Jorge Pullin: Okay, so our speaker today is don't worry shoe will speak about complex critical points and curve geometries and we're in San EPL sprint format for you.
Dongxue Qu: Hello everyone.
Dongxue Qu: Thank you so much for being here it's my pleasure to get to spend some time with you also send the whole he and.
Dongxue Qu: Communities to offer me this opportunity to report my recent work, so this work in collaboration is missing, to try and have won the paper is appearing, you know few weeks we are finalizing the paper.
Dongxue Qu: So this is a plow today's talk First, I will show you the motivation with this work and the previous already that's.
Dongxue Qu: Nice to introduce the chaos been for model in details and then use real and the complex credit points in the show you the real and the complex creative points in the chaos before model then in the end, I will use the other three and help protect them to show our numerical results.
Dongxue Qu: So first is the motivation and the previous or results, as we know, the semi classical consistency is important, the requirement that you look at quantum gravity.
Dongxue Qu: Today, I will focus on four dimensional lauren's a equals B form formulation, the definition of the House before model will be introduced to your moment.
Dongxue Qu: The semi classical approximation gills as large as in politics, oh spin for multitude there are many people, contributing to this area that, as in politics older spin for multitude it relates to graduate calculus.
Dongxue Qu: We are going to use numerical nicer to study the chaos info magnitude.
Dongxue Qu: Recently, there is a lot of progress in your marks on speed for models, for example as well to see form is the on the 15th Jason both plus booster this.
Dongxue Qu: being formed with normalization the effectiveness being for model and our previous work about is in Celtic expansion, a word hacks on pit road.
Dongxue Qu: Speeding form on live chat symbol, by using Monte Carlo method to study the US being phone propagator this work will extend our previous nicer when numerical a computer the ice and topic extension or spin form amplitude unseen simply show complex.
Dongxue Qu: So what they consider those that are the spin for mounted to the answer palatial complex by taking into account some orgy.
Dongxue Qu: There is an argument that the PR else being formed attitude seems to be dominated only by flight ready geometries in the semi classical region, this is called the flight in his problem livio come back to give some details about flatness problem, but actually this argument is not true.
Dongxue Qu: Because they found some courage geometries, and that is courage of our our numerical without to show that this occur, the geometries contribution and not smart EP is being formed amplitude.
Dongxue Qu: So this is a one or a result, the horizontal axis is that second go the vertical axis is proportional to the absolute value or amplitude.
Dongxue Qu: This Green point is the amplitude at fly to john this rather points are amplitude at occur, the geometries.
Dongxue Qu: And you can see, this empty to the actors occurred geometries are comparable to the amplitude at the flatter job geometries even for this law is the point.
Dongxue Qu: That empathy deficit angle is around 10 to the negative for the amplitude is still around the point of file.
Dongxue Qu: So it means in the spin for the life of here in spirit, form the last spin parameter Lambda it to shoot a beer fan at expansion parameter, then for any large or the fan Atlanta, they are always exist, a relatively small Pepsi the NGOs such that the amplitude is not small.
Dongxue Qu: In the parameters base and we're also founded this non BLU Ray jim's it contained the Code, the geometries and this occur in the geometry is ambiguous and not small, they also found that the effective action it's equal to the rejection, plus the high curvature corrections.
Dongxue Qu: We want to show this curl the geometries account from the complex creative points and the compliance creative points has been or located by the argument for the flatness problem.
Dongxue Qu: let's let me use this watermark example to show what's going on here, so this is a easy a simple integral if are equal to zero this integral is just as the also literary ocean integral.
Dongxue Qu: And the action here is the items X square mangoes are times X plus one square here are is greater or equal to zero Lambda is much greater than one here both are and the Lambda a parameters.
Dongxue Qu: Then they can solve the critical point so you can see what our is equal to zero, the Creator point is real creative point one are is not equal.
Dongxue Qu: To zero than this critical point is a complex great point so as simple integral we can compare to the amplitude that directly, and this is the result so compare the initial.
Dongxue Qu: integrations you can see, we just to replace this X by the critical point accuracy and from this result you can also see we this Lambda should be off finite number.
Dongxue Qu: We can't adjust the Center this Lambda to infinity, because if we insist Center this one into infinity than this amplitude will be zero anyways so it doesn't make sense to send Lambda to be infinity.
Dongxue Qu: Now they choose this Lambda to be a constant and applause, to the absolute value Oh, the amplitude is a function of our.
Dongxue Qu: Then, this is the attitude add to the real creative point, and these are the amplitude at the complex creative points and this attitude as a complex query the points and not small.
Dongxue Qu: So that's come back to our result warehouse similar conclusion so this point is from the inside the flatter geometry.
Dongxue Qu: It to Chris bond to the real creative point this points are the career the geometries which correspond to the complex creative points and the amplitude at these complex creative points and not small.
Dongxue Qu: So analyst I want to use this simple example to show you how the complex credit points contributed to the attitude.
Abhay Vasant Ashtekar: And that, why do you call it real critical point isn't it imaginary.
Dongxue Qu: confused because of lonely lonely souls of Korean point, you can see, this is the form, for the cream point.
Abhay Vasant Ashtekar: right but are equal to zero, it is imaginary right or equal to 02 imaginary, so why do you call it real critical point, I just want to make sure i'm not missing something.
Hal Haggard: or equal 00.
Abhay Vasant Ashtekar: Yes, this is 00 i'm so sorry.
Abhay Vasant Ashtekar: stupid, thank you, thank you.
Dongxue Qu: I can OK, so the similar idea already appeared in the in this works.
Dongxue Qu: And in the deltas remodel our without also make a closer and problem relaxed and a full file path to move when numerical a reduced the spin.
Dongxue Qu: Up to the to integral or reggie geometries and the here, we also prove this effective action is equal to the reggie reggie Action Plan something like a high character correction.
Dongxue Qu: Okay, so nice to let me talk about everything in details, so there are men is spin for models what we use today here is the API is beautiful model so yeah four dimensional triangulation.
Dongxue Qu: It includes four simple X tag phaedra and the triangles and yet here's the deal, you know it's too complex, we use the word hacks day to day notice for simplex.
Dongxue Qu: We use oriented address to denote attach pager and we use oriented business to denote the triangles, so there are two types so triangle triangles.
Dongxue Qu: Will our wives, the internal face they use H to label it and boundary faces we use be to label, it was being formed, as you to beans to eat face, then it means there are two capsules beans, the internals beans G H, and that the boundaries means GB.
Dongxue Qu: Then the speed formatting you can be writing in the integral representation with this information and the here gauge the internals being a some the wearables and the.
Dongxue Qu: SL to see group or gv it's the integrate integrated variables, this is the last two cpu one is also inter integrated wearables and here JP kezia, be they are boundary data.
Dongxue Qu: We try not to integrated all integrated awesome so we can consider them as the bear parameters so here only the internals been stamped now to the boundaries beans.
Dongxue Qu: So this is the detail the expression for the spring form action and the spin for the spin for my action in the continue to spend for MAC has a continuous speech freedom so for each TV.
Dongxue Qu: For each TV, there is a scaling get freedom, so it is that to do get fixing them they fix the first component, I would say to be one.
Dongxue Qu: And for each way, there is a continuous the gate for it, there is a continuous SL to seek it freedom, then they choose one was a group element to be identity.
Dongxue Qu: At each way there is, as you to get freedom, so we choose was the group element jv program he along the edge he to be upper triangular matrix.
Dongxue Qu: Their House are falling real power tradition here je je not an orphan not will be the critical point oh action.
Dongxue Qu: And this X and the way they are real numbers, so therefore this spin phone action is a function in terms of all these real variables and that this action will be analytic continued to the whole morphic function and all these variables will be complex wearables.
Dongxue Qu: Then in the El que je by the error spectrum the classical area will be much greater than LP square it implies large means.
Dongxue Qu: This motivates us to understand that the largest being regime by as the semi classical regime to probe the semi classical regime this deal both the boundaries beans GB and the internals been suggested by Lambda this man, there should be much greater than one.
Dongxue Qu: Then they apply the so by this point the actually the skilled, then they apply the person's submission to the EPA is being formed amplitude we got to this form, and now the internals beans are the integrated wearables and they are continues.
Dongxue Qu: So, then, we will how the jewel creative point that the integral in the spring form amplitude will follow the falling form and then here are in the boundary data.
Dongxue Qu: bases je je because he he be and the X are the integration variables, they are all the real variables.
Dongxue Qu: The real creative point will be the solution to the critical equations this as a critical equations, and that is critical equation includes the derivative or action.
Dongxue Qu: Also included the they will to action with respect to internal spins then this solution, they will give us the reggie geometries subjected to the flight nice construct.
Dongxue Qu: This is of lightness constraint and this fight in his constant seems to tell us the spin for magnitude is dominated only by the flight ready geometries in the semi classical region.
Dongxue Qu: So let's come to a concrete example to show how the boundary did had determine the ready geometries so we use this doubt has three triangulation, there are three fourths in places, and they share a common internal facing.
Dongxue Qu: The all the ids they are on the boundary, then the boundary Atlantis will determine the reggie geometry on the artist rate.
Dongxue Qu: So here, it means this are is parameter, it means is the boundary data gap, because it be, and then it will determine the boundary edge lenses and then determine the reggie geometries also attach phaedra and the triangles we used to hear us based like.
Dongxue Qu: So now we know the boundary did have you determine the ready geometry, then there are two regions one.
Dongxue Qu: The first day region if we fix the boundary data are this boundary data in the midst of lighter ready geometries on the triangulation.
Dongxue Qu: Then the dominator contribution will from the real critical point.
Dongxue Qu: And the address redeem if we fix the boundary data are, which are the myth, the curl the geometries then it means there is no real critical point.
Dongxue Qu: In this case, the attitude of will be surprised, so in the first region, the amplitude is power, logically, and the in the secondary Jim the amplitude is exponential decay.
Dongxue Qu: Then the vendor if we also like to the are very late means we need an interpolation between these two regions in order to clarify the contribution from the curve that geometries so then we introduced the use of the complex critical points.
Dongxue Qu: For the complex creative points, we need to consider the large land the integral, this is a large land integral if we see the deltas re triangulation then it's 124 dimensions.
Dongxue Qu: And the here New Orleans X under the action as our X, they are the analytic function for our belongs to you X belongs to pay.
Dongxue Qu: Then you cross cake it's all compact neighborhood are not X not here are not is the parameter and it meets the flatter it geometry.
Dongxue Qu: X not is the corresponding real critical point, then they can do the analytic extension to the variable X and the action as or X.
Dongxue Qu: Then the complex critical points, they are the solution or the complex quid pro quo equation, this is a complex critical equation.
Dongxue Qu: Okay, let me use this graph to show what's the relation between the real creative point and the complex creative point.
Dongxue Qu: So, what are you cold what are not, we have a real critical points if leaky form data our from our mouth, then this real critical point of view, more smoothly from X axis to the complex pulling So this is the relationship between the real creative point and the complex query the point.
Dongxue Qu: Then the we held a large long, that is, in particular, expansion for the integral, so the left hand side is the integral in the real.
Dongxue Qu: In the real integration domain and the red hand with that in the ass in politics expansion add to the complex career point now, you can see the dominator contribution from the complex query point.
Dongxue Qu: So this as an article expansion interplay so the two regions, I mentioned earlier, so first a review What are his are not is the real quick it's the flight geometry.
Dongxue Qu: Then the real part of the action and to the flatter geometry will be equal to zero, then this is intoxicated patient will be powerful.
Dongxue Qu: If our is not equal to are not, then the real part whoa the action at the complex acquitted point will be less than zero, so we have attempting factor this eat times Lambda to this easy to the Lambda times the real part of the action.
Dongxue Qu: So here, there is a important remark, we can consider this one or London is a fanatic expansion parameter like each bar in the quantum mechanics.
Dongxue Qu: So, although this age bar is a dimensional, but if we choose the way truth, the units each bar is just a small number, we will never let age by equal to zero so similarly here within our like Lambda to be finished it.
Dongxue Qu: Then, give them i'm a fan at the Lambda E to the lamb that hands the real part or action, maybe not.
Dongxue Qu: Maybe not small, for example, if we choose the real part of action is equal to negative one hour Lambda then this damping factor will be equal to eat to the negative one, which is not a small number.
Dongxue Qu: Okay nast maybe, let me use.
Dongxue Qu: Use some examples to show our numerical result.
Dongxue Qu: So this is our reveal this is the deltas re triangulation and like it has a serif or sunglasses and it to share a common.
Dongxue Qu: interface, and the here, we already know the boundary data will determine the boundary at lenses and then determine the reggie geometries.
Dongxue Qu: So, then we can numerical a constructed the boundary data and again the flight geometries and the computer the real critical points, these are part of the date has we got for the boundary data and the real critical points.
Dongxue Qu: So the algorithm or for the for the deltas three triangulation here, we already House a real critical point, and then we will vibrate the less this out to six if we very this less it will give us of family or boundary data.
Dongxue Qu: And then video numerically opportunity family or career geometries, so this is a ranger or the less variation and the corresponding deficit angles.
Dongxue Qu: Then, for each delta the Dempsey tango not equal to zero, it means it's a real creative point will be absent.
Dongxue Qu: Then they can numerical, but we can numerical a computer the complex creative point which is satisfied the da complex critical equations.
Dongxue Qu: By using the Newton like a recursive procedure, so this is a steps of how to numerical a computed the complex critical points.
Dongxue Qu: So first of the need of a linear rise, the complex critical equation at X not so this X naught I will call it a pseudo real critical point because.
Dongxue Qu: It is X not satisfied with the real part of the action equal to zero, and the first of the real to action with respect to G and C I couldn't do.
Dongxue Qu: But the the real to action visit respect to the eternal spins and not equal to zero, then we got the solution we call it a diva Similarly, we can keep a linear right in the complex a critical equations and then we get the one the solution that they wanted to, and the car so on got the.
Dongxue Qu: We will call this solution theon will approximated the complex a critical equate of the complex critical point and the practically we use this procedure for four times so n equals four.
Dongxue Qu: Because when we want to solve the complex a critical equation, then they put we use this the root or action and to the complex critical point.
Dongxue Qu: The maximum value or the due to action at the complex critical point to be the absolute error and this absolute error realize the on the Pepsi dangles and the how many times we repeat the whole steps.
Dongxue Qu: Here, this is the table, we got four different that's it angles and the corresponding errors, you can see, this errors us more enough.
Dongxue Qu: Once we can numerical a computer's a complex a critical point for many are Chris bond to the career that geometries we can numerically computed the action.
Dongxue Qu: And that the difference delta from the reaction so here, this is reggie action and it's real.
Dongxue Qu: So it to me, is a part of this reality we actually are multiplied by the imaginary unit, so it means it's a real part of the action will come from the real part old delta I.
Dongxue Qu: Then it means the horizontal and the vertical axis will be proportional to the absolute value oh me too, so we got to this graph well Lambda equal to 10 to the 11 and a gamma equal 2.1.
Dongxue Qu: The horizontal axis is a deficit angles and the This point is the amplitude at a fly to geometry and it's a come from the real quick points in this read points.
Dongxue Qu: They are the amplitude at has occurred geometries correspond to the complex critical points so you can see the amplitude that does occur, the geometries are comparable to the attitude at the flatter geometries.
Dongxue Qu: Even for this point so low is the point that devastated angle is around 10 to the negative for the amplitude it's still around 2.5.
Dongxue Qu: So it means the amplitude at this current geometries they are not small.
Dongxue Qu: And this blue curve it from the best fit poll on your function or delta I so when numerical live feed it to the Lambda times the real part or doubt I.
Dongxue Qu: And II to the items Lambda the imaginary part of your time, so we got to the best of feet function for Delta.
Dongxue Qu: And the here is the best of feed the coefficient and the corresponding featuring hours are listed here, and you can see, the best the feet errors, they are also small, so this without his trust it can be trust.
Dongxue Qu: Then the then the effective action will be equal to the reggie action, plus the high courage for corrections.
Dongxue Qu: And the user parameter parameter space, we are also how the contract loss this the to the Lambda times the real part of delta I, which is.
Dongxue Qu: proportional to the absolute value or the attitude and from this graph you can see, the non global region, it contains the curve, the geometries.
Dongxue Qu: And this attitude for the curve, the geometries they are not small and it means the ranger older Dempsey, to angle so for the nice surprise the altitude, is not an issue as long as this Lambda large but finite.
Dongxue Qu: And the similar for this contour plot, we can also see the ranger or deficit angles, are you locked if it's a small so but anyways from these two graphs we want to show this non BLU Ray James content, the sacred geometries, and that is currently geometries and not smart.
Dongxue Qu: So our results for the art history triangulation also make the cause and problem of relaxed so for calls and problem now usually we will consider the amplitude MED content eight terms.
Dongxue Qu: So it means each word hacks will contribute one positive reaction and the one negative already action this eight terms, corresponding to to continuous for some facts orientation all the.
Dongxue Qu: same directions and the six this continuous force blacks orientation.
Dongxue Qu: So what we consider the orientation, although for some places, then the flatness constant will change to this form.
Dongxue Qu: Here I will call this delta as as as the orientation dress that deficit angle, and this is, it can be positive, can be negative, they are the opposite orientation and to the floor simplex we.
Dongxue Qu: Then, give them the boundary data or not, the tread the orientation dress that that's the tango can be computed bit different.
Dongxue Qu: that's it is different orientations and the we found only this to continuous orientation gail SAS tool real critical point.
Dongxue Qu: And at that point, the orientation are continues, that the other six the discontinue orientations, the other orientation dressed deficit angles and not equal to do.
Dongxue Qu: then add to this point, we can get as far as in politics, so amplitude for the deltas three triangulation so here this I are is a rejection this delta and the delta I plan on something like the high quitter corrections.
Dongxue Qu: For this two different a complex creative points and that this too complex critical point is very close to that are two real critical points so by this point from this act in politics or the attitude for Dell has three triangulation the cause and problem is relaxed.
Dongxue Qu: Then let's go to the one file pack them so for one fact to pack the moon.
Dongxue Qu: it's one for simplex its refining have one for syntax into file for some places by inserting or internal statistics, so this is a simple visual complex for one file pack them.
Dongxue Qu: Then you can see very the internal set is point six and the file internal segments this rather segments I internal segments, then there are ton.
Dongxue Qu: Of boundary triangles for them for this 123 up boundary triangles and the term internal triangles, for example, this one to six and the 136 they are the internal triangles.
Dongxue Qu: Okay, then for the one file pack them the draggy geometries are determined by the boundary data Plaza they'll file Atlantis for this hour and six.
Dongxue Qu: Because we focus on the neighborhood Oh, the flag geometry, the real critical point so inside that neighborhood we can locally, change the wearables from the less to the errors by using heroines formula.
Dongxue Qu: And the here this attitude we pick high profile internal address as the integrated variables so, for example, this.
Dongxue Qu: One to it means the triangle, Chris bond two or 12126 and this G once read it corresponds to the triangle 136 so we came up with this file internal spins as the integrated variables, we also defend this day.
Dongxue Qu: This day is the integrated the integrated variables are jade park we use this H bar to label the other file internal spins other than this file.
Dongxue Qu: Then the focus on the 194 five dimensional integral in this day here K trades not it is equal to zero.
Dongxue Qu: Then, for this D so external parameter the boundary data and this case this internal spins then are not will determine the flatter geometry, and it will give us the critical point with the same orientations.
Dongxue Qu: nice to have it fixed.
simone: Yes, now infinitely many flop geometries.
simone: I mean I don't know what you leave your family there is measuring only boundary valuable to also the bulk variables in this context.
Dongxue Qu: So in this one, the external parameter content, the boundary data J, because the B and also the internal spins the truth, as well, yes, which was a file the internal spins as the perimeter.
simone: And for fixed about the recipients now they're infinitely many bulk configurations, which are flat right isn't it.
Dongxue Qu: i'm right.
simone: Okay, thank you.
Dongxue Qu: Right so here we're done They fix the boundary data and the intuitive way to form this internal Atlantis.
Dongxue Qu: If lead the form the internal Atlantis then it means the internal spins are different later this there are 212 and the song, because we have our internal.
Dongxue Qu: Internal spins than this file, all of them are deformed then this are parameters are also deformed here all the information we use the Monte Carlo method to deform, though.
Dongxue Qu: And the folder welfare tractor move there are four degree of freedom of information for delta are which keeps the geometry of flight.
Dongxue Qu: And then there is only one degree of freedom doubt are this GR occur, the geometries bids, the smart Pepsi the angles, all these devotees dangles are less than 10 to the negative sweet.
Dongxue Qu: And the answer this point, the real creative point of will be absent So although the one factor more complex is completed, we can also we can still apply the similar process theater as Darren has read.
Dongxue Qu: triangulation to computed the numeric to numerically computed the complex creative points for many.
simone: or another.
simone: Question when the sample do these divergent also.
Right.
simone: Are you using wireless is now in so with some cut off or.
Dongxue Qu: Yes, we have some cut off like in case the Bible that returns a true some cut off and, besides, here, in the end I can show you the result is the integral depends on the edge lenses the internal it lenses so.
simone: actually already knowing how it the villagers as a function of they got off, I think there will be a new and interesting results that were excited produced so far right.
simone: Tell us what is this scaling factor.
Dongxue Qu: So here we're fixing the boundary data and.
Dongxue Qu: We pick up the firewall the internal spins.
Dongxue Qu: As the integrated wearables and the what we calculated here is this date, not the amplitude.
Dongxue Qu: Not to the empty to the for the moon.
simone: Or, I understand it, I understand Okay, thank you.
Dongxue Qu: So here what we calculate is adjusted this Z and.
Dongxue Qu: Then they will you answer to this and say into this attitude.
Dongxue Qu: And then we can numerically computed the complex creative points for many different are, and then we thought to the actions and the.
Dongxue Qu: delta I so for this one file pack DEMO we also how similar result with data through triangulation.
Dongxue Qu: This the horizontal axis is the average or 10 deputy tangles and the word, a call, I think the word require access is proportional to the amplitude so this Green point is also the amplitude at the flight geometry geometries and the this.
Dongxue Qu: The right points and the attitude at the career the geometries so you can also see this empty to that occur, the geometries they are not small it's a comparable to the amplitude at the flight john tree.
Dongxue Qu: And these are the counter Plus, and we also have similar without the range Oh, the Dempsey tangos for those nine surprised the amplitude it's not banishing and, besides the render older Dempsey tangles will be enlarged if it's a smoke.
Dongxue Qu: Then we inserted the as an extension see back to the attitude we obtain the integral or whether ready geometries so here is the amplitude at it.
Dongxue Qu: So this result is around the complex quitter point to be calculate so here this action is also the reggie action class something like stuff high creature corrections.
Dongxue Qu: And here we change is a wearable from the internals beans, to the internal at lenses that out so, then this are will be a function or out.
Dongxue Qu: And here this coefficient that can be get but the numerical without so if are you cold one, then they got to the coefficient is this and the visa as smart as the feet hours.
Dongxue Qu: So, then they come to the summary, the APR is being formed and the tools, allow the curtain ready geometries there's a smart exit angles, so therefore the flatness problem is not there.
Dongxue Qu: And the curl the geometry is crisp on to the complex creative points there's a complex credit points as laterally away from the real integration to me.
Dongxue Qu: This ready geometries with the smart deficit angles, are sufficient for approximating arbitrary smos kuroda geometries.
Dongxue Qu: So the dominator contribution to the spin form attitude will be proportional to eat to the effective action here the effective action is the.
Dongxue Qu: Actual or the curly geometries classes occurring for correction or order, there are 10 square plus higher order, so this is effective action, this is a reaction and the folder Darrell has three triangulation our without also make the cause and problem relaxed.
Dongxue Qu: Now for one third TAC toe with numerical a reduce the spin for montacute to integral or reggie geometries So this is the form of the spin form anti to the fall flat file.
Dongxue Qu: And folder our to our numerical mastered how so can be applied to the others being for models.
Dongxue Qu: And the vehicle so calculated the orbits herbals for them for the correlation functions and we can also calculate more complicated complex and to do the lattice requirement we ferment and the calculated the classical limit.
Dongxue Qu: We also plan to calculate the latter definitely tangles and the higher order corrections.
Dongxue Qu: So that's all thank you.
Jorge Pullin: questions.
Carlo Rovelli: hey.
Carlo Rovelli: Make make a comment just.
Carlo Rovelli: Stop it's not really a question is a compliment it's a it's sort of just.
Carlo Rovelli: I want to say congratulations, this is, this is really fantastic and it's like Christmas, I mean it's.
Carlo Rovelli: It seems to me that this was not very beautiful but more importantly they're compatible with everything that the values previous results they don't they don't show that businesses are the wrong.
Carlo Rovelli: They show that there is a coherent clearance story.
Abhay Vasant Ashtekar: It seems to me they're incomplete like Carlo.
Abhay Vasant Ashtekar: The previous is an incomplete, because they.
Abhay Vasant Ashtekar: did not look at this complex.
Abhay Vasant Ashtekar: Critical ones isn't that what it shows.
Carlo Rovelli: Is a question was.
Carlo Rovelli: To the question where they're curve geometries represented answers, yes and, and the reason they were sort of the suspicions that they were not represent this by by taking one particular limit first we lose them.
Carlo Rovelli: So it's just by not taking that particularly be the first, but they are there, so it seems to me that this is a.
Carlo Rovelli: I mean that that's the point of view that wasn't religious of course machine has been arguing for that for a long time it's not.
Carlo Rovelli: it's not you but it's a this I found the presentation extremely clear extremely clean and I just wanted to congratulate, because I think it's very good, very good work.
Dongxue Qu: Thank you.
Abhay Vasant Ashtekar: I want.
Abhay Vasant Ashtekar: My my feeling is exactly the same, but I do think that.
Abhay Vasant Ashtekar: The previous work was incomplete, because I think that one did not realize the value of this complex critical points, so it is not that of course is no contradiction, but I think that was incompleteness which is feeling here is that not do not agree carb load that incompleteness statement.
Carlo Rovelli: yeah yeah I mean he was.
Carlo Rovelli: peaceful political star completed a.
Carlo Rovelli: conceptual things yeah I mean this is this is completely new for me, I mean I didn't know about that and and it brings together it.
Carlo Rovelli: To my mind, explains why previous results seemed incompatible with one another, but they're not, this is not this was extremely extremely clarifying I mean so i'm doing press the.
Hal Haggard: Right.
Abhay Vasant Ashtekar: question about your third point, how can I.
Hal Haggard: Just a quick point on what you were just saying I don't want to make to larger claim, but these complex critical points are what we were finding in the effective spin phones as well, so if by previous we mean just a year ago, then I would.
Abhay Vasant Ashtekar: know.
Hal Haggard: We were finding.
Abhay Vasant Ashtekar: That i'm in previous meeting you, and then there are the first tension between flatness problem I mean that they should practice problem first our roles that's what I meant by previous.
Hal Haggard: Okay, great.
Abhay Vasant Ashtekar: Michael my question about the third point here, I still don't quite understand that.
Abhay Vasant Ashtekar: I mean, in your class the deficit angles were still very small, like us, as you said, 10 to the minus four.
Abhay Vasant Ashtekar: And so, so why is it that you can get Arabic and first of all, this is just a single simplex right.
Abhay Vasant Ashtekar: you're not you're not doing in many, many force influxes.
Dongxue Qu: Now for this spectrum, we have file for some places.
Abhay Vasant Ashtekar: And the 490 5% business okay.
Abhay Vasant Ashtekar: yeah but, but for the previous lot so so So if you want to five foot for simplicity, even then, so can you just explain why is it that if, in fact, you have.
Abhay Vasant Ashtekar: very small deck is dying or 10 to the minus four you can still get arbitrary curvature I just missed that I thought that that meant that the coaching side is also small I mean.
Not arbitrary.
Dongxue Qu: Yes, so, first I want to claim for the arbitrary is most appropriate geometry than the depths it and going to do so, as long as you're how enough that for some places, then we can use it as smart Dempsey tangles to.
Abhay Vasant Ashtekar: The correct exactly exactly so you're not that's not a statement about the.
Abhay Vasant Ashtekar: Either one for simplex or five four sentences, but if you had many, many forces, please.
Abhay Vasant Ashtekar: read it.
Abhay Vasant Ashtekar: Yes, I do Okay, thank you.
Jorge Pullin: This morning.
simone: Thank you m so two questions.
simone: First, is about the.
simone: Numerical methods, so I understand you're not doing it in exact evaluation, but some approximate methods right, can you tell us something about the control, you have over the errors like are the homogeneous Lee reliable, or are there regimes in which.
simone: The arrows are smaller and regimes in which they're bigger how much is your control over their proxy mission you're doing in these new metrics.
Dongxue Qu: So first and there are two errors, if there is the errors, then there are two hours first days of the absolute error from the calculating the complex critical points So here we choose the new Newton Newton like recursive procedure, then, if we repeat the whole steps.
Dongxue Qu: Like many times, then the hour will be small, here we are only.
simone: in identifying the precise location of the critical point.
Dongxue Qu: I, yes, so we will defend the absolute error at the critical point so if it's good enough for them this maximum values to be equal to zero.
Dongxue Qu: But anyways there will be errors, so what we can do is to decrease this errors and for us, I think, equal to four is good enough.
Dongxue Qu: For this absolute error is smart enough So here we only choose an equal to four, but if you wanted to bite her you can also increase this to be file to be as light as the the computer can do that and the time is not too long.
Dongxue Qu: So this is the first hour, we have and about NASA error is from the feature works, so this is a feature of ours, and here the fit carries also small, so I think that the errors here is not a problem.
Jorge Pullin: Okay, there are two hands raised and start with Dean, Joe.
Dongxue Qu: Ah, OK.
simone: I can come back to the words.
Ding Jia: you're going to go ahead, please go ahead.
simone: Okay, and okay and there's no question was so I think, as I said, this is very clear and very nice way of thinking of these exponentially surprised.
simone: configurations as being somehow protected in some sense but existence of a complex critical point but, in your opinion, what does this bias like, how can we now.
simone: use it to move forward with this model, you pointed out to these possibility of an organization of higher order corrections to the rejection and could this be now use the, for instance in computing correlations and seeing whether.
simone: The properties that would have been expected from the original may be naive viewpoint that it was reggie all along, including the curve, the configurations.
simone: can still be made to work like could we test the things like they grab it on correlations or something like these, has an appropriate to semi classical regime, do you have ideas in practice how to use this now.
Dongxue Qu: Yes, so good that they are, they are they plan to calculate to like the coronation function and to choose observable maybe the depths tangos we plan to do that, yes, it's a it's a good idea, maybe, maybe look into it.
simone: Because this correction terminate you have gives you like a quantitative control over these corrections.
simone: So, whether the regime really existing which is beans are large enough to be semi classical but not too large to be flat in yet be GR like you can do with this modeling you have.
Dongxue Qu: Right right.
simone: But then also, we will need to control the the somehow they the arrows over the integrations, I suppose, as well, because when you start looking for correlations.
simone: you read also maintenance right.
simone: egress understand correctly.
simone: is not something that is affecting the analysis here is just identification of the southern point that.
Dongxue Qu: Yes, yes yeah CINCO CINCO CINCO about to that and I agree with everything you said yes that's it correctly.
Jorge Pullin: Okay, thanks yeah.
Ding Jia: Thanks I don't know you've question I was just wondering.
Ding Jia: Why the allowed to deficit NGOs are just small Is it because of.
Ding Jia: lattice or the boundary did or or some parameters, or some other reason why kind of large deficit bang goes.
Dongxue Qu: up so first I think your question is related to this one so as what I said, if you want to approximate smooth curve, the geometries, then we need more.
Dongxue Qu: simply says, with the smart exit angles Okay, and our without shows i've lost as to how this smart that's a tangles we can approximate to the.
Dongxue Qu: Account prosecuted, that is most current geometries so this that smart if they got sick smart FC tangos enough so we don't need more larger definitely tangles.
Dongxue Qu: Larger deficit NGOs who is also something we plan to do we plan to calculate button here, I think that there's more depth to the angles, are enough to approximated occur, the geometries.
Ding Jia: agree in principle is enough, however, in practice, guys you're definitely angle is a 10 to the minus four.
Dongxue Qu: mm hmm.
Ding Jia: On to approximate some geometry was debating with other one that you need just too many.
Dongxue Qu: So the point is if the depths it angle.
Dongxue Qu: So if the Dempsey, the angle is too large, then the expert, then the amplitude of view exponential decay, it is surprised so actually we don't we don't need a large FC bangles.
Abhay Vasant Ashtekar: Okay, what I think.
Abhay Vasant Ashtekar: Is isn't it related to the boundary data, I mean it's amazing I give you a boundary data which corresponds to.
Abhay Vasant Ashtekar: very, very good geometry, then you would get.
Abhay Vasant Ashtekar: Is which are larger.
Dongxue Qu: Yes, but to this that's a tango so now to contribute to to the amplitude they are suppressed.
Abhay Vasant Ashtekar: depends on the boundary data.
Dongxue Qu: Right so.
Abhay Vasant Ashtekar: The statement is about the boundary data.
Abhay Vasant Ashtekar: Because you're giving kind of oh.
yeah.
Zichang Huang: Sorry, I want to say something in addition so i'm actually actually, as you say that if you have like a small graph which have not enough.
Zichang Huang: park degree of freedom, the T deaths angle, will be decided by the boundary data and and then, what I want to say, in addition, is that we have already developed a algorithm that can calculate the.
Zichang Huang: Where is the critical point the complex critical point when the depth angle is about like two or four so.
Zichang Huang: In that case, actually, you can see that the critical point that come to us critical point is really far away from the real plane and.
Zichang Huang: The the real part helps action at the combat critical point is is rather small and as don't you said if if this thing happens here at large large.
Zichang Huang: Large large graph of its many warehouses, it means that this type of configuration just contribute a little to the whole fancy champion.
Abhay Vasant Ashtekar: You said that because you put a boundary data, and this is what hours are you saying that no matter.
Abhay Vasant Ashtekar: The boundary data is.
Abhay Vasant Ashtekar: The digital angle, will always be small.
Zichang Huang: or no, no, it also depends on the depends on the graph, for example, like this delta three just three word has HIV and the tango is totally decided by the data.
Abhay Vasant Ashtekar: Right, so that is what the question was asked about why this calculation what is getting related to the mind the sport and it seems to me that the primary reason is the boundary data is or incorrect.
Dongxue Qu: Yes, what I said is correct, I agree with you, yes, and I think I also saw the last question so from this graph it's very clear the the amplitude will decay if we increase the the deficit angle and this depth that angle is to determine the Panda bear the boundary that.
Ding Jia: Now, if you want to.
Ding Jia: impose bounder data is that correspond to large Delta.
Ding Jia: Yes, would you what would you do, would you change your lattice or something else.
Dongxue Qu: Oh Carson for you want to get a large Pepsi tango so you, you need to change that that the boundary did.
Dongxue Qu: Here is we don't need the large tax it angles, because of the amphitheater will surprise.
simone: You, we also you know you may also argue that you don't want large delta anyways because then even classically reggie calculus departures from GR like we know that regardless.
simone: reproduces jar in the meeting which you have many simply says, with very small they're facing angles among each other, otherwise radio, the classical level, you know policymaking the continuum theory so maybe you may argue that anyways you're not so interested in those.
simone: So here the worry was not the word was that there was only exactly zero allowed, but he only is malls are allowed a priori it's not.
simone: Of course, it will become a matter of limits and see and these analysis, makes it possible to study that continuity, but.
Ding Jia: it's a question of balance, you want practicality and you want to.
Ding Jia: correctness, then the question is how how small it is small, I mean is 10 to the minus for.
Ding Jia: small or large need those many blogs that maybe it's not.
Ding Jia: So, so I guess, then the question, my question is a what's a good value to pick for Delta, do you want it to be 10 to the minus two or 10 to the minus one or 10 to the minus three or four.
Ding Jia: To make students suppose I wanted to some calculation, I want to make it practical I can't have too many building blocks.
Dongxue Qu: I think of from the graph is a clear like so like if you extend the data to maybe 10 to the negative three or 10 to the negative to interview decrease to maybe zero the amateur the baby, maybe tend to the zero so.
Ding Jia: given your boundary later.
Dongxue Qu: Yes, it's my binary there's.
Ding Jia: Other sort of boundary data.
Ding Jia: Would order the daughter change.
Dongxue Qu: Now I think you need to decide the so what what is the smallest one the smallest ambiguity, you want to get so it depends on the model.
Ding Jia: But model you mean the action or you mean the lattice or something will parameters.
Dongxue Qu: depend on the parameters, the boundary data is waiting for the delta three so for different models, I think you need to choose a different parameters.
Ding Jia: parameters you mean the Lambda and the other partner or do you mean.
Dongxue Qu: here for the outhouse rate, it means is a boundary data it if it's one file path mood, it means that the boundary data plus that the long day they fix the here, there is a file.
Ding Jia: Internal spins yes.
Ding Jia: No, no suppose I chose, I chose different value that already.
Ding Jia: To some other avenues that question is uh what kind of Delta, would you get how do I know what kind of data, would you get.
Dongxue Qu: To the numerical calculation that you will get a different attitude.
Ding Jia: Right is it an easy calculation.
Dongxue Qu: So from this two examples I think it's easy to get to this amplitude.
Okay.
Abhay Vasant Ashtekar: Okay.
Abhay Vasant Ashtekar: The other people that questions yeah.
Jorge Pullin: Francesco has, for a while.
Abhay Vasant Ashtekar: yeah please.
Francesco Gozzini: Yes, yes, have a couple of questions, thank you i'm sure for the story, this is very, very interesting, I appreciate a lot that are different American the one that we use.
Francesco Gozzini: And when I think that your results are perfectly as color say they are perfectly compatible with what I I was involved recently.
Francesco Gozzini: And when we act we weren't just interested in searching for different things, and in fact they think that well i'm not commenting on the partner, because it is is, if not working, but for the delta free, I think that these various low suppression in in the deficit angle would.
Francesco Gozzini: be seen, for example.
Francesco Gozzini: From i'm mentioning the work of Jonathan.
Francesco Gozzini: You want to say something about it.
Francesco Gozzini: So this could be seen in fact from from the formula applied to the case, but it is very nice that you can apply your meeting young American realtors to confirm these and I have a couple of practical questions so The first one is why you to go to such large values of London.
Francesco Gozzini: So 10 to the 11 because I remember, for example, if i'm not mistaken in the work about the relation propagated.
Francesco Gozzini: To use the higher the higher powers of Lambda, but it was like 10 to the six so is that a technical reason why now you go to 10 to 11.
Dongxue Qu: Because we want to see the suppression so because we want to see, at which point it feels price so which was.
Francesco Gozzini: So say that to that we pick Lambda 10 to the six.
Francesco Gozzini: I guess that we are going to see the separation at very, very, very low value of.
Dongxue Qu: regret that, but a heater relaunch to show this graph with the suppression.
Dongxue Qu: Which is a surprise right so which was this large land.
Francesco Gozzini: So you wanted okay you wanted to reach.
Francesco Gozzini: values of delta was not very pretty colors is say okay.
Francesco Gozzini: I thought, maybe it was related also to the Monte Carlo proximity, because you have not discussed to the year or so that I think the you know, discuss the errors that may come from the Monte Carlo simulation because it does it does a statistical.
Francesco Gozzini: Calculation so.
Dongxue Qu: Right so, first I want to clarify for the deltas three I didn't use the Monte Carlo Messer only the one file practice we use with a multiple Monte Carlo method to do the defamation so, then why.
Dongxue Qu: I didn't realize the the errors from the Monte Carlo yes.
Francesco Gozzini: So you could read the.
Francesco Gozzini: Like semi analytically the date of the case with your like a new procedure.
But.
Francesco Gozzini: OK OK, and a quick question and then.
Francesco Gozzini: For the.
Francesco Gozzini: stage.
Francesco Gozzini: Well, I think I guess that complex critical points mean.
Francesco Gozzini: Complex expectation values so do you have control, I mean expectation Belize and observable our physical.
Francesco Gozzini: Predictions of the theory that to have control on.
Dongxue Qu: Oh okay so.
he's.
Dongxue Qu: So I use this graph to show the relationship between the bureaucratic point and the pump X great point so as long as the the complex the creative pointed in the analytic region region, then, then, then you can send out to the complex career points.
Dongxue Qu: and
Francesco Gozzini: Yes, but my question is that do you have control on the imaginary part institutional bed.
Yes.
Dongxue Qu: Yes.
Dongxue Qu: Yes, as a matter of a partner for the Bismarck for the observers.
Francesco Gozzini: And this is always the case for this critical points or it depends on the observer I.
Dongxue Qu: Think it's always it's always small yes.
Francesco Gozzini: Okay okay thanks.
Hal Haggard: bye bye if you're speaking you're still muted.
Abhay Vasant Ashtekar: Thank you, I will I had a question about the.
Abhay Vasant Ashtekar: ding and.
Abhay Vasant Ashtekar: Apollo point about being and Simone his comments.
Abhay Vasant Ashtekar: It has to do with them.
Abhay Vasant Ashtekar: I mean I don't understand the philosophy, so I would just like to understand it a little bit better.
Abhay Vasant Ashtekar: So, supposing I.
Abhay Vasant Ashtekar: actually took a geometry, which is very close to the black hole horizon or near that big magnifying him everything regular but curve, which is very, very large there.
Abhay Vasant Ashtekar: And I wanted to approximate I mean I wanted to get the geometry should be allies in some semi classical approximation and so, then my boundary that I would be very different from the flag boundary data that was given to us right so, then the.
Abhay Vasant Ashtekar: I mean, some are similar they seem to think that what it is OK, because the veggie calculus will also say that you get that kind of geometry one would need many, many simply says, and therefore could also be approximated with small, that is, the triangles.
Abhay Vasant Ashtekar: Is that the point of view Simone I mean I that that somehow I need many, many.
Abhay Vasant Ashtekar: What is the LIFE like in our case, in order to approximate something which is a stronger which region and that they would always be approximated with small deficit angle, but many, many of them, as opposed to a few different angles, are quite large.
simone: Right, in fact, even I would go even farther and see even smaller the hero angles, you would like, which to me kind of always makes sense, it also from the point of view quantum gravity right because we have these kind of.
simone: compact invocation of the extensive curvature which is now included in a in a periodic connection, so one makes sense, even from that point of view, to look at the configurations, in which.
simone: The extensive curvature is more on the on the parts so to avoid the missing information in this competition so to me that looked always quite consistent.
simone: Good then.
simone: Whether we did have control over the corrections, of course.
Dongxue Qu: So I think near the singularity this semi classical method and may fail because of the lack J, as in politics should feel if it's near the singularity I think there is a paper right and by me send me to try to prove this try to argue but.
Abhay Vasant Ashtekar: But what do you mean by near the city right, I mean you still find it is the curvature is very large, but it is still small compared to the plank curvature.
Abhay Vasant Ashtekar: Right, I mean like like in the near the big big bang right the downside of inflation, the curvature is 10 to the minus 12 times planter richer but it's still the curvature is still something like.
simone: A calculus in.
simone: In classical calculus you would would you would see more than exploding angles, is the need of exploding number of simply says when you're progressing in order to be able to describe what's going on there right.
Abhay Vasant Ashtekar: Now that makes complete sense to me so.
Abhay Vasant Ashtekar: All lower days, people used to think that Well, I can I can just consider.
Abhay Vasant Ashtekar: fuse fuse and.
Abhay Vasant Ashtekar: This is even in the strong coverage at ease and that I understood that, but what you're saying now makes complete sense to me, but I just wanted to make sure if there is a consensus.
simone: What when.
simone: Did you go sorry.
Carlo Rovelli: I guess.
Carlo Rovelli: there's no consensus.
Abhay Vasant Ashtekar: And there's no consensus.
Abhay Vasant Ashtekar: On but anyway.
I might.
Abhay Vasant Ashtekar: Even know.
simone: Mine was a statement that will classic gardens, which can be used as intuition, but it doesn't mean that the same thing is gone so.
simone: An idea, like the one that can.
Be.
simone: sure.
Carlo Rovelli: So some.
Abhay Vasant Ashtekar: Consensus, so let me.
Abhay Vasant Ashtekar: So Simone a presenter, an idea which is to say that well if I wanted to have reproduce some geometry in a stronger which region again is small compared the plan plan plan curvature 10 to the minus protest Parker which are, but it is Jewish because.
Abhay Vasant Ashtekar: This tend to dismiss defy times the average on this solo monsters near the horizon, the solomons blackboard, so in that case scenario would say that I would need many, many.
Abhay Vasant Ashtekar: simplicity and there are many, many what it says and small deposit and.
simone: In classical reggie calculus I won't go as far as saying we must have that in Spain forms that I don't know, but if you want to have some Jewish average IQ is, I guess, we would need that is just to be precise, think.
Abhay Vasant Ashtekar: Okay, but why are you so timid, I mean what why so let me be aggressive and let me say that well if it is to energy calculus Why is not the same thing true in.
Abhay Vasant Ashtekar: With the women in exactly for the reasons you send me the extrinsic or whichever is has to be small and therefore you need many, many of them because next music, which is very large here.
simone: Well, as as these discussions are showing it.
simone: We might be losing the precise relation to reggie calculus or really because of these analyses of complex critical points so it might be that we still get some interesting dynamics, which makes sense to us this kind of questions without having a.
simone: Very precise in relation to the calculus let's.
Abhay Vasant Ashtekar: Forget about logic algebra just take your relation with a sense of extrinsic are which have been small because of the way they.
Abhay Vasant Ashtekar: Look what would the way we do it and therefore to get large exceeds the curvature you love it down so, namely right, I mean so so what, why is that argument and what, why are you being so timid, I mean why why aren't you saying that.
Abhay Vasant Ashtekar: i'm just pushing both sides to extreme just to say I mean not just about just about anything can happen isn't your logical argument seems to suggest that I would need the district, with a large number of thing but tablo says not right.
Abhay Vasant Ashtekar: So it was good to know that you're.
Carlo Rovelli: not putting my mouse things.
Abhay Vasant Ashtekar: So what is that guy looks.
simone: Like he's acting.
Abhay Vasant Ashtekar: Now you just want the Community to know that at this point, there are different views and.
Carlo Rovelli: opinions, and I am saying that you're you meet somebody saying something.
Abhay Vasant Ashtekar: Is not saying Okay, so let me say my opinion okay.
Carlo Rovelli: Opinion so don't know.
Carlo Rovelli: Engine Simone is saying something else okay.
Abhay Vasant Ashtekar: So I said that simoni said that small extrinsic motivators because of the way that we do our or disk utilization and, therefore, if i'm in a region where it says it gets extremely large, then I would need.
Abhay Vasant Ashtekar: Lots of that implies that I would need lots of synthesis and if somebody says no that's not the case, then I would like him to explain why not.
Carlo Rovelli: Can I can I can I interject here and the monitor, allow me to say something I think.
Carlo Rovelli: Some of the different problems here one problem it's a.
Carlo Rovelli: Given the amplitude of quantum reality, how do you recover the classical limit that's one problem.
Carlo Rovelli: A completely different problem it's how you study the quantum theory and we should not confuse this to.
Carlo Rovelli: complete the and how do we study nature with this amplitude.
Carlo Rovelli: same thing in my way.
Carlo Rovelli: I guess, if I have.
Carlo Rovelli: The quantum field of the of the hydrogen atom and they want to recover the classical orbits of the of the electron I know that, for instance, if I go for large one two numbers large in I do this is a bore things or I can use.
Carlo Rovelli: wastebaskets but also, I need large numbers.
Carlo Rovelli: Of course, smaller and smaller orbits of the electron around the atoms the classical one Sir I I might play with the math but i'm not doing physics Okay, they are not just.
Abhay Vasant Ashtekar: Not just.
Carlo Rovelli: they're not just.
The.
Abhay Vasant Ashtekar: corner states that.
Carlo Rovelli: I would just.
Carlo Rovelli: I would just think the three different questions, one is how do we get the classical limit and that's what we're discussing today, which is a.
Carlo Rovelli: let's insist is a wrong physics, because the right physics in nature is not classical is an approximation.
Carlo Rovelli: So, the second is the well they might be strong classical intermediate one strong curvature regimes which are still completed classical.
Carlo Rovelli: OK, I will cover those ones that's an interesting question Okay, a separate question is what happened when the curvature start coming close to the quantum.
Carlo Rovelli: To blank and scale and then we definitely do not want to recover the any classical limit.
Carlo Rovelli: So we definitely want the theory to say something strongly different than the classical theory so that point if we have a amplitude We trust the amplitude not the limit for large J that's what I.
Carlo Rovelli: And I want to say so let's not confuse the two and the three the three is a quantum commoner if I want to happen at the end of the operational black hole I need.
Carlo Rovelli: The to look in the amplitude Sir very much away from the classical limit like if I want to know the spectrum of Adrian at home, I want to look exactly as a way as possible from the from the classical limit because they wanted the sweetness.
Carlo Rovelli: In the in the in the low.
Carlo Rovelli: curvature regime that's all what we have heard, is fantastic, and I think what what has been asked here it's a What about a stronger curvature where i'm still a way when I still don't want to look at, I believe that.
Carlo Rovelli: That quantum effect the negligible well in that case, it seems reasonable to me that.
Carlo Rovelli: There is that case there is a regime in which I can take a triangle issue sufficient is small.
Carlo Rovelli: To have sort of small as holly saying deficit angle Simone is saying that is the angle and and.
Carlo Rovelli: And and and the hedo angle so and I can I can.
Carlo Rovelli: I can use the same results for doing the classical approximation, but this does not mean that if I want to look at genuinely quantum.
Carlo Rovelli: physics at a very high curvature I need to have a lot of have.
Carlo Rovelli: A very fine triangulation I think it goes the other direction okay so.
Abhay Vasant Ashtekar: All my happy that there are some hidden questions put you in a moment, but my question was about only two.
Abhay Vasant Ashtekar: I never talked about frequent by question or the only I kept saying that well.
Abhay Vasant Ashtekar: You go near the big bang, I mean I don't set up inflation, where the courage is still pending Romans 12 times plan curvature.
Abhay Vasant Ashtekar: So it was really about to not about clear now i'm not asking about what is happening at the big bang so then i'm extremely happy to address unless you object again due to the to realize that there is consensus on this issue.
Abhay Vasant Ashtekar: That on this issue there's consensus which says that do recover such things.
Abhay Vasant Ashtekar: What would need lot of synthesis.
Abhay Vasant Ashtekar: to recover the geometry in this regime where that the temperature where the corrosion about 10 to the minus 12 times plant curvature, which is still very, very large but, but since away from Clinton.
Abhay Vasant Ashtekar: And where we trust classical general agility and therefore nice resume it seems to me that you agree that what one would need lots of.
Carlo Rovelli: to recover the full theory to the full classical generativity yes, I don't know when there are cases in which.
Carlo Rovelli: In which.
Carlo Rovelli: I mean what we know is that it will work, you know what it seems things to be clearly pointing at is that with a sufficiently fine triangulation will record the classical.
Carlo Rovelli: classical question but let's not forget that there are there are other results that.
Carlo Rovelli: That indicate that some some some aspect of the classical theory can be also recover the.
Carlo Rovelli: wi fi regulation older older calculations of the gravity propagate over we're done with a single vertical.
Abhay Vasant Ashtekar: yeah but program propagated or just because of initially this was very beautiful that everybody clarify that that if the if the data is the boundary data corresponds to your flight space, then you know to triangulation is is fine.
Abhay Vasant Ashtekar: But I that's why I was going away from and i'm saying that the boundary corresponds to still classical stronger which region, and then, when needs many, many of these things.
Hal Haggard: john I don't want to jump ahead of you, but I have a response directly to add by should I Okay, so I just wanted to recast your question in in a more general language, because I think we have the perspective that is very general on this now, so you can ask whether.
Hal Haggard: What Why are these critical points arising, and one way of seeing it is that we have a system with second class constraints with with week constraints that we're imposing.
Hal Haggard: And if you ask when I impose a week constraint, in general, when it is my semi classical limit valid.
Hal Haggard: You can see that the there's an interaction between the oscillations of your amplitude and the constraint itself, and you can you can ask when can I get a critical point under that constraint.
Hal Haggard: And that very general consideration leads to exactly this regime that Simone de was mentioning and that Dong shoe is exploring, which is a regime where.
Hal Haggard: The product of the emirati parameter the spin and the deficit angle, has to be less than or order one, and so this is something mission was already finding in the awesome topics and 20 years ago, or maybe Last, but not so long ago.
Hal Haggard: But the point is that that if you want constrained critical points it what you're saying I think is is just mathematically you can show it.
Hal Haggard: That is a that you need you need small deficit angles, if you're going to be talking about large jays and.
Abhay Vasant Ashtekar: Baraka greetings one was image a parameter a better idea of what was the 30.
Hal Haggard: The the scale of your boundary geometry the J, the scale of the day.
Hal Haggard: So I think that what don't shoes showing very much fits into that that framework, and I think that framework just shows that you do indeed need small deficit angles.
Abhay Vasant Ashtekar: Fantastic side so i'm delighted that there is consensus because.
Carlo Rovelli: Like cloud Ukrainian and I were.
Carlo Rovelli: arguing the.
Carlo Rovelli: front end.
Abhay Vasant Ashtekar: Absolutely yeah, but I think that.
Abhay Vasant Ashtekar: You can you can do whatever I mean there's a mathematical statement and then you can play with it the way you want somebody may want to keep them on the same as what would use a black hole entropy but then it is.
Hal Haggard: Exactly exactly.
Abhay Vasant Ashtekar: that's wonderful Thank you.
Jorge Pullin: Okay john has been patiently waiting.
Jon: So one of the things I found interesting in this work is.
Jon: This this plot right here that you have.
Jon: showing how the Lambda i'm sorry via the deficit angle, the maximum allowed deficit angle depends on Lambda I think I haven't seen that studied before.
Jon: In the PR all model and actually I find that dependent that that that dependence more interesting than than just the maximum allowed delta to specific Lambda and i'm wondering if you've tried to quantify exactly how the maximum.
Jon: deficit angle depends on Lambda i'm sure it depends on the triangulation and stuff like this.
Jon: But if one could get a handle on exactly how it depends on Lambda or some estimate of it then maybe for a specific geometry is when could have an estimate of how many simplicity is you, you need to approximate it.
simone: Whether it depends on gamma rays were right too much discussion we have been happening.
Jon: Is that too yeah.
Dongxue Qu: yeah So those are it to depend on aws Lambda right so um I think address question is like how much it depends.
Jon: The functional forum is there some estimate on the functional forum of of delta as a function of Lambda I.
Dongxue Qu: Think kids but to use the last slide to show it.
Dongxue Qu: may be the last one.
Jon: it's not so obvious to me from from this equation.
Sorry.
Dongxue Qu: Maybe this one, it will show the.
Dongxue Qu: hmm.
Dongxue Qu: So we put this action into this and get you the this integral maybe this shows up functional dependence.
Jon: That shows the dependence of the amplitude on Lambda.
Jon: Which is a well studied thing, but what what I was curious about is is the maximum Delta.
Dongxue Qu: Delta.
Jon: approaches course there's no actual maximum.
Jon: show the slot for giving us this quick fall off at a.
Jon: Certain delton so i'm wondering how that you know effective drop off changes as as Lambda increase, of course, is doing the zeros Lambda goes to infinity but i'm just wondering if there's any idea of how it goes to zero.
Dongxue Qu: I think it really depends on the model we used that could different models, the the different models what's the Max and taxi the angles, make it the decrease.
Dongxue Qu: And we need to so like one or.
Dongxue Qu: I think it depends on the models, so the maxim that's it NGOs will depend on the models i'm not clear, I don't know I come to see us like a.
Dongxue Qu: Right So yes, I will think I will consider that that one will depend on the models so i'm not sure the Jenner answer for that one for the maximum Dempsey dangles.
Jon: You have a you have an expression expression for any one model.
Dongxue Qu: um so each model, I think I will try to pull out to the the amplitude with the depth that angle and then to decide at which part I need to cut off that like makes it that depth angle to.
Stop all.
Muxin Han: Right just just one common for jon's question I think what you can do to determine the maximum.
Muxin Han: That language well Firstly, you need to choose a smallest amplitude.
Muxin Han: You want to do is decide the largest alumna Okay, then suppose you choose the the amplitude is an older one where I mean to be 0.3 say point three and 0.3 is approximately to the minus one.
Muxin Han: yeah and then you just let the real part of the this action to be something like my overland yeah and then you can just solve yeah it's just a a doll just square eight others where the real part you pose to while we're Lambda and then you saw adult.
Jon: very nice that's very simple relation.
Muxin Han: yeah for the cpl this case yeah.
Hongguang Liu: and also this a dependent on certain models so it's changes I think for 33 and the technology so one family.
Hongguang Liu: it's different for different.
Zichang Huang: Translations yeah.
Thank you.
Jorge Pullin: more questions.
Jorge Pullin: Okay let's thank the speaker again.