Self-Reference, Dimensionality & Scale of QM Effects (contd.)

0:00 In the parameter space. So the context of the aeroplane was in suppressing the noise or vibration in the aeroplane, if I remember. Yeah, yeah. So all these methodologies. Now, it strikes me that the combinatorial hierarchy is somewhat similar, because one of the things that is worked out by the hierarchy to which a lot of attention is paid are the coupling constants. Okay? which to some extent by the processes of the hierarchy are self-organized to work out the coupling constants. So my view is that there's a definite connection here between these things. And of course, also going back to Wilson's theory, you are essentially mapping the Hamiltonian and the Southern point with the critical points. And these critical points are, again, parameters in the parameter space, like critical temperatures, critical masses, and other things to which you can attach particular bulbs. So, all these solutions are in the parameter space. Now, so once we'd actually done and agreed that, we all thought we'd know a lot more about how we'd all been working, okay? And we began to look for this boundary condition. Now, this boundary condition, we'd often thought that, and you think too, that the universe starts from nothing. Okay? So, what about putting nothing in the boundary condition? So, essentially, let's say this is going to start with the Schrodinger equation. You see? That's the Schrodinger equation in this particular case. So, you say, well, what can come out of that? Well, it turns out it looks like nothing, but in fact it's everything. okay, because what does this mean

2:30 well this means that there is there is no dynamic evolution so it essentially means and I you know, I think in fact that his intuition might have been exactly right his first intuition the first vision, well that was there was the time everywhere that there was there essentially is no time The time, there's no time like the, literally, in this, in this universe, there is no time like the present, right? There's no time like the present. Literally, there's no time like the present. Now, this doesn't mean that the universe can't evolve. Oh, no. Because, suppose, suppose now, we normalise this, we normalise this spectra, and then people want, then the solution, then it turns out that the solution to this equation and the normalisation is now this is the solution because this must be a complex this thing must be a complex concept if you normalise it, it has to be that, you see, and what is this parameter well this parameter just happens to be the very phase so this universe can evolve in the very face parameter space. There's something wrong. It's just some arbitrary function of that. Yeah, but you can give us another interpretation. The equations you've written down mean that psi is a function of the coordinates because those are the things that don't depend on time that are left behind. But the normalization condition that you've used is to integrate psi, over the space and say 1. It's equal to 1. It's the integral that's equal to 1 not psi, psi, star. Well, why not? This could be the whole universe. That's not the normalisation they use in quantum mechanics in general. That's all I'm saying. You've got the integral of the space. But in this case there is no space. There's no space? Not yet. Yes, there is. That's what your partial derivative is. Oh, okay. Well, my idea was the only thing associated with the universe as a whole is the very phase. So in the very phase, this thinking can evolve in the very phase, prior to

5:00 space. You know, I wonder if the very phase... Because this is a... Psi is a constant, but it's a complex constant. Does size depend on some origin? You gave it a time to help. Well, let me No one understands what you're talking about. Does psi have... Should psi have a function of t, x, y, z, q, 1, q, 2? Is it just a different number? Please let me go on. Please let me finish the argument. You don't get a dynamic evolution, but you do get a geometric evolution associated with the parameter space. Okay? What is the parameter space? Well, the very phase, it turns out. The very phase is the parameter space. The very phase comes from integrating real space around the loop, right? Yeah. You have to have that real space parameter, and you have to be able to go around a loop in order to have very phase. So you've got such a primitive place that there is no space yet. Well, yeah, but this essentially goes around the loop. Now, the nice thing about this is that in this particular case, any theta... Yes, I know, I know. But you have to interpret it now. Any theta, any of these thetas will actually fit. Okay? So this particular solution is always renormalizing. It doesn't matter what happens to that. Okay? They're in the parameters. Peter, is it fair to say that the space in which you're thinking of this integration as occurring Space space. It's not space space. It's essentially in the Hilbert space. Okay? The side is not so much a wave function extended throughout space. There's a vector in the Hilbert space. So in that case, the size, size, star is quite valid. The size, size, star equals one is quite valid. It's just as a vector. And because of this condition, any theta fits it. And so it's all... And this represents a standing wave. But since this, any theta fits, you could say that in this particular space you have complete phase entanglement at this particular point, zero.

7:30 At this particular, at this position represents. So, now this is very nice. If this is completely degenerate, then you know that all the solutions associated with this angle, which you can think, in relation to the very theory are all non-trivial. Okay? And this tells you you've got, in some sense, an exquisite geometrical topological property because if you remove from this space all the degenerate points then you get a very highly entangled topological property of this particular point. of the zero energy point. Now, which means that in some sense you've got very high coherence here. So this is a very highly coherent in the quantum magnetic sense point. Now, if it's highly coherent, then you, in some sense, have got the conditions. You've got the conditions, because you need spatial coherence and temporal coherence. and to a certain extent from the very phase you know that there's the potentiality to record if you go around a loop if you go around a loop and it's going around a non-trivial loop from wherever you were to wherever you're going to go that there will recorded in the phase will be the time recorded in the phase will be where the thing went in space and what are the quantum states what are the quantum states that it went through now you say well the question is why does it go why does it why does it go does it make any loops at all well it makes loops in the quantum holographic condition because we've still got to take into account the Heisenberg commutation relations which model Heisenberg uncertainty which under these particular conditions are this optimal process

10:00 of quantum holography. So this particular solution would seem to evolve in the potential landscape of the very face space. Okay? And so, and of course it turns out in the very face space, you can of course do logical operations. I mean, if you have a potential hill, say, okay, and you approach it this way and you go around it, and you come back this way, you're facing this way. So, effectively, you've converted a 1 into a 0. Or a minus 1. Or a minus 1, yes. It's wonderful. So this is a... This is a... This is an evolution of geometric origin in the parameter space, OK? And it evolves in the parameter space Because the parameter space contains unstable critical points. Now, there's a look of... No, I don't. Thank you. And as Tony told us, there's a boundary, really, between, certainly in two dimensions, between chaos and essentially quantum mechanics.

12:30 Or at least... Well, actually, it has to be at least three, I believe. Okay. Unless you're under this great planet, though. Okay. That's my understanding. So, in other words, if you have a differential equation with only two variables in it and they're continuous, it cannot be chaotic. It can't be chaotic if it's linear, but it can be chaotic if it's non-linear and it's discrete in two dimensions. But once it's three dimensions or more, you can have as much chaos as you like, as long as it's non-linear. So long as it's non-linear. Okay. But we said in relation to Wilson's theory, you're looking for attractives, okay? Now, DuBois discovered that... if you look at what the space looks like that he essentially used to do his factual intelligence and you sort of map it out then it has all the arms of the particular chaotic solutions there's a special point which you could consider to be computer universal. This is a so-called slide, so I don't take too much sense to that. But there is a point at the centre here in which all the solutions are mapped onto. And it turns out that this particular point is concerned with the gold mean. I don't know what you mean by mapped onto there's there are all these all these things are effectively mastered in front of it I mean in a chaotic system trajectory well these are the these are trajectories falls into the stranger tractor Yeah, but there's one very special strange attractor in this thing which is associated with the gold amine that they all fall into. Well, let's see, what have you got here? You've got a vertical picture of the logistic iteration.

15:00 Yeah. Where you're taking the coupling parameter and increasing it as you move down the page, right? And you're plotting the orbits as horizontal. So what does this point mean over here, this one where the lines are perverted to it? Well, it appears that all the things that all go back to there or come from there. So it's a sort of universal, it's a universal attractor in this space that all the other attractors are connected to. Now, if I could just elaborate on Luke's question, the coupling constant is increasing as it goes down the page or up the page? Down. Down. in a regime there where the cup of constant is relatively small. Yeah, this is a period two orbit along the horizontal line. And that point isn't part of the orbiting along the horizontal line. Right, it's just all these. But then he's got extra trajectories of lines out there. I don't know. That's what I was getting to. What is this feather there? That says even the very weakest ones are also attracted there. Is that what that feather is doing? Yeah, I think so. I'd like to get the original picture, but there are two ways to do this. One is you choose an initial value, and then every time you up the coupling constant, you plot starting with the initial value. Then you get a lot of extra lines. I think that's what this is. The way people often draw it is they choose an initial value, then they move the coupling constant up, but they keep tracking it at the, without just one initial value. And as you go down, you're going in and out of regions of chaos. But this one is very special in the sense that they all go, all the trajectories. Yeah, fine. But where the lines are, you aren't chaotic. No, no, this happens to be fractal. Right. This happens to be fractal. Well, it's fractal down below. Yes, and there are some pieces of fractal. But these fractal structures are part of this chaotic map. It's the disconnected fizzy bits that are chaotic. But this particular point seems very special,

17:30 and it's concerned with the number, which is the golden mean. Now, this particular attractor the same property as the attractor we selected when we selected. In some sense you can have any standing wave there and that standing wave includes all these things to do with Okay. Now, to show that that's the case... We have about ten minutes to go back then. We have about ten minutes to go back then. Okay. More or less finished. Jaguar discovered that, of course, the, the, sorry, the, sorry, Michael, wrong one, at this particular point, this particular point corresponds to a unimodular, a unimodular, unish operator of that particular form. Now, I'm not sure whether this is actually right, but there appears to be, if this is actually correct, if this is actually correct, now for the Weinberg angle, then in fact, and these two points, this is then a special universal critical point in Wilson's book. in Wilson's sense, okay, then at this particular point, this is the point which is effectively going to dominate and cause this space, cause the evolution of this space, because it's, so the Big Bang will in a sense start from here and it appears that it's associated with the electro-weak interaction.

20:00 And you can do a lot of other you can do a lot of other modelling on these particular conditions. And nearly all these... Well, the other thing I forgot to mention was that all these mappings that I've been talking about are, in a sense, self-referential. In quantum polygraphy, the map that the Heisenberg, that you tune the parameters to, achieves phase conjugation. Conjugation is when you map the image of an object onto the object itself, for example. In the reference to this golden mean, this is essentially a mapping of the... I see some text there which will sort of turn on a small light in my head, which may be entirely in a moment. I know what a Sierpinski gasket is, but I don't know what a Sierpinski matrix is. Do you know what it is? I'd have to go back but this is 1, 1, 1, 0 oh I see and that's some kind of generator for the gasket probably yes, yes, ok and of course you know that x squared equals y squared equals 1 and also this sorry, oops the other thing you can map onto this of course harmonic oscillator, the quantum mechanical harmonic oscillator. And, of course, it needs to be a quantum harmonic oscillator, which is essentially an elliptic orbit. So immediately you get out of this the capillarian orbit as a possible solution to this problem, but but you can also get out the corresponding... It's not the Keplerian one. It's the other one where the centre of attraction is the centre of the ellipse. It's the one you get when you have a potential which is equal to R square. Well, not if you...

22:30 It is elliptical, but it's not the Keplerian ellipse. How about it, doesn't it? Yeah, that's what he says, yes, and it's true. I'm saying the harmonic oscillator isn't there in the lips, it's the other, it's the central one. Okay, well, I'll take that up with Walter, because Walter was convinced that, in fact, he's, Walter happens to be a descendant of Johannes Kepler. He's got a stake in this. Well, no, I don't think he has. I mean, no, come on. I mean, you know, that really is just not the way to do science to say that somebody is prejudiced. Are you almost done, Peter? Because I want you to finish, but I do have a question. I have a question. Yes, okay. Yeah, let's. Shall I do the question? I was, you know, I've been convincing myself for several years that a co-occurrence of R82 is a representation of a photon, okay? Yeah. And I see something like this, and I really, you know, the caption, the second sentence of the caption of that figure, and I'm wondering, it says the photon. Could we say a photon could be considered as, I mean, should I, is that picture, that statement encouraging me to think of a photon as a co-occurrence of a B0 and a W0, is that what or is it saying a photon is to some extent this angle is where you go from an unstable state which is this which is this which is these particles to the stable state when you say gamma, that's photon This is an extract from something, this one. Yes, yes, this is an extract from Du Bois' book on hyper-incasity. I'm sorry? It's a book on hyper-incasity. It has a generalization. Oh, it's an extract from Du Bois. It's an extract from Du Bois. It's an extract from Du Bois.

25:00 It's a linear combination. I don't know if co-occurrence can be accredited to a linear combination. Yeah. That's all that's going under. Okay, right. associated with the U1 group in the standard model, which is ST2 plus ST3 plus U1 minus some z-factor. And associated with the U1 is their particle as a particle. And associated with the ST2 are three particles. And some linear combination of those associated with the U1 These particular arguments. But can I finish this thing? Yeah. Some linear combination of the one associated with the U1 associated with SV-2 functions as a physical photo. That's what they're saying. Okay. Thank you. Peter? But the intention, the, sorry, yes, sorry. Have you ever seen the film Dom, Doc, and that magic was? Okay. Well, I, immediately when I see the Golden Ration, I think of that film. I was a child when I saw it, I was very impressed. And in fact, it's an iteration. And what you're going to reproduce is another rectangle, it's the left one. If it has the same ratio, that's the Bowen ratio. It's one way to define it. It makes a real neat picture. Yeah, yeah, sure. Peter, you said something quite early on. you and I still have some grip on things which I'd like to comment on we said that quantum mechanics is chaotic now my understanding of chaos is that it is generated by deterministic equations different equations for example or different situations, which are functions of time and you just iterate them and you get, under certain parameter sets, which is what you said, chaotic behaviour. Now, there was a theory at one time, which I didn't pay very much attention to, called the theory of hidden variables

27:30 which was supposed to explain the sort of randomness in quantum mechanics because there were variables underneath it all that you didn't measure so you didn't know they were there and they were fizzing about and they were creating the uncertainty but I gather that the whole edifice disallowed eventually, it was proved that it couldn't do it given those hidden variables I can well imagine that you would get chaos out of quantum theory standard quantum ideas because they could be their parameters could be such or the laws governing could be such that the observed effects were chaotic I couldn't believe that but the statement quantum mechanics is chaotic. I wasn't sure what you meant. Well, certainly this particular point, since it's uni-modular and it's connected to all these other... Around this area, you can effectively point to any chaotic trajectory. I agree with you, but I mean, Barry's thing is about quantum chaos. Yes, but I can't really imagine what quantum chaos is. There is something that people call quantum chaos, which is meant to be the analog in quantum mechanics of whatever doesn't manifest itself as chaos in the classical system. So your wave equations, or whatever they might be, are k-alpha? No, no, no. Is that what you're saying? No, I said it's the analog. It's the analog. The idea is that you might have a classical system

30:00 which would be treated classically chaotic. Suppose you wrote that hypertonin that was equivalent in the quantum theory. Would there be some signature in the quantum theory that you produced that you had started I mean, the way people look at properties of spectrum and say that they could recognize that in a kind of system. Yes, but the spectrum could be fractal. Yeah, or it could be something usually a little more sort of like whether the eigenvalues follow up or some distribution or something. Well, I mean, Barry, when he was first investigating this, I think it was a speculation rather an actual proof that quantum chaos concerned an unknown dynamical system where he identified the quantum Hamiltonian as having no time reversible symmetry or having time-reversal asymmetry, and it concerned the imaginary values or the phases of the eigenvalues of the Riemann-Zetta function. The zero is the Riemann-Zetta function. And there's been a lot of new work on that to show that, in fact, the Riemann-Zetta function is a solution to a particular kind of quantum mechanical system. And the eigenvalues do have fractal properties. Yeah, and the eigenvalues do have fractal properties. So the intention with this idea is to get Schwemp and Binns to, in fact, put it into a much more rigorous mathematical context. But the phrase quantum chaos is then a sort of short hand for this particular class of the line. Peter, could we wind up rapidly? Yeah, yeah, sure.

32:30 have you finished are you finished is that the final slide can we fire all the questions oh yeah I've been waiting since the first I just have to bring this one out it's not really a criticism You started off by saying with a received wisdom that in quantum mechanics there is this ambiguity of the phase. When you measure things, you measure the amplitude of the way it functions, but you can't measure the phase. Now, people always said that for many years and they're still going on saying it after something which I heard about a few years ago. statement is, that by measurements at an instant, you can't measure the failures. But Harunoff showed me, and I think it comes from him, but if not, it will be somewhere at a meeting to a sort of wake for David Bowen, which we had at a day long conference, that you can produce measurements which do measure both the amplitude and the phase to a certain extent, but the measurements have to go on over a finite time. if you're going to measure the phase absolutely accurately then the measurement has to go on for an infinite time but in between you can have measurements which last a finite time and we've told you quite a lot about the phase now I think that that needs to be taken into account of the earlier remark that the phase is totally well I mean it's very useful in in the holographic universe because you can use you can use this as the reference phase, as the reference phase for the holography, okay, and the nice thing is in a self-organized universe where phase conjugation, I think the universe is essentially phase conjugate and is mapping onto itself, you can consider that this arbitrary phase

35:00 in some sense is a measurement standard, okay, is the measurement standard. Now, if in a self-organizing universe where this is the measurement standard, okay, you can measure things, all measurements can be measured against the standard, but they can't actually, you can't actually measure the standard, you can't measure the standard itself. So that would, in the holographic years, that would be the function that this arbitrary phase would essentially I think I see what you're saying, but it seems to me that the number of times that you referred to phase with the adjective arbitrary in front suggests that you haven't really taken on board, but I'm saying that the phase is not arbitrary because given measurements over a period, you can actually find out something about it. Yeah, but in the case of the universe itself, I don't think you could, because it being in itself, you know, in the ultimate, I agree with you, depending on, in some subsystem, in any subsystem, you could probably do what you, you say, but in the universe as a whole, there will be this, this would, this, this, you can consider this to be the measurement standard, because in any measurement, you have to have a measurement standard, And I don't think that has really been taken on board in quantum physics to incorporate the measurement standard in the model of measurement. Can I just underline this business about measuring the state function? I mean, if you just stuck to measuring size, size, star, now that is the size, you function, coordinates sometimes times, and it's treated as if psi, psi star in other words, multiple psi squared is a probability density of getting these coordinates to try and measure the covariance. Now, if you think about it I'm talking about ordinary statistics and you want to measure a probability density you've got to do lots of experiments and they take time and you create a histogram and you go on bashing weights. So, you even have to take a lot of time just to evaluate that amplitude. You also need many copies of the sentence. Oh, yeah.

37:30 Because it's right away from the sentence. That's right. But if you don't have many copies, your experiment is meaningless. So, I'm not sure that you're saying you have to take a lot of time to. And also, because it's big. but this is how you can think of the universe as actually working this is what the second quantization is about thank you