Inflation & De Broglie-Bohm Fluctuations / What is De Broglie-Bohm Theory?

0:00 The first step is briefly something I've talked about a lot, so I'm going to indicate one myself.

2:30 The four rules away from the square is the probability that the law dictates the function. This is quite quick. Am I in the way? Yes, you're in the way. So, um, so these four rules are fundamental. And I want to sketch how, in the context of a certainly very popular cosmological theory, evolutionary cosmology, there is an opportunity to, in a sense, grow quantum fluctuations in the very early universe by means of current astronomical observations, in particular the measurements of the cosmic microwave background. And I'll say a little bit, not as much as I want to, and I haven't thought about this much, I want to call on Mike instead of the dry garden dairy, who ignores the literature in the short distance of this year, and consider the knock on the back of Mike's hand on what people imagine Mike to be saying. So, now, briefly, why should one... Doubt that the whole world is fundamental in those situations, and actually the quantum theory has a way of constructing the logic of straightness and solubility, while two arguments have always struck me on it, it seems to be the same. There is a non-locality in quantum theory that happens to be hidden from a, hidden from direct use by statistical quantum noise. I want to conclude that in the context of the general deterministic invariable theory, we don't have to be non-local, I want to conclude that if there is a distribution of invariable, it could be the distribution of quantum mechanics, but considering the general arbitrary distribution of the step-on-the-line deterministic equations, we'll get into the same thing.

5:00 So what we do, I'm suggesting, is that we suggest that the equilibrium distribution of quantum possibilities is something special about them, even though it's not very important, but it happens to rank among those elements. Another argument, and it goes back a long way, is that the honor of Hawking's case points to a deep connection between quantum and eternal life. Gamma and relapse of light showed how the thermal matrices in fact arrived in directions of quantum-lactic fluctuations of the human being's field. Smolin made the same argument, but then suggested that perhaps the quantum fluctuations are, in some sense, really just physical fluctuations in fact. So anyway, it was just suggested, I don't approve anything, it was suggested to me that quantum probability is directed at the spatial equilibrium stages, and the physics that we're looking at is not fundamental, and that our belief is that it is invincible in the general non-equilibrium system, particularly in classical physics, because we don't have the physics to solve equilibrium. Before I move on, I'd like to comment on some interesting work on deriving a quantum square into an axiom. What would I say about that? It seems that one can derive a quantum probability from an axiom. Say these types of activities that are relevant actually have to do in relation to thermal physics. One interesting question is that it might be interesting to look at which of those actions failed in one exhibition.

7:30 One can actually ask these questions concretely and deploy both theories because, for instance, if I had a piece in which I assume the neutral equilibrium distribution is invariable to time zero, you would talk of a quantum probability and it would show data as acting. One can, as described on here, consider the hardest of non-experimental institutions in the circle, the ones that cover statistics to the outcome of its benefits, but are not the ones that can cover statistics. And so one could ask, well, what is happening there? What should we actually be saying? And it may well come to the conclusion that, frankly, very few of them know the reality of how they can live in a time-lapse world. So, what I propose then is thinking about looking for some evidence of non-equilibrium physics in the early universe and or very short distances. So, the rationale for the first one in the early universe was... Our current physics is electrostatic on the natural state of it and having a rhythm by relaxation processes in an early and non-electrolytic distribution. There is a, there are tons of studies trying to get new relaxation processes in specific cases to destroy bone theory. Another rationale is that, well, the second point about why one might think about directional distances is that, at the grand scale, there are supposedly very strong gravitational fields fluctuating between the joints of space-time, and one might speculate it's been speculated that the quantum-mechanism of space might have been stabilized by gravity. It's a particular model of that.

10:00 Anyway, now the point I want to make in this talk is just the following, that inflationary cohomology can be viewed as probing for rules, at very short distances in the ocean. So, to show you that, a little sketch of inflationary cohomology. There are many different versions of inflation. They have been common but in the other universities we have a classical spanning space-time and that is described by Holmes' field theory and in certain conditions, which I won't bother to specify because they are actually different in different models, but the procedure they have in common is that there is a period where these Because of common field theory effects, you have the energy density of matter is constant, and if you put that in the Einstein equation, you get an exponential expansion state. So the idea is that soon after the big bang, Something fun happens at the level of quantum field theory. You know, the theory of what's stated expands exponentially and then things settle down to the world order and expand the cosmologies of the community. There's an early theory of exponential expansion. Now, in this theory, the extent of the factor by which space expands in this theory is huge. It's usually only 10 to the 6th, and often it's much bigger, which is what's called chaotic inflation, and it's crazy numbers like 10 to the 10 to the 5th. Huge factors in space that expand in time. So what that means is, with the topological, with some of these models... Cosmological length scales today originate from distances shorter than the Planck length at the start and the end, in many, many forms. Now, what happens is that during this period of exponential space, there is a scalar field, a quantum field associated with it.

12:30 At that time, and quantum fluctuations in this field generate small perturbations in the energy density, the energy density state is not perfectly homogeneous between the quantum fluctuations in this field, and these microscopic density perturbations get stretched up to very large number scales, which is the best way to understand this state. And later on... At the time when most electrons are 100,000 years later, when protons and electrons combine into four atoms, you have a plasma that is not densely, it's not perfectly homogeneous, there are four densities of perturbations that originate these atoms, quantum perturbations. And these densities of perturbations affect... Well, when photons no longer interact with matter, the photons now, as they leave this plasma, the small differences in density affect the frequency of the photons, the different lengths from the gravity of the field, from doctor effects to the motion of this plasma. So what you've got is this scenario where early quantum fluctuations during the period of exponential expansion lead to small perturbations in energy density, which later are imprinted on the microwave background, which is more variable in intensity. So, well, so just to the beginning, growth of density specifications, what we're talking about is just after this inflationary period, we're talking about some classical density specifications, one has a density contract with fractional deviations of the linear density of the universe. And what you do is you use Fourier modes, but here it's some large volume.

15:00 The linear regime of small-density perturbations, even though it's evolving independently, so it seems to work even if it's in low-density perturbations. Yes, now, the details are complicated, but the underlying message is simple. Given some initial, some initial perturbations, okay. There's a well understood formula in them to calculate how these perturbations evolve in time, and for instance, it's known that in certain situations, if they would go like 48 times the time, it would be about 1,000 times the perturbation that would go to life actually, and that's what we've established as well. Now, the point is that given some input at a very early time of the density perturbation, we want to move on forward and calculate the density perturbation at the time of last gap in the program. And once you have that, there is then a well understood formula for calculating the distortion in the temperature of the microwave vacuum. This is the density difference between the cohomology and the vacuum. The only thing that we need for our telephoto... Now, how do probabilities come in? So, if probabilities come in, one thinks about a probab... one has this density concept, delta x, which is the fractional unit, the density of the unit, and one thinks about a theoretical probability for this variable. One wants to... Now, the thing is, in the universe, of course, there is just one extent of the density distribution, so what one does, one has a theory where you have one prediction for probability distribution, you relate it to the actual perturbation received. By assuming that there's some sort of large-scale quantum kinetics in the universe, in space and in the universe, for very large quantities, you have a large number of regions interpainting the realizations of random variables. That's the assumption in this way.

17:30 So what it means is that you can use the state of physical averages of the theoretical probabilities to find the state of the averages of the very large quantities. And in this context, they usually assume a Gaussian distribution between independent modes, the probability distribution is not observed in these modes, and each distribution probability for instance, for example, the density constant, the probability distribution as a result of K is just Gaussian. Okay. Um, and typically, this, well, okay, you know, there are, this thing is, there's a power thing, typically there's a power there, but the point is, there's a key point here, is that one usually assumes, is usually assumed that the initial, uh, probability is assumed that the galaxy is just there, um, and, again, I'm not... The details are important from the two points of T at the end, why it's so important. So, okay, so, let me how long this stuff is specific to density perturbation. Now, I told you that once you have an input to the density perturbation in the moment of time, one can calculate the probability that my hypothesis is perfect or less than the density of this quantum. It's done in very striking ways. Now, the calculations show, and this is standard, and it's not more than tenfold, you'll find this, that this tendency to distort them is a lenient because the distribution of these don't pay to distort the equations, they just matter to one. What that means is, in this vision, close to the mitoscopy, in it, there is also a Gaussian random variable, which is zero. Which means you have complete statistical information about the, what you have is over the time you have these variations of temperatures, and one can measure the temperatures at different points and look at the two-point correlations from them, which what one again does, the statistical averaging is only one.

20:00 So, anyway, so I'm just going to introduce you to Tom. So, this is what we were actually So far, the intractable deviations of temperature of all the temperatures might be fine, and they seem to follow a Gaussian principle, which means, specifically, that higher-order correlations can be obtained in two-point correlations. Some people are considering various reasons that there might be a non-Gaussianity. And so far they've constructed a measure of non-galactianity given the data of the temperature areas of the sky, what it can do in the day-to-day surface of non-galactianity, and so far we've measured a zero in the data so far. Now, the point, now I'm getting into the main point, which is that in inflation, these initial perturbations have a quantum origin. During inflation there is a scalar field, which is called the intercalar field, and during this period of exponential expansion, For various reasons, again, objecting to the spontaneity of symmetry breaking, it doesn't really matter, but the total field can be written as breaking to a uniform classical mean which is revolving in certain order, plus a term that is treated to a good approximation between one and two.

22:30 And, essentially, while we're aware that the people get different reasons for what's going on really and often, because this thing has been expanding so much, any particle associated with this thing is so diluted that you've essentially got the groundwork to keep the nucleus human, to keep the fluctuating field of the groundwork. So... On one hand, and of course this is what's known as quantum space planning from the scientific experience of Stanley and his students at the University of New York, nevertheless there is a similarity with quantum space planning as well. Looking at the 4A road, the ground state is a product of the Egyptian road, which we make away from the floor of this road by a sort of tail. They don't have a galaxy before, even on this standing in the background, and with a width between two sub-widths of 90 centimeters. Now, what happens is that there is a bit of a sponge. I've never really seen a piece of this kind of sky earlier. So the way people, what are people starting to derive is a prediction for fluctuations at a physical level. So the informal fluctuations, what one usually does is one says, well let's... To define a classical fluctuating field that could be seen to mimic these quantum fluctuations, what one usually does is say, take Fourier components of this classical field and just get the least of them, the r and s, with these quantum fluctuations to the true way of finding the expected factors. And then the next step is to derive fluctuations in the energy density. Well, only from the time that we get back to a negative scale can we get to that kind of time. So, A gets very large during the period of the regression time. A through the energy density is a half final square. That implies that the density comes out through these fluctuations and density is proportional to the time duration of this field.

25:00 And having defined this field in this way, as many of you use quantum fluctuations, what ends up with this is the initial density comes out, for example, is proportional to the time duration of this R-net field, where these are wavefront fields. Now, what is often seen as a suggestive inflation is that not only are these fluctuations with regard to destruction, but the actual amplitude squared is proportional to the modulus of the wave vector, and certain vectors, which leads to the approximately what we see on the screen. So now, what I want to say is that the picture I'm presenting, the picture we have in this place, is more than just a fluctuation between some fields in the same period, generated by many events in such a period, by a well-earned amount of time, and weighed someplace in the 10 to 10.9% of the time. So there's a sense in the context of the equation, whether the equation is true or not, as we know, in the context of the model, the temperature distortions of the microwave sky are an influence of primordial quantum mechanics. For some reason, what I wonder, my message is that there's an opportunity here to probe quantum mechanics. In the very early universe. As I said, in some of these models, the expansion tank is so large that these anisotropies that we see originally come from length scales shorter than the Planck banks, and there's now a small industry of people who have various ideas about what happens in Planck and physics with the Planck banks, whether it comes to the beam of addition, or part of the spin theory, or whatever, with an effect.

27:30 The quantum fluctuations, the quantum mechanics, the physical changes, the field theory, so there are a lot of changes in mathematics and mathematics in the new mind. It's hard, I think, to use the word for fraction as a fraction, but the fluctuations are still the opposite. Now what I'm supposing is that these things should be developed as a probe, not as a kind of a ticket to the early universe, but as a possible great quantum theory. Now, I can't really say that one... Okay, so the natural steps change when we consider explanations. With an initial non-equilibrium distribution, one runs into the immediate problem that there is no natural non-equilibrium. Now, one wouldn't want to say, well, some of the observations use what they used to use. So one wants to look for a particular signal that might be explained by quantum non-equilibrium in a similar way as not other ones. Now, one obvious signature is non-Gaussianity, that if the probabilities are not given by the modulus of the fact that we're going to the square, the fluctuations will not be done. Now, it is expected that there will be a small amount of non-Gaussianity, just from nonlinear events and varying changes. But here there is a possibility of a large non-Gaussianity. And there are two forms. One is, remember we have the ground state wave function as the product over mode. Now, it could be that it actually could be a product over mode, where each mode is out there for delivery. One problem with that is that it can be shown that if the actual quantum state is the wave function, it's going to be the product over ground state mode. If each word has an opposite, then the position of the energy state is the limit of any distribution of the flow.

30:00 So what I'm saying is, you wouldn't be able to tell whether the flow is not in the sine squared or the sine squared is not what you're talking about. Even so, nevertheless, one might make logical answers to this question, but I would say... Another possibility, more striking, is that, well, more generally, we also have a lot of products that are both, and I'm trying to figure out what particular signature subjects might have on the background, and I'm afraid I don't think I have much to say about that at the moment. One sort of concrete, sort of natural initial state, one could use certainly the drive home theory, is instead of saying the initial state is this uncorrelated product of a vacuum of probability, one could say that one has the product structure that we can suggest in some pathology. Multiplied by something that is not a product, to the mode of the entire system. And again, what one has to do is, in his own theory, to exist in this world. Stately, one can easily jump in the standardization of conservation into a system. In the 14 years of his experience in the system, the question is, is there some specific signature that one can find out of it? So, a different result for the alphabets that have been obviously backed up in the way that we've been talking about. So, anyway. So, in conclusion, the information clearly provides a window on early quantum substations, which is very true. Not only for them, they are massively useful in non-Galaxy analysis. I think I've said before all the people that are already here. And so that's kind of it. Thank you. Well, the printer itself is an interesting idea.

32:30 And furthermore, even these people, I think, are very good at it. And I feel like they're going to be involved with that some time. We can back that up. All of these are supposed to be, and it appears to me that, in the time that people are looking for, there cannot be a difference between non-linear multiplications versus invariant multiplications, versus an underlying invariant, because non-linear multiplications can't work. I haven't thought about that. What I can say is that people have considered that the course is what is typically treated as a free field, or it is not treated as a free field. There are self-insurrections in it, or there are self-insurrections in it. And people were found, I don't think it's a general result, but to some level they were found, that because of this huge expansion, this enormous exponential expansion, that these interposed... Interactions between the results of the same paper or the same thing. That is the common result that I think people justify. I don't know if there was, then I would go with the diseases between them. Thank you for your attention.

35:00 I'm not suggesting that there might be another type of physics, but I'm not suggesting that there might be another type of physics. Which, in a way, causes a conflict between manuals and now, obviously, what is what you're aiming for this time of year. Strictly speaking, you have to turn the logic around and use observations to explain what is what you're aiming for. But, on the other hand, if you decide to, for example, consider the use of a computer, Where you have small deviations from science where perhaps there are small differences. Then you have something specific. There's still an alteration in terms of growth of science where there's some growth in a broad way. And one might hope to derive some particular conclusion from it. If you have a quantum, for example, you're dealing with a size square on a larger scale, but not size 1, but on a larger scale, a very small scale, then, unfortunately, that may lead to a string theory, which is not necessarily a concern, I would say. Well, this is very difficult. Yes, it's very difficult. I think everything, I don't know if this will be correct, but everything you've said seems to be true. Of course, there's equilibrium and non-equilibrium. You never speak of equilibrium and non-equilibrium. And it's not good for you to, you know, think about what happens if you don't speak of equilibrium and non-equilibrium.

37:30 Right, what happens then? It's because of these two segments and simply want to encapsulate it before we break the fuse that we begin to come to the thermo-tech and get to the thermo-physical context of mathematics and mathematics theory. And later on, the cultural business has expanded its violence and observance of factors to be part of authenticity. Eventually the problem is that they're so diluted that we essentially have to adapt to them. In geometry, we tend to think of it as complex and exciting. And some of those people, I don't know if you've heard of them, but they're quite complex. These kinds of things give you an idea of what it takes to understand something that is not in the field, that is not in the field of thinking about it. So that is the argument that we can give to the decreases of the stuff we've been talking about today. Thank you very much. And there's quite a lot of people holding what's called a filter theory of what's being called a quantum physics theory. It's a very specific word for a very specific word for a theory. So, um, you know... Well, that's my kind of thing, but I'll try to use it. Um, what I want to do is give you a little bit of a question about the school of learning. My remarks are of a degree of introduction to mathematics and physics. I'm sure plenty of you know the same idea of the school of learning theory.

40:00 The school of learning theory is going down in the fellowship in the future, and we're going to know how to do that. And everything I'm going to say around it will be in the next class today. So the whole point of the hearing in the end is having a few of the different distributions of our knowledge today, generating what I've tried to do, and what I've tried to do, and what I've tried to do, and what I've tried to do, and what I've tried to do, and what I've tried to do, and what I've tried to do, The reason this equation works, I mean, it generates a whole ton of space, it's a ton of equations, you've got those equations in some cases, you've got those equations in some cases, you've got those equations in some cases, you've got those equations in some cases, you've got those equations in some cases, The question I'm going to raise is, what can we find to support our science, science theory, mathematics theory, physics theory, all the other elements of your notion of mathematics? In particular, our speakers are supported by the theory of the characteristic of an architect, the fact that he learned the first guidance of all the missions of physics, both conservative and not conservative in and of itself.

42:30 Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. Now that we have done all of these things, I would like to start with the quantum mechanics of the story. So some of the features top of the magazine of the De Bruyne moment theory, well it's a famous act and it has shown very well that there is truth to some of the features of mathematics and we know there are. Civic things to say about chaos, which is a predictive thing to do, and to think of chaos as something that's always going to happen, and what it is going to happen, and vice versa. I've tried certain violations down from now, which is quite a bit of an environment within the 12th century. It's very orderly, I must say. There are very civic things to say about it, and civic terms, for example, there's a math thing called a step-up, which predicts that no government is going to be working out the symmetry of the climate. It was ruined, so it's hard to explain things like it now, because it's so much better for you.

45:00 Now, first of all, in America, the problem is that you don't know how to do it, and I don't think that's a problem. The black satellite sphere in the city of Alberta, which is in the western part of the country, it's in front of you, so you don't know where it's going to be, so all that has to be done is to look at it, and look at it, and look at it, and look at it. The idea in the sort of own theory would be that a person doesn't need to go to a physics class. Mathematics is a field that you have to be going to to study physics. For example, you can have a job serving an education in mathematics and algebra. It's a very good place. You won't have to go to a physics class if you don't need to go to a physics class. But other than that, it's very interesting to look at the theory. The other equation comes from certain equations, so to say, that quantum mechanics is a global equation, whereas the idea was to send four of the students back to a hundred and thirty-three, forty-five-thousand-and-thirty-thousand years, and that's when I was providing some of the following definitions of the equation for quantum mechanics. It wouldn't have to be in that airfield, it wouldn't have to be in that room. However, um... String theory and algebra can be used in a variety of fields, including mathematics, geometry, algebra, mathematics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics. So, in the absence of an academic issue, there is no relationship between quantum mechanics theory and quantum physics theory. That's a useful idea, that quantum mechanics is connected to different types of mathematics.

47:30 That's what he's doing, that's what he's doing. You know, what I've been trying to do is kind of tell you that it's difficult to go through, because you always have the divergences between them, and it's hard to use them. And so on and so forth, and we put it at the bottom. So I ended up using that as a way to get to the bottom of the story. And I'm assuming that's how it was suggested. It was actually sort of a theory, and then that's how I found it. So, both of these problems have come to me. There are a number of different types of students, but I'm not going to go into too much detail about each of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. I'm going to focus on one of them. So, one last thing we need to invoke is the place of the study. Not the one that I'm talking about, but the one that I'm talking about. The mathematics of science. The mathematics of science. The mathematics of science. The mathematics of science.

50:00 The mathematics of science. The mathematics of science. All of those are the ones that I'm going to be talking about today, which is the quantum mechanics of physics. And by the way, we can take the current, everyone can take the current. The question is why? Well, that's one of the last ones we're going to be discussing. Now, the physics of physics is kind of like salt, isn't it? It's a question about how it's going to come about in the future. It's not just about that. You have to take the current and use the color of the theory to do that. The method of expression is very unparalleled. It is the end of the third order, and it is also the last phase of the quantum expression of the state, given that it is one moving state. Here, by quantum state, we are referring to the gas state, which is the gas coming into the field. It is one moving state, and the other is the light state, and the third is the liquid state, and the fourth is the liquid state. So, okay, that's the step four. Why should the college attend a government university in the States? If one looks at the time, I think the answer might be the government university in the States, the White House. One of the benefits here, and although the government didn't have the possibility to do so, there was a function in the form of the college. So it's just another kind of theory. All of these terms are used in the course of the course of the course of the course of the course of the

52:30 So it's a variety of things going on in the world, but one of the new things that we're going to have to do, there are two ways we can do it. One is to invoke mathematics as a learning system, or in case you want to do it as a learning system, for example, to see if you're going to go from there into a learning system, which is good to do. There are a number of different types of questions that can be answered in the lecture. The floor plan is very specific. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. I have some questions that I would like to ask you. And what we're after is a projection theory that's going to lead to some of these things and some of these things are going to be out there and go out there and do it from time to time to involve them in the discussion side by side and then go on and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and do it again and Our idea is to communicate something moving along with the rest of the equation of physics, using a vector, where you often can. Our assumption is that doing all the things by the conventional expression means that zero contains a very much zero.

55:00 Now as far as we know of our own frames, well we must have the same formula for the exact frame, so I don't think it's the same. From that point, the theory of quantum mechanics was very much clearer than the theory of quantum mechanics, but even for that theory of quantum mechanics, the theory of quantum mechanics was very much clearer than the theory of quantum mechanics, and the theory of quantum mechanics was very much clearer than the theory of quantum mechanics, and the theory of quantum mechanics was very much clearer than the theory of quantum mechanics, and the theory of quantum mechanics was very much clearer than the theory of quantum mechanics, and the theory of quantum mechanics. The idea here is that the number of the number of the number of the number of Let's consider a special case from the 19th century when we test the probability of an issue that a function dies once it is entered in the string of time. And it turns out that the sign is at the first element here. The first one is the term of the current mark. The fourth one is the term of the function of the time period. And the fourth one is the term of the expression of the modified value of the string of time. And I suppose, I don't know if this is going to work, but in the action, for the first time, I'm going to start to try and understand the concept of A. Well, A is going to be the same as A, but it's not going to be the same as A.

57:30 I'm going to try and understand the concept of A, but it's not going to be the same as A. I'm going to try and understand the concept of A, but it's not going to be the same as A. These terms can actually be used to state the language of mathematics. So I'm going to go to the next slide, and I'm going to give you a little bit more detail. So the positions are made up of the terms that you know I'm going to use. So in terms of the artificial theory, this is where we're going to explain, we're only going to explain the fact that we're going to talk about mathematics, the terms we've got. This doesn't show that it's wrong, it just shows that it's true. There are many ways to explore the history of physics, including the fact that I myself described the reasons for the origin of physics, the origin of the direction of physics, and the third way, which I list in this presentation, is that many of the countries featured in the division of physics have done so, partly down the path of science, clearly. And if you thought about physics, you knew that you didn't have any way to explore it in mind. Key terms may include mathematics, geometry, algebra, analysis, quantum mechanics, relativity, cohomology, mathematical physics, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra,

1:00:00 And chemistry out there, it's a very complex factor, I would say, if you look at it directly. They're never there, it's just a set of steps. It turns out that things don't come out of this context. In terms of the area, it's far back from the context. The size of the place where we go down suggests that it's still not something that we can study, so it's going in the following way. So what we're doing is we're putting things in the context of the next energy term. In fact, what we're doing is introducing both geolanguages here. This is an interesting example. If we were to design a course for this, we'd start by illustrating it. And then we'd write a new line for it. That's what we mean by geolanguages right now. So we have this kind of language. But the next one I'd like to share with you, is something we've done to do with scale regression, which I'm going to explain to you in just a moment. The socio-operative work is done with a range of forms, and so it's going to affect what we will be talking about in the next few minutes or so.

1:02:30 So any of you who have a lot of time to do this should be able to understand the common sense of quantum physics. So, thank you very much. Oh, and what do you like in fitness? I mean, people don't really do much to it, they stay at home most of the time. Key terms may include mathematics, geometry, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra, algebra. However, if you don't focus your analysis on the theory, then if you don't focus on the theory, you're trying to look at the battery theory, that's why you're trying to look at the theory, you'll start getting attracted to the theory, so you'll start looking at the theory, so you'll start getting attracted to the theory. So, to be very brief, the Polygon theory is not really necessary. It's probably not going to be a suggestion, but it's certainly something that we might say that it's a kind of theory that we are interested in for the Polygon theory. The special focus on the Polygon theory is not necessarily going to be a suggestion. The second point is that we lack a certain kind of initial justification for this theory. But each of those can be identified, depending on the topology or field that you have to use, such as the state of the universe and the state of the universe.

1:05:00 So if you took the promise that if you wanted to come to a new town, you'd have to be outside of your home, you'd have to be outside of your home, you'd have to be outside of your home, Thank you for your attention. There's something more involved in the mathematics of physics, though. For example, when you tell a story, the first thing you need to figure out in a country is if you can learn a number of things from each other. Because we want to be able to test this, the fact that we're able to tell them to go to the other end of the whole of the equation. And we hope to be able to contrast them in many ways. Thank you for your attention. Thank you for your attention.

1:07:30 I'm happy to be here, but this is the start of my lecture, so why don't you do the next thing I ask you, and I haven't done it for a long time, but Simon is going to do it for me. Thank you, I just got in. So, can I just ask, what happens if you use the Eden-Bigner coordinates instead, and then work backwards from that, and then recover the standard, if any, and the expression for that? I hope you enjoyed this video, and I'll see you in the next one. And we've got an answer here, if you remember, I want to find out if you've got quite a few numbers here, because you've never read this before, so I'm just going to find something about it. I mean, the point being is that it's a much bigger representation of what we've been talking about. We've given you something intractable in the mid-tier, which is probability. And we're going to come back to that and then make this difference. Well, what we're using now is a very common thing in the mathematics of physics, isn't it? That's the combination of the last, last, and second statements, isn't it? And just that way we understand it, isn't it? That's how we think of it, in the mathematics of physics, isn't it? I'm not sure I can do a pretty cool... No, but just let...

1:10:00 Side by side, you're using that as your cue, and you're wrong. It doesn't have any obvious meaning. It's simple, I'm not afraid of you. I'm happy to be here tonight. Thank you. I shall attempt to exemplify some of the conjectures outside the context of these memories, but before I do so, I would like you to say something about the conceptual context. I think it's particularly appropriate for your sessions that you can learn some more about these things. I'm certainly right in the thought that what's not in theory, but what is in terms, would give you the, if you'd like to get it as well, there are two parts. I'm not going to go into that because it's a very boring approach, but it's often a nice thing to know to look at. And that is expensive. Discussive and conceptual conventions of physical theory tend to confine the notion of individuality to the formal structure of the theory. They concentrate essentially on what is being said rather than on how it is being said, the way it is being said. At least in my opinion, some of the analogists who read the respective models will admit that depending on who actually fires the gun, a lot of the students get the sense that the fire in the gun has an actual compaction or an actual effect. But, it is through the verbal and visual vocabulary that the words go in search, by which we come to ideas and create meaning.

1:12:30 The results have remained quite unacceptable. Consider, for instance, the quantum-chemical density, the one-size-square density, which provides a critical touchstone, as you will note. Both the conventional and the software-developed clouds, as you can see on the screen here, It's composed out of, for some reason, distribution of points, the configuration space, which apart from the shape of the density, it produces a lot of structural features. By contrast, we have the de Gaulle-Bohm approach, and see this graph, this cloud, the other hand, is a vacuum. It's permeated by connections that make these points. Each and every point is clouded by a time-ordered amount of people, of course, of a continuum that continues to lead to a path. So, these connections, these paths, in the Breuil-Bohm approach, we produce fundamentally what we might call some of the narrative dimensions into the theory. And we articulate, in a visualizable way, the motor patterns of the framework. This expressive capacity of quantum theory, in the right reading, gives an appearance of quantum dynamics that will seem to be unavailable. Thus, the original quantum physics trajectory says things about the quantum's appearance. So the original quantum physics trajectory... Now, the thing about quantum mechanics is that it is not, as you said, a theory of physics, and instead really initiates a novel discourse on the, what are called, the only instruments of quantum mechanics. For instance, this surprising feature, which happens to exist in our literature, is that there is no cross-link between the properties of the axis of symmetry, indicating that there are particles of each lift.

1:15:00 The main confines to the expected semi-intuitive half-play, and this objective will include a restricted type of non-locality, which acts alongside the overarching non-locality of potential. But as we've already heard, these are discussions on the non-renewedness of potential and their minds. The very virtues of the De Bruyne's own approach. Why? Well, because, clearly, it undermines the very means by which is the narrative of De Bruyne's own approach, and what I can add is that I actually like the way I tell these stories. So it is an interconnected... While not unique, and clearly their ontological status would be comparable, an exercise in which the qualitative value is greatly reduced, the status of this trajectory, I suggest, would be more akin to the pointing vector, that is to say, that the notion of entities resulting from the imperative of the continuity of conservation is what it is. But their actual substantial physicality as local and unambiguous quantities need to be maintained. But the GTV, which is very well known for its F2, are not. They are more like the conduction code of the mathematics. And like a conduction current, they are fixed definitively by a constitutive equation. This equation will provide a strong physical constraint over and above the one exposed by the continuity equation. In other words, the trajectories have an equivalent of Ohm's law, which is a guiding feeling regarding the selection of physical objects. Since this relation actually provides the typical principle that determines the current density in terms of the phase in a relationship.

1:17:30 This, of course, is a very difficult question. So the question of the uniqueness, therefore, should be rephrased. Whether these effects are unique or not should be rephrased in terms of whether the constitutive equation for current densities is in fact complete. This question... Feats suggested can be answered if you just remember a physical unit, or the Dirac equation, which provides a key physical principle that needs to be taken into account, certainly for spin half-sciences. And as has been shown, this will result in modification of the Hauser-Kirchhoff equation, and therefore of the appearance of a spin. And the perfective potential that we have already seen in the guidance relations. So this I shall re-show, or take on, reminding you that what I now propose to think of as the constitutive equation, the complete constitutive equation, The vector potential actually appears in the form of this here, I'm assuming that we are being unconfident in this case, and still the constant vector is a vector. So this completion is actually the expression for the current density that adds to the complexed terms. It's right there. These are gradients of the takeaway function of a selectivity component, the electric field. So, what are the consequences of this? Well, one interesting consequence of this completion is that purely quantum mechanical quantities acquire features that are strongly subjective of the lectures they have. That's what we understand as the physical attacks against theta as we see here. The effect of the Lorentz covariance that survives in this number of characteristic limits. I've started to bring the density alongside all the same things as the phase of the wave function, but the two ingredients of the wave function that play disparate roles in the original formulations of the Borei-Bohm now act in an equal footing.

1:20:00 The projections of course are modified by this. The subjects that are being obtained by integration of this guidance relation are of course difficult, but it is good again to remember that the mod sine squared, the actual cloud itself, is undouched, that's what I'm saying, not that it's changed, but the connection within this cloud is the vacuum system, the way it's made up. The analogy of electromagnetism endures further, and the electric and magnetic-like fields that appear from this particular form of combination appear naturally. They actually emerge from this particular form of both completion, regulation, and re-giving the amount of material. So, three of the rest, like four, that is produced, that is most of it, both these magnetic and magnetic-like fields play key stories, key parts in the story that is told as we continue today. And what I shall show you now is that, is this story seemingly told by me today. And what I shall do is that I shall begin by showing you Through a succession of calculations, subjective calculations, how the newly modified double-snip projectors emerge. In this way, I shall do, shall I say, what I call the subjective calculations which are really following each other, each sequence which culminates in a series of double-snips. I've gone, I guess, to the same time. So, I shall start there, I hope, by showing you the objectives that we know from the use of the off-the-wall guidance dimension for a single, for a single dancing wave function, stationary and symmetric.

1:22:30 I shall then show you what happens when you get this thing moving to give it a boost. I shall then show you what happens when the telephones are deformed asymmetrically, and finally what happens in two positions, and at the end I shall show you how this is positioned to then be modelled in the U.W.S. project, throughout the thesis of the event. Okay, so now on to the graduation. Congratulations! I'd like to push everyone further to review the last one, Rotary of the Basics, the Basics of Mathematical Calculation, which is an inter-based assumption, which I'll go into in a minute. So we assume that we begin with an eigenfunction of all of these things. All the wave functions that we're going to be getting suggested are based on a two-dimensional time-dependent Gaussian of A n to the r, which is presented here by the expression of the phase and the time-dependent half-grain in that geometry. All the initial points that were put up for the project would take on the surface of a constant density. So, we've done it as a kind of ensemble. Projectors in these pictures now begin, are becoming more difficult because their configurations say as much about the physics of the collection as what happens to the brilliance or the throttling sound. So it's important to keep an eye on the overall configuration of the project. It's rather like you plot magnetic fields in terms of field lines. If you want to plot a little series of ensembles, an ensemble, you get an idea of the configuration of the field. Equally, as I've got to mention here, we too have projected the start of quantum mechanics. So I believe that there's a lot of things actually applying all of the calculations that you've been saying.

1:25:00 And I won't have time to get into it, but you can take my word for it. But it's definitely not good enough for this. And finally, all the subjects in the computer that you see have been contributed by numerically integrating the values here. Okay. So, let me begin now by showing you what happens when a single symmetric Gaussian... Stationary Gaussian is what we serve. This is the canonical ensemble of projections, the constant density of which the Gaussian is vertical, so we've got so many, I'm giving you how many here, and these projections can be thought of as being in the wave function's best way, wave function's best way. If we work out the electric and magnetic-like field here, as I've already told you, it's the climate-conducting theorem. This here is an issue of inversion motion. The single kinetic element in this inversion motion, these trajectories are linear, and the speed of all this is constant. There is no acceleration. In other words, we are moving in a real field, a field 3, in that situation. The gauntlet in this picture, in this extended, galantonic picture, emerges as the generator of American science. The circularity in the circular aspect of the electrical picture appears to be to a level of non-sense. In other words, these objectives are somewhat like a captive idea. Each project has no notation, but the ensemble does in fact produce such an effect. Very briefly, here you have a mental picture of what these fields now look like.

1:27:30 By the way, these deconjectures are always set towards the between the brain and the astral space of the brain. The effective potential is simply in the secret direction, in the cone. Electrically and magnetically I told you to go like so, and then I told you to go to zero. And each trajectory, the speed of each trajectory is a constant, but it does depend on the initial distance. R0 is the initial distance from the center of the wavelength. So this is the beginning of a series of calculations that we need at the point of direction. The inertial motion... All of this is unaffected by the second stage of the calculation. The second stage concerns now imparting a propagation to a wave function. To impart a propagation to a wave function, a force is just like a Galilean boot. This is really kind of quite straightforward. This is getting the wave function moving in the x direction. This is to say, the projection, the modified projection there is, I'll just rotate it, the rotated version of the 1 meter spectrum, the angle of rotation is dependent on this angle beta which is the angle between the directional motion of the wave function and of the original projection. In a minute, when the wave function speed is much greater than the trajectory speed, the angle of rotation extends towards the angle between the trajectory and the wave function. So, these here are the chocolate-hating trajectories for three different speeds. I've covered some of them for ease of recognition. Again, circular initial ensembles, so canonical ensembles. Here the wave function is going at 0.8 times, twice, and five times the speed of the trajectory, the speed of the trajectory of the trajectory. And the way canonical ensembles have been chosen for this to be played on the half-width of the geometry.

1:30:00 So for those things, you know, how these actually have rotated, if you concentrate your attention on that red one, you see that the position direction is here if you put a red one to you, so it's protecting you from that way, because now it's going to be in your ear. So this is not, so we can actually do that, here, sorry, it's not perfect, but I think it's a good way to do it. In the x direction. In the x direction, in that direction. So, a moving wave function, the unity in the electromagnetic light force, in this condition, is still zero, so the inertial motion is still the same, but it seems that it is a different way of working. Let me now show you the result of turning a wave function into an asymmetric product, another wave function. But, I'm taking the x and y direction, the wave function of a hydrogen pathway, the x and y direction, therefore we have the physical expenditures in the level of the wave function, but, for the rest, we will fall on the ground to dust. Here, now, we see that... The subjectives are no longer linked. The differences between the evidences exist at different times. They are exactly the same, but here we have a few more of them, which is a better way to see the code. So a race like force does not vanish here, and for a short time we get the subjective basis. So, the asymmetric wave functions, by the way, are not all found in an ellipse plan, taken on the road of some of the various functions of the ellipse, 3 to 1, 3 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to 2, 1 to

1:32:30 What we do actually find is that we tend, as exotically, towards the Deploy-Bowles original character field. The vector potential here became the denominator 2 squared, whereas the gradient of the face became the denominator 2, and each here became the radiate, as they would have done without the vector potential, or with the derivative force. I'm going to mentally take a few positions in progressive stages. Let's begin by taking a few positions on these two galaxies, separated by distance a. But imagine that what we did was separate the things here. So we have the two components of the two positions overlapping each other. Of course the situation is identical to the very first paper. I've shown you how to get on such and such a generous position to get the subjective results of it. But that's a new level. Imagine now an infinitesimal separation, so a superintensive separation between a wave function and an infinitesimal. So first approximation, clean elliptic form of Gaussian, more or less elliptical, and we expect to see the Lorentz force keep in. So it would account for such an unresolved separation of the position, we get the subjective on its side. A long way away if we look at it. But, if we carry on separating further, then of course the people will resolve effectively the canonical ensemble that we need to take to be topologically different. It can break up into two circles. So, the two positions that have been resolved now actually consist of a cross-sectional protected array of circles around each. Each piece. And let me show this here first. This is actually the De Bruyne version. This is the intuition. The two pieces are resolved now. But these are predicted to be yet without the vector potential. The uncompleted version.