Jorge Pullin: Our speaker today is going to be Dr Martin dissolve was back speak about causal structure and spin folks.
Pierre Martin-Dussaud: Thank you Thank you and good morning good afternoon everyone i'm glad to give the seminar today about causal structures, beans phones, and this is based on some work that they have done in collaboration with Agenda Yankee.
Pierre Martin-Dussaud: At penn State University, although i'm currently located in Europe, so the underlying question, the thing wants to answer here is this form, whether because that energy is a fundamental or an emergent property of space time.
Pierre Martin-Dussaud: Should we take it causality as one of the basic ingredient of our theories, or should be just some imagine property at some level.
Pierre Martin-Dussaud: And so to answer this question.
Pierre Martin-Dussaud: This is my plan i'm going to start from scratch.
Pierre Martin-Dussaud: And look at the kinematics of general general relativity and then they will build on top by adding a series of liars adding some discreet ness then look at.
Pierre Martin-Dussaud: The implementation of the degrees of freedom on the show faces then introduced on dynamics then introduce some quantum aspect with patentable.
Pierre Martin-Dussaud: And I think at this level, we will have the student quite a bit about what is the causal structure know these theories and we will be able to go to spin films and look at presenting this framework.
Pierre Martin-Dussaud: So let's start from scratch.
Pierre Martin-Dussaud: With.
Pierre Martin-Dussaud: The kinematics of general relativity so kinematics because i'm not going to talk about the Internet equation yet just look at the.
Pierre Martin-Dussaud: Mathematical structure that we are starting with that's a manifold em and rents your metric G buying rental I mean the signature is of this fall.
Pierre Martin-Dussaud: So into N minus minus minus into.
Pierre Martin-Dussaud: It I can be plus or minus one and usually people fix a convention but I don't want to make any choice at this point I want to keep it general.
Pierre Martin-Dussaud: Because general relativity stops said whether the signature, for the time should be one minus one so let's keep it general will be helpful.
Pierre Martin-Dussaud: To be careful in our analyzes, and so what is a course on structure in this framework for their cost structure is the light code structure than this, I need that every point of the manifold I can define locally light go.
Pierre Martin-Dussaud: To be a bit more mathematical.
Pierre Martin-Dussaud: This slide Cone is given by an equivalence class.
Pierre Martin-Dussaud: There are three equivalent classes on the tangent manifold.
Pierre Martin-Dussaud: And this classes, they are correct rise by the sign of G of the you, you were you is one of tangent vectors that the sign of the norm, of the different vectors and this can be have three types screen to eat if it's time like zero if it's no and minus eat it spaceflight.
Pierre Martin-Dussaud: And this is the cause of structural it's the ability to distinguish what, what are the directions of time, and what are the direction of space.
Pierre Martin-Dussaud: And so aside remarket as the sport at this point is that there is no time arrow.
Pierre Martin-Dussaud: there's sometimes causality maybe, especially in quantum foundations community is very much related to the ID idea that there is a time arrow, but this is not the case in GR.
Pierre Martin-Dussaud: There is no way to distinguish a priori what is fast and what is future if you wanted to do so, then we need to put some extra ingredient like some vector field, and we will say the spectrum, from the point is pointing towards the future or what's the custom.
Pierre Martin-Dussaud: This is arbitrary.
Pierre Martin-Dussaud: So.
Pierre Martin-Dussaud: We have seen how did you arrive at the causal structure from the metric and another question is can do the other way around Okay, thank you.
question.
Pierre Martin-Dussaud: yeah So the question is, can we do the other way around, I mean if I could you let Cone structure everywhere.
Pierre Martin-Dussaud: yeah.
Pierre Martin-Dussaud: You were asking me to repeat that yeah please.
Deepak Vaid: yeah no, I just wanted to yeah sorry, no, I just want to clarify the.
Deepak Vaid: statement that you made about there'd be no no direction of time in in general activity, I mean naming in already metric general relativity the metric, for example, cannot be degenerate right, I mean.
Deepak Vaid: So if you if you have a metric at a certain point, if you do have a light pole in in local locally flat coordinates let's say.
Deepak Vaid: So if you if you move move to any other patch of that of that space time.
Pierre Martin-Dussaud: Is.
Deepak Vaid: Not change.
Deepak Vaid: Unless.
Deepak Vaid: Something like a horizon, maybe so.
Deepak Vaid: If your space time doesn't have anything ready and then how can you say that.
Deepak Vaid: You don't have a ton of time in generativity.
Pierre Martin-Dussaud: i'm not sure I got your question, there was some trouble in the connection and some moments in life that was for me on.
Deepak Vaid: My question.
Pierre Martin-Dussaud: Can you.
Pierre Martin-Dussaud: say it again in short sentence.
Pierre Martin-Dussaud: Okay yeah.
Pierre Martin-Dussaud: it's don't.
Deepak Vaid: Be.
yeah.
Pierre Martin-Dussaud: Yes.
Because.
Deepak Vaid: The question in the chat okay.
Pierre Martin-Dussaud: yeah sorry I don't know if.
Pierre Martin-Dussaud: The problem of connection is on my side on the back side, but I wasn't able to get through the question and I think.
Pierre Martin-Dussaud: yeah what's this.
Pierre Martin-Dussaud: yeah I cannot really answer that question and I don't get the next question.
Pierre Martin-Dussaud: yeah the boy was yet to point out that in the kinematics if we just look at the kinematics just from the data which is contained in the metric you cannot recover the.
Pierre Martin-Dussaud: You can find in future or past direction, and the question is in the other way around, if I if I give you like construction everywhere, my name manifold can you reconstruct the metric.
Pierre Martin-Dussaud: And that question, there is a beautiful answer which is measurements feeling anonymous theorem tells you schematically.
Pierre Martin-Dussaud: That the metric can be reconstructed from the causal structural plus the conformance factor which is, can I wanted to get everybody manifold which can be understood, like as the local view.
Pierre Martin-Dussaud: And so, this is a way to say that the information which is contained in the causal structure captures almost all the information that you have in the metric and so it's really.
Pierre Martin-Dussaud: contains a lot of information it's really important and that's why I think it is a very interesting question to ask whether the quantum level.
Pierre Martin-Dussaud: This is still the cadences.
Pierre Martin-Dussaud: What are the degrees of freedom at the bottom level button called is called structure.
Pierre Martin-Dussaud: So now let's go to let's start to add some ingredients to our summary CB and let's add goodness.
Pierre Martin-Dussaud: So I will start with a very simple example to dimension, and then I will go to four dimensions so let's start with the two dimensional differentially mobile manifold and the game is to democratize it and we get a complex of triangles so each triangle.
Pierre Martin-Dussaud: Has a boundary which is made of segments, and the segments themselves the boundaries, which are the points, and then we go into the digital space.
Pierre Martin-Dussaud: and by this I mean that we replace each triangle by about X each segment by an edge and it's all by face and we get the drawers can enter all right simple now let's do four dimensional differentiable manifold with Lorenzo metric.
Pierre Martin-Dussaud: So when we just pretend it will get four sentences complex of four sentences so it's not very easy to imagine geometrically what this is so let's need to be able to abstract.
Pierre Martin-Dussaud: Normally, and so this for synthesis, this is the structure, they have a boundary which is made of five dre dre and then training all sing one imports.
Pierre Martin-Dussaud: And we are going to assume that the Detroit raw space like.
Pierre Martin-Dussaud: So if the trade right our space like it means that to neighboring for simplicity's or necessarily time like separated, and this is nice, because then, when I go to the jewel picture.
Pierre Martin-Dussaud: So, which vertex represents for simplex to neighboring vertices on are linked by an edge, but this, because this is timeline I can put an arrow on it, and this arrow will tell me.
Pierre Martin-Dussaud: distinction between past and future so instead you what I got is a jeweled skeleton with the local time hours.
Pierre Martin-Dussaud: So, initially, I had a four dimensional different table manifold with Lorenzo metric and by doing this procedure, I am now a discrete setting with your skeleton with local time hours, but in between, I have dropped the control factor at all we retain the causal structure.
Pierre Martin-Dussaud: And here, you see that I have an hour now, which is my edges and so these are all in a sense, is distinguishing past from future, but this is a.
Pierre Martin-Dussaud: This is.
Pierre Martin-Dussaud: If I flip all the arrows I will get an equivalent to generation so there's no there's a global two gentlemen here.
Pierre Martin-Dussaud: Right so.
Abhay Vasant Ashtekar: So why do you put out was at all.
Abhay Vasant Ashtekar: Just lights that without any direction, I mean exactly like in classical general relativity you could also put an arrow, which is to say, but one of the columns his future directed what nicely, and besides, we don't, so why are we doing it here.
Pierre Martin-Dussaud: Well i'm doing it because, if I if I if I only have two vertices, I think, indeed I could just push a single line, but if I want to consider path in my graphs.
Pierre Martin-Dussaud: I need to be able to identify some order so if I wanted to yeah to to go from this vertex, for instance, to this vertex I needed the arrows to know which path, I can go through to have some cause any order trajectory.
Abhay Vasant Ashtekar: Within that is true, also the continuum.
Pierre Martin-Dussaud: Well, if I don't have.
Abhay Vasant Ashtekar: To go from one point to another.
Abhay Vasant Ashtekar: Along the park.
Abhay Vasant Ashtekar: I just don't want to spend too much time, but that was basically the confusing part to the question.
Pierre Martin-Dussaud: If you want the arrows is necessary to see my light construction, you should take this text, for instance.
Pierre Martin-Dussaud: It has five it is attached to five edges, but I can say that these three edges corresponds to the past client code when these two edges on top correspond to the future might code.
Pierre Martin-Dussaud: So this is where my cousin structure is implemented is a way to to divide my class of edges in two classes, the class of past and.
Pierre Martin-Dussaud: Like let go in and change my life that's why.
Abhay Vasant Ashtekar: it's perfectly fine just that you made a big distinction, the classical theory.
Abhay Vasant Ashtekar: And you are breaking that distinction here.
Abhay Vasant Ashtekar: Because in the classical theory also I could have put you know the to light codes.
Abhay Vasant Ashtekar: I could I just label one of them is future.
Abhay Vasant Ashtekar: The whole point is that I thought your main point of the classical theory.
Pierre Martin-Dussaud: Was that.
Abhay Vasant Ashtekar: Richard has not asked me to do that.
Abhay Vasant Ashtekar: And, in particular, I cannot do it consistently is the manifold is not time oriented, but now you are violating your own principal principal and you are saying that well, I would like to talk about this arrows and therefore I know what his future past which is perfectly fine with me.
Pierre Martin-Dussaud: But I just want to emphasize that this is something that if.
Abhay Vasant Ashtekar: You could add then also classically.
Abhay Vasant Ashtekar: But he chose not to.
Abhay Vasant Ashtekar: Do good content mechanically.
Abhay Vasant Ashtekar: yeah indiscreet said okay.
Pierre Martin-Dussaud: yeah Okay, I think yeah I agree.
Pierre Martin-Dussaud: And so.
Pierre Martin-Dussaud: This graph this little skeleton as some properties and you can encode some coastal information, and let me just make the remark that.
Pierre Martin-Dussaud: It has the property of the causal sets if I perform the transitive completion of this course on set of the graph I transitive completion, I mean that i'm an ad arrows between any two vertices for which there is a causal path.
Pierre Martin-Dussaud: And so, from the George Clinton, I can construct because will set by your by completion, but the other way around it's not true by if I only constitute the causal Stephen losing information.
Pierre Martin-Dussaud: There are several your skeleton that they have the same concept that was just a site remark to relate this construction with them things that can be family or for.
Pierre Martin-Dussaud: Many of you who have worked.
Pierre Martin-Dussaud: OK, so now we have the causal structural, which is implemented in a district setting on the graph, which is the jewel once connected.
Pierre Martin-Dussaud: And that is me at the next a way to distinguish between past edges and future marriages, but this is one way to implement.
Pierre Martin-Dussaud: The causal degrees of freedoms, but there's another way to implement it on the so face geometrical structure, and this is important because you know in there are several way to formulated general relativity and depending on which.
Pierre Martin-Dussaud: way you want to be either Einstein is bad or Einstein cattle, you will get different cultural theory and so it's very important to have a choice and what are the relevant degrees of freedom that you want to start with.
Pierre Martin-Dussaud: And in spoonfuls, for instance, we are, are we do have degrees of freedom which live and so faces, and this is coming from the penske formulation of general relativity, and so we would like to do the same thing here, trying to see what's happening, if I and code causality on so faces.
Pierre Martin-Dussaud: So that's The goal of the of the slide.
Pierre Martin-Dussaud: yeah so that's what we wanted to we want now to look at faces and more precisely wedges which all that to other things to do this, we must make some algebraic description of the graph and so i'm going to define this object which is epsilon the orientation.
Pierre Martin-Dussaud: it's the orientation of the edge with respect to a vertex V2 which it is attached and i'm going to say that it is minus one if the edge is implement like your range edges here.
Pierre Martin-Dussaud: And i'm going to say to one if it's outgoing like like for the future are going blue on the spiritual.
Pierre Martin-Dussaud: that's compatible and so, if you give me your one skeleton I can compute the orientation epsilon for all the edges.
Pierre Martin-Dussaud: Can I do the other way around, if I give you a set of orientations for given graph without a rose, can you reconstruct the arrows on the edges and the answer is yes, provided that this constraint is satisfied so it's very simple constraint and just says that.
Pierre Martin-Dussaud: For the same edges, the orientation, with respect to the different two different vertices to which it is attached should be the opposite.
Pierre Martin-Dussaud: So if if one edge if I take one edge, it is attached to two vertices and so, if it is in going for one to be outgoing for the other, this is just what is causing constraint tells me.
Pierre Martin-Dussaud: And this is a consistency condition that I must satisfy if I want to construct the global cause of structural on my graph from the data given by the orientation.
Pierre Martin-Dussaud: Okay, so now let's look on the left side of the slide and let's we want to do the same thing, so now the wedgies they I can define an orientation of the wedges so it's epsilon of the face F attached to the vertex the.
Pierre Martin-Dussaud: And I can say that it is ITO if it is, including some time region so that corresponds to the pink wedges so for the pink wedges like this one, it is bounded by two edges, which are pointing in the same direction, either future here on the past here, and so I say that they are cockrell.
Pierre Martin-Dussaud: And when they occur, and all that it is closing region of time and in that case, I will say that the orientation, so we don't remember that's the the parameter that enters in the signature so it's either one or minus one.
Pierre Martin-Dussaud: And so, when it's Anti Fraud all like the green wedges here, I will say it is minus eater, and this is in closing for region of space.
Pierre Martin-Dussaud: In sometimes you may be familiar, also with the distinction between phoenix and thick wedges, and this is exactly this can we can say that the Co cornel West wedges they will corresponds to stick what is one year to Colonel they would correspond to finances.
Pierre Martin-Dussaud: So that's a way to.
Pierre Martin-Dussaud: To do the orientation and So you see, in a sentence on the wedges I have distinction between time and space.
Pierre Martin-Dussaud: And under the edges of distinction between past and future which is carried by the arrows and now I can go from one description to another, and the way I do that is by this relation.
Pierre Martin-Dussaud: Can I can check it's easy to check, so the orientation on the wedges is the product of the orientation and edges, which are neighboring it and, as he, as a proportional effect.
Pierre Martin-Dussaud: And this relation enables me to translate from the description on the surfaces to a description on the edges, but it's not completely objection it's actually a map which is one to two and the reason is because, on the wedges I have no time that's the same story, as before, while.
Pierre Martin-Dussaud: you're on the edges, I have a narrow, which is the next train information that they get.
Pierre Martin-Dussaud: So now, I ask again the question as before, for the edges, I have a question for wedges if I give you a set of wedged orientation, can you we construct global causal structure.
Pierre Martin-Dussaud: Is it possible to have from.
Pierre Martin-Dussaud: wedge orientation we construct such a graph with arrows which are when when the fan, yes it is yes that's an extract causal constraints which is this one.
Pierre Martin-Dussaud: So it's not surprising that I need constraint, because now information about the causal causality is implemented on the wedges they have more and wedges that I have edges, I have 10 wedges for each foot vertices why, before I had five edges for each for each politics.
Pierre Martin-Dussaud: So I have this cold constraint that my data most satisfied So what is this, it means that if I take a cycle, so the cycle, what is it a cycle it's a sequence of wedges that closes so, for instance here if I look at these three pink wedges they define a cycle, because they close.
Pierre Martin-Dussaud: And the goal constraint says that if I make the take the products of the orientation around the cycle.
Pierre Martin-Dussaud: I should get this number, which is eaten.
Pierre Martin-Dussaud: To the power of the cardinality of the cycle, so in this case, it would be three in the example I have given 123.
Pierre Martin-Dussaud: And so, this is a causal constraints which must apply to each vertex for all the cycles around it, and if this constraint is satisfied then from the orientation of my wedges I can reconstruct the full causal graph but that's the conclusion of the slide.
Pierre Martin-Dussaud: Which is that the causal structure of the complex can be encoded by assigning in orientation, that is to say sign over to the web deeply edges, or the wedges satisfying some color constraints.
Pierre Martin-Dussaud: And in the future, my talk, I will use this code constraint on the left, quite often so that's why I put a star here for you to remember.
Pierre Martin-Dussaud: If you don't treat get the what it really means to compute it doesn't matter just understand that this is a constraint on my possible data to reconstruct the full causal structures.
Pierre Martin-Dussaud: So.
Pierre Martin-Dussaud: Now.
Deepak Vaid: yeah.
Pierre Martin-Dussaud: there's no question.
Deepak Vaid: About by audible or if it yeah can you hear me.
Pierre Martin-Dussaud: So far you.
Deepak Vaid: Can you hear me or if.
Pierre Martin-Dussaud: I can.
Deepak Vaid: yeah Okay, so I have a question about the previous slide.
Deepak Vaid: me go back to the previous slide yeah.
Deepak Vaid: So first, can you just.
Deepak Vaid: elaborate on on the box in the middle.
Where you pay that.
Deepak Vaid: yeah what what exactly is going on.
Pierre Martin-Dussaud: yeah So if you give me.
Pierre Martin-Dussaud: If you can give.
Pierre Martin-Dussaud: US Union station on the edges, so a set of none of these numbers.
Pierre Martin-Dussaud: Some too complex, with this data, I can compute what is the orientation of the wedges so I can go from the right to the left by just making the.
Pierre Martin-Dussaud: product of them, so, for instance let's give an example, if I take this to arrange I think these two ranges to arrange arrows.
Pierre Martin-Dussaud: These are both incoming with respect to this vertex so this means that the orientation is minus one the both cases and so.
Pierre Martin-Dussaud: There is a wedge in between, and the orientation that they're getting to this, which is the product of the federal interesting so minus one times minus one that's one times, etc.
Pierre Martin-Dussaud: So this means that the wedge in between is equal to eat and so that's why the Cindy cochran Oh, and in closing the prevention of time that's why i've color coded in pink here.
Deepak Vaid: Okay, and so what about what about those spaces.
Deepak Vaid: Okay, so you're saying that the which.
Deepak Vaid: which has one time, like i'm sorry one in going arrow and one outgoing arrow or where one edge is blue and one he is orange.
Deepak Vaid: Yes, although your paper like.
Pierre Martin-Dussaud: In this case, in this case, if I take one which is incoming and one which is outgoing if I take this formula.
Pierre Martin-Dussaud: I will get minus.
eater.
Pierre Martin-Dussaud: And this means that you did.
Pierre Martin-Dussaud: In closing original.
Deepak Vaid: space.
Pierre Martin-Dussaud: And that's why.
Pierre Martin-Dussaud: he's.
Reading here.
Deepak Vaid: yeah.
Deepak Vaid: Oh okay so so that's okay that's the language for that you.
Hank Chen: Actually, can also ask a question on this page so presumably Okay, so you have these constraints and then you're like essentially the definition of how you assign orientation your faces right in the box in the middle.
Hank Chen: And you also have the constraints so then you're given triangulation I can assign lazy two variables two edges two faces and stuff like that are satisfied, this constraints right.
Hank Chen: So are there, like redundancies in this assignment like maybe I can re label edges re label faces in a certain way and i'll get the same kind of structure.
Pierre Martin-Dussaud: i'm not sure I get your question because there's I don't see what you're thinking taking talking of when redoubling.
Hank Chen: Really yeah so, for example, you fix some vertex labels, for example, right, and you know from the ordering you, you get an edge labels are, then, what I can do is, for example, just rotate the entire.
Hank Chen: You know the entire door complex right like cyclically relabeling my edges.
Yes.
Pierre Martin-Dussaud: Certainly, yes, certainly, so if you have not been really talking about what is the concrete way you wanted to level you're doing too complex, so, but if, of course, depending on the level that you choose, you may have some.
Pierre Martin-Dussaud: Some redundancy in some sort of symmetry in the numbers that you're assigning.
Pierre Martin-Dussaud: Yes, yes, here, I was in a sense, I was working without.
Pierre Martin-Dussaud: coordinates without levels, I was this F was was a.
Pierre Martin-Dussaud: was just a name for one specific face but i'm not.
Pierre Martin-Dussaud: it's not a coordinate it's interested intrinsic description of the face.
yeah.
Hank Chen: Okay, fair enough, will you be talking about that then.
Pierre Martin-Dussaud: or no i'm not going to.
Pierre Martin-Dussaud: Mention.
Pierre Martin-Dussaud: Many you what you have in mind, maybe, is that I could give like numbers are to the vertices like I J K and then the edges, are going to be level by two.
Pierre Martin-Dussaud: numbers and the faces are going to be novel by the set of edges, which are around surrounding it, yes indeed, if we would have relations.
Pierre Martin-Dussaud: of redundancy and centuries, but i'm not joking at that.
Hank Chen: Okay okay yeah Thank you.
Hank Chen: intrinsic what I wanted to.
Pierre Martin-Dussaud: Welcome
Pierre Martin-Dussaud: So now.
Pierre Martin-Dussaud: You can ask a question.
yep.
Muxin Han: Sorry.
Jorge Pullin: Maybe you can continue okay.
Muxin Han: Well, I think.
Muxin Han: I think it's better no.
Muxin Han: Sorry for that So my question is.
Muxin Han: So, whether this orientation is there any relation between the orientation that you assign here on the complex with the classical notion of time orientation.
Muxin Han: The classical that we know we know that cuz I mean, for example, either you have certain validation that word classical Kathy have a classical notion of penalty manifold, then you can make the sanitation, a complex or something like that.
Pierre Martin-Dussaud: Sorry, I don't understand the question I don't get a hold of.
Muxin Han: US and questions alright so.
Muxin Han: So I mean we know classical generativity this notion of time orientation.
Muxin Han: Right certain magical becomes different major consistently a time or.
Yes, it is.
Muxin Han: yeah and, and here I guess on on the complex sometimes you can make consistently this orientation on all those areas like satisfying your constraint, sometimes, but will you talk for certain complex so whether.
Muxin Han: You know the these two notions related.
Pierre Martin-Dussaud: Whether whether the notion of time or the integrity is related to the causal constraint here is the question.
Muxin Han: Yes, yes.
Pierre Martin-Dussaud: I would say, I think, no because.
Muxin Han: The.
Pierre Martin-Dussaud: question of timing integrity.
Pierre Martin-Dussaud: is somehow a global notion.
Pierre Martin-Dussaud: The possibility to assign.
Pierre Martin-Dussaud: Time orientation which is consistent everywhere on the manifold locally, you can always do it.
Pierre Martin-Dussaud: And so, its global notion to check the consistency when sometimes you can't do it is yes.
well.
Pierre Martin-Dussaud: But here are the skills of constrained by your local conditions.
Pierre Martin-Dussaud: For the edges it's conditions, which is a local local on the edges and straight it's local niche dot X, so I think it's right I don't see him directly.
Muxin Han: But there will be certain reflection of the time, the ability.
Muxin Han: To set up.
Pierre Martin-Dussaud: yeah yeah if you if you consider so here again here i'm considering to complexes which are simple enough meaning i'm not thinking about.
Pierre Martin-Dussaud: i'm not thinking about clothes time like girls have this kind of thing in this case I could have some obstructions and some troubles with my constraints that's true yeah but i'm not considering anything pathological here.
Eugenio Bianchi: If I can jump in quickly to the rescue machines question machine on the right hand side that there are these edge consultant this this age construction this one assumes time orient ability, with the one on the web address introduces additional variables, and so we have additional constraints.
Muxin Han: So, so you mean this is something in the.
Muxin Han: So what we mean by additional, so this is some constraint, in addition to the time orientation that's what you mean.
Exactly.
Muxin Han: But what that basically means for this additional somebody you know but classically in classical generativity we don't have so I mean what will be the path of analog for for for these additional.
Pierre Martin-Dussaud: classical no constraints.
Pierre Martin-Dussaud: Yes, you don't have you don't have it, because.
Pierre Martin-Dussaud: If you take the metric, then you always have a well defined causal structure for today any metric and locally, you can find it here.
Pierre Martin-Dussaud: We are not getting a metric that we are giving a set of wet orientation and then the question is from the set of course orientation, which is very large because I have for each vertex I have 10 numbers 10 numbers which are either tell minus data and so.
Pierre Martin-Dussaud: I must, the question is from this 10 numbers can can I would construct some light construction can, this is not always true it's only true if this goes on constraint is satisfied.
Abhay Vasant Ashtekar: I.
Abhay Vasant Ashtekar: got an interview, because it seems to me that.
Abhay Vasant Ashtekar: I mean we're often thought people used to do you speak.
Abhay Vasant Ashtekar: Construction was like in the causal factor by the standard causes sets you can we can just take a continuum and you can take a continue with it lorenzen metric and in the causes set case just pick some points and.
Abhay Vasant Ashtekar: And then you'll get some relations so.
Abhay Vasant Ashtekar: I think you're doing the same thing here you, namely you're you're saying is that Well, I can just take a continuum metric, if you like, and I can consider a lot is a metric you want to be, and then I can just put.
Abhay Vasant Ashtekar: The superficial decomposition of that, and then the statement would be that well that's impressive decomposition will have the property that the your your cause of constraint is automatically satisfied.
Yes.
Abhay Vasant Ashtekar: So I think that's a statement, and so this just automatically satisfied and so.
Abhay Vasant Ashtekar: it's nothing new is the converse question is going to be the important one, like for causes sets for causal saves the question is always that okay after you're finished all your restrictions and axioms Is it true that every causes said he's embeddable in classical space time.
Abhay Vasant Ashtekar: So similarly here, you might ask at the end of the day, that you give me all these constraints and is it true that I can embed this into a lot easier and.
Abhay Vasant Ashtekar: Better idea is this.
Abhay Vasant Ashtekar: Just simply show complex that again are too complex that.
Abhay Vasant Ashtekar: That it is a later question, we may or may not complete, but at this stage, a statement is that there's no.
Abhay Vasant Ashtekar: constraints are getting will be automatically satisfied if you consider.
Yes.
Pierre Martin-Dussaud: Yes, yes, if I stopped from a metric manifold that I can make this construction and because of constraints will be satisfied, but now.
Pierre Martin-Dussaud: At some point I wanted to get rid of the scaffolding and just start all over again studying by considering that my wet orientation or the fundamental.
Pierre Martin-Dussaud: degrees of freedom from which I should reveal because of structure and then this cause cause of constraints appears as a necessary condition the famous satisfy.
Pierre Martin-Dussaud: Okay.
So let's move on.
And let's.
Pierre Martin-Dussaud: introduce some diamonds.
Pierre Martin-Dussaud: So there are several ways to introduce the dynamics depending of the action that you want to start with here, going to consider the action the action in the continue so, for which there is a metric can be defined connection.
Pierre Martin-Dussaud: And now that we are in this group setting there's an equivalent formulation of Latin the action for the discrete setting, which is called the first order rejection and that was introduced by by reading the 90s.
Pierre Martin-Dussaud: And for this setting you have an action which is the following here to describe it, what are the oldest terms.
Pierre Martin-Dussaud: So you have some of our older four sentences and also some of our older wedges the triangles that belong to a force in fx.
Pierre Martin-Dussaud: And then you have some language multiplier new for each for simplex then these determinant of gamma not saying what gamma is because that's not very important for what's for for for what photos but just to let you know it's somehow closure constraint.
Pierre Martin-Dussaud: And then what are my variables variables or the length of the segments s.
Pierre Martin-Dussaud: Also valuable angle between the tetrahedron.
Pierre Martin-Dussaud: let's see so that's associated to each where there's such a dinosaur angle and this quantity theory of the triangles that can be created from the length of the segments.
Pierre Martin-Dussaud: And now the question i'm asking is where is causality in these variables.
Pierre Martin-Dussaud: What are the variables that carry the causal structure.
Pierre Martin-Dussaud: And, of course, from the lens of the segments.
Pierre Martin-Dussaud: I can get some information because of structure, for instance, I can look at the sign of the length and if it's positive or negative it's going to tell me that.
Pierre Martin-Dussaud: The memphis time Narco space like but you're we we make the assumption that all the train graphs based like and so all the men's positive, and so this sign of the length is not going to give them directly and information on the cost structure.
Pierre Martin-Dussaud: So more directly even causes structure is given by the side of the that you do an angle sita, and this is what I call the orientation structure.
Pierre Martin-Dussaud: So i'm going to give an excellent that's the orientation to the sign of fetal suppress of minus one, and this is really where I wanted to see a causal structures.
Pierre Martin-Dussaud: Now just aside remotely.
Pierre Martin-Dussaud: because someone is shania admit this.
Pierre Martin-Dussaud: remark listen I think it's important you could also compute the dial angle, starting from the length of the segments.
Pierre Martin-Dussaud: And by doing some thing equivalent to the spherical good silo, and this will give you another notion of orientation and because it, but this is somehow indirect both wants to go into that direction, what they want to focus now is on the sign of the data wrangling data.
Pierre Martin-Dussaud: And so.
Pierre Martin-Dussaud: This epsilon enters into the possible variables of my action and a prayer he can take any values for.
Pierre Martin-Dussaud: Any of my wedge on my too complex.
Pierre Martin-Dussaud: Now what's interesting is that if I make a variation of reaction with respect to the different variables, I give the equations of motion and the consequence of the equation of motion is the causal structure, because of constraints.
Pierre Martin-Dussaud: So, starting from an arbitrary orientation structure my website is not imposing the equations of motion of the first order rigid action.
Pierre Martin-Dussaud: I get the causal relation, so another way to say is that the causality is a consequence of the equations of motion and okay now medical level, I have no cost structure for my too complex, the existence of a consistent cost structure is imposed by equations of machine.
Pierre Martin-Dussaud: So that was the dynamics now that's but, so far, everything was classical so now let's go to the quantum theory and quantum theory use the path integral method, so we have still.
Pierre Martin-Dussaud: Simply stack complex four dimensional teacher complex with the boundaries imagine.
Pierre Martin-Dussaud: The purpose of my quantum theory is to us associated to compute an amplitude a associated to this boundary and to some state on these boundaries, and this is how I computed.
Pierre Martin-Dussaud: i'm using the first order reggae action, so I take the exponential of it, and I make the integration of the different variables, so we are will get the constraint, which is coming from the lagrange multiplier, and here I have any integration of other lens and the data domain.
Pierre Martin-Dussaud: And I wanted to extract the causal structure from despite integral, so the way I do is I rewrite the integral by saying that the Daniel angle sita is epsilon things room and so that is the sign of the the angle and rose the know of the gods positive.
Pierre Martin-Dussaud: So, by doing so, I can write me up this way.
Pierre Martin-Dussaud: I have now with some over this possible orientations and even internal which is for row on the positive.
Pierre Martin-Dussaud: Now I can make several comments.
Pierre Martin-Dussaud: First, this year.
Pierre Martin-Dussaud: and sending over all possible configurations of epsilon assigned to wedges, and this is, including both causal and non causal configurations.
Pierre Martin-Dussaud: By causal configuration, I mean configuration which satisfied this cause of constraint, the non causal one I will call them spurious.
Pierre Martin-Dussaud: So i'm sending over different causal histories and not histories as well.
Pierre Martin-Dussaud: Now second remark, he said, the presence of these non causal mysteries contributing to the amplitude depends on the certain choice of variables.
Pierre Martin-Dussaud: It is because I have chosen the first order rejection which comes with a dado angles sita as fundamental variable that I can I can ask such configurations.
Pierre Martin-Dussaud: You can compare with a standard richer calculus for which you only have the lens and, in this case, if you do the patenting wall, you are only something of course on the streets you don't have spare your stance.
Pierre Martin-Dussaud: Now, if you do the semi classical image, the non causal configurations are going to be suppressed that's because, as I said just the slide before.
Pierre Martin-Dussaud: The causal constraint is a consequence of the equations of motion.
Pierre Martin-Dussaud: In the six in classical in the spirit stance or kill.
Pierre Martin-Dussaud: And one could say, well, maybe I could suppress the spurious stems directly at the quantum level by restricting the range of integration.
Pierre Martin-Dussaud: In other words, I could define a causal amplitude by summing only, although this configurations which satisfy the causal constraint.
Pierre Martin-Dussaud: And why should I do this.
Pierre Martin-Dussaud: For three months, the choice of including the spiritual stamps or not depends on what we want to compute is it a projector on the physical space or causal propagating.
Pierre Martin-Dussaud: This point was made in disgust normally by tighter boom that also later bye lean and we're at 20 years ago.
Pierre Martin-Dussaud: And then there was this comparison comparison, which was met with a just the particle wave function which.
Pierre Martin-Dussaud: solves the client golden equation.
and
Pierre Martin-Dussaud: What we, what we are using usually is the feminine propagator but the famous perpetrator has an order of time it's the time ordered propagated.
Pierre Martin-Dussaud: And so, independent propagator I have somehow fixed causal structure and what I get is appropriate to w, which is a green function for the client golden equation.
Pierre Martin-Dussaud: And this Green function can be obtained as a path integral by restricting over only this path which or time order, whichever a fixed cost structure.
Pierre Martin-Dussaud: And if I don't restrict this patentable, I would get what's called Adam our function and you're not done malfunctions can have a client Gordon equation, and this can be seen as a projector or the physical event space.
Pierre Martin-Dussaud: So typically this is similar kind of thing which is happening year.
Pierre Martin-Dussaud: yeah I can restrict or not my son to cause of configurations.
Pierre Martin-Dussaud: Okay, so we have started from.
Pierre Martin-Dussaud: The kinetic session yes.
Seth Asante: So, like in one of recent referral, so I came back he tried to describe.
Seth Asante: angles in learn tense space time and in those facetime sometimes you can get complex angles right, so in that sense that, if the title angles, are complex, then, how do you assign like a sane because he i'm thinking you guys in the angles here are real right.
Seth Asante: So.
Pierre Martin-Dussaud: yeah so.
Pierre Martin-Dussaud: yeah so you're the day one angles, are real numbers, they are positive or negative, they can take any value, but real values.
Pierre Martin-Dussaud: So I know that it's your mom you have several Convention when you wanted to find the ranch an angle and for one Convention, you can also indeed consider them as been imaginary numbers.
Pierre Martin-Dussaud: But you're not forced to do this.
Pierre Martin-Dussaud: it's a convention.
Seth Asante: So I mean like.
Seth Asante: Raphael he inputs like, if you want to have an activity of angles, you know, then you are forced to have a complex angles and some of these things, yet so in one sense, do you mean like you're not forced to do.
Pierre Martin-Dussaud: yeah you're not forced to do this.
Pierre Martin-Dussaud: yeah I.
Abhay Vasant Ashtekar: Just make a quick game are coming.
Abhay Vasant Ashtekar: Through this discussion.
Pierre Martin-Dussaud: But what was your remax.
Abhay Vasant Ashtekar: Does not related to this discussion, so is there a silence I talk to you have to the discussion so many mark is that this possible all that you're doing is really very, very beautiful and.
Abhay Vasant Ashtekar: I just want to say that this last idea that you expressed is something that was also found when people did the.
Abhay Vasant Ashtekar: spin form bark integrals in cosmology.
Abhay Vasant Ashtekar: And when we did that we, we had the exactly the same distinction between the final propagate and and I just said, the question is whether you want to get.
Abhay Vasant Ashtekar: A solution in the physical space or whether you want to cause a propagator So those are those ideas were kind of explore some detail in the case of.
Abhay Vasant Ashtekar: spin form cosmologists, and so it might be very good to go back and look at them from this very beautiful general point of view.
Pierre Martin-Dussaud: Is Thank you yeah yeah I wasn't aware of that session discussion that.
Abhay Vasant Ashtekar: I can send you the difference yeah.
Pierre Martin-Dussaud: Thanks, thank you.
Eugenio Bianchi: Can I add something quickly so seconds I was racing this point that it looks like there's maybe a tension with disrespect.
Eugenio Bianchi: That is working, so the tension is resolved by the fact that Dr love that they either angles you're referring to are really boosting words in the old the day trader are assumed to be space like so there's never.
Eugenio Bianchi: An angle between something space like and something thing like, so in that sense, we just need the real objects just.
Pierre Martin-Dussaud: awesome yeah.
Seth Asante: I see.
Hal Haggard: yeah follow up on that.
Also.
Hal Haggard: I was gonna guess that that was the resolution and i'm just curious do we know that what kind of restriction that imposes on the on the floor simplex triangulation like it can we cover a general general space time with with that kind of triangulation.
Pierre Martin-Dussaud: And my guess is yes, but I don't have.
Pierre Martin-Dussaud: Any Q amp to to back my statement, so I think it is quite general.
Pierre Martin-Dussaud: My intuition is just coming from lower dimension examples when i'm trying to triangulate just to surface I can always take my triangles to be quite flat so that my they are indeed on space like tense.
Pierre Martin-Dussaud: So that's just my team, efficient, I have, but I know i'm not around to make this more precise.
Pierre Martin-Dussaud: Okay, so what we have done so far, was started with.
Seth Asante: The kinematics of.
Pierre Martin-Dussaud: General relativity.
Pierre Martin-Dussaud: And then we have many discreet, and then we have seen how to implement the cause of information on the surfaces.
Pierre Martin-Dussaud: And then we have put some dynamics on it and seeing how the equations of motion impose the causal structural.
Pierre Martin-Dussaud: And now we have done the math integral and that goes to the quantum world and so now I think we're ready to go to the skin fold theory and try to see how this translate in the case of spin for models, so I will recap.
Pierre Martin-Dussaud: What is the skin for model in the case of the pm.
Pierre Martin-Dussaud: So we start with the network, which describes the quantum geometry of space and the idea is that if we let it evolve get it's been film, which is the portal geometry of space time.
Pierre Martin-Dussaud: And the game is to compute the transition amplitude w from the initial speed network to the finals in that book, this is a some over all possible to complexes which are in between.
Pierre Martin-Dussaud: And so we need to compute the spin from amplitude for fixed topology fixed too complex, and this is what we do, we associated to each wedge the variable which is Su variable and we are going to integrate overage.
Pierre Martin-Dussaud: And then we have two products, the underground we have first product on the face and there's a delta function typically telling my that my.
Pierre Martin-Dussaud: faces must be flat if i'm making the product around all the wedges on my face, and then there is another product which is the product of all the vertices have some function Avi, which is the vertex mtg.
Pierre Martin-Dussaud: So the vertex amplitude is a function of my wet variable and it can be expressed as an integral over some new variables, which are located on the edges and which belong to SF DC.
Pierre Martin-Dussaud: And so, for each edge I have such.
Pierre Martin-Dussaud: As variable and then i'm making the product for all the wedges around my vertex, then this is a product of K and K is the wedge interview.
Pierre Martin-Dussaud: So i'm going to.
Pierre Martin-Dussaud: i'm going to have to describe the webcam did you so okay depends on both the wedge valuable and yet variable.
Pierre Martin-Dussaud: And here, it is again it's just the same formula.
Pierre Martin-Dussaud: And it is the okay it's a bit complicated expression and i'm not going to go into full detail, but just this is a semel bernstein's right the other set of integrations other variables, which on cpu one.
Pierre Martin-Dussaud: And here I am using the current state representation, you understand why very soon, and they have the exponential I S, which is the wedge actually.
Pierre Martin-Dussaud: So the winter action as this.
Pierre Martin-Dussaud: As this form.
Pierre Martin-Dussaud: And now the question i'm asking, so this is a wedge amplitude and we have seen from the analysis analysis before that's causality leave on the wedge can leave on the wedge, and so the question is where is because editing coding in this expression.
Pierre Martin-Dussaud: And for the stem this matters to go to the semi classical image and, in this case we realized that this through Gary them Morally speaking it's going to be in a semi classical you need to dial angle at the wedges.
Pierre Martin-Dussaud: And so, this is where i'm expecting to see the causal structure appearing in this wedge action, because the sign of it to tell me whether the wedge will be space and closing or timing time.
Pierre Martin-Dussaud: So now, this is what what I do i'm just rewriting the wedge amplitude by making.
Pierre Martin-Dussaud: The making the seven year, which is a semi rural new parameter that I am introducing excellent which can be minus one on one.
Pierre Martin-Dussaud: And i'm defining this causal wedge amplitude which is leveled by epsilon and it is exactly the same formula, as before, except that I can ensure you sing in the epic run a theater function and so see this is the TV side step function and the argument of it is epsilon times the wet action.
Pierre Martin-Dussaud: And so, in a sense, this function is going to select me all you want a half of the wedge amplitude.
Pierre Martin-Dussaud: And it's it's only keeping me either the Spaceport all the time, part of the magenta.
Pierre Martin-Dussaud: And so, now I can write go back to the vertex amplitude.
Pierre Martin-Dussaud: And the vertex amplitude can be now composed.
Pierre Martin-Dussaud: into three terms.
Pierre Martin-Dussaud: and
Pierre Martin-Dussaud: These terms are some of the different possible configurations for the orientation and the wedges which are surrounding is the decks amplitude and here this three terms.
Pierre Martin-Dussaud: The two first one, they satisfy the causal constraints.
Pierre Martin-Dussaud: But for the value of this nature, which is different.
Pierre Martin-Dussaud: Either you take one equal minus one remember this nature was not fixed, so I try rhian i'm sending over both possibilities and then there is this last term in the vertex amplitude which corresponds to all the possible configurations of excellence which do not satisfy the causal constraint.
Pierre Martin-Dussaud: And I call them spurious turns.
Pierre Martin-Dussaud: And now, in the semi classical demons.
Pierre Martin-Dussaud: This is what I get all the spurious terms, they will go to zero.
Pierre Martin-Dussaud: And then the causal one for each one will go to e to exponential to the I rejection.
Pierre Martin-Dussaud: And the middle term for the the minus I to the rejection, and this is the usual semi classical image that we recover for the vertex mtg.
Pierre Martin-Dussaud: Now, from the vertex amplitude we can go to the global too complex and look at the fools painful amplitude.
Pierre Martin-Dussaud: And with our analysis, we also have similar decomposition.
Pierre Martin-Dussaud: Three terms.
Pierre Martin-Dussaud: And now I am sending you over all possible configurations.
Pierre Martin-Dussaud: For the orientation of my wedges of all the wedges the metro complex.
Pierre Martin-Dussaud: And again, I will have causal terms and spiritual stamps and the more because sometimes I would have a distinction between the one forward to the signature is one Jonas, for which the signature is minus one.
Pierre Martin-Dussaud: So now, I could also make this.
Pierre Martin-Dussaud: choice of only keeping and defining a causal informatica tool by only keeping the two first terms which are causal.
Pierre Martin-Dussaud: And this way I would define some courses P phone, which would be in a sense of propagator of the networks with a time evolution and we some clothes structural imposed attacks fundamental level.
Pierre Martin-Dussaud: But if I want.
Pierre Martin-Dussaud: To have yet projector on my physical states, then I should consider all the times, so that the hamiltonian constraint is in satisfied.
Pierre Martin-Dussaud: Now i'm preaching to the end and I would like to make some connection.
Carlo Rovelli: i'm sorry.
Pierre Martin-Dussaud: Okay, yes I.
Carlo Rovelli: got confused.
Carlo Rovelli: In this.
Carlo Rovelli: formula here the last term the school use one.
Carlo Rovelli: it's not it's it's expressed in the classical unit or not.
It is.
Pierre Martin-Dussaud: Yes, yes it is suppressing the classical image yeah.
Carlo Rovelli: OK, so the.
Carlo Rovelli: The suppression.
Carlo Rovelli: In the classical meaning does give globally, the full amplitude should be just given by two terms, so to the forward and backward propagating one.
Carlo Rovelli: So strong results just not just the individual.
Carlo Rovelli: So.
Eugenio Bianchi: getting into a single vertex.
Car.
So sunny.
Eugenio Bianchi: I think it was referring to a single vertex when he was seeing suppressed.
Pierre Martin-Dussaud: And I was not, I mean on the I mean, yes, I know.
Carlo Rovelli: you're here, I understand here is that.
Pierre Martin-Dussaud: One and now.
Carlo Rovelli: The question is the last semester.
Pierre Martin-Dussaud: And I think it is still suppressed know semi classical minutes because in a semi classical It means the.
Pierre Martin-Dussaud: Because of the constraint is going to be boast.
Pierre Martin-Dussaud: yeah the cause the cause of constraints, is going to be imposed.
Pierre Martin-Dussaud: Everywhere in made to complex at each of our tomato complex and so i'm expecting to have because of constraint, which is satisfied that each protects it might.
Carlo Rovelli: make sense, yes, before we understood it to your.
Carlo Rovelli: objection to never.
Eugenio Bianchi: Let me say again within the same for a single vertex standard PSI Villa we know the past, it does this produce terms, and we know that in the semi classical mimic that they are suppressed.
Eugenio Bianchi: Now, if you have a general too complex.
Eugenio Bianchi: The Formula one gets disbanded that gets a sketching yet in the box, so this one is without imposing it without modifying the payroll in any way.
Eugenio Bianchi: But then the Senate define us is this proposal, it was discussing of selecting only causal that is solving this course of constraint.
Eugenio Bianchi: Then the last term the speediest one would just not appear in the list because the speediest once and the ones that violate the cause of constraint and so by construction it wouldn't appear not.
Eugenio Bianchi: given me to do the semi classical limit is not even there in the full theory that did some modification of the model.
Carlo Rovelli: And why why in the classical theory.
Carlo Rovelli: that's w.
Carlo Rovelli: missing a step sorry, is a key step why the classical theory, so why the classical limits, when a compute this w here, I cannot have.
Carlo Rovelli: Some verses that comes with a day but wonder some comes with a dipole minus one.
Carlo Rovelli: which they don't belong night at the first note of the second.
Pierre Martin-Dussaud: i'm saying, is it possible that in the classical image, I have configurations, for which to neighboring vertices disagree on the value of the signature.
yeah.
Carlo Rovelli: Maybe not me, I will expect not and I understood that you showed that not but now it was.
Carlo Rovelli: For one of the previous.
Carlo Rovelli: It has everything to go to the process so suppressed, so do you still have to, but now, when you some everything you ever.
Carlo Rovelli: get all the first one it's a prompt of assumptions two things.
Pierre Martin-Dussaud: Yes.
Carlo Rovelli: yeah what.
else are the next steps.
Pierre Martin-Dussaud: Okay, I.
Pierre Martin-Dussaud: don't know.
Carlo Rovelli: But I just.
Pierre Martin-Dussaud: Not yeah.
Pierre Martin-Dussaud: I need to think about this.
For.
Muxin Han: The last little search terms.
Muxin Han: But both on both cross that qualified should just be answer the phone.
Pierre Martin-Dussaud: Yes, exactly, so it is in this previous terms, I also have done, for which I am the causal structure is called constraints which is satisfied that each of our text but.
Pierre Martin-Dussaud: It with a signature, which is different here are these into equal minus one is a signature, which means that it is the same for all the bonuses my.
Pierre Martin-Dussaud: Might complex, but in the spirits configuration I could have a mixed and this yeah.
Carlo Rovelli: so well, she.
Carlo Rovelli: Is a senior senior argument that this gets depressed right.
Muxin Han: Well, well, I have a similar argument for it's not suppressed.
Muxin Han: So this is some something yeah, this is actually my my next question that because I had a similar study by early like probably 10 years.
Muxin Han: ago was study the time yeah the time understanding time orientation from from steam forums and bite us in politics, my semi passive analysis yeah and and the strategy was.
Muxin Han: What the argument was we we can define some semi semi classically time oriented place steamed bonds space time bye.
Muxin Han: bye the criterion that that all the semi classical in connections coming from the magical interpretation belongs to the ice all one three plus.
Muxin Han: All the subgroup as a subgroup of all one three which preserving the time orientation and so that also do the constraint certain kind of constraint on the allowed complex order that such kind of.
Muxin Han: semi classical be informed facetime here yeah and that constraint, I think it's a little bit yeah it's quite a lot of similar as your calls or constrain that because it's just some some political science and.
Muxin Han: Some some constraint like that so i'm just wondering, have you ever.
Muxin Han: studied the semi classical approximation of these sounds and.
Muxin Han: put them how it relates to in connection with your although considering.
Pierre Martin-Dussaud: yeah.
Muxin Han: yeah because you know i'm the classical at the time orientation relates to inbound right.
Muxin Han: And you can have seemed almost by default only when you have time oriented.
Muxin Han: Only you can have time orientation awkward the other requirements, but one of the requirements is time orientation, so that we can define the model so that you have sinners and you have.
Muxin Han: Seen connections belongs to, so to speak, yeah and but that prompts the bombs it's not it's not obvious from the semi classical analyses of.
Muxin Han: CMOs you can have.
Muxin Han: Seen connections belongs to so once per class and also seem to think that also I mean connections, you know to actual one three minus.
Muxin Han: Only when you have some site requirements of science.
Muxin Han: And that's desperately a requirement of the complex so that you're you can have all the connections, the last last one we pass.
Muxin Han: So I mean that that's condition is a lot similar.
Muxin Han: yeah from mom maybe it's lot similar as you're constrained so i'm just wondering.
Pierre Martin-Dussaud: Okay Okay, I think I should I should take a look at this work of viewers, to see to understand presenting what is the argument and whether we can make it here yeah.
Pierre Martin-Dussaud: So let me mention.
Pierre Martin-Dussaud: A few works which are which can be connected in the way to what has been done here first there is this paper my nine years and collaborators about the.
Pierre Martin-Dussaud: divergence is of spin phones.
Pierre Martin-Dussaud: And they have shown that.
Pierre Martin-Dussaud: Basically I can invest and there's, the results are saying that some of the spiritual terms are they imagined here, not all of them, but some of them, and this is the arguments that they gave in this paper.
Pierre Martin-Dussaud: Another paper, I would like to comment on this this reading and writing paper which is 20 years old and in which they were trying to implement because it for the buried crane model.
Pierre Martin-Dussaud: And in their case they were considering wedge amplitude which add an explicit expression of the small, so it is using the side function and what's nice about the same function is there is a direct way to write it as the sum of two terms.
Pierre Martin-Dussaud: which are related distinguished by an orientation absalom, and so they were also making the suggestion that maybe we could fix because of constraint, the because the structure of the too complex and so only keep one of the two terms in the sun.
Pierre Martin-Dussaud: And the last paper, I would like to comment on this proposal by Jonathan angle and zip for of the ransom proper vertex amplitude.
Pierre Martin-Dussaud: And so they have motivations which will be different than ours, they don't really talk about causality, this is not precisely the question they want to address the but they want to.
Pierre Martin-Dussaud: Address is well is to say in EPL model we are basically working with two sectors of lipinski in the question is.
Pierre Martin-Dussaud: Maybe I should just recover only the sector of the Einstein Gilbert, and so I need to kill, one of the sector and they make a proposal, the way to do it.
Pierre Martin-Dussaud: And the proposal is in the amplitude, for example, today, introducing this projector pie, and the spike in the industry, basically as a feature function, just like we are doing and so that proposal consensus, very close to our proposal, but it is not exactly the same.
Pierre Martin-Dussaud: The way that the argument of this data is not.
Pierre Martin-Dussaud: The same and our proposal, so they all other works which are related to the understanding of causality and spin foams and you're not putting some names and forgetting probably many others not, I have no time to go through all the list.
Pierre Martin-Dussaud: And i'm just reaching the conclusion that miracle few of the lessons which I think are important for us.
Pierre Martin-Dussaud: Which is that, first of all that's management CRM that's causality which exhausts almost all of the information contents of the gravitational field and so that's why we should care about understanding, where risk was ality in autumn granting.
Pierre Martin-Dussaud: seven points because it can be represented by arrows on the edges, the jewel skeleton.
Pierre Martin-Dussaud: and, more importantly, because it can also be included on the wedges, but in this case you have more variables, and so you need to satisfy a new causal constraint.
Pierre Martin-Dussaud: And that's the natural way to implement because ality and after the density of the surfaces and so that's why it's interesting for speed format models.
Pierre Martin-Dussaud: Now this cause of constraint can be derived from the equations of motion as we've seen.
Pierre Martin-Dussaud: In the patented wall what can restrict or not, the same to cause all the stories only but that choice depends on what one wants to compute either the projector or propagator.
Pierre Martin-Dussaud: And that's for the naive back into role, but we can basically do the same thing with skin folds in that case we are.
Pierre Martin-Dussaud: it's like we are.
Pierre Martin-Dussaud: revealing some structure within the plural modalities nowadays we are able to decompose it as a some of the different terms and.
Pierre Martin-Dussaud: These terms correspond to different orientations structure, some of them do have a causal well defined consistent causal structure, but not all of them that's the basic lesson that I wanted to give thanks all for your attention.
Ding Jia: Thanks, we have for the last talk I enjoyed it a lot um my question is about.
Ding Jia: how you think of the simply show manifolds to you have a continuum picturing my work, do you think of it as exclusively discreet, and in particular.
Ding Jia: So there's a picture, there is an understanding in the standard reggie calculus There is a continuum and see if I talk about a matter particle it could propagate inside of the simplicity.
Ding Jia: And then, in this case, when I consider the causal relationship between two simply says.
Ding Jia: I will consider all these continuum paths connecting the two sentences and ask if there is anyone that's called me if there's not to their calls will be separated.
Ding Jia: And this gives me a cause a relation i'm all the simplest is, I wonder if this notion of conservation would agree with yours.
Ding Jia: Because it seems, you only allow you know the.
Ding Jia: The every for each to simply says that our neighboring you only allow one path.
that connects them.
Pierre Martin-Dussaud: Again, which I get all of your question, correct me if.
Pierre Martin-Dussaud: i'm beside the point.
Pierre Martin-Dussaud: In this case, when you have a democratization, we are making the assumption that he tried rye all space like and as a consequence to neighboring.
Pierre Martin-Dussaud: Forcing wishes are necessarily timeline like separated and so, if you take to simplex that touched one another yeah the first and second time megabits but.
Pierre Martin-Dussaud: You can recover notion of space like separated, but if that's if you take for synthesis which are away from one another, if you are to synthesis which are far from one another, with no time like path that connect them, then you can say that they are spaceflight.
and
Ding Jia: Maybe it would be either, if I can draw a picture I not sure if.
Ding Jia: I can do that can I use the whiteboard tool to draw a picture.
Jorge Pullin: Drawing yes okay.
Ding Jia: So, think of 2d mean kosky space time.
Ding Jia: And the live calls are 45 degrees lines so yeah take this point, this is a live call.
Ding Jia: This this simplex that's within the local now, I have another simplex that's outside of the light called so these services are causally disconnected and the continuum Victor However, I can consider in another simplex.
Ding Jia: relates these two in this way.
Ding Jia: Maybe another simplex.
Ding Jia: So it seems, in your nose, am I right that.
Ding Jia: A and B are closely connected, because here, it is a quarter past years is.
Ding Jia: There are these causal parts related IMP well.
Pierre Martin-Dussaud: I think if I follow the arrows that you have drone I agree that A and B are closely connected, but then I think that the way you have drone the triangles is not very accurate and Just to give you an example, the the triangle, a that you are drawing.
Pierre Martin-Dussaud: Is not.
Pierre Martin-Dussaud: That we are considering that as time like edges.
So.
Pierre Martin-Dussaud: we're not constantly in this case.
Pierre Martin-Dussaud: We are considering cases where the edges all space like so you should make it very flat something like that.
Ding Jia: And can I prove in the case imagine if all the edges are space like and I proved that the continuum notion of consolidation agrees with your notion.
Pierre Martin-Dussaud: depends what you mean by agreeing if you start from the continue continue framework with manifold with a metric, then you make a decision democratization and so these decks conversation is going to be a normal of your more feasible.
Pierre Martin-Dussaud: towards simply share complex and then this metric can be translated in a very precise way as.
Pierre Martin-Dussaud: Some some causal.
Pierre Martin-Dussaud: structural relations between neighboring for synthesis and, of course, my construction it's going to be a consistent.
Ding Jia: As an example, yeah.
Ding Jia: These are all space like urges.
Ding Jia: i'm not like going.
Ding Jia: Over the vertex acts.
Ding Jia: As a dashed lines.
Ding Jia: And now I have a.
Ding Jia: triangle towards space like.
Ding Jia: If this is.
Ding Jia: agreeable I hope it's clear that this be obeys your condition all edges are space like this, I all of these triangles obey your your condition.
Ding Jia: Yes, however, it seems.
Ding Jia: I can have a causal path.
Ding Jia: connects from A to B, even though in the continuum understand up outside of this router like oh.
Pierre Martin-Dussaud: yeah that's true but somehow this picture is bit misleading because he was super imposing the continuous picture and the picture.
Pierre Martin-Dussaud: Cone.
Pierre Martin-Dussaud: The time that the light comes, you should only take them seriously very locally, because he go globally, I think you have to run.
Pierre Martin-Dussaud: into problems when you are super imposing these two pictures.
So.
Ding Jia: I understand.
Ding Jia: Your sentences, if you treat the cause of you take the understanding of scripture that I agree you can't then just a random introduce.
Ding Jia: A continuum picture, but I know it seems, unless I can have up or something's you're saying the continuum Victor has something wrong that part I didn't understand.
Ding Jia: Because this is very similar to the mikulski style is everywhere flat, and all these different angles vanish I don't see any problem with a continuum picture.
Pierre Martin-Dussaud: Okay.
Simone SPEZIALE: perfect in your drawing you can probably see that some of your arrows represent the space like movements right, I guess you you didn't draw they're all.
Simone SPEZIALE: There will be time like, but then the next one will be space like right, so we can see explicitly where they going outside of the litecoin is.
Ding Jia: Happy they're all they're all time.
Simone SPEZIALE: Now those ones, yes, but then, when you go from me aren't you going from the middle points of the triangle, to the next one, if you do it that way let's say you can right exactly now you see that you have a space like arrow.
Simone SPEZIALE: Center right minded you are in our body centric away, so to speak, there, we can clearly see why your picture is is allowing us to go faster than light.
Simone SPEZIALE: I agree with what you're saying that.
Pierre Martin-Dussaud: All the arrows the timeline whenever you.
Simone SPEZIALE: know not not the ones may make that you will make the notion of you.
Simone SPEZIALE: Know like burn oil.
Simone SPEZIALE: Then.
Simone SPEZIALE: There is okay, this first arrow goes from the.
Simone SPEZIALE: Center of these lower triangle, to the Center of the next triangle, yes, then when you go from the Center of triangle to to the Center of triangle three you could say that's a that's a space like are probably so that way, then we understand.
Simone SPEZIALE: Where these going faster than the speed of light is coming from.
Simone SPEZIALE: Because it is going faster than the speed of light, we agree with that right.
Pierre Martin-Dussaud: yeah but if if the if the segments on need space, like the two triangles next to one another, should be related by a time like relation necessarily a construction.
Simone SPEZIALE: If what.
Pierre Martin-Dussaud: If the length of the segment either segments are specified.
Simone SPEZIALE: There are no Of course not, I mean look at these exemplary.
Simone SPEZIALE: shows you very nice, you know you have two triangles they're both space like but one is to the left of the first one and going from the Center of one to the Center, of the other one is not a time like religion.
Simone SPEZIALE: You know this triangle to interact with.
Pierre Martin-Dussaud: Three but that's.
that's.
Ding Jia: Not what they are imposed.
Simone SPEZIALE: Right and i'm not sure they must have in mind that they did in order to have the structure, they want probably these do or regulation has to be built differently, I was just trying to give more details to this example that you pointed out, which.
Pierre Martin-Dussaud: I think it depends on the technical details of your construction so maybe.
Pierre Martin-Dussaud: Maybe we can discuss this.
Pierre Martin-Dussaud: later.
Ding Jia: yeah.
Pierre Martin-Dussaud: If you want to be.
Abhay Vasant Ashtekar: happy with the onset of what.
Ding Jia: i'm I think everything is only an empty I said was look we're clear to me, and I still it still seems to me, if one doesn't use him on his way of drawing arrows but you spell we're trying arrows, then the continuum notion of causality disagreed with a description of causality yeah.
Ding Jia: Thank you.
Jorge Pullin: Okay bye.
Jorge Pullin: I.
Abhay Vasant Ashtekar: don't want the same lines, but I think my question is more or.
Abhay Vasant Ashtekar: Less.
Abhay Vasant Ashtekar: strongly enough, I mean, I assume that that if you actually have a spacetime just given to you with a metric and we just introduced a desensitization back.
Abhay Vasant Ashtekar: Then, your notion of causality would actually agree with the with the notion of causality in the underlying space that but now this last discussion even drive some question about that, but let's suppose.
Abhay Vasant Ashtekar: argument that in fact it is a case that impact your notion of causality agrees in the space.
Abhay Vasant Ashtekar: And then the converse question is an interesting right, I mean, namely that if you just given discrete structure with your notion of consistency between the surface and the line causality appear the condition that you wrote down.
Abhay Vasant Ashtekar: Then, is it always the case that you could embed that this key structure into a continuous space time.
Abhay Vasant Ashtekar: With the you know when so self induced causes structure would agree with us, and these are kind of question that is kind of key, for example, for calls to set.
Abhay Vasant Ashtekar: aside non causal says, but they cannot the cause a lot of puzzle says that you cannot embedded law in space time.
Abhay Vasant Ashtekar: So the same question what advice for you, I mean I could just write down some causes sets are not conceptually your script sets.
Abhay Vasant Ashtekar: And it may may or may not be true, and maybe this is related to this whole idea about a semi classic ality that you talked about but that came in, in the context of dynamics, but i'm saying that they may be question, even before will do context of dynamics that in fact.
Abhay Vasant Ashtekar: That you weren't gonna magically you are allowing say something much more general.
Pierre Martin-Dussaud: yeah yeah i'm not.
Pierre Martin-Dussaud: Aware of the examples that there are in coastal sets where you cannot make this reconstruction, but is it something very pathological, but they are constructing.
Abhay Vasant Ashtekar: You know I don't think.
Pierre Martin-Dussaud: I would imagine that he's always possible to embed any reasonable.
Pierre Martin-Dussaud: directed graph, this is what we have here they're actively seeking love raft we're managing the manifold I think this is.
Pierre Martin-Dussaud: yeah my intuition tells me this genetically be possible.
Abhay Vasant Ashtekar: manifold the metric which is margin and noodles.
Abhay Vasant Ashtekar: manifold yes, and the question is whether.
Abhay Vasant Ashtekar: There is a cat is a metric says that.
Abhay Vasant Ashtekar: The causal relations that you are imposed on the discrete structure are in fact in use by that metric.
or not.
Abhay Vasant Ashtekar: So I mean it would be.
Abhay Vasant Ashtekar: Good to how clean answer to this question, maybe it is easy because you're doing something slightly more spacious right because you're allowing only spatial.
Abhay Vasant Ashtekar: Space like that I had drawn.
Abhay Vasant Ashtekar: And so that might be that initial structure might seem silly simplify your life but that I think would be clarified right in the beginning, then one or two be able to understand better the distinction between what is happening in kinematics versus what is happening.
Abhay Vasant Ashtekar: And I just repeat everything the as far as i'm concerned, I think, various points that you raised about consistency and also category it's actually a couple was asking about those points are discussing this cosmological spread forms.
Abhay Vasant Ashtekar: And I just also put another reference in there, so it might be worth.
Abhay Vasant Ashtekar: Looking at those things to see oh.
Thanks.
Abhay Vasant Ashtekar: This one to make to segue into is really, really beautiful I liked it a lot thanks.
Jorge Pullin: Oh.
Hal Haggard: I also really enjoyed the talk, I have two very broad questions, and I can make them more specific if if need be, but i'm curious about your thoughts on on tunneling.
Hal Haggard: In particular i'm thinking if we pick out a grain of space time that's completely space like say a tetrahedron, what do you make of the fact that it could potentially quantum mechanically tunnel into something that has you know time like edges and things like this.
Hal Haggard: And then maybe related is the question of of the role of pair production in quantum gravity, so we know in particle physics, we can pair produce.
Hal Haggard: And, and it seems here that pair production would have to be related to these causal issues so i'm interested in your thoughts on those two topics.
Pierre Martin-Dussaud: Okay, better better prediction you mean prediction of.
Pierre Martin-Dussaud: What working with you.
Hal Haggard: Know i'm thinking of a spacetime pair production, so if we took a cosmological model.
Hal Haggard: And we actually imagined that it it branched into two two universes and some.
Pierre Martin-Dussaud: logical like maybe you.
Hal Haggard: say exactly yeah i'm curious on your thoughts about what you're you've told us says about that kind of possibility.
Hal Haggard: The thing I have in mind is the how to Martin fineman propagator things you were saying is saying right, because we know that those topics are related to pair production in the particle physics right.
Pierre Martin-Dussaud: yeah well The second point is, I think, only a matter of topology for the manifold at the beginning.
Pierre Martin-Dussaud: And I have not many, many strong assumption on the topology so.
Hal Haggard: I don't think that's quite right, I think you know if you have a topology where with a branch.
Hal Haggard: We can even think about this in 2d if we have a cylinder that branches into two cylinders.
Hal Haggard: Yes, at that place where that topology change happens.
Hal Haggard: is required that the causal structure is also.
Pierre Martin-Dussaud: A complicated I maybe yeah it might be that in such cases it's true at the moment where the two legs of the trousers rise, maybe at this moment, many one could expect to break the causal structure locally so yeah i'm not thought about this, but that's yeah.
Abhay Vasant Ashtekar: yeah I think the metric would become degenerate, for example, I mean it's like holly said, in that case, and so there'll be a problem with that, so the metric will not be lauren.
Abhay Vasant Ashtekar: yeah okay.
Pierre Martin-Dussaud: yeah so we would have.
Francesca Vidotto: Somehow.
Pierre Martin-Dussaud: It, we would not have.
Pierre Martin-Dussaud: To light comes at.
Pierre Martin-Dussaud: All we just we don't maybe just one part of the right code and.
Pierre Martin-Dussaud: If we only have instead of an issue if you only have like the past part of the litecoin I think the description discrete description that they have just grabbed steelworks.
Pierre Martin-Dussaud: I mean, there is no breaking of the causal constraints tailbacks if I only have one part that's indicates, where I have a vertex.
Pierre Martin-Dussaud: Which is a terminal of ethics in that sense, like all the five edges are converting tweet and, in this case the structure is because of constraints to bikes but maybe there are some other tricky thing.
Pierre Martin-Dussaud: yeah and I think he wants to give him this question and the first part of your question was can you again.
Hal Haggard: It was about tunneling of.
geometry.
Pierre Martin-Dussaud: Yes, in which case where you would consider like to vertex which.
Pierre Martin-Dussaud: means.
Hal Haggard: The simplest possible example would be in a in a mink 2d makovsky space, if I had an interval that was.
Hal Haggard: Initially space like we could imagine it tunneling into an interval that became time like.
Pierre Martin-Dussaud: Yes, so that would be somehow, I have a wedge, which is a time and closing disease, it is switching to a wedding retreat space in closing can service providing would be described by the two complex, which has two vertices and.
Pierre Martin-Dussaud: I can assign an orientation to all the wedges around both my vertices.
Pierre Martin-Dussaud: And maybe maybe indeed.
Pierre Martin-Dussaud: Maybe, indeed the tooling which you want to describe with corresponds to a case where.
Pierre Martin-Dussaud: No.
Pierre Martin-Dussaud: No, I think the custom constraints should work also each vertex.
Pierre Martin-Dussaud: So yeah.
Pierre Martin-Dussaud: No, I think the the case you were describing can perfectly the model by you too complex, we were defined global cause of structural.
Pierre Martin-Dussaud: engineer to write these down to show myself.
In trouble here.
Abhay Vasant Ashtekar: yeah but the issue is really about Batman we can buy dancers, in the question is whether dynamics actually gives you a non trivial amplitude for now.
Abhay Vasant Ashtekar: Where I think this distinction, but how was making between the hallmark of a system.
Abhay Vasant Ashtekar: To find them propagator is not this is critical, and so the question is, what are calculating also want.
Abhay Vasant Ashtekar: To say about.
Abhay Vasant Ashtekar: If one is calculating the.
Abhay Vasant Ashtekar: Product right, I mean if you're calculating.
Abhay Vasant Ashtekar: Then I think that this would not happen, but for calculating something which is more like a farmer propagator then this umbrella, so the question is what, what do you want to calculate is a question, and I think is very interesting questions yeah but conceptual that different.
Pierre Martin-Dussaud: The different thing you need is to relate to that we are contributing to some of survival and, for instance, in the case of the propagator of a particle when we have the fan man propagator.
Pierre Martin-Dussaud: The observable side, maybe more easy to understand, because we can imagine, indeed, that when a particle is traveling to the background causal structure is fixed.
Pierre Martin-Dussaud: So, for that reason we should indeed keep the feminine propagator and so restrict the patenting role to only the one which one time order but that's because in sense I have an independence between my particular the background, because of structure in the case of gravity.
Pierre Martin-Dussaud: What it'll do I am I am able to measure.
Pierre Martin-Dussaud: It possible, is it possible, for instance, that they have observable, for which I fixed because of structure.
Pierre Martin-Dussaud: And the only thing the only degrees of freedom, which is changing, which is quantum really would be the control factor is some other kind of of question that that should be answered, and that can be I think only be really answered in the context of a specific.
Pierre Martin-Dussaud: experiment in specific upset all that he wants to compute.
Hal Haggard: i'm really interested in this topic, because it seems to me that we need to identify regimes somehow we want a causal things to be suppressed in a certain semi classical limit.
Hal Haggard: But we don't want to lose the quantum effects, all together, because that seems like a really interesting avenue for quantum gravitational phenomena and so.
Hal Haggard: part of what i'm wondering, and we don't need to answer it now, but i'm just wondering if we can separate out those two regimes like we want, we don't want to lose the quantum effects that's all.
Francesca Vidotto: yeah Let me mention That was my question and my worry, in the sense that we have seen, and that, especially when families involved.
Francesca Vidotto: We need to consider a vector geometries and possible in your young components.
Francesca Vidotto: In the amplitude so I worry if you ever thought about this and whether the construction that you're imposing these artificially suppressing these and therefore, as I was saying, making you lose the quantum effects, you want in the dynamics.
Pierre Martin-Dussaud: i'm not sure.
Pierre Martin-Dussaud: Of the answer to that we, I remember, we thought about this with a genuine but I don't remember what was the conclusion and an original, if you remember what is the contribution of Euclidean part and how it appears.
Francesca Vidotto: It will be interesting, maybe to to use your prescription and redo the calculations and see whether you're not getting the for process or, if you are getting into them it's even more interesting because you should ask why so.
Eugenio Bianchi: yeah.
Pierre Martin-Dussaud: yeah.
Eugenio Bianchi: yeah.
Sebastian Steinhaus (he/him): yeah hello, thank you for your talk and I wanted to first some of the comments bit on causes sense, because the kingdom.
Sebastian Steinhaus (he/him): If you consider, for example in an element called set actually most of these concepts are not meant for like at all so many of them forward to this class of so contrived on butchers common sense.
Sebastian Steinhaus (he/him): And they are very peculiar it's basically just have like three slices of which these concepts are because the elements sit and they're connected.
Sebastian Steinhaus (he/him): And they have huge difficulties actually you know you can't even define the same sentence three dimensional process two dimensions works, but everything beyond that you can't really decide with that so.
Sebastian Steinhaus (he/him): there's a lot of structure there, so you know the accidents are very simple there's a huge set of concepts and they have huge difficulties of actually singling out particular manifold like policies with the dynamics.
Sebastian Steinhaus (he/him): that's a German so.
Pierre Martin-Dussaud: Okay, is this the statement is most console set cannot be constructed from manifold Is this the statement that you're saying.
Sebastian Steinhaus (he/him): Yes, men for like content sets if you consider all an element instance our very last class I don't know whether it's completely.
Sebastian Steinhaus (he/him): helpless classified.
Pierre Martin-Dussaud: Again it's interesting.
Sebastian Steinhaus (he/him): Because what they do is they, they sprinkle metaphors and from that get concepts and from that they try to estimate properties that metaphor like it's happening particular so.
Sebastian Steinhaus (he/him): But that wasn't really my question, which is like you know this from these rather abstract structures, many objects can rise and it's not really obvious whether this would correspond to some continuing like.
Sebastian Steinhaus (he/him): causality or like manifolds so that's like the challenges they are facing.
Sebastian Steinhaus (he/him): My question is a bit unrelated and technical because it was a typical circus analysis you formulate this in terms of the boundary data like spins and the 3D novels and from that interaction conditions they must satisfy all that to get.
Sebastian Steinhaus (he/him): The.
Sebastian Steinhaus (he/him): salad dressing classical approximation and we can stop the force attacks, so you have a solid condition is a different kind of.
Sebastian Steinhaus (he/him): way of prescribing that you obtained for simplex have you thought about translating these notions like you know when you can basically them say me.
Sebastian Steinhaus (he/him): And what kind of sense of three dimensional bounty data or the 3D normal vector associated with the tetrahedral leads to a cause for subjects I mean the question is kind of one to one because.
Pierre Martin-Dussaud: So, so if you fix just the boundary of your complex like, which is a set of the trade war with john to one another, you fix it and you have some notion of causal structure on this boundary which is going to put some constraint matata possible nice to meet that you had in the bulk.
Pierre Martin-Dussaud: But these constraints is not going to be.
Pierre Martin-Dussaud: very strong like for a fixed causal structural on the boundary you have really many possible belt and which are happening.
Pierre Martin-Dussaud: And so, because you can always add in the belt.
Pierre Martin-Dussaud: topology which is more complex like by adding more vertices and by adding more that is inside you just have more and more degrees of freedom that enables us to play with and to add some some orientation structure and.
Sebastian Steinhaus (he/him): So you can split yeah I was just referring to one simplex see.
Sebastian Steinhaus (he/him): Just.
Sebastian Steinhaus (he/him): One yeah so it says, because he provided a different way of saying that you know certain various providers if it's not suppressed, and the same classical and.
Pierre Martin-Dussaud: that's yeah So yes, you just consider just one vertex when you fix the boundaries what he's done, for instance, you do the computation of them are, and then the collaborators on the semi.
Pierre Martin-Dussaud: classical limits for just one vertex.
Pierre Martin-Dussaud: You are providing some information on the boundaries that this.
Pierre Martin-Dussaud: is going to allow.
Pierre Martin-Dussaud: To because of structure in yen, which are corresponds to the to southern points and these two columns structure.
Pierre Martin-Dussaud: The correspondence actually the same structure, but it is described with a signature, which is different, this is the way we understand with our framework is the way we understand if you seven points that appear.
Pierre Martin-Dussaud: In the the Center tech savvy PR and you have to several points been to several points they correspond to a saint causal structure, but with a signature itar which is different, it can be equal to plus one minus one, I think.
Pierre Martin-Dussaud: yeah, this is the way we understand.
Sebastian Steinhaus (he/him): yeah very interesting and.
Sebastian Steinhaus (he/him): How what vector geometries eliminated francesca's question and fit into this picture.
Sebastian Steinhaus (he/him): press, but if you only get one.
one.
Pierre Martin-Dussaud: yeah.
Pierre Martin-Dussaud: yeah, so I would give you the same answer from Francesca I need to think about this again more.
Pierre Martin-Dussaud: carefully before Thank you.
Pierre Martin-Dussaud: you're welcome.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay let's thank the speaker again.
Pierre Martin-Dussaud: Thank you, thank you.
Pierre Martin-Dussaud: I think that there's been questions and references in the chat so please Georgia don't close the zoom before I can.
Eugenio Bianchi: I.
Pierre Martin-Dussaud: can hear.
Pierre Martin-Dussaud: You good you got them a genuine okay perfect yes thanks.
Jorge Pullin: Okay, if you don't have them, let me know, and I can send them to.
Pierre Martin-Dussaud: Thank you.