Lecture

0:00 Thank you very much for your time and I hope to see you again in the next lecture. In fact, I would love to give two books. And one is philosophically right, and the other is physical theory, but maybe I can give, short and daily, a given book. They're probably related, but let me begin with the beginning. I'm struck by a discrepancy, a contradiction between two points of view, one that people actually use to work with. And one that they teach. One that is professed and one that is practiced. And this conflict between what physicists do and what they say has persisted since the very early days of quantum theory. There are still people who think that Schrodinger discovered quantum theory as well as Eisenhower. And of course his theory never worked. He got oscillations with certain frequencies which are not the frequencies seen in nature. Instead, one has to have the arbitrary rule to look at the differences between those terms, and that's what comes out of the question. Whereas in Heisenberg's quantum theory, that doesn't have the arbitrary rule, that follows from the mathematical populace of the theory. Turning to the equation, when I go over to the calculator, unfortunately you can drag with it parts of the terminology. Heidenberg imitated Einstein as closely as he could and spoke about what this is to do with operations and the relations between these operations, turning the theory to an older form of physics, going back to before Francis Bacon, in which one postulates things that exist and tries to work out how the universe would think, right, in those postulates. And I will call these two approaches to a physical theory, these two kinds of theories.

2:30 Practic in one case, a kind of theory based on operations and practice, and untic in the other case, a kind of physical theory based on beings. The first one, the theory that worked, was a practical one. And if you go into the laboratory and watch a physicist trying to predict, for example, the number of photons from this polarizer that we get from this polarizer. This is the birth of quantum theory in the hands of Malus in 1805. The general rule is, I'll try to put this rule in a way that applies to the original Malus experiment. But also the most advanced particle physics of today involving particle creation chambers, accelerating rings, colloid, particle beams, collision beams, and conflict chambers. But this is first looks at how the system is produced. And there's a general catalog. There are a number of ways to produce the quantum system. This is one way of defining where the left one is and to say how you make it, how to eliminate the left one. Then there are a catalog of ways to detect the same system. They play these against each other. Perhaps the most important relation is the statement that nothing from this source gets to this source, the accruing version. Partly, this relation by techniques that Galois developed to a lattice. In fact, a pair of lattices in relation to Cleveland called the Galois connection.

5:00 And in that lattice, you find atoms, which correspond to ideal modes of preparation and detection. These are as sharp as possible. These are modes which are counted by as few counters as possible. In quantum theory. And this relation of occlusion holds just in the case for distance zero. One of the ways of stating the quantum principle in terms of operations of this kind is to say that this lattice has a certain symmetry view. If you really believe in classical physics, this lattice is always a product of binary matrices. A bunch of yes or no decisions. The system is at this point, you face space, or it's at this point, or this one, or this one. Preaching these, you have a yes or no question. You put all these together and you're going to get an exact specification of the system. Clearly, this lattice is not simple. There's a huge number of invariant binary sub-lattices. The quantum principle is to state that they're simple, that the relativity group of the lattice, I mean, is simple, that it's, in fact, a simple league group. And all of the paradoxes of quantum theory are built into this idea that, on one hand, there's continuous infinity, Of ways of preparing a system, they form a lead group. And on the other hand, it's a lead group. There's a 45-dimensionality required to describe that. It can be with photons. You have an infinite number of possible polarizations. And yet, the amount of information that a photon can carry is one bit. And all that we analyze may be a two- or a dozen-picture. The lattice is infinitely wide and moves too far. This is the simplest case of what is simply S-O-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2-A-S-U-2- From this leap of characterization follows things like analysis law, which is that in the two-dimensional case of, say, photon polarization, the probability of transmission is given by the square of a matrix element of this kind, and that turns out to be the square of the angle between the two, between the polarizer and the angular.

7:30 The probability of a photon that has gotten through the polarizer, getting through the analyzer, is cosine squared theta, and if you get a square for a moment, it looks like this, I guess, and if you square, it looks like this, and what you expect from constant physics, when you get down to ultimate precision, is that if the angles are exactly aligned, the thing gets through with 100% probability. And if there's at least a bit of a discrepancy between the labels, since this is part of a sharp description of the state, you should reject all of both of them. For example, if you were sending broom handles down a bench, and you had a lap comb, a picket fence that they had to get through, if they're exactly lined up, they get through. If they're at least a bit offline, in the ideal case, they don't get through. So, you have to understand how this conception of a delta function like transmission probability arises when the fundamental thing is cosine theta. And, of course, it arises from large numbers. For example, if you send two photons down the bench, the probability of them locating true is cosine to the fourth theta. If you send ten photons down the bench... Let's say 20 is cosine to the 40th theta, and as you look at higher and higher tolerances of the cosine, the peak gets more and more exaggerated, and when you send in the number of photons down the bench, in order for them all to get true, the two polarizers have to be exactly aligned in the classical physics. The classical physics emerges from quantum physics in an easy way, and once that has happened, you no longer need to discuss The input and the output, reduction and detection separately. Just the statement that transition is allowed at all tells you there's a one-one correspondence between these.

10:00 And the equivalent pair of the two is called the state of the system. When you go to the limit of deterministic physics, the state arises as a description of how the thing is made. The state is, as it were, the information about the past which is efficient to predict the future exactly. Let me regress to my childhood. I remember riding the 3rd Avenue L with Jack Schwartz while we were excited for high school. He was explaining to me what theoretical physics was about. And we didn't have a blackboard. They didn't have blackboards in the 3rd Avenue L. So, he made a quick gesture in the air, which I think was a top act. And here is the real world of experience, and what theoretical physics does is intervene at some point and extract symbols, a symbolic description of the situation. And then computation takes over. It processes the symbols and comes up with a symbolic complex, which is compared to reality at this point. And the two agree you have a successful physical theory. And what I didn't realize at the time, it had only come to realize slowly over the years, is that this implies a fundamental accord between the way symbols behave and the way the real world behaves. It implies that nature is symbolizable. And of course, symbols have a property that they can't hold a party equal. If you can't tell an A from an E, you're rightly too small. And you write larger until every reader can infallibly tell it to apart. So in the symbolic level of description, we're always operating in a macroscopic domain, where there's many photons that are necessary to make sure the cosmology works. And it just happens that this game of mapping symbols with experience doesn't work really with photons. The most successful theory yet does not predict what will happen to a photon. Instead, it just gives you the odds. And the ability to give odds is just a property that comes with the law of large numbers.

12:30 Almost anything at a microscopic level ends up giving correct odds at the macroscopic level, because the experiment's walking them. And so, it's clear how the concept of state arises, of why has it persisted so long, since it's clearly A single limit of the quantum situation. Why do we insist on ascribing it to resist a mistake? One answer is historic. We could look back to the most influential formulations of quantum physics. For example, the book of Dirac on principles of quantum mechanics, or the book of Vermeulen on mathematical foundations of quantum mechanics. The process of kind 1 and process of kind 2. And process of kind 1 is this. This is the process of kind 1, where you look at the system and come out with symbols and make a measure. And the process of kind 2 is this, where the system evolves. And what I realized, fairly frankly, and thought it might be a good I don't have a point to hang this kind of discussion on, but I never noticed that complement can't count. That there are not just two processes that intervene in the evolution of those systems. There are three. And that's either 50% off or 33% off, depending on which way you count. But it's a significant error. And of course, the three are the beginning of the experiment. The middle of the experiment and the end of the experiment. The prediction is typically, in Hawking's theory, a matrix experiment. And for some reason or other, if you look at him unmistakably, he says there are two ways to intervene. Namely, in the measurement, K can change, and then he gives an incorrect rule, an incorrect description of the measurement. But this was back in 1932, so he can be forgiven. He has a measurement turning pure state into a mixture. And of course, this is a result of not using the measurement.

15:00 He's lumping all the output beams into one. And no one would do a measurement if they were going to lump all the output beams into one. You do a measurement to use the output. So what he should have said is that A changes into B, where B is in the measure, with a certain probability. This is a change of kind one and is not predicted by quantum theory. We only give you odds. We don't know the outcome of this experiment. The change in the form of a change of kind two is described as a passive sign. A, he said, change of kind two, you may review the unitary transformation. And, of course, it's not really related to what goes on in the laboratory. No one knows what A is at the beginning of an experiment. There's no A out there waiting for us to process. Where did this idea come from? I'm busy looking back at classical mechanics. And astronomy, in fact. In astronomy, A is the position of the planet at the beginning of the experiment. And when you're becoming naive about acquiring this information, you look and there it is. You get a state given to you by God as a form. So it's okay not to mention how we know it. It doesn't change the planet to get its name. And in these processes, whatever you're doing changes the symbol. So if this looks like it's more physical, then you can leave out beginning the experiment. If you think that is annoying enough, that is correct. To get the history right. This little part of the Williams book, well, that actually wasn't what I was going to do. When I first read Wigner, he expressed me with some pride. As well, in general, the flow of information was in this case, he was the one who provided this section of the men's book. And this is how terribly significant it is in fact. In fact, if you look through the book, you'll find that in general, it's consistent with the idea that this is the state of the system. Now, there's nothing wrong with calling it the state or sliding tub or cable or anything like it. Except, if you call it a state, you have to think it's all the system.

17:30 In effect, you acquire this information by looking at the polarizer, not the postcard. You do not begin the experiment by looking at the postcard. You begin the experiment by setting up the polarizer and adjusting it. That takes an infinite amount of information, I think. We're adjusting at a continuous angle. We're investing infinite information here. And infinity information is there, but just in the analyzer. And you get out one bit of what one does or does not make the transition. Whereas, think of it this way. God gives you infinity of information at the beginning, and you get out, if you're correct in one insight, you get out this one bit of whatever it goes, and the theory doesn't predict that, it gives you the odds. So, people get along with a phenomenal description. By misreading the word state, we mean the mode of preparation. In fact, if you look at Dirac's book, he starts by saying, systems have states. And then many, many pages later, there's a footnote. Of course, by the state we mean the way in which a system is prepared. And if you look at Fanon also, he's perfectly explicit. By the state of the system, he means the way in which, he means the ensemble from which it's selected. Which is just a particular choice of mode of preparation. You imagine a big warehouse full of systems and you choose from it. It's an idealized mode of preparation, easier to describe than a hotel room. But in every case, in application, you learn not to limit the system for the state, in quantum theory, although one does in classical physics. Okay, then, what are the problems with this mode of description, the ontic formulation of quantum theory? The first one that comes up is raised immediately in the book after this. Namely, if the problem is the measurement, so to speak. The problem of measurement is the following. Clearly, measurement is a dynamical process, an interaction between the observer and the system. A dynamical process is a process of kind two. In classical physics, there's no process of kind one. All measurements are dynamically described. The process of measurement is important in the dynamical knowledge. There's again a slight misstatement. He says that since a measurement is a dynamical process,

20:00 you can feed in the parameters of the measuring system as numbers, expressing the dynamical process. But in fact, we know that in a measurement, the system interacts with microscopic variables of equipment. And what is fed in are not numbers, but quantum variables. You can't treat them as numbers, they change, but one of the principal components is leaving out the unpredictable reaction of the instrument to the system. But that aside, the effect of changing attention from the system to system plus experiment is not to eliminate the need for a process 1. In classical physics also, you begin by observing where the system is before you evolve and observe where the system ends up. So you eliminate the process one on the system level, but only to create two more approximately one on the method system level, the level of the experiment. And it's just that in astronomical physics, one has learned to ignore those. But of course in quantum physics, we cannot. So the very first step in formulating the problem of measurements is law. One does not ever replace measurements by dynamics. One only replaces measurements at one level and measurements at another level. We're all into these three stages, even back in classical physics. In classical physics, you thought of the system as an unmoved movement. It gives information to you, which you write in your notebook, but it's not changing the process. One slightly idolizes the system in the measurement process and wants to be more realistic and recognizes it as a reaction. So I speak of the non-Hawking dimension. There's no such thing as eliminating measurements in favor of dynamics. We can only replace values at one level by measurements at another level. Another problem, another way of putting the same problem, is the problem of the collapse. If you think that this creature is the state, then inevitably you think the state is changing during the experiment.

22:30 It does in classical physics. And so you think this other thing which creeps up here is something that evolved from this in the course of the experiment. It does in planets. But in any measurement system, classical or quantum, It's completely up to you how you begin the experiment and how you end the experiment. These are both free choices and determinants in both classical and quantum physics. It just happens that in classical physics, unless you choose this exactly right, your transition will occur. So you don't bother looking at what kind of physics. You only calculate what kind of physics it is. In quantum physics, you don't have this option. Almost any place you look, you'll find the system if you look long enough. You only have a probability, and almost never is that probability zero. So the fact that this is an independent variable from this is unavoidable in quantum mechanics. It is not the case that the polarizer rushes down the optimal bench and becomes the analyst in a photon experiment, which is why it will apply when you say it's initially evolved into the planet's fate in some mysterious way. There is no phenomenon in nature corresponding to the collapse of the wave function. The phenomenon arises when you try to describe experiments with only one end. You leave out the fact that you have to make an initial determination of how you produce the quantum. One-handed experiments I like to think of as like one-handed practice. And eliminating both ends of the experiment, Eliminating measurements all together is like fathoms and zolomites. It doesn't work. I'll ask you, but I wish you would. This is all very fine, but at some level one has to understand why you handed that in, or appeared to that in. First of all, that's a perfectly valid question, but of course it would employ any statement I make. And I don't really think the job of physics will ever be ended. If I answer that question, this leads to another one. And I think in unprecedented physics, we start with this as a possible one and leave it for the next generation, understanding more deeply where it comes from.

25:00 Perhaps in the second half of my talk, I'll indicate where this more processional view of nature leads. Let me just mention that, yes, please. I want to ask a couple of related questions, which is beyond the light. When you do this kind of management thing, do you review the IE chart? Well, yes, I do. We make a lot of chart on paper. Oh, my God. We found that I have T-more. And I have T-more certainly helping me always to fit in my, I think always in my, yeah. And then that evolves into A to T. It doesn't evolve into B. And then that's C, B, where it should evolve to A. And if you ignore that, well, you've got two choices. Either you believe the same evolved from A, obviously, by then A to C, and then B to F, or you believe that the polarizers are interdependent and can't be analyzed. Yes, you're speaking the same language. You're thinking of this as the state which evolves. It is not. It's a description of the initial polarity. Nothing more, nothing less. Look at how the quantum physics is actually done in practice. The quantum physics does not look at the polarity to make a prediction of its behavior. Yeah, but it's not true that the state doesn't evolve. The state doesn't exist. It doesn't evolve. There's no such thing! Systems don't have states in quantum theory. Any law in the world has a now in relativity. One can formulate theories which give much the same experimental results as special relativity, imagining there is a now out there. For example, though, Ray Fitzgerald's theory is almost as good as that. But that doesn't mean there is a now. And if you think there is, well then you're scratching your head. Where do you go from here? Systems don't have states. There's no reason to think they do. What about health writers that define measurements? Would you still believe in a health writer that defines a measurement? Oh, I believe in these creatures also. It's just a question of what their relationship to experience is.

27:30 The whole of the mathematical apparatus, the ordinary textbook and quantum theory, is all relevant and applicable. But what you do with it is not what is described in the book. You don't treat it. As if you were looking at the state of the system and watching it evolve. You talk about that, and then at the very end, you convert the probabilities and compare apparatus and emission, the injection chamber, with apparatus and the counting chamber. What people call a state. It's in the red. This is the important relation. This is that which is an equivalent. A lot of different descriptions of equipment are all the same for predicting the future. So that's why we're going to go to the Galois lattice of this relationship. That signals out what is important about the description. Because, of course, the operations are irrelevant as long as they're essential aspects. Exactly. You identify things at this end which are not distinguished at this end. Conversely, you identify things at this end which give the same, no matter what you do, effect. And the fact that these things are not distinguished suggests that... The better looking thing that's counting in that state is the system. It's a guess, isn't it? And the suggestion is wrong. I mean, the system carries on. I mean, there is no way to extract from a photon information about how it was made of anything more than one big company. And the way it was made has infinite number of bits in it. But it's not totally wrong to say that it simply remembers how it was made. But it's closer to wrong than to right, because remembering very little about how it was made, and classically it remembers everything important but how it was made. It's different between almost nothing and almost everything. That's it. You can see that it must be formally correct.

30:00 What I feel is that there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. Yes, there is a difference between what we use in theory and what we don't use in mathematics. And we will, I'm sure of it. And you're just looking ahead for the next problem. And I'd like to do that also. But we don't need to do it. But on the other hand, one can do it, because it's only one. Absolutely. As long as, and you can do it in honesty or dissonance. One can imagine the system at this stage, and to a certain point, and then drop that and do it right. I mean, all the textbooks are written that way today. Or you can be honest and begin with saying, don't mention state, just think of input and output, input and output, input and output, input and output, input and output, input and output, input and output, input and output, input and output, input and output. We talked a lot about modus operandi, but that's a linguistic game that many people don't want to play. Process is also a nice omnivore. It's very hard to do a misplaced concreteness. If you speak of these as in the process and out of the process. There's not a state of mind in this book. The state of mind of one wouldn't work if one carried it through consistently. And the only reason all the textbooks survive is that they don't do what they said to be served.

32:30 And by the way, this is not a new point of view. Berkeley explicitly made this very very explicit fact in two papers. First, he pointed out That the view of destruction would want you to do, identifying this with the state would be a completely other great decision, if you don't as well say that the fact of the matter is what the state is. And this is, for example, a hard number. We're also refusing to give up the idea of the state. Maybe the system has two states. And if that helps, we'll use the first one I'm going to speak about. Peter Bergman got it right back in the 60s. There are two important papers, one with Harnell Bergman. And liberals, pointing out this peculiar ambiguity, why you choose this to be the state and not that to be the state. And then, in a subsequent paper, in the series that Mario Wille edits, he points out maybe the resolution is that the idea of state doesn't belong in quantum theory. And I think it's a shame. That you couldn't carry out the conversation you learned today. In fact, I think Einstein's greatest mistake was not the cosmological concept. I think that was his third greatest mistake. The second greatest mistake was thinking that was his greatest mistake. Greatest mistake was not realizing that quantum theory is an operational theory like his favorite theory of relativity. Just didn't keep it up. I don't know what you should do, but you know the answer, the answer is nonsense all the time. I think he had his chance. Do I have time now to indicate the general, the next step in physics? If this is right, then the situation today is rather disgraceful, in that you have things like old schools of research, or the many worlds of interpretation, or the career history, or consistent histories, these are all attempts to solve a problem that doesn't exist, the collapse of the state. And what should we be doing? Now, this, what I've said so far, I think is true. It doesn't make sense. But I'd say now, it might be true, but the odds are enormously against you if you're trying to see which way physics is going to go. And hindsight is what's going to allow you to be first. Still, I find the question irresistible. What should we be doing?

35:00 The world is really to be described with verbs rather than nouns, putting it that simple. But for all this process, then where the hell did the atomic period come from? Why has it been so successful? Because the problem is that there are elegant particles. There really seem to be. If you look at how that reflects out here, you see that certain processes... Come in chunks. They're in processes of creation and dilatation. Have units to them. They're elementary processes of creation. The other hand, other processes don't come in chunks. In practical physics, you can move something as little as you like. There's no elementary translation process. Processes or translations can be divided into infinitesimal parts. Whereas processes of creation either go or they don't go. And you're down to the electron level. Well, the obvious assumption, the obvious step is to suppose not that there is an elementary part of it, but there is an element of the process. Maybe there is one elementary process, or a small number, or a finite vocabulary, or an infinite countable vocabulary of the elementary processes, which terms in which all processes can be finitely expressed. I think underlying the present infinitesimal theory is a really quantum theory. Broke before, for quite a few decades now. And they wrote a book about it called Quantum Motivation, back in 96. What I want to talk about today is how that book has grown, which wasn't written before. And this is largely the result of, as I said, years. It's the result of going to a meeting where a guy alone was getting an honorary degree at Columbia University. So ridiculous. And I was walking behind one of his friends, who's the head of the geology department in the United States, and I heard him say, well, it's relative.

37:30 And I sneered. Everyone knows this is just a cocktail party version of general relativity. To hear the word general relativity, it must mean there's a general principle about everything relative. I even wrote a paper with a little chapter about this pointing out that the relativity has its aspects. And Oscar Klein, who we dealt with long ago, called relativity for the invariant theory, and Rob, as you well know, founded a special activity on the theory of the invariant relation defined by future and time-like vectors. So, it is certainly not the case that any physical theory worth the name will always know it. On the contrary, we only begin a physical theory by describing those things which know the absolute. Even in quantum theory, the concept is more of a preparation. It's something everybody is supposed to be able to agree on, an absolute. But I listened a little longer, and it turned out that, first of all, this was the interpretation given by the Dalai Lama's school of Tibetan Buddhism. But the whole bootstock of all this emptiness, namely that the viewpoint, the observer, influences all observations, that everything is made from, every observation is made from the point of view, there is no absolute essence left over after you take into account the observer. There really isn't everything in a modern sense. And this very attractive notion is much more attractive than beginning with some attributes and so on. So I tried to go back to the process of relativization to see if we could be pushed to the limit. We didn't have to relativize everything. I did re-remember an important paper by Ian Miller and David, back in 1952, where they discussed the process of group contraction, which is how you get from a good theory to a bad theory. How do you get from special relativity back to Galilean? You introduce a parameter, Steven White, to take the limit as it goes to infinity, in this case. You introduce a parameter into the commutation relation to the reality of a theory. And then you go to the limit.

40:00 And the algorithm changes its structure completely, you know, to a singular limit. You begin with a simple algebra, and you end up with one which isn't even semi-simple. And reading through Fittler's master-like position, for example, I spotted a footnote to a paper of a really old acquaintance of mine, Cervant Siegel, 1951. That's a paper I really earned you to read. It's a remarkable insight for a seminal paper full of many, many years. The main idea is that, first of all, this idea of group contraction turns simple Big groups, like the one at the foundation of the quantum principle, is the non-semi-simple big groups, and Siegel encourages us to invert this, to look around, for example, the non-semi-simple groups. Whenever you see one, this is what you should be going past. You have to make that group simple. You have to find the fundamental physical framework which is allowed to go from single to zero, infinity, whatever it is. It's remarkable that all the important conceptual, epistemological allusions in physics can be cast in the terms that Ziegler describes, not just the example that Wigner put to the right. I don't know why Wigner stopped with the speed of light. Einstein's constant is also a stabilizing constant in the sense of Ziegler. Let me explain why stability is an important concept here. That a non-semi-simple algebra is unstable in the sense that you make the least change in structural constants. You come to the algorithms with a totally different structural non-isomorphic unity. Simple algorithms are stable. You make a small change in a structural constant, it doesn't change the algebra at all. You don't have your own isomorphic. It's just as like changing your units and your reference vectors. And implied into the paper is the principle that maybe physical theory should be stable. Maybe you have something with experiments, and experiments always have little errors in them. If you leap from experimental data to unstable theory, you're going to fall into experimental data. The only hope you have, I mean, it might be right, maybe God loves that theory. And he puts it there for you to discover, and you have the zero and the nine.

42:30 But maybe that's not the case. Maybe theories are things we make from the data, and we should make them stable, therefore. Unstable theories are useful. Hyperdynamics is a useful theory. You can call it unstable, but it can't really be right. In fact, when England tries to compute hyperdynamics, they're including stabilizing viscous terms to make it possible. The original theory just isn't conceivably right. And it is, of course, it is, followed from the atomic theory, by then the atoms go to zero, and the number of them go to infinity. Hydroponamics is some kind of only stable limit for particle theory. So the main rule is, look for the much more simple rules, and then make them simple, by reducing constants like t and h bar. But Zico gave a couple of examples of how present-day physics is unstable, and therefore, Very, you know, 100% probability right or wrong. That doesn't mean it's wrong. 100% probability is not the same as certainty. But it's damn close. And, first of all, he pointed out that the Heisenberg communication equation is unstable. If you write P comma Q with lines of A and R, then you also have to write P comma I with zero, Q comma O with zero. This is remarkably similar to the connotation relation that occurred in the Galilean rule of space and time. And there you fix it by putting in little counter terms. You say, this isn't zero, it's just very small. And so you do the same thing here. You end up with p comma i, with some multiple of q, q comma i, and some multiple of q. This is a stable commutation relation on the simple field, where Heisenberg's original relation is not stable. And moreover, by writing these down, by making these constants to be small, you guarantee that quantum theory is preserved. It's just that these constants are small, so we have to be a little more careful here at the moment. But our case here goes on and on. Under serious advising, I can't find anything wrong with it. I really think Hawking is wrong in the sense of Galilean physics. We may not be out of it, but it's there.

45:00 Yeah, that's it. I don't know because I'm aware of it. Obviously, this doesn't make sense if I'm not aware. It doesn't make sense. Just as in special relativity, the... The new group that I've written down here is either either SL3 or SL1-2, depending on the signs you get these constants. It just happens that exactly this theory came up. I didn't realize that it meant you really were going to do quantum mechanics, but it turned out that you missed one. To do that, you introduce operators I, J, and K over a real field, with actually real quantum mechanics with an SO symmetry. But it turned out to be predictive. It led to a gauge theory, which is the Georgi-Glashow unit-like theory, or the Leukoelectromagnetic theory, several years before it dates down to time. I'm sorry, I apologize for the fun with that. I know a lot of the wrong word. I mean, you can always start to develop people right here and study them there and there. The thing I was the one that was talking about was that projection. And then there are other... So this is why I used to do it. Quantum theory is wrong. I don't think people will not be disappointed to hear it, but it gives you research for it. Well, I just have a couple of comments. One positive is that, one is that you have to avoid using them and say that you put it up to the point that they all need to focus on. They don't see you sometimes having a negative conversation. A negative conversation is that By the way, even if you look at so-called non-communicable geometry, they're usually over a complex fluid space. They haven't stated why a distant future can be a collision. They haven't adopted Siebel's program. It's true they're deformed.

47:30 I'll let you repeat that. That means they're not solving any of the capabilities of the existing field. They're doing mathematical speculation. There's a mapping between the knowns and the absolute ones, but I mean, there aren't any absolute ones. Absolutely. That's like saying quantization is not good. It's a heuristic process. You're lucky you guessed right, but I don't know a better game than that. So, this was one of the experiments. I think it's worthwhile tracing this through the root, right? We're at about a few minutes. This ultimately is representative of the present-day optical theory, and you have seen that throughout our time. It goes back to Newton and Leibniz, if I get into the argument, who discovered the calculus. But the instability of Heisenberg's relation is the instability of Newton's, or Leibniz's, relation to the differential complex. I take it seriously. The differential calculus is an unstable theory. Anyone who's ever tried to put it on a machine knows it's unstable. In order to estimate a derivative, the same precision, it's impossible to estimate the derivative with the same precision as you estimate x. You need to look at two x's which are put together, and then the accuracy on the difference is one way down. One ends up doing the prior difference method and trying to arrange that they give results close to that of the calculus. But the calculus itself is unstable. So this suggests that underlying Heisenberg theory is a more algebraic theory yet. Now, let me begin.

50:00 Where's the erasing thing? It's sitting behind there. I had no idea. I remember I was nervous at the erasing thing because I'm not sure. And I didn't know I had a chance to look at it. But I can guess. Oh, yeah, right now. Well, the theorem is about a percent of the journalist who wrote the book. Kind of an example in the last chapter. Let me say what I think was wrong. Okay? The possible problem is there exists an elementary process from which all processes are composed. And I have in mind a parallel to the usual way in which you make atoms out of particles and molecules out of atoms and so on. And in this case, you put together processes out of little bits of processes. And before you can even begin such a game, you have to decide on the statistics. What are the, what is, what is the statistics of the elementary process? And we only know the two kinds of statistics. Yes? Are these supposed to be the word process, elementary process, or, you know, percent, you know, all those kinds of things? Well, in physics you always have to take something that is underlined mathematically. But if you're smart, you take it to be something that everyone knows the meaning in practice. And I'm assuming everyone knows the meaning in practice of practice. Until I heard your first part of the quote, I knew it was worth a thought. It's something you do. Really, it's something you do. It isn't very closely related to a problem that Simon is writing about right now. But you can start with binary relations or monadic existence assertions as your fundamental entities. And I'm definitely starting with a relation of a very special kind called an operational process, a relation to now and a little bit later, representing an action, a process, a doing, a word, not now.

52:30 So we shouldn't take that there exists in the initial form of a verb. Right, exactly. This is really regarded as a description of a language. In a language, there's the idea of an elementary process. And then, the next question is, what are the statistics? And you have to make, you have to answer, I think, the only way to play the game, is you get as close to the real theory as you can. Guaranteed, you go over to it in the corresponding limit. I like to think of algebra as a deformation, in the sense of Siegel and Euler-Wendigel. Well, if you look at classical physics, We learned to express all the processes there in the language of set theory. The closest thing in set theory, in quantum theory, is perimeter action statistics. I don't know if you realize how close to R the algebraic structure of set theory is exactly the algebraic structure of rational algebra. Restricted to an orthogonal basis, an orthogonal basis. Now this is important in rational algebra. As a common language, the placing set theory for quantum physics was first determined by a beautiful talk that David Bowie gave at Columbia University in the 50s, and it really inspired me down the years, and I have the same thing, is it almost right, almost up to infinity formation, which is what I've learned in the last couple chapters of Quantum Affinity and expounded on since. Part of the thing that bothered me back then is the fundamental relation of graphs and algebra for forming the actual statistics is unstable. Let me remind you of the correspondence between graphs and statistics and costal epistemology. This corresponds to the statement of the algorithm making the algorithm back to the first. When the first saw, the rule was larger. You know it's the left of the algebra. The rule had a basic operation that you wrote in a question, and it wasn't always defined.

55:00 The only rule that was tremendously influenced by the theory of probability is that it happens well. In this book, there's something come out. Like, there was a little pencil he called as a private expense before he wrote the book, which I came across in The World of Mathematics by Kazim Rumi. And I think it's absolutely critical. It's a beautiful example of practical It happens almost at the beginning of every theory, when people have to understand what they're talking about. They go to practice. Then they hide that. They tear up their notes to present the postulation on their point of view. You don't find in Boole's book what a class is. He must do his classes. But in his little note, 30th in the Catholicism library, he says what a class is. A class is defined by... The process by which is select from a population of large individuals having something in common. The class is defined by a lot of things. Today, of course, people will be infiltration, the projection of the world, meaning a sort of white source as implicitly included. I don't know if I should say this, but I can't, or I will try to give the relation to the rationality of the cosmology. In the rationality of the cosmology, you have a product, which I'll write it this way, which has a component that appeals to zero. And I'll just say one thing, and this corresponds to Boole's original operation. You can get a consistent mapping between the two theories. You can then try zero and undefined. Not the null set. The null set is perfectly well defined, but it's represented by 1, because 1p is 0. This is a kind of viewing operation, and adding the empty set to something doesn't change it. This recognition that logic needed a symbol for the undefined, first regarded as the most important discovery, at least when he was young.

57:30 And it enabled him to turn pool of logic into an algebra. He said this was as important for logic as a zero for it. But because he used a plus sign on this operation, he had to use a symbol infinity for the absorbed development. And here I'm drawing on Piano's work, which comes after this one. And this is unstable, and if you make the least deformation in it, you get this. By an adjustable change in scale. And this no-motor is a Grasmann algebra. This is a Kripit algebra. Kripit algebra is just a very slight deformation of a Grasmann algebra. And it related the Grasmann algebra to the quantum theory of the quantum oscillator, which is related to the classical theory of the quantum oscillator. This is a quantum quantization. So back in the 80s, even yesterday. With Ernesto Rodriguez, who wrote a paper on quantum logic, found that they're not going to grasp the natural, but at a separate level. In the very same year, I discovered last year, Frank Wojcik was working on carriers of electricity and fractional quantum law. He gave us the statistics for these carriers. There is no relation to any of the statistics that have been used before in physics. And it has to reflect the operations on the carriers on a corporate algebra. He did this before I did. It's certainly a dependency. That is, you know, what I'll do with the board now. Keep pushing. I'm going to put it down. Great. That's fine. It only describes statistics. What do I mean by statistics? I'll give you a concept which works for all the examples I give you. I'm not going to give you a general view of the world. You start with a vector space, which you think of as the one quantum modes. The one quantum space, you might guess, and you just bring this over. And you go over from this to algebra.

1:00:00 We try to have many and go from one to many. This process was given a name by the famous Scottish magician William Hamilton in 1840. He called it quantification, going from the one to the many. It is not quantization. It doesn't introduce any constants. It's not a deformation, for example. And moreover, it's not going from a wrong theory to a better theory, the way quantization works. It's just going from the period 1 to the period 9. And the end result is now a vector a. And you can represent the quantification process by a method, q, which turns vectors here into operators here. And since this turns vectors into numbers, it has the transformation properties of a form. So it's convenient to put a vector on it. And in further direction for the next seven cases, this is a one-body mode, and this is the creation operator, or, yes, at the moment, and the annihilation operator, as it's best written this way. To quantification, the philosophy goes from a one-body mode to creating an annihilated body in the familiar cases. And this all wasn't maybe to convert operators of one-body theory into operators of many-body theory, which represent two different values of a quantity. And in the Graston case, the Fermi-Dirac case, and he is the Graston algebra on the vector space theory.

1:02:30 Sorry, these are the load vectors of the ensemble.