0 00:00:02,450 --> 00:00:06,670 Jorge Pullin: Okay. So our speaker today is Victoria Cabell, who will speak about quantum reference frames. 1 00:00:08,080 --> 00:00:12,390 Viktoria Kabel: Thanks for the introduction and thanks for inviting me to speak here. 2 00:00:12,530 --> 00:00:24,189 Viktoria Kabel: So I'm gonna be speaking about quantum reference frames. But I wanna focus on in particular the relation between quantum reference frames and gravity. So quantum reference frames in space-time. 3 00:00:24,260 --> 00:00:25,600 Viktoria Kabel: and 4 00:00:25,790 --> 00:00:40,770 Viktoria Kabel: after an introduction to the general framework to quantum reference frames, I wanna speak about in particular joint work with my Supervisor Joseph Bruckner, with Esseb and Castro Reese and Kantrina and boyfriend Vila, which you can find on the archive 5 00:00:40,780 --> 00:00:54,650 Viktoria Kabel: on how to combine quantum reference frames with gravity. But before I delve into what quantum reference frames are I think we should first talk a bit about why we should care about quantum reference frames. 6 00:00:55,000 --> 00:01:19,940 Viktoria Kabel: and I think there are different kinds of motivations you may have. For studying quantum reference frames, the one that's may be most common in the quantum foundation community is an operationalist motivation which is essentially saying that in practice any reference frame that we use is ultimately just a physical system, like a clock or a ruler, and usually it's one that should ultimately be described by quantum theory. 7 00:01:20,040 --> 00:01:28,560 Viktoria Kabel: So it's quite natural to think what happens if the reference frame is treated as a quantum system in the theoretical description as well. 8 00:01:29,520 --> 00:01:41,589 Viktoria Kabel: That's not the only motivation, though I think you could equally arrive there by starting from quantum gravity. From the problem of time, where we learned that we actually need a reference frame in order 9 00:01:41,660 --> 00:01:46,080 Viktoria Kabel: to even describe evolution and time, or even just variation across space. 10 00:01:47,400 --> 00:02:11,019 Viktoria Kabel: And then, I think, a third motivation actually comes from gauge theory or from trying to quantize gauge theory where reference frames allow us to construct gauge invariant observables through dressings, even though these dressings are not commonly called reference frames. But we're going to see at the end of the talk. How the kind of quantum reference frames that emerge in linearized gravity actually also act as dressings. 11 00:02:12,840 --> 00:02:23,420 Viktoria Kabel: Now, as I said, in the quantum foundations community, it's mostly this operationalist mindset that motivates the study of quantum reference frames, and it also fits 12 00:02:23,520 --> 00:02:42,939 Viktoria Kabel: kind of well with what I would call the first in principles approach to problems such as quantum gravity. And by that I really just mean that we take the principles of known theories, such as quantum theory, gr quantum field theory, maybe even QFT. On curved spacetime. And just see how far we can push them. 13 00:02:43,270 --> 00:02:55,830 Viktoria Kabel: So it's actually kind of a conservative approach. You may argue, because we're assuming that these basic principles hold even beyond the regimes of applicability of these theories that we have tested. 14 00:02:56,570 --> 00:03:08,800 Viktoria Kabel: and for the study of quantum reference frames. Really, the following 3 principles were going to be particularly important from the quantum theory side, it's the linearity of quantum theory and the superposition principle. 15 00:03:08,970 --> 00:03:20,799 Viktoria Kabel: And then we're also gonna add, in the relativity of certain physical quantities, like position, momenta directions, and so on, which arise ultimately from the symmetries of the equations of motion. 16 00:03:20,930 --> 00:03:27,140 Viktoria Kabel: If we combine these principles, we quite directly arrive at the idea of a quantum reference frame. 17 00:03:28,310 --> 00:03:45,280 Viktoria Kabel: and I think this first principle approach is really a complementary approach to top down approaches to quantum gravity, where by top down approach, I really just mean any theory which aims to find a more fundamental theory from which then, the known theories can be derived. 18 00:03:46,150 --> 00:03:51,680 Viktoria Kabel: Sorry can I ask a very naive question just about these motivations? 19 00:03:52,530 --> 00:03:56,320 Simone: So one of the principle of quantum mechanics. I think it's also the fact that 20 00:03:56,480 --> 00:04:01,129 Simone: the system is split in 2, and one is the quantum system we observe. 21 00:04:01,350 --> 00:04:04,789 Simone: and another one is the observer that we have to treat classically. 22 00:04:05,160 --> 00:04:10,540 Simone: because otherwise we don't know how to explain things like the collapse of the wave function. 23 00:04:10,890 --> 00:04:14,510 Simone: So you're kind of giving up that principle or 24 00:04:14,620 --> 00:04:21,130 Viktoria Kabel: no. No, I think that's actually an important principle as well. Also, for for the quantum reference frames, it's just not one that 25 00:04:21,360 --> 00:04:30,860 Viktoria Kabel: kind of directly motivates them. This is not an exhaustive list principles. It's just supposed to be the ones that are most relevant to quantum reference frames. 26 00:04:31,890 --> 00:04:39,700 Simone: Well, let let me rephrase my question, then, if you want to treat the the observer also as quantum. This is what you want to do right? 27 00:04:40,490 --> 00:04:46,469 Simone: Well, not not necessarily the observer, I think directly. 28 00:04:46,530 --> 00:04:47,820 Simone: Okay, thank you. 29 00:04:48,330 --> 00:04:49,430 Viktoria Kabel: No worries. 30 00:04:51,680 --> 00:05:08,949 Viktoria Kabel: Alright. If Darren aren't any other questions regarding the motivation, I wanna come to a quick overview of what I'm gonna talk about. So as I said, I wanna start with a basic introduction to what quantum reference frames are really using a very simple example of the translation group. 31 00:05:09,050 --> 00:05:27,719 Viktoria Kabel: And then I want to talk about 2 different ways. We might want to combine quantum reference frames with gravity. The first one is to just take the formalism of Qrfs, and then add in some gravity by treating the quantum reference frame, or one of the systems acting as a quantum reference frame as a massive object. 32 00:05:27,730 --> 00:05:41,430 Viktoria Kabel: and then the other direction that I want to talk about is kind of trying to go the other direction, starting from a general relativistic description, and seeing if we can get out a notion of quantum reference frame from there upon suitable quantization. 33 00:05:41,590 --> 00:05:53,269 Viktoria Kabel: And then, of course, I'm going to close with a quick, summary outlook and connections. So if we want to understand what a quantum reference frame is, we first have to understand what a classical reference frame is. 34 00:05:53,320 --> 00:05:59,079 Viktoria Kabel: And for the following part of the talk, I just really want to focus on the simple example of the translation group. 35 00:05:59,400 --> 00:06:06,809 Viktoria Kabel: So usually reference frames are important in classical physics. Whenever we have a symmetry like an invariance under translations. 36 00:06:07,070 --> 00:06:20,900 Viktoria Kabel: and the symmetry can then be understood to a free choice of the position, reference, frame, or by the position reference frame. Here I really just mean choosing with which particle we align the origin of our coordinate system. 37 00:06:22,280 --> 00:06:32,710 Viktoria Kabel: and we can then say all we can equally describe our system by lining the 0 point with the blue particle. That's the reference frame of the blue particle, so to speak, or with. 38 00:06:32,880 --> 00:06:37,939 Viktoria Kabel: can describe everything with respect to the orange particle. But the physics is going to be the same. 39 00:06:38,860 --> 00:07:05,489 Viktoria Kabel: Now, if we want to take this to the quantum level, we first have to quantize all of the systems that we have. So we just put cats around everything. So of course, a bit more subtle than that. So we're gonna describe everything in terms of quantum states of the particles we're gonna assume for now that these are perfectly localized particles in an eigenstate, and they're gonna be living in generally distinct Tobit spaces for each of the description. 40 00:07:06,750 --> 00:07:19,739 Viktoria Kabel: and then, if we want to go from one reference frame to the other reference frame, we would expect all the usual properties of the classical reference frame to remain because it's essentially the same system just described in terms of quantum theory. 41 00:07:20,180 --> 00:07:28,430 Viktoria Kabel: And we can implement this classical like change of reference frame on the quantum level with a simple translation operator. 42 00:07:28,970 --> 00:07:51,790 Viktoria Kabel: I should add here that for technical reasons, we're not applying the translation operator on all of the systems, even though we could simply translate everything by the distance XA between the blue and the orange protocol. But for technical reasons, we're using this parity swap operator here. To exchange the positions of the 2 reference frames. 43 00:07:51,790 --> 00:08:04,830 Viktoria Kabel: the blue particle and the orange vertical. And essentially, this is just mirroring the position of the new reference frame with respect to the origin, and then exchanging the labels so that the new reference frame ends up in the 0 point of the coordinate system. 44 00:08:08,040 --> 00:08:10,790 Viktoria Kabel: Now. this is still 45 00:08:11,000 --> 00:08:23,730 Viktoria Kabel: not much surprising. This is just the standard quantum translation, and this operator can describe any situation where we have classical, like reference frames. But any type of quantum system. 46 00:08:23,840 --> 00:08:26,630 Viktoria Kabel: in the rest of our setup. 47 00:08:26,700 --> 00:08:30,230 Viktoria Kabel: But the really interesting. yeah. 48 00:08:31,520 --> 00:08:40,170 Laurent Freidel: So just just a question here. What can you comment on? Why, you take that option versus just the one where you translate back? 49 00:08:40,690 --> 00:08:49,189 Viktoria Kabel: Yes, so it becomes clearer when we change between a proper quantum reference range where the particle is in a superposition. 50 00:08:49,310 --> 00:08:55,820 Viktoria Kabel: So maybe I just comment on that when we see the operator there, because then it becomes a bit clearer, I think. 51 00:08:56,490 --> 00:08:57,290 Laurent Freidel: Okay. 52 00:08:58,190 --> 00:09:12,879 Viktoria Kabel: So the really interesting features of the quantum reference frame transformations, namely, arise when we want to jump into the reference frame of a particle that's in a proper quantum state, that's in a superposition, or even spread out further across space. 53 00:09:13,430 --> 00:09:36,839 Viktoria Kabel: And there. It's maybe a bit less trivial to know how to go into the reference frame of such an object. But we can already have some guiding principles. The first one is probably that in its own reference frame each particle should still be in the origin of the coordinate system. That's kind of what we mean by a reference frame, and it also doesn't really make sense that with respect to itself, the particle is at different distances from itself. 54 00:09:37,290 --> 00:09:39,939 Viktoria Kabel: It's always going to be a distance 0 55 00:09:40,180 --> 00:10:04,129 Viktoria Kabel: And then the second thing that we want to retain is that the physically relevant quantities, like the relative distances, should remain the same in each of the reference frames, and since the orange particle and the blue particle are in a superposition of relative distances, and we want to retain that in the new description it's now gonna be the blue particle that has to be in a superposition, so that the relative distances 56 00:10:04,130 --> 00:10:13,390 Viktoria Kabel: remain the same. So we can already see one interesting feature of these quantum reference frame transformations, which is the superposition becomes a frame-dependent quantity. 57 00:10:14,120 --> 00:10:42,989 Viktoria Kabel: and similarly, entanglement becomes a frame dependent quantity, and in this simple scenario is actually quite intuitive, because we know that in this frame of reference the orange particle is closer to the blue particle whenever it's further away from the gray wave function. And in order to ensure this in the reference frame of the orange particle itself, we're gonna have to use an entangled state, so that whenever the blue particle is closer to the orange one, the grey one is further away and vice versa. 58 00:10:43,830 --> 00:11:00,840 Viktoria Kabel: And now we can implement the transformation from this State to this state, using a very similar operator to the one that we used before with a minor modification, and that is that we turn the distance by which we translate into a quantum operator. 59 00:11:01,120 --> 00:11:28,990 Viktoria Kabel: So what this essentially does is a quantum controlled translations. It reads off, what is the distance XA. One or XA 2, between the 2 reference frames, and then it translates accordingly. So it might do a different translation in each branch of the superposition. And this is also the technical reason why we have to use the parity swap, because if we try to both control on the position of the new reference frame and shift it, we run into problems. 60 00:11:32,600 --> 00:11:33,750 Viktoria Kabel: So 61 00:11:34,610 --> 00:11:45,600 Viktoria Kabel: really, a quantum reference frame transformation in this approach to quantum reference frames can really be understood as a quantum controlled translation or a quantum controlled symmetry transformation. 62 00:11:46,790 --> 00:12:00,819 Viktoria Kabel: and in this sense the quantum reference frames generalize the classical reference frames to extend to particles that are in a superposition of positions, and we can equally use the same operator for any quantum state of the 63 00:12:00,940 --> 00:12:03,130 Viktoria Kabel: reference frame here. 64 00:12:03,710 --> 00:12:13,629 Viktoria Kabel: and then we might add to the classical symmetry principle which said that we have an invariance under translations. We might expect that 65 00:12:13,860 --> 00:12:22,450 Viktoria Kabel: this actually carries over to the quantum level, so that we might have an invariance even under these quantum controlled translations, under these superpositions of translations. 66 00:12:24,460 --> 00:12:34,639 Viktoria Kabel: And if this is true, then we find it. Whether something is any superposition or entangled actually depends on the frame. It's maybe not a purely physical feature. 67 00:12:37,670 --> 00:13:04,650 Viktoria Kabel: And I just wanna mention here how the principles that we saw earlier really almost directly lead to this idea of the quantum reference frames under quantum symmetries, because what we have to put in is simply the symmetries of the known physical theories. Like the translation invariants, we add in the linearity of quantum theory, because we now consider superpositions of different translations, and if we assume an invariance under that, we end up with the quantum symmetry. 68 00:13:05,710 --> 00:13:24,049 Viktoria Kabel: Now, the translation case is really just one of many cases that you can study and quantum reference frames have studied for many different symmetry groups like the Galilei groups, spin rotations, conformal transformations. Lorentz boosts and asymptotic symmetries, and really it should extend to any type of symmetry that you could think of. 69 00:13:24,440 --> 00:13:40,449 Viktoria Kabel: I should also mention here that I presented one particular approach to quantum reference frames, which is mainly centered around Vienna and around people that used to be in Vienna. But there's also other approaches to quantum reference frames like the so-called perspective neutral approach. 70 00:13:40,580 --> 00:13:46,920 Viktoria Kabel: or a more operational approach that deals more with algebra observables. 71 00:13:48,550 --> 00:13:56,260 Viktoria Kabel: But I think for the discussion here. Actually, all we're gonna need is this one approach to quantum reference frames. 72 00:13:57,270 --> 00:14:04,050 Viktoria Kabel: So I think, if there are any more questions on quantum reference frames. This would be a good time also, if the 73 00:14:04,490 --> 00:14:09,000 Viktoria Kabel: parity swap operator was not clear. I'm happy to pull up on that. 74 00:14:09,640 --> 00:14:18,020 Ding Jia: II do have some critical remarks to make. Should I save them to the very end? Because I suspect that it'll lead to many discussions? 75 00:14:18,630 --> 00:14:24,010 Ding Jia: I mean, if you think it's more for discussion. Maybe we can discuss it at the end. Yeah. 76 00:14:30,350 --> 00:14:38,300 Viktoria Kabel: all right. If there are no questions regarding the general idea, we can finally turn to how we can combine this with gravity. 77 00:14:38,490 --> 00:14:54,279 Viktoria Kabel: And, as I said, the the first direction we want to, I want to talk about is really taking this formalism of quantum reference frames that we just saw, and adding in a bit of gravity, by considering a massive object as one of the particles. 78 00:14:55,210 --> 00:15:07,759 Viktoria Kabel: and we can imagine the following scenario, you just take a massive object like the earth. You put it in a superposition of 2 different locations, and then you ask yourself, how is a particle going to move in this mass configuration 79 00:15:08,060 --> 00:15:25,499 Viktoria Kabel: 2 caveats to add here? Firstly, of course, we're not gonna put the earth in super position. But there are actually some attempts at putting at least small massive objects of maybe the plank mass in a superposition in Vienna. So maybe in 10 or 20 years we can actually 80 00:15:25,540 --> 00:15:35,819 Viktoria Kabel: do experiments of this kind. And the second point is that if you don't want to adhere to a particular approach to quantum gravity. Then our current theories 81 00:15:36,040 --> 00:15:42,350 Viktoria Kabel: just quantum theory, and tr alone. Don't tell us the answer to the question, how does the particle move. 82 00:15:42,360 --> 00:15:48,700 Viktoria Kabel: because none of these theories tell us what is the gravitational field sourced by this mass configuration and superposition. 83 00:15:50,090 --> 00:16:07,219 Viktoria Kabel: So if we don't want to assume anything beyond the current theories. We can still give an answer to this question if we just assume this extended symmetry principle. So the idea of using quantum reference frames. To study the scenario is to just jump into the reference frame of the earth. 84 00:16:07,240 --> 00:16:19,420 Viktoria Kabel: and because superposition is a frame dependent feature, we can actually go into a reference frame where the massive object is definite, and then solve the problem there, and then go back and infer the 85 00:16:19,870 --> 00:16:23,380 Viktoria Kabel: the motion of the particle in the original reference frame. 86 00:16:23,670 --> 00:16:31,860 Viktoria Kabel: So I wanted to quickly go through the argument. But it's really, essentially, mathematically the same as the quantum reference frame transformations that we just saw. 87 00:16:32,280 --> 00:16:44,499 Viktoria Kabel: So in the first step, we use the quantum reference frame transformation operator to change into the reference frame in which the gravitational source is definite. So it's like replacing the orange particle from before with the earth. 88 00:16:44,920 --> 00:16:52,149 Viktoria Kabel: Now, this is a scenario that we can both describe theoretically with our known theories, and that has been tested experimentally. 89 00:16:52,530 --> 00:17:05,100 Viktoria Kabel: We could, of course, describe everything in terms of Qt. On curves facetime. But this is maybe a bit of an overkill A simpler solution is obtained by assuming that the particle moves in a superposition of semi-classical paths. 90 00:17:05,240 --> 00:17:17,520 Viktoria Kabel: where the path address given by the geodesic motion in the now-fixed space-time background. and we can also calculate the quantum phase that is picked up while the particle moves through the gravitational field. 91 00:17:18,319 --> 00:17:32,719 Viktoria Kabel: and we find that the particle moves in a superposition falling towards the earth. And this is something that we can be pretty sure of, because there are actually experiments, using neutrons moving in a superposition of paths in the gravitational field of the earth. 92 00:17:33,730 --> 00:17:39,530 Viktoria Kabel: And if we now just add this one additional ingredient, namely, the extended 93 00:17:39,840 --> 00:18:00,500 Viktoria Kabel: symmetry principle, that is, we assume that the change of quantum reference frame is the symmetry of the equations of motion. We can transform back and infer the dynamics and infer, if we just apply this inverse quantum reference frame transformation to the state that we obtain, we see that the particle will move in a superposition of paths in this frame, as well 94 00:18:00,650 --> 00:18:04,300 Viktoria Kabel: towards the 2 different locations of the massive object. 95 00:18:05,840 --> 00:18:11,839 Viktoria Kabel: And, as I said, the one big assumption that we do have to put in is this extended symmetry principle? 96 00:18:13,010 --> 00:18:36,209 Viktoria Kabel: So we can see the argument as a whole over here, and the idea is kind of to avoid saying anything about the quantum nature of the gravitational field over here and going this deep tour. Using the extended symmetry principle. But you could, of course, have arrived at the same results, and probably a lot of you would have expected exactly this result. By simply assuming that the 97 00:18:36,360 --> 00:18:41,690 Viktoria Kabel: mass configuration and superposition, also sources of gravitational field and superposition. 98 00:18:41,960 --> 00:18:51,189 Viktoria Kabel: So, in a way, you could see the argument with the extended symmetry principle as a coherence check for the quantum nature of the gravitational field. In this context. 99 00:18:52,930 --> 00:19:07,759 Viktoria Kabel: while this is something you would probably expect from theories like linearized quantum gravity and the linearized regime. There are actually some approaches or some models, or for quantum gravitational scenarios that do not agree with the extended symmetry principle. 100 00:19:07,800 --> 00:19:22,319 Viktoria Kabel: So in a way, we can say, if you believe strongly that the extended symmetry principle should hold, then maybe you should. Not believe in collapse models or semi-classical gravity, because they break that, and this is quite easy to see, because 101 00:19:22,340 --> 00:19:33,289 Viktoria Kabel: no matter which model you pick, it should have the same predictions for the reference frame in which the earth is definite, because this is something we can describe with known physics, and that has been experimentally tested. 102 00:19:33,330 --> 00:19:46,530 Viktoria Kabel: But while the extended symmetry principle tells us that the protocol falls in a superposition of paths. A collapse model would say that the superposition of the massive object cannot be upheld for a decent time frame. 103 00:19:46,630 --> 00:19:52,210 Viktoria Kabel: so the particle will either fall towards the right hand side, or the left-hand side with a certain probability. 104 00:19:53,450 --> 00:20:13,099 Viktoria Kabel: So this does not satisfy the extended symmetry principle. Similarly, if you were a strong believer in semiclassical gravity in all regimes, then you would predict that the particle wouldn't move at all, because the average of the gravitational field is going to be 0 in the middle of the 2 locations of the earth. 105 00:20:13,260 --> 00:20:16,650 Viktoria Kabel: So again, this cannot obey the extended symmetry principle. 106 00:20:17,640 --> 00:20:35,460 Viktoria Kabel: So the idea really is just to give an example of how we can use these first principles. Really, the symmetries of the equations of motion, plus the linearity of quantum theory, and then push them to new regimes and see. Oh, they're in conflict with certain approaches. 107 00:20:35,560 --> 00:20:41,930 Viktoria Kabel: and we can actually make predictions that we would otherwise have to pick a certain approach to quantum gravity. For 108 00:20:45,640 --> 00:20:46,750 Viktoria Kabel: now 109 00:20:47,570 --> 00:20:57,209 Viktoria Kabel: this is really just one direction in which you can combine quantum reference frames with gravity. But there is another way that you may want to go. 110 00:20:57,410 --> 00:21:07,010 Viktoria Kabel: and that is starting from a general relativistic framework and asking whether we can actually derive quantum reference frames from within there. 111 00:21:10,040 --> 00:21:23,560 Viktoria Kabel: So this is what I want to talk about. And the last bit of this talk. and for this particular example, we're still going to consider a situation that's quite similar to the ones before we have a bunch of endpoint particles 112 00:21:23,570 --> 00:21:29,659 Viktoria Kabel: in a region of space-time. But now, importantly, we're going to consider a bounded region of space-time. 113 00:21:30,910 --> 00:21:38,469 Viktoria Kabel: and we're asking ourselves to question whether we can derive quantum reference frames from within this setup described by general relativity. 114 00:21:38,650 --> 00:21:53,199 Viktoria Kabel: and the goal is really twofold. First of all, this would give us quantum reference frames formulated in a language that's much closer to general relativity formulated in a field theoretic language rather than just standard quantum mechanics which we've been using so far. 115 00:21:53,710 --> 00:22:04,540 Viktoria Kabel: and secondly, we would expect that this would give us more general quantum reference frame transformations, because general relativity has a much larger symmetry group. Ultimately the diffumorphism group. 116 00:22:05,450 --> 00:22:17,299 Viktoria Kabel: Now, of course, the issue is, if we want to derive quantum reference frames, we're going to have to quantize the theory, which is a bit hard in full general relativity. But we can go a first step by looking at linearized gravity. 117 00:22:17,870 --> 00:22:26,920 Viktoria Kabel: And we find, and this is what I want to explain in more detail now that if we consider linearized Dr. In a bounded region of space time. 118 00:22:26,970 --> 00:22:33,309 Viktoria Kabel: Then quantum reference frames emerge naturally as edge modes at the boundary of space-time. 119 00:22:35,750 --> 00:22:46,490 Viktoria Kabel: Now this is actually quite in line with also some recent work by Philippine and others, where they relate reference frames on the classical level to edge modes 120 00:22:46,780 --> 00:22:48,939 Viktoria Kabel: engage theory or gravity. 121 00:22:49,650 --> 00:22:54,780 Viktoria Kabel: But before I go through the derivation, I want to just give a brief 122 00:22:54,820 --> 00:23:06,930 Viktoria Kabel: intuition for what edge modes are for those that are not familiar with them, and I think they can actually be motivated most easily with, an example by Carlo Rebelli. 123 00:23:07,080 --> 00:23:18,609 Viktoria Kabel: with a translationally invariant theory of n particles. So the idea is really just to consider a bunch of spaceships, and they're floating out there in outer space. And there's really nothing else 124 00:23:18,790 --> 00:23:27,629 Viktoria Kabel: in the universe. There are no planets with respect to which you can describe the position of 2 spaceships. There are no other spaceships around but the system that you have. 125 00:23:28,070 --> 00:23:39,089 Viktoria Kabel: And in this context it would really be redundant if you used all 5 positions of the spaceships to describe the system, because it doesn't matter if all the spaceships are over here or over here. 126 00:23:39,330 --> 00:23:45,999 Viktoria Kabel: so you can get a full description of the physical degrees of freedom by focusing on the 4 relative distances 127 00:23:46,070 --> 00:23:47,669 Viktoria Kabel: between the spaceships. 128 00:23:48,890 --> 00:23:54,820 Viktoria Kabel: Now you could imagine that 2 of the spaceships go off to explore another part of the empty universe. 129 00:23:55,130 --> 00:24:14,889 Viktoria Kabel: and you can make the same argument. Now you're left with your 3 spaceships, but it's kind of redundant to describe the position of all 3 of them. So you restrict yourselves to 2 relative distances between the 2 of them. Similarly, for the spaceships that have gone away. If you just describe this one subsystem, all you need is the relative distance between the 2. 130 00:24:15,610 --> 00:24:35,270 Viktoria Kabel: But in splitting this total system in the 2 subsystems, now we've lost some information. We've lost the information that describes the relative distance between the 2 fleets of spaceships themselves. And if we ever want to bring them back together, this information is gonna be relevant. It's gonna be relevant what their relative position is. 131 00:24:36,410 --> 00:24:53,409 Viktoria Kabel: and the idea of edge modes essentially can be boiled down to saying, Well, if we describe a subsystem, we can retain this information on how to couple to other subsystems by introducing an additional degree of freedom. It could be something like the distance of the spaceship to the boundary. 132 00:24:54,730 --> 00:25:09,150 Viktoria Kabel: Now, usually one doesn't call them edge modes unless it's a local gauge symmetry or a generally covariant theory. So to see why it's called an edge mode or a boundary mode. I want to look at a second example, which is electrodynamics. 133 00:25:09,910 --> 00:25:21,389 Viktoria Kabel: and the idea is essentially the same like you have the U. One gauge symmetry of electrodynamics. You don't need to describe the entire electromagnetic field. It's enough 134 00:25:21,490 --> 00:25:38,920 Viktoria Kabel: to describe everything in terms of gauge invariant. Wilson loops so we just integrate electromagnetic potential along a closed path. And if we have the information along all the closed paths in our total space time, for example, then we're going to have all the physical information we need 135 00:25:39,250 --> 00:25:41,120 Viktoria Kabel: for our electromagnetic field. 136 00:25:41,540 --> 00:25:52,369 Viktoria Kabel: But things change if we want to look at subsystems. If, for example, we introduce a wall that splits our space time into 2 regions, and we're only interested in the region in front of the wall. 137 00:25:52,880 --> 00:26:03,579 Viktoria Kabel: If we now were to use only the closed loops. To describe the electromagnetic field. We're losing all the information of the loops that were crossing the boundary beforehand. 138 00:26:03,920 --> 00:26:11,969 Viktoria Kabel: and he's what remains of these loops itself the half Wilson loops. They're not going to be gauge invariant observables anymore. 139 00:26:12,100 --> 00:26:31,000 Viktoria Kabel: because they transform. And in particular they change for gauge transformations that don't vanish at the boundary. The change of this half Wilson loop under a gauge transformation depends on the gauge parameter lambda at the boundary where the Wilson loop crosses the boundary. 140 00:26:31,760 --> 00:26:44,839 Viktoria Kabel: And again, just as we can retain this additional information, by adding additional degree of freedom in the case of the rockets. We can now add, in this additional degree of freedom, the gauge parameter at the boundary 141 00:26:44,930 --> 00:26:47,479 Viktoria Kabel: to our description of the subsystem. 142 00:26:47,650 --> 00:27:06,689 Viktoria Kabel: and this will allow us to later couple back together the sub regions plus it allows us to get a gate. Invariant description of even the half Wilson loop, because if we equip the gate parameter with the right transformation properties, it will actually cancel out any transformations of the half Wilson loop that we saw here. 143 00:27:09,710 --> 00:27:13,020 Viktoria Kabel: and a similar idea of 144 00:27:13,120 --> 00:27:27,789 Viktoria Kabel: edge modes emerges in the context of generally covariant theories, and in particular in linearized gravity. And as we dare have the diffumorphism group as a symmetry group, we would expect something like coordinate fields 145 00:27:28,090 --> 00:27:34,289 Viktoria Kabel: to arise as edge modes, just like the gauge parameter, would arise as a boundary mode in electrodynamics. 146 00:27:35,170 --> 00:27:50,660 Viktoria Kabel: Now. The crucial difference is, however, that while these et modes are usually added in by hand through an additional boundary term in the action, for example, in electrodynamics or other gauge theories. They actually emerge quite naturally in linearized gravity. 147 00:27:50,720 --> 00:27:56,110 Viktoria Kabel: and one could say that they emerge from the space-time background itself. 148 00:27:57,740 --> 00:28:13,889 Viktoria Kabel: So let's look at this a little bit more closely. So, as I said, we're considering linearized gravity in a separation of space-time with endpoint particles. And we're gonna perturb around a flat space-time background to, for instance, second order in the gravitational coupling. 149 00:28:14,680 --> 00:28:20,270 Viktoria Kabel: Now the flat space time background in the tetrahed formulation 150 00:28:20,310 --> 00:28:33,989 Viktoria Kabel: can be really characterized fully by 4 coordinate fields. X. Mu. So the idea is kind of that. Your tetrad will just be given by the derivatives of these coordinate fields at each point in space time. 151 00:28:34,540 --> 00:28:42,999 Viktoria Kabel: Of course, this only holds up to the internal rotations that come with the tetrahed formalism which are characterized by Lambda. Here. 152 00:28:43,990 --> 00:28:54,710 Viktoria Kabel: similarly, the connection for flat space time is, of course, going to be 0 again up to internal SO, 1. 3 rotations which give rise to this additional term here. 153 00:28:55,330 --> 00:29:01,330 Viktoria Kabel: and we're going to see that these coordinate fields and Lawrence fields survive in the description 154 00:29:01,380 --> 00:29:09,809 Viktoria Kabel: only at the boundary of space-time, where they then act as reference frames or as edge modes at the boundary of space-time. 155 00:29:11,360 --> 00:29:18,239 Viktoria Kabel: And, as I said, we're gonna consider perturbations around the slide space-time background which are denoted by F and Delta here. 156 00:29:19,650 --> 00:29:30,429 Viktoria Kabel: and this entire scenario can be described by an action. We're using the Hilbert Pelatini action, plus some matter action with the which depends on the path of the particles. 157 00:29:31,490 --> 00:29:40,459 Viktoria Kabel: Importantly, I just want to stress here. We don't have to add in any boundary terms. But we will see that these coordinate fields kind of survive on their own. 158 00:29:41,760 --> 00:30:01,879 Viktoria Kabel: Now, the emergence of edge modes can most easily be seen in the covariant phase space formulation. So just wanna very briefly give an interlude explaining why we wanna even use the covariant face. And the idea is really just to get a manifest the covariant description of face space. 159 00:30:01,880 --> 00:30:21,079 Viktoria Kabel: This issue is usually, if you go to the Hamiltonian framework, you have to do a Legendre transformation which already picks out a preferred time, direction. Whereas, if you describe the phase space in terms of the symplectic form, as is done in the covariant phase, space formulation. You can derive the directly from a variation of the action 160 00:30:21,370 --> 00:30:33,040 Viktoria Kabel: and the symplectic forum. Here I've given an example for just end point particles also gives you all the information that the Hamiltonian approached us. And it's directly related to the Poisson bracket. 161 00:30:34,310 --> 00:31:03,319 Viktoria Kabel: I also wanna point out what this both face d means because we're actually looking at a field space. So a point in phase space is gonna be given by an entire field configuration of the fields and their conjugate momenta across all of space-time. So the geometry of the face space is actually gonna be described in terms of symplectic form, where the exterior derivative is really a field space exterior derivative, which is closely related to variations 162 00:31:03,350 --> 00:31:04,510 Viktoria Kabel: of the field. 163 00:31:07,680 --> 00:31:21,759 Viktoria Kabel: So if we return to our setup and linearize gravity, we can directly derive the symplectic form, as we just saw from a variation of the action, or from a variation of the Lagrangian, and I'm going to spade you the technical details. 164 00:31:21,860 --> 00:31:32,240 Viktoria Kabel: but if we derive the symplectic form, we can automatically read off what are the ingredients? What are the constituents of the phase space. And how are they related? 165 00:31:32,640 --> 00:31:39,529 Viktoria Kabel: And what we find is that the symplectic form for our bounded region here actually splits into 3 parts. 166 00:31:39,810 --> 00:31:56,290 Viktoria Kabel: we first have, we have a matter part describing the point particles, a part describing representational radiation, and then we also have this boundary term which will describe our coordinate fields and Lorentz fields at the boundary. 167 00:31:57,630 --> 00:32:01,380 Viktoria Kabel: and these also already enter within the other 168 00:32:01,790 --> 00:32:25,519 Viktoria Kabel: terms of the symplectic form. So if we look at, for example, the matter part of the symplectic form, it almost looks like the symplectic form for the endpoint particles that we saw in the last slide, but with one important difference, and that is that it's not the position of the particles themselves which which enters, but a kind of relative or dressed position of the particles with respect to the coordinate fields. 169 00:32:26,930 --> 00:32:34,839 Viktoria Kabel: Similarly, if we look at the symplectic form for the gravitational radiation, we find that the first order, perturbations. 170 00:32:34,920 --> 00:32:51,560 Viktoria Kabel: Don't enter with the standard exterior, derivative, but with a kind of covariant field space exterior derivative, and the issue intuition behind that is really just that you're subtracting any variation. 171 00:32:51,580 --> 00:32:56,430 Viktoria Kabel: the gravitational radiation that could be absorbed by the coordinate fields. 172 00:32:57,240 --> 00:33:03,150 Viktoria Kabel: So it's also, again, a kind of relative variation with respect to the coordinate fields. 173 00:33:03,940 --> 00:33:23,009 Viktoria Kabel: And then, finally, and most importantly, we find that we automatically without having to introduce any boundary terms, find that the in the action find that the symptic form contains this boundary term describing the coordinate fields X mu, which provide a reference frame for the diffumorphism group. 174 00:33:23,170 --> 00:33:29,909 Viktoria Kabel: and these Lorentz frames at the boundary which provide a reference frame for the internal SO. 1, 3. Symmetry. 175 00:33:31,510 --> 00:33:34,230 Viktoria Kabel: and these fulfill several roles. 176 00:33:34,510 --> 00:33:41,919 Viktoria Kabel: I want to focus on the coordinate fields for the remainder of this talk, but you could really make similar arguments for the Lawrence frames. 177 00:33:42,020 --> 00:34:04,320 Viktoria Kabel: But the coordinate fields firstly, render the entire symplectic form invariant under the few morphisms. So it's on automatically invariant, not just under the few morphisms that act in the bulk, but also on the large diffum morphisms that act non-trivially at the boundary, because these changes are absorbed by the coordinate fields. 178 00:34:05,240 --> 00:34:16,609 Viktoria Kabel: Secondly, as we saw, they provide a reference for the point particles path through the dressing in the symplectic form, and similarly a reference for the variations of the gravitational radiation. 179 00:34:17,020 --> 00:34:28,789 Viktoria Kabel: And finally, and this is a special feature of generally covariant theories rather than just gauge theory. They are actually what defines the location of the boundary itself. So one can also see them as a kind of embedding fields 180 00:34:28,969 --> 00:34:32,559 Viktoria Kabel: after region into a background spacetime. 181 00:34:35,750 --> 00:34:51,039 Viktoria Kabel: But we can also read off from this description is the momentum conjugate to these coordinate fields, and we can explicitly find a definition of the momentum in terms of the bulk degrees of freedom in terms of the second order. Perturbations of the 182 00:34:51,710 --> 00:34:52,980 Viktoria Kabel: connection. 183 00:34:53,840 --> 00:35:10,700 Viktoria Kabel: and these have 2 important features. Firstly, they actually provide us with a conserved quantity. So if we integrate this along the edge this gives us a conserved quantity, and if we then also send the boundary to infinity, this actually agrees with the adm momentum. 184 00:35:11,420 --> 00:35:24,570 Viktoria Kabel: and secondly, if we go to the quantum theory, the definition of the momentum will actually have to be imposed as a constraint on the physical States. Which relates the bulk and the boundary degrees of freedom. 185 00:35:25,900 --> 00:35:27,080 Viktoria Kabel: So. 186 00:35:27,530 --> 00:35:46,899 Viktoria Kabel: having talked enough, I think, about the classical theory, I now want to turn to the implications for the quantum theory. And because we're using linearized gravity. And we've described everything in terms of the symplectic form, we can already make quite easily a few statements of what the quantum theory of the setup should look like. 187 00:35:48,100 --> 00:36:08,349 Viktoria Kabel: So the first one is that because we saw the symplectic form splits into these 3 independent parts describing matter of radiation and the boundary degrees of freedom, we would expect the same to hold true for the kinematical Hilbert space, which should be partitioned in a tensor product of some bulk, degrees of freedom, matter, and radiation, as well as the boundary degrees of freedom. 188 00:36:09,310 --> 00:36:22,469 Viktoria Kabel: Secondly, as I was already alluding to, we're going to have to impose this momentum definition as a constraint. This will give us an equation that relates to bulk and the boundary degrees of freedom, and in particular. 189 00:36:22,610 --> 00:36:29,129 Viktoria Kabel: will actually provide us with a relational Schrodinger equation at the boundary, so it will give us the 190 00:36:29,420 --> 00:36:40,920 Viktoria Kabel: evolution of the physical state with respect to the coordinate fields. X. Mu at the boundary, so an evolution in time and in space, so to speak, because you have to form 191 00:36:40,930 --> 00:36:43,100 Viktoria Kabel: coordinate fields here 192 00:36:44,540 --> 00:36:55,489 Viktoria Kabel: and finally. And this is really what brings us back to the original motivation of this talk. We can derive the quantum reference frame transformations for these boundary degrees of freedoms 193 00:36:55,520 --> 00:36:58,430 Viktoria Kabel: if we send the boundary to infinity. 194 00:36:59,880 --> 00:37:12,810 Viktoria Kabel: So let's do that. Let's consider a bounded region in space-time. But we're sending the boundary off to infinity. There is a slight technical issue that arises, because if we send the boundary to infinity, one of the coordinate 195 00:37:12,810 --> 00:37:27,560 Viktoria Kabel: values is also gonna at least one of the coordinates is also gonna diverge because it's gonna be infinite. But we can deal with this by simply splitting the coordinate fields into a finite and a divergent part. So we introduce some fiducial coordinates X 0. 196 00:37:27,560 --> 00:37:49,440 Viktoria Kabel: And then the coordinate fields at the boundary are gonna be completely described by global Lawrence. Rotations of these past some finite and angle dependent translations. So by now, the boundary we're considering for a given cauchy hypa surface is gonna be like a sphere. So we just have different translations for every angle on that sphere. 197 00:37:49,730 --> 00:37:53,119 Viktoria Kabel: And of course, this holds up to order one over row. 198 00:37:54,730 --> 00:38:03,369 Viktoria Kabel: These actually, these global orange rotations and finite angle. Dependent translations are what characterizes the asymptotic symmetries of the boundary. 199 00:38:04,460 --> 00:38:27,480 Viktoria Kabel: Now, as we saw, the whole bit space splits into this tensor product of bulk and boundary degrees of freedom. So at least formally, we should be able to expand the state in terms of an Eigenbasis of the coordinate fields. So we're just using these 2 described states peaked around some classical configuration, Omega and Q. 200 00:38:28,860 --> 00:38:53,959 Viktoria Kabel: And we can now consider 2 states where the reference systems. The coordinate fields are in 2 different configurations. So we're considering one quantum reference frame peaked under configuration. Q. 0 and omega 0. And then we're considering another one which is any superposition of different configurations. Qi. And again, for simplicity, just leaving the Omega 0 the same. But you could do the same argument for the global orange rotations. 201 00:38:55,680 --> 00:39:06,319 Viktoria Kabel: And now, so far, we've just been considering the kinematical states. If we want to deal with the physical habit space, we also have to impose the momentum constraint. 202 00:39:06,540 --> 00:39:23,059 Viktoria Kabel: This can be done through a projector which is essentially just the delta function of the constraint. But we can write this in terms of this exponential here, and this again, is just the definition of the momentum. Conjugate to the coordinate fields in terms of the bulk degrees of freedom. 203 00:39:24,410 --> 00:39:34,940 Viktoria Kabel: And if we now look at the physical inner product of these 2 States, this will give us the quantum reference frame transformation that maps us 204 00:39:34,940 --> 00:39:56,800 Viktoria Kabel: from this reference frame in superposition to the reference frame and the definite configuration. Q. 0. And really, the way to read this equation more intuitively, is that DNA product kind of compares the 2 States. Science phi. But in order to compare them at first, has to rotate them so that they're described. With respect to the same reference frame. 205 00:39:56,800 --> 00:40:05,310 Viktoria Kabel: this rotation is then implemented by the matrix element of the projector, which will give us a unitary 206 00:40:05,630 --> 00:40:08,799 Viktoria Kabel: implementing. The change from the reference frame qi. 207 00:40:08,830 --> 00:40:11,179 Viktoria Kabel: To the reference frame. Q. 0. 208 00:40:11,230 --> 00:40:22,389 Viktoria Kabel: But importantly, it's not just one unitary. It's, in fact, a sum or a quantum controlled unitary, where for each branch of the superposition I, we apply different 209 00:40:22,810 --> 00:40:26,340 Viktoria Kabel: transformation. QQI. To Q. 0. 210 00:40:26,420 --> 00:40:46,039 Viktoria Kabel: We can again formally write this out, and we see that this actually looks a lot like the quantum translation operator with 2 main differences. Firstly, these translations, qi, or angle dependent translation. So at every point of the boundary you can actually do a different translation. Secondly, the H. Mu 211 00:40:46,120 --> 00:40:51,690 Viktoria Kabel: will tell you how this translation acts under gravitational degrees of freedom in the bulk. 212 00:40:53,720 --> 00:41:05,149 Viktoria Kabel: So this really gives us a quantum controlled point-wise translation from within the framework of quantized linearized gravity, and as such. 213 00:41:05,280 --> 00:41:10,740 Viktoria Kabel: it generalizes the quantum control translations that we saw before. 214 00:41:11,390 --> 00:41:21,250 Viktoria Kabel: So, in a way, you could see this as a strategy to derive or justify quantum reference frame transformations from within a general relativistic description. 215 00:41:23,440 --> 00:41:42,779 Viktoria Kabel: So before closing, I just want to quickly summarize this part of the talk, because it's been quite long. We've seen that in linearized gravity we quite naturally get these coordinate fields as edge modes at the boundary of space-time, and I argued that 216 00:41:42,780 --> 00:42:00,890 Viktoria Kabel: judging from the form of the symplectic form. These are to be included in the quantum description as well, and this actually has some advantages. First of all leads to a relation or Schrodinger equation through the momentum constraint. So we actually get a evolution with respect to these reference fields, and the such, they really 217 00:42:00,970 --> 00:42:06,919 Viktoria Kabel: also act as the kind of reference quantum reference frames that you would want as a solution to the problem of time. 218 00:42:07,470 --> 00:42:21,049 Viktoria Kabel: And, secondly, we also find that at asymptotic boundaries we obtain quantum reference frame transformations for pointwise translations and rotations. If we had included the global Lawrence rotations as well. 219 00:42:21,300 --> 00:42:26,580 Viktoria Kabel: And if you wanna see any of the details there. Given our paper on the Archive 220 00:42:30,120 --> 00:42:56,810 Viktoria Kabel: so altogether, I hope that I could explain to you how quantum reference frames generalize the idea of a classical reference frame, at least in the simple scenarios considered here. And particularly, I think, the key takeaways that the quantum reference frame changes are implemented by quantum controlled symmetry, transformations giving rise to these extended symmetry principles, and that superposition and entanglement become frame features. 221 00:42:57,320 --> 00:43:14,009 Viktoria Kabel: which is also crucial because this allows us to study problems that you interface between quantum physics and gravity, like that of a massive object in superposition from a new perspective that allows us to solve the problem without making any assumptions about the quantum nature of the gravitational field. 222 00:43:14,320 --> 00:43:20,099 Viktoria Kabel: But we also looked at the problem from a different angle, and saw how quantum reference frames. 223 00:43:20,320 --> 00:43:28,720 Viktoria Kabel: or the asymptotic symmetries arise as edge modes at the boundary of space-time and linearize general relativity. 224 00:43:31,070 --> 00:43:45,170 Viktoria Kabel: Now, I think the field of quantum reference frames. Is really connected to quite a lot of different research research research directions in and around of quantum gravity. We already saw how they're related to edge modes. 225 00:43:45,630 --> 00:43:58,970 Viktoria Kabel: I think there is also a good case to be made that they can eventually be connected to the material reference frames in quantum gravity in particular, the ones that you might use and look quantum cosmology to describe cosmological evolution. 226 00:43:59,260 --> 00:44:28,359 Viktoria Kabel: and there are also 2 other directions. I just wanna briefly mention the first is the idea that some recent research by Witten and others has shown that if you have quantum field theory on curved spacetime, and if you include an additional reference degree of freedom, something as simple as a quantum clock, this actually solves a lot of problems within the quantum field theory description, and in particular gives you a finite entropy, for example. 227 00:44:28,470 --> 00:44:42,269 Viktoria Kabel: and I think that if we see that these reference frame emerge already naturally in linearized gravity. Maybe these can also act as the kind of regulators that they do in this area of research. 228 00:44:42,750 --> 00:45:08,320 Viktoria Kabel: And I think another interesting direction that we could barely touch on here. Is that the reference frames will generally be conjugate to some momenta or other charges, or conserved quantities. And this would actually be interesting to investigate further, because, if we understand, in a trash of neuter charges and charge sectors at the quantum theory, this could actually relate us back 229 00:45:08,380 --> 00:45:11,189 Viktoria Kabel: to an area where quantum reference frames 230 00:45:11,390 --> 00:45:16,860 Viktoria Kabel: were originally studied in quantum information theory, which is the study of super selection sectors. 231 00:45:17,420 --> 00:45:30,269 Viktoria Kabel: But yeah, I think these are just a few examples of how quantum reference frames are connected to other areas. I'd be very curious to hear your thoughts on that or any questions that you have, and I would like to thank you for your attention. 232 00:45:32,120 --> 00:45:35,240 Hal Haggard: Thank you, Victoria, for such a nice summary of your work. 233 00:45:38,480 --> 00:45:53,450 Hal Haggard: So I also wanted to explicitly thank you, Victoria, for for leaving enough time for us to have questions at the end. We've we're trying to encourage more and more of our speakers to keep it to this length. So thank you very much. 234 00:45:53,800 --> 00:45:57,609 Hal Haggard: Ding had his hand raised first. So, Ding, why don't we start with you? 235 00:45:58,160 --> 00:46:04,140 Ding Jia: Thank you. I'm going to make some very critical remarks 236 00:46:04,320 --> 00:46:08,789 Ding Jia: up to make clear something. It's nothing against you personally. 237 00:46:09,000 --> 00:46:12,110 Ding Jia: because these mistakes were made by 238 00:46:12,370 --> 00:46:19,589 Ding Jia: your collaborators and other people. They're in the works. They're old works. They're already there and just pointing them out. And 239 00:46:19,800 --> 00:46:22,000 Ding Jia: and it's nothing against you. 240 00:46:22,020 --> 00:46:36,600 Ding Jia: Don't think you're introducing any new mistake. Secondly, I sincerely hope that you can point out that that the mistakes are actually mine. So that though, there's something for me to learn, and I'd be really happy if that if that happens. 241 00:46:36,760 --> 00:46:40,669 Ding Jia: basically are 2 criticisms. If you could go to the 242 00:46:40,790 --> 00:46:42,640 Ding Jia: motivation slide 243 00:46:42,990 --> 00:46:46,050 Ding Jia: we mentioned operationalism. 244 00:46:46,160 --> 00:46:48,929 Ding Jia: Yes. here, I think 245 00:46:49,100 --> 00:46:53,140 Ding Jia: personally, this point is wrong. In practice. 246 00:46:53,550 --> 00:47:05,860 Ding Jia: Any reference frame is a physical system. Think this this is a really wrong Ngr. Example, if you study a black hole, we introduce a coordinate system. TR. Theta Phi. 247 00:47:06,620 --> 00:47:10,019 Ding Jia: This is not a physical system. We don't have any physical field. 248 00:47:10,100 --> 00:47:13,300 Ding Jia: The town is divided of of RT. etc. 249 00:47:13,680 --> 00:47:18,979 Ding Jia: This is a mental construction. It's our invention. It's not a physical system. 250 00:47:19,570 --> 00:47:24,559 Ding Jia: and it's misleading. It's a mistake. So say that this is a classical reference frame. 251 00:47:24,730 --> 00:47:26,610 Ding Jia: because it's not a physical system. 252 00:47:26,830 --> 00:47:30,190 Ding Jia: Therefore there's there's no mo, no motivation 253 00:47:30,420 --> 00:47:35,609 Ding Jia: to generalize this kind of artificial mental invention to a quantum system. 254 00:47:35,850 --> 00:47:40,390 Ding Jia: Therefore, this is not a valid motivation to go to a quantum reference frame. 255 00:47:41,370 --> 00:47:52,859 Viktoria Kabel: And secondly, maybe, can I quickly reply to the question. And you say, the second point, yeah, I think I mean, this is really just in practice, if you do any actual measurement 256 00:47:52,900 --> 00:48:10,510 Viktoria Kabel: like, of course, there are much more general coordinate systems, and even without TRI could think of jumping into the reference frame of a particle moving at the speed of light which will practically never be possible. So it's really just the mental construct of the reference frame. But the idea is really that 257 00:48:10,810 --> 00:48:21,329 Viktoria Kabel: the reference frame that we actually can use in experiments and with respect to which we calibrate our measurement results that is always going to be physical. So in TR. It's going to be. 258 00:48:21,960 --> 00:48:27,579 Viktoria Kabel: I don't know whatever system you use to send your light race to the next 259 00:48:27,640 --> 00:48:43,109 Viktoria Kabel: planet, or to collect the light rays that come to you from a distant galaxy into your telescopes. And it's really just referring to those. Of course, there are coordinate systems and reference frames that are used in theory that are never realized in practice. 260 00:48:44,200 --> 00:48:52,150 Ding Jia: Even if that's true, I still think the statement. The claim is too strong because you're saying in practice, any reference ring is a physical system. 261 00:48:52,270 --> 00:48:56,880 Ding Jia: I can think of practical situations where I use a a artificial. 262 00:48:56,890 --> 00:49:00,420 Ding Jia: a mental reference. Right? It's not a physical system. 263 00:49:00,920 --> 00:49:04,029 Ding Jia: right? I think it boils down to what you mean by in practice. 264 00:49:04,220 --> 00:49:13,160 Ding Jia: What I meant is really just in in the laboratory, or if you're an experiment, I can think of non physical system that are used. 265 00:49:13,660 --> 00:49:16,900 Ding Jia: I can set up a coordinate system in the middle, in a love department. 266 00:49:17,280 --> 00:49:22,199 Ding Jia: And this describes you. You know what experimentalists do. That's very practical. 267 00:49:23,980 --> 00:49:27,930 Viktoria Kabel: right? But if you actually try to measure it you would have to use 268 00:49:28,110 --> 00:49:31,459 Ding Jia: like, I still use an artificial reference room. That's not a physical assistant. 269 00:49:34,120 --> 00:49:42,240 Ding Jia: Next point. This is more important point. Could you go to the slide where you show a picture of Earth and the party going. Superposition. 270 00:49:42,340 --> 00:49:43,060 Viktoria Kabel: Hmm. 271 00:49:44,230 --> 00:49:54,960 Ding Jia: yes. I think the core idea of quantum rifles, right is to identify points across different configurations in superposition. 272 00:49:55,060 --> 00:49:56,710 Viktoria Kabel: I completely agree 273 00:49:56,810 --> 00:49:59,669 Ding Jia: here. You're showing showing us 274 00:49:59,740 --> 00:50:05,799 Ding Jia: a party going to Earth. and there are different configurations for these physical objects. 275 00:50:05,970 --> 00:50:17,719 Ding Jia: and there are different ways to identify those different pictures. It's like you have one picture and another. You're stacking them on top of each other, and either put the party at the same position 276 00:50:18,000 --> 00:50:22,770 Ding Jia: with the earth that is in position for infinitely many other ways to do this. 277 00:50:22,920 --> 00:50:26,010 Ding Jia: and this is the guard here of quantum reference frame. 278 00:50:26,250 --> 00:50:27,500 I think 279 00:50:28,080 --> 00:50:31,250 Ding Jia: this structure is totally superfluous. 280 00:50:31,290 --> 00:50:42,479 It doesn't make any difference to the physical theory. for the following reason. In quantum physics there are 2 combinations. There are either integral formulations 281 00:50:42,900 --> 00:50:55,370 Ding Jia: non path, integral formulations. Let's discuss them in turn. Let's consider path integral formulation of the quantum theory. What does it need to define the theory? We have a set of configurations? 282 00:50:55,970 --> 00:50:57,600 Ding Jia: If you sum it over. 283 00:50:57,840 --> 00:51:05,590 Ding Jia: we have a map that tells us, like some pitches for each configuration. and then we sum the complex 284 00:51:05,940 --> 00:51:07,630 Ding Jia: to obtain numbers. 285 00:51:07,930 --> 00:51:11,530 Ding Jia: the end. The results can either be a complex amplitude 286 00:51:11,580 --> 00:51:16,980 Ding Jia: or real probability depends on whether you single path into a double bathroom to go. 287 00:51:17,330 --> 00:51:23,329 Ding Jia: And that's a cool story. It tells us what exists in the world apart into a configurations. 288 00:51:23,480 --> 00:51:27,080 Ding Jia: But the dynamic allows are through the amplitude map 289 00:51:27,580 --> 00:51:30,929 Ding Jia: and what the the physical predictors predictions are 290 00:51:30,980 --> 00:51:33,879 Ding Jia: the probabilities. That's full story. 291 00:51:34,110 --> 00:51:40,420 Hal Haggard: Ding. Why don't you leave it there and let Victoria respond. I just want to make sure other people get a chance to ask questions. 292 00:51:42,180 --> 00:51:52,699 Viktoria Kabel: Yeah, yeah. I mean, with the identification. I completely agree. And we actually have a paper and production where we relate everything. 293 00:51:53,340 --> 00:51:59,940 Viktoria Kabel: more directly to this role of quantum reference frame as identifying objects across the branches. 294 00:52:00,190 --> 00:52:08,199 Viktoria Kabel: I'm not sure what what the issue is with. The 295 00:52:08,220 --> 00:52:09,720 Ding Jia: the issue is. 296 00:52:09,900 --> 00:52:16,989 Ding Jia: You can identify the path into a configuration points the passing configurations in any way you want. 297 00:52:17,800 --> 00:52:20,470 Ding Jia: it doesn't change as a result of the path into your 298 00:52:20,840 --> 00:52:23,830 Viktoria Kabel: oh, yeah, I mean, that's what I 299 00:52:24,180 --> 00:52:32,599 Ding Jia: however, you identified. The result of the passenger is the same. So it's a superfluous structure to introduce quantum reference frames. 300 00:52:32,920 --> 00:52:49,320 Viktoria Kabel: Yeah, I mean, to some extent, I agree. But I think it's superfluous in the same sense that reference frame, and general relativity as a Pufflow's or the gauge parameter engage theories of perflus. But I think it's just because the description without it is so inconvenient 301 00:52:49,380 --> 00:52:53,580 Viktoria Kabel: that we often like to use these reference frames, and 302 00:52:53,590 --> 00:53:16,360 Viktoria Kabel: if we already use them, we might as well study them at the quantum level as well, because I think actually studying Pr in terms of particular reference frames, instead of just using a non local different variant description has told us a lot about Dr. That we would have maybe not understood without it, and I think, similarly, you don't necessarily need to quantum reference frames for a full description. I completely agree with you 303 00:53:16,360 --> 00:53:23,830 Viktoria Kabel: on that, but I think they can still give us more understanding, because we can look at the problem from more and different perspectives. 304 00:53:25,070 --> 00:53:30,039 Hal Haggard: All right, let's leave that discussion there for now Simone was next. 305 00:53:31,570 --> 00:53:33,190 Simone SPEZIALE: Thanks. 306 00:53:33,280 --> 00:53:50,590 Simone SPEZIALE: 2 2 questions, but they should be quick first. One is that I got cut off at some point. So if you could please repeat what was the tension or contradiction you mentioned between this extended symmetry principle you assumed at some point, and maybe semi classical quantum gravity. 307 00:53:51,020 --> 00:53:54,530 Simone SPEZIALE: Right? Please repeat that. 308 00:53:54,540 --> 00:54:10,180 Viktoria Kabel: Yeah, this is just. If you imagine that you have a scenario where the particle is directly in the middle between the 2 locations of the massive object and superposition? And if you really just use semiclassical gravity as your full description of this. 309 00:54:10,180 --> 00:54:24,560 Viktoria Kabel: then it would predict a gravitational field that vanishes in the middle of the configuration right? Because it's just the average. So it would predict that the particle doesn't move at all, which is in contradiction to the prediction. You get through the extended symmetry principle 310 00:54:24,810 --> 00:54:26,900 Simone SPEZIALE: amazing. Okay, thank you. 311 00:54:26,950 --> 00:54:44,930 Simone SPEZIALE: And the other question is coming back to my initial question. You said that. No, you're not saying that every observer should be treated as quantum. You are still happy in treating observers as classical, so we don't have to worry about collapse. But then my question is, if we are happy with the observers being classical. 312 00:54:45,040 --> 00:54:59,979 Simone SPEZIALE: Who is then going to use this quantum reference frame? What are they going to be relevant for? Could you pinpoint some questions that a classical observer would need this reference quantum reference frames in order to answer. 313 00:55:00,840 --> 00:55:01,900 Viktoria Kabel: and I think 314 00:55:02,220 --> 00:55:12,790 Viktoria Kabel: in this sense, in practice I see them more as a tool. It's kind of like you go into the reference frame of a vertical moving at the speed of light. You're never actually gonna find an observer 315 00:55:13,160 --> 00:55:22,719 Viktoria Kabel: who realizes this reference frame, who can actually measure things? But you kind of use it as a tool to make predictions. And similarly, leaders? 316 00:55:23,160 --> 00:55:37,480 Viktoria Kabel: Probably not. Gonna we're not gonna be able to put our measurement up, or at this is actually in the same configuration as the quantum reference frame. But we can kind of use it as a tool and then make predictions there and worries me. Is that in the 317 00:55:37,560 --> 00:55:45,139 Simone SPEZIALE: in this tool. I mean, how can you compare these 2? Because, you see, the problem is that the classical observer sees the collapse 318 00:55:45,220 --> 00:55:55,109 Simone SPEZIALE: in this quantum reference frame? If everything is quantum, there's never gonna be any collapse. So how can this be a practical tool? Because somehow we will have to. 319 00:55:55,230 --> 00:56:18,309 Simone SPEZIALE: So these are my initial questions like, Are you motivated by trying to complete the quantum mechanics, so that you have a unitary theory that includes the observers and the collapse. And if not, II kind of would like to see. You know precisely how is this tool going to be used by the classical observer which sees something that is inherently not described by unitary processing quantum mechanics. 320 00:56:19,270 --> 00:56:28,390 Viktoria Kabel: Right? I think. Okay, so as soon as we we talk about collapse, I think this is going more into speculative regime. The quantum reference frames. 321 00:56:28,560 --> 00:56:53,680 Viktoria Kabel: considered so far, really, just assume the unitary evolution. I think there is maybe one comment to be made. It maybe doesn't directly address your question, but in a sense you could say that in the reference frame of whatever object you choose, it behaves kind of classically, and this is because the state of the reference frame itself always factorizes out. 322 00:56:54,320 --> 00:57:08,650 Viktoria Kabel: So in the sense. As soon as you go into a reference particular particle, you could treat that as classical, and thereby please momentum. You don't know its position. Why is it classical? 323 00:57:08,850 --> 00:57:17,770 Viktoria Kabel: Right? II. This is assuming that this is not actually a flying state, but a coherent state. if we and so I mean there would be a spread 324 00:57:19,470 --> 00:57:31,049 Viktoria Kabel: right. But you could find the coherence that a state that is very closely peaked around. X equals 0. It's a free particle it will spread will grow inevitably. 325 00:57:31,720 --> 00:57:38,250 Simone SPEZIALE: Not for a coherent state. Yeah, for a free particle. Yes. you're you're you're thinking of a 326 00:57:38,400 --> 00:57:43,370 Simone SPEZIALE: of a closed orbit. Couldn't stay like the harmonic oscillator. But if you have a free particle it spread rose. 327 00:57:43,520 --> 00:57:52,299 Viktoria Kabel: Okay. But then, but then, additionally, the reference frame itself probably won't evolve, because with respect to itself, it doesn't really make sense 328 00:57:52,680 --> 00:57:55,990 Viktoria Kabel: for it to evolve in its own recognized. 329 00:57:56,170 --> 00:57:59,129 Simone SPEZIALE: Thank thank you very much. Very nice. Thank you. 330 00:57:59,440 --> 00:58:00,980 Hal Haggard: Laurent was next 331 00:58:02,970 --> 00:58:07,000 Laurent Freidel: II think. Carlos was maybe before now. 332 00:58:07,210 --> 00:58:11,890 Hal Haggard: Well, you had unmuted before you raised your hands. II don't mind either way. 333 00:58:12,840 --> 00:58:34,089 Laurent Freidel: Okay. Well, just first. Thank you for this. You know. Very clear talk, Victoria. And and the connection between, you know, reference frame edge mode maybe it's a question of clarification, and and they can help to answer. Maybe the both previous questions. So if I understand as part of your results. 334 00:58:34,090 --> 00:58:44,319 Laurent Freidel: what you're showing is and maybe most people are really aware of it is that the gravitational field has different components in it. Right? It does the spin 2 components. 335 00:58:44,340 --> 00:58:47,220 Laurent Freidel: But it's also as it's a Newtonian component 336 00:58:47,790 --> 00:58:53,989 Laurent Freidel: which you know in in regular quality. Theory is is kind of usually not quantized. 337 00:58:54,080 --> 00:59:02,729 Laurent Freidel: And you can think of these Newtonian component or the other component of the of the gravitational field as quantum reference frame. 338 00:59:02,760 --> 00:59:13,689 Laurent Freidel: and and it's not kind of I mean. Tell me if you agree with that for me, it's not kind of optional to introduce them is that if you really want to talk about what is the radiation, you have to separate what you mean. 339 00:59:13,690 --> 00:59:33,260 Laurent Freidel: you know the audition is relative to a Newton and Company. So let's say, you know, in the linearized regime you are with, okay, maybe it's possible to to have an absolute split. But in general you know, in full non gener, it's not going to be possible, because the speed to the gravitation of addition is going to back react 340 00:59:33,270 --> 00:59:44,439 Laurent Freidel: under Newton potential. So anyway, if you want to comment on that, because I think that's one of the conclusion you're you're raising there at the end that you, you know, in the gravitational case, it's it's not really an option. 341 00:59:45,990 --> 00:59:54,790 Viktoria Kabel: right? I think I agree in general, I'm a bit confused. Why, you say the radiation with respect to the Newtonian potential cause, I think it's also with respect to the 342 00:59:54,950 --> 01:00:07,399 Viktoria Kabel: coordinate fields that it has to be defined. So there is kind of 3 layers. There is kind of the background, coordinate fields, which are kind of redundant, and then we also do the split into the 343 01:00:07,580 --> 01:00:10,679 Viktoria Kabel: coulombic part and radiation part. 344 01:00:11,280 --> 01:00:17,119 Laurent Freidel: But at the end you did have a coordinate, you know, edge mode coordinate that came from the gravitational field. 345 01:00:18,430 --> 01:00:28,399 Viktoria Kabel: Yes, but I wouldn't necessarily say it comes from the Newtonian part of the gravitational field, or I think that maybe maybe we understand different things. By the. 346 01:00:29,650 --> 01:00:32,790 Viktoria Kabel: if you just mean a flat spacetime background. Then I agree. 347 01:00:33,070 --> 01:00:39,070 Laurent Freidel: But I mean, I mean, thatometric contains spin, 0 spin one and spin 2 components. The spin 2 is the 348 01:00:39,090 --> 01:00:57,130 Laurent Freidel: new potential. If 349 01:00:57,480 --> 01:00:59,050 Laurent Freidel: okay, that's 350 01:00:59,090 --> 01:01:01,970 Laurent Freidel: by by the speed 0 component. 351 01:01:02,680 --> 01:01:17,929 Laurent Freidel: I mean you, you haven't really explained too much in your talk. Maybe you can expand on that. What do you call the radiation yet this Delta? You knew that you could audition, but didn't really. Initially we understood how you define that and how you expect the the coordinates from the gravitational field? 352 01:01:18,890 --> 01:01:23,439 Viktoria Kabel: Right? Right? I mean very briefly. What is it? 353 01:01:26,000 --> 01:01:41,589 Viktoria Kabel: Right? I mean, there, there's more splits going on. So first of all, there's the the split into the background fields that are kind of the coordinates associated to the flat solution, and then there are perturbations. But these perturbations are then also split into first order and second order. Perturbations. 354 01:01:41,830 --> 01:01:45,349 Viktoria Kabel: and the first order. Perturbations are, gonna be the 355 01:01:45,470 --> 01:01:57,689 Viktoria Kabel: gravitational radiation and the second order. Perturbations are gonna be the ones that come from the matter. So you could see them as kind of columbic parts, maybe, as well as the ones where 356 01:01:58,190 --> 01:02:02,100 Viktoria Kabel: the gravitation of radiation itself is sourcing more. 357 01:02:02,150 --> 01:02:03,600 Viktoria Kabel: more gravity. 358 01:02:04,210 --> 01:02:05,579 Viktoria Kabel: This would be d 359 01:02:06,100 --> 01:02:07,890 Viktoria Kabel: different degrees of freedom. 360 01:02:10,650 --> 01:02:13,590 Hal Haggard: Let's move on to Carlos, who's been waiting patiently. 361 01:02:19,160 --> 01:02:22,900 carlos alex souza da silva: Thank you very much, Victoria, for your talk. 362 01:02:23,390 --> 01:02:25,370 carlos alex souza da silva: like questions 363 01:02:25,620 --> 01:02:30,179 carlos alex souza da silva: is about if is it possible 364 01:02:30,240 --> 01:02:32,969 carlos alex souza da silva: to conceive quite reference frames 365 01:02:33,020 --> 01:02:39,160 carlos alex souza da silva: beyond space? Time? Talking was about what reference frame is in space time. 366 01:02:39,530 --> 01:02:46,539 carlos alex souza da silva: and I would like to ask you if it's is it possible to conceive quant reference frames beyond space time. 367 01:02:48,290 --> 01:02:54,090 Viktoria Kabel: I mean, I think in general, the the abstract formalism of quantum reference frames. 368 01:02:54,650 --> 01:03:03,530 Viktoria Kabel: If you really see it in terms of these quantum systems, you could do it for any symmetry group, so you could also do it for any kind of internal symmetry group 369 01:03:03,680 --> 01:03:09,359 Viktoria Kabel: which I would then maybe describe as quantum reference frames. Not in space time. 370 01:03:11,210 --> 01:03:14,549 Viktoria Kabel: So the framework works really for any any group. 371 01:03:14,950 --> 01:03:17,409 carlos alex souza da silva: Okay. thank you very much. 372 01:03:18,710 --> 01:03:19,720 Hal Haggard: Joe's. 373 01:03:23,280 --> 01:03:29,929 Joe Aziz: Thank you. For the talk. I wanted to ask if there's any ideas or 374 01:03:30,720 --> 01:03:39,720 Joe Aziz: attempts for some experiment that might show whether the extended symmetry principle is really a symmetry of nature 375 01:03:40,500 --> 01:03:50,630 Viktoria Kabel: right? So we actually thought about whether we can maybe do something like this. But with a clock instead of the particle 376 01:03:51,110 --> 01:03:55,339 Viktoria Kabel: and then, if the clock takes in a superposition of 377 01:03:55,470 --> 01:04:02,540 Viktoria Kabel: different ticking rates due to the gravitational field. So you're going to have to place it a bit closer and a bit further away. 378 01:04:02,990 --> 01:04:15,510 Viktoria Kabel: The mass configuration. If we could actually test that, you could see that as a test of the extended symmetry principle, however, the numbers that we got from our experimental list of trust 379 01:04:15,520 --> 01:04:29,289 Viktoria Kabel: what they could achieve were were unfortunately still very far away from we can actually measure. But theoretically you could think of experiments that could test that. It's just. We haven't found a feasible one yet. 380 01:04:29,500 --> 01:04:38,140 Joe Aziz: Do you? Do you have any idea of how unfeasible it is! Is it borderline impossible, or is it like. 381 01:04:38,820 --> 01:04:42,669 Viktoria Kabel: I don't remember the exact timescales? I think 382 01:04:42,920 --> 01:05:01,820 Viktoria Kabel: it was. At least you would have to measure like small time differences of like. I don't know 10 to the minus 30 or 34, which is quite beyond what we can measure right now, but it's also much closer than the Planck time, which is maybe where people generally would expect the quantum gravity, thanks to kick in. So maybe it's 383 01:05:01,860 --> 01:05:03,610 Joe Aziz: little bit more hopeful 384 01:05:03,640 --> 01:05:05,959 Viktoria Kabel: than certain other approaches. But 385 01:05:06,050 --> 01:05:22,050 Viktoria Kabel: I think there might actually be scenarios if one thought about this more where it's more realistic to test this, because actually putting a massive object in superposition is something that people expect to be able to do in like 1020 years time. It's just gonna be quite light. 386 01:05:23,790 --> 01:05:24,919 Joe Aziz: Okay, thank you. 387 01:05:26,800 --> 01:05:27,720 100. 388 01:05:29,180 --> 01:05:31,419 Alejandro PEREZ: Hi, thank thank you. I've 389 01:05:31,730 --> 01:05:58,220 Alejandro PEREZ: for the nice talk. II arrived a little bit late, and so but I think, question. I mean, the question is, I want to ask you question, but it's related to the beginning of the of your talk. So even in this quantum mechanical setup where things are much simpler and much explicit. I so you evolve this translation operator that will relate different reference frames at the quantum level 390 01:05:58,650 --> 01:05:59,520 Alejandro PEREZ: I 391 01:05:59,680 --> 01:06:10,940 Alejandro PEREZ: and there a lot of factor ambiguities is, is this transformation actually defined? Well defined, I mean free of ambiguities 392 01:06:11,570 --> 01:06:16,930 Alejandro PEREZ: because of factor ordering. II mean, I mean this translations where your parameter now is an operator. 393 01:06:17,120 --> 01:06:22,129 Viktoria Kabel: Yes, yes, I think it's actually not so much of a problem, because, it's different systems. 394 01:06:22,250 --> 01:06:29,610 Viktoria Kabel: It's XA and Pb, to enter in the translation operator. And these communities. Yeah, yeah, but you, you seem to. 395 01:06:30,040 --> 01:06:46,019 Alejandro PEREZ: Is that the case for any? If if the group was done, Abelian or I mean if you go to the if you really, this is the reason why we're using the parity swap. It only becomes problematic 396 01:06:46,030 --> 01:06:49,219 Viktoria Kabel: if we want to translate the reference frame itself. 397 01:06:49,280 --> 01:06:55,299 Viktoria Kabel: Because if we use different operators associated to different systems. 398 01:06:55,440 --> 01:07:16,440 Viktoria Kabel: This should generally be commuting. Maybe you can think of some example where the momentum of particle A does not commute with the position of particle B, but usually the different subsystems commute among one another, and then the only problem that you would have is if you wanted to move, particle a cause, then you would have a X Apa. 399 01:07:16,740 --> 01:07:26,609 Viktoria Kabel: and then you would run into the problems, which is why we use the parity swap to deal with the reference frame itself. And this way we obtain a unitary, well defined operation. 400 01:07:27,630 --> 01:07:29,189 Alejandro PEREZ: Okay, A/C, thank you. 401 01:07:30,790 --> 01:07:31,780 Hal Haggard: Wolfgang. 402 01:07:34,530 --> 01:07:51,629 Wieland, Wolfgang Martin: just 2 short comments. So one to to lower. I think we are in in complete agreement. In fact, one of the motivations for for our for this project or this research was, in fact. 403 01:07:51,780 --> 01:08:19,120 Wieland, Wolfgang Martin: to to say that even in linear, so even in linearized gravity, if you look at the entire face space in a bounded region. We have to quantize everything, not just the radiation field inside, but also the boundary modes that will then inevitably show up as additional edge modes at the boundary of our domain. And it's true, of course, that in the linearized regime we have this 404 01:08:19,120 --> 01:08:27,299 Wieland, Wolfgang Martin: need split between radiation and and columbic modes which then at the non perturbative regime. 405 01:08:27,300 --> 01:08:44,850 Wieland, Wolfgang Martin: become where this, where it's not not anymore possible without a background to introduce this separation into radiation modes and and columbic mode. So it's ambiguous. 406 01:08:44,859 --> 01:08:53,319 Wieland, Wolfgang Martin: And then another comment, perhaps, on on this earlier question by Dean 407 01:08:53,540 --> 01:09:01,440 Wieland, Wolfgang Martin: would say, the difference is that in the case of the super post super position of. 408 01:09:01,460 --> 01:09:11,400 Wieland, Wolfgang Martin: or in the case of, a microscopic object in superposition, in a spatial superposition. What 409 01:09:11,760 --> 01:09:34,749 Wieland, Wolfgang Martin: it's not true that that even in the path integral, these 2 configurations would be equivalent gauge equivalent, because they, in fact, connected by a late large gauge transformation by large diffumorphism that doesn't vanish at infinity. And we know that these are not gauge, but they are generated by finite 410 01:09:34,750 --> 01:09:45,870 Wieland, Wolfgang Martin: charges that have that are non vanishing. So it's it's not true that they are gauge dependent gauge equivalent. So this, I think, answers the 411 01:09:46,020 --> 01:09:48,129 Wieland, Wolfgang Martin: answers. This concern. 412 01:09:49,300 --> 01:09:52,670 Wieland, Wolfgang Martin: okay, these are the 2 comments, thanks. 413 01:09:54,760 --> 01:10:01,889 Hal Haggard: Victoria. We're now 10 past the hour. Are you okay on time. I'm happy to keep hosting. We can continue discussion. 414 01:10:02,070 --> 01:10:04,209 Hal Haggard: Frank for me. Okay. 415 01:10:04,600 --> 01:10:12,679 Hal Haggard: then, Ding, just before I take you again, I'll ask if anyone else who hasn't asked a question has a question they'd like to ask. 416 01:10:15,830 --> 01:10:17,950 Hal Haggard: and if not ding, why don't you go ahead? 417 01:10:18,920 --> 01:10:23,039 Ding Jia: Thank you. Seems I'm I'm playing the role of of the badbox. 418 01:10:23,490 --> 01:10:31,520 Ding Jia: which I'm happy to 3 responses to people sent to. To my question. First of all, I'll mentioned 419 01:10:31,540 --> 01:10:42,769 Ding Jia: to address my concern. One is considered radiation. I'm not sure difficulty seeing how it addresses the concern. The 2 concerns, first. reference rooms don't have to be physical. 420 01:10:42,860 --> 01:10:48,869 Ding Jia: Second, quantum reference frames do not make difference to the physical results. I don't see how 421 01:10:49,380 --> 01:10:53,330 Ding Jia: bringing radiation to the picture addressed any of the concerns. 422 01:10:53,780 --> 01:11:01,230 Ding Jia: Second Wolfgang. Answer, Stuart. I'd be typically seeing saying a lot. There are 423 01:11:01,360 --> 01:11:13,620 Ding Jia: configurations differing by large gauge transformations, and and so it it addresses the concern. I suppose it's the second concern quantum reference rooms do not make any difference to 424 01:11:13,970 --> 01:11:15,930 Ding Jia: physical results in a path integral. 425 01:11:16,480 --> 01:11:21,490 Ding Jia: In my understanding, in the passenger sum over other configurations 426 01:11:21,680 --> 01:11:25,049 Ding Jia: I assign complex. I send over the complex numbers. 427 01:11:25,800 --> 01:11:29,800 Ding Jia: and the concern is that 428 01:11:30,010 --> 01:11:37,239 Ding Jia: you know whatever way you identify points across the configurations, it doesn't make any difference to the end results. 429 01:11:37,840 --> 01:11:42,620 Ding Jia: I don't see how thinking of large page transformations change anything. 430 01:11:42,790 --> 01:11:50,240 Ding Jia: Final response to Victoria. If you replied to my second concern by saying. 431 01:11:51,240 --> 01:11:53,589 Ding Jia: if we consider quantum reference frames. 432 01:11:53,610 --> 01:11:58,250 Ding Jia: There are some questions that are easier to solve. I'd like to press Victoria 433 01:11:58,430 --> 01:12:01,080 Ding Jia: to come up with explicit examples. 434 01:12:01,090 --> 01:12:07,570 Ding Jia: examples that we encounter in quantum gravitational research in theories of quantum gravity. 435 01:12:07,920 --> 01:12:08,900 Ding Jia: A. 436 01:12:09,540 --> 01:12:17,410 Ding Jia: Could you give me an example or some examples where quantum reference frames solves a previously difficult problem. 437 01:12:19,280 --> 01:12:23,459 Viktoria Kabel: right? I mean, I think maybe going backwards onto questions 438 01:12:23,660 --> 01:12:26,369 Viktoria Kabel: at the risk of forgetting the first one 439 01:12:26,710 --> 01:12:35,360 Viktoria Kabel: as an concrete example, I think this is an example. Of course you can solve this if you just assume that the gravitational field is in a superposition here. 440 01:12:35,420 --> 01:12:43,699 Viktoria Kabel: But I think if you push it harder and harder. You'll say you consider a black hole in superposition. I'm not sure if you would 441 01:12:43,910 --> 01:13:02,079 Viktoria Kabel: get this from any current approach, because then you can't use linearized gravity anymore. And then I don't know if you can actually practically derive the motion of a point particle for this particular state from any approach to quantum gravity. I mean, I think in theory you should be able to do it. But I don't know if 442 01:13:02,540 --> 01:13:07,299 Viktoria Kabel: there are the technical capabilities to actually complete this. So I would say. 443 01:13:07,380 --> 01:13:16,679 Viktoria Kabel: depending on what you want to put in and how much technical, difficult. Do you want to go through this? This would be an example where they can help us understand the situation. 444 01:13:17,280 --> 01:13:25,160 Ding Jia: I'm not sure it solves. I mean, it's full series of quantum gravity. So we consider 445 01:13:25,520 --> 01:13:33,860 Ding Jia: path integral with gravity coupled to a point particle. And you're considering, you know, semi classical situation. So I saw for set of points. 446 01:13:33,990 --> 01:13:40,450 Ding Jia: if a boundary condition is that there's 2 set of points that are competing in their contribution to the Bathroom Bureau 447 01:13:40,480 --> 01:13:42,010 Ding Jia: have a superposition. 448 01:13:42,530 --> 01:13:49,959 Ding Jia: and it's just solving the classical equation of motion for the set of points under certain boundary conditions. 449 01:13:50,050 --> 01:13:55,610 Viktoria Kabel: Yeah. But then you're kind of putting in that assumption, right? That it's it's kind of a superposition just after 450 01:13:56,760 --> 01:14:01,469 Ding Jia: condition that says I'm not saying anything in the bulk 451 01:14:01,480 --> 01:14:02,970 Ding Jia: in the bogus salt 452 01:14:04,080 --> 01:14:05,300 Ding Jia: start putting in. 453 01:14:07,560 --> 01:14:11,529 Viktoria Kabel: But I think when you solve it. You're you're putting in more assumptions. 454 01:14:11,820 --> 01:14:19,840 Viktoria Kabel: I'm just trying to say you can solve it with less assumptions if you use quantum reference frames. I think I think in the end I wanna come back 455 01:14:19,870 --> 01:14:32,189 Viktoria Kabel: because I think to some extent you have good points. I think in the end you you can use different approaches. It's just different ways of solving the same problem. I'm not trying to argue. The quantum reference frames are the only way to solve it. 456 01:14:33,460 --> 01:14:44,490 Ding Jia: I'm arguing. So you you made a point, considering quantum reference rooms make some problems easier. So you haven't made that point to me. At least, you haven't given me a valid example 457 01:14:44,640 --> 01:14:45,800 Ding Jia: shows this. 458 01:14:46,990 --> 01:14:59,299 Viktoria Kabel: Yeah, I would. I would have to look at how you actually solve this problem with the path integral formulation, because I'm not familiar enough with that. As for the other point, with the 459 01:15:00,590 --> 01:15:03,220 Viktoria Kabel: large gauge transformations, I think. 460 01:15:03,230 --> 01:15:11,390 Viktoria Kabel: But again, I'm not super familiar with the path integral approach, but I would expect that the boundary conditions are somewhat different, and and this would probably affect your 461 01:15:12,710 --> 01:15:14,030 Viktoria Kabel: your results 462 01:15:16,930 --> 01:15:21,190 Viktoria Kabel: if if the frames are related by large gauge transformations. 463 01:15:21,400 --> 01:15:33,590 Ding Jia: Sounds good to me. Actually sorry. It's not clear. Yeah, it's not clear what the original 464 01:15:34,070 --> 01:15:36,440 a reply mint to me, the the 465 01:15:37,520 --> 01:15:42,830 I mean the logic isn't clear. So why thinking of large gauge transformations? 466 01:15:42,940 --> 01:15:45,110 Ding Jia: Maybe they change boundary conditions. 467 01:15:45,550 --> 01:15:52,550 Ding Jia: But but why does it justify quantum reference frames? Why, it makes quantum reference frame to make a difference. 468 01:15:52,650 --> 01:16:06,220 Viktoria Kabel: I think I think in the end this all boils down to the empirical significance of symmetries, which is a very subtle topic. And in the end your symmetry is never gonna if it's really a symmetry, it doesn't change the 469 01:16:06,270 --> 01:16:09,130 Viktoria Kabel: physical situation by definition, right? 470 01:16:09,780 --> 01:16:25,220 Viktoria Kabel: So you could always get rid of the symmetry, you could always argue that it's that it's a redundancy. But as soon as you enlarge your system, then some symmetries will not look like symmetries anymore from the perspective of the larger system. 471 01:16:25,220 --> 01:16:41,190 Viktoria Kabel: because they move your system with respect to whatever external structure you've introduced, and as such they suddenly become measurable, they suddenly become empirically distinguishable. And you always kind of have to bear in mind both perspectives in order to even make sense of the different reference frames. 472 01:16:42,550 --> 01:16:49,379 Viktoria Kabel: But again, this is just one way of looking at it. You could always remove the gate redundancy. But then you have other problems like non locality. 473 01:16:51,460 --> 01:16:56,510 So let's go to Wolfgang's hand, because I assume it's related to this. And then vessel, I'll come straight to you. 474 01:16:56,770 --> 01:17:06,129 Wieland, Wolfgang Martin: Yeah, just a very quick reply. So in the path, in the path integral, we sum over configurations modulo gauge. 475 01:17:06,210 --> 01:17:08,140 Wieland, Wolfgang Martin: But what is gauge 476 01:17:08,400 --> 01:17:22,640 Wieland, Wolfgang Martin: is is answered by by the analysis that Victoria gave in this talk so a large gauge transformation that or large diffumorphism that does not vanish 477 01:17:22,730 --> 01:17:31,680 Wieland, Wolfgang Martin: infinity. Or if we're in a bounded region does not vanish at the boundary is is not a gauge transformation, and 478 01:17:31,830 --> 01:17:35,270 Wieland, Wolfgang Martin: in the example of this planet, in superposition 479 01:17:35,780 --> 01:17:43,079 Wieland, Wolfgang Martin: you would they? These configurations differ by large gauge transformations, so they are not. 480 01:17:43,120 --> 01:18:07,380 Wieland, Wolfgang Martin: Gauge equivalent configurations. Now that raises the question, then what are the variables in the path in the world that you sum over that that that distinguish these configurations, and these are precisely the the boundary modes that are part of the 481 01:18:07,890 --> 01:18:25,550 Wieland, Wolfgang Martin: part of your gravitational degrees of freedom, which are not which are what Laurent said in in the classification in terms of spin degrees of freedom or the spin 0 or spin, or the Newtonian potential. If you wish, that are part of 482 01:18:25,550 --> 01:18:39,910 Wieland, Wolfgang Martin: of what is quantum in your quantum theory, they're just not in the in the linearized regime. They just don't show up as radiative modes, but as different degrees of freedom. And then 483 01:18:39,910 --> 01:18:45,919 Wieland, Wolfgang Martin: I think the the just, there's a clarifying remark. 484 01:18:45,920 --> 01:19:13,289 Wieland, Wolfgang Martin: The the viewpoint from from this part of the physics community from that part of the physics community, from this operational viewpoint is to have physics, principles that go beyond the singular approach. So he, when Victoria was introducing this symmetry principle that needs that. We want to have satisfied. This is not just about the path integral approach. This is 485 01:19:13,290 --> 01:19:24,990 Wieland, Wolfgang Martin: something that we can use to discriminate, discriminate different approaches to quantum gravity, and that in includes, for instance. 486 01:19:25,070 --> 01:19:37,669 Wieland, Wolfgang Martin: models in which there would would be a collapse which is which is incompatible with the path integral approach. So we try to introduce 487 01:19:38,510 --> 01:19:44,520 Wieland, Wolfgang Martin: new principals that can then classify different 488 01:19:44,930 --> 01:19:51,629 Wieland, Wolfgang Martin: different approaches, and that can serve us as a guiding principle. 489 01:19:51,940 --> 01:19:54,479 Wieland, Wolfgang Martin: I think that is the viewpoint. 490 01:19:54,950 --> 01:20:04,380 Hal Haggard: I imagine there's more to say in this discussion. Let's sit there. Thanks. I'll take Vesa's question, and then and perhaps we'll we'll conclude after that. 491 01:20:06,420 --> 01:20:23,810 Veso: Yes, thank you very much. How. And first I would like to express my gratitude to Victoria. It was a wonderful talk. and for the seminar I was able to so look at the slides yesterday, but it wasn't a season. Usually I would be able to graph 492 01:20:23,890 --> 01:20:28,509 Veso: the talk just looking at the slides, but I really enjoyed the way she explained it. 493 01:20:28,750 --> 01:20:33,900 Veso: And I would like to say few comments, basically, that 494 01:20:34,030 --> 01:20:47,810 Veso: I noticed that Don was kind of saying, well, we don't know what where we're going or what the difference does it make? And I would like to quote Einstein on this, that if we knew where we're going we wouldn't call it research. 495 01:20:48,030 --> 01:21:08,359 Veso: And basically the thing is that different approaches. Of course, when the ultimate description of a system should not depend on the choice of coordinate frames, but having different frames, would help you sometimes in calculations having different approaches, helps. You understand the description of the system. 496 01:21:08,440 --> 01:21:19,920 Veso: Actually, somebody asked Victoria earlier whether she was going towards solving the measurement problem because this could be a key towards the measurement problem ultimately, because 497 01:21:19,930 --> 01:21:38,710 Veso: classical systems, yes, when everything is definite there, but in quantum system, I mean, we have a little bit uncertainties. And how do we quantize? Quantify? This uncertainty is not so clear, and maybe quantum reference frames can help us with that. So I would like to thank you. And 498 01:21:39,200 --> 01:21:40,829 Veso: wonderful job. Thanks. 499 01:21:41,790 --> 01:21:42,850 Viktoria Kabel: Thank you. 500 01:21:44,240 --> 01:21:50,829 Hal Haggard: Wonderful. That's and a nice note to end on. Thank you. Also from the organizers. Victoria is a very nice seminar. 501 01:21:51,540 --> 01:21:53,430 Viktoria Kabel: Thanks and thanks for inviting me.