2 of 6 (contd.)

0:00 There is a probability that we are now going to expand here, and the probability is that we will be able to look at all of this in the future. You can see that it is very precise. It is in the alias, but it is very precise. It is precise because in the alias, you do not have the state of the system, but as soon as you have the state of the system, it is important to know the state of the system, because it allows you to think again. On the other hand, you know that the state of the system is in the past. It is possible that it is the state of the system before. You have your system which is in a state of Psi, which is the name of our first lecture. You say to yourself, well, I have just one measure, boom! I'm going to teach you, whether it's here or there, certain probabilities given by the previous lecture, after your first lecture. You can already see that it corresponds to what we did earlier. You can also see that it's a way of probability, because it's very easy to understand that the sum of u is the length, if the length of Psi is a way of summing up. Everything is possible here, I'm sure you will get something, and on the other hand, you know that if your vector C before the measure is in one of the 8, well at that time, you will get a Y number with probability 1, a J number, the J is different from the Y, with probability 0, and that was the 2nd part. So the idea is to see what we can do with this formalism. I don't know if you can see it, but I think you can see it. The important thing is that we are going to try to illustrate it. First, to make a link with what I said yesterday, you can see that if we try to look at the theoretical theory that I am going to describe now,

2:30 well, Newton's method of reality is that the conditions of the system in physics... I gave you an axiom 2, a part of the evolution, that you can find in a computer operator, and I mentioned to you that it can be linked to an equation. This part of the evolution is governed by an equation. Of course, there is another part of the evolution, an axiom 4. My particle is polluted with calcium-2, which is usually blue, copper, copper. I find that, from time to time, there are measurements that break this beautiful image by things that, first of all, are not deterministic, the notion of randomness, and on the other hand, which are very brutal. There is not, until now, the phenomenology of the calcium-4 in terms of an equation that we could solve. For those who have heard it, I will talk about it later, because I don't know the coherence. So in the end, we find ourselves in a problem of decision-making. If I told you about a system that is about to evolve, you would say, but what am I going to do? Am I going to measure it or am I going to make this decision? Theoretically, they don't decide for you. Theoretically, they don't decide for you. What they decide is a kind of knowledge of how to do things. For the moment we have this problem, these two axioms. These two axioms make two coherent evolutions appear, but they are coherent between them, they work very well, perhaps to succeed in the evolution of our physical life, etc. And an example of coherence that we have, the coherence of science and science, the coherence of the theory, is precisely in the axiom K, the reduction of the wave path. What is the reduction of the wave path? These are the ones I'm talking about at the beginning.

5:00 It's the fact that you have, before the measurement, a number here. You effectuate the measurement. You fall on a number here. So, now, if I calculate the measurement of a number here, we're sure that we're going to get a vector of 8, because there's another probability. If there's a probability of 0, we're going to get a vector of 1. So, you see, this is an example of coherence. If you don't worry about this reduction, This is something that changes a lot of people, including physicists who have accepted the paradigm of physics, but you see that what I see here and there has lost all the part of the system that is given to life, it has lost where it is, hence the parallel universes that make up this thing that we are going to see that we do not need. The only thing to notice is that if we had not projected On the 3rd vector of the array, we would have a problem because, if we perform the measurement immediately after, we would expect that it would be late, that we would obtain the same value, otherwise, by continuity, we would have reduced a period of time after which the new measurement, so by continuity, you would find the same values. This is exactly what we are talking about here. Another example of coherence is the evolution. As I said before, limitarity preserves the norm of physics, and so it preserves the sum of the numbers that are preserved, so it preserves well that your probability remains the same for all of us. So there are several reasons why it works very well together, and so you can play in general what we do in the physical-physical field. We have been evolving almost all the time with such and such. If you want to talk to us about quantum algorithms, for example, we are going to talk about them in the next few weeks.

7:30 But what I'm telling you is that we're just starting to make some basic evolutions in which we're only doing measurements. That is to say, within a measurement, as soon as you find the result, you have something to say, now I'm going to do this other measurement. You can have fun doing these evolutions that are managed only by the action plan. Once again, these two actions that are coherent with each other, and that give you two different visions of the evolutions of a system, are very important to us. What is formalism and, if you will, what will be a little bit the regularity of formalism. So, first of all, if you know that you are doing well with, from the beginning, with the probabilities, you have to introduce a notion which is called the notion of probability amplitude. I have a question about these two axioms. Is it correct to say that what describes axiom 4 is implicit as a particular case the possibility of axiom 2, but what axiom 4 does is identify it as the measures? No, axiom 4 is outside of axiom 2, totally outside. For example, evolution in axiom 4 is not a land, it is a land of information. This evolution that gives, let's say, measures, is not an evolution in the sense of... Absolutely not. It is not included in the equation of change. It is one of the problems of the theory. It is like that, like that, but you cannot validate it by the equation of change. Absolutely not. Absolutely not. And you leave the system to yourself. You look at it. Yes, it's Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus is Venus, Venus

10:00 That is to say, this idea that measurements change the system, etc., it's informal, it's not the actual consequences. It's the fact of switching from psi to ui. It has changed in random ways. But it's not a change in the sense of... No, it's a brutal change. Brutal. There is a before and an after, there is nothing... You see that... So this is going to be the core. I also gave you a probability law, which is actually a square module. You see that the big difference between a classical situation and a probabilistic one is the density of a gas mold. The density of a gas mold is the probability law that we use. The 10 start to evolve. But here, you see that the part of evolution in the second part does not speak of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of

12:30 That is to say, we know the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, the square root, This is a square root. I'm not going to tell you how to do it. You know that in an equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation, you have to take the root of the square root of the equation We need four vectors of the most common geometric structure, the spinorium, and two of these vectors give us the mass of the Earth. That's how we discovered the electron wave, theoretically, before we discovered the electron wave. So this is a general spinorium, and I'll send it back to Daniel for an internet, there. So it's an amplitude of probability that we have seen. And, uh, well, I wanted to talk about a very bad case, so I can't have much time. Paroxysm is the idea of probability, the fact that we sum the probability amplitudes, and not the probabilities, to find the square So you have to imagine that a big part of quantum mechanics is that we don't sum probabilities, we sum entities, we take the square modules afterwards. And of course, it's an entity. That's for the square. Another remark that I would like to make, and then we'll talk about equations,

15:00 a very small remark, is that a way of putting together the axiom 2 and the axiom 4, so the two axioms that I'm talking about in quantum physics evolution, is to say that after all, there is only one evolution, which is the one given by axiom 2. But what evolves is not something that is really determined in the system, what evolves is the density of the probability, roughly speaking, of the probability, and so you have a probability that evolves in a way that is quite determined, and simply by evolving this probability you say that it is true, because the effect of the future is repeated in the same situation. In the past, we also have a kind of evolution that deals with variability. We could do a little analogy, but here we have a probability that is evolving. And another remark that I intend to develop is that when we look at how these things have evolved, In this way, the game is also increasing. That is to say, if you want, you see that the same probability becomes deterministic if it goes from 0 to 1. In this case, the probability disappears. So the quantum evolution, whether it be in the 20th century or not, is something that, on the contrary, always enlarges the probability of having very strong situations. So, with an idea like this, by showing in our lectures, we will be able to have a link between this randomness, this randomness that we are talking about here, and the notion of predictability and sensitivity to the conditions of the system. So, implications. I have already said an interesting part about this.

17:30 I have some notes that start to come to me. So, as we saw earlier, if we were to interpret this first step as the sum of the capitalized states, it would not be equal to a capitalized state. So, I like to use an analogy, which is not so much an analogy by the way. The logic is due to musical notation. So you know, if you take... I think it's good to understand... When you write the music, you have two strings, one string by an instrument, and the other. So this, I'm going to call it the H1 system, or the H2 system. So inside H1, you have... a little bit of the composition, because each instrument can play two notes at the same time. So you have a plus, And then, you have the product of the social dance, the two instruments of the dance. So, throw that away quickly, I'll write it in a financial way so that you can find it. What does all this mean? So that means that we can only hear the violin that plays C, or the piano that plays E. So that, you see, will be the violin that plays C and the piano that plays E. That will be the piano that plays E and the piano that plays G. You will even be able to hear a piano that plays mi and sol and a violin that plays do and si. You can see that you have a factorized state.

20:00 You will never be able to hear the state of this formula. That is to say, if you take the sum of the two factorized states, if you try to represent this in musical notation, and to see what this means to you at the acoustic level, You will notice that you are out of the paradigm of musical notation and that an agreement like this is literally impossible to find. This is an example in which I note that quantum mechanics consists, in the case of a work with a game in general, it consists of a set of symbols, which we have had for a long time, but in a completely symmetrical and equivalent way. That is to say, if we have this, it is very important. And this is a novelty. This is something that is not in the physical domain. It is from this point of view, for example, that the mathematical state is not reducible to the mathematical state. There is really a change. If you want, these implicit states can no longer be represented in a way that is interpreted by the mathematical state. So, I'm going to stop all this. But I'm not going to go into too much detail about them. So, first of all, it's in a way a classic theorem. That is, the idea of Bell was to say, well, let's suppose that I have hidden variables, that in my case, I have something that's not the same. Can I put in a gauge, a gauge of p, so that we can see that we can measure the relationship? All of these terms can be used to determine the measure of equality or neutrality.

22:30 So, this is a very interesting topic. If you look at the general program, it is a bit like what follows the PR article. The PR article is a bit more sophisticated than what we have learned, because, of course, there are concepts in physics and mathematics, and also in mathematics and mathematics at the same time, and, of course, in the whole passage of the 40th century. In the 1960s, there were so many extraordinary things that, well, people remember very well this bizarre thing that we saw in the school of physics. And so, the violation of the law and of the law of the computer, we do not hear in the meantime, but we succeed in implementing it experimentally. So, what is it about? If you want, in an ancient icon, after Schrodinger, Altenberg and others... There are two characters who have arrived who are now called Alice and Bob. I find it unquestionable. I don't know if it's a good title, but what I mean is that we can no longer talk about Callis and Bob. Alice and Bob are two people, two systems that exist as we want. They will have fun with each other. Eventually, they won't exist anymore. But for now, they are classic. And we assume that they will measure each two quantities. All of these are measured on each of the centers, because we have exactly the same system, the quantity of each of them, the quantity, as you know, as the position of the speed in a mathematical model. So for Alice, you have the and for Bob, you have the S and C. But I'm going to suppose that these quantities that are measured, that are measured, that are measured, that are measured, that are measured, that are measured, that are measured, that are measured, that are measured. Each one of them contains two values, which is very important.

25:00 If you have two values, you don't need to have a good teacher or even a good teacher. So it's the same as a teacher of physics and a teacher of mathematics. If you have two values, you don't need to have a good teacher or even a good teacher. So, from these four entities, you have two values. I'm going to associate the quantity as follows. qs plus rs plus rt minus u. So it's easy to show that either q plus r is equal to zero or q minus r is equal to zero. You can find that these entities, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Qs, Each of these measures is carried out independently, in the classical world, for example, in mathematics, geometry, physics, and so on. I don't want to go into too much detail about the history of mathematics and physics, for now, I don't want to go into too much detail about the history of mathematics and physics, for now,

27:30 and I simply say that I suppose that Alice Borg uses this measure in a number of ways, and that in each of the situations, the values taken by the entities are given by another probability. Each of these terms has a probability of having this value which corresponds to our probability of having a value. I have thus produced a notion of probability to which we correspond. So if I calculate the hope of the expression for the value, it is a sort of RST. I put the probability and then I put the value. If you calculate the elementary, since this number is less than or equal to 2, this will be less than or equal to 2 times the sum of the probability. And this, of course, will be 2 times the sum of the probability. On the other hand, if it is a hypothesis, suppose that E is equal to S, S is equal to S, S is equal to S. Esperance and reality, minus Esperance. The power of truth.

30:00 If Alice and Sylvain are classical people, the virtues are the virtues of life. And at the end of the day, how can we learn from them? We have to be able to give the meaning of this to the authentic. This is the usefulness of science. What will become, now, of the experience of the interior universe of the paradigm of quantum mechanics? What will become of the virtual reality? What will become of the future of quantum mechanics? That's what you can explain. It's in detail. That's why I'm not going to go into it. So, I'm going to go back now to the notion that we have taken the law of quantum mechanics and the quantum mechanics of quantum mechanics. One of the consequences of the action of the measurement is that you see that you will have another probability that will not be there. And this is not a reference to a priori. All this is a reference to a measurement of the observable system. There is therefore an aspect of the analysis of the whole of mathematics and mathematics of France. Look, if I construct the quantity under the parachute, it's perfect, but it's not the same thing under the parachute.

32:30 Suppose I calculate the height acting on this, and then the scale produces with this. When we take this in the rotation of the standard equation, we make the scalar term, and then we have to find a number like this, in the sense of the miracle of Dirac, this pole of the scalar term, the joint that reverses things, the magnitude of this, the joint of this and this, and then the scalar term that falls. So, by definition, you see that the definition of this number, I will explain it in more detail later. Uj is an autonomous base. The vector C decomposes. On the other hand, it is an autonomous base vector 3. Therefore, O acting on Uj is the number of Uj in Uj. On the other hand, it is an autonomous base. Uj is the square root of Uj, Uj is Uj, Uj is Uj, Uj is Uj. When you put all this together, you calculate. The so-called average value is generally called decomposing psi on it. After two decompositions, you will have Y, C1 bar, Cj, O acting on Y, and all the summation on Y and on Y. Simply to develop the psi-tpx like this, and the psi-a, I obtained the bars because I am in a complicated context. When you think of UGIT as lambda UGIT, it is the sum of UGIT, UGIT, CELTA, UGIT, LAMBDA, UGIT, UGIT, CELTA, UGIT, LAMBDA, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT, UGIT,

35:00 All of this is the sum of these two lambda i, but it's the square, you know, on the base, you have this, and in fact it's the i, which is precisely the scalar product, the vector's scalar product on the base, which is the vector on the base. So this is the sum of the lambda i of the square. So now that's a difference. The Law of Probability, as you can see, is exactly the same as the law of motion. So, this is, in fact, an expectation of your observability. And so, you see that one of the consequences of the action of case and of certainty is associated with the Law of Probability in the same way as the law of evolution. It is simply that if we calculate an expectation in relation to this Law of Probability, This is my algebraic and mathematical state. But you see that the meaning that we have made is not at all rare. The notion of probativity is to say, well, I'm going to do the measurement on the system that is going to be here, I'm going to do the measurement on the same state as in the previous one, and I'm going to compile it like this.

37:30 You have a link between a statistical idea on a set of events, so that you can repeat the events, so that you have a kind of average over time, which, in your mathematical form, identifies itself with another probability on something that is in space, in the space of time. So in fact, this kind of probability is a bit like a kind of algorithmic hypothesis, in which you mix... The average on time versus the average on space. And it is on this game that we are going to associate these entities here, the identity of the mathematical mechanism. If in any case we have the catalogue, we will have the mathematical equation here, and we will be able to determine which one is the right one. So, for that, we are going to... Thank you for your attention.