give an idea of ​​the structure underneath. Those numbers that repeat themselves. Where, if you're really smart, you might start to realize that yes, there's something deeper than just these elements. So our hope as theorists is to look at this equation and see if maybe we can find patterns in it that suggest there might be something deeper underneath.

And they are there. So let me give you an example. This is the equation that describes the strength of electricity and magnetism. And it's almost the same as the equations that describe the forces for the strong force and the weak nuclear force. You can see. I just changed lyrics. It's a little more complicated than that, but not much more complicated than that. The three forces really do seem similar. So you might be wondering, well, maybe there aren't three forces in the universe. Maybe those three forces are really just one force. And when we think there are three forces, it's because we're looking at that force from slightly different perspectives.

Maybe. Here's something else, which is surprising. These are the equations for the 12 matter fields of the universe: neutrinos, electrons and quarks. Each of them obeys exactly the same equation. Each of them obeys the Dirac equation. Again, you might be wondering, well, maybe there aren't 12 different fields. Maybe they are all from the same field and the same particle, and the fact that they look different is, again, maybe simply because they are seen from slightly different perspectives. Maybe. So these ideas that I have been suggesting are called unification. The idea that the three forces actually combine into one is what is called grand unification.

And it's very easy. It is very easy to write a mathematical theory in which all of them are just one force, which from our perspective appears to be three. There are other possibilities here. You could say, well, this is the question and these are the forces. And the equations are different, but not that different. Because, ultimately, they are both just fields. So you might be wondering if maybe there is some way in which matter and forces relate to each other. Well, we have a theory for that too. It is a theory called supersymmetry. And it is a beautiful theory.

It's very deep conceptually. And in a way, you know, it smells like it's the right thing to do. Finally, you might be really bold. You might say, well, can I combine everything? Can I just get rid of all these terms and write just one from which everything else emerges? Gravity, forces, particles, the Higgs, everything. I have something for you if you want that too. It's called string theory. Thus, we have the possibility of a theory that contains all this in a simple concept. And the question going forward, of course, is: are they correct? You know, it's very easy for us theorists to have these ideas.

And I should say that these ideas are what have driven theoretical physics for 30 years, but we want to know if they are right. And we have a way to tell them that they are right. We do experiments. So I should say, if you want to know if string theory is correct, we don't have any way to test it right now. But if you want to know if some of these other ideas are correct, then that's what the LHC should be doing. The reason we built the LHC was to find the Higgs in the first place. Well, it worked and, secondly, to test these types of ideas we had to see what lies beyond.

So the LHC has been working. It has been running for two years. It has been working like an absolute dream. It is a perfect machine. Two years. This is what you see. Absolutely nothing. All these fantastic, beautiful ideas we've had, none of them appear at all. And the question from now on is: what are we going to do about it? How are we going to advance understanding the next layer of physics when the LHC sees nothing and our ideas just don't seem to be the way nature works? I have to tell you, I often don't have a good answer for this.

My impression is that most of my community is a bit shocked by what happened. There is certainly no consensus in the community to move forward. But I think there are three answers that several people have had that I would like to share with you. And I think these three answers are reasonable to some extent. The first response to the LHC not seeing anything is the following. You little children are so pessimistic. Everything is doom and gloom with you. You need a little more patience. You know, I didn't see anything last year and I didn't see anything this year.

But next year, something will be seen. And if not next year, it will be the following year when something will be seen. It's usually my illustrious senior colleagues who have this... and you know what? They could easily be right. It could easily be that next year the LHC will discover something surprising and put us on the path to understanding the next layer of reality. But it is also true that these same people predicted that he would have already seen something. And it is also true that this cannot last much longer. If the LHC doesn't see something within, say, a two-year time scale, it seems very, very unlikely that it will see anything in the future.

It's possible. It just seems unlikely. So I sincerely hope that the LHC discovers something next year or the year after that. But I think we have to prepare for the worst, which may not be the case. OK. Answer number two. Answer number two, which is also from similar people, well, all our theories are very beautiful. They absolutely need to be correct and what we really need is a bigger machine. 10 times bigger will be enough. Once again, they may be right. I don't have a good argument against it. The obvious rebuttal, however, is that a new machine costs $10 billion.

There aren't many governments in the world that have $10 billion to spare for us to explore these ideas. There is one. One is China. And if this machine is going to be built, it will be built by the Chinese government. I think the Chinese government would find it extremely attractive if the entire community of particle physicists and engineers currently working at CERN and Geneva moved to a city slightly north of Beijing. I think they would see it as a political and economic gain, and there is a real possibility that they will decide to build this machine. If they do, it will take about 20 years to build.

So let's wait a little longer. There is a third answer. And I have to say that the third answer is kind of the camp I'm in. I should mention up front that it is speculative and probably not supported by most of my peers. So this is really just my personal opinion at this point. This is my opinion on this. This is the equation that we know is correct. This is kind of the basis of our understanding. But even though we know it's right, there are a lot of things in this equation that we haven't understood. There are many things to me that are still mysterious in this equation.

So while there seemed to be hints of unification in this equation, perhaps they are just red herrings. And maybe if we work harder to try to understand this equation better, we'll find that other patterns emerge. So my answer is: I think maybe we should go back to the drawing board and start questioning some of the assumptions and paradigms we've held for the last 30 years. In fact, I'm quite excited about the lack of results for the LHC. Know? It seems good to me that everyone was wrong. You know, it's when we make mistakes that we start to progress.

So I feel pretty happy about this and I think there's a very real possibility that we can start thinking about different ideas. I must say there are clues here. There are clues for me to mathematical patterns that we haven't explored. In this there are signs of connections with other areas of science. Things like condensed matter physics, which is the science of how materials work, or quantum information science, which is the attempt to build a quantum computer. All of these fantastic topics have new ideas, which sort of feed into the kinds of questions we ask here. So I'm pretty optimistic that in the future we'll be able to make progress, maybe not the progress we thought we would make a few years ago, but just something new.

So that's the end of my talk. The bottom line is that this is the greatest equation we have ever written. But I hope that one day we can offer you something better. Thank you for your time. There is nothing discrete about the Schrodinger equation. The Schrodinger equation has something to do with a smooth field-like wave function. Discretion is something that arises when you solve the Schrodinger equation. So it is not integrated into the heart of nature.