I will discuss a few of the questions facing fundamental physics that might be answered before the 100th Lindau meeting.

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Well, thanks, it’s wonderful to be back in Lindau and to talk to all these excited and brilliant young researchers in science and I’m going to talk about frontiers in physics. Now, there are many, many frontiers in physics and since I was only given half an hour, which is usually just enough time for me to get going and get through the jokes, I decided to concentrate on one frontier in my own subject, elementary particle physics. where we’re in a very anomalous situation. Throughout most of the 20th century, we explored the fundamental constituents of matter and tried to understand the fundamental forces of nature and arrived at a marvellous theory called the standard model, really should be called a standard theory, it is a comprehensive theory of the 3 forces that act within the atom and the nucleus. Electromagnetism, the strong nuclear force and the weak nuclear force. And together with our good understanding due to Einstein of gravity at large scales, we have a pretty good theory which explains just about everything we’ve observed and has been tested with enormous precision and beautiful experiments for the last decades. With extraordinary precision, we physicists are proud of the precision we bring to bear on fundamental questions and the precision in testing electromagnetism is often one part in a million or better and the same is beginning to be true for the strong and weak interactions where we can test the standard model to better than one part in a hundred, often to one part in ten thousand, quite remarkable. This theory is well founded, well tested, shows no particular place where it might break down unless we go to extraordinary short distances. It is an incredible achievement of physics and of science. There have been many, many Nobel prizes given for contributions to this theory and many of them are sitting in the room today, it works. We could work as far as we know from the smallest length imaginable, the Planck length, where gravity becomes a strong force and we use it to describe stars, galaxies and the structure of the universe as a whole. It is an incredible achievement and yet we have many reasons to believe, many problems both observational and theoretical with the standard model, we recognise its deficiencies and we have been searching for decades for indications of what the new physics, that might explain some of these problems, theoretical and observational, are. So I’m going to concentrate on the frontiers of our knowledge in elementary particle physics and on the problems, the 3 problems I will discuss briefly, they are the problem of unifying the forces of nature, these forces seem to fit together. We have important clues that they might fit together and how they fit together is a major problem. The problem of the mass scale - what sets the mass scale for the weak interactions – which, that scale leads to the masses of the elementary particles as well as the masses of the carriers of the force. And there there is a major problem which I will describe. And then a problem which is, we must address since our friends, the astronomers, observers and astrophysicists have told us with what appears to be great confidence, we accept that the universe is full of a new kind of matter never seen on earth, called dark matter, and it is incumbent on particle physics to explain what the dark matter is. These are 3 of many problems, 3 of the most fundamental ones I believe that we face and I will then discuss as a theorist one speculation, one new principle, in fact a new symmetry of nature called supersymmetry which, as it turns out, has a possibility of addressing all 3 of these problems. It is a rather revolutionary new idea, this new symmetry of nature, that, we speculate, might exist and explain these problems, because as I’ll explain to you it is an indication of new quantum dimensions of space and time itself. And the marvellous thing is that we’re faced with these problems, theoretical, observational, and we have fascinating new speculations as to the solution to these problems which are quite dramatic and wonderful and we have the possibility of answering, of determining whether these speculations have any validity with the construction and now the running of the Large Hadron Collider at CERN which, as you know, has begun to collect data in the last, during this year. So let me start with the problems, the first problem is: How do the forces of nature unify? We have these 3 forces that act within the nuclei and if we look at them they look quite different in nature. The strong nuclear force is immensely strong, the weak of course weaker and electromagnetism, which we’re all much more aware of in daily life, a force that acts within the atom, is even weaker. So how can they be unified? Well, one clue came from our understanding of the strong force and the others as well, that these forces vary with distance. That if you look at the nature of the forces as the objects experiencing the force get closer together, the force can change and indeed the strong force gets weaker as one goes to higher energy which is the way you probe shorter distances. That’s why we need these high energy accelerators to look very closely inside the nucleus. And the same is true of the other forces and according to present day observation and calculation and observation, these forces are coming together. The strong force is getting weaker, the electromagnetic force is getting stronger. It was for theorists an immediate consequence of constructing the standard model to have the theoretical tools to do what experimenters so far cannot do, and extrapolate the high energy and see what happens if you were to do experiments at even higher energies, and that extrapolation showed remarkably that the forces seem to come together and to unify at a very high energy scale. Not only that but the nature of the elementary constituents of matter, the quarks and leptons that are the basic constituents of matter in the standard model, which we have observed and measured their properties, fit together very neatly as if they could all come from a unified form of matter and a unified force at these very high energies. Unfortunately, this very high energy is way beyond where we can directly probe today, but this might be a clue as to what is going on and especially since gravity, an incredibly weak force at ordinary energies, which is why I can hold this up with a little electrical energy and the whole earth is pulling down on this pointer. I am resisting the earth, gravity is a very weak force. But at very high energies, indeed at the same energy where the other forces seem to unify, gravity becomes an important quantum force. Well, this is a clue to all sorts of other speculations which I will not discuss now, but it might be taken at minimum as a clue, that all the forces do indeed unify at this very high energy. However, that’s not the only conclusion, it could be a coincidence. Now, you never know, for a theoretical physicist and tries to imagine what new physics there might be – it is very important to decide whether experimental observations and theoretical extrapolations of this sort are important clues or coincidences. I cannot tell you how you make this decision. This is what's called intuition or experience or wisdom or foolishness. Problem number 1. That extrapolation I showed you was done 30 years ago, after the completion of the standard model. A problem for those who think that it was a clue to unification is that after 30 years of much better experiments, high precision experiments that enabled to extrapolate better and much better calculations that improve the accuracy of the theoretical extrapolation: It doesn’t work. If you here plot the inverse couplings, so this is the strong force which has the smallest inverse coupling, and this is electromagnetism, and this is on a logarithmic scales of the theory tells you that things very logarithmically, so these are straight lines and we extrapolate to very high energies and these 3 lines do not meet at a point. What do you conclude? Well, it could be a clue that something is missing. We’ve left something out and the forces still would unify if you put that back in or it could be a clue that the forces don’t unify, either one. Now we turn to the second problem, the mass scale of the electro weak, the weak force that acts within the nucleus, which is transmitted by a heavy particle called the W meson which we’ve just, Carlo Rubbia, who is here, discovered at CERN. And it is very light compared to this natural scale where the forces might unify, the so called Planck scale that Max Planck first introduced and recognised as a fundamental scale of physics, the scale where gravity becomes a strong force. The W mass is smaller than the Planck scale by 10 to the minus 16. Also the famous Higgs boson, for which the LHC was partly designed to finally confirm its existence, discover it, is also equally light and these 2 facts are related very closely. Now, there are a lot of small numbers which we don’t understand, like this and there are small numbers like this, which we do understand. Our understanding of the nuclear force has explained by the way why the proton mass is so much lighter than the Planck mass, an even smaller number. But how can we possibly explain such a small number here? And it could be an important clue that some physical principle, some symmetry, some new physics is missing in our understanding that would allow us to explain such a small number. Or it could be that we can’t explain it and we simply have to measure it and adjust carefully this mass, the mass of the Higgs, or the mass of the W to 1 part in 10 to the 16th. Now theorists assume that eventually we’ll be able to calculate such things, and if we can’t at the moment, there must be some new physics missing. That’s a very theoretically motivated problem. Now I come to an observational problem and that is dark matter. So the astronomers over the years have told us, based on many different arguments, that the universe is full of a new kind of matter we don’t see on earth, that doesn’t radiate and we can’t see it directly, called dark matter, they observe looking at the rotation of stars and galaxies, that there is some missing mass that holds the stars in place, a halo of dark matter. But there are many, there’s much evidence for dark matter from many different sources and, in my opinion, that evidence by now is incontrovertible. There is a beautiful event that occurred in the universe where 2 clusters of galaxy collided, and here you see the gas of 2 different clusters seen in the x-rays, and the blue stuff is, what astronomers deduce, is the dark matter that really holds those galaxies within the cluster. And the stars can be seen in x-rays, the dark matter can be seen because it bends light, it acts as a gravitational lens and the fact that in this collision the stars and the dark matter behave differently, the stars have much more friction because their interactions are much stronger than the dark matter, is one of the proofs that really the only way to explain all the observations of dark matter is by some new kind of matter, not modifying Einstein’s equations or something like that. And there’s one other very important piece of evidence that was provided by the measures of the cosmic microwave background, starting with COBE for George Smoot and John Mather, who are here, received the Nobel prize a few years ago, and their measurements of the distribution of density fluctuations, temperature fluctuations of the cosmic microwave background, leads to a beautiful quantitative agreement with a standard cosmological model, which, among the rest, determines the matter and energy distribution of the universe. And, based on this and much other evidence, there is clearly no doubt that the universe has, most of the matter in the universe is in the form of this so called dark matter, much more than ordinary stars or other forms of baryons. So astrophysicists tell us that most likely, in fact, this dark matter is made out of what we call WIMPS, Weakly Interacting Massive Particles, and the problem for particle physicist who have never produced such a particle in the laboratory or observed it, is to answer what are the WIMPS. So those are 3 problems: unification, the mass scale of the electro weak interactions and dark matter. Now I want to tell you about a theoretical speculation based on a new symmetry. Physicists love symmetries, they’ve learned in the 20th century that in many ways the secrets of nature are often symmetries. Starting with Einstein and his theories of relativity, special and general, to the standard model which is completely based on local gauge symmetries of nature. The easiest way of describing symmetries is to describe them as transformations of some kind of space. For example rotational and variance. You all know that the laws of physics are rotationally invariant. That means if I do an experiment in my laboratory and then I rotate the laboratory and I do the experiment again, I get the same answer. If I rotate it back I get the same answer, the laws of physics are invariant under rotation. There are many other symmetries of space time. They have marvellous consequences, they are the reason that we have conservation laws. The symmetry of the laws of nature under translations in time and space lead to the conservation of energy and momentum. The invariance under rotations lead to the conservation of angular momentum. The invariance under the change of phase of a complex wave function describing charged particles leads to the conservation of charge. And symmetries underlie our modern understanding of all of physics, and indeed local symmetries are at the basis of all the forces, including gravity, that we have discovered and understood. So I’m going to discuss a new symmetry that we’re speculating about. We haven’t yet observed it, it might be there. It’s a very beautiful new symmetry and therefore we give it the name supersymmetry. It´s super. Now again I will describe this symmetry as a rotation of superspace, so that’s what supersymmetry is, it’s simply rotations in superspace, but of course I have to tell you what superspace is. So, ordinary space consists of X, Y, Z and time. We live in a 4-dimensional space time and we describe particles moving in space as time goes on, fields that are functions of space and time, wave functions, quantum mechanics that are functions of space and time. And symmetries transform or rotate space time, spatial rotation of X axis to Y axis is a symmetry of the laws of physics in ordinary space. So what is superspace? Superspace has new dimensions, now you might have heard of new dimensions of space. People speculate that there might be 6, 7, 1, many new dimensions of space. Well, superspace has new dimensions but they’re a little different and I label them with Greek letters, ?. So there are new dimensions, new directions, you can move in, but the difference is that these are quantum dimensions. You measure distances along these dimensions not with ordinary numbers like 1, 2, 3, inches, metres, but with anti commuting numbers, numbers whose multiplication law is anti commuting. Well, mathematicians, you know, invent such things, they’ve invented all sorts of crazy numbers which we use, like square root of -1, that’s a pretty strange number, and you can easily invent such numbers mathematically. These numbers are actually quite lovely and simple and fun to work with because multiplication is easy. For example: So the multiplication tables are kind of simple. There turns out a natural generalisation of ordinary space and space time of Einstein, to superspace, where in addition to these ordinary dimensions, measured with ordinary numbers, you have anti commuting quantum dimensions. What is good about that? Well, you can think about the symmetries of such a space time with new quantum dimensions and rotations that rotate ordinary dimensions into these new quantum dimensions. And those are very interesting because, you know, in physics there are 2 kinds of particles. One are called bosons and the other are called fermions, after 2 famous physicists. Bosons are particles like the quanta of light photons, the carriers of force of the weak interactions of W and Z mesons, the hypothetical Higgs meson. Fermions are the constituents of matter, quarks, electrons, neutrinos. And they differ in one fundamental way, that their statistics is opposite. Bosons are described by ordinary classical statistics, they’re indistinguishable particles and if you exchange the 2 you don’t notice the difference, whereas with fermions they’re also indistinguishable, but if you exchange 2 identical fermions, the wave function that describes them gets a minus sign in front of it. Just like this minus sign, you exchange them, you get a minus sign. You don’t notice that because when you calculate probabilities you square the wave function, but it has a fundamental effect on the properties with systems of many fermions, and in fact it is the underlying reason for the stability of matter, it leads to the Paulie exclusion principle. In all of our theories until now of matter, we’ve had these 2 kinds of matter, bosons and fermions, and no connection between them. Supersymmetry relates them, because when you do a supersymmetric transformation like this, you turn an ordinary dimension into a quantum dimension, a boson into a fermion. And if you have a field or a wave function which depends on both x and ?, you can tailor expand it and it stops because ?2 = 0, and you´re really describing 2 ordinary fields or wave functions with different statistics because ? is anti commuting, if ? is an ordinary commuting object, then ? is an anti commuting object. So in supersymmetric theories for every particle there’s another particle, for every boson a fermion, and that means that the quark is accompanied by a squark, the electron by a selectron, the photon by a photino. We give these particles funny names because we’re embarrassed that we haven’t seen them. So you might say, ok, beautiful idea, but doesn’t work. But we live in a very complicated state of nature, the vacuum, which is full of fluctuating fields. This is a picture of a vacuum according to quantum chromodynamics at the scale of a proton. And the symmetry, that underlies the law of physics, might not be visible apparent in the vacuum. Just like this room, by the way, is not rotationally invariant. If I look out this way I see you, and if I rotate 90 degrees I don’t see you. This room breaks rotational invariance. Now, one thing we’ve learned in the 20th century is that there are many symmetries of nature, exact symmetries of the laws of nature, that are not manifest, that are broken in the vacuum, so it could be, in fact it´s quite natural that supersymmetry could be broken in the vacuum. And if its broken at a very energetic scale, at very short distances, then all of these new particles would be heavy and we might not have seen them. That’s the only way we could reconcile the exact symmetry of the laws of nature with the fact that we haven’t seen these super particles. Now, supersymmetry is beautiful and I haven’t had time to describe why it’s so beautiful, why it helps you to solve so many theoretical problems, why it’s a wonderful thing for string theory and all sorts of other aesthetic reasons. I want to explain why it helps solve the 3 problems I’ve mentioned, unifying the forces. Remember it didn’t work, but if you take the standard model and say something is missing, what's missing is supersymmetry, you supersymmetrise, and it´s absolutely immediate, because you´re adding a symmetry and make the minimal supersymmetric, the standard model, you discover then you´re adding new, all of these new particles, and they change the evolution of the couplings, and now the couplings meet to 1% accuracy at these extremely high energies. So that is a clue, maybe, that the forces do unify and you have supersymmetry broken at a TeV, or it’s a coincidence. Number 2. If you take a supersymmetric extension of the standard model, then you have a way of explaining this very small number, you relate this very small number, the mass of the W particle or the Higgs particle to the mass of fermions, which we know why they’re so small. So you protect this mass of the Higgs essentially from becoming so very big, and you actually get new predictions. You predict not just 1 Higgs but 2 Higgs, a very clear way of distinguishing this from the standard Higgs mechanism. So that’s either an important clue again for supersymmetry at a TeV at the scale of the electro weak mass scale, or there are other explanations. None as compelling in my mind as supersymmetry, but they are possible. Number 3. Supersymmetric extensions of the standard model naturally produce a heavy particle, neutral, that is weakly interacting, the so called lightest supersymmetric particle. If you produce these supersymmetric particles, they will decay, but the lightest one cannot decay. So it will behave just like the dark matter particles we’re looking for. And in fact we can calculate what that mass or we can estimate quite easily what the mass of that particle would be, because we have a theory, a quite successful, of how matter was created in the universe. We start with the Big Bang, a very hot state, matter is created from energy. If you have a high enough energy, you can create anything. It can annihilate as well, it´s in thermal equilibrium until the universe gets cool enough that the matter is diluted enough, so that the particles and their anti particles can no longer meet, except rarely and annihilate. That leads to one TeV, if you have one TeV supersymmetry then you’ll get 90% dark matter. That’s again an important clue for supersymmetry in a TeV, or it could be something else, so we don’t know. So we have this beautiful speculation that helps unify the forces, explains the mass hierarchy, predicts a candidate for dark matter and, best of all, just at the LHC where we can determine whether this speculation has any validity. We have this wonderful machine, we have these exquisite detectors which are functioning extremely well, and we can search for Susy, which predicts many, many new particles, one for everyone we know at the very least, with known couplings, unknown masses, high rates, complicated signals. This is an example of what a Susy event might look at, at one of the detectors. What you see here are jets of particles that you can identify, but you can see just by looking at this event, that everything is going upwards, not very much is going downwards. And if you add up all the energy, you would find missing energy, that would be a sign of dark matter coming out, not doing anything much and invisible, but by the missing energy you can detect its presence and start to measure its properties. So the message is, when you read in the newspaper a few years from now that physicist at the LHC discover supersymmetry, I want you to remember that this discovery is tantamount to the discovery of quantum dimensions of space and time. We will then know that we do not just live in ordinary space, we actually live in a space time with extra quantum dimensions. So that’s it. Actually its not the end, the fun is just beginning. Thank you. Applause.

# David Gross (2010)

## Frontiers of Physics

# David Gross (2010)

## Frontiers of Physics

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