0 00:00:02,320 --> 00:00:07,480 Jorge Pullin: Okay. So our speaker today is Flaminia Jacomini, who will speak about quantum reference frames. 1 00:00:09,310 --> 00:00:18,630 Flaminia Giacomini: Okay, thanks a lot for the introduction. Thanks a lot, because it's very nice in position. I'm very happy to be able to keep this stores here with my research. 2 00:00:19,040 --> 00:00:36,180 Flaminia Giacomini: So yes, the main topic of the talk today is the contraction strains, and I will introduce you to a formulation of this topic. and I will give you some argument why they can provide us a relational perspective on the classical spacetime. 3 00:00:37,440 --> 00:00:48,290 Flaminia Giacomini: And so first let me just clarify some terminology, since we are from we all have different backgrounds. 4 00:00:48,560 --> 00:00:50,100 Flaminia Giacomini: So 5 00:00:50,730 --> 00:00:56,700 Flaminia Giacomini: the you. We have our 2 main theories of physics that are quantum theory, and generally 6 00:00:56,750 --> 00:01:00,320 Flaminia Giacomini: which both rest on a classical notion of spacetime 7 00:01:00,600 --> 00:01:14,860 Flaminia Giacomini: mit ctl, and but then it is a widely shared expectation that the interface between these 2 here is the this classical notion of spacetime is no longer sufficient, and we have to replace it with something else. But we do not know what the what is this Something else, one? 8 00:01:14,950 --> 00:01:20,420 Flaminia Giacomini: And of course this question has been explored in in quantum gravity 9 00:01:20,470 --> 00:01:31,890 Flaminia Giacomini: in many different ways. and typically the quantum gravity literature focuses in the high energy regime. where and 10 00:01:32,100 --> 00:01:45,440 Flaminia Giacomini: many different approaches to to quantum gravity from Luc on to and the Black Hole. Physics discuss many ways in which spacetime can become kind of. For 11 00:01:45,790 --> 00:01:48,740 Flaminia Giacomini: this is not the approach that i'm going to take in this talk 12 00:01:48,810 --> 00:01:57,120 Flaminia Giacomini: here. I'm going to focus instead in the low energy regime, where gravity is perturbative, and we can meaningfully talk about quantum particles. 13 00:01:57,170 --> 00:02:04,080 Flaminia Giacomini: So, for instance, the the simplest thing we can consider is to have a must in a one to super position. 14 00:02:04,140 --> 00:02:09,039 Flaminia Giacomini: and this is the sense in which I will talk about no classical spacetime. 15 00:02:09,419 --> 00:02:12,930 Flaminia Giacomini: and I will refer you in particular on some 16 00:02:13,080 --> 00:02:14,930 Flaminia Giacomini: more 17 00:02:15,200 --> 00:02:21,310 Flaminia Giacomini: concrete aspects which lead to some physical scenarios with an immediate physical meaning. 18 00:02:25,460 --> 00:02:32,840 Flaminia Giacomini: So let me first give you some overview of the the general question that we're going to ask. 19 00:02:33,790 --> 00:02:37,270 Flaminia Giacomini: So in general relativity we have, I sensitive questions 20 00:02:37,320 --> 00:02:45,330 Flaminia Giacomini: that connect the metric of the space-time to the matter through the through these questions. 21 00:02:45,760 --> 00:02:46,600 Flaminia Giacomini: and 22 00:02:47,390 --> 00:02:57,940 Flaminia Giacomini: these are questions are valid Whenever I have a classical. however, quantum theory tells us that matter is quantum. 23 00:02:58,600 --> 00:03:10,690 Flaminia Giacomini: So ideally, we would like to have quantum stress, energy, cancer here on the right hand side. But if we do so, then we cannot solve this question anymore in the fullest generality. 24 00:03:11,260 --> 00:03:24,820 Flaminia Giacomini: And again, there are different ways of approaching this problem. What i'm going to do here is to consider a linearized version of the since the questions where it is meaningful to just put a quantum stress and an answer. 25 00:03:25,190 --> 00:03:31,490 Flaminia Giacomini: And, for instance, this is a situation that can be realized by a mass in a possible position. 26 00:03:31,720 --> 00:03:40,400 Flaminia Giacomini: So I must. I'm thinking a. And then one could think, okay. But this is not really an on-classical space time. 27 00:03:40,500 --> 00:03:47,630 Flaminia Giacomini: But fundamentally, what I have here is a quantum source of a gravitational field 28 00:03:47,860 --> 00:03:48,700 Flaminia Giacomini: so 29 00:03:48,810 --> 00:03:53,140 Flaminia Giacomini: at the fundamental level. I cannot have a classic space sign. 30 00:03:53,240 --> 00:04:03,380 Flaminia Giacomini: and I can measure that. For instance, if I put a quantum clock, and the quantum clock will detect a difference according to whether the mass is here or is here. 31 00:04:05,230 --> 00:04:13,050 Flaminia Giacomini: Why is this interesting? So one of the reasons that I find this interesting is that experiments are making their way 32 00:04:13,100 --> 00:04:20,649 Flaminia Giacomini: towards realizing this situation in a laboratory, and in particular, there are 2 different directions in which experiments are pushing 33 00:04:21,250 --> 00:04:30,500 Flaminia Giacomini: on the one hand. Here on the left hand side of the slide. Then experiments are trying to measure the gravitational field that is sourced by 34 00:04:30,590 --> 00:04:47,250 Flaminia Giacomini: lighter and lighter objects. And, for instance, in in this paper from 2 years ago, the Asper Mayor Group, Vienna, measured the gravitational company, so the gravitational interaction between 2 spheres that we, as little as 90 milligrams. 35 00:04:48,010 --> 00:04:57,520 Flaminia Giacomini: on the other hand, is that there is a a an effort that tries to show that quantum properties, all for more and more microscopic objects. 36 00:04:58,030 --> 00:04:59,720 Flaminia Giacomini: and 37 00:05:00,480 --> 00:05:10,860 Flaminia Giacomini: 2 examples of what has been achieved in recently are this paper, where they this quantum interference of 38 00:05:10,940 --> 00:05:16,290 Flaminia Giacomini: of heavy molecules. and also some 39 00:05:16,340 --> 00:05:30,380 Flaminia Giacomini: instead. Here, where they try to push the size of the superposition, and they actually achieve at the single out of level super position, size of half a meter. And is that an object that is put in a quantum square position and not an interferometer. 40 00:05:30,800 --> 00:05:42,600 Flaminia Giacomini: Now the hope is that in the future the experiments will bridge this to regimes, and we'll actually measure the gravitational field that is source, but want to monitor. And this is, of course, very hard. 41 00:05:42,640 --> 00:05:48,280 Flaminia Giacomini: and not something that we're going to do tomorrow, maybe in 1020 years. 42 00:05:48,310 --> 00:05:50,970 Flaminia Giacomini: But and there are serious limitations 43 00:05:50,980 --> 00:06:04,580 Flaminia Giacomini: currently through the experiments that are, for instance, in coherence and scattering. And in this paper of the Mas Marcus as per my year, that you can find the current status of the experiments on this. 44 00:06:06,070 --> 00:06:06,880 Flaminia Giacomini: So 45 00:06:07,100 --> 00:06:15,750 Flaminia Giacomini: this is clearly not the regime of traditional quantum gravity approaches, and then one could that, or what? How could this contribute to to quantum? 46 00:06:16,460 --> 00:06:29,260 Flaminia Giacomini: And I here identified 3 reasons, and These reasons are personal, of course, so other people will have different reasons. and at least i'm here from the the most conservative one to the 47 00:06:29,280 --> 00:06:30,890 Flaminia Giacomini: a more ambitious one. 48 00:06:31,920 --> 00:06:34,480 Flaminia Giacomini: So the first reason is that 49 00:06:34,520 --> 00:06:47,720 Flaminia Giacomini: it's to date. We do not know which experimental observation that we will be able to realize in the lab. In the say, short to midterm, will prove in a compelling way that gravity has gone through features 2. 50 00:06:47,800 --> 00:06:59,050 Flaminia Giacomini: But we are going to have experiments soon, so it is very important to understand exactly what we can deduce on the gravitational field if we perform this type of experiments. 51 00:06:59,420 --> 00:07:01,260 Flaminia Giacomini: and this is still an open question. 52 00:07:02,270 --> 00:07:17,920 Flaminia Giacomini: The second reason why I find this interesting is that there are conceptual local questions, infant and gravity that are also shared in this regime. and, for instance, the lack of a classical space time, as I try to argue towards you before, but also like 53 00:07:17,970 --> 00:07:34,840 Flaminia Giacomini: a quantum time, because time you want to using quantum class can see that time is also in a constant superposition in this regime. Cause i'll be what happens to the notion of causality observables, and how to partition the Hebrew space into local sub algebra or subsystems. 54 00:07:34,970 --> 00:07:48,890 Flaminia Giacomini: and work on to information the sense. And the third reason why I find this interesting is that this is a research that uses quantum information tools for for the most part. 55 00:07:49,140 --> 00:07:53,740 Flaminia Giacomini: for instance, quantum information theorems or protocols. and 56 00:07:53,750 --> 00:08:06,080 Flaminia Giacomini: by its very nature quantum information does not depend on a specific regime of the physical theory, but just on probabilities that are measured in the lab and offers principles. 57 00:08:06,400 --> 00:08:10,520 Flaminia Giacomini: So the hope for the future is that 58 00:08:10,570 --> 00:08:28,210 Flaminia Giacomini: we can find some internal tests of the consistency of a here in the interface between quantum and gravity, by making some further experiments in this in this regime. But then out of logical considerations, then this can give us indication. This can point 1, 2 59 00:08:28,330 --> 00:08:32,169 towards how we should deal with the theory at higher energies. 60 00:08:32,620 --> 00:08:39,659 Flaminia Giacomini: and on this it will be very important to to work together with quantum gravity researchers. 61 00:08:40,020 --> 00:08:41,840 Flaminia Giacomini: So this is also an invitation. 62 00:08:43,830 --> 00:08:57,070 Flaminia Giacomini: Now let me get more into the the core of the topic of the talk, which is quantum production, strength. And now what i'm going to do is, I will tell you about quantum reference frames 63 00:08:57,130 --> 00:09:05,090 Flaminia Giacomini: in a regime where there is no gravity. So this will be just fully neural, logistical Galileo relative to quantum mechanics. 64 00:09:05,580 --> 00:09:11,590 Flaminia Giacomini: and later i'm going to connect it with some gravity arguments. 65 00:09:12,230 --> 00:09:21,040 Flaminia Giacomini: But to do that first, let me just set the stage and let me review what we usually mean by a reference frame. 66 00:09:21,220 --> 00:09:26,270 Flaminia Giacomini: So a reference frame is usually a set of access, and the state of motion. 67 00:09:26,410 --> 00:09:34,930 Flaminia Giacomini: and the it is a very useful tool in physics, because it helps us to fix the point of view from which observations are carried out. 68 00:09:35,530 --> 00:09:43,560 Flaminia Giacomini: In addition, we also know that it doesn't matter which reference frame we take. But if we can write the laws of physics in any reference frame. 69 00:09:44,380 --> 00:09:45,250 Flaminia Giacomini: so 70 00:09:45,890 --> 00:09:56,330 Flaminia Giacomini: then we can connect the different descriptions that we give in its frame via a reference frame transformation. So imagine now that 71 00:09:56,440 --> 00:09:57,430 Flaminia Giacomini: you know 72 00:09:58,010 --> 00:10:03,980 Flaminia Giacomini: just some of quantum mechanics. We want to make a a reference to transformation. 73 00:10:04,250 --> 00:10:08,580 Flaminia Giacomini: This is included in a unit address for information. 74 00:10:08,830 --> 00:10:12,410 Flaminia Giacomini: So, for instance, here I have a translation or a Galilean boost. 75 00:10:13,860 --> 00:10:26,530 Flaminia Giacomini: and what I would like you to focus your attention on is that this parameter here X 0 and V gives us the relation between the oil reference frame and the new reference frame. 76 00:10:26,640 --> 00:10:33,140 Flaminia Giacomini: So this is the amount for which to translate, and this is the amount by which I boost. 77 00:10:33,610 --> 00:10:45,050 Flaminia Giacomini: So the the the relative velocity between the initial and final reference train, and there are a position to initial a final reference frame. And here these are just parameters. 78 00:10:45,390 --> 00:10:50,080 Flaminia Giacomini: They are not operators. They are not dynamical quantities, they are just a parameter. 79 00:10:52,070 --> 00:10:52,850 Flaminia Giacomini: Then 80 00:10:53,130 --> 00:10:56,400 Flaminia Giacomini: we also know that if we have a Schrodinger question. 81 00:10:56,560 --> 00:10:59,580 Flaminia Giacomini: if we perform a reference transformation. 82 00:11:00,300 --> 00:11:08,980 Flaminia Giacomini: the Schrodinger question is again mapped to a different Schrodinger, but formally the same Schrodinger question, but with a different from Miltonian 83 00:11:09,000 --> 00:11:13,540 Flaminia Giacomini: that is connected to the initial Hamiltonian by this relation. Here. 84 00:11:15,030 --> 00:11:29,350 Flaminia Giacomini: and this is a statement of the covariance of physical laws. In this the quantum mechanics framework. In addition, we say that the reference frame transformation is a symmetry of the dynamics. 85 00:11:29,370 --> 00:11:40,330 Flaminia Giacomini: If the final functional form of the final Hamiltonian is the same as the functional form of the Hamiltonian before the transformation. 86 00:11:42,620 --> 00:11:43,640 Flaminia Giacomini: so now 87 00:11:44,890 --> 00:11:52,950 Flaminia Giacomini: imagine that we have this very simple system that is made up of 3 different reference frames a, B and C. 88 00:11:53,490 --> 00:11:57,670 Flaminia Giacomini: Now imagine, in, for instance, initially, we are in, C. 89 00:11:58,150 --> 00:12:12,390 Flaminia Giacomini: If you want to take a relational perspective, and we would like to take it because we know that well, since we are in interested in generalizing this to gravitational framework. We want to incorporate the relational view that comes from Gr. 90 00:12:12,600 --> 00:12:14,790 Then the 91 00:12:15,370 --> 00:12:23,150 Flaminia Giacomini: we are going to have 2 meaningful to physical degrees of freedom, and when the center of massive is of freedom does not matter for us. 92 00:12:23,320 --> 00:12:34,180 Flaminia Giacomini: and the relation, because of the position between a and C, and between B and C. So these 2 yellow vectors. 93 00:12:34,960 --> 00:12:41,400 Flaminia Giacomini: But now, if we, for instance, want to switch the oranging of the reference frame to 94 00:12:41,720 --> 00:12:44,300 Flaminia Giacomini: 8, then we're going to have 2 95 00:12:44,350 --> 00:12:57,560 Flaminia Giacomini: other vectors that represent the relative position between C and a and between the and a. So basically the amount of information that we have here is the same in the perspective. It's just reshuffled. 96 00:12:59,120 --> 00:13:02,390 Flaminia Giacomini: Now, the question that you are going to ask is 97 00:13:02,480 --> 00:13:03,300 Flaminia Giacomini: so. 98 00:13:03,310 --> 00:13:09,800 Flaminia Giacomini: If you think about it. When we make a measurement, we use physical systems, and we also 99 00:13:09,870 --> 00:13:12,490 Flaminia Giacomini: take as reference physical objects. 100 00:13:13,060 --> 00:13:23,080 Flaminia Giacomini: So if we take the operational perspective that preference frames are physical systems, then we also know that physical systems are ultimately quantum systems. 101 00:13:23,680 --> 00:13:30,130 Flaminia Giacomini: So we are going to ask the full question. Can we attach reference, frame 102 00:13:30,240 --> 00:13:35,010 Flaminia Giacomini: 2. Some object to the position of some object that is in a quantum state. 103 00:13:35,430 --> 00:13:44,660 Flaminia Giacomini: so does it. Does it make sense to consider reference frames? Does that, you know, quantum superposition, or even in town, will relative to each other. 104 00:13:45,990 --> 00:13:51,640 Flaminia Giacomini: And this is the question that we ask when we talk about confront reference trains 105 00:13:53,780 --> 00:14:00,320 Flaminia Giacomini: so more specifically. We want to start from a situation in which we are in C, 106 00:14:00,490 --> 00:14:10,070 Flaminia Giacomini: and we describe the quantum system of a B which can be. You know it's going to superposition of in town world, anyone from State. 107 00:14:10,660 --> 00:14:12,610 Flaminia Giacomini: And then we want to switch 108 00:14:12,620 --> 00:14:15,320 Flaminia Giacomini: to a quantum reference frame 109 00:14:15,340 --> 00:14:18,510 Flaminia Giacomini: that is centered in the position of a. 110 00:14:20,050 --> 00:14:31,340 Flaminia Giacomini: and in this case what we will see is the quantum state of B and C. That can again be as a fully general quantum state in a one to superposition or in time. 111 00:14:34,090 --> 00:14:34,950 Flaminia Giacomini: No. 112 00:14:35,060 --> 00:14:46,150 Flaminia Giacomini: let me set up the formalism by giving you a classic like a classic of reference transformation as an example, and then generalizing it to a one to superposition. 113 00:14:46,880 --> 00:14:57,900 Flaminia Giacomini: So this is, I. I will consider a special translation in one dimension. where, initially we have seen. That is the origin of our initial reference frame. 114 00:14:58,020 --> 00:15:06,360 Flaminia Giacomini: and we have a quantum state of a that is localized around some Position X one and the state of B that is here, I 115 00:15:06,680 --> 00:15:09,770 Flaminia Giacomini: through it as localized, but it can be any one from State. 116 00:15:11,090 --> 00:15:12,090 Flaminia Giacomini: So now. 117 00:15:12,310 --> 00:15:22,790 Flaminia Giacomini: if you want to move the origin of the reference frame from C to a. What we do in some of quantum mechanics is to apply a unitary operation. 118 00:15:22,940 --> 00:15:29,510 Flaminia Giacomini: That is, a a translation operator. where we translate System B by X one. 119 00:15:29,940 --> 00:15:43,760 Flaminia Giacomini: And then, since we also want to say that system, c. Is localized at minus X, one from the perspective of system. A. Then we add this additional operator that we call a parity swap operator. 120 00:15:44,210 --> 00:15:45,250 Flaminia Giacomini: That's 121 00:15:45,260 --> 00:15:57,150 Flaminia Giacomini: whose action is exactly what I just said. So it sends X to one of sacks, and so a to C. And this is to realize this part of the transformation. 122 00:15:58,610 --> 00:16:06,140 Flaminia Giacomini: So now what happens if, instead of having this state. Here I have a state that is like that 123 00:16:06,340 --> 00:16:19,980 Flaminia Giacomini: where B is again a general state. And here, just for simplicity, I through it as localized. and a is in a quantum superposition of 2 different positions. X, one and X 2. 124 00:16:20,210 --> 00:16:25,390 Deepak Vaid: Hi flamenia. Could you possibly just go over that again? 125 00:16:25,480 --> 00:16:27,860 Deepak Vaid: Once more a little slower. 126 00:16:28,720 --> 00:16:31,080 Flaminia Giacomini: Yes. From which part 127 00:16:31,140 --> 00:16:34,460 Deepak Vaid: the the previous slide. Yeah, this this, this. 128 00:16:34,580 --> 00:16:40,770 Flaminia Giacomini: Yeah. Okay. So here you have a quantum state of a, and I want to set up B 129 00:16:40,920 --> 00:16:53,120 Flaminia Giacomini: mit Ctl. And and a is a state that is localized around some position. X one. So here, basically you, when you change your reference frame. You just want the classical quantum mechanical relation to hold 250. 130 00:16:53,440 --> 00:17:10,760 Flaminia Giacomini: So what what you do is you apply a translation operator here. So when I apply this translation operator to X 0. This translates X 0 by a minus X one. So I get x 0 minus x one when I apply this part. 131 00:17:11,119 --> 00:17:13,069 Flaminia Giacomini: and when I apply this part. 132 00:17:13,240 --> 00:17:17,210 Flaminia Giacomini: I apply it to the at X, One, a. 133 00:17:17,400 --> 00:17:22,390 Flaminia Giacomini: So like this operator sends X to minus x, and swapped a with C. 134 00:17:22,660 --> 00:17:34,020 Flaminia Giacomini: So if I get minus x one and the swap a to C. So I get this this state here. So if I put the 2 of them together, I will get this whole state. 135 00:17:34,190 --> 00:17:35,450 Flaminia Giacomini: This is clear. 136 00:17:37,850 --> 00:17:42,600 Deepak Vaid: Yeah, I I I guess the only part is this: this parity swap operator. It's not. 137 00:17:42,920 --> 00:17:47,220 Deepak Vaid: It's not completely clear what it's doing. and why it's needed. 138 00:17:47,820 --> 00:17:56,350 Flaminia Giacomini: So this is needed. So what he's doing is just what I said. So it sends X to minus X, P. To minus P. And so up the labels a and C. 139 00:17:57,680 --> 00:18:00,420 Flaminia Giacomini: So this is its action that's by definition. 140 00:18:01,240 --> 00:18:02,410 Deepak Vaid: Oh, okay. 141 00:18:02,860 --> 00:18:10,330 Flaminia Giacomini: and why it's needed. It's because it's just out of the like relational reasons. 142 00:18:10,440 --> 00:18:24,210 Flaminia Giacomini: Because, if so, imagine if I I send in C and the Ca: at some position X. From my perspective. Then, if I stand here, then I want to describe 143 00:18:24,610 --> 00:18:27,050 Flaminia Giacomini: the former orange in of 144 00:18:27,160 --> 00:18:32,280 Flaminia Giacomini: my reference frame. As to being in my office, and it's a. 145 00:18:32,670 --> 00:18:40,410 Flaminia Giacomini: and I want to label the C instead of a. So basically this is the reason why we need to introduce this operator. 146 00:18:42,070 --> 00:18:44,060 Deepak Vaid: I I see. So I mean when you 147 00:18:45,280 --> 00:18:47,720 Deepak Vaid: take some position, X. And make that the 148 00:18:47,820 --> 00:18:52,500 Deepak Vaid: origin, then the other. The origin goes to 106. So that's where the parity comes from. 149 00:18:52,770 --> 00:18:54,660 Flaminia Giacomini: Yes, exactly. Yes. 150 00:18:54,710 --> 00:18:56,620 Deepak Vaid: yes, okay. Thanks a lot. Yeah. 151 00:18:56,990 --> 00:19:00,670 Simone: And why? So? Just to follow up on this. 152 00:19:01,990 --> 00:19:08,040 Simone: So Why, Don't, you just apply? Use the translation operator for both systems a and B. 153 00:19:08,190 --> 00:19:15,000 Simone: Why do you we with the swap instead of just writing it at the same parameter acting on both a and B, 154 00:19:15,350 --> 00:19:20,720 Flaminia Giacomini: so you can have an alternative formulation where you have 155 00:19:20,810 --> 00:19:26,850 Flaminia Giacomini: 3 differently the spaces of a, of B and of C. And the 156 00:19:26,870 --> 00:19:32,250 Flaminia Giacomini: origin of the reference frame is always assigned symbolically Position 0. 157 00:19:32,430 --> 00:19:41,330 Flaminia Giacomini: And then you can write this operator in a different way, and this extended over space. So that initially you, this this has 158 00:19:41,420 --> 00:19:44,190 Flaminia Giacomini: origin 0. Say, let me just write it. 159 00:19:46,030 --> 00:19:49,920 Flaminia Giacomini: Okay. And here I end up in this 160 00:19:50,140 --> 00:19:55,070 Flaminia Giacomini: state. and I can find a unitary operator that maps this. 161 00:19:56,290 --> 00:19:58,470 Flaminia Giacomini: To this it's equivalent. 162 00:19:58,870 --> 00:20:10,500 Flaminia Giacomini: But then the okay. So the thing is that then this is not very useful, because then, of course, this is not a full hill, but space. It's just symbolically there to say I am at the or engine. 163 00:20:10,620 --> 00:20:21,280 Flaminia Giacomini: So India. It's not really needed. And this is a just, a more compact definition of the the full thing. But it's a mathematical equivalent. 164 00:20:24,240 --> 00:20:25,550 Flaminia Giacomini: It applies 165 00:20:25,580 --> 00:20:27,700 Flaminia Giacomini: answer to the question. 166 00:20:31,540 --> 00:20:36,520 Flaminia Giacomini: Okay, I guess it does. Okay. So 167 00:20:38,530 --> 00:20:41,280 Flaminia Giacomini: should I go through this light again. then? 168 00:20:42,290 --> 00:20:45,290 Deepak Vaid: No, I'm: I'm: Good. But 169 00:20:45,310 --> 00:20:49,800 Flaminia Giacomini: okay. so okay. So when we have a superposition, then 170 00:20:49,970 --> 00:20:58,860 Flaminia Giacomini: what we are going to do is just to up linearly superpose the action of the operator 171 00:20:59,130 --> 00:21:03,290 Flaminia Giacomini: for each single position of it. So what's the question now. 172 00:21:03,510 --> 00:21:10,900 Flaminia Giacomini: here we have a that is delocalized, so there is no single X that we can use to perform the translation. 173 00:21:11,100 --> 00:21:17,710 Flaminia Giacomini: But then we can take seriously the linearity of quantum mechanics and say, okay, I don't have a single. 174 00:21:18,320 --> 00:21:27,550 Flaminia Giacomini: a single coordinate by which to translate. But I can just linearly superpose all possible positions of system. A. 175 00:21:28,080 --> 00:21:30,730 Flaminia Giacomini: And so what happens is that 176 00:21:31,380 --> 00:21:39,570 Flaminia Giacomini: when a is in X one, then B will be translated by X, one and C will be in minus one. 177 00:21:39,630 --> 00:21:48,100 Flaminia Giacomini: but when a is in x 2, then B is translated by x, 2, and C is also in minus x 2. 178 00:21:49,320 --> 00:21:55,530 Flaminia Giacomini: So in this is a in quantum information language, a quantum controlled translation 179 00:21:56,020 --> 00:22:04,210 Flaminia Giacomini: where the controlled system, so the one that tells us by how much to translate is the quantum reference Train a. 180 00:22:04,810 --> 00:22:17,350 Flaminia Giacomini: So mathematically. What happens is that the parameter of the transformation becomes an operator. and they are the the Hilbert space that corresponds to the hill, best space of the quantum reference frame. 181 00:22:18,930 --> 00:22:29,320 Flaminia Giacomini: And an immediate consequence of this transformation is that superposition and entanglement become quantum reference dependent. 182 00:22:29,620 --> 00:22:34,830 Flaminia Giacomini: And you can see here an example. This is a product state. So this is not entangled. 183 00:22:35,000 --> 00:22:41,830 Flaminia Giacomini: and after I mark it to the new quantum reference frame of a, I get an entangled state. 184 00:22:44,710 --> 00:22:45,680 Flaminia Giacomini: Okay. 185 00:22:45,810 --> 00:22:46,750 Ivan Agullo: is this. 186 00:22:46,900 --> 00:22:59,510 Flaminia Giacomini: Is this similar to to to a quantum date generating bill. Yeah, yeah, it's it. It. You can see it as a as a quantum gate. So of course, this is an if you need dimensionally this space, it's continuous variables. 187 00:22:59,550 --> 00:23:07,160 Flaminia Giacomini: but it is basically a quantum controlled superposition of gates. So that's what it is. 188 00:23:07,450 --> 00:23:23,700 Simone: Do just to understand the the standard description in which the frame is a non dynamical as you are seeing, and so not quantum imposed. How is he recovered the replacing these operator X. A. With some expectation value? Or do I need to do something else? 189 00:23:24,060 --> 00:23:26,760 Flaminia Giacomini: So what? 190 00:23:27,020 --> 00:23:45,770 Flaminia Giacomini: So the the believe meeting which you can recover the the usual translation. Actually, here, you don't do anything but you only restrict the space of states of the quantum reference frame to be coherent states, meaning that they are localized both in position and momentum. 191 00:23:47,010 --> 00:23:50,010 Flaminia Giacomini: So basically, these are the states of minimal dispersion 192 00:23:51,260 --> 00:23:57,920 Flaminia Giacomini: and acting with this operator on this. 193 00:23:58,490 --> 00:23:59,650 Flaminia Giacomini: That's the mean 194 00:24:04,400 --> 00:24:16,850 Simone: I don't understand why I mean, Sorry. Just me. Okay, One step back. Do we agree that the standard description of the translation. These X hat is just a a free parameter and not an operator. 195 00:24:18,640 --> 00:24:20,910 Simone: Okay, now, how 196 00:24:22,850 --> 00:24:31,710 Simone: okay? Now, if I act with this operator or an acquaintance state. This is not the same thing as replacing that I, that operator with the some classical parameter right? 197 00:24:31,900 --> 00:24:48,290 Flaminia Giacomini: So you you have the proper to the down a coherent state center, that on Xmp. And the both the X operator gives X coherent state and P. Operator acting on the coherence, it gives P. Coherent state. 198 00:24:48,380 --> 00:24:51,240 Flaminia Giacomini: So the the 199 00:24:51,380 --> 00:24:54,750 Simone: is not an eigenstate of these operators. 200 00:24:54,890 --> 00:24:59,870 Flaminia Giacomini: It's not, but it's approximately true, so you can. You can make this replacement. 201 00:25:00,950 --> 00:25:06,660 Simone: Okay. But this approximation is part of my question. So it is not enough right? You also need 202 00:25:06,830 --> 00:25:13,800 Simone: what? What is the some sending H bar to 0? Maybe. 203 00:25:14,030 --> 00:25:32,890 Flaminia Giacomini: No, no, it it's a okay. So this is we have in a. So the the user. Which one does the the possible way which one does the classical limit in this type of the descriptions. It's more like an operational way. 204 00:25:32,890 --> 00:25:45,880 Flaminia Giacomini: E. C. 205 00:25:45,880 --> 00:25:53,400 Flaminia Giacomini: And if the state is localized within a single slot of the measurement apparatus, then you are in the classical limit. 206 00:25:54,050 --> 00:25:58,010 Flaminia Giacomini: And so it it is more a matter of 207 00:25:58,060 --> 00:26:16,070 Flaminia Giacomini: the interplay between the resolution of that. Your measurement and the type of state that you're considering. And then, once you apply the of the the operator on the subset that you choose of the Hilbert space that's defined the state of the your reference frame. 208 00:26:16,070 --> 00:26:24,040 Flaminia Giacomini: When in this case you want to take the link of the classical to the classical, different strength, then you're fine you you are in the plastic, you 209 00:26:27,060 --> 00:26:34,770 Simone: I see. So, strictly speaking, you will recover translations with this, with parameters, to begin with. Okay, I understand. Thank you. 210 00:26:34,820 --> 00:26:35,510 Yes. 211 00:26:38,330 --> 00:26:41,370 Flaminia Giacomini: Can I also a question? Sorry. 212 00:26:41,850 --> 00:26:52,180 Florian Girelli: So just before for you slide again. So if I want to know if I want to do a frame. 213 00:26:52,190 --> 00:26:56,620 Florian Girelli: a a change of frame, I mean, like here i'm in what i'm in. 214 00:26:57,120 --> 00:27:00,210 Florian Girelli: And so what I need to do is to do a measurement 215 00:27:00,300 --> 00:27:07,730 Florian Girelli: of oh, I I mean, we we need to measure what this parameter recorded a parameter before. But this this guy needs to be measured. 216 00:27:07,880 --> 00:27:18,530 Florian Girelli: and if I measure it, this is gonna affect all the all the systems. And so, then how can you have a nice transformation like that? Because when you measure, or you kind of. 217 00:27:18,690 --> 00:27:30,760 Florian Girelli: you know, to performing the systems. And so I think we we looked at that. We Steve, about that and the transformation where we're very complicated. So how can you make it so nice here? 218 00:27:30,930 --> 00:27:41,410 Flaminia Giacomini: Yes, no, no, that you are perfectly right. So it's true, but it is a different question. So here we are assuming we have infinite resources for the reference frame. 219 00:27:41,580 --> 00:28:00,090 Flaminia Giacomini: And the the question that you're asking is, what happens if I actually want to operationally, Consider the like really setting the measurement and understanding how these 2 quantum references are related by communicating, for instance, between each other. And then you have a problem of limited resources. 220 00:28:00,090 --> 00:28:18,240 Flaminia Giacomini: and we it we still do not know what happens in this formulation. What we know is how this formulation is connected to the like we call it. Sometimes the quantum information approach by back to through the spectrums. 221 00:28:18,240 --> 00:28:32,340 Flaminia Giacomini: and it's so it's a different way of taking a group average. In our case we take a coherent group averaging and in the other in in the quantum information case, you take any. 222 00:28:32,560 --> 00:28:52,410 Flaminia Giacomini: And basically this means that your so if you have a conserved quantity that, for instance, in this case could be the total momentum. Then you're going to have a at the composition in this, for different values of the like, and square the composition, block the composition in this for different values of the total momentum 223 00:28:52,410 --> 00:29:07,340 Flaminia Giacomini: mit ctl, and and you take all of them the direct sum. Well, in our case we would have a projection on the total momentum equal to 0. So, mathematically this is the relation between these 2 approaches. Physically, I think that we still need to do some more work, 101 224 00:29:07,340 --> 00:29:24,640 Flaminia Giacomini: erez Agmoni, to incorporate also this other question in this approach, and the the conservative way of seeing that is how to map. So I make measurements only from the lamb frame. And then I want to map a set of relational variables into a different set of relational variables, 150, 225 00:29:24,640 --> 00:29:34,580 Flaminia Giacomini: and that's without a asking the question, how which measurements I have to make in order to to set up really the problem in an operational way. 226 00:29:39,020 --> 00:29:53,340 Florian Girelli: Oh, okay. So basically, you're saying that's that's the question. That is open. What? What I was asking. I mean that you need to. Yeah, but we we, we, we, we we we we looked at that, and the the transformation. We're very bad. And it was I was very 227 00:29:53,700 --> 00:30:00,020 Florian Girelli: that this this is a very complicated yeah. 228 00:30:00,270 --> 00:30:01,310 Florian Girelli: All right. Thank you. 229 00:30:04,570 --> 00:30:06,560 Flaminia Giacomini: Okay. 230 00:30:07,410 --> 00:30:11,180 Flaminia Giacomini: Okay, it's not. Now, what what I I give you is 231 00:30:11,250 --> 00:30:20,220 Flaminia Giacomini: the simplest transformation, so the the special translation. But actually you can come up with other transformations, for instance, the 232 00:30:20,270 --> 00:30:28,580 Flaminia Giacomini: superposition of like boosts, etc. But all the transformations that we found so far roughly, have this structure here. 233 00:30:28,740 --> 00:30:39,680 Flaminia Giacomini: where we have on this side just a standard reference from transformation that can be special translation, both so accelerate transformation to an accelerated reference frame. 234 00:30:40,010 --> 00:30:47,040 Flaminia Giacomini: and this would be the parameter of the transformation. But then this parameter is controlled 235 00:30:47,110 --> 00:30:52,180 Flaminia Giacomini: on an additional Hilbert space. That is, the state of the quantum reference frame 236 00:30:52,490 --> 00:31:01,720 Flaminia Giacomini: that can be, for instance, position, velocity, or also some effective acceleration with acceleration is a bit more complicated than this is just an approximate form of what we find. 237 00:31:03,350 --> 00:31:04,480 Flaminia Giacomini: So now. 238 00:31:05,420 --> 00:31:10,390 Flaminia Giacomini: what happens if on top of that we also want to include dynamics. 239 00:31:10,400 --> 00:31:15,320 Flaminia Giacomini: So we want to give the quantum reference frame also Hamiltonian. 240 00:31:16,640 --> 00:31:28,000 Flaminia Giacomini: So let's just consider, for instance, a transformation that is, we can call it extended Galilean transformation. This is a terminology from Daniel Grimberger. 241 00:31:28,860 --> 00:31:32,820 Flaminia Giacomini: that is, of this form. Then you just shouldn't go to put it 242 00:31:32,920 --> 00:31:46,330 Flaminia Giacomini: for a standard reference from a transformation we can take the Schrodinger question, and then we transform the Hamiltonian. This reading the question, as I wrote in the one of the first lines according to this law. 243 00:31:47,900 --> 00:31:48,760 Flaminia Giacomini: No. 244 00:31:48,910 --> 00:31:53,080 Flaminia Giacomini: And, for instance, this can be a translation or a boost. 245 00:31:53,640 --> 00:31:54,500 Flaminia Giacomini: No. 246 00:31:55,550 --> 00:32:00,810 Flaminia Giacomini: if I start with a free particle, Hamiltonian for some particle. B. 247 00:32:01,060 --> 00:32:09,250 Flaminia Giacomini: If I apply one of these 2 transformations so like translational boost, then I end up with another free particle, Hamiltonian. 248 00:32:09,760 --> 00:32:16,780 Flaminia Giacomini: And so this is this means that these 2 transformations are as image of the dynamics. 249 00:32:17,220 --> 00:32:22,020 Flaminia Giacomini: And now what we want to ask is what happens with quantum preference frames. 250 00:32:22,250 --> 00:32:24,830 Flaminia Giacomini: Basically the logic is exactly the same. 251 00:32:25,240 --> 00:32:36,610 Flaminia Giacomini: and in just that as following the recipe that I gave you, we are going to promote this parameters to operators on the Hilbert space of the quantum reference rate. 252 00:32:37,370 --> 00:32:43,490 Flaminia Giacomini: So x 0 goes to excel operator, and V. 0 goes to PA, divided by am. A. 253 00:32:44,940 --> 00:32:45,990 Flaminia Giacomini: But then 254 00:32:46,030 --> 00:33:05,290 Flaminia Giacomini: the we can step by the same. So this is the the the final Hamiltonian is still related to the initial Hamiltonian. Exactly in the same way. The only difference is that we will have a Hamiltonian, not only of Particle B, but also of the one from 255 00:33:05,430 --> 00:33:07,020 Flaminia Giacomini: that is possible. A. 256 00:33:08,310 --> 00:33:18,930 Flaminia Giacomini: And in particular one can find 2 transformations that correspond to a superposition of special translations and superposition of Kerle and Boost. 257 00:33:19,050 --> 00:33:23,890 Flaminia Giacomini: such that a free particle Hamiltonian of this type is mapped 258 00:33:23,950 --> 00:33:31,060 Flaminia Giacomini: to a a free particle. Hamiltonian, where the Hamiltonian of a is replaced by the Hamiltonian of C. 259 00:33:31,080 --> 00:33:32,590 If you haven't. 260 00:33:33,010 --> 00:33:38,400 Flaminia Giacomini: and this is the sense in which we talk about extended symmetries of the dynamics. 261 00:33:40,970 --> 00:33:51,870 Flaminia Giacomini: Okay. So now I promised to give a connection to to the gravity. and there are, I I will do it in 2 different ways, and I will be very brief. 262 00:33:52,190 --> 00:33:54,160 Flaminia Giacomini: So the first one 263 00:33:54,200 --> 00:34:03,120 Flaminia Giacomini: is more like first principal approach, and then I I would like to tell you about an actual experiment that was done recently. 264 00:34:03,820 --> 00:34:04,880 Flaminia Giacomini: So 265 00:34:05,270 --> 00:34:11,420 Flaminia Giacomini: the the first one, that is that quantum reference trains can actually lead to 266 00:34:11,570 --> 00:34:17,800 Flaminia Giacomini: for a generalization of the I. And this can be done in 2 ways. 267 00:34:17,889 --> 00:34:22,980 Flaminia Giacomini: So one way is to consider a classical gravitational field 268 00:34:23,020 --> 00:34:25,850 Flaminia Giacomini: here, and then just delocalize 269 00:34:25,860 --> 00:34:35,100 Flaminia Giacomini: a for instance, like in another interferometer. So in a superposition of 2 different heights in the gravitational field. And 270 00:34:35,330 --> 00:34:47,530 Flaminia Giacomini: so, if I put a clock, for instance, on top of this particle. Then the clock will pick differently, according to whether it is in this path or this path. 271 00:34:48,460 --> 00:34:53,620 Flaminia Giacomini: And now, with quantum preference frames, we can find a transformation 272 00:34:53,760 --> 00:35:11,760 Flaminia Giacomini: to the quantum reference frame that is associated to the position of this particle in the interferometer, such that we can make the metric locally minkoskian at the origin of this conference frame. So basically at the position of this particle, even if it's possible, is in a particular position 273 00:35:12,840 --> 00:35:20,530 Flaminia Giacomini: and a bit more ambitiously. We can instead consider a quantum superposition of 2 different space times 274 00:35:20,950 --> 00:35:27,710 Flaminia Giacomini: That, we say are microscopically distinguishable, meaning that there is a they are going on. 275 00:35:27,790 --> 00:35:30,630 Flaminia Giacomini: they are. 276 00:35:31,420 --> 00:35:36,510 Flaminia Giacomini: and then we can have a particle that is entangled with the 277 00:35:36,540 --> 00:35:42,390 Flaminia Giacomini: with the position. Sales is mass. The detail means the the space and configuration. 278 00:35:42,800 --> 00:35:51,550 Flaminia Giacomini: And then, again, we can find a quantum reference from transformation that to the quantum reference stream centered on this particle here. 279 00:35:51,790 --> 00:35:56,800 Flaminia Giacomini: such that the metric is local limit. Costs can at the origin of the quantum reference frame. 280 00:35:58,440 --> 00:36:02,550 Flaminia Giacomini: So what does? What are the consequences of doing this? 281 00:36:02,680 --> 00:36:14,170 Flaminia Giacomini: So in in this simple it's simpler case. We can device a test for the this Einstein equivalent principle for conference 282 00:36:14,220 --> 00:36:21,680 Flaminia Giacomini: that uses an adventure from gene quantum clocks in particular. This is some work that I need to the master's student 283 00:36:21,860 --> 00:36:30,130 Flaminia Giacomini: we found we we used and tangled clocks with with, so that entangled in these other interferometers. 284 00:36:30,470 --> 00:36:33,900 Flaminia Giacomini: and we found that if this 285 00:36:34,130 --> 00:36:46,860 Flaminia Giacomini: extended I principal for consumer reference frame is not valid, then it doesn't even make sense, even from an external perspective, to assign a time to this quantum clocks. 286 00:36:48,290 --> 00:36:53,590 Flaminia Giacomini: And now and he said the in in this in this case here 287 00:36:53,770 --> 00:37:09,700 Flaminia Giacomini: this is instead contained in these other paper. we propose this generalization of guest and equivalence principle, as a way to reconcile the ice and equivalence principle and the principle of linear superposition. 288 00:37:10,350 --> 00:37:11,180 Flaminia Giacomini: And 289 00:37:12,350 --> 00:37:29,080 Flaminia Giacomini: this is so. The the incompatibility between these 2 principles who are coming from, and one coming from general relativity was one of the way that the it was used by Roger Peros to argue for the spontaneous localization 290 00:37:29,080 --> 00:37:37,410 Flaminia Giacomini: of the wave function in the presence of a superposition of gravitational fields. And so. 291 00:37:37,640 --> 00:37:49,180 Flaminia Giacomini: because these 2 principles cannot go together, so he argued, one has to abandon one of them, and he wanted to put general relativity first, so he abandoned the principle of leadership position. 292 00:37:49,350 --> 00:38:00,020 Flaminia Giacomini: But what we say is that this is not necessarily so, provided that you are fine with extending the Einstein principle to this more general configuration. 293 00:38:01,050 --> 00:38:03,920 Flaminia Giacomini: And okay. 294 00:38:04,450 --> 00:38:16,240 Flaminia Giacomini: Now, this is the more conceptual part. Now let me come to a more concrete question. What happens if you put a quantum particle in a quantum superposition of 2 positions. 295 00:38:16,460 --> 00:38:31,610 Flaminia Giacomini: and this is not a new question. This was raised at least in 1,955 set, 57 by Richard Feynman, and the Championship Conference, and he proposed a for the experiment in which amass was put in a quantum superposition. 296 00:38:31,940 --> 00:38:41,260 Flaminia Giacomini: and he concluded that if you believe in quantum mechanics up to any level. Then you have to believe in gravitational quantization. In order to describe this experiment. 297 00:38:41,670 --> 00:38:51,660 Flaminia Giacomini: Now, he meant gravitational quantization. In a very precise sense. He meant that the state of the gravitational field is in a constant superposition. 298 00:38:51,750 --> 00:38:53,300 Flaminia Giacomini: Nothing more than that. 299 00:38:54,500 --> 00:38:58,960 Deepak Vaid: Can I? Can I ask a question about the previous slide? 300 00:38:59,160 --> 00:39:00,680 Flaminia Giacomini: Hmm. It's fine. 301 00:39:06,740 --> 00:39:12,540 Deepak Vaid: Okay, so I mean, I probably miss something. But when you say that. So you have 302 00:39:12,930 --> 00:39:16,000 Deepak Vaid: an observer who is 303 00:39:16,150 --> 00:39:18,230 Deepak Vaid: in a superposition of trajectories 304 00:39:18,510 --> 00:39:24,310 Deepak Vaid: to it. It's the same, fully following observer. But along moving around 2 different trajectories. Is that correct? 305 00:39:24,760 --> 00:39:28,320 Flaminia Giacomini: So we are not talking about observer. We are talking about particle. 306 00:39:28,680 --> 00:39:31,820 Deepak Vaid: sure, sure. Okay. So some system. 307 00:39:32,490 --> 00:39:33,180 Flaminia Giacomini: Yeah. 308 00:39:33,760 --> 00:39:44,930 Deepak Vaid: Okay. And so the the notion is that this extended equivalent principle that you're saying is basically that you can describe the 309 00:39:45,180 --> 00:39:48,180 Deepak Vaid: the whole system, the the earth. 310 00:39:48,640 --> 00:39:52,250 Deepak Vaid: and the you know the freely falling particle. 311 00:39:52,990 --> 00:39:59,210 Deepak Vaid: either by looking from the particles perspective, and seeing the earth in a superposition. 312 00:40:00,630 --> 00:40:05,210 Deepak Vaid: or from the earth's perspective. And seeing the particle in the superposition. Is that is that correct? 313 00:40:05,430 --> 00:40:13,430 Flaminia Giacomini: You're okay, but the left hand side now right the right hand side. So this is entangled. So basically. 314 00:40:13,480 --> 00:40:16,090 Flaminia Giacomini: if I if I stand so 315 00:40:16,350 --> 00:40:28,980 Flaminia Giacomini: okay, so this this is: I do it for a very special case. But in general yes, I can take a quantum reference frame that is centered on the particle that is entangled with the the space time 316 00:40:29,100 --> 00:40:30,000 Flaminia Giacomini: we did 317 00:40:30,340 --> 00:40:40,170 Flaminia Giacomini: so I I have for take space time, one state of state of a set of particle in space, and one plus space and 2 state of particle is based in 2 318 00:40:41,760 --> 00:40:46,150 Deepak Vaid: right. But now Penrose's argument, I think it 319 00:40:46,210 --> 00:40:48,510 Deepak Vaid: based on the fact that 320 00:40:49,270 --> 00:40:53,100 Deepak Vaid: you, you know you have these 2 systems which are 321 00:40:53,260 --> 00:40:56,450 Deepak Vaid: very different in mass. And 322 00:40:56,760 --> 00:41:02,710 Deepak Vaid: so when you, when you look at the the earth in this position, right, and you calculate the 323 00:41:03,430 --> 00:41:07,950 Deepak Vaid: the gravitational potential energy to do that separation. Right? 324 00:41:08,440 --> 00:41:11,190 It's it's made. It's many times larger than the 325 00:41:11,790 --> 00:41:17,660 Deepak Vaid: change in the gravitational potential energy of the particle in the 2 locations as seen by the earth. 326 00:41:20,440 --> 00:41:30,690 Flaminia Giacomini: so he has different ways of arguing. One is in terms of this energy difference between the 2 configurations. And then he said that this leads to an unstable state. 327 00:41:30,700 --> 00:41:36,580 Flaminia Giacomini: But there is also another way in which he argues really from first principles, that these 2 328 00:41:36,660 --> 00:41:55,360 Flaminia Giacomini: principles of gravity, gravitational theories, and quantum mechanics are not compatible one with the other, and then he needs a. And then you need to abandon one another way that he uses is that it is impossible to define a single killing vector if you have. 329 00:41:55,360 --> 00:42:04,900 Flaminia Giacomini: or that the volume of the shield is different, according to which amplitude you're in. So there are several arguments that 330 00:42:05,160 --> 00:42:08,800 Deepak Vaid: But the thing is that even if you take this extended equivalence principle. 331 00:42:10,110 --> 00:42:17,400 Deepak Vaid: the fact that there is this. this, this difference in the gravitational potential energy is in the 2 cases 332 00:42:18,100 --> 00:42:20,280 Deepak Vaid: that pack doesn't Go away right? 333 00:42:20,880 --> 00:42:22,690 Flaminia Giacomini: No, but this is not a problem. 334 00:42:26,550 --> 00:42:28,690 Flaminia Giacomini: because it I mean 335 00:42:29,180 --> 00:42:39,940 Flaminia Giacomini: So things dico here. If you make a measurement such that you record information about the the value of the computational potential, or anything like 336 00:42:40,180 --> 00:42:41,920 Flaminia Giacomini: like anything you want. 337 00:42:41,990 --> 00:42:45,380 Flaminia Giacomini: Yeah. But if you don't do that, then 338 00:42:45,790 --> 00:42:59,100 Flaminia Giacomini: you're fine, and it's not enough to become entangled so like to to be, for instance, subject to a different traditional potential in order for the State to go here. Otherwise, we wouldn't even have autumn interferometers. 339 00:43:03,320 --> 00:43:06,630 Deepak Vaid: Okay, okay, thanks. 340 00:43:07,080 --> 00:43:07,670 Yeah. 341 00:43:10,330 --> 00:43:13,070 Flaminia Giacomini: Okay. So 342 00:43:15,190 --> 00:43:16,680 Flaminia Giacomini: okay. So the 343 00:43:16,730 --> 00:43:21,980 Flaminia Giacomini: So this is what 5 one meant for the what, when they must in your particular position. 344 00:43:22,140 --> 00:43:35,390 Flaminia Giacomini: Now this discussion led to a long literature after 1,957, and was revived that Don't have time to go through this literature, but was revived in 2,017 by a proposal one 345 00:43:35,550 --> 00:43:39,840 Flaminia Giacomini: so 2 papers that came out on the same day on the Archive. where 346 00:43:39,930 --> 00:43:54,280 Flaminia Giacomini: 2 masters. So it's. It's basically a slight variation of this protocol where 2 masters become entangled via their gravitational interaction, and they use a quantum information theorem in order to say that the gravitational field is not classical. 347 00:43:57,840 --> 00:44:09,710 Flaminia Giacomini: No, there were many reactions. I I will not go through the argument in at all. But there were many reaction to this paper, and with positions being also opposite 348 00:44:09,950 --> 00:44:29,840 Flaminia Giacomini: from like this doesn't, tell us anything about gravity to this is an experiment that can should get sprinted with cloudy phones, and I think both of these positions are a bit extreme, but there are many interesting observations that can be made on this set up, and that can inform us on features of the gravitational field in this regime. 349 00:44:30,420 --> 00:44:32,450 Flaminia Giacomini: And here are some. 350 00:44:33,890 --> 00:44:34,740 Flaminia Giacomini: So 351 00:44:35,920 --> 00:44:36,730 Flaminia Giacomini: no. 352 00:44:38,570 --> 00:44:41,100 Flaminia Giacomini: I want to put one more observation here. 353 00:44:41,270 --> 00:44:44,270 Flaminia Giacomini: So we have seen with quantum reference frames. 354 00:44:44,590 --> 00:44:49,680 Flaminia Giacomini: that for entanglement and superposition are quantum reference to independent. 355 00:44:50,090 --> 00:45:05,930 Flaminia Giacomini: And now the question that I want to ask is, can it be that also? The superposition of gravitational field is a relative concept that it is not something that is just given a priority, but it depends on the specific formulation that we take. 356 00:45:05,990 --> 00:45:19,390 Flaminia Giacomini: and the specific quantum corrections that we take. And I don't have an answer for that. So this is just a question. and that we we have just started to think about 357 00:45:19,450 --> 00:45:21,630 Flaminia Giacomini: what the possible answer could be. 358 00:45:21,830 --> 00:45:32,280 Flaminia Giacomini: and they want to show you, as a final example, one possible way of understanding this question in a very concrete set up that is. 359 00:45:33,140 --> 00:45:38,340 Flaminia Giacomini: in particular. This is an experiment that was done at Stanford last year 360 00:45:38,590 --> 00:45:50,460 Flaminia Giacomini: by the group of. and that measures the gravitational. So this is another mix fountain. So If you should imagine a cylinder that is, 10 meters height. 361 00:45:50,590 --> 00:46:02,410 Flaminia Giacomini: where particles are sent in a quantum superposition of 2 different heights in the gravitational field, just focus on the red particle. We don't care of the blue particle for what concerns us at the moment. 362 00:46:03,360 --> 00:46:15,240 Flaminia Giacomini: and then what they did was to measure the face shift. So at the end of the interferometer basically the particles go up. But then they go down, and then you measure and 363 00:46:15,800 --> 00:46:29,870 Flaminia Giacomini: and this interference factor, and we we can look at it here. In a feeling for new frame is includes a gravitational action difference. But this gravitational action difference is not the gravitational action difference of the earth 364 00:46:29,890 --> 00:46:35,330 Flaminia Giacomini: that they can feel that out. But it's the gravitational action difference produced 365 00:46:35,440 --> 00:46:51,740 Flaminia Giacomini: by a Tunstan mass this half doughnut here that we is 1 0 and the displaced at the top at the very top of this interferometer. So this is the source mass of which causes the gravitational phase shift here. 366 00:46:52,390 --> 00:47:02,260 Flaminia Giacomini: and this is the first experiment that measured a phase shift that went beyond deliver approximation of the gravitational potential. 367 00:47:04,940 --> 00:47:07,390 Flaminia Giacomini: So it measured the higher order corrections. 368 00:47:08,470 --> 00:47:09,500 Flaminia Giacomini: So now. 369 00:47:10,180 --> 00:47:25,150 Flaminia Giacomini: what what did we do? So we took everything that we know from current experiments. And what do we know from current experiments? So we know that the master is localized, that sources the gravitational. Here, then, this has been verified up to this scale. Here. 370 00:47:26,280 --> 00:47:35,210 Flaminia Giacomini: then, we know that the equivalence principle is valid up to experimental resolution. then we know that there are gravitational waves. 371 00:47:35,320 --> 00:47:36,690 Flaminia Giacomini: We have measured that 372 00:47:37,460 --> 00:47:45,560 Flaminia Giacomini: then these experiment has measured this gravitational phase, shift between the different parts of the denatom takes in an interferometer. 373 00:47:46,310 --> 00:47:56,750 Flaminia Giacomini: and then we know that we can take classical gravity, and we can take quantum theory, and we can put them together in this experiment, and they work perfectly well. There's no contradiction at all. 374 00:47:57,810 --> 00:47:58,740 Flaminia Giacomini: And 375 00:47:58,900 --> 00:48:07,400 Flaminia Giacomini: so now we ask, okay, so previously, this experiment doesn't show that just by itself that the gravitational thing is going to. 376 00:48:07,550 --> 00:48:08,470 Flaminia Giacomini: But 377 00:48:08,680 --> 00:48:16,680 Flaminia Giacomini: what are we missing? Which principles are we missing that could be tested in order to 378 00:48:16,750 --> 00:48:32,910 Flaminia Giacomini: take this to a configuration in which the gravitational field is in a quantum superposition, so which which assumptions are releasing here. and in particular, we laid down 3 fundamental principles, and I here focus on 2 of them, because. 379 00:48:32,930 --> 00:48:36,330 Flaminia Giacomini: like these, 2, are sufficient to prove the point 380 00:48:38,050 --> 00:48:44,850 Flaminia Giacomini: to to show that this experiment is equivalent to one in which the gravitational field is in a quantum superposition. 381 00:48:45,250 --> 00:48:55,900 Flaminia Giacomini: and these 2 principles are the existence of the gravitational of gravitational fields, which we mean as any massive particle that is well localized at Position X. 0 382 00:48:55,900 --> 00:49:11,710 Flaminia Giacomini: sources a gravitational F. G. With some functional form X minus X 0. So here we are, just assuming that the localized particle sources a gravitational field, and it doesn't assume anything about the particle that is not localized. So, in a quantum superposition 383 00:49:12,350 --> 00:49:25,820 Flaminia Giacomini: mit ctl. And and the other principle that we can take is the quantum relativity principle, namely, that the laws of physics take the same form in every reference frame, including quantum reference frames. So the reference strains associated to 1, 2 particles, one. 384 00:49:26,770 --> 00:49:31,660 Flaminia Giacomini: Let's see what happens if we map the yeah. This experiment 385 00:49:31,790 --> 00:49:35,240 Flaminia Giacomini: using these 2 principles. So 386 00:49:36,090 --> 00:49:45,700 Flaminia Giacomini: in particular we want to take. So the tungsten mass source is the gravitational here Here we and we know if we have measured it, and we have. 387 00:49:48,410 --> 00:49:50,890 Flaminia Giacomini: we have. 388 00:49:52,830 --> 00:49:55,220 Flaminia Giacomini: We also assume it with the first principle. 389 00:49:55,330 --> 00:50:03,410 Flaminia Giacomini: and then. Now we want to take a quantum reference from transformation to the quantum reference frame centered on the atom in the interferometer 390 00:50:03,890 --> 00:50:18,710 Flaminia Giacomini: mit ctl, and in this quantum reference frame the album is in a fixed position, but the source mass is in a part of the superposition of 2 positions; and then, if the laws of physics are prevalent, this is the sorts months in a quantum superposition this 150, 391 00:50:19,070 --> 00:50:23,230 Flaminia Giacomini: and so it should be considered as the source of the of a traditional field. 392 00:50:23,790 --> 00:50:30,990 Flaminia Giacomini: and hence, if the interference. If the experiment shows some some interference pattern, which should. 393 00:50:31,210 --> 00:50:36,030 Flaminia Giacomini: then we can conclude the 394 00:50:36,190 --> 00:50:39,850 Flaminia Giacomini: Now, I don't want to say that this experiment proves 395 00:50:39,960 --> 00:50:50,450 Flaminia Giacomini: mit ctl. And that the gravitational field is in a constant superposition. But what I want to do is to take a first principle approach and say which set of principles, we should 250 396 00:50:50,530 --> 00:50:56,280 Flaminia Giacomini: take in order to show that the gravitational field can be in a constant superposition state. 397 00:50:57,690 --> 00:51:04,860 Flaminia Giacomini: And so this is more as an inspiration towards future experiments than to claim something on current experiments. 398 00:51:06,390 --> 00:51:10,170 Flaminia Giacomini: So this is all that I want to tell you and 399 00:51:10,710 --> 00:51:19,840 Flaminia Giacomini: mit Ctl, and so to recap from an experimental perspective. We do not know which observation would prove in a compelling way that gravity has quantum features one. 400 00:51:20,520 --> 00:51:28,680 Flaminia Giacomini: And so it is interesting to explore how much we can know about the gravitational field that we are forming these experiments 401 00:51:29,550 --> 00:51:37,750 Flaminia Giacomini: from a theoretical perspective. We do not know how to reconcile the fundamental principles of general relativity and quantum theory. 402 00:51:38,270 --> 00:51:42,410 Flaminia Giacomini: However, we can device thought experiments in this regime 403 00:51:42,660 --> 00:51:52,570 Flaminia Giacomini: that can help us to solve some open questions and test the internal consistency of general relativity and quantum theory in some concrete physical scenarios 404 00:51:52,810 --> 00:51:55,280 Flaminia Giacomini: and the results. And thank you for your attention. 405 00:52:00,660 --> 00:52:03,820 Parampreet Singh: Okay, thank you for being here. Are there any questions 406 00:52:07,500 --> 00:52:08,280 Parampreet Singh: you one? 407 00:52:08,720 --> 00:52:25,990 Ivan Agullo: Yes, I have a a question. I mean these something and I have been discussing with by I know junior, and a few weeks ago, and and and one of the confusion that at least I have, and I think they also share it about this type of experiments, and 408 00:52:26,150 --> 00:52:29,110 Ivan Agullo: what they the last about gravity 409 00:52:29,540 --> 00:52:39,110 Ivan Agullo: is that you know there is no gravitational wave production, you know, in this kind of match configurations, so only the columbic 410 00:52:39,170 --> 00:52:49,380 Ivan Agullo: or the source part. You know the part of the gravitational field that is attached to the source. You know we are not introducing 411 00:52:49,720 --> 00:52:56,110 Ivan Agullo: the degrees of freedom, of gravity by itself, but only the coulombic part which 412 00:52:56,250 --> 00:53:00,730 Ivan Agullo: you know it never involves, so to speak. 413 00:53:01,000 --> 00:53:12,500 Ivan Agullo: a Hilbert space for gravity itself. These experiments. You know, this gravitational field can be formulated in the Hilbert space of matter. You, don't need independent degrees of freedom of gravity 414 00:53:12,670 --> 00:53:16,350 Ivan Agullo: to Spain. This experiment, so I don't understand what 415 00:53:16,820 --> 00:53:25,830 Ivan Agullo: this experiments can tell me about the Hilbert space of gravity, or the quantum mechanics rapidly itself, because they are not not involved. And 416 00:53:26,210 --> 00:53:40,900 Flaminia Giacomini: okay. So one caveat is that you should not think about only the experiment that has been proposed so far. But we are thinking more broadly in terms of all experiments that could involve masses in a quantum school position 417 00:53:41,010 --> 00:53:54,870 Flaminia Giacomini: mit ctl. And so, secondly, there are some consistency arguments that you can make as soon as you take a must in a quantum superposition and space like separated operations. So in that case already you can see much more 2, 418 00:53:55,120 --> 00:53:58,870 Flaminia Giacomini: because so there is a sort of experiment that's 419 00:53:58,920 --> 00:54:07,460 Flaminia Giacomini: the 420 00:54:07,580 --> 00:54:10,010 Flaminia Giacomini: where you can consider a communication product. 421 00:54:10,490 --> 00:54:20,250 Flaminia Giacomini: and you put a massive particle in a on to square position and far away from it. You put a test particle that it's initially localized in a truck. 422 00:54:20,550 --> 00:54:24,740 Flaminia Giacomini: Now at the time is equal to 0. So basically this 423 00:54:24,770 --> 00:54:30,720 Flaminia Giacomini: a cycle equal to 0. B has the can make the decision whether to open the truck or not. 424 00:54:31,780 --> 00:54:43,680 Flaminia Giacomini: and notice that we assume that the mass was prepared in a content superposition long before the experiment started. So all the gravitational degrees of you know, had dissipated away. 425 00:54:43,850 --> 00:54:48,560 Flaminia Giacomini: So basically. The only possible interaction is news onion at this level. 426 00:54:49,050 --> 00:54:56,220 Flaminia Giacomini: But then a at some point can decide to make an interference experiment and recombine the superposition. 427 00:54:57,100 --> 00:55:06,250 Flaminia Giacomini: And basically according to how fast she so it's it's it's it is a complicated. There are some complicated conditions, but 428 00:55:06,260 --> 00:55:14,200 Flaminia Giacomini: according to how or how she does it, then she can do it as lowly enough so that she does not emit any gravitational radiation. 429 00:55:14,450 --> 00:55:22,540 Flaminia Giacomini: and she can see and it. And then she might see interference at the end. So basically the question is. 430 00:55:22,670 --> 00:55:29,490 Flaminia Giacomini: can a know whether be open the track before a live processing time? So this is the question that you ask. 431 00:55:29,770 --> 00:55:40,160 Flaminia Giacomini: and you find that so you didn't need to invoke anything except for you on an interaction up to that point. But in a linearized quantum gravity description. 432 00:55:40,260 --> 00:55:42,860 Flaminia Giacomini: If you do not include 433 00:55:42,950 --> 00:55:46,290 Flaminia Giacomini: the quantum flip questions of the gravitational field 434 00:55:46,510 --> 00:55:56,580 Flaminia Giacomini: which limits visibility to be considered and tangled with a. and the emission of gravitational radiation in a quantum superposition 435 00:55:56,740 --> 00:56:01,270 Flaminia Giacomini: which limits a's ability to get which for information. 436 00:56:01,620 --> 00:56:04,920 Flaminia Giacomini: then you run it to faster than light signaling. 437 00:56:05,660 --> 00:56:13,620 Flaminia Giacomini: So this is this is the case in which simply Newtonian interaction, plus basic like separation, forced you to include 438 00:56:13,660 --> 00:56:25,200 Flaminia Giacomini: in a specific description of gravity, some dynamically. So in some really quantum features of quality, in order to, not to, not to, not to have problems with and signaling. 439 00:56:26,310 --> 00:56:27,480 Flaminia Giacomini: So 440 00:56:27,980 --> 00:56:37,920 Flaminia Giacomini: there are a direct caveats to to to be made, because the we can, we can say we we can actually say I like we can see more. 441 00:56:41,200 --> 00:56:54,030 Ivan Agullo: I should read that that argument in more detail. Thank you. I I I I think the paper 442 00:56:54,200 --> 00:56:55,720 Parampreet Singh: I think Lee has a question. 443 00:56:57,900 --> 00:56:59,180 Parampreet Singh: You are muted 444 00:57:03,690 --> 00:57:06,760 Lee Smolin: well. How do you 445 00:57:07,410 --> 00:57:17,670 Lee Smolin: you know that there are gravitational theories where the speed of the of the graviton is faster than the speed of light. Does that affect any of these arguments? 446 00:57:19,100 --> 00:57:20,760 Flaminia Giacomini: Well, in that case. 447 00:57:21,000 --> 00:57:25,280 Flaminia Giacomini: so I think that as long as it's finite. 448 00:57:25,480 --> 00:57:30,950 Flaminia Giacomini: then you can reach up for the argument in order to include a different 449 00:57:32,290 --> 00:57:32,890 Okay. 450 00:57:36,100 --> 00:57:45,310 Flaminia Giacomini: But i'm not sure. One would have to put the numbers, and that since the conditions are a bit delegate, then it could be that something doesn't work in that case. 451 00:57:45,980 --> 00:57:46,970 Lee Smolin: Yes. 452 00:57:48,280 --> 00:57:54,240 Lee Smolin: so why do you say we don't know how to 453 00:57:55,180 --> 00:58:01,370 Flaminia Giacomini: Well, I do not know any way to to reconcile them, like the notion of space-time for instance. 454 00:58:01,540 --> 00:58:07,120 Flaminia Giacomini: or like, because it has a different role in gravity and quantum theory. 455 00:58:07,360 --> 00:58:09,350 Flaminia Giacomini: So there are. 456 00:58:10,460 --> 00:58:18,270 Lee Smolin: Well, what if we say that it's necessary to give up the idea of space time in order to reconcile. 457 00:58:18,580 --> 00:58:27,350 Flaminia Giacomini: Yeah, I would be favor of that. But then we have to find out how to talk about events, for instance, in without without the space time. 458 00:58:27,550 --> 00:58:28,900 Lee Smolin: What's the problem? 459 00:58:29,680 --> 00:58:30,310 Flaminia Giacomini: Yeah. 460 00:58:30,620 --> 00:58:33,390 Lee Smolin: Why is that a problem? 461 00:58:34,530 --> 00:58:39,870 Flaminia Giacomini: Well, because we do not know how to talk about events? If we don't have space-time like, how do we find like? 462 00:58:40,110 --> 00:58:43,780 Flaminia Giacomini: How do we replace, for instance, the crossing of word lines, or. 463 00:58:44,180 --> 00:58:50,400 Lee Smolin: you know, causal says kind of picture. We do know how to talk about events. 464 00:58:52,480 --> 00:58:55,630 Lee Smolin: So this is for us to go in that direction. 465 00:58:57,290 --> 00:59:02,320 Flaminia Giacomini: I don't know. I mean there are. There are many. There are other things that one can consider right 466 00:59:03,550 --> 00:59:10,020 Lee Smolin: right. But isn't your argument for considering that exactly. 467 00:59:10,580 --> 00:59:12,700 Flaminia Giacomini: I I guess it's some possibility. Yeah. 468 00:59:13,520 --> 00:59:17,950 Lee Smolin: okay, I want to go a little bit stronger than you. But very good. Thank you. 469 00:59:20,040 --> 00:59:21,650 Parampreet Singh: Okay. Any other questions. 470 00:59:24,510 --> 00:59:27,010 Parampreet Singh: Yeah. Deepak. Yes, go ahead. 471 00:59:27,860 --> 00:59:32,320 Deepak Vaid: So I it for me again. Thanks for. 472 00:59:32,810 --> 00:59:34,630 Deepak Vaid: and I can talk. 473 00:59:37,880 --> 00:59:47,660 Deepak Vaid: No. I mean again, maybe I missed it. But did you provide a prescription for constructing a quantum reference frame 474 00:59:49,410 --> 00:59:51,500 Deepak Vaid: in a generally covariant manner. 475 00:59:52,020 --> 00:59:52,870 Flaminia Giacomini: Hmm. 476 00:59:53,960 --> 01:00:06,060 Flaminia Giacomini: Not so. So actually, that's a very interesting question that I would be interested in in in exploring. We so far do not have prescriptions to construct that one from reference frame. 477 01:00:06,670 --> 01:00:20,840 Flaminia Giacomini: and especially in a covariant, not not even not realistically, but not in a in a covariant way. Not you like even being worse. And but that's of like, yeah, that's an important question that we should solve at some point. 478 01:00:22,110 --> 01:00:27,610 Deepak Vaid: right? So I mean I until one can do that in some, in some sense 479 01:00:29,710 --> 01:00:34,380 Deepak Vaid: we, you know we can't really understand what 480 01:00:34,420 --> 01:00:37,230 one of your offensive friends are telling us about. 481 01:00:38,920 --> 01:00:40,940 Flaminia Giacomini: Sorry I didn't understand the question 482 01:00:41,380 --> 01:00:49,410 Deepak Vaid: I can until we we can construct quantum reference frames in in a matter which is 483 01:00:50,050 --> 01:00:51,950 Deepak Vaid: covariant, or which. 484 01:00:54,290 --> 01:00:56,420 Deepak Vaid: you know, respect the 485 01:00:57,120 --> 01:01:01,320 Deepak Vaid: this principle of covariance in some sense quantum covariance. 486 01:01:04,310 --> 01:01:09,960 Deepak Vaid: right? We we can't release and say what? What quantum reference they are telling us about. 487 01:01:10,030 --> 01:01:14,120 Flaminia Giacomini: Yeah, no, I I agree. This is all yet to be done. Yeah. Yeah. 488 01:01:14,280 --> 01:01:14,970 Flaminia Giacomini: Yeah. 489 01:01:15,300 --> 01:01:23,350 Flaminia Giacomini: So that's why I said this: this is just more like motivation for future work, whether presented than an actual result that 490 01:01:23,850 --> 01:01:24,750 Flaminia Giacomini: so 491 01:01:26,140 --> 01:01:30,350 Deepak Vaid: sure, sure in in in fact, I mean 492 01:01:30,510 --> 01:01:34,270 Deepak Vaid: I I guess this will probably sound very simplistic. 493 01:01:34,610 --> 01:01:38,850 Deepak Vaid: but the way that I often tell people 494 01:01:38,950 --> 01:01:41,160 Deepak Vaid: why quantum gravity is necessary. 495 01:01:41,600 --> 01:01:46,340 Deepak Vaid: like, you know, completely lay people in a very non-technical manner. 496 01:01:46,870 --> 01:01:52,510 Deepak Vaid: is that I say that well. you have this notion of superposition. 497 01:01:53,350 --> 01:01:57,470 Deepak Vaid: but that relies on the existence of some coordinates. 498 01:01:58,560 --> 01:01:59,730 Flaminia Giacomini: Yeah. 499 01:01:59,910 --> 01:02:02,790 Deepak Vaid: And and so. 500 01:02:04,170 --> 01:02:04,890 Deepak Vaid: if 501 01:02:04,910 --> 01:02:08,070 Deepak Vaid: you know, those coordinates themselves are 502 01:02:08,090 --> 01:02:15,930 Deepak Vaid: not not well defined, or they they are. They are fluctuating, or or they're in some sort of superposition themselves. 503 01:02:17,090 --> 01:02:21,760 Deepak Vaid: or or as in what you do, you basically turn the coordinates into operators, right? 504 01:02:23,490 --> 01:02:25,520 Flaminia Giacomini: Yes, yes, yeah. 505 01:02:25,620 --> 01:02:26,350 Deepak Vaid: So 506 01:02:26,570 --> 01:02:31,840 Deepak Vaid: right. So so so then, and the the idea of superposition becomes 507 01:02:33,800 --> 01:02:36,620 Deepak Vaid: really at the very least observer depend. 508 01:02:36,770 --> 01:02:43,460 Flaminia Giacomini: Yeah, exactly. Yeah, yeah. And that's of course, just the stuff. I mean, there are many important questions. 509 01:02:46,110 --> 01:02:47,110 Deepak Vaid: Okay. 510 01:02:47,520 --> 01:02:49,110 Parampreet Singh: Okay, Any other questions. 511 01:02:50,000 --> 01:02:53,050 Adrià Delhom i Latorre: I have one. 512 01:02:53,770 --> 01:02:55,720 Adrià Delhom i Latorre: So for me. I wanted to 513 01:02:57,110 --> 01:03:07,960 Adrià Delhom i Latorre: to see if I I was thinking of something like. So if you take a classical particle and you describe it in a quantum reference frame, it will look like a quantum system, right. There is no way of this thing. 514 01:03:09,420 --> 01:03:12,440 Adrià Delhom i Latorre: Okay. So in that sense it appears to me that that 515 01:03:14,140 --> 01:03:17,600 Adrià Delhom i Latorre: whatever kind of experiments that you can do with quantum reference frame 516 01:03:17,700 --> 01:03:20,900 Adrià Delhom i Latorre: to To look at the gravitational field. 517 01:03:21,100 --> 01:03:23,630 Adrià Delhom i Latorre: You will always be in this 518 01:03:24,110 --> 01:03:31,900 Adrià Delhom i Latorre: you you will always be unable to distinguish whether there is a classical reference, a frame describing a quantum gravitational field, or the opposite right? 519 01:03:33,800 --> 01:03:38,700 Flaminia Giacomini: Or a classical gravitational field seen from a quantum reference frame. 520 01:03:39,210 --> 01:03:44,560 Flaminia Giacomini: Yeah, yeah. So yeah, I I I do not have the full answer to this question. 521 01:03:44,820 --> 01:03:51,120 Flaminia Giacomini: because it's like one would have to probably more complicated configurations. But for the synchronous ones. Yes. 522 01:03:51,840 --> 01:04:00,020 Adrià Delhom i Latorre: yeah, yeah, of course. I mean, I was thinking only of one part of the legal and one friend. No. I also thought that probably if You' more stuff becoming more tricky. But thank you. 523 01:04:03,610 --> 01:04:09,680 Parampreet Singh: Okay. If there are no further questions, that is time for me to thank you very much, for 524 01:04:09,880 --> 01:04:13,020 Parampreet Singh: Thank you very much for having me.