Aspects philosophiques de la classification des symmetries

0:00 It is now half past three on the afternoon of the 29th of May, 2006, and I'm sitting in the little cafe just across from the IHPSD at 13 Rue de Four, and in 45 minutes the seminar with Alexander Gouet on philosophical aspects of the classification of symmetries. Philosophical aspects of the classification of symmetries will begin there and that will be the next thing to be heard on this tape and it will continue over onto the other side.

5:00 What is the same in different minds, etc. So it's always the invariance of this idea, the invariance of that idea. It's exactly the idea of symmetry. The automorphism group was exactly the same in physics in several languages, but the language I chose, it's going to ask me questions about symmetries as much as it informs us about objective properties. We're talking about symmetry of phenomena. Well, only indirectly. In fact, most phenomena... When we talk about symmetry, we generally talk about symmetry at the level of laws, so we are already talking about symmetry at the level of abstraction, of generality, of superiority.

7:30 This has been defended by Wiener, the Wiener physicist, who defined symmetries explicitly as laws of laws, or metanoids. I'm going to talk about symmetry in physics, I'm going to talk about symmetry at this level of generality. Well, if we wanted to push the thing, we could say, well, objectivity. All of this is happening at this level of generalization and not necessarily at the level of quantum phenomena. We can imagine that someone who is interested in realism, for example, instead of clinging to talking about the realism of objects, should talk about the realism of structures at a higher level, since that is where the objective part is found, if we believe in the objectivity criteria of the novel. It's not a thesis on realism, it's just a clue. The question of symmetries in the development of laws. In the history of physics, sometimes, strategically, one approach has been more used than the other. In recent physics, the B approach is particularly fruitful. That is to say that we explore models by imposing constraints. In this case, symmetries would be constraints for the development of models. But, of course, when this approach does not work very well, we derive models and deduce symmetries from them. The two approaches are always the same, but we must say that this approach, which in particular was very fruitful when people were convinced that space-time symmetries were first and therefore that any model should respect space-time symmetries and that, in a way, space-time symmetries were of superior objectivity, the approach has been extremely fruitful.

10:00 It's almost implicit, but it's not automatic, which justifies the small project today, which is to discuss the articulation of the concept of symmetry, law and objectivity, which has been discussed recently. Symmetry and objectivity have been very little discussed in the lecture today. So what I'm going to discuss today is the classifications of objectivity, variance, symmetry and symmetry. Not always, no. But today, it will be mostly structure of law. It depends on the structure of law. One thing is on groupoids, but it's probably the same thing. But another thing, because in groups, it's a variation under transformations that is reversible. And if it's not reversible, what is the objectivity? Well, it's just a question. We have to be careful. Does symmetry, as a property, we're talking about transformation groups that describe symmetry? It describes a property, but it is not necessarily the property. It could be that there are certain things in a property that cannot be represented by groups, and we will have to say too much because our description tools are insufficient or inappropriate. Hermann Welch was the one who defended groups at 100,000 at the time. He never said that symmetry was a group of transformations, but symmetry is described in a group of transformations. It's a case by case, to be sure. For example, there are very few symmetries. It's still not frequent.

12:30 For example, a group is a multiplication of a partial number, so it's a totally different structure than that of a group. That means that all elements cannot be multiplied with all elements. There are other types that could not be. They have as many elements as there are objects in the group. So they have many, many different elements. It would reduce our discussion on objectivity a little bit, but it is one of the most confusing factors in the literature of the time. What is very important in this paper? Because there is popular wisdom, a kind of thing that physicists say to each other, and that global symmetries are related to conservation principles. Local symmetries, ah, those are constraints. What is popular wisdom? That the criterion can capture. There we will see that the standard definition of the criterion works very badly to find this popular wisdom, but we can imagine other things. I have to discuss this criterion since the criteria that are more philosophically rich in terms of objectivity, etc. We often use this criterion in our lectures. In standard definition of local and global symmetry, which is the same everywhere, the function of space and time is to be constant, the same, everywhere, for all time.

15:00 In some places, there is a global symmetry of the sky, a local symmetry of the sky, the potential of the sun, for example. This is the example of space and time. To define a point to which it turns. There is no need for any dependence on this space-time. A reflection, which is supposedly a global symmetry, you need to specify the axis of the strange. In the traditional definition of global symmetry of the sky, there is actually no dependence. A reflection is very different from a transformation, for example, of a potential potential in the global case, which does not seem to be well sought after. But the examples themselves are clear. Capturing, showing how a rotation, a rotation of a reflection is not a transformation of a potential that depends on each other. We can therefore modify this symmetry as a point-to-point transformation with a partially defined operator.

17:30 I hope you found this video useful. If so, please like, share, and subscribe to our channel. In this new version of the computer, the dependence on space-time is evacuated from the computer. Questions like, oh yes, but what is local symmetry? Is this a dependent on space-time? No. You look at the number. So we can imagine that we can continue to talk about global local symmetry in very strange topologies, theories of the more complex connection to space.

20:00 This distinction will seek the intuition of physicists anyway, because it is exactly this distinction that works in non-neutral theorems. If my memory is correct, it is the least transparent. Yes, non-neutral theorems in full here, because they are theorems. In philosophy, everyone should know that. Physicists, because there are physicists in physics in the room. And then here, I will make the vulgarized version on the table for equations. Key terms include the function of the parametric system that we will not call plagiarism, deducing the behavior of indeterminism. The third theoretical theorem of transformation is a distinction between the systems represented by its physical action,

22:30 and the global one for the systems represented by the plagiarism of it. In the case of conservation, movement, etc., local symmetries are associated with an indeterminism. The key point, whose definition was not quite explicit to start with, If we associate it directly to Lagrange's theorem, we come to a very interesting theorem. Indeterminist in the sense of subdeterminism. If there are too many variables... If the Lagrangian completely describes the system, we assume that if we have the good Lagrangian, we have all the classical information,

25:00 the system is indeterminist, then we can interpret it. We can say, ah, there may be many variables. Maybe in the middle of the earth, it's a mathematical theorem. What it tells us is the equation for the number of variables. I took the Oxford-Hitlerian rock. There is a distinction between analytic symmetry and physical symmetry. There are functions in magnitude or in form, especially algebraic transformations. Usually nothing new, but of course in a physical model, a lot of analytic symmetries correspond to physical symmetries. Well, up to this point, nothing has been said. It's new and interesting. But in a particularly surprising passage in Roche, in 1987, he tells us that they are more or less abstract. There are certain analytic symmetries. We can deduce the symmetries in this lecture. The first theory of neuter is quite simple. A Lagrangian symmetry is a formal symmetry, since the Lagrangian is not like a physical quantity, like the mass, the energy, and so on.

27:30 The theory of neuter is based on the invariance of the Lagrangian to a conserved quantity. A conserved quantity is something that is conserved in the neuter. I say to myself, well, there you have it. It's obviously totally in the way. It's quite surprising when you say that for the first time. The result, which is a bit like a rock formation, is that we can easily believe, for example, that the invariance of the phase in one of the charged fields leads to the conservation of the charge. The invariance of the phase in a physical quantity is a bit like a rock. At a certain point, we realize that the theorem of Noether in his book of the Enzymes, the principle of physical conservation, the formation on the quantum theory of Lagrangian, is in fact giving us the information that does not allow us to deduce what is sometimes said.

30:00 An active translation is like moving a translation, for example, an active version is to move the thing, a passive version is to move the coordinate system. It's absolutely physical to the extent that it's a symmetry. The physical, analytical power of Roche is infinite. There are things that are of formalism, models that represent physical things. It's not a physical correspondence. It wouldn't be objective. It would have more or less a part of objectivity.

32:30 But after that, you have to reinterpret everything, to trivialize everything. Objection is the formula of Hamiltonians who force entities, and not laws.

35:00 There, sometimes, there are all kinds of variables. In general, if you see objects, we say that symmetries, you can at least try to find the right mathematical structure.

37:30 That's what Roche does. It means that there is a kind of mathematical model, and I believe that there is another approach. But you see, this kind of example, Kantian's, can attack the example I just discussed about representation. I don't think that working on physics as a machine to produce the equations of movement, which will not be verified in nature, What's the difference? We think that classical space adds time, and something like space-time is not classical, but it doesn't work because there is symmetry that doesn't have a physical meaning. Yes, we have changed time and space. What is space? Maybe everything.

40:00 Mathematics and physical structure. For example, Newtonian space-time, classical, more time-metric, more space-metric, more refined structure. This allows us to differentiate, to have the symmetry of the references. This is not a point-to-point constraint of the variety towards spacetime points, and yet it is a geometric representation. What is there without mathematical representation? That is to say, we can say that in physics, we work with this physical object, it is already mutimized. That is to say, there are physical things that are not mutimized. We say, well, it's a thing in itself. There is a speaking value, which is essential. If Petriloge, in the physical model, is a physical symmetry of the real world, we will see if reality is compatible with that. We will see that there is a scale of entities, of hierarchical objectivity, inside our model. We can be an anti-realist like Van Felsen and believe that there are entities more or less significative inside our model. So we can say that if there is a planetary symmetry that does not have a physical form, it is simply not a model. It's still false. If you say, I have a model that has a local symmetry, that generates an indeterminism, but that this indeterminism is apparent because there is, because in fact, I don't really believe that there is too much variation in the model, you could say, for economic reasons, that there are too many things that have a strong function in a physical model.

42:30 For example, it may be necessary to have a surplus to make a point theory. But therefore, there are parts of our theories that are objectively written for essential functions. I'd like to clarify a little more about inter-symmetry, symmetry whose transformations are non-spatial-temporal. By these symmetries, we separate spatial-temporal, we say, somewhere, external-external, dividing between geometric symmetry and spatial-temporal symmetry. Since we dare to interpret it geometrically, there is a great program called Geometrization of Everything, which interprets theories that are in appearance non-geometrical, like geometric theories. So, internal-external, external-external, the first... The nature of space-time transformations requires different phases of operations, such as charge conjugation, which do not depend on each other.

45:00 It's a troubling question for a major philosopher. I've written his reasoning. Premise 1 is that an interpretation is a sufficient and possible condition. So, internal signatures do not denote unification. Externally and internally, it would be more than a simple distinction in the field of transformation, it would be a distinction between what could allow an ontological modification of what could not. What does an ontological modification mean? It means that, in fact, in a way, they are not really, they may only include internal signs. And then there is the left hexagon, active, the real part, that this word is still the transformation, genuine transformation. The distinction between active and passive is physical, that is to say, with the active one, there is an external actor.

47:30 In the case of active, there is an actor who does something. It is passive as a re-coordination of the problem, that is to say, active implies symmetry, it is conserved, from the pencil to the stylus. This is just a change in representation. Of course, if you can't formulate a reasonable interpretation, you can't have a quantifier in your system that transforms, that can interpret in a passive way.

50:00 Of course, Van Hels didn't have the imagination to do that. A possible world could look like a reasonable system, but that's where the problem of Van Hels' argument comes from. What does a reasonable transformation mean? There is a kind of rotation, an ontological multiplication. It is a pencil, the same thing, if I identify such a symmetry. In order to be able to say it rationally, I need to have an easy interpretation. Mathematically, there are many cases where we will not be able to know because it is a passive field of the type in our representation. But I want to know, for example, if supersymmetry is a reunification between fermions and bosons.

52:30 And he will say no, because there is no passive interpretation. There are other types of unifications. They are made up of similes, not a passive-solid interpretation, so they are unifications. Mathematically, the equivalence between them is the interpretation of formalism. It is sometimes discussed when we have both and when we don't have both. For example, the paradigmatic cases of unification are the space-time similes. You know the space-time. The interpretation of a passive-solid interpretation is to talk about the same thing during the transformation. Let's create a change in the super-symmetry. It's seen as a re-coordination. According to the type of symmetry, it's a re-coordination only between the effects.

55:00 But we say, listen, the electrical quantities are measurable, they are all... What we say is that the indeterminist is capable because there are non-physical variations in the system. And then we reinterpret the symmetry as being that it is only the description of the same physical state. All descriptions correspond to the same metaphysics. We take caution. We could take caution if we want to have the theory reduced. But we work with the theory to reduce when we are... But that's one case. For example, in general relativity, we have a more general notation. I don't know if it's correct. Attention, attention, attention. Yes, yes, yes, that's it. Yes, that's it. That's exactly the change I wanted to give you. General relativity under the amortization effect of the variety of space-time. In theory, there are too many determinists.

57:30 That's exactly it. If we interpreted all the variables as being physical, we wouldn't believe that general reality is a determinism because of the large number of variables. In space-time, we have a... If we were in hypomanity, we would say the same thing. In France, it's the same thing. And that's why I think there's a problem with general reality. Well, there's not a problem, but we have to pay close attention to what we consider to be physical in general reality. And it's a philosophical difficulty. All these theories could be very different from the standard theory. It's a real problem of physics. It's important. But it's the same kind of question. There is a danger in the internal and external criteria to try to distinguish the space-time of physics. There is a danger from the beginning. Because Lagrangian is dependent on the variable of relativity where we are always talking about space-time.

1:00:00 Even if we make our arguments, it's sure. The dynamic theory of space-time in Einstein is a bit like science fiction. The symmetries of space-time, the symmetries of physics. It's purely mathematical, it brings up Einstein, where he underlines, I mean, I want to understand it like that, but I'm not sure I understand it exactly like Einstein. It's quite spectacular. Intern-extern. So, already, we read that, we go to the question, we create a moment, we have an argument. It's not a title, the unification of intern-extern theories, but in fact, it's a little bit like that. I clean up Einstein. There is something in a space whose symmetry is represented by a group of transformations. The group of transformations. In other words, the transformations became transformations plus space.

1:02:30 The points of space would no longer be identical. Because here, the points of space were identical, except for the places where the figure was. So, by saying, yes, space plus the types of points, which correspond to the orbits of the group of points, in fact, we could have more types of points than just... Here, there was the figure of space, the points that were not in the figure, the points that are in the figure.