Jorge Pullin: Okay, so our speakers today are joining the water and he can make it in, I think, Joel is going to go first. They're speaking about quantum reduce Luke gravity.
Gioele Botta UW: Okay, so first of all, thank you very much for people see me to speak at the same seminar today, I'm going to present the award that we are doing in collaboration with the professor Orlando ski and Manuel
Gioele Botta UW: De Luca, and the topic would be one more useful gravity that basically it's an attempt to that Manuela Francesco john Franny build the long time ago to try to extract physics from the full deal
Gioele Botta UW: So,
Gioele Botta UW: As I said, the, the first stop them to build this Kramer was from Francesco in the manual in 2013
Gioele Botta UW: And the goal at the beginning was just to be like a bridge to connect to the cosmological set or difficulty or Andrew quantum cosmology.
Gioele Botta UW: But little by little during the year. This program showed that it could be much more general to with respect to the initial idea and I would like to say that there there is already
Gioele Botta UW: Consistent realization of this program that was actually perform in a framework that it's useful to studies very clearly see matter space, times the people who are
Gioele Botta UW: We're doing this work are Manuela Daniella and Siena. And one interesting things that emerged from this works is that
Gioele Botta UW: When you're taking into consideration the degrees of freedom of the full theory. For example, in the fate of the black hole there can be
Gioele Botta UW: Many surprises with respect to municipal space model. So what we want to do is basically created the same program to study the cosmological set
Gioele Botta UW: Of the food theory and then the stalker. Are you in the first part, I will try to give you a general overview of this program.
Gioele Botta UW: And I will try to explain you the mathematical consistency of the program and I will try even to give a physical intuition be behind the square quantum or use gravity framework.
Gioele Botta UW: So first of all, let us think about the classical general relativity in classical general relativity. If we want to start the the full Einstein equation. Basically, we are not fixing up glory any specific background.
Gioele Botta UW: We are in the if we are doing this, we might just try to solve the full Einstein equation. But as far as I know.
Gioele Botta UW: There is not still a way to get the full solution of this equation because they are really complicated. So what is a strategy to
Gioele Botta UW: extract some some physics from general relativity, basically we are considering some symmetries, in the sense that we have in mind the physical model that we want to study. For example, I don't know cosmology and black hole. We had some symmetries.
Gioele Botta UW: To, for example, to our line element, we have a simplification, a drastic simplification of the Einstein equation we are able to solve them and we are able to extract some physics, but there could be another way that may be classically
Gioele Botta UW: Is just something that is not so useful. But the is basically the way that in quantum reduce look gravity were trying to derive the full quantum gravity in a way that is compatible. So what is this way.
Gioele Botta UW: We can even think to start from the full Einstein equation and perform against fixing
Gioele Botta UW: A gauge fixing. In this sense, in this case I'm I mean we are trying to select the coordinate system through an age fixing. In this way, we are keeping all the physical degrees of freedom of the theory.
Gioele Botta UW: For example, we might write the matrix in a blog diagonal for and these are resolved that the old four dimensional matrix can be putting on the diagonal from from different grand
Gioele Botta UW: We can write the matrix in this way, and the first of all, we might try to solve. There is an equation near it's not clear, there will be any advantage is probably not.
Gioele Botta UW: But what I want to say is that even for from here, we might impose some symmetry reduction and we can extract some physics in the usual way.
Gioele Botta UW: This will be the pop that we will follow in quantum radio spoke gravity, because it seems that from this pop there cannot can arise, some simplification, with respect to start from the theory, not in any engage
Gioele Botta UW: One result that I will use in the form of the goal will be that a any three dimensional matrix can be diagonal eyes, and these are resolved first proved by young in 1984 and then by we can grant in 2009
Gioele Botta UW: So let's see. The main difference from the old formulation or Francesco dwelling from the formulation that we are trying to implement
Gioele Botta UW: In 2013 Francesco under Manuela can see there the setting. Basically, they weren't starting from the full face space parameters by the Arctic are variables.
Gioele Botta UW: And they were can see the ringer reduce it space where the connection and the flow and then see taste riots were diagonal
Gioele Botta UW: But the problem was, what was the problem about this this frame or it was that
Gioele Botta UW: To be able to build a face space in such a way, we cannot rely only on the gauge fixing because the component that we are getting rid of connection and then the face buyers are too much.
Gioele Botta UW: So to access to our face face like this, we have to impose like a mix of symmetry reduction engage fixing
Gioele Botta UW: But when we're imposing symmetry reduction engage fixing. First of all, we have to we have to check in both cases you the face space is per server during the revolution during the day by day dynamics.
Gioele Botta UW: And the answer in the case of Francesca Manuela was that the space, space could be preserved by the dynamics if and only for the curvature Skylar was set to zero. And these basically was
Gioele Botta UW: Was the same by considering only homogeneous space time. So, this the simulators that were compatible with this framework was basically the one connected to homogenize
Gioele Botta UW: And in this in the, the old, the war by Francesca Manuela were concentrated in extracting physics from some kind of homogeneous cosmology.
Gioele Botta UW: So what we are trying to do now. Now we are trying to work in a different way of relying only on gauge fixing and the problem, even if the starting point. At least this similar it is much more complete complications. First of all, what we are doing these a partial gauge fixing
Gioele Botta UW: So we are using the girls constraint and special different markings constraint to fix the gay
Gioele Botta UW: What we are asking by our gauge fixing basically whoever imposing free gauge fixing six gauge fixing condition.
Gioele Botta UW: With the first free gauge fix the issue on basically we are somehow stigmatizing the triads.
Gioele Botta UW: And with the second free gauge fixing condition we are getting rid of the same metric of diagonal component of the trials.
Gioele Botta UW: So through the six gauge fixing condition. What we want can see there is the gauge fixes space where they can actually get our connection of all the components.
Gioele Botta UW: But the diagonal triads and, but the truth is only the diagonal component this somehow is a quick is equivalent to consider a space on the diagonal matrix, but I want to stress that the diagonal triads.
Gioele Botta UW: Condition, it's even stronger than the diameter condition. So we walked like to work with the space, space.
Gioele Botta UW: First of all, we have to check if the partial gauge fixing is well defined what well defined the, I mean that like
Gioele Botta UW: We have to do to have a well defined HP existing we have to set maximum one good fixing condition for each constraint. And this is exactly what we have done.
Gioele Botta UW: And second, the gauge fixing should be accessible. So, for example, like a show every year.
Gioele Botta UW: If we want to start the general relativity by fixing the gauge, we might be able to prove the diametric using a certain number of diploma Diplo more feasible.
Gioele Botta UW: Can be written in a specific way that was basically we can grant show that the old free diagonal matrix can be set in a diagonal form.
Gioele Botta UW: And basically we are using these results that to say that the gauge VC is accessible on the first lives of our space time
Gioele Botta UW: But the problem are different because the not trivial issue now the gauge fixing can be preserved by the dynamics. So somehow I'm asking. It is possible that the dynamics even preserve you are in all the evolution this coordinate system.
Gioele Botta UW: And the second important issue is how we can deal with the gauge fixing that the one to level because by implementing the edge fixing basically
Gioele Botta UW: We are considering a second class system and didn't we second classes and what the quantum level, if not something straightforward.
Gioele Botta UW: So what is the what we have done until now. So first of all, we have consider some method to deal with second class system. The first one that is basically the one that
Gioele Botta UW: is presented in many textbook is the one of the direct market to basically the direct rocket consisting a modification of the possum rocket
Gioele Botta UW: And in this way, we, we are we have an object that is able to to exclude from the dynamics. The flux of the second class constraint because second class constraint will not are not preparing usually the
Gioele Botta UW: The, the face space. What is the problem of these approach. Well, the problem is that classically once we are able to impair this and maybe that is the direct my athletes and we can work.
Gioele Botta UW: We can work with the rocket probably without any relevant problem. But if we want to go one, two, there is a big complication because
Gioele Botta UW: You see the structure of the, the fact that it's much more complicated and then find the representation of the quantum algebra or this
Gioele Botta UW: Rocket in 3D and not trivial task. So we decided to don't consider for the quantization the direct Crockett another
Gioele Botta UW: Way that we consider is the gauge on fixing basically the gauge on fixing is a procedure where
Gioele Botta UW: You are allowed to keep your posts on bracket structure. So this is good for example for the quantization.
Gioele Botta UW: But the object that now is the one that is making the job to preserve the pre spaces them into
Gioele Botta UW: Indeed, if you have an animal, turn off your phone of your system. If you are able to perform the gauge on fixing basically your amid Tanya will be modified.
Gioele Botta UW: Will be modified in such a way that usually is not trivial. Because in the new term can arise, even some non local paraffin one size non local of the
Gioele Botta UW: It's usually much more difficult task. And the other problem that you want. If you want to rely only on the gauge on fixing
Gioele Botta UW: Basically, what happened is that whoever new orleanian but not only because the your gauge fixing condition become basically a first class system with these new on with dawn.
Gioele Botta UW: And so then you should want is basically a new system. So you have to perform a reduced quantization, and it is completely not clear if you can rely on the tools developer to one ties.
Gioele Botta UW: Ties the general relativity, not to do quantum gravity. So probably you have to
Gioele Botta UW: Try to invent a new kind of quantization and might be completely know
Gioele Botta UW: The other strategy that we we
Gioele Botta UW: We can see there was the weekly implementation of the gauge fixing condition by these, I mean that
Gioele Botta UW: We have our engaged fixing condition we promote them to operate or and we impose them weekly on the state that should be physical, because this is how
Gioele Botta UW: These a procedure is supposed to work. But the problem, of course, in this case would be, which are the physical state of open to gravity.
Gioele Botta UW: And this is a question that we don't have the answer, because it's now the full spectrum of the Hamiltonian is not known. And even if we will have the full spectrum of them is doing and probably this procedure would be not
Gioele Botta UW: So relevant. So in this case, what is our strategy, our strategy basically play both on the classical and quantum level.
Gioele Botta UW: So classically what we want to do is to use the gauge on fixing procedure to find the modified Hamiltonian. Why this week because we know that at least classically these armies Dorian served our face base that we are considering
Gioele Botta UW: On the same time on the quantum level since we are performing a partial gage speaks in
Gioele Botta UW: We want to impose weekly these constraints that now our operator on the Keenum article states of the theory and ask that this is equal to zero. End of the states that will span our
Gioele Botta UW: Gauge fix the space or the one where an elated and up late this condition, then if we have classically disarming Tanya composed by the normal Hamiltonian of the system plus the gauge on fixing their they then goal is to quanta is designed to anyone because
Gioele Botta UW: These will be Demi, Dorian, that we will use to preserve our space. So the dynamic should preserve
Gioele Botta UW: The evolution of our system. And since we perform a partial beach fixing this should be some, something that we are allowed to do
Gioele Botta UW: So let's see, first about what are the progress progress progress connected to find
Gioele Botta UW: These new one is, Dorian, let's say, so to perform the gauge on fixing procedure. Basically, it is possible to show that you have just like the person bracket. You have just to embarrass the direct matrix of your system.
Gioele Botta UW: So this is a direct matter that we were found, and until now, what I have to say is that we were not able to have an explicit solution of these
Gioele Botta UW: Of the inverse of these operator, but recently we were able to prove one things that is if we started the differential. The most general differential problem associated to these operate or
Gioele Botta UW: We are able to reduce the problem to solve these free see the systems of partial differential equation.
Gioele Botta UW: And we with the with the technology of 50 we were able to classify this system like a general icing metric hyperbolic system.
Gioele Botta UW: This system. Our study the literature and for the system we have the guarantee that this solution MCS this unique and the pen continues beyond the initial data so
Gioele Botta UW: At this point, we know that our direct ma Catholics over an inverse. So it exist dynamics with preserving our, our face base.
Gioele Botta UW: Indeed, we can start the construction at least have the kinematics because we know that the space, space can be up a space that is accessible to our gauge fixing and
Gioele Botta UW: Of course, if we want to compute the full dynamics of the model we need an explicit solution. And this is something that we are still trying to get
Gioele Botta UW: So now let's see on the quantum part. So now that we know that we are allowed to build the kinematics. Since, like I said, there is a dynamic to preserve our workspace.
Gioele Botta UW: What we have to do is try to find the solution of this to constrain operator equations. So, what we have. What this is something that that among whale and Francesco did already in the past and basically their idea was the following. So we have shown that we can write
Gioele Botta UW: A face space when we're basically the matrix are the metrics are diagonal. So, let us fix these a coordinate system orthogonal coordinate system.
Gioele Botta UW: And once we we fix the free direction of these orthogonal coordinate system attempting solution at least to try to check is the one
Gioele Botta UW: Off cubic off to be graph. Indeed, they were able to show that in the larger limit this cubicle graph. Our solution of both constraints, so they can can see there are they, where they can be considered a basis of our engaged fix that in workspace. This cubicle graph.
Gioele Botta UW: Despite their simplicity
Gioele Botta UW: They can be represented in such a way that for each edge is associated on your
Gioele Botta UW: Ajay saw another reducible representation of a suitable that is different from each edge.
Gioele Botta UW: So what does it mean this this means basically that we are able to represent even some non trivial geometry in the sense that, here we are, we just
Gioele Botta UW: Fix coordinate system that is accessible to gauge BC. So basically we're not getting rid of any physical degrees of freedom and we have found a solution of these constraints.
Gioele Botta UW: That basically give us the passivity to represented even non homogeneous geometry, of course, then another important thing is that you from the states.
Gioele Botta UW: You want to start the sun symmetric sector of the theory we have even a nice geometrical interpretation, because we have just to play with the J number in the sense that if we want to consider and I'm watching us.
Gioele Botta UW: Some basis states to some our present on emerging as a topic geometry we have just to concede, they're the same J on each direction. Another important things that Erica will explain better
Gioele Botta UW: Later, is that these states doesn't have intertwined. So, I mean, there are some intertwine and bottoms are some phrases that
Gioele Botta UW: Become not relevant in the calculation of physical quantities. So these. What does it mean, this means that the the calculation with respect to the full theory.
Gioele Botta UW: Can be much more simplified. I want to repeat again that this solution is not the more broadly is not the most general solution that we might be able to get from this equation and the solution that is
Gioele Botta UW: Extract by comes by neglecting
Gioele Botta UW: Terms of the order one over j
Gioele Botta UW: So now that we have the structure of how our of the event space that we are considering we have to understand
Gioele Botta UW: The relation between the full to Rio period or and the in the operator of the quantum to use local gravity.
Gioele Botta UW: So earlier, there was this approached by a manual and Francesco
Gioele Botta UW: Manuel and Francesco they were considering the full theory operators, for example, let us concentrate on the hashtag live on those key volume.
Gioele Botta UW: And they were somehow projecting these operators to okta only on the red, you said space.
Gioele Botta UW: But this this projection was like a gap because with this project shown basically they they jump from the operator of the full theory and there is the
Gioele Botta UW: operators who are the so color and you said operator is was not so clear because it looked like that.
Gioele Botta UW: If you are asking to your operator Justin from the full to adjust to see what is going on there. They're reducing the universe space, you might lose some information and these actually was the case.
Gioele Botta UW: But the one important the result that they get is that these reducing volume acting on the most general graph in this case our graph with the six volleying graph with all different J.
Gioele Botta UW: at Giza volume. That was the Yahoo and as this is really easy for. So this was really great for calculation, because the volume in the pool theory is one of the
Gioele Botta UW: The, the object we present the a lot of challenges. But what so the problem of this approach, in my opinion, was the following. That is was not clear. The relation with the full operators.
Gioele Botta UW: And another problem was that the projection of these non elementary operator was done component by component. So they were not projecting the wall volume but they were just projecting one by one the flat sees when they were with what the volume is
Gioele Botta UW: Is written, but this year is that, and this is basically will be the, the topic of the continuation of the stalker.
Gioele Botta UW: And try the new approach that basically, in my opinion, fill this gap that was pre present
Gioele Botta UW: He just couldn't see them. The full theory operator, for example, even here. Uh, let's think about the article and Osceola
Gioele Botta UW: And we disappear, a tour er directly without any project shown on these gauge speaks and Hilbert space and there is on to feel cow was really interesting because it show that
Gioele Botta UW: If we are in the larger limit these full theory operator reproduce it. Sadly, the result of their IT. YOU SAID, OH Perry or
Gioele Botta UW: But of course he show that if you are not in this letter G mean there might be some extra components that are somehow the memories of the fact that these operators are exactly the food to reappearing or so these. So these are result is nice because somehow
Gioele Botta UW: validate the procedure that they will and Francesco they were using because basically, as I said in the lounge. I mean, the
Gioele Botta UW: The action of the operator is the same, but then if clarify water basically better the relation between the operator of the full theory.
Gioele Botta UW: And the one which are on the reduced to space. And in this case, they are what are these operators. They are the full to reopen rate or and we don't need any kind of project from
Gioele Botta UW: And in this case, the message is that the computations are possible. So let's let us try to assume this full framework so
Gioele Botta UW: If we start from full quantum gravity and we can see them get some gauging bar and state and we try to act for example with the volume operator, we are not able to get
Gioele Botta UW: An explicit expression of the eigenvalues of the volume and the end, even if we want to compute the dynamics, even in this case.
Gioele Botta UW: We don't have many, many chance to find to find some explicit result. But there is even the other issue because as far
Gioele Botta UW: As I know there is not a systematic way from starting from the gauging bar and state of the food theory and do some kind of a reduction of symmetries.
Gioele Botta UW: At the level of states we tell our to study some somehow some symmetric sector of offload quantum gravity.
Gioele Botta UW: But what happens if we are going to fix the gauge so fixing the gauge, we are choosing these that they called generalized orthogonal system to
Gioele Botta UW: Keep track of the fact that here we are not imposing any symmetries. This is just something that we access to, again, fixing
Gioele Botta UW: So we are fixing the score Vinay we are looking for solution of our game speaks in condition adapted to the score. We need system and we get our
Gioele Botta UW: To because states that are law, but it by a different J on each age we are acting on this kind of stayed
Gioele Botta UW: With the full theory operator here. I represent that they actually have
Gioele Botta UW: One really important operator, because the volume is at least kinematic observable. So they asked if anyone does give all was acting on six violin nodes.
Gioele Botta UW: And here we have the expression of the volume. But what is basically to have a physical intuition measure this formula of the volume.
Gioele Botta UW: Basically this is the classical let's say this critize form will have the volume for some time for a boy, basically.
Gioele Botta UW: So what we are doing here, basically we are considering all the topology, which are compatible by when we, when we fix a generalized orthogonal system.
Gioele Botta UW: And we are just basically refine this kind of topology with the local cool toys, which can be in principle we can ever, in principle, even different edges.
Gioele Botta UW: Here as I want to remind we are in a larger limited and the fact is that here the calculation are possible. So here we might even forget
Gioele Botta UW: About studying some symmetric sector of the theory, we might just try even to compute the full dynamics of the model because here the dynamics is compute about if it's solvable. This is something that should be investigated.
Gioele Botta UW: So this is one of the one application of this framework, the other application was one that has been explore. So we start from by fixing this coordinate system.
Gioele Botta UW: And we are choosing among all possible coordinate system, one that is adapted to the symmetry of this system that we want to study. For example, we want to study a nicer tropic
Gioele Botta UW: Homogeneous geometry were true, setting a Cartesian system and for each direction we are assigning one j all the j in one direction to reproduce
Gioele Botta UW: Or more generic and it should be the same, but on each direction are different. And in this case, they actually go live under skee ball Uma acting on of states.
Gioele Botta UW: Made like this is giving us this simple formula. So the again volume. The volume is the square root of the problem of the free J.
Gioele Botta UW: So what does it mean these the here, it means that we're refining, some of our topology connected to these amino acids in an easy topic and homogeneous geometry with some kind of
Gioele Botta UW: red rectangle Lloyd and what we can do now. Now we have, we're basically refine our first line of our space time because here we are talking still about kinematics.
Gioele Botta UW: And then we can, for example, try to use a coherent state prescription to extract some pieces from the model for example what had been done until now was, for example, to the this tour I to the team unclear in states adapted to reduce it states speak it on a classical
Gioele Botta UW: Unusual on a classical Yankee one space, time, and the last step that has been performed until now was to compute the expectation value of the Hamiltonian
Gioele Botta UW: On these kind of states and the results were basically that the amount of Francesco get back the loop one cosmology Hamiltonian from junkie one but
Gioele Botta UW: I mean my opinion extracting quantum cosmology like these. It can give a better perspective of what is even look quantum cosmology, from the perspective of the of the full year.
Gioele Botta UW: So my this is the last slide of my part of the talk. So after this consideration, in my opinion, want to reduce low gravity of the potential to be considered.
Gioele Botta UW: The leading or during j of the full to rewritten specific coordinate system. It has the potential. I want to stress this because there are still some issue that we have to
Gioele Botta UW: To solve for example first of finding these extra pieces of them is, Dorian, and then investigate back there. The structure of these in our space to check if there are more general
Gioele Botta UW: Solution that might lead to something even less three well done now.
Gioele Botta UW: The important things to keep in mind is that the coordinate system that plays the most important role in this construction is accessible through luggage fixing. So we're not imposing any cemetery, but we are considering all the physical degrees of freedom.
Gioele Botta UW: And I want to stress, even that the quantum reducer gravity can represent an ideal arena to study the full discrete version of general relativity, because we have some indication that in this life changing it somehow. What you are the model that you have in your end is some
Gioele Botta UW: Some classical democratize general relativity. This is something that you can see by study the homogeneous cosmology, so
Gioele Botta UW: This is a more or less of speculation, because we have some indication. But if not, but it's something that we we should investigate
Gioele Botta UW: In a more careful way but for sure. These, these should be considered not just a model, but the framework because it's not just for your in states model because, as I told you, one can even completely forget about
Gioele Botta UW: I've seen bit about extracting a symmetric step sect or by coherence states from the full year but he can just focus to study the
Gioele Botta UW: Different quantum dynamics, but the main message is that in this case the corporate the quantum computation circle civil and these might open some possibilities to extract some some new results from this gage fixed version of quantum. Thank you very much.
Jorge Pullin: So we do questions at the end, and
Gioele Botta UW: Like you
Gioele Botta UW: Prefer for me.
Gioele Botta UW: The same
Jorge Pullin: Questions while setting up
Ilkka Mäkinen: Can you make me a co host. Again, I got disconnected at someone who I think I lost my co host stop those
Jorge Pullin: Are you
Ilkka Mäkinen: Thank you.
Ilkka Mäkinen: Do you see the slide.
Just go ahead
Ilkka Mäkinen: Okay.
So I
Ilkka Mäkinen: First of all, I'm very glad to to to have this chance to
Ilkka Mäkinen: Present my work here in this
Ilkka Mäkinen: On time, so
Ilkka Mäkinen: In this
Ilkka Mäkinen: Second part of the talk, I
Ilkka Mäkinen: Talk about the technical details of these free south of China already advertised, Richard.
Ilkka Mäkinen: Richard very promising doubly clarifies how these very simple
Ilkka Mäkinen: Or pay those off the quantum reduced model related to the operators have the full theory.
Ilkka Mäkinen: Was precisely this
Ilkka Mäkinen: Simple structure of the of the operators which makes it possible to do such calculations in the quantum theory boosting framework, we took me to not really be practical to to attempt in the in the full theory framework.
Ilkka Mäkinen: So this
Ilkka Mäkinen: Michelle, even the first and
Ilkka Mäkinen: Their best of quantum theory goes to gravity these triggers or indeed were introduced by project in the affairs of the phone theory down to this creep boost him but space and then from this interesting never particularly clue, or how this
Ilkka Mäkinen: Simple structure your managers on the projection
Ilkka Mäkinen: And then it's
Ilkka Mäkinen: Very interesting to
Ilkka Mäkinen: Find that
Ilkka Mäkinen: Most of us are simply the full or painters have proper quantum gravity acting on the
Ilkka Mäkinen: On the state or federal boost model.
Ilkka Mäkinen: So that the more precise statement of the relation is that if your
Ilkka Mäkinen: Thoughts are on it and you act in a state in the Holy Ghost him but space.
Ilkka Mäkinen: Keeping in mind that the
Ilkka Mäkinen: Space in virtual goes to face or maybe by and large spins. Can you find that in the in this place out there is some time or moving or the enjoy nature.
Ilkka Mäkinen: agrees with the simple action or three boost or better, and then generally there is also some correction term beaches or lower order in which we can tell for neglect in the very large speeds.
Ilkka Mäkinen: So it's
Ilkka Mäkinen: The show. So it's actually not necessary to think of, of doing any
Ilkka Mäkinen: Protection for and
Ilkka Mäkinen: Procedure or from the privilege of bears from the first one so simply consists of
Ilkka Mäkinen: Remembering that you are here in the logic speed limit for these things on you can keep on the term of reading order EJ
Ilkka Mäkinen: Result.
Ilkka Mäkinen: But however as
Ilkka Mäkinen: We go on and see that in this way we do not always exactly
Ilkka Mäkinen: The same covered the three books are
Ilkka Mäkinen: Formulated in the US or version of of quantum gravity. And so, in particular for them to boost memory or
Ilkka Mäkinen: Find a slightly different version from the one that that initially wasn't
Ilkka Mäkinen: Proposed in order to know paper.
Ilkka Mäkinen: Okay, so
Ilkka Mäkinen: John had been previously mentioned what the structure of these trade offs him birds basically spotlight like me who are quote trolling me for more details. Since these pieces in bed space. Obviously so.
Ilkka Mäkinen: Central ingredient or 30 South that I'm presenting here.
Ilkka Mäkinen: So this
Ilkka Mäkinen: Is free bros bros base with subspace of the Kenai multicultural bunch base of the full theory and the bases states which spanned these pre Boston space. I've got harassed by these three
Ilkka Mäkinen: Requirements here. So we're first of all have a cubicle graph those edges are aligned in the x y and Zed directions or some fixed background coordinate system.
Ilkka Mäkinen: Then we assume as I've already said that the
Ilkka Mäkinen: Edge of the graph is labeled by a large spin quantum number.
Ilkka Mäkinen: And then before this call our numbers on this. Your purpose and passion matrices which were with the edges we assume that the magnetic indices of the
Ilkka Mäkinen: Big number three states them maximum and minimum value.
Ilkka Mäkinen: So Jay Jay or minus jape with respect to the direction of the edge.
Ilkka Mäkinen: To explain more
Ilkka Mäkinen: Clearly, what I'm going with respect to the dissection of the edge. Let me introduce some notation here. So I've been marked by this state with subscript i that state which diagonal register squared online momentum and the AI component. And so here is either x y or center.
Ilkka Mäkinen: And then with this d matrix with subscript i i did not the matrix elements of the bigger matrices in this
Ilkka Mäkinen: In this basis here.
Ilkka Mäkinen: And we have this notation icon crimes that are
Ilkka Mäkinen: Both function of of what I might call the initial post spill network stake in this way here in the bottom of the slide. So they simply a product of these
Ilkka Mäkinen: Nice matrices of where these. So the sigma our size they are either plus or minus one. And then here, this is x y or set depending on what the direction or this edge, he is
Ilkka Mäkinen: Indeed, us, as I've already mentioned, there are no intertwining of any kind in world in the state. Even though in the early
Ilkka Mäkinen: Papers, but when they were defining the states that they will include there something that they're called treat boost in depth whiners book. These are actually not necessary, and they don't carry any information. So you can't just
Ilkka Mäkinen: Do you find a space like I did here. I'm not
Ilkka Mäkinen: Not on
Ilkka Mäkinen: Board, these are
Ilkka Mäkinen: Fake intertwined.
Ilkka Mäkinen: So then this year, though I found this spin networks that is not actually a spin network state in the sense that this virtus news nightly news team in quantum gravity, because these are
Ilkka Mäkinen: The state here is not to gauge for him.
Ilkka Mäkinen: Okay, so these are the steps on those models. And how are the basic operators. Well I brochure here the
Ilkka Mäkinen: Whole on on the on the flux or payers, which are the fundamental affairs of the theory and here are
Ilkka Mäkinen: So this, this symbol archaea nice at these offers on these
Ilkka Mäkinen: Those offers. That's pretty solid from this project that I mentioned earlier. So from then because of these projects and then hold on, on the operator also enhance this properly induce has to be maximum or minimum. So we have here one
Ilkka Mäkinen: Is S S one with India's minus x minus s and these are the on the
Ilkka Mäkinen: four components of the whole normally operator which we consider in the US well formulation, or this model.
Ilkka Mäkinen: And then the action of this opera is very simple and it's basically just a
Ilkka Mäkinen: Multiplication law. And so, you either add or subtract
Ilkka Mäkinen: The speeds.
Ilkka Mäkinen: Then in addition to her family. We have different boost flux operator.
Ilkka Mäkinen: Which is defined on before surfaces me try and do on to
Ilkka Mäkinen: coordinate directions of this background coordinate system. So we have
Ilkka Mäkinen: Serve is there one, one of the background coordinate is constant on the surface.
Ilkka Mäkinen: And then for the surveys, we have this
Ilkka Mäkinen: Very simple.
Ilkka Mäkinen: will boost flocks of REACH simple new parts of by one on the on the Indies is here available on there and then
Ilkka Mäkinen: You see on the
Ilkka Mäkinen: Surface is not properly aligned against the edge or or if this internal
Ilkka Mäkinen: Index of the flocks doesn't agree with me or other things.
Ilkka Mäkinen: So since not
Ilkka Mäkinen: flocks offer is dialogue on Earth. And then on the upper starting construct from the logs refining something involving them or they are also
Ilkka Mäkinen: Simple. In fact, day after diagonally in this
Ilkka Mäkinen: Model.
Ilkka Mäkinen: So this is the
Ilkka Mäkinen: Basic Structure of the mobile I'm
Ilkka Mäkinen: Go on to
Ilkka Mäkinen: Discuss how we can actually see that this structure simply found was, if we paid for.
Ilkka Mäkinen: All of the foods we are in. We are projecting or troublesome them in any way and simply apply these
Ilkka Mäkinen: operators in the in the
Ilkka Mäkinen: In the reduced Hilbert space.
Ilkka Mäkinen: We start with them with the alarm on the offer. So I had first hand. He had the simplest possible example, the full on the upper case being one half.
Ilkka Mäkinen: And
Ilkka Mäkinen: So the, the inspired with how this slide might look this calculation is actually very simple. And I
Ilkka Mäkinen: Run it on these here precisely to show how how simple this basic mechanism is which which underlies the these results.
Ilkka Mäkinen: So here I'm acting with this offer on the
Ilkka Mäkinen: Whole number to reach us here in this is Jay Jay and then basically just by
Ilkka Mäkinen: By
Ilkka Mäkinen: Mathematics. This side is this this so called collection Gordon series where the seas are the collab Squadron coefficients of su to
Ilkka Mäkinen: We can we can now look at all the possible values of the Indies. A and B refresh left LM bill bears are the rasa, or
Ilkka Mäkinen: Okay, I use us as a shorthand for the last one half.
Ilkka Mäkinen: In this case, though, there's only one term in there. Some over okay and we immediately get these, these are
Ilkka Mäkinen: pretty psyched which agrees with the reduced multiplication, while that I showed on the previous slide.
Ilkka Mäkinen: If LM bare bones are mindless we
Ilkka Mäkinen: Have a slightly more complex.
Ilkka Mäkinen: Calculation. So now,
Ilkka Mäkinen: Now best values of the total spend time possible and and then at first, it doesn't seem to be accomplished. Very much so. We have here. I wanted his second term here where this whole long memories of the proper ghost form and then we haven't we haven't done. There's a whole on Mondays.
Ilkka Mäkinen: Are
Ilkka Mäkinen: Not perfect from the point of view of the Holy Ghost model because he has a magnetic indices are neither maxing mountain or minimal
Ilkka Mäkinen: However, if we can now insert the explicit values of the lead score and coefficients we find started that in the limit of large Jay is coefficient of the would approach this one, one, the coefficient of the arm that becomes very small
Ilkka Mäkinen: So in this case, will find that
Ilkka Mäkinen: That lead in order in Germany gets to the
Ilkka Mäkinen: Simple
Ilkka Mäkinen: Rules to multiplication wall for the whole on on there.
Ilkka Mäkinen: And then in the in the remaining guys well one, one of the good news is, for us, and the other is mine was
Ilkka Mäkinen: Will learn that each of these organizations appear in Branson from the
Ilkka Mäkinen: Song to humor is entirely often lower order in Jay compared with the leading terms in in these two equations.
Ilkka Mäkinen: Solving see here. If we look at the terms of living order. Enjoy. Then we got these simple one multiplication, the law for the whole on the operator.
Ilkka Mäkinen: Okay. So then here I
Ilkka Mäkinen: show what happens in the in the general case.
Ilkka Mäkinen: Not
Ilkka Mäkinen: Completely jammed down because we still have to assume that the spin off the alarm on the opera burner is small compared with the spin of the state that we are acting on or if this assumption is not met, then the
Ilkka Mäkinen: Priests and retry clan here is not valid.
Ilkka Mäkinen: But here, basically, they're
Ilkka Mäkinen: The same thing happens. So we have here one term.
Ilkka Mäkinen: The days of the
Ilkka Mäkinen: Criticizing hold on Monday I marks a mile and a bunch of times where they are not maxima and then we'll figure out the
Ilkka Mäkinen: Values of this coefficients here. Then we'll find that out that you need in order. This book has for phase one, and on the other, don't have five patients, which are smaller in the in the limits of large J.
Ilkka Mäkinen: So therefore, we
Ilkka Mäkinen: Will find fault for this.
Ilkka Mäkinen: Component of the whole economic opportunity again for the simple multiplication. The work leading order, J.
Ilkka Mäkinen: And then in the spring one heart example will also find that on the diagonal
Ilkka Mäkinen: On film and skill every side which can be neglected then then Chase, very large.
Ilkka Mäkinen: And he went, nice. So if you
Ilkka Mäkinen: Remember this multiplication wall which I
Ilkka Mäkinen: Showed for the original
Ilkka Mäkinen: Version of the
Ilkka Mäkinen: Kudos call on within when you'll see here this result is not exactly the same, because every
Ilkka Mäkinen: Component of the whole line on the operator volleyed operator in the reduced Hilbert space.
Ilkka Mäkinen: So this somehow
Ilkka Mäkinen: Some testers in the room, the triggers multiplication lot of the whole a moment. This
Ilkka Mäkinen: Quantum number which determines the action of the operator is actually the mud likely to the story so
Ilkka Mäkinen: The magnetic index of
Ilkka Mäkinen: Of this diagram one or components are not good.
Ilkka Mäkinen: Enough.
Ilkka Mäkinen: Okay, so let me
Ilkka Mäkinen: Move on to their flocks on air.
Ilkka Mäkinen: So here the
Ilkka Mäkinen: Flux operator is basically some of these operators, we try called j and which act like the left and right environmental factors are fans of su to depending on if they locked on the beginning or ending point off the edge.
Ilkka Mäkinen: So that
Ilkka Mäkinen: The matrix elements of the J or pay that are basically just a su to China. So time you
Ilkka Mäkinen: Will immediately find that if you apply the child or pay that are free tools to allow me like this then then one of the components out to dry have gone on the accused us to eigenvalue J or minus Jay and thunder either dog dog that I have gone only, but here the
Ilkka Mäkinen: Crease on his of all the square foot of Jay only while here that
Ilkka Mäkinen: Again, but like in value of the diagonal. One is Jay
Ilkka Mäkinen: Well, of course, here it's probably a bit much to say that you can simply neglect the term of all the square root of j in the in the limit of large Jay, but if you have some
Ilkka Mäkinen: Or pay them like the volume of Baylor, for example, there are the components of the child or pay that are involved and you will find that the leading term in that case will always come from, from these
Ilkka Mäkinen: components of J rich diagonally, and which pre service form of the pre, post hole on it.
Ilkka Mäkinen: Okay, so since I don't seem to have very much time left. So let me jump straight to them falling off base because these
Ilkka Mäkinen: These face out here is that
Ilkka Mäkinen: One that they don't want to skip because of
Ilkka Mäkinen: where it's at.
Ilkka Mäkinen: That level, Mr mood seems a little
Ilkka Mäkinen: Remarkable how how simple the volume of the columns here, considering how how complicated it can be in some other instances in the fourth theory.
Ilkka Mäkinen: So here, if we're if we're consciously ago. And this was kind of six Poland feel calm nodes that we have in this and produced spill network states them that are stuck are live on those good volume operator is basically the square foot of this operator, which I can't hear you will be
Ilkka Mäkinen: So the earliest awesome combination of theism J operators that I had on the previous slide.
Ilkka Mäkinen: Well, if we take this offer that you will be under we apply it to this state here where we now have a decent
Ilkka Mäkinen: Product or six do matrix for this season. And does that belong to this mode.
Ilkka Mäkinen: Then we indeed find the term of what you need in order in jail comes when
Ilkka Mäkinen: When all of these offers out by your grandmother on the corresponding do matrix. So the this this diagonal term here. Witches of orange. A third
Ilkka Mäkinen: And then we will have dense on the chart of all the J squared on it.
Ilkka Mäkinen: So that
Ilkka Mäkinen: Was great squared volume.
Ilkka Mäkinen: Therefore, our to buy a gun lobby at Linden order in Jay and then just by
Ilkka Mäkinen: By making a symbol or a lot. They really simple, at least calculation. With perturbation theory, you can extract the square foot from this and find that the actual volume operator itself also has a diagonal doctrine that you need in order on on this note here.
Ilkka Mäkinen: This I
Ilkka Mäkinen: emphasize again that you can compare these
Ilkka Mäkinen: Two sides of it, the fact that in
Ilkka Mäkinen: In the full thing on it.
Ilkka Mäkinen: That you want to provide them value or pay later on we'll solo spin metabolic state we usually cannot even find the matrix elements or the volume of very explicitly except in some very simple
Ilkka Mäkinen: Special games.
Ilkka Mäkinen: Okay, so
Ilkka Mäkinen: Next I
Ilkka Mäkinen: Have a few
Ilkka Mäkinen: words about the humble Estonian which we obviously
Ilkka Mäkinen: Need to do this easily if you want to study the dynamics of this model.
Ilkka Mäkinen: So for the your end I'm part of the homemade Estonian there doesn't seem to be very much mystery and just take that
Ilkka Mäkinen: You're Canadian part of filaments Hamiltonian using this graph, preserving more press creature and shown in the drawing.
Ilkka Mäkinen: With me if you have all these
Ilkka Mäkinen: Are
Ilkka Mäkinen: also assume that these spin off the loop is one half. Then we
Ilkka Mäkinen: Find that, again, the leading term in the action or this offer that you spark. This so called to produce tommy. Tommy and which pro
Ilkka Mäkinen: Has been constructed in in in these more bound by by projecting the operators involved in the fall theory Hamiltonian
Ilkka Mäkinen: Then
Ilkka Mäkinen: Then, further where Banshee I'm part of the Hamiltonian there.
Ilkka Mäkinen: Seem to be many different
Ilkka Mäkinen: Ways of how you might try to deal with this.
Ilkka Mäkinen: But first of all, you're still months construction, which
Ilkka Mäkinen: Might might be technically more complicated than you might like. But in principle there. I promise you that there is anything, probably the
Ilkka Mäkinen: Temporary this this so called
Ilkka Mäkinen: Well, what I might call them French and go reach an operator, which has
Ilkka Mäkinen: Previously
Ilkka Mäkinen: A few years ago, being constructed by
Ilkka Mäkinen: By the Warsaw group where the idea is that that these
Ilkka Mäkinen: In depth knowledge now appears are still or MC on both of the Hamiltonian. It can be approximated by fed just formula there, you have this lengthen deficit angles of some tetrahedral.
Ilkka Mäkinen: Composition of space.
Ilkka Mäkinen: Pieces.
Ilkka Mäkinen: So if you are now in the
Ilkka Mäkinen: Ghost and found bug thing is not very clear how this idea could be applied. Third, because you are
Ilkka Mäkinen: Wonderful full theory. This operator would call that intertwined or on from there shade of what the value of angle is
Ilkka Mäkinen: Well, in the
Ilkka Mäkinen: In these triggers to spin metro state. We don't have any in depth whiners and then it's not clear how how how you could have some interesting notion of angle there.
Ilkka Mäkinen: More. For this reason, we have something to look for a different approach to to
Ilkka Mäkinen: One dies in this in that role of the feature scale or gamer. So working over
Ilkka Mäkinen: What we do is we basically just tried this in the ground here as a function of the trial and then try to
Ilkka Mäkinen: Try to quantify this this function which we get in terms of the elementary
Ilkka Mäkinen: Operators or from or from quantum gravity and this
Ilkka Mäkinen: Is
Ilkka Mäkinen: Something this
Ilkka Mäkinen: Is our approach to the garbage truck is still a work in progress, but we hope that we should have some
Ilkka Mäkinen: Completed
Ilkka Mäkinen: Results from it.
Ilkka Mäkinen: And in addition there. Of course, these terms.
Ilkka Mäkinen: That join and mentioned reach me too.
Ilkka Mäkinen: Must be included in the Hamiltonian because of the Dodge big thing and
Ilkka Mäkinen: Unfortunately, we will also need to find some way to do it first before we can say that we really have a
Ilkka Mäkinen: Complete
Ilkka Mäkinen: Control of the dynamics here.
Ilkka Mäkinen: Okay, so let's move them.
Ilkka Mäkinen: More to the conclusions. So on this slide, I simply
Ilkka Mäkinen: Summarize this
Ilkka Mäkinen: Precisely so I presented here which are
Ilkka Mäkinen: He's not doing some
Ilkka Mäkinen: Simple approach or fearful boost model can't convince him simply ask them.
Ilkka Mäkinen: Is not operators or false theory acting in the
Ilkka Mäkinen: Interface ghost here about space and
Ilkka Mäkinen: There isn't any needs to think of them in terms of any transaction or anything like that. The only thing that happens here is that you remember that you are working here with larger volumes of the screens and you on the key terms of leading order in the check.
Ilkka Mäkinen: So please
Ilkka Mäkinen: Yes, very solid very
Ilkka Mäkinen: Nicely clarifying clarifies the relation between the Phantom three doors model and performs theory as far as the offers. Well of course there are still many other
Ilkka Mäkinen: Questions.
Ilkka Mäkinen: For the morning that you should try to answer it before we can claim that we completely
Ilkka Mäkinen: Understand this
Ilkka Mäkinen: Is what triggers to framework from the perspective or for granting probably
Ilkka Mäkinen: So in in the female market called neither will come with us always
Ilkka Mäkinen: Try to understand better and more
Ilkka Mäkinen: Precisely what what we are actually doing when we post these days, fixing the constraints.
Ilkka Mäkinen: In particular, we are
Ilkka Mäkinen: I think we should
Ilkka Mäkinen: Consider whether there might be some more general so motions of this game speaks in constraints that might be interesting to to look at because the
Ilkka Mäkinen: title of this talk.
Ilkka Mäkinen: Defined as the Holy Ghost invoice based is for sure, not the most general set of solutions to the isn't he isn't gauge weeks in conditions.
Ilkka Mäkinen: Nothing that I
Ilkka Mäkinen: Wouldn't
Ilkka Mäkinen: Should be understand better is how to systematically constructing semi classical stands for this model. There are, of course, some proper sounds in the in the existing literature for how to build this, but I think
Ilkka Mäkinen: At least for me, it seems that suffer from the same
Ilkka Mäkinen: Problem that the operators previously suffered, namely that this CONSTRUCTION SEEMS seems kind of
Ilkka Mäkinen: Arbitrary or ad hoc and it is not
Ilkka Mäkinen: completely clear whether the states actually have the deaconess properties that they they are supposed to have
Ilkka Mäkinen: And then for for with dynamics as I wish I mentioned on the previous slides, we
Ilkka Mäkinen: Should
Ilkka Mäkinen: find some way to deal with this is going to be extinct dances should be included in the Hamiltonian
Ilkka Mäkinen: And that the for this.
Ilkka Mäkinen: Approach of constructing the curvature of bye bye and directly franchising is as a function of the trial and I
Ilkka Mäkinen: Think that we have
Ilkka Mäkinen: Finished three. Sorry about that.
Ilkka Mäkinen: And then one one final thing which which I want to mention here is that even though, as I showed in this talk. If you're looking at the
Ilkka Mäkinen: Sort of key now mechanical action of of operators such are still growing. And then, then there is this very nice.
Ilkka Mäkinen: split between the leading order term which gives you back the simple action or three boost or better. And then the terms of lower order, but then it doesn't seem completely clear to me if
Ilkka Mäkinen: If
Ilkka Mäkinen: If it's still enough to only consider leading or attention when we move on to to investigate the dynamics of this model and are the thesis.
Ilkka Mäkinen: Trademark finish and forth on my own behalf and joy and less. Thank you for your attention.
Jorge Pullin: Any questions.
Klaus Liegener: Hey may, may I ask a question.
Klaus Liegener: Very nicely said about this very important requirement that jays of the state should be very large. In order for the conversation to work and to be
Klaus Liegener: Connected to the full theory. Now, if I'm interested in is the nomics I would imagine and principal the exponential of the Hamiltonian or two computers flow so many iterative application of adding these loops.
Klaus Liegener: And this would mean many, many interesting applications of which applications of the DJ one half, which ultimately what bring even a very large Jade were very small g is the portal at least
Klaus Liegener: Is very small so
Klaus Liegener: My question would be if they already know. I said in one sentence. This States face preserved under the action of the dynamics.
Ilkka Mäkinen: I bind us. Yeah, I think you're absolutely right. It's on the functions limit. He served in any precisely my fam optical sensor. That's how. However, I think that
Ilkka Mäkinen: That, you know, if you think of it in terms of repeated actions of the hormones only and then you can still
Ilkka Mäkinen: Make a rather large number of actions before you
Ilkka Mäkinen: Go out of this.
Ilkka Mäkinen: Free post hubris space. So then we might hope that this new info.
Ilkka Mäkinen: Dynamics.
Ilkka Mäkinen: doesn't preserve the space for arbitrary mom finds it might still preserve it for some finite
Ilkka Mäkinen: finite time but but still a long enough time that you might see some interesting dynamics happen or over this time interval, but but I agree with you that you shouldn't expect that that will be preserved for for arbitrary long times
Klaus Liegener: Thank you.
Norbert Bodendorfer: I have a question in the similar direction of this large J expansion, which is that you would typically consider physically realistic quantum state be composed of many small Jace instead of a few large Chase.
Norbert Bodendorfer: And in very simple models, we can really keep track of that you find that the computation at large chain. It does not give the same result as the computation, with many smaller JS. So how do you
Norbert Bodendorfer: In some sense,
Norbert Bodendorfer: What is your opinion that this framework relies so heavily on this lunch tray assumption when you actually are interested in the physics of many small, geez.
Ilkka Mäkinen: Okay.
Ilkka Mäkinen: Of course, at this point, when we haven't done any uncredited calculations here about physics or what what I am not value is on the kind of speculation and it's not actually backed up by any
Ilkka Mäkinen: Serious confirmations.
Ilkka Mäkinen: What what I expected.
Ilkka Mäkinen: With what what will happen is that that you
Ilkka Mäkinen: That
Ilkka Mäkinen: You have done correct or proper value chain to most would be something which is
Ilkka Mäkinen: Larger on bandwidth one, let's say,
Ilkka Mäkinen: About them that this
Ilkka Mäkinen: Characteristic month or Carter is the volume corresponding with this while you have drones can be very small compared with the microscopic scale. So in some sense, you'll still have many
Ilkka Mäkinen: Many small quantity of space to us to personnel that first one that they would be labeled by speaking one horse being one but but they
Ilkka Mäkinen: Don't have some JV to
Ilkka Mäkinen: The Chase much larger than one but still small enough that you need to have a lot of such wanted to make up the entire
Ilkka Mäkinen: Plant based geometry that you want to consider.
Gioele Botta UW: And can I add something.
Gioele Botta UW: To to what model. You're referring, for example, to, I don't know the new merch scheme in Lupin cosmology that is basically is made up by having a sale of the minimal j that are that are basically the during the dynamic something like this.
Norbert Bodendorfer: So what I'm referring to isn't a specific and vertical computation to get with master student, which appeared last year.
Norbert Bodendorfer: Where you can we have something like a loop quantum cosmology model, but you have many of them so you can study realisation there.
Norbert Bodendorfer: And they just see that if you work with large Chase, but you work with a non normalized Hamiltonian, meaning the one essentially that you are working with
Norbert Bodendorfer: Then you get a different result for observers, then if you would work with a small many small J state and the Hamiltonian you're working with.
Gioele Botta UW: I see it now, because this is a result that of course we should check and later you can give us maybe a reference it would be nice to check but
Gioele Botta UW: If I have to talk about with respect to quantum cosmology. I think that they die. I mean to have some model of reference to make comparison there. I think there are no issue. Bu alarms or or small J, like you said here when we are talking about Latin J. For example, in the
Gioele Botta UW: Definition of our airspace just
Gioele Botta UW: neglect the correction that are going to lock by one over j
Gioele Botta UW: And you have if you neglect this correction when you are satisfied with Sarah. Sarah thing error even j equal to 100 equal to 1000 something like this. If you are going to check
Gioele Botta UW: Toward I don't know area or volume of the quantum of this space time these Jay are related, but it's really, really, something's more, maybe if you are going to check to all many Planck length.
Gioele Botta UW: An area of J.
Gioele Botta UW: Correspond now. You didn't do the calculation, but it should be something really close to the planck length so
Gioele Botta UW: I mean, doesn't seem such a strong restriction, at least from, from the point of view of
Gioele Botta UW: Cosmology insane cosmology, because until now are the only model where we have some kind of control the normal genial setting, I can say anything to because
Gioele Botta UW: There are more more than the nature and modeling injured from the full year, as far as I know. So with respect to the school mammalogy it doesn't seems to me such a big restriction. But of course, I would like to check your work or understand better whatsoever.
Norbert Bodendorfer: I mean to make precise what I'm, what I'm standing here is so first of all, the model is, of course, much simpler as compared to yours, but that doesn't mean that the correct that the conclusions shouldn't generalize to more complicated.
Norbert Bodendorfer: Case and the conclusion just is that if you work with many small spins, you get a different result. Then if you work with few large spins. If you use the same opinion.
Norbert Bodendorfer: This is clearly nothing that one wouldn't expect if you look say contents matter, our soul is just an energy computation in such a quantum gravity setting there.
Norbert Bodendorfer: And the second observation is that you don't get away by using say intermediate the large Jace. Because what you find that already read normalizing from something like Jake with one half to Jake to one that gives you already almost 90% of your correction so
Yeah.
Norbert Bodendorfer: You know,
Norbert Bodendorfer: Since you already make the error.
Norbert Bodendorfer: ended up using largest
Gioele Botta UW: Most likely, yeah. Yeah, I totally agree. But this is somehow something that we expect because I can give you an example. What he could present here of the volume. Basically it's some kind of expansion of the volume.
Gioele Botta UW: Around J. Right. And this is exactly going in the direction of what you said, because the form of the volume, like you're seeing here basically just a classical democratized volume. And if you plug in these in the Hamiltonian, you will get a result. But just imagine to go to some
Gioele Botta UW: Small that you want to give some smaller J, the volume will not be the same anymore. There will be the spark with some extra pieces. And if you plug in these in me, Tony and
Gioele Botta UW: Of course, the dynamic will be different. But this basically is going to the direction that
Gioele Botta UW: There's more Jay are the ones that are controlling the quantum gravity effect indeed here. We are not claiming to have some framework that is able to control quantum gravity Reggie, my statement was more like the this framework and
Gioele Botta UW: Give you an understanding of these correct is classical general relativity at this point. But of course, not a framework that can describe ever dream of one to grab it. So I think that your conclusion with ours is not incompatible. It depends on
Gioele Botta UW: What regime of gravity. You want to explore
Jorge Pullin: More questions.
Jorge Pullin: Okay, let's thank the speakers again.