WEBVTT 1 00:00:01.480 --> 00:00:05.599 Welcome to the quart Side Quantum Physics Podcast, an exploration 2 00:00:05.679 --> 00:00:10.880 of the fundamental structure of reality where quantum laws govern matter, energy, 3 00:00:11.199 --> 00:00:16.239 and information. Here, uncertainty is a feature, not a flaw, 4 00:00:16.719 --> 00:00:19.239 and understanding begins with the smallest scales. 5 00:00:27.600 --> 00:00:30.839 Picture yourself, just for a second, floating out in the deepest, 6 00:00:30.879 --> 00:00:32.520 most absolute void of space. 7 00:00:32.799 --> 00:00:34.799 Oh wow, okay, setting. 8 00:00:34.439 --> 00:00:37.799 The scene right. I mean, you are light years away 9 00:00:38.159 --> 00:00:42.039 from the comforting glow of any star. You're just drifting 10 00:00:42.119 --> 00:00:46.799 toward this ultimate cosmic abyss, a black hole, the point 11 00:00:46.799 --> 00:00:49.799 of new return exactly. And for decades, the way we've 12 00:00:49.840 --> 00:00:53.479 imagined this journey, it's really been defined by just sheer 13 00:00:54.320 --> 00:00:55.479 inescapable terror. 14 00:00:55.640 --> 00:00:57.320 Yeah, absolute terror. 15 00:00:57.039 --> 00:00:59.640 Because you approach the event horizon, and that's that invisible 16 00:00:59.640 --> 00:01:02.679 boundary right where the escape velocity actually exceeds the speed 17 00:01:02.679 --> 00:01:05.079 of light, and you just know that once you cross it, 18 00:01:05.400 --> 00:01:08.480 there is no going back. None. You are locked in gravity, 19 00:01:08.640 --> 00:01:11.280 which is, you know, the fundamental force that anchors us 20 00:01:11.319 --> 00:01:13.799 to reality every day. It's warped and twisted into this 21 00:01:13.920 --> 00:01:15.280 unfathomable monster. 22 00:01:15.480 --> 00:01:16.040 It really is. 23 00:01:16.120 --> 00:01:18.799 It pulls it you so violently, Yeah, drags the actual 24 00:01:18.840 --> 00:01:21.719 geometry of space and time inward like this rushing river, 25 00:01:22.159 --> 00:01:24.719 and as you fall deeper into that absolute darkness. You know, 26 00:01:24.760 --> 00:01:28.760 the classic century old view of physics dictates this really 27 00:01:28.879 --> 00:01:32.879 terrifying final act, the singularity. Right, your destiny is just sealed. 28 00:01:33.319 --> 00:01:36.840 You and literally every single atom of your body are 29 00:01:37.120 --> 00:01:40.640 doomed to be dragged toward the exact center and just 30 00:01:41.040 --> 00:01:45.599 crushed by infinite gravity into a mathematical point of absolute. 31 00:01:45.079 --> 00:01:48.519 Nothingness, right, which means the fundamental laws of reality to shatter. 32 00:01:48.640 --> 00:01:52.680 Everything that makes our universe coherent basically ceases to exist 33 00:01:52.959 --> 00:01:53.439 right there. 34 00:01:53.560 --> 00:01:54.359 It's terrifying. 35 00:01:54.439 --> 00:01:57.040 I mean, it really is the ultimate apocalyptic scenario, right, 36 00:01:57.040 --> 00:01:59.280 And I don't just mean for you the person falling 37 00:01:59.280 --> 00:02:03.560 in but or our entire mathematical understanding of the cosmos. 38 00:02:03.079 --> 00:02:04.959 Because the master just breaks exactly. 39 00:02:05.040 --> 00:02:07.359 For the longest time, the physics community has kind of 40 00:02:07.359 --> 00:02:10.840 just accepted with the sort of grim resignation that at 41 00:02:10.840 --> 00:02:14.759 the heart of a black hole lies this catastrophic, irreconcilable 42 00:02:14.840 --> 00:02:16.919 breakdown of the laws of nature. 43 00:02:16.719 --> 00:02:17.759 Like a glitch in the matrix. 44 00:02:17.919 --> 00:02:21.520 Yeah, a place where the elegant equations that govern the 45 00:02:21.560 --> 00:02:24.960 motion of galaxies, the orbits of planets, even the ticking 46 00:02:25.000 --> 00:02:27.080 of clocks. They simply throw up their hands. They just 47 00:02:27.080 --> 00:02:30.400 output a string of infinities and surrender completely the. 48 00:02:30.319 --> 00:02:32.680 Literal end of the line. But and this is what 49 00:02:32.719 --> 00:02:36.639 we're getting into today. What if that fatalistic assumption is wrong. 50 00:02:36.639 --> 00:02:39.400 Which is a huge question, right, What if. 51 00:02:39.240 --> 00:02:42.520 This assumption we've clung to since like the nineteen sixties 52 00:02:42.560 --> 00:02:45.240 is just fundamentally flawed. What if the universe is actually 53 00:02:45.319 --> 00:02:49.199 far more resilient and doesn't allow its own underlying geometry 54 00:02:49.520 --> 00:02:51.360 to just be torn apart so violently. 55 00:02:51.479 --> 00:02:53.639 It's a completely paradigm shifting idea. 56 00:02:54.080 --> 00:02:56.759 So welcome to our exploration today. We are taking you 57 00:02:56.840 --> 00:03:01.039 on this intensive, totally mind bending journey into the absolute 58 00:03:01.080 --> 00:03:04.199 cutting edge of theoretical physics, a new fun one. We're 59 00:03:04.199 --> 00:03:08.680 going to unpack a brilliant theoretical framework that really challenges 60 00:03:08.719 --> 00:03:12.000 absolutely everything we thought we knew about the darkest, most 61 00:03:12.039 --> 00:03:15.879 mysterious places in the cosmos. We are exploring the mathematical 62 00:03:15.879 --> 00:03:19.759 possibility that the terrifying breakdown of reality inside a black 63 00:03:19.759 --> 00:03:21.680 hole just doesn't actually happen. 64 00:03:21.800 --> 00:03:25.439 Yeah, we are going deep into the profound theoretical calculations 65 00:03:25.479 --> 00:03:29.599 of Francesco di Filippo and his recent structural models suggests 66 00:03:29.639 --> 00:03:34.919 that by combining two very specific, almost seemingly opposing cosmic 67 00:03:35.000 --> 00:03:39.439 phenomenal quantum evaporation and internal repulsion. The universe actually has 68 00:03:39.479 --> 00:03:43.080 a built in mechanism to cancel out the apocalypse inside 69 00:03:43.120 --> 00:03:43.919 a black hole. 70 00:03:44.159 --> 00:03:47.039 Cancel the apocalypse. I love that, right, and. 71 00:03:46.960 --> 00:03:49.879 It's a revelation that I mean, if it's fully realized, 72 00:03:49.919 --> 00:03:54.000 it could reshape half a century of theoretical work. It 73 00:03:54.080 --> 00:03:56.560 fundamentally alters our understanding of space time. 74 00:03:56.759 --> 00:03:59.240 I am so ready for this. But Okay, before we 75 00:03:59.280 --> 00:04:01.599 can really talk about it how the apocalypse gets canceled, 76 00:04:01.960 --> 00:04:04.800 we need to understand the anatomy of the apocalypse itself. 77 00:04:04.879 --> 00:04:07.120 We have to know what we're saving the universe from. 78 00:04:07.280 --> 00:04:10.439 Exactly. When physicists talk about the center of a black hole, 79 00:04:10.520 --> 00:04:14.560 these this word that sounds almost medical. They talk about pathologies. 80 00:04:13.919 --> 00:04:17.079 In space time pathologies, Yeah, like a disease in the math. 81 00:04:17.240 --> 00:04:20.600 Right, the complete breakdown of Einstein's theory of general relativity. 82 00:04:20.920 --> 00:04:22.800 And there are really two main culprits we need to 83 00:04:22.800 --> 00:04:23.480 look at, right. 84 00:04:23.319 --> 00:04:26.000 Two distinct ways the machinery just grinds to a halt. 85 00:04:26.240 --> 00:04:29.240 Yeah, And the first, the most famous one, is the 86 00:04:29.279 --> 00:04:32.959 curvature singularity. Let's build this from the ground up for everyone. 87 00:04:33.079 --> 00:04:36.759 Sure, So to really understand the curvature singularity, we actually 88 00:04:36.800 --> 00:04:39.519 have to rewind all the way to nineteen fifteen, back 89 00:04:39.560 --> 00:04:42.000 to Einstein's formulation of general relativity. 90 00:04:42.040 --> 00:04:43.120 Okay, setting the clock back. 91 00:04:43.319 --> 00:04:47.680 Yeah, before Einstein, Isaac Newton basically taught us that gravity 92 00:04:47.920 --> 00:04:52.519 was this mysterious invisible tether, right, just pulling objects together 93 00:04:52.959 --> 00:04:57.519 across this static, unchanging stage of space and time. 94 00:04:57.480 --> 00:04:58.879 Like objects on a flat table. 95 00:04:59.040 --> 00:05:03.639 Right. Einstein completely dismantled that stage. He proposed that space 96 00:05:03.680 --> 00:05:06.879 and time are actually fused into a single dynamic, four 97 00:05:06.920 --> 00:05:09.680 dimensional fabric we call it space time. 98 00:05:10.040 --> 00:05:12.040 And gravity isn't a pull in that model, is it? 99 00:05:12.160 --> 00:05:14.560 No, not at all. Gravity is the actual curvature of 100 00:05:14.560 --> 00:05:18.279 that fabric. The physicist John Archibold Wheeler had this perfect summary. 101 00:05:18.600 --> 00:05:22.040 He said, mass tells space time how to curve, and 102 00:05:22.120 --> 00:05:24.120 space time tells mass how to move. 103 00:05:24.519 --> 00:05:26.360 There's such a great way to picture it. And the 104 00:05:26.399 --> 00:05:30.399 mathematical engine driving that relationship is Einstein's field equations. 105 00:05:30.040 --> 00:05:33.920 Exactly specifically governed by something we call the stress energy tensor. 106 00:05:34.279 --> 00:05:37.839 The stress energy tensor. Okay, let's unpack that. That's essentially 107 00:05:37.879 --> 00:05:40.519 like the master ledger of any given region of space. 108 00:05:40.759 --> 00:05:42.160 The ledger's a great way to put it. 109 00:05:42.160 --> 00:05:44.920 It accounts for the energy density, the momentum, the pressure, 110 00:05:45.000 --> 00:05:48.920 the sheer stress, basically whatever matter or radiation is hanging 111 00:05:48.959 --> 00:05:52.519 out on that spot, and that ledger dictates exactly how 112 00:05:52.560 --> 00:05:55.120 sharply the local space time has to been around it. 113 00:05:55.240 --> 00:05:59.120 Precisely. Now, if we fast forward just one year to 114 00:05:59.240 --> 00:06:03.720 nineteen sixty, a physicist named Carl schwarz Child is actually 115 00:06:03.759 --> 00:06:06.600 serving in the German Army during World War One. 116 00:06:06.439 --> 00:06:09.120 Which is wild to think about. He's doing this math 117 00:06:09.160 --> 00:06:10.120 in a trench. 118 00:06:10.560 --> 00:06:13.839 Literally amidst artillery fire, and while he's stationed at the 119 00:06:13.879 --> 00:06:17.560 Russian Front, he manages to find the very first exact 120 00:06:17.600 --> 00:06:21.360 solution to Einstein's incredibly complex field equation. 121 00:06:21.639 --> 00:06:24.120 Just doing casual genius math while dodging bullets. 122 00:06:24.519 --> 00:06:27.720 He calculated the geometry of space time around a perfectly spherical, 123 00:06:27.800 --> 00:06:31.920 non rotating mass, and a solution was brilliant, but it 124 00:06:31.959 --> 00:06:33.439 contained a really dark secret. 125 00:06:33.519 --> 00:06:34.439 The math got scary. 126 00:06:34.759 --> 00:06:36.839 The math showed that if you take a mass and 127 00:06:36.879 --> 00:06:39.600 compress it into a small enough radius, which we now 128 00:06:39.639 --> 00:06:44.399 appropriately call the schwartz Child radius, the escape velocity of 129 00:06:44.439 --> 00:06:46.759 that object actually reaches the speed. 130 00:06:46.439 --> 00:06:48.639 Of light, and that right there is the event horizon. 131 00:06:48.439 --> 00:06:49.920 Or the event horizon, yes. 132 00:06:49.759 --> 00:06:52.279 Which I mean that's terrifying enough on its own. It's 133 00:06:52.279 --> 00:06:55.120 a one way membrane in the universe. But the event 134 00:06:55.160 --> 00:06:58.600 horizon isn't actually the singularity. The horizon is just the 135 00:06:58.639 --> 00:07:00.959 point of no return exactly. 136 00:07:01.160 --> 00:07:05.279 The real problem is deeper. Schwartz Schile's equations sure that 137 00:07:05.399 --> 00:07:08.959 as you travel inward past that horizon, toward the exact 138 00:07:09.040 --> 00:07:12.319 center of the mass, the radial coordinate of zero or 139 00:07:12.399 --> 00:07:16.240 our equal zero, the denominator in the equations actually drops 140 00:07:16.279 --> 00:07:16.759 to zero. 141 00:07:16.959 --> 00:07:20.199 And I mean, any middle school math student knows you 142 00:07:20.279 --> 00:07:23.319 cannot divide by zero. It just blows up to infinity 143 00:07:23.319 --> 00:07:24.120 on your calculator. 144 00:07:24.160 --> 00:07:26.800 It does. It blows up. But for decades, physicists kind 145 00:07:26.800 --> 00:07:29.720 of debated whether that infinity was a true physical reality 146 00:07:29.800 --> 00:07:31.920 or maybe just a quirk of the coordinate system they 147 00:07:31.920 --> 00:07:32.360 were using. 148 00:07:32.720 --> 00:07:36.040 Oh, like how longitude lines converge at the north pole, 149 00:07:36.319 --> 00:07:39.319 Like the Earth doesn't physically end or break at the 150 00:07:39.360 --> 00:07:41.800 north pole, it's just where the greed we drew on 151 00:07:41.839 --> 00:07:42.680 it gets kind of weird. 152 00:07:42.839 --> 00:07:45.920 That is an excellent distinction, and honestly, it took the 153 00:07:45.920 --> 00:07:48.920 physics community quite a few years to look that out. 154 00:07:49.240 --> 00:07:50.839 So how did they figure out it wasn't just a 155 00:07:50.839 --> 00:07:51.600 grid problem. 156 00:07:51.920 --> 00:07:55.319 Well, they eventually developed mathematical tools to test it. They 157 00:07:55.319 --> 00:08:00.279 looked at things called curvature invariance, specifically one called the Kritchman's. 158 00:07:59.720 --> 00:08:01.600 Scalealer the Cretchman scaling. 159 00:08:01.720 --> 00:08:04.759 Yeah, these are quantities that describe the absolute curvature of 160 00:08:04.800 --> 00:08:09.079 space time, completely independent of whatever arbitrary coordinate grid you 161 00:08:09.160 --> 00:08:10.240 try to overlay on it. 162 00:08:10.319 --> 00:08:13.600 Okay, so it's the raw physical reality exactly. 163 00:08:14.000 --> 00:08:16.759 And when you calculate the Kretchman scaler at our equal 164 00:08:16.920 --> 00:08:21.639 zero inside a schwartz Child black hole, it genuinely physically 165 00:08:21.680 --> 00:08:24.560 diverges to absolute mathematical infinity. 166 00:08:24.759 --> 00:08:26.839 Oh wow, So it's not a trick. 167 00:08:26.639 --> 00:08:29.959 No trick. The physical curvature of space time and consequently 168 00:08:30.000 --> 00:08:32.960 the tidal gravitational forces become infinite. 169 00:08:33.159 --> 00:08:36.360 So if you were falling in feet first, the difference 170 00:08:36.399 --> 00:08:39.279 in gravitational pull between your feet and your head would 171 00:08:39.279 --> 00:08:42.720 become infinitely vast, right, stretching you perfectly thin. 172 00:08:42.639 --> 00:08:44.480 The famous spaghanification process. 173 00:08:44.559 --> 00:08:47.679 Yes, right, affectionately notice spaghetification. But it's not just about 174 00:08:47.679 --> 00:08:50.720 getting stretched like a noodle. The actual density of the 175 00:08:50.759 --> 00:08:52.919 collapsing star becomes infinite, doesn't it. 176 00:08:53.039 --> 00:08:56.600 Yes, the volumet occupies shrinks to literally. 177 00:08:56.360 --> 00:09:02.440 Zerous zero volume, infinite mass. It's a true ue curvature singularity. 178 00:09:02.519 --> 00:09:04.960 It is a literal point where the fabric of reality 179 00:09:05.000 --> 00:09:08.679 is torn and Einstein's equations simply cannot function anymore. 180 00:09:08.759 --> 00:09:11.799 They cease to yield any physical meaning whatsoever. 181 00:09:11.360 --> 00:09:13.799 Which means we have no physical laws to describe what 182 00:09:13.919 --> 00:09:17.799 is actually happening in that infinitesimally small space. The predictive 183 00:09:17.799 --> 00:09:20.120 power of physics just stops cold. 184 00:09:19.840 --> 00:09:22.919 It completely stops. But as you kind of hinted at earlier, 185 00:09:22.960 --> 00:09:26.440 the curvature singularity is actually only one half of the pathology. 186 00:09:26.720 --> 00:09:29.639 There is a second horror lurking in the dark down there. 187 00:09:29.720 --> 00:09:31.600 Yes, and this is the one that really messes with 188 00:09:31.679 --> 00:09:32.559 physicists heads. 189 00:09:32.919 --> 00:09:37.000 Oh many theoretical physicists find this one far more deeply troubling. 190 00:09:37.399 --> 00:09:39.519 It's called the Kachi horizon. 191 00:09:39.200 --> 00:09:42.399 The Cachi horizon. And to understand why this one is 192 00:09:42.440 --> 00:09:45.919 so terrifying, we really have to talk about something incredibly 193 00:09:45.960 --> 00:09:49.080 fundamental to science, determinism. 194 00:09:48.480 --> 00:09:51.039 The absolute core of classical physics. 195 00:09:51.159 --> 00:09:54.120 Right, Because in classical physics, if I know the exact 196 00:09:54.240 --> 00:09:57.360 initial conditions of a system, like the position, the velocity, 197 00:09:57.399 --> 00:09:59.960 the forces acting on every single particle in a room. 198 00:10:00.720 --> 00:10:05.080 I can use a mathematical operator, a Hamiltonian to evolve 199 00:10:05.120 --> 00:10:06.639 that system forward in time. 200 00:10:06.840 --> 00:10:09.960 You can predict its exact future with absolute certainty. 201 00:10:10.080 --> 00:10:14.840 Exactly. It's the ultimate clockwork universe. The present perfectly dictates 202 00:10:14.879 --> 00:10:15.799 the future. 203 00:10:15.919 --> 00:10:17.639 And that is the foundation of what we call the 204 00:10:17.679 --> 00:10:21.440 initial value problem. In physics, we define a slice of 205 00:10:21.480 --> 00:10:25.399 space time a Cauchi surface, which basically represents the entire 206 00:10:25.519 --> 00:10:28.799 universe at one specific frozen moment in time. 207 00:10:28.720 --> 00:10:29.639 Like taking a snapshot. 208 00:10:29.679 --> 00:10:31.480 Like a snapshot. Yeah, and if you know all the 209 00:10:31.559 --> 00:10:34.480 data on that surface, general relativity basically guarantees that you 210 00:10:34.519 --> 00:10:37.320 can uniquely determine the entire past and the entire future 211 00:10:37.320 --> 00:10:40.960 of that universe. It's the bedrock of cause and effect, which. 212 00:10:40.720 --> 00:10:43.639 Makes sense to us intuitively. I mean, a shattered glass 213 00:10:43.679 --> 00:10:45.759 on the floor implies someone dropped it a moment ago 214 00:10:46.000 --> 00:10:50.679 cause and effect. But a Cauci horizon represents the absolute 215 00:10:50.759 --> 00:10:52.440 death of that determinism, doesn't it. 216 00:10:52.440 --> 00:10:56.159 It really does. A Kauci horizon is this boundary that 217 00:10:56.279 --> 00:11:00.399 forms deep inside certain types of black holes, specifically black 218 00:11:00.440 --> 00:11:03.080 holes that are spinning or have an electric charge. 219 00:11:03.279 --> 00:11:06.120 Okay, so not just the basic spherical ones, right, And. 220 00:11:06.039 --> 00:11:07.559 If you were to fall into one of these black 221 00:11:07.600 --> 00:11:11.000 holes and somehow cross the Cauchi Horizon, you would enter 222 00:11:11.120 --> 00:11:14.320 a region of space time that is fundamentally decoupled from 223 00:11:14.360 --> 00:11:14.759 the past. 224 00:11:14.879 --> 00:11:17.320 Decoupled meaning what exactly, meaning the. 225 00:11:17.360 --> 00:11:20.399 Data from your initial Cauchi surface the present moment you 226 00:11:20.440 --> 00:11:23.120 just left behind is no longer sufficient to predict what 227 00:11:23.200 --> 00:11:23.879 happens next. 228 00:11:24.000 --> 00:11:27.559 It's a complete failure of the predictive power of science. Yeah, 229 00:11:27.639 --> 00:11:30.960 you cross that line and literally anything could happen, and 230 00:11:31.000 --> 00:11:34.039 no equation in the universe could predict it none. It's 231 00:11:34.039 --> 00:11:36.639 not just that we don't have enough information, it's that 232 00:11:36.679 --> 00:11:40.440 the mathematical link between cause and effect is totally severed. 233 00:11:40.799 --> 00:11:43.080 Reality just becomes arbitrary, precisely. 234 00:11:43.679 --> 00:11:46.679 And for a long time, the general consensus was that 235 00:11:47.240 --> 00:11:51.120 these pathologies, the singularity in the Cauchi Horizon were simply 236 00:11:51.519 --> 00:11:54.840 the inevitable, inescapable fate of gravitational collapse. 237 00:11:54.919 --> 00:11:56.720 It's a depressing dead end for the universe. 238 00:11:56.799 --> 00:12:00.399 Yeah, and this fatalism was really locked into place nineteen 239 00:12:00.440 --> 00:12:03.440 sixty five by Roger Penrose, who, by the way later 240 00:12:03.559 --> 00:12:05.399 won the Nobel Prize for this very work. 241 00:12:05.519 --> 00:12:08.759 Right, Penrose's singularity theorem, And we really need to dig 242 00:12:08.799 --> 00:12:11.080 into the mechanics of this theorem because it's the exact 243 00:12:11.120 --> 00:12:15.039 thing Francesco di Filippo's work is challenging today. Penrose didn't 244 00:12:15.120 --> 00:12:18.559 just guess that singularity's form. He proved it mathematically. 245 00:12:18.679 --> 00:12:22.399 He did. But, and this is key, mathematical proofs always 246 00:12:22.440 --> 00:12:26.879 rely on assumptions, always. So Penrose utilized this brilliant piece 247 00:12:26.919 --> 00:12:30.200 of mathematics called the racial Doury equation. It was developed 248 00:12:30.200 --> 00:12:33.720 by Amal Kumar Ratioturi about a decade earlier, and this 249 00:12:33.759 --> 00:12:36.919 equation describes exactly how bundles of light rays behave as 250 00:12:36.960 --> 00:12:38.840 they travel through curved space time. 251 00:12:38.639 --> 00:12:39.960 Okay, tracking the path of light. 252 00:12:40.279 --> 00:12:43.679 Right and Penrose combined this with the concept of trapped surfaces. 253 00:12:43.840 --> 00:12:47.080 These are regions inside a black hole where gravity is 254 00:12:47.120 --> 00:12:50.279 so intensely warped that all light rays, whether they are 255 00:12:50.320 --> 00:12:53.840 pointing inward or trying to point outward, are dragged inexorably 256 00:12:53.919 --> 00:12:55.000 toward the center. 257 00:12:54.840 --> 00:12:58.919 Because space itself is literally flowing inward faster than the 258 00:12:58.919 --> 00:13:01.559 speed of light. It's like trying to row a boat 259 00:13:02.159 --> 00:13:06.039 upstream against a waterfall. Doesn't matter how fast you row, 260 00:13:06.320 --> 00:13:08.720 the current of space time is just carrying you down 261 00:13:08.759 --> 00:13:09.480 into the abyss. 262 00:13:09.559 --> 00:13:13.039 That's a perfect analogy. Yes, yeah, But to mathematically guarantee 263 00:13:13.039 --> 00:13:15.320 that these light rays eventually converge to a point of 264 00:13:15.519 --> 00:13:20.480 infinite density, a singularity, Penrose had to make one absolutely 265 00:13:20.519 --> 00:13:22.679 critical assumption about the nature of gravity. 266 00:13:22.720 --> 00:13:23.840 Okay, what was the assumption? 267 00:13:24.080 --> 00:13:28.159 He had to assume that gravity is strictly universally attractive. 268 00:13:27.879 --> 00:13:30.879 Which sounds obvious, right, Gravity pulls things together, and apple 269 00:13:30.919 --> 00:13:34.320 falls to the Earth, the Earth orbits the Sun gravity pulls. 270 00:13:34.519 --> 00:13:37.879 It sounds totally obvious. But in the language of general relativity, 271 00:13:37.919 --> 00:13:41.200 stating that gravity is purely attractive means imposing what are 272 00:13:41.279 --> 00:13:44.919 called energy conditions on that stress energy tensor we mentioned earlier, 273 00:13:44.960 --> 00:13:49.320 the space ledger. The ledger. Yes, specifically, Penrose relied on 274 00:13:49.360 --> 00:13:50.600 the null energy condition. 275 00:13:50.720 --> 00:13:52.399 The null energy condtion. Yeah. 276 00:13:52.440 --> 00:13:55.559 In simple terms, this condition demands that the energy density 277 00:13:55.559 --> 00:13:59.039 of matter and radiation, as measured by literally any observer 278 00:13:59.159 --> 00:14:01.480 moving at the speed of lilfe light must always be 279 00:14:01.639 --> 00:14:04.039 positive or zero, never negative. 280 00:14:04.480 --> 00:14:07.799 Okay, So as long as energy is positive, gravity acts 281 00:14:07.840 --> 00:14:10.759 as this sort of focusing lens. It pulls light, rays 282 00:14:11.200 --> 00:14:13.000 and matter together exactly. 283 00:14:13.360 --> 00:14:16.639 And if gravity always focuses and you have a trapped surface, 284 00:14:16.960 --> 00:14:21.600 Penrose proved incontrovertibly that those paths must eventually end. The 285 00:14:21.639 --> 00:14:26.519 space time manifold must be incomplete. A singularity is absolutely unavoidable. 286 00:14:26.679 --> 00:14:29.759 Wow, Okay, well wait, if the geometry is scaling to 287 00:14:29.840 --> 00:14:34.000 infinity at the singularity, and the mathematics guarantee this inevitable 288 00:14:34.000 --> 00:14:37.360 collapse as long as gravity is pulling, how do physicists 289 00:14:37.480 --> 00:14:40.240 even begin to study the interior of these things? 290 00:14:40.360 --> 00:14:41.960 That is the million dollar question. 291 00:14:42.080 --> 00:14:44.799 Because you can't just stick a telescope inside an event horizon. 292 00:14:45.200 --> 00:14:46.960 You can't send a probe to map out a catchy 293 00:14:47.039 --> 00:14:49.360 horizon and expect it to beam the data back out 294 00:14:49.399 --> 00:14:50.480 to the one way membrane. 295 00:14:50.480 --> 00:14:51.799 No, the signal would never escape. 296 00:14:52.039 --> 00:14:54.519 Right. So to study a domain where space and time 297 00:14:54.559 --> 00:14:58.120 were just mangled beyond our normal comprehension, you need a 298 00:14:58.240 --> 00:14:59.480 very specialized kind of map. 299 00:14:59.559 --> 00:15:02.559 Right do you need a map that captures the entire 300 00:15:02.799 --> 00:15:06.000 causal structure of space time, extending all the way out 301 00:15:06.000 --> 00:15:08.480 to infinity, while bringing it down to a scale that 302 00:15:08.519 --> 00:15:10.120 the human mind can actually. 303 00:15:09.799 --> 00:15:11.679 Process, Which sounds impossible. 304 00:15:11.840 --> 00:15:14.840 It does, but in theoretical physics. That tool is known 305 00:15:14.840 --> 00:15:19.600 as a Penrose diagram, or more accurately, a Penrose Carter diagram, 306 00:15:19.799 --> 00:15:22.960 honoring both Roger Penrose and Brandon Carter, who developed them. 307 00:15:23.120 --> 00:15:25.200 Okay, and this is where Defilipo comes in, right. 308 00:15:25.360 --> 00:15:29.159 Yes, it was by meticulously studying one of these diagrams 309 00:15:29.399 --> 00:15:32.720 that DeFilippo began to see a way out of the apocalypse. 310 00:15:33.080 --> 00:15:37.559 I find Penrose diagrams utterly fascinating because they require such 311 00:15:37.600 --> 00:15:40.799 a massive shift in how we naturally visualize the universe. 312 00:15:41.440 --> 00:15:43.639 I mean, normally, if we try to graph space and time, 313 00:15:43.720 --> 00:15:45.799 we draw an X axis for space and AI. 314 00:15:45.679 --> 00:15:47.879 Axis for time standard Cartesian coordinate. 315 00:15:48.000 --> 00:15:51.200 Right, but space goes on forever, and time goes on forever. 316 00:15:51.279 --> 00:15:52.919 You can't draw infinity on a chalkboard. 317 00:15:53.200 --> 00:15:57.000 You cannot. So Penros and Carter utilized this really clever 318 00:15:57.320 --> 00:16:02.120 mathematical technique called conformaltification conformal compactification. 319 00:16:02.120 --> 00:16:02.720 Okay, Yeah. 320 00:16:02.759 --> 00:16:06.720 They apply to a series of mathematical transformations, specifically wild 321 00:16:06.759 --> 00:16:12.440 transformations that artificially shrink infinite distances in space and infinite 322 00:16:12.480 --> 00:16:16.799 stretches of time, basically compressing them so they fit neatly 323 00:16:16.840 --> 00:16:19.080 within a finite boundary on a page. 324 00:16:19.279 --> 00:16:22.639 Let's try to visualize this for everyone. Imagine taking the 325 00:16:22.840 --> 00:16:26.320 entire four dimensional history of the universe, right from the 326 00:16:26.399 --> 00:16:29.759 absolute beginning of time, through the formation of every galaxy, 327 00:16:29.879 --> 00:16:32.480 the birth and death of every star, all the way 328 00:16:32.519 --> 00:16:34.799 out to the infinite cold death of the cosmos, the 329 00:16:35.639 --> 00:16:38.919 whole thing. Now, imagine taking that boundless reality and creatively 330 00:16:38.919 --> 00:16:42.279 squishing it down into a single, flat, two dimensional piece 331 00:16:42.320 --> 00:16:45.360 of paper, forming a diamond shape. It's almost like taking 332 00:16:45.399 --> 00:16:48.840 a massive three D movie universe and flattening it into 333 00:16:48.879 --> 00:16:51.000 a single comic book panel where you can see all 334 00:16:51.000 --> 00:16:52.240 the plot to acitic lands. 335 00:16:52.440 --> 00:16:54.840 I really like that comic book analogy, but we have 336 00:16:54.879 --> 00:16:58.720 to emphasize what the specific map preserves. Like a Mercator 337 00:16:58.799 --> 00:17:01.799 projection of the Earth distorts the size of land masses 338 00:17:01.799 --> 00:17:05.359 near the poles right, but it preserves navigational angles. 339 00:17:05.119 --> 00:17:07.960 Right greenland looks huge exactly well. 340 00:17:07.960 --> 00:17:11.799 A Penrose diagram massively distorts physical distance and time, but 341 00:17:11.920 --> 00:17:16.480 it perfectly preserves causality. Specifically, the path is of light. 342 00:17:17.599 --> 00:17:20.440 On a Penrose diagram, a array of light will always, 343 00:17:20.559 --> 00:17:24.519 without exception, travel at exactly a forty five degree angle. 344 00:17:24.359 --> 00:17:27.440 Which is the crucial detail because nothing can travel faster 345 00:17:27.519 --> 00:17:30.240 than light. So if light always travels at forty five degrees, 346 00:17:30.480 --> 00:17:32.759 the path of any physical object with mass like you, 347 00:17:33.000 --> 00:17:36.440 or star or spacecraft must travel at an angle steeper 348 00:17:36.440 --> 00:17:38.640 than forty five degrees, pointing generally upward. 349 00:17:38.839 --> 00:17:42.000 Exactly and upward on the diagram represents the forward flow 350 00:17:42.000 --> 00:17:42.319 of time. 351 00:17:42.400 --> 00:17:45.000 Okay, So the edges of the diamond represent infinity. The 352 00:17:45.000 --> 00:17:48.319 bottom point is past infinity, where time begins. The top 353 00:17:48.359 --> 00:17:51.160 point is future infinity, where time ends. The left and 354 00:17:51.240 --> 00:17:52.839 right corners are spatial infinity. 355 00:17:53.079 --> 00:17:57.039 You've got it, and by mapping a black hole this way, 356 00:17:57.440 --> 00:17:59.960 you can literally trace the path of a collapsing star. 357 00:18:01.079 --> 00:18:03.400 You can see the event horizon form, which is usually 358 00:18:03.440 --> 00:18:07.119 represented as this forty five degree line sloping inward. 359 00:18:07.240 --> 00:18:09.920 And once you cross that forty five degree line, moving 360 00:18:09.960 --> 00:18:13.400 strictly upward in time and forward in space, your causal 361 00:18:13.480 --> 00:18:17.640 future inevitably intersects with this jagged horizontal line at the 362 00:18:17.759 --> 00:18:19.079 very top of the diagram. 363 00:18:19.119 --> 00:18:22.799 And that jagged line is the curvature singularity. It is 364 00:18:22.920 --> 00:18:26.119 the literal end of time and space on the map. 365 00:18:26.319 --> 00:18:29.319 You hit that line and your worldline simply terminates. You 366 00:18:29.400 --> 00:18:32.680 cease to be boom game over gameover. Yes, but that 367 00:18:32.839 --> 00:18:37.039 is just the standard diagram for a simple, non rotating shortschild. 368 00:18:36.480 --> 00:18:37.880 Black hole, the basic model. 369 00:18:38.079 --> 00:18:38.279 Right. 370 00:18:38.640 --> 00:18:41.519 But Francesco di Filippo wasn't looking at a simple black hole. 371 00:18:41.559 --> 00:18:44.599 He was investigating the theoretical collapse of a Riisner Nordstrum 372 00:18:44.599 --> 00:18:44.960 black hole. 373 00:18:45.039 --> 00:18:46.720 Raisner Nordstrum. Okay, and how is that different. 374 00:18:46.880 --> 00:18:49.279 This is a black hole that is perfectly spherical, but 375 00:18:49.359 --> 00:18:52.680 it carries a net electric charge, and the Penrose diagram 376 00:18:52.680 --> 00:18:55.880 for a charged black hole is drastically more complex. 377 00:18:55.799 --> 00:18:59.960 Right, because an electric charge actually changes the internal geometry. 378 00:19:00.319 --> 00:19:02.960 Instead of just a single event horizon and a jagged 379 00:19:03.000 --> 00:19:05.960 singularity at the end of time, a charged black hole 380 00:19:06.440 --> 00:19:08.960 has an outer event horizon and an inner horizon. Yes, 381 00:19:09.119 --> 00:19:11.880 And that inner horizon is exactly the Cauchy horizon we 382 00:19:11.880 --> 00:19:14.920 were carerified of earlier. Right, the boundary where determinism just 383 00:19:14.960 --> 00:19:15.759 dies correct. 384 00:19:16.160 --> 00:19:19.119 On the Penrose diagram for a Riisner Nordstrom black hole, 385 00:19:19.720 --> 00:19:23.079 the singularity isn't a horizontal line cutting off the future. 386 00:19:23.160 --> 00:19:26.440 It's actually a vertical a vertical line. Yeah. And because 387 00:19:26.480 --> 00:19:30.000 of the strange geometry of that inner horizon, classical mathematics 388 00:19:30.000 --> 00:19:33.759 suggests that crossing it might actually lead into entirely new, 389 00:19:33.920 --> 00:19:36.880 completely separate universes or out through a white hole. 390 00:19:37.000 --> 00:19:37.599 A white hole. 391 00:19:37.720 --> 00:19:40.720 Yeah, but as we established, crossing that Kauchi horizon means 392 00:19:40.799 --> 00:19:44.799 your future is entirely unpredictable anyway, So it's a huge problem. 393 00:19:45.000 --> 00:19:49.400 So de Filipo is staring at this incredibly complex, deeply pathological, 394 00:19:49.440 --> 00:19:53.519 conformal map of a charged black hole. He sees the 395 00:19:53.559 --> 00:19:57.680 outer horizon, the inner Cauchy horizon, and the vertical singularity. 396 00:19:58.200 --> 00:20:00.839 But then he begins to introduce two fun mentally different 397 00:20:01.160 --> 00:20:04.240 cosmic phenomena into this purely classical map. 398 00:20:04.400 --> 00:20:07.119 Yes, he introduces the quantum world. 399 00:20:07.200 --> 00:20:10.839 And this is where the underdogs enter the arena against 400 00:20:10.839 --> 00:20:14.599 the undisputed heavyweight champion of the universe, infinite gravity. 401 00:20:14.839 --> 00:20:17.440