What is Categorical Relativity? — Discussion led by Marc Lachieze-Rey (contd.)

0:00 So, the PQ product, it comes with a very high speed. Well, first of all, the idea is that a blockable observator, because it blocks the speed, it will not be so fast, in any case, it will be a dry train. I see the observator as a link. If you have the length of the universe, the length of the length of the universe, you have the metric length, which is the integral of the metric, which we call the time. It's simply the metric length, which is induced by the metric that we are talking about here, it's an equation of your own, so the time will be induced, and the speed is the tangent vector, you can say it that way, either it's the normalized tangent vector in the metric. Either you can say it's the derivative of the proper time, it comes back the same. It's a normalization. As long as it's normalized, in fact, it's... It can be like that, yes. But it's not a vector at all. It's not a vector at all. What I want is to spherize tangents. It's a vector. It's not a vector. It's a vector that always has a number. So the second question is... Now, we are given a point, an indicator like this, and if there is a material that we can write, and if we imagine that I throw it, that I throw it into the universe, it depends if you ask the observator to be free, so that you have a geodesic degree, and if he is free, we are given a point given only a geodesic degree,

2:30 There are two directions in the universe, and Hawking is the only one. Yes, there is no other direction. Okay, I don't understand. On the other hand, if you assume that there is an engine, that's why, for example, we go on Earth. Because we are free and the Earth is free. But if I put an engine, I take an object, I can start moving. And so, in the transmission, there is... I would like to ask you a question. Is there any other topic you would like to talk about? I think this is the goal of our group of work, to answer these questions. I am sure that yes, I have some ideas. I know that there is a whole literature of ideas. For example, it is well known that in terms of cobordism, it says something. What is cobordism? These are the categories. Does it add anything more than relativity itself? I don't know, but I think we should continue these lectures from this point of view. For example, there is another point of view. I have an idea which is... And finally, the cohomology groups, that is to say, in terms of space-time, we should not define the cohomology as a morphism between these two things. There are some things that happen in mathematics. It's a bit the spirit of the Italian geometry. I don't know if someone did it, I don't know if it leads to something. So I think we can have a lot of ideas. The goal is to talk about this group and then to be able to decide if they are good and if they are not good enough for the project. Our question is very specific. The idea as a local is that it is more structured in terms of geography. If it is local, it is good.

5:00 I think that the relativity in the local point of view is perfectly described. Thank you for your attention. Thank you for watching. I'm not sure, because the P is something, at the moment, there is no concept of displacement, there is no concept of stability, nevertheless the P, when we are going to interpret it as an observator, it is something that is perfectly localized. And so all the arrows that arrive on P... This is what I would call a process of localization, that is to say, you will be in any high point Q of space-time, you have the omega cube arrow and you will say to yourself, here is the relationship between this distant point of space-time and Q and P, what can be the other localization for this thing? It's perfect. No, no, no. A priori, all points in a space-time are the same. You have a variety. It depends on the metric structure. All points are strictly equivalent. And then the metric structure, considering that it has been added, so the points remain equivalent except that each point carries the value of its metric. This is a part of a master's degree, so what are the relations between these two subjects going to be like? I would really like to answer that question, but I don't know how to answer it. Maybe it's not... in this approach, it was to think of the point as... I agree with you, I agree with you. P is not a point, except that it corresponds, from the way we see it until now, it corresponds to a point with a vector, let's say, in relativity.

7:30 An observator, that's it. An instantaneous observator is a point with a vector in its point. It is a fundamental notion for relativity and as we talked earlier about the role of the observer, I think that there is a very big parallel between relativity and quantum physics. In these two theories, there are two things. There is physical reality, physical objects that identify the real. In relativity, these are covariant objects, such as the impulsion energy tensor, the speed vector, and so on. In quantum physics, these are the wavelengths of quantum fields. And then there is what an observer can know about it. An observer can never know the totality of a thing. So in relativity, how can you know a thing, a pulsing energy tensor, than by making contractions with... Speakers also include speed, and as they are not defined in the same way, they must be transported. So, the knowledge of relativity is done first by a transfer from the observed object to the position, and then by contraction of your own speed. So there is a very big parallelism and in both cases, the observer plays the role of a kind of machine that makes pass real quantities, fundamental in this theory, to what we can observe. For example, when we observe the shift towards the wheel here, what is the shift towards the wheel here? It is something that is different. I'm going to start with a kind of process of my own speed, something variable, a vector square by the speed of the probe, so I can't do that because it's not difficult, but I manage to do it. Give me the plan, there's never too much to lose, there's never too much to lose.

10:00 The speed of the observer. I didn't look at that point, but yes. No, no, no, no, no. Remember what I told you earlier, is that if I have two points, remember, a point, well, two observers, a observer is a point with its value. The relative speed, I don't know, because the speed of P, I don't know. The problem is that if it happens, it's not going to be there.

15:00 I'm going to look for a half-passable one. No, no, it's a good idea. No, but then I'm going to get to the point where I can express myself in this format. This arrow is something that defines us. It's the composition, but instead of defining them, arrow by arrow defines them, globally at the top. So it already exists in the category at the beginning. So, if we have, for example, the Coup d'Avélien, the Coup d'Avélien is not only a set of Coups d'Avélien, it is the composition of Coups d'Avélien.

17:30 That is to say, it is given with all the richness, it is not given with the whole structure of the system. It comes spontaneously to the mind, it is constant, it is very good.

20:00 For the rest, it is always, I always interpret it as a number.

37:30 This is the date for the next lecture. I know there are people who don't like this date, so we can ask ourselves the question of changing it. What is the date? It's Tuesday. Tuesday. So, who doesn't like Tuesday's date? In general or in particular? Excuse me? In general or in the village?

40:00 This Tuesday, I know it doesn't suit you, but it doesn't suit you either, it doesn't suit the others either, it doesn't suit me, it doesn't suit you either, so if for example, are there any days in the week that are better for you? Monday. Monday is better? No, not all at once. Thank you for watching this video. We had the table of the 28th, we have another table which is the 12th of December, I suppose it's the same, we were obliged to set the dates in advance, it was a matter of reservation of the room. You can't be consensual. Then, I think we won't have a problem with that at the CETO. We'll probably do the answers at the APC, at the University of New York, and we'll be able to do that. What remains to be done is maybe to set up a work for next time. I think we have enough time to come back to this article. To clarify what we have seen today, Thomas, there may be a place to make a passage.

42:30 There is an interesting list to explore, maybe like that, I don't know, or you can buy it. Ah, that's a good question. This formula is interesting. It's not easy to think of a formula of this kind. It's not easy. Well, I don't know. There are several solutions for the next question. Can someone tell us something special about, I don't know, I don't know if you have already explored the categories. Thank you for your attention. I think it's better to stay on the relativity side, because that's what we're going to be able to do in the future. Among others, but already there are very simple things that are given the definitions, we will see how they apply to the language of science, and then we will stop talking about it. Does anyone want to present that to us? Or maybe it's our conscience. So, what I propose is to make another proposition, that I select a part 2 of Barrett and Crane. I'm going to choose one or two, and then I'll send a list of the paper's coordinates by mail, and then we'll take it for the next time, and we'll talk a little bit about today's coffee to see if we really don't know anything or anything.

45:00 And then, I don't know which one it is. Thank you for your attention.