Theorie quantique de l’objet

0:00 In fact, I wanted to say that this session is part of a program of the RACHAF called Program of the System and I would like to share it with you at the National College of Philosophy and from the SRES-MARC. In particular, what I will talk about here is part of a chapter of this program in which we will try to analyze to what extent it is possible to reactivate contemporary scientific and philosophical knowledge. I don't know much about quantum mechanics, but I have heard that philosophy and nature are two different things that have the same universal approach as physics, but they are considered in the same way as mathematics. My way of interpreting this quote is very simple. I try to use universal laws as an example. The theory of the law of the body, the version of Schelling, says that we are not primitive.

2:30 L'ensemble de notre savoir ne consiste qu'en théorie, c'est théorie empirique, qu'est parce qu'en prendre conscience comme des théories nécessaires. Toute théorie, quel que soit par ailleurs son contenu, peut donc être élevée à la dignité des théories a priori. N'est pas une différence qui entrait primitivement aux théories, devient une théorie a priori. Or, s'il faut qu'il soit possible, donc on propose la caractéristique qui vise à dégager les configurations mathématiques qui garantissent la consistance rationnelle de la nature. These are the various forms of nomological necessity. Speculative physics aims to highlight the rational necessity of physical theories itself. Speculative physics aims to push back as much as possible the speculative facticity of physical theories, that is to say, to transform the empirical or a posteriori characters into a rational necessity after theory. This is why this project, which is guided by a kind of amplification of the principle of reason, aims to counter the insurmountable forces of facticity. Well, the forced operation of the project should allow us to locate the possible points of impasse. That is to say, if we can analyze to what extent this theory comes from a methodological remark,

5:00 given that it is a theory of some kind, the way, in my opinion, to locate it is necessary, and to identify the conceptual impasse of the previous theory. It seems quite banal in the case of mechanics that do not yet understand the conceptual approach. That is because we do not yet understand the classical mechanics. What do we not understand in mathematics by quantum mechanics? From a strictly theoretical point of view, I say that on this point, if we do not understand, in my opinion, quantum mechanics, it is because we do not yet understand quantum mechanics. The fourth remark is that this kind of speculative and theoretical deductions is not an ontological or mathematical deduction, in the sense that both quantum mechanics and quantum mechanics are different. We can make a list of different modalities, modalities, we find those that assert something beyond the subject, pure chaos of the second level, which is what it consists of, but does not represent it.

7:30 This gradation goes from the most idealistic version of the theory to the third version. This third version, we find that it says that the laws of nature, except those that are transcendental, that is to say that they exist, but in the rational laws there are laws of nature. These are laws that we cannot deny. The fourth position, quite original, is the position of Meillasson, according to which it is possible to demonstrate the absolute necessity of the factuality of these laws of nature. This is what he calls an irrational principle. These four possibilities, I would say, are the regulatory postulates of physics. This conception imposes a... I believe that the advent of a new theory is not a revolution or a scientific event. That is to say, a theoretical future that, as a moment of inauguration, a new historical sequence, inaugurates a new paradigm that would be incommensurable with the present paradigms, that is to say, impossible, but rather the consequence of a rational necessity, an impenetrable limitation between rational and quantum mechanics.

10:00 As for quantum mechanics, I agree with the observation that quantum mechanics, both classical and quantum mechanics, is an abstract conformalism. Mechanics is a machine in which I can introduce objects, and the machine is going to give me a certain number of objects, etc. So I can introduce them in classical mechanics. In a certain way, mechanics should be understood as a general theory of physical objects. So we can ask the following question, is it possible to remove a formalism of mechanics from such a theory of generic objects? Is it possible to make a purely conceptual reading of the formalism of mechanics and to draw a theory of the object? Well, the answer, in my opinion, is significative, and that this is only possible for quantum mechanics. There is no such thing in classical mechanics in which one can find a notion of objectivity in quantum mechanics.

12:30 And that, on the other hand, in classical mechanics, there is no such thing. And in fact, we can understand a movement thanks to... We do what it takes to make the start of mechanics really an object theory. I will take the opportunity to make a certain cartography of the current state of physics. In the research program, in the first place, we have a theory. In the second place, we have in physics, particular objects. In particular, we have two types of objects. We have material objects. The forces in physics are described by what we call the million-to-two particular theory. General relativity, which is the theory of things, and the theory of Young-Mills. So we have an abstract theory of physical objects, which is quantum mechanics. Two types of objects, material objects and signals. And now we can introduce these objects into our machine. This is what we call quantum theory and quantum gravitation. These are the various instances that should be of this form. Let's move on to the mechanics. In the presentation of the theory, I will focus on a central point of quantum mechanics, in which we can locate the minimal difference between quantum mechanics and classical mechanics, which is the following.

15:00 You know, in classical mechanics, the position and quantity of the exact movement can be predicted at any time. The position and quantity of the movement of the system. Against quantum mechanics, the position of a system characterized by the quantity of the movement well defined cannot be predicted by the theory. In general, the quantity of movement and the position can be predicted only to certain entities. Einstein, Kodol, Rosen argued that the position and the quantity of movement in the system can be predicted with accuracy. The quantity of movement and the position are well-defined objective properties, but quantum mechanics cannot predict them. So we have to conclude that quantum mechanics does not provide a complete description of physical reality. That is to say, in the art of biology, there would be elements of physical reality that are part of the theory. These moments are elements of physical reality, but the theory does not allow me to know them. Well, the path I will follow today is the following. First, we will define what I call the quantum theory of logic. Then we will show that, according to this theory, the quantity of movement and the position cannot be of objective property. This means that the classical description of a physical system by means of the position and the quantity of movement is not objective. And that, on the other hand, quantum mechanics provides a complete and objective description of the state of a physical system.

17:30 Well, since we are in the International Center for the Study of Contemporary Physics, I will send you some canonical references. And, in fact, this quotation by Deleuze and Guattari represents, in a fairly clear way, this issue. Even in quantum physics, the demon of Heisenberg does not express impossibility, but he measures exactly the sublime interpretations of thermodynamics, of relativity, of physics, of perspectivity. He does not constitute a relative, but on the contrary, what can be released, what can be released. We will see in the air in what sense this idea that we will find in quantum mechanics. Well, so I'm saying that quantum mechanics can be interpreted as an object theory, so what problem can an object theory give us? Well, the problem is as follows. As you know, multiplicity is not a pure chaos, it is consistent, leaving completely alien sensations. It has been clearly understood by Whitehead. Process and reality, sometimes we see an elephant and sometimes we do not. That is to say, multiplication can discern objective configurations.

20:00 An object can be discerned by its own determinations. That is to say, by objective properties that allow it to identify and recognize it. An object does not only have its own determinations, but in addition, an object in itself, it presents itself in the form of profiles, keys or facets. We never see an object... But we only see object profiles, which is by means of this different terminology of Frege, we can say that the same reference can have several donation modes. That is to say, the three in the morning and the three in the evening are different donation modes, the presentation of the same preference. In other words, the sensitive multiplicity consists of creating a multiple of profiles of an objective unit, which is characterized by a set of objective properties that guarantee the identity of the object. We can therefore, from what we have just said, enumerate the constitutive categories of the notion of object. I will summarize. In the first place, we have a determination, that is to say an object has objective properties that characterize it. In the second place, an object is phenomenal, that is to say an object is present. In the third field, there is a unit, i.e. the different profiles are connected by means of certain scientific transformations of the object, i.e. an object, and finally we have a notion of identity, i.e. the objective properties are invariant vis-à-vis the transformations that allow the profiles of the object. I change, I turn the object in order to have access to its different profiles, but there is something that remains identical.

22:30 We can therefore recover the definition proposed by Alain Badiou in The Law of the World when he says that by object we must understand what is current in the appearance, or what authorizes to speak of this being as being inflexibly itself. So what is the theory of the object of its surface? To explain the relationship between the properties of the entity of the object, the multiplicity of these problems was first addressed by the transcendental tradition. In the transcendental tradition, we postulate, ontologically, the unit that is necessary to assemble the multiple sensitive systems in an object. And it also contains the operations that allow us to render the effect at the time, the unit of the pre-pushed perception, the multiplicity of non-ethical sensitive data put together by the data. And in contemporary philosophy, there are, we can see, tentatives in progress to find a solution, to continue a theory of the object. From this subject matter, I am going to give an example of the Yoneza letter in theory and category.

25:00 I discovered the idea that there is a theory of the object in suicide in the letters of Yoneza in the books of Guérino Manzola and Toposov Music. And the content of these letters, the conceptual content of these letters, may appear very unknown. It may be completely characterized by Isomorphism. The objects that are connected by the relationship. So, according to the genesis of Ionetta, the appearance of an object in a category can be completely characterized by all the relations it maintains with other objects. Being is reducible to what other objects have. And what we see depends on the type of relationship that is admitted in the category. If I take an object and I put it in another category, the object will manifest itself in a different way. Because then we have the position of value. Badiou, in a certain way, returns to a certain transcendental tradition by saying that the relational network is not enough to constitute an objectivity but that, on the other hand, it needs an entity that is no longer useful but that provides, in a certain way, this operation of constitutions. So, according to Badiou, a category is not enough. It is necessary to add to the category what can be called a constituent object. And a category that is included in such an object is what we call an Anthopos, so we can say that an object in the philosophical sense of the term exists, and not in a category, but in an Anthopos, and that such an object constitutes and declassifies the parts, that is to say that the components are therefore not united in a set of parts, and not united in a set of remarkable books by François Valle, the part that I am reading, so I am not able to read it myself, given that François Valle...

27:30 So, after this long introduction, we will now move on to the physical object, which is a configuration that has different profiles, in the first place, and in the second place, a physical object is defined by the set of its objective properties. This set will be called the Eidos of the object. The set constitutes the Eidos of the object. The objective properties, by definition, in terms of their objective, must be invariant with respect to the operations that occur. In other words, given that I am a computer scientist, the objective quotient must be invariant with respect to the objective quotient. These operations, the operations of modifying the profiles without modifying the objective quotient, will be named here to observe without modifying the objective quotient. We thus recover the definition proposed by Hermann Weil. Objectivity means invariance with respect to the group of automorphisms. In this characterization, there is a central problem. Given any object, what are the automorphisms of the object, that is, what are the rational transformations to have access to these different properties without modifying the object, that is, without modifying the whole of its properties?

30:00 For its application defense of invariance by Kalman Baye, he said, reality may not always give a clear answer to the question what we have. So this is the problem to which we can propose a solution. So I repeat, given an object, we can perform different types of transformations, different points of view, in order to observe different properties of the object. For example, I turned the object around and I can observe the object. Nevertheless, the fundamental idea that I want to convey is that for a given object, there is only a certain amount of information that is accessible. For example, if I take an object that exists in time, I will observe it at different times of time. In other words, in my terminology, I can say that the temporal evolution that allows me to observe the temporal axis of the object. On the other hand, if I have an instant object, an object that exists, it cannot be observed in time.

32:30 Another example is the following. If I take an object that is aligned with the axis, I cannot rotate the object around the axis. This means that the rotation around the axis is not an automorphic. So I repeat the intuitive idea of the following. Even the object that establishes what these automorphics are, there is not a set of automorphics Now I'm going to develop this idea, I'm going to introduce a certain terminology, we are going to say that an object participates in a way that is specific to a certain number of what I would call universal ideas or operations. That is to say, there are ideas or there is a concrete object that participates in a certain way, for example, we are going to say that there is an object that rotates around the axis, in a certain way, a rotation around the axis. The idea of rotation around the axis is an object that can participate in this idea. In a certain way, in Whiteheadian language, we will say that the idea of rotation around the axis is an eternal object that makes an ingression in a certain way in the object. The idea of universal operation is in the object. The ingression of such a universal operation in the object is a high operator of the object. So we have the following representation.

35:00 Different objects, we have what I am calling ideas or universal operations, and these ideas make an ingression in objects, and the result of this ingression is the definition of what I am calling an object operator. So we can say that an object can be characterized by the way in which it participates in certain ideas or universal operations. Yes, if we have two different objects, so we have what I am calling ideas or universal operations, for example, the state. These ideas make a question in the object and define what I am calling an auto operator of the object. That is to say, we have something of the order of the universal which is shared in the object and which assumes the form of a concrete operator. So, two different objects can differ because... Different ways of the same idea or because they are part of a different idea. This object does not participate in this idea. So 10 different objects can differ. Either because they are part of a different idea.

37:30 We'll see. But basically, it means the following thing. If this is a universal idea, rotation around the axis, for example, it means that this object turns around the axis in a certain way. And this object turns around the axis in another way, that is, we have something in the universal order called rotation around the axis, but each particular object, so I am describing this situation differently from the same universal idea, that is precisely what will define the nature of the object. The difference we are talking about is, for example, the question of knowing if for one it is an automorphism and for the other not, or is it the difference that counts? No, in this case, they are all automorphisms of the object. Okay. In fact, the automorphism of the object is generated by the auto operators. It comes after. Can you give an example of what kind of difference these two turn according to the same operation? Well, for example, I can have a D and I can have another D. I can turn this one around the axis. I will see different numbers here. So we can say that these two objects turn around the axis of a different person. And in fact, we will use these differences to characterize and differentiate them. All of this is important enough to be able to continue with the lecture. In fact, the object is only the set of determinations of the regard of these objects in the system.

40:00 In this case, there is an objective determination that is not the regard of the cause of the multiplicity of the participatory. But what is in the object itself? Yes, I am making a definition of characterization completely in French. I was talking about the properties of the object in French. For example, I was continuing with this example. We can imagine that this die has the same color in all the faces. And we can imagine that this other die has the same number in each face. Each face is colored in a different way. The number is an objective property because it doesn't change when I turn the dice. But the number is a profile. When I change the dice, the numbers change. However, for these dice, the number is an objective property because I can turn the dice and I always see the same number. However, the color changes every time. The color now becomes a profile. I observe a different color. And to follow the measure, I have to clarify the line. So the same characteristic... I have not yet finished explaining the general theory, and then we will show in what sense this theory is in a certain way filled by quantum mechanics and not by classical mechanics. That's why I don't know what it is.

42:30 In fact, in physics, as I said, classical mechanics or quantum mechanics are theories that do not correspond to objects. So I can introduce there what I want. I can introduce my object, it can be a particle, it can be a planet, it can be a space. I am in the process of making this a little bit intuitive, but maybe afterwards, if it is not clear, I do not know. That's something that I ... Imagine, for example, that the color is not the same. Imagine that the light is there and the color is there. Yes. In this case, the color will not be ... This is the definition itself of what I'm trying to write for myself. And conversely, you would agree that what you call a profile, right? It's any character that can not be a variant by any operation. Yes, but for this object, it's a variant. That's why I called it a profile of objects. No, I'm talking about profiles. Ah, sorry. What you call a profile, for a given object, it's any character that... In this case, there is at least one operator. No, it's not as general as that. It's not as general as that, but I want to answer you. We will see that there is a kind of correlation between the objective properties and the profiles. This idea of characterizing the properties of the object from the regression of something of the order of the universal is a language that I learn from the category theory.

45:00 In the category theory, for example, if I come together, there are elements. For example, the element A. A language that is very subtle in theory is to say, well, there is something that we can call a universal element, there is a universal element, and instead of pointing this object A as an element of this set, I said, in fact, this object A, I'm going to write it as a certain ingression of this universal element. So it has a certain function. This universal object can make an ingression in the whole in different ways. It can make an ingression with this other function. So instead of describing the elements, I describe the functions. So language means that each element of the whole is only one way that has the universal element to make the ingression in the object. I am reproducing this language in the case of mechanics. There are different operations for the same object. Yes, but what differentiates the objects? There are different universes, there are different universal operations. That is to say, there is a whole set. And each object will participate in a certain number. They are already given? Yes, they are universal. That is to say, they are there for any object. Yes, but the universal is different. That's the point. No, no, no. There is a whole set. There is a whole set of ideas.

47:30 I think that the atomicians are aliens. They are not aliens. In any case, they are two different things. Yes, they are there in the economy of any object. So now we are going to go into the core of all this. We have two ways, according to everything I have just said, to characterize an object. Either by the objective properties that make up its eye, an object has objective properties and these properties allow us to differentiate them, or by the ways in which it participates in certain universal ideas and operations. I have given two different characterizations. An object is characterized by its objective properties. Where an object is characterized by the way in which certain ideas or universal operations. What I want to do now is to unify these two different ways of characterizing an object. By using this approach, I mean that an objective property of an object is a quantum of how an object participates in a certain idea or a universal operation. That is to say that each objective property of the object characterizes how the object participates in a certain idea or a certain universal operation. The second fundamental postulate is the following. The auto-operator resulting from such an ingression is the generator within the object's automorphism. We can put these two postulates together by saying that the objective properties of the object define the auto-operators that generate the object's automorphism, i.e. the operations.

50:00 Until now, I have said several things. I have said that an object can be distinguished thanks to its objective properties, and then I have said something a little more obvious. The object can be characterized by the way in which it participates in the universal cooperation. Now I am trying to bring these things together, that is to say that each objective property of the object specifies how this object participates in a certain universal cooperation. For example, the property, we can call it, characterizes how this object is defined by this objective property. Why? Because an objective property is nothing else than a quantity that... The idea is that the operator, a universal operation, is an operator of the object, which results in the ingression of the object. The popular design is that this operator, and I remind you that an automorphism means a transformation that allows me to observe. So now I am intriguing the notion of objective property and the notion of profile. How a universal property makes an ingression in the object. And the operator that results in such an ingression generates a transformation of the profile. These are the two postulates that will necessarily lead us to quantum mechanics.

52:30 That is to say, we cannot assume these postulates within the framework of classical mechanics. Classical mechanics does not satisfy these postulates. One last time, we have universal operations. An object participates in a certain way in a certain number of universal operations. Each objective property of the object specifies how the object participates in a certain operation. And the operator who decides to observe the different profiles of the object. So now I will repeat that. I will say that the operations that synthesize the multiplicity of these profiles are induced by the doses of the object itself, and not by a function of the constitutions. That is to say, the operations, the automorphisms that allow me to observe the different profiles are generated in a certain way or are induced by the properties of the object. So, it's the idos of the object itself, if you will, the In Hegelian language, we could say that the letter of the object, i.e. its eidos, is the whole of its properties, which is the generator of each of its objective properties in the eidos.

55:00 These are the automorphisms that allow us to see these differences. A remark, we can say that everything is phenomenalized, even the eidos, which is the generator of the phenomenization, because an objective property, far from being a kind of hidden essence, is only a variant profile, i.e. there is a kind of distinction between profiles. An objective property has nothing else but an invariant profile, but it is something that can be seen in the object. Well, now I can answer. I am saying that this object is characterized by this property here. This property specifies how an idea-operation makes an ingression in the object. This ingression defines an object's auto-operator. This auto-operator generates an automorphism, and this automorphism is an operation that does something on the object. So, for example, it turns the object. So everything that changes with respect to this operation is a profile. So they are linked to an operation? Yes, that is, each operation defines what I called in the paper a profile orbit. That is, a high operator generates a certain kind of information. And this information is nothing but a different profile orbit. So I call a profile everything that belongs to a profile orbit generated by a high operator. So now, I insist again, it's... Objective properties and profiles suddenly become intricate, so to the question of what are the profiles of an object, I answer, well, you have to see, you have to analyze the operations generated by these objective properties, so each objective property will generate an operation, and this operation there, so each element of this set is a profile.

57:30 An anniversary operation that is not associated with a property, because precisely it leaves nothing to be used, it is usable, at this point we have profiles that appear. Well, for example, if I apply this property to this object, this property here, it is a property that does not belong to its Hilbert space. In this case, no, no, no, because as I said before, you cannot apply any operation to any object. For example, if I have an unidimensional object, I cannot rotate it, so I am saying that this object does not participate in the rotation around the axis. If I can turn it around the axis, it participates in a certain way in this operation. It's not possible. If I have an instant object, if I have an object that is in an instant, I cannot observe it in different ways. So it does not participate in the universal idea. For an object, it is participating in an idea. I would say that being an object means participating in a certain way that is proper to it in a certain number of ideas. This object, what is this object? It is a physical configuration. The object is, in a certain way, characterized by the properties peta and p phi that determine the universal operation. An object is nothing but a configuration that participates, in a certain way, in a certain number of universal operations. And when I say in a certain way, that's what determines the object. But there are no object-based configurations? The object is only participation? The object is only a configuration that participates in a certain number of universal operations. Well, there are properties, there are properties that I can't say are objective properties of the object.

1:00:00 They are things that belong to it, but it's like a number on a dice. Well, I can't say, if I take a dice and I see a number of them, I can't say it's a property of a dice. But still, it's something of a dice, it's a profit. That's the closest thing to an accident, let's say. It's a profit that belongs to a profit orbit generated by an operation. For example, in a dice, we're going to... These objects participate in the linear rotation around the axis, in some ways. Why? Because the rotation around the axis generates a profile orbit. And this profile orbit, what it writes, is the number 1, the number 2, the number 3, and the number 4. If I rotate the D around this axis, I will see the profile 1, then I will see the profile D, then I will see the profile 3. This is the universal rotation operation around the axis of some of the properties of the object. The elements of this orbit are the non-objective properties of the object. And if we talk about the orbit of the object itself, is it part of the object itself? No, it's a different way of saying what I'm about to say. What is part of the objective properties are the generators of this orbit, not the orbit. But the orbit is generated by an operation, and this operation is characterized by... So it's a different way of saying the same thing. What is a property of two is the whole orbit. But instead of numbering the orbit, what I give is the generator of the orbit. That is, the auto-operator that generates the automorphism. No, it's the same thing. That is, it's a little more technical, but when I say an operation, a generator of an operation, it's an infinitesimal operator.

1:02:30 Then I can concatenate this operation in a finite way. Okay, so I can do... No, I'm trying to make it as pedagogical as possible, but, for example, a temporal evolution, the parameter that generates the temporal evolution is a continuous evolution, so there is a whole set of infinite profiles, the property of an object, so an object that has a certain energy, such as I can observe, for example, this view here, there are different numbers in each face, but there is always the same color, so we can say I look at the view and I observe and the color is... Thank you for your attention and see you in the next lecture.

1:05:00 They are first classified, they are first continuous, the position, the speed, the energy, the temporal evolution, then it is more normal to start a continuous separation. And an object? Yes, the point, because it is the rotation around the axis, the level of the axis, the rotation around the axis. And an object in which the properties do not vary, it is an essence that does not participate in ... What is an object? I don't know, but you can imagine an object that is always green, always with an A, always with an E. There are no variations? It's not possible, because if this object participates, for example, it has an objective property, it is green. What I just said is that this property characterizes how an operation is done in the object. So, of course, there is an operation that must change something. So, formally, it doesn't exist. If I can say something about an object, the property that I am throwing at it specifies how this object participates in an operation. So, of course, there is an operation that must change something, okay? This is the consistency of everything I am saying. There is no object that is completely separate. It is the same thing as saying that there is no object that is not of determination. All objects have a determination that allows me to say, here, there is an elephant. I would rather say the definition of being, which is completely indeterminate. An object has determinations, and what I'm trying to do here is to define what a determination is, and a determination is nothing else than a quantity that specifies how an object participates in a certain operation. For emphasis, there is a certain terminology that is, in my opinion, in general, there is a certain terminology that exists in the theory of Scholes, when we have a symmetry operation, This is a phantasmatic direction. Why? Because an automorphism of an object in a certain way is an evanescent operation, that is to say, I have an object, I turn the object and the object does not change, so there is a certain inertia vis-à-vis the operation, so I did something and there is no effect, so it is as if the object was in the process of evaporating from my operation, so we can rewrite the following, we can say that the consistency of the object...

1:07:30 Therefore, what is common in the phenomenological distribution of these products is guaranteed by the idos, which are nothing else than the generators of phantasmatic transformations of the universe, that is to say, of quantum transformations, without modifying the object by the use of these products. For now, we will show in what sense this set of concepts represents, in a certain way, what we see in quantum mechanics. In particular, what happens is the following thing. All of these properties configure what I have called the eidos of the object. What we will see now is that there is an internal structure in the eidos. The eidos cannot be a collection of any number of properties. There are certain constraints of the algeoric type that the eidos of an object must satisfy. And the constraint is the following. For the moment, I have said two things about the properties of an object's objective. In the first place, I have said that the objective is a variant vis-à-vis the homomorphism of the object. It means that if I turn the object, the objective property is already there, I added that an objective property is also the generator, in a certain way, of one of these automorphisms. So the objective property plays a role. On the one hand, it is an invariant, and on the other hand, it is something that specifies how the object reacts vis-à-vis a certain automorphism. If we put these things together, we get a result quite... That is, an objective property is an objective, so it must be a variant.

1:10:00 A variant in relation to what? A variant in relation to the automorphisms. But these automorphisms are generated by the other objective properties. So an objective property must be a variant in relation to the automorphisms generated by the other objective properties. So the different objective properties come into relation. Let's imagine that the Eidos is composed of objective properties F. These are the properties that allow me to characterize this object. F is an objective property, so it must be invariant. It must be invariant with respect to the object's automorphism. However, these automorphisms here are generated by the objective properties themselves. So that means that the property F must be invariant, I want to write it like this, with respect to the automorphism generated by our property G. I will write it this way. That is, each objective property must be invariant with respect to the automorphisms generated by the other objective properties that define the same object. A constraint is very, very strong. For those who know a little about physics, the operation at the technical level, the operation that represents this operation, is what we call the fish hook. Given the objective properties, if I take the fish hook, it means that it is the transformation of a property by the automorphism generated by another property.

1:12:30 So what I am saying is that we are talking about a kind of self-consistent clause of the Eidos, which is the following, all the objective properties that belong to the same Eidos must be compatible or fully measurable. In technical terms, again, it is said that the Eidos of the object must constitute an algebra of commutative fish. This is the technical terminology. Any property must be invariant with respect to the general operations caused by other properties of the same object. We can show in physics that if we take the quantity of movement P, we can define the quantity of movement in this physical term as the objective property that generates the movement of the object in a direction that we will call Q. This is the definition of the quantity of movement in this physical term. It is a quantity that generates, in our terminology, a transformation of the variable Q. This means that the transformation generated by the quantity of movement of the variable Q is not zero, because Q is not a variant of the operation generated by P. So the conclusion we must draw is that Q and P cannot belong to the same object. Defining an object such as its idos is constituted by the quantity of moment P and the Q-variable which is affected by the transformation generated by P. So, if I have an object serviced by an idos to which the quantity of moment belongs, that means that the Q-variable is transformed by the operation generated by P.

1:15:00 Well, this is nothing more than the principle of uncertainty. In other words, the position and the amount of movement in a system cannot belong to the idos. In other words, the amount of movement P and the position cannot be objective properties of the same object. It is inconsistent. This is a direct consequence of the postulate proposed. A remarkable conclusion is that for this object, the different values ​​of the position must be interpreted as different profiles of the object. In general, I'm talking about the amount of movement. If we introduce a time parameter in the system, which I haven't done until now because it's not necessary, if we introduce a clock, instead of talking about the amount of movement, we can talk about speed, and instead of talking about the automorphism generated by the amount of movement, we can talk about spatial displacement in space as time goes by. That is, we go from this quite abstract characterization to a characterization in terms of a temporal evolution. To do this, we have to introduce a temporal parameter measured by a revolver. In these cases, we can say that the different possible positions in a system characterized by a well-defined movement quality must necessarily be interpreted as different spatial profiles of the system, that is, non-objective properties of this system. In the end, it means that an object that is in a well-defined state of movement cannot ever be in an instantaneous objective position. And this is nothing more than the quantum version of the paradox of these names. Something that is moving cannot be found somewhere, which is a completely ambiguous result. But it is a result that we achieve thanks to quantum mechanics.

1:17:30 In classical mechanics, we believe that an object that has a certain speed can be found somewhere. From the point of view of quantum mechanics, this is inconsistent. And for us, now, this is quite reasonable. This is an object with a well-defined quantity of movements. So if we take a D, it doesn't make sense to ask what the objective phase of D is. A D doesn't have an objective phase. In the same way, if I take a B, it doesn't make sense to ask what the objective phase is. Because the position is a profile, it's not a product of the object. Nevertheless, if I take a D, even if a D doesn't have a privileged phase, But this does not mean that this phase is the objective phase and we will obtain a non-positive phase. In my opinion, this does not mean that this is the objective phase. There is a complete analogy between the two. I can make a measurement of the position and I see that the system is in a position. This does not mean that the object is only a profile. Referring again to the canon, the characterization of Tedeschi and Guattari in this situation and the next,

1:20:00 Even a single particle has an associated wave as a flow that defines the co-existence space of this object. I think this is a very correct formulation, the co-existence space. The data I just drew is nothing but a figure that represents the co-existence space of all possible positions. But there is a co-existence. Here we have the definitive answer to the question of what an object is, according to what I just explained. I will repeat it one last time by including all the elements. An object is nothing more than a physical configuration that actualizes, in a certain way, a certain number of universal operations. Each universal operation emits in the object in a particular way that is characterized by one of the objective properties of the object. The emission of this universal operation defines a self-operator of the object. This self-operator generates an automorphism of the object. And in particular, if the object is characterized by the property quantity of movement, the operator that I find in the object is the generator of position transformation. This means that the position cannot be an objective property of the object. It is only a property. I tried to argue that quantum mechanics, in accordance with classical mechanics, is a general theory of any physical object. Well, what is a physical object? As I just said, it is a physical configuration defined by its leader, that is to say, by the set of its objective properties where each of these objective properties specifies how the object participates in a universal idea of operation and as the ingression into the object of one of these universal operations defines an out-operator that generates an automotivation of the object, that is to say, a transformation that permutes the different properties of the object. If we accept this definition, we say... In a completely conceptual way, without any technicality, the principles of uncertainty, that is to say, if the quantity of movement is the objective property of the object,

1:22:30 then the position cannot also be the classical description of a physical system by means of the position and the quantity of movement of an over-determined description. Because it includes not only the objective properties of the system, but also the non-objective properties. And the conclusion is that, on the other hand, the complete and objective description mechanism of the bizarre system, you know, the reference of... A point of detail. When you talk about the quantity of movement, you always assume that it is constant, that it does not vary in the course of time. I choose the example of an object characterized by a quantity of movement well defined, but it is only an example. Otherwise, it would not be an objective property. Of course. I can choose an object that has the position in the objective quantity. And the whole situation is reversed. The position is nothing but a property that specifies the transformation of the amount of movement. That means that the amount of movement is a profile in a system that has a well-defined position. There is a kind of encryption between variables. Each variable has another variable that is associated. So if one is an objective property, the other is a profile. If the second is an objective property, the first is a profile. In geometry, it is called a symplectic implication of a pair of variables. I chose an example here. So it would lead you to say that an object that is immobile, in the same position all the time, this position is part of your objective property. Your criterion does not allow you to say in general if certain characters are objective or not.

1:25:00 The position can be as good as the quantity of movement for that. I don't know if I have to answer, but in fact... The formalism of quantum mechanics is very flexible and it allows all possible elements between the two extremes. That is to say, as soon as I position a moment's quantity, I can find a situation where neither the moment's quantity nor the position are objective properties. That is to say, for example, the position is, up to a certain measure, an objective property, and up to another measure, a profit. That is what we call the Ranschart physics, objective properties that are not... This is the generalization of what I have just said. You can understand these cases with the concepts I have just presented. ... that mix objective profit and profit, at least objective profit and at least unprofitable profit. No, not at all. The only thing that is necessary is that the balance between profit and objective profit is respected. To respect this balance, we can respect this balance without being completely... The system is consistent. For example, if a quantity of the position is not a complete objective property, it means that the transformation it generates is not a complete transformation of the gauge. It means that the quantity on which this transformation takes place is not completely... it means that around it, this quantity is also a property of the object. So it generates a transformation of the gauge. And these certain measures are the terminals of our test. Yes, of course. In fact, the exact formulation of the principle of uncertainty is the mathematical formulation of this balance. In the principle of uncertainty, it is a mathematical expression that allows all possible distances between the two extremes. Between the extremes in which we were completely objective, completely in profile, the opposite of all the intermediate situations. So it's really a mathematical expression.

1:27:30 Yes, you have to create the object. By the way, to talk about an object, you have to create it, if you want. Create it, if you want to create it, in an experimental context, you have to create it. That is to say, any object, well, it's the same thing as saying that the objective properties of this clock depend on the person who made the clock. Yes, of course. And if we had made it from a different person, the objective properties would be different. An object, well, it's different. So the objective properties of the object depend on how we made the object. The consequence of what you say is that the observables in the sense of measurement etc. are not at all a criterion to say that it is objective, not because I measure the instant state, the position of the instant state of the system that this position is an objective characteristic. Exactly, it is the example of the 2. The measurement has no precedence. Yes, if I make a move of 2 and I get a 3, it does not mean that the 3 is an objective characteristic of the 2. If I check a piece, and I pass it, and I get a pile, it doesn't mean that the pile is the real property of the piece, right? It's just a profile. And in quantum mechanics, it's exactly the same thing. If I get a system that is in a well-defined position, it's not the right position. It's big and it's possible to be precise. But there's something complicated in quantum mechanics. I'm talking about this here, and I'm not able to explain it. There's the fact that, of course... A measure modifies the system in a certain way. A measure is a physical procedure. And as a physical procedure, it must be modelled with the tools of physics, in particular with the tools of quantum mechanics. All this has brought about a series of complications that have not yet been resolved. But that's another chapter.

1:30:00 It's not only dead or alive. Well, in fact, that's what happens in physics. In physics, we always take the example of the quantity of the moment of the procession, but, well, a system can be characterized by any real law, right? It can be, I don't know, energy, for example. So, I don't know if that's the question. To characterize an object, it can say something about the object. To determine it, it can say something that determines it. So I'm trying to define... What is the property of an object? All I'm trying to say is to give you a definition of what a property of an object is. The relationship between its mental and its operations. The relationship between the operations of objects and the relationship between the operations of objects. No, in my opinion. No. I believe that quantum mechanics is a logic, if you will, a logic that seems very physical. Obviously, given a theory of the physical appearance, it has epistemological consequences, if you will, depending on how the worlds are, we will have access to these worlds in some way or another, so quantum mechanics has consequences of the epistemological type, in the experimental sense of the term, so I think a transcendental analysis of quantum mechanics is quite relevant, that is to say an analysis that analyzes the transcendental conditions...