Jorge Pullin: Okay, so our speaker today is we'll see a minimalist will speak about clock dependence and unitary in quantum cosmology.
Lucía Menéndez-Pidal de Cristina: hi Thank you very much for allowing me to speak today, and so we talked about codependency new verity in quantum cosmology.
Lucía Menéndez-Pidal de Cristina: This is a work I have been doing in collaboration with Stephen guillen and it's part of the two papers, one is published and the other one is impress.
Lucía Menéndez-Pidal de Cristina: You want to have a look at them.
Lucía Menéndez-Pidal de Cristina: And so, how is this going to be so, first I plan to do a small introduction on the concept of the problem of time for the people who are not familiar with this issue.
Lucía Menéndez-Pidal de Cristina: Then, once I have talked a bit about the problem of time we will analyze this problem regarding a specific cosmological model that we have studied in these papers.
Lucía Menéndez-Pidal de Cristina: These more that we will personalize it the classical, this is the second section, and then we will want is it and we will look specifically.
Lucía Menéndez-Pidal de Cristina: about the role that in third place in the quantization and once we have one dies or mothers, we will organize it in different ways.
Lucía Menéndez-Pidal de Cristina: We will look at what effect these quantization have on the dynamics specifically looking for effects such as similarity resolutions and bounds, and when, at the end, I will conclude.
Lucía Menéndez-Pidal de Cristina: So, with no further delay, they suddenly introduction so first what is a permanent of time, the problem of time is.
Lucía Menéndez-Pidal de Cristina: An issue, so to say that stems from the different morpheus and variants of Dr so generativity your know so beautiful theory, it is different movies and mean variance and.
Lucía Menéndez-Pidal de Cristina: These leads that when we want to have an action for dinner relativity we have these terms, these I hope you see my mouth or the words to split know these N and N, a which are the legs under shift.
Lucía Menéndez-Pidal de Cristina: Which are lagrangian multipliers in these action, so if we want to have an action principle which is well defined, we must add the additional constraint that what is multiplying the likens multiplier has to be zero.
Lucía Menéndez-Pidal de Cristina: or variation and theories not well defined these new equation classically they don't create.
Lucía Menéndez-Pidal de Cristina: Many problems, but when we want to go and dice GR and when I say one dies and waving my hands a beat and i'm saying we put had some everything which is.
Lucía Menéndez-Pidal de Cristina: Everything into operators, we now have a wave function, or the universe or facetime or whatever, this means to us and this equation these eight equals zero turn to an operator times the function equals zero.
Lucía Menéndez-Pidal de Cristina: And there is no, this is not equivalent to establishing your equation in the sense that because is equal to zero, there is no clear evolution, that we can interpret from here, and the question is how do we make.
Lucía Menéndez-Pidal de Cristina: The observable so far, in theory, or the important quantity of our theory evolves, and this is a an ongoing problem in physics.
Lucía Menéndez-Pidal de Cristina: Sorry Okay, yes, so there are possible approaches to the problem of time, especially regarding the study of simplified models, which is what we're going to do in this top.
Lucía Menéndez-Pidal de Cristina: One approach is to choose time or o'clock before quantization, and this is usually referred as reduced quantization and what people do is, we have some extra constraints in the very simple models and the mother, we will study we have one extra strain.
Lucía Menéndez-Pidal de Cristina: That we can solve classically which.
Lucía Menéndez-Pidal de Cristina: Basically, is almost of choosing the gate and we only want is what we call or what we consider are the two degrees of freedom.
Lucía Menéndez-Pidal de Cristina: And the ambiguity is in the edge fixing and doing this sort of procedure might lead to different quantum theories and we have some ordering issues.
Lucía Menéndez-Pidal de Cristina: and for the sake of simplicity, we will not talk about this approach, but it's something that people do, and there are plenty of very nice paper about this.
Lucía Menéndez-Pidal de Cristina: But if we don't want you to sign the form quantization we don't want to fix against things like that we can to stay after quantization.
Lucía Menéndez-Pidal de Cristina: In our case, we are simpler model, we will have an equation, which is the winner definitely equation that again has some ordering issues that we will try to.
Lucía Menéndez-Pidal de Cristina: have an answer to and then, once we have the winner defeat equation, we have basically two choices, the first one would be.
Lucía Menéndez-Pidal de Cristina: tools, one of the dynamic of variables of or will or the equation as clock and then build an inner product and he was based around the remaining the dynamic of variables, which is what we will go answer at.
Lucía Menéndez-Pidal de Cristina: This, of course, has some ambiguities, because these points to, why do we choose one dynamic a viable and not the other, this is a question we will try to emphasize.
Lucía Menéndez-Pidal de Cristina: In the stock and the other answer is we do what is called the direct competition program which I.
Lucía Menéndez-Pidal de Cristina: I expect to some of you to be familiar with, which is we start with the kinematics space that is too big and we're trying to reduce it to a physical space when he sees not free from ambiguities.
Lucía Menéndez-Pidal de Cristina: And why am I talking about this, and what do I think this is important it's because these problems are theory independent in the sense that all of these issues appear in the quantization schemes as know quantum cosmology and other ways to look.
Lucía Menéndez-Pidal de Cristina: At quantum reality as long as it's one of the standard geometrical approaches to the quantum reality if we have a wave equation, like the will of the equation, or something similar to this, we will have this.
Lucía Menéndez-Pidal de Cristina: Time or clock choice issue, and I believe personally that these questions i've sometimes overlooked, for the sake of simplicity of the models.
Lucía Menéndez-Pidal de Cristina: But just emphasizing that all of these issues are also be an inner mother is not look one two cosmology, but they also appear in the quarter cosmology setting.
Lucía Menéndez-Pidal de Cristina: So what are we going to do with the problem of time we will choose the cosmological model first.
Lucía Menéndez-Pidal de Cristina: Because the metric is easier than.
Lucía Menéndez-Pidal de Cristina: Of course, then we will quantities more than using the word delete equation that we write soon we will, because we are not.
Lucía Menéndez-Pidal de Cristina: We do not want to discriminate between dynamic and variables, we will this model we have several has everything and because I have is that we can.
Lucía Menéndez-Pidal de Cristina: use as club because it's a very simple model, and we need to see all the possible choices and see which theories, we obtain and what are the difference.
Lucía Menéndez-Pidal de Cristina: When we compare the series there and then we will compare a little bit to what happens when we try to choose to do quantization of the same model and, at the end, we will study singled out there is an ocean, which is the main reason why people usually.
Lucía Menéndez-Pidal de Cristina: Try to quantify scarcity, to begin with.
Lucía Menéndez-Pidal de Cristina: In our case it's going to be the big one singularity or the current.
Lucía Menéndez-Pidal de Cristina: OK, so now let's talk about their mother didn't beat so the ingredient of our mothers are the full week we start with a flat if in our that the metric.
Lucía Menéndez-Pidal de Cristina: which has a following nine elements So you see, we have the labs function, and we have escaped factor, and then we have a flat spatial metric.
Lucía Menéndez-Pidal de Cristina: And the matter component is a free massive scale fec standard of quantum cosmology and then there is a small difference we use a cosmological constant that comes from Union model activity.
Lucía Menéndez-Pidal de Cristina: From people that are not familiar with the new model T and the new, modern identity is like standard car, but we reduce are the different more feasible to the ones that fix the determinant of the metric these way it's GR but we.
Lucía Menéndez-Pidal de Cristina: also imply that the demeanor of the metric is fixed so at first glance, it looks like we are losing.
Lucía Menéndez-Pidal de Cristina: Some of the full the full Murphy some environments, because we are restricting the type of be more feasible, but the full different markets and invariance can be restored by adding additional fields, and this is a very well.
Lucía Menéndez-Pidal de Cristina: explained the old paper have no and the divine.
Lucía Menéndez-Pidal de Cristina: And this this version of the model of gravity which we add extra fields to recover the full difficulties and environments is called sometimes parameters, you know modern gravity and it's the action.
Lucía Menéndez-Pidal de Cristina: I have here, so this is the standard action of tr, this is a similar would have already from Dr plus or cosmological constant that now.
Lucía Menéndez-Pidal de Cristina: Is a integration constant and the extra fields, so we see these variables are former going to get there, and this is our specific.
Lucía Menéndez-Pidal de Cristina: matter component which, in our case is the free Masonic scale defeat, so if we take the section of modular gravity and we particularly to our model we find this.
Lucía Menéndez-Pidal de Cristina: in which a is our skin factor we have London.
Western Physicists: Cindy.
Lucía Menéndez-Pidal de Cristina: Can you repeat the question sorry.
Western Physicists: Lambda the cosmological constant is a fact functional space and time excellent here.
Lucía Menéndez-Pidal de Cristina: No, no it's a constant but it's an integration constant.
Western Physicists: So what does it mean I mean in an action i'm not used to seeing the integration costs and don't have to see constant.
Lucía Menéndez-Pidal de Cristina: Okay, so what i'm trying to say with this is that it is a constant, but the difference between the usual cosmological constant that we have.
Lucía Menéndez-Pidal de Cristina: Is that these constant is constant over a solution of the equation, but you can have a unit with universities or solutions with different values of the cosmological constant.
Western Physicists: And then go so, then this is not the standard action principle is something else in a standard of constants and and fields that you don't worry so is a Lambda is a is a dynamic environment will always confused.
Lucía Menéndez-Pidal de Cristina: It is a dynamic environment.
Lucía Menéndez-Pidal de Cristina: But it turns out to be a constant of motion.
Western Physicists: It turns out by the equation of motion, or it is to start with i'm confused of the rule of the Games here, what are the variables es que ella it's a functional of the metric the field, the ta is a things and in London, what it's a.
Western Physicists: it's a field is a it's a part of the face space is not part of the face face and i'm confused what am I supposed to vary with expecting me to walk my sorry.
Abhay Vasant Ashtekar: I think.
Abhay Vasant Ashtekar: I think Lambda is supposed to be space time constant but still no medical variable.
Western Physicists: image.
Abhay Vasant Ashtekar: Is this is a constant space time but.
Western Physicists: Always face.
Abhay Vasant Ashtekar: Value these not.
Lucía Menéndez-Pidal de Cristina: Exactly.
Western Physicists: So unless supposed to vary the actual is better handle so if there's an equation.
Western Physicists: Which is the p zero.
Western Physicists: Is there the equation da da Brazil.
simone: No, not equal zero equal you know squirrel to the letterman.
Western Physicists: yeah is a part of the equations.
Lucía Menéndez-Pidal de Cristina: And this is why this is fixed because you have this data equals them I don't remember the full details but.
Lucía Menéndez-Pidal de Cristina: But this this extra condition X, that the determinant is fixed I.
Western Physicists: am asking what what this is an actual and find value in the actual with respect to what.
Lucía Menéndez-Pidal de Cristina: The values of.
Lucía Menéndez-Pidal de Cristina: Of the series, so I don't think I don't see where the problem is exactly you can formulate your question.
Western Physicists: If I get the action of the standard model, there are some things which are full dynamic variables, or something which are both constant.
Western Physicists: The dynamic of variables, so the theme is defined by the minimization of the action with respect to the dynamical variables and not by the medium a.
Western Physicists: musician without respect to the constants.
Western Physicists: So those ladder.
Lucía Menéndez-Pidal de Cristina: That is a dynamic.
Lucía Menéndez-Pidal de Cristina: variable of the theory it's you add the dynamic of rappers to this theory Dana sorry.
Western Physicists: easily obtained by varying the actual respect the London.
Abhay Vasant Ashtekar: Yes, D alarm, be a key equal to minus square root of Japan to Kappa times two.
Western Physicists: Okay, so this is the this was this was a question so it's it's gonna have a.
Western Physicists: A an associate integration.
Western Physicists: Yes, okay.
Lucía Menéndez-Pidal de Cristina: But at the end as which happens, and we will have to momentum that are going to be constant of motion and land is going to be one of them, so.
Lucía Menéndez-Pidal de Cristina: Once we get the momentum to the.
Western Physicists: To the field.
Lucía Menéndez-Pidal de Cristina: Yes to the field turns out to be constant of motion and the same thing happens to lana So you see here that in this simplified model we just have a which is it.
Lucía Menéndez-Pidal de Cristina: London T are conjugated viable and.
Lucía Menéndez-Pidal de Cristina: And that turns out to be constant, but because of our specific.
Lucía Menéndez-Pidal de Cristina: Because on the setup of this exercise.
Western Physicists: Okay.
Lucía Menéndez-Pidal de Cristina: Okay.
Lucía Menéndez-Pidal de Cristina: So why this is clear we just pointed a very important point, which is that London is a dynamic a variable of the model and hence it adds.
Lucía Menéndez-Pidal de Cristina: A degree of freedom that we can work with and just to finish V zero is integral over the spatial part of the metric which we assumed to be silent and standard and valleys of effort, which is valued over are so now that we have.
simone: Actually, before you go before you guys, can I ask a question concerning Guild so this.
simone: Yes, and.
simone: sort of me speaking, if my intuition is right, you need these additional fields, because by working with the things determinant your, so to speak, losing one equations of motion because one of the 10 components of demetri good on you don't very respected.
simone: But if you use a first order formulation.
simone: Then you don't have such a problem because even though you have gotten rid of one of the major components that you still have the.
simone: The conjugate momentum, so to speak, that is present in reverse order for money, so I don't know if you ever looked at.
simone: Our this formulation of.
simone: Using decades you wouldn't need any extra fields.
Lucía Menéndez-Pidal de Cristina: You mean firstly the formulation of any modern gravity.
simone: Right.
Lucía Menéndez-Pidal de Cristina: I haven't looked into that I need to know.
Lucía Menéndez-Pidal de Cristina: But now I will.
Lucía Menéndez-Pidal de Cristina: Thank you.
simone: see whether index is he works at a similar problem for other reasons, and it turns out that there were no needs of extra fields in the first one.
Lucía Menéndez-Pidal de Cristina: OK OK OK, no, no, then I will look into this closer.
Lucía Menéndez-Pidal de Cristina: Okay, so now that we have our actual we can do a change of wherever and.
Lucía Menéndez-Pidal de Cristina: So we will define me, which is basically proportional to eq this has been to be very important variable of our system which is conjugated momentum PV and then leave the London, which is basically the cosmological constant we had multiplied by zero and hence we need to modify the.
Lucía Menéndez-Pidal de Cristina: land is a conduit to to meet a D and we have the canonical relation to the fossil record of it and and the cause one and we will just redefine the field.
Lucía Menéndez-Pidal de Cristina: With a constant of represent it so that it looks a bit more beautiful and the take out of this is that the cosmological constant happens to be a constant of motion so it's constant have a one solution in face to face.
Lucía Menéndez-Pidal de Cristina: But the specific value of this constant can change, and this is a big difference between gravity and Dr.
Lucía Menéndez-Pidal de Cristina: If we do this change of variables, we find that the hamiltonian of the theory has this form in which, until that is just a function of any of our internal labs.
Lucía Menéndez-Pidal de Cristina: And we have to quadratic momentum and one medium term because of these libraries will decline in once again, we have to imply.
Lucía Menéndez-Pidal de Cristina: What to have an additional constraint, which is what is inside these brackets has to become zero and so now slowly thing if we work in the the choice image and tinder equals one, then our meeting T and TAO are directly related in the sense that.
Lucía Menéndez-Pidal de Cristina: They.
Lucía Menéndez-Pidal de Cristina: Were these derivative equals two one so basically we can use little tea as something that neighbors how are viable change, we can have we have deep I have tea.
Lucía Menéndez-Pidal de Cristina: But he is not just the coordinate like TAO in the matrix it's a dynamic a viable of our system.
Lucía Menéndez-Pidal de Cristina: And just to emphasize again we is proportional to wake up, so we will call it a volume and it's kind of measures, the volume of for universe, you know i'd be kind of wavy but it's proportional to wake up, the most important part.
Lucía Menéndez-Pidal de Cristina: So just here we have the solutions to the equations of motions for Lambda equals zero and what we see what these university standard and has a big bug singularity.
Lucía Menéndez-Pidal de Cristina: And also be printing and very deep, so this is a disease of the subscribers always has to be positive.
Lucía Menéndez-Pidal de Cristina: And the most important things about this equation, rather than the form of this equation is where the big bang and the beacon similarities well, and for that to be perfect sorry.
Lucía Menéndez-Pidal de Cristina: First of all, is that we can express everything as a function of D, but we can also express everything as a function of fine, we can do a change of variables.
Lucía Menéndez-Pidal de Cristina: And, and if we want that we can do Steve as club fires clock and also V as Look, we have to pay a bit of attention to where.
Lucía Menéndez-Pidal de Cristina: The clocks are monotonic but basically any variable that is monotonic in the interval interested in, we can use it as a tool to measure how the rest of the viable change, and this is standard India.
Lucía Menéndez-Pidal de Cristina: And it's a very nice feature of Dr, so to say, and this is why I have here expressed all of the possible values with respect to one another and.
Lucía Menéndez-Pidal de Cristina: The difference between all of these clocks basically, is where the singularity is with respect to the clock, so if we look at the big bang or request singularity would see it is at the finite T did what what is quantity one equals zero, but it is at an infinite logarithmic of the.
Lucía Menéndez-Pidal de Cristina: Entities also add an infinite fi.
Lucía Menéndez-Pidal de Cristina: And also, we are interested in what happens in spatial infinity I eat when he was infinity especially spatially infinity seats at an infinite time infinite volume, but very interestingly finite.
Lucía Menéndez-Pidal de Cristina: fields I just i'm going to skip a couple of states, we can visualize this better so in this light, we see this much better, so if we if you look at the dotted line, which is the question of motions for universities positive cosmological constant, so this is V of tea, and this is via five.
Lucía Menéndez-Pidal de Cristina: We see that the becomes zero at define it, but then goes to infinity as it goes to infinity but the opposite happens with the field, so we read spatial infinity as a finite value for the field and we read the singularity as when five equals infinity.
Abhay Vasant Ashtekar: Why do you call it spatial infinitive is.
Lucía Menéndez-Pidal de Cristina: We will.
Abhay Vasant Ashtekar: be confusing terminology because space is really.
Lucía Menéndez-Pidal de Cristina: Okay, yes.
Abhay Vasant Ashtekar: that's, not to mention space.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: What does spatial infinity me.
Lucía Menéndez-Pidal de Cristina: When I when I mean spatial in SCI fi movies, is not the most correct term but, again, think of anything better I mean we goes to infinity.
But.
Abhay Vasant Ashtekar: Now, on he goes to infinity spaces.
Abhay Vasant Ashtekar: Yes, and going back to Carlos question because it's often confusing I mean is your theory restricted within an Hello gnomic constraint, which says that Lambda is positive.
Lucía Menéndez-Pidal de Cristina: In the big, no, no, no, no.
Abhay Vasant Ashtekar: Why are we just looking at some class of solutions.
Abhay Vasant Ashtekar: I mean so yeah but.
Abhay Vasant Ashtekar: You go to contagious Lambda positive sector right.
Lucía Menéndez-Pidal de Cristina: No know so okay so we're looking at the disclosing a solution with Linda positive, because then, when we do the numeric.
Lucía Menéndez-Pidal de Cristina: We do restrict ourselves with universe that have only done the positive, but when we went eyes, we do not restrict the sign of Lambda, at least in the beginning, sorry university.
Abhay Vasant Ashtekar: Since all the content is become.
Abhay Vasant Ashtekar: can become imaginary in your last transparency.
Lucía Menéndez-Pidal de Cristina: Sorry.
Abhay Vasant Ashtekar: The good as your last some content is in your last transparency under square root.
Abhay Vasant Ashtekar: node will become like, for example.
Lucía Menéndez-Pidal de Cristina: Key, yes, but.
Lucía Menéndez-Pidal de Cristina: yeah, these are the solutions, only for Linda positive for London negative some of these quantities do not have the same the same expressions.
Lucía Menéndez-Pidal de Cristina: But we have also calculated the same.
Lucía Menéndez-Pidal de Cristina: disabled.
Abhay Vasant Ashtekar: So, if I understand right in the first part you give us the general action in general idea.
Abhay Vasant Ashtekar: In the second part you.
Abhay Vasant Ashtekar: For some reason, you are sticking yourself to only one sector of classical solutions, but in the third part you're going back to the full theory is that what is happening.
Lucía Menéndez-Pidal de Cristina: Yes, I mean I could have put the solution for all cases of Langer JESSICA solution, but I thought it was just putting too many way too many equations on.
Lucía Menéndez-Pidal de Cristina: It and I just wanted, so I just wanted to the point that I wanted to make is that the singularity is always no matter the sign of Lambda at define it.
Lucía Menéndez-Pidal de Cristina: But infinite value for the other blocks, where the point vehicle infinity is at infinite value of the blocks the possible flux dmv but a finite value of five audiences this happens for all landers but it's just.
Lucía Menéndez-Pidal de Cristina: Is it just that, because then in the numeric we're going to study mainly positive numbers.
Lucía Menéndez-Pidal de Cristina: I thought it was better to already have an idea of what the classical songs shouldn't do that, then we can compare.
Abhay Vasant Ashtekar: But isn't it true i'm going to be confusing here but isn't it to the negative Lambda they're all just non-secular solutions.
Abhay Vasant Ashtekar: Because you got the opposite sign up for the energy density and therefore I mean effective energy density.
Lucía Menéndez-Pidal de Cristina: I don't think so, I think this is.
Lucía Menéndez-Pidal de Cristina: How we did to.
Lucía Menéndez-Pidal de Cristina: protect the universe we're singing I was calculating the proper time and observer would take to reach the point of equals zero and these independently on the sign of Monday spine night so it's always similar.
Abhay Vasant Ashtekar: like that.
Lucía Menéndez-Pidal de Cristina: Yes, so these are the classical trajectories and Why did I put a lot of emphasizing this thing is also because there is conjecture.
Lucía Menéndez-Pidal de Cristina: don't show Okay, which is the snow clock and fast clock conjecture, so this comes okay this comes from.
Lucía Menéndez-Pidal de Cristina: Work so when door knowledge, the first time, these West thought about was in a beeper of content in La.
Lucía Menéndez-Pidal de Cristina: And what the doing this work they basically define what they mean by slow and fast clock.
Lucía Menéndez-Pidal de Cristina: And what they mean is i'm just going to read this out loud because going to be simpler, so if X is a dynamic a viable use to express the vibration, of the remaining parameter for universe, like a glock.
Lucía Menéndez-Pidal de Cristina: X is slow, at the point at the singularity if this singularity is reached at the finite value of X and not whether it's been advised basically not plus or minus infinity, and this is a bit.
Lucía Menéndez-Pidal de Cristina: Not very strictly defined because to define these in a full perfect mathematical rigor.
Lucía Menéndez-Pidal de Cristina: We have to talk about intervals, in which the clocks are defined, and so on and so forth, but the important stuff on what they want to emphasize is that.
Lucía Menéndez-Pidal de Cristina: tea the tea clock because we read the singularity at finite T T is slow at the singularity and a singularity is important because it is pointing with our space time breaks down when there is the other important point of the theory which is.
Lucía Menéndez-Pidal de Cristina: What i've named specialty basically when T equals infinity and this point can also be analyzing these fast slow clock thing, and it would be fast at this point so.
Western Physicists: So my question here it's a stupid question so don't don't think as an intelligent person try to make more of it.
Western Physicists: Why, why is it the terminology why slow fast in this way and not reversed.
Lucía Menéndez-Pidal de Cristina: Yes, it's also yes, I also thought he was confusing, but basically when they say fast, I think it they mean the clock ticks fast enough.
Lucía Menéndez-Pidal de Cristina: To rebel the singularity whereas if it's too slow it's not going to take fast enough and it's going to reach the singularity too early, I mean.
Western Physicists: It really does the same thing which one is them to use the opposite.
Western Physicists: sorry if I.
Western Physicists: Suppose the universe ends at some point.
Western Physicists: And i've two blocks, which I would pull fast, because if they had more faster in one which I couldn't go slow, because they had moved slower okay It may very well that the one that goes to infinity.
Western Physicists: Is a fast one, not a slower.
Lucía Menéndez-Pidal de Cristina: It is confusing I also said.
Western Physicists: Okay.
Lucía Menéndez-Pidal de Cristina: Okay, so but it's it's to use the terminology, they use they mean by by it's yeah I also I if I would have discovered is I might have used the opposite the Convention.
Western Physicists: said thanks yeah.
Lucía Menéndez-Pidal de Cristina: But so when a clock is too slow, just to emphasize it because it doesn't take fast enough to repel the singularity or spatial infinity.
Lucía Menéndez-Pidal de Cristina: And the difference, the main difference between the street clock is that these lower the singularity whereas feis fast at the singularity but then it's low at spatial infinity because he treats his specialty vidya define it value and V is its own thing because it's fast everywhere.
Lucía Menéndez-Pidal de Cristina: For V, you have to redefine so when we be redefining Var log V all the time, so I will be probably using a abused.
Lucía Menéndez-Pidal de Cristina: Language when I mean the most of the time, I mean log of the is easier to work with quantities that are defined in between minus infinity to infinity and he's defined to be positive, so we will be working with a lot, most of the time, so when I say we.
Lucía Menéndez-Pidal de Cristina: I mean the log of me because it pushes the singularity frequency and when the logs minus infinity and it wasn't we didn't have this infinity.
Lucía Menéndez-Pidal de Cristina: And this is also what we see here, so the clock face slow, especially 50 but faster the singularity and o'clock D is slower the singularity but fast, efficient feet.
Lucía Menéndez-Pidal de Cristina: And the reason.
Lucía Menéndez-Pidal de Cristina: Why this is the paper this contract to control and what they say basically.
Lucía Menéndez-Pidal de Cristina: When we have this little clock the dynamics are gated and then, when we want is the theory.
Lucía Menéndez-Pidal de Cristina: Using the slow clock that's the norm, of the state has to be when we find everywhere, if we demand any therapy and these will artificially extend the solution to the whole domain of the clock that was previously truncated.
Lucía Menéndez-Pidal de Cristina: Because theory finished in a finite value for this clock and this will have the consequence that it will.
Lucía Menéndez-Pidal de Cristina: resolve single singularity resolutions these basically what they.
Lucía Menéndez-Pidal de Cristina: They said in the work that demanding unitary it artificially extend the range, in which the theories were defined the theory has to be well defined everywhere in points were classically wasn't 25.
Lucía Menéndez-Pidal de Cristina: And these will of course need to inevitable departures from the classical theory and singularity resolution and we're going to verify these three more work.
Ivan Agullo: So let's let me ask a question about that and and are they saying that that a to resolve singularity in the quantum theory do mass use as low block.
Lucía Menéndez-Pidal de Cristina: Yes, well it's not maybe it's not exactly that statement what they say is, if you use a slow clock you reserve the singularity.
Lucía Menéndez-Pidal de Cristina: it's not that you must use it.
Lucía Menéndez-Pidal de Cristina: it's kind of the reverse if if you use it, you always have the singularity.
Lucía Menéndez-Pidal de Cristina: And what we find in our work.
Ivan Agullo: And do they say something Hello fast lot.
Lucía Menéndez-Pidal de Cristina: Yes, that fast clocks do the opposite because o'clock is past basically means that the theories classically will be fine everywhere, so you don't have to extend the artificially these.
Lucía Menéndez-Pidal de Cristina: Were the where you wave functions defined by demanding unit it so you don't not expect your steer your quantum theory to divert from the desktop theory and have this quantum behavior so you do not expect cigarette resolution these cases, and he is also what happens.
Lucía Menéndez-Pidal de Cristina: It will happen, for example, difficulties fast, and it will not sign the singularity in our case.
Abhay Vasant Ashtekar: We only don't understand why you keep calling it artificially because the statement is that I mean I got a hilbert space and I go to your.
Abhay Vasant Ashtekar: evolution operate on it either the evolution continues forever it doesn't want me forever there's nothing artificial about extending it or not, extending it's a question about whether the Community to operators unity evolution doesn't stop I mean this is not.
Lucía Menéndez-Pidal de Cristina: me but.
Lucía Menéndez-Pidal de Cristina: Okay, what I want to say here, maybe the right word to say it is.
Lucía Menéndez-Pidal de Cristina: You are extending the face face.
Lucía Menéndez-Pidal de Cristina: Because you're.
Lucía Menéndez-Pidal de Cristina: Because you're demanding that you series unitary.
Abhay Vasant Ashtekar: But, but the quantum mechanical it, there is no face face on a mechanical dead space illiterate unitary the first speaker but space and the statement is that.
Abhay Vasant Ashtekar: The evolution continues, I mean in the in the United States, so there's nothing.
Abhay Vasant Ashtekar: Stopping it would be adding.
Lucía Menéndez-Pidal de Cristina: Yes.
Lucía Menéndez-Pidal de Cristina: That still.
Abhay Vasant Ashtekar: I think I can sharpen the question I had, I mean the comment if I look at just even classical TV.
Abhay Vasant Ashtekar: there's a spacetime description and there's a Facebook.
Abhay Vasant Ashtekar: MySpace time description stops at some place.
Abhay Vasant Ashtekar: And you can ask about the face space description, and so you can ask if you give me time.
Abhay Vasant Ashtekar: hamiltonian vector field on the Facebook.
Abhay Vasant Ashtekar: With generates dynamics with respect to this time, and you can ask is the hamiltonian vector field complete or is it not complete.
Abhay Vasant Ashtekar: And if it's not complete, which is what you think slope law what finite time if you did not complete, then diameter and vector few different geometry just tells you that this Hamilton electrical can be can be continued.
Abhay Vasant Ashtekar: So.
Abhay Vasant Ashtekar: I mean, this is the thing.
Abhay Vasant Ashtekar: Technically it's not a.
Abhay Vasant Ashtekar: it's a comment about me or you're not.
Lucía Menéndez-Pidal de Cristina: About yeah very good comment.
Western Physicists: Can I also interject a sink to a crucial point here, since you say now we're going to verify this conjecture.
Western Physicists: My reaction to this conjecture is that it's not relevant and it's not interesting and is not what one has to do period because.
Western Physicists: If the solutions if the histories of the theory are such that there is a slow clock so variable that is bounded.
Western Physicists: Then.
Western Physicists: There might be a unitary operator that moves the speed toward the shifting that variable but that's not.
Western Physicists: that's not the.
Western Physicists: way the the the state evolves in general, so there is no reason to demand the unique guarantee in that evolution period, so if if if I study a particle in a box.
Western Physicists: And they use the X mts variable.
Western Physicists: And I say, well, as we use X as a variable as a time variable to access o'clock fine but X is mounted So if I demand that the evolution is unitary eggs I just do something wrong.
Western Physicists: So, demanding that the problem I have is that demanding in the charity.
Western Physicists: Why should we demand unitary there's no reason, so the idea that we should demand the clarity or and then good look, this was all the singularity because, of course, there is also where it is allow us to go past the single point, which is the boundary.
Western Physicists: My resourcing well it did I don't know, maybe it does, but it doesn't it does not but that's not what we should do physically, obviously, it seems to me we should simply not demanding maturity in that variable.
Western Physicists: period.
Lucía Menéndez-Pidal de Cristina: Yes.
Western Physicists: We want to find it in other ways, without this demand in the singularity.
Western Physicists: Then I think that's the way we're doing to gravity for for decades, so why do you want to do something else.
Lucía Menéndez-Pidal de Cristina: I mean, because you need clarity is one of the main principle of quantum mechanics basically if you don't happy with.
Western Physicists: Another one is the main thing about the military at every time.
Western Physicists: There is a.
Western Physicists: Are symmetry in the face space which correspond to the time evolution is it's a main thing, under certain conditions, which are not realize that, for these clocks.
Western Physicists: This this ideology Oh, we should choose a broken then imposing iterative just roll period, and if there are other ways of defining quantum theory perfectly consistent in your venture new some of them present to the medical.
Western Physicists: And, and it makes no sense to ask any clarity with respect to o'clock that comes down stokes doesn't the so I you know they said.
Lucía Menéndez-Pidal de Cristina: The problem I mean this is a thing so.
Lucía Menéndez-Pidal de Cristina: it's I think the main philosophical question about all of these approaches, is whether integrity is really something that we should impose to are.
Western Physicists: appearing what we're not.
Western Physicists: it's not not by choosing an arbitrary clock and pretending to be unitary with respect to two o'clock that this is not the right unitary I just gave an example where it goes wrong.
Western Physicists: it's a seal so far is even super clean super Nice would you present the generativity is the relations between variables Okay, now we want to the quantum theory that is fun to religion within these variables that in the classical it goes to those fine Certainly, we do not want.
Western Physicists: A theory where necessarily.
Western Physicists: Where the system doesn't grow classically necessarily it should go over to the candidate, why it might have been some cases but demanding it as a principal makes no sense whatsoever to be.
Lucía Menéndez-Pidal de Cristina: But then, how would you.
Lucía Menéndez-Pidal de Cristina: analyze anything if you don't have a coherent probability interpretation, so this is my.
Western Physicists: making it clear and for ability interpretation.
Western Physicists: Without a unitary evolution in some variable.
Western Physicists: it's.
Western Physicists: Written two books and explaining how to do that and other people, probably this audience and I read another book so how's the present.
Western Physicists: So I don't understand this a priority request that I choose a variable which happened to end at some point that I demand is really to be unique to that variable industry, making mistake so.
Lucía Menéndez-Pidal de Cristina: When this is the thing I mean i'm not saying that this is the answer to to the to the problem statement saying that this is one approach and usually, when people study.
Lucía Menéndez-Pidal de Cristina: This type of cosmological models based very simply, and very nice me sometimes these tools, the dynamical variable that they liked the most and use it as clock and then.
Lucía Menéndez-Pidal de Cristina: Most of them being played at the series indeed to have like a coherent interpretation of that and the point is are the things that I want to do later, is that, then the dynamics of the theories are very dependent on this very nice choice and.
Lucía Menéndez-Pidal de Cristina: And, and what does this tell us about these approaches that maybe we, I mean there are things that maybe people overlook and have to.
Lucía Menéndez-Pidal de Cristina: think a bit more about this and and me.
Lucía Menéndez-Pidal de Cristina: But they don't I don't have an answer I didn't have a theory of quantum gravity that solves the problem of time.
Western Physicists: Whether there are there are there.
Western Physicists: So why looking at a 1983 it's a what 40 years ago I mean since then, there are a lot of work on other ways of dealing with the problem of time that don't require unitary do just an arbitrary chosen.
Western Physicists: Independent variable.
Lucía Menéndez-Pidal de Cristina: yeah yeah but I mean this is, many people are studying these type of models.
Lucía Menéndez-Pidal de Cristina: and doing this, this.
Lucía Menéndez-Pidal de Cristina: doing the we're done with the question and then they choose, environment and the clock as a clock i'm in the extract some consequences of that.
Lucía Menéndez-Pidal de Cristina: So we just wanted to point out the necessity of looking at the clock to scare me, I mean.
Lucía Menéndez-Pidal de Cristina: Maybe you don't do it that's fine.
Western Physicists: I get some time I think some.
Western Physicists: quantum because we're logical models that they're very delicious sure.
Western Physicists: They are that they're choosing an independent variable and evolving in that variable precisely because it's possible to to have unique URLs that variable as as as a band was saying, if you look at the face space issue, there are some flow if you choose this is.
Western Physicists: me dorian classically a flow in the face space, which is, which continues, which you don't know anything anywhere, then there's nothing wrong in in a study that initial part mechanical, but if you choose a flow the end somewhere.
Western Physicists: Then there is no reason to so it's not that every time you choose a block.
Western Physicists: And you do something wrong.
Western Physicists: i'm not.
Western Physicists: Saying every time it was a clock, you must do something right.
Western Physicists: So I just wanted to put that strongly there.
Western Physicists: that's that's some of the radiology when 40 years ago.
Western Physicists: In fact, oh let's in demand in the charity or that's wrong in general, it might be right, in some cases, but depends, case by case.
Lucía Menéndez-Pidal de Cristina: mm hmm.
Lucía Menéndez-Pidal de Cristina: OK, so I guess in this theory, both I and T.
Lucía Menéndez-Pidal de Cristina: would be bad choices of club, according to what you're saying.
Western Physicists: I should think about because I don't remember.
Western Physicists: Okay okay that's better but it's something like that, yes.
Lucía Menéndez-Pidal de Cristina: OK OK OK.
Abhay Vasant Ashtekar: I don't agree with.
Abhay Vasant Ashtekar: Some of the things that i've been saved, but maybe we should let the speaker initial then.
Lucía Menéndez-Pidal de Cristina: We can increase the discussion because it's a very interesting discussion and So yes, taking into account.
Lucía Menéndez-Pidal de Cristina: we're going to choose the three clubs and see and see what theories, we obtain and then we can comment, maybe on these things and regarding the.
Lucía Menéndez-Pidal de Cristina: resource for finding similarities of Russian and I just wanted to point out some people that have done.
Lucía Menéndez-Pidal de Cristina: That have either worked in this model of working very similar model so, for example, our last game sd card, they have.
Lucía Menéndez-Pidal de Cristina: Basically, the same model, but with a fixed cosmological constant that they studied in the local tumor cosmology setting and then comparing it to the standard winner David quantization and the use of five o'clock.
Lucía Menéndez-Pidal de Cristina: Then we have preventable that use the same more than we used.
Lucía Menéndez-Pidal de Cristina: To use the T clock and also dylan and to look.
Lucía Menéndez-Pidal de Cristina: They use the the clock so have you ever seen like these mothers in our models have been analyzed using different terms of look, and then we have a very interesting work.
Lucía Menéndez-Pidal de Cristina: From boivin which willa in monday's call up and what else decal.
Lucía Menéndez-Pidal de Cristina: They looked at the at the senior model with a fixed cosmological constant using a generalized the moment opportunities semi classical and they also found results that are compatible with ours.
Lucía Menéndez-Pidal de Cristina: So now we can entice them all.
Lucía Menéndez-Pidal de Cristina: Okay.
Lucía Menéndez-Pidal de Cristina: So.
Lucía Menéndez-Pidal de Cristina: we're how are you going to do this, we will take the classical constraint, and we have to turn it into a an operator constraint.
Lucía Menéndez-Pidal de Cristina: And to do so, we replace we when we can see that this quadratic terms they kind of look like a metric multiplying the momentum with the metric being.
Lucía Menéndez-Pidal de Cristina: The winner words that mean the word metric and we can change the Sturm replace it by the lab last week climbing operator minus eight Square.
Lucía Menéndez-Pidal de Cristina: box.
Lucía Menéndez-Pidal de Cristina: And Okay, so this is not free of ambiguity, because we always have the ordering and the greatness and our take on the ordering ambiguity that we want our theory to be.
Lucía Menéndez-Pidal de Cristina: Government and the change of coordinates in these five and MySpace and to do so, we use this operator, but of course the other choices can we make made and.
Lucía Menéndez-Pidal de Cristina: Again, this one is on another thing that requires an answer from quantum theory, but what we find these with a different equation with then against an operator light on our reflection of the universe, which is going to be a variable have wi fi and T equals to zero.
Lucía Menéndez-Pidal de Cristina: And the problem of time here is how to start time evolution from this equation, and really try to apply the answers A and B.
Lucía Menéndez-Pidal de Cristina: And the answer a, which is to clock starts with all of the blocks defying the are good clocks or maybe not from what we saw previously, but we will ignore these for the moment and be the quantum theory with respect to all clocks.
Lucía Menéndez-Pidal de Cristina: So first i'm going to assign the scholars to every block so it's a bit simpler, the Decalogue series always going to be orange and then, if I click blue and vic look.
Lucía Menéndez-Pidal de Cristina: Like think.
Lucía Menéndez-Pidal de Cristina: So, if we look at the clock theory, we can rewrite the winner delete equations that it looks like a shredding equation, with the derivative with respect to T.
Lucía Menéndez-Pidal de Cristina: And an operator, which we call he was a senior at the hamiltonian because it's a sharing an equation, we want to Australia in a product which is this one, with it, of course, on the remaining variables and this factor comes from the determinant of the matrix.
Lucía Menéndez-Pidal de Cristina: If, instead, we decided to go with the five very nice clock, then we have something that looks a bit similar to a client government equation.
Lucía Menéndez-Pidal de Cristina: And this is obtained by multiplying the first winner the equation, we had by effectively Square and we find the second or the derivative with respect to find my.
Lucía Menéndez-Pidal de Cristina: equal to an operator multiplying our function of the universe, because this is the second order formulation, we need a client Gordon in a product on the remaining variable which is going to be this one.
Lucía Menéndez-Pidal de Cristina: And here, these one of the V comes from the normal kind.
Lucía Menéndez-Pidal de Cristina: Of fight with constant surfaces and so now we have these minus thing standard kangaroo in the product, and if we analyze the V clock.
Lucía Menéndez-Pidal de Cristina: Then we have this second order equation, in which we have another operator with me today called F multiplying my Fine, and again, this is the second area formulation, so we need to use a blank or type in a product which, in our case is going to be this one.
Lucía Menéndez-Pidal de Cristina: So very nice now, we have our theory.
Lucía Menéndez-Pidal de Cristina: The solution of the wheeler delete equations are basic functions, so there are basic function of imaginary and real order.
Lucía Menéndez-Pidal de Cristina: And this, these are the expiration factors that then we'll be playing everything and so alpha beta gamma and epsilon are parameters that.
Lucía Menéndez-Pidal de Cristina: are going to be constrained for two main reasons, the first is, we want to have a nice quantum theory, we will require normalize ability.
Lucía Menéndez-Pidal de Cristina: Which means we will only consider states that are finite norm and the dean of products, we have previously defined.
Lucía Menéndez-Pidal de Cristina: And then the big one, which is time independence, we want our theory to be unitary but the unitary with respect to the clock, we chose for experience, and this is going to constrain my alpha beta gamma and epsilon.
Abhay Vasant Ashtekar: Again isn't Lambda positive.
Lucía Menéndez-Pidal de Cristina: So here, not so here the integral over Lambda is over the horror via line.
Abhay Vasant Ashtekar: OK, so the square root of Lambda in the boat.
Lucía Menéndez-Pidal de Cristina: Man, yes, it can be a real and unreal and in the papers it's a better explained, but there is a convention to define the rest of functions with this kind of complex argument, but we have to make the choice of there somewhere.
Lucía Menéndez-Pidal de Cristina: But.
Western Physicists: This is a choice T as o'clock or I got lost in the world.
Lucía Menéndez-Pidal de Cristina: So sorry, these are the solution of the way that equation, without making any traces This is intended on the this alpha beta gamma and epsilon the we look different with respect to different properties.
Western Physicists: So when you when you say time independence is the classical theory time independent was spectral choice blocks.
Lucía Menéndez-Pidal de Cristina: So when I say Okay, so this is maybe the framing of the slide was is not helpful in this case.
Lucía Menéndez-Pidal de Cristina: So when I say we, I have three theories, I have one we live it equation, but I have three ways of interpreting.
Lucía Menéndez-Pidal de Cristina: yeah, this is the solution of my will read the question without with my interpretation and then depending on the interpretation i'm going to restrict the solutions, first of all, what.
Western Physicists: classically in the theater traditions.
Western Physicists: classically is their time independence with respect to the three choices of time.
Lucía Menéndez-Pidal de Cristina: Time independence of what.
Western Physicists: You know time independence in the classical theory.
Western Physicists: Is the dynamics, independent of time.
Western Physicists: For each one of the three possible choices of time.
Abhay Vasant Ashtekar: The only two choices right.
Lucía Menéndez-Pidal de Cristina: There in the classic sense theory everything can be.
Lucía Menéndez-Pidal de Cristina: wrote as a function of everywhere variable.
Western Physicists: Right, but is it time independent the dynamics I don't think so.
Lucía Menéndez-Pidal de Cristina: But i'm independent What do you mean by an independent JESSICA theory.
Western Physicists: Well, the same missing the quantum theory, if there is a unitary.
Western Physicists: evolution time and means that there is a.
Western Physicists: classical symmetry for time shifted.
Western Physicists: me.
Abhay Vasant Ashtekar: So tell me done in flow in both of those variables depends on us.
Lucía Menéndez-Pidal de Cristina: But this is, this is the thing that we were discussing before right not are viable are the same classically because of the flow degenerate now.
Western Physicists: defend this quantum mechanical it says all time independent classical.
Abhay Vasant Ashtekar: Work time independence.
Abhay Vasant Ashtekar: should not be perhaps is the wrong terminology in this like that i'm just each he just wants yeah we can strike that.
Lucía Menéndez-Pidal de Cristina: Yes, I checked your time independence.
Abhay Vasant Ashtekar: I think that.
Abhay Vasant Ashtekar: The floor.
Abhay Vasant Ashtekar: And the classical face space, the floor preserve the simplistic structure.
Lucía Menéndez-Pidal de Cristina: Okay, maybe now.
Abhay Vasant Ashtekar: Does the law is the law that's what she wants to ask.
Abhay Vasant Ashtekar: or you're still unhappy.
Western Physicists: yeah I mean maybe it's the same questions before, why do we demand any charity in evolution of a variable, this is the same question just before it gets when we don't.
Abhay Vasant Ashtekar: Think about is a mathematical pressure classically I got hamiltonian from a flow, which is hamiltonian.
Abhay Vasant Ashtekar: With respect to both charts up time and, as far as I know, there are only two tons of time not three so so the classical the flow is.
Abhay Vasant Ashtekar: Is those this you know the background structure which is a simplistic structure or mechanically.
Abhay Vasant Ashtekar: She wants to say that there is structured in America solicit given medical structure which is simplistic structure quantum mechanical insurance to say is that the cinematical structure is in a product and does the flow presented a product they just asked is another magical question.
Abhay Vasant Ashtekar: Are you still unhappy.
Western Physicists: That it seemed to me doesn't flow.
Western Physicists: revolution in the classical limited keeps the flow, but this flow does not is not well defined everywhere in in classical face face.
Abhay Vasant Ashtekar: The face basic is actually well defined but somehow the space time interpretation breaks down.
Abhay Vasant Ashtekar: The curvature blows up, but the floor.
Abhay Vasant Ashtekar: is well defined.
Western Physicists: space.
Western Physicists: If I follow flow.
Western Physicists: evening when along a slow time motion why why doesn't the flow end and the singularity.
Abhay Vasant Ashtekar: yeah so you can just say that.
Abhay Vasant Ashtekar: Okay, so in space time it doesn't it's.
Abhay Vasant Ashtekar: Not in face because I mean the statement is that the particular dynamical way, I mean, these are kind of thing that you have talked about Karma barbers shorts in singularity that you can just define variables, which you can continue across, even though the.
Abhay Vasant Ashtekar: The space time picture is actually singularity.
Abhay Vasant Ashtekar: So you can have faith based on which hamiltonian flow you.
Western Physicists: know there are some cases in which you can comment on.
Western Physicists: Maybe we shouldn't let me check oh go ahead yeah.
Abhay Vasant Ashtekar: Let me check I know some.
Abhay Vasant Ashtekar: some cases it can so that's good so in this case the statement is in the classical face face if this continues she's she's just asking if you like, the mathematical question.
Abhay Vasant Ashtekar: Does it continue with respect leave a product.
Okay.
Lucía Menéndez-Pidal de Cristina: So.
Abhay Vasant Ashtekar: I think I think we should never finish and then, once again.
Lucía Menéndez-Pidal de Cristina: Okay, so what the way i'm going to.
Lucía Menéndez-Pidal de Cristina: constrain.
Lucía Menéndez-Pidal de Cristina: This alpha beta gamma next in on these parameters are by two ways normalization This is with respect of the chosen theory, so we have three theories, we have the V clock.
Lucía Menéndez-Pidal de Cristina: The clock and the clock and we want first our states to be normalized and then we, we want to take that our theory is in integrity, with respect to the chosen clock and so what this requirement means is the following so normalization is easy.
Lucía Menéndez-Pidal de Cristina: We just want.
Lucía Menéndez-Pidal de Cristina: The norms.
Lucía Menéndez-Pidal de Cristina: To be conserved.
Lucía Menéndez-Pidal de Cristina: Whether or not we conserve to not be infinity and in the teeth look theory, this means.
Lucía Menéndez-Pidal de Cristina: We have no real basic function so let's just as a reminder gamma and excellent i'm multiplying will order vessel functions.
Lucía Menéndez-Pidal de Cristina: So, in particular theory normalization implies that we have no real basic functions in the week looks theory is the same requirement and the fight clock theory, we have we still can have.
Lucía Menéndez-Pidal de Cristina: Real order basic functions, although they have a weird and just as an aside, usually Llangollen either products are not positive definite and these cases not different than that so but it's easy to solve this problem, because the way of the how the vessel functions.
Lucía Menéndez-Pidal de Cristina: Everything the theory the inner products are ready, separating positive norm and negative norm state, so we just if we modify the new product only on the negative non state, we find the positive.
Lucía Menéndez-Pidal de Cristina: Definitely my product everywhere, but this is just an aside, so now, the big one, which is time independence and what I mean by that independence is in the theory the theory this.
Lucía Menéndez-Pidal de Cristina: lean product should be independent of the in the fight theory, it should be independent of fighting the V theory, it should be independent of V.
Lucía Menéndez-Pidal de Cristina: And this requirement translate into the self for joining this of the previous operators that I presented a few slides ago which are eight D and F, so we see that, with the three theories, we have built here.
Lucía Menéndez-Pidal de Cristina: requiring that our theory has been very evolution is is equivalent to a same for joining this problem, and this age DNS are different operators.
Lucía Menéndez-Pidal de Cristina: And to sell for joining this requirement is with respect to the front end to type in a product, and how does this translate.
Lucía Menéndez-Pidal de Cristina: So, in general, these operators are symmetric and they will fall into silica theories, the ones that are already sent for joint like F, which will be already super joint.
Lucía Menéndez-Pidal de Cristina: And the ones that are not sephora joined the meeting for don't extensions like G and H, and there are some operators that are not for joining and not have made sense, which i've extension, but it's not the case.
Lucía Menéndez-Pidal de Cristina: In our work it happens at eddie's already sent for joint so our week looks theory is already unitary so we don't need to do anything else.
Lucía Menéndez-Pidal de Cristina: But eight and D are not sephora joint and if we want them to be said for joining, which means, if we want our theories, to have.
Lucía Menéndez-Pidal de Cristina: A conserve the norm, over time, we have to introduce some boundary conditions which are the ones that I present here, and the important thing is these limits in the boundary condition, because they look very similar.
Lucía Menéndez-Pidal de Cristina: But one of them is a boundary condition around the point equals zero, which is where the, these are the two o'clock worse slow.
Lucía Menéndez-Pidal de Cristina: and for the fight like cereals and the boundary condition that week was inventing which was where the fighter was slow classically going back to the vedanta my conjecture.
Lucía Menéndez-Pidal de Cristina: What did this theory what to discern this boundary condition will, for the allowed best and function, it means that we're only allowed real combination of imaginary or the best function So here we only have three a combination of these vessel functions.
Lucía Menéndez-Pidal de Cristina: And we have one parameters different extension which is produced by these parameters data and gaba zero in this case, why is a function of K and your inflection of them so remember here this fight it and fight side are the allowed state of two different.
Lucía Menéndez-Pidal de Cristina: quantum theories.
Lucía Menéndez-Pidal de Cristina: And so we see that the conclusion of this is that.
Lucía Menéndez-Pidal de Cristina: If we employ me directly, the allowed states are going to look very different from theory theory and of course it will have impact on the dynamics.
Lucía Menéndez-Pidal de Cristina: Just as a wrap up so i'm a bit late, so I don't know how much time I have left.
Lucía Menéndez-Pidal de Cristina: But I still have one of the dynamics that they want to show, so I might just go a bit faster than that seat.
Lucía Menéndez-Pidal de Cristina: But just to let you know this is important in the theory the boundary conditions that requires zero, which is we're dressing, the talk was not.
Lucía Menéndez-Pidal de Cristina: In the faith theory the boundary conditions as equals infinity which is just the word o'clock westlaw.
Lucía Menéndez-Pidal de Cristina: And what we can conclude from this is such an interesting place the boundary condition if the field is not already unitary at this low point of the clock.
Lucía Menéndez-Pidal de Cristina: and different blocks, of course, need to boundary condition, but we can ask yourself is this an artifact of the way we're trying to quantum theory So what about the conversation, and we have looked a bit on this.
Lucía Menéndez-Pidal de Cristina: and basically when we looked at the data quantization we are in the following scheme, first we have to wait until it equations.
Lucía Menéndez-Pidal de Cristina: which implies the existence of two operators which equals one and CEO and cto is basically see one multiplied by the square but this apparently is not trivial because we Square, it is a non trivial faith based function.
Lucía Menéndez-Pidal de Cristina: If we start with these will delete the equation, and we want and we interpret the second or the derivative again as a box operator these motivates two different kinematic inner product so see one would motivate the.
Lucía Menéndez-Pidal de Cristina: kinetic in the product one here with were multiplying by V because it's the box operator have a different metric and the cto would motivate these type of Connecticut in a product, so we basically by multiplying the theory.
Lucía Menéndez-Pidal de Cristina: By a non non.
Lucía Menéndez-Pidal de Cristina: Non trivial faith based function in our case, we square we find out.
Lucía Menéndez-Pidal de Cristina: To different giving medical interpreter, to start with.
Lucía Menéndez-Pidal de Cristina: And now demanding so for joining this with this particular kinematic and in a product.
Lucía Menéndez-Pidal de Cristina: off the operators see one and see to will turn out to the corresponding to say for joining this problem of sequel operators in this case the one.
Lucía Menéndez-Pidal de Cristina: Of the one is equivalent of separate Jonas, of the one which is very simple operator and for joining us of see to is a clear answer for joining us on the.
Lucía Menéndez-Pidal de Cristina: mat if you compare the one and he basically the only difference lives here, in which we have a square instead of the.
Lucía Menéndez-Pidal de Cristina: derivative with respect to five Square and here there is a.
Lucía Menéndez-Pidal de Cristina: There is a.
Lucía Menéndez-Pidal de Cristina: hard to explain these, but these operator basically the same operators.
Lucía Menéndez-Pidal de Cristina: But in one dimension less and between the D one and the ah.
Lucía Menéndez-Pidal de Cristina: There is a.
Lucía Menéndez-Pidal de Cristina: Another team to variable with respect to be but rewriting going on but it's very simple, in any case, the two is even simpler because it's a one dimensional operator that would correspond to the one that mentioned reduction to the GP in which we're changing this deep to lana.
Lucía Menéndez-Pidal de Cristina: Using the free it as well.
Lucía Menéndez-Pidal de Cristina: So what can we can go from the forum, all of these if we have our two wheeler the equations that implies one and see two and we want our operators to be super job with respect to the kinematic in the products, and this is something that is usually.
Lucía Menéndez-Pidal de Cristina: A requirement when we do do quantization we find a set for joining this problem, which is basically equivalent to the previous version is problem we had.
Lucía Menéndez-Pidal de Cristina: Yes, so this is what I explained this like this is for joining us problem remains in vr quantization and the thing is that we multiply the width of the equation by faith based function, but this shouldn't have very.
Lucía Menéndez-Pidal de Cristina: An impact or naive need with within thinking will have an impact, because the important stuff is that.
Lucía Menéndez-Pidal de Cristina: The two equations have exactly the same solutions which are the basic functions and, but if you multiply by a non trivial faith based function, you find.
Lucía Menéndez-Pidal de Cristina: Different kinematic are in the product and, at the end defensive vaginas problems.
Lucía Menéndez-Pidal de Cristina: And the question would be, how do we choose between the different with a different equation, possibly these what is the right one, so it, the problem we have several jamison new date is not only a problem of.
Lucía Menéndez-Pidal de Cristina: The approach, we chose that was choosing first o'clock and then colonizing but, rather, it also appears in the other frameworks, like the quantization and just.
Lucía Menéndez-Pidal de Cristina: To say that our work is not a contradiction of the artistic work of homes, Nice and lock.
Lucía Menéndez-Pidal de Cristina: In which they developed a framework that allows for clock changes because in their framework, they have only one way to delete the equation.
Lucía Menéndez-Pidal de Cristina: And they do click changes inside, these were the equation that gives them the theory and in our case because of this non trivial multiplication we have two different winner the equation so it's a slightly different scenario.
Lucía Menéndez-Pidal de Cristina: So now, I can start talking about the dynamics very quickly.
Lucía Menéndez-Pidal de Cristina: So, first the dynamics of the V theory, and this is to recall the dinner solution for which is this combination of basic functions, now we have only imaginary order as a function and because here we are free to choose.
Lucía Menéndez-Pidal de Cristina: We are going to focus on states where i'll phase zero, so we have here on the beta and there is a normalization constant going on here that I am ignoring so this would not be.
Lucía Menéndez-Pidal de Cristina: Equal exactly it's going to be X of proportionality thing anyway So how are we going to build semi classical states is by changing this beta to a gosh which is going to be big.
Lucía Menéndez-Pidal de Cristina: Around have some values Casey which means K classical and the classical so if we do this if we take if I was zero just for simplicity, now we change these two ago and.
Lucía Menéndez-Pidal de Cristina: We expand these coefficient these expectations value around equals zero we find these series.
Lucía Menéndez-Pidal de Cristina: Which is very, very similar to classically expanding the solutions we found longer going one of the first lights around V zero So you see the first difference starts appearing around order for him V What this means is that.
Lucía Menéndez-Pidal de Cristina: This theory doesn't show strong divergence from the classical theory at least, if we choose the states of course undefeated to other states but.
Lucía Menéndez-Pidal de Cristina: What this means from similarities versions perspectives is that we cannot say that this the resource the similarity resolution and the other dynamics for the other theories are going to be a bit different.
Lucía Menéndez-Pidal de Cristina: So for the D theory, we have these type of states.
Lucía Menéndez-Pidal de Cristina: Which we're going to render semi classical again by shaping this lamp this alpha as caution this parameter we're going to set it to zero for simplicity, but, for example, preventable in their work they analyzed the different forms of.
Lucía Menéndez-Pidal de Cristina: offer this sufficient distinction factor and they didn't find a strong dependence on the results on these fake factor.
Lucía Menéndez-Pidal de Cristina: Anyway, so if we change these I will caution again beat around the classical and learn the classical we can study expectation values of the of tea, which is the important quantity and the criteria for simulators notion is meant to be that this V.
Lucía Menéndez-Pidal de Cristina: is always greater than zero and finite in our case.
Lucía Menéndez-Pidal de Cristina: So just.
Lucía Menéndez-Pidal de Cristina: To also recall that the basic functions at small arguments of this is going to be the limit returns to zero.
Lucía Menéndez-Pidal de Cristina: look like playing waves and again with the we have a pre factor with applying the best function, which is the square root of Lambda.
Lucía Menéndez-Pidal de Cristina: And is minus so it's going to cancel or compliment very nicely these exponential.
Lucía Menéndez-Pidal de Cristina: So, very close to the singularity or five classical looks like a superposition of playing waves of independent of lander that are either outgoing from the singularity or in going to the singularity and these.
Lucía Menéndez-Pidal de Cristina: superposition is basically what is going to trigger singularity resolution, so this is one of the curves.
Lucía Menéndez-Pidal de Cristina: We found for V, and so the solid lines are the classical theory, in which we goes to zero, and the dotted lines are different.
Lucía Menéndez-Pidal de Cristina: expectation values for a difference in classical state basically the width of the ocean is changing, and what we observed, is that of course the specific curve depends on the choice of goshen but the.
Lucía Menéndez-Pidal de Cristina: way that the dynamic is always the same, we stayed very close from a classic a solution, and then the quantum session separates.
Lucía Menéndez-Pidal de Cristina: Never reaches zero or which, which is a boy or the orange remains positive and then bounces back, and it is a classical curve that you see when you see a bounce.
Lucía Menéndez-Pidal de Cristina: So we can see that the DC resolves the singularity and, last but not least, the fight clock theory that had this state, so we do the same business.
Lucía Menéndez-Pidal de Cristina: But now we study expedition values of V that are going to be a function of fine and we want to serve quantum singularities emotion, but you will have several quantum we collapse, ie or V is never going to reach in the director is going to stay finite so what I mean is this.
Lucía Menéndez-Pidal de Cristina: So we see first we start very closely to the classical solution, then the quantum session starts expanding very quickly, but then slows down, for it is a fine line to value and then goes to the other branch and is exactly.
Lucía Menéndez-Pidal de Cristina: A reflection again but not from equals zero rather from V equals infinity and this very this rapid.
Lucía Menéndez-Pidal de Cristina: Growing phase in which the quantum solution grows faster than the classical solution, for example, this was observed in this work of boiled it I that only looked at some of the journalists momentum.
Lucía Menéndez-Pidal de Cristina: Just to point this out.
Lucía Menéndez-Pidal de Cristina: And yeah, so this is another observation, we studied in the in the fight clock series, so we had in the previous like via fire, now we had we have to fight and we can also study.
Lucía Menéndez-Pidal de Cristina: And we see here it is again a transition between one branch of the and the other brands of the so deep stops being a function of a single valued, whether or not the I mean the expectation, one of the four disciplines christie's and then because we have to fight and fight your fight.
Lucía Menéndez-Pidal de Cristina: These are blocked off the two of them with respect to each other, which is very nice again, so the solid line is the classical theory of tea.
Lucía Menéndez-Pidal de Cristina: And in this case of what the quantum solution would be doing is evolving, I think, in this way, so we would start from the singularity go close to classical solution, and then there would be.
Lucía Menéndez-Pidal de Cristina: The quantum social separates from the classical theory and we go to the other branch and go back again to the same.
Lucía Menéndez-Pidal de Cristina: person visiting degradation of the dynamics the structures know stone divergence from the testicle see that the clock serves a singularity under the cloak sean's a quantum leap collapse.
Lucía Menéndez-Pidal de Cristina: And the important thing is that the quantum behavior can be interpreted as a reflection from the boundary either as equals zero y equals infinity.
Lucía Menéndez-Pidal de Cristina: As already says it's up to where the boundary condition is because of the day, but when a Venetian what are they seeing the theory diverges from the classical theory and far from the boundary the classical and quantum course always look very similar.
Lucía Menéndez-Pidal de Cristina: yeah yes, so this is a recap, of the features of all the clock.
Lucía Menéndez-Pidal de Cristina: So the V clock theory, we saw that the the clock was.
Lucía Menéndez-Pidal de Cristina: Was unitary this the quantum theory from the for the vehicle was unitary from the beginning, so there was no binary condition and hands, because in urban urban nation nothing denied there's an ocean and knowing producer ocean if eating.
Lucía Menéndez-Pidal de Cristina: equals infinity i'm gonna put this here to be clear on this legal entity resolution.
Lucía Menéndez-Pidal de Cristina: That the clock is not very different from scratch the quantum theory, so we need the wonder evolution, to make a janitor and these one recognition needs to security solution.
Lucía Menéndez-Pidal de Cristina: And the fight clock is not either from the beginning, so we need a vulnerable position, but now this boundary condition resolves infinity instead of this.
Lucía Menéndez-Pidal de Cristina: So yes, so what I wanted to show here is that the problem of time has many neurons and need very complex, I think that quantum cosmology is in good testing ground to do this type of a philosophical questions.
Lucía Menéndez-Pidal de Cristina: And that, in this scenario i'm using this quantization procedure you need directly require month at what are the thing that lead to different theories.
Lucía Menéndez-Pidal de Cristina: And these unique parity requirement are present in different compensation schemes, not only this relational quantization that we chose but also direct quantization.
Lucía Menéndez-Pidal de Cristina: And also, at the end of the day, seen it or solution seems to be not only a feature of the theory, but the feature of the choice of club and what they want to give attention to is that clock change block choices should be given.
Lucía Menéndez-Pidal de Cristina: More attention when studying these type of cosmological models and that's it, thank you for listening.
Lucía Menéndez-Pidal de Cristina: have more questions.
Jorge Pullin: Any questions.
Abhay Vasant Ashtekar: The main questions that he had.
Jerzy Lewandowski: I will be also happy to make a comment, but my comment is very general so.
Jerzy Lewandowski: Maybe there are more important questions and comments.
Abhay Vasant Ashtekar: No, please go ahead.
Jerzy Lewandowski: Nobody yeah so when we consider hamiltonian constraints system from the.
Jerzy Lewandowski: From this first point of view which wasn't the first slide that is that we first saw the constraints and then we construct the reduce face face.
Jerzy Lewandowski: Then he writes this this on the on the left hand side, then.
Jerzy Lewandowski: Actually, all the time, well then, you have this issue of what is the evolution, because we receive not to have, so we have to introduce some questions, we can we can go, we can introduce relational observable.
Jerzy Lewandowski: and effective hamiltonian the the no framework i'm not talking about anything different than this, but, but then, when we look at this from the point of view of gauge transformations then we find that actually all choices of time our gauge equivalent.
Jerzy Lewandowski: Well, at least locally made maybe the face space has some complicated structure of non trivial fiber bundle maybe maybe that would require some.
Jerzy Lewandowski: This statement would require some some modification, but if, if we look at this locally and then this if this fiber bundle defined by the action of of.
Jerzy Lewandowski: The constraint is we consider as a trio and then every to a time functions are just gauge equivalent.
Jerzy Lewandowski: So what okay so every time functions I gauge equivalent, then there is no issue of have chosen clock, so what what is the clock actually the clock is not the time function, this is the momentum conjugate to the time function.
Jerzy Lewandowski: Which region, so we can fix one time function and and in this way we fix gauge transformations and instead we can consider all the conjugate momentum.
Jerzy Lewandowski: And I wonder whether this point of view it changes anything or or explains anything but, but that is the bottom line is that this point of view.
Jerzy Lewandowski: Well, it makes this issue of choosing clock function committee relevant.
Jerzy Lewandowski: yeah this is, this is my my very general.
Jerzy Lewandowski: comment on the clock functions.
Abhay Vasant Ashtekar: Speaking in classical period contemplating.
Jerzy Lewandowski: Well, I was thinking about classical theory.
Jerzy Lewandowski: So it depends a little on on whether we first South classical constraints and then quintiles or whether we agree with the first one ties and then then so so we have more ambiguity in would we do.
Abhay Vasant Ashtekar: It, so I think classically everybody understands, I mean, I agree with what what you said so there's no issue, I mean they're just different descriptions right.
Abhay Vasant Ashtekar: Of the same phenomenon classically.
Abhay Vasant Ashtekar: I mean you're given a solution if you like, just slicing it.
Abhay Vasant Ashtekar: To say what you mean by time evolution and I would say that, why do you want to talk about time evolution at all.
Abhay Vasant Ashtekar: So we can talk and physician ambiguous, but even if you talk about transition aptitudes it's our initial state in a final state, and so you have to define what do you mean by initial state in the final state.
Abhay Vasant Ashtekar: And so, in the classical picture that would correspond to gauge fix surface initially engage fixer is fine by gauge fixed me, which has been a time.
Abhay Vasant Ashtekar: In a year to give me a time q1 and q2.
Abhay Vasant Ashtekar: Talking about.
Abhay Vasant Ashtekar: The transition amplitude for.
Abhay Vasant Ashtekar: You know, from time 5125 to from even to be to etc, etc, but classically I think there's no problem, the question is about really quantum mechanics.
Abhay Vasant Ashtekar: But I think will be good to.
Abhay Vasant Ashtekar: know a lot of discussion in the beginning about.
Abhay Vasant Ashtekar: about the issue of your Daddy so maybe we can.
Abhay Vasant Ashtekar: understand that.
Jorge Pullin: All the Western through this our hand up.
Western Physicists: yeah I haven't so physical.
Western Physicists: machine, I want to say that.
Western Physicists: I mean I complained about the motivations.
Western Physicists: At some point in the middle of your talk, but the decisions were beautiful, I mean it's spectacular beautiful, I would say you really analyze this.
Western Physicists: it's very nice, because if you have a system or simply nothing you can do anything and complex in after you can.
Western Physicists: You can look at all the various options, and this is a this is remarkable i've never seen such a such an extensive analysis of.
Western Physicists: Of the of the question so so congratulations very, very nice and I have some questions, if you look at the at some point to write it will of the integration, in fact, the right two versions will.
Western Physicists: Just take one, this is an equation, I mean you can view this you can think of extended free space right before before reducing the linear space of this I know which this equation is defined that.
Western Physicists: That space there if I demand a pie by fee lavender TV and see to be SOFA jointed that has a it's a it's a well defined hyperspace Is that correct.
Lucía Menéndez-Pidal de Cristina: story, can you rephrase.
Western Physicists: The question that extended the in the space, not the not the physical One the one the one the arbitrary functions of the three variables.
Western Physicists: Extended his bonus if I if I didn't know that pie, all the free moment in time to three variables, to be self a joint that will define the it has a wonder if I hit the pro product that correct.
Lucía Menéndez-Pidal de Cristina: I don't know because we so in when we did.
Lucía Menéndez-Pidal de Cristina: i'm going to call interpolation and block approach so when we went from this with a different equation, we didn't analyze within analyze it we we chose o'clock directly and then studied the healer space we constructed from the clock, but then, when we did the direct quantization.
Lucía Menéndez-Pidal de Cristina: So we started with, for example with these winner that equation, and then we had our head space and we had a inner product, which was involving vt and fi and there we didn't ask for each individual moment to be said for joined, rather we asked for this big seat.
Lucía Menéndez-Pidal de Cristina: To be said for joint and with respect to the new product, we found and that was non trivial.
Lucía Menéndez-Pidal de Cristina: But we ask and all the individual and ddp and ddp and ddp to be super tight.
Lucía Menéndez-Pidal de Cristina: I my phone.
Western Physicists: Up isn't truly sold that don't extend that same space, the obvious l to.
Western Physicists: heal her.
Western Physicists: structure makes every sense of the joint and we just imagine, this was a.
Western Physicists: magic, this was a hamiltonian in a in a in a time of evolution and you have three independent variables that that be nobody would make any complicated mess about about the Hebrew problem.
Western Physicists: The question we just just try to understand why whether.
Lucía Menéndez-Pidal de Cristina: I don't know I don't want to put.
Western Physicists: Okay.
Abhay Vasant Ashtekar: The question is really.
Abhay Vasant Ashtekar: If you don't have the syllable space why'd you do that, hopefully, what i've done this alternative see had.
Abhay Vasant Ashtekar: lasik earlier that this operator bye bye bye bye spread of V and you minus by splitting your order to buy the new spread noisy use I use it for the eyes pop.
Abhay Vasant Ashtekar: Up Monday and God so Carlos Gilbert space you're using it here, implicitly, and similarly for them for the volume one by itself is going like is going from zero to infinity, but you are using one, a lot of volume and.
Lucía Menéndez-Pidal de Cristina: Then, yes.
Abhay Vasant Ashtekar: So sometimes answer answer the question is yes.
Abhay Vasant Ashtekar: Yes, yeah use that space to write down this.
Abhay Vasant Ashtekar: So this operator.
Lucía Menéndez-Pidal de Cristina: Yes, yes, yes, yes, no, no you're right, yes, they have to your wedding fun and it was again right the operator to begin with.
Abhay Vasant Ashtekar: Why did you go on Carlos you know next.
Western Physicists: semester comments.
Western Physicists: When we you talk about ambiguous when we take classical theory and promoted or pumpkin seed always have the greatest so the factor of the greatest is not is not particularly worrisome by itself, I mean if I if I write.
Western Physicists: The classical theory of Monaco see later like a quantum theory and.
Western Physicists: I can do it in a way you just completely wrong or we can do it in a way in which there is a zero point.
Western Physicists: Energy open do we, which is not zero point energy, I mean, these are well known, ambiguous in quantum theory, so the fact that ambiguity says.
Western Physicists: it's normal and that usually we solve this ambiguity is when they were physical systems by by X, the other inputs, I mean we have reason to believe that this is the right thing in this wizard believe is wrong theory so.
Western Physicists: it's not that the presence of ambiguity by itself should worry as much should be true interest us.
Western Physicists: A lot more yeah that's what I was saying.
Western Physicists: So it might be let's just put it as a tax there's some obvious reason for which one of your choices of the fall when it's when it's right or wrong or physical roads.
Western Physicists: I don't know, maybe because we expected political action to be some Regina not it's another region, for instance.
Western Physicists: On physical ground we use this all the time when we build the political theory there's no, we know that there's no unique machine that given a classical food was appointed to.
Western Physicists: The way we think about that is that somebody was mentioning a moment ago um I don't want to go into that in any, but I think one can work on extended here the space.
Western Physicists: Work in terms of partial observable and working terms of physician attitudes.
Western Physicists: and
Western Physicists: and never asked the question.
Western Physicists: of a unitary time evolution in a specific time variable I think this is a I think if you want to go to work on to reality, we should.
Western Physicists: get out of the shading variation and Union data because that's just not it's it's a it's cautious with generativity dramatic and generativity we don't have a preference time, so we should learn how to work with different types i'm not saying that this solves a problem or this.
Western Physicists: takes anything away from what you're doing I think what you're doing it's beautiful because it opens up a beautiful.
Western Physicists: system where we're kind of realize that but I, the only.
Western Physicists: coral I have is this was strong ideology which are less, we have a physical healing space with a unitary solution we haven't a theory no so as well.
Western Physicists: In my opinion, I think we can have a theory.
Western Physicists: Even in cases and you know unlimited papers there's a table with colossi long ago in which obviously there is no unitary time evolution in any.
Western Physicists: In any variable because this is a classical theory, where the histories are closed or sort of go round and round perfectly well defined, you can do the quantum theory it's predicted utilization anti to.
Western Physicists: see a well defined in the space is like here is much more simple that.
Western Physicists: You can do everything consistently, it has a clock right classical limit I wouldn't see any problem and there is no.
Western Physicists: Variable with respect to which there is a unitary kind of illusion, so I think do all this beautiful math that you work out should be resolved in a way in which may forget this requirement and see physically which one is the right set of.
Western Physicists: Because you have a you do correction to the classical trajectories assumption right isn't should be wrong if the difference one another, which is what I get so the question is, what are the physical ingredients, the extra physical ingredients.
Western Physicists: Like you know.
Western Physicists: classical limit in some sense it's also supports them.
Western Physicists: Which which tell us which one is the right prediction.
Western Physicists: That is just appointments not not.
Lucía Menéndez-Pidal de Cristina: lucky number, I see, I think I see what you're trying to say, and this is also one of the takes the takeaway of the full talk know how, how do you trust these models, how do you.
Lucía Menéndez-Pidal de Cristina: How can you trust it that what we're doing is correct, if, when we do another way we make another choice, the reserves are are completely different and I guess.
Lucía Menéndez-Pidal de Cristina: What you're trying to say is that we need some extra information.
Western Physicists: In our learners.
Western Physicists: Yes, we always do when we go to plug in theory, the many examples we stumbled upon it, and even even a lukewarm to cosmology.
Western Physicists: in which one was following some procedure and then at some point, they were waiting me this gives a.
Western Physicists: stroll panto collection, where you don't expect them okay so let's backtrack and say there was a wrong choice at some point we have to do another choice, so this is a physical ingredients, I suppose board would say a compliment heritage, what is.
Western Physicists: The name of it.
Western Physicists: I mean the use of classical music, for instance I don't know is this bounce a large volume physical reasonable I don't I don't have sufficient understanding that you will have your models predicts that the systems come back for a large volume.
Lucía Menéndez-Pidal de Cristina: Yes, it's very puzzling this balance from now.
Western Physicists: i'm a physicist, so I say Okay, so there are some choices this in choosing the mental model.
Western Physicists: And I have some independent research I don't know i'm not sure I would say, maybe say something wrong, but as an example.
Western Physicists: And some reason to believe that when the universe, is very large and far away from a bump in the gym so my quantum theory should not affect that so, then I made a wrong choice of some point so fine, so what I do take a chance.
Lucía Menéndez-Pidal de Cristina: These.
Western Physicists: These will do so.
Lucía Menéndez-Pidal de Cristina: The ways to go out of these now i'm wow Okay, so I am I am only going to choose a Blocker.
Lucía Menéndez-Pidal de Cristina: That does the thing I want, and in this case I am interested in singularity resurrection and for example of these three clocks the only one that gives me singularity is emotion is a decline, which is shown.
Lucía Menéndez-Pidal de Cristina: Here and.
Lucía Menéndez-Pidal de Cristina: So I would say that the clock is correct, no but.
Lucía Menéndez-Pidal de Cristina: But then I mean I don't have any strong a reason to believe that there is a simulated version in the universe, because there's no proof of that observation.
Western Physicists: We want the theory which is consistent with what we expect is not, I think, is wrong idea Lou we just take some formal mathematical to see your we take a simplified we close our eyes cool I mean, of course, we we choose our models on basics of physics, the real problem here is not.
Western Physicists: The real problem here seems to me, is we follow generativity at some point something goes wrong here it is something clearly the role.
Western Physicists: And the end nobody goes wrong, but we expect this to be deep enough to Regina because those some some back of the envelope calculation, we know that we're keeping a quantum regions or something should happen.
Western Physicists: Is there a position that tell us what could happen there, yes, there is.
Western Physicists: A.
Western Physicists: If once a year, but the same position applied with a different choice doesn't do anything here and tell me that the university is very large is going to come back, they say, well, fine but that's not the theory that matron reasonably tools.
Western Physicists: And that's just a general way of thinking specifically I, I think that.
Western Physicists: I would love to see the hill display the food, he was space which.
Western Physicists: Is solution of the.
Western Physicists: I mean the The alternative is to work in the full human space use us partially observable as they are some symbols to find it up there and.
Western Physicists: A computer to position ourselves by.
Western Physicists: By the extractor projector as a symmetric silent of the projector on the.
Western Physicists: On the on the solution of the so I wonder if this can be translated the sincere all the mathematics work out maybe this.
Abhay Vasant Ashtekar: And I can it can all be translated.
Abhay Vasant Ashtekar: To constantly be.
Western Physicists: This way yeah.
Abhay Vasant Ashtekar: So I just I mean, I agree with Carlos don't know philosophy appear that.
Abhay Vasant Ashtekar: We do have a lot of experience, about passage to classical from classical theory to quantum theory and we should use that.
Abhay Vasant Ashtekar: But conversation is not a crime that one.
Abhay Vasant Ashtekar: There are physical books, but I would I would add one more thing that, namely.
Abhay Vasant Ashtekar: These physical inputs will also reflect prejudices, because that is our our intellectual prejudices about what future is like because you know anytime you're going beyond the.
Abhay Vasant Ashtekar: Beyond the President they're going to be significantly be on the page and tried to construct new theory, there are going to be expectations and so singular entity faces in your data and so.
Abhay Vasant Ashtekar: This is going to be a prejudice or whether singularity should be resolved or not, and I think you know we look on gravity believe that.
Abhay Vasant Ashtekar: There are no physical singularities and video universe, and so they should be resolved.
Abhay Vasant Ashtekar: So you'll be said, there is no observational evidence yeah but then, what we are trying to do is, of course, say that if it is resolved, then you know, can we have some observational evidence about that in like in a smaller.
Abhay Vasant Ashtekar: You know about the singularity resolution so.
Abhay Vasant Ashtekar: And in fact mainstream cosmology is also don't think that that is in humanity, I mean very when they say our big bang theory for to what phase after after inflation.
Abhay Vasant Ashtekar: But I think with respect to the transition aptitudes I mean the thing is that, in order to calculate transition athlete you they're going to be you still have to solve the condom constraints right because you like to get to envision amplitude between physical states.
Abhay Vasant Ashtekar: And so I think that, therefore.
Abhay Vasant Ashtekar: Depending on your framework, then depending on which clock you choose the initial and find the state is going to be.
Abhay Vasant Ashtekar: it's going to be different right because, in one case.
Abhay Vasant Ashtekar: In other words, you're choosing initial state in which the time is constant so.
Abhay Vasant Ashtekar: So, but nonetheless sense yeah I got three different clocks and yeah directly and just the middle of the talk I got confused.
Abhay Vasant Ashtekar: So there are three choices, so you could just you know.
Abhay Vasant Ashtekar: Say clock and the clock and then see what happens to fly or tea clock and by five o'clock and say what happens to be in both cases.
Abhay Vasant Ashtekar: and expertise evaluate V as a physical observable and you can calculate the functionality.
Abhay Vasant Ashtekar: And so, if you like this extra machinery that you are having a quote unquote unity evolution.
Abhay Vasant Ashtekar: can be just regarded as a way of calculating the position attitude, just like what you know find Monday was a major in the space of parts and this, this is in the products that providing a measure to calculate the TV and YouTube.
Abhay Vasant Ashtekar: From from initial state to find the stick, so there are meaningful questions you can ask and I, I also believe that.
Abhay Vasant Ashtekar: The fact that there are no boundaries, you know direct quantization ambiguity is is not the obvious contradiction and ambiguity is, you will, for the average and I can I can.
Abhay Vasant Ashtekar: monetize the radio moment them in different ways and get different answers experimentally, we know, one of them is right.
Abhay Vasant Ashtekar: So we shouldn't worry about coordination ambiguity is.
Abhay Vasant Ashtekar: zero level when you say yes, you got this.
Abhay Vasant Ashtekar: gap when Jesus was a little bit metric and P, a P, plus B equals zero, I think, to use the gauge covariance I mean the wear and tear up appointments, but we G is.
Abhay Vasant Ashtekar: lonely differential geometry natural choice, but otherwise everything depends on which coordinate see choose on what you were.
Abhay Vasant Ashtekar: configuration space here chosen and that's what you're using and I think that we're choosing the laplacian with respect to the.
Abhay Vasant Ashtekar: metric gap and I don't think that.
Abhay Vasant Ashtekar: I mean I don't consider that to be a choice in the sense that.
Abhay Vasant Ashtekar: Any other choices, but just breaks covariance so.
Lucía Menéndez-Pidal de Cristina: uh huh yes.
Abhay Vasant Ashtekar: Yes, so so but, but these are choices that we will guiding principles for problems but there's other things about you know singularity resolution happening or not happening, and so on, I should just add that in.
Abhay Vasant Ashtekar: lukewarm smiles yes, there is a simulated resolution also for the fight fight time.
Abhay Vasant Ashtekar: Not for not for not for the.
Abhay Vasant Ashtekar: Not in Villa deducted but for the for loop on this quality video.
Abhay Vasant Ashtekar: and also for five.
Yes.
Abhay Vasant Ashtekar: So I didn't I agree that this mathematical which so therefore I also don't want to engage the new database as being the you know something that we want, but other.
Abhay Vasant Ashtekar: Because, technically speaking, but space and then solutions to this constraint equation, so you need in the product.
Abhay Vasant Ashtekar: And you can use some guiding principles to get that you need in the product, and then you said a utility and then you can take a semi classical limit and just to make sure that it agrees with the classical period the usual.
Abhay Vasant Ashtekar: regimes and then see what happens at the widget widget class 25th I agree that that philosophy.
Abhay Vasant Ashtekar: I see that Stephen Julian is also in the audience or was at least maybe Stefan you want to add something, since you have been thinking about this and also.
Steffen Gielen: I think initially it's true that it seemed to us at these choices, a flop level arbitrary in terms of demanding unitarian, but I think the fact that you see the same ambiguity is in direct quantization us kind of strengthen this.
Steffen Gielen: These results, I mean that was something we were quite puzzled about for quite some time and also given the results of Philips arena and collaborators, how can this be.
Steffen Gielen: And here, you can understand that if you redefine the laps right suddenly you have a different operating the quantities, from the perspective of direct quantization.
Steffen Gielen: Which is also known that you see to the best of my knowledge, right at some other labs choice is important, but then this can be another it's another way of seeing general parents right so classically we can choose arbitrary.
lapses.
Steffen Gielen: yeah I think that's the only comment I have.
Okay.
Jorge Pullin: Any other questions.
Jorge Pullin: Okay let's thank the speaker again.
Lucía Menéndez-Pidal de Cristina: Thank you.