Philosophy of Physics Discussion Group — David Finkelstein

0:00 Thank you. just for a few days, and I think another one tomorrow morning, a talk entitled Two Quantum Theories. Is that correct? Well, a quantum process. That's what it's called. Two quantum? Two quantum? An elementary process. I think that's the number there. Oh, that's right. An elementary process. That's the question. A very big method. In fact, I would love to give two talks, and one is most algorithm-oriented, the other and maybe I can shorten both of them and give them both. They're closely related. Let me begin with the beginning. I'm struck by a discord, a contradiction, between two quantum theories, one that people actually use and 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 earliest days of quantum theory. There are still people who think that Schrodinger discovered quantum theory as well as Heisenberg. And of course, his theory never worked. He got oscillations with certain frequencies, which are not the frequency seen in nature. Instead, one has to add the arbitrary rule to look at the differences between those frequencies. And that's what comes out of the action. Whereas in Heisenberg's quantum theory, that's not an arbitrary rule that follows from the fundamental of oscillates of the theory. Schrodinger's equation went over to quantum theory. But unfortunately, it dragged with it part of the terminology. Heisenberg imitated Einstein as closely as he could and spoke about what physicists do, operations, and the relations between these operations. Trinning adhered to an older form of physics, going back to before Francis Bacon,

2:30 in which one postulates things that exist and tries to work out how the universe would be according to those postulates. And I will call these two approaches to a physical theory, these two kinds of theories, Practic in one case, that's the kind of theory which is based on operations and practice, and Antic in the other case, that's a kind of physical theory that's based on beings. Okay, the first quantum theory that worked was the Practic one. you go into the laboratory and watch a physicist trying to predict, for example, the number of photons from this polarizer that will get through 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 malice experiment of the oblique polarizers, but also the most advanced particle physics of today, involving particle creation chambers, accelerating rings, target rooms, collision kitchen rooms and counting chambers. The physicist first looks at how the system is produced. And there's a general catalog of ways to produce the quantum system. This is one of the parts of defining what an electron is. So you say how you make hot filaments and all that business. Then you have a catalog of ways to detect the same system. and you play these against each other. And perhaps the most important relation is the statement that nothing from this source gets to this source, the occlusion relation. Ultimately, one can parley this relation by techniques that Galois developed to a lattice. In fact, a pair of lattices and a relation between them called the Galois connection. And in that lattice, you find atoms, which correspond to ideal modes of preparation detection. These are as sharp as possible. These are modes which are counted by as few counters as possible, for example.

5:00 And those are the things you can call bras and caps in quantum theory. And this relation of occlusion holds just in the case where this is 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 group. If you really believe in classical physics, this lattice is always a product of binary lattices. A bunch of yes or no decisions. The system is at this point in the phase space, or it's at this point, or this one, or this one. Pretty easy, 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 sublattices. The quantum principle is a statement that it is simple, that the relativity group of the lattice I mean is simple, that it's, in fact, a simple e-group. And all of the paradoxes of quantum theory are built into this idea that on one hand, there's a continuous infinity of ways of preparing the system. a Lie group. And on the other hand, it's a Lie group. So it's only a plant dimensionality required to describe it. If you, with photons, you have an infinite number of possible polarizations. And yet, the most information that a photon can carry is one bit. To hold up an analyzer, you get through it or it doesn't get through it. And the lattice is infinitely wide and only too high. This is the simplest case of a simple e-group, SU2, I guess it is. Okay, now, in ontic formulations of a physical theory, you generally, at some point close to the beginning, describe what's called the state of the system. You postulate the existence of these states. And so I should show how the idea from the theory of this kind we're not mentioned. From this B group characterization follows things like Malice's 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 comes out to be the square of the angle between the two,

7:30 between the polarizer and the angle wire. The probability of a photon that has gotten through the polarizer, getting through the analyzer, is cosine squared theta. And if you forget the square for a moment, cosine theta looks like this, I guess. And if you square, it looks like this. And what you expect from classical 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 bit of a discrepancy between the two angles, since this is part of a sharp description of the state, you should reject all the protons. For example, if you were sending broom handles down a bench, and you had a lab comb that they... a picket fence that they had to get through. If they're exactly lined up, they get through. If they're at least 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 a cosine theta. arises from large numbers. For example, if you send two photons down the bench, the probability of them both getting through is cosine to the fourth theta. If you send 10 photons down the bench, or let's say 20, it's cosine to the 40th theta. And as you look at higher and higher powers of the cosine, the peak gets more and more exaggerated. And when you send an infinite number of photons down the bench, in order for them all to get through, the two polarizers have to be exactly aligned and you have classical physics. 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 production prior production and detection separately. Just as the statement that transition is allowed at all tells you there's a one-one correspondence between these and the equivalent pair of the two is called the state of the system. When you go over to the limit of deterministic physics, the state arises as a description of how the thing is known. So the state is, as it were, the information about the past,

10:00 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 in high school, to his home in the Bronx. what theoretical physics is about and we didn't have a blackboard, they didn't have blackboards in the 3rd Avenue L. So he made a picture, a gesture in the air, which I think was a top hat. And here is the real world of experience. And what a theoretical physicist does is intervene at some point and extract symbols, a symbolic description of the situation. And then computation and the imagination takes over, and he processes the symbols, and comes up with a symbolic output, which is compared with reality at this point. And the two agree you have a successful physical theory. And what I didn't realize at the time, and I've 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 the property that they can be told apart uniquely. If you can't tell an A from an E, you're writing too small and you write larger until every reader can't infallibly tell the two apart. So in the symbolic level of description, we're always operating in the macroscopic domain with as many photons as necessary to make sure the classical logic works. And it just happens that this game of mapping symbols with experience doesn't work for individual photons. The most successful theory we have does not predict what will happen to a photon that gets through a polarizer and comes to an oblique analyzer. Instead, it just gives you the odds. And the ability to give odds is just a property of consequential law of large numbers. Almost anything at the microscopic level ends up giving correct odds at the macroscopic level often enough. And so it's clear how the concept of state arises. Why has it persisted so long since it's clearly a single limit of the quantum situation? Why do we insist on ascribing to the system of state? One answer is historical. You look back to the most influential formulations

12:30 of quantum physics. For example, the book of Dirac on the principles of quantum mechanics or the book of Phenomen, Mathematical Foundations of Quantum Mechanics. In Phenomen's book, there's a famous paragraph where he speaks of process of kind one and process of kind two. And process of kind one is this. This is the process of kind one, where you look at the system and come out from the symbols, you make a measurement. And the process of kind two is this, where the system evolves. And what I realized fairly lightly, and thought might be a good point to hang this kind of discussion on, but I had never noticed that phenomenon can't count, that there are not just two processes that intervene in the evolution of the physical system in quantum theory. 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 quantum theory, a matrix of the experiment. And for some reason or other, if you look at the moment of the statement, he says there are two ways to intervene, mainly in the measurement, A can change, and then he gives an incorrect rule, measurement, but this was back in 1932, so he can be forgiven. He has measurement turning a pure state into a mixture. And of course, this is the result of not using the measurement. 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 a thing you're measuring, with a certain probability, which is given by analysis law, also called Born's Statistic Principle. This is a change of kind one and is not predicted by quantum theory.

15:00 We only give the odds. We don't know the outcome of this experiment. And the change that he called of kind two, he described as a passage of time. Changes into UA, where U is a unitary transformation. And, of course, this is not the least related to what goes on in the laboratory. No one knows what A is at the beginning of an experiment. There is no A out there waiting for us to process. Where did this idea come from? Others are looking back at classical mechanics. At astronomy, in fact. In astronomy, A is the position of the planet at the beginning of the experiment. and one can be totally naive about acquiring this information you look and there it is you get its state given to you by God as it were so it's okay not to mention how you know it it doesn't change the planet to get its state and in these processes whatever you're doing changes the symbol so this looks like it's more physical and you can leave out the beginning of the experiment if you think as Benoemann does to get the history right little part of the Neumann's book was not actually written by the Neumann. When I first met Wigner, he expressed to me with some pride that while in general, the flow of information was from the Neumann to Wigner, in this case, he was the one who provided this section of the Neumann's book. And this is not a terribly significant fact. In fact, if you look through the book, you'll find it's in general consistent with the idea that this is the state of the system. Now, there's nothing wrong with calling it the state or a sliding tub or a kangaroo or anything you like, except that if you call it the state, you have to think it's of the system. And in fact, you acquire this information by looking at the polarizer, not the photon. You do not begin the experiment by looking at the photon, you begin the experiment by setting up the polarizer and adjusting it. That takes an infinite amount of information, ideally. You're adjusting a continuous angle. of information here, and infinity information there, but just in the analyzer, and you get out one bit, the photon does or does not make the transition. Whereas, if you think of it this way, God gives you an infinity of information at the beginning, and you get out, if you correct for a moment slightly, you get out this one bit of whatever it goes, and the

17:30 theory doesn't predict that, it gives you the odds. So people get along with the phenomenon description by misreading the word state to mean the mode of preparation. And in fact, if you look at Dirac's book, he starts by saying systems have a state. And then many, many pages later, there's a footnote. Of course, by the state, you mean the way in which the system was prepared. And if you look at the phenomenon also, he's perfectly explicit. 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. That's an idealized mode of preparation, easier to describe in a hot dog. But in every case in application, we've learned not to look at the system for the state in quantum theory, although one does in classical physics. Okay, then what are the problems with this motor description, the ontic formulation of Haunton theory? The first one that comes up is raised immediately in Phenomen's book after this, namely, it's the problem of measurement, so-called. The problem of measurement is the following. Clearly, measurement is a dynamical process, an interaction between the observer and the system. Dynamical process is a process of kind two. In classical physics, there's no process of kind one. All measurements are dynamically described. Why on Earth do you need a process of measurement in quantum theory if it's dynamical in origin? There's, again, a slight misstatement. He says that since a measurement is a dynamical process, you can feed in the parameters of the measuring system as numbers and express it as a dynamical process. But in fact, we know that in the measurement, the system interacts with microscopic variables of the equipment. And what is fed in are not numbers, but quantum variables. You can't treat them as numbers. They change. Phenomenon at this moment is leading 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 one. In classical physics also, you begin by observing where the system is

20:00 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 processes one on the metasystem level, the level of the experimenter. And it's just that in astronomical physics, one has learned to ignore those. But of course, in quantum physics, one cannot. So, the very first step in formulating the problem of measurement is wrong. One does not ever replace dynamics, sorry, measurement by dynamics. measurement at one level, but measurement at another level. There are always these three stages, even back in classical physics. It's just in classical physics, you thought of the system as an unmoved mover. It gives information to you, which you write in your notebook, but it's not change in the process. One slightly idolizes, defies the system in the measurement process. And in quantum theory, one is more realistic. One recognizes in a reaction. So, I speak of the non-problem of measurement. There's no such thing as eliminating measurements in favor of dynamics. You can only replace measurement at one level by measurement at another level. And then another problem, another way of putting the same problem, is the problem of collapse. If you think that this creature is the state, then inevitably, you think the state is changing during the experiment. 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 for 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 three choices of the experimenter in both classical and quantum physics. It just happens that in classical physics, unless you choose this exactly right, no transition will occur. So you don't bother looking where the planet isn't. You only count where 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 the quantum theory. It is not the case that the polarizer rushes down the optical bench and becomes the analyzer

22:30 in a photon experiment, which is what you imply when you say the initial state evolves into the final state 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 and you leave out the fact that you have to make an initial determination of how you produce the, the quantum, the photon in this case. A one-ended experiment I like to think of as like one-handed clapping and eliminating both ends of the experiment, eliminating measurements altogether is like clapping with no hands. even more interesting. Can I ask you a question? Oh, you should. This is all very fine, but at some level, one has to understand that why do we have the dynamics, or appearance of the dynamics, in the physical world? First of all, that's a perfectly valid question, but of course it will apply to any statement I make. and I don't really think the job of physics will ever be ended if I answer that question it would just lead to another one and I think in our present day of physics we start with this as a postulate and leave it for the next generation to understand more deeply where it comes from 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'll ask a couple of related questions, which will probably answer later on . When we do the standard measurement thing, at least if we do the IE picture, I always do. When you say do, do you mean in the laboratory or on paper? On paper. We start with IFT norm. And IFT norm certainly doesn't evolve from the B. It evolves into, yeah. And then that evolves into IFT. it doesn't evolve into B, and it's A of T, B, and if you ignore that, well, you've got two choices.

25:00 Either you believe the state evolved from A of T into A of T and then B initially, or you believe that the polariser zooms down the bench and changes into the analyzer. Yes, but that's why you have to turn on a statement from the beginning. You're speaking the state language. You're thinking of this as the state which evolves. It is not. It's a description of the initial polarizer. Nothing more, nothing less. Look at how the quantum physics is actually done in practice. The quantum physics does not look at the photon to make a prediction of its behavior. Yeah, but is it not true that if the state doesn't evolve? The state doesn't exist. How can it evolve? There's no such thing. Systems don't have states in quantum theory. Any other 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, the Lorenz Fitzgerald theory, before Einstein, was almost as good as that. But that doesn't mean there is a now. And if you think there is, you'll end up scratching your head. Where did it go to? Why don't you see it? systems don't have states. There's no reason to think they do. What about operators that define measurements? Would you still believe in an operator that defines a measurement and what evolves? Oh, I believe in these creatures also. It's just a question what their relation to experience is. The whole mathematical apparatus of ordinary textbooks 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're looking at the state of the system You talk about that, and then at the very end, you convert the probabilities and compare apparatus in the emission, the filament, the injection chamber, with apparatus in the counting chamber. Yeah, I just wanted to clarify this point. You say systems don't have states. The states really description of the preparation. What people call a state. It's explicit in the end. But it's not, it's a bit more subtle than that, because preparation contains all sorts of facts, which are not relevant. Right. That's why this is the important relation. This is that with an equivalent. A lot of different descriptions of equipment are all the same for predicting the future. That's why when it goes to the Galois lattice of this relationship, that signals out what is important about the description.

27:30 So that pushes one in the direction of saying the statement about the system, because all sorts of different preparations, whether the operations were red or blue. are irrelevant as long as some essential aspects of it. 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 with it. And in fact, these things are not distinguished. It suggests that the relevant thing that's carrying that state is the system. So in some sense... It's a guess, and the suggestion is wrong. The system carries... I mean, there is no way to extract from a photon information about how it was made of anything more than one bit content. And the way it was made has an infinite number of bits in it. So it's not totally wrong to say that it just remembers how it was made. But it's closer to wrong than right. It remembers very little of how it was made. And classically, it remembers everything important about how it was made. It's different between almost nothing and almost everything. Can I just present the idea in a slightly different way, I think you agree with it, and it might help to be able to see the point. If you put anything in terms of about ventricles, and it just does quantum mechanics, using the about ventricle theory, don't bother able to construct a healthy space. that's a fair description right absolute approach so we can see that it must be formally correct as a point of view as far as we're giving back everything what do you at the end of the day you need to know you need to understand why the Hilbert space that we do have and they work in our theories in our experiments Well, it's very well to give up things. The fact is, you don't need to understand that to do physics. No, fair enough. You really don't need to. You might want to, but you don't need to. Yes, we have an agreement. Tomorrow we might need to, when we discover the present theory is wrong. And we will. I'm sure it's wrong. Good. We agree. And you're just looking ahead for the next problem. And I like to do that also. But we don't need to do it. Today we don't. But on the other hand, what can we do with physics using only the other space and not using the other space? Absolutely. and you can do it either honestly or dishonest. One can imagine the system has a state until a certain point and then drop that and do it right.

30:00 So, which is what, I mean, all the textbooks are written that way today. Or you can be honest and begin with saying that, don't mention states, just speak of input and output, input and outtake modes. In Latin, they speak of channels, which is a perfectly fine way of avoiding the implications of the state. I like to use the word mode rather than state because we're not talking of a status quo of the system. We're talking about modus operandi. But that's a linguistic game that many people don't want to play. Process is also a nice ontic word. It's very hard to do a misplaced concreteness. if you speak of these as input process and outtake process. This is a processional description. It's a practical description. It's not a state or ontic description. The state or ontic one wouldn't work if one carried it through consistently. And the only reason all the textbooks survive is they don't do what they say. And by the way, this is not a new point of view. Bergman explicitly made this very, very explicit back in the 60s first he pointed out that in view of this structure for quantum theory, identifying this with the state is a completely arbitrary decision. You could just as well say that the detector tells you what the state is. And this is, for example, Aharonov, who also refused to develop the idea of the state, maybe his system has two states, as if that helps. Who is the person named Peter Bergman? Peter Bergman got it right back in the 60s. There are two important papers, One with Ahareoff, Bergman, and Leibovitz pointing out this peculiar ambiguity. Why did 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 Bunge edits, he points out maybe the resolution is that the idea of state doesn't belong in quantum theory. And I think it's just a shame that he couldn't carry out this conversation with Einstein. I think Einstein's greatest mistake was not the cosmological constant. I think that was his third greatest mistake.

32:30 And the second greatest mistake was thinking that was his greatest mistake. The greatest mistake was not realizing that quantum theory is an operational theory like his favorite theory of relativity, just as he pulled out. Heisenberg brought this issue to him, you know, for the answer that Einstein gave. He's nonsense all the same. He had his chance. Do I have time now to indicate the next step in physics? If this is right, then if the situation today is rather disgraceful, in that you have things like, you know, whole schools of research devoted to the quantum potential, or the main world's interpretation, or decoherence theory, or consistent histories, these are all attempts to solve a problem that doesn't exist, the collapse of the state. And what should you be doing? Now, this, what I've said so far, I think is true in some important sense. But I say now, it might be true, but the odds are enormously against it. This is trying to see which way physics is going to go. And hindsight is much more reliable than foresight. Still, I find the question irresistible, what should we be doing if the world is really to be described with verbs rather than nouns, put it in its simplest terms? All this process, then where the hell did the atomic theory come from? Why has it been so successful to suppose that there are elementary particles? There really seem to be. If you look at how that reflects itself here, you see that certain processes come in chunks. They have a process of creation and annihilation, have units to them. They're elementary processes of creation. On the other hand, other processes don't come in chunks. In present-day physics, you can move something as little as you like. There's no elementary translation process. Processes of translation can be divided in infinitesimal parts, where there's process of creation either go or they don't go when you're down to the electron level. Well, the obvious assumption, the obvious step is to suppose not that there is an elementary particle, but there's an elementary process.

35:00 Maybe there's one elementary process or a small number or a finite vocabulary or an in terms in which all processes can be finitely expressed. Maybe underlying the present infinitesimal theory is a really quantum theory. And this is something I've been groping for, for quite a few decades now. And I even wrote a book about it called Quantum Relativity back in 96. What I want to talk about today is how that book is wrong, its fundamental flaw. and this is largely the result I must say it's weird it's the result of going to a meeting where the Dalai Lama was getting an honorary degree at Columbia University so ridiculous and I was walking behind Robert Thurman who was the head of the theology department or something like that at Columbia and I heard him say all is relative and I sneered everyone knows this is just of general relativity. They hear the word general relativity. It must mean there's a general principle that everything is relative. Feynman wrote a paper, a little chapter about this, pointing out that even relativity has its absolutes. And Oscar Klein pointed out long ago that we just called relativity theory invariant theory. And Rob, as it's well-known, founded special relativity 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 all is relative. On the contrary, we always begin a physical theory by describing those things which shall be absolute. Even in quantum theory, the concept of mode of preparation is something everybody is supposed to be able to agree on. It's an absolute. But I listened a little longer and it turned out First of all, this was the interpretation given by the Dalai Lama's school of Tibetan Buddhism to the old Buddhist doctrine that all is emptiness. Namely, that the viewpoint, the observer, influences all observations. That everything is made from, every observation is made from a point of view.

37:30 there is no absolute essence left over after you take into account the observer. They really meant everything is relative in a modern sense. And I tried, you know, this very attractive notion, it's much more attractive than beginning with some absolutes and so on. So I tried to go back to the process of relativization to see if it could be pushed to its limit. Could you relativize everything? I dimly remembered an important paper by Eden New Antigna 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 you get from special relativity back to Galilean relativity. You introduce a parameter, the speed of light, and take the limit as it goes to infinity, in this case. You introduce the parameter into the commutation relations of the algebra of the theory. And then you go to the limit, and the algebra changes its structure completely in the limit. It's a singular limit. You begin with a simple algebra, and you end up with one which isn't even semi-simple. And reading through Vigga's masterful exposition of this example, I spotted a footnote to a paper of a really old acquaintance of mine, Irving Siegel, 1951. And that's a paper I really urge you to read. It's a remarkable, insightful, seminal paper full of many ideas. The main idea is that, first of all, this idea of group contraction turns simple Lie groups, like the one at the foundation of the quantum principle, into non-semi-simple Lie groups. And Siegel urges us to invert this, to look around for examples of non-semi-simple groups. Whenever you see one, this is what you should be relativizing. You have to make that group simple. You have to find the fundamental physical parameter which has been allowed to go to a singular limit, zero, infinity, whatever it is. It's remarkable that all the important conceptual epistemological revolutions in physics can be cast in the terms that Siegel describes, not just the example that Wigner puts forward. I don't know why Wigner stopped with the speed of light. Pi's constant is also a stabilizing constant in the sense of Siegel. Let me explain why stability is an important concept here. Steele proved that a non-semi-simple Lealgebra is unstable in the sense that if you make the least change in its structural constants,

40:00 you come to Lealgebers of a totally different structure, non-isomorphic to the original one. Simple Lealgebers are stable. To make a small change in a structural constant, it doesn't change the algebra at all. The non-algebra is isomorphic. It's just as light change in your units. in your reference vectors, and so on. And implied in Sewell's paper is the principle that maybe physical theory should be stable. Maybe they have something to do with experiment, and experiments always have little errors in them. If you leap from experimental data to an unstable theory, you're going far beyond the 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 to zero in on it. 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. Hybrid dynamics is a useful theory, even though it's unstable. But it can't really be right. And in fact, when anyone tries to compute with hybrid dynamics, that was putting in stabilizing viscous terms to make it possible. The original theory just isn't conceivably right. And it isn't, of course. It follows from an atomic zero and the density and the number to go to infinity. Hydrodynamics is some kind of unstable limit of the particle theory. So the main rule is look for the non-semi-simple groups and then make them simple by producing constants like C and H bar. And Siegel 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 raw 100% probability is not the same as certainty but it's damn close and first of all he pointed out that the Heidenberg commutation relations are unstable if you write P comma Q minus O H bar then you also have to write P comma I is 0 Q comma I is 0 this is remarkably similar to commutation relations in the Galilean group 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.

42:30 You end up with p comma i, the sum multiple of q, q comma i, the sum multiple of p. This is a stable commutation relation. It finds a simple group where Heisenberg's original relation is not stable. and moreover by writing these down and making these constants to be small you guarantee that quantum theory is preserved. It's just that these constants are small and we have to look more carefully to find them. But I take Segal's argument under serious advisement. I can't find anything wrong with it. I really think quantum mechanics is wrong in the sense that Galilean physics is wrong. We may not be out of its domain of validity yet, but it's there. Is that going to be a linear transformation of, dare I say, the whole space? Obviously, this only makes sense if I was an operator. It's no longer central. And when you do that? Just as in special relativity, the velocity is no longer commuted. They were central back in the old theory. What's the representation of this? Well, the new group that I've written out here is either SO3 or SO12, depending on the signs you give these constants. It just happens that exactly this theory came up in quaternion quantum mechanics, way back, when I is elevated from the center to becoming a dynamical variable. So I sort of lit up when I saw this. I didn't, I swear, I didn't have anything like this in mind when I did quaternion quantum mechanics. I didn't realize it was stable than the usual theory. I did realize that it meant you really were doing real quantum mechanics. Quaternion quantum mechanics turned out to be a misnomer. To do it, you had to introduce operators i, j, and k over a real field. It was actually real quantum mechanics with an SO3 symmetry group. be predictive. It led to a gauge theory, which is a Georgie Glashow unified theory of the weak electromagnetic theories, several years before they stumbled on it. I'm sorry, I apologize when I stumbled, but I don't know what a wrong word. I mean, their research was the result of a very careful study of Fermat's data. Ridiculous. I was the one who stumbled on it. I was just projecting. Okay, then, so this is one instability. Quantum theory is wrong.

45:00 you might not be disappointed to hear because it gives you research work. Question? I just had a couple of comments, one positive and one negative. One is that you would be glad to know, maybe you already know, that there is a huge program, part of quantum gravity programs, non-community geometry, where they call these the formation parameters. Of course. And they stabilize the system in that way. The negative comment is that the mapping between... By the way, even if you look at so-called non-community geometry, Hilbert space. They haven't stabilized this particular combination relation. They haven't adopted Siegel's program. It's true they're deforming. The problem that I see is that... Let me repeat that. That means they're not solving any of the instabilities of the existing theory. They're doing mathematical speculation, I would say. The mapping between the non-simple to simple and the mapping from the other way around, simple to simple is not unique. Absolutely. That's like saying quantization is not unique. It's a heuristic process. If you're lucky, you guessed right. But I don't know a better game in town. So this was one of the instabilities. I think it's worthwhile tracing this to its root. Do I have another few minutes? This ultimately is represented in present-day Kroker theory. I even got the sign right. It goes back to Newton and Leibniz. Let's not get into the argument, but we discovered the calculus. But the instability of Heisenberg's relation is the instability of Newton's or Leibniz's relation to the differential calculus. And I think it's serious. 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 is impossible to estimate the derivative with the same precision as you estimate x. You need to look at two x's which are close together. And then the accuracy on the difference is one way down.

47:30 One ends up doing finite difference methods 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's theory is a more algebraic theory yet. Now, let me begin. Where is the eraser? It's hidden behind the... It's not a bad idea to hide the eraser, by the way. I remember I had this nervous habit of erasing things I'm not sure of. And that gives no one a chance to look at it. It's not still right. Oh, yeah, I'll tell you now. Well, the theorem about to present, what the germs of the theorem about to present, grew out of the book, out of an example in the last chapter. But let me say what I think was wrong. Okay. The postulate one 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. Only 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 is the statistics of the elementary process? And we only know two kinds of statistics. Are we supposed to take the word process as an elementary concept? Or do we understand it in a normal sense? Both. In physics, you always have to take something as undefined, mathematically. but if you are smart, we will take it to be something which everyone knows the meaning and practice of. And I am assuming everyone knows the meaning and practice of practice. Until I heard your first part of the talk, I knew what practice was. It is something you do. Really, it is something you do. This is very closely related to a problem that Simon is writing about right now.

50:00 whether you start with binary relations or monadic existence assertions as your fundamental entities. And I'm definitely starting with a relation with a very special kind called an operational process. A relation between now and a little bit later. Representing an action, process, doing, birth, not now. So, we shouldn't take that that exists in any sort of romantic way. Right, exactly. This is really to be brought in as a description of the language. In the language, there's the idea of an elementary process. Thank you. And then, the next question is, what is the statistics? And you have to answer, I think, as close to the old theory as it can to guarantee that you go over to it in the correspondence limit. I like to think of what I'm doing as a deformation in the sense of Siegel and Inuid Wigner. Well, if you look at classical physics, you learn to express all the processes there in the language of set theory. The closest thing to set theory in quantum theory is Fermi-Drax statistics. I don't know if you've realized how close the two are. The algebraic structure of set theory is exactly the algebraic structure of Grasman algebra restricted to an orthogonal basis, an orthonormal basis. This importance of Grasman algebra as a common language replacing set theory for quantum physics was first drilled into me by a beautiful talk that David Bohm gave university in the fifties and really inspired me down the years and what I have to say today is it's almost right, almost up to a little deformation, which is what I've learned in the last couple of chapters of quantum relativity and expounded on since. Okay. One thing that bothered me back then is the fundamental relation of grasp and algebra or Fermi-Drax statistics is unstable. Let me remind you of the correspondence between Grassman's statistics and classical theft theory.

52:30 This corresponds to the statement of... The observation I'm making now goes back to Peirce. When Peirce saw Boole's logic, he noticed it wasn't algebra. Buhl had a basic operation, which he wrote as a plus sign, and it wasn't always defined. He only...Buhl was tremendously influenced by the theory of probability in setting up his logic. In his book, this doesn't come out, but there was a little pamphlet he published at private expense before he wrote the book, which I came across in the world of mathematics by Casner and Newman, which I think is absolutely critical. It's a beautiful example of practical thought. 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 and present a postulational ontic point of view. You don't find in Bull's book what a class is. He postulates classes. But in this little note, a very thin pamphlet that he published, he says what a class is. A class is defined by the process by which you select from the population at large individuals having something in common. A class is defined by, well, today the closest thing to it would be the filtration, the projection operator, leaving a sort of white source as implicit in the theory. and then there's too much to say let me give the relation between Grasping Algebra and Classical Logic in Grasping Algebra you have a product which I'll write this way which has a property that PRP is zero and I'll just say blatantly to Boole's original operation. The zero, you get a consistent mapping between the two theories. You get that to a zero from the undefined. Not the null set. The null set is perfectly well defined. And it's represented by one. Because one P is P.

55:00 This is a kind of union 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 his most important discovery, at least when he was young, and it enabled him to turn Boole's logic into an algebra. He said this was unimportant for logic as the zero for arithmetic. But because he used a plus sign for this operation, he had to use a symbol infinity for the absorptive element. And here, I'm drawing on Piano's work, which comes after Boole. 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 longer is a Grassman algebra. This is a Clifford algebra. Clifford algebra is just a very slight deformation of a Grassman algebra. and it's related to Graspin Algebra the way the quantum theory of the harmonic oscillator is related to the classical theory of the harmonic oscillator. This is a quantum quantization. So back in the 80s, it seems only yesterday, with Ernesto Rodriguez, who wrote a paper on quantum logic founded not on Graspin Algebra, but on Clifford Algebra. In the very same year, I discovered last year, Frank Wilczek, working on carriers electricity in the fractional quantum Hall effect suggested the statistics for these carriers which is no relating to any of the statistics that have been used before in physics and it has the effect that the operations on the carriers form a Clifford algebra and he did this before I did and certainly independently Okay. What do I do with the board now? Keep pushing. Can I put it down? Great. That's fine. Thank you. Okay, so let me describe statistics. What do I mean by statistics? I'll build, I'm using a concept which works for all the examples I need. I'm not sure it's the most general in the world. You start with a vector space, which you think of as the one quantum modes.

57:30 If you want to call them states, be my guest, but you're just screwing yourself up. And you go over from this to an algebra, which represents many, okay? You're going from one to many, okay? This process was given a name by the famous Scottish logician, William Hamilton, in 1840. He called it quantification, going from the one to the many. Again, 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 does. It's just going from a theory of one to a theory of many. And the end result is an algebra A. And you can represent the quantification process by by a mapping, Q, which turns vectors here into operators here, and since this turns vectors into numbers, it has a transformation properties of a form, so it's convenient to put a dagger And in Fermi Dirac and Bose and Einstein cases, this is a one-body mode and this is the creation operator for, yes, for that mode. And the annihilation operator is best written this way. Creation. annihilation to quantification of a process which goes from a one-body mode to a creator and annihilator for that body in the familiar cases. And this also enables you to convert operators of one-body theory into operators of the many-body theory, which represent cumulative In the Graslin case, in the Fermi Dirac case, A is the Graslin algebra over the vector space

1:00:00 V. Sorry, these are the mode vectors of the ensemble. The operators, the algebra for the in the Morphism Algebra, linear operator in the Graskin Algebra. In the Bose-Einstein case, let me just write down the characteristic to communication relations. And then for Bose-Einstein, it's rather similar. only with commutators. You don't even have to write down the first one. It's an identity. And there's a special form, this sublectic form, which you learn from the classical theory and use to construct a commutation relation And then at the same time, I will not give the form of Clifford statistics that Wilczek gave, which is complex. He was not trying to stabilize the existing physics, just trying to understand superconductors or fractional quantum Hall. I have to get rid of I because of what I've learned from Siegel. And so I start with the real vector space and the commentation relations then are sign squared equals norm sign. That's the end of the story. And I call this Clifford statistics.

1:02:30 And it's the real form of a complex theory that I call Clifford Wilczek, or Wilczek-Clippert. Statistics. And Wilczek didn't let the story die back in 1980. He'd been publishing more and more physical papers applying Wilczek statistics problems, as recently as 1999 or so. You know, the big difference between this and this is that this is a projective statistics. All these statistics give rise to representations of the permutation group. Here, if you swap two elements, you just change a sign of the wave function. That's a scalar representation, practically trivial. Change in sign is nothing in quantum theory. It doesn't change anything physically. And here you don't even change the sign of the waveforms. It's swapped in particles. Antisymmetric, symmetric. And here you get a two-valued representation of the permutation group. If you have a swap like one, two, it doesn't get plus one or minus one, phase in general, but its square is minus one. In this representation of the permutation group, this projective representation of the permutation group, first appears in literature rather recently. I think it's 1898 in the work of the Austrian mathematician Wiemann. Maybe it should be called Wiemann-Wilchek Statistics. Wiemann was simply cataloging the, what he called, representations of the permutation group, and he discovered this. He tried to give a catalog of all the projected representations of the permutation group back in 1898. He missed a couple, and the famous Isaiah Schuer fought them and completed the cataloging in 1911. And sort of basic in his catalog structure is the Wilczek-Clifford statistics.

1:05:00 He was looking at complex representations, unitary representations, rather than real. So he did discover exactly this, and Wilczek cites his work. And there's been a rather large mathematical literature on projected representations of the permutation group. It's just somehow I didn't notice it until around, sorry, 1898, 1998. Why projective? Why can't you? Is there any specific reason why you have to have projective representation? Absolutely. Just as for the rotation group, if you want to catch all the representations, so to speak, you need the projected ones. There are these double-valued ones because of the topology of the rotation group. And there are double-valued representations of the permutation group, so to speak, because of its topology. and in fact if you think about it for a moment any representation of the orthogonal group is also a representation of the permutation group because the permutating axis is an orthogonal transformation and this representation of the permutation group is exactly the specialization of the spinner representation of the orthogonal group to axis permutations so I think it's perfectly fair to say that Wiemann discovered spinners in 1898 in 1911, two years before Cartan discovered them and named them. And they arise from the theory of ensembles. Spinners do not describe an individual. A spinner describes an ensemble of objects with a very peculiar statistics. Their swaps are represented by elements of equivalent algebra. The construction is very beautiful. Let me describe it. I'm simplifying it slightly. There are some arbitrary choices of sign that Schroeder made and they can be stripped out to give a more symmetric statement as follows. You want to represent permutations of objects 1 to n. Associate with each of the objects a Clifford unit. I1 to I n. It's a matter of taste whether you take these squares of plus 1 or minus 1. You get pretty much the same representation either way. and Clifford also waffled. I'm pretty sure there's a deep physical question involved that will settle the sign ultimately. And my favorite today is to say that I squared is minus one. I think this was Clifford's first choice. Then the swap of, say, one, two is represented by I one minus I two.

1:07:30 It's as simple as that. Projectively represented. It could also be represented by I two minus I one. That's the other sign. And you can get it from one to the other by going around the permutation group and coming back again. Okay, that's, so you can think of the gammas of the Dirac equation as representing permutations of some structure inside every spin and a half particle that we have not yet been able to resolve unless maybe they're quarks. And it's rather amusing that this double value representation, permutations, does not arise until you have more than three objects. For less than three objects, all the representations are equivalent to single value forms. As soon as you have four objects, like the four axioms of space-time, you acquire double value representation of the permutations. And that's when spinners begin, at the number four. So, I take as my quantum version of set theory, Clifford Algebra, in the sense that instead of the original product of Boole, Peirce, Peirce, and Grassmann, instead of that product, which corresponds to a partial pore. Undefined unless it's actually disjoint. That's why it's partial, not a full operation. This Grasman product is a quantum version of pore, partial operation. and the Clifford product is the graspedness of Clifford. Corresponds exactly to XOR, which is always defined as a true operation. And this is the stable logic. This is the unstable logic. This is enough to sketch out all of set theory that operates on one level. The Boolean theory. That is the least interesting part of set theory. The important part of set theory is the way in which you make new units out of old sets. The operation that Peano designated by Iota,

1:10:00 and which turned into the successor operation of his theory of the natural numbers, and which he thinks then as representing the passage of time. Okay, time is of the essence. Okay. And then in set theory, this is represented nowadays by putting the things involved inside of races. This goes from many for one, e pluribus unum. So you can think of set theory as Clifford or Graspin algebra provided with an operator for making new units out of old higher degree elements. It's a graded algebra with an operation for making grade 1 elements out of higher grade elements. Linear in the quantum theory. Okay. There isn't time to write down the rather obvious axioms that I ought to obey. They follow directly from those of the Brace postulate of classical theory. Okay, the next step. So this is my candidate for the universal language of quantum And it's as universal as set theory. They simply, that's the worst part of theory, it's too easy. You can take any theory of existing quantum theory based on a classical continuum and rewrite it in Clifford algebraic terms, based on the idea of underlying events that have Clifford statistics. Still, there's something of a unification going on. It really is vindicating Siegel's idea that this process of deformation is a process of unification. And perhaps at a later time, I can tell you how it goes. Or if you're interested, send me an email and I'll send you the current manuscript in process. Thank you. So what is the deformation parameter? I'm lost a bit. Oh, thank you so much for asking. I had to leave it out for the end of time. In fact, I do end up identifying Iota with a kind of temporal succession operation. There's a built-in unit of time, and that's the deformation parameter. Originally, I rather egoistically called it Tav,

1:12:30 fundamental time. It's the last letter of the Hebrew alphabet. And its literal meaning, back in the Phoenician, or the Canaanite language, was a musical note. Which is very appropriate for a given of time, I thought. But even in latex, it's rather hard to get the letter tav. Hard to ship it around the world anyway. So lately I've been using chi. Because when the idea of a quantum of time was posed by Margenau, back in the 20s, he called it the chronon. And that begins with a chi. And it turns out if you push the theory, you end up not only with a fundamental time, but a fundamental energy. The simplest elementary particle has a cap to its energy spectrum and to its mass spectrum. And since there is a cap to the particle masses and around the Higgs mass, I suppose a chi is around the time associated with the Higgs mass. that's one of the deformation parameters. It takes two. If you saw how many unifications go on, you wouldn't consider it a waste of parameters to accomplish them all with just two deformations. The other one, n, is the total number of cronons in the universe, roughly speaking. And the existing theory is the limit as this goes to zero and this goes to infinity. I'm sorry, H stands for in mass, no, no, in the mass. This is mass with the Higgs mass. So how did you write this? Because the elementary particle mass spectrum seems to stop. There seems to be nothing above the top quark or the Higgs mass. They're about the same size. I must say also that my choice of Higgs comes from quaternium quantum mechanics. There, again, IH turns into a fundamental field that I called eta, which turns out to be the Higgs field of the unified weak electromagnetic interactions. And the mass associated with this is the deformation parameter. so I figured it worked once I'm going to try it again but it's still quite a soft part of the theory and going back to states and systems briefly going back to states and systems systems don't have states again systems don't have states do polarizers have states

1:15:00 polarizers have states things used to make I have to really ask at what depth you're asking the question in our ordinary experience of polarizers, all that counts about them is the angle. And pretty much, you tell me the angle today, it might be the same. If you think of them as a rigid rotator, and you really subject them to, say, no external forces, then for practical purposes in the laboratory, they're rigid-binded, they have states. If you ask them more carefully, of course, I have to recognize a polarizer is a large quantum system. And then I'm looking at the internal degrees of the polarizer. They're not supposed to be important in its use as a polarizer. And then it doesn't have a state any longer. So it's a question relative to the degree of resolution of your observation. And it's the same tree for people? Absolutely. So doesn't this... Or relatively, as the case may be. So doesn't this deny us a standing point at which we can, for instance, construct a prose theory of people? That's right. Eisenberg called quantum theory non-objective physics. He didn't mean that it was mood-dependent. He meant there were no objects in it. So what price neuroscience? Pardon? What price neuroscience? What? What price neuroscience in that case? I'm sorry, I still can't understand the question. Where does that leave any attempt to construct a physical theory of observers? Well, again, it's a question of what you mean by a theory. If you're looking for a final theory, quick, go into some other game. I think that's kind of, the whole point of this is a final theory. But if you're looking for a theory that works, then at every level of experiment, you start with some place where naive language works. Where you look at something and you can describe it and get away with it, enough for other people to get the same object out of it, to check the same piece of equipment out of the equipment shop. Okay, I don't think I put that clearly enough. I don't mean an underlying micro-physics final theory. I mean theory of biology and neuroscience and psychology that explains and analyzes human perceptions and thought processes and so forth. If essentially we're having to take those perceptions and thought processes as basic, then we seem to deny the possibility of explicating those. Is that something you're happy with? Well, first of all, you're going through stages, your question, that took me many, many years.

1:17:30 And use the word basic, for example. That suggests that physics has a basis. And we're looking for the basis, the things that are basic. And I deny this. I used to believe this, and I thought that was what we were hunting for. But today I think that physics is just another strategy for the survival of organisms in a universe which is not totally hospitable, but fortunately creates little gardens. But hang on a second. Organism is a state of a certain physical system. We're not emitting organisms into our ontology fundamentally. Well, I don't have an ontology, and I don't have states. And so my organisms don't have states. Ascribing something as state is indicating So what do you mean when you say there are organisms? Well, it is important. Well, what do you mean by it? Oh, I'll be naive. I mean the same thing. Because there are physical systems with states. You must be naive at a certain point. You have to talk to people. And if you want to be my organisms, my description would include complete happiness about using the word state at a fundamental level, not just... But notice you wouldn't have to use the word state to describe... First of all, if nothing... By all means, feel free to use the word state in the macroscopic domain. It works there. I have no objection at all to speak of states of planets when astronomers are using the term. If you're a quantum cosmologist, however, you'll have trouble if you think that planets have a state. There's no problem now in making a quantum cosmology. The problem is entirely in thinking that the cosmos has a state. Well, apples don't have them. Why should the cosmos? There's this remarkable, famous aphorism, I think of Laplace. He was asked where God enters into the spirit. this hypothesis. He was lying, he was a bald lie, namely elsewhere, he speaks of a supreme intelligent being who does his experiments on the universe, gives initial values, and predicts the future. Of course, that's Laplace's God. And of course, it's just a deification of Laplace, as so many gods tend to be, self-deifications. And there's no difficulty making a quantum god. If you really want to do quantum cosmology, you can. But a quantum god does an experiment on the universe, creating it way back in the remote past, including us and all our propensity to do experiments. And then he looks at the end result. I mean, he's a quantum god. He works with things like this. If you think this is the problem, then that is not a solution.

1:20:00 But if you think of this as the basic form of physics, there's no more problem with a quantum god than with a classical one. The root is always the correspondence principle. could get away with God, so can a quantum physicist. You just have to decontract, deform Laplace a little bit, and you get the correct quantum cosmology. I think I've lost the fact about it, because I'm asking, but I don't know if we're getting any further. You have to imagine God looking over your shoulder after you've done the experiment. And you relate his results to your results in the way he described by . And he checked that quantum theory is consistent this way. you and God will get the same results after the fact. God, I guess, ends the general observing demon. I think I have a question. So is the main reason why you're not taking states as describing yourself in the physical, because that way of doing the physics doesn't work? That's the basic reason. Right. And also, if you look carefully, When people tell you how to find the state, when people who use it consistently tell you how to find it, they find you don't look at the particle, at the system at all. And back in classical physics, the one feature of the state is that you find out about it from the system. So it's totally misleading to use that word for this very important concept in quantum physics. You look at the apparatus to find what people finally plug in for the state when they come to using quantum mechanics. But I mean, that's the standard more known as a margin for macro physics as well. It's something different here. And what you seem to be saying is that the difference is if you treat systems as having states, it doesn't work. Yes, what you said is correct. That's the way you would put it. But fortunately, most people doing quantum mechanics don't treat systems as if they have states. They only say they have states. And they treat them differently. And what's interesting is that most people don't. But it seems that there is a program that's treating everything at the level of, say, the Emirates interpretation. And so if one can think that works, then that would be a counter argument to you. But if you look at all these interpretations,

1:22:30 the theories are one-ended experiments, or worse, no-ended experiments. There's always a crucial link to experience missing, they're not really physical theories. They put in that missing link, the program collapses, they end up postulating what was they hoped to prove. You really, those theories are badly put. Wait a minute, take a second, pilot-way theory, pilot-way theory, pilot-way theory, pilot-way not completely pose, and if you look carefully, there is no way to get the pilot wave by looking at the system. Bone pointed this out at the beginning. There's a missing point in this system. How do you explain that the pilot wave happens to coincide with the probability it is? You never could solve that. You measure it, and it works. Great. You put it in, and you have something equivalent to the Uevo quantum theory, just like that. I mean, the language conflicts with the operational practice. course, you could learn to do that. But first of all, you've given up an important symmetry of the quantum theory. You may have faces that say, yes, you should. I understand why it's like that, but it's the charging coherence that I thought you'd do. Look carefully for the operational meaning. You'll find a missing point or a missing postulate. Are you saying that an operational version of quantum theory has no missing bits at all? Well, it does predict the result of the experiment. Quantum theory is incomplete. We have love incompleteness. And moving because there's this incomplete building in downtown Atlanta. They never put the roof on. It's very pretty at night. The way I look at this is that physical theories have pragmatic bridge principles, which say say, this theory, which is something written down on paper, actually has this relationship to this real physical object. Now, that pragmatic link is something that I take to be perhaps not ultimately cash out at all. That doesn't matter as far as use of the theory concerns. As long as you have a story which people can come to agreement as to how they've used the theory and so on, you could use the theory, but acceptably. Now, I would take any operational physics to have that pragmatic link in that. And in that respect, not to be any different in the sense that you have this set of axioms,

1:25:00 perhaps, if you axiomitize the theory, or perhaps not axiomitized. But regardless, you have some mathematics written down on paper. You have connections between that and the stuff over here. Whether you're operationalist or Bohmian or whatever, or just someone you used to the theory, you have that relationship. It's not cashed out in logic, and precisely because that would be a category of mistake to worry about that sort of aspect. So how is the operationalism you're saying, is the only way to do this better than, say, Bohmian or just Copenhagen? Well, first of all, I surely don't think it's the only way to do it. It's just the only found that works. And I'm sure it's wrong, in fact, and that tomorrow, if we're lucky, we'll find a way which is as different from this as relativity is from classical physics, but works even better. So the last thing I want to do is claim that this has some kind of God-given validity. It's not the only way to do things. It just is operational in a more complete way than most of the theories put down for competition. In fact, there are all of them that I know. This is a separate question, really, now. You're saying that to pursue... Let me put it differently. In it, the link, what you called it correctly, the pragmatic link in the theory between symbols on paper and experiences is absolutely crucial. And all previous physics was made at a level where it could be handled very easily. You didn't have to say too much about what the state was. Of course, the camera looks at the star and sees its state. Gets its position today in velocity after a few years of study. And that is not the way it is for the quantum pretension. They are not the objects of naivety of perception. And the way in which you determine them has to be spelled out carefully. Right, but all that comes down to is you have the theory on paper, you have the perimatic limit to experience, and you can draw it here, say, for the Bohmian theory has this to the object, a more operational theory has the line somewhere here, perhaps. is in the logical descriptions of the language there is perhaps in some sense a shorter meaning precisely not

1:27:30 something that can be measured there is experience and there is experience a little bit more structured namely in an operational theory you begin by distinguishing between yourself and the system and experiences with yourself and your apparatus. And you've completely blurred that distinction. And the usual language also blurs it. When you speak of the state of the system, there's a clear implication that it's something you learn from experiences with the system. And the interpretation given of quantum theory, it is not. It's learned from experiences with yourself and your apparatus. And one easily slips into the stakes, thinking that by using the word state to refer to yourself it's only in phenomenological theories that distinction has to be made if you're taking the God's eye point of view however you have to make the distinction between God and the universe, so it's always there aren't you just denying that we can make certain sorts of inferences you're denying that we can infer what the state is from observations of larger things but why should we apart from just the general instrumentalism why should we accept that step make sort of certain sorts of inferences to gain knowledge. Well, you're saying you're denying that you can gain knowledge of the unobserved in virtue of certain inferences. I'm not denying that I can. I just don't know how to do it. I don't know how to get the psi function of a photon from any process I do in a photon. I have to look at how it was produced. Maybe someday someone will know how to get the psi of the photon and maybe even predict whether it will get through the analyzer. Then I'm wrong. What's the difference between looking at the analyzer such and such, and looking at the state directly using some sort of different sorts of eyes, you know? I mean, what difference does it make whether we can actually observe the state itself, or do we have to observe something which is causally... Surely, you're not asking the difference between looking at myself and looking at the photon. You're asking how that difference can be important. Well, sort of, I am, yeah. between you and the fauchan, obviously, because we're not interested in... Wouldn't you even say it's an important difference? It depends on what sort of story you're telling, yes. Morally, it's important, the difference between you and the fauchan.

1:30:00 But epistological... You can't make that decision seriously. Of course you can. You say you experience yourself, right? You said something along that line. Quite blatantly. I don't think it's in great detail. You don't experience yourself at all. You don't experience yourself at all. There's no such thing as a self in that argument. sense perceptions if you follow Hume. So in that sense, there's no distinction between you're just trying to observe something and picking yourself out. There's no observant. Well, in thermodynamics, it's very important to be able to tell the system from the heat path. Sure, sure. I mean, you can make these sort of distinctly. My point is simply, it's hard to deny or you need very good reasons to deny knowledge planes of the unobserved when you can argue for a sort of continuum between the observed and the unobserved and I just don't see why the fact that you have to look at a polariser to see how the microsystem behaves or what its states are means that you can't have any knowledge of the state of the microsystem itself I mean I agree that it was actually presented as a perfectly consistent very lively presentation of an instrumentalist approach to quantum mechanics. No, no, I deny it's instrumentalist. I really think this is the way things are. It's a state of the way things are, but all you've said is that all we can make claims about is... The world is a process, not a collection of things. I deny it. This is a fundamental description. If you say the world is a process... You're constructing an ontic model in which process is the object. A ontic-like process, right. Why is it practical and not ontic in that case? Because what I'm talking about are practices. You've made it ontic. The theory is ontic, by definition. All theories are writable. When you write them down, you have things. That's the purpose of a theory, to have something to make a computer with. The question is what you're talking about. finger. Yes, my finger is a very good replica of a thing. Look what I'm pointing at. I'm pointing at processes, not objects. Yes, what I'm pointing with is a readable approximation to a thing, otherwise I wouldn't be able to use it as a pointer. You have to be able to read my papers, so I write with large letters. Very good replicas of objects. But of course,

1:32:30 if you read them too intensely, you'll explode the page. You have to read them not using very high-resolution gamma rays. You have to read them rather gently if you want someone else to be able to read it after you. There are no objects, really, but we need to pretend they are for daily life, including making theories. The real world is unsymbolizable. Evolution requires us, for example, to protect our internal DNA as if it were a symbol, as if it carried meaning, like we're too cold. So it passes a test for an object. We know it isn't an object, but we very much want to make sure it passes for one. And our theories are not that different from our DNA. Does a process have a state? If it's in the world, does it have a state? Nothing has a state. We give some things states. They're a rather naive question. question. Now you're boasting. If you're taking the process as basic, a kind of basic question would be what is being processed? That is indeed. That's a little like saying that if we're taking space-time as fundamental, what is now? It's a question that arises but I don't know whether you're conditioning. You used a lot of theories where the idea worked. Oh, you see it differently because you were saying that we have the same sort of the theoretical idea of what the process is because that's what it makes you clear. I seem to have a different one from you because my pre-theory of the process is not going to happen to the thing. Well, I'm pretty willing to say, for example, that the process that malice carries out in an optical bench happens to a photon. So, the process happens to the quantum system. I have no problems with that. I don't see why any... I guess some people do. People who like collapsing wave functions probably don't believe the system exists. You say, you believe there is a system? Pardon? You believe there is something as a system? I have no problem with that, of course. You believe, I mean, when you have a preparation... Electrons sometimes.

1:35:00 ...and you have a detection operation, you believe there is some system that moves between the two? Of course, yeah, absolutely. Every physicist, most physicists do. It's a moral necessity. Why do you believe that, Rob? What's the difference between believing in the existence of the system and the existence of its properties? You're believing in one and not the other, and I can't see why there's more evidence for the existence of one than the other. Well, the evidence of the existence of the system are all the ways you have of producing it, ways of catching it, and the way they relate to each other. It behaves just as if the system was going from there to there. And now the idea of property... It's also just as if the system going to connect that had its state. That's exactly not the case. That's the point. It is not as if it had a state. But it doesn't behave that way. If it had a state, you might be able to say, well, it's what it's going to do. The state almost by definition, classically, determines a future behavior. and the past, perfectly symmetric. And here, nothing determines the future behavior. Since things just happen. Is it indescribable? Is what indescribable? The system always has to... It's unsymbolizable. You can say something's about it, but it does not behave the way symbols do. Symbols obey classical logic. They're undisturbed when you look at it. Can we put down a letter, but you can't predict the behavior of the object by manipulation on the letter. The correspondence between symbols and ecturality is not as close as Newton thought. So the symbols never behave as do physical systems that they use to describe the basket of things. Now you're trying to hide a bushel under an ant. There, the arrow can be as small as you like, we thought. There was never any science that is something fundamentally wrong in assigning symbols to states. And it doesn't work in quantum theory. The only way I know to handle mathematics is by watching people do it, and it's always done at the macroscopic level. Now, they don't have to get the chain, we're getting the quantum computer. But even there, in order to say you're doing mathematics, you end up with printed out to so yes

1:37:30 I'm convinced that mathematics is an extreme macroscopic limit of physics Hittgenstein said something like that and he said that mathematics is altered physics it's the part of physics which is the most stable he meant quite the opposite it was supposed to be a damning comparison of that way of thinking about mathematics he was saying that he was talking about the normative role the hardness of the logical must and how that hardness can't possibly be like the hardness of a super hard material because they're just quite different types of things. So he was completely disagreeing because his whole line was that you can't explain mathematics in that case because then it's a contingent question whether a causal or some sort of process goes right or wrong. Whereas in mathematics, it's either right or wrong, necessary truth, and that can't be mapped into causal physical language. people disagree with that, but that's what I guess I'm saying. Just a couple of comments on this thing. Surely, physicians produce symbols. That's not all that they do. One can try to make that ball that is involved in reflection. I wouldn't, yeah. I realise that thoughts are also involved. I did, there's also a thought. And they can be thought of a symbol to... Right. Now, you almost seem to be in a position saying, perhaps you're happy, you're very serious. But in order to think accurately, of what has happened to quantum systems, we would have to have quantum variance. No, even then it doesn't work because of the theorems about the impossibility of quantum cloning. The very idea of one quantum system doing what another one is doing is inconsistent. Well, not precisely what it's doing, but to even approximate what the quantum system is doing, we would have to only do a quantum forecast. No, you can't even approximate closely. I mean, one photon doesn't behave like another one when they come to the polarizer. the noise will approximate one with another. Well, I take that point. It really happens. I take that point. What I'm trying to hear about is, you seem to have a general thesis about the nature of representation, that the quantum domain is not representable in anything like stable... We're very fortunate that we have these processes where one end is macroscopic. And the other end is nevertheless in the quantum domain. We can produce photons with almost sharp polarization.

1:40:00 You know, it's like a bit more marbling at how clean you can get dishes with a dirty towel. That's the story of our life. The way I'm at a loss is to how to state your plane. It seems to be that systems don't have states. Well, another way to state it is that there's no such thing as representation that one can only mimic. Well, of course, for example, one can represent Roman numerals by Arabic. Representation works in the symbolic domain. It's just the representation of physical actuality is fundamentally limited. One can go so far and no further. And there are big errors when you try and go further. Whereas in classical thought, many of us thought those errors could be reduced. He really thought, classically, that the world could be regarded as a symbolic process. The symbolic process are very special behaviors of magnetographic systems. The world isn't a bit like them, deep down. Now, Colonel, we may say this isn't instrumentalism. An instrumentalist might also say that there is no basis by which to correctly represent the unreservable. Well, I think... You would agree with that statement. Right, but instrumentalists might not say that. I think when people, people who use quantum theory, usually don't characterize it as instrumental. It usually presented as a criticism of theory. It merely predicts the result of experiments. It can't be right. The world couldn't be that way. Now, I would ask such people, if a theory predicts the result of all experiments as well as can be predicted, what else do you want? What else do you mean by a description of nature? What is not an experiment? What is left out? The instrumentalist criticism itself is deeply flawed. We're looking for a theory of a classical biblical kind. Let me just work within your own framework for a minute. Along the way, you've dismissed the consistent histories framework. It seems to me that actually consistent histories is precisely the sort of set up your opinions. to, whereby the projections by which one defines the history space are the state preparation, state measurement configurations and the historic objects.

1:42:30 The point about consistent histories is it's giving us some guidance on how to conditionalize in between state preparation and state measurement. What if I were to do a measurement in between, with the probability to go from here to here equal the sum of probabilities to go from here to here, and then to there, plus from here to here, and then to there, plus from here to here, and so on. This is the consistency condition. Now, it's a remarkable fact that you can satisfy the consistency condition so long as you restrict yourself to certain sorts of configurations and not to others. What are those configurations? Well, they need to be not too fine-brained. And it's quite a good idea if they've got something to do with configuration space rather than something completely inaccurate. And it seems to me you have to buy into all of that. You have to say, yes, indeed, what we are getting at in that form is something like the most that can be said, which describes entire history including human observers and so on. And in a way, I would be happy with that sort of an analysis of quantum mechanics and quantum mechanics if one had a point of which if there's some, as it were, precise criteria for why so far and no further. And what's more, if one had a precise consistency condition satisfied as opposed to an approximate one. But the point that the thing is approximate, when there seems to be fast, even before the definition in the history space, suggests that one can't make a fundamental theory out of it, but not a precise fundamental theory in this way. But I've noticed that consistent history's approach in an attempt to eliminate the collapse of the wave function. Now, there are two possibilities. One is that they succeed in eliminating the collapsible wave function. Then that makes a theory suspect because wave function doesn't collapse. It's not the kind of thing that evolves, so happen and collapse. Wave function are the kind of things that happen. They're things you do to the system. They don't evolve, they don't collapse. The other possibility is they don't succeed in eliminating the collapsible wave function. What's the point? You don't have to mention the state at all. Well, what is the history you're talking about? It's a sequence of configurations.

1:45:00 Roughly, it came to your sequence of measurement preparation and measurement detection. I'm sorry, is that the classical level? But it tries to push that classical level as far as it can be done. And it goes down quite a long way depending on the particular nature of the setup. So if it's a two-slit experiment, we'd better not be imposing values for positions, even coarse-grained positions of the product that's in between preparation and detection. But in all of the circumstances, it gives you as precise a description as possible. But the point is, there's fudge. This approximation runs through it, and it seems to be in the limit. there will not be any precise characterization of how fine-brain those histories can get. That's just, this is not the basis for fundamental theory. I don't see how you can reject this framework. I must say it's on the basis of what you're saying. Thank you very much. It sounds very apt to your purposes. Right. Now, on what basis are you insisting one can do no better? Pardon? On what basis do you insist one can do no better? I wouldn't insist on that, on the contrary. I'm not sure what you mean by not do better. Are you trying to beat the kind of the relationship? No, but what can do better in a never-ending extension of the consistent history of studies? What can do better? One can infill a description of the quantum process. And one does so, of course, without defeating the uncertainty principles, and, of course, without getting rid of into terrorism. Why do you legislate against that further move? I have to reconsider that. I'm sorry. Thank you. There's maybe one exception of this list of blind allies that I've mentioned. All right. Let's see what we'll do. This is kind of back to what you're saying that... By the way, if I'm right, you can beat the uncertainty relation. What takes the place of the Heisenberg unstable of the algebra is the algebra of the rotation root. And what takes the place of P comma Q of I is something like one component.

1:47:30 the commutator two components of angular momentum. And you know perfectly well that even though LP and LQ don't commute, there are modes where both have eigenvalue zero. For example, the single model has all three zero. And if I'm correct, the Heisenberg commutation relation is just a restriction of a relation like this in case where this has a large value. So we got to rethink that we can't beat the uncertainty relation which has a very high spin in a certain direction and with more intelligent apparatus we'll be able to do much better. But a careful statement of the uncertain relations on the right hand side we have an exactation value. Right. We've left out a right hand side. Is this kind of... In your response I think to Claire you said one of the reasons it didn't make sense to talk about the state of a spectrum was that it was part and part of the concept of state do, and there wasn't a description that told you what the system was going to do. But even more than that, it's the phrase of the system. There's a strong implication that you learn it from the system. Sure, I understood, but I accept another line of what you're saying, the way we learn that information is different, but even within that description, there's a problem you're identifying. Now, presumably, someone who believed in wave function collapse would respond, it does tell us the description of what the system will do, but it tells us a probabilistic description. Now, are you saying the notion of a probabilistic physical law is incoherent? Of course not, no. I think the laws of quantum theory are as coherent as we're going to get and they're probabilistic. So then how does your objection work? That wasn't my objection. My objection was simply that that kind of analysis is overlooking the boundary between observer and system. Going back to an older form of theory where that was unmentioned. Right, okay. But then we sort of want to distinguish when we say the system data state we're distinguishing between something that is, let's say, metaphysically OTAs mean that it's extravagant. That's something that simply doesn't make sense. So when you're saying wave function doesn't collapse, it seemed to me that you wanted to say it's simply senseless to talk that way rather than saying it's a metaphysical extravagance to talk that way. It makes sense that it would be foolishness. It would be a bad theory. Now which of those issues do you want to hold? Do you want to say that it's just senseless to talk about the state of the system? Or do you want to say the idea of collapsing is a result of thinking that it's of the system.

1:50:00 There's no such thing. The state is something you did at the beginning and there's something you do at the end and it doesn't evolve out of that. One doesn't collapse into the other. But there are two ways in which there may be no such thing. If I say there's no such thing as an invisible elephant sitting on that light, I'm not saying it's logically impossible for there to be an invisible elephant sitting on that light. I'm just saying it's absurd. If I say on the other hand there's no such thing as somebody in this room who is moving while yet staying still, I'm saying it just doesn't make sense to talk about that. Now, when you say there's no such thing, which of those statements do you want to make? I'm saying it's a question language which is deeply flawed. I guess that's another way of saying it makes no sense. But yet, there are businesses who do talk about it. All the books. I mean, the exceptions are, I think, the book of Flint, that came out in the 40s and then 60s again, presents quantum theory entirely in matrix terms. And of course, Feynman's path integral does not talk about the state of the system. So avoids this question. but most of the books in quantum physics begin with a postulate the system has a state described by a vector in the liberate space and leaving out the operational fact that you don't look at the system to find the state but this is sort of my point operationally we don't do it that way so that might make the state an excessive concept but unless you want a commitment that all things are necessarily to be defined operationally then I don't see how you can extrapolate from that the state is senseless well I don't want to take such a strong position and the concept of state is very fundamental and yet the concept of experience is left so vague that it can cover both the actual practice in which you look at the apparatus to get the state and all the mental imagery in which you think of the state as the system. Is it really true that you look at the apparatus to get the state? I would say you look at the measurement of the apparatus it's not the preparation of the apparatus to get the state. Because you take an ensemble, and over an ensemble, you have a different preparation. Imagine someone gives you a device that says, to choose what state this prepares. One thing you could do is analyze the preparation operators, get into the deep open box and look at it. But you wouldn't do that. What you would do is you would put into place some non-measurement measurement operators, and make them a different type of measurement, and therefore deduce the state. But those are measurements made on the system, not on the preparation operators.

1:52:30 the two talk to each other all the time. You learn about inputs by looking at outtakes, you learn about outputs. Nevertheless, you end up with two lattices with a duality between them. And you hold one of them describing the input and the other one describing the output. But you have to keep track of it. And it just happens, the way the terminology has been set up by people like Giles and Ludwig, who write completely consistently, they define the where he stayed at the beginning as the description of the input process, and they call test the description of the outtake process. And Durant also has a footnote, and von Neumann has a paragraph, all to this effect at some point in their texts. It's just a matter of convention. But what's worrying me is it is a way, so the word state is going to be used to describe how two types of places talk to each other. I would like to suggest that if you can talk that language, call this the state, call this the etat. All right. What's striking, though, is that these objects, either eyebrow objects, but the state and the... Etat. Etat. It has an etat. Etat. But both objects are to do with the way these two operatrices, is talk to each other. If you believe in systems, then the way they're talking to each other is by our system. So obviously, both these objects have to do with this system. Absolutely. But you're saying a lot of the systems. Well, of course, there's a difference between the apparatus and the system. It's a crucial distinction. If you just see... I mean, maybe I agree with that. Sorry, in phenomenological theories, it's a crucial distinction. And all the theories have to have a phenomenological part. to you, and I might sort of send you emails, for example. So I would talk to you, and we'd establish some analog of these two devices. And what those analogs would describe would be the sequence of zeros and ones in email. So they would be of the email in that context. So it would work in classical physics. Exactly. But why do you say it doesn't work in? Because in classical physics, the state determines a eta and conversing. and in quantum physics there isn't almost any gives a positive result for almost any state if you just keep reading long enough

1:55:00 probability zero is a very rare case isn't this just saying in fact probability zero is the case of probability zero isn't this just saying if we want to treat states of being probability system then the footnote is the wrong thing to say can't I just say instead is a state is a primitive property of a system represented by Hilt's perspective, full start. And then say in my dynamic laws, that state interacts in certain ways with other systems and evolves in time in certain ways. I mean, I grant, if I make that sort of double-think of saying both the state is a property of a system and the state is, by definition, a property of a measurement device, then that's going to be coherent. But you're saying you have to reject it first. As long as you stay within a symbolic system, you'll have no problems, but you'll also have no contact with measurements. Why not? A measurement device, just another system. The fact that people can understand each other is an incredible miracle resulting from millions of years of evolution, and ultimately we have to get back to a naive domain where we know what we're talking about, where perception and symbol are almost automatically connected. You can't mathematize semantics. Why not? that's tantamount to saying the artificial intelligence program for instance I mean they're saying artificial intelligence and saying that you can't that you can't cover semantics I'm denying that accomplishing it by artificial intelligence is mathematicising it that's exactly the difference operates with a machine in real time and real life. It's not a symbolic system. Semantic properties are supposed to explain the theory form of science. Symbols are not mechanical laws. It's very important that we're free to make postulates about how they combine. I may have If Ms. Skolkin, of course, I have no doubt that one could replace a human being by a machine in a working physical experiment, and I've no doubt that the machine could be programmed to apply quantum theory correctly. But if you, in that case, where upside function enters the computation, you'll find the

1:57:30 machine looking at the apparatus, not at the system in question, not at the photon. Is it okay if we used to look at one system to produce a property of another system? Because you do that with so many classical physics. Right. But there is this one correspondence which enables you to forget which of the two you're talking about because it simply doesn't matter. And in quantum physics, one often falls into the trap of thinking one can speak naively about what exists when your perception does not tell you what exists. You can't see what a system is. it and then you know what it will be, or you detect it and then you know what it was. There is no is in quantum theory, any more than there is in relativity. I think probably we should call it to an end. I did want to end with just one story about David. This is told me by Hilary Park. of the sailing trip they took together in 1960, 61, 62, a longish conversation there, which of course they're hearing of to jump in quantum logic for the next 20 years, so I think, let's not go fishing. Seven of us are really dangerous enough. Thank you. Thank you. Maybe you could take the question in the middle of the book. What? No, I don't remember the music every year. I'm interested in the other thing. Yeah. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you.

2:00:00 Thank you. Thank you. Thank you. Thank you. Yeah, I'm sorry. I think it's just a pragmatic process. It's a great thing. I would go to you now. They need to be encapsulating all the three of the characters. It's just a little easier to do that. What can do then? What can together do without them? It's just a minor stage of the system. We call them kangaroos. They call them bird works. A person like Chris, who doesn't believe that repeat will be at the same stage of your individual system anyway.

2:02:30 It's a highly relevant concept. Which, in example, does this electron really belong to? Chris Luke's. Even in the case where it's a pure state, whereas, you know, like the Romanians, they say that it's a pure state, and they don't think it's a pure state, they would both believe it's the same pure state. Whereas Chris Luke says that he doesn't possibly know. I don't think it's going to be a bit of why Chris Weeks thinks that would be happening. But then it's sort of out to your argument if you keep it You must think about that. This is the person who . Thanks for your comments. OK, so I appreciate receiving reprints, current thoughts. Thank you. Thank you. Thank you.

2:05:00 Thank you. Thank you. Thank you. Thank you.

2:07:30 Thank you. Thank you. Thank you.