Daseinization and the Redemption of Quantum Theory (contd.)

0:00 I mean, the truth object moves around. Just bear in mind there's no reduction of the state vector here, right? There's no measurement, there's nothing like that. And for better or for worse, you've simply got logic. And what happens is, they say, the state vector, sorry, the truth object moves around. And so the truth values change in time. And what may be totally true at one point, this notion of total truth, completely untrue, what is totally true at one point may become partly true later on. and so on. I mean, there's nothing very special about that. So it's basically, it pushes you, I'm sure it works ever in this context, but you basically end up in a there is no reduction. No reduction statement, no, at all. This is the whole point. We're not talking about measurement. I wonder if I could just step in there and push this perhaps in a slightly different way so it's related to the diameter of the issue. But let's go back to the Roley-Bone. Now, I know that the rolling ground starts with an ontology of configurations that you may not find very interesting, but nonetheless, the reason that you get a kind of a contextualism, and indeed you get a contextualism which allows for avoidance of all the difficulties associated with developed ocean speck of paradox, is because of the way the equations of motion work both for the wave function and for the variables, and because you can construct a very detailed theory of measurement of it. And that's telling you what you mean by the self-egmental difference. Some of them can be measured non-contextually, some of them are measured contextually. And this is not at-hoc. This is a feature of the dynamics of the theory. And this reminds me a little bit, for example, pushing it even further. There is a tradition in the literature, I don't think it's very well, I don't think it's widely accepted, perhaps, that goes back to people like Bickman, to the effect of the very commutation relation itself, the canonical commutation relations with quantum mechanics have something to do with the dynamics of the theory. It's not enough just to say, well, I've got some generalization of unitarity. The devil's in the details. It's, I'm going to introduce certain kinds of forces in quantum mechanics, and because of Irish, let's say in a Lagrangian context, and because the forces are of a certain kind, it turns out that the P, the position, and the velocity operators stand on certain commutation relations. Now, your operation is entirely kinematical, and this is, it is problematic. Well, I'm not sure we see it. If you're looking in the state space, and the observables, but not systems evolve over time. Well, as I said, the time evolution

2:30 is very easy to implement. I mean, it's the same as ordinary quantum mechanics is. I mean, not in the Bohm interpretation, but ordinary quantum mechanics, quantum mechanics is normally There's nothing different about it. I mean, the analogue of the state moving around is that the truth object moves around. It's just, there's nothing special about that, but it's certainly all in there. Nothing's missing. It's true that, what is true of this approach, is that it's that opposite of picking a particular context as you do in poem. Same to as all of them. I've always, personally, I know it's just a different perspective. I always argue with Julian Barber about this. I don't like using configuration space because I think it's so limited also. It's so very classical in context. I mean, the use of configuration space comes from classical physics. And I think Bohm was trying to, in a sense, to go back to classical thinking. Now, maybe that's right, I don't know, but I don't think myself is going in the wrong direction. We want to get away from classical physics. I mean, you may say, well, isn't this going back towards classical physics? Of course, it's not remotely, actually. The use of the topos is a dramatic change. Jeremy. I think you didn't say out loud in the talk what exactly is the assignment of truth. On that slide, we've seen what these problems are. I was out of Skipper. I was out of every second. I put it on there. Yeah. We know that a projector is now a sub-object of sigma. That's what it looks like. Right, so could I try to say in words what... Okay, so there is a comparison. So what we said a long ago, I think, was that if you had a projector that you were thinking of as an event for property or proposition or value of an observable, and we had a state of psi, We said that the truth value of the proposition that in this state, this projector is true, this proposition is true, this property is possessed, or the value of the observable lies in that ring, the truth value was something very odd when you first hear it. it was a collection of weakenings or widenings of that projector, which was formerly a sieve.

5:00 But the idea was, it's to be those coarsenings or widenings of that projector that include the state. And therefore all further coarsenings, and closed under further coarsenings. That's what I said. Now, that is maintained in the new scheme, but now you speak of these coarsenings as just one aspect of a more general idea. Yeah, that's right, that's right. so now you're looking at all the capital W's in early W so the truth object is sort of what it was the truth object is the same there was a weakness in what we did we discussed it at the time if you remember was that our projections had to actually belong to the W before we could talk about the truth values whereas here it doesn't have to do that for example if you read a book on Topos theory about using Topos logic to represent languages you'll find this scheme fits perfectly what we did didn't So yes, it's a generalization, but the basic idea is the same. All that's hidden, of course, in this notation. This is meant to look like little x belongs to something. What it's saying is the truth value is still mathematically saying something belongs to something else. It's just that it's in a topos. And you have to do this delta operation to get out of the quantum logic. So the basic idea is the same, but it's the biggest perspective. The truth object moves about because in third-degree evolution of psi, the collection of all the... That's right. ...sides are going to vary. Sorry, just... I've got three names, and I think I'm going to have to restrict them to that, and I would ask people to keep their questions as short as possible. The notion of truth in the context of a total sphere, is that still in terms of correspondence or only as coherence? Personally, I'm a passionate believer in coherent theories of truth, because I'm not really a realist at all. Physicists aren't meant to admit this. I think the whole of physics reeks out for coherent theories of truth, actually. having said that now in a technical sense what do you say in a topos

7:30 is it correspondence or coherence what do you say someone asked you that question well you your son might know the answer I mean I mean it's a good question I mean it seems to me coherence is a more natural interpretation the thing is of course that truth in a topos is mathematics is not the notion of coherence corresponds to the philosophical notions truth in a topos means what it means mathematically, so you're really asking how does it map across into the world. I don't know, maybe I shouldn't be so glib about saying it's coherent. I'm not even sure whether it would prefer one or the other. I honestly don't know. It's a good question, but I don't know how to think about it in general. One thing that typically happens when one tries to construct a general framework is to learn something about what makes the difference between one and the classical. So, if you look at pro-lexions, or if you look at half-lexions, you learn what's different, but presumably, you learn what's different from one of those classicals from your framework to the quotient-specific theorem that translates into maybe no classifier? No points. No points, yes. Can we see how that impacts, for example, the dynamics, and we have dynamics now, we've got sequences of truth values assigned, why is it that no points gives you determinists, and I say, well, I suppose it's because, in classical physics, I said if you had to take little s, you could construct the truth object T s, no difference. I mean, they were just different ways of looking at the same thing. In quantum mechanics, this is no longer true. You don't have any microstates at all in that sense. A quantum state does not tell you how things are. But you can still reduce this construction that Jeremy and I did to construct what we call a truth object, which plays the analogue of the truth object in classical physics. But there's no longer any points in which you derive it. I mean, that's where it comes in. It's the asymmetry between little x belongs to capital A. It doesn't no longer make sense. But A belongs to something else. It does make it's the asymmetry which you get in the top of Peter

10:00 well yes I mean in fact in a sense it goes across rather well if you take the example of the C-Store algebra technique earlier. It's very easy to take some out of us about, and you can certainly, yeah. But if you ask does it solve the ultraviolet renormalisation problems, the answer's quite well, because it doesn't. Yes, I mean, quantum filter theory fits in just as well as quantum quantum mechanics does in this scheme. The stories that don't do all the quantum gravity theories people have talked about in answer to the earlier question, the question is whether you can learn anything from that, it's terribly interesting, and you can certainly fit them into this scheme in a technical sense, but Well, I think you'll agree with me that although this was the last seminars of the series it was anything but the least I wish you'd given us a wonderful talk to end our series and thank you very much for dealing with the questions so well as well Thank you, I really enjoyed coming here I have to prevent my officers for a number of reasons Thank you.