Jorge Pullin: Okay. So our speaker today is Flaminia Jacomini, who will speak about quantum reference frames.
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.
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.
Flaminia Giacomini: And so first let me just clarify some terminology, since we are from we all have different backgrounds.
Flaminia Giacomini: So
Flaminia Giacomini: the you. We have our 2 main theories of physics that are quantum theory, and generally
Flaminia Giacomini: which both rest on a classical notion of spacetime
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?
Flaminia Giacomini: And of course this question has been explored in in quantum gravity
Flaminia Giacomini: in many different ways. and typically the quantum gravity literature focuses in the high energy regime. where and
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
Flaminia Giacomini: this is not the approach that i'm going to take in this talk
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.
Flaminia Giacomini: So, for instance, the the simplest thing we can consider is to have a must in a one to super position.
Flaminia Giacomini: and this is the sense in which I will talk about no classical spacetime.
Flaminia Giacomini: and I will refer you in particular on some
Flaminia Giacomini: more
Flaminia Giacomini: concrete aspects which lead to some physical scenarios with an immediate physical meaning.
Flaminia Giacomini: So let me first give you some overview of the the general question that we're going to ask.
Flaminia Giacomini: So in general relativity we have, I sensitive questions
Flaminia Giacomini: that connect the metric of the space-time to the matter through the through these questions.
Flaminia Giacomini: and
Flaminia Giacomini: these are questions are valid Whenever I have a classical. however, quantum theory tells us that matter is quantum.
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.
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.
Flaminia Giacomini: And, for instance, this is a situation that can be realized by a mass in a possible position.
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.
Flaminia Giacomini: But fundamentally, what I have here is a quantum source of a gravitational field
Flaminia Giacomini: so
Flaminia Giacomini: at the fundamental level. I cannot have a classic space sign.
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.
Flaminia Giacomini: Why is this interesting? So one of the reasons that I find this interesting is that experiments are making their way
Flaminia Giacomini: towards realizing this situation in a laboratory, and in particular, there are 2 different directions in which experiments are pushing
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
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.
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.
Flaminia Giacomini: and
Flaminia Giacomini: 2 examples of what has been achieved in recently are this paper, where they this quantum interference of
Flaminia Giacomini: of heavy molecules. and also some
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.
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.
Flaminia Giacomini: and not something that we're going to do tomorrow, maybe in 1020 years.
Flaminia Giacomini: But and there are serious limitations
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.
Flaminia Giacomini: So
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?
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
Flaminia Giacomini: a more ambitious one.
Flaminia Giacomini: So the first reason is that
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.
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.
Flaminia Giacomini: and this is still an open question.
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
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.
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.
Flaminia Giacomini: for instance, quantum information theorems or protocols. and
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.
Flaminia Giacomini: So the hope for the future is that
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
towards how we should deal with the theory at higher energies.
Flaminia Giacomini: and on this it will be very important to to work together with quantum gravity researchers.
Flaminia Giacomini: So this is also an invitation.
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
Flaminia Giacomini: in a regime where there is no gravity. So this will be just fully neural, logistical Galileo relative to quantum mechanics.
Flaminia Giacomini: and later i'm going to connect it with some gravity arguments.
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.
Flaminia Giacomini: So a reference frame is usually a set of access, and the state of motion.
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.
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.
Flaminia Giacomini: so
Flaminia Giacomini: then we can connect the different descriptions that we give in its frame via a reference frame transformation. So imagine now that
Flaminia Giacomini: you know
Flaminia Giacomini: just some of quantum mechanics. We want to make a a reference to transformation.
Flaminia Giacomini: This is included in a unit address for information.
Flaminia Giacomini: So, for instance, here I have a translation or a Galilean boost.
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.
Flaminia Giacomini: So this is the amount for which to translate, and this is the amount by which I boost.
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.
Flaminia Giacomini: They are not operators. They are not dynamical quantities, they are just a parameter.
Flaminia Giacomini: Then
Flaminia Giacomini: we also know that if we have a Schrodinger question.
Flaminia Giacomini: if we perform a reference transformation.
Flaminia Giacomini: the Schrodinger question is again mapped to a different Schrodinger, but formally the same Schrodinger question, but with a different from Miltonian
Flaminia Giacomini: that is connected to the initial Hamiltonian by this relation. Here.
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.
Flaminia Giacomini: If the final functional form of the final Hamiltonian is the same as the functional form of the Hamiltonian before the transformation.
Flaminia Giacomini: so now
Flaminia Giacomini: imagine that we have this very simple system that is made up of 3 different reference frames a, B and C.
Flaminia Giacomini: Now imagine, in, for instance, initially, we are in, C.
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.
Then the
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.
Flaminia Giacomini: and the relation, because of the position between a and C, and between B and C. So these 2 yellow vectors.
Flaminia Giacomini: But now, if we, for instance, want to switch the oranging of the reference frame to
Flaminia Giacomini: 8, then we're going to have 2
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.
Flaminia Giacomini: Now, the question that you are going to ask is
Flaminia Giacomini: so.
Flaminia Giacomini: If you think about it. When we make a measurement, we use physical systems, and we also
Flaminia Giacomini: take as reference physical objects.
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.
Flaminia Giacomini: So we are going to ask the full question. Can we attach reference, frame
Flaminia Giacomini: 2. Some object to the position of some object that is in a quantum state.
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.
Flaminia Giacomini: And this is the question that we ask when we talk about confront reference trains
Flaminia Giacomini: so more specifically. We want to start from a situation in which we are in C,
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.
Flaminia Giacomini: And then we want to switch
Flaminia Giacomini: to a quantum reference frame
Flaminia Giacomini: that is centered in the position of a.
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.
Flaminia Giacomini: No.
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.
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.
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
Flaminia Giacomini: through it as localized, but it can be any one from State.
Flaminia Giacomini: So now.
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.
Flaminia Giacomini: That is, a a translation operator. where we translate System B by X one.
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.
Flaminia Giacomini: That's
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.
Flaminia Giacomini: So now what happens if, instead of having this state. Here I have a state that is like that
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.
Deepak Vaid: Hi flamenia. Could you possibly just go over that again?
Deepak Vaid: Once more a little slower.
Flaminia Giacomini: Yes. From which part
Deepak Vaid: the the previous slide. Yeah, this this, this.
Flaminia Giacomini: Yeah. Okay. So here you have a quantum state of a, and I want to set up B
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.
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.
Flaminia Giacomini: and when I apply this part.
Flaminia Giacomini: I apply it to the at X, One, a.
Flaminia Giacomini: So like this operator sends X to minus x, and swapped a with C.
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.
Flaminia Giacomini: This is clear.
Deepak Vaid: Yeah, I I I guess the only part is this: this parity swap operator. It's not.
Deepak Vaid: It's not completely clear what it's doing. and why it's needed.
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.
Flaminia Giacomini: So this is its action that's by definition.
Deepak Vaid: Oh, okay.
Flaminia Giacomini: and why it's needed. It's because it's just out of the like relational reasons.
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
Flaminia Giacomini: the former orange in of
Flaminia Giacomini: my reference frame. As to being in my office, and it's a.
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.
Deepak Vaid: I I see. So I mean when you
Deepak Vaid: take some position, X. And make that the
Deepak Vaid: origin, then the other. The origin goes to 106. So that's where the parity comes from.
Flaminia Giacomini: Yes, exactly. Yes.
Deepak Vaid: yes, okay. Thanks a lot. Yeah.
Simone: And why? So? Just to follow up on this.
Simone: So Why, Don't, you just apply? Use the translation operator for both systems a and B.
Simone: Why do you we with the swap instead of just writing it at the same parameter acting on both a and B,
Flaminia Giacomini: so you can have an alternative formulation where you have
Flaminia Giacomini: 3 differently the spaces of a, of B and of C. And the
Flaminia Giacomini: origin of the reference frame is always assigned symbolically Position 0.
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
Flaminia Giacomini: origin 0. Say, let me just write it.
Flaminia Giacomini: Okay. And here I end up in this
Flaminia Giacomini: state. and I can find a unitary operator that maps this.
Flaminia Giacomini: To this it's equivalent.
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.
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.
Flaminia Giacomini: It applies
Flaminia Giacomini: answer to the question.
Flaminia Giacomini: Okay, I guess it does. Okay. So
Flaminia Giacomini: should I go through this light again. then?
Deepak Vaid: No, I'm: I'm: Good. But
Flaminia Giacomini: okay. so okay. So when we have a superposition, then
Flaminia Giacomini: what we are going to do is just to up linearly superpose the action of the operator
Flaminia Giacomini: for each single position of it. So what's the question now.
Flaminia Giacomini: here we have a that is delocalized, so there is no single X that we can use to perform the translation.
Flaminia Giacomini: But then we can take seriously the linearity of quantum mechanics and say, okay, I don't have a single.
Flaminia Giacomini: a single coordinate by which to translate. But I can just linearly superpose all possible positions of system. A.
Flaminia Giacomini: And so what happens is that
Flaminia Giacomini: when a is in X one, then B will be translated by X, one and C will be in minus one.
Flaminia Giacomini: but when a is in x 2, then B is translated by x, 2, and C is also in minus x 2.
Flaminia Giacomini: So in this is a in quantum information language, a quantum controlled translation
Flaminia Giacomini: where the controlled system, so the one that tells us by how much to translate is the quantum reference Train a.
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.
Flaminia Giacomini: And an immediate consequence of this transformation is that superposition and entanglement become quantum reference dependent.
Flaminia Giacomini: And you can see here an example. This is a product state. So this is not entangled.
Flaminia Giacomini: and after I mark it to the new quantum reference frame of a, I get an entangled state.
Flaminia Giacomini: Okay.
Ivan Agullo: is this.
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.
Flaminia Giacomini: but it is basically a quantum controlled superposition of gates. So that's what it is.
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?
Flaminia Giacomini: So what?
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.
Flaminia Giacomini: So basically, these are the states of minimal dispersion
Flaminia Giacomini: and acting with this operator on this.
Flaminia Giacomini: That's the mean
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.
Simone: Okay, now, how
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?
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.
Flaminia Giacomini: So the the
Simone: is not an eigenstate of these operators.
Flaminia Giacomini: It's not, but it's approximately true, so you can. You can make this replacement.
Simone: Okay. But this approximation is part of my question. So it is not enough right? You also need
Simone: what? What is the some sending H bar to 0? Maybe.
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.
Flaminia Giacomini: E. C.
Flaminia Giacomini: And if the state is localized within a single slot of the measurement apparatus, then you are in the classical limit.
Flaminia Giacomini: And so it it is more a matter of
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.
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
Simone: I see. So, strictly speaking, you will recover translations with this, with parameters, to begin with. Okay, I understand. Thank you.
Yes.
Flaminia Giacomini: Can I also a question? Sorry.
Florian Girelli: So just before for you slide again. So if I want to know if I want to do a frame.
Florian Girelli: a a change of frame, I mean, like here i'm in what i'm in.
Florian Girelli: And so what I need to do is to do a measurement
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.
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.
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?
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.
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.
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.
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.
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
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
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,
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.
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
Florian Girelli: that this this is a very complicated yeah.
Florian Girelli: All right. Thank you.
Flaminia Giacomini: Okay.
Flaminia Giacomini: Okay, it's not. Now, what what I I give you is
Flaminia Giacomini: the simplest transformation, so the the special translation. But actually you can come up with other transformations, for instance, the
Flaminia Giacomini: superposition of like boosts, etc. But all the transformations that we found so far roughly, have this structure here.
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.
Flaminia Giacomini: and this would be the parameter of the transformation. But then this parameter is controlled
Flaminia Giacomini: on an additional Hilbert space. That is, the state of the quantum reference frame
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.
Flaminia Giacomini: So now.
Flaminia Giacomini: what happens if on top of that we also want to include dynamics.
Flaminia Giacomini: So we want to give the quantum reference frame also Hamiltonian.
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.
Flaminia Giacomini: that is, of this form. Then you just shouldn't go to put it
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.
Flaminia Giacomini: No.
Flaminia Giacomini: And, for instance, this can be a translation or a boost.
Flaminia Giacomini: No.
Flaminia Giacomini: if I start with a free particle, Hamiltonian for some particle. B.
Flaminia Giacomini: If I apply one of these 2 transformations so like translational boost, then I end up with another free particle, Hamiltonian.
Flaminia Giacomini: And so this is this means that these 2 transformations are as image of the dynamics.
Flaminia Giacomini: And now what we want to ask is what happens with quantum preference frames.
Flaminia Giacomini: Basically the logic is exactly the same.
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.
Flaminia Giacomini: So x 0 goes to excel operator, and V. 0 goes to PA, divided by am. A.
Flaminia Giacomini: But then
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
Flaminia Giacomini: that is possible. A.
Flaminia Giacomini: And in particular one can find 2 transformations that correspond to a superposition of special translations and superposition of Kerle and Boost.
Flaminia Giacomini: such that a free particle Hamiltonian of this type is mapped
Flaminia Giacomini: to a a free particle. Hamiltonian, where the Hamiltonian of a is replaced by the Hamiltonian of C.
If you haven't.
Flaminia Giacomini: and this is the sense in which we talk about extended symmetries of the dynamics.
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.
Flaminia Giacomini: So the first one
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.
Flaminia Giacomini: So
Flaminia Giacomini: the the first one, that is that quantum reference trains can actually lead to
Flaminia Giacomini: for a generalization of the I. And this can be done in 2 ways.
Flaminia Giacomini: So one way is to consider a classical gravitational field
Flaminia Giacomini: here, and then just delocalize
Flaminia Giacomini: a for instance, like in another interferometer. So in a superposition of 2 different heights in the gravitational field. And
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.
Flaminia Giacomini: And now, with quantum preference frames, we can find a transformation
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
Flaminia Giacomini: and a bit more ambitiously. We can instead consider a quantum superposition of 2 different space times
Flaminia Giacomini: That, we say are microscopically distinguishable, meaning that there is a they are going on.
Flaminia Giacomini: they are.
Flaminia Giacomini: and then we can have a particle that is entangled with the
Flaminia Giacomini: with the position. Sales is mass. The detail means the the space and configuration.
Flaminia Giacomini: And then, again, we can find a quantum reference from transformation that to the quantum reference stream centered on this particle here.
Flaminia Giacomini: such that the metric is local limit. Costs can at the origin of the quantum reference frame.
Flaminia Giacomini: So what does? What are the consequences of doing this?
Flaminia Giacomini: So in in this simple it's simpler case. We can device a test for the this Einstein equivalent principle for conference
Flaminia Giacomini: that uses an adventure from gene quantum clocks in particular. This is some work that I need to the master's student
Flaminia Giacomini: we found we we used and tangled clocks with with, so that entangled in these other interferometers.
Flaminia Giacomini: and we found that if this
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.
Flaminia Giacomini: And now and he said the in in this in this case here
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.
Flaminia Giacomini: And
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
Flaminia Giacomini: of the wave function in the presence of a superposition of gravitational fields. And so.
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.
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.
Flaminia Giacomini: And okay.
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.
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.
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.
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.
Flaminia Giacomini: Nothing more than that.
Deepak Vaid: Can I? Can I ask a question about the previous slide?
Flaminia Giacomini: Hmm. It's fine.
Deepak Vaid: Okay, so I mean, I probably miss something. But when you say that. So you have
Deepak Vaid: an observer who is
Deepak Vaid: in a superposition of trajectories
Deepak Vaid: to it. It's the same, fully following observer. But along moving around 2 different trajectories. Is that correct?
Flaminia Giacomini: So we are not talking about observer. We are talking about particle.
Deepak Vaid: sure, sure. Okay. So some system.
Flaminia Giacomini: Yeah.
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
Deepak Vaid: the whole system, the the earth.
Deepak Vaid: and the you know the freely falling particle.
Deepak Vaid: either by looking from the particles perspective, and seeing the earth in a superposition.
Deepak Vaid: or from the earth's perspective. And seeing the particle in the superposition. Is that is that correct?
Flaminia Giacomini: You're okay, but the left hand side now right the right hand side. So this is entangled. So basically.
Flaminia Giacomini: if I if I stand so
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
Flaminia Giacomini: we did
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
Deepak Vaid: right. But now Penrose's argument, I think it
Deepak Vaid: based on the fact that
Deepak Vaid: you, you know you have these 2 systems which are
Deepak Vaid: very different in mass. And
Deepak Vaid: so when you, when you look at the the earth in this position, right, and you calculate the
Deepak Vaid: the gravitational potential energy to do that separation. Right?
It's it's made. It's many times larger than the
Deepak Vaid: change in the gravitational potential energy of the particle in the 2 locations as seen by the earth.
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.
Flaminia Giacomini: But there is also another way in which he argues really from first principles, that these 2
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.
Flaminia Giacomini: or that the volume of the shield is different, according to which amplitude you're in. So there are several arguments that
Deepak Vaid: But the thing is that even if you take this extended equivalence principle.
Deepak Vaid: the fact that there is this. this, this difference in the gravitational potential energy is in the 2 cases
Deepak Vaid: that pack doesn't Go away right?
Flaminia Giacomini: No, but this is not a problem.
Flaminia Giacomini: because it I mean
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
Flaminia Giacomini: like anything you want.
Flaminia Giacomini: Yeah. But if you don't do that, then
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.
Deepak Vaid: Okay, okay, thanks.
Yeah.
Flaminia Giacomini: Okay. So
Flaminia Giacomini: okay. So the
Flaminia Giacomini: So this is what 5 one meant for the what, when they must in your particular position.
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
Flaminia Giacomini: so 2 papers that came out on the same day on the Archive. where
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.
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
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.
Flaminia Giacomini: And here are some.
Flaminia Giacomini: So
Flaminia Giacomini: no.
Flaminia Giacomini: I want to put one more observation here.
Flaminia Giacomini: So we have seen with quantum reference frames.
Flaminia Giacomini: that for entanglement and superposition are quantum reference to independent.
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.
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
Flaminia Giacomini: what the possible answer could be.
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.
Flaminia Giacomini: in particular. This is an experiment that was done at Stanford last year
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.
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.
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
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
Flaminia Giacomini: that they can feel that out. But it's the gravitational action difference produced
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.
Flaminia Giacomini: and this is the first experiment that measured a phase shift that went beyond deliver approximation of the gravitational potential.
Flaminia Giacomini: So it measured the higher order corrections.
Flaminia Giacomini: So now.
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.
Flaminia Giacomini: then, we know that the equivalence principle is valid up to experimental resolution. then we know that there are gravitational waves.
Flaminia Giacomini: We have measured that
Flaminia Giacomini: then these experiment has measured this gravitational phase, shift between the different parts of the denatom takes in an interferometer.
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.
Flaminia Giacomini: And
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.
Flaminia Giacomini: But
Flaminia Giacomini: what are we missing? Which principles are we missing that could be tested in order to
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.
Flaminia Giacomini: like these, 2, are sufficient to prove the point
Flaminia Giacomini: to to show that this experiment is equivalent to one in which the gravitational field is in a quantum superposition.
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
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
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.
Flaminia Giacomini: Let's see what happens if we map the yeah. This experiment
Flaminia Giacomini: using these 2 principles. So
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.
Flaminia Giacomini: we have.
Flaminia Giacomini: We also assume it with the first principle.
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
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,
Flaminia Giacomini: and so it should be considered as the source of the of a traditional field.
Flaminia Giacomini: and hence, if the interference. If the experiment shows some some interference pattern, which should.
Flaminia Giacomini: then we can conclude the
Flaminia Giacomini: Now, I don't want to say that this experiment proves
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
Flaminia Giacomini: take in order to show that the gravitational field can be in a constant superposition state.
Flaminia Giacomini: And so this is more as an inspiration towards future experiments than to claim something on current experiments.
Flaminia Giacomini: So this is all that I want to tell you and
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.
Flaminia Giacomini: And so it is interesting to explore how much we can know about the gravitational field that we are forming these experiments
Flaminia Giacomini: from a theoretical perspective. We do not know how to reconcile the fundamental principles of general relativity and quantum theory.
Flaminia Giacomini: However, we can device thought experiments in this regime
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
Flaminia Giacomini: and the results. And thank you for your attention.
Parampreet Singh: Okay, thank you for being here. Are there any questions
Parampreet Singh: you one?
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
Ivan Agullo: what they the last about gravity
Ivan Agullo: is that you know there is no gravitational wave production, you know, in this kind of match configurations, so only the columbic
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
Ivan Agullo: the degrees of freedom, of gravity by itself, but only the coulombic part which
Ivan Agullo: you know it never involves, so to speak.
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
Ivan Agullo: to Spain. This experiment, so I don't understand what
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
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
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,
Flaminia Giacomini: because so there is a sort of experiment that's
Flaminia Giacomini: the
Flaminia Giacomini: where you can consider a communication product.
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.
Flaminia Giacomini: Now at the time is equal to 0. So basically this
Flaminia Giacomini: a cycle equal to 0. B has the can make the decision whether to open the truck or not.
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.
Flaminia Giacomini: So basically. The only possible interaction is news onion at this level.
Flaminia Giacomini: But then a at some point can decide to make an interference experiment and recombine the superposition.
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
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.
Flaminia Giacomini: and she can see and it. And then she might see interference at the end. So basically the question is.
Flaminia Giacomini: can a know whether be open the track before a live processing time? So this is the question that you ask.
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.
Flaminia Giacomini: If you do not include
Flaminia Giacomini: the quantum flip questions of the gravitational field
Flaminia Giacomini: which limits visibility to be considered and tangled with a. and the emission of gravitational radiation in a quantum superposition
Flaminia Giacomini: which limits a's ability to get which for information.
Flaminia Giacomini: then you run it to faster than light signaling.
Flaminia Giacomini: So this is this is the case in which simply Newtonian interaction, plus basic like separation, forced you to include
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.
Flaminia Giacomini: So
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.
Ivan Agullo: I should read that that argument in more detail. Thank you. I I I I think the paper
Parampreet Singh: I think Lee has a question.
Parampreet Singh: You are muted
Lee Smolin: well. How do you
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?
Flaminia Giacomini: Well, in that case.
Flaminia Giacomini: so I think that as long as it's finite.
Flaminia Giacomini: then you can reach up for the argument in order to include a different
Okay.
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.
Lee Smolin: Yes.
Lee Smolin: so why do you say we don't know how to
Flaminia Giacomini: Well, I do not know any way to to reconcile them, like the notion of space-time for instance.
Flaminia Giacomini: or like, because it has a different role in gravity and quantum theory.
Flaminia Giacomini: So there are.
Lee Smolin: Well, what if we say that it's necessary to give up the idea of space time in order to reconcile.
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.
Lee Smolin: What's the problem?
Flaminia Giacomini: Yeah.
Lee Smolin: Why is that a problem?
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?
Flaminia Giacomini: How do we replace, for instance, the crossing of word lines, or.
Lee Smolin: you know, causal says kind of picture. We do know how to talk about events.
Lee Smolin: So this is for us to go in that direction.
Flaminia Giacomini: I don't know. I mean there are. There are many. There are other things that one can consider right
Lee Smolin: right. But isn't your argument for considering that exactly.
Flaminia Giacomini: I I guess it's some possibility. Yeah.
Lee Smolin: okay, I want to go a little bit stronger than you. But very good. Thank you.
Parampreet Singh: Okay. Any other questions.
Parampreet Singh: Yeah. Deepak. Yes, go ahead.
Deepak Vaid: So I it for me again. Thanks for.
Deepak Vaid: and I can talk.
Deepak Vaid: No. I mean again, maybe I missed it. But did you provide a prescription for constructing a quantum reference frame
Deepak Vaid: in a generally covariant manner.
Flaminia Giacomini: Hmm.
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.
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.
Deepak Vaid: right? So I mean I until one can do that in some, in some sense
Deepak Vaid: we, you know we can't really understand what
one of your offensive friends are telling us about.
Flaminia Giacomini: Sorry I didn't understand the question
Deepak Vaid: I can until we we can construct quantum reference frames in in a matter which is
Deepak Vaid: covariant, or which.
Deepak Vaid: you know, respect the
Deepak Vaid: this principle of covariance in some sense quantum covariance.
Deepak Vaid: right? We we can't release and say what? What quantum reference they are telling us about.
Flaminia Giacomini: Yeah, no, I I agree. This is all yet to be done. Yeah. Yeah.
Flaminia Giacomini: Yeah.
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
Flaminia Giacomini: so
Deepak Vaid: sure, sure in in in fact, I mean
Deepak Vaid: I I guess this will probably sound very simplistic.
Deepak Vaid: but the way that I often tell people
Deepak Vaid: why quantum gravity is necessary.
Deepak Vaid: like, you know, completely lay people in a very non-technical manner.
Deepak Vaid: is that I say that well. you have this notion of superposition.
Deepak Vaid: but that relies on the existence of some coordinates.
Flaminia Giacomini: Yeah.
Deepak Vaid: And and so.
Deepak Vaid: if
Deepak Vaid: you know, those coordinates themselves are
Deepak Vaid: not not well defined, or they they are. They are fluctuating, or or they're in some sort of superposition themselves.
Deepak Vaid: or or as in what you do, you basically turn the coordinates into operators, right?
Flaminia Giacomini: Yes, yes, yeah.
Deepak Vaid: So
Deepak Vaid: right. So so so then, and the the idea of superposition becomes
Deepak Vaid: really at the very least observer depend.
Flaminia Giacomini: Yeah, exactly. Yeah, yeah. And that's of course, just the stuff. I mean, there are many important questions.
Deepak Vaid: Okay.
Parampreet Singh: Okay, Any other questions.
Adrià Delhom i Latorre: I have one.
Adrià Delhom i Latorre: So for me. I wanted to
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.
Adrià Delhom i Latorre: Okay. So in that sense it appears to me that that
Adrià Delhom i Latorre: whatever kind of experiments that you can do with quantum reference frame
Adrià Delhom i Latorre: to To look at the gravitational field.
Adrià Delhom i Latorre: You will always be in this
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?
Flaminia Giacomini: Or a classical gravitational field seen from a quantum reference frame.
Flaminia Giacomini: Yeah, yeah. So yeah, I I I do not have the full answer to this question.
Flaminia Giacomini: because it's like one would have to probably more complicated configurations. But for the synchronous ones. Yes.
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.
Parampreet Singh: Okay. If there are no further questions, that is time for me to thank you very much, for
Parampreet Singh: Thank you very much for having me.