Structure of the Standard Model from Combinatorial Hierarchy

0:00 A combinatorial perspective on a standard model. Do you want me to start? Yes, I think I just introduced you to us. Yes, I call this a combinatorial perspective on a standard model. but the point is that the hierarchy algebra which some of us are involved in and all the work associated with it claims a variety of successes that bring it directly into the ambit of the standard model for particles so we can't ignore the theory and hopefully they shouldn't need to ignore us. Since what we're demanding is a quite new general dynamical background of philosophy, we need to look at what the critical successes of the standard model are to see how far we have to go to incorporate them or satisfactorily replace them with our methods and see whether there are some which effectively rule out our approach altogether. I'll come back to that. The point is that if there's some things that you can calculate using the quantum theory, which are incompatible to our principles, then our principles go by the board, period. So that's what we looked at. In particular, some of the results that are used or implied in the standard model are not specific to that model, but the general results are quantum physics. So, do you have to have quantum physics? Because we don't. We don't want to. Well, look at all that seems in tall order. Perhaps it is. but we do have to remember that people thinking about the standard model usually imagine it embedded in a whole background of quantum mechanics which is as it were prescribed thinking prescribed thinking now we taking our cue from things

2:30 in quantum physics and in the study of particles go all the way think that adopt a philosophy which sets the dimensionless constants as the first physically interpretable things to be encountered and having a primary position that isn't quite what is done the standard model would be taught but on the other hand I think It's a real part of the way they think. But these properties are, the coupling constants are very primary. You might well say, well, why can't this obsessive ignoramus, that's me, learn quantum mechanics and its connections with relativity, learn it properly and just get on with it without having to pull everything up by the roots in this boring way. Now, I've given the answer to this many times. I'll give it again, briefly. It's because quantum physics doesn't work unless we agree to use different mathematics for two classes of things, the two classes being according as they have or have not to do with measurement or observation. you have to switch from one mathematical treatment to another merely because associating it with the notion of observation now I'm not of course denying that there is a profound truth that they were trying to get at the point is that merely justifying it by an appeal like that is merely to make the thing work by a verbal trick really essentially it's a verbal trick jump from the discrete to the continuum or the continuum to the discrete. I'm not saying that you couldn't give explanations. I mean proper discussion of the trick so it doesn't remain a trick. It's no longer a trick. I mean, von Neumann said, well, there's this infinite regress. Finally, in order to understand the observation, we'll finish up with the operation of the human mind. That's a logical possibility. exactly embraced kindly by the quantum

5:00 physicists, in fact it was dropped like a hot brick for reasons one well understands it would take us to put it mildly into strange waters so as things stand a model has been introduced into what a would-be articulated sphere of discourse and once you let in such a model it proliferates to permeate the whole sphere Now, the things I would like to be talking about I shall not get very far, needless to say I will briefly write 7 out of 6 down on the board because if I write on the board then you have time to read it whereas if I put it on one of those things you don't A little short. It's a scratchy short. What are the coupling answers? The statistical background of the hierarchy should have struck there considered in relation to the vacuum and the vertical particles. How did we get to quantum theory, given that we didn't start there, considered in relation

7:30 I call them the first time, the rest of the area. What is mass, oh, photon on space-time, energy bank, what is mass, quartz, and, um, fixed. The standard model symmetries. The main thrust of this is what I'm saying is to consider how it is that there are a variety of questions that I would normally ask about logarticles and the standard model, which the development of the model shows to be inappropriate. that's one of the things you're not supposed to ask you seem to want I'm reminded of a remark I've heard attributed to Dyson who said that the last part of learning quantum physics in general was to realise that there are some questions that you may ask and others that you may not and you have to learn not to demand answers to the second tool I understand this was said seriously you'd think it wasn't very satisfactory as a general principle I shall find myself maintaining that there's an important range of questions that fall into the second class, the kind you're not supposed to ask, that the hierarchy approach would explain why they're inappropriate. Sorry, I've got confused with the grammar. There's an important range of them can see from the hierarchy of breaks why it's inappropriate to ask them. In fact, it provides

10:00 a theoretical background in which they never arise in the first place. So that has to be set against the obscurity of the position ones that are being asked to take up. So we've got two kinds of questions, really. First, the first is defensive and negative. The second Are there any calculations which are essential to the field as the combinatorial approach, which we could never see our way to obtain, sorry, which are essential to the field, that's the quantity of the standard model field, which we could never see our way to obtain in combinatorially, or most generally, because if they are, that would vitiate our claim to be able to advance towards as much as we need as a continuum, constructively. in practice we couldn't break free of the quantum theoretical presentation of classical physics and then secondly more positively what results or methods are there which arise naturally for us for which the standard model has to strain or can't get to at all well of course pre-eminent among those is the calculation of the coupling consciousness about which we continue to remind ourselves and Clyde produced his masterly analysis of in the last few days. Right, so my question now, what are the coupling constants? Not at all obvious. What we're saying is that we have to get any dynamics we want for purposes of comparison with the standard model from the bare dimensionless numbers of the hierarchy from such pretty basic ideas as to come from the construction of those numbers. In other words, dynamics has got to emerge from this background of this very vestigial background of a small number of numbers with together, of course, with the structure, mathematical mathematical structure within which they were calculated. People usually start by telling you coupling constants specify the strengths of the fundamental fields or fundamental interactions.

12:30 Now this could mean that there are ratios of some experimental measures of those fields. But this interpretation works quite well for comparison of the electromagnetic and the gravitational fields. The higher artifact a good approximation to the large number which gives the strength of the gravitational field in terms of the electromagnetic this doesn't give us an obvious meaning for the pure numbers found from the hierarchy of standing alone or indeed for those that are the conventional picture doesn't really it's very cagey about telling how you do it how you jump from those ratios from ratios to the expressing the properties of field, the strengths of field. You can look into the simplest levels, which for us have characteristic numbers 3 and 10, try and form ratios of the strength of the strong field, but the concepts on which it's based are best vague. I mean, there's no clear line deriving from the conventional theory. We're not in the position of providing one at the moment. Right, so now we begin to get some insight, and because of the statistical background of the hierarchy and the bacterial fluctuations, it appears to be necessary to have a residual half-H of action which cannot be eliminated, and which is attributed to the Heisenberg-uncertainty relation. to be imposed on us by the theory of spectra. I should want to look at that in a bit more detail. This half-page is called the zero-point energy. It simply arises from supposing that if you know the position of a thing, then you have to associate an energy with that statement.

15:00 And the physical reality of this is re-emphasized by the fact that its interaction with the electron gives rise to very small but extremely exact spectral displacements of lower energies, spectral displacements of spectral lines at lower energies, called the land shift. But these are very small because of their appearance in expansion series of the increasing powers of prime-structicons. So here we see that the really high cost detailing for their mental values that the, well I must say the standard model is that modern physics, quantum physics, quantum theory gives us, do depend on precise use of this very structure of skeradons in accordance with the principles I was talking about. And by contrast, you look and you think, well, now, such things as that will certainly be all the, there'll be pages of stuff, standard continuum theory of getting the appropriate Lagrangians and all that kind of thing. and you just don't look for it if you don't find it isn't there it doesn't seem to be necessary so it's quite a good thing to show why this is one of the cases the curious way they carry on is what from our point of view we would expect this is where the hard stuff comes well this dependence on this carciosis is related in people's minds with a more general belief in the background of how do you call them particles? Things, but collectively called the vacuum. And since the vacuum has no ordinary spatial concomitants the particles are said to be virtual.

17:30 And something like this seems to be a logical necessity. You've got to introduce these new kinds of things, and they're not particles in any normal space. But they will give us, if we look at it, they will give us the beginning of an answer to this question, what really is the fine structure process? Now, I've actually presumed a quote from Peter Brodens, one of the papers of his I had, because he looks at questions like this and comes up with statements which are clear and down-to-earth and straightforward and quite unlike what you normally find in the complicated circumlocution. of the state-of-state theorists. Though I may be doing an injustice, I haven't read through. When I look on the Internet, I get through the first 20, and then I go to the further ones, and I get about through about three or four stages, and then I give up. Well, I do some of the stuff. I do find that. But it doesn't seem... The kind of questions that one would think to ask and answer. Now, what he says is the idea of an alpha, thinking of these things collectively, is that if you have an isolated charge, it still interacts with the vacuum to produce virtual bosons, photons or whatever, by emission or absorption. And where another charge is present, the bosons can be emitted by one and absorbed by the other in a two-way process. Virtual interaction with the vacuum is similar to real interaction with a real field, which is, of course, a distribution of real charge of some kind. The vacuum acts as a virtual field. And then, again, the measurement of the coupling between charge and field is the coupling constant alpha. In the electromagnetic case, this is the primary case, obviously. In the case of a coupling involving one charge emitting or radiating a photon,

20:00 and another charge absorbing it in a mutual process that goes both ways simultaneously, the rate of the interaction, or the probability per unit time that the process will happen, is proportional to alpha. He quotes a friend, Mike Holden, for saying that the particle with charge e randomly radiates phonons at a rate that is a constant of nature. Scattering and emission absorption are essentially the same process on a final diagram. So if you want to get into a final diagram and then to imagine that you're talking in some kind of spatial picture and that's the way to do it. Okay, so the reason you can't find your ratio as a natural definition of constant is because you're really referring to absorbing and the emitting process, two things. There are your two things that can give you a ratio. Each has its own characteristic process type. So what I'm saying is that for very strong reasons, the theorists need to be able to say that the alpha is a property of the particle, in this case, the electron, itself, which exists independently of other entities. It hasn't, in the initial thinking of it that way, it doesn't have to be expressed in ratio. And if and only if they can do that, can they construct an interaction with other particles with similar attributes. Since the effects of these from a single electron are not seen, they're said to be virtual, and the background in which they had their being is called the vacuum. You can't say that they're an imaginary construction because the effects of them are real enough. So a strange ontology of virtuality is born which seems to be invoked and without discussion that one would have thought necessary for such a philosophically extravagant innovation. Well it is weird isn't it? Introducing a sort elementary reality, after all the talk that philosophers give about phenomenology and that. Well, besides my contention for the way into this mind field, is to find, is to see it in the need to have the alpha as a real property of the electron in isolation.

22:30 well now in computational physics spirituality comes as no surprise and no special provision for it has to be made the construction process that generates the hierarchy proceeds by discrimination stimulated by the arrival of a continual supply of new entities from inverted commas outside we know beyond what we're able to infer from the construction procedure itself. In order to avoid presuming to have knowledge that we cannot yet have, we think of the background or the outside as being random. But that's merely a way of working, that doesn't asserting anything about their nature. It's merely to say that where we don't know, we will use the random statistical process. If we find something funny going on which is different from the randomness, then that will be evidence of something, some structure, which exists out there in the Vars-D-D. But the variations of the, variations from the statistical norm are the only intimation in the first place that we can have on them. So we could say that the hierarchy of construction involves a continuous sampling of this background, which may display a variety of naturally occurring weightings, some of which we may choose to interpret as spatial distributions of some kind, determining things like the number of chairs in this room, to things of no physical importance like that, and perhaps other things that are of great importance. But the important thing to realise is that we're not, in no sense are we searching into a pre-existing spatial framework.

25:00 While the discrimination of entities of such things in a statistical background are like what they're postulating about the vacuum, no spatial structure. So we can call those things virtual by very similar verbal construction. But now what we have to pay for this simplicity is never to have an objective or observer independent reality that exists independently of the construction process that is something that we are fixed with and i would think we might say that the standard model has the same problem and deals with it, has to deal with it differently, it certainly is less aware of the logical situation it's found itself, it's worked itself into. What is remarkable is that the standard model has had to furnish itself with something so like what we, from our basic principles, got. Now, how was the time? I think that's all right. Oh, a little more than that. About 25. About 25 we've been going to take that back. Yeah, okay. So it got over half an hour, so. Now, this is slightly in a way of being a digression. okay if we hadn't a background dynamics how would we get back to quantum theory well I'll start by saying the unique change made by the quantum theory is the appearance of spin I won't elaborate that it could be discussed but probably you'll see what I'm getting at Now, the combinatorialists have to search for its combinatorial origin.

27:30 And they have such questions as to whether it represents angular momentum, or what to be said later, when more structure has appeared. A long time ago, twenty, twenty-five years ago, we maintained that thinner rows, or at least that's, I'd better say, I maintained. I got to hot water so I didn't have landed until I entire other people with this particular hot water that's only partial, that's an example of a partially mixed measurement and that spin arose because there were certain changes at the level by two vectors which required two operations to secure them at that level, which could be performed in one operation at the level of four vectors or two by two matrices. At the time, we blindly associated this fact with the half-angle rotations that were introduced to spin. But it's now, but it was clear that we really had to put it much more abstractly than that. And that if we were successful, perhaps the geometrical interpretation can be added on afterwards to taste like sugar and orange. Now all this depends on the irreducible asymmetry between the 0 to 1 symbols in the algebra. Things are different from what we had with Boolean algebra. However, we consider to column two vectors, and the trick I argue is to consider two column vectors and use the up and down positions to convey the asymmetry by not treating them as equivalents, top and up and down as equivalents. The rule we take is that we only use vectors as operators which have one in the top place. I'll go through this, though, it's, um, it, um, I found it so indigestible, though he doesn't, he doesn't really say there's absolutely nothing in it, but it, it drove him into, um, inventing, uh, what it would call aspect, and it led to the introduction of the Quaternions.

30:00 I mean, if we get a process like this, these are performed by discrimination, the vectors which I go on again, meets the focus disallowed by our rules, and therefore we look for pairs of allowed operations that will replace them. And we find that one and only one pair does in each case, and these are Feeding, something like that. These can be replaced by two-by-two matrices, namely, because these are double transformations, and we were searching for a way of representing them by single transformations. so that you get the effect that you wanted of a double operation by a single operation if you consider the thing by changing the level. actually has got an intervening state before you get to quaternions of presenting this in his notation which is different from this and more difficult to hold in the mind but less objectionable from all of you appearing to derive physically significant things from what has to be, or what looks very much like a special representation. However, I can give that brief thing, but I think I won't. Time's getting on. Well, now, 20 years ago this argument was something of a wild surmise, with so much stripped away from what we thought were obvious physical interpretations

32:30 of this algebra, it seems reasonable that it is indeed necessary that something so fundamentally experimentally, should have its mathematical counterpart in something so simple. What I think about spin demands a digression. People will say, we all know the history of the concept, and whereas it may be helpful to have these combinatorial ideas, they can only add to what has been well known since Zommerfeld, Haldsvitt, and Ullenbeck and Pauli and the others. Well, this is really an example of the outlook that I think is at best misleading. It always seems to me to ask where fundamental innovation really comes from. several different kinds of root cannot be right. I expect this complacency about the multiplicity of origin which affects the view that quantum theory unifies everything as a solid base. Most people would say there is an understanding of spin within mainstream quantum theory with its continual basis, and that therefore see it arising purely combinatorial as it must be wrong. And this and obviously I'll need to explain why this view is not correct. We find that the discussions of the origin of the fine structure constant in the spectral theory require inevitably a ratio of the mechanical to the electromagnetic force that comes in naturally. but there's simply a variety of mechanisms which this ratio has to be applied to determine and they're all different first was due to Zollerfeld who introduced a correction for the relatively dictated mass of the rotating electron into Hamiltonian it was at this stage that the core model was superseded while Zollerfeld's mechanism was replaced

35:00 not corrected for but scrapped although it's still put on as relevant to the picture by Holtzman and Uhlenbeck who assigned an angular momentum to the electron the better to fit the spectral observations at that stage the necessity of the factor to emerge which they didn't explain and which they didn't know the need for Heisenberg said yes But where is for factor two? And indeed, where was it? I don't know what one's here to tell it now is that Dirac put the electron angular momentum on a sound basis as a deduction from hotter mechanics by taking a four-dimensional linear form for the wave regression for the Hamiltonian. The, uh, quite straightforward, um, in the book on Eddington, which, there was a copy of which, my copy of which I found again after I've seen it destroyed in the past years back, which I recommend as containing an awful lot of good stuff, summarized the position as follows. He said, Dirac's approach in this paper, the quantum theory of the electron for society, is that not to summarize in the first paragraph. It is to find why nature had chosen, not a point charge, but a spinning electron as a building bridge. That's a quotation from Dirac. He then proceeds to this is now a quotation from Clyde here. He then proceeds to relate this with the necessity of making the theory of Lorentz invariance. It is clear now what was perhaps not clear in 1928, that neither requirement evolved the other uniquely. to have half integral spin. Other spins are possible, and the choice is experimental.

37:30 Achievement is to have shown how the two requirements can be combined. combine. That's sort of Clyde's usual general way of describing the situation. I would tend to put it more strongly by saying that there are various red herrings here. I mean the attempt to produce space and time symmetry to produce a four-component weight equation is all a bit of a muggle. That's from my point of view, you don't need to introduce a combination of space and time and therefore you don't need to introduce Lorentz and Variance. It isn't the case that Lorentz and Variance is the sort of thing that you sign up for and then it works always under all circumstances. relevant here. There aren't any rapidly moving objects. Well, there was, of course, a relatively collection of domitiles. But, and moreover, the point about the linearized equation of Dirac may have been thought by him to be important because it introduced space-type symmetry but what it really was doing was drawing an algebra in which the Pali matrices were natural which are discrete entities, and which now could be connected with the spin. Now where this all connects up with interpreting the spin as angular momentum is really a very complicated question. And to which I think there is really no very clear answer. There are connections, but to quote Bill Rowland again with these discussions of these things, angular momentum comes quite a long introduction of angular momentum comes quite a long way. or a few more, it is succeeded in introducing time structure constant and derivatively massive charge, then you can think about something as angular momentum.

40:00 This again is a sort of sub-asside, but I'll burden you with it. Thinking about how we get to quantum theory and how much it imposes on us, I want to point out, well it really trifled this to my attention as well. There could always have been a much simpler road into the quantum theory which didn't involve the dubious philosophy of states and observables. If we consider like the harmonic oscillator, an oscillating system, essentially a system in which there is repetition. We're not talking about continuum time at all. We're talking about things as oscillating. And it's not unnatural to use a mathematical device of saying, well, now let's represent things which are essentially discrete by real numbers, and let's suppose that they are on the background of things which are complex numbers, which we can characterise by the expression. But let's say that's just a device. We are looking at the world, we see that we've got some strange discontinuous things to deal with, so we produce some discontinuous mathematics. A mathematical fact. There's no harm in that. That's a good old philosophy of science. You look for a theory which has some characteristics you want to represent in your system. This is not my way of trying to analyze a situation, but it seems to me to fit in this case. And as Clive said the other day, I as the usual imaginary quantity

42:30 of algebra and the way in which this plays an essential role is still a mystery. He was quoting himself the other day, I was saying this well, from this point it was not a mystery at all, it was a down to earth kind of thing, you use some mathematics which has a particular property there's something puzzling in the world you represent it by this trick you don't put anything, you don't find anything profound in it in particular there's nothing about states and observables. That was all forced on as an attempt to say, ah, now we have a continuum, now, sorry, now we have a consistent mathematical theory which describes what used to be called the continuous and the discrete states. And as I pointed out before, this is done at the expense of a model. So here's a way of doing it without all that presumption. Right. Now, the simplest case of a theoretic system, it's the harmonic oscillator, and the energy is that's now because the frequency yet it's possible to show that the condition which comes from this equals E S gives you a number E of the form half has emerged. We write the observable A, and here I ought to be spending more time and say that I'm using a conventional notation which I shouldn't be justifying. that A was re-utilising the fact that everybody here almost would be more familiar with all this than I am

45:00 changing this equation into the direct form A S equals there's a sequence of steps of these finite steps that Diandra was deliberately incorporated to reproduce and the remarkable thing is that they go in double jobs so this formula with a half comes in Well, I must admit that I was much edified by doing this, multiplying it out by myself, and finally I didn't give this answer. And I constantly tried with puzzlement. He said, oh, well, you've forgotten that you're dealing with an anti-commuting answer, perhaps, you know? I said, oh, good Lord, do you mean to say that all this stuff about anti-commutation means you have to do the simple algebra differently, and now, you know, the light dawned. I was able to laugh at myself. So this is where the notorious half comes in. I think it does. It depends on the representation of energy as a square term. And it's fortunate that Tony's not here. Of course, he would be jumping up and down and saying, but according to me, it's necessary. The square form is necessary, but never mind. He's not here. So this half, you say, well, this issue was supposed to be dealing with Hamiltonians. What's that, physically, what's that half mean? And then there's a sort of slightly embarrassed silence. And people start going back to where we were a bit before, talking about zero-point energy. following our earlier track, they give them to virtual particles and all that stuff. And in other words, so that there is an intrusion. I mean, what you might call angular momentum has got something to do with this. In spite of Clyde's assuring me that this was one argument which produced one half of the argument

47:30 about angular momentum which did or did not come from Karp-Smith and Nurendek produced a quite different theme which was not mathematically related whilst they apparently are related in some obscure way and so really the more you look into this the more of a can of worms it is it's rather complicated to see what the right steps are but I think it's highly significant. It's pleased me anyway to see There was something as simple as this, which gave you the most essential number of quantum theory. And you didn't have to even go into the hydrogen atom, let alone did you have to go into all the stuff about states and observables. That, again, why I got into this was because it seemed to me necessary The combinatorial theory could start from the abstract basis of discrete set of numbers with appropriate mechanical, with appropriate rules of construction or background algebra without, and yet, and didn't have to, wasn't constrained to go through the conventional quantum mechanics. They could do that all much later without logical thinking of hearing. I think you've got about five minutes, Ted. In fact, if it's actually possible to do this at all, I'll ask you the incredulity, really. Why have you all had people like me, anyway? I've got a hearing problem today. I think you've got about five minutes, Ted. Oh, is that all? You're not strongly restricted to that five minutes, I'm just warning you, this is how it's time-telling. I won't go, I've run over. So, I've got to tell you, if it's actually possible to do this, then I ask for the incredulity why we all had to spend so much time and sustain our persistence through so much confusion

50:00 and perplexity in coming to terms with the current philosophical stance of the quantum theory. It could have all been like that. there is quite a lot more I should like to be able to say and can't I'm going to jump ahead and deal just with one thing which is in this section what is mass the standard model theorists quite openly admit they have no theory of mass but in the sense of the sort of basic definition of the term I mean we may suspect they won't have even if they find the Higgs particle it's a case where one has to stand outside the range of continuum concepts for insight now I go along with Peter Rowland who has a step-by-step creation of a digital numerical value of mass and charge treated mutually in a sense which the novelist tried to realize that by mutual I mean you couldn't have one without the other with a build-up to a top stop with 137, in which case E and H, and therefore M, fit into the picture of starting the coupling conferences. Now, he doesn't have a stop to his progression, we do, which is well not for us. He has a complicated combinatorial theory to come from a step-by-step list, however well now what is mass all the other quantum numbers all the other properties of particles seem to fit in more more or less as what I like to call descriptors

52:30 not for one value, they either exist or they don't exist mass is stiff, mass and charge I suppose, but we usually think of charge as one of them it's usual to think of charge as a descriptor, and leave all the varying to be done by the mass so what is this strange thing I'm going to the extreme I try and justify myself. The picture that seems to fit the bill is strange. We want to identify the three basic quarks with our combinatorial triad of discriminately closed subsets. That's a sense of a gouger-braic basis in which we'd like to make a connection. I do know there are more than three quarks, but I think in a sense there are three most basic ones, and the theory started with three. given something like the build-up mass. And of course it does, it does evolve mass via h. Given that, we get one value of mass. How do we get a, I won't say continual mass, but how do we get at least a series interpreted it as mass, and which we know to be the same kind of thing. See if you're looking at a body, a classical body, you don't have to say why it's the same, why different observations of what you call mass to be the same kind of thing, it's obviously But yet, we do. Now, I invoke the notion of our notion of levels, and I observe that at the electromagnetic level, where this appears,

55:00 there is this number which is a limiting number. Now, what numbers are there which could be physically exampleable, which are not limitable, which are not limited, but which are capable of having different values. And my suggestion is that things like the corks, and there may be other things, they don't have this limiting value. They're capable of wandering about. No one hopes no one will get values of mass, or we might. So that within the algebra, There are things, there is a limit, and within which there's some freedom of play, which is not bounded, essentially, and irrevocably bounded. And it's the irrevocable boundedness that you want to get away from. Now, I pitch this, what I'm talking about now, within the context of what is named some remarkable distinction, doing what he called composition and extension. How do we begin to introduce composition and extension together? In which case, we have, if the way is open to define mass, that's because we have no bridge between those, that we have a way open, that we have no way open to define mass. Now, I'd suggest the following bridge. What I've just mentioned, that the quarks have variable values within a constraining alpha. And they're the same kind of thing because we're interpreting them differently. Peter speaks of different values of e-square because he regards the charges of fundamentally variable. It doesn't very much matter. So to put it very anagorically, no, not anagorically, mystically, almost, theoretically, almost, elusively, perhaps, I would say that extension and composition

57:30 can become connected by treating these things the separable corks have flexibility to change and the basic alpha does not you could say, putting it as I said, this is our picture of the origin of mass through the relinquishment of space of space or extension and I'm seriously proposing this of the two concepts. Incidentally, it explains the otherwise odd experimental unreality of the quarks as particles. And if that argument is true, then the quarks won't manifest themselves as spatially determined particles because they're still components of the process by which we build up a connection between extension and composition and thereby compose things as happening in space. Now, I'm not even going to apologise for the strange argument I've just produced. I would say that I have thought about it and it's the only thing that feels to me to have the right power to bridge the composition and extension, that's fundamental, and characteristically, we want to embed it into a physical thing, into a physical picture, which I think is an advantage. Well, there you are. I'll stop on that note. Thank you very much, Ted. Thank you. I've got several points I could make. Concerning your factor 2, you mentioned a lot of things like, which to me are all connected, like the filled vacuum, the vacuum, the 8 crossover 2 you get in the vacuum. The one you get in the Heisberg uncertainty, the one you get in the harmonic oscillator, the one you get in spin.

1:00:00 Has he talked to me? Yeah, I think so. I'm sorry. Peter, look, I apologize generally. It's really not my fault. I've tried to get my ears burned out. Should I speak very loudly? I think so. Yeah, the fact of two, you have many cases of it that half, harmonic oscillator, Heisenberg uncertainty, vacuum, zero point energy, spin, they're all basically the same and if you introduce anti-commutivity it will appear. And anti-commutivity in theory, it will always appear. That half will always appear because there will always be that doubling. But as I was saying on a previous occasion much our letter mentioned about the factor two. Any of those dualities, to use that word, any of those dualities between conjugation and conservation and all that kind of thing, conservation, non-conservation, or dimensionality or non-dimensionality or real and complex, all of those will introduce that factor two. And so when you say there are different, seem to be different ways of generating that spin thing, there are because they're all versions of the same thing. They're all basic versions of fundamental duality. Wherever that duality is, there will always be that factor too. So it makes perfect sense that there are many different approaches, but they are really all the same approach. And they don't depend on... You can switch from one to another. If you have a duality, which is whether it's dimensionless or dimensional, for example, you introduce anti-commutivity, which is basically introducing dimensions, then that's a way of generating the factor two. But you could also do it by conservation and non-conservation, Newton's laws, etc. And that is just another way of introducing the basic duality that produces the factor two. it's always a choice of two choices so that factor always comes in because of it the basic situation doesn't require expression in terms of states and observables no, not at all

1:02:30 and nothing to do with it it's no different to saying kinetic and potential energy or something like that, it's the same sort of thing it's just a fundamental duality which will come in, and that heart doesn't require states and observables at all Are you coming back immediately, Harry? Are you coming straight back? Yeah. Just in this recent thing that you said about mass and alphas, well, the calculations I did of masses didn't have a changing alpha. It was a fixed value because the alpha wasn't the primary thing. If you write down... m over alpha. That's not really anything to do with alpha. That's really sort of some sort of fundamental mass which if you take the electron mass and alpha they sort of cancel each other out at the same time. The electric properties and you just get a fundamental mass. so I did believe that was the same value it wasn't changing so I agree with you on that it doesn't change, not for that alpha changes when you're measuring alpha but it doesn't change for determining masses of particles so I agree with you on that I don't even react to my motor physics about the reality of about the sort of click space. You mean it's all in one package? Space comes with the particle, you mean? It comes with peculiar... well, it comes out of our model. Yeah. So I'm alleging, or I ought to say, I am, and we'll come up with this, but it's in that way, but the basic thing is that you've got something which in its nature unspecified and in those forms, and something which is exactly specified, and it's the connection putting the best together, to get both in the same picture, which enables you to get the concept to a third. I'm not sure I understand it yet. I need to read it. I need to read it before I can actually say anything about that. But I agree with you that quarks are not actual particles. They're only part of a structure. And when I wrote that wave function down, it's not possible to regard quarks as actual separate particles if you write down the wave function like that.

1:05:00 because you've got three parts of a momentum vector which are necessary at the same time. You can't separate one any more than you can separate three dimensions of space. Peter, a question for you. When you pick up forks in your model, do you pick up along with them the representations of SU3 and so on that standard model have? Yes. Effectively, you can transfer almost straight off. to do is put the covariant derivative in instead of P, and you get exactly the perfect standard model representation. It's really easy to do the SU3. The difficult one is the SU2. But the SU3 is very easy in this model because once you write down the wave function of a bearing like that, you can immediately just then put in the covariant derivative instead instead of P. And you can see immediately how it operates. You get an A term, but you get an A naught term. Can you explain that in one of the papers? I explained it in a different paper, which I can send you. In fact, one I've just sent, one I've just given in Liege. I can send you that one. Great. Because that explains that well. So I'll write that down as well, Liege paper, because Yeah. It's very easy to do SU3. SU2 is a lot harder. It's a lot more messy, but SU3 is very easy. I have a question for both Clyde and Ted. This is because Clyde, in his talk, said something which surprised me rather, which was that he's very happy that his new calculation fits so accurately, the measured value of the fine structure constant, and that, as I understood it, he now feels that an approach, which is in a certain sense with philosophical justification behind it is actually a better approach than the calculation directly to physics. Now, that's what I understood, Clyde, to say.

1:07:30 I didn't hear him say it in a while. No, I didn't use that word, but I used it in a certain sense, and I tried to make clear what I was imagining him to be. Now, this is in direct contradiction to the approach Ted's taking here today, I thought. Maybe I'm wrong. I wanted to ask both Clyde what his reaction to that was and Ted what his reaction to Clyde's statement was in any other way. I'm actually puzzled by Clive's treatment of that, particularly where he says there's a first stage which has no theoretical significance. You simply observe the number. I don't actually quite understand his motive, and then he builds on it and says, ah, the elaboration of this thing gives you cause for self-congratulation. I don't really know what his motivation for that is. It does puzzle me. All I say, that's all I say. Well, I think to answer you, Keith, in a brief manner, it surprises me that you see any great inconsistency with what I've been saying and what Ted has been saying this morning. See, I thought he was taking much the same time. I mean, this specific point may be a difference between us, but it's a detail. I'm prepared to, in order to fix on a constant, I'm prepared to sell out the credit for getting the rough number. I understood you to say that you wanted the constant to come out as a significant structural That's very solid. That gives it a kind of mathematical solidity. If it happens to correspond to something else, it's a separate investigation. Yes, I see what I was doing. I was probably doing wrong here, actually. I was trying to answer physicists who might have said to me, Oh, how do you know you're calculating the fine structure constant? And I would want to answer for that. Well, look, at the first stage, I'll give you that free.

1:10:00 It's almost there. But I now realise a better course of action would be to take the whole calculation and say, well, I've got a constant and it has this for seven significance, this value for seven significance. And if you want to think it's the fine structure constant, you can. And indeed, if it works at 37 significant figures or 2,342 significant figures, it would be very hard for anyone to say that's not the fine structure. Well, except that I haven't got all of the seven. So, in a sense, it is numeral, numeral, but then there's some... It depends on your theory. I could assert that the spur of 2 plus the spur of 3 is equal to 5, and you'll find it works to a few decimal places. not 4,300. That was my thought. Yeah. I'm still not clear. Oh, take all the answer, really. Do you think it's fundamentally different from here? Absolutely. Yeah. Yeah. Agreed. Another question? Project the physics in as soon as you can. Yes. I guess that's the present. and being a process and generating process, and he attempts to take concrete purpose to someday convince him to use abstract algebra. It's unlikely, but... I think it's unlikely, yes. The attempt has been made in the past. I don't want to sound ungrateful to Pierre because in the very early stages, it was his approach which convinced us to me that there was something that happened with the culture you thought was this? I was always opening, you know, the, um, uh, universe and so on. I now don't want to have anything to do with it. It was a great help to us at a certain stage in the development in, in, to me, in convincing me that, I mean, at that particular historical stage, the aims are often not very clear.

1:12:30 Well, shall we meet here at 3.30, which time are you doing? Now. Now. Should have been about half an hour ago. So perhaps I should probably close the meeting. They're going for the bun shop to begin this afternoon's discussion. When is 10? I'm sorry, I've left this boat because I'm in track home to pick up the den tomorrow from the... I'll stay on the night. I'll stay on the night. I didn't want to go on that morning and I thought she would be away. As it is, I received a great chance to stay tonight. I have a talk. Possibly. Thank you.