Generic Predictions & New Developments in Loop Quantum Gravity — Discussion

0:00 That, and you get naturally one of the KQ because you can't get anything else. You get an estimate for the amplitude, and you can use that to estimate the number of non-local fluctuations then. This we feel is very, very, very rough. We don't feel we have good control over this. These things are sitting there for a long time. Things might build up. Well, this just gives us a sort of first check that's not ridiculous to get something that looks down there. The idea of using the noiseless subsystems to get to the standard model, Does it supersede now the idea of using the non-local correlations of the quantum mechanics via Nelson? That's a different idea. And that idea, I wouldn't say supersedes. So for people who don't know what he's talking about, one of the things that we looked at when we started thinking about the effect of this non-locality could somehow have something to do with quantum mechanical non-locality and so we have one result which we published was actually the first thing we published about it which which i think it's fair to say that as far as the ground state is concerned which has no nodes the result seems to hold up but there are questions about whether it holds up for excited states which and we don't have anything more to say about it. There's a paper in preparation I can show you and we can continue our discussion about the weak points of that. So I'm not making any claim about that here. But thanks for mentioning it. Last question. Perhaps it would not be correct to say that you have time in your picture from the beginning, but get time from this local moves but the notion of move is obviously a metaphor so my question is you're not really deriving time in this approach it seems like you have time there from right from

2:30 the start it's just discretized space time but still have the notion of evolution it's central I'm not saying it's a bad thing, of course, but just to make things clear from a philosophical point of view. Well, also from a physical point of view. Because after all, walk and move, if it has any physical meaning, some sort of motion, not in a background space, then obviously. That would be wrong to say. Yeah, no, no, no. So, I'm certainly very deliberately, I, I, I, I, I, so, there, in loop quantum battery, there's an approach to dynamics that goes through the Hamiltonian constraint, and raises all the, all the issues about the Hamiltonian constraint in a specific years of time, and throws some time picture, okay? There are people like, and Carlo Rovelli is one of them, who strongly believe that time, quote, emerges from that in some appropriate sense, and I'm not so convinced that it does. I don't have a convincing argument that I can't, but certainly it's a very challenging thing. It's very easy to show that in a little model with some harmonic oscillators talking to each other. What would be required to show that in a real theory is pretty amazing. And it's one of these things where a quantitative difficulty of doing any calculation maybe is indicating that you're on the long track. That's my view. So, I've confirmed the point of view where dynamics is formulated in the path in the world, personally, and that's why I present it that way, and therefore in the path in the world there are histories, and each history has a causal structure, and in that sense time is built in. Now, from then it goes two different directions. For the kind of results that I talked about here, one doesn't need more than that. And one doesn't need to decide the deep problems about the nature of time.

5:00 If you ask me what I think about the new problems of the nature of time, which maybe is what you're doing, I think that we're all wrong. I'm convinced more and more, and this is completely orthogonal, and what I try to do in the seminar is present results that point to connections with physics and cosmology. But my sense is that I've never heard a convincing proposal for the really fundamental issue of time in quantum gravity and quantum cosmology and I'm more and more suspicious that there's a deep issue and that the deep issue, and this is maybe what people say when they're going nuts. on the present moment and all that stuff. So depending on how much time you give me, I can embarrass myself in that direction. But again, I want to emphasize that if you anything about this has nothing to do, hopefully, with these results, but my sense is that, if you like, the scene of the crime is in the following assumption. is in carrying over to these kinds of theories the assumption that it's useful to talk about evolution in terms of separating kinematics from dynamics. So if you separate our kinematics, you believe you can specify the configuration space, the space of all possible configurations at one time. And then solving dynamics is just finding a path for a series of steps that is distributed through the configuration space. And my sense is, A, that you've already lost the game when you do that. And B, in all of these kinds of theories, you should worry because, you know, functions in R3, which is, you know, the Hilbert space for simplest particle mechanics, is very different from the Hilbert space I've described.

7:30 Even though it's easy to state, you know, a basis given by all embeddings of all labeled graphs in a three manifold, there are issues of computability. If I give you two quantum states in some representation here, do we, you know, how many steps does it take to compute the inner product? But if you, you know, there's issues, it's not just the graph isomorphism problem, it's the graph embedding homomorphism problem, you know, one or two embedded graphs topologically or diffeomorphically the same, which is an unsolved problem in topology. And if there's no algorithm to decide when two embeddings of graphs are diffeomorphic, then there are problems of computability in the definition of the theory that I've stated. And these kinds of musings lead me to wonder... Another way to say this is there's this sort of, you know... To me, there's a problem if you're planning dynamics, if you believe you're doing a fundamental theory and your fundamental dynamics down at the Planck scale, which is supposed to be elementary, asks you to do a very complicated calculation to compute what's going to happen in the next Planck time and a Planck volume. If you have to do a calculation which involves the solution of an empty hard problem to involve one Planck time and one Planck volume, then there is something wrong in my estimation. And therefore, finding a way to formulate dynamics without the notion of the prior existing configuration space or prior existing Hilbert space is very attractive. And that suggests some more, I don't know what the word to say, some more, some stronger role of time in the formulation of the dynamics. Then the problem is, if in the space of configurations everybody can be possibly connected to everybody else do you have something like relativistic there's a number of questions

10:00 anyway the best the best thing that I can say about this problem is we've tried to have some interesting discussions about it at Perimeter one very interesting discussion we had involved the philosopher Roberto Montevera Unger who's a professor of law at Harvard It's not going to be transcribed, but it's there on our web page, and we have... I should look at it. Yes, yes. I mean, this scares me very much because I would like the problem of quantum gravity to be solvable, you know, now. It's enough already. But if part of it is the problem of time, then it does seem to me more and more that we're being asked to invent something really new. and really new means, well, let me just, I mean, one of the ways that Andre put it in these discussions, he's extremely articulate, is he said there's a kind of poison gift from mathematics to physics when you represent physics mathematically, and the poison gift is when causal implication is replaced by logical implication. Because every time you make a mathematical model of evolution, what you're really doing is replacing causal implication in the real world, replacing it by logical implication in some mathematical system. The logical implication is timeless. So you've done something strange. And the alternatives seem to be to just buy that, in which case you have one or the other of the paradoxes of timelessness. believe that there's something intrinsic about nature which is not representable mathematically, or go the way to be intuitionists and look for foundations of mathematics in which time itself plays some essential role. And that's where I've come to, but I don't know how to move on from that. So let me stop talking.