Fantastic. So, well, I would like to start by thanking the organiser and my colleagues in physics for letting me taking part of these beautiful experiences, some for tonight. I cannot see all of you in person, but there we are trying to do our best. So. So what they will describe today is an attempt to construct a theory that describes all fundamental particles and all their interactions. Now, this is probably the most ambitious conceptual enterprise ever attempted by humankind.
And it could well be that it is far from what we can do. And we are like maybe a group of dogs trying to understand the rules of chess. So it seems quite hopeless. But that doesn't mean that we shouldn't try. And even if we don't achieve that, it could be that we learn a lot of things on the way. And that's what physicists should do. Now, as we will see, this will lead to a full theoretical inspired solution to the problem of quantum gravity.
And also, it will lead to very surprising consequences. So if we want to answer this question here, the first thing we need to understand is what are the fundamental blocks of matter? And in order to do that, we need to look at the atom. And here I drew the classic big dude of the atom, which is an electron orbiting around a nucleus formed by a neutron and a proton. Now it turns solve that if you tried to split the electrons into more fundamental particles.
You cannot do that. So the electron, as it is, is fundamental. So we believe it is fundamental. And that is one of the fundamental particles in the universe. On the other hand, the proton and the neutron are not fundamental. And if you split them, you see that inside them there are more elementary particles that are called quarks. The neutron course, two down quarks and one up. And these cars, two up works and one down. And these quarks are the fundamental particles.
So the complete picture is that actually the electron is part of a family of fundamental particles, which are called leptons. We have the electron neutrino and other particles similar to the electron and the neutrino. And also the quarks, the two quarks that we saw before are part of a family. Both of quarks, you see d the s unbe.
Now, all these particles that I have listed here and also there, antiparticles, they form all the matter of the universe, all the tangible and matter like the table, the computer, et cetera. And they are called fermions. So the particles that form the tangible matter in the universe. This article ferments now in our modern view of particle physics. It does? S that also the fundamental forces, gravity, electromagnetism, etc are mediated by particles.
They are not tangible. You can put a lot of light in a room and you know, you have no obstacle in doing that. And there are fundamental particles that are responsible for the forces. These are called boatswain's. And here there is a picture of the fundamental forces that we know so far. So we have gravity, which is, of course, responsible for the formation of black holes or for the earth orbiting around the sun. And this is mediated by the gravid, done by a particle called they cannot be done.
Then we also have electromagnetism, which we have seen in the previous dog. And that is mediated by the photons. These two are the most well known forces. And then there are two other forces that are a little bit less known. So one is called the nuclear strong force, and it is the force that keeps together the three quarks inside them, the protons and neutrons. And then we have another force, which is called the nuclear weak force. And it is responsible for for like nuclear reactions, cetera.
And for instance, it if it makes possible for these Pickworth to jump into our youthwork. Now, if you look at these four forces. Ladies are mathematical, the reason of why gravity is very different to the other three forces. However, luckily, if you look at the item and other scales that are laid, the atomic scale at the atomic level, we can completely forget about gravity.
And for instance, if you compare the orders of magnitude of the gravitational force and the weak force there, there are this nuclear weak force, the nuclear weak force extend to the 36 times bigger. So it is huge compared to the gravitational force. And the nice thing is that if we forget about gravity, right, we will say that we will completely forget about gravity, then all the fundamental particles and their interactions are very well described by what we call a quantum field theory.
And we have more or less seen what a quantum field theories in the previous dog. So a quantum field theory is a framework that describes how particles interact with each other in a way which is consistent with quantum mechanics and special relativity. OK. And for instance, QED is a simple example. The simplest example of quantum physics. And in a quantum field theory, the way to to deal with particles, et cetera.
Is that each particles and hear of a particle. I mean, both fermions or boatswain's are represented by your field. So here photons I like the particle of electromagnetism, is represented by SMU, new, as we have seen in the previous stock, and also electrons, etc, are represented by by another field. And then the statement is that this quantum theory tells you that the interactions between these particles firmly on Serbo Sense are dictated by a LeGrande Jones for those spheres.
And here. I have read them for you in our extremely compact way, best under the Lagat Anjan for the standard model of elementary particles. This little bit looks very much like the QED leg. But this is a big generalisation of the QED Leggat engine. What actually the figures are not just functions, but thorough mattresses. OK, so this is the complication of of the system Standard Model and Cucina, which is part of it.
And one way to interpret what I like Ranjani is telling us is that the laggard engine gives you a set of basic rules and tells you what are the probabilities for basic processes to happen. So this Leggat Anjum, for instance, is telling us that an electron can meet one of these said boatswain's, and then it can become a positron. And this legat engine tells you what is the probability for that thing to happen.
And actually, as we have seen in the previous lecture, this Lagat John predicts really with huge accuracy what happens at accelerators and this Lagrangian and the standard model to work needed an extra Volson, which was called the Higgs boson. And this was exactly found at accelerator's. So this was probably the biggest triumph of theoretical physics of the last decades.
So we really have a very nice modern that describes all these particles, all these elementary particles and how they interact with these three forces. If we forget about gravity. Okay. So this is very nice. No. However, he here. We see that we have some kind of conceptual problem. So we've may be happy that we can make measurements. The standard model is renormalise Sobol. So we can make predictions. We can go measured. These predictions are accelerator's and we are extremely happy.
However, we know that the standard model cannot exist by itself. And a very simple reason why this cannot. The standard model cannot be the whole story is because the particles of the standard model, they do cupper to gravity. OK. If you have a lot of electrons, they would make gravitational field and electrons feel the force of earth as well. And it turns out that although you can forget about gravity at length, the scale of of the atom, actually at some point gravity will become important.
And the standard model will break down. And in terms of energy, basically we have calculated the energy scale at which this happens. And basically, this is a calculation which is dimensional analysis. So that is a unique combination that involves quantum mechanics through hate bar. Relativity through the speed of light and gravity through the Newton constant. That, that, that and that gives you an energy. And when you translate this energy in these dunce's, this becomes this.
This does this plan length, which is about ten to the minus 33 centimetres, so that we expect that the standard model at these distances break down because of these distances. We cannot disregard of gravity anymore. And again, let let me repeat the same. So although gravity at Lusha Scales is well described by Einstein's theory of Jennet other lefty bitin theory of general relativity, these phages are very small in this case.
And if we tried to construct a quantum field theory for gravity, once we actually run in, you fit into infinities. As mentioned in the previous talk. And again, as we have just seen, I am here. So I, I wrote down some of these integrals that were computed by Belmont some time ago. So you can consider, for instance, the scattering of gravitons in general relativity. And the problem with gravitons is that good habitants are point like particles in the usual approach to general relativity.
And they can't get too close to each other. And if you compute processors like the scattering of good evidence, then these you are led to integrals that are divergent, not disintegrate. Dustin, it's not really a problem, but the integral is that you get two two loops are actually a problem. And an utterly unimportant note is that we do have these infinities in the standard model, too. But those we can cure because the theory is renormalise simple.
The problem with gravity is that you cannot cure these infinities. So the infinities that come from the fact that gravity don't sort of point like are much worse. In the case of general relativity. So we need a different approach to the problem. And the approach of string theory is to try to step back and try to answer the question of what is the form of the element that is particles are the points that carbon like CDO they mentions or are they something else?
And in a string theory, we propose that theory scale and not to the list again, because fundamental particles, they are not really points, but they are like very little, really tiny strings. And then let's say that you take this as a fact. So you say that the particles are are lethal strings, then what you have to do. You have to sit down and you have to construct a relativistic theory of strings are suppose to point particles,
which is consistent with quantum mechanics. So it's a theory of strings consistent with reality, with general relativity, with quantum mechanics. And actually, it turns out after 20, 30 years, you often find out that you don't have much of a choice. The theory is pretty unique. And there are a few ingredients that you need to have. So you will always have open strings that that is strange that a start on end in two different points. You have closest Trigg's ladies.
And then you have some objects which are called deep rings, at which the strings can start and end as shown in the picture. And this is a useful mothers offer strings where you have different of these deep brains. The places where streak's gonna start and open and end sorry. And you have a string that can go between one brain and another one strings that can go between the same brain as here and also closer strings.
And the beautiful thing is that if you study the properties of these of these strings, these strings have exactly the correct properties of the fundamental particles that formed matter, leptons and quarks. Well, these are strings give you the game boatswain's unclosed. The strings give you they could have written so that we have a framework that only Fi's all particles and forces. In addition, there would be how you get excitations of the strings.
So this will be Kiger, an extra degree of freedoms that come with with the string theorists. Now, there is another reason also, which is very easy to see with the picture of why instinctively we don't have Infinity's anymore. So imagine that you can see the scattering of two tons if they are just in like a general approach, which are a standard approach to one to gravity. Here you have to gravitons and you see that to grab it does collide in to give one graviton time runs from left to right.
And here in you, Shortall approach to quantum gravity, the gravity does can get really close to each other. So here you see this point is some simple, really sharp. However, in a string theory, gravitons are this open and strings and as close to string. Sorry. And as they move on time, we have these tubes and we have two tubes joining into a third tube. And this interaction is something much softer than a point particle interaction.
And because of that, string theory is freed from the infinities that you get in in quantum gravity. Of course, not everything is beautiful in a string theory. And a string theory comes with several other features that I will describe in the second part of the talk. So the first feature is that each predicts supersymmetry. This is a remarkable, really too surprising symmetry between fermions and boatswain's so utterly.
String theory does suggest that there is a symmetry between the particles of matter and the particles of interactions, which is extremely surprising. It also predicts the total number of dimensions of space time, and I think neither physical theory does this in such a clean way. The third point, which is a bit bad, is that it is extremely hard to make computations with.
And I would try to explain why. And it was probably the richest physical and mathematical distractor amongst any theory invented by humankind. And this could be a good thing or a bad thing, depending on your taste. So for the remaining 20 minutes of of this stock, I will try to give a glimpse of these three aspects of string theory.
So the first one is the number of dimensions and very sexual are very cute and a small sorry and a small computation that tells you how to compute the number of dimensions in a string theory. So the first question we can ask is, what is the mass of the graviton in a string theory? So we have this closest train that represents the graviton. And we can ask what is the mass in a string theory? And actually. OK. We would need a few string theory lessons to do that.
But the end of the computation is something very simple. And it's just given by a bunch of harmonic oscillators, which you all met in quantum mechanics. And the total formula for the mass of the graviton is B minus two times the sum, which looks very much like the energy of of the harmonic oscillators. Minus two. And here so here in this forum, Wolf, we have the input of quantum mechanics.
This is basically a quantum mechanics computation. But then we have these finally some here, which is one minus two, plus three, minus four, etc., which is obviously divergent, but this can be done in a legal way. If we introduce a will later Epsilon and then say this Epsilon two CDO, so each term of this, some we multiplied by E to the minus epsilon end. And of course, for any positive epsilon, this is exponentially dum dum.
So the sum is convergent. And then you do the sum and at the end you take the limit of Epsilon going to. And that gives you this very beautiful one quarter. And if we take this, the fact that B sum is equal to one quarter into the most formula for the good we've done for the string string you could have. We get this nice and result for the mass of the graviton in a string theory. However, general relativity implies that the good that we've done must be massless.
And this was one of the questions with the photons a few minutes ago, because gravity is also a really long branch force and graviton smooth at the speed of light. They have to be massless and this is quite a sequel to CEDO can only work if the sequel to 10. So if string theory is consistent with quantum mechanics and general relativity already in 10 dimensions.
And this is a funny thing, because if you go to IKEA and buy a piece of furniture, they will give you three dimensions for the furniture. So we actually expect that for their mansions land with uncrate last time. And we are finding them. So very not the right question is. If a string theory predicts 10 dimensions, why do we see on before? And the answer is that not all of them have to be large.
And we can think of a garden hosted by. And if we look at the whole spike from really far away, it will look like a one dimensional object, right? Like a one dimensional line. Basically, if you look at the whole spike from 20 metres per winner, if you with close to it, you will see that there is a long dimension, a large dimension which is similar to to ah to the rear line times, a composite dimension that goes around the surf there.
This is the pipe itself. So a two dimensional spike has a large dimension. I love Kompa Dimension, which is basically a circle. And the idea with the string theory is very much the same out of bestand dimensions. Four dimensions can be very large. And they have to be very large. Basically a three plus one Minkowski space. But then the other six dimensions are wrap up, right? Curl curl up in a six dimensional compact.
Many for. And one of the kind of features of a string theory is that actually there are a bazillion ways to curl up six dimensions. And the predictions for the theory of what happens in these four dimensions depend very much on how you carve up these six dimensions here. And just to give you some flavour for the kind of things that is important.
So here we have this correspondence that the shape of these six dimensional, many full issing, one to one correspondence with how particles interact in four dimensions. And for instance, some of these interactions are proportional to something very mathematical as the number of straight lines that you can fit in this many force or some specific commentary integrals that you can do in the cycles of these many forms. So these started with a car, complicated mathematical questions to answer.
But then, OK, we have this relation here and we are saying that different many forms give you different physics in four dimensions, different predictions of a string theory for what should happen in the real world. So to say. So we can ask, is that a way of roughing the six extra dimensions such that in four dimensions things the theory looks exactly like the standard model.
And the answer resect on extremely car and it is impossible to get models that being for, they mention, looked exactly like the standard model. But it is too easy to get similar models and an important problem here. Is that why, one, they mention I combat many force and took on? Do they mention a Kompass remaining force at a piece of cake? Six, they mention, are many folks at extremely rich Honokaa.
Do a study and then assess this mathematics. Kosten been developed yet not even for for their mentions. It hasn't been developed yet. So we may be sent to these sub, go away from the maths necessary to understand six dimensional many faults. But still we can learn a lot from from this perspective. So this perspective between physics in four dimensions on unna geometry, in kager dimensions has led to do a lot of beautiful results in physics. But I won't have time, much time to go through this.
But but you can ask me questions such as the. So, no, let me. Let me end up. So the last three minutes with with a few comments about a string theory. So the first comment is about predictability in a string juries. Now, one of the dreams of a string theory was that if we did a theory of four strings, which was consistent with quantum mechanics and general relativity, this theory would be unique. And actually, this bringing is basically truth with the caveat that I would mention in.
But the theory is almost unique except for a discrete choice. So there are five different types of string theorists, but they are believed they are. Do I link this between them and they are believe to be different corners of a single eleven dimensional theory, which is called M theory, which is even more complicated than a string theory. But there is a sort of uniqueness of a string theory.
However, the problem is that there are many, many, many classical solutions with the spaces of the form of flood Minkowski space time like here. Times are six dimension and many fold because there are many six dimensional in many forms that are consistent with the portions of motion of a string. And the metric is actually the geometry. Actually, one of the fears of string theory. But we have many others and there is an abundance of luck.
So basically the situation that we have here is that you have only one set of equations, but we have many solutions to those situations. And the universe may have chosen in principle any of these solutions and a rough estimate of how many solutions are there. Gives you 10 to the 500. And I think it is fair to say that this is just too big of a number. But I think my personal opinion is that this is because we don't really understand string theory properly.
What do we really need to understand whether there are further constraints? So let me tell that in here. Let me know what started my conclusions, saying that string theory has achieved many things. So, of course, I just spoke for like 30 minutes. But it unifies or non fundamental particles, some forces under one framework, as we have seen it cures the divergent problems of gravity. And it is a complicated theory, but it is a quantum theory of gravity which is consistent.
And there are many other achievements that I didn't have time to explain. It has social problems. For instance, it kind of predicts supersymmetry that has not yet been observed in nature. It predicts extra dimensions, an abundance of buckworth. And also the mathematics that we need has not been developed yet. And the important question, of course, is whether a string theory, is this really true or not? And why at LHC, we will certainly not be able to prove fury.
There is string theory. It could be that LHC may provide some evidence for the ideas that feature in a string theory, for instance, supersymmetry. And you know, the maths is incredibly calm. And this enterprise may take Comverse of years. But if we do see, we would have found definer theory, which is a theory that unifies all fundamental particles. Some forces under one framework and all the laws of nature must follow from it.
And this will give a new conception of spacetime. We could understand things like that, quantum mechanics of Blackhorse or the origin of the universe. All of this on deeper scientific questions and probably applications that we can even imagine. Thank you very much.