The topological nature of electrons / discussion

0:00 Thank you. No, it's OK. It's all right, no, I'll put it down there. That's why the William had to order for now. The case is not there. No, no, no, it's OK. I don't like it. It's more stable than mine, that's your thing. It's OK, don't worry. Thank you. and words to tell you who I am, where I'm from. I was home in China, and I had my university education, master education in China in solid state physics and metal physics. When I came to Chavez University of Technology in Gothenburg to do my PhD, I was doing micro-analysis of semiconductors. And in that period of time, after I finished the semiconductor, I moved to semiconductors, this experimental work, and then moved again to semiconductor films, and our biomaterial systems, model catalysis systems, and eventually now I'm working on semiconductor physics to produce new lighting source. At the same time, I work as a company and be responsible for technical development to develop another kind of lab.

2:30 It's really my pleasure to be here today, just to present the work I've done in my spare time. It's my gratitude to George, to give me this opportunity to celebrate the... So... I beg your pardon? Well, the topic of my talk will be... electrons with the polytron. As usual, when we talk about other polytron, we don't really talk both at the same time. We talk about a real one in our universe, not the other universe. I will speak more about electron than the polytron. When it comes to the connection of the electron and the polytron, then I will point out what is the connection. But the The basis is that whatever theory you have, or description of the electron, it should be put on the same footing as for the potential. Ah, yes. That's better. This is very strange. I have deleted it, but somehow it came back again. It's not the wrong version of this. Because when I was putting it, it says this mold is called the electron. I thought that was funny. When we talk about electron, there is a mold for moving in the electron. I'll jump this fast. This is my name, Chiu Hong-Ku. I'm from Godfrey University, Department of Physics. So, yeah, that was even worse. It was even worse. I was too playful. The content that we talked about is the paper I published sort of recently in Fisk's essays. This is the cover page. You've got a paper and this is the cover page of the paper.

5:00 And this is the brief content of the paper. The title of the paper is The Nature of the Lecture. I feel it's kind of, in a way, impressive, but anyway, I took the title. So I start the paper with describing the concept of electron from the world when it is conceived into the history, how do you see the history of electron, in two perspectives, one is like time sequence view, the other one is the event, the time sequence and also the event sequence, and then it was sort of theory to have developed during the years. And based on that, I asked myself, what is actually missing? Do you mean something? And it seemed like it did. So I was working hard to get the structure and then to see if it's possible, based on this structure, put all the properties of the electron into the structure, as well, more or less, I execute with it, and we see, and then this, yep, I use this one as kind of working hypothesis, see, this is true, and what is going to happen, and then the formulation is going to be a self-consistent test, and as a consequence, at the same time, and then afterwards, so So we refine the postulate, we rewrite the postulate again, and I describe what is the implication of the work, and then I conclude with some comments. But I will not go directly for this one, rather it will be kind of a junky step. There will be a lot of things missing. Hopefully, one second. If you can follow the text, if you want to do it, or you can read it afterwards. The whole thing is actually based on this equation, and I, let's see, it's probably difficult to visualize it at once, or at once, what this equation is. Actually, it's the

7:30 parameter equation for what is stripped, this one, and I got it from Hermann Weil's book, or the concept of a dark green surface. So then I will come to change this one to the structure of the electron, I can call it, because as you see, you have two parameters here, the sizes here, and the rest is this kind of phase or time. So by varying these sizes you have a different kind of structure so this is a bit of logical yeah this outline would be first of all so the electron has been knowledge what it is and there I will not give like a technical justification for why we have to work on this thing because if say my reasoning is like at once, if you don't have one good reason, you need many reasons. In this case, probably you also need a lot of reasons to say, well, you have to work on this thing, or some other people do think it's necessary. But anyway, I would just say, somebody think it was a question. And then, I'd like to point out the two views. One view is a one-flag particle, which is kind of orthodoxy, and the other one is, we can find the topological structure which is not just a void. And then, in following that, we will see what we call something simple. And then, while the subtlety comes, the set in, in the world, in the simple structure, And then we mentioned something subjective, whether it's good or not, we'll have this open for discussion. Then the postulate is, I named that structure as hippieus helix, the question is, will it be an electron or not? And then I will tell you, in this part it's going to be the formulation briefly going through how we derive all the properties of the electron we have set here. And then in

10:00 terms of physics, geometry and topology, and then later we will think, I would like to draw your attention to say that this is a topological structure which has been overlooked perhaps in mathematics or in physics, surrounded by everybody or everybody else. And then there will be some discussion on, based on the structure, some discussion about arts, mathematics, and physics in terms of perception. And eventually we'll come back again to compute the equation for describing the electron in this parameter equation with all the constants set. And finally, I would like to share with you what's in the cycle, something I have thought after this work was done. Yes. So, the way normally electron is described was electron is a point-like particle, a particle, point-like. When you say it's a point, it's imprecise, because you can also have a geometric point. When you say point-like, it seems like more precise than actually inherently imprecise. But it has a mass, we denote that there's a mass, but there's an M, and a negative charge E, and we know also from relativity theory, the mass would change with velocity. And we also know from constant scattering, we have constant wavelength of electrons, which is H, T, Y, and Y, M, C, where this relative reliance in vacuum and mass of the electron are not constant. And after the other one, you have the wave particle to the galaxy, you also introduce Dirac, introduce the wavelengths for the electron as Dirac wavelengths, that replays the function of this mass and velocity. Then eventually, if you want to put in order to introduce an atomic spectrum, one has to introduce the concept of spin, which is one-half, which is one, and the magnetic moment of each bar divided by 2mc.

12:30 In 1930, Schrodinger derived the significance of the right theory, but not many people believe in this kind of mathematical aspect. Anyway, we put it here. In his work, when he has this If you have this kind of tripling motion, the frequency is 2mc divided by H-bomb, and L-tune is similar, but I mentioned some word that has linked or complemented in it. And this is well-known, Dirac developed Dirac equation, where there is a current entity which was not as old in the beginning and later it turned out. it has to be an antiparticle of the electron, named positron, and there is an association of the electron to the positron. And this was later, after the war. So, a matter of measurement, well, actually, first, the interpretation, because later there is an obvious magnetic moment associated with the electron. The measurement revealed it was not this much, and then they come to quantum electron dynamics to make this correction. So as I said, I will not give technical justification why I could do it. I happened to find a sentence written by Roger Penrose in his reading book, World to Reality, where he talks about reality talks about the questions what and why questions and answers I'll try to read it hopefully not too boring the modern science will be cautious in the tempting answer to the why questions as best as well as versus to what yet the questions as to what and why are frequently supplied with answers it is considered acceptable to do so provided that the questions are not asking about reality at its deepest levels. Well, we expect an answer to such a question as the following. What is a cholesterol molecule that's made of? And why is uranium nucleus unstable?

15:00 Yet, some other questions were my post that caused more embarrassment. What is an electron? He felt this kind of... First of all, it's a question. And secondly, it's kind of an embarrassing question. Well, hopefully the answer is not embarrassing. And then there is, there are some more questions posed by a theoretical physicist. He asked, what is really an electron? What is the structure which gives a spin? Why there must be a positron? And what is the mass? Why and how the electron manifests with properties? And what is the interaction between two electrons, or between the electron and the positron at a shorter distance? In these questions he said, in fact, the history of the electron showed that although there has been a tremendous progress in detailed applications of the electron theory, the progress in the foundation of physics is very slow. Yeah, another person, this paper I found after everything was done, so I thought it was still quite illustrating to present again. It's fair to say that there is today an implicit, explicit tendency of not encouraging inquiries into the specifics of shape and topology of particle structures. This work, this work philosophy is based on perhaps a vague conviction that the pursuit of such a knowledge has no meaning for what the goal is believed to be outside of human knowledge. In fact, point particle rather than the finite size parental structure are now declared to represent physical reality and some other things. In characterizing the present situation, it can be noticed that the physical theory is usually dominated by the use of point particle obstructions, yet no physicist truly believe in the reality of point particles. It's merely used as work hypothesis. In virtue, it's mostly only preventing the two-way imagination from going wild and making structure assumptions about the final part of the structure. Like, I understand. I mean, if you spend all your life doing this without getting in the way, so that's going to be a tragedy. So, when you think about the electron, I'm thinking about it's kind of, must be from

17:30 sort of the beginning. So Jonathan says, and probably has all that in person. And after that, let that be light, there must be the electron. So there has to be something which is simple, which is kind of strange. But then I would like to invite you to explore the simplicity and to the complex structure, see what it is. Well, yeah, let's say, go back to God. They accept that if there is God, he is a great mathematician. And another one, Einstein said, something has roared. So the laws and nations have not exhaust God. Something with God. And there's one more. He said, physics is simple but subtle. And the question is, how the simplicity and subtlety will be combined to get something really is quite the thing. First let's start with say if you get the simple structure you can get is a point. Probably nothing more simple than this. So you move the point you can get a line and move line, you can get a surface. Moving the surface, you get a cube or any other three-dimensional objects. So this is one with complexing the point. And let's continue with this one. So it can also extend, we can also get a curved line from a point and this one you can continue with another one which will be a circle by moving a circle one way over another so you can get a sphere that's by spinning but if you do a more So if you translate it, you get a cylinder, or you get a torus. So these are the most, probably the most common objects, or geometrical objects we have seen.

20:00 And then the question is, is there anything we can call a subtle? The other thing I can see is here you get the Euclidean geometry and with patograph theorem. but this one it comes something special that's the pie because you have the same terms of the sphere is to to my heart and these things are also in my perspective with that but then if we come come back to here and ask another question what happens if this guy is not lucky he goes one turn without going to to the stopping point. So what you get is something that has two times. So if you start somewhere like here, it goes around once, but without enjoying the end because it's unlucky, then you have to have the second chance in order to get to a point so you get two times something and this one let's see what's special with this one yeah i call it i call this one because it goes like if you start it is not to first of all it's not two dimensional object You can see, if it is to the mansion, then they go back by to the pipe. You have to lift the third dimension in order to not meet your starting point. So you go once, you have to either up or down to that place, below or above, then again. So it's like half way, half, one circle up, one circle down. Like helix, but it's close. It's too close. close. So first of all, I have 4 pi periodicity instead of 2. Secondly, I realized after several months of work, this thing actually is the edge of the nebius strip because you can see the edge itself. There is kind of reality there. And the third thing, it has a handedness. Everybody

22:30 knows how made of him is a strip. So you have a long strip of paper, you join the end, but not glue them together, but rather twist it first, then glue. But you have two ways. One way is you do this, and the other way you do that. Then you've got left handed, right simple object which possesses a parity. So this is more easily simplified by actually looking at the two movement strips because it's in a mirror relation. So this one gives you one hand in this, the other hand in this. It's very easily done with the program because earlier, before there was the program, it was very hard to imagine what was going on there in space. And the reason I got this structure was that I once read this cartoon book, Sidney Harris, he said, the trouble with me is that things are only one side in the other question. But I thought it was a question with me earlier was I did not realize there was handedness in this object. I thought there must be something very interesting associated with the structure. Yeah, so then it comes to what I call the postulate. I said the topological structure of the electron is close to term helix, like that, that is generated by circulatory motion of a mass-like particle, mass-less particle, at the speed of light. So I made a MATLAB drawing here to start out like this and one about like this. So then I tried to see if the structure will give the properties of the electron and the starting point was from here so if a particle we call electron has a mass and then it has energy and it also has a frequency on each bar so then you can do follow uh de Broglie's quantizationization where you have two pi r equals to wavelength of the wave associated with with the electron, and in this case, you just write two parts, four parts that, you get this one, and then, you try to derive, you derive the radius of this

25:00 uh, felix, in, in relation to the constant wave length, and, and you, you got spin, you got a magnetic moment, which will be, if you just think of a coil, of currents going twice, like that. So that's exactly the thing we measure here. Eventually it's actually, well, I didn't do the rest. You will get charge times the radius. That's the end result. Now if you have this structure, so we know that the electron and post-translation The first thing is, they both have the same mass, but in terms, because they have the radius here, and the relation to their mass, the statement that they have the same mass will be equivalent to the statement of radius, so they have the same size. And secondly, because one has a positive charge, one has a negative charge, that thing can be associated with the widening of your structure. So here it introduces a winding number and the parity, the sticker, which will be widened right-handed or widened left-handed. I compare this population with the Rack equation, so what you see is both will give you a spin and a magnetical moment of the electron, and both have the relation, the association of the electron and positron. And what about that is the spindle in the Rack equation is actually the same as as this helix because both has four pi very opposite in the case of the rapid version you have two components describing electron spin up and down two describing like a position up and down but in this case in this case you have you have two structures one left and right you can spin while the other states and then there is this uh like I have said, it's a circulatory motion. That one can be associated with

27:30 sharing the state of the momentum. Yeah, what you got is, you got one frequency, which is the state of the momentum frequency, which will be twice as the delaying frequency of the electron. with the structure and also five structure constants. So I can derive also the five structure constants which will be the classical radius of electron in the classical electron dynamics and this radius this is the radius of this one and this is half-flip of this structure. So then by doing your integration, because I told you the magnetic moment, let's bring I do charge times the radius, but one concept above is based on like two terms ideally drawn structure. So one term is complete overlap, but in reality it's not possible to have, But if both turns have the thickness, it's not possible to have the complete overlap. So then, what it meant is that if it's something like, you have to say, you have first turn like this large, and second turn slightly larger than the first one, then the momentum, will attempt, like, each, the whole value, or the radius in measurement, should be the average of all the radii over pi. So what you have is basically to integrate all the angles from this one. So after this, you will get a relation where the R will be 1 plus alpha divided by pi, like this. And then this alpha will be defined as the half width of this structure to the radius of it.

30:00 So it's like, on one side, if you cut this one like this here, on one side it will be like this, on the other side it will be like this. Something like this. So that, because we know alpha is e squared divided by h bar c, so if you have a geometrical meaning for this one, there must be a geometrical meaning for the charge, because I cannot find geometrical meaning for this one and that one. So that means, if you think, if you ask yourself whether this one is more fundamental or this one knows which one is more fundamental or which one is less fundamental. It seems to me this one and this one is more fundamental and this one is less. So then what you derive is you actually derive charge square as exactly a twist of this structure. So it comes out like if you write it like this. So I'm going to continue with this one, see, here I found a little bit, yeah, I try to explain where the test comes from. So the test will be eventually e squared divided by pi h bar c. So then you can associate charge or charge square with twist of the structure. Eventually, you can also state that, say, that's based on Heisberg's argument, when he argued about the existence of fundamental length in 1930s, he said, well, you have to have a fundamental length because length and mass cannot be formed only by H and C, co-dimensionally. It has to be related somehow either like length, like this, it has to be like this. and he suggested that since length is more sort of intuitive to us, so we should introduce length as the format length instead of a kind of format of math. So if we see this structure

32:30 here, and it resembles the kind of curvature formula in mathematics. If you simply take, well, let's say if this is curvature and this is radius of curvature, then it's the worst proportion. And then if you take the action of the electron as the unit, and the speed of light as unit, you identify the curvature of the mass, and the radius of curvature So you, for example, you can expand the concept to a general meaning, but we can see how valuable it's going to be. But in a way it makes sense because the heavier the mass you have, the more curved the space you have. And also the heavier the particle, the smaller the particle, in a way it makes sense. I also checked the transformation properties on the structure. And not like Lorentz transform or other, but just three discrete transformations, charge parity and time reversal. It turned out that since you have the charge associated with twist, in other words, associated with parity, so the charge parity will not be individual or independent operations it's going to be one combined operation so this one will become one operation and time reversal operation still in independence and these operations forms like a community operation if you can act this And then the way dividing left and right is also different, you see. In this case, the left is not the right. When we see our hands, the left is not, because there is a mirror symmetry something with it. I cannot move my left hand to my right hand, except if I put my right

35:00 hand in a mirror. That basically says the right is not the left, but if you somehow inverse the right, it will not be inverse left. But rather it should be the inverse right is left, and the right is inverse left. So then this was basically content-wise, it was basically the first version of the paper. Then I submitted to a journal and I got criticism and said but everybody knows the election of the points so you cannot have this one with continuity and so then I said I thought I have to explain why they have such a large electron where you do have high energy scans where you see them as a point then I wrote an additional section there you can see here and for every probably cool, we have this relation. And if we put this relation to electrons in this work, we have also this relation. So then if you replace mass with this one, you get the size as a function of energy. So the higher the energy you have, the smaller the size you have. That means when we apply two electrons of very high very small. That's why when you analyze your data, you see whether they are very, very small, tends to be up to, say, 16 if you get to 200 gigawatts. We come to some implications of the work which is not so tightly related to the structure. The first thing is, because of the finite size, you get the finite self-emotion, self-mass, not like the classical election dynamics, where if you are in cross-zero, there will be a singularity. And then, you can also try to categorize particles, because this one is half spin, and it has two tons. but if you have one term, you have a spin image, and so on. And here, it is also possible through this relation,

37:30 and relation to fine structure constantly, to introduce the fundamental length. So, yeah, well now I've looked through the statement that this structure has been overlooked. People have not, in my understanding, people have not noticed this 2,000 helix thing. Rather, they have seen this one a lot. I think in almost all calculus books you can find Memeus' strip as a very interesting example to inspire students. And like in mathematics, in art, in Firewall Hits, if you want to go home, you'll know that. And even this is the non-tribunal Fagabondal in terms of Fagabondal theory. So yeah, there's a new book written by Clifford Pickover. It's specifically talked about Lincoln's trip. It's going to be quite soon, so you'll see. It's quite an impressive book. be claimed from its read, one book a year for some topics, different topics. Yeah, another aspect which you recognize is not theory. So when you see the first, like, the classification nods, the first five nods, this is not nods. And then the second one is this one, a nod table. Well, I reckon there's something missing here, because as you said, We have this one, right? Not, not, not. And this is something between not, not, and not. If we say not, not, not, it's not, not. So this is something exactly in between a knot, knot and a knot, which is this structure. So, this one should disappear. So, you see, first of all, you have one simple ray, and then you make 12 knots.

40:00 In between, actually, this one should be there. That was a problem, but because this one, well it depends how you say it, right? But this is two-dimensional object, and this is three-dimensional object. That's why when people start topology, they restrict themselves from two-dimensional space. They say, well, what's special if you make another term? circles, it appears it's still one. But if you lift yourself to three dimensions, and then it won't be different. But you're still topologically equivalent. In fact, topologically, you look at the complement of the knot. And that is that the complement of the knot depends on the embedding. Yeah. That's the topological. So what does that mean? It means that your argument is true. If you are embedded in a certain space, the complement is different. And you look at the complement as a topological thing. Let me decide. One thing I found from Bohm is that physics is a form of insight. and such, it's a form of art. So because in trying to understand this object and its relation to the nervous trip, it took me like half a year to see what is actually these things are, these things are. So I have learned to comment on something about this ambiguous figures and I call the couple of double perception. Typical examples. The first one is the negative. two, I think these are well known things. But if you look at this for a while, then things start to jump, because that's because of the perspective reversal, because your eyes perceive two different like visible images, the alternative, those automating them. And then the second one is this mass or head, but there are different names for this thing.

42:30 But anyway, this is based on the figure and ground reversal. So in this picture you see this as a figure, the rest as a ground. Well, if you take this one as ground, that one as a figure, then you have a totally different perception of the picture. So, and this is again, but this is another kind of reversal, it's the Rival Shemata reversal. So here you have two things, you have two things, if you focus on one thing, you see one, you see one, you see it. If you see the other one, you see another one, but I think a lot of people know... It's the same woman but after many years. So basically, if you identify this small black dance feature as I, this is Nose, you see a very beautiful young woman here, this is a kid, or if you identify this as Nose, this is his mouth, you see a little lady in the picture. But sometimes it's very difficult for some people to see both. But after some training I think it's possible to see both. When you're old enough. Psychologists say that when old people will begin to see this one, young people will begin to see this one. They have to make choice. So this is another kind of reversing. If you see this as a curve, or you see this one as a surface, because normally if you draw a geometric object, it's a cube, which is simply draw like this, but actually they can as well be afraid without concept. This kind of perceptual reversal is, I call it the boundary and in-close reversal. Because you have, let's say, if you put it in the right terms, you put a manifold and you have a boundary for a manifold. So, for both, let me continue here. So, yeah, that comes in a relation, simple, simple-simple-simple-minded relation.

45:00 I mean, there's mathematics and there's physics. They are kind of connected one way or another. Each one is connected to the other. There's no, like, one-way street connection. So, let me try to, for this statement I need another equation. Because this equation gives you the surface. Its generator is a segment. To move the line segments in space like that you get a surface but in in the helix case your generator is a point so this means this means say this one defined width of the band this this one can determine the diameter of it or the radius. Now I try 6, not saying this one is a real number, this one is constant. So that means I only do like this. So it's also interesting if I ask people how fast you can draw the biggest helix, and the biggest trip, if you imagine how we draw it, it would be very, very slow. But in this case, I can draw it very, very fast because I would create a new algorithm. Because this is one-sided surface and it has a list and has a good thing. So that equation would be the same as this one, And that's just the only difference is you have only one value for this one. So that gives me the conclusion. Different topological objects may share the same complete description. Or conversely, same topological objects may have complete different descriptions like this one. So if you turn this one, or draw it out and bend it anyway, analytical expression will be a little bit different, but it's still the same

47:30 for the logical company. And then, with that kind of reversion, as I said, voluntary and enclosed reversion, the association actualized of the Tufts theory. So that in those senses you see the connection of art in terms of perception, and the connection to mathematics in terms of observation, and in this one we need something about measurements, because, say, if you have a system with boundaries and with interior, the boundary itself could be the boundary or the interior. But when you're outside, you don't really know what you have. you're asking why you want to measure these results and I measure the other. There's no compromise but actually that there is full contents in your learning program. So that after this has been done and I was trying to, well the motivation for doing this was, first of all, I didn't feel comfortable at this point like concept. There are a lot of things I didn't understand. I thought probably it would helped me to understand more. And I think one of the things is the superconductivity, because we try to, when I work for superconductivity, if I know how experiments we can produce material and measure, and what sort of PC you get, and then you measure again, and then synthesis, you don't know what's going on, nothing to guide you to, like, high temperature. So I think in case if you understand the electron, there should be some help to understand some connectivity. But again, I've been thinking some new experiments, because most of the aspects of electron was more or less well established. All experiments should be done. But there are some things we're missing still missing. And that would look at the issue of asymmetry between a charge molecule and a magnetic molecule. Because in this case, I had lots of great thoughts, it's really dirty. But it looks to me, if you have a charge molecule like this, then you cannot have a magnetic molecule. Because it's the same structure.

50:00 From the magnetic molecule quantization condition, you have the charge times the molecule strain. But here you have a charge squared, which gives you the constitutive condition. Or the file structure constant. And then, when I taught my philosophical people, friends, and I said, well, this is something I felt very interesting. They asked me, what is useful? And I couldn't answer. and one day I found one from an Asian Chinese philosopher. He said, everyone knows the usefulness of the useful, but no one knows the usefulness of the useless. So I think in this spirit, I really admire George to bring us together here to discuss something sort of totally, probably to other people in justice. but we will see if we can find anything useful later. And as my personal pursuits to this subject, it seems like I have gone through the history of the electron, the theory of the electron and the philosophy and mathematics to get this done, this thing done. And my conviction to Art of Einstein's belief is that you know it will be sufficient to really understand the electron. And I think there was also another statement he made in the 50s where he was asked, nowadays you know people found lots of particles in this and that in the 50s. He said, what's your opinion? He said, I'd rather to understand the electron first. And then another interesting incident was I spoke to a mathematical physicist. I said well I've done this thing and I told him probably it's interesting because I'm not trained as mathematician I'd like to see the mathematical context of this work. He said this is not possible. It's impossible. You're inventing alternative medicine. If you're doctor, which is, he meant, contractual dynamics. And then I said, well, the difference between science and medicine is, for medicine, the

52:30 consequence could like kill the patient, because the patient does not have knowledge of what is going on. But with science, I can only influence people who understand. If they don't understand, this one doesn't exist. to talk to people, it's not like commercials, but this thing can only be communicated to people who understand. When they understand, they will know what is right and what is wrong. I don't have a possibility to poison them. So then, there was another thing, I thought I would probably send him a mail and say that, because he said impossible, and I said impossible you're associating the electron charge with the twist or you say the electron John's square. It's square, actually it's square. And obviously that leads to the question, well how is the electric field associated with this topology? Yeah, yeah, I'm working on that. I presume you were, yeah. I know how to work it. Right. What's your direction on that question then? Well, because, let's see, let's start with the mathematics of these space curves. But Gauss worked on this space curve in a higher dimension, yes, Gauss is in a higher dimension. But there was like more complex work done by some of the people using Los Angeles in the 60s, I think George White's time. That's a pretty long paper and it was also pretty difficult to suggest. And then it was a shot of a concise version. So we were, let me see, I find everything right. So first, you would define the twist. And then you have the book. The motivation for, let's see, this is on page 451. So, what you have is you have a, what he called, he defined as a writing number, and a connection

55:00 with a writing number, and a twist number. So, and the twist number is defined as the twist divided by two five. What it does is, if you have a script, like a piece of paper, it's very simple. So yeah, this one is flat, there's no twist. So if you turn it, like, two pi, then you get a twist. But, well then you divide it by two pi, that's just number one. So, and you can do it any other ways. Like, you get more two numbers and less two numbers. And then, in a way, the two is kind of complex, because you kind of get something between them. And then there's an 18 number, a writing number, he finds. And his work was more concerned with the biological subject, which is the supercolors of the DNAs. And then when Francis Crick saw this paper, the Roman Catholic average portion, I think it's so cool is that after Francis Crick's paper, the average biologist should be able to understand this. So then, because of the dimensional things of everything, so this one is associated with charge squared, not charge. That's something interesting. I saw George has a book upstairs, it's the physicist's conception of nature, that's the one dedicated to Dirac. There, Dirac had a paper. He was discussing about the phi structure constant, which is e squared divided by h bar c. And he said, well, this one is the nationalist, and this one is the square, and this one. And what he was talking about is do we believe, let's see, well, if we do it the other way, so it will be alpha times h-bar c, like this.

57:30 So now the question is, if this thing is fundamental, well, why is it more than the square root? you cannot you cannot start a square root and I go to the square because this this thing will be very uncomfortable in a way so that is it there's some it has some something you probably have to start think this one as an entity rather than this one but I don't understand myself In classical dynamics, what we always measure when we are claiming this one is more elementary than this one. But in classical dynamics, actually your expansion is actually this one. You don't really have a charge. You have a charge squared as a kind of fundamental entity. When you do a normalization, it is charged squared. It's not a charge itself. Well, the same is during classical mechanics. What we actually measure is the force. So you can say, okay, it's the field times the charge, but the field itself is proportion to the charge of the source. Yeah, great. So that's also an interesting thing. If we have our quorum of quorum line here as well, this is the force. And then the potential will be still in the square and will be par. So we have no idea if we want to put together in the cycle, which will be connected to my brain. it's kind of difficult to conceive. So you have one chart here and one chart there. And when you say, well, this guy produced a field, what if you don't care about this one?

1:00:00 And you say, well, this is my test charge. The definition of a test charge is, you say, this one does not include the distribution of this field. It only maps how large this field is without influencing this one. So then you move this around, and afterwards you get this one. But what happens if you say, well, I don't have test charge. And how do you get test charge squared in that case? Without just arguing for the dimensions, which will be, these things will combine the other force. Well, I'm going to skip the concepts and units. Okay, well, time is moving on. We've got two more speakers. Thank you very much. Can I respectfully request a German to move? Can I respectfully request a German to move tomorrow afternoon? Do you want to go tomorrow afternoon? Yes, I do. We haven't looked. Would you like to have a break? Yeah. Mark and the other one. Do you have another one? Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. So we have one of the talks after that. Let's read this after that. That's fine. Let's get it up. Er... Sorry, man. Sorry, man. Sorry. Thank you. There we go.

1:02:30 The only problem is that I tried to start from the stick that I got this morning, and I couldn't get it, but I suspect, at about 90% of that, that is a problem with my stick. Why don't you use your own computer? No, I need to print out basically to have my crib sheets. I think probably if I haven't prepared this talk to about 9 o'clock this morning, maybe I could do it out. That's great. Jim's going to go right now. We'll get shorter tones. What about that? I'm going to go right now. Yeah, I really have that idea. It's brilliant. It's brilliant. It's brilliant. It's brilliant. It's brilliant. It's brilliant. It's brilliant. It's brilliant. Stephen, do you want to try my laptop tomorrow? Um, the key to use is to... We've just got one talk. We've got one talk. Yes, I know. I realise that. We've just got one talk. OK, well we'll see if we can switch it.

1:05:00 Are you going to have to shake back my adaption? That's OK. Oh, you have his hand. That should be fine. That should be fine, yeah. Sorry, yeah. Yeah, I mean they do. What's the day is it? Uh, Napoli. Napoli. Napoli. Oh, it's a bit better. Yeah. Could you give them a... Could you give Ray a something? Oh, yeah. I think it's more... You just want to do a... You want to do a lot of things a dooblick. Well, it worked, it worked for Eliza Doolittle. Having told everybody, I'm an anarchist, I don't know. I'm not trying to be a referee. Okay, so, well, as ever, before I forget, I want to thank George for, inviting me here yeah I should also say I don't know whether you know I mean having the opportunity to talk you know meetings like this you know where we have I mean that was in kind and given us nice lots of time to speak I mean this is a kind of great motivation to actually do the work you know so having an opportunity to speak is actually helps one forces one i suppose to think it's hard about what one is trying to do so um uh just to say like some of the other people here i'm i mean like nick i mean i i sort of see a bit of parallels in there because i started off in i was actually a PhD student of Dennis Sharma in Oxford in the 1970s doing Classical General Activity.

1:07:30 I went through agonies in the last year trying to decide whether to carry on with the subject. I had a post-doc opportunity at Dant with Stephen Hawking, which would have kind of involved in quantum, quantum GR, and I couldn't get my head around quantum mechanics at all, despite, you know, little courses and stuff. So, I, that was sort of partly influential in deciding to change fields to something more, let's say, societally useful. So I've been, last 25 years or so, I've been doing climate, weather and climate research, and in fact Basil asked me I mean if there's time and he said I've got a kind of public talk I give on verbal warming and I could I could maybe I could maybe give some of that later on if you're interested so that's what I've been doing but um you know it's a bit like a Jesuit education I think if you do if you do sort of fundamental physics it never quite you know you can't actually quite shake the oven as hard as you try And so, you know, the sort of stuff about what does quantum mechanics mean in the context of gravity and so on is sort of has been dogging me. And I suppose what I'm going to try and bring to the table is some perspectives, which sort of have been brought from my own more professional work on non-linear dynamics applied to the atmosphere. I mean, after chaos theory, in a sense, I mean, modern chaos theory arose from actually a good colleague and friend of mine, Ed Lorenz, this is L-O-R, this is Lorenz without the T, who actually, you know, derived one of the prototype chaos models by trying to understand the unpredictability of weather. And, of course, the great achievement he made was to show that this unpredictability could be explained with a very low-ordered, unendful system. So, more cognitive stuff in the second talk. Well, actually, if it's acceptable. So George, for example, sent around an email asking us to, you know, not perhaps launch into all the technicalities right at the beginning, but say something about motivation and basic What I thought I'd do is maybe spend, hopefully, I don't know, 20 minutes or something, just talking about the motivation for what I want to talk about.

1:10:00 And I won't talk about any kind of mathematics as such, I don't know if there's any equations in these first few slides. So I'll maybe get to the point, you know, where the maths might start and then leave that for tomorrow. And then if there's still interest, I'll talk about finding change due to the muscle of the function. So, but I wanted to, you know, because I don't want to kind of run out of time tomorrow, and I don't want you to get, you know, you'll start, I think, to lose concentration if I used to do an hour and a half of this stuff. So let me kind of break it up. So I'm going to spend 20 minutes trying to describe, this is my hobby if you like, which I entitled the mysteries, plural, of entanglement. And that's come from basically a quote. So the first few slides are just quotes. And the first... So the two mysteries are taken from Roger Penrose's recent Megatone. I'm sure some of you have seen it. I'm still kind of curious that almost everything is in this book, except perhaps the most important stuff you did, There's nothing about some theory, so that's an interesting, psychological question. I will ask him next. Yes, I think it's because it's established, it's uncontroversial. Oh, he only wants exciting stuff. Anyway, so here's the question. It seems to me there are two quite distinct mysteries presented by quantum entanglement. So number one is the one that he says everybody is aware of. And this is something that perplexed us from the moment that everyone was discovered. I'll show you. How will we turn and then EPR and so on crystallize the mystery? And how do we make sense of this idea of non-locality, essentially, in terms of ideas that we can comprehend? But then he also, he also poses this one, which he says is something which people don't tend to ask, but, you know, if you take Schrodinger evolution seriously, then all the time, you know, as the world, the universe evolves, things are just getting more and more entangled.

1:12:30 everything's getting entangled with everything else and it's becoming a kind of horrible clutter of entanglement and it goes on and on, it increases increases, but yet, why do we kind of seem not to really notice in our direct macroscopic experience of the world sort of ever increasing entanglement so this is his second mystery I want to present let's say proposals to both of these two, and in a sense they're both They are proposals, they're not by any sense of the word mainstream proposals, but this isn't my job, so in terms of my career, it doesn't depend on it, so in terms of I don't really care if it's crazy. So the first point is to make the claim, and I try to give some justification to this claim, but we will be able to understand quantum entanglement conceptually. Therefore, as and when, let's say, quantum theory can be recast and embedded in a non-linear deterministic theory of some larger type. Now, the particular type I want to talk about are ones where there are very strong dynamical restrictions on, let's say, dynamically allowable states. and in particular the restriction is to a very small dimensional subset of states so this will become more obvious what I'm talking about very shortly now the second point which is definitely more controversial is that on the basis that as and when we can do this then I think we will find that we do indeed notice entanglement in our direct experience of the world and we already call it something, we call it gravity So, I am proposing that gravity is not some sort of extra force that we quantize along with electromagnetism and weak and strong interactions and so on. It's actually a basic property of quantum theory, but not quantum theory as we understand it now, but quantum theory as we will understand it hopefully in a sense which will make entanglement more understandable conceptually. so in some sense I do see this proposed as a little bit like when we go from Newtonian physics where gravity is a force into GR where gravity is not anymore a force

1:15:00 it's just a property of the state vector in other words metric, it's the curvature so in this framework gravity is no more a part of the Schrodinger Hamiltonian or something like that it's just a property of the state vector of the entanglement So, let me just, so I'm going to, so this second point will really come in the second tomorrow, so we'll sort of really get back to these basics, because the whole motivation for this was this first issue about how to make sense of, of, um, so I've got, uh, just like the previous speaker, a few kind of quotes to start with, I mean, uh, I think there's no better person in the field than Bell himself. So this is from his paper Free Devils and Local Causality, which I got from his book, Unspeakable and Unspeakable, in quantum mechanics book. So he says, to start with, quantum mechanics is not locally causal and cannot be embedded in the locally causal theory. So that's, you know, that's essentially the message from from the Bell theorem, that the bone inequalities, which satisfy if you have a locally causal invariable theory, are violated and therefore non-locally causal. Now, he then goes on to sort of emphasize the point that that conclusion, the conclusion of this sentence here, depends on treating certain experimental parameters, like the orientation of polarization filters or orientation of Stern-Gerlach as free variables. In other words, you derive the bell inequalities for hidden variable models by kind of assuming, well, the hidden variables, they don't know exactly what measurement you're going to do, but they're kind of prepared for any particular choice of Sto-Gallard orientation you may choose to do. Okay, so the whole derivation of the inequalities treats these experimental parameters as free variables. Now, Bell points out in this paper that, and he's quoting from, I think, a paper by

1:17:30 Shimoni and others, about sort of the metaphysics of this issue about free variables so he says in this matter of causality it's sort of an inconvenience that the real world I mean I think he's this paragraph is slightly said slightly tongue-in-cheek but it's like it's like it's not as I can understand but he's responding to a paper let's say by Shimoni which which which raises the kind of metaphysical question about what is free variables really mean so he says in this matter of causality it's a great inconvenience that the real world but it's given to us once only. We cannot actually know what would have happened if something such as one of these experimental parameters had been different. Because we can't repeat an experiment changing just one variable. You know, at the very least, you know, if you do the experiment of changing a variable, it'll be at a different time. So the hands of the clock will have moved or the moods of Jupiter have moved or something. So this notion, you know, what does it mean to think of, say, free variable uh is kind of is metaphysically kind of loaded with difficulty but in the sense bell then goes on to say you know frankly i'm not this is my interpretation of trying to read this i think he's going to say well this is kind of interesting from a philosophical point of view but you know i'm a physicist and i don't really care about these philosophical issues as far as where I'm dealing with physical theories, and physical theories either have free variables or they don't. So, you know, he says physical theories are more amenable, if you like, than the real world in this respect. We can calculate the consequences of changing the free elements in a theory. They may only be initial conditions, but they may be certain parameters and so on. But we can explore the causal structure of the theory. So his claim is that, you know, The Bell Theorem, Proof of the Bell Theorem, is really an analysis of certain kinds of physical theory, and I've sort of emphasised that point because it's something I want to come back to, because for me this issue is a sort of, it's an interesting one, the fact that, you know, in reality we can't actually keep everything fixed and just change the the parameter of some experiment, because things at the external world would have changed.

1:20:00 But the question is, can one try to address this issue within a framework that Bell himself would have felt comfortable with, in the sense, are there certain kinds of physical theory for which these types of Shimoni-type metaphysical questions are brought to the four. Now, this is the last bit of the quote. He says, contemporary quantum theory, as it is practiced, do have three external variables. So that's fine as far as contemporary quantum theory. But what I want to address here is, if you like, a different kind of physical theory. Now, at this stage, I don't want you to even think about whether or not this type theory is something in which quantum mechanics can be embedded I mean I will make the claim later on that perhaps it can but at this stage let's not go down that road of whether this has got anything to do with quantum theory or not but just try to think about the consequences of the Bell theorem with respect to this kind of physical theory now the kind of physical theory I'm talking about is, this is the famous Lorentz, the meteorologist Lorentz, attractor. So it's a chaotic model. Now, I should at this point say that many people have, or at least a number of people anyway, have addressed the issue of whether chaotic dynamics can in some sense be brought to bear on the Bell problem. And the general concern, for example, Penrose in one of his early David Deutsch discusses it, I'm sure a number of other people did. And their view is, no, this is irrelevant as far as the Bell theorem is concerned. The Bell theorem addresses wholly different issues than have got to do with chaos. However, when people of that type, Henry's Deutsch and others, talk about chaos theory, they're basically talking actually just about the differential equations. So this flow is described by three non-linear coupled ordinary differential equations. And when people talk about chaos theory, they refer to just those three differential equations

1:22:30 as the defining systems. However, when I was brought up as doing maths at university, I was told, you will mark down if you try to solve an equation without taking a differential also considering the boundary conditions or the initial conditions. So a system was not only the differential equation, it was the boundary or initial conditions as well of the climate system. And what I want to do is to consider a system which is governed by those differential equations, but a system which, let's say, is initialized or lies on the invariant set, or in this case the attractor set, of those differential equations. Now, chaos is often used to just denote some sort of unpredictability, and I want to slightly get away from that perspective, because the unpredictability is not something I consider to be of primary importance. And I'm going to actually use a phrase that Lorentz himself used in his, sorry, where are we? Yeah, Lorentz himself used in the title of his paper, the 63 paper, on chaos. He didn't call it chaos. The word chaos only came about in the 70s when people rediscovered Lorentz's work. He called it deterministic non-periodic flow. And I want to call this system I'm talking about is on attractor deterministic non-periodic flow. So I'm talking about flow that is on this sort of invariant set of the system. Just as an aside, This is something I have been unable to actually ascertain rigorously whether this is true or not. I've contacted a number of my colleagues of a more mathematical nature than I am to ask whether they think it's true, and everybody says they think it's true, but nobody seems to have come up with a definitive proof. It's known, for example, that the Mandelbrot set, which is that sort of quadratic mapping of the Argand plane, produces a fractal. that's known to be, so membership of the Mandelbrot set is known to be recursively undecidable in general and my belief is the same is true also of these dynamical system attractors

1:25:00 so for example if you wanted to prove rigorously that a point P, sort of a random on the plane, lies on the attractor then one condition for example would be that the trajectories, the orbits under the set of differential equations from P would have to repeatedly pass through an arbitrarily small matrix of P. That's clearly something that it's going to be, let's say, difficult to do by that time recursively. So I think this is true, that this meant... So if you're not on P, you can recursively determine that you're not on P, but knowing that you are on the If the P is on the attractor, it's something that is unlikely likely to be an uncomputable or an undecidable proposition in the final decision process. So that's a side-to-side, but we'll come back to that again. Now, so just I wanted to say, I said that I'm trying to de-emphasize this word chaos some unpredictability, and emphasize other aspects. And I'm emphasizing some of these other aspects because of the relevance, the possible relevance, to the bell of inequality and such. So one particular sort of key thing, I think, and there's something that certainly, you know, Lorentz, nobody before Lorentz had guessed it might not be true, was that, you know, some is interested in turbulent fluid mechanics. And it's known, you know, if you look at a turbulent fluid, it's got potentially zillions of degrees of freedom. And the view was that to explain the complexity of turbulent flow, you needed zillions of of Kaplan's differential equations to describe those zillions of degrees of freedom. And, you know, what he was able to show was that completely non-periodic behavior, so nothing repeating itself, looking apparently random, behavior could be generated through motion on a very low-dimensional subspace, You know, for example, n dimensions in a state space that could be 2CM, for example. So this, for me, is getting away from unpredictability and saying one of the key aspects is that

1:27:30 you can generate complicated, very complicated, apparently random behaviour on a sort of invariant set, which has very low potential, very low dimension, compared to the number of degrees of freedom that the system may have in reality now a second second aspect or second property of this type of deterministic non-periodic flow non-linear a non-linear property is that you can and this is actually used in practice a lot in in sort of the practical studies of chaotic systems is that you constructors will reconstruct the whole geometry and shape of the attractor in face-to-face by just monitoring or measuring one of the degrees of freedom of that system so for example with the Lorentz system that's just got three components you could just take the Z component and just look at you know measure the z, the value of the z with a certain, every sort of t seconds or something, measure z. So you produce a time series of just one of the degrees of freedom. From that time series, you can reconstruct the whole three-dimensional, or the attractor as it lives in three-dimensional state space. So this, in a sense, is quite a dramatic thing if you think about it. I a bit like saying, if you're listening to Beethoven's Fifth Symphony, could you reconstruct the entire symphony by just taking one of the second violins out and looking at the musical score? Well, you could. I mean, all you've had is the musical score and the second violin. So, you know, this is, in some sense, runs contrary to perhaps one's intuition. But here, it's like saying you can take just one degree or three thing out and solve it And you can know enough about the entire system from that just about one degree of freedom. I just put here shades of Mars principle. I mean, this kind of vaguely reminds me of, you know, looking at the inertia of just one little particle locally. In some sense, that's, if you believe in Mars principle, it's telling you something about the mass of the whole universe.

1:30:00 Jim, are these theorems? These are theorems. This is called the Tarkin's Embedding Theorem. in non-linear dynamic subsistence theory. Yes, indeed. What's a DOF? Oh, sorry, degree of freedom. This is a degree of freedom. So, in other words, one of the many dimensions, if you like, that make up state space. We saw, for example, if you had a gas and you would just follow what molecule of the gas was sufficient in a long time, you would be able to... of the one of the yes that's right if it was if it had this underlying um so what's going on by this underlying type of oh i mean it has to be governed by a loader yes yes that's right and it has to be non-linear absolutely absolutely it has to be known yes it's less counterintuitive that you think you have a bunch of jazz musicians and you know them very well then you could actually sort of except another way of sort of looking at this this I mean it sounds related to this second point here is that you could take one of these degrees of freedom one of these direct directions in state space, even though energetically, you know, it explained like a zillionth of a percent of the energy of the total system, so it would be very unimportant. If you perturb it in an arbitrary way, you will almost certainly, with probability one, in the sense with respect to the continuum measure, if you like, with your state space, we'll take that system off the attractor so the attractor lives actually for these for these chaotic type systems the attractor is actually in measure zero has zero measure with respect to the continuum measure so this has a fractal structure in this low dimensional space so if you sort of slightly move the state off the perturb the state in some arbitrary way maybe what you think was

1:32:30 small perturbation. It will take it off the attractor as a probability. But then it will go back to the attractor if you let it evolve. Well, if you allow the system to evolve under the differential equations, it will then go back towards the attractor. What am I trying to say here? What I want to... I'm going to come back to Bell in a second. back to your your point what i want to think of here is is a system which if you like is the is the is is the is the is the system is the is the um is the attractor set itself so i want to think conceptually for what i want to think about here i want you to as an intrinsically defined set independent of how it's embedded in in this euclidean state space um this reminds me you know when one tries to talk to you know people lay people about you know people often ask why how come the universe you know you say the universe is somehow finite but it's got no no boundary so you say well imagine you're an ant on a on a on the surface of a football machine. That football has no boundary, but it's finite. And then you say, well, you have to just imagine the universe as a three-dimensional...