L'univers dans lequel le futur pourrait précéder le passé… (l'univers de Gödel)

What if you could walk, not towards tomorrow, but towards yesterday? What if the future, the present, the past, were only fixed points, of a space already drawn? This is proposed by an amazing solution to Einstein's equations, imagined in 1949 by Kurt Gödel. But who is this man? Well, actually, Gödel is a mythical name of mathematicians. The genius who, in his youth, had already shaken the foundations of logic with his famous incompleteness theorems. But what we know less, is that he also ventured into the depths of general relativity, with a confusing idea. A rotating universe, allowing loops in time. A universe where we could, in theory, go back to our own past. So is it just a simple mathematical curiosity? Maybe. But this model has a particularity, and no less. It perfectly respects Einstein's laws of relativity. It is therefore, in theory, of course, a possible universe. And it is not a coincidence that Gödel conceived it. He wanted to question the very reality of time. For him, change, becoming, the arrow of time. All this could only be an illusion of our perception. A kind of mirage created by our consciousness, and not by the fabric of the universe. This strange model probably does not describe our cosmos, but it pushes physics into its refraction. It forces us to ask a radical question. Is time real? Or is it just a mental construction? In this video, we will plunge into the universe of Gödel. A world without past or future. We will discover how a software revolutionized cosmology. And why his vision still fascinates physicists, philosophers, and even science fiction writers. Get ready to question what you think you know about time. Because in the universe of Gödel, time is waiting for no one. Welcome to this new video. Today we are going to talk about a subject that I have never dealt with on the channel. So it's brand new. I hope you will like it. And just before, I have a small bid to make you part. 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That means that you can put it in pause at any time. If for example you go on vacation. So please. If you feel that you need to speak. Need to confide. Well do not wait. And otherwise you will always have my videos to avoid you. And besides. Would not we go back? Then. But before seeing exactly what the Godel universe consists. we will stop for a few minutes on this man, Kurt Gödel, whose intelligence seemed to flow beyond the boundaries of the conceivable. Born in 1906 in Brun in the former Austro-Hungarian empire, Gödel grew up in a German-speaking bourgeois family. Very early, he is distinguished by an exacerbated sensitivity, a prodigious memory, and above all, an obsessive questioning. Why does something exist, rather than nothing? Can we base all human knowledge on logic? He is passionate about mathematics, not as a tool, but as a key to breaking the very structure of reality. At only 25 years old, Gödel publishes what many consider to be the most important text of logic of the 20th century, the Theorems of Incompleteness. While mathematicians dreamed of a perfectly logical, complete and self-sufficient system , Gödel comes to break this dream with relentless rigor. He shows them that there are mathematical truths that cannot be demonstrated, that in any formal system powerful enough to contain arithmetic, there will always be true but indisputable propositions within the system. It's like building a perfect machine to do puzzles, and discovering that there are pieces that will never fit into the framework, even if they exist well. In other words, logic is not enough to explain everything. There are holes in the tissues of rationality. And even mathematics, this solidly reputed foundation, rests on a form of irreducible incompleteness. But Gödel was not just a mathematician, he was a philosopher, perhaps even the last great classical metaphysicist of the 20th century. Contrary to the positivist software of his time, he thought that mathematics was not a human invention, but the discovery of a world of eternal truths, accessible to the mind by intuition. He believed in the soul, in the beyond, and in a deep order of the cosmos, even if invisible to the eyes of ordinary scientists. Gödel did not seek to understand how things work, he wanted to know why they exist. And he shared this quest with another giant, Albert Einstein. But how did they meet? Well, in fact, in the 1940s, the two met at Princeton's Advanced Studies Institute. In New Jersey. Every day, they walk side by side, talking about gravity, causality, time. Einstein had shocked physics by proving that time depended on speed and gravity. But Gödel, faithful to his love of reasoning pushed to the extreme, asks himself an even more confusing question. And if, according to Einstein's own equations, time simply did not exist? So here's what happened. In fact, Gödel found in 1949 an exact solution to the equations of general relativity. A universe in global rotation, coherent from the point of view of the laws of physics, but where time forms loops. In this universe, the future can join the past. It becomes possible, in theory, to travel through time. Not thanks to a machine, but simply by following certain curves of space-time. These closed time curves are like the paths of the cosmos, which come back to themselves. Gödel, as a pure logician, does not say that our universe is necessarily like that. But he asks a fundamental question to Einstein. He tells him this. If your equations allow universes where time loses all objective meaning, then what is time, really? And that's where it all starts. Because, in Gödel's mind, time does not flow. For him, this impression of the past, present and future is an effect of perspective, an emerging phenomenon. Reality, it would be timeless. Like a frozen crystal where all moments coexist. And that's where a crazy idea emerges. Eternalism. The world does not unfold. It is quite simply that. Time is not a river, but a landscape that we explore through our consciousness. Einstein himself, at the end of his life, will say about a deceased friend, For us, convinced physicists, the distinction between past, present and future is only an illusion, if it is not. And now, we're going to get into the details. We're going to dive into this unique cosmic model, where space-time itself is in rotation, and where the laws of relativity allow time loops. Welcome to Gödel's universe. A world where the future can join the past, and where logic flirts with the vertigo of the eternal. And this world starts from a question. And it's the whole universe spinning. Not the planets, nor the galaxies, but the universe itself. The fabric of space-time. The frame, the decor, the background. It was this dizzying idea that Kurt Gödel proposed in 1949. But Gödel is not a physicist like the others. Besides, he is not even a physicist to speak properly. He is above all a logician, a mathematician and a philosopher. Famous for his incompleteness theorems, which shook the foundations of mathematics in the 20th century. But concretely, what are these discoveries? Well, what Gödel discovers is that Einstein's equations are more flexible than we think. They do not describe a universe. They admit an infinite number of possible. Curved, flat, empty, filled worlds, and even, why not, in rotation. And precisely, Gödel finds an exact solution. An infinite homogeneous universe filled with matter, and where space-time itself spins on itself. But it is not the matter that spins in a static space. It is the fabric of space-time that is caught in a global rotation movement. Like a giant vinyl. Or even better, imagine that you pour a little milk into a cup of black coffee. And if you shake the spoon, the liquid starts to rotate. And the milk starts to form spirals in the mass of coffee. In Gödel's universe, milk is light, and coffee is space-time. The light, which normally goes in a straight line, now follows curved, twisted, spiral trajectories. And that's not all. In this spinning coffee, if you go far enough, you can go back. Not back spatially, but back in time. When the coffee returns to its starting point, then it is in the present, but also in the past. And like a cup of coffee, welcome to a universe where time becomes circular. But why circular? And not another form? Well, in fact, it is one of the strangest consequences of Gödel's solution. In a spinning space-time, it is mathematically possible to trace closed curves of time. In other words, time loops. Paths that, while moving forward every moment to the future, return to their starting point in the past. It's as if, by moving straight forward, we were making a big circle in time, and we were coming back before we left. Gödel does not propose it as a science fiction experience. It is a rigorous solution, logically deduced from the laws of general relativity. And the craziest thing is that Einstein accepts this solution. He is even troubled, and he will say this. Gödel opened my eyes to implications of my own theory, which I had not seen myself. Because deep down, that's the real revolution of Gödel. He does not only propose a spinning universe. He proposes a universe where time loses its directional arrow. In this world, there is no more absolute distinction between past, present and future. Everything is relative, deformable, revisitable. And it goes much further than the deformations of time due to speed or gravity. Here, it is the very structure of time that is questioned. And for Gödel, this is not a bug. And it is proof that time does not exist fundamentally. And so, what is time for Gödel? Well, a logical illusion. In fact, Gödel, influenced by Plato's philosophy, thought that time was only an appearance. An effect of perspective. A reflection of our limited consciousness. But that, in the ultimate reality, everything is already there. Eternal. Frozen. Beyond change. And that physics, through its own equation, begins to confirm it. Well, for the moment, we will not go too much into the subject, since we will talk about it later. But we will talk about it quickly. First, good to remember of course, Gödel's universe does not describe our observable cosmos. We know that the universe is expanding, not rotating. In any case, no evidence suggests a global movement of the fabric of space-time. But that's not the main point here, no. The point is that the laws of general relativity allow such a world. And so, it does not exclude time travel. And that's crazy. Because Gödel created a kind of theoretical mirror. A mirror in which physics looks and sees its own paradox. Basically, Gödel's universe is a bit like a giant thought experiment. But written in pure mathematical language. It does not say, here is the world as it is. It says, here is what your theory allows. And if it bothers you, then maybe you should change the theory. Or change our conception of time. But how do we change our conception of time? We talked about time loops, but concretely, what is it? Imagine a world where, always walking straight, without ever turning around, you end up falling back into your own past. A world where time, instead of flowing like a river, closes like a ring. Where the very idea of ​​cause and consequence becomes blurred. And where your future could literally precede you. Well, that's what the universe proposed by Gödel reveals. But this universe, it is authorized by general relativity. It is not necessarily validated, but it is authorized. But why? What about Einstein's theory, which was used by Gödel? Well, in fact, in his model, general relativity authorizes what physicists call Closed Time-like Curves. Closed because these lines of space-time close on themselves. And temporal, because by following them, we always remain in the domain of the possible for an observer made of matter. No need to travel faster than light. Nor quantum magic. In other words, these are trajectories that follow time normally. At every moment. But they still return to their temporal starting point. A bit like if you were moving forward in the future. And that by progressing for a long time, you would fall back to the moment of your departure. In this universe, time is no longer linear. There is no more privileged direction. There is no more absolute present. Each observer has his own present. There is no more clear distinction between past, present and future. And especially, the future can, in theory, influence the past. It is a world where causality becomes local. And no longer universal. The effect can precede the cause. And the cause can depend on what it is supposed to produce. A closed, perfect, destabilizing logical loop. But what does it change concretely? Well, it's a real conceptual revolution. In fact, these temporal loops are not just side effects of relativity. They are a direct consequence. But Gödel did not invent them to make science fiction. He highlighted them as a natural property of Einstein's equations. Finally, provided that the universe is rotating. And that's crazy. Because it means that general relativity, our best theory of time, allows us to travel in the past without breaking any fundamental law. But is it coherent? What about temporal paradoxes? The most famous of them, the grandfather paradox. What happens if you go back in time and prevent the birth of one of your grandparents? But also the letter you receive before you even wrote it. Or the object that self-creates, appearing in the past because you sent it from the future. All these scenarios trouble us. Because they question our intuition of causality. And yet, they are not necessarily forbidden by relativity. On the contrary. Some physicists, like Igor Novikov, even proposed a principle to save logic in this type of universe. It is called the principle of coherence of Novikov. And this principle says that. In other words, yes, you can go back in time. But you will never be able to cause paradoxes. Because events will adjust spontaneously to respect the coherence of the overall story. For example, you can send a letter into the past. But only if it is this letter, which at the origin, made you want to write it. Or, you can go back in time. But only if your actions do not alter what has already been. It is as if the universe had a sense of narration. As if each time loop told a story that holds. Even if it defies our linear logic. No contradiction. No parallel universe. Just stories closed to themselves, where cause and effect are linked in a strange but coherent dance. But a mechanic without a time arrow, is it really possible? To ask this question, it actually comes back to wondering if time has ever had a direction. And we know that in quantum mechanics, the fundamental laws are reversible. It is us, with our memory, our perception, that gives meaning to the arrow of time. Godel's loops, they do not need an arrow. They form a cyclical mechanic, where the universe turns on itself. And where every event is both cause and effect. We then leave the image of time in a straight line. To enter a circular version, perhaps even more fundamental. In reality, Godel did not really believe that our real universe worked as its solution. He knew that our cosmos is not in global rotation. But he had a more subtle goal. In fact, by finding this solution, he wanted to show that Einstein's equations are stranger than we think. That they allow realities that have no equivalent in our daily experience. And above all, that they say nothing about what time really is. In fact, Godel's loop does not only teach us that time travel is possible. It pushes us to rethink what time itself is. Perhaps time is not a river, but a labyrinth, or a spiral, or even a broken mirror. Each fragment of which reflects a different aspect of reality. Godel, like a metaphysical clock, gives us this idea. Time may not be what we believe. And our present may only be a dot on an infinite loop. And even if this vision seems to conform to Einstein's ideas, it is not in reality. Because the real problem with Godel's universe is that it looks like nothing to what we observe. First, it does not extend. We saw that it was spinning, but in fact, Godel's universe is static. There is no Big Bang, no expansion, no galaxies moving away. And yet, all around us, we observe galaxies fleeing from each other. Traces of expansion in the cosmological diffuse background. And even proof of an ultra-fast inflation phase, just after the Big Bang. So already on this point, Godel's model does not match the cosmic history that we reconstruct today. Ok, it does not extend, no. Instead, it rotates on itself. But the problem is that it rotates too much. Well yes, in Godel's universe, all space-time is in rotation. But in our cosmos, this idea is contradicted by very precise observations. For example, the cosmological diffuse background, the Big Bang's fossil light, is almost perfectly isotropic. That means it does not present any privileged direction. If there was a global rotation, it would leave visible traces in this light. However, this is not what our devices detect. In other words, we clearly do not live in Godel's universe. But does this mean that this solution is useless? Well, not at all. On the contrary. In fact, Godel's universe is like a giant thought experiment. It serves to show us the direct consequences of Einstein's equations. And even if it does not describe our universe, it allows a universe where time itself can loop on itself. It's a bit like a theoretical model of a mythological animal. It does not exist in nature. But it reveals what is possible within the laws. It is also a way not to be too divided in research. Because Godel's universe has shown that a cyclic universe can exist. But that it does not exist. At least, this is not what we observe at all. And that, we could have guessed it from Godel. Simply because this genius is a mathematician. And not an astronomer. And there is the big difference. Godel was not there to map galaxies. He was not there to predict observations. He wanted to question the foundations of reality. And even today, this reality is now general relativity. So, he tests this theory. He will question its smallest foundations. And in particular, time. He will go so far in his mathematical predictions, always valid in the context of relativity of course, that he will describe in his book that change is an illusion. And that the past, the present and the future coexist. In fact, through his model, Godel proposes a blocked vision of time. Not a flow, not a succession of moments. But a complete structure, frozen, out of sight. In which the events are already there. Whether we lived them or not. So in fact, Godel's universe is not impossible. It is even widely authorized by relativity. But it does not correspond to what we see around us. It is important to note that these works have not been useless. They opened a huge philosophical gap. That of a non-linear time, of a world where the present loses all absolute meaning. It's like the universe sends us a sign. This sign, we say that the equations of physics describe possibilities. But that reality, it chooses among these possibilities. But in the end, time, what is it? Is it a reality? An illusion? Or a trap of our own brain? Because by playing with the equations of space-time, Godel discovered something strange. Something disturbing. Not only a mathematical property, but a question of time itself. This is where these works make all their sense. Because in the end, Godel did not want to predict a universe. He wanted to question our perception of time. In fact, he knew very well that his universe, in rotation, does not look like ours. But that was not his goal at all. In reality, his goal was to show a possibility contained in Einstein's laws. And to ask a question, at least, confusing. If these laws allow a universe where we can travel in the past, then what does that say about the real nature of time? In the end, wouldn't that be an invention of our mind? And for that, we were lucky that Godel was not only a math genius. Because he was also deeply influenced by idealist philosophy. Especially by Leibniz, who affirmed that time was not a substance, but a relationship. And by Parmenides, a Greek philosopher of antiquity, for whom change was an illusion. And Godel shared this vision. For him, time was not a fundamental ingredient of reality. It was a mental construction. A way for our consciousness to structure events. He wrote that the flow of time had no objective meaning. In other words, the past, the present and the future exist simultaneously. It is in fact our mind that selects a now, and imagines that it slides into the future. And what makes Godel's position even more fascinating, is that Einstein himself was not far from thinking the same thing. As we quickly saw earlier. In a letter written after the death of his friend Michel Bessot, he says that for convinced physicists, the distinction between past, present and future is only an illusion, if it is not. It is a famous sentence, often quoted, but rarely taken seriously. And yet, in the context of relativity, it takes on a huge weight. Because relativity has already suppressed the idea of ​​a universal present. Well yes, as you may know, time is relative. What is now, for you, can be the past or the future for someone else. Depending on its speed or its position in space. And Godel, as a good logician, pushes this observation to the end. Imagine a film already recorded. A complete reel, with each scene already there. From start to finish. But we, spectators, we only see one image at a time. The present seems to slide from one scene to another. But the film itself exists in its entirety. Already written, already frozen. Maybe the universe is a 4D film. And what we call time, is simply our way of reading it. And that's what we call a universe block. A space-time already complete. And where each moment coexists with the others. But then, why do we feel like time is passing? Well, this is where neuroscience and physics meet. Some think that the impression of the present, which slides to the future, is an effect directly related to our memory. We remember the past, not the future. In fact, our brain records events in a certain order. And it recreates a temporal narrative. A kind of timeline that gives meaning to our experience. But all of this happens in our brain. Because in equations, nothing moves. Time does not flow. It is there, placed, structured, like a 4D geography. And if Gödel was right, what would it change about our vision of time? Well, if his universe is proven, and that time is an illusion of science, then it means that each moment of your life already exists somewhere in space-time. Your childhood, your distant future, this video, everything is there. Inscribed in the fabric of the universe. And if we push logic a little further, it also means that dying is not disappearing. It is simply leaving a region of time for another. Gödel, who was a believer, saw in this vision a form of rational eternity. A mathematical consolation to one of the most worrying and terrifying phenomena of the universe. Death. But of course, all of this remains speculative. Real time may not be a total illusion, nor an objective river. But physics, and in particular relativity, forces us to admit that our conception of time is imperfect. And that's exactly what Gödel did with his spiral universe. He does not describe the real cosmos, but he asks the right question. What we call time, is it a fact of nature, or an effect of perspective? So in fact, time for Gödel is not a dynamic dimension, but a fixed structure. There is no absolute present. Simply because the past, the present and the future are all equally real. And our consciousness, for biological reasons, can only perceive it for a moment at a time. So what should we remember from all this? Well, Gödel's universe, In fact, when we think of him, we often think of the man of mathematics. A logician who has proven that all truth can not be demonstrated. But by proposing a universe where time loops on itself, he has also touched on one of the greatest mysteries of our reality. What leaves us is not a simple cosmological model. This is not a serious alternative to our Big Bang. No, it's a reversal. An enigma. An intellectual provocation. A way to tell us that we better look at our equations. Because maybe in it, time has no place. Maybe the change is an illusion. And that the whole universe is like a book, written in one block. And as we could see, Gödel's universe puts in tension two visions of the world. The intuitive, linear, human vision of time, therefore the universe in which we are, with the reality that we live. And the deep, theoretical, mathematical vision, where time is not a fundamental dimension, but a projection of our consciousness. It's completely confusing. But that's exactly what Gödel was looking for. To question what we think is obvious. But even if Gödel's universe does not describe our cosmos, he left traces in science, in logic, in literature. And above all, he reopened the oldest philosophical question of all. Does time pass? Or are we going through an immobile universe? And if Gödel was right, then the future already exists. The past never dies. And everything that has been, is, and will be, everything is there, somewhere. In the silent curvature of space-time, waiting to be discovered, or forgotten. If you want to continue your question about time, I put a video that is linked right here. Otherwise, if you want to totally change the subject, I put a playlist here that you can launch without thinking, as usual, and fall on a subject that interests you. Thank you very much for following this video. If there are any who are interested in becoming a script, do not hesitate to send me an email at contact.yt. Thanks to all those who join the channel, who subscribe, who subscribe to my podcast. Thank you all. It was Zebros, see you soon.