Jorge Pullin: Okay, so I think we can start this morning, we have a panel black hole of operation we're going to be three dogs one by mid autumn haley first by hashtag or second and Carla already third speakers will try to limit them to 15 minutes each.
Jorge Pullin: I suggest, if there are questions during the docks we keep them short to clarification type questions if a discussion on shows was just move them towards the end, so please go ahead.
Ahmed Almheiri: hey thanks thanks a lot for the invitation to participate in this panel.
Ahmed Almheiri: i've been tasked to talk about some results from two years ago on reproducing the page curve from gravity pathological.
Ahmed Almheiri: So let me talk about that.
Ahmed Almheiri: So I titled The talk is entropy plucking radiation and the question about how how to compute this entropy.
Ahmed Almheiri: To begin see, let me, let me first talk about something that some of us have been calling the central dogma of black holes.
Ahmed Almheiri: This is the idea that you should think of a black hole as a.
Ahmed Almheiri: Normal quantum system.
Ahmed Almheiri: whose number of degrees of freedom scales, as the area of the horizon divided by 14 Newton and which evolved unitary under time evolution.
Ahmed Almheiri: Here I mean that, in the sense that.
Ahmed Almheiri: A black hole is coupled to its environment and then the total system, the combined system is evolving under time evolution that's.
Ahmed Almheiri: The question is whether this assumption is justified, and so this talk is going to be about evidence for this.
Ahmed Almheiri: assumption or dogma.
Ahmed Almheiri: Let me first began about what we know about michaels so we know the black holes have thermal entropy and this terrible entropy is assigned by the gravity pathological.
Ahmed Almheiri: The way, you see, this is the way you define entropy as you first write down a canonical partition function, which is defined as a trace of eating the mind has been ah so it's it's it's a trace of some Euclidean or some evolution Euclidean time that's that's the beta here.
Ahmed Almheiri: And what we learned from.
Ahmed Almheiri: quantum mechanics and quantum field theory is that a trace of of this type can be written as a path integral.
Ahmed Almheiri: Here the theory that we have is gravity so as the pattern to go of gravity so here it's some.
Ahmed Almheiri: This is the integration mentor on the metro on metrics you have some action of the ground of gravity, which could be less in ice and every action and there's also a partition function of the matter living on some on the space time which i'm going to leave implicit just said about.
Ahmed Almheiri: This integral is a hard integral to do, but when we were doing it is by restricting to sign up points.
Ahmed Almheiri: In the central point of this path integral is the so called Euclidean cigar geometry.
Ahmed Almheiri: I should have emphasized that this pathological should is to be evaluated, given the falling boundary conditions and infinity in particularly you have an s one okay that's that's supposed to correspond to the gradient time direction.
Ahmed Almheiri: Now this is again the Center point the relevant data point for this interval is this you put in cigar which.
Ahmed Almheiri: famously everyone knows that the metric on this is just the analytic continuation of the short short solution.
Ahmed Almheiri: Something amazing about this.
Ahmed Almheiri: about the Center point is that if you plug the solution back into the action and then differentiate with respect to the temperature or apply this differential operator on logs in a beta.
Ahmed Almheiri: that's that that's just a formula of extracting a thermal entropy what you find is that is the area of the horizon.
Ahmed Almheiri: Of the black hole which is the area of the tip of the score plus the entropy of the matter outside i'm going to ignore this second term.
Ahmed Almheiri: The upshot is that we have this is the upshot is that you get a finite entropy for from this configuration, which corresponds to a black hole.
Ahmed Almheiri: Steel shot here is that the gravity patentable assigns a black hole a thermal entropy.
Ahmed Almheiri: and enhance it seems to suggest that a black hole has area of a 40 minute and number of degrees of freedom.
Ahmed Almheiri: And now, if we assume that a if we take the black hole to be a quantum system, then this result suggests that we should assign the black hole hilbert space of this dimension area over 14 years.
Ahmed Almheiri: Now.
Ahmed Almheiri: it's it's a it's a theorem in quantum mechanics that the whole moment entropy of a.
Ahmed Almheiri: quantum system is capped out by the thermal entropy of that system in this case, this means that the maximum volume and entropy the quantum black hole can have is the area over as the area of horizon divided by 14.
Ahmed Almheiri: Just some intuition and this theory it's just that the volume and entropy of identity matrix measures, the uncertainty you there is in the quantum state and the maximum uncertainty, you can have.
Ahmed Almheiri: is really just a total possible states.
Alejandro PEREZ: So I have.
Alejandro PEREZ: I have a question just.
Alejandro PEREZ: Because you're going to the Euclidean aren't you calculating the entanglement entropy of the outside only aren't you calculate something that has to do with the outside.
Ahmed Almheiri: So far, I did not to period in time when I interviewed so far I computed the thermal energy.
Ahmed Almheiri: And and best to get.
Alejandro PEREZ: But when you go to the acadian the this restricts yourself to the outside of a black hole which is the only place where this week rotation makes sense.
Ahmed Almheiri: sure.
Ahmed Almheiri: I agree, you can interpret this as saying that this is the thermal entropy of the black hole as you from the outside.
Ahmed Almheiri: i'm okay with thinking about it okay.
Alejandro PEREZ: Thank you.
Ahmed Almheiri: Okay.
Ahmed Almheiri: So the upshot so far is that the gravity pattern ago told us that the black hole again I see from the outside, to like has thermal entropy have given by the area of 4G Newton if we add this extra ingredient of saying that.
Ahmed Almheiri: quantum mechanics applies, then, then this would say that the following entropy of the black hole has to be kept up by the area over 14 years.
Ahmed Almheiri: Okay, but somebody else we know.
Maybe.
Laurent Freidel: And I.
Laurent Freidel: just remind me tomorrow agree with what you're saying, maybe just a point over when you when you saying you know we're perceiving that.
Laurent Freidel: There, but space dimension is is bounded by the area, maybe we'll do here is that in some sense this is kind of the project of quantum gravity will prove that and, and this is.
Laurent Freidel: This is what's hot right So if you are postulate that you can you can submit maybe it's good to acknowledge here that I mean there's an entire community of people that have.
Laurent Freidel: tried to address in what sense, you could make sense of that object from this, I can only go quantization number two vertical position, etc.
Laurent Freidel: That.
Laurent Freidel: Was it's kind of not, this is not skip it's a huge it's a humongous assumptions to do that, and it will be, you know, having a CEO of quantum gravity means understanding how that comes true.
Ahmed Almheiri: I more or less agree, however, what I would say is that the results from the gravity pathological is one data point towards that result.
Ahmed Almheiri: And that's that's basically the what i'm taking what i'm using so far.
Ahmed Almheiri: So, so the gravity particle so the thermal entropy is viewed from the outside and.
Ahmed Almheiri: That.
Ahmed Almheiri: If you were to believe that that is actually that that that really should be thought of as a thermal entropy.
Ahmed Almheiri: Then.
Ahmed Almheiri: Well it's really what I have on on this.
On this.
Laurent Freidel: The keyword uses belief and it's you know until you have a connection between more or less space and mechanical definition in the semi classical calculation.
Laurent Freidel: which you know are leaving to complete different room at the stage, so this is media where i'm pointing out is a point of.
Laurent Freidel: of convergence like if you were focusing on In what sense, these two stories have anything in common, then the two communities which are here, and can you know talk to each other and face the social problem, which is really to look for proof of this essentially will be.
Ahmed Almheiri: If I if I, if I can summarize what.
Ahmed Almheiri: I think, roughly speaking what you're saying is that what's what's the microscopic origin for this for this terminal entropy, for example, you can think of it like that maybe that's what you meant by.
Ahmed Almheiri: well defined the quantum states in a in a some sort of lauren TIM quantization of the theory that's fair, the only.
Ahmed Almheiri: From my from my side of the world in a Community that's been.
Ahmed Almheiri: Further evidence of this of this conjecture comes from you know counting micro States using the brains and so on, so forth, and string theory and maybe i'll learn some some other.
Ahmed Almheiri: Similar kinds of competitions from the loop quantum gravity perspective, maybe, as I, as I hear the other talks but i'd be happy to discuss this point more.
Ahmed Almheiri: During the discussion session.
Ahmed Almheiri: OK.
Ahmed Almheiri: So now black holes evaporate and they do so by emitting hawking radiation.
Ahmed Almheiri: As hawking taught us that there is this pure creation process that happens across the horizon, we have entangled pairs they get admitted and from the outside.
Ahmed Almheiri: It appears that the black hole just shrinks and gets well transforms into just.
Ahmed Almheiri: Is blue hawking quanta that i'm drawing.
Ahmed Almheiri: The option of the calculation is that.
Ahmed Almheiri: The being time and entropy of the outside world, if you will have all the radiation does grows with time.
Ahmed Almheiri: But there's an assumption in this in this calculation Okay, so this one i'm calling Hawkins assumption, there are two steps to this kind of condition, the first step is to.
Ahmed Almheiri: declare that the state of the radiation is what you get from a matter path integral on a on what i'm calling the black hole saddle so you first solve for.
Ahmed Almheiri: The classical solution for what the space looks like and then you evaluate the matter path and to go on that and that prepares for you some states.
Ahmed Almheiri: After you get the state of the of the matter, which is the state that I just described in on the previous slide you have hockey quanta outside that are entangled hawking quanta inside.
Ahmed Almheiri: Then you compute the entropy of the radiation outside okay so i'm going to call this the hawking interview so it's basically just equal to the matter entropy of the radiation outside.
Ahmed Almheiri: In equations rocky speaking it's it's what i'm saying these two points are what I have here at the bottom you first there's some density matrix, which is a density matrix of.
Ahmed Almheiri: Its density matrix of the matter in some gravitational cycle and then the way you complete the entropy is that you, you take this density matrix of the matter in the gravitational subtle and you plug it into the usual formula for entropy trace romar grow.
Ahmed Almheiri: And when you do this, you get in well as I just said, the entropy just grows with time for all time that's the hawking answer now, the issue is that.
Ahmed Almheiri: The thermal entropy of the black hole again as you turn the tide.
Ahmed Almheiri: Just decreases with time until for all time until it goes to control it goes down to zero.
Ahmed Almheiri: And Hanks after these two lines cross there seems to be a problem.
Ahmed Almheiri: In particular, and this would predict well first it looks like the black hole is getting the this is this is inconsistent with the.
Ahmed Almheiri: With what we said about how quantum black holes should behave in particular about the number of States here, it says that a black a small black hole can be can have.
Ahmed Almheiri: can be entangled more than it's then it's thermal state case okay can be entangled the amount of entanglement can be more than what the black hole has room for.
Ahmed Almheiri: And so what this says is this makes a prediction, which I think is a very serious problem it predicts that in.
Ahmed Almheiri: In this theory that you can have light objects, with an arbitrary number of.
Ahmed Almheiri: Internal states okay arbitrary large number of internal states.
Ahmed Almheiri: Okay, because you know it's the black hole becomes very, very small here it's entanglements can be very, very low.
Ahmed Almheiri: Okay.
Ahmed Almheiri: And after the black hole disappears completely again, it looks like.
Ahmed Almheiri: black hole formation evaporation can take a pure states and star into a mixed state of the radiation and this evolution is not unitary.
Ahmed Almheiri: I can ask why is this a paradox well it's a paradox, because so far, it seems that a set of trusted assumptions lead to unpalatable conclusions, in particular, it looks like.
Ahmed Almheiri: One perspective, you can take is that quantum mechanics broke down you've evolved a pure state to a mixed it that's one perspective, you can do.
Ahmed Almheiri: Another perspective is that it's it's.
Ahmed Almheiri: it's address again, do you have these low mass high entropy objects and then there's then there's one here, the question is where are those high degeneracy small mass objects why didn't we see them yet.
Ahmed Almheiri: there's old work by Steve getting that says that you should have seen these.
Ahmed Almheiri: You should have seen signatures of these subjects and identity, for example.
Alejandro PEREZ: Okay, my question for maybe this is a question for later, but as you agree that the beginning, your your.
Alejandro PEREZ: Account concerns the exterior of the black hole So how can that be the full story of what is going on, when you never say anything about what happens with with what falls into the singularity.
Ahmed Almheiri: Well, the quick answer to that question is just um.
Ahmed Almheiri: Well, first let me ask you a quick question are you are you.
Ahmed Almheiri: what's your comment about the second point here or just about the entire thing.
Ahmed Almheiri: But apparently.
Alejandro PEREZ: it's about your assumption.
Alejandro PEREZ: That you agreed, I mean they understood you're telling a story from the outside, only all your story is about the radiation outside and the size of the black hole becoming smaller a scene from the outside.
Alejandro PEREZ: What about everything, I mean you're hawking pairs that fall into the singularity without saying anything about those, how can I know i'm not missing something really big.
Ahmed Almheiri: that's that's that's fair but but I don't think that changes anything i'm saying on this in this slide in particular.
Ahmed Almheiri: This is that, from the from i'm not making a statement about what physics looks like for a person on the outside it either looks like quantum mechanics broke down.
Ahmed Almheiri: Okay, or it looks like there are met, there are these high degeneracy small mass objects, so what i'm saying is that independent of what happens on the inside.
Ahmed Almheiri: If we're saying that Hawkins answer.
Ahmed Almheiri: is unchanged from the perspective of the outside, then you have a problem.
Alejandro PEREZ: Okay, I don't agree with that.
Alejandro PEREZ: Because they don't say anything about it.
Alejandro PEREZ: But Okay, we can yeah I can stop sorry.
Jorge Pullin: yeah.
Abhay Vasant Ashtekar: I think we should let him finish, because it is a time for discussion.
Laurent Freidel: But maybe before I think, if I may say something you say trusted assumption, I think it really depends on which Community, for instance, one assumption which people make.
Laurent Freidel: Is the assumption that the space is split there is, it can be split into utensil product, and if you.
Laurent Freidel: Are quantum gravity's you know that this is wrong, that is, we know that this assumption is not valid i'm not saying that it resolved or the paradox, but.
Laurent Freidel: What is clear is that inside on these products there's already an assumption that we know is not valid, which is essentially.
Laurent Freidel: The assumption that the image and constraints, you know which is military constraint is not taken into account.
Laurent Freidel: so that you know you have to say so, you know in relieving that assumption doesn't mean you're breaking of quantum mechanics it means revisiting the solving in the light.
Laurent Freidel: Of the fact that the space is not split between the Interior and exterior, would you agree with that that would be, it will be less dramatic statement which is is more accurate reflection of you know, the proper knowledge of we have about quantum field theory, in addition to.
Ahmed Almheiri: Okay, let me, let me say two things, the first is that I don't trust the assumptions Okay, so this is trusted sort of in the past, if you will.
Ahmed Almheiri: or said differently.
Ahmed Almheiri: It it's the trusted here is that this.
Ahmed Almheiri: Is that.
Ahmed Almheiri: Well, let me just get this out of habit that I don't trust this the assumptions made to four second point is that, yes, I mean there's also.
Ahmed Almheiri: A comment also touching on the previous question that the inside, is important, I agree, and I, I do agree that hilbert space on the inside, and the outside is not split but.
Ahmed Almheiri: I think it doesn't fit for for different reasons not not not for this, not for the usual reason reason of just.
Ahmed Almheiri: Because of hamiltonian constraint and so on and so forth, as far more solid reason which i'm which I will get to in a second and how these are great questions, but we should leave them for me.
Jorge Pullin: yeah folks we're at 20 minutes now, so we should let me finish.
Ahmed Almheiri: Okay, thank you okay so so far, this is the the what we saw so far, the promise of.
Ahmed Almheiri: gravity path also predicts a black hole evaporates it's on the path and go because it comes from the quantum fluctuations about the saddle and that leads to the bottom of entropy being larger than the area of a 14 year 10.
Ahmed Almheiri: At some point in the evaporation but then this this conflict with the other with the the other constraint that we found from quantum mechanics.
Ahmed Almheiri: And so that you can ask what is the weakest link, so you can see that maybe quantum mechanics are not apply it just breaks down.
Ahmed Almheiri: And that would that would imply that that thermal entropy is not a bound in the form of an entropy or you guys a quantum mechanic does this continues to apply, but then you just have some other reason for why volume and entropy is not bounded by federal entropy.
Ahmed Almheiri: um I think this is too drastic I think it's I think it's just that this calculation is wrong, like it sometimes the resolution that i'm sort of advocating for is that.
Ahmed Almheiri: This resulted, that the volume entropy is logged in the area code just comes about because because of some mistake in a sense.
Ahmed Almheiri: Let me first tell you the answer and then i'll justify it.
Ahmed Almheiri: The answer is that there's there's simply, this is a new formula for computing the entropy of the of the radiation which comes from the gravity pathological nothing, nothing.
Ahmed Almheiri: Like nothing new has been pulled out of a hat.
Ahmed Almheiri: And the formulas to follow it so there's a new contribution from the gravity pattern ago.
Ahmed Almheiri: When it says today is that there are two possible formulas that you can apply to compete, the entropy of the radiation, the first is what hawking applied just the entropy of the matter outside that's just a standard formula.
Ahmed Almheiri: And another formula is what i'm going to call the the island formula for the entropy it says that the entropy of the radiation outside is not just the entropy of the outside mode.
Ahmed Almheiri: But it's the Union of the entropy of the outside, along with some region inside the black hole called the island which i'm going to call the island so it's a matter entropy of the radiation Union island, plus the area of the boundary of the island okay.
Ahmed Almheiri: So far this island is not picked it's not just an arbitrary place in the interior of the black hole but it's fixed by some condition the condition is that the surface X extra Mises this functional here, which is sometimes called the generalized entropy functional.
Ahmed Almheiri: So, giving some radiation outside of you want to compete, the entropy all you have to look for the island with extra Mises this.
Ahmed Almheiri: And then.
Ahmed Almheiri: Another what the prescription tells you again from the gravity article is that the actual entropy of the radiation is the minimum between these two contributions between the hawking answer and this new island answer.
Ahmed Almheiri: Well, the hawking answer we saw it just grows with time, while the island answer it turns out that.
Ahmed Almheiri: The matter entropy term though the radiation Union island is actually a small number it doesn't do anything really.
Ahmed Almheiri: The radiation basically because all of the radiation outside is purified by the radiation and the island, so this is just some small number.
Ahmed Almheiri: And the dominant piece comes from the area of X, which is actually very close to the event horizon and since the black hole is shrinking This gives you a number, this is just a decreasing function of time which traces the thermal entropy of a black hole.
Ahmed Almheiri: Taking the minimum between these two tells you that the interview would rise initially and then come back that and.
Ahmed Almheiri: So you get the page and it transitions will this transition is sometimes called the page.
Ahmed Almheiri: And hence the thermal entropy bound is satisfied.
Ahmed Almheiri: And the way you get to this formula is by relaxing Hawkins assumption, so how about hawking did was that he computed the density matrix of the matter where you first you.
Ahmed Almheiri: You restrict to the quantum state on the givens on the black hole Seidel, then you take a dense matrix and you plug it into terrestrial mongrel we went over that.
Ahmed Almheiri: The new method says hang on this is you can't do this prematurely Okay, so you cannot take the density matrix of the outside and just plug in a saddle what you have to do is first.
Ahmed Almheiri: write down the function for the entropy trace role or grow where row is the fourth density matrix and then consider several points.
Ahmed Almheiri: Sarah point evaluation of the full function here of trace logo.
Ahmed Almheiri: And when you do that, you find that there are various contributions is a contribution coming from the hawking silo and there's a contribution coming from the island sorry.
Ahmed Almheiri: Is that there's a one title font is the hottie answer and there's another style font which gives you the island answer.
Ahmed Almheiri: For the experts this, so the entropy You can write it, you can you can complete it by using this replica trick we take row to the power of N, the question is whether you take expectation what.
Ahmed Almheiri: Expectations are here I mean you, you plug in a gravity saddle then race to the end, or you take the gravity cycle of em copies of this system.
Ahmed Almheiri: The The thing that this the second term gives you is that you can have a wormholes that connect them with the different copies Okay, when you have multiple copies in sharepoint can connect with different companies.
Ahmed Almheiri: And so.
Ahmed Almheiri: What what you then find is that.
Ahmed Almheiri: When you do this, that.
Ahmed Almheiri: You you do end up satisfying this the development entropy is bounded by the thermal entropy and, in essence, we didn't need to assume quantum mechanics anymore.
Ahmed Almheiri: What we're finding is that the gravity pathological itself consistent by itself, the answers that it gets are consistent with quantum mechanics we don't need to impose this condition.
Ahmed Almheiri: And I was going to give a very brief.
Ahmed Almheiri: example very simple and brief example for this effect of how we're almost coming to fix things, but if the.
Ahmed Almheiri: organizers feel that I went to for every time we can go to the next talk should I keep going.
Jorge Pullin: Just the more I haven't read more than 20 minutes now.
Jorge Pullin: 25 actually.
Ahmed Almheiri: So so deep So do you want to skip this last part or.
Jorge Pullin: move through it as quickly as you can.
Ahmed Almheiri: Okay okay so um Let me give you the quick a quick example of the House so let's let's consider a abstract version of a completely evaporated Michael so here's oops sorry.
Ahmed Almheiri: He should think of time going upwards, and the black hole so in some sense detached from the space time again, this is a cartoon.
Ahmed Almheiri: And inside, so this this this thing that branches off of the universe we're calling that the Interior and these blue this blue line is supposed to represent.
Ahmed Almheiri: hawking particles inside entanglement hockey particle outside now let the abstract this abstraction in terms of this picture Okay, so this picture is again the black hole detaching from our universe and there's entanglement between inside and outside.
Ahmed Almheiri: suppose you want to compute the not the entropy but the purity which is trace row squared of the outside Okay, the exterior density matrix is given by taking the state.
Ahmed Almheiri: Cat bra then tracing out interior, what does tracing out meet it means that you're attached interior using gravity pathological.
Ahmed Almheiri: Now, when you compute terrestrial squared you have to multiply two matrices by.
Ahmed Almheiri: Just multiply the students matrices and that's this cross contraction here and I have two factors of the gravity path indigo for the inside.
Ahmed Almheiri: Now you let the gravity path and go do connect in all possible ways one possible ways to trivial way we just connect on this point at this point.
Ahmed Almheiri: And this gives you this picture here, which is, which gives you an answer for the purity of just want to recap, a it tells you that the outside is mixed.
Ahmed Almheiri: However, there's another connection that you can have where where the bra on one side can can connect to the cat, of the other that's that's that's a so called replica wormhole.
Ahmed Almheiri: contribution which can be rearranged to just two factor eyes to be just this, which is just trace rope all squared and that's that's just equal to one, so this new contribution tells you that that the purity.
Ahmed Almheiri: That the outside is actually pure and that's a good approximation when K is marked.
Ahmed Almheiri: Okay, so that's pretty much all I had to do some final comments.
Ahmed Almheiri: The origin of the.
Ahmed Almheiri: The gravity pattern or give us an answer, consistent with the central dogma.
Ahmed Almheiri: The origin of the area terms of resolving the island, because the same as what you get from given talking it's like the it comes from the Ukrainian section of the pathological on the horizon.
Ahmed Almheiri: And just with given talking there's no microscopic understanding and final point is that the gravity pathological is good, it is good at computing numbers, like the entropy but it's not as good as is not good at.
Ahmed Almheiri: Writing down the exact state of the hockey radiation that's pretty much everything I had Thank you.
Jorge Pullin: Thank you, please, don't share your screen.
Abhay Vasant Ashtekar: So while i'm sharing the screen, I can just ask a quick question.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: Is it the case that the island knows about insight, you know in some sense, you were always outside, but the island know something about the inside the black hole.
Ahmed Almheiri: um yeah, so I would say slightly differently, I would say that.
Ahmed Almheiri: The radiation, so when you consider the entry to the radiation it had a contribution from the island from the inside the black hole which was important for the to get the right answer What this means is that the radiation knows about the inside.
Ahmed Almheiri: Given that the entropy of the radiation dependent on the inside panted knows about the inside, and I didn't have time to talk about this, but you can actually show how actions on the radiation can actually modify the state of Interior, let me keep it at that.
Jorge Pullin: Thank you, thank you let's go to the next speaker of is digger.
Abhay Vasant Ashtekar: So what I would like to do is just have.
Abhay Vasant Ashtekar: provided.
Abhay Vasant Ashtekar: A broad perspective from lt from look on guy we decide, and I think that I hope that we can make connections with automobiles you're saying and and have some discussion on that as well.
Abhay Vasant Ashtekar: So I am but, and so what i'm trying to do here is the.
Abhay Vasant Ashtekar: How does general consensus just come from many, many researchers and the body market larger taken from this particular review article about from about a year ago slightly less than a year ago.
Abhay Vasant Ashtekar: OK so.
Abhay Vasant Ashtekar: Let me start with a preamble as to what I would like to.
Abhay Vasant Ashtekar: communicate.
Abhay Vasant Ashtekar: I think that there is a broad consensus in between LPG about two points, one is that for this black hole quantum black holes that two things that are really important one is singularity resolution, which I think is something that is ignored in many other approaches.
Abhay Vasant Ashtekar: And the point in from Luke kind of cosmology, we know that there are many, many examples in which the singularity result.
Abhay Vasant Ashtekar: And that is reserving space, time is then much larger than the classical space time that we started out with, and then the quantum state can evolve to the blank reggie all the way to scribe plus in this larger space that.
Abhay Vasant Ashtekar: I will, what I want to emphasize that we didn't look on gravity details of how to describe plants can physics in the black hole context are still work in progress, there is a word in very different directions and i've only instead some of the major contributions appear.
Abhay Vasant Ashtekar: But they all sort of point to the fact that the singularity.
Abhay Vasant Ashtekar: are buying to the don't have one thing in common, which is singularity resolution, and that is that our results would say that's in you, that is resolved with varying various degrees of assumptions and approximations.
Abhay Vasant Ashtekar: And the second thing is really irrelevant notion of.
Abhay Vasant Ashtekar: The main point here is that there are no event horizons and, as I will see in some more and more clearly what forms and evaporates and dynamic of horizons and these dynamical horizons a timeline during the evaporation process.
Abhay Vasant Ashtekar: And lot of confusion can arise because of explicit or implicit assumption that there's an absolute event horizon, out of which nothing can come up.
Abhay Vasant Ashtekar: As a result of these two things the black hole you operation can unitary without having been invoked various.
Abhay Vasant Ashtekar: To us exotic idea, such as the long time ago quantum Xerox machine and, more recently, fast gamblers and little bit in between the two firewalls etc, and also one does not have to worry about this whole issue about quantum Baraka.
Abhay Vasant Ashtekar: I must start, I will not discuss full card number gene.
Abhay Vasant Ashtekar: But already there is some tension at the semi classical Virgin, which was hinting at by month, so I would like to address that.
Abhay Vasant Ashtekar: And I will summarize LPG viewpoint on this tension so first I like to explain what was in these first two points appear they'll hugely viewpoint up here and then the semi classical or iijima.
Abhay Vasant Ashtekar: So again, let me just begin with the Hawkins argument, just like what am I did I started with hawking's argument using Euclidean part, integral and i'm talking here about the lorenzen space that.
Abhay Vasant Ashtekar: So in the external feel approximation, this is was hawking's original original calculation.
Abhay Vasant Ashtekar: There are three assumptions one is that one users can refuse to give up on a black hole background space time and approximations or assumptions are the space, time is to get classically.
Abhay Vasant Ashtekar: The test quantum field is really a test on the field, so they know back reaction on the condom geometry.
Abhay Vasant Ashtekar: And the matter field collapses is a classical and is distinct from the desk on the field consider.
Abhay Vasant Ashtekar: So year that typical sort of idea, the status collapsing and studies never considered as part of a system.
Abhay Vasant Ashtekar: What one is looking at is really giving some scale if he loves guy minus evolving it and see what happens, what happens on a on a purchase and things like that, and what happens in a plastic, which is if it's like that, and what happens on Skype list as a whole.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: If you want to include back reaction, then.
Abhay Vasant Ashtekar: This really is to address the second part.
Abhay Vasant Ashtekar: I want to emphasize that there is no detailed calculation, you went today about including a bank reaction and hawking just drew this diagram and this diagram really did not come from any detailed calculation, I want to emphasize that, because it is often forgotten.
Abhay Vasant Ashtekar: This is the general expectation that is based on the physical body weight their jurisdiction that lead hawking to propose.
Abhay Vasant Ashtekar: That the space time diagram should be like that, basically, the strength of the singularity decreases, if you like, as a black hole shrinks and.
Abhay Vasant Ashtekar: Then the and then, finally, the blackboard string so people say, well, I don't know what happens here, but, in the final picture, there is really an absolute born boundary.
Abhay Vasant Ashtekar: And in one of the elements slides, even though you're talking, most of the time, the premium domain it looked like there was also an absolute boundary of here and things though particles were coming out or falling in outside at Bob boundary.
Abhay Vasant Ashtekar: Because of future boundary include space to improve the singularity.
Abhay Vasant Ashtekar: I think the statement is that the state, the state on sky minus does determine state on Skype Plus, but the converse is not true, or the state on Sigma one will determine state and save my final appear.
Abhay Vasant Ashtekar: Sick my initial determines the Conversely, I cannot give me you want this backward in time here.
Abhay Vasant Ashtekar: and
Abhay Vasant Ashtekar: I can change his mind about this diagram and, in fact, the new diagram their proposed nursing unity, but surprisingly, the Orient original diagram is still very heavily used.
Abhay Vasant Ashtekar: In many, many of the arguments, and it is still a shoe that for that the correlations should all be restored before this last Ray which is called the the US of the event horizon.
Abhay Vasant Ashtekar: Because this is the future boundary of the past of infinity and that statement is that interesting July dissolve This assumption is just wrong and this really, for example, all the things about.
Abhay Vasant Ashtekar: quantum monogamy are really deeply rooted in this assumption because idea here is that yoga some party of going out his partner is falling in if you are the restore purity then something else will come out before this year.
Abhay Vasant Ashtekar: If there is no singularity then things can come out after this the partner, the partner, more could just come out and in the larger space time and therefore there's no issue about monogamy information does purity does not have the video store right up to here.
Abhay Vasant Ashtekar: So again, the last quickly against in United is illusion and, as I just mentioned, that Hawkins take two in the in the papers, with a Pope and strong and strong measure that I vidyo singularity.
Abhay Vasant Ashtekar: But this diagram is still used by others, very much and it looks awesome guy with his expectation is amazed making what I do models that I was just mentioning before, so the kind of diagram that one expects and book quantum gravity is a diagram like that yoga squared minus.
Abhay Vasant Ashtekar: And then, again in this diagram is a problem that start is not part of the system, so in look on gravity would like to consider the.
Abhay Vasant Ashtekar: collapse occurring because of some skis collapse of the same scale of field and gravity plus Gala field is a proper system, so we got a closed system up here and so these are the tick Shell some notion, if you like, which false and then five form some classical to just follow black hole.
Abhay Vasant Ashtekar: But what really happens is that there is a dynamic and horizon an article horizon he just a word to Bob.
Abhay Vasant Ashtekar: For two spheres, each of which is a modular track surface and so the dynamic and horizons transforming here.
Abhay Vasant Ashtekar: At the Left end of this of this profile of the of the collapsing matter.
Abhay Vasant Ashtekar: And then it grows, so this dynamic horizon is black line and it actually grows it's difficult to see here this because I think I should have drawn this ticker and then the statement is.
Abhay Vasant Ashtekar: True, that wrong sorry I should have done this ticker and then you're grown much more clearly.
Abhay Vasant Ashtekar: It groans grows and his face like in this thing and then it becomes paying like during the time when the black hole is actually evaporating.
Abhay Vasant Ashtekar: And if the singularity is actually result, then you would have a trap region appear and anti trap region appear, and then the statement is that the more school just come up, I mean the statement is a partner most which failing should just come out up here.
Abhay Vasant Ashtekar: done a lot of open work that is going on is about completely condom region and we can talk about it.
Abhay Vasant Ashtekar: Okay, so the expectation is really that.
Abhay Vasant Ashtekar: First of all, the important thing is to consider that the dynamical horizons and then the expectation is that.
Abhay Vasant Ashtekar: That the classical singularity will be resolved and will be replaced by genuinely contemplation and correlations between the most which went out at infinity.
Abhay Vasant Ashtekar: In during the hacking radiation can be restored, because of partners could go through, and really uptown appear, and so they don't have to be restored before this last Ray before the last way appear some area in the semi classical reggie.
Abhay Vasant Ashtekar: So now, let me go to the second part, which has to do the semi classical regime.
Abhay Vasant Ashtekar: And I want to say now don't forget about really the singularity and this part has nothing to do with the single idea resolution or with whole.
Abhay Vasant Ashtekar: Finally, the purification complete takes place but there's an issue already at the stage that was already hinted at and that I would like to consider.
Abhay Vasant Ashtekar: So I really had the space time appear in the semi classical regime so i'm not wearing the entering the condom.
Abhay Vasant Ashtekar: regime at all so here is a game in which, for example, the black hole is shrunk but the size of a million times plant plant a billion times plant plant and therefore you know we can just assume that I got semi classical.
Abhay Vasant Ashtekar: In fact I would consider explicitly a solar mass black hole to just go to lunar mass and I think most everybody in the audience who probably agree that this really is macroscopic and semi classical physics should actually hold.
Abhay Vasant Ashtekar: And so the idea here is that there is a time you, which is green up here, I hope you can see, this time, great in green appear.
Abhay Vasant Ashtekar: And the statement is that a deed is really started the syllabus and by this time it has really acquired the Lunar mass, the process is should be well described by a semi classical gravity.
Abhay Vasant Ashtekar: And this process of our tech something like 10 to the 64 years, and so a large number of moore's escaped infinity during this time, and the total state on this.
Abhay Vasant Ashtekar: The total state on Sigma appear, first of all, was pure and historical state on the manifold like that is also pure because you know, the more which are outside are correlated with the Boards with an inside.
Abhay Vasant Ashtekar: So in this region, I got a flat regional space time before the Shell collapses, then I got the Korean appear I got radiation which is coming in.
Abhay Vasant Ashtekar: And radiation which is falling in and releasing which is going up so inside I had not only the radiation which is falling in the partner mode, but also the radiation which made.
Abhay Vasant Ashtekar: The black hole, and this is often ignore the the total state which is pure if you include what failing, plus the what is.
Abhay Vasant Ashtekar: What caused the collapse, plus the partner mode, which are failing and the partner mode and and the model which goes up all the three together will give you a pure state on this, and then the statement is that the problem state appear will appear.
Abhay Vasant Ashtekar: So the updated information parallax, however, is still there, which is that.
Abhay Vasant Ashtekar: This process takes about 10 to 64 years and just back up the envelope heuristic calculation will say that there are a lot of moore's which are actually emitted appear to infinity during this time and see even if the state is pure.
Abhay Vasant Ashtekar: There is an apparent still information parallax, namely the Lunar mass black hole has radius of only point one millimeters so period is only point one eight millimeters and the masses about 10 to the minus seven times the quarter mass.
Abhay Vasant Ashtekar: Now the radiation which went out these boards are calling about solar mass solar mass minus 10 to the minus seven times so otherwise invalid.
Abhay Vasant Ashtekar: And what is it inside is only 10 to the minus seven service solar masses, so they let you budget, so, in fact, all these more Sapir are going to be correlated the more Sapir.
Abhay Vasant Ashtekar: Then there's a shoe on my thing that there is an energy by your problem, because I got so much more energy here than in here.
Abhay Vasant Ashtekar: Are in terms of.
Abhay Vasant Ashtekar: More in terms of boards that we looked at here I got a black hole or the I got a dynamical horizon radius is the only about one millimeter point one millimeter up here.
Abhay Vasant Ashtekar: And in fact I got more violent point one millimeter mode is realistic, then, and then I allow the maximum wavelength, which is about point one millimeter because that's what I think is the maximum size here.
Abhay Vasant Ashtekar: Then the master be about 2010 to the 22 times Luna master is the same argument that the energy budget here does not seem to be appropriate to really account for entanglement with the Boards which went on.
Abhay Vasant Ashtekar: And therefore, the idea here is that.
Abhay Vasant Ashtekar: The put differently, the horizon area should account for the total entropy of everything that is consistent considered contained inside the horizon, and this is way too small competitor and property associated with warm water went out.
Abhay Vasant Ashtekar: and sought This suggests that a significant amount of purification should take place before this time before the Lunar module the thing.
Abhay Vasant Ashtekar: And this general belief is enshrined in the face scrub that restoration of correlations to start begin at the base time in the black hole is shrunk only to have the mass and not the Lunar month, he.
Abhay Vasant Ashtekar: Does he places something goes wrong with the usual space time semi classical picture, even when the black hole is macroscopic even vanity shrinking from half of its solar mass to the.
Abhay Vasant Ashtekar: The lunar month, but I would like to say that in fact there is noticeably there is no problem at all, there is a simple resolution.
Abhay Vasant Ashtekar: And the simple resolution is that when when evolves the semi classical equations I will use a semi classical you equation one saws them inside the vision appear.
Abhay Vasant Ashtekar: One finds the region, which has been closed for the dynamic and horizon, one finds that what happens is that this is a very slow dynamics appear that is happening because of the unfolding radiation, which is very slow between the time that the black hole is.
Abhay Vasant Ashtekar: Then, to the 64 years is what it takes maybe when a black hole is.
Abhay Vasant Ashtekar: Solar master black hole that is Luna mass up here, but during this time, these surfaces that I did the surface, as I got appear.
Abhay Vasant Ashtekar: You can take them to be coachable you could scale up equal constant surfaces or I can just take it to be R equals constants surfaces is all spiritual symmetric.
Abhay Vasant Ashtekar: And when I can actually solve the semi classical equation and show that these surfaces devil up astronomically long next intend to the 64 years and stretching some tend to the 62% 64 years up here.
Abhay Vasant Ashtekar: And therefore, the radius appeared is only point one millimeter but inside, in fact, these are extremely long.
Abhay Vasant Ashtekar: And so the slow dynamical evolution in the semi classical phil's been falling one more to get stretched.
Abhay Vasant Ashtekar: Roughly like what happens in inflation, except that this is even much, much more conservative because inflation this happens very quickly here, the text into the 64 years, and therefore the becoming for right and we can easily accommodate and have them inside the dynamic and.
Abhay Vasant Ashtekar: Once we do this.
Alejandro PEREZ: sorry about I have a comment on this, this is true, if you take frequency metric modes, if you take modes with angular momentum, then they get because you get an infant contraction in the transverse direction, then you don't get the symphony redshift.
Abhay Vasant Ashtekar: OK so i'll talk about that, just a day okay so let's just let's consider the sense but it gets the.
Abhay Vasant Ashtekar: magic box one moment, so that, so the state is that there are enough boards in order to be put my argument that.
Abhay Vasant Ashtekar: That there'll be no problem.
Abhay Vasant Ashtekar: we'll talk about the other one in.
Alejandro PEREZ: The radiation, the Organization has the modes without not.
Abhay Vasant Ashtekar: Yes, so so.
Alejandro PEREZ: In fact well.
Abhay Vasant Ashtekar: Right so.
Abhay Vasant Ashtekar: that's why I got myself in semi classical region i'm not telling about what is happening as you approach the singularity please wait until the last boss like.
Abhay Vasant Ashtekar: Once we replace the.
Abhay Vasant Ashtekar: The statement is that one can use it like how many these boards once we replace the event horizon dynamical horizon and study the back reaction.
Abhay Vasant Ashtekar: When space time geometry inside the dynamic and horizon that tension with information loss and semi classical rich in the semi classical region disappears.
Abhay Vasant Ashtekar: And there is no reason for the semi classical arguments, not to be valid for doing their math backwards, I think alexa would agree with.
Abhay Vasant Ashtekar: These statements, what happens before beyond semi classic ality is what is being debated, but in the semi classical regime, I think one would agree with this.
Abhay Vasant Ashtekar: That there is no there's no there's no paradoxically, in fact, that it better be the truth, because we know that the state of fear is is pure and therefore the statement is that these more switch paint out should be correlated with more which I went in, and they should be no problem.
Abhay Vasant Ashtekar: But then don't do we have long live gremlins, and this was alluded to to about Steve getting's.
Abhay Vasant Ashtekar: With lot of internal states, first of all I would like to say that this would happen long lived in the remnants of this time.
Abhay Vasant Ashtekar: Or are there already in the back, page time when the black hole a strong, to have the solar my side, I agree that this reminisce then would have a look from outside, with a size up about a kilometer but for him.
Abhay Vasant Ashtekar: For this lunar mass, it will be point one millimeter and I can shrink it down even further and make it in a point.
Abhay Vasant Ashtekar: And astronomy for life, so they will be there are kind of small microscopic objects which is completely the semi classical regime which have.
Abhay Vasant Ashtekar: Long which are lots of mods and this highly entropic objects is really not not an issue at all, and the reason for that is that such objects can exist, but to develop their astronomic a long, long legs.
Abhay Vasant Ashtekar: They need 62 to 64 years to grow, and they cannot therefore be instantaneously created in the particle accelerators or calculations.
Abhay Vasant Ashtekar: So I don't most of us don't agree with his arguments about effective field theory and we can discuss about.
Abhay Vasant Ashtekar: So let me just summarize that many of the look what i'm guy with using it seems that several of the standard difficulties disappear if one recognizes that this that this that in the classical GR.
Abhay Vasant Ashtekar: Already the event horizons are useful very useful idealized idealized notions, but they are not very useful to analysts actual physical processes.
Abhay Vasant Ashtekar: For example, the event horizon can form and grow in flat reaches of space, time is explicitly shown, for example in the white space so use of this event horizons as absolute boundaries for the entire evaporation process causes unnecessary confusion.
Abhay Vasant Ashtekar: And the second thing is that there's no reason to abandoned semi classical guy with the veil away from the plank regime.
Abhay Vasant Ashtekar: And one has to carefully study the geometry inside the dynamic of horizon and a very interesting I haven't used to understand the relation between this semi classical description and the recent part into lana's.
Abhay Vasant Ashtekar: That might just told us about up at a certain level I don't see a contradiction because i'm not saying that the entanglement entropy is.
Abhay Vasant Ashtekar: there's something incorrect about the entire entanglement and probably being large I think i'm always saying that one to really be calculating or different kind of entropy in order to.
Abhay Vasant Ashtekar: To to understand the pacemaker and perhaps also if you actually way to make measurements in your scribe This is something that doesn't matter from knoxville Henry Max will argue the new notion of entangle entropy might be more appropriate and it also uses.
Abhay Vasant Ashtekar: Investigation the singularity dissolve and is replaced by position surface that separates the trap region from an entity region.
Abhay Vasant Ashtekar: And however, none of the investigations in lukewarm gripe is complete and there is no unanimity nanometer on exactly how the correlations really stop now there's one recent result, and this is not fully, but this is going towards addressing what.
Abhay Vasant Ashtekar: Alex was talking about, namely that one can actually consistently evolve, the test contact fields even across singularities including all the wars, the non spiritually symmetric boards.
Abhay Vasant Ashtekar: And the team you knew that he normalized the meaning of such boards continues to be well defined distributions just like very well defined distributions away from the singularity and this analysis provides.
Abhay Vasant Ashtekar: US for technical tools to rival the nature, the nature of space time satisfying quantum einstein's equation.
Abhay Vasant Ashtekar: across what are the classical singularity so let me stop you.
Jorge Pullin: Thank you about it please and share your screen.
yeah.
Jorge Pullin: So let's move on to our third speaker already please share your screen.
Carlo Rovelli: Coming writing.
Jorge Pullin: Or if it go ahead.
Carlo Rovelli: Okay wonderful.
Carlo Rovelli: Thank you, how to get some of you have read since goodbye.
Carlo Rovelli: we're a bit late so i'll try to be shorter, or I think I can stay less than 15 minutes, I want to make three points.
Carlo Rovelli: about the topic we've been discussing, which are these three.
Carlo Rovelli: The first one.
Carlo Rovelli: refers directly to the difference between what's happening outside and what the bicep it's a two different pictures here and I.
Carlo Rovelli: To me it seems that the picture that I presented this it's.
Carlo Rovelli: physically reasonable.
Carlo Rovelli: But if so after that presented a very strict series of deduction that forces us away that, so I want to point out where I see the confusion comes in, in a very specific point.
Carlo Rovelli: And therefore, and this is, I think, is before the central dogma assault will come after it's the same phenomenon itself that it's a it's wrong.
Carlo Rovelli: Then I will sort of go a little bit more in the picture what happened to black hole and argue the second point that the problem of what happened to black hole Sir.
Carlo Rovelli: it's actually three different physical problems and we met a separate the three i'll show what I mean and then, very briefly, the third point I will illustrate what I think it's a.
Carlo Rovelli: The scenario that seems more likely to me, which is in the general framework, the by a by mentioned and, of course, as I said, nothing is certain and sure and complete in this in this story, so let me start by by the first point.
Carlo Rovelli: Central dogma is a full stock Missouri for the Italian all here should be any false doctrine.
Carlo Rovelli: And I think in in the full story is that the number of internal internal says the full number of states of black hole real black hole I say in a moment, why I insistent real.
Carlo Rovelli: it's bounded by the rice on area and echoing a little bit What about is gonna say i'm just going to sharpen what by.
Carlo Rovelli: said this comes from a number of confusion, the key one is exactly the confusion between event horizon and.
Carlo Rovelli: dynamical arise or trapping arise on whatever you want to call the the fuzzy local definition of their eyes on that doesn't require to go to the far future which is related to the last of my points you're stationary evolving black holes if you assume, to start with.
Carlo Rovelli: That black hole is forever like the diamonds and, therefore, that is sort of something like a sharpshooter black hole forever there's an event horizon, then you do the calculation for its.
Carlo Rovelli: entropy, which is the one and a half minute did, which of course is correct and you get the terminal into the black hole which of course is correct.
Carlo Rovelli: And that's a black hole that's a terminal and entropy that governs what the enterprise about Heaton work exchanges for something.
Carlo Rovelli: So this is the hidden market changes with a black hole for somebody outside interacting with black hole as long as it stays in this approximation and block, it is.
Carlo Rovelli: described by an effective event horizon so before it's evaporate we operate is also the station or any book we go out for this a punctuation which are guy from this regime something else happened, and then, as I was arguing between the moment.
Carlo Rovelli: It is the full stop may tell that let's do the page curve and to all the survey said values many tentative of sort of go around and justify the page curve.
Carlo Rovelli: which I believe a lot justified the main confusion is between 2 million empirical phenomena and probably so allow me just many of you are this is completely obvious with.
Carlo Rovelli: My leaders to remind what the two are for lyman entropy when you have to system say MB.
Carlo Rovelli: A pure state of the two system, so I A and B you trace of a B you get, of course, the density matrix of the a system, you can see the standard entropy, and this is different from zero because there's information in be that you're not looking at.
Carlo Rovelli: The monocle entropy.
Carlo Rovelli: In the simplest, most when picture recounts the dimension of the face space which in quantum mechanics kinds the log into the dimension.
Carlo Rovelli: So far, so good, and then Asp net computed the terminal claim to be a shorter black hole and he got a number which will agree with them.
Carlo Rovelli: And then, he said, careful and, of course, the following man entropy.
Carlo Rovelli: Is bounded by the thermodynamic going to be, because, of course, you cannot have a larger dimension, you cannot have more end to be from here, then how big is the MySpace and be seems obvious right and that I just copied it from earth made the.
Carlo Rovelli: slide slices here this bounce is fine grained phenomenon to be and, therefore, is a theory.
Carlo Rovelli: That the phenomenon to be is less than the terminator right, the problem is too serious is that they have a hypothesis right So are we in the hypothesis of the theorems and one day potus is that the.
Carlo Rovelli: degrees of freedom are all accessible, so let me give you a counter example to this theorem which shows the DCM is false, when you go outside it's about us.
Carlo Rovelli: These are very simple counter example I had one in my old paper, but this is not mine come from Francesco I forgot his name apologies Francesco.
Carlo Rovelli: you hear you have three system A, B and C sees the guy here see for catalog.
Carlo Rovelli: And you compute the following my name to be okay, when you trace over add, in other words Cardinal get entangled with a baby.
Carlo Rovelli: So there is some information some entanglement between the couple of the system and Canada Okay, which is computed by for lomond entropy Okay, then you take the system ab and you just separate the be part of a part until they are very far away it's the space like separation.
Carlo Rovelli: And now going to interact just with a okay interacting with a it will be a thermodynamic lined up because the sun microscopic things and so.
Carlo Rovelli: there's an entropy associated to this interaction Okay, which counts the number of degrees of freedom of what have a obviously not to be.
Carlo Rovelli: Because because it's just because, if I if I put energy into it doesn't go into be because there's basically it's a very it's too far isolated from one another.
Carlo Rovelli: So the thermodynamic of entropy that panel says sees is just determined by the number of degrees of freedom of a.
Carlo Rovelli: But nothing beats that there is an entanglement between, so there is a lack of the impurity in what color measure.
Carlo Rovelli: Due to an entanglement with internal and B, which is far away so that's a clear cut no relativistic without any doubt case in which the fulfillment and to be is larger than the thermodynamic of entropy and remember what was in the slide there is a feeling that this is impossible.
Carlo Rovelli: Okay.
Ahmed Almheiri: So.
Carlo Rovelli: So this is no, no, no, I got to the end, and then we discussed.
Carlo Rovelli: So it's, of course, the serum is a serum, of course, all calculation was correct, but the Syrian has any hypotheses hypothesis and old ways of freedom are accessible right.
Carlo Rovelli: So why is it still relevant to a black hole because that's exactly the situation in which we're in a black hole the beast system it's whatever happens let's say on the rise, or around horizon oriented in the membrane parody whatever you want to think about that.
Carlo Rovelli: As long as you are in this part of space time if this part of Skype plus if you want.
Carlo Rovelli: To take this away.
Carlo Rovelli: As long as you're in this part of space time the degrees of freedom with which are interacting so to that that react you back to whatever you saw inside are all of these.
Carlo Rovelli: So the terminology claim to be corrected computed by the calculation of the half represented right this essentially fully you're here, this is a nearly stationary.
Carlo Rovelli: traci black hole which you can do that calculation correctly, there is this nickname, but this has nothing to do with the fact that that can be a.
Carlo Rovelli: Following and entropy that counts the the entanglement between whatever is outside would have been inside, and this is exactly what I was talking about right when those.
Carlo Rovelli: authorization that flows out to Skype classes also if you want the the other walking pointer that flows inside.
Carlo Rovelli: And pile up inside and that's a phone or meant to be that keep growing, even if determining a nickel entropy goes back, of course, as soon as there is a quantum.
Carlo Rovelli: gravity transition and you go somewhere else, I mean, because at the end, there should be some quantum gravity things to go somewhere else.
Carlo Rovelli: Then, in the past of the quantum gravity region so when the observer is here, then we're not in that approximation anymore so it's then we you get back the information.
Carlo Rovelli: That you have there and where is the key here the key here is exactly what I said, namely because you can because you can get information through the quantum to position.
Carlo Rovelli: The interior of the black hole is not screams from Skype last, so this is not an event horizon, this is a dynamical arise and or.
Carlo Rovelli: copyrights so is something which it's likely the sharpshooter matrix locally okay or fame locally around the black hole local everything is because keep it around the black hole.
Carlo Rovelli: back the future is different, but why is everybody, why is everybody getting confused on that or let me remind you and event horizon just the past.
Carlo Rovelli: or future infinity a trapping horizon for instance that's one of the definitions is a region where they are without cognos surfaces decreases right.
Carlo Rovelli: So physical black hole that's why I said a real black hole if you define the black hole as an event horizon.
Carlo Rovelli: Then you're lost because you're killing quantum gravity because quantum gravity says may very well says that there are no event horizon and here is the here is the detail, so this is a standard classical.
Carlo Rovelli: picture of a collapsing star right the blue region is where you enter in a in a quantum.
Carlo Rovelli: gravity situation where you can take it when the curvature because blank and, for instance, then you you go outside the classical approximation reliably but careful if there's hogging radiation, the arises shrinks right.
Carlo Rovelli: The local horizon the dynamical so shrinks and so at some point, it becomes plunking.
Carlo Rovelli: In the curvature it's off the order of the rising to the minus two so when the curvature when when the horizon become small the curvature outside their eyes and his plan can so quantum gravity just believing quantum field space time with trivial but.
Carlo Rovelli: background, but the same effect on the metric the shrinking of the reason implies that we're in a quantum gravity outside horizon, which means that the classical prediction that the event the races in the interest is not reliable.
Carlo Rovelli: is an assumption about quantum gravity, which might be wrong.
Carlo Rovelli: So that's why to believe that when you.
Carlo Rovelli: When the black hole presumably ends it's evaporation suddenly all what is inside of disappeared nothing and we find just because it's a small mouse it might necessarily be that we are near.
Carlo Rovelli: mean costs good everything is appears it's an iPod disease, which is not granted by anything is a nonsense.
Carlo Rovelli: or, in other words to assume that whatever happened to my screen flows from Skype wow so it's wrong hypothesis it doesn't fall off on absolutely anything.
Carlo Rovelli: So there's nothing wrong in animate calculations, except in the point where he said, necessarily, the number of states for nominating to be bounded by the.
Carlo Rovelli: By the thermodynamic late.
Ahmed Almheiri: i'm sorry I need to ask a targeted traffic clarification question about that point.
Ahmed Almheiri: So you agree with.
Ahmed Almheiri: With just a quantum mechanics quantum mechanical statement that the whole moment entropy has to be is more bounded by the log of the dimension of the hybrid space.
Carlo Rovelli: Independent, which in this case of the accessible degrees of freedom lot of all degrees of freedom.
Ahmed Almheiri: i'm not sure what I mean so so you know I just have a helmet space with some dimension D and I, and I have a quantum state.
Ahmed Almheiri: Sometimes a matrix I just asked him about the whole nother what what is the upper bound on the volume and entropy of their identity matrix of some system.
Ahmed Almheiri: i'm doing i'm This is just abstract.
Carlo Rovelli: it's a it's a short is little with me his number of degrees of freedom, of course, but the temple dynamic and to become a smaller than that that's the point.
Ahmed Almheiri: Sorry, the only thing i'm sorry to the family dynamic entropy in a system without hamiltonian or rather when hamiltonian tribute is just a it's just the longer the dimension of a hybrid space.
Carlo Rovelli: No that's the point is a logo two dimensional of the subspace have a space.
Carlo Rovelli: That include the the accessible states look is not the number of degrees of freedom is not the dimensional favorite face of A and B together it's only the number of degrees of freedom of a you see because bs no, I know I don't interact with it that's the point that's a subtlety.
Ahmed Almheiri: Okay well one one quick question because I let you keep going, but in this on this slide as well known as a small limit of what an SPS as to what, maybe, let me ask that.
Carlo Rovelli: As following one is the trace of an ad.
Carlo Rovelli: Of the state of ABC Okay, of which I consider the the the the the trace of rolla grow.
Ahmed Almheiri: But that's phenomenal see is that right.
Carlo Rovelli: yeah after after racing away and be.
Carlo Rovelli: So this entanglement is amount of the entire world between see and the couple system.
Ahmed Almheiri: And what is St as thermal of what.
Carlo Rovelli: Now i'm here okay sees here it's exchanging heaping work with a only a.
Carlo Rovelli: Okay, and so it's just the number of degrees of freedom of is the longer, you have the number of degrees of freedom, the space of a.
Ahmed Almheiri: Okay, so this has nothing to do with.
Carlo Rovelli: Technically, nothing that you said is vulgar but at some point, you said, and this suggests that right i'm not saying that you said anything wrong.
Carlo Rovelli: I was listen very carefully to you as this suggests that so we assume that at the end of your and at some point you flush the serum Okay, and in this theorem the.
Carlo Rovelli: The following month that the main to be that you're referring to it's a second second entropy right is a.
Carlo Rovelli: Fine, and but the phenomena entropy you you wanted to to use in this argument is this fool number of states of the black hole and that doesn't follow.
Carlo Rovelli: Because the black hole it's the Union if you want of the boundary which is like a here, which is what the term in the temple dynamic a to be in the inside, which is what.
Carlo Rovelli: carries the degrees of freedom that contributes to the following interview, but not to the claim to be noticed that I am only.
Carlo Rovelli: i'm like i'm saying exactly the same thing that I said accepted instead of doing it.
Carlo Rovelli: In the detail of of gravitational situation or just abstracting where the where the subtle with appointees of disagreement.
Carlo Rovelli: In other words, there are degrees of freedom inside the black hole that contribute to the phenomenon to be, but, of course, not to the.
Carlo Rovelli: table dynamically.
Carlo Rovelli: Maybe I should go ahead and the.
Ahmed Almheiri: episodes Please go ahead, thank you.
Carlo Rovelli: Because, because they are the two points I way faster than the other two points.
Laurent Freidel: Just can I.
Laurent Freidel: Just sorry, just a quick remark on that what you're saying is very true for an order to use the system, but then i'm going to say exactly the same thing, I said to me, it is not true, in a gravitational system, there is no gravitational.
Carlo Rovelli: Well it's a it's a discussion.
Laurent Freidel: No, but it Okay, but Okay, but it's also yeah it's a discussion based important to add the.
Laurent Freidel: The the assumptions clear, so this this point again there's an amateur new constraints that being a and D and, in fact, he sent me to sign is the reason why I met is talking about the logo so.
Laurent Freidel: At some point, I would put both of you in if you take into account the fact that a bit space is not split a lot of your problems and products seems to deserves and maybe then you can you know agree more.
Carlo Rovelli: I don't see any paradox i'm saying that the phenomenon to be.
Carlo Rovelli: That measure the entanglement of a far distant observer so there's no issue about.
Laurent Freidel: You but you're forgetting that these far distant observers entangled through them into constraints to two a's and thankful to be that's just.
Carlo Rovelli: Whether it's a.
Carlo Rovelli: Whether entangle us not irrespective of that i'm saying the phenomenon to be can be large and it can be much larger the feminine article, and you know just a little bit can be no mostly larger, in fact.
Carlo Rovelli: it's The point is that is perfectly, but the point is that the page curve does not have to go down.
Carlo Rovelli: there's no reason for the face curve page curve to go down, we can have a very small horizon right here, various well let's say anything about with a very small arise, and of course the time and I meant to be go down a lot, because this was our rice and doesn't.
Carlo Rovelli: have a lot of temperature, but like to be as we know.
Carlo Rovelli: It nevertheless an enormous amount of information stored inside that's what i'm saying.
Abhay Vasant Ashtekar: there's no release or modify that by finish a page called human pace car for the entanglement and, probably, which is what it was, whereas Emma is not talking just about entitlement entropy just just want to.
Ahmed Almheiri: I think I am I think I about we can talk about other OK OK.
Alejandro PEREZ: I can I.
Alejandro PEREZ: Can I make a comment, please so imagine, in this sense of what Todd was saying, imagine a black hole, that is, that is microscopic.
Alejandro PEREZ: So do you trust quantum field theory in personal time on it and you feed it with stuff with some material continuously so that if.
Alejandro PEREZ: You compensate the evaporation, then you can have an entanglement entropy that includes the radiation entropy of the hockey radiation, that is unbounded it can be as large as you want.
Alejandro PEREZ: While the area of the black hole is always saying in this situation, nobody doubts about quantum theory and we know that there will be unitary evolution from months that from one slice to another one.
Alejandro PEREZ: And so, in that regime even I mean, even though I agree with neuron in that regime that what you're saying around it's also going to be as small as it's going to be a very small correction that it's not really relevant so.
Alejandro PEREZ: entanglement entropy can be very, very, very large and that doesn't lead to any contradiction, we are in the situation where everything is absolutely clear in this example.
I agree.
Jorge Pullin: Please continue.
Carlo Rovelli: yeah we have women.
Carlo Rovelli: discussion time after so let me just make it to this was the first point, point one, let me guess the point to a point i'll be fast about this, so I want to emphasize that I believe that if you want understand what happened to black holes.
Carlo Rovelli: We have to solve sweet physical problems, not one and unless we saw all three then we haven't understood it.
Carlo Rovelli: which I call ABC and my collaborators here always.
Carlo Rovelli: tease me because they confuse which one is a B and C, because I put them in the road.
Carlo Rovelli: So see is that matter suppose we have a star the star getting side become very compressed this what happened at sea.
Carlo Rovelli: Be is what happened in the rise and when the rise up with a plan caramel with some quantum effects effects horizon he it's what happened to an observer, this is an observer that falls in its away from the stories away from the riser at some point goes there.
Carlo Rovelli: The universe is not at infinity physics tell us should tell us what happened to this observer, whatever it is, I mean it's gonna die but we're all gonna die, so it doesn't change anything.
Carlo Rovelli: So is it disappearing what happened, so there are three different physical problems here and the a problem by has mentioned, is a huge amount of work into quantum gravity and not only look into morality.
Carlo Rovelli: Which with a number of variants and with a number of things which are not completely clear, but they also suggest that a problem can be looked at just in the case of the evolution of classical beyond the article zero singularity all them.
Carlo Rovelli: Those in those sort of paper with different techniques suggest that you go from this drop the region to this anti trapper the region of sort of another another.
Carlo Rovelli: structure solution here, I like this color white hole by doesn't like the white calls for some reasons it's it's an Anti tropical region.
Carlo Rovelli: That you that you get when you use quantum mechanics and when you lose quantum gravity loop on to gravity different techniques and across to go close that.
Carlo Rovelli: In fact, this is an old lady goes back to the 50s one can write a metric an effective metric that goes through, one can guess an effective metric.
Carlo Rovelli: The loan cube I was talking about, which is the sort of the article constant or cables constant surfaces that approach, the singularity get squeezed to a minimum and then grow the The other side is sort of like a like a bounce or something like that they see.
Carlo Rovelli: physics, is the physics, of a star that gets more and more compressed at some point the density because, again, this is where you expect.
Carlo Rovelli: The lukewarm to gravity to bounce the density of bound the curvature.
Carlo Rovelli: And this is when you expect the balance and the balance is possible because, of course, the balance wouldn't be possible in the tropical region because of causality but it's possible if you go into it drop the region.
Carlo Rovelli: So you can bounce up in the ante track the region, and then the third problem, which is a separate problem is what happened in the region here.
Carlo Rovelli: Because you see if you if you continue to from a tropical island to trap injuries and then, if the story in some way bounces so what happened here, are you going in we go into a different universe, and I think here.
Carlo Rovelli: There is a key.
Carlo Rovelli: Class classical physics result.
Carlo Rovelli: which goes back a few years, been recently extended to.
Carlo Rovelli: arrange on nordstrom which is you can actually have a classical solution outside the black hole that continues from the sort of the previous to the to the future.
Carlo Rovelli: spacetime region so, in other words, there is a space time like that that solves the classical ice and equations everywhere except in a Fini quantum gravity a quantum region, and we know that quantum mechanics allows tunneling, so there is nothing that tell us that this is impossible.
Carlo Rovelli: Provided that the curvature sufficient yeah we are sufficient in a quantum gravity rejects the standard quantum mechanical penalty so.
Carlo Rovelli: This is a reasonable picture of what happened there is a time during which the black hole last if we believe.
Carlo Rovelli: hawking theories or two of em cube in terms of the regional master.
Carlo Rovelli: There is a what I would call a white hole that forms which is anti tropical region which is should be connected to the nonprofit the region, so there should be a.
Carlo Rovelli: And trapping horizon here and there are arguments which I don't have time to go into that the duration of this facie as much longer conservation of information, essentially, is a is an for so I close with what I see the scenario just basically repetition of the same.
Carlo Rovelli: same slide, this is a scenario which it's obviously compatible with quantum mechanics it's compatible with the ice and equations.
Carlo Rovelli: Everywhere, which, in a team region, so the only thing we need for quantum gravity to validate that.
Carlo Rovelli: Is that there is an equation and violated when things becomes an order H bar so when the curvature becomes becomes blanket for a little paneling for a little town in time this has been studied by a number of sorry this has been studying now has been started using.
Carlo Rovelli: This platform for monies mess of the transition for this position actually is be standing up look want to grab it in the in the covariance.
Carlo Rovelli: picture I don't want to go into that I will just mention this and mentioned also that there is a lot of feminists phenomenology been studied that the scenario here is that this.
Carlo Rovelli: remnant are very long leading which by the way, is the reason you cannot produce them at.
Carlo Rovelli: CERN right, I mean there is this.
Carlo Rovelli: old argument, by getting that you cannot have a small.
Carlo Rovelli: Mass object, with a lot of.
Carlo Rovelli: With a lot of internal degrees of freedom, of course, you can Okay, is it just have to be long living that support, and these are lonely OK so.
Carlo Rovelli: The phenomenology which is being explored is relate that to dark matter of two older more little things around, there is the possibility of.
Carlo Rovelli: signal that come on from that there's a lot of literature on that I just want to say that it exists, so I summarize I just.
Carlo Rovelli: been going long, first, I believe that the central document is a false false dogma, because it does not follow from the correct calculation at half men as presented because there's no reason the following my name to be which include includes.
Carlo Rovelli: The entanglement with interior to be bounded by the thermodynamic on entry, which only counts the number of degrees of freedom that can affect us and therefore any other eyes.
Carlo Rovelli: Second point, there are three regions feelings physical problems that the tunneling through the singularity the bounce of the Star and what happened at the.
Carlo Rovelli: At the black hole provide some become wider horizon and the likely scenario is this this one which a lot of uncertain aspect on it, we don't know exactly the duration of the black hole face it could be shorter been suggesting shorter have some, as you know, Alex.
Carlo Rovelli: has long been accessible to have someone information is lost in micro copy degrees of freedom.
Carlo Rovelli: that's a possibility, there are a number of things which are not clear, this has to be extended to care and so on and so forth, but this is a scenario which doesn't contradict.
Carlo Rovelli: quantum fields in space time where we were is reliable doesn't contradict unity already doesn't completely relativity it's perfectly consistent with quantum mechanics generativity.
Carlo Rovelli: i'm not sure is real, but I don't see any much more plausible than this other stuff here.
Jorge Pullin: Under God alone For those of you who are not regulars here the Center has been running for many, many years, and so we have some traditions that predate soon, so we thank our speakers, the traditional way so let's thank our speakers.
Jorge Pullin: And I thought we could start with some questions on one of the speakers and then I made this our guests, do you have any questions for carly.
Ahmed Almheiri: Many I guess.
Jorge Pullin: strike one or two.
Ahmed Almheiri: Okay um.
Ahmed Almheiri: So the first is, let me just.
Ahmed Almheiri: I lost my zoom.
SEC.
Ahmed Almheiri: Can you guys hear me.
Jorge Pullin: We can hear you do you want to share something Carlos should ensure yeah.
Carlo Rovelli: Do you want me to close it my slides later.
Ahmed Almheiri: No, no, no it's fine for now so first a comment on something that I think was in Hong Kong.
Ahmed Almheiri: sad about so you can you can have a situation where you have a black hole which you're constantly feeding.
Ahmed Almheiri: Can you constantly dealing with pure matter and it continues to evaporate and.
Ahmed Almheiri: I never evaporates away you get a steady state solution and but the phenomena entropy of a black hole at least.
Ahmed Almheiri: SV from the outside, looks like it's growing arbitrarily large because it because it keeps building up entanglement with all the hawking radiation that emits.
Ahmed Almheiri: And you might have said that well that's that's life that's a you should just take this is, it is that the interpreters keeps growing.
Ahmed Almheiri: At so two comments, one comment is that it does it violates the central dogma, which is also an assumption, it violates that entered that from the outside, it looks like the entropy of the black hole is exceeding external entropy.
Ahmed Almheiri: The other comment is that that's actually that answers just simply the wrong answer in the sense that, if you do the calculation.
Ahmed Almheiri: And the way that I was describing it using the gravity pathological there's a new contribution that comes in and the entropy of the radiation, you find that it gets capped out at the thermal entropy even in that case.
Ahmed Almheiri: So.
Ahmed Almheiri: In some sense, so this is a it's something that comes out of the of the pathological, this is not something that I pulled out of a hat so i'm curious about about that possibility for that scenario which is like I.
Abhay Vasant Ashtekar: said.
Alejandro PEREZ: In quiet.
Abhay Vasant Ashtekar: spaces cry and dad or maybe you should go.
Alejandro PEREZ: No, no company subjects right yeah.
Abhay Vasant Ashtekar: So I took I could just take the business can calculate entropy entropy is, in other words you're calculating some entropy, but that is not the entropy that our calculate and the best way is to avoid this issue about the hilbert space.
Abhay Vasant Ashtekar: And just focus on observable so I can just considered an algebra observable associate described right and calculate the entropy and that interview keep growing.
Ahmed Almheiri: I disagree, I mean you can compute literally trace roller girl, and you computed in this careful way, using the gravity path and ago.
Ahmed Almheiri: But.
Abhay Vasant Ashtekar: I can just calculate so glad.
Abhay Vasant Ashtekar: You gave me this I mean I don't need to know anything about entanglement I can just calculate the.
Abhay Vasant Ashtekar: I just need to calculate this is.
Abhay Vasant Ashtekar: Just a piece of scrap.
Ahmed Almheiri: i've been I I I think I agree with you, and what we want to calculate so they would you what would you want to calculate is traced roller girl of the region far away from the black hole right.
Ahmed Almheiri: This is what we want to compute.
Ahmed Almheiri: Yes, and what i'm saying is that when you compute that quantity their contributions they come in which.
Ahmed Almheiri: and complete rest what role I bro as trace route to the end of the deck angles to one you get contributions which are wormholes connecting the different copies, but if you get connected inside the black hole like.
Abhay Vasant Ashtekar: that's that's the seven Euclidean calculation that gives you some concepts, I agree with that, but I could just calculate it in algebraic using a device called a few serious crime.
Abhay Vasant Ashtekar: And I would not get that I would actually get just you know the thermal the interpret corresponding to thermo status and the.
Abhay Vasant Ashtekar: Space it's crying or the.
Abhay Vasant Ashtekar: Space I got a thermal density metrics there that's what I would get.
Ahmed Almheiri: But don't you find it odd that that calculation, it has in it a contribution, which is exactly what you're saying, but it also has another contribution.
Abhay Vasant Ashtekar: yeah therefore yeah calculated something else I mean adults in normal systems which are not gravitational various calculation give you the same answer.
Abhay Vasant Ashtekar: But once you got include gravity and, particularly, you know non trivial things like black holes, then the same calculation that you're used to in five space time and you know quantum field in fact space type etc would give different answers, I think that.
Abhay Vasant Ashtekar: does not happen very often.
Ahmed Almheiri: I find this really weird because I thought.
Ahmed Almheiri: I thought coming into this community that you guys would be more weight to gravity, but here you're telling me i'm going to ignore the new thing that gravity tells me.
Alejandro PEREZ: But can I make a comment.
Alejandro PEREZ: which goes along the same lines, I suppose, if the black hole is very large, if you take a slot and you're feeling it in the way I proposed.
Alejandro PEREZ: And you take a slice some some spatial some cushy surface, for the past part of the and then you take another one to the future, then.
Alejandro PEREZ: Because the black hole is large, then, to a very, very good degree of a of accuracy, they will be unitary evolution of the quantum fields, from Sigma one two Sigma to, and there is absolutely no paradox, then it can compute.
Alejandro PEREZ: The entanglement entropy is true, there will be a diversion term proportional to the area I can pull that off, but.
Alejandro PEREZ: You know I could regularize this in some in some way and that entropy will be growing.
Alejandro PEREZ: Due to the fact that I am producing more and more hawking radiation and there is absolutely no paradox, even this don't you agree, because I know.
Alejandro PEREZ: That inquisitive in theory, the evolution from one segment to the other is just perfectly unitary our why way.
Alejandro PEREZ: Why should it be a paradox when there is nothing and it's absolutely everything is absolutely clear in this situation in the regime where quantum field theory is an extremely good approximation.
Ahmed Almheiri: I agree that there are there's no obvious reason for why should this trust the quantum field.
Alejandro PEREZ: i'm saying there is no paradox there.
Alejandro PEREZ: is no problem there is no need to go to your calculation, I mean, in my view, I mean I mean this is, this is my confusion.
Ahmed Almheiri: No, but but but.
Ahmed Almheiri: What i'm what i'm saying is that is that once you do the calculation carefully, irrespective of what answer you want to get.
Ahmed Almheiri: And all i'm saying is that there are contributions that come from wormholes that change the answer that are different from from the naive.
Ahmed Almheiri: expectation that quantum field theory on a fixed background gives you the right answer, because this is an observation, the question is whether, whether you want to trust the calculation or not.
Abhay Vasant Ashtekar: I think this is really the interpretation of the calculation, not the calculator itself right, I mean again, as I was saying that, I mean I.
Abhay Vasant Ashtekar: I agree that this community will trust Dr Jason things much more, but we trust so much that we also believe that when you include gravitation then.
Abhay Vasant Ashtekar: The physic the same physical concept in absence of gravitation can split into distinct physical concepts and just to have this is who had the slide appear on the loop on the screen.
Abhay Vasant Ashtekar: I mean, why would you not be calculating in the just the just the the entanglement entropy of the the yeah entanglement and drop in between just a in and and and and see and if you create any calculation and not with the combined system A, B and C.
Abhay Vasant Ashtekar: In other words, this extra time that you're getting a nuclear and calculation you're getting some answer but it's not clear to me that that answer is the same as the the entanglement and entropy between the original system A, B and C.
Ahmed Almheiri: um well in terms of the picture here all you, all I can maybe draw some pictures for you, but i'm saying in terms of the pictures here, I would say that the calculation is set up, from the beginning to compute only the entropy of see okay.
Ahmed Almheiri: And then, what you find is that it, it also includes being the game in some way because that's and that that comes in, from gravity I can have some pictures if you'd like but.
Carlo Rovelli: interpretive see a, namely see has a density matrix is that what you're saying.
i'm.
Ahmed Almheiri: For me see is some region far away from the black hole and i'm.
Carlo Rovelli: Saying that's here we are, we are together and and and and there's a density method associated to it.
Ahmed Almheiri: Correct is it Okay, if I drop.
Ahmed Almheiri: My share my screen is.
Carlo Rovelli: shown in any take this away just one, second, you cannot do it, while i'm doing it.
Alejandro PEREZ: So why we wait so so you're doing the calculation, but there's something happening inside of the black hole is Could you give more details eventually about this, I mean inside I don't know what the week rotation mean I don't know what.
Alejandro PEREZ: What the sale cleon subtle, are you didn't give many details.
Ahmed Almheiri: You know, because we have 15 minutes is not enough.
Alejandro PEREZ: You know I said.
Ahmed Almheiri: Let me first joined.
Alejandro PEREZ: But, did you do get it, you get what what is the point of my question so normally when you go to the occasion you only get some you only get the exterior well where the identity continuation gives you a real metric.
Ahmed Almheiri: If you go if you go to the interior, then you continue to learn to time, then you get the Interior.
Carlo Rovelli: I think I handle has a point here it's a.
Carlo Rovelli: The way you derive your first calculation, the easy one, the one you used to derive the epidemic and to be European spaces boundary.
Carlo Rovelli: And the boundary it's a nice to close on this one, if I remember right which is essentially.
Carlo Rovelli: The riser going from future past or future and then close because you do the tabernacle thing you close the past the future right essentially that's that's it.
Carlo Rovelli: um you know it's clean version of the old, what is it hawking hartle.
Carlo Rovelli: givens first to the book events, thank you.
Ahmed Almheiri: Talking that's that's.
Carlo Rovelli: Given talking Thank you it's a it's a clean version of that.
Carlo Rovelli: which of course it's nice it's correct it gives a temperament and you came to be but.
Carlo Rovelli: Point is at how are you saying is that which Termini McCann to be discovered, it is given it up an article and to be of a black hole which is assumed to be stationary okay it's key point of the thing, where you cut away the interior you forget interior okay.
Carlo Rovelli: And so you're asking if you're outside Okay, and there is some DEMO dynamical effect of the horizon, what are the thermodynamic effect of the rising.
Carlo Rovelli: And that's fine the one and effective horizon give a quantity, which should correct the colon entropy and will agree it's all fine the point of disagreement is that this has nothing to do with the fact that this calculation doesn't see some physics and the physics is.
Carlo Rovelli: physics, which is not captured by the analytical continuation of the exterior of the horizon, because is the physics, of the entanglement.
Carlo Rovelli: Between the outside and not the boundary but something which goes inside and which only comes becomes effective for an observer, when the the rise is not an arise on anymore, so when you come we come out from the.
Carlo Rovelli: Let me make a comment, since I.
Ahmed Almheiri: bought flow and.
Carlo Rovelli: Then, and then i'll shut up shut up.
Carlo Rovelli: To medical physicists are super good, but obviously and you're one of the best so once you give them a problem they find solution of it okay.
Carlo Rovelli: If you take the central dogma and you want to justify ag i'm sure that somebody sufficiently good find the calculation that.
Carlo Rovelli: But the point is, as you said that the central dogma is an assumption, you said it so in your in your end this assumption which physically.
Carlo Rovelli: is not justified so what's the point of making assumption getting in trouble, because it seems to be then and then climbing mirrors to find a very smart arguments that makes it compatible with a race that just assumptions wrong.
Ahmed Almheiri: I disagree well so.
Ahmed Almheiri: That well I don't want to go into some overview of the entire.
Ahmed Almheiri: field of string theory media cmt and blah blah blah all that stuff but i'll tell her there are lots of there's a lot of evidence pointing to that central dogma and and well.
Ahmed Almheiri: we're trying to come up with all of us are trying to come up with the best description fitting all of our data points we might disagree on which data points should have higher credence versus others.
Ahmed Almheiri: i'm saying here for the for this talk was just about how the gravity pattern, you know, gives us answers consistent with the central dogma that's really everything that i'm saying right.
Abhay Vasant Ashtekar: So we had a talk with Maxwell Maxwell have you know, a year ago and I had a long correspondence with him and don model as well.
Abhay Vasant Ashtekar: And, Dom completely agreed at that time is that, in fact, what is being calculated in the islands is not entanglement entropy.
Abhay Vasant Ashtekar: And that entanglement and probably will continue to grow and we didn't see any problem with that at all, he said that what one is calculating.
Abhay Vasant Ashtekar: isn't entropy which is kind of more relevant in terms of actual observations mia's cry and that I understood mean seven observe your observable something that you construct so so even within stream for your dog has the same.
Abhay Vasant Ashtekar: same.
Abhay Vasant Ashtekar: munition as you.
Ahmed Almheiri: Can I drop the kind of draw a picture.
Abhay Vasant Ashtekar: yeah please.
Abhay Vasant Ashtekar: explain to me that you disagree with don and why.
Ahmed Almheiri: I i'm pretty sure don agrees with me.
Ahmed Almheiri: about this.
Abhay Vasant Ashtekar: like to share the message.
Jorge Pullin: draws does any of the other speakers have a question.
Abhay Vasant Ashtekar: Any questions to speaker so.
Ahmed Almheiri: Okay, I can you guys see my screen.
Ahmed Almheiri: Yes, okay i'm doing something okay i'm going to draw a picture the the physical significance of the picture might might be not very clear to everyone, but I but.
Ahmed Almheiri: i'll tell you which features i'm trying to offer is going to get the message across so.
Ahmed Almheiri: let's do something like this, so here.
Ahmed Almheiri: Is the usual cigar geometry okay.
Ahmed Almheiri: that's me let's imagine breaking it up, I will not breaking it up, but.
Carlo Rovelli: What is the boundary what is the boundary.
well.
Ahmed Almheiri: as well.
Carlo Rovelli: physically physically, what does that.
Ahmed Almheiri: represent asana boundaries goes, all the way to infinity.
Ahmed Almheiri: Know there's a boundary there this one oh so the next one.
Alejandro PEREZ: Is from the heart, I think I got no.
Ahmed Almheiri: No, no, the manifold here asymptote to s one cancer RD say.
Ahmed Almheiri: Okay, so this is one direction and RD every point here is is is a D minus one sphere and are the radio radio direction this is ours or shorter radius are we good so far.
Carlo Rovelli: Short radius i'm confused, what is the show.
Abhay Vasant Ashtekar: These are you creating.
Carlo Rovelli: The show she called in acumen.
Ahmed Almheiri: This Euclidean black hole.
Abhay Vasant Ashtekar: You clearly black hole that's the point and therefore.
Ahmed Almheiri: Are we good so far, this is a Ukrainian Blanco.
Ahmed Almheiri: No.
Carlo Rovelli: I don't understand what is the boundary physically, what does it represent is is that the reason or is cry.
Carlo Rovelli: No else there's nothing of that there's no scrape it some.
Carlo Rovelli: Some about infinity boundaries it space.
Ahmed Almheiri: I don't have a boundary i'm drawing the cigar geometry and as i'm talking flat space.
Carlo Rovelli: So is there an area so we're here in the boundary.
Ahmed Almheiri: Areas here.
Carlo Rovelli: Where.
Ahmed Almheiri: The horizon is here this point here.
Abhay Vasant Ashtekar: In the.
Carlo Rovelli: analytic continuation of the outside of the horizon Is that correct.
Correct.
Carlo Rovelli: So this already cuts away, whatever happens inside horizon is not the analytical intuition, of the inside of the reason.
Ahmed Almheiri: Current good.
Carlo Rovelli: So the boundary I shouldn't focus is not the right one, is the left one and that's the reason area there okay good.
Abhay Vasant Ashtekar: Okay, going back.
Alejandro PEREZ: yeah it's.
Ahmed Almheiri: Very good now imagine.
Ahmed Almheiri: flattening this this cigar so that so i'm going to draw this to go like I said as a as a disc okay.
Ahmed Almheiri: This point here's RS.
Ahmed Almheiri: And this guy's at infinity.
Ahmed Almheiri: got it okay.
Ahmed Almheiri: If you.
Ahmed Almheiri: If you consider a slice.
Ahmed Almheiri: Like a you know here's because it is like this that's like this slice here.
Ahmed Almheiri: that's like a slice of the outside of the black hole three agree.
Ahmed Almheiri: yeah let's imagine, for the moment that we want to compute the entropy of.
Ahmed Almheiri: Some region outside the black hole this red region here.
Ahmed Almheiri: Okay, so that in this picture that's like a red region here.
Ahmed Almheiri: Very good, how do we compute entropy so one way to do it is to say, let me just consider the state of the matter Okay, I did fix the geometry.
Ahmed Almheiri: I consider the state of the matter and then compute you know trace route to the end and then take it goes to one blah blah blah let's do something much simpler let's just consider n equals two.
Ahmed Almheiri: Okay, this is the thing called the purity.
Ahmed Almheiri: When you do, that is, you consider two copies of the system because it's trace route squared.
Ahmed Almheiri: there's matrix multiplication of the two roles, which means that you, you draw cut along the region, you want to complete the entropy of.
Ahmed Almheiri: Nine you identify.
Ahmed Almheiri: do some identification like that.
Alejandro PEREZ: Okay.
Ahmed Almheiri: This is trace role Square.
Ahmed Almheiri: This is how you complete the.
Ahmed Almheiri: density with the purity of the matters.
Ahmed Almheiri: Of this region, assuming you've quote unquote turned gravity off okay so you're just doing ethical manner on fixed.
Ahmed Almheiri: On a fixed gravitational background.
Ahmed Almheiri: Okay, so this is what I would call computing trace.
Ahmed Almheiri: expectation by your role Square.
Ahmed Almheiri: expectation, but I mean plugging into gravity gravity saddle.
Ahmed Almheiri: But now what what what i'm saying is that this is too quick, this is not the thing that you should compute I think you should compute is trace.
Ahmed Almheiri: row squared and then evaluate everything by several points, but what does this quantity look like, so this thing is, again, let me drop in a different page machinima from here.
Ahmed Almheiri: You can again the setup of the problem is that you consider the same thing, without with the right identifications.
Ahmed Almheiri: And you consider all possible sound points.
Ahmed Almheiri: One central point is what we had here, which is so here gravity was killed him like this, so gravity is filled and like this.
Ahmed Almheiri: But there's another side appointed turns out where you develop a wormhole.
Ahmed Almheiri: that connects the two discs.
Ahmed Almheiri: This is something that you find in the gravity pathological but it's it's, a thing that you find if you evaluate it this way.
Alejandro PEREZ: But in the in the Lawrence and gravity party and there are there are things there that you don't you don't see in this Ukrainian verse right there are many metrics that don't have that are not real when you when you've complex if I time I mean there is no week rotation gravity so.
Ahmed Almheiri: But but but there's something something amazing that comes out of this potential so let's let's consider this let's consider this picture okay this picture you can draw it in the following way.
Ahmed Almheiri: here's my desk i'm going to use a so called quotient picture, which means that.
Ahmed Almheiri: Here is a well should immediately definitely.
Ahmed Almheiri: Have a branch cut here is the branch what that tells me that that makes identification between this part of this part.
Ahmed Almheiri: But the fact that have a wormhole here connecting the two sheets tells me that I should have another.
Ahmed Almheiri: set of branch points in our branch.
Ahmed Almheiri: This picture is supposed to represent this picture.
Ahmed Almheiri: Is that clear.
Ahmed Almheiri: I will address your question in a second and 100 verses is this clear.
Carlo Rovelli: You.
Carlo Rovelli: know I mean this is technicality So what are you.
Carlo Rovelli: Understand you're enthusiastic about this.
Carlo Rovelli: Calculation very good.
Please.
Ahmed Almheiri: Let me get the message across what i'm saying is that when you compute this quantity there that you can get a contribution from gravity that connects a wormhole on the first sheet to the other sheet that's my first point and I hold.
Alejandro PEREZ: Some sort.
Alejandro PEREZ: of some sort of Euclidean quantum gravity.
Ahmed Almheiri: For now, for now let's go for it for another two years okay and and.
Ahmed Almheiri: i'm saying that I can represent this picture as this picture here.
Ahmed Almheiri: that's what i'm saying.
Ahmed Almheiri: Because it is a branch God is just supposed to represent the fact that I have a connection to the two sheets, maybe I shouldn't belabor this point, but the upshot is.
Ahmed Almheiri: The when you actually try to find a solution for this, you find that the location of of this wormhole is actually not in not in Euclidean space.
Ahmed Almheiri: When you actually look for look for a solution, you find that the location of this this branch cotton these branch points is actually in renting space, so when you go and then draw a picture of the black hole.
Ahmed Almheiri: here's my Lawrence Ian black hole.
Ahmed Almheiri: here's the.
Ahmed Almheiri: The region outside, we will continue the entropy off what you find is that the space time develop these branch points here actually.
Ahmed Almheiri: The looks that looks something like this, they move into the Lawrence in section and they give you a picture like this.
Alejandro PEREZ: How I mean by what procedure you see this thing that this warm whole turns into something inside.
Ahmed Almheiri: Good it so what we're trying to do is we're evaluating this quantity via sharepoint right, and so you need to look for this, the solution of einstein's equations and the solution of ISIS equations it determines the location of these branch points.
Ahmed Almheiri: And the location, you find is not in the completed section, you find it that it's in the orange in section like it's literally just an output of the calculation.
Alejandro PEREZ: solution of htc equations or.
Alejandro PEREZ: subtle point of.
Thomas Thiemann: view is.
Thomas Thiemann: Just something over Euclidean metrics, how can you find the right.
Ahmed Almheiri: No i'm not i'm not doing i'm I have, I have some.
Ahmed Almheiri: Some into some some path integral to the I.
Ahmed Almheiri: g.
Ahmed Almheiri: And i'm just looking for configurations that extra that extra miles, the actual.
Ahmed Almheiri: And you find that, given the boundary conditions of the problem, the configurations that that extra eyes the action are not purely Euclidean configurations they have interesting part.
Alejandro PEREZ: So you're saying, are you saying that the picture you drew have a warm hall is not quite right, because that would be no cleaning configuration.
Ahmed Almheiri: Exactly exactly this is just for intuition so.
Alejandro PEREZ: So, so this is just to keep bookkeeping type of language, but what you're doing something else, yet it's not really that.
Ahmed Almheiri: it's it's I think the right thing to say is that it's just it's the laurentian continuation of a Euclidean World War.
Okay.
Ahmed Almheiri: Let me, let me, let me take a.
Abhay Vasant Ashtekar: Look at the tier one one game.
Abhay Vasant Ashtekar: picture, and we know why, of course.
Ahmed Almheiri: that's it that's all I wanted to start back I realized how much time we spoke, you can have a wormhole in in the in the Ukrainian section okay there's a location of the wormhole.
Ahmed Almheiri: That what get continued is the is the location of the wormhole not it's not Assad the continuation of the Euclidean wearable space time no but the location of the wormhole gets continued tolerant in space and that's why you get a picture like this.
Alejandro PEREZ: Okay, in the in the in the warm whole picture this wormhole is connected regions where the spheres, have a radius which is larger than the radius of the horizon.
Ahmed Almheiri: that's.
Alejandro PEREZ: But then.
Ahmed Almheiri: Okay, fine that's that's a good point.
Ahmed Almheiri: There, in the case where this calculation actually applies the island and just outside the horizon, but that's that's a detail.
Jorge Pullin: let's see since we.
Jorge Pullin: are a mark, can we take a few questions from the audience raising your hands was soon, please, to keep some order.
Ahmed Almheiri: me, let me answer.
Abhay Vasant Ashtekar: Now, I think, just before you can share, I mean that.
Abhay Vasant Ashtekar: You don't know to do the lorenzen integral that you are the complex metric integral that you wrote down it'll actually be no control the bottom thing that you wrote down.
Abhay Vasant Ashtekar: So long as it is the premium domain also like a geezer all European domain, there is some semblance of control of that, and you can do this, you know some.
Abhay Vasant Ashtekar: Some subtle point approximation, etc, as soon as you go to complete lorenzen domain, I mean I is it that they didn't deal just thought well if I am is never be well defined but nowadays uncontrollable beta five so i'm not sure that the argument supply at all in this case.
Ahmed Almheiri: We set up a like this, nobody knows how to do this and people don't really know how to do it so first time points.
Abhay Vasant Ashtekar: yeah but.
Ahmed Almheiri: What i'm observing is that there's a subtle point which is in the in the endurance etc.
Abhay Vasant Ashtekar: Right, but now exactly going back to what Carlos say now, the question is of interpreting this side of things.
Abhay Vasant Ashtekar: So it may be that what what is doing is really calculating the entropy that really has to do with the surface degrees of freedom as in Carlos language.
Abhay Vasant Ashtekar: Because i'm in one is taking for granted, this is exactly the point I was trying to debate, but it was too vague, that when you do the actual calculations.
Abhay Vasant Ashtekar: The new elements that are coming and those new elements might tell you that the country that you calculated is not the usual quantity in you know.
Abhay Vasant Ashtekar: The cloud space time or space times without any.
Abhay Vasant Ashtekar: horizons, but it may be a different continent, so it may be that you are calculating this quantity and that country, and it seems to make complete sense if you say that that that quantity is really the the the degrees of freedom of the black hole horizon that interact with.
Abhay Vasant Ashtekar: Experience and everything seems to.
Abhay Vasant Ashtekar: make complete sense, so the.
Abhay Vasant Ashtekar: question that for us, is really the interpretation.
Abhay Vasant Ashtekar: Of the last step, you did, which was really stepping up completely stepping out of the pre mice that one started out with in Green Party interiors.
Ahmed Almheiri: II I.
Carlo Rovelli: had one.
Ahmed Almheiri: question is set up by your initial setting up a question.
Abhay Vasant Ashtekar: like this absolutely.
Ahmed Almheiri: And this, the initial setup was this computation and then we went and then we just see what gravity wants to tell us.
Carlo Rovelli: If you want me to.
Ahmed Almheiri: reinterpret the result of the end that's that's.
Ahmed Almheiri: required like a duck it's a duck to.
Ahmed Almheiri: me so.
Carlo Rovelli: I mean you're doing gravity right now suppose is an extra field or there's an extra volume of encyclopedia Britannica which is thrown in.
Carlo Rovelli: Your calculation does doesn't know anything about that, I mean if you what What do you mean is that what we are worrying about is that own a black hole we work all those also on the block on geometry, there is also another field, whatever that poking evaporate.
Carlo Rovelli: And that.
Carlo Rovelli: create additional entanglement between the outside and the inside.
Carlo Rovelli: And this depends, of what else i'm throwing inside so of course there's more entanglement with inside if I saw more thing inside, how can your playing with some functional integrals gravity alone known anything about that it doesn't.
Ahmed Almheiri: It does it does it does so there's there's gravity pathological also has a matter pathological in it, and that that is sensitive to things like throwing throwing things inside.
Carlo Rovelli: The intensity, I mean I smell something inside and immediately after I saw something.
exciting.
Ahmed Almheiri: It is, it is not insensitive.
Carlo Rovelli: I know.
Abhay Vasant Ashtekar: I.
Carlo Rovelli: don't think we're convinced let's put it this way it's a.
Carlo Rovelli: Beautiful probably should.
Carlo Rovelli: follow it, I don't think we're convinced that is relevant for the difference between the 10 million and we came to be the following Monday to be.
Abhay Vasant Ashtekar: yeah I think that a new elements that are coming in exactly when you went to the complexes and you and you're trying to do the.
Abhay Vasant Ashtekar: And then the physical interpretation I mean if I just say that what you're calculating is, in fact, the number of degrees of freedom on the exterior of the intro pencils are extremely which actually.
Abhay Vasant Ashtekar: agree with the which can interact with the degrees of freedom on the surface, the black hole, then everything is perfectly fine so and I don't see how your calculation.
Abhay Vasant Ashtekar: is telling you that you're not being.
Abhay Vasant Ashtekar: I mean you're putting new elements in the calculation, and so the physical interpretation, at the end can.
Abhay Vasant Ashtekar: can be different from the traditional physical interpretation or the traditional calculation.
Ahmed Almheiri: I don't know how to answer that I mean it's just yeah it's time.
Abhay Vasant Ashtekar: yeah, but I think it is I.
Ahmed Almheiri: mean this is this is.
Abhay Vasant Ashtekar: Why we do that all the time right, I mean in general activity that that certain calculation that you do in space of relativity can give you to like, for example, like, I mean even within general it up, you know you can calculate the.
Abhay Vasant Ashtekar: The mass of the space time, for example, by having planets go around you can calculate it by what happens to.
Abhay Vasant Ashtekar: The mass if you actually have a bunch of test particles and you've observed that Judas separation and you get different answers, and when I mean.
Abhay Vasant Ashtekar: We and the statement is that yeah I mean there's nothing wrong, I mean it does you know in newtonian theory, you might get exactly the same answer.
Abhay Vasant Ashtekar: But in general relativity if it is not station in space time, particularly, you will get different answers and we say yeah That is because the concept as bifurcated and we're to really carefully price as to which that.
Abhay Vasant Ashtekar: The given calculation, which can separate really first to even though you've done in $30 for both coalesced and gave us the same answer.
Abhay Vasant Ashtekar: So you're you're doing a certain calculation, but it seems to us that the physical interpretation you're given to it at that sticking to the starting point is not necessarily relevant because or is not justified, I should say because you're putting new elements in the calculation.
Ahmed Almheiri: The gravity person that's putting them in it's not me.
Abhay Vasant Ashtekar: No, no, but I mean the same thing that one is.
Abhay Vasant Ashtekar: yeah okay I, I think that it's not I mean it's true that it's a gravity part integral, but you are evaluating it by putting in new elements which is not.
Abhay Vasant Ashtekar: which are not dead, the guy with you, I mean in the beginning, when we are associated the meaning using the ingredient party to develop that was perfectly fine.
Abhay Vasant Ashtekar: What what in what thermodynamic entropy meant, but now you're doing something else.
Abhay Vasant Ashtekar: And therefore, when you do that, it may well be that you know, this seems completely justified to us to say that yeah so very interesting calculation and look what this calculation gives us is really.
Abhay Vasant Ashtekar: The entropy associated with the degrees of freedom which interact with the with the surface of a black hole and if I say that, then I mean we would all there's no contradiction with anything.
Abhay Vasant Ashtekar: and also the pace car going down and so on everything seems perfectly right.
Abhay Vasant Ashtekar: that the number of degrees of freedom which can interact with the black hole is going down as a reassurance.
Abhay Vasant Ashtekar: And so to us it's it all looks completely sensible and it's an interesting and fascinating calculation that one can get.
Abhay Vasant Ashtekar: To the number of degrees of freedom that interact with the surface of black hole in this particular way, but I don't see why one is compelled to say that that's not what it is, I mean.
i'm.
Carlo Rovelli: Not here to convince one another right we're.
Carlo Rovelli: Here next change.
Carlo Rovelli: Point of View so it's not the point is not to get to a consensus point is to present present different views that come from different ways of viewing a problem and to sort of listen to one another, so that's that's it.
Ahmed Almheiri: we're all we all understand each other's points yeah.
Ahmed Almheiri: um.
Ahmed Almheiri: You know.
Jorge Pullin: Though we did some other questions, yes.
Abhay Vasant Ashtekar: yeah yeah let's take questions the audience sorry I.
Jorge Pullin: just had a hand in for a long while up.
Ding Jia: Thank you, I just have a quick question to I meant about seto points, I wonder, you have any selection principle if, in the gravitational path integral.
Ding Jia: There are multiple set of points, for example, I mean, in the context of.
Ding Jia: more general case not necessarily this this is model you're considering for simple because.
Ding Jia: I can do a gravitational potential in general, give us some boundary conditions and for some boundary conditions are multiple set of points to use some over all of these in your semi class calculation or do any way to select the relevant ones.
Ahmed Almheiri: I think I just do things well not just need, I think the right thing to do is to well.
well.
Ahmed Almheiri: In this setting you just you try to list all this, one can do the integral so we can look at several points and then you just.
Ahmed Almheiri: In theory, have to consider all of them, and then the doll and then you pick up the dominant one, so the selection criteria is just what's the best approximation, for your integral.
Ahmed Almheiri: And in this case well there's a transition between the not hawking versus the wormhole or island answer at the beach time.
Ding Jia: Since you're saying you do some or all of these, but some are dominated so these make make major contribution.
Ahmed Almheiri: In this in this particular calculation, we only have to sell points when.
Ding Jia: i'm asking you know more general case for the organization, but in theory to use all of these or do you select some.
Ahmed Almheiri: You some of our some of our everything and sometimes you also.
Ahmed Almheiri: well.
Ahmed Almheiri: Yes, you some of all of them, and then you well and that's it and then your answer is going to be dominated by whichever one dominates if that happens, or maybe the some we something to something mean.
Ding Jia: Think.
Jorge Pullin: of your.
Edgar Shaghoulian: hey sorry i'm going, can you scroll down to the picture, with the island in the black hole, I want to see if I understood the.
Edgar Shaghoulian: perspective of the other speakers so i'm in was trying to argue that you set up a computation to compute the phenomena entropy of.
Edgar Shaghoulian: The radiation far away from the black hole and what you land on what's represented in this picture is that the answer for that question.
Edgar Shaghoulian: is roughly given by the semi classical entropy of this region are this radiation region Union the island region, and I think what other speakers were saying is that.
Edgar Shaghoulian: You can interpret this computation as computing the entropy of the degrees of freedom that interact with the surface degrees of freedom of the black hole.
Edgar Shaghoulian: So by that is it meant that really what your computing is the fun moment entropy of the radiation Union the island region is that a way of rephrasing what the other speakers are saying.
Edgar Shaghoulian: As opposed to the semi classical entropy of the radiation Union the island.
Abhay Vasant Ashtekar: yeah, I guess, I mean i'm not sure exactly but something along those lines that exactly yeah.
Edgar Shaghoulian: yeah yeah and just to make sure also just it so both of a in chrome is very important that.
Edgar Shaghoulian: You sort of disagreed with the the central dogma, the number of states of a black hole is more than either a over 4G I mean that didn't that was just motivational intimate discussion, but nevertheless when can take votes and see where they went, but.
Edgar Shaghoulian: It was very important that that was not the number of states have a black hole in your guys's discussions is that right.
Abhay Vasant Ashtekar: yeah so in my view, I mean you know, there is a difference, I mean this is first surprising to me, but there is a difference between the old black hole in the new black hole.
Abhay Vasant Ashtekar: In the black hole we just form of course there is nothing outside I mean let's suppose that there is there's a scale of physical Apps and that's black oldest form there's a Korean state Wisconsin on sky minus from the black hole, then the state, but is that.
Abhay Vasant Ashtekar: yeah, then I think, then the the the area of the black hole.
Abhay Vasant Ashtekar: You could take it to be the gravitation entropy so because it is really just the surface degrees of freedom which interact with with outside.
Abhay Vasant Ashtekar: So there's nothing inside so, then it is a total entropy but, as the evaporation proceeds more and more things will fall in and then he is no longer.
Abhay Vasant Ashtekar: The the total entropy of what is contained inside the horizon, but rather it is.
Abhay Vasant Ashtekar: It is really associate degrees of freedom of the horizon which interact with the with the external world so there's always the degrees of freedom which interact with the external world but for a new black hole.
Abhay Vasant Ashtekar: So to say there is, it can also be taken to be the total entropy but as a black hole becomes old evaporation proceeds then it's no longer the case.
Carlo Rovelli: In fact, I think, by and I got to this in dependent ways of thinking, but as.
Carlo Rovelli: For me, also the big surprise, or the big point of all that was the distinction between a lot of black hole in a young black hole so to black hole with the same area classically.
Carlo Rovelli: A very different geometries depending if they formed the just now by a collapsing something with that area or long ago with a much bigger area, and they have shrunk by hawking radiation.
Abhay Vasant Ashtekar: To the job it inside the horizon yeah.
Carlo Rovelli: clock, in fact, something pretty magic is to in classical generativity which is they're very different matrix inside just right the metric and is very different.
Carlo Rovelli: But from the outside, you do not see the difference at all okay unless something happens quantum mechanically that transform the horizon, that kills the horizon innocence that.
Carlo Rovelli: Has a second sequence, that the risers there's an event horizon so is this point, the crucial one, I mean unless we one realizes that.
Carlo Rovelli: What may happen physically is that the rhinos is not an event horizon.
Carlo Rovelli: One doesn't see one one cannot start discussing what happened at the singularity and the bias was insisting the physical problems will have a singularity singular solution.
Carlo Rovelli: All the calculation of Atlanta, which are very nice very good, in fact I won't learn more about them and it says about they're all in.
Carlo Rovelli: The implicit assumption that the reason is an event horizon so it's everything seeing from from.
Carlo Rovelli: From the outside, without going past the quantum gravity transition what happened, it was quite quantum gravity transition that's what I would like to know, I mean if if if those methods could say something about not a stationary.
Carlo Rovelli: object stationary object, this is an is on arrival doesn't end evaporation the physical problem that I think we should all address is what happened at the end of the evaporation.
Carlo Rovelli: Not as long as this thing is evaporating because if you keep thinking Oh, we just have to understand what happened at longer this thing is about breathing we're just always avoiding the physical problem.
Carlo Rovelli: And it seems to me that we have means I mean look what when certain we have men study what happens at the end of their preparation, so when you got to the.
Carlo Rovelli: To the the little wavy line in the in the in the picture, which is, which is are there.
Carlo Rovelli: In there it's completely different where the actual distance between the reason and the end the article zero on the left side is short or large.
Carlo Rovelli: A black hole has a huge spatial distance between the rise on the inside, a young and in this distance is what it's completely lost in the kind of calculations that treat the rise, the black hole as a stationary object.
Carlo Rovelli: With an event horizon.
Carlo Rovelli: I shut up how long ago with a very curious to know what is Hello question to shut up.
Hal Haggard: And so I actually had a somewhat technical question for you mad it's about the nature of the saddles so I suspect, you know this recent work of.
Hal Haggard: can save it and siegel and also at Whitney has been thinking about these things about this follows up on work old work of yarmulke and referral sorkin about the viability of certain complex metrics as saddles.
Hal Haggard: And so I was curious about these island saddles and whether you know that, whether they satisfy these sort of viability criteria and of local and sorkin and and whether we can think of them as really complex saddles that are related to a lorente and metric.
Ahmed Almheiri: But that's a great question, unfortunately I don't know.
Ahmed Almheiri: What the answer is for these configurations that he talked about, but I do know that some people are thinking about this and.
Ahmed Almheiri: well.
Ahmed Almheiri: So far, I remember that some some class of them satisfy this and well there was one example, which is luckily not relevant to any evaporating black hole, but something about.
Ahmed Almheiri: Maybe some something about.
Ahmed Almheiri: Being entangled with with a with a with a with a designer clothes universe, which I think has some problems.
Ahmed Almheiri: related to what within pointed out.
Ahmed Almheiri: base I I I don't have a straight answer for you, maybe somebody else has thought about this, I agree that it's a very interesting thing to the to investigate, to see if that rules out these these configurations or it's more support.
Hal Haggard: yeah i'd be curious if you have an opinion.
Hal Haggard: You know, speaking of wormholes that we could think of wormholes and all sorts of and physical situations right where you would have to have negative energy, and you know they could be very unfair physical.
Hal Haggard: And, and this would be a criterion for rejecting physical versions I i'm not saying that yours are i'm just saying that that it seems interesting to figure out whether we can eliminate them on this basis.
Ahmed Almheiri: yeah.
Edgar Shaghoulian: yeah no it's a great question, I think that all the things that descend to an island saddle and the semi classical space time as Ahmet has drawn here, I think all of those are always going to satisfy that condition, but that hasn't that hasn't been shown.
Edgar Shaghoulian: them they're crazy or wormholes you can draw that wouldn't descent to something simple in the original facetime and those probably will be rolled up early some of those.
yeah thanks.
Jorge Pullin: Well folks has been over two hours by now, and our speakers are start sort of looking tired by now so i'd like to thank the speakers again.
Abhay Vasant Ashtekar: let's make one comment about.
Abhay Vasant Ashtekar: That just just wanted to, I mean I one of the good thing that might come out of this is really you know this calculation was done in which the end of the.
Abhay Vasant Ashtekar: If, like, I mean I Scott was saying that in the lorenzen domain, there is a.
Abhay Vasant Ashtekar: The dynamical geometry inside the horizon and that dynamic law right geometry is pretty dramatic and.
Abhay Vasant Ashtekar: And that somehow could be captured by some idea like this, where what is really calculating.
Abhay Vasant Ashtekar: doing a nuclear and calculation doing this complex thing, etc, but that is captured in the physics, of what is happening.
Abhay Vasant Ashtekar: But again, in our view, then that would be correspond to calculating the the entropy of the surface degrees of freedom yeah so I, because here there's no.
Abhay Vasant Ashtekar: dynamical geometry in sight right and all these geometries or is that right, first of all, that all the job, it is a nuclear domain domain are not really dynamical.
Ahmed Almheiri: Well, if you continue to learn to me our dynamical now.
Abhay Vasant Ashtekar: Why, I mean So what is the geometry that you're down up here just inside the horizon, I mean, how does it compare that's that that would be fantastic.
Abhay Vasant Ashtekar: So does it compare in any way with the geometry that we find out anybody finds by just looking at.
Abhay Vasant Ashtekar: The solving aisense equations with the with the special intensity given by the flux.
Ahmed Almheiri: Would you say that that maximum extent that short shelf.
Ahmed Almheiri: Space time.
Ahmed Almheiri: dynamical black hole or not.
No.
Abhay Vasant Ashtekar: wrong.
Abhay Vasant Ashtekar: um but that dynamic that that that analytical intuitive sense.
Abhay Vasant Ashtekar: yeah, no, no, but they're not none none none none, I mean like like this surfaces developing long astronomical next is this dynamic, I mean that kind of non trivial phenomena that that.
Abhay Vasant Ashtekar: So just comes out of some you know very conservative calculation in semi classical gravity just taking the solving nice tense equations with you know stress in terms of informing matter.
Ahmed Almheiri: I thought I thought that the eternal torture black hole.
Ahmed Almheiri: The length inside does grow arbitrarily large.
Abhay Vasant Ashtekar: No, but this is really time dependent mass right, it is.
Ahmed Almheiri: I understand I understand I understand that aspect but I, but I was just pointing out that even for the eternal black hole that the length of the interior does grow arbitrarily large.
Abhay Vasant Ashtekar: But but you're not to eat a black hole in the picture.
Ahmed Almheiri: I know I know I know.
Abhay Vasant Ashtekar: I was, I was really referring to the picture up here.
Abhay Vasant Ashtekar: But, but no, but the dynamical in the sense of our time.
Abhay Vasant Ashtekar: dynamic in the sense that semi classical solving the semi classical equations right to this specific answer you get white that kind of metric and we just not charging metric is it's not if, like this metrics i'm not source free, whereas classical is source free so that was different.
Abhay Vasant Ashtekar: Now.
Ahmed Almheiri: I think I think there are actually well um.
Abhay Vasant Ashtekar: Oh, but then you.
Ahmed Almheiri: know our examples of this calculation for the national black holes, you can send your reference.
Abhay Vasant Ashtekar: Okay, thank you.
Abhay Vasant Ashtekar: So sorry honey I just.
Jorge Pullin: Okay, thanks everyone, and perhaps you can repeat this at some point in the future.
Abhay Vasant Ashtekar: Thank you and thank you very much john with for.
Abhay Vasant Ashtekar: Both parties patient.
Abhay Vasant Ashtekar: patience and everything, thank you.
Ahmed Almheiri: This is a lot of fun thanks guys.
Jorge Pullin: bye bye bye bye.