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Jorge Pullin: Okay. So our speaker today is Victoria Cabell, who will speak about quantum reference frames.
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Viktoria Kabel: Thanks for the introduction and thanks for inviting me to speak here.
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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.
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Viktoria Kabel: and
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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
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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.
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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.
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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.
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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
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Viktoria Kabel: to even describe evolution and time, or even just variation across space.
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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.
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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
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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.
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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.
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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.
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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.
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Viktoria Kabel: If we combine these principles, we quite directly arrive at the idea of a quantum reference frame.
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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.
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Viktoria Kabel: Sorry can I ask a very naive question just about these motivations?
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Simone: So one of the principle of quantum mechanics. I think it's also the fact that
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Simone: the system is split in 2, and one is the quantum system we observe.
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Simone: and another one is the observer that we have to treat classically.
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Simone: because otherwise we don't know how to explain things like the collapse of the wave function.
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Simone: So you're kind of giving up that principle or
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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
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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.
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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?
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Simone: Well, not not necessarily the observer, I think directly.
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Simone: Okay, thank you.
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Viktoria Kabel: No worries.
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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.
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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.
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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.
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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.
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Viktoria Kabel: And for the following part of the talk, I just really want to focus on the simple example of the translation group.
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Viktoria Kabel: So usually reference frames are important in classical physics. Whenever we have a symmetry like an invariance under translations.
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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.
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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.
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Viktoria Kabel: can describe everything with respect to the orange particle. But the physics is going to be the same.
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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.
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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.
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Viktoria Kabel: And we can implement this classical like change of reference frame on the quantum level with a simple translation operator.
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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.
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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.
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Viktoria Kabel: Now. this is still
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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.
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Viktoria Kabel: in the rest of our setup.
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Viktoria Kabel: But the really interesting. yeah.
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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?
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Viktoria Kabel: Yes, so it becomes clearer when we change between a proper quantum reference range where the particle is in a superposition.
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Viktoria Kabel: So maybe I just comment on that when we see the operator there, because then it becomes a bit clearer, I think.
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Laurent Freidel: Okay.
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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.
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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.
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Viktoria Kabel: It's always going to be a distance 0
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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
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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.
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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.
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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.
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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.
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Viktoria Kabel: So
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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.
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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
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Viktoria Kabel: reference frame here.
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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
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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.
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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.
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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.
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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.
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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.
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Viktoria Kabel: or a more operational approach that deals more with algebra observables.
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Viktoria Kabel: But I think for the discussion here. Actually, all we're gonna need is this one approach to quantum reference frames.
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Viktoria Kabel: So I think, if there are any more questions on quantum reference frames. This would be a good time also, if the
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Viktoria Kabel: parity swap operator was not clear. I'm happy to pull up on that.
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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?
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Ding Jia: I mean, if you think it's more for discussion. Maybe we can discuss it at the end. Yeah.
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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.
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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.
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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
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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
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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
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Viktoria Kabel: just quantum theory, and tr alone. Don't tell us the answer to the question, how does the particle move.
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Viktoria Kabel: because none of these theories tell us what is the gravitational field sourced by this mass configuration and superposition.
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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.
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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
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Viktoria Kabel: the motion of the particle in the original reference frame.
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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.
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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.
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Viktoria Kabel: Now, this is a scenario that we can both describe theoretically with our known theories, and that has been tested experimentally.
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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.
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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.
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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.
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Viktoria Kabel: And if we now just add this one additional ingredient, namely, the extended
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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
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Viktoria Kabel: towards the 2 different locations of the massive object.
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Viktoria Kabel: And, as I said, the one big assumption that we do have to put in is this extended symmetry principle?
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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
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Viktoria Kabel: mass configuration and superposition, also sources of gravitational field and superposition.
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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.
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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.
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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
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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.
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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.
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Viktoria Kabel: so the particle will either fall towards the right hand side, or the left-hand side with a certain probability.
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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.
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Viktoria Kabel: So again, this cannot obey the extended symmetry principle.
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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.
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Viktoria Kabel: and we can actually make predictions that we would otherwise have to pick a certain approach to quantum gravity. For
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Viktoria Kabel: now
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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.
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Viktoria Kabel: and that is starting from a general relativistic framework and asking whether we can actually derive quantum reference frames from within there.
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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
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Viktoria Kabel: in a region of space-time. But now, importantly, we're going to consider a bounded region of space-time.
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Viktoria Kabel: and we're asking ourselves to question whether we can derive quantum reference frames from within this setup described by general relativity.
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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.
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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.
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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.
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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.
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Viktoria Kabel: Then quantum reference frames emerge naturally as edge modes at the boundary of space-time.
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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
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Viktoria Kabel: engage theory or gravity.
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Viktoria Kabel: But before I go through the derivation, I want to just give a brief
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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.
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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
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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.
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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.
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Viktoria Kabel: so you can get a full description of the physical degrees of freedom by focusing on the 4 relative distances
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Viktoria Kabel: between the spaceships.
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Viktoria Kabel: Now you could imagine that 2 of the spaceships go off to explore another part of the empty universe.
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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.
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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.
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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.
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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.
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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
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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
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Viktoria Kabel: for our electromagnetic field.
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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.
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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.
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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.
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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.
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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
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Viktoria Kabel: to our description of the subsystem.
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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.
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Viktoria Kabel: and a similar idea of
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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
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Viktoria Kabel: to arise as edge modes, just like the gauge parameter, would arise as a boundary mode in electrodynamics.
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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.
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Viktoria Kabel: and one could say that they emerge from the space-time background itself.
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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.
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Viktoria Kabel: Now the flat space time background in the tetrahed formulation
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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.
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Viktoria Kabel: Of course, this only holds up to the internal rotations that come with the tetrahed formalism which are characterized by Lambda. Here.
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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.
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Viktoria Kabel: and we're going to see that these coordinate fields and Lawrence fields survive in the description
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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
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Viktoria Kabel: of the field.
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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.
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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?
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Viktoria Kabel: And what we find is that the symplectic form for our bounded region here actually splits into 3 parts.
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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.
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Viktoria Kabel: and these also already enter within the other
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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.
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Viktoria Kabel: Similarly, if we look at the symplectic form for the gravitational radiation, we find that the first order, perturbations.
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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.
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Viktoria Kabel: the gravitational radiation that could be absorbed by the coordinate fields.
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Viktoria Kabel: So it's also, again, a kind of relative variation with respect to the coordinate fields.
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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.
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Viktoria Kabel: and these Lorentz frames at the boundary which provide a reference frame for the internal SO. 1, 3. Symmetry.
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Viktoria Kabel: and these fulfill several roles.
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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.
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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.
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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.
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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
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Viktoria Kabel: after region into a background spacetime.
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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
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Viktoria Kabel: connection.
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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.
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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.
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Viktoria Kabel: So.
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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.
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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.
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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.
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Viktoria Kabel: will actually provide us with a relational Schrodinger equation at the boundary, so it will give us the
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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
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Viktoria Kabel: coordinate fields here
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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
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Viktoria Kabel: if we send the boundary to infinity.
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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
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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.
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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.
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Viktoria Kabel: And of course, this holds up to order one over row.
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Viktoria Kabel: These actually, these global orange rotations and finite angle. Dependent translations are what characterizes the asymptotic symmetries of the boundary.
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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.
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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.
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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.
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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.
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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
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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.
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Viktoria Kabel: this rotation is then implemented by the matrix element of the projector, which will give us a unitary
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Viktoria Kabel: implementing. The change from the reference frame qi.
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Viktoria Kabel: To the reference frame. Q. 0.
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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
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Viktoria Kabel: transformation. QQI. To Q. 0.
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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
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Viktoria Kabel: will tell you how this translation acts under gravitational degrees of freedom in the bulk.
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Viktoria Kabel: So this really gives us a quantum controlled point-wise translation from within the framework of quantized linearized gravity, and as such.
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Viktoria Kabel: it generalizes the quantum control translations that we saw before.
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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.
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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
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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
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Viktoria Kabel: also act as the kind of reference quantum reference frames that you would want as a solution to the problem of time.
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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.
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Viktoria Kabel: And if you wanna see any of the details there. Given our paper on the Archive
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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.
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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.
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Viktoria Kabel: But we also looked at the problem from a different angle, and saw how quantum reference frames.
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Viktoria Kabel: or the asymptotic symmetries arise as edge modes at the boundary of space-time and linearize general relativity.
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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.
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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.
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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.
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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.
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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
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Viktoria Kabel: to an area where quantum reference frames
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Viktoria Kabel: were originally studied in quantum information theory, which is the study of super selection sectors.
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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.
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Hal Haggard: Thank you, Victoria, for such a nice summary of your work.
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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.
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Hal Haggard: Ding had his hand raised first. So, Ding, why don't we start with you?
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Ding Jia: Thank you. I'm going to make some very critical remarks
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Ding Jia: up to make clear something. It's nothing against you personally.
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Ding Jia: because these mistakes were made by
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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
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Ding Jia: and it's nothing against you.
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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.
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Ding Jia: basically are 2 criticisms. If you could go to the
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Ding Jia: motivation slide
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Ding Jia: we mentioned operationalism.
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Ding Jia: Yes. here, I think
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Ding Jia: personally, this point is wrong. In practice.
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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.
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Ding Jia: This is not a physical system. We don't have any physical field.
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Ding Jia: The town is divided of of RT. etc.
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Ding Jia: This is a mental construction. It's our invention. It's not a physical system.
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Ding Jia: and it's misleading. It's a mistake. So say that this is a classical reference frame.
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Ding Jia: because it's not a physical system.
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Ding Jia: Therefore there's there's no mo, no motivation
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Ding Jia: to generalize this kind of artificial mental invention to a quantum system.
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Ding Jia: Therefore, this is not a valid motivation to go to a quantum reference frame.
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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
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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
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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.
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Viktoria Kabel: I don't know whatever system you use to send your light race to the next
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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.
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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.
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Ding Jia: I can think of practical situations where I use a a artificial.
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Ding Jia: a mental reference. Right? It's not a physical system.
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Ding Jia: right? I think it boils down to what you mean by in practice.
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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.
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Ding Jia: I can set up a coordinate system in the middle, in a love department.
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Ding Jia: And this describes you. You know what experimentalists do. That's very practical.
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Viktoria Kabel: right? But if you actually try to measure it you would have to use
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Ding Jia: like, I still use an artificial reference room. That's not a physical assistant.
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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.
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Viktoria Kabel: Hmm.
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Ding Jia: yes. I think the core idea of quantum rifles, right is to identify points across different configurations in superposition.
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Viktoria Kabel: I completely agree
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Ding Jia: here. You're showing showing us
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Ding Jia: a party going to Earth. and there are different configurations for these physical objects.
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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
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Ding Jia: with the earth that is in position for infinitely many other ways to do this.
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Ding Jia: and this is the guard here of quantum reference frame.
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I think
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Ding Jia: this structure is totally superfluous.
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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
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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?
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Ding Jia: If you sum it over.
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Ding Jia: we have a map that tells us, like some pitches for each configuration. and then we sum the complex
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Ding Jia: to obtain numbers.
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Ding Jia: the end. The results can either be a complex amplitude
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Ding Jia: or real probability depends on whether you single path into a double bathroom to go.
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Ding Jia: And that's a cool story. It tells us what exists in the world apart into a configurations.
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Ding Jia: But the dynamic allows are through the amplitude map
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Ding Jia: and what the the physical predictors predictions are
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Ding Jia: the probabilities. That's full story.
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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.
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Viktoria Kabel: Yeah, yeah. I mean, with the identification. I completely agree. And we actually have a paper and production where we relate everything.
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Viktoria Kabel: more directly to this role of quantum reference frame as identifying objects across the branches.
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Viktoria Kabel: I'm not sure what what the issue is with. The
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Ding Jia: the issue is.
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Ding Jia: You can identify the path into a configuration points the passing configurations in any way you want.
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Ding Jia: it doesn't change as a result of the path into your
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Viktoria Kabel: oh, yeah, I mean, that's what I
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Ding Jia: however, you identified. The result of the passenger is the same. So it's a superfluous structure to introduce quantum reference frames.
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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
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Viktoria Kabel: that we often like to use these reference frames, and
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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
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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.
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Hal Haggard: All right, let's leave that discussion there for now Simone was next.
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Simone SPEZIALE: Thanks.
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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.
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Simone SPEZIALE: Right? Please repeat that.
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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.
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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
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Simone SPEZIALE: amazing. Okay, thank you.
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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.
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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.
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Viktoria Kabel: and I think
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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
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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?
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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
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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
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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.
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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.
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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.
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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.
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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?
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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
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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.
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Simone SPEZIALE: Not for a coherent state. Yeah, for a free particle. Yes. you're you're you're thinking of a
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Simone SPEZIALE: of a closed orbit. Couldn't stay like the harmonic oscillator. But if you have a free particle it spread rose.
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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
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Viktoria Kabel: for it to evolve in its own recognized.
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Simone SPEZIALE: Thank thank you very much. Very nice. Thank you.
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Hal Haggard: Laurent was next
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Laurent Freidel: II think. Carlos was maybe before now.
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Hal Haggard: Well, you had unmuted before you raised your hands. II don't mind either way.
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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.
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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.
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Laurent Freidel: But it's also as it's a Newtonian component
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Laurent Freidel: which you know in in regular quality. Theory is is kind of usually not quantized.
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Laurent Freidel: And you can think of these Newtonian component or the other component of the of the gravitational field as quantum reference frame.
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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.
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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
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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.
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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
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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
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Viktoria Kabel: coulombic part and radiation part.
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Laurent Freidel: But at the end you did have a coordinate, you know, edge mode coordinate that came from the gravitational field.
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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.
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Viktoria Kabel: if you just mean a flat spacetime background. Then I agree.
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Laurent Freidel: But I mean, I mean, thatometric contains spin, 0 spin one and spin 2 components. The spin 2 is the
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Laurent Freidel: new potential. If
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Laurent Freidel: okay, that's
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Laurent Freidel: by by the speed 0 component.
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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?
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Viktoria Kabel: Right? Right? I mean very briefly. What is it?
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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.
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Viktoria Kabel: and the first order. Perturbations are, gonna be the
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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
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Viktoria Kabel: the gravitation of radiation itself is sourcing more.
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Viktoria Kabel: more gravity.
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Viktoria Kabel: This would be d
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Viktoria Kabel: different degrees of freedom.
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Hal Haggard: Let's move on to Carlos, who's been waiting patiently.
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carlos alex souza da silva: Thank you very much, Victoria, for your talk.
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carlos alex souza da silva: like questions
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carlos alex souza da silva: is about if is it possible
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carlos alex souza da silva: to conceive quite reference frames
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carlos alex souza da silva: beyond space? Time? Talking was about what reference frame is in space time.
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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.
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Viktoria Kabel: I mean, I think in general, the the abstract formalism of quantum reference frames.
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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
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Viktoria Kabel: which I would then maybe describe as quantum reference frames. Not in space time.
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Viktoria Kabel: So the framework works really for any any group.
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carlos alex souza da silva: Okay. thank you very much.
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Hal Haggard: Joe's.
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Joe Aziz: Thank you. For the talk. I wanted to ask if there's any ideas or
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Joe Aziz: attempts for some experiment that might show whether the extended symmetry principle is really a symmetry of nature
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Viktoria Kabel: right? So we actually thought about whether we can maybe do something like this. But with a clock instead of the particle
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Viktoria Kabel: and then, if the clock takes in a superposition of
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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.
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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
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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.
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Joe Aziz: Do you? Do you have any idea of how unfeasible it is! Is it borderline impossible, or is it like.
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Viktoria Kabel: I don't remember the exact timescales? I think
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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
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Joe Aziz: little bit more hopeful
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Viktoria Kabel: than certain other approaches. But
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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.
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Joe Aziz: Okay, thank you.
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100.
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Alejandro PEREZ: Hi, thank thank you. I've
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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
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Alejandro PEREZ: I
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Alejandro PEREZ: and there a lot of factor ambiguities is, is this transformation actually defined? Well defined, I mean free of ambiguities
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Alejandro PEREZ: because of factor ordering. II mean, I mean this translations where your parameter now is an operator.
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Viktoria Kabel: Yes, yes, I think it's actually not so much of a problem, because, it's different systems.
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Viktoria Kabel: It's XA and Pb, to enter in the translation operator. And these communities. Yeah, yeah, but you, you seem to.
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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
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Viktoria Kabel: if we want to translate the reference frame itself.
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Viktoria Kabel: Because if we use different operators associated to different systems.
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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.
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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.
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Alejandro PEREZ: Okay, A/C, thank you.
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Hal Haggard: Wolfgang.
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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.
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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
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Wieland, Wolfgang Martin: need split between radiation and and columbic modes which then at the non perturbative regime.
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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.
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Wieland, Wolfgang Martin: And then another comment, perhaps, on on this earlier question by Dean
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Wieland, Wolfgang Martin: would say, the difference is that in the case of the super post super position of.
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Wieland, Wolfgang Martin: or in the case of, a microscopic object in superposition, in a spatial superposition. What
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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
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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
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Wieland, Wolfgang Martin: answers. This concern.
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Wieland, Wolfgang Martin: okay, these are the 2 comments, thanks.
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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.
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Hal Haggard: Frank for me. Okay.
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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.
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Hal Haggard: and if not ding, why don't you go ahead?
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Ding Jia: Thank you. Seems I'm I'm playing the role of of the badbox.
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Ding Jia: which I'm happy to 3 responses to people sent to. To my question. First of all, I'll mentioned
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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.
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Ding Jia: Second, quantum reference frames do not make difference to the physical results. I don't see how
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Ding Jia: bringing radiation to the picture addressed any of the concerns.
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Ding Jia: Second Wolfgang. Answer, Stuart. I'd be typically seeing saying a lot. There are
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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
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Ding Jia: physical results in a path integral.
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Ding Jia: In my understanding, in the passenger sum over other configurations
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Ding Jia: I assign complex. I send over the complex numbers.
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Ding Jia: and the concern is that
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Ding Jia: you know whatever way you identify points across the configurations, it doesn't make any difference to the end results.
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Ding Jia: I don't see how thinking of large page transformations change anything.
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Ding Jia: Final response to Victoria. If you replied to my second concern by saying.
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Ding Jia: if we consider quantum reference frames.
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Ding Jia: There are some questions that are easier to solve. I'd like to press Victoria
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Ding Jia: to come up with explicit examples.
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Ding Jia: examples that we encounter in quantum gravitational research in theories of quantum gravity.
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Ding Jia: A.
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Ding Jia: Could you give me an example or some examples where quantum reference frames solves a previously difficult problem.
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Viktoria Kabel: right? I mean, I think maybe going backwards onto questions
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Viktoria Kabel: at the risk of forgetting the first one
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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.
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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
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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
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Viktoria Kabel: there are the technical capabilities to actually complete this. So I would say.
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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.
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Ding Jia: I'm not sure it solves. I mean, it's full series of quantum gravity. So we consider
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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.
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Ding Jia: if a boundary condition is that there's 2 set of points that are competing in their contribution to the Bathroom Bureau
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Ding Jia: have a superposition.
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Ding Jia: and it's just solving the classical equation of motion for the set of points under certain boundary conditions.
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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
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Ding Jia: condition that says I'm not saying anything in the bulk
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Ding Jia: in the bogus salt
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Ding Jia: start putting in.
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Viktoria Kabel: But I think when you solve it. You're you're putting in more assumptions.
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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
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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.
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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
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Ding Jia: shows this.
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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
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Viktoria Kabel: large gauge transformations, I think.
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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
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Viktoria Kabel: your results
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Viktoria Kabel: if if the frames are related by large gauge transformations.
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Ding Jia: Sounds good to me. Actually sorry. It's not clear. Yeah, it's not clear what the original
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a reply mint to me, the the
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I mean the logic isn't clear. So why thinking of large gauge transformations?
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Ding Jia: Maybe they change boundary conditions.
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Ding Jia: But but why does it justify quantum reference frames? Why, it makes quantum reference frame to make a difference.
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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
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Viktoria Kabel: physical situation by definition, right?
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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.
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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.
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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.
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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.
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Wieland, Wolfgang Martin: Yeah, just a very quick reply. So in the path, in the path integral, we sum over configurations modulo gauge.
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Wieland, Wolfgang Martin: But what is gauge
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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
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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
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Wieland, Wolfgang Martin: in the example of this planet, in superposition
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Wieland, Wolfgang Martin: you would they? These configurations differ by large gauge transformations, so they are not.
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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
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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
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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
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Wieland, Wolfgang Martin: I think the the just, there's a clarifying remark.
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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
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Wieland, Wolfgang Martin: something that we can use to discriminate, discriminate different approaches to quantum gravity, and that in includes, for instance.
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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
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Wieland, Wolfgang Martin: new principals that can then classify different
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Wieland, Wolfgang Martin: different approaches, and that can serve us as a guiding principle.
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Wieland, Wolfgang Martin: I think that is the viewpoint.
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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.
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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
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Veso: the talk just looking at the slides, but I really enjoyed the way she explained it.
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Veso: And I would like to say few comments, basically, that
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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.
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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.
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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
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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
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Veso: wonderful job. Thanks.
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Viktoria Kabel: Thank you.
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Hal Haggard: Wonderful. That's and a nice note to end on. Thank you. Also from the organizers. Victoria is a very nice seminar.
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Viktoria Kabel: Thanks and thanks for inviting me.