Jorge Pullin: Okay, so let's figure it this way chick Kaminski will speak about the volume operator and quantum cosmology.
Wojciech Kaminski: Okay, so thank you very much for allowing me to speak in international loop quantum gravity seminar. So because the
Wojciech Kaminski: Reason that I'm presenting in fact quite elementary I will start with the
Wojciech Kaminski: Short Introduction. So put the resulting some broader context in the loop on to cosmological so
Wojciech Kaminski: Let us start with the classical Friedman Robertson worker model with new Muslim scholar field. So in this model we have on the thought degrees of freedom to for scholar built and to for the
Wojciech Kaminski: Geometry.
Wojciech Kaminski: And from all the
Wojciech Kaminski: Constraints this on the one left this equation to until we can of course some of these constraints using the parameter ization through this color field and then the classical Hamiltonian is given by the plus minus square root of this
Wojciech Kaminski: Function Tita entities just be square city square
It of course
Wojciech Kaminski: In the classical era. We can afflict ourselves on the one sector say plus or minus. And we see that the super selection in the quantum Tiara will some problems.
Wojciech Kaminski: Okay, so
Wojciech Kaminski: So, let us go to. So I'm not sure but I have do I share the screen with you or the screen is not visit
Jorge Pullin: Your screens visual
Wojciech Kaminski: Okay so perfect. So, let us shot to describe look on to console log jam. So, of course, under the simplest model for the lambda cosmological constant equal to zero and flat.
Wojciech Kaminski: A special section. And so of course you want to Kasparov now we know that it's not just symmetry, the direction of flow quantum gravity, but it's quantization of this mini super space.
Wojciech Kaminski: Model inspired by the math thoughts of continuity and of course this is a question, can we update from quantum gravity and the area of the hot topic now.
Wojciech Kaminski: But so there are some positive and negative results. But as this relation of quantum cosmology and look completely rocked it is not completely clear. So we can ask whether we should
Wojciech Kaminski: Trust prediction of quantum cosmology, whether it's still called in the future of constant gravity and
Wojciech Kaminski: So having that you might let us understand that in fact in the full gravity is very complicated. So we are not usually not able to get some reason every prediction on that and Tina.
Wojciech Kaminski: For example, if you want some practical results. Usually we get the kids just through the slope quantum cosmological this, as we know, not
Wojciech Kaminski: Obtained steal from quantum gravity or welcome to class manager concerns as a testing ground for some methods. You see in use our method that should be used in a full look quantum
Wojciech Kaminski: Okay. And so let me here shortly described this QC models. So I will, in fact, skip the most of the constants and keep on the essential details for the essential for what I will be talking about. So, let us concentrate on this case lambda equal to zero equal to zero.
Wojciech Kaminski: And then the physical space after all and actions because we confess reduced to the CD lattice. And then we can also be seen lattice leaders to the symmetric one, then the hill, but space is given by the sequence.
Wojciech Kaminski: spanked by the integer positive integer numbers with this a bit
Wojciech Kaminski: Change scholar product. So this video is important because it's lead to some
Wojciech Kaminski: Specific behavior of the era and
Wojciech Kaminski: This evolution operator is given by the square root of some operator data. And here we are at the impose this super selection.
Wojciech Kaminski: That we choose on the plus square root of the data is a so called Jacoby operator. So it's a difference operator when we this H plus minus r shifts by one modified accordingly and zero and B C C zero and we are some functions of the volume. So it's represent
Wojciech Kaminski: The schema space is represented in the volume, I can say
Wojciech Kaminski: And in what follow for me will be only important the syntactic behavior of these functions.
Wojciech Kaminski: Of course, this is a special model. And recently, there were introduced new model what this difference equation is of the higher order is it's there are five terms in this defense equation and
Wojciech Kaminski: So I will not consider that the the stock. But probably the feature that I will be speaking about is also present
Wojciech Kaminski: Okay, so this
Wojciech Kaminski: Model is what is important for the for this behavior and some syntactic expansion of dysfunctional CC zero and ba.
Wojciech Kaminski: And let us not this. That is a question four or five and six that we in fact need a bit more
Wojciech Kaminski: Terms in discussing some results on the need that the sea is behaving like the volume plus collection, we also need this correction up to the V2 minus one, we need to control the behavior of that.
Wojciech Kaminski: And surprisingly, such a strict the behavior is common in the URL and models like APS and all and also some of it will come to smaller
Wojciech Kaminski: Okay.
So,
Wojciech Kaminski: So I promise that I will put this model these results about the ill defined that less of the volume in some broader context of this context is in fact the semi classical unit because once we quantum
Wojciech Kaminski: Quantum we concise cosmological the slope quantum cosmology way we want to somehow come back to the classical or semi classical dynamics, because this is something that we compare with the
Wojciech Kaminski: Evolution that we see in the universe.
Wojciech Kaminski: And in fact, the quite interesting features of these models. So first of all, so this is
Wojciech Kaminski: Mostly based on the metrics. Some of them are proven analytically. So it's also still not completely clear.
Wojciech Kaminski: Audio for not knowledge but states that are picked on the high end abjure
Wojciech Kaminski: Are also picked on the high volumes, so it's it's not that, you know quantum cosmology, we have these bounds and the bounce if the if the energy is
Wojciech Kaminski: Huge the bounce Oculus also for the large volume lot the larger and larger, the larger volume of the box. And if we look at this in the full year transport picture then
Wojciech Kaminski: The volume operators.
Wojciech Kaminski: Is changed into derivative and this shift is changing the multiplication by it to ice.
Wojciech Kaminski: And the these high volume.
Wojciech Kaminski: Limits corresponds to the high momentum. So then it is very similar to the lock the meeting the spin thumbs, Something that usually sculpt
Wojciech Kaminski: Semi classical human, but of course semi classical limits may have many different meanings. So, moreover, and not only even if we don't
Wojciech Kaminski: Restrict the very high end address, we see that the for the lifetimes.
Wojciech Kaminski: As into the behavior of the waste package. They also move to the large volume and they enter again in this region of high moment and
Wojciech Kaminski: Of course, they're like additional asset, these two limits are additional properties have no control customer luxury. But if we want to compile into classical GR
Wojciech Kaminski: In fact, you would mostly be interested in the limit of small curvature that in this Fourier transform picture correspond to the limit of care to do
But
Wojciech Kaminski: So how
Wojciech Kaminski: We deal with semi classical dynamics in the
Wojciech Kaminski: Low quantum cosmology something some prescription
Wojciech Kaminski: That some of that was also determined by
Wojciech Kaminski: The way.
Wojciech Kaminski: Supported by some numerical simulations and some of them. Also, there are some analytical computations, but one
Wojciech Kaminski: Consider CDP coherence states peaked at the given faceplates point
Wojciech Kaminski: And then one compute the expectation. The value of the city operator in discussion states and then one is get the example that we would call this function.
Wojciech Kaminski: Will be effective data and the square root of that will be effective Hamiltonian. And of course it's divisible that if we
Wojciech Kaminski: Take the different versions of coherent state, then this effective Hamiltonian can change. So, one needs to have a knowledge about the dynamics in order to capture the light cookin states that will give the
Wojciech Kaminski: Data that we can task and, moreover, if we don't care about lower order terms. You can also compute this data effective
Wojciech Kaminski: In the naive, but very direct way without
Wojciech Kaminski: Spending a lot of effort on the computation of expectations about you just take the form of the operator as the place
Wojciech Kaminski: Operator volume by D and shoots by to IC
Wojciech Kaminski: But that's a bit bigger and bigger D, however.
Wojciech Kaminski: There are some special cases when these bigger ambiguity.
LSU Rel: How can I please ask a question in the previous slide. Yes, yes. So my first command it like equation eight, it is true, like this kind of a thumb rule which one can use for
LSU Rel: Especially flat models, but I think like such a tumble really doesn't work for closed models or open models like a cold one or equal to minus one. This is just a comment.
Wojciech Kaminski: Comment about equation seven or eight
LSU Rel: That's I'm going to ask you about equation seven. So I'm trying to understand. Again, like what is the ambiguity here because
LSU Rel: I'm not much I don't much remember what Martin did, and though it was very extensive work. But in the case of Victor, the virus work which are more familiar with like he was, I think, quite careful in looking at
LSU Rel: That the current states which he has chosen, which were sharply pig, which were sharply picked under the assumptions, he had made. They had the right
LSU Rel: they preserve the Hamiltonian flow for the teat operator very nicely. And that is what we checked.
LSU Rel: In the numerical simulation and I agree. Like, you will come to the point that numerical simulations didn't capture the infrared tail, but I'm trying to understand what is analytically wrong in Victor Tavares calculation. So
Wojciech Kaminski: That's a good question. So first of all, I'm not sure.
Wojciech Kaminski: So,
Wojciech Kaminski: The question. Okay, so we compute summer. So there were several
Wojciech Kaminski: Estimates and three speaking I still don't know.
Wojciech Kaminski: Which so surely because we now know that this volume is easy needs.
Wojciech Kaminski: It's it's busy that they need to be some touch in this computation some some estimates that we're not correct. So I
LSU Rel: Went through Victor Paris calculation in lot of detail and we we are writing paper from very long time on something what he was doing. I do not see where
LSU Rel: This will be caught because one is making only the approximation that
LSU Rel: To derive that Hamill, the effective Hamiltonian that v is much greater than the plank volume.
LSU Rel: So whereas your concern is more at the infrared limit. So I understand the point you will make. But what I'm trying to understand is
LSU Rel: In the calculations of what Richter has done at least. And I think Martin's calculations will be probably similar
LSU Rel: How will we catch this, I'm just, I'm just curious about this. I myself. Want to see whether this term plays that you will come to plays an important role phenomenology Kelly. That will be great if that can be done, but
LSU Rel: Some of you have to extract this term from the way effective dynamics has been derived
LSU Rel: And does it have any non negligible effect. I don't think so.
Wojciech Kaminski: No. So I agree that
Wojciech Kaminski: I expect that this
Wojciech Kaminski: Semi classical dynamics is after all right.
LSU Rel: Okay, you say that
Wojciech Kaminski: Yes, yes. So, but, of course, I expect so.
Wojciech Kaminski: I don't think my results really spoil this. So the other. It's funny. The interpretation in terms of the expectations value because
Wojciech Kaminski: Okay, so we can, I think,
LSU Rel: I think maybe we can continue this because I again for the freedmen equation which Victor, the virus obtained was from the expectation values of the volume and
LSU Rel: I'm just feeling too right now understand
LSU Rel: How your result changes that I know like at a fundamental level your result is is correct and true, but at the effect of dynamics level of what he did. I do not see like where it spoils the approximation. He made
Yes.
Wojciech Kaminski: So I agree. I also don't know and it would be great to pick up exactly the point where this approximations are not valid. And he says,
LSU Rel: Yeah, okay. I agree. I agree. Maybe at very large volumes.
LSU Rel: I don't know. I have to think about this, but I think this is some
LSU Rel: Some good venue to investigate for someone
Wojciech Kaminski: Yes, I agree. Okay, thank you. I only would like to comment Okay, but maybe to make this comment at the end of my talk.
Wojciech Kaminski: So let me remind I will come back to this point at different because okay so but now i i would like to continue. And the point is that if we
Wojciech Kaminski: If we restrict cipher, the negative cosmological constant, then we are in some case that is well studied by mathematician. So there are some tea or of passion.
Wojciech Kaminski: Type of differential operators. The tell that this evolution in the case when this term that is at the front of the square of the leading volume. The term is
Wojciech Kaminski: Always non zero, then we know how to how to write the semi classical evolution and the semi classical behavior is well captured by this
Wojciech Kaminski: Evolution of this effective dynamics and even if we disregard distance of the so this our returns in this specific case does not influence dynamic so much in the lunch volume.
Wojciech Kaminski: So,
Wojciech Kaminski: The evolution for lambda equal to zero so indifferent, because there is a point when these terms in front of these queries banshee. However, for the sake close to the bounce so
Elliptic region.
Wojciech Kaminski: This this evolution is also a dependent on this additional detail.
Wojciech Kaminski: And
Wojciech Kaminski: So it's not natural questions that one should
Wojciech Kaminski: Answer as, Can we trust the semi classical dynamics. So by elliptic region. I mean, the points, points of the face space where the
Wojciech Kaminski: The stamps at the Liddy volume powers is invaluable and
Wojciech Kaminski: But by asking this question, we are the posing that semi classical dynamics is in some sense local. So, this
Wojciech Kaminski: Can be so effective.
Wojciech Kaminski: Coming Tatyana that is completed.
Wojciech Kaminski: Excellent. So it's some local function of the of the DNC that
Wojciech Kaminski: That we don't need to know this effective Hamilton far from the region that we are interested in
Wojciech Kaminski: And the second question, of course, this can be extended to the lifetime of some topics and of course numerical studies suggest that it's really true. So if we take the
Wojciech Kaminski: This effective Hamiltonian equal to just, just the square root of the things that we computed
Wojciech Kaminski: And the last transparency, then we get to the correct evolution of the copyright states.
Wojciech Kaminski: Covered in this question. It's not only limited to the
Wojciech Kaminski: Two kosmala cosmology. It's one can ask it in a more general settings, for example, on some lattice new quantum gravity and this is also the way one can try.
Wojciech Kaminski: To compare look quantum gravity, which will come to cosmology. So looking just at the semi classical subject is. And of course, this little question whether
Wojciech Kaminski: This approximations are really true. So whether these dynamics is local and whether we can trust this affected come into the house. So under I was speaking about some of the skills I think half a year ago on international quantum gravity seminar, but
Wojciech Kaminski: So we were not completely successful. And that's why I was led to evaluate this semi classical dynamics open to a small village, and thank you, Justin, what is happening.
Of course,
Wojciech Kaminski: One can speak about
Wojciech Kaminski: Two ways to approach the problem of the semi classical evolution. So, one can try either to attack the problem directly. So look for the
Wojciech Kaminski: Evolution.
Wojciech Kaminski: So try to estimate the quantum evolution by semi classical evolution and of course this is in some songs better because one can imagine to do it all scientists Latisse quantum gravity or okay I not there to sell full of quantum gravity, but smile.
Wojciech Kaminski: But in the case of local to cosmological there is another way, because we have a lot of knowledge about the Eigen functions of this detailed, very thorough
Wojciech Kaminski: So we can you mentioned through look for the some properties of it functions of data. And if we understand the same way I guess functions well enough, you can build the wave packets out of them. And by studying the behavior of this waste packets by
Wojciech Kaminski: Looking at the behavior of agriculture.
Wojciech Kaminski: Okay. And I will say what Tyler
Wojciech Kaminski: What are the results. And of course, let me first.
Wojciech Kaminski: Remind how the
Wojciech Kaminski: This Eigen functions of detail operator.
Wojciech Kaminski: Console logical constant equal to zero and zero looks like. And of course, nice picture is not the real I can function, but it captures the properties
Wojciech Kaminski: So the three jewels, and the first region is something like the
Wojciech Kaminski: Girl or decay of this I can function in the forbidden ritual. So it's looking like the if we have web approximation. Then we have probably the region and the way function is vanishing there.
Wojciech Kaminski: And it's the same here and this part is, in fact, responsible for these bows acuity at the large volumes.
Wojciech Kaminski: But this expansion is true for large enterprises. So then there is a second part that is
Wojciech Kaminski: I think it's well capture of my picture because it's
Wojciech Kaminski: Not well visible in the volume that presentation but if one go to the full year at transform, then one see that this there is some like intimidation.
Wojciech Kaminski: part where the its corresponding to the turning point in the web approximation. And it's also the expansion from the large images, but there is a term that is
Wojciech Kaminski: There is some behavior of the function that is through not only for the larger existence in fact true for other and actually
Wojciech Kaminski: But it's something we have your for the large volume and this part is very sensitive to these details of the Hamiltonian. So to these higher order expansion that I was showing a few slides ago. And of course, then
Wojciech Kaminski: If one a match, say the static point with this entity behavior, one can get a lot of information about their
Wojciech Kaminski: Scattering you know control personal agenda. This is the way. Well, how it's done.
Okay.
Wojciech Kaminski: So I because for me this this last
Wojciech Kaminski: Part is the most interesting. I will just maybe sketch some method how to
Wojciech Kaminski: Capture captured the essence of the behavior of these functions. So, let us introduce some some the Omega function. So, in fact we regarded as serious in the inverse powers of v.
Wojciech Kaminski: And they will call efficiency. These theories are given by this week and
Wojciech Kaminski: Numbers.
Wojciech Kaminski: So this is
Wojciech Kaminski: Where we want that these CDs satisfy equation nine
Wojciech Kaminski: And in fact, if we take this equation and one plug in the serious one consult with record separately.
Wojciech Kaminski: And there are two solutions d omega plus minus and the first term is given by this plus minus i omega. So, if we look at this, the Omega, the first term is
Wojciech Kaminski: Ito plus minus i omega divided by
Wojciech Kaminski: Ok and now how we define this approximate
Wojciech Kaminski: Functions. So we take the product of the amount of course we need to make some location to have some people defined. But the bigger championship. We take the more exact.
Wojciech Kaminski: Is satisfying the equations of the, I guess.
Wojciech Kaminski: Okay, so now we the summer general to learn how to if we had the approximate solution, then we can produce from this approximate solution some real solution of the
Wojciech Kaminski: Equation.
Wojciech Kaminski: With the same as synthetic expansion and enough to have the enactment of this approximate solutions we combine we write our equation in terms of the
Wojciech Kaminski: Vector, but first of the differential equation and then we built out of these vectors. The matrix and in terms of these metrics we can determine whether
Wojciech Kaminski: We can produce such as exotic solutions are now and this is the second point, but as our error is decaying as fast as we want. We always can do that. In our case, so we are getting two solutions of the synthetics given an equation nine
Wojciech Kaminski: And in fact this is V two plus minus i omega, because this is a supporting behavior of he to some of i omega divided by
Wojciech Kaminski: So it to i omega divided by the when we take the SAM. It's about a two plus minus i omega Garrett d and this is exactly a question.
Wojciech Kaminski: Okay, but these are solutions that does not suck. They do not satisfy our symmetric assumption at the zero. So in order to have the icon functions. We need to impose this additional condition, but of course we can create this er mega as a linear combination of the
Wojciech Kaminski: Of the storm solutions with the given us insulting behavior. And if we do that, we see that
Wojciech Kaminski: This era god he
Wojciech Kaminski: Has the given veer off. So it's not growing too fast growing like get to absolute value imaginary formiga because now this year mega are defined not on the for real omega defined for and the complex accept some special points where our method is failing.
Wojciech Kaminski: And moreover,
Wojciech Kaminski: If we
Wojciech Kaminski: Take a bit of attention to these functions will not use the data exactly generalize it functions for the positive part of the spectrum of tea. In fact, if we have these tools are synthetic solutions, then one can prove that the spectrum is the whole positive real life.
Wojciech Kaminski: And exactly the T omega era, I can function.
Wojciech Kaminski: OK, so now I really present some
Wojciech Kaminski: Strange argument about that will lead us to the
Wojciech Kaminski: Problem with the volume operator. So, let us assume that we have a function that is in the domain of the some positive power of their fault. So then
Wojciech Kaminski: Thanks dysfunction, we can define some function depending on on back. I went, oh my god, it's a complex number that is defined by this equation.
Wojciech Kaminski: At what else and that that nothing's the B2B side if in our Hilbert space because we assume that science in the domain of P2P
Wojciech Kaminski: And also be to minus beta your mega if you never hit backspace because of the growth of your mega so and the function that is growing slower than and the negative power of V as in our Hubert's faith because of the scribes turn be of be in this color.
Wojciech Kaminski: So we, we see that we have function that the Palomar click. So this one can check the column or taking this trip.
Wojciech Kaminski: So we need to assume that image that are part of that is smaller than down into more of a symmetric because he omega is under depending on omega squared. So there is no
Wojciech Kaminski: Dependence on the side.
Wojciech Kaminski: Okay, but if the evolved function also belong to the domain.
Wojciech Kaminski: Then we can construct similar function. Now let's call it fit.
Wojciech Kaminski: For them about that steak.
Wojciech Kaminski: And he's enjoying the property. So it's hella Murphy King Street and symmetric, but now from the Eigen function expansion. We can rewrite this fit.
Wojciech Kaminski: In the for say omega positive EFF EFF oh my god multiplied by these two minus it omega. This can be for the evolution of correct
Wojciech Kaminski: However, we can now analogy Talia extended again to the collar strip. But now this extension. We know that sequel to it to minus the omega, if that is not symmetric, of course.
Wojciech Kaminski: It's too much to say to somebody. It's not symmetric unless F zero
Wojciech Kaminski: But this minute that Peter size zero that side is not in the positive part of the spectrum of cheetah. And so we get the result. And the result is that the stage.
Wojciech Kaminski: That initial using the domain of and the power of the polio token status domain and the devolution on the support that are non positive part of the spectrum of data but festival. We assume about the topic is positive and it's positive of the model that we are considering and
Wojciech Kaminski: In the most of them.
Wojciech Kaminski: There is no one zero, I can vector for Peter Thomas mean that there is no states that enjoy discovered to peek in there and the power of you and
Wojciech Kaminski: So this is a positive result. And in fact, if you look carefully for the literature.
Wojciech Kaminski: That people will not exceed that okay not expecting that before but exactly because in all number customer relations there. There was no
Wojciech Kaminski: Small sign of this
Wojciech Kaminski: Infinity is because this is not belong to the main because expectation. The value of some power of volume is teaching
But
Wojciech Kaminski: Because there was no numerical final that everyone was thinking that smaller some technical talent will be on consult
Wojciech Kaminski: So there is a tension. So first session is exactly this numerical simulations. And the second is, there's also some results about exactly models.
And
Wojciech Kaminski: We would like to understand what is the
Wojciech Kaminski: Relation of this result about linking up with some exact for the computation of the funnel. So let me just say about this numerical simulations.
Wojciech Kaminski: Cause I'm not
Wojciech Kaminski: I have no
Wojciech Kaminski: Eggs that
Wojciech Kaminski: Claim about that, but I can suspect some key. And number two, to explain. Let let us say that the same properties also present for the ability to read
Wojciech Kaminski: And the will of the purely one can if
Wojciech Kaminski: We've been simplified version one is defined in this equation that Tina. And then if we change the valuable to x equal to log out of the volume, then the state is just a special part of the clown God don't turn and our
Wojciech Kaminski: Super selection rule.
Wojciech Kaminski: Just telling us that we divide the wastebasket into positive and negative moment and we
Wojciech Kaminski: Evolved evolve positive movement that we decide to be because client garden has left and right moving parts. So we about positive movement that we do right and they get people into with delta
Wojciech Kaminski: And
Wojciech Kaminski: Let us know. Consider a Gaussian stating this
Wojciech Kaminski: Era.
Wojciech Kaminski: And of course, if we just agreed upon, it's no longer smooth audition Regional Council was of course smoke in the
Wojciech Kaminski: In the moment weaponization but we about it, it will be not smooth and people to see right and that we can take the Fourier transform, and look how it's what are the properties
Wojciech Kaminski: And stand out that the Fourier transform.
Wojciech Kaminski: It has the very special behavior.
Because
Wojciech Kaminski: The Fourier transform for at least for lunch. X is dominated by this behavior at people to zero. So, does not move part of the of the states.
Wojciech Kaminski: And so one can even give them the exact property of the full year transform. So the leading term behavior is like the one over x square with the coefficient that is proportional to the very bottom of this side, the Fourier transform. SIGH at zero.
Wojciech Kaminski: And there are some lower order times
Wojciech Kaminski: So if we now back, come back to the volume representation. So let's assume an X equal Logan, he
Wojciech Kaminski: Then I will state has some very long tail that became like one over logo squared up and of course one of the local square d even squared is not integrated with the
Wojciech Kaminski: Powers of the
Wojciech Kaminski: So our state for tea not equal to zero. It's not belonging to the domain of the volume anymore.
Wojciech Kaminski: But now we can look closer at this time that the style and not is that the style is proportional to the reproductive of Psyche zero. And if I were
Wojciech Kaminski: The
Wojciech Kaminski: gumption state was picked and some Peasy on. So, usually in America simulation, as far as I understand one taking p. So, this gives Mayra will be similar to the inner the students that are using it would be similar to the balance volume.
Wojciech Kaminski: So this is usually quite large. And in addition, the star is proportional to eat to mind knows that it's extremely NY a smaller and
Wojciech Kaminski: So the conjecture is that it's not integral part is so small that it's not visible in America for malicious, of course, in principle of 100 feet, but we want to take very non classical
Wojciech Kaminski: States for something that you speak to close to the
Wojciech Kaminski: Like
Wojciech Kaminski: Okay, so also when
LSU Rel: I ask a question.
Wojciech Kaminski: A bit differently.
Wojciech Kaminski: can divide this
Wojciech Kaminski: Notion into
Wojciech Kaminski: One.
Wojciech Kaminski: By
Wojciech Kaminski: Writing mode so
LSU Rel: Can I ask a question from the
Previous
Wojciech Kaminski: And this fee is behind
Jorge Pullin: Our question here.
Wojciech Kaminski: Knife. He saw all the time gulshan and keep moving along classical projector.
Wojciech Kaminski: But there is also the reminder to remind, there is a difference of this say 16 and the original real estate and this is small. So it's like extremely small city detail, but
Wojciech Kaminski: Despite that, it's so small. It's a small city for the problem with the volume.
Wojciech Kaminski: And now in the summer will not as one either argue or it was like assumption that we can take the states when this error key is negligible.
Wojciech Kaminski: So it's not introducing and the problem with the expectation value of the model. And of course, if I do that, then the evolution follows classical trajectories. But now we know we cannot do that. So, it
Wojciech Kaminski: Is small but the expectation value of the volume in LTC fee, though, we cannot. I mean,
If we look
Hello.
Jorge Pullin: Hello.
Yes, so
Jorge Pullin: They had a question here for you. Yes.
Wojciech Kaminski: So I just got
LSU Rel: To go back some slides.
LSU Rel: On the conjecture slide.
LSU Rel: Non integral part of the tail is
Wojciech Kaminski: So it was so it was not so
Wojciech Kaminski: Happy. It was not
LSU Rel: Previous slide. So I, I would like to understand like this non integral integral part. Like, how does it depend on omega like is does it decrease the amplitude of the tail. Does it decrease as omega increases.
Wojciech Kaminski: What you mean by omega
LSU Rel: Or or you have this model, right, with much less killer field. So the omega is the frequency of sci fi or theta.
Wojciech Kaminski: So okay, so then they will have the
Wojciech Kaminski: somehow related to the p
LSU Rel: Yes, or your PSP fight. Yes.
LSU Rel: Please.
Wojciech Kaminski: Yeah, so a piece so
Wojciech Kaminski: P conjugated to x axis low volume.
LSU Rel: Yes. Right. Right. That's what I was saying. So x is longer term of volume.
LSU Rel: As far as I remember, that is conjugate to I think we'll be fine.
Wojciech Kaminski: Yeah yeah
LSU Rel: Exactly. So that is omega. So from your expression before the conjecture. It seems that the higher psi. We take smaller is the amplitude of the scale.
Wojciech Kaminski: So,
Wojciech Kaminski: If
Wojciech Kaminski: I think in general, it's only for really lower
Wojciech Kaminski: Right, exactly.
LSU Rel: Exactly. So you see, this is another reason like in the new metrics we were always having large
Wojciech Kaminski: Maybe I was not successful, but they were
LSU Rel: So the point is for larger and larger purifies this tale is actually having smaller and smaller amplitude. Now you want to take them.
LSU Rel: If you want to take a really macroscopic universe and then want to apply these ideas to that, then P Fi at least let let us say the analogy with k code one universe then the PMI has to be extremely large
Yes.
LSU Rel: This is not going to have any physical effect.
Wojciech Kaminski: Yes, no, I completely agree.
Wojciech Kaminski: Sounds strange
LSU Rel: It's a strange artifact of choosing the volume operator, I agree to that, but I would also like to comment on the fact that you can like, as you will.
LSU Rel: As you probably mentioned about lambda greater than lambda, positive, positive cosmological constant case which up and Thomas did and Thomas and you did. One can also take
LSU Rel: And and and one, one can also define an operator v in a different way. Let us say, like, if these are bonded operator which you find like
LSU Rel: Then one can define f inverse inverse of that expectation. Well, if we and that can serve as one regularization have a new volume operator, of course, like this has to be found judiciously. But in principle it is possible, yes, I
Wojciech Kaminski: agree with that.
Wojciech Kaminski: Because the small in the in the space for
Wojciech Kaminski: It will be negligible.
LSU Rel: So I agree. First
LSU Rel: One can take this analytical strategy but secondly for realistic cosmological models.
LSU Rel: This tale will probably have no effect.
Wojciech Kaminski: Yeah, so
Wojciech Kaminski: It, it has no effect.
Wojciech Kaminski: Because we always need to take something like semi classical so the point is that we should not trust.
Wojciech Kaminski: We should maybe not complete semi classical objects that we can make so
LSU Rel: Let me just mentioned that, let me just mentioned that with my collaborators here at Ellis, who, like in the last couple of years.
LSU Rel: Very small p five cases also like P 550 P 520 and so on, p equals 2015 was a best we can do with whatever supercomputing resources were available to us because in the
LSU Rel: In the 40 or space the lattice is too large. And you see, even those in America simulations would never see this, because to perform those simulations.
LSU Rel: We had to cut off even the caution part the tail of the ocean part of the way function and this tales will be completely lost. So what I want to emphasize is that even if we want to find about this tale numerically. It's an extremely challenging task.
Wojciech Kaminski: Yes, yes, I agree.
Wojciech Kaminski: It's made me not.
Wojciech Kaminski: To look for that.
Because I
LSU Rel: Can look at this paper which like Peter dinner. Me and
LSU Rel: My stolen by Jason mega mega one way road where we took very, very non caution extremely wide states. Our goal was not to show the factor dynamics is true, but there is a bounce, even for those dates.
LSU Rel: And you can see like numerically. We still have to do approximations and then cut off the tails so that
LSU Rel: Even the best supercomputers can perform the simulations. So I think it's also technically challenging to see this effect.
Wojciech Kaminski: Yeah, yeah. So I short because if one look here. I think it's extremely small number. Yeah, okay, you beyond the normal, it's not accidental.
Wojciech Kaminski: Yeah, okay. Okay, so, so let me
Wojciech Kaminski: So yes, I was, I think I was here so that, of course, the on the smoke part the volume.
Wojciech Kaminski: We have completed. Nice and peaceful, loving the semi classical trajectories and this is if one and now take into account the reminder to spoils the expectation of the volume, then this is all about the mothers just telling that that on this like smoke.
Wojciech Kaminski: Version of the white part of this without absolute value that can be everything is fine and
Wojciech Kaminski: So we see that in some sense.
Wojciech Kaminski: This semi semi classical
Wojciech Kaminski: It can be done. It's not a semi classical evolution is not complete local
Wojciech Kaminski: But as the parent mentioned it's a we hope and
Wojciech Kaminski: This is something that I expect we can even prove that you send me locally on some class of bounded operators and in fact for the Phantom the smaller than the luxury of pizza but the good operator. So good operator is no problem with the infinite
Wojciech Kaminski: Okay, so let me
Wojciech Kaminski: Conclude so of course concludes, I would say something like the physical consequences. And of course, as I mentioned, it's, it's a bit artifact. Yes. So, um, the problem is that
Wojciech Kaminski: In the men their
Wojciech Kaminski: Application of Groupon to cosmology, we are using expectations value of the power from the volume.
Wojciech Kaminski: And one of these is the best metric. So in this metrics we look
Wojciech Kaminski: What kind of geometry, the quantum field.
Wojciech Kaminski: Effectively fields, if, if it's
Wojciech Kaminski: Evolved in the quantum universe and deposits
Wojciech Kaminski: This is extremely complicated problem. So it without some approximations that is basically know how to solve. No hope to solve it. So we just make approximations and some of them are quite hard to justify and
Wojciech Kaminski: So now they are a bit harder because the answer. Exactly. Getting the expectations value of the powers of the volume that time in PDF. So of course the question is
Wojciech Kaminski: Can we somehow correct these approximations that we can still test them and what should be the place with these independent quantities and we working on that one. So, and I think we have some answer, it should be. You should have usage. But to the point is that these
Wojciech Kaminski: Effective
Wojciech Kaminski: Volume from the previous slide is a
Wojciech Kaminski: Nice proposition for so I just this one. Yes, so it's nice proposition for the fees that we should put instead of this is defined expectations about
Wojciech Kaminski: Okay. And so let me mention shortly that. So as I said, it's probably a bit artifacts. So this is defined volume isn't
Wojciech Kaminski: Some other fact that there is. So first of all, it's not always happens. So for a positive cosmological constant. It's not clear.
Wojciech Kaminski: So then, but then it's not a big issue because nevertheless in the fight even for this semi classical
Wojciech Kaminski: Or so equal for the semi classical evolution. Well, the volume become infinity in the final time so no one is looking for the expectation value of the podium always we are taking some bandit operator.
Wojciech Kaminski: However, for London smaller than, you know, there is no problem. So there is no
Wojciech Kaminski: The expectations value of the volume is well defined for Hall if we take the good enough state it's well defined for the whole evolution and
Wojciech Kaminski: So it's not here with this new hyper mobile, what are
Wojciech Kaminski: What is the fate of without. But in some sense. If we look at the proof with this.
Wojciech Kaminski: Analytic attention. I think it should also hot for this new model.
And
Klaus
Wojciech Kaminski: Young, your thoughts so many people. So it was proposing two stages.
Wojciech Kaminski: So that they have five letters and of course
Wojciech Kaminski: There is a reason. So if, if we look at this evolution without
Wojciech Kaminski: Absolute value has no problem. We've done a promotion. So we see that the original restriction to this super selective super selection factor this class.
Wojciech Kaminski: And I need to finish my talk with the conjecture that if we take the if we come back to the group of an IP again and we
Wojciech Kaminski: Chose constant loop and also some other we MP3, it is. But if we choose evolution and upset about lists that are mixing sectors. So evolution is not be affected by October.
Wojciech Kaminski: Then
Wojciech Kaminski: I expanded it to the it's no problem with divulge
Wojciech Kaminski: So, thank you.
tpawlow: Actually if you can hear me. And I can make some comment.
Okay, well,
tpawlow: First of all, I would like to add a little bit more information to the outlook page.
tpawlow: So first of all, regarding the positive cosmological constant, we very abundant using the powers of the volume or volume itself. Because essentially, it was clear that it is not a good operator.
tpawlow: Namely, even if you look at the trajectory then system reached the infinite volume at the finite time and that indicates already many of the problems on the operator level.
tpawlow: So instead we already were forced to use some
tpawlow: Functions of volume work for that was calling essentially regular eyes or compact version of the volume operator. So that already.
tpawlow: Sort of answers. What is happening for positive cosmological calls and then those problems were observed as much more severe and steps were already taken to
tpawlow: solve these problems. So that's one thing. Second, this
tpawlow: Problem is essentially a result of connecting unifying or merging couple of the components of the model. So first of all, there is this particular choice of group averaging, namely taking the just the positive frequency, the composition choosing scale our field as a time
tpawlow: So it's essentially the
tpawlow: Details of a group of urging and the
tpawlow: Type of choice and, for example, other time choices like we tested it with the radiation with that deals and they seem to be free from this problem.
tpawlow: So this is something I wanted to add just to show that essentially there is quite a lot of ways.
tpawlow: potential solutions.
tpawlow: Another thing is that I'm very happy that vojtech mentioned, it is that, essentially, we have the same topics of accuracy towards they will or the wheat solutions which essentially reduced to the
tpawlow: Kangaroo equation with only the volume operator bank represented us. I suppose exponent of x. That would be the anello
tpawlow: And I would suppose that we can then use the fact that we actually know how to make like an equation work to also correct certain details of the approach we applied for LTC to
tpawlow: Implement the ways the problem was solved that.
tpawlow: Okay, that's, that's it.
Yeah okay I
Wojciech Kaminski: I agree, which topic is so I was mentioning this this
Wojciech Kaminski: Lambda Deacon hero, we use the compact defied volume. Yeah, so, so good. The traumatic stress.
Wojciech Kaminski: Disorder. I've gotten there.
Hello.
MH: Hi water. This is mostly in time here.
MH: We're good. Yeah. So my question is, do you think the same problem carry over to the BU theory as well because seemed seemed to me the info theory, the evolution of volume is seems not unified. Well, there seems has less this domain problem. What do you see, I mean, in
MH: Theory. I mean, what I see is, I mean, in theory, you can define the physical Hamiltonian
MH: Using using task and skater field and and the volume operator is also define us the network and and and sweet and both of the market finance the network.
Wojciech Kaminski: So, so this is very good question. And of course, I have no idea.
Wojciech Kaminski: So we founded our class, we were trying to estimate, you know, say,
Wojciech Kaminski: Okay, you know, maybe not fully try but if not, if you come to me gravity and we always were some are failing to estimate unbound operators.
Wojciech Kaminski: But of course the question is whether they smell some
Wojciech Kaminski: Of the special happening that Phoebe free Dr. From these are the behavior.
Wojciech Kaminski: But in general, I would say that something like that can happen.
MH: Well, I'm gonna say, more specifically, what exactly what is what exactly the quantity we need to see in order to detect this problem. So, and, you know,
MH: You must you mentioned you know this work by Andy and clouds and well. And there's also an hour reason work with someone about and passing the law of
MH: Gravity, I realized to effective dynamics of cosmology. But I mean, can you somehow let let let let me, let me know.
MH: What, what kind of computation, which may detect this problem you for theory.
Wojciech Kaminski: Yes, I see the, the easier easiest way would be to look at this 13 like in this class will at the feet.
Wojciech Kaminski: So looking for the
Wojciech Kaminski: What is done. So we can estimate the
Wojciech Kaminski: It will deplete we can estimate this behavior of for the large volumes by the by the spot that correspond to too small and that
Wojciech Kaminski: So,
Wojciech Kaminski: So why I was not doing the same way in the in the slope quantum cosmology.
Wojciech Kaminski: Broadly, because from
Wojciech Kaminski: Because of some Malaysian as because in their little quantum cosmology. We don't have good knowledge about the behavior of the
Wojciech Kaminski: Eigen functions for the smaller. And so usually people who are estimated from village and they just that is for an empty not equal to zero. So, there is no uniform
Wojciech Kaminski: Description of the Center for when they go to zero went in there with the good case we had so maybe one should think this funky Allah if if you would have some knowledge about
Wojciech Kaminski: Low does you know and that
Wojciech Kaminski: States then invisible, it should be.
Wojciech Kaminski: Integrated one should see this behavior of the volume but
Wojciech Kaminski: I think you quantum gravity is much more complicated. So I
Wojciech Kaminski: Would be, it would be great if you would do that.
But
LSU Rel: Like, just to interrupt like David Craig has written a very nice paper. Some years ago, in which he has
LSU Rel: He has completed all the things that you need for all QC look at back and functions that it's everything is analytical
Wojciech Kaminski: I thought he found the
Wojciech Kaminski: Right.
LSU Rel: Yes, so it's a single lot of paper. I think like three or four years ago and but it was
Wojciech Kaminski: Somebody who
LSU Rel: Was for solar LLC. Yes.
Wojciech Kaminski: Yes, so
Wojciech Kaminski: So to two. Okay, so to bridge these two questions actually fun look to look for the silver, but there are the functions are so different graphs are really have to estimate
Wojciech Kaminski: It was really complicated to show that
LSU Rel: That's true. So, but, but I think like he managed to
LSU Rel: Do some estimations just some some simple programming with mathematical
Wojciech Kaminski: Okay, so I should look at that. Yeah.
Wojciech Kaminski: Yeah, so to to come back to the machine question.
Wojciech Kaminski: Okay, so this if one can speak about something.
Wojciech Kaminski: Positive in the
Wojciech Kaminski: Resulting it's exactly that we should make be terrific. What we dream in the foot to the
bakery.
MH: Okay, thank you.
Jorge Pullin: Any more questions.
Jorge Pullin: Okay, let's watch again.