Causality and Relativistic Spacetime / Temps, Ignorance et Irréversibilité Logique

0:00 Thank you. I don't know what you want to say. You were just like a curve. You were just like a curve. What do you mean? In this moment, the hypothesis, is that what we call an event, that is what we call what we call habitually with one position and one instant, It's a point in the space-temps. Yes, and what you said earlier, is that this course corresponds to a suite of positions in the space-temps. Yes, it's a suite of positions in the space-temps. Yes, it's a suite of positions in the space-temps. I am an ensemble of positions in the space-temps. An ensemble of suits? An ensemble of positions. A one dimension. Pardon? Well, if you want, And... Okay. C'est ça, il définit ? Non mais tu vas voir, on va y arriver à ce cours du temps. Bon, j'anticipe pour répondre à Etienne. J'anticipe pour répondre à Etienne, parce qu'il va être content. Donc, moi, je suis une courbe continue de genre de temps. Maintenant, puisque j'ai une courbe continue de genre de temps, je sais que j'ai une métrique. Donc, je peux calculer la longueur métrique between two points, the length of my curve. So I know how to calculate the length of the length of an interval like this. It's by definition what we call the length of the time. So the length of my curve, the length of my curve gives me the length of the time. If I have another curve, the length of this curve is the length of the time. It's exactly what I've written here. So, to be able to do that, you have to have a metric. But you can see that and that, it has nothing to do.

2:30 First of all, it's not a function, I can only do that. Now, I can take an origin here and call it the length of the metric along my curve, the tempo. But obviously, if there is another curve that is part of this point and it arrives there, this, this, this length, we have no rapport with this, etc. So, there are things that are also really interesting, which are also really interesting. Yes, of course, there is no difference in all these concepts between the reality of general and the reality of science, but here, we can imagine a situation a lot more tordues, Yes, of course, of course. But for what he is talking about, he can say the things that he is talking about in general, he is talking about it. A good thing, yes. Yes, there is no difference. Sauf that if you want, you can imagine... In fact, this notion of tempo, you can have, say, a group like this and the other sort of asymptote. And how do you choose what you count as a group each time? Wait, the only thing that we call the temporal, which is a very mauvaise notation, it's just the length of the metric, which are just the intervals. Everything that we can define in relativity, which resembles a time, it's between two points along the course, which is the length of the course. We call temporal. For a short term. Yes, I have another curve. Here I have an interval of time which has nothing to do with that. Here it will be, I don't know, 10 seconds, here it will be 1 second, and if I go very far, it will be 0,0. Yes, but the problem, if you take it as particle, But if there is a problem, because it's like the same particle, it's a ballad. But the particle, or she follows this line of time, or she follows that path. Yes, but these two versions coincident here. And then? That's a particle, that's another one. So between these two...

5:00 Here, let's say, two particles are immis. Here, they join them. For one particle, it takes 10 seconds. For the other, it takes 10 seconds. Sauf that the time for one particle, we'll see later, it doesn't have a sense. Well, it can give you a sense, but I think that... And that's another thing. I don't want to say that in the notation, in the signification, and in the two senses, in the two senses, in the signification. So, one thing that is very well defined in relativity, it's the time proper. But you see that the time proper of an observator, it's something that defines the length of the universe . if there is an event that is happening here so, here is my line of the universe in this moment, I don't know I can't tell you anything at the kitchen, they are trying to cook a coffee if you want to do this is that it happens in the same time that or in the same time that or in the same time that there is no way to say there is a time probe that is not connected to mine. So, we will see that there can exist in some cases some means of synchronization. I will come after. So, what we call a time probe, it is something which is defined only for me here and only for my course. If, in this moment, in the same place where I am, there is a person who passes, It will be this. What he calls a second, it will be this, for example. It has nothing to do with the second, the cosmos which passes here, which is another universe, is my second to me. And when we find ourselves here, to replace our second by year, for me, for example, it will take, for example, three years for the cosmos, Well, he'll be like that, and he'll be like one, two years. All right. That's something that is already true in relativity restreint, which is completely validated by experience every day,

7:30 with the rayons cosmic, the accelerators, the cosmos, the navigation spatiale, the GPS... Pardon? Oui, oui, le cosmonaute, lui, il n'a aucune... Le cosmonaute, il vit normalement, rien de spécial, il a son temps propre. Tout va bien pour le cosmonaute, tout va bien pour moi. Ce temps-là n'a pas plus... Mon temps propre n'a pas plus de valeur que le temps propre du cosmonaute. Alors, il est. Il est. Mon temps propre est. Ça dépend ce que tu entends par « est ». Oui, bien sûr. That is the time. Now, the structure causal. I want to show what we call the structure causal in relativity because it is also interesting. And in which way, it is independent of the time. So, in each point, we can demonstrate that if we have a variety and it exists in each point, we have this cone-like all the curves of the time inside. In one other point, we have a cone like this, and finally, in each point, we have a cone and all this. This structure has nothing to do with the top top, because the fact that the curves and the length are not, we don't care about it, the only thing that counts is that they are in the same direction. that is to say the whole structure of this structure, which is what we call the structure causal. If I change the metric, obviously it is defined. If I change the metric in this way, you have seen that it will never change the sign of the vectors, it will never change the genre of the curve. So if I take another metric, that is to say another curve, this curve, this curve, this curve, rest inchangé. Alors que les temps propres, eux, sont complètement modifiés. C'est-à-dire que si je remplace la métrique par une autre, ça veut dire que ce que j'appelais avant pour moi-même 10 secondes, ça va devenir une heure, enfin bon, tout est distordu du point de vue des mesures de temps propres. Donc, je change complètement les mesures de temps propres, je change complètement la métrique,

10:00 mais cette structure causale reste invariante. C'est ça que tu parles. Alors là, je reviens à la discussion de tout à l'heure. Si tu n'avais pas supposé l'orientalité, tu n'aurais pas de structure causale, parce que tu aurais des choses qui pourraient flipper. Mais ça peut flipper. Par exemple, quand tu as... Alors, maintenant... Donc ça, j'y arrive. J'y arrive tout de suite, je pensais y arriver plus tard. Ça, c'est donc la structure causale de ton espace-temps. So we can analyze the space-temps from the point of view of the structure causal. So you see, for example, we can analyze the structure of the genre-temps. In general, we can very well have the genre-temps fermé. It's to say that you have a structure causal like this. So, it's called... Alors, est-ce que tu acceptes, comme solution de la relativité générale, des espaces-temps dans lesquels il y a des courbes de temps fermé ? Oui ou non ? Ça, c'est un choix. Alors, si tu veux, justement, c'est là qu'on en arrive à classifier les structures causales. Par exemple, on va dire qu'un espace-temps est appelé causal, ou respectivement chronologique, s'il n'existe pas de courbe causale fermée. Courbe causale, ça veut dire soit de genre temps, soit de genre lumière. On appelle ça causale. Et un espace-temps est qualifié de chronologique, c'est il n'existe pas de courbe de genre temps fermée. Je vous donne un exemple tout de suite d'un espace-temps qui serait non chronologique. C'est très facile. Je prends un cylindre comme ça, où le temps s'écoule comme ça. and the space is like this. It is obnoxious to the equation of the relativity general. It is completely orientable, but almost all the curves of torque are fermées. What we call the space anti-deucitaire,

12:30 it is the same thing that it is going to deform. We have something like this. So the space anti-deucitaire is non-causal and non-chronologique. It's a perfectly possible solution to the relativity of general. The space-time Goddard is also interesting because there are no longer term fermé and no longer term ouvert. So, question, is it, in the name of a principle that we call a principle of causality fortes, je ne sais pas quoi, est-ce que l'on doit admettre ou pas des espaces-temps où des cours de temps sont fermés ? Actuellement, il n'y a absolument rien dans la physique qui suggère d'interdire ça. C'est-à-dire que des espaces-temps où ce genre de choses arrivent, il n'y a absolument rien de pathologique, absolument aucune conséquence observable Sauf qu'on peut dire qu'a priori, ce n'est pas physique. Ça, c'est ton choix. Il y a des tas d'autres choses qu'on délimine. Non, non, mais je suis d'accord. Les potentiels avancés de matchmaking. Vraiment, tout à fait d'accord. Ce que je veux dire, c'est que c'est un choix qui est ouvert. C'est-à-dire que tu peux dire que ce n'est pas physique pour des raisons personnelles à toi. Non, je suis général. Non, non, mais il y a des gens qui disent non, qui disent qu'il faut les admettre. There is even, actually, all a courant that says that the structure of the material, the microscopy properties of the material, are ultimately liées to the existence of certain curves of time, of course, at a small scale. So, if you want, it's not at all a show evident. And what we need to do is, actually, let's say, it's a debate. It is to say, if we impose on the solution of the general relativity of the spaces of time, or chronological, then there are things much more subtiles. We can call it weakly causal or weakly chronological. weakly causable, that means that we are not only allowed to be closed, but we are allowed to be closed, which, without being closed, will come back to a little bit of a village.

15:00 We have some very special conditions, because we feel that we need to admit it, for in general, and as you said, it's a lot of people to admit that it's time. The problem is that it's the fundamental idea of the time when we build and when we build the time in the physical. So you can imagine that in the mathematics, it's useful, because it's the relations that are purely formelles, that are useful, and that's what it is. But then, when we pass to what is physical, we have to discuss seriously. Yes, but to respond to what is physical, if you do a model of space-temps today, where there are things like that, first, if there are things like that, it doesn't mean that there are particles that follow these lines of time. That's it, go further. Imagine, there exist in your space-temps, and there are particles that follow this. There are books in the entier, for example, Tom, who study this kind of situation, who study what we need in Einstein's equations to make things like that be permitted and all. So, in a situation like that, you can look at the consequences observation of this machin, there is absolutely nothing which contradicts Aucun paradoxe du brouillage temporel et aucun paradoxe de l'échose temporel. Ce qu'il faut voir aussi du point de vue du bon sens, c'est que là encore, dans ces notions-là, pour l'instant, on n'a pas mis une notion d'interaction. Si on essaie de mettre des notions d'interaction, on se retrouve face au problème de définition que j'ai mentionné la dernière fois. Donc, en fait, la problématique qu'il va y avoir, c'est pour voir si on avait des paradoxes, de toute façon, on est obligé de faire certaines approximations. It's a problem which is complicated, and in this sense, it doesn't contradict the good sense, because when you talk about, for example, of the potential retarding, in general, you have a lot of difficulties to define, there are some spaces in which you don't know how to do, but in general, it's much more difficult. And if you want to emphasize something in a problem at this level, you're still facing the same problem, so it's not at all obvious.

17:30 It's not. Just to complete it, I think that everything I've said here, and I think that the last remark of Mark, that it's part of the work on the quantitæs in the expression mathématiques. The code can do what we want, because it's not the case, it's the expression mathématiques. But then, we are taken by the physical constraints it is to define what we are talking about. Yes, but wait, just one, the physical which you speak is a physical which comes from an acceptation implicit. It's not a good sense, Michel, because I think that... One particle that follows a course is a very good model to represent certain systems and it's not a mathematics. It's not a mathematics. It's not a mathematics. The question is, what Hawking appelle le principe de protection chronologique, c'est le principe par lequel il est excusé lors de la situation. La première question, la deuxième question c'est si on allumait ces possibilités, est-ce que par souci de cohérence on ne doit pas aussi admettre les ondes avancées in the first place, and we're going to say the causality there on the list. Alors, là, j'essaie justement de présenter la causalité d'une manière qui est purement spatio-temporale. C'est-à-dire, je présente ici la causalité comme, vous avez bien vu, comme une propriété de l'espace-temps purement, sans m'occuper des relations, on pourrait dire, material, physical, interactive, between the phenomena. It's a choice, and it's like that is what makes the relativity general. The relativity general distinguishes the content of the content. It's maybe a limitation which is not good, but in all cases, it's like that. So, for answering your question, if you want to distinguish the ones avancées and the ones retardées in relativity general, you can't just simply not. which is something that goes towards the future. It would mean that you can define the future chronological

20:00 everywhere in the points. So, there is a function of time. In the space of Mikovsky, a function of time exists. In many spaces of time, a solution of the general relativity exists, but there are many places that do not exist. For example, around a black trou, the space-time, if it exists, it doesn't matter, but for the moment it is part of the solution. You can't define what is that avancer retarder. And it's exactly... It's related to the problem that you mentioned earlier. You can't define it, it doesn't have a sense. I've been talking recently about the problem of the retarder of the electromagnetic classically. We've got to explain it recently, to try to define it in situations of relativity general. because the definition is not evident. I have an example of that. When we say to define a potential avance or a potential retarder, in fact, it means that we define a certain type of function. This function will be an equation of champs with its conditions at the bottom. Or, when you do that, you modify the conditions at the bottom and your problem cannot enter into the problem which is even a unique solution. So there are problems. It's not like an argument sufficient to eliminate. The problem is that when we say that we have a physical intuition, in fact, what we are saying is that the physical intuition that we have, is that we know that we have a mathematical model mathématiques qui peut rendre compte de ce que nous on appelle l'intuition physique. Ensuite, lorsqu'on essaye de raisonner sur quelque chose de ce type, on extrapole ce modèle mathématique en disant ça va contre mon intuition. Mais en fait, ça ne va pas contre l'intuition. C'est pour ça que je dis que ce n'est pas simplement une histoire de représentation mathématique. C'est que pour aller plus loin de cette intuition-là, on est obligé complètement de sortir du cadre dans lequel on voit les choses. Donc on a, en quelques Or, just the math, at this moment-là, we say that we can't do this extrapolation. So, in fact, if we try to answer things out of a case, I would say, if we look at a good sense, the good sense, if we look at these extremes, we say that this good sense, from the point of view of the translation in the theory,

22:30 is a good sense local. If I want to translate this consensus from a global point of view, for example, with an experience of thinking about the potential retarding and things like that, I am embêté because I have no traductions mathématiques who allow me to do it. This is a consequence of the fact that the general rule means local. And if you want the global rule, you are obligated to impose. So, like the relativity general gives a certain structure of the space-temps, a very great liberty. A priori, you think that you are too big because some solutions are going to your sense. They are going to your sense of Michel Paty. So, you have two solutions. There is no sense of physicality. There is no sense of physicality. There is no sense of physicality. Yes, but just... It's exactly the wrong sense. I'm sure. So in this case, you have two solutions. You arrive at a prediction which offers the good sense. For example, Einstein... So, when you arrive at a prediction which offers the good sense, you can say, or maybe I refuse and this, I would say, it's Poincaré-Lorens at the end of the Matthew of Cech, or maybe I put in cause my good sense and it leads to something new. Let me finish. You have a good sense. And the sense of physical, it's not a good thing. Well, I'm not a good sense. And I pretend that it has a sense of physical and even very strong and strong. Just a question. You are very partisan, Michel. What is there, like, an experiment possible to detect this kind of thing? Well, just a question. what is there as an experience possible to detect if this kind of thing exists or not? And what kind of consequences can it have in the physical? It's to say, what can we say about the existence of the four fermées? Before I say that, I'm going to talk about the problem in two. It's to say, I consider this part where the particle, in a way, is that in a way, I've already talked about it here. L'affirmation, une particule remonte dans le temps. Quel moyen a-t-on de s'apercevoir si c'est vrai ou pas, ou si rationnellement ? Réponse, aucun.

25:00 C'est-à-dire, là, du point de vue physique, l'idée d'une particule qui remonte dans le temps ne viole aucune expérience, ne viole, à mon avis, pas le bon sens non plus, enfin en tout cas pas le mien. Donc, il n'y a absolument aucun problème. And there is absolutely no problem to imagine in particular that. That's a question of orientation, I agree. But here, there is still a difference topological. Of course, that exists. If you want, that will exist. You say that it doesn't contradict, but is there evidence positive, that you can say that this thing exists? For the moment, it's not possible. This thing is completely admissible. Nos viols, to my opinion, have no sense nor observations, but you can choose to refuse it. What is it that you do when you do something that is only admissible without a sense of observation? No, but it's the question. What type of physique? Well, it's what type of physique. And I'm going to bring you to the end of the 19th century where you have something, a problem, etc. it was to abandon the time and space, to replace it by something else. You would have to say, it's contrary to the good sense, I refuse. But if you admit it, you would have something new, which was the reality of the same. Here, in this moment, there is a lot of reflection on the role that could play. And if you want, there are people who say, what is a particular element? How do you see that? You know, there is a lot of people who try to interpret the material, what we call today material, as a sort of nœud, singularity in the geometry. Is it just something like that, it is not a good candidate to describe the material, the foundation of the material? Well, it's an open problem, I'm not going to arrive, I don't know anything, but it's an a list explorée, interesting. At the moment, in relativity, yes. But everyone thinks that the relativity is only a version provisory of the physics. So in the ultimate version of the physics that everyone seeks, maybe it doesn't exist, but I don't know. But from our side, one thing I would say is that if there is a ultimate version of the physics,

27:30 it will be contrary to what we call today the physical sense. There is something that we are today evident, which will be violated. I don't know what, maybe it's the return of time, the conservation of energy, I don't know. But if the particles are in the future, there is no separation between the contents and the contents. Yes, yes, that's what I want to say. I want to say that today, everyone seeks a new theory. And among these new theories, there are many who seek to reduce the substance of the world which is today distinguishing between geometry and content, to reduce the one and the other. That is to say that the particles are in fact the singularities or the noeuds of the geometry, or to say that the geometry does not exist, but that the relations between particles, that is the relation relation. Well, I think that at all, if we reduce everything to a single substance, it would be something to unify. And what we call it a geometry or particle, if we arrive at a single substance, it would be the same. So, in this program, suppose that we are interested in the program to reduce the particle to a geometry. It would mean what? It would mean that we have to consider a sort of singularity, or a nœud of the geometry, which have properties of stability, which make us consider it as particles. So, wait, wait a second. So, for a long time, people say that it should be something of topological. Because first, a topological structure in an space is something stable. For example, if I have a torque with a trou, I can deform it as much as I want, the trou will stay. So this is a sort of, when we are at 4 dimensions, we will have a singularity topological, it's something stable, and so these are good candidates to represent the particles. In addition, if I have a trou and an anti-trou, when they meet, it will give another thing. So, we feel something there would be nice to describe the particles. And how to have, at the level of microscopy, the topological structures well defined and stable? Well, there are many people who think that it should make intervenir the curves of jantan fermé, for example.

30:00 It's one of the hypotheses, and it's true that it's very efficient, but it's not even physical and physical. Yes, it's very efficient. In fact, at the point of view mathematical, it's a sort of an acronym, it was a continuous content, because since Gauss, I believe, it is something that does not exist in mathematics pure. Of course, it is not sufficient in mathematics pure, but... Because each continuous, you can look at it as an space geometrical, with its own intersect, Intrinsècle. Intrinsècle, c'est-à-dire cette idée de l'espace comme un contenant contre l'esprit des humectes et des manières pour ce qui est de l'espace, pour ce qui est de l'espace. Aujourd'hui, il existe des moyens d'interpréter la relativité d'un point de vue comportment relationnel. C'est-à-dire, ici on décrit tout en termes d'espace, temps, variété, mais il existe une propriété qui s'appelle la covariance, qui est en fait l'invariance ou le difféomorphisme, et finalement tu t'aperçois qu'en relativité, bien sûr on passe par ce genre de dessin en général, but when you do the measures of time, of space, of angles, of anything, in fact, it leads to things purely relationnels, that is to measure a certain field of material compared to another field of material, even if this field of material is called method. So, in fact, you have already, to interpret the general relativity as it is, from a point of view purely relationnel, by eliminating all the geometry. And when we read Einstein, it was already a point of view, it was forgotten, it was never, it was never, it was never, it was never, it was never, it was very rarely presented like that, but there is today a way to look at the relativity as relational. And if you read the book of Rovelli, it's exactly this point of view that he has. And what is the interest of doing that? Well, there is an interest in it, it's that it allows to quantify it. Because otherwise, why quantify the relativity? Well, today, all the physicists are a bit unsatisfied with the physics, because of the one hand, we have the interactions that are quantified, and of the other, the interactions that are not. and the other side of the quantic, we have an space-temps that we can't consider as dynamic,

32:30 and the other side, yes. So everyone would like to synthesize that. And one of the ideas that is very interesting, it's to quantify the relativity, to quantify the gravitation. The problem is that when we quantify things, today, we quantify in space and in time, with a time and space well defined. But there, you see that space and time, it's not defined. So how to do a quantification without having this one? Well, one of the possibilities is that if we have a description of a relation relation, we would know, and we already know, we have a theory of quantification, we have a version of the quantification of the relativity general, we would know how to quantify all these things, when we have only the fields that are... There is no evolution in the time, there is no evolution in the space, there are only relations, that is to make sense of coincidence between the champs. By convention, by commodity, there is one of the champs that we call horloge. So if we have an ensemble, even non-ordonnée, between the horloge in a position 1, the horloge in a position 2, I can write in any order, the horloge in a position 3, like that, with my system in position X, etc., well, that, if it is a story, there is no time there, it is an ensemble of coincidences, and finally, we realize that we can reconsider all the physics like that. Just to emphasize that the problem at the level of the certification, it is not that at the beginning, it is not that at the beginning, is that we want, and also for the technique of the quantification, but we want to quantifier in preserving the covariance of the theory. It is to say in preserving the fact that we have no observateurs privilégiés par rapport à un autre. And that, it is something that we don't know, if we are in a space space temporel fixed, it is something that we have So there are also theories that they do, but the problem is that the base is the but of this way. Yes, go ahead. I think it's clear. But my question is, is that we can talk about it or something else?

35:00 It's what we do already in physics, in theory quantique, in the aspect of the history. If we talk about coincidences like that, we have a suite of coincidences, so that implicitly it is construed in a form. It's an horloge. Yes, but if you want to talk about it, if you want to talk about it, you want to talk about it. You have chosen a certain system like an horloge. That's going to be clear in what I'm going to say. Because now, I think you have seen that each variety is associated with a structure causal. which is defined by the intermediary of the matrix, but not only by the intermediary of the matrix, but by the intermediary of the class of all the matrix which is related to each other by a transformation which we call transformation conforme. That's why in general relativity, structure causal, the same as I defined here, is equal structure conforme. And what's interesting is that there is a theory which is called Arthur H. Weig, who suppose, who rajoute a sort of ansatz to the physics. The physics is invariant of an echel. Can we build a physics invariant of an echel? Yes. Weig l'a fait en 1917. It gave him the opportunity to introduce a quantity called a connection, which has played a great role. but what is interesting is that when we have a structure, if we want to construct a physical variation of an echel, finally, it means that if we replace, change the echel, it means what? It means change the length of everything that exists in the universe. Longueur and duration. It means multiply the metric by a number. So, we introduce precisely There is a new invariance in physics, a variance of the scale, and this invariance will be the action of a certain group, which will be either the group of dilations, or, if we want to be larger, the group of conformes. All this has been done very properly by Weim. This gives a great theory, and a theory where we have not only a structure Riemannian, a structure metric, but a conforme, which is something more large. And there's something very interesting. I'll take five minutes to talk about it.

37:30 Because when we make a measure temporelle, what do we measure? In fact, we don't measure time. I make a measure temporelle, I measure the time we need to go from an end to an end, well, locally, let's say for three movements. So, during my turn, I make three movements of my arm, so I will say that it takes a third of a second. So, what do I do? To measure the duration of seconds, I call it delta t in seconds, I measure the proper time that I need to do this movement, I call it delta t if you want, and I divide by the amount of time that I need to do a tour, which by convention is called a second. Now, suppose that I multiply my metric by a certain factor, which means that the duration of my movement is multiplied by this factor. But the duration of what I call a second also. So, finally, all the measures of time, what we call measures of time, it's not a measure of time, it's the same for the length of time, it's the measure of a duration divided by the duration of an etagon. what we call the zone. And that has been marked, obviously, for very long time. I think already, I think, in the 17th century, there are some texts. Pardon? In the 18th century. So, it's well known. And all this code, absolutely, in saying that if I multiply the metric by the same number, it doesn't change anything. The problem is that, when we talk about transformations conformes, we multiply the metric by a number Alors, est-ce que ça a une importance ? Ça a une importance, oui. Si je compare une durée que je mesure chez moi à une durée de la seconde qui serait ailleurs, est-ce qu'on peut faire des choses comme ça ? Ah oui ! Regardez, j'observe, je suis là, j'observe une galaxie loin dans le passé. La galaxie, elle a une horloge. Il y a des horloges dans la galaxie, c'est quoi ?

40:00 C'est des atomes. Pourquoi les atomes sont des horloges ? Parce qu'ils émettent. Frequence, c'est l'ensemble des périodes. Je vais parler en termes de périodes. Un atome, je peux le considérer comme une horloge qui émet un tic-tac toutes les fractions de secondes. Disons toutes les secondes. Donc, j'ai un atome dans ma galaxie qui émet un tic-tac. C'est le signal électromagnétique correspondant à une respectrale. Je mesure la respectrale ici. Cela veut dire quoi? It means that I measure this duration, and I compare it to the same thing, the same atom, which is the same thing. And what do I find? Well, I find a difference. I call it a redshift. I find a difference in how I interpret it. I interpret it in general, by the expression of the universe. But I can say that there is a function omega-2 here, which has a certain value, such as the rapport omega-2 to my position on omega-2 to the galaxy, which is what I call the redshift 1 plus z. This interpretation stays completely. So I can very well interpret, it's what would say the law of the grand monde, instead of saying, Yes, you suppose that you have a function omega-2, there are certain values in the universe. And what you call expansion, you can very well interpret it in saying that the second varies, finally. The second varies with the time, I don't say that it's economic, that it's elegant, but it's absolutely equivalent. And if you want, it's a physics, at this point, a variant of scale. It's the realisation of a physics in a variant of scale. And, in a certain way, it's equivalent to an antigen. It's less beautiful, it's less elegant, there's not any equations that are so nice. There are still problems with the mass, or something like that. The mass? Yes, but it's a problem, except if you think it's integral. I'm not going to go into detail. The theory of Veil, which was proposed by Veil, was contradicted immediately by Einstein. Why? Because the idea is that if you take an atom, you make a bubble in space 100, that means that the frequency of this atom, because it makes a bubble,

42:30 in virtue of what we call the synonyms of the collection, but it doesn't matter, it doesn't have the same frequency. So it doesn't work because we know that in the same place, the atoms have this. So we replace the theory of Veil, what we call the theory of Veil, an integral, to know that the connections that make the transport have no longer power, and it ensures that when you do the transport like that, fermé, there's no variation. version affaiblie de la théorie de Vey, qui est effectivement la seule compatible avec l'expérience, mais qui permet quand même encore ce genre de choses. Bon, c'est un peu une curiosité, mais c'est pour vous dire quand même qu'on peut aller encore plus loin dans le débarrassage du temps de l'article général en remplaçant le temps par quelque chose qui est le temps Well, I'm only talking about the time-propes here. Now, to finish, just, I wanted to see... We talked about the time-propes, which is something very local and very personal, but we would have a desire, of course, to find something in relativity which are the properties of the time normal, to be able to say that there is something in this moment, and even in the galaxy, to be able to synchronize the environment. So it's interesting to see in which conditions and how we can do that. First of all, the time-propes cannot serve this. Why? Supposing that I am here, I have my time-propes which is like this, and I would say that I would like to take the time-propes as a measure of time in the universe. I observe a galaxy which is there. How do I observe? There is a rayon lumineux here, and I can say that to measure chronologically, to measure chronologically my galaxy compared to me, to define a time, I will take the time proper. The problem is that the time proper along this thing is zero. So it would mean that the galaxy, when she has a rayon lumineux at 14 milliards of years, but I would say that it is contemporary, it is in the same time as I am. So the time proper cannot serve as a basis to define something

45:00 that would be the propriety of the time. So it will have to find another thing. So we can see that in Relativity, we can define... Well, here it is, it's a little bit, but... On a plusieurs procédés qui permettent de définir du temps dans l'espace-temps. Qu'est-ce que ça veut dire définir du temps ? Ça veut dire, en gros, couper l'espace-temps en tranches comme ça, et on va dire, chacune de ces tranches-là, on va appeler ça des tranches à temps constant. Bon, en général, on ne peut pas faire ça. For that we can do it, it is necessary that the space-temps has a condition that will be hyperbolical. What is the condition of global hyperbolicity? It means that there exists in the space-temps what we call a surface of Cauchy, C'est-à-dire une surface telle que, une surface causale si vous voulez, une surface telle que quand on prend des conditions initiales sur cette surface, toutes les équations différentielles d'un certain type aient des solutions. Donc si l'espace est globalement hyperbolique, ce qui est une condition supplémentaire qu'on impose, à ce moment-là, on peut faire une foliation comme ça. There are a lot of solutions to the relativity general that do not verify that, including solutions for today to describe the space-temps. So it is something that we cannot do in general. In other hand, for a solution enough simple, we can do it. When we do the cosmology, for example, the space-temps real, maybe there are no black objects of objects very passive, which make the structure of space-temps very complicated and in all rigueur, we can't do that. But when we do the cosmology, we don't forget the details, we're going to fix it. And finally, the solutions cosmology of the rest of the general, they are relatively simple. Why? Because we say, we demand, in a row, that it is a large scale, isotope, what we call the cosmology principle. It's a contrainte that we make. And if we have a space-time very simple, of course, we will be able to do something like that. The problem is that we can do it in several ways.

47:30 We choose one, why? Because, even in virtue of the cosmological principle, which, of course, will greatly restrain the solutions to the reality of general, the cosmological principle tells us that the space is homogenous, that is translated mathematically into that the space-temps has the sections spatiales to maximum asymmetry. So these sections spatiales to maximum asymmetry, because they exist in virtue of the principle that we have imposed, we are going to choose, it is to say that we are going to do a foliage of our space-temps by these sections-là. It is quite natural, since they exist, we are there, because they are there, and we are doing this foliation. And we will name it to space, and we will numerate it by a function, which we will call a function temporelle. And in addition, we will choose the function temporelle in a very astuce, that is to say that we will imagine here an observator, the observator terrestre, this observator has a time-prop, and then we will choose the time-prop of this observator as a function temporal. So it is very practical because we just define a function of time, which is valid in all the universe. We define what we call the space, and this time-prop coincide with the time-prop. We call it time-prop. who are there, are in Europe, they are not at all at all with that. Other restrictions, just, I finish that. Now, I can tell you that I am here at the value of the time cosmological, let's say, 13,5 milliards. Now, we have all the points in the universe which is at the value of 13,5 million dollars, the same value as for me, in the time cosmic. And I say, I'm interested to know what's going on in this moment, for example, in the galaxy Andromed. The galaxy Andromed is the long of this year. So, here is the galaxy Andromed, here is its story. There is, in general, one way and one way of defining the synchronization.

50:00 It's Einstein who showed that, quickly. I'm somewhere, and I wanted to know what happens when something happens, at the moment of my anniversary, what happens in the galaxy? How to do it? Procédure, j'envoie un signal ici, en supposant qu'il est réfléchi tout de suite, donc je l'émets à un instant t1, je l'émets à un instant t2, et par convention, je vais associer à ça un temps t, tel un temps t, qui est la valeur ici au temps t1 plus t2 sur 2. d'accord, ça paraît logique c'est la procedure de synchronisation d'Einstein on s'aperçoit que tout ce que l'on peut faire en termes de synchronisation dans la pratique spatiale et tout ça marche comme ça et finalement on s'aperçoit aussi que on n'arrive pas à inventer c'est ça qui paraît naturel il n'y a pas tellement d'autres moyens de synchronisation donc si je calcule if I calculate in the space-temps what are the events which are contemporains the problem is that I will find those events that are not at the same time cosmological as mine so it is to be afraid this time cosmological is not a function of the type temporel which is defined in all the universe which has certain proprieties but it is to be afraid because the events at the same value of the time cosmique contemporary events, simultaneous, in no sense of the term. It is to say that we are always, well, always, with certain conditions enough simple, we are always able to define things that have a certain propriety of the time. For example, here, a time which is called, it allows us to define a certain chronology, but two events simultaneously in a sense, practical and physical, have not the same value of this time. So, there is no doubt, and we always have to do things, but what I wanted to say is that we can define, in relativity, there is one thing which is so well defined, it's the structure causal, a space-temps is defined, the structure causal is defined.

52:30 She also defines the temporal, but which is not valid individually, subjectively and locally. In some cases, in some cases, we can always define the temporal structures, They have notions that have a temporary character, such as simultaneity, chronology, etc. But, attention, they are not, they have never, all the proprieties that we would like to add in time, they have relations, you see, they are independent of the structure causal. And finally, we realize that we can even, since there is an invariance conform, on can define the structure causal, even in the conditions where it is impossible to define a time, even the time-prop, because if I say that I have something that will not be a variety rimanian, but a variety conform, I have no metric, I have simply a class of metric defined at a constant près, so I have not even a time-prop. not only I don't have a function temporal global, but even at the level of individual, I don't have a function. However, I have a structure called the structure causal, which is defined. So the idea, and I will end up here, that, finally, the structure causal, is still what is the most fundamental. So, when we want to, for example, quantify or prolong the relativity general, On s'aperçoit que c'est très difficile. Pourquoi ? Parce qu'on a trop de choses et, entre autres, ce qui nous gêne, pour des tas de raisons, c'est le temps. Donc, point de vue possible, puisqu'on arrive à définir une structure causale indépendamment de toutes ces fonctions, de toutes ces histoires de temps qui nous embêtent, Prenons, faisons l'hypothèse que ce qui est fondamental dans l'espace-temps, dans la physique, dans la reactivité, c'est la structure causale. Et oublions pour un moment le problème des mesures de temps et de durée, essayons de faire la physique avec la structure causale, And at the end, if we can quantify it or do something new, we can ask if we can find the time or not.

55:00 So there is an actual branch of physics that says that we are going to take a causal structure, formal, and we will see what we can do. What is the structure causal? What I did not say is that when we have an expression like this, between two events, there is a relation that is, yes or no, there exists a curve temporal, or a curve causal between the two. So if there is a curve causal between the two, since we have an orientation temporelle, we will, by definition, or by convention, we will call something future and future, or to be more known, if we are A and B, and we will say, if it goes in the sense AB, we will say that P is greater than Q, and if it's like this, it's not like this, it's not like this, it's like this, it's like this, it's like this, and it can also be in the position where there is no relation causal between Q and P. Well, all this means that if I consider all the points of the space-temp, other than all the events, it is a relationship of partial. The relationship of partial, it is well known in mathematics, so, hypothetically, a structure causal, it is an ensemble partially ordained. So, what is it... Now, all the conditions that I have talked about earlier, There are many others. I can now transcribe them in the language of the partials, or in the language of the categories, since the categories are perfectly adapted to describe the partials. So, I say now, an espace-temps causal, it's an ensemble partially ordonné. What can I do with an ensemble partially ordonné ? In the same way, it's also the same thing that a topology. It's also the same thing that a logique. Because that, I can consider it as an implication, so it defines the rules of logic. There are lots of points of view, but it's very rich in the structure.

57:30 And what can we do? We can obviously quantify that. It gives us what we call the Spine's reasons. It's very interesting. What does it mean to quantify? That means that we replace, if you want, the relations of order, which are there, by operators. And these operators... We're going to take the quantifier the most element that you can imagine. It's an operator of spin. And so, we're going to define something called the space of spin. Well, it's not done by this point, but it's done by itself. Another interesting thing is that I'm giving an ensemble partially ordained. So what is it? C'est un ensemble de points, et puis entre certains des points, il y a des relations d'ordre, mais entre d'autres, non. Question. Si j'ai quelque chose comme ça, quelles sont les conditions que doit vérifier ce machin pour que je puisse définir quelque chose qui ressemble au temps ? So why can I define what we call the chain causals like that? In which conditions I can define, along these chains causals, the functions that will correspond to what I have the habit of calling the time-propes, such as there is still a condition of compatibility, when I have these chains like that, etc. In which conditions I can define the functions that will allow me to say these events, these events-là, are simultane or intérieur, these functions of time. which I find very interesting, I work a lot, so that I'm interested, but it is to ask the question, when we have a causal structure, taken from this point of view, well, it is defined mathematically, it is a definition, I don't say that it is that, but in this sense, a causal structure is something that is defined, is defined, in which conditions, from this structure causale, we can find notions which are temporal, which is a temporal, a possibility of synchronization, a possibility of chronology or things like that. And so, it's a very active branch, and also, the intérêt, it's that it's something that can be quantified more easily than a variety. The idea is, of or something like that, if really the reality is that, when we look at it with a little

1:00:00 bit of a flou, well, of course, we will find a variety. And if it is quantified, well, there is a relationship between these operators which will be related to non-computation, so there is a link to everything, obviously, with the geometry non-computative. And what What's interesting is that these new ideas are coming out. We see that all the interesting tools of mathematics, which have been developed, like the geometry of the commutative, the categories, the logics, the fibres, etc. Finally, the new structures on which we arrive, we can consider it from all these points of view at the same time. So we have a very rich mathematical arsenal which allows us to attack that. Obviously, there are a number of interesting results which, for the moment, are mainly curious. But when there are curiosities mathématiques which accumulate and give a kind of image, we can say that maybe this image is a configuration of a future reality. Two little remarks. I was struck by the vocabulary here, to see that at the end of your speech, you return to the words like category, substance, etc. Wait, category, it was in another sense. It was in a mathématic. But... If you use the same words, when you want to see it, you return to the vocabulary, it's on the vocabulary, For me, in the world, there is a substance. The question is to know if this substance is geometry plus matière, plus, I don't know, energy noire, what you want, or is it all reduced to the geometry, or is it all reduced to the material, or is it that everything is reduced to something that we haven't done yet, and that we call matter, in a certain case, geometry? And it's exactly in this problem. One of the great results to do is that the oxidation of the water is not neutral. Evidently! Dès qu'on fait de la physique...

1:02:30 Attends, mais moi, je me situe tout ça... Just to... I'm going to sit in a line that starts by Heinrich, which starts by Heinrich, by Marx, by Einstein, and by others. I have a remark on Rénaud. There is something that, in my sense, is impossible to do, which is that, from the moment you are doing research in a domain where the concepts are not yet elaborated, Obviously, there are no words to design these concepts, which is why they are vulgarizing, that is to give a representation which is, I would say, close to what we have described without being exact, these words do not exist anymore. The concept does not exist anymore. And all the problem, I would say, of the vulgarization, in a noble sense, The most noble of the research is that we can't, in any way, with enough precision, because the concepts that we are talking about are not defined with enough precision. There are no techniques. There were a few years ago I had to read a book of messiah, messiah was entered in the retreat, and he had a book on the cosmology of the universe. And there was a book that I had a lot of plu, and I didn't have the impression that I found it in what you said. It was to say that he defined what he meant as an observator fundamental, which is in movement with the expansion of the universe, and he said that if there is a certain observator, all the observators who are like this live the same history of the universe. How can they be considered the same cosmos? That's what I said. The observator that I took here, I suppose, but it's very technical to define this, C'est-à-dire, un observateur, j'ai oublié de le dire, définit naturellement une direction temporelle, qui est la direction de sa vitex. C'est-à-dire, pour un observateur, sa ligne d'univers, c'est le temps. Ensuite, localement, dans l'espace-temps, tu peux définir le complément orthogonal de cette direction. C'est ce qu'on appelle l'espace. Mais c'est défini localement. Après, tu peux le prolonger comme ça, tout comme ça, tu ne sais pas.

1:05:00 If you have a surface of constant courbures, you can, theorize, there is a family of observators that are orthogonal to all the surface of constant courbures. So what you call this famous observator. But it's totally artificial. So you have selected that. And I repeat that for these observators, for each one, the cosmic time is the time. But for me, the simultaneity, still, is not quite appropriate. So, I think it's these observators that I have taken, but as it's technique, I have left my definition. Would you agree to say that if we want the relativity, we have no hypothesis like the principle of psychology? Yes, yes. Well, I don't have to worry about what we need to do. Oh, it's to say... I don't have to worry about it, even the causality. Ah, yes, the causality. You give me a variety, but the causality, I give you one. Yes, it's true. Yes, it's true. Yes, because the causality, it's that. It's between two points, I know if they are or not liable. The question is, is we have to do these expectations in the world? The principle cosmological, which is necessary for us to have a cosmological perspective. And in this case, does it allow us to find the cosmological perspective, or are we going to find the cosmological perspective, or are we going to find the cosmological perspective, and we develop all the possibilities of the world? That's the question. But the concept cosmological, if you want, for me, it's not even a hypothesis. It's rather... The cosmological perspective, it's a particular regard that we have on the universe. For example, if I look at the Earth, I know there are mountains, there are valleys, etc. But, globally, I would say that the Earth is round. That doesn't mean that I make an hypothesis that it is really round. I would say that I look at the Earth. Yes, but what I'm saying is that I'm saying, and I'm listening to the first time, and I'm listening to it, and I'm listening to it, it's that the general relativity doesn't allow me to trancher between the different hypotheses, the different solutions that you've mentioned about the substance.

1:07:30 It's to say, if we take all the general relativity, then we can say that the geometry is pure, or the geometry is pure. it's the geometry pure. On is obligated to make the material. In other words, we can say that it's only material. You can consider that the field gravitation, that you call the symmetry, is a field that makes part of the collection of the material. And when you say, you see an event in relation to the geometry, in fact, you see it in relation to the geometry. It's to say that you see it in relation to the geometry. And it's to say that you bring everything to represent the champs compared to the others. You bring everything to the coincidences between the values of champs. It's true that these values of champs you represent by the points of space-temps and from this point of view, if you want, the points of space-temps are a role in a kind of system of coordinates that you use by commodity but that doesn't exist properly. There is no difference, there is no difference. And when you read Einstein, he was already... Yes, he was already... But he was already, more or less. And he was often in the mess... ... when you see the mess... But it's not the mess... It's not the mess... It's not the mess... Well, I don't talk about the problems of singularity, etc. But that's another thing. You know that we have an expansion model, and when we try to produce an expansion in the past, if we take, say, a family of solutions that we have some reasons to take because the material had a certain proprietor, we arrive at a singularity, that we had called Big Bang, and the people, during the last century, have been enormously overwhelmed because of this singularity. on essayait de léviter et tout sans succès. Aujourd'hui, qu'est-ce qu'on pense ? On pense qu'on arrive ici à des zones où la courbure est tellement forte qu'on ne peut pas appliquer la relativité. Si on rentre dans le domaine où la gravité doit être décrite de manière quantique. Donc, les solutions, tout le monde pense,

1:10:00 almost everyone thinks today that the solutions to the models of Big Bang describe this part-là, but that part-là, we can't describe it until we don't have found a quantum version of the gravitation. So, there are a lot of people who say that already, they have already advanced in the quantum gravitation to be able to describe it. For example, HTK, with their gravity in a group, they start to say that they can apply here these operators of the geometry of geometry which allow them to understand perfectly what happens at a moment like that, without singularity. So it's very controversial, but it's very interesting also. Question about the time cosmology, because it seems to me that in a certain sense, it's, how to say, it's an attempt to reintroduce In some sense, it works very classic. Of course, it's the idea. The time, the object, it doesn't exist. But we have so much the habit of reasoning with the time that, when we do the relativity, we try, in a way, to reintroduce the notion of the object. It's a bit like, in physics, we know that the particles, it doesn't exist. But we can't stop using these notions that we have so much the habit. fundamental or just how much you think? Dès que tu fais de la cosmologie, en fait, le temps cosmique, c'est quelque chose que tu utilises tout le temps. C'est tellement commode. Mais attention, il y a tellement de contresens possibles puisque ce n'est pas vraiment un temps de simultanéité et tout ça, il faut être très prudent. Donc moi je dis que les étudiants, si tu veux, je leur dis n'utilisez pas ça. Vous l'utiliserez le jour où vous aurez bien dominé la question You immediately do the contresens. You do it as if it was a time, and then you go on a thing erroneous. I'm completely agree with that, but just to come back to a little bit earlier, I think you would agree with that. What do you mean? It's not necessarily the time that you use when you talk about the physics that you use. When I talk about the physics, I don't use the time. There, there's no time for me. There are some time. There are some curves, there are some curves, I have to say here, I have to say today, the time is something that is not defined for me in relativity. I agree that in some cases, we can restore something that will remind

1:12:30 what we have used to call the time, but again, once again, it is always dangerous. To reintroduce, reinterpreter solutions to the general relativity with terms, say, newtonians, like the time, the time, the time, the time, all of that, often we can do it, often it's common, but it's always extremely dangerous. The contresens is always there. It's exactly like in the physics quantic. You say that the particles are there, they are there in the same time. It's a question, it's what we abandon. It's not true. It's not true, it's not true. But the vocabulary exists already. Wait, wait. The vocabulary exists already. All the words that I've used here, the curve temporelle, the curve spatial, the curve of the time fermé, the time proper, it's perfectly defined. When you're talking about the universe hyperbolics, you say that the time is cool like that, and that's why it's incert. Well, wait, wait, but what's it going to say to you? It's not going to respect the universe. When I'm talking about the universe, I don't know if I'm talking about the universe, There are curves of the time, that's what it means. That's all, there's nothing else to say. We'll come back to the debate a little earlier. We'll come back to the pause. Just with the question, when you talk about the space-time, you said that it was quite well with the topology. Yes, yes. So, that means that the topology is rather the character? Yes and no. It's not the same thing. Is that, finally, I have the impression that the big debate about this affair of the court or the fletch of the time, is that it's a local property or is that it's the local property of a global property? That's what I have to say. I think that's what I have to say. I think that's what you call the fletch of the time. I don't think that's the same thing you said. The course of the time. The course of the time. For me, there is no part in the course of the time. The question... The time, but there is a single course of the time. You're going to tell me if you agree with this one. Wait, listen. In each point, there exists a cone like this.

1:15:00 In each point, I can, if my space is orientable in time, future, past, which will be continued in every space. Is this choice you call the course of time? In your sphere, you have to call the line, you have to call the line, you have to call the line and you have to call the line, and you have to call the line You have a vector like that, which has a component X0, which can be positive or negative. So it is called the future director or the base director once you've defined the future and the past. If you don't have any other, you don't have a P in the sense and a F dans the other. Everything is connected to the same way. I don't know how to do it. It's not the only thing you want to do here. It's not the only thing you want to do here. It's defined in the same way. You can boucler. There's no orientation global. No, it's local. But what you want to do is to say that in all points, there is a procedure that allows to talk about the future and the future. Here it is a pure convention. That's to say, what does the relativity mean? It's that there is a choice possible that is coherent globally. Localement, in all points. But localement, in all points. What does the relativity mean? At any moment, the relativity is obligated to make this choice. I want to call the future and the past, that's why I call the A and B. So there are the vectors directed towards A and directed towards B. I call it conventional. If you want to call A future and B past, no problem. If I prefer to call B future and A past, no problem. You will describe exactly the same physics. Sauf that for the one, the Big Bang is in the future, If you want to have A and B cohérents between them when you take place, then you have a condition global. So, it's happened two times. What? It's happened two times. It's happened the first time when you eliminated the organization. It's happened the second time when you introduced the organization. And that's it. It's happened the second time. It's happened the second time. No, no, no. Because the time that we live, it's not the condition that I impose on the last time. No, no, no. It's a commodity that I give you to be able to talk about it. Yes, but that's artificial.

1:17:30 It's artificial. If you have no idea that the relativity is the theory of cosmology, you can. Well, we could try to understand, for example, the cosmology. And so, I think that the fact of the totality, the totality in cosmology, what happens, for example, Well, what I wanted to say in my exposé today is that there is a notion of flèche of the time which has been written by Genman in the book of Jaguar, which is an excellent book. He said that there is a large flèche of the time, which comes from the truth of humans, and that in the past, the universe was in a state quite determined. while in the future, it is in a state of total indifference. I don't know what to say, the word determined and indifference. If you define it, I would say that. No, no, no, it's defined with the function of the cohesion scientific. So it's something that I'm going to say. So it's... No, I'm not so sure. It's a condition initial, which is a condition of low entropy, essentially, that you are in a state high or low equilibrium and a state of low entropy. At epsilon près, the entropy of the universe, in particular, is strictly constant. The variation of the entropy of the universe is epsilon. You take an initial state, but in the future, you suppose there is no predestination. Because if you were doing the contrary, you would have an event that would be exited by the condition that you gave in the future. And that, in fact, there isn't. And so this condition is global, it can intervene the past and the future. And it's that, after him, it's that the financial issue. So, I have really the impression that... It's going to be reflected in a local property, of course, because we have to see this, this fledge, we have to see it locally. To answer, just to answer. I don't think it's the bordel of cosmology. I don't think it's the future, it doesn't mean it's the future.

1:20:00 I forgot a moment, I forgot a moment, the language relativist, I forgot a moment the language relativist, I forgot a cosmology with the cosmic time, as if it was a normal time. I don't know what I'm going to say. So, to start, thank you Marc for inviting me. I wanted to talk a little bit different on the theme, both on what I wanted to talk about, and also on the theme of the language, I have not been able to do this part of the second part of the exposé. So, I will do it, I will take a look at the exposé, which is there, you can see, It's an exposé, not at all misageable, but still there. I'm perfectly sure what I'm going to say. It's an exposé on the time. I just want to say that this is a time that is not known, which is related to the non-community. And I want to point out all these stories. I will start by you exposing the introduction and the conclusion, and then in the formalism. because there is in the middle of a complex mathematics that would be necessary to understand the conclusion. So I will actually do two times the same conclusion. One time at the beginning, one time at the beginning, one time at the beginning. And then the second time at the end, where they come from.

1:22:30 So, as it is of coutume to begin by the poésie, I begin by the very great poésie on the time. The two words the most important that you are describing in the 20th century, the time worships language and forgets everyone like the most lips. And, well, the aspect moral, the forgiveness, is not exactly an intérêt to remember, but it's the aspect-là, the liant between language and language, and language compris in a sense quite particular. This is what you will see, this is what you will see, this is what you will see, this is what you will see. This is just a title of the paper. We are going to start and here is the plan of this exposé. So, as I said, we will talk about some of the problems at the beginning of the time. In this room, it's not as necessary as it is because it has been developed several times. what are the problems, the different temporalities and the problems that we have done. However, I will quickly move on to this first part. I will then go directly to the conclusion of the third part, without even exposing the second part, which is the first part, in the way to present the result of the principal result, which will be already complicated

1:25:00 as a conceptually conceptually. And then, if it's possible, I will, at least, try to return to this conclusion by the way that we are proper and the way that we need to take, that is to expose the formalism of the Sanjeev-Franci-Etoile and Fogelman and Fogelman, which is behind. So, for you to situate a little, You came here to hear me on the basis of the basic notion of the mechanism of the theory in the theory of the theory of the theory of the theory of the theory, this morning I was talking about the basic notion of the basic notion of the theory of the general theory. There is a formalism other than... If I... There is a formalism other than the formalism that you have seen which allows to place in the sense of a way a way to formulate the theory of the concept, and a certain way to formulate, when we talk about the reality of the general, in general, we have a certain version of the theory of the space-temps, and it's the formalism of the Algernon-Céphalus that we are interested in. But to start, I'm not sure. I'm at this first part where I pose just a few questions about the time. And the first question very interesting when it comes to theory. It is, for example, to note that the time in which it comes to theory, this time is not at all a physical which interests us. It's a parametric, a little bit too paramétrique, and one of the manifestations irritant of this fact is that in a mechanical quantic, the order of the which, for us, is an order temporalisier,

1:27:30 between A and B, and between A and B, there is a certain point of view. The order of the measures can be different from the temporal, from this variable T, which is the temporal variable of the mechanicality, which is what we call the time, the time of the mechanicality. It is to say that if we have two operators, we have the right, and there is no problem, to measure something, and then to measure later, in another physical time, another operator has the price, with the price strictly less inferior to T. and the interprétations standard of the mechanics of the principle of all the formalism and all, they have absolutely no objection to make at this point of the show. There is no problem. You see all of the sudden that this variable T of the mechanics of the principle... What do you mean by that? You mean that it comes from the principle of the mechanics of the principle? Ah, ça vient justement du fait que ce T n'est pas du tout le temps qui définit, c'est le temps de l'évolution unitaire d'un système. Donc, bon, il y a un système, il y a les observables de ce système, il y a l'évolution qui est définie avec cette variante T, puis dès qu'on fait la mesure, l'évolution recommence parce qu'on redéfinit, on prépare l'état, on prépare un autre état. On fait une mesure puis on recommence toute évolution, parce que l'état a volapsé. L'ordre des mesures n'est pas décrit par cette variable T. Ce qui se passe à l'intérieur d'une évolution immunitaire est décrit par T. Mais l'ordre des mesures, pour le fait, n'a rien à voir avec le T. Je voudrais juste comprendre le sens du mot LATER. Oui, plus tard ici, c'est-à-dire dans le ton de l'expérimentateur au labo. Tu vois, moi je suis au labo, j'ai un observable qui correspond à la vérité, et puis j'ai un autre qui correspond à la déprime, enfin c'est à peu près les It's a delayed experiment, it's a delayed experiment, it's a delayed experiment, it's

1:30:00 to say that in fact you have to be conditioned by something which is later, something which is later. So, let's say, the lesson that I will tell you about this transference is that this simple time of the evolution of the human being is not the time that we are looking for. Do you understand that the order of measurement is not the same thing to measure? But after, you can choose the direction you want, it's a consequence of the reversibility of this. and then we will not have taken the cable. I will try to change the world. If it doesn't touch it. So, that's the first constat. Because it's not complicated. It's on the same system. A and B, it's on the computer, it's on the same system. It's like the lecture experience, it's to say that you have the same system, you... You have the first one, so you have the first one? Yes, it's to say that the measures are not... You see, instead of measuring directly A, a operator, 1, and another 2, you can very well find a field experimental where you will measure something that will give you the value of a certain observable here. and then later, in the middle of the measurement of the lab, you will measure something that will give you a certain information on that. And in the middle of the measurement of the lab, it will be one or two, while in the time of this system, it will be the same. But is it that it comes from the reversibility of the planet?

1:32:30 No, it's just the fact that... Can you give an example concrete? For example, a collision between two atoms? No, it's a collision between two atoms. But this T is a pure convention. It depends on the fact that the T is a pure convention, the T is a parameter of evolution. We can't see how it is. In fact, it's not a direct show, but if I go, I'll go back to the show, because to make an exposé on a direct show, it's not a chance than what I would like to do. But the point of the start is that this T is a conversion, is a parameter of an origin human being. which would be called another letter. Yes, we can call this T alpha and it will always be the one that will be the one. This is not something that we satisfy when we ask the question about it. It's the T of Schrodinger. Yes, but the T1 and the T2 are not the same T as the T of P. Well, that's it. Let's continue. For the start points, so that you know, it was not the end of the day. I was on the first one on the phenomenon. So we are looking for the start point. Where do we find this time that we are interested? this time that I have indexed in the two circles, which will allow us to understand the time that we live in our lives. For example, we could start with the phenomenal time. Phénoménal, disons. Il y a eu cette très belle citation de Valle qui est reprise par exemple par Ackman dans son livre récent sur la relativité, The Rise of Relativité, où Valle, après Husserl, évidemment, après Husserl, évoque le problème de définition des points temporal. And Valle, here, uses this idea, quite conscient, of what we see,

1:35:00 to pose the possibility of the points temporal, like the regions of the region. The exact points are not even in the situation. and I'm not absolutely for that concept attending to the definite and it's only the purely for arithmetic, arithmetico and arithmetic concepts of the real number. Alexei, ce que tu dis me rappelle la discussion qu'on avait hier c'est le passé du présent comparé au passé tout court comme le diagramme qu'il avait monté. Oui, moi je l'ai dit que Val quand même a prévoir le Husserl je crois que Val le sera à faire of the name of Baell, who has nothing to do with Cerf, but he is referring to the diagram of Cerf, the diagram of retention and retention. It is exactly the same. Yes, it is exactly the same thing. So, another citation, for continuing on Baell, well, again, again, it is a point of departure, not an exposure on Baell, because to be really precise, you have to say something more about Baal, about what they really thought about it, etc. If we... and that's going to be important for the next one, if we try to think about the phenomenon that we don't know about it, what we are interested in is this idea of talking, and I will come back to the conclusion, but with the conclusion, we will follow this first part of our production, and then we will see what we will talk about. And then we will see all this through a mathematical formalism. And then the last thing, this is a citation, also quite familiar with Dirac, sur la méthode, qui introduit mon utilisation de normalisme, et ça, c'est l'ambiance que Marc disait ce matin, pour pouvoir parler d'une dérelation du temps. Délation à partir de quoi expliquer l'espace-temps, mais à partir de quoi et comment. Ça, c'est une formulation

1:37:30 The most powerful advice would be to perfect and generalize the mathematical formalism that force the existing basis of theoretical physics, and how to reach the success in this direction to try to interpret the new mathematical features in terms of physical evidence. So, we're going to try, this is for the second part, if you want, so that it will be possible, we're going to try to present a formalism, a formalism mathématic which will allow to derive everything in fact something that we will interpret all this will pass as I mentioned before the beginning, all of this will happen in the field of interpretation of information. It is to say that I will start from a certain formalism which will talk about systems, information about these systems and the facts. It will not be very important for the variation of the time, but for the interpretation that's very important. I'll read it all the time, because I pass to this 3rd part, where I explain the explicities of this story. So, in lieu of doing 2, I do 3 all the time. So, it's all about to say that most of your questions are legitimate, so if you have more questions about reformalism, please wait for a moment to see if there is no response to a question about reformalism. But I want to talk about the sense of all these encounters. So, what do we do in these approaches that are both operationally, I put a terminology, a certain terminology that comes from the domain of the physical, to explain each other of these terms, maybe this would be a bit long, but let's say, I talk about an approach

1:40:00 which is part of an informalism, which is what I suppose, I suppose cooperation, that is to say that we are going to talk about the systems, the operations of these systems, that is to say what we can observe on these systems, what we can do with it. So if we observe something, we have a value. It is a framework, or a framework, a cadre in which we can try to deriver, to try to deriver the theory of physics from a certain position or action operative. It works also well for the coronary of the quantum field. There are several options, several axiomatics, etc. So, here it is, it is, for me, to start from a light What does that mean? It's not a particle for the moment. So it's a certain number of characters that we can observe at the end of the system. The state, the state of the system. there is an agent of the domain that is built, well, that I will pass for the moment. So you can come back to this point? I don't see the difference between Sigma and Compess. between sigma and what? It's not that. That, you call it how? Sigma? No, the higher. Yes, that's the one. The set? Yes, that's the one. The ensemble of the states, you call it how? Sure, we already know. Yes, that's the span. Yes, yes, that's the span. What is the number of the letters? It's a G? Non, non, ça c'est un esgotique. Quoi ? Esgotique. L'ensemble des États, il y a une structure d'espace vectoriel. Donc ils se confondent avec son span ? Non, non, non, non. Les coefficients. Non, les États sur le truc, tu vois, ça peut ne pas être complet. complexe dans le sens de coefficient complexe dans quel sens ?

1:42:30 Oui, oui, je le sais. Non, mais ça peut très vite, ça peut être utile. Bon, je vous propose quand même, dans cette conclusion, je vous propose de parler pour l'instant, because the past few people talk about ideas, and then we will refer to the journalism with the part 2 for comment. So, for the ideas. For the ideas. Here is the fundamental problem of the approach operation. It is a system with the observable system. But how do we know... How do we know... If you measure the same thing, it is to say that you have your system which is a very large number of things that you can measure, that you observe. There is no rule of identification. You measure A, let's say number T1, and then number T2, you measure a number of things, because all this stuff is in the sense of observable, so number T2, you measure everything. And then you want... It's observable or not? C'est observable. C'est observable. Attendez, non, non, je n'ai pas dit d'abord. Non, j'ai dit AT1 vous mesurez A, et AT2 vous mesurez la prime. Et il faut qu'il y ait un principe par lequel vous pourriez identifier ces choses-là. Donc, pour dire qu'en fait vous mesurez la même chose, you have to add to this algebra, to this algebra, to this algebra, to this algebra, a principle of identification through the ground. For the moment, we observe it. Why do you observe it? You are saying that I measure the observable A at 1. But in fact, you can also have the other point of view, which is that A at 1 is an observable. J'y arrive, j'y arrive justement. J'y arrive comme conclusion. J'y arrive. Donc, cette vision, cette vision, disons préliminaire, je trouve, c'est qu'il faut, s'il y a une algèbre avec ses observables, il faut qu'il y ait une loi qui identifie à travers le temps, disons le temps pour l'instant est posé.

1:45:00 At the time, there is a law of identification of these observes. So, a law of identification at the time. A law that is supposed to be dynamic, because it is a law that is supposed to be the time. But it's the time in the arrow. What is the arrow? No, it's the time in the arrow. So, it's the arrow. of Aragh on the Algebra local, it is to identify the procedure of observation as the same thing, the same thing. And this procedure of identification should include, and this is a consequence in general, include the ETA. In fact, it is to say that because of the ETA, there is no dynamic law which is like this, there is always, in a way, the ETA. It is to say that a dynamic law cannot use ETA. Well, I'm not sure why, but... In general, in general, it says that without talking about the state, we can't do the law dynamic. And it's there that begins a problem. If we postulate the time and if we want to identify the observable through the time, and that it's impossible to do without talking about the state, because the state should be very different, in which sense is it that it has to identify the observable? Because if everything depends on the Etats, it is to say that if I am in an Etat, it identifies my observable with something, and then if I change the Etat,

1:47:30 I will not measure other things, I will measure the same thing but in an Etat different. But it is impossible. So in general, it is invalid, the possibility of identifying things as being the same thing. So, we have to do something other than that. The last phrase is to say that we have need of topology faible. Yes, that means that we have... On a besoin d'une topologie faible parce que justement c'est elle qui va faire interner les états. Mais je vais expliquer ça. Une fois que j'explique le lien entre les alliés, c'est quoi, les phénomènes, on va voir quoi. Donc, ici, je viens de vous rappeler ce que j'ai dit ici. On cherche une procédure d'identification qui sera interne à cet algèbre. So if we take the algebra and we post it from the exterior, or we impose a changement temporaire, it does not work. So we need to find something inside the algebra. And that's where we find this object very interesting. Well, I will perhaps... I will perhaps... I will perhaps... I will also announce this hypothesis that is called the hypothesis of the thermodynamics. And then I will, as I just said, I will proceed in two terms to explain the first time quite quickly, and then the last time with more information. So, this is really one of the two components of this exposure. In the nature, there is no time physical, of variable T, which would correspond to a preferred time. Parmi tous les états équilibres, il n'y a pas d'état préféré a priori. Toutes les variabilités, par conséquent, sont équivalentes. Bon, je vais expliquer sur le contrat suivant ce que c'est signifié. Toutes les variabilités sont équivalentes. Mais, et on peut trouver le système d'un orquel parmi les états équilibres.

1:50:00 But if the system is in an état of omega, then a certain variable temporaire is chosen by this état of omega. And it is from there that we can emerge in the same time. C'est-à-dire que si on a le système dans un état donné, cela fait émerger quelque chose qu'on va appeler « non ». Et il faut quand même tout de suite donner un commentaire sur ce que vous venez d'entendre, pourquoi est-ce que c'est tant, et qu'est-ce que ça veut dire les états d'équilibre, etc. Donc je vais le faire tout de suite. because it prolongs a little what I said, that what I said implies that we can't define a time based on the geometry of the space-time. And, just the few cases where we can define a time, it comes from a system, where we can define a time by a process of... ...and, in a certain way. So, in fact, So we have a system in a state of equilibrium. Is that the same thing that the time is completely free and independent? And if we have a state, we already have a certain time. Is it the same thing that the time is independent? The time is not dependent. The time is not dependent. Yes, what I just said, if we have an algebra, if we impose a curve of time unidirectionnel, with a continuum, it does not work. This is not possible. However, the best way to find a time in this kind of system, is to take an operator with an hectare. I understand. but you say that there is no time to prefer, etc. That means that it's a free parameter. You can choose time or whatever. No, I didn't say that. No, no, I didn't say that. For the moment, I said that the time depends on the state.

1:52:30 One second on the subject. Yes, if you want, I have a comment on the formalism, because I have a lot on the formalism, but... Just a comment on the hotel. I know if it's possible. How do you define the notion of temperature? The notion of temperature here? There's a difference. It's to say that... Is there a difference in terms of temperature? Yes, it's a story. How do you define the temperature? How do you define the temperature? It's the real problem. No, no. There's no problem, it's just a parameter in the definition that I will write. Yes, I will call it a certain beta in this definition, which I call temperature. But after I show you how this generalizes the function of Gibbs. And it's because I show you how I identify this beta with the vector of Gibbs. But the word temperature here is just the generalization of the word temperature in Gibbs. So, if we have this condition, then... Yes, if the number of liberties is finished, it's the same thing that it does. So, it's a... So, it's a generalization of the condition. So, that's the term of Dumita Takisaki, which is unfortunately not very, very known as the philosophy of science, which is still one of the very big theories of the physics mathematics of the 20th century, is that if we take an état, let's say, that's correct, as I said, on an algebraic observable, It is an état. N'importe quel état c'est grave, si on agit ou des observables, est un état disons d'équilibre à une certaine température bêta par rapport à un certain groupe

1:55:00 d'automorphismes de cet âge général qu'il génère lui-même. et génère un groupe d'automorphismes et c'est là que j'aurai besoin de ma partie 2 pour vous expliquer tous les détails mais c'est à dire qu'en gros ici on gardait ce symbole gamma t, vous voyez ici un t, c'est bien ce t qu'on cherche c'est à dire c'est une variable unidimensionnelle qui va devenir ton, qu'on va interpréter en ton It's a group of parameters, yes, it's a group of parameters, and it's there that I need a part of 2. So, in fact, on prend sur an algebra of observable, that's very important. On prend n'importe quel algebra of observable. On prend un état assez correct. And it's true that this état is an état of equilibrium thermodynamic. It generalizes the thermodynamic. at a certain temperature compared to a certain time that this time is defined by himself. You see how many things we obtain just from an algebra with an etat. What is this miracle? there is a lot of miracles in the notion of algebra. So in fact, the force of this theory is really... It's not simply the objects of functions complex on an espace. So, for you to repeat again the conclusion, the term defined as this parameter t of gamma depends on the state. If the state changes, the time changes. So, if the state changes, the time changes. What is the change in the state? It's a change in the information that I have. So change in the state, it means change in the information. And that, if we sort, because I told you earlier, each Etat is correct to define a time. But in fact, there are many Etats who define the same time.

1:57:30 But it's a weight or it's a stability? No, no, no, I'm going to define it. No, no, I'm going to define it. I'm going to define it. but if we start from this ensemble of states which are defined in the same time, it is to say that we can go a little further and then we can find another time, and that is called the folium, the states, which each folium will define the same time. Do you think that I can consider an etat as a field of vectors? Which would be a generator of this flow? Is it correct? What do you mean? A etat. You just said that it is a generator of a flow to a parameter. Well, in a variety, the generator of a flow and a parameter is a vector, so what does that mean? Well, yes, because the setup is the function of the science. Well, it's a vector. What I'm interested in the most, is that if our algebra is a algebra that corresponds to what we believe today for the world, It is to say, if it is an algebra of a phenomenon of 3-1, and in part 2, I will show you what it means. So, if it is not any algebra of these two, but the algebra of which he describes the theory of quantum mechanics, which is the algebra of the quantum mechanics of quantum mechanics, Well, we found that the spectrum of this time varies from zero to infinity. So, it's all the number of zero to infinity. Which is, for us, normal. However, what is this? Because this is an algebra non-commutative for operators and observers. It is to say that from this non-commutative, because for example if we take an algebra

2:00:00 or the cumulative abelian, of the type 1, or even an algebraic abelian, but fiché in a mechanical system standard, the spectrum of this time will be gelled, that is to say 0. That is to say that when we have this non-community and the infinite number of liberties, we have no It depends on the Etat. It is a time non-commutative, if you will, which is linked to the thermodynamics. So you see that the thermodynamics in this vision is intrinsically linked to the non-commutative of the observance, of the observance. The spectrum of the time, that means that it's an operator? Yes, the time, in fact... Ah, no? That allows you to access to a time operator? No, the time... Wait, two seconds, I'll show you how to define it in the part 2, how to define it. But the spectre, you still have a question. Yes, yes, yes. No, in fact, it's not the spectre of T, it's the spectre of S. It's another spectre. Excuse-moi, because if T is the parameter of a continuous group, it can't be something else that... Non, mais c'est pour ça que je vous dis, c'est un fait, c'est un sperme d'autre, strictement, enfin rigoureusement parlant, c'est le sperme d'autre chose que peut-être, mais c'est pas ce peut-être qu'on va, en fait, qui va vous intéresser, c'est un peu autre chose. Okay, well, that's for finishing my conclusion, which is, again, the development formel. But now, you can see what I need in the development formel. At least, you have already plenty of questions about what means Spertre, what means Fodreman, why the states, etc. So, I'll go back to the part 2. You can define the automatism. Yes, I'll define it. I'll define it now, I'll define it, for that, by having in mind the conclusions,

2:02:30 you understand the sense of this enormous development formel that I will introduce. because that will take the 20 minutes in the race, I think. The formation, you calculate the part of an anthropologist? No, no, no, I calculate the formation of an anthropologist. But, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait, wait. I will talk about the basic notions, the algebra, I will talk about the Etats, I will introduce the types of algebra which will interest you. Just to remind you, there are some algebra of the type 3-1, what do they mean for example? And finally I will talk about these automorphisms So now you can see why I have a need to explain how I introduce the time liable to the momentum and the thermodynamics in the same time, thanks to the theory of the thermodynamics. So, I start with a linear space, the operators are on a space of Huberth, there is no problem. I define the topology of the norm on this space of Huberth. This is what I call the topology. Thank you.