Jorge Pullin: speaker today is Henry Maxfield will speak about observations of Hawking radiation that page curve and maybe
Rick
henry: Right. Yeah, thanks for the introduction and it's really a pleasure to be to be able to speak to you today and and I've been asked to
henry: Try to communicate some of the recent excitement. There's been in the sort of strings community about
henry: Progress on on new ideas and black hole information problem. And one of the things that's really exciting to me about this is that these new developments are not things that depend on on some details of
henry: UV completions of the physics and
henry: But really are.
henry: Things that are there in the low energy theory that that is quite conservative and that I think people from different approaches can
henry: Can potentially start making contact on and that's one of the reasons I'm very excited to be here today is to to get some input from from
henry: From some of you from perhaps the background that's that I'm less familiar with and and hopefully you can can make some contacts in different approaches and start a bit of a dialogue so
henry: Please do interrupt me at any time if there's something that that's unclear and I'll try to to pause regularly to to invite any, any questions.
henry: Okay, so the first
henry: Start with a, with a little bit of background. And so since the 60s and 70s with nine about your results of black hole thermodynamics from beckon seen Hawking and others that
henry: The black holes have these basic properties that look a lot like variable to federal MCS in particular one will it'll be most important today is the is the back and see hawking entropy. The area of the black hole and plank units and
henry: The immediate reaction now and you see some some thermodynamic quantity is whether you should interpret this in a statistical way whether there's a static on statistical interpretation of this so
henry: It's all question is whether this back and Stephen Hawking entropy is a count of of internal states. So let's make make that a little bit more precise with
henry: A hypothesis that we'd that we'd like to to explore and and see whether it's, it could be right or wrong. And so it's not. It's something that's a little bit stronger than just new to charity and
henry: And we thought that there's not really a very good term for this in the literature. So this is our tentative definition of what will call back and see hawking unitary it
henry: It's not a perfect name because
henry: Certainly times neither back and see nor hawking would actually have advocated this position, but nonetheless, the idea of this hypothesis is that you can
henry: If you're far for a black hole and making observations on it. So he throwing things in and measuring radiation that comes out and so forth.
henry: Then you can really think of this black hole, like any ordinary quantum system and and you can model it with some some usually Hamiltonian interaction, the outside, and in particular the dimension of that the helmet space. This describing that black hole is given by this expectancy
henry: So this is
henry: Actually
Lee Smolin: A question we will be happy to distinguish this hypothesis from another hypothesis for the purposes of the discussion.
Lee Smolin: Which is that on the next slide. I'll get various and
Lee Smolin: Okay, thank you.
henry: Okay, various options. So maybe if you've got some if you've got something that disagrees with
The options. I get on my next slide.
Lee Smolin: Thank you.
henry: Yeah, and so
henry: The immediate thing that there's
Lee Smolin: Wrongly this
henry: Is the, this is, this seems to fly in the face of standard quantum field theory in a in a black hole background with this petabytes of quantum gravity.
henry: So let's say okay this is this is sort of a strong country indication, this, this can't be. This can't be right. And so as quantitative way of asking about this is to look at look at the Hawking radiation and, in particular, look at, it's not moment entropy
henry: Over time. So you start with the collapse of black hole you start collecting the Hawking radiation and as time goes on.
henry: As you call it horrible Hawking radiation. The complete the entropy of all that often radiation is cancer. It's going to change over time. So who was in a pejorative quantum gravity that essentially the Hawking's calculation of the the state of radiation.
henry: This radiation is basically thermal at all times. So the entropy as you collect more and more and more working radiation just goes up and up and up forever.
henry: But under this hypothesis of black or you to charity. The, the entropy Hawking radiation is is quantifying an entanglement between the
henry: The hockey radiation and this black hole that we're modeling as a quantum system and that radiation, the entropy that radiation can't be larger than the
henry: Log of the total number of possible internal states. So it's bounded by the second single entry. So this would be a consequence of this black hole unity and these two things are are in conflict. So this is a plot of what the entry should look like over time. So the this curve is what
henry: Hawking would have what Hawking's calculation of the state of the radiation tells you just increases forever. And then when the black hole is gone. You have some cloud of radiation in a mixtape is this is some hypothesis at the end here is what happens.
henry: At the end of our vibration but meanwhile the black hole. It starts at some size and as it evaporates, it steadily decreases. And at some point, these two curves cross
henry: This is the time. Oh, cool, that the page time and and so here this is the long before the black hole is represented. So it's halfway gone, you have
henry: You have a discrepancy between these two ideas preservative kind of gravity is seems to
henry: Exceed given entropy that exceeds this bound. That would be a suggested by this hypothesis of vacancy for community and very importantly for us today. There's a attention.
henry: Even when the black hole is still very large and you still think semi classical physics has there shouldn't be anything wrong with with semi classical physics and so
henry: Okay, there's, there's a tension here. So here's the various possibilities system what might happen in a complete theory. So the, the red curve is as a scenario of information last so the maybe the black hole evaporates and the Hawking radiation is just mixed and and that's
henry: And that's just the way things are. And another possibility is that ok semi classical gravity applies for all time. So hockey is correct. But once the black hole becomes
henry: planking becomes very small list. There's some new physics that comes in. Maybe resolves the singularity in some way. And then, and then all that
henry: Information of the black and the black hole, if you like, I can come out again.
henry: Later, and either it could come out very very quickly in a huge explosion or it could come out over a parametric longer time.
henry: But I'll identify any of these scenarios is how to close them as as remnants and a remnant here for my purposes means that you have an object with
henry: Fixed mass or fixed energy that has an unbounded possible number of internal states. So in this case, you could start with a black hole of any size and the entropy could be as large as you like. Just by starting with a bigger initial black hole.
henry: And the third possibility is is the one that suggested by black unity and this is this page curve where
henry: First, the entropy of one woman shows up and then it starts coming down again. And this is what you would expect, have a very generic quantum system if you if I
henry: Was a good quantum system if I
henry: If I had some hot lump of metal and collected the radiation is that lump of metal cooled, then this is the curve that the boy, and what my manager P would follow for that for that. A lot of metal.
henry: Lee is that
One of these
Lee Smolin: He wanted you to distinguish is the hypothesis that the boundaries on the
Lee Smolin: Information that the channel capacity of the horizon as a child to transmit quantum information.
Lee Smolin: So it's not about on the number of
Lee Smolin: internal states best abound.
Lee Smolin: On the possibility of communicating information to the horizon to
Lee Smolin: First, yeah.
henry: Yeah, so if if one of these scenarios where it was correct, then you would have to give some different interpretation for the for what the black hole entropy what the backseat hawking entropy is telling us and and I'll be agnostic about that. But yeah, that's certainly one
Abhay Ashtekar: What, but I think that point is important in terms of, you know, some criticisms about remnants and so on, because in that viewpoint, as you just said that this is not necessarily the internal states of the blackboard, which is what you have, assuming
henry: That which i know i'm not i'm
henry: So yes, so we try and be as clear as possible. I'm not
henry: An issue. I don't want to assume this this magazine organ unit charity. I'm taking it as a hypothesis to be checked and this
henry: What this this graph has given me. Is he is a very sharp distinction that's all experimental distinction. I'll argue over the next few minutes that I can use to try and test this.
Abhay Ashtekar: No, but you did say that's it, and then we'll switch have an
Abhay Ashtekar: unbounded number of internal state. So you gotta shoot you like equating the making Stephen Hawking entropy with the internal states, and that is the distinction that was drawing basically
Lee Smolin: Yeah.
Abhay Ashtekar: We should bond because this may say, yeah.
henry: Yeah, let's say, yeah, maybe I'll say, well, it doesn't. I'm not going to refer to you much to to what the remnants. Yeah, yeah. So
henry: Yeah, okay. It would be my my definition of remnants is not going to be terribly
Alejandro PEREZ: Sorry, I guess the question is what do you mean by this healer space, whose dimension is exponential
Alejandro PEREZ: The area of the black hole.
Alejandro PEREZ: Is the hubris place of
Alejandro PEREZ: The full system or are you talking about some partial piece of it. Does it include our internal states of the black hole or not.
henry: Yeah, so it includes the
henry: internals. So yeah, let's all go back to the definition which is
henry: The last slide, which was, which was carefully worded. So the idea here is that I can
henry: Have this this hypothesis is that
henry: If I have some black hole forming and evaporating. I can
henry: I can be ignorant of the fact that there's a black hole there. I could just maybe cut out some sphere. That's a bit far from the black hole so curvature is a week and so forth.
henry: And just say whatever is inside that sphere is some quantum system with this number of possible internal states. So the hypothesis is this counts all the possible internal states. It's not some subset, there's not some somewhere I can hide extra states or so forth. This is
henry: There's a, there's a model for everything that I see as an as an observer, or an observer very far from the black hole and everything can be
henry: Everything that goes in and comes out can be modeled as an interaction with a with a system of this
space dimension.
Abhay Ashtekar: Yeah, so
Abhay Ashtekar: Different from what he was suggesting, right, I mean this is
Abhay Ashtekar: Because, guess
Abhay Ashtekar: The was interesting that this is not the nothing to do with the total number of internal states, but it could just be the available states that are available for interacts with their external world.
Abhay Ashtekar: So for example, I think what you call remnant appear might not be is not compatible with the, what you call hawking benkenstein hypothesis. I just wanted to make note of this and we can go on and as you said you're not going to
Abhay Ashtekar: fix the issue of remnant is not going to be important for your talk. So let's not spend too much time.
On
henry: Yeah, so, so important thing here is just to say, is one of these red and yellow curves. What happens is one of these greeting cards. What happens, and that is different in different theories and this is the
henry: And
henry: Good, so the the sort of outline. Today I'm I'll start off just by
henry: Sketching the the outline of what I'm going to do what. So actually what I'm going to be calculating today and and the sort of the physics that that it's going to be used as
henry: As input into that calculation, what I'm going to assume. And then the second part of the talk will be will be introducing these
henry: The new player in the game, which you are ready to go. I'm holes. And then the last piece. I'll talk a little bit about about some more interpretive issues. So, this
henry: The section two is probably the the main part in is
henry: I think
henry: broadly agreed on by people who are working in this area. The third part I think is
henry: People have strong and differing opinions on whether this is correct. So I get to sort of focus on this. The second part and just make a few comments on the last episode of part of the end
henry: So the first
henry: sort of idea or
henry: Idea to to the approaches that I'm
henry: I'm going to
henry: Look at operational.
henry: I want to prove this question about which of these curves is correct, by asking about measurements or what what experiments, can you perform and what you should
henry: What you should predict for the the outcome of those experiments.
henry: These are these are going to be very difficult sophisticated experiments. But in principle things, things that you could you could do if you were very powerful had a long time and I go to black holes so
henry: The, the key point here is that we talked about, of a moment entropy. And the last slide, but this is actually not a, not an observable that you can
henry: Directly work out if someone hands you a states and says, either. This is a thermal state or this is some pure state that I've picked, but I'm not going to tell you which there's no way that you can tell between the two possibilities.
henry: So if it's so you might want to attribute, something that you have to deduce from from something else. And if you really want to find out of alignment entropy, you need to perform joint measurements or many copies of the state.
henry: So this is the sort of experiment we going to think about doing so, one very nice way to to get hold of the violence P or a close relative is it was called the swab test something that in black hole physics was introduced by
henry: A number Haskell is you take two copies of some quantum system.
henry: Some, some state and you measure the operator that just exchanges the two systems. So with a simple definition for any to state side one inside to this defines this this operator.
henry: And this is, this is something that you really can measure. So this is the only piece of experimental data is going to be on slide. This is a graph from linker at our where they actually measure this one operator on on a transplant system just kind of keep that
henry: So if I asked if I mentioned this rope operator. And I asked him what the expectation value is the outcome on two copies of some density matrix row the expectation value is the tracer for A squared. What's guilt called the purity.
henry: And this is eat the minus the second Rennie entropy. So the second rainy entropy is is sort of morally something that's that's clearly relates to the phone I'm entropy
henry: So this is if I had many, many copies of my system. I could perform
henry: Lots of measurements, like it's poor swap measurements or the first two is what measurements on the second to and so forth, then eventually I would deduce this s to the second brain injury.
henry: And more generally, you can imagine measuring and operator I've called us sigma sigma here is a cyclic permutation. That is just doesn't just swap two systems but act as moving
henry: System one system to system to system three etc and system and backup system one and measuring this operator i if i this is on the right hand side is an expectation value of
henry: This experiment that I performed and
henry: And this expectation value is given by this. This Anthony entropy which is to find here.
henry: And in particular, I can take this in a formal limit of English to one, which is okay. The only. No, no, a function lineages then then this you have to make
henry: Some assumptions of whether you can actually do this this continuation and take this limit but this will be a sort of useful thing to have in mind that you can recover the volume entropy, at least formally bye for now having these entries
henry: Okay, so this is if you just had if you know you had many, many copies of some states, how you would hope a procedure for determining what the phenomenal entries, and it was many, many problems for the system.
henry: So that's what we're going to study what we're going to do is prepare this states uncle RO n of us. So this is the
henry: Collapse in identical black holes. So I'm very sophisticated and I put some collapsing matter in in identical pure states and very, very well separated black holes.
henry: And I let them evaporates and I capture all the Hawking radiation that emerges before some time you so you as a result of time on Skype loss, whether radiation escapes and
henry: And then I measure this sickly permutation operator.
henry: And if I for many experiments like this, then, then I could use what I call the swap entropy. There's some I go to get some outcome for this experiment and
henry: And the average outcome that I get when I go to encode in on a call this a swap entry and and if I'm sophisticated I could process this information and and find a what I call the SWAT one moment entropy that I could just get formerly by by this continuation back to English
henry: And I want to interpret this this quantity is swap entropy is
henry: As the entropy that you would use if you are in essence, it gives out and making measurements and this is the thing we're going to ask
henry: Any questions on
Yes.
Lee Smolin: Can you can you be more precise about how you will actually make a swap operator for to back calls
henry: Yeah so. Okay.
henry: This is you'd have to go and encode this hooking radiation in constant memory somewhere with some
henry: I'm not an experimental physicist, so I'm
henry: Yeah, you'd have to collect the whole you're hooking radiation and with good fidelity and keyboard is paid rotations and so forth, you have to be a
henry: pretty sophisticated experiment list.
Lee Smolin: I guess what I'm, what I'm wondering is,
henry: Operating from
Lee Smolin: Your. Sorry. I'm wondering if you make an assumption.
Lee Smolin: About A NICE AND WHAT IS IN BETWEEN THE PARKING radiation states and the internal states by claiming that by somebody
Lee Smolin: Outside operation, you can swap
henry: The, the complete states.
Lee Smolin: I'm wondering if this is where you assume what you want to eventually
Show.
henry: I'm I'm
henry: Going to say once the radiation is very far from the black hole and I collected, it's just, it's going to be a set of freely streaming photons and protons that it's going to be very difficult to collect them and so forth, but it's it's really just a state of
henry: State in in the sort of free ass and tonic Hilda space of out states.
So that's
Abhay Ashtekar: All these backwards in the same can they share this assumed Arctic region or they are different isn't Arctic
Regions.
henry: And so I'm going to idealize to put them all in different essence arctic regions as will will show that
But that I think the swapping
Abhay Ashtekar: Right.
henry: And yeah, so the the there's going to be sort of a theoretical idealization which is that are going to collect the states at squared plus in different regions.
henry: But this is going to be a really good approximation to doing that same experiment, just very distantly from black holes that are very far apart in the same essence or the region.
Abhay Ashtekar: So I don't
Abhay Ashtekar: I think it's
henry: Just it's a version of classical composition of you.
Abhay Ashtekar: But doing the same experiment will not involved swapping
Abhay Ashtekar: And and you're now doing swapping between completely different lessons arctic regions. And that I think is
Abhay Ashtekar: What is that
Abhay Ashtekar: And this even be done in principle, I mean, we're taking something which is this you know swapping two particles in the laboratory experiment or something and when
Abhay Ashtekar: Constructing space types of multiple isn't arctic regions.
Abhay Ashtekar: And we're doing doing this experiment with with swapping that it was very, very different reasons. So we are not
Abhay Ashtekar: At ease with this basic
henry: Yeah, so the, the, this, this to actually compute this expectation value. I'm going to put them in different essence arctic regions but
henry: The to perform the experiment I wouldn't have to put them in essence arctic regions, just like when we go to the LSC. We don't have to actually measure the particles that squared plus, but when we calculate the matrix from quantum field.
Abhay Ashtekar: But all those particles do have this
Idealized
Abhay Ashtekar: All these particles shared on the symbiotic region. So, and you're coming in from that region.
henry: Whereas
henry: In your voice.
henry: When we calculate some when we calculate different scattering. When we say I'm going to
henry: Yeah, but when we calculate multiple scattering experiments that happened consecutively. The legacy of course they happen all in the same space time but the but we get just as good a result by calculating as if they live in in completely independent space time because classical composition
Abhay Ashtekar: We don't do that. We do the in the same space, but we should go.
Abhay Ashtekar: These are the kinds of issues that will come up again. So we just want to
henry: Make like a thanks for thanks for sort of fell
Abhay Ashtekar: Down.
henry: Yeah, so we can
henry: revisit that later becomes important. Good. Okay.
henry: So having said what we're going to try to calculate
henry: The one to introduce the the framework and actually get going to get some gravity into the game and
henry: I get to talk about only semi classical gravity, which are defined here which is I only want to use the low energy effective theory that we that we've developed and tested so general relativity
henry: Perhaps with some high dimension operators, if you like, plus some
henry: Plus some matter on that background.
henry: And again, to use a path integral formulation of this so
henry: To be the most convenient way to present things. So when I when I compute these
henry: These expectation values. I'll be doing some pause and global metrics. So, of course, this is difficult. We can't do it directly, but we'll see how it how against a formula and the moment and some path into labor matter.
henry: And in particular, this path integral over matter is a quantum field theory on the fixed background with metric g. So I can encode that in an effective action for that.
henry: For that, for that matter. So this is then some functional of the metric only and
henry: And by a semi classical approximation here. I mean that I'm going to look for subtle points which are stationary points of this action which is some Einstein Hilbert action. The gravitational action, plus a matter of fact of action.
henry: And
henry: And the boundary conditions is the last thing that there's going to be important here is we're going to fix the esoteric geometry and
henry: In particular, the way we fixed yes and select geometry is going to depend on on exactly what we're, what we're measuring. So this is
henry: The sort of boundary conditions you would use for a scattering experiment in quantum field theory. The only difference is that it's not just the
henry: Fields that we allow to fluctuate away from the US and select boundary that those fields include the metric. And we're going to
henry: To allow allow any metric and, in particular, even though we're going to do everything in Lorenz in signature the subtle points. We're going to include hello Queen for have
henry: The Hat different apologies and this is somewhere where perhaps the it'll be interesting to discuss with with some of you perhaps
henry: The V theory will will determine whether whether this is something that's admissible or not, but
henry: We'll see the exact sort of topology change that that we're going to to include. But this is sort of important to mark hours.
henry: There's some new technologies that are going to come in and this is is is certainly an assumption that that's going to do. We're going to make is that these technologies that are admissible as subtle points in the pathological
henry: And in particular, we because he only wants to use this low energy theory, we don't want to include a geometries that have regions have very strong curvature sort of planking curvature, where we expect
henry: The corrections to this low energy theory of to become important. So we're going to stay. We're going to stay in regions where where you're actually to the tested GR and matter. And we know that this is a good effective theory.
Laurent Freidel: Okay, sorry.
Laurent Freidel: I do have a question about that. Like, it seems to me the neurons in geometry. These two assumptions are kind of
Laurent Freidel: mutually exclusive. That is, if you want to start from an orange and geometry and you can have topology change, then you will have to have a region which, you know, they will have their UI curvature, which is fine, but so
Laurent Freidel: I think I will. Yes, assumptions are kind of not concern.
henry: Yeah, so I'll maybe I'll
henry: We'll get to exactly what the sort of new technologies are that we're going to include and
henry: And then I'll maybe I'll ask you to to ask the question again or or or comment on
Alejandro PEREZ: On that when we were going to get to this I have, I have a question. So, so, so if the problem is the one about information. And so we know that there are pair creation around the black hole and
Alejandro PEREZ: One that would make hockey radiation. The other one is going straight to the singularity. So how can an approach where you'd completely avoid you know strong caricatures, or UV questions be something that reasonable to do
henry: And confused. So that's what we, yeah. So this is, in particular, why began to focus on on. So we're going to focus on on collecting hooky radiation up to some time that's
henry: Where the black hole is too large. So we're not going to wait until the black hole is small and the way began to avoid strong curvature is will be
henry: The way that the calculation. Avoid the original strong curvature will become clear in the next couple of slides.
Abhay Ashtekar: So what is the
Abhay Ashtekar: Thing that you are driving yet. I mean, you're not
Abhay Ashtekar: So, since you're looking at the semi classical regime until you is last, which I think is very, very good thing to do.
Abhay Ashtekar: Because there are many issues. We don't understand already in that region.
Abhay Ashtekar: But if you're going to do that, then certainly you're not addressing issues of identity. So what exactly are you interested
henry: So the, the point here is that the the before the when the black hole is still large so before this endpoint.
henry: Then the semi classical approximation is still good. But nonetheless, there's a sharp distinction between
henry: The page curve which will be suggested by black hole unit charity and these red and yellow curves that would be that are given just by preservative kind of gravity on the on the black background so there's
henry: Yeah, it's a semi classical gravity seems to have nothing wrong with it. And yet, there's this very sharp distinction, so
Alejandro PEREZ: If not for an emulator that fall into the black hole that fall into the singularity inside if you, if you look at some cushy surface and you try to think about unitary evolution, then you have a piece of your state that goes to the UV curvature achieve
henry: Yes, but
Alejandro PEREZ: The Blacklist microscopic
Alejandro PEREZ: That is a question about the high caricatures and and and it's not clear to me why semi classic The semi classical approach.
Alejandro PEREZ: Actually resolve this issue of information. It might be some other issues. If I think about the geometry outside and it's evolution, maybe, but here we're talking about the unit evolution of the quantum state.
henry: Yeah, so it's important here that we are asking questions only
Abhay Ashtekar: About the
henry: About outside and what riches strapless and
henry: And perhaps the the avoiding strong curvature point will become
henry: Perhaps I can make you happy. In the next in the next couple of slides. So I'm going to start just start off by describing just Hawking's calculation and his language. And that, in particular, is something that it's insensitive to the some
henry: Though the strong curvature effects.
henry: That's good.
henry: We jumped.
I'm sure
henry: Yeah, so
henry: I can is a review of something everyone knows, so I'll, I'll go through very quickly. It's, it's how you actually do Hawking's calculation. So the way I phrase. This is to have some just
henry: A fixed black hole background of a collecting black hole. And I just want to do quantum field theory on this background. And what I'd like to measure is the expectation value of some observable that subscribe plus and
henry: And the state of what happens on squared plus is going to be determined by some initial state on squared minus, which I choose. So the way to do this calculation is you take this operator and you just do the Heisenberg evolution.
henry: Back to square minus. So I define the operator squared plus Heisenberg of all back described minus perhaps it's just free matter on his background and
henry: And okay, there's some of the scatters off the black hole of atmosphere and some that comes
henry: That sort of 3D propagates back back through that the origin back describe back sky minus and then once I've done this Heisenberg evolution.
henry: I evaluate this operator in the in the initial state described, which is to find a squared minus. So,
henry: Then you can start so maybe there's operators and expectation value of some particular mode of Hawking radiation.
henry: And it's going to give begin by the bobby voelker efficient it's if it's a free field.
henry: And in particular, because I'm doing this this Heisenberg evolution, which is, it is all happens to the past of the horizon.
henry: I don't have to worry about this drunk amateur region. So this is completely independent of what happens to the geometry of the here.
henry: What happens to the fields in here. I don't need to put any boundary conditions. I don't need to define whether they need to do anything. I'm insensitive what goes on here.
henry: Okay, so this is something that's familiar for
All of us.
Alejandro PEREZ: But we could say that we could compute this petition value is this operator with reduced density matrix in which you trace out the until that call. And that didn't see the matrix with not evolve, you need a precisely because you're tracing out the inside
henry: Which is worth it. Yeah, so this is why I've really focused on on
henry: Computing expectation values of observable so that I can them.
henry: So I'm not going to be sort of computing density matrices as an intermediate thing.
henry: It's another way you could do calculation, but that's
Alejandro PEREZ: If the Blackwell evaporates, then they would be of syllables that might not be necessary, like your idealized situation that only has new the exterior of the black hole.
Alejandro PEREZ: So,
Alejandro PEREZ: If I am in the US into the future, when the black hole has already elaborated then there will be some O's which will meet the height curvature
henry: Really. So yeah, this is why I'm only going to do observation that happened early enough times that the black hole is too large and it's
Alejandro PEREZ: The region is infinitely
Late
henry: So yes, I'm only going to insert operators that have support that is that on Skype last before some retarded time especially that I can do this.
Abhay Ashtekar: That's, that's one of the sort of things sort of peculiar to visa is true that hawking did that calculation, the simplest context or you but I mean we should really consider something which is great dynamical formulation of the black hole right not an eternal
henry: Absolutely. We will
Abhay Ashtekar: We will get there, you'll get good thank you.
henry: Um, but yeah. So the reason to introduce this is just to just to rephrase the same calculation this familiar hawking calculation, but in in pathological language rather than Hamiltonian language, just to make sure we're on we're on the same page so
henry: The path internal description of this is to use an informal ism because we're not making a complete description of final states. In particular, we're not defining what the status on this. We don't want it to.
henry: measure things or form a complete measurement on that singularity and so forth. So the correct way to do this is this in in Australia Kelly's formalism.
henry: So that means that we we do a path in trouble over over to copy spacetime. So if you like this, Heisenberg evolution that we did have the operator back described minus is
henry: By conjugating with the time evolution operators, you owe you Decker, and this path and you're on the right hand side is roughly speaking, computer you and the path into on the left hand side computer you dagger.
henry: And we again to glue these two slices. So this is going to be weighted by each of the items, some action and this is going to be rated by each of the minus i time some action with some operator insertion
henry: So I'll call this the the brass space time that does this forward evolution and the cat space time that does the backward evolution. Other way around probably would be better.
henry: And these two things get identified on this on some future Casey surface sigma plus
henry: With this insertion of the right waiting that defines this operator.
henry: So in particular, I'm doing the path integral energy on this geometry that does not include regions, a strong curvature and one set of words you can use to describe this as this identification in the black hole interior is is tracing out the interior. The language that you can use.
Abhay Ashtekar: It is the scribe also identified. I'm not clear on what exactly are we
henry: Identify yeah so we're identifying here. For this example, we're identifying all the way along this sigma plus, which includes the entirety of scribe plus
henry: The only difference is, we're going to insert this operator. Oh, so. So this is the thing that's relevant for
Abhay Ashtekar: Oh, it's just, why is that operator not also on the left hand side, if it would identify it.
henry: It's sort of this is this point here is the same as the as the point here, if you like.
henry: I was just saying in quantum mechanics, I would have some forward.
henry: Branch of for what evolution in time, I would insert some operator x or P or whatever I want to measure and then I would have a backward evolution. I'm just, I'm just redundant.
Abhay Ashtekar: OK, so the operator is inserted have both copies in both copies
henry: Or it's
Abhay Ashtekar: Just explain
henry: And there's just one operator inserted at the at that kosher service.
henry: Yeah.
Abhay Ashtekar: Exactly. Okay.
henry: Good.
henry: So and so, okay, we should now ask about how you do how the entropy works with this calculation with this path interval formalism.
henry: And now this operator. Oh, is not something that's just acting locally. It's not just some waiting of local fields, but it's something that x more the X non locally. Is this the swap operator. Yes.
henry: So I have now two black holes. Each of them has a full what evolution and a backward evolution with
henry: With similar sort of
henry: Identification going on, except now that the definition of my operator oh involved. This swap between systems. So that means I identify things in this red region and the green region in a in a slightly different way.
henry: So just, just this red and green arrows are the definition of this operator acting on Skype plus this is a swap operator economically radiation.
henry: So this is, this is the sort of picture you to the Hawkins calculation of quantum field theory on a fixed background and asked, What is the
henry: This will be the second rainy entropy calculation or the trace of RO u squared or the expectation value of the swap operator, you do the path integral on this background to compute that.
henry: In principle, and the answer you get as of course there's thermal entropy of Hawking radiation that increases forever.
henry: Okay, so, as pointed out, we should
henry: Actually have dynamical gravity in this picture, and I'm not going to go through all the details because
henry: Until we win the black hole is still large we know
henry: Roughly, what happens is that is that the black hole evaporates, so we'd no longer just have this
henry: The, the space linebacker should have a short field, type background or something like that. But we have an event horizon that shrinks over time.
henry: Eventually, it becomes plank in. So there's this endpoint, or call. So the endpoints are think of as a region of the geometry where where the characters become plankton, where the black hole is smaller than plankton and
henry: And I don't really know what goes on once. So the singularity. I think of just as the region where I don't think my effective field theory is valid anymore.
henry: And this endpoint is against some region where I don't think that's like to feel theory is valid anymore.
henry: And I really don't know what goes on in the future here unless I know something about the UV theory. So in particular, there's some no congruence. That's the future of the endpoint elaboration.
henry: Where, where I don't know what really what goes on to the future of that and this, this means this scribe plus is not going to be complete. It is only going to, it's going to terminate some evaporation time
henry: And and I'm not going to ask what happens to the future of that because it's going to depend on on exactly what happens in the singularity and so forth.
Okay.
henry: So this is how we're going to avoid any of these sort of UV assumptions and you can play the same game as before. And again, there's going to be a path integral, which now includes some
henry: Some metric fluctuations and so forth. And then the picture looks sort of much the same. And
henry: Okay, I think we should
henry: Hopefully that's certainly
henry: A sketch of what goes on. But hopefully, hopefully that's something we're all happy with.
henry: Okay. And so the actual calculation, then, is going to be competing this swap entry. So this is basically these these boundary conditions, again, to be the ones appropriate to do this calculation.
henry: So I've drawn these boundary conditions where there's this swap operator that's applied on some region.
henry: Up those up to some time you and
henry: And to the future of that region. There's going to be some identification. This shift between the, the same copies
henry: So there's some Cosi slice that is going to be as intellectually identified in the without this swap but then inside when these
henry: black circles. I can include my principal any geometry. I like as long as it's going to be a subtle point for this. For this I sent Hilda plus matter effective action. So these are the boundary conditions.
henry: Okay, so one Southern point here is going to be. There's two copies of the sort of the 90 subtle point that we got from
henry: Just preservative subversively including the background and effects of talking radiation and this gives me is entropy that just goes up and up and up for it. And it was a killer is it doesn't agree with back and see what community.
henry: Now, the whole point of this, this talk is to tell you that there is actually
henry: Under the assumptions. I've sort of outline. There's another subtle point which are called a rapid and I don't expect you to get the details from this. This is what the whole next section is going to be talking about
henry: job to do fairly swiftly, that's okay.
henry: It doesn't get done. Maybe what calculation, you're doing for these
Abhay Ashtekar: For which these are central points because
Abhay Ashtekar: Previously, there was only one a symbiotic region.
Abhay Ashtekar: Now, I mean after identification. There's only one Jackson Pollock region, but here you will after identification. There are multiple regions, is that correct
henry: Yeah, so it's so it's against the model these multiple black holes. I'm going to make an idealized situation where they live in separate space times, but this is actually good approximation to very well separated black holes all in the same space time
henry: Where I do measurements distance
Abhay Ashtekar: Finite yeah it is the point that I strongly disagree with them. And I think that's a vertical regions that are some reasons, but we should go.
henry: Okay, so, yeah, we could, if you prefer, we could do not have this measurement as an essence Arctic region, but some sphere that's
henry: Paramount really distant from the black hole.
Abhay Ashtekar: But the last one should be the same space time
Abhay Ashtekar: As the bike.
henry: Yes. And this this this calculation will under
henry: Cluster decomposition. If you like will be the
henry: Parliamentary well approximated by by this. I think this is really no different from doing estimates from doing separate S matrix calculations for different scattering that we might do at the ad agency and Rick
henry: They, you know, we don't have to include Rick in our scattering sermons to get this matrix of the LLC and we use different pockets of surplus, but this is perhaps maybe get to the, the, the central point and we can discuss them afterwards. I'd be happy to discuss for
henry: As long as you like, but
Simone Speziale: I'm sorry, just slowly side.
Simone Speziale: The other points.
Simone Speziale: Sorry.
Simone Speziale: You could be this other points from some classical action. But if I understood correctly, you're using an action which is
Simone Speziale: Some effective action in which in principle you should integrate exactly over the matter fields. So I suppose you don't really know it explicitly
Simone Speziale: So the subtle sir what conjecture. The or the really the result of an
Simone Speziale: Explicit calculation, and if so,
Simone Speziale: What is the explicit form of these action.
henry: Yeah, that will, this is what we're going to talk about in the next
henry: Little while yeah and the, the, the things that make this a subtle point of really going to be very generic properties of any of any local field here on the background.
henry: Yeah, yeah. So the important calculation is only that these are the, the, this picture on the left hand side is to set a
henry: Boundary conditions that I'm
henry: Looking for subtle points with these boundary conditions.
Laurent Freidel: May be another question, but
Laurent Freidel: That might become clear is that you're, you're essentially the region is now, which is a very Lawrence in concept. So are you going to replace that
Laurent Freidel: Because they're not surface can can can accept radiation. So are you going to replace this not surface by something occasion, which cannot accept radiation or are you going to keep this entity region still Lawrence him.
henry: Yes, and solid region is going to be the RNC and so
Laurent Freidel: In the end,
henry: This subtle point is actually is the subtle points are strictly speaking going to be geometries that don't have a real metric everywhere. They're going to have a complex metric, but this is something that happens in if you do an integral. If you do in a cemetery integral, then this
Laurent Freidel: Will be the essence arctic regions.
henry: It's gonna be awesome topic either ensign
Yes.
henry: Okay, so here's the
henry: Here's a sketch of the geometry.
Alejandro PEREZ: Repeat without the boundary conditions.
Alejandro PEREZ: For determining the subtle points. Yeah.
henry: Yeah, so the boundary conditions are on on screen minus. So I have I have these several copies of square minus where the, the state of the matter is defined by whatever my favorite initial states of
henry: Matter is that forms of collapsing backup. The clappers forms of backup some some state of matter on squared minus pure state.
henry: And then there's these regions spray, spray you if you like that the region of scribe plus up to retire time you and
henry: I'm going to say that these these regions exists and and the matter fields are identified in this way and meta fields here would include some drivers on fluctuations as well.
henry: And identified by the green curves and then finally there's there's going to be some ass inside at Cosi slice that meets scribe plus at time you
henry: I can and and as syntactically, that will be identified it without this swap. So this piece here will be asking you identify with this piece, but I'll be I going to
henry: Not going to insist that this identification continues forever. A deep into the space time. I'm just going to say that's what happens as an
henry: IP that's
henry: Clear that's
Alejandro PEREZ: Then, you know, somehow you have under control. How many cells. There are how many solutions to your boundary conditions they are without knowing explicitly this action does effective action.
henry: And I wouldn't say necessarily know that you've got all the solutions. Okay, you might hear we argue that we've gone for 40 years without knowing about, about one of the solutions. So there may be others.
henry: But I'd
henry: Rather fridge very generic matter content.
henry: Then there is a subtle point that looks like this is what I'll claim and hopefully motivate in the next couple of minutes.
henry: Maybe I'll um I'll push on to make sure we get to the main the main punch line and then
Yeah.
henry: Good. Okay, so, so here's the picture of what the replica level. So it's this sort of a lot to absorb in in in Congo.
henry: So,
henry: This looks a lot like the the subtle point that just appears from conservative quantum gravity. The, the acid call that the the Hawking subtle point on it gives you the standard
henry: State of that makes radiation. But there's one crucial difference and the difference here is that we this this future Cosi surface. So it's got three parts. There's this the piece of scribe plus we're performing the swap
henry: Then there's some other piece, which I call sigma x exterior piece and then there's a third piece, which has become known as the the island. So this is some some some partial Cosi slice that's bounded by gamma, which is a sphere.
henry: And and the rep who wormhole is
henry: Says that this interior piece on the island is identified with this swap. So there's a swap that we impose on the outside, which is imposed by the boundary conditions, but on the inside, with something of a different geometries.
henry: So we're going to allow this so you can dynamically include a swap. If you like this is this is a possibility, that's included in there. Some of the geometries.
henry: Yeah, so this is
henry: This is what the subtle point looks like.
And
Laurent Freidel: Having an ego swap internally, does that change the topology or
Laurent Freidel: It just seemed to purge inside
henry: Yeah, it does change the topology and we'll see, in particular, if you will, the, the, a lot of the analysis or go on near this near the surface gamma and is that surface gamma, which introduces some some
henry: Some different topology.
henry: That it's not so it's a little bit different from a lot of discussions of topology changing Lorenz Ian quantum gravity because we're not talking about starting with some topology having a region, and then some different topology to the future.
henry: This this topology changes happening on this the future point of this in in contour, if you like. So it's so it's perhaps a slightly unfamiliar thing but it's, it is a different topology.
henry: So this is
henry: Yeah, I could work. I will totally told us here, but
henry: Let's do this apology is basically a cylinder food. Yeah, so the boundary condition here is I think it's a I think it's a three sphere which well yeah
henry: That's leave that for now.
henry: Yeah, and in particular this location gamma. The of where the swapping so you can you can vary this Cosi slice exactly what the coach two slices on this island without changing the action. Let's just, let's just
henry: Essentially a gauge trace, but the location of gamma the splitting surface that's something that really changes the geometry and will change this this action and effective action and we have to
henry: Locate extra eyes over the location of gamma, as well as the metric and so forth, to find the extreme and so that location is going to be determined dynamically by demanding that we have a subtle point
henry: So the plan for for motivating the existence of the subtle points.
henry: So the, the
henry: The clearest argument for these thus far is involves a slightly formal procedure which says that we, first of all, so this is just n equals two version we're performing a swap on on to black holes, but we've got this generalization web form of cyclic
henry: cyclic permutation on n black holes and we can actually reformulate the the path interval
henry: For for that n copy or and replica calculation, such that it makes sense for for any and it's just a different language that there's a natural continuation of this
henry: And then you can ask what happens to this when n becomes close to one, and we look for the condition that there's a subtle point and that condition is is that there's
henry: This gamma is what's called a continuous stream or surface. And then the last part is to is to look for some kind of extreme or surface in it of operating black hole.
henry: And that's then evidence that that that the typical wormholes will exist to find it. And we can talk more of the end about about efforts to to
henry: To get other piece of evidence together these exist and find it.
Eugenio Bianchi: I shouldn't question. Yes.
Eugenio Bianchi: Can you
Eugenio Bianchi: Clarify, what are you holding
Eugenio Bianchi: Fixed when you do this, but in Tehran. I already fixed the mass of the black hole of the temperature. That's what is what is fixed.
henry: So what yeah
henry: Strictly speaking, we're holding fix the initial state of sky minus
henry: Which is
henry: And
henry: And the time of which we're making the the observation.
henry: But are you kidding. Well, let's see.
Eugenio Bianchi: In the result. What does it depend on you get up and generate additional partition function does it depend on the temperature on the mass
henry: And it's, it's going to be more or less independence of
henry: The so you could do this with a, with an initial state. That's some thermal ensemble of of black holes, if you like, and so forth. But
henry: But in the end, all that's going to matter. It will the crucial thing that's going to matter is this geometry late times
henry: And that's going to settle down to to more or less the same thing, which is just an app that something, it looks locally like short she'll just add a vertically of evolving as evaporates and with a
henry: With a with it and restate if you like so. So these details and not that important in the end was yeah we'll see precisely what it depends on that.
Abhay Ashtekar: Since you're considering identical black hole. So on each crime mind is identical initial conditions, is that correct
henry: That's correct.
Abhay Ashtekar: Thank you.
DLT-H0: Sorry. So here is here in the original calculation of all and that was in Ukraine extinguisher and and the inner product has to be interpreted as a placeholder average
DLT-H0: In order to make sense in the
DLT-H0: Product, but here.
henry: Okay, so
henry: Rich pieces that is something that we should I didn't get to the third part of the talk is to talk a little bit about about the interpretive piece but
henry: Okay.
DLT-H0: So, so you're going to do.
DLT-H0: Is it's a similar
henry: This is, this is why I'm having to use the what I call this swap entropy, rather than formally defined for mobile entropy, but
henry: Let's, let's, um, let's, let's, I think we're only the issue aside for now I want to make sure I get to the the
henry: main point here, which I
henry: Do I have. How much longer do I have to get go through this
henry: I just want to the time and it's
Jorge Pullin: Well, there's no time limit, in principle, but, you know, people get tired after a while.
henry: Of course, yeah.
Abhay Ashtekar: And I think we're reaching about 11 o'clock, so I think it on another 1520 minutes. I think we should
henry: Say, I'll make sure we
henry: Get through
Abhay Ashtekar: This piece of the talking. I don't say anything at all about the last part, then I wouldn't be too unhappy. I can never
henry: Do it. Yeah, the paper will be submitted to the archive for this afternoon. So, so if you
henry: Pay for this is based on with on or off.
henry: So if you can put your interest. Okay, so, so the first thing I should do to get to this is to tell you what I mean by contextual surface.
henry: And then we'll then we'll, we'll sort of perform the rest of this derivation say how is this thing appears. So this is very closely related to what to go back and think and sit back and 60s, 70s. Yeah.
henry: Which is the
henry: The generalized entropy which is
henry: Now any surface or its equivalent. You can think of it as a functional either of the the island, or if it's bounding surface gamma basically equivalent information up to gauge
henry: And the generalize entropy is going to be defined as the area of this surface gamma which bounds. The, the island, plus the entropy of of matter that's both in the island and Australia. So, this
henry: The things I noticed that this region, our Union Square you is the piece of the space time, excuse me, piece of the space time that's getting swapped here. So both the island and screw you have the same funny swap they're going on for their implications.
henry: So the definition of a kind of extreme or surface. It's that it's just stationary point. If I wiggle gamma a little bit. These around then.
henry: Then to first order variations this this functional is is stationary. Yeah. One important property of this this now. Pray do evidence for is this is a really natural quantity, you should consider an effective field theory, it's something that you find a couple of independence and so
henry: I went through the evidence. Now take your time.
henry: And this quantum extreme or surface rule that you end that will gain all that all just sketch the derivation of is it's compute this what von Lohmann entropy
henry: And you, first of all, look for an island which is bounded by this quantum extreme of surface gamma and this is going to be in in the original Hawking.
henry: The original unperturbed geometry, a single copy geometry you look for this kind of extreme surface.
henry: And
henry: Then if you have several possibilities kind of extreme surfaces you you minimize over the generalize entropy and that basically the swap entropy is given by the generalized entropy
Maciej Ossowski: Of some kind of extreme or surface.
henry: This is, this is the rule, and this is
henry: The sort of ancestry of this rule is in AS, EFT and computing entanglement entropy and so forth in his work and lots of people that, but it's really a statement about about semi classical gravity.
henry: As far as we can send you this book. So this formulation of this rule is was written down first by angle hot water.
henry: Okay, so let's derive this rule and the derivation is again an ancestor basically given the given talking pathological calculation of the of the black hole that
henry: We've got yeah so that's that's the given token calculation is a version of this that has if you want symmetry. We don't have here.
henry: And so what we're going to do is just look for subtle points for this. This path and school that have a replica cemetery. So the, the, the boundary conditions themselves have some info.
henry: Symmetry and in psychology from using the the boundaries. So I'm just going to assume that that isn't spontaneously broken or or look for settles that don't spontaneously break out so much. That's a very natural thing to look for and
henry: So there's going to be an identical copies of some geometry that are going to be joined in this way.
henry: And the first thing I going to do is imagine fixing the geometry this this single copy geometry with the identifications and I going to perform the path integral of the the matter that lives on this geometry on this end copy geometry.
henry: And because it's because of this swap identifications. This is basically just a calculation of the entropy of the matter.
henry: So it's given by this up to some definitions and logs and normalization, and so forth is basically the the matter Rennie entropy of
henry: Sorry, this should be sky you union i is the island. So it's the entropy of the regions that are being that are being swapped operated and this and you have this single copy piece which is just some normalization factor that appears
henry: So that's the easier piece.
henry: And then the second piece is the gravitational action on the end on the end copy and replica geometry.
henry: And because we've got an replicas, and the the gravitational action is is local. You might just say, well, it's n times the matter action on each individual copy
henry: On each individual piece, but that's not quite true, because there's something going on at this this glowing locusts and this this correction term accounts for what's going on a gamma. So here's a picture of the geometry near gamma. So, so there's
henry: Gamma lives at the tip of these cones.
henry: And and this is going to
henry: So the geometry here is actually going to be sort of locally you kitty so
henry: Rather than gluing these two guys to space times together like this. You can imagine there's there's a contour in time that goes up and bends around it comes back down again and we're looking at the horizontal piece where the time looks, you can do this.
henry: And then the geometry locally looks like this. Each individual copy looks like a cone, but the identifications glue them together like this. So the total glue geometry is Smith.
henry: And
henry: And because there's this and this, this chemical defect on each individual geometry. That's why you need this correction.
henry: So,
henry: Apologies. It's a little bit quick but
Laurent Freidel: That's
henry: The basic idea. Yes.
Laurent Freidel: Can I ask a question about that which goes back to my original question about singularity, because I think this is where you
Laurent Freidel: So here, here we are. That's what we're discussing when you're going to change you're creating a singularity. Now, since you're in the in the quantum gravity audience we know in quantum gravity that some of these two variable, the clinical defect angle and and the area of our, our conjugate
Laurent Freidel: Which
henry: Is exactly why.
Laurent Freidel: Right, which means that, in fact, you can't fix one and the other together without violating the uncertainty principle. So so so now there is some kind of stone. I mean, it's so this calculation somehow enters the deep calling machine but there should be a lot of
Laurent Freidel: quotation mark because of that thing like you know you're really getting at the core of of trying to fix both a variable and it's conjugate variable which is impossible. So you're really interested with them. We
henry: Said, we're not fixing the area. So what I'm going to do is take have any metric that looks like this.
henry: Which okay it's going to get to make it complex so that it
henry: That it looks locally Euclidean and but this is going to be the the action on any given geometry with this.
henry: Particular with this correction term, but when I actually extra eyes and look for a subtle point that's going to include variations of that area.
henry: So that area is not something that I'm fixing. It's something that's going to be dynamically determined
henry: By varying the equations and it will indeed it'll have fluctuations. So the subsequent will have some width and I'd have to include in principle that one of the fluctuations of that area and so forth. So it's
Laurent Freidel: I think it's bringing
Laurent Freidel: In some sense, what I'm asking is where you see the Heisenberg principle at play, because this way so you are you fixing any to fixing n typically speaking the area cannot be
Laurent Freidel: Defined
henry: So we're fixing n. And so the area is just as an operator, if you like. It's a function in the in the
Laurent Freidel: Passenger languages and
henry: The geometry.
Laurent Freidel: And
henry: Then there's an uncertainty principle. But there's an uncertainty principle just tells me that the subtle point is not sharp. It has some width.
henry: And that's
Laurent Freidel: With it with his curiosity to do with you choose the precision with which you choose. And I mean that's inversely proportional to that the uncertainty principle.
Laurent Freidel: You can't you so you know you you can't arbitrarily choose the with event and you choose have a it's that's that's the main point where classical quantum different but
henry: I
Laurent Freidel: Agree with these two variables are completely can actually contribute
henry: To each other. Yeah, I agree. Um, yeah, yeah. This
henry: Is yeah this is the same in the end as well. Okay.
henry: And yeah, it certainly has a finite with maybe we should think more carefully about how that
Laurent Freidel: That's, um, I think about
henry: That. So I mean, at this point of view, it's, it's just it's a function of the geometry and we're looking to extra mile as a function of the geometry and you can then ask what the Hacienda is, if you like, what the second yet how why this is
Laurent Freidel: Uh huh. Yeah.
henry: But yeah, it has
Laurent Freidel: To do you ever come across the nation. In fact, that's the thing you ever control the ocean or you're, you're just looking at the classical yes
henry: Yes. So this is, um, yeah. And this is in fact this is a very sort of a natural continuation of your destination, if you like, of the given talking calculation. So it's really you can continuously go from this, to back, back to the givens token calculation. If you like quotes
Abhay Ashtekar: So, so the answer is that you're using classical action.
henry: Yes, I'm using. Well, I'm using a classical action as the waiting that appears in a functional integral and I'm evaluating that functional integral by looking for a subtle point and I can then subsequently
henry: Check that it's a good subtle point by evaluating the, the, the ice and if you like, or the looking at the width of that song.
So,
Abhay Ashtekar: Like, do that.
henry: Yeah, it's, yeah, I'm not going to talk about it today, but yes, it's the subtle point is is
henry: It doesn't have any any zero modes or anything like that.
Abhay Ashtekar: Okay, glad it's not, there's not
henry: This gluing if you don't want. Sure.
KALLAN BERGLUND: You're now that you're actually putting together these identified portions of the Kashi surface. Could you talk about the causal structure of these diagrams. Because, like, what's going to happen to information as it passes across, it's going to get stuck on the boundary
henry: Yeah, that's a super interesting question and yeah so empathy. So this, this is going to really matter if I want to ask what happens to somebody falls in and ends up to the future of this of this splitting surface gamma and then
henry: My answer for now is that the I'm not, I'm not exactly sure what the the right way to think about it is you have to, you have to because we're
henry: Putting this splitting surface on this future gluing piece of the console. We're really excluding anything that happens to the future of it. So you'd have to do something a little bit different. Okay, so some ideas of how to do that, that, that I won't go into now that
henry: The yeah that that is certainly not care at the moment. And it's one of the with the
KALLAN BERGLUND: Interesting questions to thanks for bringing that up. Thank you.
henry: Okay, so let's just quickly finished the this this derivation
henry: So we've got these
henry: This this effective action of the gravitational action, plus the matter effective action has two pieces. One is just n copies of the original action.
henry: And this is the, the, the only pieces left at n equals one. So you just get back to the
henry: The, the path and tour for a single replica. That is just if you like computing the normalization event of the of the Hawking state. It's just the computing the trace of the Hawking density matrix or something, something trivial like that normalization.
henry: So this gives us a
henry: What we expect for the Hawking subtle point. But then we have these correction terms that appear lead linear order close to n equals one.
henry: And and these two pieces you'll recognize as basically this generalized entropy they add up to this generalized interviewing. So you can see now that extra mile. This. This action is going to be the same thing as extra
henry: The generalized entropy on the on the background of the original geometry.
henry: In other words, looking for kind of extreme surface. And if we find a kind of extreme will surface in this background, then
henry: I'll take that as as good evidence that say there's certainly some finite range of and then for which there's for which these replicable replica geometries exist and
henry: actually constructing that that n equals two, n equals three is is is that much harder task that has been done in certain cases, but it's
henry: More challenging
henry: So that's the basic structure of the argument.
henry: And the last punchline is just to say that there is a kind of extreme ourselves in our operating back to this is a calculation you can do very explicitly in, in, in simple models, but
henry: But is that you really understand the features that lead to this are extremely generic and and really all that matters is the
henry: Yeah, it's a very generic features of quality also is back or background again to enter silly to this.
henry: I'm not sure if I want to
Laurent Freidel: Do you
Laurent Freidel: Like to make that calculation you need to define the interview matter which means you require you record of at some point because
Laurent Freidel: It's moving right so
Laurent Freidel: I guess you're doing the calculation, where the matter is kind of free. We need to have a complex in which you can make sense of the second element.
henry: Yeah, so, so, so it's very, very important here that this generalize entropy is is a cut of independent quantity. So it's something that I can define an effective field theory. So I have some sub blinking cuts off.
henry: Where the theory is well described by Einstein Hilbert plus plus some matter to find out that sub Lang can cancel.
henry: And if I change the location I cut off then then each of these terms individually will will change every normalized, but the
henry: But there's a lot of evidence now for the idea that this that some it's really a well defined thing and if
Laurent Freidel: It's an assumption or or because you know what you would need, you would need to not only include the area but Dixie curvature excavation square. I mean, there's anything after
Laurent Freidel: That guy becomes
Laurent Freidel: As you were saying the areas of quantum
Laurent Freidel: Operator, which he has some secrets any complicated spectral so so
henry: I absolutely yeah yeah so when it, when I say this area. I really
henry: It's a bit of a shorthand that really designed to inhibit action has harder of the corrections and so forth. And that will give you some new geometric functional in this area and so forth.
henry: And but the there's a there's an expansion parameter which is you have parametric control what a buy order in the size of the black hole in units of the cutoff and the cutoff is something that's going to be much smaller than a black hole, but much bigger than that.
henry: And
henry: And there's in specific models, you can really go compute how this thing gets normalized, and it's
And it's kind of independent
henry: But
Laurent Freidel: The Bay Area very complicated non local function.
henry: Yes.
henry: But if the black hole large compared to cut off scale is parametric well approximated by the area. So the area is good enough, but
Um,
Abhay Ashtekar: Yeah, so she tried to that sort of finished in about five minutes because then we can at least 10 minutes of discussion.
henry: Yes. So let's, um, there's been lots of great questions as we go along. So alum and perhaps I won't. So this is the this is in the end it's
henry: This is a calculation that you'd have to go and do. But the important point here is that if you want to find the extreme of this generalize entropy. You might think it's dominated by this area to them because of the small Judaism.
henry: But that's it actually does matter entropy plays a very important role in this context, and that is to extremism. This in going direction and
henry: And this is related to the fact that the time evolution as synthetically becomes some exponential boost close to the horizon that's that's unfamiliar from various different context.
henry: Okay, there's a there's a calculation that's the really relies on the generic six good details. Okay, so the punch line then is that we have these two subtle points. There's the the naive one from conservative back reaction.
That we
henry: Know, and love in some version. And then there's this new guy and this guy dominates is a dominant subtle at early times but this one becomes dominant elite times and in particular for computing the swap entropy
henry: You end up with the page curve on the notes so particular this generalize entropy that's giving you the swap entropy in this second case is
henry: Up to some parameter very small corrections is the magazine is the area of black hole.
henry: Okay.
henry: Now let's just make a brief comment and before. Well, I'll um I think I'll say virtually nothing about these last few slides, but
henry: We're happy to have discussions with people offline or in some future moment. And it's going to be in the paper that comes out today.
henry: So that the slight puzzle here is that Hawking's calculation, which is just the single replica thing we haven't done anything to modify
henry: No changes being made and this density matrix that hawking gave still, I don't have any, anything to say about corrections to that. But nonetheless, we've got these corrections to these replica things
henry: That give us direction so they swap entropy. So how should we resolve this, this sort of apparent contradiction is we you can't change the entropy without changing the state.
henry: So the resolutions that the to copy density matrix for two sets of Hawking radiation is not just to independent copies of the density matrix, when in fact they're correlated
henry: And they're correlated in a, in a very special way.
henry: They're correlated in in this sort of way that says that the end copy identity matrix is not just n copies of some density matrix, but it's
henry: A statistical mixture of various possibilities for some assemble all era, if you like. They're super selection sectors and this is a this is what you get by.
henry: By looking at Myspace interpretation of this and this goes back to old ideas of Coleman and getting stronger and talking and so forth in the 80s.
henry: Talking about baby universities and so forth, slightly different from what they're talking about, then various ways that the central idea is more or less the same.
henry: And this allows a single copy of The Walking Dead Sea matrix to be given by an ensemble of matrix of density matrices, each of which gives the page curve but statistical mixture doesn't
henry: But that means that the information loss from hawking the Hawking would predict is, in principle, an observable because you can't. This is a sort of the hill.
henry: Definition of a super selection sector is that is that you don't, you can never observe super positions of different soup selection sexist, you always end up essentially measuring which super selection sexy living
henry: That was
henry: That last part was extremely quick and it's probably better to have discussions about about that sort of interpretation. Another time and
henry: Lots of people will probably disagree with that interpretation as well. But given time. I think I should leave you there, and with a few different open questions. Thank you for all your discussion and questions and so forth and invite them.
henry: Further discussion now and and in the future.
henry: Thanks for your attention.
Jorge Pullin: So I have to go in a couple of minutes or bike and you manage the q&a
Abhay Ashtekar: Yeah, that's, I was able to take over. Now, so, um, so thank you very much. First of all that. But this wonderful talk. So let's thank Henry
Abhay Ashtekar: We now have the floor, open for questions and people saw the people had to leave already, but those want to stay and stay as long as you want.
Abhay Ashtekar: So please go ahead and ask questions.
Muxin Han: So I have a question about the this awesome average. Can you be more details about about what parameter you are averaging at and and what kind of ensemble will be in the Europeans.
henry: And so
henry: In the end, so what we can actually compute our various moments, if you like to this ensemble, we're not
The
henry: And
henry: From this point of view, the sets of parameters seems to be basically you average over the whole black or less matrix. There's an exponentially larger number of parameters and it's very
Muxin Han: Well, but, but here in
Muxin Han: New York, you're not in the contact areas to an SI K
henry: So you si k has has actually yeah I'm
henry: Going to do this yet, but there's an ensemble is really
henry: Is really just a property of the fact that there are spacetime wormholes and this was not long, long, long before AS, EFT was realized that perhaps not have the same language, but it was realized that this leads to soups election cycles and so forth by
henry: So in the context of black holes. This was explained by filtering skin strawman germ, they had a proposal that is in some ways an ancestor of them are ethical and also had some problems of itself, but the basic idea was the same.
Muxin Han: Okay. But, but, you know, in case you have to
Muxin Han: I think my question is, what are the system of this ensemble.
henry: So, so this this ensemble really emerges from from the fact that there's this interior of the black hole that that remains on observed at which you know you conventional language would just lead to inflammation loss for the esoteric observer.
henry: But
henry: Yeah, but there's so the fact that they're super selection sectors emerges from the fact they are entangled with this other system that's an observable.
henry: But as an esoteric observer. The only way you can prob. This system of baby universities of black hole interiors is is via
henry: You'd ask themselves, which perform a set of computing operators, so you can define this entanglement.
henry: Without any quantum superposition or quantum statistics as or classical statistics and and the fact that you get some interesting statistics is because, because these wormholes actually modify the inner product on this baby universe of its base.
henry: I don't want to go too deeply in it. Sorry. It's a little bit high level and vague, but I'd be happy to speak about it in more detail offline if you'd like.
Muxin Han: Okay.
Yeah.
Muxin Han: Well, okay. Okay, so probably we can. Yeah, I think.
Abhay Ashtekar: Any other questions, comments.
Abhay Ashtekar: Yeah, so I think you should go back to just the previous slides just a one or two where you had this summary. Nope. So
henry: This one, yes.
Abhay Ashtekar: Yes.
Abhay Ashtekar: No.
Abhay Ashtekar: I'm adding you just showed, and maybe one before because you had that the pace car again that drawn in that light.
Is
Under the previous section.
Abhay Ashtekar: Yes.
Abhay Ashtekar: Yes. So I think just so that we understand the basic the basic claim is that
Abhay Ashtekar: First of all, you are saying that taking the optimize that. In fact,
Abhay Ashtekar: That the the radical curve is the is the entropy associate with radiation and somehow they're supposed to be an assumption here that the idea of the black hole is
Abhay Ashtekar: Comes the internal degrees of freedom. Is that what the assumption is
henry: There is, that's, that's not an assumption, but rather a hypothesis that we're that we're testing and
henry: And
henry: The. Yeah, so the framework is we're making this particular set of measurements and the assumptions are that we can
henry: We can use semi classical gravity with this path in trouble, and in particular the pathological allows for topology changes because the very old idea and
henry: And and the conclusion is that it supports at least some version of this interpretation that the
henry: That the entropy of the black hole is counting and tell states or at least that if you try to observe entanglement by by these sorts of measurements as a 4K radiation that it can't exceed the
henry: The pregnancy or the entropy
Abhay Ashtekar: Okay, which is at least
henry: As an indirect
henry: Way of
henry: Is an indirect but strong indication that that in some sense the vaccine or entropy is counting internal states.
Abhay Ashtekar: So your final conclusion will be done by so if, in fact, somebody had the view that, in fact, did not counting the internal states and there is a way to convey to the states, etc.
Abhay Ashtekar: Then, in some sense, the parallax itself doesn't arise, and you would not have anything to say about that is that right
henry: So if some if
Abhay Ashtekar: If one point takes the point of view that, in fact, it's legitimate for a young black hole to, sort of, you know, an approximate approximately that the
Abhay Ashtekar: Back in Pakistan entropy is some major victory states, but as a black hole evaporates I shrinks it is no longer
Abhay Ashtekar: A measure of internal state.
Abhay Ashtekar: And
Abhay Ashtekar: I mean, you, you do have a pure state, as you say, like me, as if you take a draws surface in the regime semi classical region that you're talking about, you do have your state.
Abhay Ashtekar: And therefore, you know, if I just look at the black outside the horizon, I get some entropy that would correspond to the entropy that is shown the red car, and it's a pure state. So therefore, the entropy inside must be
Abhay Ashtekar: Just by identity.
Abhay Ashtekar: The same because the total status bill and therefore we can just take the point of view that, that means that the area shrunk so much more than half. Then
Abhay Ashtekar: The Bakken Stein Hawking. The API is not a measure of the total number of internal states and therefore there's no contradiction at all.
henry: So I have in mind here. Maybe you start with a very, very large black hole and you evaporated down until the smallest back whole way you still trust a semi classical prediction.
henry: Then there's a sharp distinction between the traditional point of view, if you like, of information lost that the the entropy of hogging radiation is still very, very large because it's entangled with an observed system and the entropy is all the radiation is he's actually small because
Abhay Ashtekar: Somehow the radiation is not right.
henry: The
Abhay Ashtekar: System is very
henry: But there's but some early hawking quantum is actually purified by some very late or quantum and this is the body's experiments with doing the swap experiments as a way to try to verify whether which of those two is the case.
Abhay Ashtekar: But supposing I just look at you know you're there and I just look at
Abhay Ashtekar: I mean, you also looking at the regime in which semi classical approximations on valid because you're not to enter into the plank regime, etc. So I just look at a point which is just about the intersection point that they that you see at the two girls.
Abhay Ashtekar: So it's semi classical Reggie know about about about about. Yes, that's something that I mean maybe closer to the intersection point, if you like, but about somebody that. Right. Exactly. Yeah. Somebody's day
Abhay Ashtekar: And so you. I mean, I would just say that, well, in that case, and I draw kosher surface all in the semi classical regime without having this can kind of calculations.
Abhay Ashtekar: And then from the point of view of the total state is pure semi classical approach to patients perfectly valid in and therefore the entropy which is sort of a registered on that exterior exterior part of the black hole, which is very large. Now,
Abhay Ashtekar: Must be equal to the entropy which is inside because of the total status here.
Abhay Ashtekar: And then it directly contradicts your picture that the
Abhay Ashtekar: The entropy is actually
Abhay Ashtekar: Decreasing
henry: Yes. So that's this is. Yeah. The main point is that is in sharp distinction to getting this result at the same time.
henry: When the, the point of the talk was to say that that this result has some support from a semi classical calculation.
Abhay Ashtekar: Right now have any
Abhay Ashtekar: Not agreed that complete contradiction with the purity of the total state.
henry: Um,
Abhay Ashtekar: If I, if I look at
Abhay Ashtekar: This
henry: So this is why this universes are important is the yeah my conclusion of the of the third part is that okay the entanglement is still there in some sense okay in a strict sense, the, the, the von entropy is given by the red cap.
henry: Right. But if you really to do this.
henry: Experiment at by collapsing black holes collecting radiation and you were, you were an experimental is trying to find the Hawking dollar matrix, if you like, or the
henry: Or the the matrix. If you think it's evolving peer to peer then then you would work out all the parameters by experiments and your experiments will be explained by a model that gives the green curve.
Abhay Ashtekar: And
henry: The reason for that is that there are super selection sectors and the you're the, the red curve is encounter.
henry: Is counting entanglement with with is counting a statistical mixture of a super selection sectors, whereas experiments or waves will land you in one swoop selection sector and so that that's that particular type of entanglement. This is in principle in knots observable.
Lee Smolin: Question by me.
Abhay Ashtekar: Yeah, please. I think
Lee Smolin: So I think I'm trying to get the same thing that you're trying to get at.
Lee Smolin: You, you have a hypothesis and you shown that the because of these new style points you can maintain a consistent descriptions your hypothesis in semi classical half integral
Lee Smolin: I have a different hypotheses. My hypothesis is that the singularity is eliminated is a baby universe. There are large amount of state there.
Lee Smolin: And they're not accessible to an external observer. So that would you called Hawking, whether they can see new the charity is false because the third scribe size does not have access to the large number of states in the
Lee Smolin: Ad universe. Now, do I understand right that what you given is a consistency argument for your hypothesis, but it's not an argument against my hypothesis.
henry: And yeah, but it's a yeah it's so sharpens
henry: What the conditions might be and it gives you a
henry: So it would suggest, at least the on the your hypothesis. There's, there's some reason why there's subtle point is forbidden. And that's, I can't. That's a reasonable point of view. Perhaps this subtle point doesn't sit on the counter of integration or perhaps
henry: Perhaps you've got some UV theory that in the IR doesn't allow for these sorts of ology changing SOLID POINTS. And that's, that's a reasonable point of view.
henry: And yeah, it's that it's the the sort of new development is saying that these are certain assumptions about what the the infrared theories is saying the word leads to the green path.
Lee Smolin: Okay, I think I understand that i i don't know how strong that is because my understanding is that we need ultraviolet physics to understand the absence of the singularity, so that I wouldn't expect to resolve the question that level you're resolving
henry: Yeah, as well. So this was the, I think the the why I wanted to focus on this version of the information puzzle. You may not think it's a positive this is this version of the this dichotomy that is happening when the black hole is still large and that's it's important that there's a
henry: If the information puddle was puzzle was just based on a disagreement about UV physics then then we were shooting in the dark. Because, because ultimately there is, there are several options that we don't know which which
henry: Which is going to be correct, or whether it's something completely new but the
henry: That it's, it's an interesting question purely because it only depends on the PS3. It depends on the infrared physics.
Lee Smolin: Yes, whenever I have
Laurent Freidel: A question.
Lee Smolin: Go ahead. Go ahead.
Laurent Freidel: At
Neev Khera: Some point. You had mentioned
Neev Khera: That there is a clinical defect.
Neev Khera: So that doesn't that mean that there's a curvature singularity and the semi you shouldn't be using semi classical physics there.
henry: And yeah, so the the conical defect here is that if I have this this end copy geometry, maybe two copies
henry: And if I were to just look at the geometry on a single copy, then it would look like there's a conical defect.
henry: But the reason for introducing that is because when you glue these replicates together in the in this in this way, the actual the full geometry is smooth so
henry: You take two cones with a pie deficit angle like this and you you slice them open. And then you glue them together, you're going to end up with a flat piece of paper.
henry: And that's the that's why there's, it's kind of a defect mechanical defect is there precisely so that the metric is the physical
henry: Actual record metric
henry: Yeah, okay.
Abhay Ashtekar: Is that okay, leave. Thank you. Okay, so that some other cancers are raised, but I don't see it. I just had an answer, raise, but I don't see any of them.
Laurent Freidel: Okay. I have a question.
Abhay Ashtekar: A lot on physically
Laurent Freidel: Unless somebody says,
Abhay Ashtekar: No, I think you're, you're the only one out now.
Laurent Freidel: So yeah no to I think need to answer your question, I understand what you're trying to do. You're trying to say whatever you use theory.
Laurent Freidel: There is some price to pay. That is, there's some consistency condition Indian father that we have to take into account.
Laurent Freidel: So I think what he's trying to say is that if you make it, but this is my baby universe you you're, you may be contradicting something that is in fact purely in the
Laurent Freidel: Slide, which is good. So we need. We didn't have a test. Now, it might be as anybody saying that in fact the southern point is not accessible from the contour
Laurent Freidel: Some but but I think it's something to face, right, is it do I properly represent your point of view. Yeah. Yeah. Okay. Thank you. Yeah. Now,
Laurent Freidel: Let's go around that point of view, and I want to go back to. So let's take seriously that there's really, you know, semi classical test that we should make our quantum gravity theory past and we should take them seriously. And I want to go back to the
Laurent Freidel: Aspect okay so so usually it is true that you know the measure the Fukushima radiation matter is explanation minus x divided by screwed of the determinant of the action.
Laurent Freidel: Okay, so usually we we it's enough to compare the action. Right. So, in the absence of topology change it's it's enough to compare the action because some of the other term is clearly sub dominant
Laurent Freidel: Term is craziness of the minute because, you know, these two. Usually you compare actions which are kind of the same substrate. So the number of modes doesn't change.
Laurent Freidel: But now, so it sounds like a technical question. I think it's a very, very important point is that now what you're comparing is really two measures on two different spaceflight.
Laurent Freidel: Which means that there is no reason to believe that the number of modes that tend to the action or the number of zero mode attended the session in one space time topology is the same or comparable to the other one.
Laurent Freidel: So, so I you know I understand this is the first type of your calculation. But I think to be really credible, you really have to compare the full quantum measure that is
Laurent Freidel: You see what I'm saying. It could be that in the other topology. There's new wealth of zero mode which somehow makes the comparison not valid or or reinforce the comparison. You know, it could be both ways. Is that, is that clear what I'm saying that is
henry: So you're suggesting that there's a sale sort of one live determinant of metric fluctuations that
Laurent Freidel: In advance
henry: One relative to the other.
Laurent Freidel: Which might be completely different. Right. So, so it's true that you will now to look at, at some frustrations, you know, scheming in the first apology versus fluctuations community over topology.
Laurent Freidel: And now you want to look at essentially the, the size of zero modes, because the other ones, which I've been to some sense infinite action right
Laurent Freidel: And and whether there's an assumption you what you're saying is that some of these two determinants at the same amount of zero moles and and that's, you know,
Laurent Freidel: I mean, there's been a lot of work in the past about people looking at feats propagating in topology change. And there's a drastic drastic things that can happen.
Laurent Freidel: So would you agree that this is the first step, it's a possibility argument, but unless you really get control on
Laurent Freidel: On this determinants or or the fact that there is in fact something comparable right each a different space time becomes very hard to compare the physics. So that's just one point I want to, to put out like if I take your point of view. Seriously, which I do, then, you know,
Laurent Freidel: That's, that's, you know, I before we can conclude that this is really what's happening. You have to be able to prove that there's a way to compare us to the movies on this.
henry: Yeah, thanks for that comment that some yeah I initially I think I didn't see any reason why they should be any physical zero in on because there's no symmetries of the space times and so forth. So
Laurent Freidel: Nobody we
Laurent Freidel: Gauge modes there. So the question is, besides
Laurent Freidel: The size of the group drastically depend on the topology of this place so
Laurent Freidel: Yeah, and listening to me the answer, but it's, you know, we were talking in Phoenix. Plus, you know, I mean, orange unit minus
Laurent Freidel: Right and listening. It's an easy thing to compare these two
Abhay Ashtekar: Okay, I think.
Abhay Ashtekar: This. Do you understand
Abhay Ashtekar: And we
henry: Know what an exciting thing as some yeah
Abhay Ashtekar: Yeah, I think I imagine you agree.
Abhay Ashtekar: So I think mission, use your hand was raised again. Is that correct or not. Yes.
Muxin Han: So my question is, is why here, you use flat and Ruby instead of all unary renew entropy
henry: And yeah, so the
If I was really competing
henry: Rainy entropy. Entropy. Then I really shouldn't allow these theoretical wormholes on employees.
henry: Because
henry: The I can an alternative way to compute things is that I first of all, compute the Hawking density matrix. And then I, you know, compute all the components of the identity matrix. And then I
henry: Compute the tricks of the square, whatever it is, by, by hand. So, you know, this hawking calculation I don't know any way to modify it.
henry: And and so I don't think
henry: To my mind, and this is a this is
henry: Perhaps the sacrilege. In some circles where the
henry: In this is really goes against a DSC fit, for example, is that really this
henry: This swap entropy
henry: Doesn't seem to me to be at least without some new ingredient is not directly interpreted as a the actual true vendome and entropy and the actual
henry: That
henry: The reasons about soup selection sectors and so forth. I said, for the the sort of formal definition of the phenomena entropy really still follows the red curve but but it's that that's in principle.
henry: That answers the question.
Yeah.
Abhay Ashtekar: So let me just not a good couple of questions and then
Abhay Ashtekar: Because nobody else has a handle handle that is raised
Abhay Ashtekar: What machine you're you're you're
Abhay Ashtekar: You're done. Right. I can lower your hand. Yeah.
Yeah.
Muxin Han: Yeah, I think.
So,
Abhay Ashtekar: The first thing is that I mean this. I know to go back to this thing about one space time versus
Abhay Ashtekar: To space stamps and you brought in things like the, you know, what happens in certain and so on.
henry: So forth.
Abhay Ashtekar: But I think this is very different because
Abhay Ashtekar: Supposing I mean because we're talking about huge timescales. First of all, so if in fact these black holes were all
Abhay Ashtekar: Residing in the same space time
Abhay Ashtekar: Then I think
Abhay Ashtekar: They will actually be drawn towards each other There cannot be an equilibrium if in fact you are just using Ice dance equation and nothing else.
Abhay Ashtekar: And I mean,
Abhay Ashtekar: We're talking about. I mean macroscopic black holes like that. I mean, in order for them to reach this lose half the Mars is absolutely gigantic period of time.
Abhay Ashtekar: Compared to even like history of the universe. And then we're not a black holes actually which start out very, very far essentially extremely far
Abhay Ashtekar: They come together and they collide and there's a whole dynamics between
Abhay Ashtekar: Them. And that, I think it's completely ignore where we actually consider two different space times and do all this identifications so that is what confuses me and I was just wondering if you have any comment on
That
henry: And so I imagine that. So, this requires a very sophisticated experimentalists who has a very long time available to him so
Abhay Ashtekar: That, that's what you need to
Abhay Ashtekar: You could search
henry: Which is and and they need. In fact, if you really want to tell the difference between the right Kevin, the green curve hashing need to do the experiment exponentially many times. This is really an incredible thing but
henry: So you could you can make an argument that they won't have time before the before the university case but no
henry: This is really, in principle, that I can. I could do these, these two black holes I can, I can have
henry: I can I have one friend who collapses a black hole that lives in the small black hole that lives in orbit around alphas and tour I and I do my black hole in orbit around the sun and keep them far apart. And if that's not far enough apart for you, then I can put it in the
Abhay Ashtekar: I don't know, but you can keep my hand in that should be included in the action.
henry: Or just prepare them in the vacuum a deep space.
henry: If you're worried about the black holes colliding before before the
Abhay Ashtekar: Before the preparation.
henry: For the evaporate, then you could just put them further apart.
henry: Parameters are further apart and any other scale are interested in
And
Abhay Ashtekar: Know, I think that time scale for which, if I take a macroscopic blackboard, which we are all interested here.
Abhay Ashtekar: Because we
Abhay Ashtekar: Want to remain the semi classical domain and so on.
Abhay Ashtekar: Then I think the time skills that will be if you just calculate right i mean
henry: These black holes will actually
Abhay Ashtekar: Come together. So I think that some dynamic and effect will be there, whether they will actually collide or not, but it will be patients that we grew up in ways that we all kinds of things which are not included in the
Calculation.
henry: That
henry: That's, that's true. I'm really, I'm thinking of this is a really a theoretical thought experiment.
Abhay Ashtekar: With Thailand.
henry: And I want to put them perpetually further apart than any other scared in the problem. I know that I that's something practically. I'm not going to be able to do that. But in principle that's
Abhay Ashtekar: I can go
henry: There anything that the only difference by the from the NFC and quantity is apparently the time scales here a parametric much, much longer than
I think
Abhay Ashtekar: We should discuss this because, because I do think that the
Abhay Ashtekar: Near the intersection point appear, but a macroscopic black hole, you will have to
Abhay Ashtekar: You like to live for, you know, it takes so long that solar mass black hole actually will come together. If all you have a new words is to Solomon's black holes and nor experimenter, who is actually putting them apart or repulsive force, they will actually come together, way before
Abhay Ashtekar: This this intersection point is actually reached
Abhay Ashtekar: Okay, let's just let's go back and let's talk about that either.
Abhay Ashtekar: So I think that that Lee and Laura were asking questions, just for us to understand
Abhay Ashtekar: I think I understood Lawrence, LawRENCE, point of view.
Abhay Ashtekar: But still you would agree that
Abhay Ashtekar: That there is no contradiction right with the idea that the total state is pure with respect the one nominee entropy and therefore
Abhay Ashtekar: The one I want to entropy
Abhay Ashtekar: A big the growing is not a contradiction.
henry: And not it doesn't
henry: Contradict anything
henry: Anything that I said today.
Abhay Ashtekar: Okay, that's good. So the statement is that the because the total status pure, therefore, I could just take the point of view that the that the in the semi classical approximation that you are looking at. Right.
Abhay Ashtekar: Sometimes calling me infrared but semi classical approximation.
Abhay Ashtekar: That the total status field. Therefore, the outside entropy must equal the inside entropy and therefore the black hole area does not capture the inside and
Abhay Ashtekar: That's the point. I can take me. I'm talking about here and entropy being the one I might be. You can pick you agree with that. Is that correct,
And
henry: That's what is
henry: Suggested by this calculation. Yeah.
Abhay Ashtekar: So you're saying that is incorrect, is what is the distance calculation.
henry: So I'm
Leaving
Abhay Ashtekar: Yeah, no, I think that
Abhay Ashtekar: Was everybody agreed. Right. That is so please go ahead
henry: I'm
henry: Sorry.
henry: The question was whether I agree the volume and entropy follows the red curve essentially sister.
Abhay Ashtekar: Well, I follow each, the water, the
Abhay Ashtekar: Yeah, probably. Yeah, but I'm on. I'm on entropy, we mean, not the one eyed man entropy is interrupted the radiation is following, something like that.
Abhay Ashtekar: But that is not a contradiction because the state is still pure I'm saying something stronger. So maybe, maybe, please let me try to say it again.
Abhay Ashtekar: The state total state is still pure in the semi classical regime and therefore what the number of states inside the black hole are not at all measured by the area of the black hole.
Abhay Ashtekar: This is just as invalid argument appear and we're talking here about the entropy. The usual
henry: If the entropy follows that red curves. And yes, I agree with
Abhay Ashtekar: Okay, so I think both Laura and you'd like to say something. So I think a lot on his hand first. As far as I could say, so a lot of these guys.
Laurent Freidel: Yeah, in fact I wanted, I wanted to maybe give some some light on on on your question about, I think,
Laurent Freidel: Please find this one property with anybody wants to say I want to relate it to a debate that has been going on in quantum gravity for a long while, right, the debate. It's a between Luke quantum gravity versus going
Laurent Freidel: There is the debate whether, when you should, there's always been this question whether, when you want is gravity. Should you do it.
Laurent Freidel: You know, given space time where you know quantum mechanics, like gravity second quantum you know just second on ties or should you include the former third quantization.
Laurent Freidel: Okay, that that allows topology change on your slide. So I think about what your questions are are are in the context where you assume that some of quantum gravity can be dealt with in the first quantities matter. In that case, you follow the right care and
Abhay Ashtekar: In the semi classical energy
Abhay Ashtekar: When you're talking about something radical about what I'm really saying is that so so whereas we blue curve is is in the context of these third quantization.
Laurent Freidel: At some point you you allow superposition of disconnected slices or topology change their what's surprising in terms of
Laurent Freidel: In what every saying and I know that resolution is that, you know, I, you know,
Laurent Freidel: Up to now, this debate has been going on forever. And it seems to be no point to resolve it, because it seems a very deep autumn question what what angry seems to be saying is that
Laurent Freidel: This question whether we should first point is your second point is that is a second point is the third month identity as some semi classical implication
Laurent Freidel: In this blue curve like which which seems really radical. I think that's what you're, if I understand property.
Laurent Freidel: I mean, do I represent properly every point of view. And then I think your, your question is that we, it seems like it's a very deep quantum question whether we should circle on title 31 times but
Laurent Freidel: Maybe there are certain observable, which are semi classical observable, which are sensitive to that shows that a fair representation of both the puzzle and
Laurent Freidel: Yes, sir.
henry: Yeah, I think perhaps I wouldn't use the same language. But if you if I interpret your word is third quantization as being as the allowing topology change this sort then. And that's a very good yeah and that's
Abhay Ashtekar: I think that the characterization. This is very similar than to saying you know that various things that outcome particular about a string community before getting this on that there should be large quantum gravity effects in in this in the semi classical idioms in which
Abhay Ashtekar: Order the semi classical gravity horse.
Abhay Ashtekar: Right. Am I agree. I agree. And that's isn't the same spirit and that is exactly what I wanted to
Abhay Ashtekar: Kind of highlight or and
Abhay Ashtekar: I also don't like the word of the language of colonization, because our
Laurent Freidel: Is the word. I mean, like, look at the theory depends on the model or
Abhay Ashtekar: No, but I'm saying that this is all within the context of
Abhay Ashtekar: What is just all second conversation was just doing a part integral and parking giggles do have this is features.
Laurent Freidel: Yes, but but it's not in the Codex have any afternoon quantization. That's what
Laurent Freidel: I mean, like, you know, quantum gravity, we assume that there's a hybrid space that we assigned to sigma, you know, which is connected. So we don't go on that.
Abhay Ashtekar: But I don't think that Henry wants to say that there is a little more space dimension of that of this I do you want to say that Henry that that they're not available space interpretation of this
henry: There is a hell of a space interpretation of this
Laurent Freidel: Election sectors right that's what
Abhay Ashtekar: For me, that would be part of second conversation right
Abhay Ashtekar: Down eyes and you know you will be charged electrodynamics their eyesight with the charge super selection set so so okay
Abhay Ashtekar: So, you know,
Laurent Freidel: I mean, I don't think you have time to talk about with the cell phones are but this alphas wherever they are, they are
Laurent Freidel: Linked to operators that, you know, Listen, God, we do have specific operators that carry neutral that allow topology change and therefore once you have this new operators, you have new quantum labels that are
Laurent Freidel: You know, the question is that here the sapphires are completely undefined and they're looking to eigenvalues have certain operators ultimately
Laurent Freidel: You have to be defined better in the economy.
henry: Okay, there is a simple model that
henry: Okay, maybe. Yeah.
Abhay Ashtekar: I mean, I really, really appreciate all the comments clarifying said, but I think Leah has been raising his hand, and I think we should quit soon. So let's at least speak now.
henry: We are you still don't think you're muted.
Abhay Ashtekar: you're muted right and
Lee Smolin: Yes. No, I'm not needed. I'm here. Yeah, I have some some questions. I love to dress, but I think they will take a little while they go in another direction, having to do with the relationship
Lee Smolin: Or the path of the formal ensembles to various assumptions about different kinds of thermal ensembles so I think I just want to thank Henry for everybody for a very clear and for being here and taking the trouble to talk with us and address us and I hope this conversation continues.
henry: Yeah.
henry: I actually, it's been a real pleasure. And if you have ever been.
henry: It's been great to take all your fantastic questions and comments. And likewise, I hope this is
henry: The start of many more conversations in the future.
Abhay Ashtekar: I mean, that's wonderful me because you said this at the beginning.
Abhay Ashtekar: Namely that you hope that there will be more conversations and you also say the dead. So I think that's really what we would also very much like I think
Abhay Ashtekar: Bringing together. And this is a great topic in which different points of view can come together. So thank you very much and let us thank Henry again.
Abhay Ashtekar: Okay so such will quit now because almost two
Hours.
Abhay Ashtekar: Okay. Bye bye.
Laurent Freidel: Thank you.
henry: Thank you.