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