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Ivan Agullo: Yeah, Thank you for here. Uh. So good morning, Everybody uh welcome. Um. Today we have a panel on. Uh. We call it a quantum information and uh quantum gravity and quantum information. And And
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Ivan Agullo: yeah, So we have three panelists, and we try to cover complimentary aspects of the relation of quantum information and and and quantum gravity, and they are, eh, Eduardo, Martin Martinez uh uh Kristina Giselle and Virginia B. Yankee.
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Ivan Agullo: The eduardo will talk about um a gravity induced entanglement, while Christina will talk about gravity, induced the coherence exactly the other way around, and and then um Eugenie will talk about uh
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Ivan Agullo: hierarchy of entitlement uh uh in in the quantum gravity, if I am, if I am uh right, so these three topics are complimentary to each other, and we hope they will generate a uh a good deal of discussions
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Ivan Agullo: as normal with panels, and they will present for ten twelve minutes each.
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Ivan Agullo: Sure questions and gratifications are welcome after each talk. Uh, but please hold a longer questions and discussions for the end of the panel, otherwise the the other speakers will have will not have the time left to to speak. And
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Ivan Agullo: uh, with no more more delay. Eduardo. Uh, please! The stage is yours.
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Eduardo Martin-Martinez: Uh, thank you. But let me share the uh slides.
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Eduardo Martin-Martinez: All right.
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Eduardo Martin-Martinez: Uh, there we go,
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Eduardo Martin-Martinez: hopefully. You see my slides full screen now.
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Eduardo Martin-Martinez: Alright, wonderful. Okay. So uh, first of all, thank you very much for the for the invitation to uh to talk in this uh in this panel
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Eduardo Martin-Martinez: and to discuss, i'm looking forward to it. Um! This is uh, i'm gonna talk about uh uh some uh opinions if you want of uh uh, the the student and I uh Dallas, Rick Perch
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Eduardo Martin-Martinez: and myself uh a half on uh, we can use entanglement and one what they can tell us. Um! What grab you can use in terms of can tell us
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Eduardo Martin-Martinez: about quantum gravity.
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Eduardo Martin-Martinez: So first of all, let me say i'm gonna say i'm not gonna say things that are uh generally accepted by yeah consensus. If you want it might be some controversial bits. So i'm looking forward to hearing the opinions and uh to hearing now as well. Um
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Eduardo Martin-Martinez: what thoughts I got. They this talk may main use uh some again. I'm really really happy to give you stock here.
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Eduardo Martin-Martinez: Okay, for the sake of time. Let's just to summarize. I hope this is entertaining. It's very simplified uh the questions that I want to discuss so kindly gravitational interaction entangled to masses, and if we can, we we we don't see the Us like the next slide. You changes like, Oh, sorry.
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Eduardo Martin-Martinez: Yeah, Not now. We yeah. But then, if I share screen, maybe i'll share the whole screen
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Eduardo Martin-Martinez: them because I was sharing the window, and apparently that was not enough.
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Eduardo Martin-Martinez: All right
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Eduardo Martin-Martinez: now. Hopefully you'll still see full screen my slide, and it moves.
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Eduardo Martin-Martinez: Yes, perfect right. Thank you so much.
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Eduardo Martin-Martinez: Alright, So that took the questions that I want to discuss is a candy, gravitational interaction and tangle masses to gravitational masses say that you have quantum degrees of freedom for the position of the masses? Can the gravitational interaction and tangle them? And if so, what does that mean um about the quantum nature of gravity. Imagine that you can actually do an experiment and see entanglement
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Eduardo Martin-Martinez: that is mediated by the gravitational interaction.
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Eduardo Martin-Martinez: So let me first present uh uh, the idea Uh: this is uh, i'm gonna base the discussion on on an experiment proposal called the Vmp. Experiment
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Eduardo Martin-Martinez: uh the Vm: The experiment basically considers two masses
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Eduardo Martin-Martinez: right? Uh, and these two masses have some position, quantum degree of freedom, and we can we assume we can prepare them in a superposition of two different paths.
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Eduardo Martin-Martinez: Now, uh, there's a person of two different paths that we have here this day that is preferred is uh interacting the two months of interacting through the gravitational introduction. And you can prove one can prove that under those assumptions the state of the masses that originally starting in a separable state end up in an entire state. Okay,
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Eduardo Martin-Martinez: so uh discussions can be found everywhere. I just right here the first paper that discusses it, and they consider a Newtonian potential, in which, of course, the the distance between the master's degree of freedom is made out of two quantum degrees of freedom
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Eduardo Martin-Martinez: to position the degrees of freedom. And uh, of course it's a quantum potential within the two masses
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Eduardo Martin-Martinez: Now, uh, of course,
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Eduardo Martin-Martinez: and you start in a separate state, as I said, and uh, after some time you end up in an entangle state. And what are the conclusions that can be extracted? So let me. Just follow um. The reasoning in this paper and several other papers uh talking about similar things
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Eduardo Martin-Martinez: Uh, the argument could go as follows: Well,
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so local operations and classical communication
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Eduardo Martin-Martinez: can not increase the entanglement between two quantum systems.
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Eduardo Martin-Martinez: Uh does give. The masses interact only gravitationally, and they get dangled in the gravitational field which is mediating the interaction. It's certainly not doing uh classical communication. So here we have some sort of quantum channel established right
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Eduardo Martin-Martinez: now. Hence the field cannot be classical, because it established a quantum channel. Everything uh uh. So this is. This is a true statement Uh, the field seems to be establishing a quantum channel, therefore, uh they feel cannot be classical, and therefore see in ex uh entanglement and experiment like this
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Eduardo Martin-Martinez: would be some degree of witness of quantum behavior of gravity
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Eduardo Martin-Martinez: now. Uh. So there's reason in that. If a third system, you know, if something is mediating an interaction between two quantum systems and establishing a quantum channel.
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Eduardo Martin-Martinez: Uh, does that mean that? Uh, there are uh local degrees of freedom? Uh that in the intermediary system that are quantum? Well uh the the Here's a couple of references where there's a theorem is proved it, which is, uh, actually easy to follow,
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Eduardo Martin-Martinez: said, Well, if a third system locally mediates interaction between two systems and the two systems can get entangled. The intermediary system has to be quantum. There's no discussion, no controversial. There has a theorem.
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Eduardo Martin-Martinez: So This is suggesting, indeed, that there's something quantum, or there are the quantum degrees of freedom um in the gravitational field.
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Eduardo Martin-Martinez: No.
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Eduardo Martin-Martinez: The question i'm gonna discuss is whether you can consider gravity to be an intermediary system. If your objective is to prove, uh that gravity is quantum with an experiment in which you can actually see entanglement mediated by writing.
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Eduardo Martin-Martinez: So uh, typically, when this is looked at, i'm using some I for this uh, often
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Eduardo Martin-Martinez: uh, it is said, Well, but You see, if gravity were not an intermediary system that has local degrees of freedom, then the interaction would be no local. And uh, we know that uh physics has to be local, because, you know, for example, you could say, you cannot really have action at a distance.
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Eduardo Martin-Martinez: Um, that's a propagates uh faster than some uh scale, for example, speed of light. So this notion of forbidden non locality should be enough to guarantee that gravity has to be an intermediate. It has to be local degrees of freedom,
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Eduardo Martin-Martinez: and for sure, then, the experiment would prove that gravity is quantum that has quantum local degrees of freedom.
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Eduardo Martin-Martinez: Now, uh, the notion goes like this mass. One couples to the field, then the field carries quantum information right? It's it's established in a constant channel for sure. So The idea is that mass one couples to the field, and then the field carries the quantum information from us, one to must, two um. Otherwise we would have known locality
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Eduardo Martin-Martinez: or actual distance in a way.
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Eduardo Martin-Martinez: Now, before discussing uh the models that I want to, I want to uh throw attention to.
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Eduardo Martin-Martinez: So operation happen at events in space time, and do not affect other events which are constantly disconnected from this is the notion of locality that uh, any theory of relativity would have um Galilean relativity established an ocean or even locality uh special relativity established. Another gr comes in another,
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Eduardo Martin-Martinez: and then we have the notion of system locality. The notion of system locality is something specific to quantum mechanics system. Locality basically says, Well, operations that independently affect the quantum systems must be separable. So you have, for example, a non, a a bipartite unitary operation.
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Eduardo Martin-Martinez: That uh uh it, it's describing the action of some local operations on Am me, then this has to be a tensor product between the two.
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Eduardo Martin-Martinez: Now, even locality is a fundamental notion in the sense that even locality is something that comes from first principles from postulation, from observation of nature. Where a system locality is an operational notion, it's a way to implement operations that are local. Um that are set to affect only one system. Um, We think quantum mechanics.
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Eduardo Martin-Martinez: No
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Eduardo Martin-Martinez: uh. The question here is, what notion of locality is the one that is, uh has value of uh first principle. If you want,
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Eduardo Martin-Martinez: let me give you a couple of um a couple of descriptions of the Bmv experiment.
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Eduardo Martin-Martinez: Uh, that has something interesting about this discussion on this distinction
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Eduardo Martin-Martinez: in particular. Let's consider, uh, we grumpy. So this is, uh, I have a classical here, a classical, gravitational field, of course, relativistic description. So here we don't have. This description is going to be even local.
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Eduardo Martin-Martinez: Uh. So there's no there's no violations of causality in this description of of gravity, of course, because it's relativistic.
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Eduardo Martin-Martinez: And uh, I have here, uh the gravitational field or perturbation of the gravitational field, written in terms of a green function that uh you choose. Now, what is sourcing the feel? And let's say that the feel is source by a small mass we'll know how to do this,
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Eduardo Martin-Martinez: the gravitational field perturbation will propagate according to the wave equation associated, or the equation of motion. If you want associated to the degrees of freedom of gravity,
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Eduardo Martin-Martinez: and we just insert this treasonary density, and we have the gravitational of generating by a mass. So this is all good. When uh this thing, this t alpha beta is a classical object. Now, when it's a quantum object, Relativity doesn't really tell you anything. Relativity at at most can tell you things about expectation values.
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Eduardo Martin-Martinez: Uh in the semi-classical regime.
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Eduardo Martin-Martinez: Um, Okay. So let's try to Let's try to describe now to masses in some quantum superposition as in the Vm. The experiment, and let me do a model here. I'm not saying it's a good one. Just the model of doing it. So the model is here. I'm going to prescribe the interaction
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Eduardo Martin-Martinez: associated to each state of the particles
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Eduardo Martin-Martinez: uh. So that's a the classical field source by each part it. So I have here uh some of two terms in the Hamiltonian, if you want,
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Eduardo Martin-Martinez: and each term it's a month right. You have the field generated by one of the paths, as in you have literally a sum of two terms that are the gravitational, the classical gravitational field generated by each of the paths. C. P. One, P. Two are, of course, the choice of part of the masses. So
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Eduardo Martin-Martinez: and you can. You can actually compute uh, what is the time? Evolution of the two masses. Right. And of course this is a relativistic description of the both original uh description Right? It's a this is in the in the non-relativistic limit. You recover the Newtonian potential. But the point here is that in this description
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Eduardo Martin-Martinez: uh, we have uh it's a description that is even local. This description uh, must be kind of know about Mass a uh before the light crossing time before the the perturbation that must a does, or whatever uh, uh, if you want back the light crossing time. Let's not call perturbation or anything. Now here, that what I've done is a prescription. You see, i'm not saying this is a good description of the experiment, where for each combination of pass
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Eduardo Martin-Martinez: I describe that relativistic but classical potential associated with it combination of past, there is no assumption whatsoever about the degrees of freedom of granting
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Eduardo Martin-Martinez: this is making no assumptions whatsoever about the existence or not of local degrees of freedom of R. In fact, the phase space of gravity here can be fit to many different theories if you want
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Eduardo Martin-Martinez: all right. So, of course, in this case the two masses evolved to an entangle state, as it should right, because we know in the Newtonian limit we had the both results. And in you know, I right in here uh negativity as a measure of entanglement, and one can see that, of course, uh the negativity can be written in terms of the propagators of the green functions.
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Eduardo Martin-Martinez: Uh, and indeed, uh, there's some entanglement. After some time this subscription.
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Eduardo Martin-Martinez: Now, again, this description made no assumption about the existence or not of quantum degrees of freedom in the gravitational field. All right,
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Eduardo Martin-Martinez: now find the coming of the masses through the gravitational interaction
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Eduardo Martin-Martinez: can be explained. So I say here does not mean that it has local quantum degrees of freedom can be explained without invoking, without needing the existence of local quantum degrees of freedom.
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Eduardo Martin-Martinez: The interaction is certainly not system. Local. Somebody looking at it would say, Well, but the unitary that you're generated is certainly not local. It's not a tensor product. It's not a interacting with the third system, and that's our system interacting with me locally. But it is
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Eduardo Martin-Martinez: now an interaction established in a quantum channel does not mean This is one of the messages that I want to transmit. An interaction established in the quantum channel does not mean that it is mediated by a quantum system,
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Eduardo Martin-Martinez: it could be a different description. I'm not saying that that different description is uh is uh, what, for example, gravity would reveal is but the point is that you can still write an interaction that is even local. That doesn't defy relativistic assumptions
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Eduardo Martin-Martinez: and yet uh can establish a one-on-one channel without assuming that the mediator, field, or whatever the field that is uh uh creating this and this quantum channel that that in this quantum channel has local point, two degrees of freedom.
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Eduardo Martin-Martinez: No,
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Eduardo Martin-Martinez: we can actually compare with a model in which we do have local quantum degrees of freedom for gravity.
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Eduardo Martin-Martinez: Now, uh,
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Eduardo Martin-Martinez: oh, this is this is supposed to show. Okay, So what we do is we we consider a a week um a week uh a week gravitational field. To this quantize we can second one. The perturbation is linear gravity, and in your gravity we can write as a quantum field. Fear you no problem.
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Eduardo Martin-Martinez: So if we actually do that if we consider, if we consider that uh gravity is quantum, and we have again weak gravity, so it's linear quantum gravity,
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Eduardo Martin-Martinez: then we can repeat the same thing. We can actually now couple the quantum degrees of freedom of gravity in our gravity has local quantum degrees of freedom to uh the different. The different degrees of you know the masses
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Eduardo Martin-Martinez: by, so that the masses generate the field associated with the path that they're undergoing.
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Eduardo Martin-Martinez: If we do that, of course,
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Eduardo Martin-Martinez: uh, we obtain this expression. This is the interaction, Hamiltonian. In that case, which is both. Again, there are quantum degrees of freedom in gravity. And uh, there's also the quantum degrees of freedom of the masses.
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Eduardo Martin-Martinez: And uh, of course, one would expect, no matter what your quantum gravity one has, one would expect that this limits a week gravity limit uh should be valid in some regime at least.
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Eduardo Martin-Martinez: Now,
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Eduardo Martin-Martinez: if we are doing the same thing as a summary. But now gravity is locally quantized, and we uh start in the Minkowski vacuum in the far past, and then we let the masses interact.
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Eduardo Martin-Martinez: Assume they're not of your position, you get something really similar to the classical case. Not exactly the same. You have some vacuum noise terms. And now, instead of having the the the radiation green functions. You have the five month propagator mediating the interaction. That's a quick sample.
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Eduardo Martin-Martinez: Now, uh the results In both cases you end up with entanglement in the massive system.
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Eduardo Martin-Martinez: But, uh, I, here is the the modeling which I actually assume that the field has quantum degrees of freedom, and here I have the modeling, which I assume that
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Eduardo Martin-Martinez: I so nothing about the decrease of freedom of gravity; and I prescribe that the model is just the superposition in terms of a sum of terms in Hi, so in coherent superposition of the classical gravitational field for each configuration of the masses.
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Eduardo Martin-Martinez: In both case this is the one that reproduces the Newtonian case. Both of them are event local. Both of them are compatible with relativistic causality.
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Eduardo Martin-Martinez: Uh, but in the first one we have one to local quantum degrees of freedom of.
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Eduardo Martin-Martinez: And the question is, is there any difference? So yeah, there are several. These are these two things i'm, not the same. If you actually assume that you have local quantum degrees of freedom. The one thing that you would see that you wouldn't see in the in the case where you have the classical or the quantum control classical case in the case that you associate, the classical
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Eduardo Martin-Martinez: relativistic still retarded, feel right. The classical feel associated with it. Math configuration.
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Eduardo Martin-Martinez: Uh, in the case of having local quantum degrees of freedom, you can see that entanglement appears between the masses,
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Eduardo Martin-Martinez: even while they are space like separated. It's not surprising. This is related to the phenomenon of internal harvesting. The two masses can get entangled by uh harvesting entanglement that already exist in the vacuum state of the gravitational field that is well known in in in in Qft. So it's A. No resulting q Oft.
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Eduardo Martin-Martinez: That, of course uh space, like separated radials of space time, contain a contain in quantum fields in space, like if you have regions of space and the degrees of freedom of quantum fields in the two regions that are space like separated, have entanglement, and that Anton can be gathered by systems of massive well system. One, two systems that are interacting with the field.
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Eduardo Martin-Martinez: So to end
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Eduardo Martin-Martinez: Um, when when we have space like separation In the case of linear quantum gravity, when we model gravity as an intermediary system. We look at one from the degrees of freedom
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Eduardo Martin-Martinez: we have entanglement harvesting from the gravitational thing. So if you want it to identify local quantum degrees of freedom of serving entanglement, while they must have paid by separated. Uh, then, if you actually do the experiment and the masses remain space like separated, and they get entangled for sure. This is a smoking gun of the existence of local quantum degrees of freedom for gravity.
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Eduardo Martin-Martinez: Now the covering proposals of this experiments work with regimes where the masses are well within coastal contact. What does that mean? Well, that means
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Eduardo Martin-Martinez: that means that in principle, if you do an experiment cut with the current proposal of Redeems right. The two masses are in coastal contact, and in principle you could explain the results of serving and tamil, and just of serving entanglement, but without appealing to the existence of local one to the degrees of freedom.
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Eduardo Martin-Martinez: Now this is not saying, this is not saying uh that there's nothing interesting about the V. And the experiment in terms of proving that gravity has something quantum about it. So let's see, Let me analyze uh here, uh how we see this, how we see what can be proved with the Bmb experiment when the two guys are still in coastal contact. So the experiment,
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Eduardo Martin-Martinez: when as prescribed, definitely proves that semi-classical gravity fails to describe the experiment. Obviously, I mean, we already kind of we already knew that. Uh, that there's no consistent way of coupling a classic on a quantum system, so that was expected. But yes, that would be experimental proof of it,
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Eduardo Martin-Martinez: and more than that, the experiment would prove that gravity can set up a quantum channel between the masses That is unc controversial.
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Eduardo Martin-Martinez: These two things will be proven if somebody does the Vm. The experiment and files entanglement in the masses.
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Eduardo Martin-Martinez: Now, what does the experiment not prove? In our opinion?
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Eduardo Martin-Martinez: Well, the experiment does not prove that gravity has quantum degrees of freedom. I can make up a model, as I did what I make no assumptions that the that gravity has quantum degrees of local quantum degrees of freedom, and also that is still even local. So it's there's no violations of causality with that modeling that you have. So in principle,
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Eduardo Martin-Martinez: I would say that gravity, having one in the of freedom cannot be proven just by finding entanglement at the end of a Vm. Experiment. Also, it does not prove that there is a quantum superposition of gravitational fields.
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Eduardo Martin-Martinez: This is often used, I think. Probably I've used in a bit language, right or quantum superposition of space, and certainly not because in the I know that this claim is controversial.
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Eduardo Martin-Martinez: But the reason why i'm making it is because, Yeah, there's no Hilbert space for the in the assumption. Imagine the model that I describe right which I associate, the classical retarded feel uh associated with the two masses uh uh, and then a sum of terms in the Hamiltonian, associated with every classical case, multiplied by the projector associated with the masses being in the particular configuration of paths that I have.
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Eduardo Martin-Martinez: That explains the experiment reproduces the Newtonian model in the normal relativistic limit is still a then local. But there's no assumption whatsoever about the face space of gravity. And certainly there's no healer space associated with the field. So even though I know that there is a controversial claim, and i'm looking forward to hearing uh other opinions about this.
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Eduardo Martin-Martinez: Um, I would say that certainly can approve that there are, uh there is a quant superposition of gravitational fields, or anything along those lines
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Eduardo Martin-Martinez: Now, finally, and I promise it's the last light uh the messages that uh I was wanting to to transmit is that the detection of entanglement to be in the experiment is agnostic to the existence of quantum degrees of freedom in gravity in the gravitational field,
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Eduardo Martin-Martinez: unless, of course, one assumes a connection between event, locality and system locality, saying that Well, if I also, if I also assume that the gravitational interaction
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Eduardo Martin-Martinez: uh with the masses has to be also system local, just a quantum mechanical assumptions, then, for sure, I agree that it implies that there are quantum local degrees of freedom. But that's an extra assumption. That is something that is made as an assumption. The experiment alone will not be able to prove it. One needs to make that assumption. And my point is that this assumption don't by first principle, there's no good reason to make it from the start, because this is the same as assuming that you, working in a framework like quantum field theory from the start where these two notions are linked,
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Eduardo Martin-Martinez: the notion of event, locality and system. Look at the are linked only within the framework of quantum theory, and if you assume that from the start you're already assuming before proving anything that gravity has local quantum, the l of freedom. And I would also argue that the experiment proves many things. But if you also
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Eduardo Martin-Martinez: can find in time between the masses while they they remain space like separated throughout the performance of the experiment, and for sure uh that is a smoking gun of the existence of local quantum degrees of freedom of gravity.
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Eduardo Martin-Martinez: Uh, that's it. Thank you very much. I hope that didn't take too much too long. Uh, thank you. Sorry.
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Ivan Agullo: Thank you, Eduardo. So we are a bit behind on time. Uh, if anybody has a very short clarification needed to go ahead. But but if you not this measured if we keep moving.
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Ivan Agullo: So, Gracie. Now please go ahead.
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Kristina Giesel: Sorry. I couldn't unmute while I was screen sharing. I'm trying again.
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Kristina Giesel: Okay, Can you see my screen. Firstly, Yes, okay. Thank you very much. Yeah. I also would like uh to thank everybody, and and especially with the committee for inviting me for this panel as if I already announced, I will speak about gravitational and use uh decoherence models
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Kristina Giesel: and um! I would like to briefly introduce a model that I was recently working on with, uh two of my Phds Rooms with a Cooper and Max Far
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Kristina Giesel: and the Long-term aim in this framework would in a sense be to to work towards the direction of Aqg. Inspired gravitational, and use the coherence models. And as a first step we considered a model one.
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Kristina Giesel: So we formulate this model in the terms of open quantum systems. So just to remind you, Ah! For an isolated quantum system, we can consider a system, Hamiltonian here denoted by Hs. And we can write down the evolution of the corresponding density matrix of the system by considering just the evolution generated by the system, Hamiltonian on some system of space, one hundred
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Kristina Giesel: erez agmoni and an open quantum systems, we ah assume that our total system can be splitted into a system, part which I call as, and some parts which we associate to the environment one hundred and fifty,
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Kristina Giesel: and which I call upside on here. And then the dynamics is enlarged in the sense that the total Hamiltonian includes the system part in the environmental parts one hundred and fifty
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Kristina Giesel: and an interaction among the two which I denoted by H in tier, and we assume that these interaction can be written as um in terms of product here of system operators, which I call as an environmental operators which I call capital, E. And I five is just some index set here which is running uh, yeah, through some index set, which is characteristic for a given open quantum model.
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Kristina Giesel: Now, if we consider this total system, we can also consider its total dynamics here written on the right button
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Kristina Giesel: and um. But it turns out often that the total dynamics is very complicated, and what one would like to achieve in such a model is that one can describe an effective dynamics of the system, degrees of freedom, one hundred and fifty
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Kristina Giesel: uh, which still encode some effective influence of the environment, and this can be described in the context of so-called master equations which consider the total dynamics shown here below the
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Kristina Giesel: and then partially trace out the environmental degrees of freedom. So that we end up with an evolution equation for the system density matrix.
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Kristina Giesel: And that's the framework in which we looked at gravitational-induced. Ah, the coherence models. And a famous situation in this context is the lindblad equation shown here on the top, which includes in the first part here unitary evolution generated by a given system. Hamiltonian. This can be corrected by some something which is usually called a lamb shift correction which comes from the interaction with the environment, and modifies, and then sends the unitary evolution.
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Kristina Giesel: And then there is a second part, including so-called lindblad operators, which I call a k here, which includes
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Kristina Giesel: in a sense also coefficients writing this part, which are time independent, and the lead blood equation, and which are just some numbers depending on K
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Kristina Giesel: erez agmoni. So now for a given open quantum model. Once you have chosen the system dynamics, Then, if you look at the Lyme integration basically uh the characteristic choices you can make for your model are the limited operators Ak: and the coefficient Scammer K. And if we think about gravitational, induced the Koreans, it would basically mean that we can choose something specific here in order to make contact to quantum gravity, one
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Kristina Giesel: erez agmoni. So let me just explain a very simple example. If we just take one limp plot operator, and so K. Is equal to one, and we take it to be proportional to the Hamiltonian of the system, and if existing some length, shift corrections two hundred and fifty.
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Kristina Giesel: If we plug this into the nimblad iteration, we get this simple form here, and if we go to the energy eigen basis. This can be easily, unaddatively solved, and we see that the row, Mm. Um. Elements here for the density matrix obtain the usual unitary evolution here in the difference of the energies, and then some additional contribution which comes with the uh squared difference of the energies which is some decay, has some decay Behavior:
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Kristina Giesel: Yeah, yeah. And this is usually called the phasing in the context of open quantum models.
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Kristina Giesel: So now, if we think about gravitation and use the coherence. Some phenomenological models take the Lynn per situation as a starting point. We
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Kristina Giesel: erez agmoni. But if you look at the assumptions that you need to take if you would like to derive the lindblad equation from the microscopic perspective. And by this I really mean you start with the total system and trace out the environmental degrees of freedom, and then go back to the nint mode equation one hundred and fifty
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Kristina Giesel: erez agmoni. Then there are a couple of assumptions necessary in order to arrive at the limitations. So first is the born approximation which assumes an initial separation of the system and the environment. One hundred and fifty
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Kristina Giesel: erez agmoni. And then usually you consider stationary state such that even for larger values of t you can write the total density matrix in this form in the system density matrix, which includes the time dependence, and then the environmental density matrix, which we can still approximately assume to be one hundred and fifty,
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Kristina Giesel: the same as the initial time
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Kristina Giesel: ere,
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Kristina Giesel: and then one step. And the Markov approximation is this short memory assumption which allows me to replace basically the density matrix here, which is involved in the integral by just row tilde of T. Such that,
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Kristina Giesel: And if we take the Markov approximation seriously, it also means that our correlation functions, which are
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Kristina Giesel: erez agmoni uh are involved in these operators. The iphone Ci for you on the button which enter in a massive creation shown above here. Um, where the first mark of approximation has already been applied, one hundred and fifty
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Kristina Giesel: um. You see, they involve these correlation functions which we get from tracing out the environmental degrees of freedom, and then they are smeared with system operators. And if these correlation functions are
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Kristina Giesel: erez agmoni peaked uh, we can extend the upper limit of the integral to infinity without changing the values of the Alpha and C Alpha too much. And this second step, in a sense, then, allows us to write down a Mathsite equation where these integrals do no longer depend on t one
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Kristina Giesel: and um. This is a step you need to do in order to go back to the Lind blood equation, often depending on the model. There's another approximation to the so-called rotating wave approximation which you apply in one hundred and one
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Kristina Giesel: uh for these exponential factors. We'd show up. If you have annihilation and creation operators in your system or environmental operators, and then you assume that only terms that these frequencies are, it will contribute to your final last site, which
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Kristina Giesel: erez agmoni. So if we consider all these assumptions, And if we want to somehow understand how A. Qg. Could enter into these kind of models, we thought we have to derive them from the microscopic perspective. One hundred and fifty,
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Kristina Giesel: and there's already existing work in this direction, using id and variables by an asteroids who blancouver Oliga, and one
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Kristina Giesel: Erez agmoni, and uh they coupled to the scale of you to linearize gravity. They also generalize this to photons, and we in a sense slightly modified the model that we started. Uh, not in the atm formulation, but in terms of ourstic are variables one
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Kristina Giesel: erez agmoni. And then in this sense we chose a classical dynamic, a reference frame, and afterwards quantized the reduced system, and then we had two D rock observables in the gym in the metal sector denoted by Phi and Pi. Here and then the usual four face-based degrees of freedom in the gravitational sector, one hundred and fifty
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Kristina Giesel: uh a positive thing about decoherence, models, and field theory is that you do not really have to put the interaction Hamiltonian by hand. But this is really given um to you by the action to start with, so We also use the usual interaction here between the energy momentum tensor of the Meta field on Minkowski time, coupled to the Pituz
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Kristina Giesel: uh Metric
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degrees of freedom,
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Kristina Giesel: Ah! The free part of the scalar field with unrelation operators a and a dagger. Then we have the um part of the gravitational degrees of freedom where we denote the emulation and creation operators by B and B. Dagger. Ah, by B and Ah, yeah, B and dagger and plus minus for the polarizations.
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Kristina Giesel: And then uh these J operators, which include the um emulation and creation operators of the scalar fields uh up to second order, and this comes then from the quantization of the corresponding energy momentum tensor one.
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Kristina Giesel: So this is our total Hamiltonian for the decoy ones model,
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Kristina Giesel: and then, um! We considered um to start the derivation of our massive creation, the so-called time contribution less um equation, which one can derive from the large once the equation which has
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Kristina Giesel: so far no approximations, and this time convolutional situation has the effect that we have a time local bus.
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Kristina Giesel: Uh, you can derive this master location order by order. As a first step we basically truncated at second order.
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Kristina Giesel: And then in all these models, what you also have to choose is a state for the environment. And here we chose a thermal state for the gravitational environment.
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Kristina Giesel: Then we basically uh, could derive from our situation, which tells us the effective evolution of the system density matrix shown here, and on the right hand side we have contribution from the system. Hamiltonian, then from including the self interaction part of the scale of field. We also have a lamb shift contribution that I was mentioning before, and then we have a dissipator which I called Kernel D first here, which is labeled for,
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Kristina Giesel: because it can be written in the first um standard Lynn platform nearly uh because, as you can see here below where the first is display it, it has operators. J. A. Jr. Dagger
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Kristina Giesel: erez agmoni, which are ordered in a sense similar to what we have seen in the lymphatic equation. But there's a big difference. And then we, these coefficients are A. B. Here are basically still time dependent. So it's no a lot of lint lad type, because we still have this time dependence here one hundred and fifty
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Kristina Giesel: erez agmoni A. B sums over from from one up to four, and these different jails we just um divided into different currents here, including different powers of, or different combinations of a and a dig of the scalar field, and the estimation here is over the polarization labels which are still included from the projection. One:
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Kristina Giesel: Um, yeah, from the projection operator which acts on these gravitational degrees of freedom which are still evoked in this final equation here.
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Kristina Giesel: So uh, we have this final mass situation, and we can, in a sense, partially also confirm the results that were there in the uh literature in the id and formulation. But uh, even
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Kristina Giesel: erez agmoni, when I have written down the situation in a quite compact form, it's very complicated. It can't be solved analytically and even numerically, it's hard to solve. So a strategy that was also followed in form. Our work is to project these full mass sake patients with the one part of the case, one hundred and fifty
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Kristina Giesel: erez agmoni. And it turns out for these few theory models. You're already in a situation where you have contributions to both divergent integrals. So already, in the simplest case, renormalization is necessary, and people have done this in the adm orders. One hundred and one
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Kristina Giesel: erez agmoni. But then, if you look at the one particle case, you have a better control, on which kind of terms will be neglected, or will be cancelled if you apply one of the further transformation approximations like, for instance, the second Markov approximation that you send one hundred and fifty
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Kristina Giesel: Erez agmoni, the upper limit of the temporal integral to infinity or the rotating wave approximation. So this is currently work in progress that we try to apply the renormalization before applying further approximations, and then still have, in a sense, the full one particular case, one hundred and fifty
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Kristina Giesel: erez agmoni. So, in order to to tell you a very um limiting case of this model um anasstopoulos, and who and also um. Then Vancouver considered that that's the reason why I call it the ahb model. They considered also the one particle case. We normalized went to the non-relativistic limit and considered one hundred and fifty
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Kristina Giesel: erez agmoni um only one-dimensional models, and then they ended up with these kind of situation which we have seen at the beginning of my talk, which was the defacing situation. One hundred and fifty
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Kristina Giesel: erez agmoni. And coming from this forward gravitational model, they could basically determine the gamma which I had just to choose by starting at the lymphatic equation which includes constants here. So the gravitational pi, the voicemail constant, and one free parameter, in a sense which is related to the temperature of the formal state that we were choosing for the gravitational environment one hundred and fifty.
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Kristina Giesel: And uh, we are currently um working on showing that we get the same non-relativistic limit also in that the model we are considering
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Kristina Giesel: erez agmoni. So let me uh conclude: why is it interesting in uh quantum gravity, to work with these gravitation and through the coordinates models. In a broader context. It allows, in a sense, a different perspective to chrome and gravity effects coming from the open quantum perspective three.
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Kristina Giesel: It is interesting in the context of matter interactions where we often assume gravity is weak
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Kristina Giesel: erez agmoni. And uh, because if we consider look fun and gravity, and spy out models in this framework, then. Um! It's interesting to generalize the existing models in the sense that we apply not that for cost, rooting our quantization. But the good quantization and the first steps in this direction in a two
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Kristina Giesel: Erez agmoni and Uh. The aim of this kind of program would be to find a Qg. Inspired models which have some characteristic properties which point back or give us the fingerprint of new quantum gravity in the the way how the coherence is manifesting in these models one hundred and fifty.
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Kristina Giesel: Thank you very much.
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Ivan Agullo: Thank you.
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Ivan Agullo: So there there will be time for questions after right to for this. Yes, there will be time for going to after now. It's just a sure a your question, and it's totally pretty short. Go ahead.
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Suddhasattwa Brahma: I I have a very good question which is before you. Make this assumptions non-relativistic, and so on you have the tcl to Naka. You must run sick type equation. So from there could you calculate the memory kernel to see how good of an approximation, a link that that approximation would be to that? I mean we is it very pipe sharp with the term
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Kristina Giesel: Erez agmoni? Yeah. So um, we can calculate it. And um, the The problem is usually that in order to judge this, you also apply the second Markov equation and send these upper limit to Infinity one.
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Kristina Giesel: And then you can basically because we have emulation and creation operators. The time dependence is mainly via exponentials.
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Kristina Giesel: Ah, and then you can use further Um: Yeah. Techniques in order to deal with these integrals, and we would like to avoid the second mark of um approximation, and therefore um, it's a bit more complicated than in the standard case. And that's the problem. We are still working on one hundred.
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Suddhasattwa Brahma: Thank you.
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Ivan Agullo: Very good. And um! You are the next
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Eduardo Martin-Martinez: You're You're muted, Virginia right?
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Eugenio Bianchi: Thank you. Can you see my screen, is it? Everything is working
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Eugenio Bianchi: uh? So i'm trying to go as close as one can get within the quantum gravity to what one call some many body conference system or a condens matter system, and try to highlight without the differences, but also try to bring in as many as the methods as one can in in this specific case. So the model system that I would like to discuss is,
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Eugenio Bianchi: uh, take the kinematic a little bit space or quantum gravity. Fix the graph, even assume that it's cubic cubic lattice and finite set of notes, for instance, uh, with some identification towards like identification,
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Eugenio Bianchi: and fix also the speeds or the spins to be equal to P. Equal to J. Not so what is left as the degrees of freedom are just in terms of these six valid notes.
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Eugenio Bianchi: The dimension of the full system is finite, and, uh, a generic state in the system is a superposition of a Uh Uh product. States of interference at it. Not
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Eugenio Bianchi: okay. So one as a tensor product structure, and one can start the standard. The uh discussion of states for this many body systems as it's done in connect matter. There's a separate question, or how to generalize all of these aspects to full quantum gravity or so to a larger portion of the kinematical space that I'm not going to address. Yeah, I want to focus on this very specific model.
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Eugenio Bianchi: And what I want to I like is that within the space within this huge space uh it's potentially large in dimension. Uh, we've got the number of uh notes or sites one can organize States in a way that is different from how we generally do for our Northern Ireland system. In our ordinary quantum system you organize states by the energy we speak about low energy States ground state.
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Eugenio Bianchi: Yeah, in quantum gravity. Uh, uh, we we don't have any immediate notion of energy that we can use, and so it's often useful to reverse the logic. Reversing the logic means, uh uh identifying properties that characterize the States and using them uh to organize, deliver space
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Eugenio Bianchi: volume, low states which are the states that we are genetically. If you pick a state of and area low states, let me uh uh uh zoom in this picture because, uh, uh, that they should clarify one of the aspects.
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Eugenio Bianchi: Uh: So yeah, i'm plotting the entropy as a function, subsystem sites, zero, subsystem zero entropy, full system, zero entropy. Uh, there's a theoretical maximum for for the entropy and the uh page Classical result is that if you pick a state at random in deliver space. It's very close to have maximum entanglement to before regions
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Eugenio Bianchi: which here would mean a volume
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Eugenio Bianchi: Now, uh,
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Eugenio Bianchi: and it's only when you lower the energy, and you get close to the boundary of the spectrum in particular, close to the ground state that you have a transition from this linear behavior in volume to a fraction of power blow behavior that is an area low, a dependence only on uh, uh,
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Eugenio Bianchi: near boundary correlations.
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Eugenio Bianchi: Okay, I update that Uh: this scheme helps with what I'm going to discuss in a moment, because all of these structures are present within this model system, and also more broadly in the larger space of look what to morality. But I cannot use energy anymore as a way of characterizing them.
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Eugenio Bianchi: Okay. So now i'm going to give examples of States in this classes, and uh, what I see as they roll up uh in the present, my present understanding of the to
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Eugenio Bianchi: uh one point, two point three point, and I or the correlation. See I'm. Focusing on two point correlations. So, for instance, you could have a region and observable in this region another region and observable cities of the region, any kind of observables, and you are interested in the correlation function, the connected correlation function
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Eugenio Bianchi: in a given state.
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Eugenio Bianchi: So let me look for that product states
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Eugenio Bianchi: the basis uh, like the recaping basis of interest liners. So it's a product state uh one can do better. One can take coherent states of the kind of query in theft. Winners like the living.
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Eugenio Bianchi: Not by no
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Eugenio Bianchi: one can even choose uh the shape of this uh semiclassic to be picked on something we've uh matching, for instance, here. Uh, I consider two big clients. I could pick each one of them on a cube
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Eugenio Bianchi: uh on the
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Eugenio Bianchi: and uh, and there's a notion of a uh uniform measure on the units here, if you want to, or a large measure of a units uh. So i'm giving you that a software, this uniform measure. You could consider all the measures
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Eugenio Bianchi: and notions of random. We respect what that measures uh, we have explored a a large class of other measures, and found that it still volume low with a different slow. So i'm going to consider just the simplest case for for illustration Here
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Eugenio Bianchi: I would be
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Eugenio Bianchi: the score
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Eugenio Bianchi: and uh variance or the dispersion. You see that the discussion goes down uh exponentially fast.
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Eugenio Bianchi: The uh average is a volume law. We want exponentially small correction. You plug it into this expression, and you'll find a typical value correlation functions so concretely you could consider angling or correlation functions for, uh uh, for cubes
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Eugenio Bianchi: are the classical geometry that source, size and a question. But the fluctuations are also correlated as a perturbation of uh, the theoretical perturbation of a background accurate, related in a State. It is low energy, or at least it is a uh uh
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Eugenio Bianchi: that you that supports that. Uh, that is well described by quantum fifty. Right? Then, you would that we would need long range correlation. So certainly the States Don't Sound.
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Eugenio Bianchi: Okay.
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Eugenio Bianchi: And as soon as the degeneracy in states of the next, your states goes down because you are getting too close, very close to the ground state. You have a transition to area law,
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Eugenio Bianchi: and you can use this notion of area
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Eugenio Bianchi: uh indication that you are a low energy, that you are uh close to the ground. State
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Eugenio Bianchi: um
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Eugenio Bianchi: The computational basis, the one that you would use for exact diagonalization of your and Mythonia the product basis that is not adapted to to look at low energies. These zero low States they don't exist at all in quantum fifty or it they don't even belong to folk space.
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Eugenio Bianchi: And uh, in a Condes matter, as I was emphasizing before they are I energy, and I would have to superpose high energy states in such We've launched this person in energy. Yeah. So I I I that are generally, I should say, to get a low energy state.
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Eugenio Bianchi: Yeah. So uh, yeah,
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Eugenio Bianchi: on the other ending one to me that you don't have any median notion of energy or energy density. But you can reverse the logic exactly as from those there's like condense matter basics, and you send tangent as a problem. And this is what we propose. Some years ago, together with Rob Myers. So we identifying the corner of the river space uh, or quantum gravity that supports any classical States, as the area low corner.
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Eugenio Bianchi: By saying, Take a region, take a larger region and take the usual information between the interior and the stereo, and this one captures an area law from long range correlations.
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Eugenio Bianchi: That this is the way, For instance, Uh, Eduardo described it before, like this experiment's great time and is produce. You stop assuming that there's no entanglement,
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Eugenio Bianchi: and there is a question uh, there is a fact. First of all, that is, in two hundred and fifty. We start with the assumption that the out of vacuum is entangled in a very specific way
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Eugenio Bianchi: allows this. We use them all the time as a basis of states. And so there's a question or a scenario, if you want uh. They thought that I want to put that for discussion. That is, uh
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Eugenio Bianchi: to area alone. A primordial face, a plan face different from the ones that we have discussed. Uh, in the recent that have been discussed in the recent literature, where one starts with zero low States, and it's the dynamics that those the analog of a quantum quench
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Eugenio Bianchi: uh in uh incompetence matter systems uh what? That would be the origin of all of the space like correlations. Now, if you wish to do this in quantum fifty or that would be no chance of doing that, because this zero low States are I energy
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Eugenio Bianchi: are allowed in Gilbert Space at this uh, uh, in this bket face. But then, as special, the real that is become important, the produce correlations and the open question is, is this a realistic scenario, where all the correlations that we see in quantum fifty-eight, and we also see in the sky are produced in this uh uh
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Eugenio Bianchi: primordial face. Okay, uh, I'll stop. Yeah, Thank you.
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Ivan Agullo: Thank you, eh? Eh? Jen? You very dressing uh any, any short uh question for Virginia before we we move to the to the, to the discussion session.
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Ivan Agullo: Okay, So so we had this, this, this three uh very interesting talks uh each of them. Uh, eh? Providing a glance to different aspects of of quantum information and and and gravity. Uh, on the one hand, eh? Eh, Eduardo? Uh, you know to us that you know.
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Ivan Agullo: Uh trying to prove experimentally this uh quantum nature of gravity can be more challenging that that that what other people uh believe this is a very controversial topic, and we will discuss more about it, but is what is very interesting. And also he made this point that you know, if we are able to make sure
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Ivan Agullo: entanglement mediated by gravity between
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Ivan Agullo: particles which are out of council contact that would be
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Ivan Agullo: uh smoking and for quantum gravity for sure,
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Ivan Agullo: and and that makes connection with the genius stock. Uh, you know, this zero law Uh um uh States. Uh second law States volume law states these transitions uh that could.
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Ivan Agullo: So there is a connection there and then uh Christine and uh, provided a different viewpoint. How gravity, you know, can, in fact, uh destroy quantum coherence Uh, of all the ships systems propagating the their own.
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Ivan Agullo: So thank you. The three of you for providing this three uh uh different and complementary uh aspects of quantum information and gravity. And now we kind of start with the discussion. Uh, I see that uh Kavlo. Ah has his hand. He was the first one. So so just go ahead. Kablo.
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Western: Okay, Um, Can you hear me? I'm talking from the Not from my computer for the Western connection one. So um, uh, Thank you, even I it's the all all three. Um presentation was super interesting, and I've learned a lot from from from all of them. There's so much to to to to take out of all this.
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Western: But I want to um uh take Eduardo invitation uh, at the beginning to to the cats welcome disagreements, and and uh, uh, uh sort of uh, uh politely disagree uh with this uh uh conclusion, I I think he he did a very good job in the in uh uh focusing on the this question of what the uh, the the the the the experiment uh shows, and I think
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Western: I think that your model is very good, because it's It's exactly what one should the uh focus on that. And so I I think I certainly agree with all your equations and the most of the things you say. It seems to me that what you show is exactly the opposite of what you um uh in words conclude that uh, for two reasons which i'm gonna say briefly, the the important is the second, but the the first one is the one, probably that creates confusion.
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Western: Um. So the first one is that it? It seemed to me you're attacking a strong man uh one of your conclusion is, if we don't do any additional assumption. We can't um uh uh derive anything from a positive outcome of the experiment.
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Western: Uh, my reaction is, of course, but this is written in all the papers uh about the the experiment, the the regional paper by
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Western: um uh, both in and others that make it very clearly. I mean, if you from the experiment itself. Nothing can be concluded. You need some more. Um, You need the existence of a field, et cetera,
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Western: and uh, my paper with my use, which are the strongly that this is evidence for a superposition of geometry. Uh makes very clearly that, uh, the experiment itself is evidence of nothing.
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Western: In fact, in physics a single experiment is always evidence of nothing, and unless you have a lot of other assumptions, and the two key assumptions here are: first of there is a field.
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Western: Unless we assume there is a field it takes, for it is nothing
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Western: now they have, and that's might be my eating events in the quantum information community, somebody who hoped to side step these assumptions. I don't know if there was somebody who's size well to size this assumptions I don't understand what they're talking about.
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Western: So if your disagreement is with the hope of side stepping these assumptions, i'm a leader right?
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Western: And somebody would tell me about this experiment proof the uh the gravity upon ties, and I would say, under which assumptions Well, it's out of this a field in the field. It's, it's, it's it's It's space time, I would say. Of course, give them double price, and we have These are good as option. Okay, Now let me come to it specific, your model, because that's my second point, and what I will focus on
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Western: and what is very good. So you say, Um, it's it's sufficient for describing what is going on. You say the way I need it. Suppose there is a thing it should call H: Okay. And I want to go to say what this is, a fluctuation of the job, and I can describe this H. Now you notice
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Western: that this field has no degrees of freedom. I I think. What you should notice is that this field has no independent degrees of freedom, and that may come back to this distinction.
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Western: Now, if there's a field, there something can be measured right. You can go hard with, stored by something that measure the electric magnetic field. So the question I would ask you is in assuming that this description is is correct, Is this thing possible?
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Western: If it is classical, it has a value in any given experimental situation, uniform in every point of space time.
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Western: So in the description you're giving is this field. Has this Feel the value in theical in any point of space time? Of course not because you show up your equations, Let's say, to understand what's going on. We're assuming that is, some of two something I
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Western: to configurations to find them uh contribution, or find that some to vectors in the space whatever uh which you can actually put us in the space of the particle in the space of the field in the space of the
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Western: slave to the particle, whatever you want, but the actual field doesn't have a single value. If it had a single value it,
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Western: there would be no interference and no effect. So the field is on classical. That's what we's, meaning by a class not being no classical.
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Western: And if we fold in the second assumption, which in this community is sort of but our bread and butter, namely, that this is this gravity, and it determines the position of so it depends what the clocks do and what the the roles do. Then
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Western: conclusion is that what determines what the clock do is not doesn't have a single value, namely, there is not a single geometry understand what it goes on with this X assumptions. We need to think of the possibility that the geometry is not doesn't have a single value.
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Western: So it seems to me that all your analysis and your field that
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Western: uh, we use it. Field show shows that this is a geometry. It cannot be a classical geometry. If um the experiments uh give the result that no one is that. And if these assumptions are formed in
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Eduardo Martin-Martinez: Ivan, can I thank you, Carlo. This is is great. Uh, you see the it's difficult, uh, always difficult, to discuss this things, because I agree, let's say, with ninety percent of everything you said as well.
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Eduardo Martin-Martinez: Uh. So that makes it. That makes it tough right to find the the the the nuance, I guess, on the on what um what I think is non-trivial here. Um, So I agree with let me first say things that I agree with. I agree that finding entitlement in the Vm. The experiment would be proof
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Eduardo Martin-Martinez: uh that the gravitational field cannot have a classical description in the way you said Right? I mean, you definitely cannot have a description of a field that is well defined in every point of space time. For sure, a hundred percent
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Eduardo Martin-Martinez: uh. The second thing is that indeed, it proves that gravity, or would prove that gravity is not classical in the sense of being able to associate a classical face space.
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Eduardo Martin-Martinez: That uh, I never said that uh that they feel is classical in the model that I consider. I call it. In fact, the the the name we use is onefully controlled classical uh as opposed to classical. But um! But here's the thing, and it's also agree with what you say so in this kind of model
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Eduardo Martin-Martinez: there's no local degrees of freedom. So first we that assumption, and we discuss the assumptions right uh without extra assumptions, what we have here is that the model number one? That would explain the experiment?
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Eduardo Martin-Martinez: Um has no assumptions about the degrees of freedom of gravity whatsoever, so you can fit any degrees. So if you can actually find a theory that fits in there like, I can complement this with some theory for the field,
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Eduardo Martin-Martinez: then uh uh, the point is is quantum. Gravity is that gravity has quantum because of the the only way in which I can complement this agnostic model about what gravity degrees of freedom are are, uh in this particular experiment.
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Eduardo Martin-Martinez: And the answer is, No, you cannot. You cannot really definitely. You can consider, uh, the existence of local quantum degrees of freedom for the field, and I agree with you in some regime. Uh, it will be described with this classically control model,
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Eduardo Martin-Martinez: but in general you cannot. Uh, I don't see a reason, at least when you can. Now, of course, one is to compliment with extra assumptions. Now my point would be. I guess the controversial points is uh whether the assumptions are uh begging the question or not, and I think that's where we would probably disagree
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Eduardo Martin-Martinez: because the main assumption that one needs to do in order to actually associate. Um uh, the existence of local degrees of freedom is this: This is something that I mean, that's um uh quantum. Locality and relativistic locality are the same notion,
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Eduardo Martin-Martinez: so you can certainly take that as an assumption, and they agree. If you take that as an assumption, I think there's no way out other than if you find entirely in the Vm. The experiment. Gravity is quantum. Ask one to local degrees of freedom. Now the question is whether you can make that assumption right, and the the point is that in the way I understand it,
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Eduardo Martin-Martinez: and that assumption together is only done, and he's done in qft. Making that assumption from the beginning is assuming that you're moving in a framework. The fact that quantum, locality and relativistic locality are connected. We'll not let's not call it relativity.
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Eduardo Martin-Martinez: The notion of coastal structure or locality in the sense of coastal structure and locality in the quantum sense are linked The frameworks in which we link the two are very particular, and in particular the framework in which we would link it
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Eduardo Martin-Martinez: um in. We gravity would be a qft, So the point would be whether making that assumption
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Eduardo Martin-Martinez: it's already assuming from the beginning that there's a qft behind the whole uh description of gravity, right? So whether the experiment can prove it or not, so maybe, if one of the assumptions is that you have these two notions of locality linked. Maybe you're assuming already that gravity can only be described through a uft, and this is, I think,
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Eduardo Martin-Martinez: the only point in which I would disagree, because I fully agree that, uh, proving that for uh showing the entanglement, deb and the not space like in time, and if you find space like in time, and that is amazing, because you can say a lot, then you can say a lot about the existence of quantum degrees of freedom of gravity. If you just find entanglement, then you know that there's no one single model that can do it. You can have a lot of models
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Eduardo Martin-Martinez: that can actually fit uh this description,
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Eduardo Martin-Martinez: because I have a description that makes no assumptions about the degrees of freedom of gravity. Now, whether you can assume you can complete that with extra assumptions, and whether those assumptions are assuming already that you feel has quantum degrees of freedom or not, I guess is my my new ones here, because I fully agree. The experiment proves that gravity established a quantum channel, which means that
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Ivan Agullo: certainly experimental proof that semi-classical gravity has no hope Right? It's uh other than that. If you assume that gravity is a field theory like in in gr, that's the experiment tells you that these are quantum field theory. I would say no, because in the first model that I paid, i'm using
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Eduardo Martin-Martinez: that what I I don't know, depending on what you mean. Right? So if you keep in mind that in the first model that I presented every path, every term in that Hamiltonian is coming from the classical field theory. So the modern is relativistic.
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Eduardo Martin-Martinez: Anything about the the quantum locality of the funeral right? And, as Carlos said it,
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Eduardo Martin-Martinez: in that case is quantum. The model is one because of the masses, so it's indirectly quantum. In a way. The quantum decrease of freedom are in matter. I'm. Not in gravity in this case it's an a few. Let's talk about the model you presented. Not that is, is there a field
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Eduardo Martin-Martinez: in the sense that it's not defined at one point in space time at at every point in space. Time, in that sense is not a you? Yes, there is a field. Is it a classical. No, it's not classical,
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Eduardo Martin-Martinez: but it's also not quantum. That's the point. It's not well. You are assuming that there might be something which is not classical as a quantum. I'm not assuming, but I don't believe that's true. I mean, I I believe that there would be a quantum field, of course, but the point is, if you look at the experiment for the agnostic point of view,
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Western: you said, there is a field.
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Western: Okay? And it's not classical. Yeah.
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Western: But what you're saying is that it might be that there is a field is not classical,
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Eduardo Martin-Martinez: but it's something else. We don't know that is neither classic or not. One zoom, for example, it could be the masses, the way masses interact again. This is not something, I think, that
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Western: all experiments, the Higgs feel the the the the, the the gravitational wave, detection, everything.
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Western: When we say this is fairly prove something. Okay, when we say uh the detection of the invitation waste proof that the line will present proved that
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Western: I can always cook up something which says, No, it does not proof. You know, that it is because it might be something which is not a it's not a quantum theory. It's not that it's something we don't know, and yet it could. It could give this phenomenal.
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Western: Yes, of course. But what is interesting in saying that the same phenomenon could come from something with knowing what it is,
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Western: and it doesn't fit in any of the way we used to describe the the way we used to describe Nature's classical in theory, classical interactions, quantum interaction want to good theory.
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Western: The experiment rules out
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Western: the possibility that there is a classical field that that describe the uh, the gravitational direction, and that this classical field that um can be interpreted as the Jo into space time that's ruled out.
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Western: And this is a Nobel prize, miss out, and the way we say that in in in most communities uh, I understand it is some communities one say, Oh, yeah, but it doesn't prove anything because of priority. It could be possible.
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Western: And that's what. If you you don't, you might not well willing to quant quantum mechanics, but that's what everybody else go for to become. And you you you! You! You want to say, Oh, but then maybe there is another thing. It's not what the mechanics can happen, or show me that theory instead of arguing that uh, oh, something else is possible.
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Eduardo Martin-Martinez: So maybe let me compare to cases right, because I think that for for conference, right the case where you find
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Eduardo Martin-Martinez: um space like entertainment. So in mind that the two masses are space like separated versus the case. We're not right there.
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Eduardo Martin-Martinez: I agree that if you are, if it's, this is I don't think it is as need pik as it may, saying, so let me. I can't give it facetious about this, so the the experiment has given the that the question is, what do you plan to prove with that experiment that we don't know right? What are we learning from the experiment? The fact that
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Eduardo Martin-Martinez: the fact that, uh, a classical field cannot be modeling gravity is well known before the experiment, right? Because we have noble results that tells you that you cannot couple
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Eduardo Martin-Martinez: one, two system to classical systems. There's a face space definition problem to begin with, So we know it cannot be a classical theory. So that is known, that is, even before doing any experiment. We know already that gravity, the structure is based on cannot be quantum lots of people, but that a lot of people disagree with that,
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Eduardo Martin-Martinez: and the No, I don't find it controversial, uh, but but but but there's a difference between theoretical expectation, not theoretical argument. What is this experiment? So that's a key point. So now let me compare to scenario the scenario where you find space like entanglement,
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Eduardo Martin-Martinez: virtual dec scenario, where you define non-space like in time you find space like entitlement. This is without making the assumption without making the assumption.
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Eduardo Martin-Martinez: That's uh, that's uh. They feel is quantum. The gravitational field is quantum. You prove that the way in which you can model that appearance can only happen by a theory that is one to local and relativistic local. So it's a positive results. So you find that that is a quantum mechanical field of planning.
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Eduardo Martin-Martinez: No, the the thing is that they compat that if you find space like entanglement like that and you. So here's the thing. The assumption in that case that I would take is relativistic locality or event locality, if you want, which is not quantum mechanics,
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Eduardo Martin-Martinez: what's that? Sorry might be something else which is not quantum mechanics. So you know that that's a difference. So in the case in the first case that I have, I can give you the something else. In the other case I don't think we anybody can give you the other case the other theory without. If I do demand that you satisfy relativistic locality, I can give you a theory for matter and gravity such that there's no gravitational degrees of freedom. There's matters, degrees of freedom, and I prescribe gravity to act in this particular way. This is Uh, this is something I can build. I can build you a theory
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Eduardo Martin-Martinez: that, uh, would satisfy this first model if you want. That would be a limit of that mode the model doesn't make. So the money is agnostic about the degrees of freedom of gravity, the first model, whereas the second is not. The second is a result that if you don't find the prediction, then you know that you've allowed Qft. So you see what I mean If you find the negative results.
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Ivan Agullo: So, Julia. And then you wanna go ahead with your viewpoint.
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Eugenio Bianchi: Uh yeah, it's on the same. It's on the same topic. I I it's a question for uh, for Edward, but also for everybody. Uh and uh,
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Eugenio Bianchi: you can just consider the Newtonian potential in this Newtonian potential. Yeah, uh, produces entanglement. We have no doubt about that. The uh electromagnetic potential one over our produces entertainment because it's uh uh, it's one over
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Eugenio Bianchi: nontrivial situation uh which can be total about some model of uh, a classical channel for gravity. It's sometimes presented that way, but I want to describe it as a description of a regime. I'm. Referring to the calf retailer, and Millbourne a model of two thousand and fourteen. So what is this?
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Eugenio Bianchi: Plus all the way around?
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Eugenio Bianchi: It's all the kind of it's a one particle makes a phone call about It's position, and it's a uh distribution of noise to the other particle. It doesn't generate an amendment. Now I don't think that anybody believes that this is our nature works, at least in our circle.
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Eugenio Bianchi: But, uh, uh,
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Eugenio Bianchi: the regime is uh when you don't just stop the two particles, and you turning interaction. The word is richer. There's uh the uh, the bodies. The two bodies are extended that they don't have a coherent for which that big mass couple studio, the big mass.
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Eugenio Bianchi: There is the coherent in the way at Christina described. So,
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Eugenio Bianchi: going from the regime where the very simple model. The Bmv model is what matches the experiment to the regime where this uh uh classic of standard model describes the experiment. There's everything in between, and part of it is, how would the experimental is still, as uh isolating systems in part of it is a good as theories we are identifying. Where is the transition? What is good enough to isolate the systems
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Eugenio Bianchi: to an amount that we can estimate? We learn something, and we learn something that goes well beyond that one uh elementary quantum mechanics case, because we use these arguments everywhere. Not just in the uh Black Hole Information paradox. We're often with this. The paradox.
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Ivan Agullo: Western has the the hand race, and uh, for a while. So
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Ivan Agullo: go ahead. We, Francisco,
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Ivan Agullo: Go go ahead, Francisco.
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Ivan Agullo: I think they're muted here.
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Ivan Agullo: I cannot hear you.
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Ivan Agullo: We cannot hear you.
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Eduardo Martin-Martinez: They they are muted, Ivan. I don't know if you hear me, but they they're muted so maybe that's why
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Carlo Rovelli: you you did it right?
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Carlo Rovelli: Sorry. Sorry There was a technical problem here. Um, I had a first of all, Thank you to all the speakers uh and uh, i'm particularly interested in uh trying to connect to what you were saying about uh a entanglement um a a, And if in general uh information in gravity, with cosmology as a genuine was doing in the end. But I wanted to ask specifically a question to to Christina, because
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Carlo Rovelli: it seems that the problem, the program that she's carrying on and studying the coherence may lead later to some interesting consequences for cosmology. So I know that this is kind of preliminary, and she, Christina was saying, Uh, okay, we have a um
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Carlo Rovelli: available, and then the next step is to have a from quantum gravity uh involved. Uh um! But I I would like to ask you, Christina, do you see already applications some way in which your preliminary results can have an effect on the way in which we do cosmology in the way in which we study perturbations, and we understand the classicalizations of the perturbation.
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Kristina Giesel: Yeah, I think you mentioned the quantum to classical transition. Of course, this is one one framework where people apply the coherence models. Um, I mean It's a bit the up with that situation, because if we do cosmology, we would like to trace out the gravitational degrees of freedom one hundred and one
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Kristina Giesel: erez agmoni. So, uh, you have to carefully think about the what you choose as the environment. But I think a first step could be, and that's also a good work in progress that we consider very simple cosmological models, like maybe Background F. And we've quantized one hundred and fifty,
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Kristina Giesel: and then consider some kind of effective model for the environment. Maybe some scalar fields, and then look uh, in a sense, how um how we could could maybe justify semi classical states that we use in cosmological models, because this would also be um a tool to understand better. Maybe the semi classical or Gaussian states use uh if we could derive them dynamically in terms of uh such a the coherence model one
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Kristina Giesel: erez agmoni, I mean perturbations. Um could also be. But I would see this rather as a second step, because it's again field theory and it's complicated, and we see already, and for quantization, that the model is very complex, two hundred and fifty.
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Kristina Giesel: So I expect, if you do this in the context of cosmological motivation to be uh it even more difficult to handle technically.
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Ivan Agullo: And Abai has a question.
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Abhay Vasant Ashtekar: Okay, So I think i'll question a comment. Actually so, Christina. And just to continue along what you're saying uh, is the use of the terrible state for the gravitational environment critical? Or could you use for some other state there.
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Kristina Giesel: Ah! I think it really depends on the limits that you're considering. So, for instance, these non-relativistic limits which they derived. I think it's It's not so important. What kind of stains you use one
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Kristina Giesel: erez agmoni. Yeah, this is, uh I I wanted to say, this: this is a specific thermal state. Uh, but you also saw in the final equation that they derived, and the number that thativistic limit that was proportional to the temperature which I uh defined the thermal state with, and if I choose vacuum, there's no effect anymore. One hundred and fifty
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Kristina Giesel: erez agmoni. So uh, that's also reason why we think you have to really look carefully how these approximations are done, because in the full one particle case, you still have a lot of interest in terms. But if you do all the approximate which are also there in the vacuum case, two hundred and fifty.
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Abhay Vasant Ashtekar: Thank you. Okay, I I kind of the the the next questions or comments I have to do with the the long discussions that we had earlier on. Uh,
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Abhay Vasant Ashtekar: so
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Abhay Vasant Ashtekar: I mean first of all, I mean the word degrees of freedom that Edward was using is not clear to me, because normally one things of degrees of freedom and gravity, especially because you're using using linearized gravity as being associated with the transverse priceless boats.
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Abhay Vasant Ashtekar: Particles are considered to be
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Abhay Vasant Ashtekar: more of a static particles than their interaction, which, in the northern Irelandistic limit would give you. Coulomb Interaction is really going to be coulomb interaction of the of the between the in in the as gravity.
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Abhay Vasant Ashtekar: And so I think that the word degrees of freedom is used loosely, and
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Abhay Vasant Ashtekar: I mean I. The point is that
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Abhay Vasant Ashtekar: if you say something like, well, if if if
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Abhay Vasant Ashtekar: if you use all of the kind of field theory that we already know that the feel is contacts. But what we know is quantize is really transverse, priceless ports in the autobiographical field, and so I think that when he is learning something new,
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Abhay Vasant Ashtekar: the entire geometry or entire diversity field is generated by matter so only coulomb interaction, if you like.
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Abhay Vasant Ashtekar: But even in that case one can see show that you know, even outside matter, you can perform experiments to show that uh this Coulombic degree, if you like, is is is quantum mechanical. Uh, I mean you could.
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Abhay Vasant Ashtekar: My last question is really about Eugenio, because I didn't understand completely his viewpoint. Uh you, Judy, are you saying that?
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Abhay Vasant Ashtekar: So? That would be
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Abhay Vasant Ashtekar: a model that, for example, Eduardo could use as a
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Eugenio Bianchi: and uh, the theory of us showing what is the next store that in the approximation is not developed.
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Abhay Vasant Ashtekar: Okay, so, then, is this what you're saying that in answer to Carlos question it, Eduardo would say that. Well, even if you see this entanglement uh
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Abhay Vasant Ashtekar: uh in in the in, not not the case where there's space like separated, but the usual you. If we solve this and development, it could be, We know that it's not classical relativity. But, for example, it could be this model as opposed to quantum mechanics.
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Eugenio Bianchi: So this specific model produces zero entertainment,
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Abhay Vasant Ashtekar: I see. So if we saw an entanglement, then we would say that this board is also going. Now, Okay, this is what I want you to understand. Okay, Thank you very much. Okay.
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Eduardo Martin-Martinez: So so it So I i'm saying this as well. If that model in particular will definitely be this proven by a Vm. The experiment. There are other models. For example, you can do a passive quantum gravity, which is a lot of freedom to choose
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Eduardo Martin-Martinez: the stochastic sector of the dynamics. If you want to the computational field, you can fit. If you with a shoe horn. I can fit a model for sure. That is not quantum. So so not classical. Obviously it's going to be stochastic in some way that is not trivial
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Eduardo Martin-Martinez: that can describe the experiment. Basically, that's the difference between a fossil f falsifying experiment versus an experiment that is open to many models, Right? The space like one. It's a falsifying experiment about Qft in the low energy sector of gravity. So you do. The space like separated one. If you don't find what is predicted. You are falsifying
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Eduardo Martin-Martinez: that there's a qft in the low energy sector of gravity that you can discard linear gravity in
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Eduardo Martin-Martinez: um. If you do, if you find in time in the Vm. The experiment, all that you're saying is that all the models that are based on to describe gravity are discarded.
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Eduardo Martin-Martinez: That's what you're saying if you're doing that. So gravity established a quantum channel. Now, in the discussion about the the existential degrees of freedom I was going. I was using these terms in the sense of okay
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Eduardo Martin-Martinez: understanding quantization in the canonical sense, right? Because I mean, i'm in with gravity as well as I'm. Like. I have a face facing weak gravity. I have a face space for gravity, and there's some sort of quantization map uh that uh maps my uh dynamical functions to uh self. I join representations of operators in a heel of space.
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Eduardo Martin-Martinez: And uh, my P. Some brackets go to commutators in that sense, because I'm. In the week in the week. Gravity sector. But what is Condes? There is a transfer space list most, and has nothing to do with this uh, with this Coulombic mode, which is really what you have to
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Abhay Vasant Ashtekar: for me. This there's a problem with this whole analysis of the experiment. I don't mean it's not worth it or something. But if you take it very seriously, it it seems to be a little bit hodgepot picture right? I mean, in the sense that the one is talking about. Uh in an analysis of experiment, because one is talking about, you know, point particles
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Abhay Vasant Ashtekar: and their wave functions. And somehow one other wave functions. I mean, are you talking about this part? I am fine. I'm saying that these are relatistic particles, and and in a regime in which there is no particle creation you can put that in,
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Abhay Vasant Ashtekar: but still you should treat them relativistically, you know. Talk about one particle sector, and not point particles coupled with this
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Eduardo Martin-Martinez: that can be done as well, and that they wouldn't change the results I can. That is easy to actually include to three third particles in a quantum field theoretical way as well, and even without restricting to a one particle sector that can be done, it would be very similar; but allowing for particle creation. No, I mean that could be completely I could
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Eduardo Martin-Martinez: I could if I wanted. I can include. If you want, I can go ahead.
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Eduardo Martin-Martinez: And Then what? What entanglement are you talking about? Of course, of course you would have. You have a state of like quantum field, say a with packet kind of in mind that you create a four-way packet one particle in that sense that's allowed to do. And then you have some device that you can model, and people know how to model these things in the low energy sector that creates a superposition of paths. And there's the interaction of the model of that. Uh that's a device that creates the path superposition. That doesn't conserve particles, for example, in only in non-relativistic approximation. It does so you could model you're gonna go a little bit away from the one person,
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Eduardo Martin-Martinez: and you could do the full treatment, of course, that way. But you can. Actually you you! You're claiming that your calculation, and we just specify all this approximate basis systematically, that not one or and is it published already? No, no, no, not at all. I mean. This is not that it can be. It's technically complicated, but what I mean is coming on. But I mean, I get it. We We know how to model those steps in particular.
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Eduardo Martin-Martinez: Um, I do have a question as well for for for for Christina. If if that's okay, I don't know if it's the time. That's okay. We are um getting out of time, but that maybe you last question.
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Eduardo Martin-Martinez: So so, Christina, there's one thing I I I enjoyed your your presentation a lot. There's one thing that is, uh, uh, commonly looked at in from the point of view of relativistic content information, right?
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Eduardo Martin-Martinez: Uh, when people like you mentioned the Anastoplas. Who uh Blenco you want uh models, and in particular, in a couple of someday look the the the these families of models um have some issues that I've been recently looked at,
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Eduardo Martin-Martinez: which are related to the fact that uh, there's no console. Some approximations on our zoom and are okay to do like. For example, we're talking about, but not only rotating with approximation in particular, are extremely incompatible with um uh the relativistic nature of the theory. This then looked at this, for for we're talking to youft now here, not not driving
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Eduardo Martin-Martinez: um. And I wonder whether uh, that's something that we're asking like typically to see if those approximations work, you have a framework in which you derive
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Eduardo Martin-Martinez: um. So again, there's some recent work uh discussing that uh that tip that the models of that of the kind of uh, the who and a stop those kind of model have these issues right? Is that something that's uh would affect you or W. Or you at all, as and because, or do you have good reasons to take those approximations and non-relativistic approximation uh rotating with approximation. What What are, What is the
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Eduardo Martin-Martinez: that? Is it Because
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Eduardo Martin-Martinez: do you have a good reason to make them? Or or is the are they done without uh justifying them typically
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Kristina Giesel: erez agmoni. Um. So I think this is one of the ideas we had in mind when we started that we really wanted to start from from from the linearized action, and then see um! What do we have to require in order to get some mass decreation? And um I mean. Of course, we also use the spawn approximation to have some manageable last situation in this sense. And yeah, I agree. We could debate that one hundred and fifty
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Kristina Giesel: erez agmoni um the non-relativistic one, I mean. I would rather say these kind of models are. Very. They're not rich in in the sense any more that I would like them to have because they are so simple. I couldn't see any fug inspired features of that. So one hundred and one
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Kristina Giesel: um
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Kristina Giesel: Erez agmoni program. Uh: yeah, people could work on, And I think people will learn something on the way in the sense how valid up approximations. Or maybe, if you do some, they are justified at the later stage, one hundred and one.
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Kristina Giesel: Yeah, the the the the literature is that thing at that point in Qft. I'm. Talking right that the coherence in uft it's certainly at a point that people are finding problems with assumptions that are done kind of by default that are inherited from the coherence in non-relativistic setup. So so yeah, there's I mean have A. D qed that I also use this Um, But again, I mean uh even writing down the operators i'm using is something which is a bit out on fox space. So it's already starting there. And uh, I guess there's a lot to do.
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Eduardo Martin-Martinez: There's a big difference between finite volume, my an infinite volume. Uh, do do you see that it? I? It's what you were also referring to it one right
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Kristina Giesel: erez agmoni. Yeah, I mean already by choosing the the thermal state right? I mean, uh, if you do this on fox space. It's It's very uh, yeah, difficult, even not possible. You have to work with Kms states. And in the final volume case, I mean, you can just choose a gift States, and it goes through one hundred and fifty,
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Ivan Agullo: very good, and and a table of raise the hand. So uh, maybe last uh intervention,
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Western: just a uh, yeah, just a short comments. Um, the final Wheeler theory.
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Western: It's a formulation of Qd. Where uh one thing at the at the field, as generated by the particles only. It's very similar to what to do out the same
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Western: um one as impression that the only the only degrees of freedom are the particles in the field is just determined by the particle. Uh. But that's wrong in in in in in a specific sense, which is a following. If you take the cost on time slice,
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Western: which is where you see where the degrees of freedom are, and you say the what the position of the particle is on the time slice that does not determine
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Western: the state of nature, because the state of nature, of course, depend on where the particles were before
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Western: so on a constant time. Slice. If you want to give data, you have to give the position of the particles plus more, which can be either where the particle with before or the field there.
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Western: So um
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Western: is not at all true that by just looking at retarded potentials
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Western: mit ctl, and I mean it's just not what we usually mean by degrees of freedom. There are things that can be in superposition, because you can have the two particles, not in superposition, say in a point. But they? Where is the position in the past? That so? The field at some time is in superposition, and the Hilbert space one
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Western: of a five minute wheel theory is not just a fuel in the space of the particles much richer, so that's where the superposition is.
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Eduardo Martin-Martinez: I do you have the right. So so um their pointer. That is important, I think. Uh It's uh they agnostic. The The first model I presented is completely agnostic about what's the dynamical sector of gravity whatsoever in that sense.
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Eduardo Martin-Martinez: So where the degrees of freedom really live or not, it's totally agnostic. So that's the point. I mean. You can fit a lot of models. Let me put it just families of models that they, the set of models for which you can actually find in time in the Vm. The experiment.
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Eduardo Martin-Martinez: It's very large, and you still have a lot of room for models that are not necessarily quantum. So particular models may have these. I, in fact, I believe that Carlos. So in in essence I agree. I believe, that eventually you can disapproval every single one of them. But I was focusing on finding
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Eduardo Martin-Martinez: um, but we were focusing on finding a particular redeem in which uh, all models uh that uh are not uh based on the assumption of a low energy sector. This qft can be this proven in the sense that it can falsify.
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Eduardo Martin-Martinez: So the the space like one, if you want can falsify the models for which you have a low energy sector of the theory that um uh, it's a qft for uh for gravity.
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Eduardo Martin-Martinez: But I agree. So that the point is that in principle just find in and we in Vm. You can fit a lot of models. Uh, maybe those models are all far-faced, but it's such a big set
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Eduardo Martin-Martinez: that they claim whether you've seen entanglement is connected one to one to experimental proof of quantum gravity is what may not be so direct, so I guess I guess it's. It's a matter of a bit. That's it. That's what it is. I'm not developing it. Everything else is facts. I think I think all that we agree with is, it's actually agree on this facts.
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Eduardo Martin-Martinez: But what is a matter of opinion is, what would you consider proof of uh experimental proof of quantum gravity?
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Eduardo Martin-Martinez: And uh, and what you need to assume in order for the experiment to be connected directly to to quantum gravity, so I guess the whole point can be summarized, and there's a larger set of theories that what could in principle fit in a model that is agnostic about the gravity sector. Like the first model I presented.
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Eduardo Martin-Martinez: That's pretty much what it is. It's very deep. So superposition in the sense of this some notion of Hilbert space for gravity, and I have a quantum super position in the same way as I have for every other single matter. Field. That is the thing I don't think you can prove with B and the entanglement
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Eduardo Martin-Martinez: as proposed. So that is, I guess that's the extent of the client.
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Ivan Agullo: Wonderful! I think it is wonderful to have all these different viewpoints, really, eh? And reaching that was the goal of this panel. And I thank you, Eduardo in particular for for for participating, and also, of course. So Jenni and Christine a couple of for the government's Abaya and uh Crunches kind of the rest.
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Ivan Agullo: Uh, I think it was uh a fantastic and and and hopefully, we will have more many more discussions like this in the future.
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Eduardo Martin-Martinez: Thank you. Thank you and I really appreciate it. And thank you, Pablo and and and everybody else who participated in this
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Eduardo Martin-Martinez: in this discussion. Uh, because I think it's really good for for us as well to be exposed to. Uh this. Well, thought arguments as well. Thank you so much.
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Eugenio Bianchi: Thank you for organizing this
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Kristina Giesel: wonderful Thank you.