Hi everyone ! Today, we’ll talk about the greatest mystery of fundamental physic, The one which impedes thousands of scientists to sleep. What we pretenciously call “The theory of everything” Theory of everything is supposedly the reunion of the infinite big and infinite small. The unification of general relativity with quantum mechanic. By the way, we more simply call it ” Quantum theory’s problem”. There’s a very famous approach to this problem: the string theory. (I already had the chance to make a video on that subject) But today, I’d like to talk about the other theory the one which is less famous than string theory but that has my personal preference: loop quantum gravity. LOOP QUANTUM GRAVITY The problem of quantum gravity is the unification of 2 theories which have both completely shaken our vision of the world in the first half of the XXth century. The 1st of these theories is general relativity, Einstein’s masterpiece. This is a gravity’s force theory. We already had a theory of force of gravity before Einstein, Newton’s, which was here for almost 250 years. That’s the one you learn at school “2 massive bodies attract each other because there is a force between the 2”. And Newton even gave us the formula which permits to calculate this force. Newton’s theory is fabulous and fantastically works for more than 3 centuries now. This is the one which permits to understand falling bodies . but also movements of planets I don’t know if you realise the prowess that represents for that epoch. Newton understands that what makes an apple fall towards the ground and what explains the movement of a planet around the sun is the same thing. (Mad stuff!) There’s one Paul Valéry’s quote that I really like and sums it well: “One had to be Newton to realize that the Moon is falling, whereas everyone sees well that it doesn’t.” In brief, Newton’s theory works greatly. And Einstein offers to replace it by something conceptually totally different. For Einstein, bodies attract each other not because of an invisible force between them but because they deform SPACE-TIME. The classic example is an outstreached drape were you place objects It’s he curve of space-time that modifies the trajectory of massive bodies et provoques their attraction Something you should keep in mind: mathematically speaking, Newton and Einstein theories are very different, but their results and physic predictions are mainly the same. You should hope so, because as we saw Newton’s theory works extremely well so Einstein’s theory better give similar results. If you calculate the fall of an apple or the trajectory of the Moon around Earth with general relativity You’ll get the same results that with Newton’s theory. Except… when the gravitationnal field becomes really intense. For example, Mercury, which is much closer to the sun than Earth, is in a more intense gravitationnal field. And here, the calculation of it’s trajectory by Newton and Einstein give slightly different results. And it’s Einstein’s calcul that sticks better with observations. It means that general relativity ameliorates Newton’s theory particulary for intense gravitationnal fields. It even predicts the existence of bodies which didn’t exist in Newton’s theory, like f.e. black holes Regions of space-time of which nothing can espace from, not even light. And of course, one of the most spectacular predictions of general relativity’s theory is the BIG BANG. The Big bang’s theory comes from the applications of Einstein’s equations to the whole universe. And it predicts that universe is not just a static arena but could be dilating or contracting. That’s what has been first observed by Edwin Hubble in the 20’s and many more after him: all galaxies of the universe recede from one another, like an elastic drape streching from all sides. If we use cosmology’s equations to go back in the universe’ past, you see that the more you go back in time, the more the Universe was contracted, dense and hot. Until 13.8 billion years ago where, according to equations, the Universe was an infinitely dense point. (as if it was born at that time) Little weird conclusion, isn’t it? We’ll later see what to think about that. LOOP QUANTUM GRAVITY The other huge revolution of the start of the XXth century is quantum mechanic. Quantum mechanic is a bit like the contrary of general relativity: a theory of the infinite small. It’s what permits to understand how matter behaves to the scale of molecules, atoms and smaller: protons, neutrons and all elementary particules. If we owe general relativity essentially to Einstein, quantum mechanics is the fruit of a collective effort of a series of geniuses who worked between 1900 and 1930. You see here the mythical picture of Solvay’s Congress in 1927. All the founders of quantum mechanic are here, and among the 29 present persons 17 got the Nobel prize. There’s only 1 woman in the assembly, Marie Curie, but well, she got it twice. What quantum mechanic tells us is that at a very small scale, matter behaves differently that what we’re used to at our scale. And the way best to realise it is to consider an hydrogen atom. A hydrogen atom is apparently simple: – 1 positively charged proton +
– 1 negatively charged electron – Between them exists a force (Coulomb’s electrostatic force) which states that opposite charges attract each other. That force looks a lot like Newton’s force, and states that an electron turns around a proton. This desciption is simple, but has a small problem: because electron can loose energy, it will turn closer and closer to the proton until it crashes on it. Like a satellite can enter the atmosphere. If that was true, hydrogen atoms would be instable, but we well see they are stable. Quantum mechanic resolves this problem by changing the way we see hydrogen. First, quantum mechanic tell us that the electron doesn’t have a defined trajectory. It’s not on a precise point on a defined orbit. It’s in a superposition of states, as if it was a little everywhere on it’s orbit at the same time The other big change is that the electron cannot be anywhere, it only has some possible levels of energy. We often symbolise it as if it only had certain possible orbits, even if it’s not what it exactly is. The electron can be on a certain level, or another, but not between them. So we give them level: level 1, level 2, level 3. Levels of energies are called “quantified”. That’s why it’s called “quantum mechanic”. This quantification of levels of energies has 2 consequences. 1: An electron can jump from one level of energy to another by emitting or absorbing a well determined quantity of energy under the form of well-defined light of wave length. You verify this every day with the colour of light which is absorbed or emited by different atoms. 2. The electron cannot go lower in energy than the 1st level which is called the “fundamental level” it especially prevents it to crash on the proton. It’s like there was a sort of repulsion force due to quantic effects which protects the atom from instability. And we’ll see that it plays an important role in our story. LOOP QUANTUM GRAVITY General relativity and quantum mechanic: the 2 huge revolutions of the XXth century in fundamental physics. Until today, these 2 theories worked perfectly well. We saw it again recently with the discovery of gravitationnal waves for general relativity and the discovery of Higgs’s Boson for quantum mechanic. Even so, these 2 theories are completely incompatible. General relativity describes a curved but smooth determinist world. On the other hand, quantum mechanic states that at the microscopic scale, the world is more discrete, probabilist, fluctuant. That is well reflected in mathematical tools used by the 2 theories which are completely different. Two so well verified but incompatible theories: physicists theoricians hate that. If we could replace that by 1 inclusive theory for both, that’d be damn better. You should know that he volunty to unify phenomenons together has always been a powerful motor of comprehension. For instance the example I gave of Newton who unifies the movement of falling bodies with the movement of planets. But there’s an even crazier example: James Maxwell, who discovers electromagnetism at the end of the XIXth century He shows that electricity and magnetism are only two aspects of something more fundamental: THE ELECTROMAGNETIC FIELD. And some years later, he understands that light if a wave of the electromagnetic field. That means that at once, Maxwell unifies 3 things that were considered independant: electricity, magnetism and light. And that allows him to understand that there must be other electromagnetic waves than visible light. We know them today: micro-waves, radio waves, X rays. In brief, unifing phenomenons is the ultimate world swagg in theorical physics. Some could argue that unifying general relativity and quantum mechanic: no one really gives a shit. As we said, general relativity is a theory of extremely heavy objects On the other side, quantum mechanic is a theory of very small objects. Well, very heavy objects are in general not very small… Yep, except that there’re 2 exceptions to this rule. The first is what happens at the centre of black holes. According to general relativity, all matter which falls in a black hole will concentrate in its centre in an infinitesimal point, a very heavy and very small thing. It’s what’s called a “singularity”. Other singularity: the 1st instants of the Big Bang. We saw before that if we use cosmology’s equations we get to the weird conclusion that 13.8 billion years ago the Universe was an infinitely dense point. But we don’t know because it was something very heavy and very small. So we cannot just use general relativity’s equations, we also have to aknowledge quantum mechanic. We need a unified theory. To understand the first instants of the Big Ban, we need a quantum gravity theory. Ok, enough of chit chat. Should we make this quantum gravity theory? LOOP QUANTUM GRAVITY To understand how we can build a quantum gravity theory, you must realize that general relativity and quantum mechanic, which we want to unify, are 2 theories not exacly on the same plan. General relativity describes a force, “the gravity force” (we should rather say an “interaction”) You can compare it to electromagnetic force. Quantum mechanic is not a force but rather a set of principles which tell us how a force will behave at the microscopic level. As we saw before with the hydrogen atom: you have the classic vision which doesn’t work and quantum mechanic modifies this vision to tell us how things happen at a small scale. So it’s not really about unifying quantum mechanic and general relativity but rather being able to apply principles of quantum mechanic to general relativity’s theory. We usually consider 4 fundamental forces in nature: – ELECTROMAGNETISM, which explains nearly all that we see around us – STRONG AND WEAK NUCEAR FORCES, which assure cohesion of atomic cores. and – GRAVITY, described by general relativity And we can do with those forces what we did with the hydrogen atom: apply principles of quantum mechanic. That way, we can for example pass from electomagnetism to it’s quantum mechanic’s version. That’s called QUANTUM ELECTRODYNAMICS. We can also do that with strong nuclear force, and obtain “QUANTUM CHROMODYNAMIC”. and with weak nuclear energy (*electroweak theory*). These 3 forces in their quantic versions form what’s called “THE STANDARD MODEL OF PARTICULES’S PHYSICS”. Because all we understand today about the behavior of elementary particules is explained by this model. All we see in particules’ accelerators until the discovery of Higgs’s Boson at the CERN can be explained by the “standard model”. Applying princips of quantum mechanic worked with the 3 first forces. So there’s only left to do it with the 4th: general relativity. But that’s where the plot thickens… I didn’t tell you how to pass from a theory to it’s quantic version. This operation is called “quantification” and there is some procedure to make it. It was described by 1 of quantum mechanic’s geniuses: Paul Dirac. Dirac offered some kind of recipe, which allows to take a classic theory and to fabricate the correspondant quantum theory. There are 2 problems with this recipe: 1) It asks us to build mathematical objects which are far more complicated that what we first had. So, the mathematical arsenal to deploy can quickly become quite frightening. 2) Dirac recipe is vague. It tells us what we need, but not how we do to find it. If we apply this recipe to the hydrogen atom, we find the quantum theory of the hydrogen atom. But if we try to apply it to electromagnetism, it already blocks. In the case of electromagnetism, the difficulty has been overcome by limiting to situations where fields are not too intense. In other words, where there aren’t too many particules which interact. That’s what’s called the “PERTURBATIVE APPROACH”. It’s a little bit like if you wanted to understand sea movements and you decided to carefully retrain to the study of waves but ignoring more global movement like currents ou storms. The perturbative approach is sufficient to understand f.e. what happens in particules’s accelerators. And we owe this approach to, among others, another genius of quantum physic: Richard Feynman. Feynman has introduced a tool which enholds his name: Feynam’s diagrams. This are small drawings which represent interactions between particules. and if you open a book about physics of particules, you’ll see some on nearly every page. So, why am I telling you this? Because the fundamental reason that makes a theory of quantum physics difficult to build is that the perturbative approach does not work with general relativity. If you still try to apply perturbative approach to general relativity, you’ll always get infinity. That means you would build a theory which will, no matter the question, answer infinity. No too practical. This result is really the birth act of different approaches to the problem of quantum gravity. Because if we had a method (the perturbative method) which perfectly worked out for the 3 first forces – electromagnetsim, weak and strong nuclear forces) but this doesn’t work with general relativity. So we need to find something else. Since here, the world is divided in 2 categories: – The ones who stick to the perturbative approach – And those who abandon it. I’m not going to talk again about string theory today, I already made a video on it. But you need to know that string theory tries to preserve the perturbative approach. For that, you change the first postulates, at the expense of introduction to some exotic things like minuscule strings, additionnal dimensions and some new particules: supersymetric particules. A good part of those who wanted to try something else than string theory decided to let the perturbative approach go and go back to Dirac’s initial recipe. That’s one of the origins of loop quantum gravity. But before I say more, I need to explain why researchers in that domain have good reasons to think that the perturbative method could not have worked anyway . General relativity’s philosophy is that space-time doesn’t exist anymore as a fixed arena where things happen, but space-time is itself dynamic and changing. A nice sentence resumes this: “In general relativity, the stage disapears and becomes one of the actors.” When you want to apply perturative approach, you have to reintroduce a sort of fixed stage where perturbations happen. For general relativity’s purists, it betrays one of its fundamental principles. So, it’s not surprising it doesn’t work well. Ok, good, but now how do we apply Dirac’s quantification program to general relativity, without using perturbations? Well, it’s hard… So hard no one has ever sucessfully done it. … until 1986. LOOP QUANTUM GRAVITY In 1986, an indian physicist named Abhay Ashtekar offers something new. He offers to reformulate general relativity. He takes Einstein’s equations and writes them differently. Mathematically speaking, the variables and equations he uses are different, but are physically the same. It’s equivalent to general relativity, it makes the same predictions. But ihis new formula makes it look more like electromagnetism. And that’s what will deblock Dirac’s application program. That, and loops of course. Ok that’s a little technical, but I have to explain where the term “loop” in loop quantum gravity comes from. We saw that general relativity’s theory covers space-time’s curve. But how do we know we’re in a curved space-time? We’re in it, so it’s not always easy to realize it. Well, you make loops. Imagine you’re on a plan, and you carry an arrow in your hand (for example a bow arrow, pointing straight) Move forward some time and stop. and take a 90° turn without changing your arrow’s position. Continue to walk straight, then take another 90° turn. without moving the arrow, and again until your initial position. In the end, your arrow is in the same position as when you started Now, let’s play the same game on a sphere, which is a curved space. Go straight. Then, turn in a right angle without changing the arrow’s direction, Go forward. Turn without changing the arrow’s direction. And come back to the initial point. Here, the arrow is not in the same direction than at start. And that is the sign of a curved space. When you make a loop in a curved space -take a turn and go back at the start- vectors find themselves in different positions. All that can seem terribly abstract, but what you should remember is that making loops permits to feel space-time’s curves, and to even measure it. So, by replacing the notion of curve by the one of loop, we can deblock the situation and to apply Dirac’s program to general relativity reformulated by Ashtekar. So I am of course not going to describe the whole theory but, by analogy with the hydrogen atom, I would like to make you sense the principal results. The most spectacular result was obtained by two reseachers: an american, Lee Smolin, and an italian, Carlo Rovelli. I told you that one of the contributions of quantum mechanic to the hydrogen atom is that levels of energies are quantified, discrete. and in particular there is a smaller level of energy. In loop quantum gravity, the same thing happens with space-time’s geometry. In loop quantum theory, geometric sizes are quantified (lenghts, areas, volumes). For example, there is a smallest possible area that a surface can possess, and it can possess certain discrete values for its area, but not for its intermediate values. So these minimal geometric dimensions are very small. The smallest lenght is approximately 10^(-35) metre, what is called “PLANCK’S LENGHT” So, we obviously don’t see the difference at our scale. What this result tells us is that if we go down to Planck’s lenght, space is not continuous anymore but discrete. It’s composed by small invisible blocks, sort of elementary bricks of finite size sort of space atoms. To represent this situation, we use a network which symbolises the way different space atoms are linked to each other. This network is a quantum state of the space’s curve – it’s called a “network of spins”. Once we understand that, there’s another essential question: How does that space evoluate?
That means: how does space-time look like? We saw in the hydrogen’s atom case that the electron could pass from one level to another. Well, it’s the same with our quantum representation of space. We can pass from one network spins to another. And to do that, it’s enough to imagine an intermediate structure which links them – we call it a “SPIN FOAM”. This spin foam is a quantum representation of space-time. And it’s important to understand that all this is not just a drawing. Behind those spin foams are equations which we associate to different elements the structure to, and that permits to describe the probability that space passes from a quantum state to another. I will of course spare you from details, but what remains is that loop quantum gravity shows us that quantum space-time is not a smooth and continuous anymore like it’s in general reativity. It’s made of elementary bricks of finite size, quantified, and which are fluctuant. -that can jump from one state to another-, a sort of boiling space-time. I described loop quantum gravity in big chunks , but now I’d like to explain the icing on the cake: how this theory modifies our vision of the Big-Bang. In the year 2000’s, a young physicist nammed Martin Bojowald applied loop quantum gravity’s equations to cosmology problems. And he created what’s called loop quantum cosmology. I of course am not going to give you all the details, but I’d just like to make you understand the lessons we get from it. Loop quantum gravity shows us that space-time is made of minuscule parts of finite size, space-time atoms. One of its consequences is that we cannot indefinitely accumulate matter in the same place. There is a maximal density that we can attain: Planck’s density. This density is monstruous. It’s 5 x 10^96 kg/m3 which is “5” with 96 “0” behind. And this maximal density changes our perception of the Big Bang. In classic cosmology, when you ride up to the Big Bang, density gets higher and higher, until it’s supposedly infinite. But in loop quantum cosmology, density cannot surpass Planck’s density, So when we go back it time, it blocks at some point. A similar thing happens with the hydrogen atom’s electron. You remember? The electron cannot crash on the proton because it cannot go beyond the fondamental level, and it’s like there was a repulsive quantum force which prevents from getting too close to the proton. It’s kind of the same thing we have in loop quantum cosmology. It’s like there was a repulsion force which prevents to surpass Planck’s density So it changes our vision of the beginning of the Big Bang. We go from a vision of a Big Bang to what would more be a BIG BOUNCE. Calculations in loop quantum cosmology show that the Universe might have been created from the collapse of a precedent universe, bounce at the maximal denisty and spread until our universe is formed. That is still speculative and the equations are a little simplified, but it is one of the possibilities. Bad -or good- news: calcuations show that the bounce erased all traces of the past in a sort of big quantum boiling. Which means that even if it was confirmed one day, we wouldn’t have the means to go back and know what the previous universe was. LOOP QUANTUM GRAVITY There, you arleady know a lot about loop quantum gravity. You should retain 2 things:
1) This is only an attempt among others 2) Everything is far from being complitely achieved in this theory. There are still a lot we don’t understand and a certain number of things which don’t have solid bases mathematically speaking And anyway in the end, it’s always experimental results that will settle and permit to state if the theory is or isn’t correct. By the way, let’s talk about those experimental results: on what can we base on to verify this theory? The first thing we can use is justly cosmology. You may know that the best proof of the Big Bang scenario is is the COSMIC MICROWAVE BACKGROUND (CMB)
– what’s sometimes called the “FOSSIL RADIATION”. And by the way this radiation fluctuates, we can hope to find traces of the first instants of the Big Bang. We’re still far from being able to discern them, but recently Abhay Ashtekar and a french physicist, Aurélien Barreau, made calculs to try to understand what the signs of loop quantum gravity would be in the CMB. It’s pretty interesting from the philosophy of science’s perspective because it means that this theory can be experimentally tested. It makes predictions, even if we still don’t have enough precision today. The other way to test loop quantum theory would be to probe space-time’s structure. The situation is rather close to what we have with ordinary matter. If I take a rock and look at it with my eyes or even a microscope, it looks smooth, made of a continous matter. But if I throw very energetic rays on it, like X rays, I can detect it’s discrete structure, it’s organisation in crystal, I can see its atoms in a way. And the same thing could happen with the discrete structure of pace-time: if sufficiently energetic rays cross it it could inform us about these famous space atoms. The problem is that we don’t know how to fabricate such powerfull radiation. But they can happen in certain astrophysic phenomenons, so we maybe have a chance to capture very very energetic radiations which hold the quantum signature of space-time. Thanks for watching this video!
If you liked it don’t hesitate to share it, so we don’t always talk about string theory. As always I wrote a small note to accompany this video and that will give you some details. Even if I can’t of course explain everything to you. If you like fundamental physics, I have a lot of other videos on the channel which talk about it. I already talked about Stphen Hawking, I talked about string theory, quantum mechanic, black holes, cosmologic constant, quantum intrication etc. One small thing I need to precise before beeing accused of it is that I’m a little partisan of this story of loop quantum gravity versus string theory, because I worked in loop quantum gravity. This was my thesis’s subject and I was lucky to work with a part of persons of whom I talked about in this video. For those who’d like to meet me, I’ll be at the Espace de Sciences on Octobre 5th in Rennes to make a conderence in Hubert Curien’s room ***The notes are in French*** You can as always see news of the channel on facebook and twitter and support me on Tipee.
Thanks all and see you soon!