0 00:00:02,250 --> 00:00:07,230 Jorge Pullin: Okay, so let's figure it this way chick Kaminski will speak about the volume operator and quantum cosmology. 1 00:00:08,340 --> 00:00:16,680 Wojciech Kaminski: Okay, so thank you very much for allowing me to speak in international loop quantum gravity seminar. So because the 2 00:00:17,820 --> 00:00:23,790 Wojciech Kaminski: Reason that I'm presenting in fact quite elementary I will start with the 3 00:00:25,440 --> 00:00:32,970 Wojciech Kaminski: Short Introduction. So put the resulting some broader context in the loop on to cosmological so 4 00:00:33,990 --> 00:00:48,570 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 5 00:00:49,620 --> 00:00:50,490 Wojciech Kaminski: Geometry. 6 00:00:51,570 --> 00:00:52,860 Wojciech Kaminski: And from all the 7 00:00:54,150 --> 00:01:11,040 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 8 00:01:12,990 --> 00:01:15,900 Wojciech Kaminski: Function Tita entities just be square city square 9 00:01:17,310 --> 00:01:18,030 It of course 10 00:01:19,170 --> 00:01:33,000 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. 11 00:01:34,470 --> 00:01:35,880 Wojciech Kaminski: Okay, so 12 00:01:40,260 --> 00:01:48,630 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 13 00:01:49,320 --> 00:01:50,280 Jorge Pullin: Your screens visual 14 00:01:50,760 --> 00:02:03,780 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. 15 00:02:04,770 --> 00:02:18,270 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. 16 00:02:20,070 --> 00:02:32,850 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. 17 00:02:34,080 --> 00:02:50,370 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 18 00:02:52,020 --> 00:02:59,130 Wojciech Kaminski: Trust prediction of quantum cosmology, whether it's still called in the future of constant gravity and 19 00:03:00,180 --> 00:03:15,120 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. 20 00:03:16,200 --> 00:03:25,620 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 21 00:03:27,150 --> 00:03:40,410 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 22 00:03:42,270 --> 00:04:04,410 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. 23 00:04:05,580 --> 00:04:21,720 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. 24 00:04:23,340 --> 00:04:28,470 Wojciech Kaminski: spanked by the integer positive integer numbers with this a bit 25 00:04:29,760 --> 00:04:34,260 Wojciech Kaminski: Change scholar product. So this video is important because it's lead to some 26 00:04:36,210 --> 00:04:39,270 Wojciech Kaminski: Specific behavior of the era and 27 00:04:40,410 --> 00:04:48,420 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. 28 00:04:49,110 --> 00:05:09,990 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 29 00:05:11,160 --> 00:05:14,040 Wojciech Kaminski: The schema space is represented in the volume, I can say 30 00:05:15,210 --> 00:05:23,100 Wojciech Kaminski: And in what follow for me will be only important the syntactic behavior of these functions. 31 00:05:24,570 --> 00:05:39,180 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 32 00:05:39,990 --> 00:05:49,710 Wojciech Kaminski: So I will not consider that the the stock. But probably the feature that I will be speaking about is also present 33 00:05:51,210 --> 00:05:52,770 Wojciech Kaminski: Okay, so this 34 00:05:54,870 --> 00:06:04,890 Wojciech Kaminski: Model is what is important for the for this behavior and some syntactic expansion of dysfunctional CC zero and ba. 35 00:06:05,640 --> 00:06:13,290 Wojciech Kaminski: And let us not this. That is a question four or five and six that we in fact need a bit more 36 00:06:14,160 --> 00:06:27,690 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. 37 00:06:28,800 --> 00:06:42,720 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 38 00:06:45,390 --> 00:06:45,810 Wojciech Kaminski: Okay. 39 00:06:47,850 --> 00:06:48,270 So, 40 00:06:49,590 --> 00:07:04,230 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 41 00:07:05,640 --> 00:07:19,440 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 42 00:07:20,490 --> 00:07:23,040 Wojciech Kaminski: Evolution that we see in the universe. 43 00:07:24,270 --> 00:07:31,920 Wojciech Kaminski: And in fact, the quite interesting features of these models. So first of all, so this is 44 00:07:33,090 --> 00:07:42,630 Wojciech Kaminski: Mostly based on the metrics. Some of them are proven analytically. So it's also still not completely clear. 45 00:07:43,710 --> 00:07:51,300 Wojciech Kaminski: Audio for not knowledge but states that are picked on the high end abjure 46 00:07:53,070 --> 00:08:04,200 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 47 00:08:05,100 --> 00:08:16,350 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 48 00:08:17,430 --> 00:08:18,780 Wojciech Kaminski: The volume operators. 49 00:08:20,790 --> 00:08:27,720 Wojciech Kaminski: Is changed into derivative and this shift is changing the multiplication by it to ice. 50 00:08:29,130 --> 00:08:32,160 Wojciech Kaminski: And the these high volume. 51 00:08:33,510 --> 00:08:42,570 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 52 00:08:43,980 --> 00:08:55,830 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 53 00:08:57,510 --> 00:09:04,050 Wojciech Kaminski: Restrict the very high end address, we see that the for the lifetimes. 54 00:09:05,220 --> 00:09:15,120 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 55 00:09:16,050 --> 00:09:26,550 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 56 00:09:27,030 --> 00:09:37,740 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 57 00:09:38,880 --> 00:09:39,300 But 58 00:09:40,860 --> 00:09:41,730 Wojciech Kaminski: So how 59 00:09:42,870 --> 00:09:46,620 Wojciech Kaminski: We deal with semi classical dynamics in the 60 00:09:47,670 --> 00:09:51,480 Wojciech Kaminski: Low quantum cosmology something some prescription 61 00:09:52,890 --> 00:09:57,000 Wojciech Kaminski: That some of that was also determined by 62 00:09:59,070 --> 00:10:00,270 Wojciech Kaminski: The way. 63 00:10:03,390 --> 00:10:10,740 Wojciech Kaminski: Supported by some numerical simulations and some of them. Also, there are some analytical computations, but one 64 00:10:11,820 --> 00:10:18,210 Wojciech Kaminski: Consider CDP coherence states peaked at the given faceplates point 65 00:10:19,920 --> 00:10:29,970 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. 66 00:10:30,540 --> 00:10:39,270 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 67 00:10:40,050 --> 00:10:58,110 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 68 00:10:59,700 --> 00:11:09,480 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 69 00:11:10,650 --> 00:11:14,970 Wojciech Kaminski: In the naive, but very direct way without 70 00:11:16,560 --> 00:11:25,020 Wojciech Kaminski: Spending a lot of effort on the computation of expectations about you just take the form of the operator as the place 71 00:11:27,300 --> 00:11:31,350 Wojciech Kaminski: Operator volume by D and shoots by to IC 72 00:11:32,550 --> 00:11:35,940 Wojciech Kaminski: But that's a bit bigger and bigger D, however. 73 00:11:37,620 --> 00:11:42,390 Wojciech Kaminski: There are some special cases when these bigger ambiguity. 74 00:11:42,600 --> 00:11:55,080 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 75 00:11:55,560 --> 00:12:06,090 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. 76 00:12:08,790 --> 00:12:10,980 Wojciech Kaminski: Comment about equation seven or eight 77 00:12:11,040 --> 00:12:18,030 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 78 00:12:18,450 --> 00:12:32,430 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 79 00:12:33,840 --> 00:12:43,680 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 80 00:12:44,700 --> 00:12:52,170 LSU Rel: they preserve the Hamiltonian flow for the teat operator very nicely. And that is what we checked. 81 00:12:53,010 --> 00:13:04,980 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 82 00:13:05,070 --> 00:13:08,730 Wojciech Kaminski: That's a good question. So first of all, I'm not sure. 83 00:13:10,200 --> 00:13:10,620 Wojciech Kaminski: So, 84 00:13:13,620 --> 00:13:18,000 Wojciech Kaminski: The question. Okay, so we compute summer. So there were several 85 00:13:19,350 --> 00:13:22,860 Wojciech Kaminski: Estimates and three speaking I still don't know. 86 00:13:24,750 --> 00:13:30,330 Wojciech Kaminski: Which so surely because we now know that this volume is easy needs. 87 00:13:34,200 --> 00:13:43,800 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 88 00:13:43,830 --> 00:13:55,410 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 89 00:13:57,150 --> 00:14:02,070 LSU Rel: This will be caught because one is making only the approximation that 90 00:14:03,150 --> 00:14:08,160 LSU Rel: To derive that Hamill, the effective Hamiltonian that v is much greater than the plank volume. 91 00:14:10,470 --> 00:14:19,320 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 92 00:14:19,860 --> 00:14:24,690 LSU Rel: In the calculations of what Richter has done at least. And I think Martin's calculations will be probably similar 93 00:14:25,320 --> 00:14:37,170 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 94 00:14:37,710 --> 00:14:41,790 LSU Rel: Some of you have to extract this term from the way effective dynamics has been derived 95 00:14:43,500 --> 00:14:47,940 LSU Rel: And does it have any non negligible effect. I don't think so. 96 00:14:50,100 --> 00:14:51,960 Wojciech Kaminski: No. So I agree that 97 00:14:53,610 --> 00:14:55,110 Wojciech Kaminski: I expect that this 98 00:14:57,030 --> 00:15:00,630 Wojciech Kaminski: Semi classical dynamics is after all right. 99 00:15:01,530 --> 00:15:02,910 LSU Rel: Okay, you say that 100 00:15:03,000 --> 00:15:07,020 Wojciech Kaminski: Yes, yes. So, but, of course, I expect so. 101 00:15:08,790 --> 00:15:18,120 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 102 00:15:19,530 --> 00:15:21,630 Wojciech Kaminski: Okay, so we can, I think, 103 00:15:21,690 --> 00:15:30,330 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 104 00:15:31,470 --> 00:15:34,350 LSU Rel: I'm just feeling too right now understand 105 00:15:36,030 --> 00:15:51,210 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 106 00:15:52,740 --> 00:15:53,130 Yes. 107 00:15:54,240 --> 00:16:03,600 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, 108 00:16:04,410 --> 00:16:08,460 LSU Rel: Yeah, okay. I agree. I agree. Maybe at very large volumes. 109 00:16:10,410 --> 00:16:13,890 LSU Rel: I don't know. I have to think about this, but I think this is some 110 00:16:15,240 --> 00:16:17,730 LSU Rel: Some good venue to investigate for someone 111 00:16:18,480 --> 00:16:26,430 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. 112 00:16:29,820 --> 00:16:42,570 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 113 00:16:44,010 --> 00:16:57,840 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. 114 00:16:58,380 --> 00:17:11,670 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 115 00:17:12,840 --> 00:17:23,580 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 116 00:17:24,360 --> 00:17:40,170 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. 117 00:17:42,030 --> 00:17:42,450 Wojciech Kaminski: So, 118 00:17:46,050 --> 00:17:58,830 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 119 00:18:00,060 --> 00:18:01,500 Elliptic region. 120 00:18:02,940 --> 00:18:08,400 Wojciech Kaminski: This this evolution is also a dependent on this additional detail. 121 00:18:10,320 --> 00:18:10,710 Wojciech Kaminski: And 122 00:18:12,810 --> 00:18:16,110 Wojciech Kaminski: So it's not natural questions that one should 123 00:18:17,280 --> 00:18:28,470 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 124 00:18:29,490 --> 00:18:35,280 Wojciech Kaminski: The stamps at the Liddy volume powers is invaluable and 125 00:18:37,290 --> 00:18:47,790 Wojciech Kaminski: But by asking this question, we are the posing that semi classical dynamics is in some sense local. So, this 126 00:18:50,460 --> 00:18:52,620 Wojciech Kaminski: Can be so effective. 127 00:18:53,730 --> 00:18:55,530 Wojciech Kaminski: Coming Tatyana that is completed. 128 00:18:57,180 --> 00:19:03,000 Wojciech Kaminski: Excellent. So it's some local function of the of the DNC that 129 00:19:06,390 --> 00:19:12,240 Wojciech Kaminski: That we don't need to know this effective Hamilton far from the region that we are interested in 130 00:19:14,010 --> 00:19:25,530 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 131 00:19:26,670 --> 00:19:31,680 Wojciech Kaminski: This effective Hamiltonian equal to just, just the square root of the things that we computed 132 00:19:32,730 --> 00:19:41,730 Wojciech Kaminski: And the last transparency, then we get to the correct evolution of the copyright states. 133 00:19:42,990 --> 00:19:46,860 Wojciech Kaminski: Covered in this question. It's not only limited to the 134 00:19:49,410 --> 00:20:00,450 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. 135 00:20:01,020 --> 00:20:12,390 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 136 00:20:13,380 --> 00:20:33,630 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 137 00:20:35,370 --> 00:20:49,380 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. 138 00:20:51,150 --> 00:20:51,660 Of course, 139 00:20:53,490 --> 00:20:54,810 Wojciech Kaminski: One can speak about 140 00:20:56,040 --> 00:21:08,070 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 141 00:21:10,770 --> 00:21:11,610 Wojciech Kaminski: Evolution. 142 00:21:12,870 --> 00:21:31,050 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. 143 00:21:32,070 --> 00:21:42,180 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 144 00:21:43,020 --> 00:22:00,510 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 145 00:22:02,280 --> 00:22:04,290 Wojciech Kaminski: Looking at the behavior of agriculture. 146 00:22:05,940 --> 00:22:08,910 Wojciech Kaminski: Okay. And I will say what Tyler 147 00:22:10,200 --> 00:22:13,740 Wojciech Kaminski: What are the results. And of course, let me first. 148 00:22:15,030 --> 00:22:17,070 Wojciech Kaminski: Remind how the 149 00:22:19,110 --> 00:22:22,020 Wojciech Kaminski: This Eigen functions of detail operator. 150 00:22:23,310 --> 00:22:34,320 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 151 00:22:35,550 --> 00:22:40,800 Wojciech Kaminski: So the three jewels, and the first region is something like the 152 00:22:42,180 --> 00:22:54,660 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. 153 00:22:55,080 --> 00:23:02,760 Wojciech Kaminski: And it's the same here and this part is, in fact, responsible for these bows acuity at the large volumes. 154 00:23:03,930 --> 00:23:11,160 Wojciech Kaminski: But this expansion is true for large enterprises. So then there is a second part that is 155 00:23:13,320 --> 00:23:16,260 Wojciech Kaminski: I think it's well capture of my picture because it's 156 00:23:18,330 --> 00:23:29,610 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. 157 00:23:30,690 --> 00:23:43,170 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 158 00:23:44,010 --> 00:23:51,840 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 159 00:23:52,530 --> 00:24:07,050 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 160 00:24:08,100 --> 00:24:15,180 Wojciech Kaminski: If one a match, say the static point with this entity behavior, one can get a lot of information about their 161 00:24:16,260 --> 00:24:21,300 Wojciech Kaminski: Scattering you know control personal agenda. This is the way. Well, how it's done. 162 00:24:22,440 --> 00:24:23,040 Okay. 163 00:24:24,120 --> 00:24:27,810 Wojciech Kaminski: So I because for me this this last 164 00:24:29,400 --> 00:24:35,640 Wojciech Kaminski: Part is the most interesting. I will just maybe sketch some method how to 165 00:24:37,650 --> 00:24:51,840 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. 166 00:24:53,580 --> 00:24:57,300 Wojciech Kaminski: And they will call efficiency. These theories are given by this week and 167 00:24:58,500 --> 00:24:59,130 Wojciech Kaminski: Numbers. 168 00:25:00,780 --> 00:25:01,410 Wojciech Kaminski: So this is 169 00:25:02,490 --> 00:25:06,870 Wojciech Kaminski: Where we want that these CDs satisfy equation nine 170 00:25:08,340 --> 00:25:14,880 Wojciech Kaminski: And in fact, if we take this equation and one plug in the serious one consult with record separately. 171 00:25:15,990 --> 00:25:28,620 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 172 00:25:29,730 --> 00:25:33,180 Wojciech Kaminski: Ito plus minus i omega divided by 173 00:25:34,770 --> 00:25:38,880 Wojciech Kaminski: Ok and now how we define this approximate 174 00:25:39,990 --> 00:25:51,060 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. 175 00:25:52,260 --> 00:25:55,830 Wojciech Kaminski: Is satisfying the equations of the, I guess. 176 00:25:59,430 --> 00:26:14,430 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 177 00:26:15,870 --> 00:26:16,680 Wojciech Kaminski: Equation. 178 00:26:18,510 --> 00:26:32,220 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 179 00:26:33,240 --> 00:26:45,990 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 180 00:26:46,830 --> 00:27:05,490 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 181 00:27:06,780 --> 00:27:15,570 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 182 00:27:16,470 --> 00:27:27,090 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. 183 00:27:27,870 --> 00:27:48,240 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 184 00:27:49,440 --> 00:27:56,310 Wojciech Kaminski: Of the storm solutions with the given us insulting behavior. And if we do that, we see that 185 00:27:58,140 --> 00:27:59,490 Wojciech Kaminski: This era god he 186 00:28:00,570 --> 00:28:21,540 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. 187 00:28:23,280 --> 00:28:25,080 Wojciech Kaminski: And moreover, 188 00:28:26,940 --> 00:28:27,540 Wojciech Kaminski: If we 189 00:28:28,770 --> 00:28:49,320 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. 190 00:28:50,580 --> 00:28:53,280 Wojciech Kaminski: And exactly the T omega era, I can function. 191 00:28:55,140 --> 00:28:57,750 Wojciech Kaminski: OK, so now I really present some 192 00:28:58,980 --> 00:29:02,970 Wojciech Kaminski: Strange argument about that will lead us to the 193 00:29:05,730 --> 00:29:18,390 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 194 00:29:20,070 --> 00:29:31,560 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. 195 00:29:32,400 --> 00:29:43,170 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 196 00:29:44,160 --> 00:30:02,820 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. 197 00:30:04,650 --> 00:30:11,400 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. 198 00:30:12,540 --> 00:30:24,480 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 199 00:30:26,340 --> 00:30:27,570 Wojciech Kaminski: Dependence on the side. 200 00:30:29,670 --> 00:30:36,060 Wojciech Kaminski: Okay, but if the evolved function also belong to the domain. 201 00:30:37,200 --> 00:30:41,850 Wojciech Kaminski: Then we can construct similar function. Now let's call it fit. 202 00:30:42,900 --> 00:30:46,260 Wojciech Kaminski: For them about that steak. 203 00:30:47,400 --> 00:30:59,580 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. 204 00:31:00,900 --> 00:31:12,120 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 205 00:31:13,110 --> 00:31:27,810 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. 206 00:31:29,070 --> 00:31:35,130 Wojciech Kaminski: It's too much to say to somebody. It's not symmetric unless F zero 207 00:31:36,780 --> 00:31:52,680 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. 208 00:31:54,840 --> 00:32:14,700 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 209 00:32:16,230 --> 00:32:17,430 Wojciech Kaminski: In the most of them. 210 00:32:18,630 --> 00:32:30,420 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 211 00:32:32,040 --> 00:32:39,030 Wojciech Kaminski: So this is a positive result. And in fact, if you look carefully for the literature. 212 00:32:40,200 --> 00:32:51,630 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 213 00:32:53,130 --> 00:32:54,570 Wojciech Kaminski: Small sign of this 214 00:32:58,170 --> 00:33:05,910 Wojciech Kaminski: Infinity is because this is not belong to the main because expectation. The value of some power of volume is teaching 215 00:33:07,080 --> 00:33:07,440 But 216 00:33:09,030 --> 00:33:16,830 Wojciech Kaminski: Because there was no numerical final that everyone was thinking that smaller some technical talent will be on consult 217 00:33:18,000 --> 00:33:29,490 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. 218 00:33:30,840 --> 00:33:31,200 And 219 00:33:32,910 --> 00:33:35,430 Wojciech Kaminski: We would like to understand what is the 220 00:33:37,290 --> 00:33:48,510 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. 221 00:33:49,770 --> 00:33:51,360 Wojciech Kaminski: Cause I'm not 222 00:33:52,590 --> 00:33:53,580 Wojciech Kaminski: I have no 223 00:33:55,980 --> 00:33:56,700 Wojciech Kaminski: Eggs that 224 00:33:59,790 --> 00:34:12,300 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 225 00:34:13,590 --> 00:34:17,310 Wojciech Kaminski: And the will of the purely one can if 226 00:34:19,380 --> 00:34:35,580 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 227 00:34:36,720 --> 00:34:38,580 Wojciech Kaminski: Super selection rule. 228 00:34:40,050 --> 00:34:47,130 Wojciech Kaminski: Just telling us that we divide the wastebasket into positive and negative moment and we 229 00:34:49,560 --> 00:35:00,600 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 230 00:35:02,820 --> 00:35:03,240 Wojciech Kaminski: And 231 00:35:04,830 --> 00:35:08,280 Wojciech Kaminski: Let us know. Consider a Gaussian stating this 232 00:35:10,320 --> 00:35:10,890 Wojciech Kaminski: Era. 233 00:35:12,150 --> 00:35:20,370 Wojciech Kaminski: And of course, if we just agreed upon, it's no longer smooth audition Regional Council was of course smoke in the 234 00:35:21,720 --> 00:35:32,010 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 235 00:35:33,870 --> 00:35:36,270 Wojciech Kaminski: And stand out that the Fourier transform. 236 00:35:38,760 --> 00:35:41,130 Wojciech Kaminski: It has the very special behavior. 237 00:35:43,200 --> 00:35:43,770 Because 238 00:35:45,420 --> 00:35:55,860 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. 239 00:35:56,790 --> 00:36:15,120 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. 240 00:36:16,620 --> 00:36:18,450 Wojciech Kaminski: And there are some lower order times 241 00:36:19,980 --> 00:36:26,580 Wojciech Kaminski: So if we now back, come back to the volume representation. So let's assume an X equal Logan, he 242 00:36:27,990 --> 00:36:41,100 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 243 00:36:42,570 --> 00:36:43,530 Wojciech Kaminski: Powers of the 244 00:36:45,030 --> 00:36:51,660 Wojciech Kaminski: So our state for tea not equal to zero. It's not belonging to the domain of the volume anymore. 245 00:36:53,070 --> 00:37:05,370 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 246 00:37:06,600 --> 00:37:06,720 Wojciech Kaminski: The 247 00:37:07,830 --> 00:37:24,240 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. 248 00:37:25,800 --> 00:37:36,420 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 249 00:37:37,230 --> 00:37:50,790 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 250 00:37:51,810 --> 00:37:55,140 Wojciech Kaminski: States for something that you speak to close to the 251 00:37:59,070 --> 00:37:59,340 Wojciech Kaminski: Like 252 00:38:03,240 --> 00:38:04,320 Wojciech Kaminski: Okay, so also when 253 00:38:04,320 --> 00:38:05,520 LSU Rel: I ask a question. 254 00:38:06,630 --> 00:38:07,800 Wojciech Kaminski: A bit differently. 255 00:38:09,330 --> 00:38:10,200 Wojciech Kaminski: can divide this 256 00:38:14,220 --> 00:38:15,000 Wojciech Kaminski: Notion into 257 00:38:16,260 --> 00:38:16,620 Wojciech Kaminski: One. 258 00:38:18,300 --> 00:38:18,750 Wojciech Kaminski: By 259 00:38:20,460 --> 00:38:21,990 Wojciech Kaminski: Writing mode so 260 00:38:22,800 --> 00:38:24,060 LSU Rel: Can I ask a question from the 261 00:38:24,060 --> 00:38:24,450 Previous 262 00:38:26,250 --> 00:38:28,050 Wojciech Kaminski: And this fee is behind 263 00:38:28,500 --> 00:38:29,670 Jorge Pullin: Our question here. 264 00:38:30,480 --> 00:38:37,650 Wojciech Kaminski: Knife. He saw all the time gulshan and keep moving along classical projector. 265 00:38:39,180 --> 00:38:54,990 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 266 00:38:56,550 --> 00:38:59,970 Wojciech Kaminski: Despite that, it's so small. It's a small city for the problem with the volume. 267 00:39:01,980 --> 00:39:13,320 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. 268 00:39:14,190 --> 00:39:28,230 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 269 00:39:29,520 --> 00:39:37,470 Wojciech Kaminski: Is small but the expectation value of the volume in LTC fee, though, we cannot. I mean, 270 00:39:40,620 --> 00:39:41,340 If we look 271 00:39:45,510 --> 00:39:45,990 Hello. 272 00:39:47,220 --> 00:39:47,760 Jorge Pullin: Hello. 273 00:39:48,360 --> 00:39:49,050 Yes, so 274 00:39:50,460 --> 00:39:53,160 Jorge Pullin: They had a question here for you. Yes. 275 00:39:53,220 --> 00:39:54,360 Wojciech Kaminski: So I just got 276 00:40:07,740 --> 00:40:08,970 LSU Rel: To go back some slides. 277 00:40:12,090 --> 00:40:13,350 LSU Rel: On the conjecture slide. 278 00:40:22,380 --> 00:40:25,530 LSU Rel: Non integral part of the tail is 279 00:40:25,650 --> 00:40:28,140 Wojciech Kaminski: So it was so it was not so 280 00:40:30,060 --> 00:40:30,930 Wojciech Kaminski: Happy. It was not 281 00:40:31,290 --> 00:40:45,750 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. 282 00:40:48,780 --> 00:40:50,190 Wojciech Kaminski: What you mean by omega 283 00:40:50,460 --> 00:40:59,670 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. 284 00:41:02,040 --> 00:41:06,000 Wojciech Kaminski: So okay, so then they will have the 285 00:41:07,980 --> 00:41:09,240 Wojciech Kaminski: somehow related to the p 286 00:41:09,630 --> 00:41:12,240 LSU Rel: Yes, or your PSP fight. Yes. 287 00:41:13,590 --> 00:41:14,040 LSU Rel: Please. 288 00:41:15,180 --> 00:41:18,000 Wojciech Kaminski: Yeah, so a piece so 289 00:41:20,280 --> 00:41:24,900 Wojciech Kaminski: P conjugated to x axis low volume. 290 00:41:24,960 --> 00:41:28,140 LSU Rel: Yes. Right. Right. That's what I was saying. So x is longer term of volume. 291 00:41:29,310 --> 00:41:34,560 LSU Rel: As far as I remember, that is conjugate to I think we'll be fine. 292 00:41:35,220 --> 00:41:35,760 Wojciech Kaminski: Yeah yeah 293 00:41:38,670 --> 00:41:48,630 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. 294 00:41:51,870 --> 00:41:52,320 Wojciech Kaminski: So, 295 00:41:54,720 --> 00:41:55,110 Wojciech Kaminski: If 296 00:41:57,690 --> 00:42:01,110 Wojciech Kaminski: I think in general, it's only for really lower 297 00:42:02,700 --> 00:42:03,630 Wojciech Kaminski: Right, exactly. 298 00:42:03,660 --> 00:42:08,760 LSU Rel: Exactly. So you see, this is another reason like in the new metrics we were always having large 299 00:42:12,360 --> 00:42:14,580 Wojciech Kaminski: Maybe I was not successful, but they were 300 00:42:15,720 --> 00:42:24,150 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. 301 00:42:24,630 --> 00:42:36,210 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 302 00:42:36,690 --> 00:42:37,110 Yes. 303 00:42:38,700 --> 00:42:41,550 LSU Rel: This is not going to have any physical effect. 304 00:42:41,850 --> 00:42:44,730 Wojciech Kaminski: Yes, no, I completely agree. 305 00:42:47,460 --> 00:42:48,330 Wojciech Kaminski: Sounds strange 306 00:42:50,190 --> 00:42:59,760 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. 307 00:43:00,330 --> 00:43:09,780 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 308 00:43:10,710 --> 00:43:20,100 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 309 00:43:20,790 --> 00:43:36,630 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 310 00:43:37,380 --> 00:43:38,100 Wojciech Kaminski: agree with that. 311 00:43:41,550 --> 00:43:46,890 Wojciech Kaminski: Because the small in the in the space for 312 00:43:48,030 --> 00:43:49,710 Wojciech Kaminski: It will be negligible. 313 00:43:51,750 --> 00:43:52,590 LSU Rel: So I agree. First 314 00:43:53,670 --> 00:43:59,850 LSU Rel: One can take this analytical strategy but secondly for realistic cosmological models. 315 00:44:00,900 --> 00:44:02,670 LSU Rel: This tale will probably have no effect. 316 00:44:04,530 --> 00:44:05,550 Wojciech Kaminski: Yeah, so 317 00:44:06,720 --> 00:44:08,970 Wojciech Kaminski: It, it has no effect. 318 00:44:10,800 --> 00:44:16,020 Wojciech Kaminski: Because we always need to take something like semi classical so the point is that we should not trust. 319 00:44:17,160 --> 00:44:23,670 Wojciech Kaminski: We should maybe not complete semi classical objects that we can make so 320 00:44:23,730 --> 00:44:30,780 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. 321 00:44:31,980 --> 00:44:44,670 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 322 00:44:45,150 --> 00:44:54,390 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. 323 00:44:55,170 --> 00:45:12,930 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. 324 00:45:15,570 --> 00:45:17,490 Wojciech Kaminski: Yes, yes, I agree. 325 00:45:19,050 --> 00:45:20,040 Wojciech Kaminski: It's made me not. 326 00:45:21,390 --> 00:45:22,500 Wojciech Kaminski: To look for that. 327 00:45:23,460 --> 00:45:24,090 Because I 328 00:45:25,470 --> 00:45:28,860 LSU Rel: Can look at this paper which like Peter dinner. Me and 329 00:45:30,660 --> 00:45:41,190 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. 330 00:45:41,520 --> 00:45:46,440 LSU Rel: And you can see like numerically. We still have to do approximations and then cut off the tails so that 331 00:45:47,940 --> 00:45:55,500 LSU Rel: Even the best supercomputers can perform the simulations. So I think it's also technically challenging to see this effect. 332 00:45:57,240 --> 00:46:09,030 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. 333 00:46:11,220 --> 00:46:15,240 Wojciech Kaminski: Yeah, okay. Okay, so, so let me 334 00:46:16,290 --> 00:46:23,400 Wojciech Kaminski: So yes, I was, I think I was here so that, of course, the on the smoke part the volume. 335 00:46:24,420 --> 00:46:42,450 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. 336 00:46:44,190 --> 00:46:50,910 Wojciech Kaminski: Version of the white part of this without absolute value that can be everything is fine and 337 00:46:51,960 --> 00:46:53,580 Wojciech Kaminski: So we see that in some sense. 338 00:46:55,260 --> 00:46:57,810 Wojciech Kaminski: This semi semi classical 339 00:47:00,750 --> 00:47:05,700 Wojciech Kaminski: It can be done. It's not a semi classical evolution is not complete local 340 00:47:06,810 --> 00:47:15,060 Wojciech Kaminski: But as the parent mentioned it's a we hope and 341 00:47:16,080 --> 00:47:33,510 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 342 00:47:35,130 --> 00:47:37,800 Wojciech Kaminski: Okay, so let me 343 00:47:39,750 --> 00:47:54,360 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 344 00:47:55,740 --> 00:47:56,670 Wojciech Kaminski: In the men their 345 00:47:58,470 --> 00:48:04,350 Wojciech Kaminski: Application of Groupon to cosmology, we are using expectations value of the power from the volume. 346 00:48:06,270 --> 00:48:12,390 Wojciech Kaminski: And one of these is the best metric. So in this metrics we look 347 00:48:13,470 --> 00:48:16,830 Wojciech Kaminski: What kind of geometry, the quantum field. 348 00:48:18,420 --> 00:48:20,520 Wojciech Kaminski: Effectively fields, if, if it's 349 00:48:22,950 --> 00:48:26,040 Wojciech Kaminski: Evolved in the quantum universe and deposits 350 00:48:28,290 --> 00:48:45,540 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 351 00:48:46,590 --> 00:48:58,320 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 352 00:48:59,370 --> 00:49:20,670 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 353 00:49:22,230 --> 00:49:23,100 Wojciech Kaminski: Effective 354 00:49:24,750 --> 00:49:27,300 Wojciech Kaminski: Volume from the previous slide is a 355 00:49:28,440 --> 00:49:39,750 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 356 00:49:41,430 --> 00:49:53,070 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 357 00:49:54,570 --> 00:50:06,360 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. 358 00:50:07,800 --> 00:50:16,260 Wojciech Kaminski: So then, but then it's not a big issue because nevertheless in the fight even for this semi classical 359 00:50:17,670 --> 00:50:29,040 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. 360 00:50:30,570 --> 00:50:35,460 Wojciech Kaminski: However, for London smaller than, you know, there is no problem. So there is no 361 00:50:36,990 --> 00:50:48,090 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 362 00:50:49,350 --> 00:50:54,930 Wojciech Kaminski: So it's not here with this new hyper mobile, what are 363 00:50:56,940 --> 00:51:05,460 Wojciech Kaminski: What is the fate of without. But in some sense. If we look at the proof with this. 364 00:51:07,080 --> 00:51:11,700 Wojciech Kaminski: Analytic attention. I think it should also hot for this new model. 365 00:51:13,650 --> 00:51:13,860 And 366 00:51:15,330 --> 00:51:16,230 Klaus 367 00:51:17,640 --> 00:51:23,130 Wojciech Kaminski: Young, your thoughts so many people. So it was proposing two stages. 368 00:51:24,630 --> 00:51:27,660 Wojciech Kaminski: So that they have five letters and of course 369 00:51:31,590 --> 00:51:37,050 Wojciech Kaminski: There is a reason. So if, if we look at this evolution without 370 00:51:39,000 --> 00:51:50,760 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. 371 00:51:52,590 --> 00:52:01,950 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 372 00:52:04,440 --> 00:52:17,160 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. 373 00:52:19,110 --> 00:52:19,650 Wojciech Kaminski: Then 374 00:52:21,900 --> 00:52:24,390 Wojciech Kaminski: I expanded it to the it's no problem with divulge 375 00:52:26,310 --> 00:52:27,150 Wojciech Kaminski: So, thank you. 376 00:52:42,840 --> 00:52:46,170 tpawlow: Actually if you can hear me. And I can make some comment. 377 00:52:47,040 --> 00:52:47,490 Okay, well, 378 00:52:48,750 --> 00:52:53,640 tpawlow: First of all, I would like to add a little bit more information to the outlook page. 379 00:52:54,870 --> 00:53:07,860 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. 380 00:53:08,370 --> 00:53:19,380 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. 381 00:53:20,610 --> 00:53:23,490 tpawlow: So instead we already were forced to use some 382 00:53:24,600 --> 00:53:34,290 tpawlow: Functions of volume work for that was calling essentially regular eyes or compact version of the volume operator. So that already. 383 00:53:35,070 --> 00:53:46,620 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 384 00:53:48,030 --> 00:53:53,430 tpawlow: solve these problems. So that's one thing. Second, this 385 00:53:55,140 --> 00:54:19,410 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 386 00:54:23,550 --> 00:54:25,350 tpawlow: So it's essentially the 387 00:54:26,700 --> 00:54:29,490 tpawlow: Details of a group of urging and the 388 00:54:30,660 --> 00:54:41,940 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. 389 00:54:44,970 --> 00:54:56,850 tpawlow: So this is something I wanted to add just to show that essentially there is quite a lot of ways. 390 00:54:58,770 --> 00:54:59,940 tpawlow: potential solutions. 391 00:55:01,050 --> 00:55:15,540 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 392 00:55:17,670 --> 00:55:31,200 tpawlow: Kangaroo equation with only the volume operator bank represented us. I suppose exponent of x. That would be the anello 393 00:55:32,040 --> 00:55:48,510 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 394 00:55:49,650 --> 00:55:51,990 tpawlow: Implement the ways the problem was solved that. 395 00:55:54,570 --> 00:55:55,800 tpawlow: Okay, that's, that's it. 396 00:55:59,100 --> 00:56:00,000 Yeah okay I 397 00:56:01,500 --> 00:56:05,580 Wojciech Kaminski: I agree, which topic is so I was mentioning this this 398 00:56:07,320 --> 00:56:16,020 Wojciech Kaminski: Lambda Deacon hero, we use the compact defied volume. Yeah, so, so good. The traumatic stress. 399 00:56:17,370 --> 00:56:18,810 Wojciech Kaminski: Disorder. I've gotten there. 400 00:56:22,530 --> 00:56:22,860 Hello. 401 00:56:23,940 --> 00:56:26,820 MH: Hi water. This is mostly in time here. 402 00:56:27,390 --> 00:56:50,370 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 403 00:56:50,550 --> 00:56:55,800 MH: Theory. I mean, what I see is, I mean, in theory, you can define the physical Hamiltonian 404 00:56:56,790 --> 00:57:08,370 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. 405 00:57:09,810 --> 00:57:14,910 Wojciech Kaminski: So, so this is very good question. And of course, I have no idea. 406 00:57:16,020 --> 00:57:21,840 Wojciech Kaminski: So we founded our class, we were trying to estimate, you know, say, 407 00:57:22,890 --> 00:57:32,610 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. 408 00:57:33,720 --> 00:57:37,830 Wojciech Kaminski: But of course the question is whether they smell some 409 00:57:39,000 --> 00:57:44,880 Wojciech Kaminski: Of the special happening that Phoebe free Dr. From these are the behavior. 410 00:57:45,990 --> 00:57:49,830 Wojciech Kaminski: But in general, I would say that something like that can happen. 411 00:57:51,810 --> 00:58:03,210 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, 412 00:58:03,810 --> 00:58:13,860 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 413 00:58:15,900 --> 00:58:25,710 MH: Gravity, I realized to effective dynamics of cosmology. But I mean, can you somehow let let let let me, let me know. 414 00:58:26,790 --> 00:58:32,070 MH: What, what kind of computation, which may detect this problem you for theory. 415 00:58:32,730 --> 00:58:42,720 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. 416 00:58:44,160 --> 00:58:46,830 Wojciech Kaminski: So looking for the 417 00:58:55,260 --> 00:58:58,740 Wojciech Kaminski: What is done. So we can estimate the 418 00:59:00,690 --> 00:59:11,070 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 419 00:59:12,150 --> 00:59:12,540 Wojciech Kaminski: So, 420 00:59:16,140 --> 00:59:21,630 Wojciech Kaminski: So why I was not doing the same way in the in the slope quantum cosmology. 421 00:59:23,160 --> 00:59:24,780 Wojciech Kaminski: Broadly, because from 422 00:59:26,190 --> 00:59:33,810 Wojciech Kaminski: Because of some Malaysian as because in their little quantum cosmology. We don't have good knowledge about the behavior of the 423 00:59:35,790 --> 00:59:47,460 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 424 00:59:48,630 --> 01:00:01,650 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 425 01:00:03,840 --> 01:00:06,180 Wojciech Kaminski: Low does you know and that 426 01:00:07,920 --> 01:00:11,010 Wojciech Kaminski: States then invisible, it should be. 427 01:00:13,110 --> 01:00:17,820 Wojciech Kaminski: Integrated one should see this behavior of the volume but 428 01:00:19,380 --> 01:00:22,740 Wojciech Kaminski: I think you quantum gravity is much more complicated. So I 429 01:00:24,600 --> 01:00:27,000 Wojciech Kaminski: Would be, it would be great if you would do that. 430 01:00:28,050 --> 01:00:28,350 But 431 01:00:31,080 --> 01:00:37,230 LSU Rel: Like, just to interrupt like David Craig has written a very nice paper. Some years ago, in which he has 432 01:00:38,880 --> 01:00:45,630 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 433 01:00:46,260 --> 01:00:47,430 Wojciech Kaminski: I thought he found the 434 01:00:51,660 --> 01:00:51,990 Wojciech Kaminski: Right. 435 01:00:52,020 --> 01:00:57,660 LSU Rel: Yes, so it's a single lot of paper. I think like three or four years ago and but it was 436 01:00:59,220 --> 01:00:59,910 Wojciech Kaminski: Somebody who 437 01:01:00,750 --> 01:01:02,490 LSU Rel: Was for solar LLC. Yes. 438 01:01:03,480 --> 01:01:04,320 Wojciech Kaminski: Yes, so 439 01:01:06,780 --> 01:01:21,030 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 440 01:01:22,320 --> 01:01:25,080 Wojciech Kaminski: It was really complicated to show that 441 01:01:25,200 --> 01:01:28,080 LSU Rel: That's true. So, but, but I think like he managed to 442 01:01:29,550 --> 01:01:33,660 LSU Rel: Do some estimations just some some simple programming with mathematical 443 01:01:33,720 --> 01:01:35,580 Wojciech Kaminski: Okay, so I should look at that. Yeah. 444 01:01:37,380 --> 01:01:41,070 Wojciech Kaminski: Yeah, so to to come back to the machine question. 445 01:01:45,360 --> 01:01:49,230 Wojciech Kaminski: Okay, so this if one can speak about something. 446 01:01:51,150 --> 01:01:52,260 Wojciech Kaminski: Positive in the 447 01:01:53,580 --> 01:01:58,890 Wojciech Kaminski: Resulting it's exactly that we should make be terrific. What we dream in the foot to the 448 01:02:00,870 --> 01:02:01,290 bakery. 449 01:02:04,230 --> 01:02:04,890 MH: Okay, thank you. 450 01:02:09,210 --> 01:02:10,080 Jorge Pullin: Any more questions. 451 01:02:15,390 --> 01:02:16,650 Jorge Pullin: Okay, let's watch again.