Abstract quantum physics - a category-theoretic view of quantum computation

0:00 It's all in apple pie order, and that's your mobile, thanks very much indeed, which I didn't have to use, obviously. Thank you for watching this video, please subscribe to our channel and give it a thumbs up. I just kept it locked and I haven't touched it since you gave it to me. Lou, thanks very much indeed for the invitation to come to dinner, but I've just come into a wall. I'm really feeling tired now, and if I'm going to get hold of her to come and check in tonight, I think I should go and do it now. So I'll take a rain check, if that's okay. Please give my very best wishes to Diana. It would have been very nice to have seen her again. Um, okay, I'll take that stuff, and you were going to print out this stuff, the, um, sort of like a meeting for me, the 14th to the 17th, that would be very helpful. It's time consuming, I can probably just get the information from the people downstairs and they administrate this office. Yeah, that would be helpful.

2:30 It works okay. It's not like I'm going to need to do any work on the file, so a PDF is fine. No, just do it as a PDF, that would be perfect. Yeah, it's just I have to do it as a computer. If you'd like, I've got a full month. I'm sure you can pick it up. No, it's been quite exciting. The last, you know, sort of two or three weeks has caught up with me. Let me see what I've got. So, making all those assumptions, you don't... Oops. Majority disabled. Take the sub to... Take the cube root of that integration and you go away. Oh, that's the stuff I was copying in first year, isn't it? Ah, we're in the fine structure concert now, aren't we? I thought you might be! No, it has to say, it is the obsession of some, you know, very interesting people. Oh, it's hugely interesting! You know, the great people have got an obsession with the fine structure concert, don't they? You think you've got some incredible, you know, it gets it all out of the great and deep people that grew up in CERN, but Cartier hasn't paid attention on the web to ask for the details. So, you know, there's some very, very, very clever people who are worried about the fine structure problem. The model I'm using is just... I tell you what, you know, it's just... You must tell me about it. Have I not seen some things that work? Well, I've just explained... I have, so I'll go on. I've announced a repeated order to Mick for a second first time. The world wants a copy of next week. Do you guys want any of this information that's just running on the meeting next week? This is the schedule for their conference, actually. Quantum gravity and quantum information, it's called, isn't it? I can make three copies. That'd be great. I can make four copies. Oh, Dr. Hooft coming. That's some big... You already mentioned, and, oh, Patini-Macropoulou.

5:00 Oh, he's got lots of big names in quantum gravity. No, no, I am very interested. No, my field is, in so far as I could do, seriously said to have a field at all, it's category theory. Oh, right. I haven't been to some academics for 25, 30 years now. Well, 25 years, no, the last time I was here. Oh, I know, it's a story. No, I did my first degree here in math and then in philosophy in 73. I did a PhD in London. I've talked about five years and then got out of academic life altogether, but retained a sort of great interest in, especially in foundations, in cathedrally, and have been sponsoring these meetings over the last ten years from the revenue of my business, which is a, well... Do you have any waxing about computing? No, not me. No, no, no, that's the one thing I never wax about. The one thing I've absolutely never waxed about is computing, quantum computing or any of that. No, absolutely not. Are you a fan of quantum computing? I don't know enough about quantum computing to tell. I know your stuff, and so far as it feeds into foundations of quantum theory, then I find it very interesting. No, the hardware side of quantum computing is something I know very little of. I don't think anybody understands the hardware side. They've got to do with our experiments. Yeah, there are these guys who've got this thing underneath the legend, either. I'm told that after... 59 or 51? Well, the last time I heard, they'd actually factorized 32. About four years ago, they could only just factorize... Oh, 15. I heard they got it up to 30-something. That may be just a rumour. But it will be... the decadence, obviously, is a tremendous technical problem. OK, so it's just the 14th, 15th and 16th. There isn't a 17th. No, 17 is on the back. Oh, sorry. I'm not looking at two sides in the attic. Oh, Lee Smolin is... Sorry, is J. Smolin... J. Smolin is not... It's nothing to do... It's not on this print of time, though. No, it's not on this print. J. Smolin is a... It's from IBM Research. ...quantum information theory. So it's nothing to do with...

7:30 Okay, so they haven't actually got titles yet, except for a couple of them. There will be some other things as well. For example, I'm doing a so-called blackboard presentation, which is like a poster group session. I'll stand at a blackboard during some designated time, and people come and talk to me. I will have a blackboard probably the size of this one, and I will divide it into two halves, and in one half I will have drawn some equations and things. And in the other half I will be willing to scribble and see how that works out. Yeah, well the thing on class is only a one-day workshop and it's the stuff that Bob was talking about today plus Samson Obranski's stuff which I, and some French contributions. It looks quite interesting but not as interesting as this. This certainly looks interesting. But Chris was really following around and called for taking skin and something like that. What about twisters? I understand twistors came out of the refinement of spin, and I'm just wondering if there's something we're missing by speaking only of spin networks, or is it just a... Oh, the whole development of twistors, which is a little different from the spin networks, but in Penrose's mind, I'm sure they're very close to each other. The key point about twistor theory in terms of complex variables and things which are... All of these connected in the sense that a light ray could get between them are touching in the twister space. So you get a different, you know, using kind of algebraic and projected geometry ideas. And you're using this extra geometry to produce lots of insights. And you've got four complex numbers. Is that what it's all about? It's not quaternary, it's actually four complex numbers. And then I saw some generalization of the like when we were at this conference two weeks ago, remarking about other ways of thinking about the source of the twisters. But there's a lot of them. Which had been right at the beginning, which of course was when Penrose was actually at Birkbeck when he did all that earlier, I can't remember if it was, just from a historical point of view, I found that absolutely fascinating, that part of Basil's talk, that had really been a quite, conceptually quite distinct way of trying to get the structure, which was much more connected with spherical and hyperbolic geometry, but also connected with some of these ideas in clever algebra, didn't rely so much on complex analytic...

10:00 There's a lot of heavy-duty machinery in the Penrose approach, all that stuff, you know, the holomorphic functions. They continue to hold over a long, long period of years a complicated discussion about that, which was published in the Twister newsletter and now collected up into a lot of books. I don't know that the Twister newsletter exists anymore. I don't think it does. It probably exists on the web, but I think it more or less disappeared. But in none of that discussion do I ever recall, and such of it as I've now followed, do I ever recall the rival approach which was there right at the beginning, in these ideas of Mounsell and David, connecting the twister with the clippered algebras, being mentioned at all, and Penrose's approach was always this completely geometric approach, except bringing in, as I say, a lot of complex upper and lower sort of holomorphic functions. And it's very nice stuff mathematically, but it's never been shown how it connects up with quantum theory. It just all remains within the framework of classical theory. But the attraction of Basel's approach was that it did seem to show some real price, and I would admit that was very well worth examining, indeed, and I'm just historic about it, it's extraordinary that nobody's gone down that road, and hardly anybody who knows about twistor theory is aware that there was at the very genesis of the subject a quite different conceptual framework. And what's, I don't understand what the relationship is between the spin networks and the twistors. The spin networks are much more abstract, just taking root theory, really. Well, the connection is that they're both ways of trying to develop a kind of direction in space without having an underlying manifold to start from, without having... We're not having a notion of points, but one is recovering points from the top down through this more complicated complex analytic machinery because directions are more fundamental and points are kind of fuzzy because you've got this kind of shear in the twisted space. There's a bunch of research by the people in quantum gravity that are kind of curious with histomological confusion going on in there.

12:30 The spin networks that they use for a long time are embedded in three-dimensional space, but of course we knew, or we discovered after we Q-deformed them, that you should think of them as embedded in three-dimensional space, just like my knots are suddenly, we're talking about spin networks that are embedded in three-dimensional space. And then... And then the people in quantum gravity realized they could use them to measure area and volume, and get quantized area and volume, so it began to look like some kind of quantized quantum geometry. It's still a three-dimensional space, but you want to get rid of the three-dimensional space. And then there's another theme that comes in a few years later, which is still ongoing, about replacing the space by, going back to replacing the space by network or by common corex. Spin phones. Yes, I've read some of it. Spin phones. And that means it's not clear now what the relationship is between spin network and spin phone, in my mind. The spin network seems a much more straightforward, I mean, plausible attempt to get at some level of structure, which is conceptually prior to the space-time manifold, but the spin-phone picture really seems to assume, I mean, well, effectively assume it. Well, it ends up assuming various things. Yeah, that's right. The way that spontaneous emulation of spin-like states fluctuating about the non-existent state can exist, you know. I'd love to get a better idea of all that, but it seems to me the neutrino is something like that, but... Oh, you're talking about virtual particles huddling around the... Yeah, well, certainly the idea of a spin cone, if I get the idea at all, is as though the... The correlation states that, I don't know, it's a question of, does light gravitationally attract light? I don't know. Should we think it does? It's got mass. I mean, it'll have mass reciprocally in an ordinary Einstein type, you know, matter to light. Well, noise is a zero s mass and the photon is a mass of a particle, and that's what one always conventionally tells.

15:00 Because it will bend the light, I think it's going to accelerate the mass, isn't it? Does the sun accelerate when Einstein's star lights up? I think it does. I think it does, but that takes one nearly to the point where if two beams of light go past one, they do that. I don't know, but the model I've got suggests they don't. Would you believe? Because they're in the light cone, you understand. It's suggesting some questions in that area, just coming out of the basic wave equation. But the problem is the conceptual foundation, the conceptual issues and the foundations of quantum field theory are incredibly hairy, I mean, we can't, you know, we don't know how to define a particle, we don't know how to, you know, an engineer can't go down that road, it's just a debug, you know, it's just not going to work in my lifetime, whereas I reckon I can handle some of this stuff, I shouldn't really venture too far. Thank you for your attention. Well, of course, we're really going to take, you know, the cosmology series. God can't just be a geometer. He has to be an engineer as well. Yes, absolutely. I would, this conversation has already, as it were, rejuvenated me a bit, actually. No, I think I am going to take a rain check there because... Well, I'm still taking the rain check. No, I would like to come very much indeed, but I think I'm going to flake out in another hour or so. I'm probably not going to slumber anywhere to stay. I'd just like to take care of that before I do anything else. I tell you what, have you got a plan where you're going? I might try and come on and join you later if you know which restaurant you're going to go to. No, I don't. I can. Oh, okay, in that case. I can go to Gretel, which is the little Italian restaurant. Do you know where it is? That's the one we sometimes... Is that the one we went to the last night at Ampere? Thank you for watching this video.

17:30 I don't know the names of these roads. No, when you say... There's this road, and if you continue on, you get to an Indian restaurant here. Margaritas. Oh, is that the... when you say this road, you mean the one that goes... as you go out of the... Well, I'm way over in town. You're over in town? Where... In Margarita. Okay. Well, I can tell you what. You're going... but you're not going to eat in Margarita. You're going to eat in this other place, Pretzel. No, this was time you were... when you... you know, there's this main road. Yeah. I forgot the name of it. Sorry. But if you continued on from Margarita, which is, you know, that drag, there's the bridge and Margarita. When you say the bridge, do you mean Magdalen Bridge? Which bridge are we talking about? Are we talking about Moreland Bridge? Yeah, when you say town, you mean the center. The punting and turning. Yeah, yeah, okay. So, I mean... You go by the Pickerel Inn. Right, okay. See, I don't recognize names of restaurants. I recognize names of streets and colleges. You keep on going along and you hit an Indian restaurant here. But there's a main road, and if you turn here... Is this going over the bridge? Over Moreland Bridge? Or... You went, you're long gone over the bridge. Here's, over here. Oh, you're on, okay, so you, when you say you're long gone over the bridge, you're long gone in this direction, going out of town. Oh, okay, in that case I do know where we're going, yeah, okay. So you're going up towards Churchill, Fitzwilliam, that's right, yeah, yeah, okay, there we were. And, um, and then there's this main road, and you turn right, uh, left on the main road. Right. And go for a few paces. Mm-hmm. And, uh, and you will find yourself walking right into the prezzo, the Italian restaurant. Okay, well, if that's definitely where you're going to be. I might try and come on and join you later, but I really do want to get myself fixed up somewhere to stay. Good chance. Okay. Well, don't tie yourselves down to going there. Otherwise, I'll see you on the 14th, whatever happens. Thanks very much. And, well, it's been great seeing you again. I'll see you again in a week. And very nice meeting you too, Nick. Indeed. Best of luck. Thanks again. I'd really like to listen to this stuff when I'm in a bit more fixed state to follow it, but as I will, and as I've got your, have you got a spare card? So it's one or two people that I could, they would come in handy. I'm certainly going to think about this category soon. Okay, thanks again, Luke. Take care. See you soon.