WEBVTT 1 00:00:02.450 --> 00:00:07.660 Jorge Pullin: Okay? So our speaker today is Salator. Privacy will speak about light con thermodynamics. 2 00:00:10.280 --> 00:00:13.670 Salvatore RIBISI: So thank you for the invitation. I'm very happy of being 3 00:00:13.870 --> 00:00:20.580 Salvatore RIBISI: here like talking to the the same, or the being following the most. At the beginning of my career. 4 00:00:20.900 --> 00:00:24.580 Salvatore RIBISI: So now, services have been. 5 00:00:24.630 --> 00:00:29.190 Salvatore RIBISI: how catching the interest of many researchers in the 6 00:00:29.290 --> 00:00:33.899 Salvatore RIBISI: in the last years and today. So I will 7 00:00:34.080 --> 00:00:41.059 Salvatore RIBISI: try to briefly review the the properties of maybe the simplest 8 00:00:41.380 --> 00:00:47.869 Salvatore RIBISI: of the no surfaces we can think about, which are light consuming Gowski spacetime. 9 00:00:48.340 --> 00:00:54.760 Salvatore RIBISI: So in this talk I will talk about the thermodynamic properties of light guns. 10 00:00:55.910 --> 00:01:03.300 Salvatore RIBISI: And so why can we? Why do live contactable dynamic properties? 11 00:01:03.810 --> 00:01:12.139 Salvatore RIBISI: So the answer comes from the fact that light comes in or be Mikoskey space types are conformal, killing horizon. 12 00:01:12.710 --> 00:01:18.119 Salvatore RIBISI: What does it mean? So we have the conformal group which is isomorphic to SO. 5, one. 13 00:01:18.990 --> 00:01:22.029 Salvatore RIBISI: and then it generator. Psi. Of this group 14 00:01:22.360 --> 00:01:30.499 Salvatore RIBISI: defines a conforming field, such that when we do, the derivative of the nintoskee matrix 15 00:01:30.980 --> 00:01:35.549 Salvatore RIBISI: through the side through any of the generator. 16 00:01:36.060 --> 00:01:42.139 Salvatore RIBISI: then what will. The result is proportional to the Nico schematic itself 17 00:01:42.370 --> 00:01:46.999 Salvatore RIBISI: with side being a scalar. So we have a function 18 00:01:47.560 --> 00:01:49.219 Salvatore RIBISI: which you can compute. 19 00:01:49.850 --> 00:01:55.900 Salvatore RIBISI: and this is the result for any of the 15 generators of the Conforma group. 20 00:01:56.310 --> 00:02:05.970 Salvatore RIBISI: Then we focus on the spherically symmetric ones. And then we only have 3. We only have 3 generators left. 21 00:02:06.190 --> 00:02:09.009 Salvatore RIBISI: which are the D, lato vector field 22 00:02:09.259 --> 00:02:15.170 Salvatore RIBISI: time translations and one of the special performance transformations. 23 00:02:16.400 --> 00:02:28.109 Salvatore RIBISI: Therefore, the most general conformance radius conformachine Fielding, because his facetime is given by a linear combination of these 3 vector, fields. 24 00:02:28.210 --> 00:02:38.219 Salvatore RIBISI: And so here you have the simple form written in terms of not coordinate. So you is the usual advanced time and either retired time. 25 00:02:38.800 --> 00:02:40.660 Salvatore RIBISI: Okay, so 26 00:02:41.100 --> 00:02:41.950 Salvatore RIBISI: with. 27 00:02:42.410 --> 00:02:48.010 Salvatore RIBISI: we want to study to to get to the point. When we find Blackton, we want to study the 28 00:02:48.260 --> 00:02:52.160 Salvatore RIBISI: council structure or given by 29 00:02:52.480 --> 00:02:55.740 Salvatore RIBISI: this family of conformal cleaning fields. 30 00:02:55.960 --> 00:03:00.179 Salvatore RIBISI: So we, we compute its norm. It's very easy to do. 31 00:03:00.700 --> 00:03:04.050 Salvatore RIBISI: And we see that it's given by the product 32 00:03:04.470 --> 00:03:08.940 Salvatore RIBISI: of these 2 polynomial of degree. 2. 33 00:03:10.290 --> 00:03:11.320 Salvatore RIBISI: So, 34 00:03:12.360 --> 00:03:14.540 Salvatore RIBISI: We see that the normal vanishes 35 00:03:14.670 --> 00:03:17.910 Salvatore RIBISI: at the root of these 2 polynomial meals. 36 00:03:18.260 --> 00:03:22.800 Salvatore RIBISI: so which are given by this to find to 37 00:03:23.020 --> 00:03:24.739 Salvatore RIBISI: past the future light comes 38 00:03:24.880 --> 00:03:31.640 Salvatore RIBISI: u equals to u plus minus, which is the root of this polynomial and the same routes apply for this polynomial. 39 00:03:33.290 --> 00:03:38.269 Salvatore RIBISI: and, moreover, the there is a sphere 40 00:03:38.680 --> 00:03:43.869 Salvatore RIBISI: in which both polynomial, at which both polynomials vanish. 41 00:03:44.970 --> 00:03:53.840 Salvatore RIBISI: which, given by the intersection of U equal u minus and v equal to e plus. So this is a sphere which is given which is at a given 42 00:03:54.260 --> 00:04:00.920 Salvatore RIBISI: model, given time and at the given radius, which depends on the 43 00:04:00.990 --> 00:04:07.080 Salvatore RIBISI: under their say, intersection of the divide goes. So we put now all this information 44 00:04:07.200 --> 00:04:10.000 Salvatore RIBISI: in a space time diagram. 45 00:04:10.570 --> 00:04:11.829 Salvatore RIBISI: So here. 46 00:04:12.210 --> 00:04:14.790 Salvatore RIBISI: yeah, we have Minkowski space time 47 00:04:14.900 --> 00:04:17.060 Salvatore RIBISI: and with the integral lines. 48 00:04:17.480 --> 00:04:21.700 Salvatore RIBISI: oh, of Xai. But this family of conformity fields. 49 00:04:22.220 --> 00:04:31.110 Salvatore RIBISI: So you see that site defines to conform a killing horizons at the past and future lightcoms of these 2 events. 50 00:04:31.510 --> 00:04:34.100 Salvatore RIBISI: or plus and or minus 51 00:04:36.290 --> 00:04:44.300 Salvatore RIBISI: each horizon, as a constant, conformal, invariant surface gravity defined via the gradient of 52 00:04:44.340 --> 00:04:46.910 Salvatore RIBISI: of the norm of sites, Esther. 53 00:04:49.060 --> 00:04:55.830 Salvatore RIBISI: and then we come at the first analogy with black holes, which are, which is, that events is pastime. 54 00:04:56.450 --> 00:05:04.600 Salvatore RIBISI: are separated as in spherical, each aspherical charge, black codes. So here you will have that region to 55 00:05:04.670 --> 00:05:08.420 Salvatore RIBISI: where the confirm activity field 56 00:05:08.590 --> 00:05:09.980 Salvatore RIBISI: is like. Like. 57 00:05:10.610 --> 00:05:15.399 Salvatore RIBISI: You will let the analogus of the outer region of a black hole. 58 00:05:16.610 --> 00:05:22.060 Salvatore RIBISI: and this would be the outside, out the horizon horizon. 59 00:05:22.290 --> 00:05:27.430 Salvatore RIBISI: and here, on the future light, colourful plans, you will have the inner horizon. 60 00:05:29.390 --> 00:05:30.414 Salvatore RIBISI: another 61 00:05:31.480 --> 00:05:37.780 Salvatore RIBISI: announce with the alright with the horizons of black hole horizons, is that the topology is the same. 62 00:05:37.990 --> 00:05:42.280 Salvatore RIBISI: namely, s. 2 cross r. So a sphere 63 00:05:42.560 --> 00:05:43.640 Salvatore RIBISI: cross R, 64 00:05:44.130 --> 00:05:47.019 Salvatore RIBISI: so this diagram also exists 65 00:05:47.080 --> 00:05:51.699 Salvatore RIBISI: in the, as also an extreme alversion, which is when 66 00:05:52.020 --> 00:05:54.329 Salvatore RIBISI: or plus, coincides 67 00:05:54.430 --> 00:05:55.900 Salvatore RIBISI: with or minus. 68 00:05:56.780 --> 00:05:59.359 Salvatore RIBISI: And so region one 69 00:05:59.400 --> 00:06:01.570 Salvatore RIBISI: shrinks to 0, 70 00:06:02.060 --> 00:06:05.550 Salvatore RIBISI: and we only have region 2, and this region 71 00:06:05.760 --> 00:06:12.759 Salvatore RIBISI: above and below, and the conforming field is time, like everywhere, but 72 00:06:12.980 --> 00:06:15.740 Salvatore RIBISI: on the future path, light on where it's 73 00:06:16.190 --> 00:06:17.670 Salvatore RIBISI: whether it's now 74 00:06:17.720 --> 00:06:20.709 Salvatore RIBISI: and the surface gravity will be 0. 75 00:06:22.260 --> 00:06:25.190 Salvatore RIBISI: Okay, starting from 76 00:06:25.430 --> 00:06:27.409 Salvatore RIBISI: this fact. So I think from 77 00:06:28.000 --> 00:06:31.230 Salvatore RIBISI: this is from these properties. 78 00:06:31.750 --> 00:06:33.610 Salvatore RIBISI: the ransom tires 79 00:06:34.150 --> 00:06:39.169 Salvatore RIBISI: found the so-called laws of light con thermodynamics. 80 00:06:40.370 --> 00:06:46.120 Salvatore RIBISI: So the 0 slope is that the surface gravity is indeed constant 81 00:06:46.260 --> 00:06:49.720 Salvatore RIBISI: on the conformal killing horizon. 82 00:06:51.010 --> 00:06:55.629 Salvatore RIBISI: Then there is the first load, which is very many results that 83 00:06:56.080 --> 00:07:01.079 Salvatore RIBISI: under conformal environment matter, perturbation. So if you perturbed 84 00:07:01.360 --> 00:07:08.619 Salvatore RIBISI: the Minkowski metric with conformal environment, you end up with a balance flow 85 00:07:09.200 --> 00:07:11.450 Salvatore RIBISI: which you can find here. So 86 00:07:12.020 --> 00:07:17.099 Salvatore RIBISI: all the quantities appear in the balance through our conformal environment. 87 00:07:17.700 --> 00:07:23.820 Salvatore RIBISI: But we have to be careful with the, with their interpretation. So we already saw what's Kappa? 88 00:07:23.960 --> 00:07:29.560 Salvatore RIBISI: Which in this formula is the equivalent of the temperature. 89 00:07:29.970 --> 00:07:36.579 Salvatore RIBISI: and is the charge associated with the with the scope for marketing field. 90 00:07:37.500 --> 00:07:46.610 Salvatore RIBISI: and the area is a conformal, invariant generalization of the area that takes into account the fact that the area of the horizon 91 00:07:46.920 --> 00:07:51.730 Salvatore RIBISI: would also increase without any matter perturbation. 92 00:07:52.740 --> 00:07:54.830 Salvatore RIBISI: So this is the remote result. 93 00:07:55.660 --> 00:08:01.330 Salvatore RIBISI: They find a second law that Gsa's that states that 94 00:08:01.630 --> 00:08:04.299 Salvatore RIBISI: this area can only increase. 95 00:08:05.500 --> 00:08:08.419 Salvatore RIBISI: and as a third law defined that. 96 00:08:09.616 --> 00:08:13.000 Salvatore RIBISI: The extreme version of the 97 00:08:13.240 --> 00:08:17.409 Salvatore RIBISI: of the diagrams of the 3 month conform opportunities 98 00:08:17.740 --> 00:08:20.200 Salvatore RIBISI: have vanishing temperature. 99 00:08:20.630 --> 00:08:22.370 Salvatore RIBISI: as we already said. 100 00:08:22.410 --> 00:08:24.780 Salvatore RIBISI: as well as vanishing entropy. 101 00:08:25.030 --> 00:08:31.059 Salvatore RIBISI: Okay? Because also the area of the my 4 kit sphere in that case would be 102 00:08:31.380 --> 00:08:32.700 Salvatore RIBISI: will be 0. 103 00:08:32.960 --> 00:08:35.100 Salvatore RIBISI: Okay, so far, so good. So this is. 104 00:08:35.350 --> 00:08:37.949 Salvatore RIBISI: if you want, like the 105 00:08:38.419 --> 00:08:42.969 Salvatore RIBISI: the setting of light or thermodynamics. 106 00:08:44.800 --> 00:08:46.200 Salvatore RIBISI: But 107 00:08:48.230 --> 00:08:54.870 Salvatore RIBISI: we have this analogy, they in their work. They also find the the meaning 108 00:08:55.540 --> 00:09:01.610 Salvatore RIBISI: of the temperature in in some circumstances, what we, what I want to show 109 00:09:01.750 --> 00:09:07.059 Salvatore RIBISI: is that you can actually find, decompose the 110 00:09:07.410 --> 00:09:09.739 Salvatore RIBISI: they might. Let me then go ski vacuum 111 00:09:09.860 --> 00:09:15.679 Salvatore RIBISI: in terms of particles associated to this conforming field. 112 00:09:16.050 --> 00:09:19.150 Salvatore RIBISI: and the the temperature that we find 113 00:09:19.420 --> 00:09:23.740 Salvatore RIBISI: is indeed related to this the composition. 114 00:09:24.350 --> 00:09:25.770 Salvatore RIBISI: So let's 115 00:09:26.040 --> 00:09:28.699 Salvatore RIBISI: clarify some points first. 116 00:09:29.160 --> 00:09:34.630 Salvatore RIBISI: So the integral lines of psi. So the trajectory of 117 00:09:34.710 --> 00:09:37.810 Salvatore RIBISI: date, the site of the I mean of 118 00:09:37.860 --> 00:09:39.230 Salvatore RIBISI: sign you, if you want. 119 00:09:40.090 --> 00:09:49.579 Salvatore RIBISI: corresponds to observers accelerating readily with a constant acceleration which is not given by by Kappa. 120 00:09:49.890 --> 00:09:54.740 Salvatore RIBISI: but is, I mean which, but it's still proportional to it. And here you are 121 00:09:54.860 --> 00:09:57.010 Salvatore RIBISI: the concept of proportionality. 122 00:09:57.640 --> 00:10:08.259 Salvatore RIBISI: however, the temperature measured by a non-devite detector will not be the temperature we are mentioning here, but the usual A over to buy. 123 00:10:08.440 --> 00:10:20.239 Salvatore RIBISI: And this is due to the fact that under the detector breaks conformal environment, so you you can try to model a scale environment detector. 124 00:10:20.520 --> 00:10:31.280 Salvatore RIBISI: The the text, the temperature Kappa. But we believe that the interest of this decomposition relies rather on global features 125 00:10:31.680 --> 00:10:36.020 Salvatore RIBISI: of the volume, then to local measurements. 126 00:10:38.070 --> 00:10:39.030 Salvatore RIBISI: So 127 00:10:41.350 --> 00:10:43.290 Salvatore RIBISI: and that'd be the same. 128 00:10:44.370 --> 00:10:48.473 Salvatore RIBISI: Let's start showing the the our 129 00:10:49.280 --> 00:10:53.370 Salvatore RIBISI: and the results of our work and the path 130 00:10:54.070 --> 00:11:04.710 Salvatore RIBISI: that leads to it. So please, if you ever have any doubts, feel free to interrupt me, because I think all the steps are easy. 131 00:11:04.800 --> 00:11:07.859 Salvatore RIBISI: But if for any reason 132 00:11:08.120 --> 00:11:12.059 Salvatore RIBISI: you you missed one, which probably means that I haven't been clear enough. 133 00:11:12.310 --> 00:11:15.439 Salvatore RIBISI: It's better for everybody than if you stop me 134 00:11:15.950 --> 00:11:17.070 Salvatore RIBISI: so. 135 00:11:17.070 --> 00:11:26.060 Ivan Agullo: So, Salvatore. Yes, just a clarification. You have 1 one such the composition for each choice of raviol conformal killing Baker Field right. 136 00:11:29.980 --> 00:11:31.300 Salvatore RIBISI: With patient 137 00:11:31.992 --> 00:11:34.559 Salvatore RIBISI: so that the composition 138 00:11:35.920 --> 00:11:37.790 Salvatore RIBISI: it's as if in the 139 00:11:38.310 --> 00:11:39.840 Salvatore RIBISI: I will. Didn't say 140 00:11:40.190 --> 00:11:42.619 Salvatore RIBISI: I mean, it's for Evan is 141 00:11:42.630 --> 00:11:48.400 Salvatore RIBISI: family of radiant conformity. I understand one such the composition 142 00:11:48.880 --> 00:11:51.340 Salvatore RIBISI: for every 143 00:11:51.460 --> 00:11:57.140 Salvatore RIBISI: given family of conformal candidates, so I have a family given by some parameters. 144 00:11:59.360 --> 00:12:05.999 Salvatore RIBISI: so every parameter, like a choice of parameter, gives 145 00:12:06.651 --> 00:12:13.670 Salvatore RIBISI: alike that our big rise to this light comes to Disco for marketing horizons. 146 00:12:13.990 --> 00:12:16.650 Salvatore RIBISI: and then you can make the composition. 147 00:12:16.840 --> 00:12:17.820 Salvatore RIBISI: But I mean. 148 00:12:17.820 --> 00:12:22.019 Ivan Agullo: Of param of parameters will will shift the position of this horizons right. 149 00:12:22.020 --> 00:12:23.390 Salvatore RIBISI: Yeah, yes. Let's. 150 00:12:23.390 --> 00:12:24.960 Ivan Agullo: So, so thank you. 151 00:12:28.830 --> 00:12:32.149 Salvatore RIBISI: Thank for the question, Ivan, So 152 00:12:32.590 --> 00:12:47.249 Salvatore RIBISI: the first step to write the Mikosky vacuum as a proposition of particle sets associated to site. We want. We need to characterize positive frequency solutions of the client or delegation with respect to inertial time on a light theme. 153 00:12:47.440 --> 00:12:53.950 Salvatore RIBISI: So to do that we start by solving the simplest equation in the history of Ifgs, which is 154 00:12:54.230 --> 00:12:58.360 Salvatore RIBISI: the scalar field, the question for a massless scalar field. 155 00:12:58.840 --> 00:13:00.800 Salvatore RIBISI: So we do that 156 00:13:01.290 --> 00:13:05.549 Salvatore RIBISI: we know, we can decompose the solution in terms of harmonics 157 00:13:06.192 --> 00:13:10.450 Salvatore RIBISI: spherical harmonics, spherical harmonics, and already a part. 158 00:13:10.670 --> 00:13:16.750 Salvatore RIBISI: We solve the equation. So the language of the question becomes an equation for its radial part. 159 00:13:17.010 --> 00:13:20.230 Salvatore RIBISI: which is solved by the hysterical business functions. 160 00:13:21.370 --> 00:13:22.340 Salvatore RIBISI: So 161 00:13:22.740 --> 00:13:24.950 Salvatore RIBISI: we now we find that we loop 162 00:13:25.030 --> 00:13:26.579 Salvatore RIBISI: for a surface 163 00:13:26.650 --> 00:13:36.900 Salvatore RIBISI: where the decomposition will be made, and we notice that since we are dealing with a non object. 164 00:13:37.420 --> 00:13:42.469 Salvatore RIBISI: the solutions are completely characterizing the union of the past 165 00:13:42.680 --> 00:13:47.170 Salvatore RIBISI: and future light, Tom, which is the red surface you can see 166 00:13:47.440 --> 00:13:55.470 Salvatore RIBISI: in this diagram. So we evaluate now our solutions in this surface. 167 00:13:57.200 --> 00:14:02.140 Salvatore RIBISI: So this surface is given by U. Equal RH. 168 00:14:02.870 --> 00:14:07.800 Salvatore RIBISI: For the future, light on and vehicle our age 169 00:14:08.050 --> 00:14:13.510 Salvatore RIBISI: in the in the past light on. So we replace this. 170 00:14:14.720 --> 00:14:21.330 Salvatore RIBISI: We replace these quantities in the solution, and we noticed that now the solution splits in 2 parts. 171 00:14:21.790 --> 00:14:23.889 Salvatore RIBISI: one which is defined. 172 00:14:23.960 --> 00:14:26.920 Salvatore RIBISI: or V bigger than RH. 173 00:14:27.290 --> 00:14:29.189 Salvatore RIBISI: And one which is defined 174 00:14:29.210 --> 00:14:34.280 Salvatore RIBISI: for you smaller than our age, which is the past license. 175 00:14:35.320 --> 00:14:36.340 Salvatore RIBISI: So 176 00:14:36.540 --> 00:14:43.859 Salvatore RIBISI: this solution, this whole solution, then, can be written in terms of a single variable which covers the whole real line. 177 00:14:45.850 --> 00:14:47.470 Salvatore RIBISI: A. 178 00:14:47.640 --> 00:14:48.610 Salvatore RIBISI: So 179 00:14:49.210 --> 00:14:51.970 Salvatore RIBISI: this a 180 00:14:52.300 --> 00:14:57.939 Salvatore RIBISI: in this case, in terms of the single variable spanning from minus infinity to plus infinity 181 00:14:58.880 --> 00:15:02.889 Salvatore RIBISI: solutions of the Glen Gordon equation. Take this forward 182 00:15:02.940 --> 00:15:04.170 Salvatore RIBISI: or day. 183 00:15:05.110 --> 00:15:07.830 Salvatore RIBISI: 5. First of all is analytic. 184 00:15:08.260 --> 00:15:13.419 Salvatore RIBISI: since it's the product of analytic function. And now the question is. 185 00:15:14.240 --> 00:15:17.010 Salvatore RIBISI: what? How do we correct? How do we characterize 186 00:15:17.110 --> 00:15:19.260 Salvatore RIBISI: positive omega solutions? 187 00:15:20.490 --> 00:15:30.120 Salvatore RIBISI: 200 equation. Again, we have to look now where this this function really solution is bounded 188 00:15:30.800 --> 00:15:37.249 Salvatore RIBISI: to, since they is, it is analytic to see where it is bounded. We have to do the expansion for large set. 189 00:15:37.270 --> 00:15:43.489 Salvatore RIBISI: We do it, and very good. So this is the the form of depression which you could probably expect. 190 00:15:44.200 --> 00:15:54.070 Salvatore RIBISI: and the solution from this solution you see that it is bounded. Once you look at it in the complex plane. 191 00:15:54.690 --> 00:16:00.530 Salvatore RIBISI: for in the for negative imaginary part of that. 192 00:16:01.610 --> 00:16:03.890 Salvatore RIBISI: so to to resume this result. 193 00:16:04.720 --> 00:16:12.359 Salvatore RIBISI: positive frequency solutions are analytic functions of that bounded in the lower half complex plane. 194 00:16:12.570 --> 00:16:14.530 Salvatore RIBISI: Imaginary part of that 195 00:16:14.580 --> 00:16:16.219 Salvatore RIBISI: is more than 0. 196 00:16:16.700 --> 00:16:18.990 Salvatore RIBISI: So very good. 197 00:16:19.630 --> 00:16:27.790 Salvatore RIBISI: This is more the same result that you would get by starting solution on a on a plane. 198 00:16:28.260 --> 00:16:37.029 Salvatore RIBISI: But okay, we. It was necessary to see if everything will be the same for the the composition on a light phone. 199 00:16:37.280 --> 00:16:38.490 Salvatore RIBISI: Now that 200 00:16:38.670 --> 00:16:41.290 Salvatore RIBISI: a this has been done. 201 00:16:41.510 --> 00:16:46.289 Salvatore RIBISI: we want to characterize positive frequency solutions associated to Xi. 202 00:16:47.720 --> 00:16:48.680 Salvatore RIBISI: So 203 00:16:49.441 --> 00:16:59.320 Salvatore RIBISI: we take account. Ordinary transformation, as you will usually do if you look in the for ringler. 204 00:16:59.540 --> 00:17:01.920 Salvatore RIBISI: for the vendor decomposition. 205 00:17:02.260 --> 00:17:06.760 Salvatore RIBISI: and under this coordinate transformation the Minkowski metric. 206 00:17:07.550 --> 00:17:11.909 Salvatore RIBISI: So this coordinate transformation is valid in the region, too. 207 00:17:12.630 --> 00:17:21.140 Salvatore RIBISI: and the Minkowski metric appears as a conformal factor, which depends on this style and row variable 208 00:17:21.810 --> 00:17:23.900 Salvatore RIBISI: times this metric. 209 00:17:24.670 --> 00:17:27.390 Salvatore RIBISI: So you immediately notice that the 210 00:17:27.859 --> 00:17:29.600 Salvatore RIBISI: conformal metric 211 00:17:30.200 --> 00:17:32.250 Salvatore RIBISI: is independent of Tao. 212 00:17:33.210 --> 00:17:39.329 Salvatore RIBISI: and so the only part of the measuring which depends on Tao is the conformal factor. 213 00:17:39.560 --> 00:17:42.400 Salvatore RIBISI: and therefore then the Tao is 214 00:17:42.874 --> 00:17:49.749 Salvatore RIBISI: I go for marketing field of the schematic. No surprises. Then the towel is actually our signing. 215 00:17:51.840 --> 00:17:52.910 Salvatore RIBISI: So 216 00:17:53.510 --> 00:17:55.150 Salvatore RIBISI: we want to study. 217 00:17:55.360 --> 00:17:58.670 Salvatore RIBISI: then the solutions which are related 218 00:17:58.690 --> 00:18:01.540 Salvatore RIBISI: with the solution. With respect to Dow. 219 00:18:02.770 --> 00:18:07.099 Salvatore RIBISI: and to do this we use properties 220 00:18:07.250 --> 00:18:09.919 Salvatore RIBISI: of of the sort of fields. 221 00:18:09.940 --> 00:18:19.130 Salvatore RIBISI: and I mean that we? We look at the way they scale under coordinate under conformal transformations. So you know how the metric transformed. 222 00:18:19.510 --> 00:18:23.659 Salvatore RIBISI: and we also know how solutions of the conformally mapped. 223 00:18:23.850 --> 00:18:26.440 Salvatore RIBISI: a Klein Gordon equation. 224 00:18:26.600 --> 00:18:28.870 Salvatore RIBISI: our transform. 225 00:18:30.430 --> 00:18:37.229 Salvatore RIBISI: And we can use this one, because, of course, we are in Minkowski. So the the rich scalar is 0. 226 00:18:38.250 --> 00:18:40.240 Salvatore RIBISI: So the solution 227 00:18:40.270 --> 00:18:51.690 Salvatore RIBISI: on the on, the in the conformal metric. Again, take this form, so we can again decompose, because of spherical symmetry into spherical harmonics 228 00:18:52.160 --> 00:18:59.730 Salvatore RIBISI: and and impose this time dependence. And then it became becomes again 229 00:19:00.170 --> 00:19:04.049 Salvatore RIBISI: the clergonal equation becomes again an equation for the radial part. 230 00:19:04.260 --> 00:19:09.220 Salvatore RIBISI: We solve it, and we get this equation, let us first lose 231 00:19:09.320 --> 00:19:12.459 Salvatore RIBISI: might seem hard to to solve. 232 00:19:13.620 --> 00:19:15.100 Salvatore RIBISI: but 233 00:19:15.400 --> 00:19:16.950 Salvatore RIBISI: we were interested 234 00:19:17.080 --> 00:19:22.600 Salvatore RIBISI: interested into evaluating the solution near this boundary. 235 00:19:22.990 --> 00:19:24.940 Salvatore RIBISI: and so near this boundary 236 00:19:25.240 --> 00:19:30.410 Salvatore RIBISI: row. If you look at the coordinate Transformation row goes to infinity. 237 00:19:30.810 --> 00:19:34.719 Salvatore RIBISI: therefore this effective potential vanishes 238 00:19:35.170 --> 00:19:44.629 Salvatore RIBISI: and and the radial solution becomes trivial, become trivial, trivial, exponential. 239 00:19:45.080 --> 00:19:48.809 Salvatore RIBISI: and this is the form of the of the 240 00:19:49.520 --> 00:19:51.739 Salvatore RIBISI: of the solution of the equation. 241 00:19:52.160 --> 00:19:55.879 Salvatore RIBISI: So now we have to bring this solution 242 00:19:55.900 --> 00:20:01.290 Salvatore RIBISI: on the again in the middle schematic through a conformal transformation. 243 00:20:02.600 --> 00:20:09.780 Salvatore RIBISI: And this is our view. So here we used the the inverse transformation between 244 00:20:10.170 --> 00:20:14.159 Salvatore RIBISI: Tau, raw, variable, and D and R. 245 00:20:15.150 --> 00:20:16.120 Salvatore RIBISI: So 246 00:20:16.260 --> 00:20:20.060 Salvatore RIBISI: phi. 2 is a solution with respect 247 00:20:20.200 --> 00:20:22.910 Salvatore RIBISI: to the toxi 248 00:20:23.840 --> 00:20:25.479 Salvatore RIBISI: in Region 2, 249 00:20:27.640 --> 00:20:31.019 Salvatore RIBISI: we can do the similar 250 00:20:31.050 --> 00:20:37.150 Salvatore RIBISI: work to for for one. And so we get the solutions here. 251 00:20:37.780 --> 00:20:40.780 Salvatore RIBISI: and the solution in region, too. Very good. 252 00:20:40.970 --> 00:20:45.248 Salvatore RIBISI: What we want to do like the reason we did that is because we want to find. 253 00:20:46.783 --> 00:20:50.649 Salvatore RIBISI: A combination of these 2 254 00:20:51.150 --> 00:20:53.580 Salvatore RIBISI: of these 2 solutions 255 00:20:54.030 --> 00:21:00.660 Salvatore RIBISI: that, is positive frequency with respect to inversion. Time 256 00:21:02.120 --> 00:21:07.490 Salvatore RIBISI: to do that, we start by. Take this complex function. 257 00:21:08.020 --> 00:21:12.890 Salvatore RIBISI: F. Omega, that you see really looks very much like 258 00:21:13.260 --> 00:21:14.780 Salvatore RIBISI: 5, 2. 259 00:21:16.270 --> 00:21:17.760 Salvatore RIBISI: And we evaluate 260 00:21:17.920 --> 00:21:22.559 Salvatore RIBISI: in the lower half complex plane. So you see that 261 00:21:22.860 --> 00:21:28.160 Salvatore RIBISI: the only problems of this function are in the real line. 262 00:21:28.230 --> 00:21:33.090 Salvatore RIBISI: So everything is well behaving on the. 263 00:21:33.360 --> 00:21:36.140 Salvatore RIBISI: on the lower health complex plane. 264 00:21:37.330 --> 00:21:41.840 Salvatore RIBISI: And so we evaluate this function close to the 265 00:21:42.140 --> 00:21:45.160 Salvatore RIBISI: close, to the real line. So 266 00:21:46.540 --> 00:21:47.330 Salvatore RIBISI: for 267 00:21:48.730 --> 00:21:54.460 Salvatore RIBISI: of course, for Z, for x, for for the real part of Z, 268 00:21:54.920 --> 00:22:02.020 Salvatore RIBISI: which is the right interval so bigger than our H smaller than minus our H. 269 00:22:02.380 --> 00:22:07.360 Salvatore RIBISI: There is no problem. You immediately see that it coincides with i. 2. 270 00:22:08.400 --> 00:22:11.949 Salvatore RIBISI: We have to do a bit of complex analysis to check 271 00:22:12.280 --> 00:22:18.360 Salvatore RIBISI: what happens when we evaluate it in in between minus our age and our age. 272 00:22:19.240 --> 00:22:20.150 Salvatore RIBISI: So 273 00:22:20.500 --> 00:22:26.719 Salvatore RIBISI: you you start by evaluating it at this point. You do all the computation by 274 00:22:27.290 --> 00:22:28.830 Salvatore RIBISI: by me 275 00:22:30.130 --> 00:22:33.360 Salvatore RIBISI: doing the right rotation in the 276 00:22:33.550 --> 00:22:42.459 Salvatore RIBISI: in the complex plane. You get the wrong sign, you redo the computation, and you finally get this result, which is that 277 00:22:43.040 --> 00:22:44.040 Salvatore RIBISI: F. 278 00:22:44.250 --> 00:22:54.469 Salvatore RIBISI: Omega. So this positive frequency solution with respect to inertial time, when evaluated between minus RH. And RH. 279 00:22:56.140 --> 00:23:02.860 Salvatore RIBISI: Gives you an exponential factor. Times a negative frequency solution. With respect to the 280 00:23:03.090 --> 00:23:04.590 Salvatore RIBISI: A 281 00:23:05.080 --> 00:23:07.890 Salvatore RIBISI: with respect to Xi in region one. 282 00:23:09.450 --> 00:23:13.969 Salvatore RIBISI: You can do the same by defining a solution which looks like 283 00:23:13.980 --> 00:23:15.410 Salvatore RIBISI: Taiwan. 284 00:23:17.950 --> 00:23:20.340 Salvatore RIBISI: And so what you get 285 00:23:20.360 --> 00:23:23.050 Salvatore RIBISI: is that FW. 286 00:23:23.310 --> 00:23:25.299 Salvatore RIBISI: And that W. Prime 287 00:23:25.950 --> 00:23:35.199 Salvatore RIBISI: are analytic and bounded in the lower half plane in terms of the Mikos people routine. Thus they are positive frequency solution. 288 00:23:35.950 --> 00:23:38.470 Salvatore RIBISI: So at this point 289 00:23:39.470 --> 00:23:46.359 Salvatore RIBISI: you can make the usual, the composition you you are used to since 290 00:23:46.750 --> 00:23:49.579 Salvatore RIBISI: Aru. So you you see that 291 00:23:50.000 --> 00:23:57.779 Salvatore RIBISI: you can take the Annihilator and Creator operators associated to 5, 2 and 5, one. 292 00:23:58.120 --> 00:24:04.450 Salvatore RIBISI: and you know that they once applied on the Nikosi volume, they they give you 0, 293 00:24:04.740 --> 00:24:08.740 Salvatore RIBISI: and by recurrence you can find that that 294 00:24:09.090 --> 00:24:15.649 Salvatore RIBISI: that then the the Minkowski Vacuum appears as appropriate state of 295 00:24:15.950 --> 00:24:19.850 Salvatore RIBISI: of the sum, I mean, of the and then you get the third mistake 296 00:24:20.600 --> 00:24:22.000 Salvatore RIBISI: of particles 297 00:24:22.200 --> 00:24:24.470 Salvatore RIBISI: belonging to region one 298 00:24:24.910 --> 00:24:27.260 Salvatore RIBISI: and belonging to Region 2. 299 00:24:28.500 --> 00:24:29.430 Salvatore RIBISI: So 300 00:24:30.290 --> 00:24:31.340 Salvatore RIBISI: so far. 301 00:24:32.008 --> 00:24:38.370 Salvatore RIBISI: There is a subtlety that I have not. That which 302 00:24:38.770 --> 00:24:42.299 Salvatore RIBISI: which is the fact that 303 00:24:42.670 --> 00:24:50.159 Salvatore RIBISI: what I have actually done is that the composition in the regions that you see in red and in blue. 304 00:24:50.760 --> 00:24:53.589 Salvatore RIBISI: in my, in my spacetime diagram? 305 00:24:54.690 --> 00:25:04.359 Salvatore RIBISI: So actually, you have particles here. So in the past horizon of Region 2, and the past horizon of region 3. 306 00:25:05.310 --> 00:25:11.040 Salvatore RIBISI: Associated 2 particles in the future horizon of region one. 307 00:25:11.970 --> 00:25:13.490 Salvatore RIBISI: So this 308 00:25:13.620 --> 00:25:16.730 Salvatore RIBISI: should be the actual decomposition. 309 00:25:17.500 --> 00:25:19.140 Salvatore RIBISI: But 310 00:25:19.650 --> 00:25:24.260 Salvatore RIBISI: we can make an identification which can be done explicitly 311 00:25:25.180 --> 00:25:27.030 Salvatore RIBISI: of the Hilbert spaces 312 00:25:27.210 --> 00:25:30.449 Salvatore RIBISI: in this surface in the past of Region 3. 313 00:25:30.910 --> 00:25:34.020 Salvatore RIBISI: And in the future horizon. 314 00:25:34.110 --> 00:25:35.380 Salvatore RIBISI: Or we can do 315 00:25:35.950 --> 00:25:42.349 Salvatore RIBISI: through this identification by studying, studying the solution in the 2 boundaries. 316 00:25:42.710 --> 00:25:47.069 Salvatore RIBISI: Then we we get the results when I show them the mode. 317 00:25:47.610 --> 00:25:48.680 Salvatore RIBISI: Okay. 318 00:25:51.400 --> 00:25:53.900 Salvatore RIBISI: so what are the 319 00:25:53.950 --> 00:25:59.690 Salvatore RIBISI: perspectives on this work like, what are we thinking about 320 00:26:00.400 --> 00:26:03.539 Salvatore RIBISI: when studying this problem 321 00:26:03.810 --> 00:26:05.920 Salvatore RIBISI: well, and 322 00:26:05.960 --> 00:26:09.660 Salvatore RIBISI: there are several. So the most immediate one 323 00:26:10.370 --> 00:26:14.319 Salvatore RIBISI: comes from the fact that the laws of light control thermodynamics 324 00:26:14.350 --> 00:26:17.749 Salvatore RIBISI: can be extended to any conformally flat space time. 325 00:26:18.400 --> 00:26:30.650 Salvatore RIBISI: and there are some. There is a list of space. That's where we know thermal properties of one 326 00:26:30.700 --> 00:26:33.100 Salvatore RIBISI: quantization with respect to the other. 327 00:26:33.580 --> 00:26:46.860 Salvatore RIBISI: and we can expect there to take me to get to have a similar decomposition of one budget with respect to particle belonging to different quantizations. 328 00:26:49.410 --> 00:26:55.899 Salvatore RIBISI: Then there is another perspective, which is probably, I mean 329 00:26:56.570 --> 00:26:59.160 Salvatore RIBISI: more. I don't know. 330 00:26:59.200 --> 00:27:00.500 Salvatore RIBISI: More involved 331 00:27:00.640 --> 00:27:05.999 Salvatore RIBISI: comes from the fact that the temperature and the entropy of conformal horizons 332 00:27:07.130 --> 00:27:18.669 Salvatore RIBISI: have been used by these authors to get wide transverse gravity using local thermodynamic approach. So they they argue that if you use. 333 00:27:18.740 --> 00:27:21.160 Salvatore RIBISI: and actually the low customeratic approach. 334 00:27:21.470 --> 00:27:23.584 Salvatore RIBISI: instead of getting 335 00:27:24.970 --> 00:27:30.570 Salvatore RIBISI: general relativity. What you actually get is a live transverse gravity. 336 00:27:30.810 --> 00:27:35.020 Salvatore RIBISI: which is generalization of unimodularity. 337 00:27:35.660 --> 00:27:48.530 Salvatore RIBISI: They evoke some mechanism which has been already managed by Paris, Sebastian, New York, and work non-conformal bar matter 338 00:27:48.780 --> 00:27:53.730 Salvatore RIBISI: will be in that case the source for the cosmological constant. 339 00:27:53.960 --> 00:27:59.299 Salvatore RIBISI: So my idea is that quantifying kind of quote unquote. The violation 340 00:27:59.620 --> 00:28:08.560 Salvatore RIBISI: light, conform thermodynamics by this nonconformal matter may give insights of this object, so maybe we can give 341 00:28:08.600 --> 00:28:10.320 Salvatore RIBISI: quantification of 342 00:28:10.730 --> 00:28:12.000 Salvatore RIBISI: a 343 00:28:12.150 --> 00:28:15.977 Salvatore RIBISI: if like. If there is an actual link between the 344 00:28:16.680 --> 00:28:19.960 Salvatore RIBISI: speculation that have been done in this paper. 345 00:28:20.130 --> 00:28:24.529 Salvatore RIBISI: and the mechanism which is being started by 346 00:28:24.570 --> 00:28:26.990 Salvatore RIBISI: these are all source. 347 00:28:27.530 --> 00:28:29.549 Salvatore RIBISI: But as that can be working. 348 00:28:31.640 --> 00:28:35.740 Salvatore RIBISI: another interesting perspective, in my point of view. 349 00:28:36.370 --> 00:28:50.299 Salvatore RIBISI: comes from the study of moving mirrors, which is usually done in one plus one dimensions. So there are several reasons, of course, why it's done in one plus one dimension. One is that that 350 00:28:50.670 --> 00:28:52.596 Salvatore RIBISI: and the 351 00:28:53.880 --> 00:28:59.350 Salvatore RIBISI: the trajectories of moving plane gives 352 00:28:59.630 --> 00:29:04.339 Salvatore RIBISI: gives like our like radiation and 353 00:29:04.570 --> 00:29:06.219 Salvatore RIBISI: bring their own. Servers 354 00:29:06.630 --> 00:29:13.269 Salvatore RIBISI: are, are not spherically symmetric. So one side 355 00:29:13.690 --> 00:29:19.340 Salvatore RIBISI: of the problem comes from the non spherical symmetricity. If you want of 356 00:29:19.840 --> 00:29:30.910 Salvatore RIBISI: of ringer observers of 5 min of ringer observers. So in this case, I think that this different decomposition, which is spherically symmetric, might help 357 00:29:31.140 --> 00:29:34.129 Salvatore RIBISI: building some models of 358 00:29:35.020 --> 00:29:37.249 Salvatore RIBISI: of spherical is in metric. 359 00:29:37.270 --> 00:29:43.539 Salvatore RIBISI: me worse, and trying to build some unitary model where you can start with the 360 00:29:43.890 --> 00:29:46.810 Salvatore RIBISI: their, their, their effects and their properties. 361 00:29:47.330 --> 00:29:58.469 Salvatore RIBISI: On the other hand, another reason, of course, is that one plus one dimensional conformatory theory is easier way, more easier way, easier than 362 00:29:58.860 --> 00:30:08.500 Salvatore RIBISI: the 3 plus one dimensional. And okay for this complication. They I don't have any help to be like this is 363 00:30:08.900 --> 00:30:10.630 Salvatore RIBISI: this, of course, a fact. 364 00:30:11.010 --> 00:30:15.500 Salvatore RIBISI: But I hope that the previous problem is can be. 365 00:30:15.550 --> 00:30:19.930 Salvatore RIBISI: can still be overcome by this by this analysis. 366 00:30:21.160 --> 00:30:22.990 Salvatore RIBISI: So there is also some work 367 00:30:23.340 --> 00:30:28.610 Salvatore RIBISI: by some collaborators where they show that where they find this conformal temperature 368 00:30:29.260 --> 00:30:34.079 Salvatore RIBISI: in the in the context of conformal quantum mechanics. 369 00:30:35.570 --> 00:30:38.690 Salvatore RIBISI: And yeah, I'm also interested to see it 370 00:30:39.180 --> 00:30:42.319 Salvatore RIBISI: like, what is the direct link from 371 00:30:42.350 --> 00:30:44.380 Salvatore RIBISI: quantum mechanics to 372 00:30:44.730 --> 00:30:46.080 Salvatore RIBISI: to to 373 00:30:46.400 --> 00:30:58.049 Salvatore RIBISI: I mean for dimension of one to fifth theory. And if there is a way to to explain this relation? Directly, because I mean events the same, they find the same temperature. 374 00:30:58.230 --> 00:31:04.394 Salvatore RIBISI: and that's similar, the composition. So I want to see what are the limits of this 375 00:31:06.050 --> 00:31:11.339 Salvatore RIBISI: of the of their analysis. And what are the the nice properties? Instead? 376 00:31:13.380 --> 00:31:25.080 Salvatore RIBISI: I didn't get into the hand, I promise. So they come with the perspective. So in another one comes from the area of measurements. In point of view, theory, where 377 00:31:25.370 --> 00:31:28.990 Salvatore RIBISI: the algebra of observables related to apparatuses 378 00:31:29.220 --> 00:31:35.740 Salvatore RIBISI: has come back support in the regional space, and we share the same features as total diamonds. 379 00:31:36.180 --> 00:31:38.869 Salvatore RIBISI: So I again. 380 00:31:39.190 --> 00:31:44.699 Salvatore RIBISI: I wonder if studying the the problem of measurements by 381 00:31:44.840 --> 00:31:48.260 Salvatore RIBISI: in in Nikosi space, and by different apparatuses 382 00:31:48.380 --> 00:31:54.960 Salvatore RIBISI: can make use of these results like, if there is, there is some link. 383 00:31:55.490 --> 00:32:02.810 Salvatore RIBISI: And then the last question I have like. I wonder how angular momentum will will enter this game, because 384 00:32:03.120 --> 00:32:07.430 Salvatore RIBISI: there are insights here and there that 385 00:32:07.890 --> 00:32:18.550 Salvatore RIBISI: there is a way to define a charge associated to angular momentum in this case. But of course, there are also complications given by extremality and 386 00:32:18.780 --> 00:32:21.740 Salvatore RIBISI: and rotating space times which 387 00:32:21.880 --> 00:32:29.999 Salvatore RIBISI: can be non-trivial, for in the case of Mikos in in the in the case of light comes. 388 00:32:30.390 --> 00:32:34.599 Salvatore RIBISI: So I wonder if there is a way to to study this problem 389 00:32:34.620 --> 00:32:39.460 Salvatore RIBISI: like accurately, but like finding some results with, but 390 00:32:39.690 --> 00:32:46.760 Salvatore RIBISI: without getting too much in trouble. And that's it, I guess. So thank you for the attention 391 00:32:46.810 --> 00:32:48.490 Salvatore RIBISI: I'm open to questions. 392 00:32:49.480 --> 00:32:51.329 Hal Haggard: Thank you so much. Savatory. 393 00:32:53.650 --> 00:32:55.259 Hal Haggard: Lee. Please go ahead. 394 00:32:55.630 --> 00:32:58.370 Lee Smolin: Yes, can you summarize your work? 395 00:32:58.690 --> 00:33:05.790 Lee Smolin: In a way the result is very simple. Tell me if I'm right, if you have an an ingoing. 396 00:33:05.990 --> 00:33:06.585 Lee Smolin: but 397 00:33:07.280 --> 00:33:09.580 Lee Smolin: near scry minus. 398 00:33:10.100 --> 00:33:24.080 Lee Smolin: and then you can find a new continuation of the wave function without singularity into an outgoing particle near Scribe, plus by making use of these identifications 399 00:33:24.260 --> 00:33:27.559 Lee Smolin: is that the interpretation of your result. 400 00:33:31.160 --> 00:33:32.020 Salvatore RIBISI: It. 401 00:33:32.240 --> 00:33:35.960 Salvatore RIBISI: Hurricane! Can you repeat? I'm not sure I'm getting the. 402 00:33:35.960 --> 00:33:38.490 Lee Smolin: If if I take them in going. 403 00:33:38.760 --> 00:33:39.230 Lee Smolin: aren't 404 00:33:39.850 --> 00:33:41.660 Lee Smolin: near sky minus. 405 00:33:41.740 --> 00:33:51.980 Lee Smolin: it's non singular region one I can transform and follow the wave function to a non singular outgoing quantum near spy plus 406 00:33:52.940 --> 00:33:54.130 Lee Smolin: is that, yeah? 407 00:33:55.250 --> 00:34:00.749 Lee Smolin: So that is, gives us a kind of definition of a quantum field theory 408 00:34:00.870 --> 00:34:05.920 Lee Smolin: involving both the region ingoing and the region outgoing, which is non singular. 409 00:34:06.430 --> 00:34:11.559 Lee Smolin: I think that that's that's a good. If I'm correct, that's a very interesting. Please help. 410 00:34:15.090 --> 00:34:16.876 Salvatore RIBISI: Yeah, okay. 411 00:34:24.320 --> 00:34:25.790 Salvatore RIBISI: I think. 412 00:34:28.540 --> 00:34:31.110 Lee Smolin: In. In other words, if I had a regular. 413 00:34:31.280 --> 00:34:42.149 Lee Smolin: a, a normal solution, which was singular in the region one, I wouldn't see that I could get this way. I can take a pure state incoming, you know 414 00:34:42.510 --> 00:34:45.630 Lee Smolin: the pastor region one and 2, 415 00:34:46.150 --> 00:34:49.480 Lee Smolin: and continue it to an outgoing quanta. 416 00:34:49.760 --> 00:34:51.469 Lee Smolin: which is non singular. 417 00:34:52.320 --> 00:34:52.900 Salvatore RIBISI: Right? Okay. 418 00:34:52.909 --> 00:34:54.079 Lee Smolin: 5 plots. 419 00:34:54.819 --> 00:34:57.599 Lee Smolin: So that gives you a non singular definition 420 00:34:57.809 --> 00:34:59.489 Lee Smolin: of a quantum field theory. 421 00:35:02.250 --> 00:35:07.300 Salvatore RIBISI: So having a a quanta which is non, which is non singular here in region one. 422 00:35:08.390 --> 00:35:11.739 Lee Smolin: Can join to Aquanta, which was non singular. 423 00:35:11.820 --> 00:35:14.459 Lee Smolin: falling in near sky, minus. 424 00:35:15.260 --> 00:35:16.729 Salvatore RIBISI: Right. Yes. 425 00:35:16.840 --> 00:35:19.490 Salvatore RIBISI: it will give you a non singularity. 426 00:35:23.170 --> 00:35:25.469 Lee Smolin: And so this gives you a definition 427 00:35:25.490 --> 00:35:29.380 Lee Smolin: of the states of a quantum field theory, which is time asymmetric. 428 00:35:29.730 --> 00:35:32.259 Lee Smolin: but which is non singular. 429 00:35:40.210 --> 00:35:43.409 Lee Smolin: I may be just wrong. Could somebody correct me if I am? 430 00:35:44.230 --> 00:35:48.750 Lee Smolin: But that's what I think you're you're saying here in this blue region. 431 00:35:50.150 --> 00:35:53.619 Salvatore RIBISI: Yeah, but I I'm I'm not sure I follow. What is the 432 00:35:53.740 --> 00:35:55.340 Salvatore RIBISI: singular part. 433 00:35:55.920 --> 00:35:57.189 Lee Smolin: Well, there is no single. 434 00:35:57.540 --> 00:35:59.040 Salvatore RIBISI: Alright. Okay. Yeah. Yes. 435 00:35:59.040 --> 00:36:00.349 Lee Smolin: That's important. 436 00:36:01.100 --> 00:36:02.240 Salvatore RIBISI: Yes, yes. 437 00:36:08.840 --> 00:36:13.899 Hal Haggard: You, Jen. You had a question also. If you wanna respond to Lee's request, feel free as well. 438 00:36:14.480 --> 00:36:15.540 Lee Smolin: Yes, please. 439 00:36:18.520 --> 00:36:20.480 Eugenio Bianchi: No, not really. I don't. I'm 440 00:36:20.630 --> 00:36:26.970 Eugenio Bianchi: don't have anything to add, though. I I I can go ahead and ask. Yeah, I saw a lot of real stuff. Okay? 441 00:36:28.260 --> 00:36:29.540 Salvatore RIBISI: Yeah. Yes. Please. 442 00:36:29.945 --> 00:36:35.619 Eugenio Bianchi: Salad. A very nice talk. I I have 2 questions one on 443 00:36:36.720 --> 00:36:54.170 Eugenio Bianchi: So conformal symmetry plays a central role here in the mathematics. I want to understand. What is your perspective on the physics? Do you need conformal symmetry to speak about thermodynamics? If your scalar field does a mass? What is the point that you would make. 444 00:36:56.497 --> 00:36:59.569 Salvatore RIBISI: So if my color field doesn't mass. 445 00:37:00.440 --> 00:37:01.830 Salvatore RIBISI: I am. 446 00:37:02.010 --> 00:37:04.614 Salvatore RIBISI: There must be some. That's where I was 447 00:37:05.350 --> 00:37:09.699 Salvatore RIBISI: kind of mentioning here. There must be a violation of something. 448 00:37:09.960 --> 00:37:12.550 Salvatore RIBISI: but this violation can be quantified. 449 00:37:13.865 --> 00:37:16.139 Salvatore RIBISI: So the point is that 450 00:37:16.610 --> 00:37:21.336 Salvatore RIBISI: I don't think this pleating will be as easy in the case of 451 00:37:23.203 --> 00:37:25.130 Salvatore RIBISI: non-form matter. 452 00:37:26.080 --> 00:37:30.329 Salvatore RIBISI: I don't know conformally invariant field theory, but I think we can get. 453 00:37:31.300 --> 00:37:34.570 Salvatore RIBISI: and we could get an insight of what's going on 454 00:37:34.960 --> 00:37:37.259 Salvatore RIBISI: by looking at the 455 00:37:37.830 --> 00:37:40.069 Salvatore RIBISI: at the lowest. So 456 00:37:40.510 --> 00:37:48.659 Salvatore RIBISI: by looking at, I think the from these lows we can see, we can see. I mean by starting it. 457 00:37:48.920 --> 00:37:55.399 Salvatore RIBISI: We might see, like what happens once the conformal environment is broken. 458 00:37:56.566 --> 00:38:00.669 Salvatore RIBISI: We can quantify, and we might get. 459 00:38:03.930 --> 00:38:07.080 Salvatore RIBISI: I don't know. Like the we can see 460 00:38:07.560 --> 00:38:11.110 Salvatore RIBISI: how thermodynamics will get modified. 461 00:38:11.580 --> 00:38:12.430 Salvatore RIBISI: But 462 00:38:12.530 --> 00:38:13.580 Salvatore RIBISI: what I'm 463 00:38:14.050 --> 00:38:16.150 Salvatore RIBISI: quite sure about is that 464 00:38:16.550 --> 00:38:23.759 Salvatore RIBISI: it cannot be the same like if you you wouldn't type. The thermodynamics wouldn't be exactly the same. 465 00:38:23.910 --> 00:38:28.319 Salvatore RIBISI: But you. So you will have a trace part coming from here from 466 00:38:28.900 --> 00:38:31.058 Salvatore RIBISI: from the mass. This end. 467 00:38:31.490 --> 00:38:33.380 IEM-CSIC: Put a lot of attention to it, but I feel like. 468 00:38:34.590 --> 00:38:39.330 Salvatore RIBISI: Okay? And so yeah, I think you will have another term 469 00:38:39.690 --> 00:38:41.990 Salvatore RIBISI: quantifying this 470 00:38:42.630 --> 00:38:44.080 Salvatore RIBISI: violation 471 00:38:44.120 --> 00:38:49.169 Salvatore RIBISI: of conformal environments. So I don't know if I'm answering, but it's like this is. 472 00:38:49.510 --> 00:38:50.829 Salvatore RIBISI: what do you think about it? 473 00:38:51.150 --> 00:39:05.300 Eugenio Bianchi: Yeah, that that's and the second question I had is, if you had thought about looking at the general boundary in this situation together with Harle and Carlo. We had considered this diamonds and affiliation of the diamond 474 00:39:05.320 --> 00:39:22.820 Eugenio Bianchi: and the fact that you can identify the fact that the region is mixed by looking at that foliation, that lens shape general boundary. This is something you can do both if you are conformal symmetry, if you don't have conformal symmetry. 475 00:39:22.860 --> 00:39:25.579 Eugenio Bianchi: but for conformal symmetry. Clearly 476 00:39:25.730 --> 00:39:28.720 Eugenio Bianchi: you can do more. Have you? Have you looked at that. 477 00:39:30.140 --> 00:39:37.095 Salvatore RIBISI: And no, I mean I I I think I see what works you're talking about. But 478 00:39:37.880 --> 00:39:40.669 Salvatore RIBISI: no, I don't. I haven't looked about the this 479 00:39:41.060 --> 00:39:43.589 Salvatore RIBISI: results like, what are the 480 00:39:44.820 --> 00:39:55.500 Salvatore RIBISI: you mean? The timel properties by looking so instead of getting the whole Nikkowski only getting the only studying the the diamond. That's what your 481 00:39:56.280 --> 00:39:57.640 Salvatore RIBISI: so Justin, you. 482 00:39:57.640 --> 00:40:05.030 Eugenio Bianchi: Can consider a foliation inside the diamond as fluation. It is adapted to the coordinates that you've introduced. Yeah. 483 00:40:06.270 --> 00:40:08.829 Salvatore RIBISI: Okay, no, I haven't. 484 00:40:09.520 --> 00:40:11.440 Salvatore RIBISI: I haven't started yet, please. 485 00:40:12.180 --> 00:40:13.330 Salvatore RIBISI: This situation. 486 00:40:13.850 --> 00:40:15.300 Salvatore RIBISI: Thanks for the remark. 487 00:40:15.790 --> 00:40:16.990 Eugenio Bianchi: Okay. Thank you. 488 00:40:19.190 --> 00:40:28.940 Hal Haggard: We have a question in the chat which I'll read out. But if the questioner would like to to follow up, please feel free. So they ask. 489 00:40:28.980 --> 00:40:34.370 Hal Haggard: why do you? Why does your surface have the interpretation of temperature? 490 00:40:34.620 --> 00:40:39.790 Hal Haggard: Is it different from the killing one? Does this interpretation make sense. 491 00:40:41.690 --> 00:40:44.720 Salvatore RIBISI: Okay, so first of all. 492 00:40:44.890 --> 00:40:46.270 Salvatore RIBISI: is a. 493 00:40:46.670 --> 00:40:49.689 Salvatore RIBISI: so the difference with the killing one is that 494 00:40:50.400 --> 00:41:01.289 Salvatore RIBISI: in this case, I mean, if I understand correctly the question, I would say, like, in this case, we don't have a Canadian field. We have something which is different, like which is not. 495 00:41:01.620 --> 00:41:08.129 Salvatore RIBISI: which is useful if you want more, general Buddy. So yeah, it's not like a healthcare field. So we have to find 496 00:41:08.520 --> 00:41:10.850 Salvatore RIBISI: a more general definition. 497 00:41:11.230 --> 00:41:20.620 Salvatore RIBISI: And the definition, of course, will be, then the properties will be weaker than those of an actual clean field. 498 00:41:21.230 --> 00:41:25.570 Salvatore RIBISI: But okay, if you look, want to see the interpretation. 499 00:41:26.420 --> 00:41:30.740 Salvatore RIBISI: the first interpretation comes from. This comes from the fact that 500 00:41:30.940 --> 00:41:38.779 Salvatore RIBISI: if you do the matter per, if you do matter perturbations, you do get a balance lower. This temperature 501 00:41:38.940 --> 00:41:40.040 Salvatore RIBISI: appears. 502 00:41:40.570 --> 00:41:42.595 Salvatore RIBISI: and then again, 503 00:41:43.340 --> 00:41:49.719 Salvatore RIBISI: a different thing. Another interpretation come from the fact that if someone really, for some reasons 504 00:41:50.250 --> 00:41:55.930 Salvatore RIBISI: you want to decompose them for ski vacuum 505 00:41:56.350 --> 00:42:04.429 Salvatore RIBISI: in terms of particles associated to these 2 different regions. So space time. 506 00:42:05.460 --> 00:42:10.509 Salvatore RIBISI: you do you see that this temperature appears 507 00:42:10.550 --> 00:42:15.539 Salvatore RIBISI: then? And this is like the second answer I will give 508 00:42:15.830 --> 00:42:23.229 Salvatore RIBISI: while staying inside Minkowski. Space time. Then, for the third answer I will go. I will leave. 509 00:42:23.590 --> 00:42:32.149 Salvatore RIBISI: Nikos is past time, and I will go to the real of conformally related geometries. 510 00:42:32.270 --> 00:42:39.269 Salvatore RIBISI: And then there there is a set of conformal transform of Y transformations 511 00:42:39.690 --> 00:42:42.260 Salvatore RIBISI: of the the Minkowski metric. 512 00:42:42.540 --> 00:42:49.000 Salvatore RIBISI: where this conformal student field becomes an actual killing field. 513 00:42:49.210 --> 00:42:50.920 Salvatore RIBISI: and then, in that case 514 00:42:51.450 --> 00:42:55.839 Salvatore RIBISI: the interpretation is the usual one, because the light guns are mapped 515 00:42:56.140 --> 00:43:02.079 Salvatore RIBISI: to actual killing horizons, and the temperature will be the temperature 516 00:43:02.320 --> 00:43:05.129 Salvatore RIBISI: measured by any 517 00:43:05.410 --> 00:43:09.420 Salvatore RIBISI: extension. You know. Stationary observers following that orbit 518 00:43:09.470 --> 00:43:13.069 Salvatore RIBISI: will be similar to the same interpretation of 519 00:43:13.420 --> 00:43:15.960 Salvatore RIBISI: hawking temperature for 520 00:43:16.250 --> 00:43:19.130 Salvatore RIBISI: for for an event horizon. If you want. 521 00:43:23.366 --> 00:43:25.193 Hal Haggard: They, they thank you. 522 00:43:26.250 --> 00:43:29.790 Hal Haggard: Are there other questions or comments? 523 00:43:33.400 --> 00:43:40.458 Hal Haggard: I have one, but it's one of these slightly unfair ones, because I'm going to ask if you know a reference. Have you seen this work of 524 00:43:41.370 --> 00:43:50.050 Hal Haggard: of Zurich and Catherine Zurich and Eric Verlinde, where they're proposing that the thermodynamics of this variety that you're talking about. 525 00:43:50.726 --> 00:43:54.689 Hal Haggard: Might be measurable in gravitational wave interferometry. 526 00:43:56.960 --> 00:43:59.699 Salvatore RIBISI: You know the answer is very simple. No, I haven't tried. 527 00:43:59.700 --> 00:44:01.275 Hal Haggard: Okay, it's fine. I I. 528 00:44:01.590 --> 00:44:03.340 Salvatore RIBISI: Definitely, a reference. 529 00:44:03.340 --> 00:44:13.709 Hal Haggard: Yeah, that's fine. I'll send it along to you. I'm very. They're they're proposing that we actually might measure these these fluctuations of space time, and that that would indicate quanta. 530 00:44:13.730 --> 00:44:21.600 Hal Haggard: And I'm very curious, you know. I I'm curious whether what we all think of that as a community. 531 00:44:21.600 --> 00:44:22.300 Salvatore RIBISI: Okay. 532 00:44:23.620 --> 00:44:26.080 Hal Haggard: Eric Longin was next, and then Lee. 533 00:44:26.910 --> 00:44:29.600 Erlangen: Yeah. Hi, this is Hannah speaking. Can you hear me? 534 00:44:29.890 --> 00:44:30.340 Hal Haggard: Yes. 535 00:44:30.340 --> 00:44:31.600 Salvatore RIBISI: Hey? Yes. 536 00:44:31.830 --> 00:44:49.529 Erlangen: Great thanks for the nice talk I just wanted to say, and I think you mentioned this, but I wanted to understand it better. I wanted to say that this situation reminds me of the quantum queue theory for an accelerated observer in the wind language. 537 00:44:49.530 --> 00:45:03.629 Erlangen: and in particular also to what is called in this quantum field theory, algebraic quantum field theory, community that these are double week month theorem, which says that in this sort of double which you have. 538 00:45:03.950 --> 00:45:33.829 Erlangen: I believe you have exactly this, this kind of thermal structure for the for the state that you have there. In this, I mean, they formulated very differently. But but I think it boils down to something like something like your this, this equation that you had. Just now this blue equation where you have the tool, this this thermal factor, and then a tensor product of the left and right States. 539 00:45:33.840 --> 00:45:42.719 Erlangen: And I wanted to know if you have any comment on this. If this is the same, if yours is sort of a generalization to an arbitrary 540 00:45:42.730 --> 00:45:44.910 Erlangen: conformal. 541 00:45:44.950 --> 00:45:48.340 Erlangen: conformally flat space times of this. 542 00:45:51.350 --> 00:46:01.140 Salvatore RIBISI: Yeah. So so first of all, I mean, I know the but I I think you didn't mention the cable theorem. It was an older theorem. 543 00:46:01.230 --> 00:46:08.219 Salvatore RIBISI: So I know that in the case of a call of a bifurcation surface you're right. There is then the 544 00:46:08.510 --> 00:46:12.209 Salvatore RIBISI: the decomposition or vacuum. I mean that they 545 00:46:12.580 --> 00:46:14.839 Salvatore RIBISI: you can see a thermal vacuum. 546 00:46:15.600 --> 00:46:20.380 Salvatore RIBISI: I mean, given, there is a global vacuum which appears 547 00:46:20.790 --> 00:46:32.089 Salvatore RIBISI: paramount in the in the 2 wedges. So so in this case it's it's not a killing. It's not a bifurcation. 548 00:46:32.170 --> 00:46:33.919 Salvatore RIBISI: It's I mean that 549 00:46:34.560 --> 00:46:38.760 Salvatore RIBISI: it's a conformal bifurcating surface. 550 00:46:38.940 --> 00:46:45.470 Salvatore RIBISI: So the difference is that here you don't have a skinny field. You have a conformal kingy field. 551 00:46:45.950 --> 00:46:53.639 Salvatore RIBISI: and yes, and you are. So this is as in the in the Arv case. What's I think it's not obvious, but maybe 552 00:46:53.920 --> 00:46:55.169 Salvatore RIBISI: I'm wrong. But 553 00:46:55.250 --> 00:46:59.570 Salvatore RIBISI: I when I looked at it, it didn't seem obvious, is that you can always 554 00:46:59.750 --> 00:47:07.830 Salvatore RIBISI: that the fact that it appears thermal. I agree. The the fact that you can always decompose it explicitly 555 00:47:08.710 --> 00:47:11.420 Salvatore RIBISI: seems to me I think it's 556 00:47:11.560 --> 00:47:15.100 Salvatore RIBISI: slightly less trivial, but the the full decomposition. 557 00:47:15.100 --> 00:47:16.350 Lee Smolin: Shouldn't reiterate. 558 00:47:17.020 --> 00:47:20.520 Salvatore RIBISI: But yeah, for it was for Kimville. 559 00:47:20.820 --> 00:47:25.479 Salvatore RIBISI: is they? I mean, that's what happens with with the reindeer kidney field in. 560 00:47:25.480 --> 00:47:26.150 Erlangen: Yeah. 561 00:47:26.710 --> 00:47:28.459 Salvatore RIBISI: There, I don't know. Thanks. 562 00:47:28.990 --> 00:47:31.200 Erlangen: Okay? So so it's a different 563 00:47:31.350 --> 00:47:35.360 Erlangen: different different feel right? Different length. 564 00:47:35.980 --> 00:47:37.890 Erlangen: Hey? Thank you. 565 00:47:38.360 --> 00:47:39.019 Salvatore RIBISI: As you do. 566 00:47:40.750 --> 00:47:42.670 Hal Haggard: Lee, did you want to go ahead with your comment? 567 00:47:42.670 --> 00:47:46.539 Lee Smolin: Well, I think I'm hardly the person to express the view of the field. 568 00:47:46.740 --> 00:47:52.700 Lee Smolin: but I do, repeating one of the older members. I do recall that there was a very similar discussion. 569 00:47:52.770 --> 00:47:57.730 Lee Smolin: maybe 2030 years ago, by people criticizing the Fermi Lab group. 570 00:47:57.890 --> 00:48:03.809 Lee Smolin: who, if I remember right, made the same proposal, and it was pointed out by Giovanni Milliona, Camellia 571 00:48:03.820 --> 00:48:07.150 Lee Smolin: and other people that they were basically 572 00:48:07.400 --> 00:48:08.980 Lee Smolin: the tab 573 00:48:09.150 --> 00:48:10.900 Lee Smolin: getting rid of the 574 00:48:11.120 --> 00:48:16.510 Lee Smolin: of the phase that makes the vacuum coherent and replacing it by a thermometer 575 00:48:16.680 --> 00:48:18.370 Lee Smolin: and vacuum, which is. 576 00:48:18.640 --> 00:48:22.660 Lee Smolin: if we're conservative members of the field, is neither right thing to do. 577 00:48:23.130 --> 00:48:28.339 Lee Smolin: You can always make more particles appear by putting in a thermal path in the vacuum. 578 00:48:31.540 --> 00:48:32.410 Hal Haggard: Thanks, Lee. 579 00:48:34.100 --> 00:48:36.870 Hal Haggard: other questions or comments. 580 00:48:44.310 --> 00:48:52.270 Hal Haggard: I'm going to take the luxury of a few minutes just because we have a little extra time. So do. If you're thinking of something, it's it's feel free. 581 00:49:03.110 --> 00:49:05.400 Salvatore RIBISI: I think I mean I'm fine. 582 00:49:05.870 --> 00:49:06.760 Hal Haggard: Okay. Wonderful. 583 00:49:06.760 --> 00:49:10.890 Salvatore RIBISI: Thanks for the yeah. Thanks for the questions. It was very nice and nice discussion. 584 00:49:11.040 --> 00:49:11.700 Hal Haggard: Good. 585 00:49:11.900 --> 00:49:14.970 Hal Haggard: Thank you, everyone, and we'll see you soon.