1 00:00:05,749 --> 00:00:03,190 okay this video will outline how and why 2 00:00:07,430 --> 00:00:05,759 to use natural units to determine 3 00:00:11,589 --> 00:00:07,440 a numerical value 4 00:00:13,430 --> 00:00:11,599 physical observable that's macroscopic 5 00:00:15,509 --> 00:00:13,440 that you would like in my opinion this 6 00:00:17,269 --> 00:00:15,519 should be taught first in physics but 7 00:00:18,870 --> 00:00:17,279 for whatever reason there's no single 8 00:00:20,710 --> 00:00:18,880 lesson there's no single chapter in a 9 00:00:22,630 --> 00:00:20,720 book there's no single lecture in a 10 00:00:24,150 --> 00:00:22,640 lecture series on this instead it's 11 00:00:26,070 --> 00:00:24,160 strewn across 12 00:00:28,390 --> 00:00:26,080 several and you start to intuit it you 13 00:00:29,669 --> 00:00:28,400 start to understand it implicitly as a 14 00:00:31,349 --> 00:00:29,679 physics student 15 00:00:33,510 --> 00:00:31,359 rather than it being made explicit which 16 00:00:35,190 --> 00:00:33,520 it is being made explicit here and 17 00:00:36,790 --> 00:00:35,200 that's because it can serve you in the 18 00:00:38,709 --> 00:00:36,800 beginning of your understanding of 19 00:00:40,310 --> 00:00:38,719 physics and even in the middle of your 20 00:00:42,549 --> 00:00:40,320 misunderstanding of physics which is 21 00:00:45,030 --> 00:00:42,559 where we all are generally this video is 22 00:00:47,110 --> 00:00:45,040 meant to change the way that you view 23 00:00:49,029 --> 00:00:47,120 physics and even the world and that's 24 00:00:50,790 --> 00:00:49,039 the point the point of view shift this 25 00:00:52,790 --> 00:00:50,800 perspective shift is the point of this 26 00:00:55,910 --> 00:00:52,800 video while it's outwardly about 27 00:00:57,910 --> 00:00:55,920 calculations it's truly about 28 00:00:59,510 --> 00:00:57,920 developing a different stance on nature 29 00:01:01,750 --> 00:00:59,520 for those of you who are unfamiliar with 30 00:01:03,270 --> 00:01:01,760 me my name is kirchey mungle i'm a 31 00:01:05,030 --> 00:01:03,280 filmmaker with a background in 32 00:01:07,350 --> 00:01:05,040 mathematical physics and i run this 33 00:01:09,429 --> 00:01:07,360 channel called theories of everything 34 00:01:11,109 --> 00:01:09,439 which is a podcast it's a podcast first 35 00:01:12,310 --> 00:01:11,119 and foremost so don't subscribe to this 36 00:01:14,390 --> 00:01:12,320 if you're not interested in the rest of 37 00:01:16,550 --> 00:01:14,400 the content and the rest of the content 38 00:01:18,469 --> 00:01:16,560 is about making comprehensible the 39 00:01:20,630 --> 00:01:18,479 different toes that exist the different 40 00:01:23,030 --> 00:01:20,640 theories of everything so for example 41 00:01:25,350 --> 00:01:23,040 wolfram's theory of everything or 42 00:01:27,030 --> 00:01:25,360 geometric unity that's coming up or 43 00:01:30,070 --> 00:01:27,040 quantum gravity well that's the 44 00:01:32,630 --> 00:01:30,080 seedlings of a toe string theory e8 etc 45 00:01:33,990 --> 00:01:32,640 etc we even cover the more larger 46 00:01:35,749 --> 00:01:34,000 philosophical ones because i'm 47 00:01:37,350 --> 00:01:35,759 interested in consciousness what role 48 00:01:39,109 --> 00:01:37,360 does that have to play with physics or 49 00:01:41,429 --> 00:01:39,119 can it be derived from physics what 50 00:01:43,590 --> 00:01:41,439 about free will what about god so you 51 00:01:44,710 --> 00:01:43,600 can think of this as largely what is 52 00:01:46,789 --> 00:01:44,720 reality 53 00:01:48,789 --> 00:01:46,799 okay let's contextualize the rest of 54 00:01:51,109 --> 00:01:48,799 this video because much of the 55 00:01:53,510 --> 00:01:51,119 misapprehension in learning comes 56 00:01:55,429 --> 00:01:53,520 generally from not understanding the 57 00:01:57,270 --> 00:01:55,439 context of what's being presented or 58 00:01:59,350 --> 00:01:57,280 worse the context isn't given to you at 59 00:02:00,550 --> 00:01:59,360 all there are time stamps here in every 60 00:02:02,789 --> 00:02:00,560 one of the toe videos and they're 61 00:02:04,389 --> 00:02:02,799 meticulously written so you can skip 62 00:02:05,910 --> 00:02:04,399 around if you like by the end of this 63 00:02:07,990 --> 00:02:05,920 you'll be able to calculate virtually 64 00:02:10,150 --> 00:02:08,000 any phenomenon as well as have some 65 00:02:12,229 --> 00:02:10,160 understanding of it specifically by the 66 00:02:14,470 --> 00:02:12,239 end of the next let's say 60 minutes 67 00:02:16,710 --> 00:02:14,480 with just high school mathematics you'll 68 00:02:18,790 --> 00:02:16,720 be able to answer the following without 69 00:02:22,070 --> 00:02:18,800 memorization in fact with derivation 70 00:02:25,030 --> 00:02:22,080 which is superior why is there only time 71 00:02:26,710 --> 00:02:25,040 so why is it that only time exists i 72 00:02:28,309 --> 00:02:26,720 could have said or i could have said 73 00:02:30,390 --> 00:02:28,319 only energy exists or i could have said 74 00:02:32,070 --> 00:02:30,400 only seconds or only length exists i 75 00:02:33,830 --> 00:02:32,080 just didn't want to come out of the gate 76 00:02:35,830 --> 00:02:33,840 sounding like a buddhist by saying hey 77 00:02:37,350 --> 00:02:35,840 all that exists is energy but you can 78 00:02:39,509 --> 00:02:37,360 equally replace that there what is the 79 00:02:40,630 --> 00:02:39,519 vacuum energy expectation i'm sure 80 00:02:42,790 --> 00:02:40,640 you've heard that this is the worst 81 00:02:45,030 --> 00:02:42,800 prediction in physics etc what are the 82 00:02:47,589 --> 00:02:45,040 bounds on extra dimensions why saying 83 00:02:49,910 --> 00:02:47,599 gravity is weak is worse than a false 84 00:02:53,430 --> 00:02:49,920 statement it's meaningless statement 85 00:02:55,509 --> 00:02:53,440 that deserves a bolded exclamation point 86 00:02:57,110 --> 00:02:55,519 great the neutron star pressure what is 87 00:02:58,309 --> 00:02:57,120 the pressure inside a neutron star by 88 00:03:00,949 --> 00:02:58,319 the end of this video you'll be able to 89 00:03:02,550 --> 00:03:00,959 answer that in almost a second 90 00:03:03,990 --> 00:03:02,560 microtubules for consciousness will 91 00:03:06,149 --> 00:03:04,000 delve a little bit into that that's 92 00:03:07,910 --> 00:03:06,159 penrose's theory why was magnetism 93 00:03:10,470 --> 00:03:07,920 understood so late that's a historical 94 00:03:12,149 --> 00:03:10,480 fact but you can actually derive it from 95 00:03:13,750 --> 00:03:12,159 fundamental principles we'll explain 96 00:03:15,589 --> 00:03:13,760 what that means what is the size of the 97 00:03:18,470 --> 00:03:15,599 earth yes you can derive the size of the 98 00:03:20,309 --> 00:03:18,480 earth approximately napkin calculations 99 00:03:22,070 --> 00:03:20,319 casmir pressure i'm sure you've heard 100 00:03:23,589 --> 00:03:22,080 that hey if you take some plates and 101 00:03:25,910 --> 00:03:23,599 then there's some mode that goes in 102 00:03:27,910 --> 00:03:25,920 between there are more modes outside and 103 00:03:30,070 --> 00:03:27,920 so the plates come together in a vacuum 104 00:03:32,630 --> 00:03:30,080 we'll also be covering knots and quantum 105 00:03:34,710 --> 00:03:32,640 gravity at least a modicum we'll also 106 00:03:37,190 --> 00:03:34,720 cover the schwinger limit and salvator 107 00:03:39,270 --> 00:03:37,200 pius's super force or the planck force 108 00:03:40,789 --> 00:03:39,280 we'll also talk about black holes now 109 00:03:42,229 --> 00:03:40,799 all of these facts look like they belong 110 00:03:43,750 --> 00:03:42,239 under the umbrella of physics except 111 00:03:45,750 --> 00:03:43,760 perhaps maybe the consciousness one 112 00:03:47,990 --> 00:03:45,760 penrose disagrees but all of them belong 113 00:03:49,589 --> 00:03:48,000 to physics and disparate fields and you 114 00:03:51,750 --> 00:03:49,599 would need to apply completely different 115 00:03:53,190 --> 00:03:51,760 frameworks to properly understand them 116 00:03:55,589 --> 00:03:53,200 that's true if you want to make a 117 00:03:57,509 --> 00:03:55,599 precise calculation then yes but if what 118 00:03:59,429 --> 00:03:57,519 you want is an estimate a napkin 119 00:04:00,390 --> 00:03:59,439 calculation then you don't need this you 120 00:04:03,350 --> 00:04:00,400 can use 121 00:04:05,589 --> 00:04:03,360 natural units now this video is akin to 122 00:04:07,350 --> 00:04:05,599 an introduction to the next video which 123 00:04:09,429 --> 00:04:07,360 is coming out perhaps a few months from 124 00:04:11,190 --> 00:04:09,439 now i don't plan on doing these lecture 125 00:04:12,710 --> 00:04:11,200 type videos like i mentioned this is a 126 00:04:15,509 --> 00:04:12,720 podcast channel don't plan on doing 127 00:04:18,069 --> 00:04:15,519 these much the next video will be about 128 00:04:19,110 --> 00:04:18,079 how to analyze and comprehend 129 00:04:24,629 --> 00:04:19,120 a 130 00:04:26,230 --> 00:04:24,639 beyond your current level of 131 00:04:28,550 --> 00:04:26,240 understanding so i'll be going through 132 00:04:30,230 --> 00:04:28,560 geometric unity and giving tips on 133 00:04:31,990 --> 00:04:30,240 learning physics and mathematics in 134 00:04:34,070 --> 00:04:32,000 general now let's get on to the approach 135 00:04:35,590 --> 00:04:34,080 of this video so number one what's 136 00:04:37,110 --> 00:04:35,600 different about this number one is that 137 00:04:39,189 --> 00:04:37,120 there will be 138 00:04:42,150 --> 00:04:39,199 quite a few digressions because it will 139 00:04:43,990 --> 00:04:42,160 be about how to think that is how to 140 00:04:45,430 --> 00:04:44,000 think about physics problems in general 141 00:04:48,629 --> 00:04:45,440 rather than how to just solve certain 142 00:04:51,590 --> 00:04:48,639 ones with natural units number two this 143 00:04:53,749 --> 00:04:51,600 is great for theory yes but and it's 144 00:04:55,110 --> 00:04:53,759 also great because it's practical the 145 00:04:56,230 --> 00:04:55,120 reason is that whenever you're dealing 146 00:04:58,390 --> 00:04:56,240 with numbers whenever you're dealing 147 00:05:00,469 --> 00:04:58,400 with units it's akin to a choice of a 148 00:05:02,230 --> 00:05:00,479 basis in the theoretical end you should 149 00:05:04,710 --> 00:05:02,240 try to construct whatever you're doing 150 00:05:07,029 --> 00:05:04,720 without reference to a choice of basis 151 00:05:08,710 --> 00:05:07,039 much of your existence in physics so far 152 00:05:11,590 --> 00:05:08,720 has taken place 153 00:05:13,110 --> 00:05:11,600 with an implicit choice of a basis when 154 00:05:14,870 --> 00:05:13,120 you're talking about some transpiration 155 00:05:17,110 --> 00:05:14,880 let's say you say it's well it's three 156 00:05:18,790 --> 00:05:17,120 meters to the left and two meters up but 157 00:05:20,550 --> 00:05:18,800 then the question is well three meters 158 00:05:22,550 --> 00:05:20,560 to the left from where two meters up 159 00:05:24,790 --> 00:05:22,560 from where and then also what is up what 160 00:05:27,189 --> 00:05:24,800 is left what are those directions per se 161 00:05:28,629 --> 00:05:27,199 now the real world per se doesn't care 162 00:05:30,390 --> 00:05:28,639 about your choice of coordinates doesn't 163 00:05:32,469 --> 00:05:30,400 care about the chart that you choose 164 00:05:33,990 --> 00:05:32,479 it's what we do in order to communicate 165 00:05:36,550 --> 00:05:34,000 with others as well as it makes it 166 00:05:37,990 --> 00:05:36,560 psychologically easier on ourselves but 167 00:05:40,710 --> 00:05:38,000 don't confuse the coordinates with the 168 00:05:42,790 --> 00:05:40,720 real world there is no detector that 169 00:05:44,390 --> 00:05:42,800 detects the coordinates in theoretical 170 00:05:46,710 --> 00:05:44,400 physics there's a saying that there's 171 00:05:49,430 --> 00:05:46,720 nothing noble in choosing a basis true 172 00:05:52,230 --> 00:05:49,440 nobility is being coordinate free number 173 00:05:54,390 --> 00:05:52,240 three it will be important for us to be 174 00:05:56,070 --> 00:05:54,400 precise so the reason is that otherwise 175 00:05:57,909 --> 00:05:56,080 you'll be confused and you won't realize 176 00:05:59,270 --> 00:05:57,919 where your confusion lies much of the 177 00:06:01,909 --> 00:05:59,280 time when you're a student and you're 178 00:06:03,350 --> 00:06:01,919 going to a professor or a lecturer or 179 00:06:04,550 --> 00:06:03,360 your tutor 180 00:06:06,070 --> 00:06:04,560 and they say well what is it that you 181 00:06:07,990 --> 00:06:06,080 don't understand sometimes you don't 182 00:06:09,909 --> 00:06:08,000 know where your misunderstanding is and 183 00:06:11,189 --> 00:06:09,919 so it's difficult to learn a subject and 184 00:06:13,510 --> 00:06:11,199 much of the time that comes from the 185 00:06:15,270 --> 00:06:13,520 subject not being explained specifically 186 00:06:16,950 --> 00:06:15,280 to you throughout this video i'll be 187 00:06:18,469 --> 00:06:16,960 throwing out tidbits perhaps different 188 00:06:19,990 --> 00:06:18,479 pieces of terminology that you don't 189 00:06:21,189 --> 00:06:20,000 understand that's okay it's for those 190 00:06:22,790 --> 00:06:21,199 who want to learn 191 00:06:24,950 --> 00:06:22,800 slightly more and i'll also be going 192 00:06:26,870 --> 00:06:24,960 through the specific steps i won't skip 193 00:06:28,390 --> 00:06:26,880 a step as often as i can and that's 194 00:06:30,790 --> 00:06:28,400 because i don't want you to be as 195 00:06:32,710 --> 00:06:30,800 confused as myself when i was learning 196 00:06:34,150 --> 00:06:32,720 much of this often steps are glossed 197 00:06:35,350 --> 00:06:34,160 over because the presenter is so 198 00:06:36,870 --> 00:06:35,360 familiar with them that they've 199 00:06:38,950 --> 00:06:36,880 forgotten what it's like to not 200 00:06:41,189 --> 00:06:38,960 understand a subject so for me when it's 201 00:06:43,590 --> 00:06:41,199 delineated specifically here you go from 202 00:06:45,430 --> 00:06:43,600 here to a to b to c rather than from 203 00:06:47,270 --> 00:06:45,440 rather than from b to d let's say then 204 00:06:49,350 --> 00:06:47,280 because the logical progression is made 205 00:06:51,830 --> 00:06:49,360 painstakingly clear you understand it 206 00:06:53,590 --> 00:06:51,840 better for example we will not be using 207 00:06:55,430 --> 00:06:53,600 this symbol 208 00:06:58,230 --> 00:06:55,440 what the heck is this 209 00:06:59,909 --> 00:06:58,240 what the heck 210 00:07:03,189 --> 00:06:59,919 is this 211 00:07:05,749 --> 00:07:03,199 now that deserves a bolded 212 00:07:07,510 --> 00:07:05,759 exclamation point the reason is that 213 00:07:09,270 --> 00:07:07,520 well is zero 214 00:07:10,070 --> 00:07:09,280 approximately one 215 00:07:12,550 --> 00:07:10,080 is 216 00:07:14,550 --> 00:07:12,560 one approximately ten ask the person 217 00:07:17,029 --> 00:07:14,560 who's teaching you please define this 218 00:07:18,550 --> 00:07:17,039 guy specifically what the heck is that 219 00:07:21,029 --> 00:07:18,560 this is not a mathematically well 220 00:07:22,870 --> 00:07:21,039 defined symbol this quote-unquote 221 00:07:24,550 --> 00:07:22,880 approximately symbol so instead what 222 00:07:27,670 --> 00:07:24,560 we'll use is this 223 00:07:29,749 --> 00:07:27,680 which means on the order of so 10 is on 224 00:07:33,029 --> 00:07:29,759 the order of 90. they have the same 225 00:07:36,469 --> 00:07:33,039 amount of digits 102 is on the same 226 00:07:38,629 --> 00:07:36,479 order of 999 for example in the interest 227 00:07:40,390 --> 00:07:38,639 of being precise technically this video 228 00:07:42,309 --> 00:07:40,400 should be titled how to approximately 229 00:07:44,390 --> 00:07:42,319 solve every physics question regarding 230 00:07:46,550 --> 00:07:44,400 observables but that's unwieldy and 231 00:07:48,950 --> 00:07:46,560 doesn't fit the title character count 232 00:07:52,070 --> 00:07:48,960 number four is will be s chewing 233 00:07:53,990 --> 00:07:52,080 exercises in favor of a point of view 234 00:07:55,510 --> 00:07:54,000 shift now generally when i watch videos 235 00:07:58,070 --> 00:07:55,520 online they're generally given by 236 00:07:59,990 --> 00:07:58,080 lecturers to university students and 237 00:08:01,510 --> 00:08:00,000 then they say okay we'll leave this as 238 00:08:04,390 --> 00:08:01,520 an exercise to you if you want to learn 239 00:08:06,629 --> 00:08:04,400 more do this as an exercise however even 240 00:08:08,469 --> 00:08:06,639 highly highly motivated people don't do 241 00:08:10,309 --> 00:08:08,479 those exercises generally you're trying 242 00:08:12,390 --> 00:08:10,319 to get an overview and the lecturer is 243 00:08:14,150 --> 00:08:12,400 used to assigning problems to students 244 00:08:15,990 --> 00:08:14,160 so they think that the viewer is going 245 00:08:17,589 --> 00:08:16,000 to actually do them but they don't and 246 00:08:19,909 --> 00:08:17,599 it's tedious and so what's more 247 00:08:21,990 --> 00:08:19,919 nourishing is to instead provide a point 248 00:08:24,230 --> 00:08:22,000 of view shift so that when you're going 249 00:08:25,909 --> 00:08:24,240 about your life you can convert all of 250 00:08:28,230 --> 00:08:25,919 these measurements that you see to 251 00:08:30,150 --> 00:08:28,240 energy for example rather than assigning 252 00:08:33,589 --> 00:08:30,160 exercises which almost no one does 253 00:08:36,790 --> 00:08:33,599 anyway so as chewing exercises 254 00:08:38,389 --> 00:08:36,800 in favor of point of view firstly 255 00:08:39,990 --> 00:08:38,399 it's easier to get this shift of 256 00:08:41,829 --> 00:08:40,000 perspective and number two it's more 257 00:08:43,670 --> 00:08:41,839 enjoyable it's fun number three it's 258 00:08:45,990 --> 00:08:43,680 more practical the fifth point is that 259 00:08:47,110 --> 00:08:46,000 it will be extremely lean and what i 260 00:08:49,350 --> 00:08:47,120 mean by that is that there will be 261 00:08:51,269 --> 00:08:49,360 little fat there will be little that's 262 00:08:53,110 --> 00:08:51,279 extraneous this is meant to be a video 263 00:08:54,790 --> 00:08:53,120 that you can watch you can re-watch not 264 00:08:56,389 --> 00:08:54,800 only when you've 265 00:08:57,590 --> 00:08:56,399 forgotten about natural units and you 266 00:08:59,030 --> 00:08:57,600 want to 267 00:09:00,790 --> 00:08:59,040 get some understanding get some handle 268 00:09:03,350 --> 00:09:00,800 on how to calculate with them do napkin 269 00:09:04,949 --> 00:09:03,360 calculations but also 270 00:09:07,110 --> 00:09:04,959 when you've lost some motivation to 271 00:09:10,470 --> 00:09:07,120 learn mathematics or physics there will 272 00:09:12,630 --> 00:09:10,480 be myriad points throughout about 273 00:09:15,350 --> 00:09:12,640 how to think about mathematics and 274 00:09:17,110 --> 00:09:15,360 physics in terms of a general approach 275 00:09:19,269 --> 00:09:17,120 to learning like i mentioned before this 276 00:09:20,949 --> 00:09:19,279 latter point will be expanded upon in 277 00:09:22,790 --> 00:09:20,959 some video that i'll release in a few 278 00:09:23,910 --> 00:09:22,800 months about going through a physics 279 00:09:25,829 --> 00:09:23,920 paper that you currently don't 280 00:09:27,829 --> 00:09:25,839 understand some theoretical physics one 281 00:09:29,990 --> 00:09:27,839 and i believe i'll be doing geometric 282 00:09:30,790 --> 00:09:30,000 unity number six now this one's more for 283 00:09:34,710 --> 00:09:30,800 you 284 00:09:36,790 --> 00:09:34,720 a part of this video that's fine keep 285 00:09:39,350 --> 00:09:36,800 pushing this comes from wheeler the 286 00:09:40,710 --> 00:09:39,360 point is not to drink from the fire hose 287 00:09:43,430 --> 00:09:40,720 that's what we think we're supposed to 288 00:09:44,230 --> 00:09:43,440 do but instead you're simply supposed to 289 00:09:45,350 --> 00:09:44,240 get 290 00:09:46,870 --> 00:09:45,360 wet 291 00:09:48,470 --> 00:09:46,880 same with watching the podcasts on this 292 00:09:50,870 --> 00:09:48,480 channel sometimes they're extremely 293 00:09:53,190 --> 00:09:50,880 technical people say well i i can't 294 00:09:55,430 --> 00:09:53,200 understand so and so that's fine just 295 00:09:57,350 --> 00:09:55,440 keep watching the first passage is 296 00:09:59,670 --> 00:09:57,360 generally to just know where are you 297 00:10:01,430 --> 00:09:59,680 going so that you can contextualize the 298 00:10:02,949 --> 00:10:01,440 understanding that comes earlier much of 299 00:10:04,870 --> 00:10:02,959 the time we're told look physics and 300 00:10:06,550 --> 00:10:04,880 mathematics you build upon it and you 301 00:10:08,710 --> 00:10:06,560 have to know the foundations otherwise 302 00:10:10,470 --> 00:10:08,720 the top will be shaky and that's true 303 00:10:12,870 --> 00:10:10,480 but it's 304 00:10:14,870 --> 00:10:12,880 it's often useful to keep going even 305 00:10:17,030 --> 00:10:14,880 when you don't understand simply so that 306 00:10:18,310 --> 00:10:17,040 you can know where are you going because 307 00:10:20,230 --> 00:10:18,320 your misapprehension about the 308 00:10:21,430 --> 00:10:20,240 fundamental steps 309 00:10:23,910 --> 00:10:21,440 come from not being able to 310 00:10:25,829 --> 00:10:23,920 contextualize it so it's fine keep going 311 00:10:27,590 --> 00:10:25,839 don't feel like i can't drink quote 312 00:10:30,150 --> 00:10:27,600 unquote from the fire hose the point is 313 00:10:31,750 --> 00:10:30,160 simply get soaked and trust that the 314 00:10:33,670 --> 00:10:31,760 learning will occur 315 00:10:35,590 --> 00:10:33,680 all right let's get into this what are 316 00:10:37,829 --> 00:10:35,600 natural units in order to understand 317 00:10:42,069 --> 00:10:37,839 what natural units are we want to know 318 00:10:43,350 --> 00:10:42,079 what are units so for example what is a 319 00:10:44,150 --> 00:10:43,360 meter 320 00:10:47,670 --> 00:10:44,160 or 321 00:10:49,590 --> 00:10:47,680 if you're being canadian a meter 322 00:10:50,949 --> 00:10:49,600 i'm based in toronto if that wasn't 323 00:10:53,910 --> 00:10:50,959 clear already 324 00:10:57,430 --> 00:10:53,920 what is a second 325 00:11:01,670 --> 00:10:58,949 now you'll get fairly frenzied if you 326 00:11:03,430 --> 00:11:01,680 think about this for quite some time as 327 00:11:06,550 --> 00:11:03,440 i have that is metaphysically what the 328 00:11:08,949 --> 00:11:06,560 heck is a second what is a meter what is 329 00:11:11,910 --> 00:11:08,959 length science actually doesn't answer 330 00:11:13,990 --> 00:11:11,920 what is questions and this is something 331 00:11:15,829 --> 00:11:14,000 that's not taught to you science isn't 332 00:11:17,350 --> 00:11:15,839 materialistic science isn't 333 00:11:19,910 --> 00:11:17,360 immaterialistic 334 00:11:21,110 --> 00:11:19,920 it's operational and this is a point 335 00:11:22,550 --> 00:11:21,120 that 336 00:11:24,230 --> 00:11:22,560 many people don't seem to understand 337 00:11:26,470 --> 00:11:24,240 including scientists science is 338 00:11:27,990 --> 00:11:26,480 metaphysically agnostic meaning that it 339 00:11:30,230 --> 00:11:28,000 doesn't actually make a claim onto 340 00:11:31,990 --> 00:11:30,240 ontology it doesn't tell you what is 341 00:11:34,069 --> 00:11:32,000 instead science gives operational 342 00:11:35,829 --> 00:11:34,079 meanings so what is a second it's 343 00:11:38,230 --> 00:11:35,839 something like nine 344 00:11:39,910 --> 00:11:38,240 comma one nine two comma i don't know 345 00:11:41,509 --> 00:11:39,920 those three seven seven zero it's one of 346 00:11:43,190 --> 00:11:41,519 those numbers you memorize as a child to 347 00:11:45,509 --> 00:11:43,200 show how clever you are let's look it up 348 00:11:49,110 --> 00:11:45,519 on wikipedia 349 00:11:50,949 --> 00:11:49,120 so let's do this wikipedia a second 350 00:11:53,910 --> 00:11:50,959 it says here the second is equal to the 351 00:11:55,030 --> 00:11:53,920 duration of 9 192 631 that's what i 352 00:11:56,790 --> 00:11:55,040 forgot 353 00:11:58,710 --> 00:11:56,800 seven seven zero periods of the 354 00:12:00,550 --> 00:11:58,720 radiation corresponding to the 355 00:12:02,389 --> 00:12:00,560 transition between hyperfine levels of 356 00:12:04,150 --> 00:12:02,399 the unperturbed ground state of a 357 00:12:05,750 --> 00:12:04,160 cystium atom a certain isotope of a 358 00:12:07,509 --> 00:12:05,760 cystium atom 359 00:12:09,509 --> 00:12:07,519 okay so then the natural question that 360 00:12:10,389 --> 00:12:09,519 comes up is why 361 00:12:11,829 --> 00:12:10,399 this 362 00:12:16,790 --> 00:12:11,839 number 363 00:12:19,190 --> 00:12:16,800 and the reason is because in london many 364 00:12:21,110 --> 00:12:19,200 decades ago someone in some back alley 365 00:12:22,790 --> 00:12:21,120 took methamphetamine on a tuesday night 366 00:12:24,550 --> 00:12:22,800 and came up with that number now i'm not 367 00:12:26,629 --> 00:12:24,560 kidding it may as well be that to 368 00:12:28,230 --> 00:12:26,639 someone studying high energy physics in 369 00:12:29,990 --> 00:12:28,240 the same way that 370 00:12:31,190 --> 00:12:30,000 well what the heck is a kilogram what is 371 00:12:32,949 --> 00:12:31,200 a kilogram 372 00:12:35,430 --> 00:12:32,959 it means you go to 373 00:12:37,190 --> 00:12:35,440 paris you go outside paris actually so 374 00:12:40,389 --> 00:12:37,200 on the borders of paris you go to some 375 00:12:43,190 --> 00:12:41,910 and you deal with people being 376 00:12:45,110 --> 00:12:43,200 condescending to you because you don't 377 00:12:47,750 --> 00:12:45,120 speak english then you duplicate this 378 00:12:50,389 --> 00:12:47,760 little metal slab that's in paris you 379 00:12:53,190 --> 00:12:50,399 duplicate it 67 times so that you have 380 00:12:55,509 --> 00:12:53,200 68 of them in total i'm just being quick 381 00:12:58,069 --> 00:12:55,519 with my writing 68 of them is in total 382 00:13:00,230 --> 00:12:58,079 then you measure yourself on a scale 383 00:13:01,910 --> 00:13:00,240 and these two numbers will coincide 384 00:13:04,310 --> 00:13:01,920 that's what it means it's an operational 385 00:13:07,190 --> 00:13:04,320 definition now physicists like to use 386 00:13:09,509 --> 00:13:07,200 units that appear in nature so units 387 00:13:11,350 --> 00:13:09,519 that appear 388 00:13:12,629 --> 00:13:11,360 and those we call 389 00:13:13,990 --> 00:13:12,639 natural 390 00:13:15,509 --> 00:13:14,000 units 391 00:13:17,030 --> 00:13:15,519 now there is some 392 00:13:18,470 --> 00:13:17,040 at least with me there's some 393 00:13:20,470 --> 00:13:18,480 controversy with what's considered 394 00:13:22,069 --> 00:13:20,480 natural because when someone comes to 395 00:13:23,750 --> 00:13:22,079 you with a 396 00:13:25,590 --> 00:13:23,760 some dish and they say this is a natural 397 00:13:27,829 --> 00:13:25,600 dish and that's unnatural well what do 398 00:13:29,670 --> 00:13:27,839 you mean that that those doritos that 399 00:13:31,509 --> 00:13:29,680 are unnatural did they come from outside 400 00:13:32,790 --> 00:13:31,519 this universe from some void because 401 00:13:34,870 --> 00:13:32,800 isn't everything in this universe 402 00:13:36,949 --> 00:13:34,880 natural aren't we a product of nature 403 00:13:39,350 --> 00:13:36,959 and so what we create is natural 404 00:13:41,269 --> 00:13:39,360 okay what a physicist means by natural 405 00:13:43,110 --> 00:13:41,279 is that it's invariant across the 406 00:13:45,269 --> 00:13:43,120 universe as far as we can tell to be 407 00:13:47,829 --> 00:13:45,279 extremely precise what we mean when we 408 00:13:50,389 --> 00:13:47,839 say natural units natural in the natural 409 00:13:51,990 --> 00:13:50,399 units is natural with respect to our 410 00:13:54,310 --> 00:13:52,000 current understanding in order to make 411 00:13:57,670 --> 00:13:54,320 certain equations simpler and remove 412 00:14:00,870 --> 00:13:57,680 arbitrary human qualities 413 00:14:03,189 --> 00:14:00,880 and not just human qualities well in 414 00:14:05,269 --> 00:14:03,199 some sense even an electron is a human 415 00:14:06,470 --> 00:14:05,279 construct in the sense that it's there 416 00:14:08,069 --> 00:14:06,480 because it 417 00:14:09,990 --> 00:14:08,079 nature doesn't parse itself out into 418 00:14:12,550 --> 00:14:10,000 these elements i mean you can say 419 00:14:14,310 --> 00:14:12,560 elementary elementary seems to be an 420 00:14:15,670 --> 00:14:14,320 objective quality because of the way 421 00:14:17,110 --> 00:14:15,680 that we define what an elementary 422 00:14:18,949 --> 00:14:17,120 particle is it's an irreducible 423 00:14:20,470 --> 00:14:18,959 representation of something so the fact 424 00:14:23,030 --> 00:14:20,480 that it's irreducible means if it could 425 00:14:24,629 --> 00:14:23,040 be reduced in this block matrix form 426 00:14:26,710 --> 00:14:24,639 then we can just decompose it and we'd 427 00:14:29,350 --> 00:14:26,720 say those elements are elementary but 428 00:14:31,269 --> 00:14:29,360 the reason why we set aside some special 429 00:14:33,990 --> 00:14:31,279 canonical place for the electron is 430 00:14:36,069 --> 00:14:34,000 because it's useful for us it makes 431 00:14:38,150 --> 00:14:36,079 our models easier to understand simpler 432 00:14:40,790 --> 00:14:38,160 outcomes razer etcetera there's plenty 433 00:14:42,550 --> 00:14:40,800 of philosophy that undergirds natural 434 00:14:43,910 --> 00:14:42,560 again this is not usually explained and 435 00:14:45,670 --> 00:14:43,920 you'll be led astray if you don't 436 00:14:47,509 --> 00:14:45,680 understand that point now here's another 437 00:14:51,030 --> 00:14:47,519 point that's ordinarily not explained 438 00:14:53,590 --> 00:14:52,550 have 439 00:14:56,829 --> 00:14:53,600 no 440 00:14:56,839 --> 00:15:02,949 they're dimensionless 441 00:15:07,269 --> 00:15:05,269 let's say slash ratios 442 00:15:09,509 --> 00:15:07,279 okay now what's meant by that again when 443 00:15:11,430 --> 00:15:09,519 you say that you weigh 68 kilograms it 444 00:15:13,189 --> 00:15:11,440 means you take 68 of some other 445 00:15:17,350 --> 00:15:13,199 reference 446 00:15:19,750 --> 00:15:17,360 then you stack 68 of them and then you 447 00:15:20,870 --> 00:15:19,760 get yourself it's actually 68 it's not 448 00:15:22,550 --> 00:15:20,880 68 449 00:15:24,150 --> 00:15:22,560 kilograms per se 450 00:15:26,230 --> 00:15:24,160 you can also think of this in another 451 00:15:27,829 --> 00:15:26,240 way if you wanted to speak to aliens 452 00:15:29,670 --> 00:15:27,839 which by the way is another 453 00:15:32,870 --> 00:15:29,680 topic on this channel not speaking to 454 00:15:36,470 --> 00:15:32,880 aliens per se but ufos then it would be 455 00:15:38,870 --> 00:15:36,480 foolish to say i way 68 of some 456 00:15:40,790 --> 00:15:38,880 product from france now you can reverse 457 00:15:42,230 --> 00:15:40,800 this and imagine an alien is speaking to 458 00:15:44,550 --> 00:15:42,240 you and you say well how much does your 459 00:15:46,389 --> 00:15:44,560 craft weigh and they say oh it weighs 460 00:15:48,150 --> 00:15:46,399 four gar bars and then you're like what 461 00:15:49,269 --> 00:15:48,160 the heck is a garbar then they say well 462 00:15:51,030 --> 00:15:49,279 that's how much 463 00:15:53,030 --> 00:15:51,040 liquid we release from our bourbons 464 00:15:55,590 --> 00:15:53,040 every two farkles it doesn't provide 465 00:15:57,910 --> 00:15:55,600 much information so instead we do what 466 00:16:00,470 --> 00:15:57,920 you see colloquially which is c equals h 467 00:16:02,069 --> 00:16:00,480 bar equals one okay let's get to some 468 00:16:03,749 --> 00:16:02,079 myths about natural units before 469 00:16:06,150 --> 00:16:03,759 exploring exactly what that means so 470 00:16:08,150 --> 00:16:06,160 firstly one of the myths is that we just 471 00:16:11,590 --> 00:16:08,160 simply set 472 00:16:13,749 --> 00:16:11,600 c to equal one to equal h bar this is a 473 00:16:15,910 --> 00:16:13,759 meaningless statement as it's written 474 00:16:19,269 --> 00:16:15,920 and the reason is it doesn't they can't 475 00:16:21,430 --> 00:16:19,279 equal one it means we're now using 476 00:16:23,749 --> 00:16:21,440 the speed of light and h bar as a 477 00:16:25,189 --> 00:16:23,759 reference for some other quantity that 478 00:16:27,430 --> 00:16:25,199 we're trying to develop if you're 479 00:16:28,710 --> 00:16:27,440 confused about this now then that means 480 00:16:30,470 --> 00:16:28,720 you're thinking about this correctly 481 00:16:32,230 --> 00:16:30,480 because it's not ordinarily explained 482 00:16:34,069 --> 00:16:32,240 it's left ambiguous 483 00:16:36,470 --> 00:16:34,079 let's look at this let's imagine what is 484 00:16:37,590 --> 00:16:36,480 the speed of let's say some car on the 485 00:16:42,389 --> 00:16:37,600 highway 486 00:16:45,670 --> 00:16:42,399 equals we would say 100 487 00:16:47,829 --> 00:16:46,550 per 488 00:16:49,670 --> 00:16:47,839 hour 489 00:16:51,910 --> 00:16:49,680 these are the units 490 00:16:54,310 --> 00:16:51,920 and that's the magnitude with respect to 491 00:16:56,310 --> 00:16:54,320 those units so if i wanted to say what 492 00:16:57,670 --> 00:16:56,320 is the speed 493 00:16:59,829 --> 00:16:57,680 sorry that's already speed what is the 494 00:17:03,350 --> 00:16:59,839 speed of light 495 00:17:06,549 --> 00:17:03,360 what we mean is two nine nine seven nine 496 00:17:08,309 --> 00:17:06,559 2 4 5 8 again it's one of those numbers 497 00:17:11,350 --> 00:17:08,319 you try to show how clever you are when 498 00:17:13,350 --> 00:17:11,360 you're a child by memorizing meters per 499 00:17:16,390 --> 00:17:13,360 second 500 00:17:19,510 --> 00:17:16,400 now look this is actually what c is c 501 00:17:22,470 --> 00:17:19,520 refers to all of this c doesn't just 502 00:17:24,390 --> 00:17:22,480 refer to the magnitude c refers to the 503 00:17:27,029 --> 00:17:24,400 entirety of it including the units so 504 00:17:29,750 --> 00:17:27,039 when someone says c equals one c equals 505 00:17:32,390 --> 00:17:29,760 one what they actually mean is that we 506 00:17:35,830 --> 00:17:32,400 are now using units where we've taken 507 00:17:39,430 --> 00:17:35,840 that two nine nine seven nine two four 508 00:17:41,669 --> 00:17:39,440 five eight meters per second and we've 509 00:17:44,310 --> 00:17:41,679 placed it in here so we've taken this 510 00:17:46,950 --> 00:17:44,320 guy and we've placed it in here see all 511 00:17:48,549 --> 00:17:46,960 of this is not ordinarily explained and 512 00:17:51,029 --> 00:17:48,559 it's because 513 00:17:53,350 --> 00:17:51,039 as an undergraduate you're especially 514 00:17:56,150 --> 00:17:53,360 used to writing with reference to a 515 00:17:58,390 --> 00:17:56,160 coordinate basis which is why i said try 516 00:17:59,669 --> 00:17:58,400 to do everything you can coordinate free 517 00:18:01,430 --> 00:17:59,679 if you have an instructor you're lucky 518 00:18:03,430 --> 00:18:01,440 enough to have an instructor you always 519 00:18:05,510 --> 00:18:03,440 ask how can you represent these 520 00:18:07,029 --> 00:18:05,520 equations coordinate free another way of 521 00:18:09,190 --> 00:18:07,039 thinking about this is that you we have 522 00:18:11,270 --> 00:18:09,200 graphs in physics and math constantly 523 00:18:12,950 --> 00:18:11,280 plot and those etchings are akin to 524 00:18:15,510 --> 00:18:12,960 choosing a unit the fact that we put 525 00:18:17,909 --> 00:18:15,520 lines with etchings means we've chosen a 526 00:18:21,750 --> 00:18:17,919 coordinate so these etchings outward are 527 00:18:23,350 --> 00:18:21,760 it implicitly a choice of coordinates 528 00:18:25,350 --> 00:18:23,360 but nature but if you look again like i 529 00:18:27,029 --> 00:18:25,360 mentioned there's no detector that can 530 00:18:29,029 --> 00:18:27,039 detect the coordinates much like if you 531 00:18:30,470 --> 00:18:29,039 take a picture with your phone and you 532 00:18:32,789 --> 00:18:30,480 then look at it on the screen and you 533 00:18:34,230 --> 00:18:32,799 zoom in you see pixels the pixels are an 534 00:18:36,230 --> 00:18:34,240 artifact of you taking a picture and 535 00:18:38,549 --> 00:18:36,240 trying to manipulate it in some manner 536 00:18:39,350 --> 00:18:38,559 the world itself is not pixelated unless 537 00:18:41,190 --> 00:18:39,360 you're 538 00:18:42,630 --> 00:18:41,200 to believe thomas campbell or donald 539 00:18:44,310 --> 00:18:42,640 hoffman another reason to think 540 00:18:46,310 --> 00:18:44,320 coordinate free is you'll start to 541 00:18:48,630 --> 00:18:46,320 construct constructions that actually 542 00:18:49,990 --> 00:18:48,640 depend on your coordinates when they in 543 00:18:51,669 --> 00:18:50,000 fact don't in nature and then you'll 544 00:18:54,390 --> 00:18:51,679 wonder why are you getting an incorrect 545 00:18:58,070 --> 00:18:54,400 answer so for example in physics and so 546 00:19:00,070 --> 00:18:58,080 on we often use let's say this 547 00:19:01,510 --> 00:19:00,080 and then we represent it in some 548 00:19:02,549 --> 00:19:01,520 symmetry this is how theoretical 549 00:19:04,470 --> 00:19:02,559 physicist 550 00:19:06,390 --> 00:19:04,480 generally reference matrices they don't 551 00:19:08,549 --> 00:19:06,400 like them so they call them symmetries 552 00:19:09,990 --> 00:19:08,559 these rows and columns but then 553 00:19:12,230 --> 00:19:10,000 you also would reference this same 554 00:19:14,870 --> 00:19:12,240 object 555 00:19:16,390 --> 00:19:14,880 with numbers in a similar manner 556 00:19:19,110 --> 00:19:16,400 however they transform completely 557 00:19:20,870 --> 00:19:19,120 differently so one is an endomorphism 558 00:19:22,789 --> 00:19:20,880 and then the other is a two form or a 559 00:19:24,230 --> 00:19:22,799 bilinear form and they transform 560 00:19:25,990 --> 00:19:24,240 completely differently and which is why 561 00:19:28,150 --> 00:19:26,000 you have transpose which is it's not an 562 00:19:30,310 --> 00:19:28,160 ill-defined object but it's a strangely 563 00:19:31,510 --> 00:19:30,320 defined object the inverse of a matrix 564 00:19:33,029 --> 00:19:31,520 is more 565 00:19:35,669 --> 00:19:33,039 copacetic but the 566 00:19:37,110 --> 00:19:35,679 transpose is a strange one so this one 567 00:19:40,710 --> 00:19:37,120 is a two form 568 00:19:43,110 --> 00:19:40,720 a bilinear form the metric in the s 569 00:19:45,270 --> 00:19:43,120 within einstein equations is a two form 570 00:19:47,510 --> 00:19:45,280 it's a bilinear form and also the 571 00:19:48,710 --> 00:19:47,520 determinants of endomorphism is a 572 00:19:50,870 --> 00:19:48,720 completely different object it's 573 00:19:53,350 --> 00:19:50,880 invariant compared to the determinant of 574 00:19:54,710 --> 00:19:53,360 a two form or a bilinear form and then 575 00:19:56,390 --> 00:19:54,720 as you start to understand this 576 00:19:57,990 --> 00:19:56,400 coordinate free you'll realize that 577 00:19:59,909 --> 00:19:58,000 there's a special place in hell for the 578 00:20:02,870 --> 00:19:59,919 person who developed the transpose it's 579 00:20:04,630 --> 00:20:02,880 an unwieldy object another one that will 580 00:20:06,549 --> 00:20:04,640 confuse you if you think in terms of 581 00:20:07,830 --> 00:20:06,559 coordinates is that the wave function 582 00:20:10,470 --> 00:20:07,840 you ordinarily think of the wave 583 00:20:14,630 --> 00:20:10,480 function as going from some rd or some 584 00:20:20,070 --> 00:20:16,390 to 585 00:20:22,630 --> 00:20:20,080 complex numbers but actually this guy is 586 00:20:23,750 --> 00:20:22,640 a section 587 00:20:25,990 --> 00:20:23,760 on a c 588 00:20:27,750 --> 00:20:26,000 line bundle and you need to understand 589 00:20:29,430 --> 00:20:27,760 bundles in order to understand it 590 00:20:31,029 --> 00:20:29,440 coordinate free so that you can do not 591 00:20:32,630 --> 00:20:31,039 only polar coordinates and you wonder 592 00:20:33,669 --> 00:20:32,640 why the heck does the derivative change 593 00:20:34,950 --> 00:20:33,679 well that makes sense when you 594 00:20:36,710 --> 00:20:34,960 understand it in terms of a principle 595 00:20:39,430 --> 00:20:36,720 bundle and then the associated bundle 596 00:20:40,950 --> 00:20:39,440 but also in terms of no longer staying 597 00:20:42,950 --> 00:20:40,960 in rd what if you want to move to a 598 00:20:44,470 --> 00:20:42,960 curved space for quantum mechanics what 599 00:20:46,549 --> 00:20:44,480 if you want to do quantum mechanics on a 600 00:20:48,549 --> 00:20:46,559 curved space this is why one should try 601 00:20:50,070 --> 00:20:48,559 their best to understand what the heck 602 00:20:51,909 --> 00:20:50,080 is going on without reference to 603 00:20:53,110 --> 00:20:51,919 coordinates and then go to coordinates 604 00:20:55,110 --> 00:20:53,120 when you're actually making a 605 00:20:57,190 --> 00:20:55,120 calculation so that's why this is a myth 606 00:20:59,029 --> 00:20:57,200 we just simply set c to equal one to 607 00:21:00,630 --> 00:20:59,039 equal h bar by the way what is h bar 608 00:21:02,390 --> 00:21:00,640 well that's a bit more abstract you 609 00:21:03,669 --> 00:21:02,400 don't need to understand that for the 610 00:21:05,750 --> 00:21:03,679 sake of this video 611 00:21:07,669 --> 00:21:05,760 but this is an ill-defined equation 612 00:21:09,750 --> 00:21:07,679 there's actually a caveat here that will 613 00:21:11,270 --> 00:21:09,760 come into play later another way of 614 00:21:14,149 --> 00:21:11,280 thinking about it is imagine you have 615 00:21:16,350 --> 00:21:14,159 one usd one us dollar 616 00:21:20,630 --> 00:21:16,360 sometimes you would say it equals 617 00:21:22,390 --> 00:21:20,640 127 yen it doesn't actually equal 127 618 00:21:25,270 --> 00:21:22,400 yen otherwise when you have a us dollar 619 00:21:27,430 --> 00:21:25,280 it would just be 127 yen what it means 620 00:21:29,110 --> 00:21:27,440 is that there's something called value 621 00:21:29,990 --> 00:21:29,120 or some monetary equivalent that's 622 00:21:31,190 --> 00:21:30,000 another way of thinking about it 623 00:21:33,110 --> 00:21:31,200 conversion 624 00:21:35,029 --> 00:21:33,120 what it means that you go here with some 625 00:21:36,549 --> 00:21:35,039 mapping let's say m and then here with 626 00:21:38,149 --> 00:21:36,559 some mapping that's that's called let's 627 00:21:41,110 --> 00:21:38,159 say m prime 628 00:21:43,190 --> 00:21:41,120 what it means is that you do 629 00:21:45,430 --> 00:21:43,200 let's say m prime 630 00:21:47,990 --> 00:21:45,440 inverse see we have to make all these 631 00:21:49,350 --> 00:21:48,000 constructions now and then that's after 632 00:21:52,630 --> 00:21:49,360 you've already done m so you've gone 633 00:21:54,549 --> 00:21:52,640 from here and then you go back up there 634 00:21:55,990 --> 00:21:54,559 they're not the same so another way of 635 00:21:57,750 --> 00:21:56,000 thinking about this is imagine you want 636 00:21:59,029 --> 00:21:57,760 to change lengths instead of using 637 00:22:00,549 --> 00:21:59,039 meters because you think meters are 638 00:22:02,950 --> 00:22:00,559 strange for some reason you want to 639 00:22:04,789 --> 00:22:02,960 measure everyone in terms of lady gaga 640 00:22:06,470 --> 00:22:04,799 so you have lady gaga here which i'm 641 00:22:08,149 --> 00:22:06,480 going to call 642 00:22:09,350 --> 00:22:08,159 lg 643 00:22:10,870 --> 00:22:09,360 so then let's say we want to measure 644 00:22:14,230 --> 00:22:10,880 someone else let's say some let's say 645 00:22:16,870 --> 00:22:14,240 goku so what is goku goku 646 00:22:19,029 --> 00:22:16,880 equals maybe one and a half lady gaga's 647 00:22:20,470 --> 00:22:19,039 in length so you take half of lady gaga 648 00:22:22,630 --> 00:22:20,480 and you stack that again on lady gag and 649 00:22:25,190 --> 00:22:22,640 you get a goku in terms of length how 650 00:22:28,070 --> 00:22:25,200 about tony robbins well that's let's say 651 00:22:30,149 --> 00:22:28,080 two lady gagas now what we're doing here 652 00:22:32,230 --> 00:22:30,159 is we're saying i'm going to make all my 653 00:22:34,390 --> 00:22:32,240 future length measurements in terms of 654 00:22:36,710 --> 00:22:34,400 lady gaga for whatever reason in the 655 00:22:38,789 --> 00:22:36,720 same way that generally speaking the 656 00:22:40,870 --> 00:22:38,799 prices on the internet can be made in 657 00:22:42,710 --> 00:22:40,880 reference to the us dollar and then you 658 00:22:45,590 --> 00:22:42,720 do some conversion to find out its 659 00:22:47,270 --> 00:22:45,600 equivalent monetary value in some other 660 00:22:48,470 --> 00:22:47,280 currency in the same way what we're 661 00:22:50,070 --> 00:22:48,480 doing right here is we're referencing 662 00:22:52,390 --> 00:22:50,080 everyone's height in terms of lady 663 00:22:54,630 --> 00:22:52,400 gaga's height and it just as foolish as 664 00:22:57,110 --> 00:22:54,640 it would be to say lady gaga equals one 665 00:22:59,590 --> 00:22:57,120 equals the usd just as foolish as this 666 00:23:01,830 --> 00:22:59,600 equation is it's tantamount to saying c 667 00:23:03,669 --> 00:23:01,840 equals one equals h bar there's so much 668 00:23:04,950 --> 00:23:03,679 that goes into a statement like that 669 00:23:06,630 --> 00:23:04,960 that's just seeing that gives the 670 00:23:08,789 --> 00:23:06,640 impression oh physicists are just 671 00:23:10,310 --> 00:23:08,799 setting it equal to one so no this 672 00:23:12,310 --> 00:23:10,320 statement is foolish and what's 673 00:23:14,549 --> 00:23:12,320 underneath that is saying hey i'm going 674 00:23:16,149 --> 00:23:14,559 to now measure everything in terms of 675 00:23:18,230 --> 00:23:16,159 the speed of light so i want to measure 676 00:23:19,590 --> 00:23:18,240 my car maybe it's a millionth of the 677 00:23:20,789 --> 00:23:19,600 speed of light i don't know i don't want 678 00:23:22,549 --> 00:23:20,799 to do the calculation right now but 679 00:23:24,870 --> 00:23:22,559 let's say it's a millionth of a speed of 680 00:23:27,590 --> 00:23:24,880 light so then i say well the speed of 681 00:23:28,630 --> 00:23:27,600 walking let's say 682 00:23:38,149 --> 00:23:28,640 is 683 00:23:40,149 --> 00:23:38,159 light units that's what it means okay so 684 00:23:42,870 --> 00:23:40,159 this is all including 685 00:23:44,390 --> 00:23:42,880 by the way this right here 686 00:23:47,110 --> 00:23:44,400 this is all 687 00:23:50,390 --> 00:23:48,549 you have to understand what's lurking 688 00:23:51,590 --> 00:23:50,400 underneath so in this example the value 689 00:23:53,350 --> 00:23:51,600 is what's being referenced when i say 690 00:23:54,390 --> 00:23:53,360 the real world that's what i mean is 691 00:23:57,029 --> 00:23:54,400 that there's something else that's 692 00:23:59,990 --> 00:23:57,039 tangible that i'm trying to represent my 693 00:24:02,230 --> 00:24:00,000 quantity in reference to so from now on 694 00:24:04,230 --> 00:24:02,240 we're going to no longer say that this 695 00:24:05,750 --> 00:24:04,240 is moving at 500 meters per second we're 696 00:24:07,430 --> 00:24:05,760 going to say that this is moving at a 697 00:24:09,110 --> 00:24:07,440 fraction of the speed of light by the 698 00:24:11,750 --> 00:24:09,120 way this should be a definition and that 699 00:24:14,149 --> 00:24:11,760 refers to the entire object there not 700 00:24:15,909 --> 00:24:14,159 just this this is just the magnitude and 701 00:24:17,430 --> 00:24:15,919 that's where this is misleading because 702 00:24:19,110 --> 00:24:17,440 it's just showing you the magnitude but 703 00:24:21,029 --> 00:24:19,120 how the heck can c equal this in the 704 00:24:22,470 --> 00:24:21,039 same way how the heck can lady gaga 705 00:24:24,630 --> 00:24:22,480 equal the us 706 00:24:30,230 --> 00:24:24,640 equals one that is myth number one now 707 00:24:33,510 --> 00:24:31,190 of 708 00:24:34,710 --> 00:24:33,520 natural 709 00:24:36,470 --> 00:24:34,720 units by the way it doesn't matter 710 00:24:40,149 --> 00:24:36,480 whether you capitalize it or not the 711 00:24:40,950 --> 00:24:40,159 advantage of natural units is that 712 00:24:44,830 --> 00:24:40,960 it 713 00:24:49,669 --> 00:24:46,630 equations 714 00:24:54,230 --> 00:24:51,590 where is the myth here 715 00:24:56,789 --> 00:24:54,240 the myth is one of these words it's an 716 00:24:59,110 --> 00:24:56,799 article it's the definite article the 717 00:25:02,070 --> 00:24:59,120 the advantage that's one it should 718 00:25:03,909 --> 00:25:02,080 actually be a advantage or an advantage 719 00:25:05,909 --> 00:25:03,919 the primary advantage is that it allows 720 00:25:08,070 --> 00:25:05,919 you to understand the world in a much 721 00:25:10,390 --> 00:25:08,080 more elegant manner that allows you to 722 00:25:12,470 --> 00:25:10,400 grasp to understand physical quantities 723 00:25:14,310 --> 00:25:12,480 much more intuitively with these napkin 724 00:25:16,310 --> 00:25:14,320 calculations and by the way i say napkin 725 00:25:18,310 --> 00:25:16,320 calculations and not back of the 726 00:25:19,830 --> 00:25:18,320 envelope calculations because when 727 00:25:21,510 --> 00:25:19,840 you're outside and you're doing one of 728 00:25:22,549 --> 00:25:21,520 these why where are you going to find an 729 00:25:24,549 --> 00:25:22,559 envelope i don't think i've written on 730 00:25:26,549 --> 00:25:24,559 an envelope or the back of one in my 731 00:25:27,990 --> 00:25:26,559 entire life and then 732 00:25:29,590 --> 00:25:28,000 okay so you take a napkin and you do 733 00:25:31,430 --> 00:25:29,600 your calculation on it what the heck is 734 00:25:32,710 --> 00:25:31,440 the front of a napkin versus the back 735 00:25:34,070 --> 00:25:32,720 it's not like you choose the front or 736 00:25:36,470 --> 00:25:34,080 the back or you can even tell most of 737 00:25:38,310 --> 00:25:36,480 the time so it's a napkin calculation 738 00:25:40,549 --> 00:25:38,320 now let's think about what did i say 739 00:25:43,510 --> 00:25:40,559 over here which is that it allows you 740 00:25:45,669 --> 00:25:43,520 to have only time or only energy etc etc 741 00:25:46,870 --> 00:25:45,679 well there's some conversion equations 742 00:25:50,789 --> 00:25:46,880 it's best to think of them in terms of 743 00:25:54,149 --> 00:25:52,149 these are the central equations that 744 00:25:56,549 --> 00:25:54,159 allow you to convert so let's give them 745 00:25:59,510 --> 00:25:56,559 a special symbol a special kind of one 746 00:26:00,470 --> 00:25:59,520 number one is e equals 747 00:26:02,710 --> 00:26:00,480 you can 748 00:26:06,149 --> 00:26:02,720 guess this e equals m c squared number 749 00:26:07,830 --> 00:26:06,159 two and then let's also make it special 750 00:26:08,950 --> 00:26:07,840 is 751 00:26:10,789 --> 00:26:08,960 x 752 00:26:13,190 --> 00:26:10,799 p 753 00:26:15,830 --> 00:26:13,200 well now i'm going to use this 754 00:26:17,990 --> 00:26:15,840 which means on the order of so actually 755 00:26:20,310 --> 00:26:18,000 let's get rid of this guy 756 00:26:22,470 --> 00:26:20,320 put him on the order of there's also the 757 00:26:25,430 --> 00:26:22,480 compton wavelength which will give 758 00:26:26,549 --> 00:26:25,440 another fancy symbol 759 00:26:27,669 --> 00:26:26,559 which is 760 00:26:31,269 --> 00:26:27,679 lambda 761 00:26:33,909 --> 00:26:31,990 and 762 00:26:36,470 --> 00:26:33,919 notice right now what have we done we've 763 00:26:38,630 --> 00:26:36,480 already set c to equal one look i'm i'm 764 00:26:40,549 --> 00:26:38,640 making the mistake notice what have we 765 00:26:43,190 --> 00:26:40,559 done already we're already going to be 766 00:26:45,430 --> 00:26:43,200 using units where c of light is 767 00:26:47,190 --> 00:26:45,440 expressed in those units as one 768 00:26:49,590 --> 00:26:47,200 so we're only making reference to c of 769 00:26:51,590 --> 00:26:49,600 light to speed of light 770 00:26:53,750 --> 00:26:51,600 that means that right here we can remove 771 00:26:55,590 --> 00:26:53,760 that because that equals one right here 772 00:26:57,269 --> 00:26:55,600 we can change that to one right here we 773 00:26:59,269 --> 00:26:57,279 can change that to one and then we can 774 00:27:01,430 --> 00:26:59,279 get rid of that because it's the same a 775 00:27:02,230 --> 00:27:01,440 zero with order equation 776 00:27:04,630 --> 00:27:02,240 is 777 00:27:05,510 --> 00:27:04,640 well the speed of light equals 778 00:27:08,789 --> 00:27:05,520 some 779 00:27:11,590 --> 00:27:08,799 spatial amount over this now since we're 780 00:27:13,750 --> 00:27:11,600 setting this to equal one 781 00:27:16,230 --> 00:27:13,760 this means that any time that you have a 782 00:27:17,110 --> 00:27:16,240 distance we can express it in terms of a 783 00:27:18,950 --> 00:27:17,120 speed 784 00:27:21,750 --> 00:27:18,960 for example you can let's imagine that's 785 00:27:22,549 --> 00:27:21,760 the earth and then we're going 786 00:27:24,549 --> 00:27:22,559 to 787 00:27:28,950 --> 00:27:24,559 one light year away or one light second 788 00:27:32,070 --> 00:27:30,630 i can either say hey that's two nine 789 00:27:34,710 --> 00:27:32,080 nine seven nine two four five eight 790 00:27:36,470 --> 00:27:34,720 meters away or i can say that's one 791 00:27:39,510 --> 00:27:36,480 light second that means that it's now 792 00:27:41,510 --> 00:27:39,520 converting distance into time any 793 00:27:44,310 --> 00:27:41,520 distance measure that you give me i can 794 00:27:46,470 --> 00:27:44,320 give you an equivalent time measure it's 795 00:27:48,630 --> 00:27:46,480 not the same it's a conversion but you 796 00:27:53,669 --> 00:27:48,640 can convert it to time 797 00:27:57,190 --> 00:27:54,389 of 798 00:27:59,669 --> 00:27:57,909 to 799 00:28:01,029 --> 00:27:59,679 time 800 00:28:02,870 --> 00:28:01,039 and back because you can do the same 801 00:28:05,190 --> 00:28:02,880 thing forward or backward and then this 802 00:28:08,710 --> 00:28:05,200 one also allows a conversion 803 00:28:12,710 --> 00:28:10,549 to mass 804 00:28:15,110 --> 00:28:12,720 so i can tell you this is one gram or i 805 00:28:16,789 --> 00:28:15,120 can give you its energy equivalent or 806 00:28:18,630 --> 00:28:16,799 you can give me some energy and i can 807 00:28:20,070 --> 00:28:18,640 tell you well that what makes up that 808 00:28:22,389 --> 00:28:20,080 energy is the equivalent of a certain 809 00:28:24,070 --> 00:28:22,399 amount of mass 810 00:28:27,909 --> 00:28:24,080 now this one is also interesting because 811 00:28:32,230 --> 00:28:27,919 it gives a conversion of length 812 00:28:35,590 --> 00:28:33,669 i noticed that i didn't explain where 813 00:28:37,590 --> 00:28:35,600 this one comes from and it's the famous 814 00:28:39,510 --> 00:28:37,600 heisenberg uncertainty equation where 815 00:28:41,909 --> 00:28:39,520 you're told that the objects of space 816 00:28:43,990 --> 00:28:41,919 and momentum don't commute however even 817 00:28:46,389 --> 00:28:44,000 this is a misnomer since it makes no 818 00:28:48,549 --> 00:28:46,399 sense to say quote unquote objects don't 819 00:28:50,710 --> 00:28:48,559 commute it should be stated precisely 820 00:28:52,549 --> 00:28:50,720 that the operations with those objects 821 00:28:54,870 --> 00:28:52,559 or operations on those objects don't 822 00:28:57,029 --> 00:28:54,880 commute how can an object be commutative 823 00:28:58,870 --> 00:28:57,039 or not without the extra structure of 824 00:29:00,789 --> 00:28:58,880 the group operation again i'm being 825 00:29:02,549 --> 00:29:00,799 pedantic because i was extremely 826 00:29:04,630 --> 00:29:02,559 confused learning all of this and you 827 00:29:08,950 --> 00:29:04,640 may be as well and as best these 828 00:29:14,630 --> 00:29:12,549 clearly it's inversed and then this one 829 00:29:17,430 --> 00:29:14,640 gives a conversion 830 00:29:21,269 --> 00:29:19,669 to mass 831 00:29:24,230 --> 00:29:21,279 now how many different types of units do 832 00:29:27,350 --> 00:29:24,240 we have here we have length 1 2 time 3 833 00:29:29,029 --> 00:29:27,360 mass 4 energy 5 momentum and we have 834 00:29:31,110 --> 00:29:29,039 four equations 835 00:29:32,470 --> 00:29:31,120 which means that we have five unknowns 836 00:29:34,310 --> 00:29:32,480 and four equations which means that we 837 00:29:36,630 --> 00:29:34,320 can represent we only actually have one 838 00:29:38,710 --> 00:29:36,640 unknown so we can represent any of these 839 00:29:40,870 --> 00:29:38,720 in terms of any quantity that we like 840 00:29:43,990 --> 00:29:40,880 and thus we can represent 841 00:29:46,230 --> 00:29:44,000 all of our quantities mass time length 842 00:29:47,990 --> 00:29:46,240 energy in terms of one or the other 843 00:29:49,669 --> 00:29:48,000 there are many reasons why a high energy 844 00:29:51,590 --> 00:29:49,679 physicist just chooses energy though 845 00:29:54,870 --> 00:29:51,600 they equivalently could have chosen time 846 00:29:56,549 --> 00:29:54,880 could have chosen length etc it's just 847 00:29:58,070 --> 00:29:56,559 for the purposes of this video and for 848 00:29:59,510 --> 00:29:58,080 you to have a different point of view on 849 00:30:01,990 --> 00:29:59,520 the world it's better to think in terms 850 00:30:04,070 --> 00:30:02,000 of energy because of a well because of a 851 00:30:07,750 --> 00:30:04,080 series of accidents the unit that they 852 00:30:09,830 --> 00:30:07,760 like to use is giga electron volts gev 853 00:30:13,110 --> 00:30:09,840 and that's the units we'll be using 854 00:30:15,110 --> 00:30:13,990 we 855 00:30:16,389 --> 00:30:15,120 will 856 00:30:21,110 --> 00:30:16,399 use 857 00:30:22,870 --> 00:30:21,120 one want to convert to gev constantly 858 00:30:24,789 --> 00:30:22,880 because if you were to give me the mass 859 00:30:26,389 --> 00:30:24,799 of this in grams i don't know what that 860 00:30:28,310 --> 00:30:26,399 means but if you were to give me it in 861 00:30:30,310 --> 00:30:28,320 terms of gev i can tell you how many 862 00:30:32,710 --> 00:30:30,320 nucleons are in here so what does that 863 00:30:35,830 --> 00:30:32,720 mean firstly notice this accident again 864 00:30:38,389 --> 00:30:35,840 it's perhaps an accident but perhaps not 865 00:30:39,750 --> 00:30:38,399 one proton 866 00:30:41,510 --> 00:30:39,760 mass 867 00:30:42,789 --> 00:30:41,520 equivalent remember it's not just this 868 00:30:45,029 --> 00:30:42,799 is something else that needs to be 869 00:30:47,430 --> 00:30:45,039 emphasized it's not the mass of a proton 870 00:30:51,669 --> 00:30:47,440 it's it's energy equivalent so once 871 00:30:53,870 --> 00:30:51,679 proton mass is energy equivalent is 872 00:30:59,990 --> 00:30:53,880 let's say i think it's 873 00:31:05,830 --> 00:31:03,350 okay we go to wikipedia and we see 874 00:31:08,310 --> 00:31:05,840 what is the mass of a proton so then we 875 00:31:09,510 --> 00:31:08,320 look at the protons mass and it's this 876 00:31:12,230 --> 00:31:09,520 right here 877 00:31:15,350 --> 00:31:12,240 and that's the same as 0.93 878 00:31:16,789 --> 00:31:15,360 gev if you just know it gigamines versus 879 00:31:18,870 --> 00:31:16,799 mega 880 00:31:21,269 --> 00:31:18,880 and why is this useful at all because 881 00:31:23,909 --> 00:31:21,279 it's almost equal to one 882 00:31:26,549 --> 00:31:23,919 so if i want it to be sloppy i would say 883 00:31:29,190 --> 00:31:26,559 equals to one but instead i will say on 884 00:31:31,990 --> 00:31:29,200 the order of one gev 885 00:31:35,350 --> 00:31:32,000 now we wanna know what is a gev so 886 00:31:38,230 --> 00:31:37,190 well you can look all of these up and 887 00:31:40,070 --> 00:31:38,240 i'm going to be giving you these 888 00:31:42,149 --> 00:31:40,080 practical steps by searching because 889 00:31:43,990 --> 00:31:42,159 that's actually what it's like to do 890 00:31:45,509 --> 00:31:44,000 physics or any research in general you 891 00:31:46,710 --> 00:31:45,519 go to wikipedia as one of your first 892 00:31:49,990 --> 00:31:46,720 sources 893 00:31:52,389 --> 00:31:50,000 so it says here ev means electron volt 894 00:31:54,070 --> 00:31:52,399 is a measure of an amount of kinetic 895 00:31:55,590 --> 00:31:54,080 energy gained by a single electron 896 00:31:57,830 --> 00:31:55,600 accelerating through an electric 897 00:31:59,909 --> 00:31:57,840 potential difference of one volt 898 00:32:00,789 --> 00:31:59,919 what that means is that let's imagine we 899 00:32:03,509 --> 00:32:00,799 have 900 00:32:04,470 --> 00:32:03,519 some potential difference here this is 901 00:32:05,909 --> 00:32:04,480 one 902 00:32:08,789 --> 00:32:05,919 volt 903 00:32:10,870 --> 00:32:08,799 and here's an electron it's at rest 904 00:32:12,470 --> 00:32:10,880 then it will accelerate a certain amount 905 00:32:15,190 --> 00:32:12,480 once it gets here it will have a new 906 00:32:17,430 --> 00:32:15,200 speed because the first speed was zero 907 00:32:19,029 --> 00:32:17,440 it will have a new speed and associated 908 00:32:21,029 --> 00:32:19,039 with that speed is an energy and then 909 00:32:23,190 --> 00:32:21,039 that energy now that it has well let me 910 00:32:25,750 --> 00:32:23,200 just do this converts to energy 911 00:32:27,029 --> 00:32:25,760 then the energy the kinetic energy of it 912 00:32:32,789 --> 00:32:27,039 is one 913 00:32:35,590 --> 00:32:32,799 why is this useful at all the reason is 914 00:32:38,549 --> 00:32:35,600 that we have now made a connection 915 00:32:41,269 --> 00:32:38,559 between one proton 916 00:32:44,870 --> 00:32:41,279 one proton's mass 917 00:32:46,710 --> 00:32:44,880 energy let's say mass energy equivalent 918 00:32:48,870 --> 00:32:46,720 remember that's important it's not it's 919 00:32:50,710 --> 00:32:48,880 energy per se it's it's 920 00:32:52,389 --> 00:32:50,720 energy equivalent we've made an 921 00:32:55,430 --> 00:32:52,399 association between this 922 00:32:57,350 --> 00:32:55,440 and one giga electron volt and then 923 00:32:59,590 --> 00:32:57,360 there's this connection which is 924 00:33:01,190 --> 00:32:59,600 implicit but i'm making it explicit this 925 00:33:02,870 --> 00:33:01,200 is what nema didn't emphasize the 926 00:33:05,029 --> 00:33:02,880 connection isn't actually here the 927 00:33:08,470 --> 00:33:05,039 connection is that this is well i'm 928 00:33:10,470 --> 00:33:08,480 going to be sloppy and say approximately 929 00:33:13,029 --> 00:33:10,480 because it's truly 930 00:33:16,470 --> 00:33:14,549 the connection is that 931 00:33:17,909 --> 00:33:16,480 this number one 932 00:33:19,830 --> 00:33:17,919 is readily 933 00:33:21,509 --> 00:33:19,840 cognitively graspable meaning that we 934 00:33:23,350 --> 00:33:21,519 can chunk it it's easier for me to think 935 00:33:24,909 --> 00:33:23,360 in terms of one lip balm than it is for 936 00:33:27,669 --> 00:33:24,919 me to think in terms of 937 00:33:28,870 --> 00:33:27,679 0.825 lip balms the reason why this 938 00:33:30,470 --> 00:33:28,880 ladder point well if it's not 939 00:33:32,470 --> 00:33:30,480 self-evident one of the reasons why this 940 00:33:34,389 --> 00:33:32,480 ladder point is important is that you'll 941 00:33:36,549 --> 00:33:34,399 see in physics constantly there's an 942 00:33:38,630 --> 00:33:36,559 effort to reduce some convoluted 943 00:33:40,470 --> 00:33:38,640 equation into linear algebra and that's 944 00:33:42,630 --> 00:33:40,480 because linear algebra is extremely 945 00:33:44,470 --> 00:33:42,640 cognitively graspable it's understood 946 00:33:47,029 --> 00:33:44,480 it's one of the few areas of math if not 947 00:33:49,110 --> 00:33:47,039 the only area of math that's well 948 00:33:51,430 --> 00:33:49,120 understood that means anytime you have a 949 00:33:53,269 --> 00:33:51,440 complex equation if you can linearize it 950 00:33:54,789 --> 00:33:53,279 you understand it much better in the 951 00:33:57,029 --> 00:33:54,799 same way that anytime we have some 952 00:33:58,789 --> 00:33:57,039 complicated phenomenon we can put it to 953 00:34:01,029 --> 00:33:58,799 something that's 954 00:34:02,630 --> 00:34:01,039 in terms of gev means we understand it 955 00:34:04,950 --> 00:34:02,640 in terms of protons 956 00:34:06,789 --> 00:34:04,960 it's akin to feynman saying that the 957 00:34:08,550 --> 00:34:06,799 number one lesson for some future 958 00:34:10,230 --> 00:34:08,560 civilization if you had to impart one 959 00:34:12,069 --> 00:34:10,240 piece of knowledge to them the best 960 00:34:13,669 --> 00:34:12,079 knowledge the best bang for your buck in 961 00:34:16,069 --> 00:34:13,679 terms of facts would be to tell them 962 00:34:18,470 --> 00:34:16,079 that the world comprises atoms and from 963 00:34:20,389 --> 00:34:18,480 that fact many other laws of nature come 964 00:34:21,669 --> 00:34:20,399 now i don't know about that because to 965 00:34:24,230 --> 00:34:21,679 me that would imply that you would have 966 00:34:26,389 --> 00:34:24,240 some fact like let's say the atom fact 967 00:34:27,909 --> 00:34:26,399 and then we have the space of all facts 968 00:34:30,149 --> 00:34:27,919 and then you have to have some measure 969 00:34:31,990 --> 00:34:30,159 on the space of all facts in order for 970 00:34:34,389 --> 00:34:32,000 you to say that this is this one fact 971 00:34:36,389 --> 00:34:34,399 implies the most facts 972 00:34:38,470 --> 00:34:36,399 and that's somewhat dubious but you at 973 00:34:40,470 --> 00:34:38,480 least understand informally what feynman 974 00:34:42,310 --> 00:34:40,480 meant it's one of the reasons why in the 975 00:34:44,310 --> 00:34:42,320 theories of everything podcast what i'm 976 00:34:46,230 --> 00:34:44,320 trying to do constantly you'll see me 977 00:34:48,230 --> 00:34:46,240 asking the 978 00:34:49,430 --> 00:34:48,240 professor who has some extremely 979 00:34:52,389 --> 00:34:49,440 intricate 980 00:34:54,069 --> 00:34:52,399 baroque equation or concept 981 00:34:56,310 --> 00:34:54,079 i'm frequently saying okay what does it 982 00:34:57,750 --> 00:34:56,320 mean in terms of billiard balls so let's 983 00:35:00,069 --> 00:34:57,760 imagine that this has a charge and this 984 00:35:01,990 --> 00:35:00,079 one does too what's going on there it's 985 00:35:03,430 --> 00:35:02,000 the same trying to reduce down to some 986 00:35:05,430 --> 00:35:03,440 fundamentals that you understand in 987 00:35:06,950 --> 00:35:05,440 order to properly understand it then 988 00:35:08,470 --> 00:35:06,960 there's another 989 00:35:11,349 --> 00:35:08,480 somewhat of an accident maybe it's not 990 00:35:15,670 --> 00:35:11,359 heisenberg said there is isospin so that 991 00:35:18,550 --> 00:35:16,390 has 992 00:35:20,390 --> 00:35:18,560 similar 993 00:35:21,190 --> 00:35:20,400 mass 994 00:35:31,750 --> 00:35:21,200 to 995 00:35:33,510 --> 00:35:31,760 units for these napkin calculations 996 00:35:35,750 --> 00:35:33,520 i'm being extremely specific and 997 00:35:37,750 --> 00:35:35,760 somewhat pedantic because much of this 998 00:35:39,030 --> 00:35:37,760 is glossed over and then you'll start at 999 00:35:41,030 --> 00:35:39,040 least if you're like me you'll start to 1000 00:35:42,790 --> 00:35:41,040 be confused at a much later point and 1001 00:35:44,310 --> 00:35:42,800 you won't realize that some of these 1002 00:35:45,670 --> 00:35:44,320 fundamentals weren't explained 1003 00:35:48,150 --> 00:35:45,680 specifically 1004 00:35:50,390 --> 00:35:48,160 now let's go through a conversion chart 1005 00:35:54,870 --> 00:35:50,400 conversion 1006 00:35:54,880 --> 00:35:58,230 here we go 1007 00:36:04,870 --> 00:36:02,150 one meter is the equivalent of 1008 00:36:06,950 --> 00:36:04,880 well on the order of 10 to the 16 gev 1009 00:36:08,950 --> 00:36:06,960 inverse ah now i haven't explained what 1010 00:36:10,950 --> 00:36:08,960 the inverses mean here at our equation 1011 00:36:12,790 --> 00:36:10,960 bolded number one and then bolded number 1012 00:36:15,270 --> 00:36:12,800 three we have an equivalence between 1013 00:36:18,069 --> 00:36:15,280 energy and mass so you say one 1014 00:36:19,430 --> 00:36:18,079 giga electron volt and that can mean 1015 00:36:21,030 --> 00:36:19,440 a certain amount of mass okay you can 1016 00:36:22,870 --> 00:36:21,040 convert between them but you can also 1017 00:36:24,470 --> 00:36:22,880 convert between the mass and then the 1018 00:36:27,109 --> 00:36:24,480 length but this is an inverse 1019 00:36:29,990 --> 00:36:27,119 relationship so that means that length 1020 00:36:31,750 --> 00:36:30,000 actually has inverse energy units so 1021 00:36:33,589 --> 00:36:31,760 anytime you give a length you can also 1022 00:36:36,470 --> 00:36:33,599 have given the same quantity an inverse 1023 00:36:37,750 --> 00:36:36,480 energy any time you have a second 1024 00:36:40,069 --> 00:36:37,760 you could do the same you can give that 1025 00:36:41,270 --> 00:36:40,079 in terms of inverse energy any time you 1026 00:36:43,910 --> 00:36:41,280 have a mass this one's simple you can 1027 00:36:45,829 --> 00:36:43,920 give it in terms of energy now this mp 1028 00:36:48,150 --> 00:36:45,839 is the planck 1029 00:36:49,190 --> 00:36:48,160 mass not the proton mass remember proton 1030 00:36:51,030 --> 00:36:49,200 mass is 1031 00:36:53,030 --> 00:36:51,040 1 gev 1032 00:36:55,190 --> 00:36:53,040 just for fun you can do the calculation 1033 00:36:57,349 --> 00:36:55,200 of a gram and 1034 00:36:59,030 --> 00:36:57,359 it's this much you can do hertz which is 1035 00:37:01,109 --> 00:36:59,040 inverse time and by the way because 1036 00:37:03,349 --> 00:37:01,119 you're in inverse time you have regular 1037 00:37:05,109 --> 00:37:03,359 energy units which means frequency is 1038 00:37:06,630 --> 00:37:05,119 actually a unit of energy anytime 1039 00:37:08,150 --> 00:37:06,640 someone gives you a frequency you can 1040 00:37:09,910 --> 00:37:08,160 just convert that straight to energy 1041 00:37:12,550 --> 00:37:09,920 we're going to be doing these by the way 1042 00:37:15,349 --> 00:37:12,560 i didn't actually do this but for 1043 00:37:20,230 --> 00:37:17,589 you can see that this is an 1044 00:37:22,150 --> 00:37:20,240 it's a dimensionless quantity it's 1045 00:37:24,230 --> 00:37:22,160 information it should be dimensionless 1046 00:37:25,750 --> 00:37:24,240 because it's dimensionless then from the 1047 00:37:27,589 --> 00:37:25,760 boltzmann constant you can get that 1048 00:37:29,109 --> 00:37:27,599 kelvin is also a unit of energy so 1049 00:37:30,310 --> 00:37:29,119 temperature is a unit of energy which 1050 00:37:32,069 --> 00:37:30,320 somewhat makes sense because you've 1051 00:37:34,310 --> 00:37:32,079 heard that temperature 1052 00:37:36,069 --> 00:37:34,320 is some function of the average kinetic 1053 00:37:38,470 --> 00:37:36,079 energy of the molecules in a room or in 1054 00:37:40,390 --> 00:37:38,480 a box but that statement alone isn't 1055 00:37:41,990 --> 00:37:40,400 enough to say that it's units of energy 1056 00:37:43,349 --> 00:37:42,000 because just because it's a function of 1057 00:37:45,670 --> 00:37:43,359 energy doesn't necessarily mean the 1058 00:37:48,310 --> 00:37:45,680 units of it are energy 1059 00:37:50,150 --> 00:37:48,320 however it does turn out to be the case 1060 00:37:51,910 --> 00:37:50,160 this means you can convert from energy 1061 00:37:54,790 --> 00:37:51,920 to temperature and vice versa all of 1062 00:37:56,310 --> 00:37:54,800 these are vice versa 1063 00:37:58,390 --> 00:37:56,320 and then one we may use later is 1064 00:37:59,910 --> 00:37:58,400 nanometers equals this by the way if any 1065 00:38:00,950 --> 00:37:59,920 of these are incorrect well then please 1066 00:38:02,390 --> 00:38:00,960 just write the correct one in the 1067 00:38:04,630 --> 00:38:02,400 comment section when you look at these 1068 00:38:06,630 --> 00:38:04,640 conversion charts online some of them 1069 00:38:08,710 --> 00:38:06,640 have a plus or minus one in the units 1070 00:38:10,710 --> 00:38:08,720 and that's because we're using this 1071 00:38:14,710 --> 00:38:10,720 symbol which means we don't actually 1072 00:38:19,030 --> 00:38:16,230 remember that this is all about napkin 1073 00:38:22,150 --> 00:38:19,040 calculations nz's we're just doing nc's 1074 00:38:24,230 --> 00:38:22,160 to be extremely concrete you can say 1075 00:38:25,750 --> 00:38:24,240 your desk in front of you is one meter 1076 00:38:27,829 --> 00:38:25,760 approximately let's say approximately 1077 00:38:30,069 --> 00:38:27,839 one meter long or you can give it in 1078 00:38:31,270 --> 00:38:30,079 terms of gev it's 10 to the 16 gev 1079 00:38:33,589 --> 00:38:31,280 inverses 1080 00:38:36,710 --> 00:38:33,599 and that means that 1081 00:38:40,150 --> 00:38:36,720 if you stacked stack 1082 00:38:43,030 --> 00:38:40,160 10 to the 16 protons 1083 00:38:49,270 --> 00:38:43,040 so you get proton proton proton proton 1084 00:38:53,589 --> 00:38:51,190 then you get your desk 1085 00:38:55,109 --> 00:38:53,599 so it gives you an extremely concrete 1086 00:38:57,270 --> 00:38:55,119 way of understanding what your desk is 1087 00:38:59,750 --> 00:38:57,280 your desk is 10 to the 16 protons 1088 00:39:02,310 --> 00:38:59,760 stacked one after the other and by the 1089 00:39:04,150 --> 00:39:02,320 way you may say well kurt isn't gev also 1090 00:39:06,150 --> 00:39:04,160 arbitrary wasn't the whole point of 1091 00:39:08,470 --> 00:39:06,160 natural units to get away from this 1092 00:39:10,310 --> 00:39:08,480 arbitrariness well yes that's true 1093 00:39:12,230 --> 00:39:10,320 except that the other part here which is 1094 00:39:14,950 --> 00:39:12,240 a great confluence 1095 00:39:17,030 --> 00:39:14,960 is that this coincides with how 1096 00:39:18,230 --> 00:39:17,040 engineers think engineers think in terms 1097 00:39:20,550 --> 00:39:18,240 of electron volts well they think in 1098 00:39:23,030 --> 00:39:20,560 terms of volts so now you've found a 1099 00:39:24,710 --> 00:39:23,040 connection between protons between 1100 00:39:26,550 --> 00:39:24,720 something that is cognitively graspable 1101 00:39:28,870 --> 00:39:26,560 between a neutron and between what you 1102 00:39:30,310 --> 00:39:28,880 can communicate with with others 1103 00:39:31,510 --> 00:39:30,320 so engineers 1104 00:39:32,790 --> 00:39:31,520 now throughout the rest of the video 1105 00:39:35,270 --> 00:39:32,800 you'll see that many different 1106 00:39:37,430 --> 00:39:35,280 quantities physical macroscopic 1107 00:39:40,150 --> 00:39:37,440 sometimes even microscopic physical 1108 00:39:42,790 --> 00:39:40,160 observable quantities are expressed in 1109 00:39:44,630 --> 00:39:42,800 terms of these fundamental ratios now 1110 00:39:46,150 --> 00:39:44,640 notice i didn't say fundamental 1111 00:39:47,430 --> 00:39:46,160 constants and that's because i'm trying 1112 00:39:51,510 --> 00:39:47,440 to emphasize the fact that they're 1113 00:39:56,230 --> 00:39:53,910 let's analyze newton's constant 1114 00:39:58,390 --> 00:39:56,240 and others 1115 00:40:00,150 --> 00:39:58,400 here's what you do in general firstly 1116 00:40:01,910 --> 00:40:00,160 you go to wikipedia so let's do that 1117 00:40:03,990 --> 00:40:01,920 right now 1118 00:40:05,430 --> 00:40:04,000 and you type in newton's constant so 1119 00:40:07,190 --> 00:40:05,440 it's also known as the gravitational 1120 00:40:07,910 --> 00:40:07,200 constant you've seen it before it's this 1121 00:40:09,510 --> 00:40:07,920 g 1122 00:40:11,589 --> 00:40:09,520 then we take a look at what are the 1123 00:40:13,030 --> 00:40:11,599 units here we go we get newtons meters 1124 00:40:19,510 --> 00:40:13,040 squared so on and so on so let's write 1125 00:40:23,910 --> 00:40:21,190 ah and even here i noticed i made a 1126 00:40:24,870 --> 00:40:23,920 mistake because often you'll see online 1127 00:40:29,030 --> 00:40:24,880 m 1128 00:40:30,630 --> 00:40:29,040 actually a length 1129 00:40:32,390 --> 00:40:30,640 and this is a common mistake when you're 1130 00:40:34,710 --> 00:40:32,400 initially doing this so this is actually 1131 00:40:37,190 --> 00:40:34,720 mass 1132 00:40:39,109 --> 00:40:37,200 and this is length squared 1133 00:40:41,510 --> 00:40:39,119 you'll see it here that it says newtons 1134 00:40:43,430 --> 00:40:41,520 meter squared so length squared then a 1135 00:40:45,430 --> 00:40:43,440 mass squared is what it's being divided 1136 00:40:47,829 --> 00:40:45,440 by then you wonder well what the heck is 1137 00:40:50,470 --> 00:40:47,839 a newton so what we do is we go into it 1138 00:40:52,310 --> 00:40:50,480 because all of these are derived from 1139 00:40:54,630 --> 00:40:52,320 something that's much simpler usually 1140 00:40:56,390 --> 00:40:54,640 mass length or time so we go here and we 1141 00:40:59,589 --> 00:40:56,400 see that it's equal to a kilogram so 1142 00:41:05,349 --> 00:40:59,599 mass times length over time squared so 1143 00:41:09,510 --> 00:41:07,349 okay now it's as simple as doing some 1144 00:41:16,950 --> 00:41:09,520 cancellations well we can remove one of 1145 00:41:20,550 --> 00:41:18,790 all right now we want to reduce this 1146 00:41:22,470 --> 00:41:20,560 even further remember there's only 1147 00:41:24,230 --> 00:41:22,480 length or there's only time or only 1148 00:41:27,190 --> 00:41:24,240 energy let's see if we can place this in 1149 00:41:29,030 --> 00:41:27,200 terms of only energy 1150 00:41:30,630 --> 00:41:29,040 we go to our conversion equations 1151 00:41:32,390 --> 00:41:30,640 there's a correspondence between length 1152 00:41:34,390 --> 00:41:32,400 and time between energy and mass between 1153 00:41:36,150 --> 00:41:34,400 length and momentum actually this 1154 00:41:38,069 --> 00:41:36,160 correspondence is between length and 1155 00:41:40,069 --> 00:41:38,079 inverse momentum and this is between 1156 00:41:41,589 --> 00:41:40,079 length and inverse mass and you can see 1157 00:41:43,589 --> 00:41:41,599 that just from the fact that there's a 1158 00:41:45,670 --> 00:41:43,599 one over and obviously that can go one 1159 00:41:47,190 --> 00:41:45,680 over there there's also another equation 1160 00:41:51,349 --> 00:41:47,200 that will come in handy 1161 00:41:58,230 --> 00:41:54,630 which is the energy time uncertainty 1162 00:42:00,390 --> 00:41:58,240 and this gives a correspondence between 1163 00:42:01,510 --> 00:42:00,400 energy 1164 00:42:02,470 --> 00:42:01,520 and 1165 00:42:04,470 --> 00:42:02,480 time 1166 00:42:06,470 --> 00:42:04,480 however looking at the equation you can 1167 00:42:08,790 --> 00:42:06,480 see that it's inverse time 1168 00:42:11,030 --> 00:42:08,800 that means that inverse time is energy 1169 00:42:12,710 --> 00:42:11,040 inverse energy is time let's now make 1170 00:42:15,190 --> 00:42:12,720 some substitutions 1171 00:42:16,390 --> 00:42:15,200 mass is the same as energy so i'm going 1172 00:42:18,150 --> 00:42:16,400 to call it gev 1173 00:42:19,670 --> 00:42:18,160 time is the same as 1174 00:42:21,349 --> 00:42:19,680 g e v 1175 00:42:24,069 --> 00:42:21,359 inverse 1176 00:42:26,470 --> 00:42:24,079 length is the same as g e v 1177 00:42:28,069 --> 00:42:26,480 inverse well length is the same as mass 1178 00:42:29,990 --> 00:42:28,079 but mass is the same as energy so you 1179 00:42:32,550 --> 00:42:30,000 can make that substitution making all of 1180 00:42:36,710 --> 00:42:32,560 these substitutions you then get that g 1181 00:42:42,309 --> 00:42:36,720 the units of newtons is actually 1 over 1182 00:42:43,270 --> 00:42:42,319 gev squared or as we'll be writing it 1183 00:42:46,230 --> 00:42:43,280 simply 1184 00:42:48,309 --> 00:42:46,240 gev to the power of negative two 1185 00:42:51,109 --> 00:42:48,319 it's all simple we look and we see that 1186 00:42:54,550 --> 00:42:51,119 it's newtons times kilograms times 1187 00:42:59,190 --> 00:42:54,560 length etc actually reduces down to this 1188 00:43:01,270 --> 00:42:59,200 so let's underline that in red 1189 00:43:03,430 --> 00:43:01,280 how about entropy well entropy as we've 1190 00:43:04,710 --> 00:43:03,440 noted above is given by formula which 1191 00:43:08,630 --> 00:43:04,720 looks like 1192 00:43:16,150 --> 00:43:10,790 and these are probabilities 1193 00:43:20,309 --> 00:43:18,630 again extremely simple now much of this 1194 00:43:21,829 --> 00:43:20,319 is made complicated but if you look at 1195 00:43:23,750 --> 00:43:21,839 it through the lens of natural units as 1196 00:43:25,589 --> 00:43:23,760 well as these conversion equations all 1197 00:43:27,270 --> 00:43:25,599 of the quantities that you know and that 1198 00:43:30,309 --> 00:43:27,280 you love and that you want to work with 1199 00:43:31,750 --> 00:43:30,319 become units of energy raised to some 1200 00:43:34,630 --> 00:43:31,760 integer power 1201 00:43:35,910 --> 00:43:34,640 how about pressure 1202 00:43:39,109 --> 00:43:35,920 again let's just look that up on 1203 00:43:41,510 --> 00:43:39,119 wikipedia that's usually the first step 1204 00:43:43,430 --> 00:43:41,520 it says here newtons per meter squared 1205 00:43:45,990 --> 00:43:43,440 that makes sense because it's newton 1206 00:43:47,750 --> 00:43:46,000 which is a force unit over some area and 1207 00:43:49,430 --> 00:43:47,760 then luckily they've decomposed it 1208 00:43:53,030 --> 00:43:49,440 further for us 1209 00:43:55,990 --> 00:43:53,040 so let's write that down that is a mass 1210 00:43:59,190 --> 00:43:56,000 over a length 1211 00:44:01,109 --> 00:43:59,200 and then we have time squared 1212 00:44:03,109 --> 00:44:01,119 which then becomes which we can now do 1213 00:44:05,589 --> 00:44:03,119 in our head but we won't do that right 1214 00:44:09,030 --> 00:44:05,599 now because we're trying to not skip any 1215 00:44:11,430 --> 00:44:09,040 steps mass becomes gev 1216 00:44:14,950 --> 00:44:11,440 length becomes gev inverse so it goes to 1217 00:44:18,150 --> 00:44:14,960 the top time is also gev inverse 1218 00:44:20,829 --> 00:44:18,160 so it's gev squared and that is the same 1219 00:44:20,839 --> 00:44:27,430 gev to the fourth 1220 00:44:31,750 --> 00:44:29,589 this tells you an extremely important 1221 00:44:34,069 --> 00:44:31,760 property of pressure it's an extensive 1222 00:44:35,829 --> 00:44:34,079 property of space-time itself this is 1223 00:44:38,230 --> 00:44:35,839 one of the reasons why it's much easier 1224 00:44:40,230 --> 00:44:38,240 or much more useful to think in terms of 1225 00:44:41,910 --> 00:44:40,240 pressure rather than force because 1226 00:44:44,630 --> 00:44:41,920 pressure is a property of space time 1227 00:44:46,710 --> 00:44:44,640 itself whereas force is some derived 1228 00:44:48,230 --> 00:44:46,720 quantity that usually isn't useful in 1229 00:44:51,589 --> 00:44:48,240 fundamental physics 1230 00:44:53,190 --> 00:44:51,599 now let's do a fun one how about speed 1231 00:44:56,309 --> 00:44:53,200 well we 1232 00:44:58,950 --> 00:44:56,319 think of it as length over time 1233 00:45:01,510 --> 00:44:58,960 and then because time and length are the 1234 00:45:03,349 --> 00:45:01,520 same in our conversion chart this just 1235 00:45:05,910 --> 00:45:03,359 becomes 1236 00:45:08,230 --> 00:45:05,920 dimensionless 1237 00:45:10,950 --> 00:45:08,240 that deserves a bolded 1238 00:45:12,470 --> 00:45:10,960 exclamation point 1239 00:45:15,270 --> 00:45:12,480 then you think well how the heck is 1240 00:45:17,510 --> 00:45:15,280 speed dimensionless isn't it the case 1241 00:45:20,309 --> 00:45:17,520 that you said over here kurt c equals 1242 00:45:22,230 --> 00:45:20,319 one you can't simply say c equals one 1243 00:45:24,150 --> 00:45:22,240 yes that's true except there was a 1244 00:45:26,309 --> 00:45:24,160 caveat in the caveat is that there are 1245 00:45:28,230 --> 00:45:26,319 these conversion equations because we're 1246 00:45:30,710 --> 00:45:28,240 placing it in terms of c which is 1247 00:45:31,990 --> 00:45:30,720 invariant it means that we can tell time 1248 00:45:33,990 --> 00:45:32,000 in terms of length and we can tell 1249 00:45:36,790 --> 00:45:34,000 length in terms of time and that means 1250 00:45:38,470 --> 00:45:36,800 that this equation is correct but only 1251 00:45:40,230 --> 00:45:38,480 when you take into account the fact that 1252 00:45:43,349 --> 00:45:40,240 c is in variance and these other 1253 00:45:45,589 --> 00:45:43,359 conversion equations 1254 00:45:48,069 --> 00:45:45,599 it's usually just glossed over so plenty 1255 00:45:50,069 --> 00:45:48,079 of preamble goes into making a statement 1256 00:45:52,630 --> 00:45:50,079 as seemingly simple as c equals one 1257 00:45:54,790 --> 00:45:52,640 equals h bar so c equals one is a 1258 00:45:56,790 --> 00:45:54,800 meaningless statement unless you're 1259 00:45:58,950 --> 00:45:56,800 specifying that you're using some of 1260 00:46:00,470 --> 00:45:58,960 these as conversions and then you're 1261 00:46:01,750 --> 00:46:00,480 also emphasizing the invariance of the 1262 00:46:03,270 --> 00:46:01,760 speed of light if the speed of light 1263 00:46:05,109 --> 00:46:03,280 depends on something else you can't 1264 00:46:08,230 --> 00:46:05,119 actually use that all of this needs to 1265 00:46:10,150 --> 00:46:08,240 be explained unequivocally first 1266 00:46:12,550 --> 00:46:10,160 it's usually not and then there's an 1267 00:46:14,309 --> 00:46:12,560 abundance of befuddlement that occurs 1268 00:46:16,390 --> 00:46:14,319 much like with the brockhead notation 1269 00:46:18,150 --> 00:46:16,400 which looks graceful however there's 1270 00:46:19,510 --> 00:46:18,160 plenty of assumptions that go into it 1271 00:46:21,670 --> 00:46:19,520 which make it 1272 00:46:23,589 --> 00:46:21,680 not terribly useful 1273 00:46:25,589 --> 00:46:23,599 let's use this to calculate a practical 1274 00:46:27,109 --> 00:46:25,599 quantity so how many protons are there 1275 00:46:30,069 --> 00:46:27,119 in you at first if you were to just say 1276 00:46:32,069 --> 00:46:30,079 well i weigh 70 kilograms that doesn't 1277 00:46:33,750 --> 00:46:32,079 give much information what we can do is 1278 00:46:34,550 --> 00:46:33,760 we can use our conversion chart over 1279 00:46:37,270 --> 00:46:34,560 here 1280 00:46:40,069 --> 00:46:37,280 and say okay well look one gram 1281 00:46:43,829 --> 00:46:40,079 is this much energy so how about a 1282 00:46:46,069 --> 00:46:43,839 kilogram so a kilogram must be 10 to the 1283 00:46:48,950 --> 00:46:46,079 26 gev 1284 00:46:50,950 --> 00:46:48,960 using this we then get that 70 kilograms 1285 00:46:52,069 --> 00:46:50,960 becomes 1286 00:46:55,829 --> 00:46:52,079 70 1287 00:46:59,510 --> 00:46:55,839 times 10 to the 26 gev 1288 00:47:01,589 --> 00:46:59,520 which is on the order of 10 to the 28 1289 00:47:04,069 --> 00:47:01,599 gev 1290 00:47:06,790 --> 00:47:04,079 that means that what comprises you is 10 1291 00:47:09,190 --> 00:47:06,800 to the 28 protons and that's a much more 1292 00:47:10,790 --> 00:47:09,200 physically meaningful quantity now you 1293 00:47:12,550 --> 00:47:10,800 have some physical intuition given to 1294 00:47:13,910 --> 00:47:12,560 you by your weight whereas if it was 1295 00:47:15,589 --> 00:47:13,920 just kilograms then you have to go to 1296 00:47:17,109 --> 00:47:15,599 paris etc 1297 00:47:19,670 --> 00:47:17,119 then you may wonder well kurt don't 1298 00:47:23,589 --> 00:47:19,680 neutrons come with protons so shouldn't 1299 00:47:25,990 --> 00:47:23,599 you times two the above yes except 1300 00:47:28,150 --> 00:47:26,000 because of this we're saying on the 1301 00:47:30,150 --> 00:47:28,160 order of so we can say there are 10 to 1302 00:47:32,470 --> 00:47:30,160 the 28 nucleons that comprise you 1303 00:47:34,870 --> 00:47:32,480 protons and neutrons bound 1304 00:47:36,870 --> 00:47:34,880 there we go simple and powerful because 1305 00:47:38,550 --> 00:47:36,880 it allows these napkin calculations 1306 00:47:39,910 --> 00:47:38,560 let's do one that you may think requires 1307 00:47:41,349 --> 00:47:39,920 plenty of work but it's actually 1308 00:47:43,750 --> 00:47:41,359 extremely quick you can do it in a 1309 00:47:46,309 --> 00:47:43,760 second so what is the pressure inside a 1310 00:47:49,589 --> 00:47:46,319 neutron star 1311 00:47:52,390 --> 00:47:49,599 firstly you have to think what is 1312 00:47:54,390 --> 00:47:52,400 happening there are neutrons as far as 1313 00:47:56,150 --> 00:47:54,400 you can see and recall that neutrons are 1314 00:47:59,670 --> 00:47:56,160 the same as protons in terms of their 1315 00:48:01,910 --> 00:47:59,680 radius and mass approximately 1316 00:48:03,430 --> 00:48:01,920 then as far as you can see all you see 1317 00:48:05,109 --> 00:48:03,440 are neutrons think about what have you 1318 00:48:06,710 --> 00:48:05,119 learned about a neutron star it's that 1319 00:48:08,470 --> 00:48:06,720 the neutrons are packed so close 1320 00:48:10,470 --> 00:48:08,480 together that they can't be packed any 1321 00:48:13,030 --> 00:48:10,480 further then you think well what is the 1322 00:48:15,910 --> 00:48:13,040 units of pressure and it's gev to the 1323 00:48:21,910 --> 00:48:15,920 fourth so we have gev times uv times gev 1324 00:48:26,549 --> 00:48:24,390 pressure in a neutron star 1325 00:48:27,990 --> 00:48:26,559 is simply gev 1326 00:48:31,030 --> 00:48:28,000 to the fourth 1327 00:48:32,150 --> 00:48:31,040 okay that's it it's just gev to the 1328 00:48:33,349 --> 00:48:32,160 fourth 1329 00:48:34,950 --> 00:48:33,359 and this is something that you can 1330 00:48:37,190 --> 00:48:34,960 verify yourself if you look up what it 1331 00:48:38,549 --> 00:48:37,200 is in pascals and then do the conversion 1332 00:48:40,790 --> 00:48:38,559 and just keep in mind that some 1333 00:48:43,190 --> 00:48:40,800 conversion charts have a plus or minus 1334 00:48:44,710 --> 00:48:43,200 one on the order because sometimes 1335 00:48:45,510 --> 00:48:44,720 people round up sometimes people round 1336 00:48:46,870 --> 00:48:45,520 down 1337 00:48:48,710 --> 00:48:46,880 now let's get through this much more 1338 00:48:50,230 --> 00:48:48,720 quickly because i'm re-recording 1339 00:48:52,309 --> 00:48:50,240 constantly there are many errors and my 1340 00:48:53,829 --> 00:48:52,319 facial hair is growing i've renamed this 1341 00:48:55,670 --> 00:48:53,839 for reasons that will become clear later 1342 00:48:58,150 --> 00:48:55,680 and neutron stars pressure is much more 1343 00:49:00,390 --> 00:48:58,160 copacetic so proportionate strength of 1344 00:49:01,670 --> 00:49:00,400 the forces so you know from perhaps 1345 00:49:03,109 --> 00:49:01,680 around high school that it's something 1346 00:49:04,950 --> 00:49:03,119 like the first charge times the second 1347 00:49:06,710 --> 00:49:04,960 charge so on and so on and so on let's 1348 00:49:09,510 --> 00:49:06,720 look at this in terms of the electron 1349 00:49:11,510 --> 00:49:09,520 charge so q1 will equal q2 will equal e 1350 00:49:14,230 --> 00:49:11,520 v is energy we know that that's 1351 00:49:16,549 --> 00:49:14,240 potential energy r is inverse energy 1352 00:49:17,510 --> 00:49:16,559 which means this equation 1353 00:49:20,390 --> 00:49:17,520 has 1354 00:49:21,349 --> 00:49:20,400 this guy here which means that this guy 1355 00:49:25,270 --> 00:49:21,359 here 1356 00:49:25,280 --> 00:49:30,230 is dimensionless 1357 00:49:36,470 --> 00:49:33,109 and this is what is usually denoted as 1358 00:49:38,870 --> 00:49:36,480 alpha which i'm sure you've heard is one 1359 00:49:40,390 --> 00:49:38,880 three seven inverse 1360 00:49:41,910 --> 00:49:40,400 this is the reason why the strength of 1361 00:49:43,990 --> 00:49:41,920 the electromagnetic force or the 1362 00:49:46,630 --> 00:49:44,000 electromagnetic interaction is 1363 00:49:49,430 --> 00:49:46,640 quantifiable it's dimensionless however 1364 00:49:52,390 --> 00:49:49,440 if we were to look up here 1365 00:49:55,270 --> 00:49:52,400 notice this this g newton 1366 00:49:57,750 --> 00:49:55,280 has negative mass dimension which means 1367 00:49:59,589 --> 00:49:57,760 that saying that gravity is weak is 1368 00:50:01,670 --> 00:49:59,599 actually a meaningless statement because 1369 00:50:03,349 --> 00:50:01,680 you need test masses you need two test 1370 00:50:05,270 --> 00:50:03,359 masses in order to say that usually 1371 00:50:07,349 --> 00:50:05,280 what's done in fundamental physics is 1372 00:50:09,510 --> 00:50:07,359 one takes the most massive of all the 1373 00:50:11,589 --> 00:50:09,520 particles the fundamental particles and 1374 00:50:13,510 --> 00:50:11,599 says well look compared to the weak 1375 00:50:15,430 --> 00:50:13,520 force which is the weakest of all the 1376 00:50:17,349 --> 00:50:15,440 standard model forces the gauge fields 1377 00:50:19,430 --> 00:50:17,359 gravity is so and so times weaker so 1378 00:50:21,510 --> 00:50:19,440 that's what's meant specifically by 1379 00:50:23,349 --> 00:50:21,520 gravity is weak but all of that needs to 1380 00:50:25,510 --> 00:50:23,359 be stated there are assumptions that go 1381 00:50:27,109 --> 00:50:25,520 into that you need a test mass and by 1382 00:50:29,030 --> 00:50:27,119 the way this guy here this negative 1383 00:50:30,950 --> 00:50:29,040 square mass dimension of the coupling of 1384 00:50:33,190 --> 00:50:30,960 gravity plays an extremely important 1385 00:50:35,109 --> 00:50:33,200 role in the non-renormalizability of 1386 00:50:36,950 --> 00:50:35,119 gravity let's calculate the average 1387 00:50:38,630 --> 00:50:36,960 speed of an electron so later we're 1388 00:50:40,150 --> 00:50:38,640 going to calculate the radius of an 1389 00:50:41,670 --> 00:50:40,160 electron and that's going to turn out to 1390 00:50:43,910 --> 00:50:41,680 be 1391 00:50:45,430 --> 00:50:43,920 this but this right now just looks like 1392 00:50:47,829 --> 00:50:45,440 junk because we haven't derived any of 1393 00:50:52,069 --> 00:50:47,839 this however from this we know that one 1394 00:50:56,309 --> 00:50:53,910 says that we can figure out the momentum 1395 00:50:58,390 --> 00:50:56,319 based on a length so then what is the 1396 00:51:03,349 --> 00:50:58,400 momentum of the average electron and 1397 00:51:13,750 --> 00:51:05,670 and that means that this is the average 1398 00:51:18,230 --> 00:51:15,910 and this number is the reason why 1399 00:51:20,069 --> 00:51:18,240 magnetism was discovered so much later 1400 00:51:21,990 --> 00:51:20,079 because electrons are moving relatively 1401 00:51:23,190 --> 00:51:22,000 slowly and we know that magnetism has to 1402 00:51:25,349 --> 00:51:23,200 do with the speed or has to do with 1403 00:51:27,190 --> 00:51:25,359 current changes thus from relatively 1404 00:51:29,190 --> 00:51:27,200 fundamental principles you can derive a 1405 00:51:31,030 --> 00:51:29,200 historic fact why was it that magnetism 1406 00:51:33,670 --> 00:51:31,040 was discovered much later well it's 1407 00:51:34,950 --> 00:51:33,680 because of this guy 1408 00:51:36,950 --> 00:51:34,960 and by the way you'll notice that i 1409 00:51:39,270 --> 00:51:36,960 spend quite a bit of time writing and 1410 00:51:41,109 --> 00:51:39,280 rewriting painstakingly almost and 1411 00:51:42,870 --> 00:51:41,119 that's because i know that clarity of 1412 00:51:45,589 --> 00:51:42,880 thought leads to this clarity of writing 1413 00:51:46,790 --> 00:51:45,599 and vice versa for myself and for you 1414 00:51:48,710 --> 00:51:46,800 and if you're lucky enough to have a 1415 00:51:51,270 --> 00:51:48,720 lecturer who's blessed in that area in 1416 00:51:53,030 --> 00:51:51,280 this notational refinement area then it 1417 00:51:54,950 --> 00:51:53,040 will translate directly to higher 1418 00:51:56,230 --> 00:51:54,960 comprehension for you 1419 00:52:00,390 --> 00:51:56,240 it's a 1420 00:52:02,150 --> 00:52:00,400 the logical placement of the words and 1421 00:52:03,510 --> 00:52:02,160 the formula matter and many of you are 1422 00:52:04,790 --> 00:52:03,520 trying to create your own theory of 1423 00:52:06,630 --> 00:52:04,800 everything you're advancing your own 1424 00:52:08,069 --> 00:52:06,640 you're not simply learning about others 1425 00:52:10,309 --> 00:52:08,079 it's one of the reasons why i try to be 1426 00:52:12,710 --> 00:52:10,319 specific in the podcast in general and 1427 00:52:14,470 --> 00:52:12,720 then also here as much as i can be given 1428 00:52:15,510 --> 00:52:14,480 the time constraints because generally 1429 00:52:17,990 --> 00:52:15,520 you're told 1430 00:52:19,510 --> 00:52:18,000 have truths so for example that a wave 1431 00:52:21,510 --> 00:52:19,520 function is a member of a square 1432 00:52:23,349 --> 00:52:21,520 integrable hilbert space okay but then 1433 00:52:25,190 --> 00:52:23,359 if you derive it is a square integrable 1434 00:52:27,190 --> 00:52:25,200 function necessarily square integrable 1435 00:52:28,790 --> 00:52:27,200 itself okay so then you limit it to 1436 00:52:30,870 --> 00:52:28,800 schwarz functions and then you say well 1437 00:52:32,230 --> 00:52:30,880 perhaps gelfon triples and so on and 1438 00:52:33,910 --> 00:52:32,240 then you realize well that only works 1439 00:52:35,270 --> 00:52:33,920 for pure states that a general quantum 1440 00:52:37,510 --> 00:52:35,280 mechanical state is actually an 1441 00:52:39,109 --> 00:52:37,520 endomorphism on a hilbert space and even 1442 00:52:40,230 --> 00:52:39,119 then when it's a pure state it's not a 1443 00:52:44,150 --> 00:52:40,240 unique 1444 00:52:45,670 --> 00:52:44,160 hilbert space you have to take a an 1445 00:52:47,670 --> 00:52:45,680 equivalence class so you generally take 1446 00:52:49,589 --> 00:52:47,680 them from projective hilbert spaces and 1447 00:52:51,430 --> 00:52:49,599 so on and the reason for me to be 1448 00:52:53,109 --> 00:52:51,440 extremely detailed is because many of 1449 00:52:54,470 --> 00:52:53,119 you are trying to advance your own toes 1450 00:52:56,309 --> 00:52:54,480 and if you're going to build them based 1451 00:52:58,710 --> 00:52:56,319 on some shaky foundation then you're 1452 00:53:01,430 --> 00:52:58,720 going to derive 1453 00:53:03,270 --> 00:53:01,440 fantastic formula and fantastic theories 1454 00:53:07,190 --> 00:53:03,280 based on 1455 00:53:08,870 --> 00:53:07,200 misleading you can it's akin to dividing 1456 00:53:10,630 --> 00:53:08,880 by zero you can prove the entire 1457 00:53:12,069 --> 00:53:10,640 universe from scratch if you divide by 1458 00:53:15,589 --> 00:53:12,079 zero what i found is that the 1459 00:53:18,150 --> 00:53:15,599 popularizers of science have generally 1460 00:53:19,910 --> 00:53:18,160 spent a significant amount of time on 1461 00:53:21,109 --> 00:53:19,920 let's say the wave particle duality 1462 00:53:22,790 --> 00:53:21,119 instead of telling you it's a quantum 1463 00:53:24,630 --> 00:53:22,800 mechanical object that behaves in this 1464 00:53:25,349 --> 00:53:24,640 manner well mainly 1465 00:53:29,829 --> 00:53:25,359 for 1466 00:53:31,349 --> 00:53:29,839 is because they want to evoke awe in you 1467 00:53:32,790 --> 00:53:31,359 and show you how unimaginably 1468 00:53:35,190 --> 00:53:32,800 intelligent these 1469 00:53:37,030 --> 00:53:35,200 esoteric physicists are for being able 1470 00:53:38,950 --> 00:53:37,040 to grapple with these concepts that no 1471 00:53:40,950 --> 00:53:38,960 one understands well you can understand 1472 00:53:43,430 --> 00:53:40,960 it too if it was explained 1473 00:53:45,270 --> 00:53:43,440 specifically to you and then you can 1474 00:53:46,390 --> 00:53:45,280 search the key terms so let's say i said 1475 00:53:47,829 --> 00:53:46,400 the word 1476 00:53:49,670 --> 00:53:47,839 gelphon triple you're wondering what the 1477 00:53:51,349 --> 00:53:49,680 heck is that well now you can at least 1478 00:53:53,109 --> 00:53:51,359 look that up on wikipedia and you can 1479 00:53:55,109 --> 00:53:53,119 gain a far better understanding of what 1480 00:53:56,710 --> 00:53:55,119 a quantum mechanical object is rather 1481 00:53:58,230 --> 00:53:56,720 than simply saying that it's both a wave 1482 00:54:00,630 --> 00:53:58,240 and a particle at the same time and who 1483 00:54:02,549 --> 00:54:00,640 knows what the collapse means and so on 1484 00:54:04,470 --> 00:54:02,559 by the way i talk about this here in the 1485 00:54:06,549 --> 00:54:04,480 quantum gravity section of the salvator 1486 00:54:08,230 --> 00:54:06,559 pious interview if you want i'll leave a 1487 00:54:10,150 --> 00:54:08,240 link in the description this is why 1488 00:54:12,230 --> 00:54:10,160 quantizing gravity is so difficult and 1489 00:54:14,790 --> 00:54:12,240 it's explained in in some pedantic 1490 00:54:16,309 --> 00:54:14,800 mathematical detail mainly because then 1491 00:54:18,309 --> 00:54:16,319 you can see okay this is why it's so 1492 00:54:19,829 --> 00:54:18,319 difficult and it it's not necessarily 1493 00:54:21,349 --> 00:54:19,839 because you're trying to mix the jittery 1494 00:54:22,390 --> 00:54:21,359 with the smooth and so on like what does 1495 00:54:25,109 --> 00:54:22,400 that mean 1496 00:54:26,390 --> 00:54:25,119 let's get to knots and extra dimensions 1497 00:54:27,750 --> 00:54:26,400 the whole point of this is to get 1498 00:54:29,349 --> 00:54:27,760 familiar with the different length 1499 00:54:31,190 --> 00:54:29,359 scales and the different energy scales 1500 00:54:33,510 --> 00:54:31,200 so let's take a look at this the mass of 1501 00:54:36,390 --> 00:54:33,520 the pion which you can look up online is 1502 00:54:38,790 --> 00:54:36,400 about 10 to the minus 1 gev 1503 00:54:41,990 --> 00:54:38,800 the mass of the electron which i think 1504 00:54:44,710 --> 00:54:42,000 we've used is about 10 to the minus 3 1505 00:54:47,670 --> 00:54:44,720 gev thinking of physics in the manner of 1506 00:54:49,190 --> 00:54:47,680 natural units and gevs etc 1507 00:54:50,549 --> 00:54:49,200 gives you concrete ways of thinking 1508 00:54:52,710 --> 00:54:50,559 about some phenomenon in different 1509 00:54:55,750 --> 00:54:52,720 respects so for example length scales 1510 00:54:58,390 --> 00:54:55,760 here these automatically imply that for 1511 00:55:01,349 --> 00:54:58,400 example chemistry 1512 00:55:02,950 --> 00:55:01,359 becomes important at what scale well 10 1513 00:55:04,549 --> 00:55:02,960 to the 3 1514 00:55:06,870 --> 00:55:04,559 g e v 1515 00:55:07,589 --> 00:55:06,880 inverse we simply take the inverse of 1516 00:55:09,510 --> 00:55:07,599 this 1517 00:55:10,630 --> 00:55:09,520 and then same with the straw and by the 1518 00:55:12,630 --> 00:55:10,640 way that's because the electron is 1519 00:55:17,589 --> 00:55:12,640 what's responsible for chemistry largely 1520 00:55:22,230 --> 00:55:19,430 we expect the scale that it becomes 1521 00:55:25,430 --> 00:55:22,240 relevant is 10 1522 00:55:27,829 --> 00:55:25,440 gev inverse and then we can simply do 1523 00:55:30,470 --> 00:55:27,839 our conversion over here to find out the 1524 00:55:32,230 --> 00:55:30,480 relevant length scale in terms of meters 1525 00:55:33,670 --> 00:55:32,240 let's now have a quick detour into extra 1526 00:55:39,910 --> 00:55:33,680 dimensions 1527 00:55:41,510 --> 00:55:39,920 we're dealing with one temporal time 1528 00:55:43,510 --> 00:55:41,520 dimension so you'll hear three plus one 1529 00:55:45,829 --> 00:55:43,520 or four plus one that plus one usually 1530 00:55:48,309 --> 00:55:45,839 means the time at some point in the toe 1531 00:55:50,390 --> 00:55:48,319 podcast i may do a single episode just 1532 00:55:52,789 --> 00:55:50,400 on extra dimensions if you're interested 1533 00:55:54,630 --> 00:55:52,799 let me know as well as extra temporal 1534 00:55:56,710 --> 00:55:54,640 dimensions what we're doing is looking 1535 00:55:58,390 --> 00:55:56,720 here so we're seeing that usually what 1536 00:56:00,630 --> 00:55:58,400 you've heard is that you compactify the 1537 00:56:02,230 --> 00:56:00,640 dimensions sometimes i think in the 1538 00:56:05,109 --> 00:56:02,240 string theory episode which i'll link 1539 00:56:07,109 --> 00:56:05,119 over here we talked about a collusion 1540 00:56:09,109 --> 00:56:07,119 compactification of 10 dimensional super 1541 00:56:10,150 --> 00:56:09,119 yang mills theory so that's what's being 1542 00:56:12,069 --> 00:56:10,160 referenced here when you hear about 1543 00:56:14,230 --> 00:56:12,079 occlusal klein resonance and then you 1544 00:56:15,750 --> 00:56:14,240 may wonder well look it says that we 1545 00:56:17,990 --> 00:56:15,760 have put some bounds on the extra 1546 00:56:20,230 --> 00:56:18,000 dimensions which is one tev but if we 1547 00:56:22,789 --> 00:56:20,240 take a look at what the lhc 1548 00:56:24,549 --> 00:56:22,799 the largest energy of the lhc is it says 1549 00:56:28,950 --> 00:56:24,559 here 1550 00:56:31,030 --> 00:56:28,960 it's 6.8 well times two so it's 13.6 tev 1551 00:56:33,190 --> 00:56:31,040 tv is just a thousand gev so then you 1552 00:56:35,510 --> 00:56:33,200 wonder well how is it that we've put a 1553 00:56:38,150 --> 00:56:35,520 bound of an extra dimension only at one 1554 00:56:40,230 --> 00:56:38,160 tev shouldn't it be at 13 tev well 1555 00:56:42,150 --> 00:56:40,240 strangely some of the theories of extra 1556 00:56:44,549 --> 00:56:42,160 dimensions have it such that the 1557 00:56:47,430 --> 00:56:44,559 standard model fields 1558 00:56:49,109 --> 00:56:47,440 stay within our three spatial dimensions 1559 00:56:51,109 --> 00:56:49,119 and then they leak out well gravity 1560 00:56:53,030 --> 00:56:51,119 mainly leaks out into another dimension 1561 00:56:57,750 --> 00:56:53,040 that's the add model not attention 1562 00:56:59,190 --> 00:56:57,760 deficit disorder but arkani hamed and 1563 00:57:01,109 --> 00:56:59,200 divali and then there's one more other 1564 00:57:02,549 --> 00:57:01,119 person and so it looks like this let's 1565 00:57:04,230 --> 00:57:02,559 imagine that this is a three-dimensional 1566 00:57:05,589 --> 00:57:04,240 slice 1567 00:57:07,510 --> 00:57:05,599 these are some particles and they're 1568 00:57:09,349 --> 00:57:07,520 moving together and then they hit and 1569 00:57:11,510 --> 00:57:09,359 then if a graviton is created well 1570 00:57:13,670 --> 00:57:11,520 graviton can somewhat come outward but 1571 00:57:15,349 --> 00:57:13,680 it can also leak into another dimension 1572 00:57:18,069 --> 00:57:15,359 and so that's one of the proposed 1573 00:57:20,230 --> 00:57:18,079 mechanisms to give an explanation for 1574 00:57:21,670 --> 00:57:20,240 why gravity is so comparatively quote 1575 00:57:23,190 --> 00:57:21,680 unquote weak 1576 00:57:24,549 --> 00:57:23,200 is that it's actually not it's somewhat 1577 00:57:26,950 --> 00:57:24,559 comparable it's just that it goes into 1578 00:57:29,030 --> 00:57:26,960 another dimension and because we're 1579 00:57:31,270 --> 00:57:29,040 confined here this is where we're 1580 00:57:32,789 --> 00:57:31,280 confined it's not as simple as looking 1581 00:57:34,870 --> 00:57:32,799 for an extra dimension like you can see 1582 00:57:36,390 --> 00:57:34,880 it just like you can see a 1583 00:57:37,990 --> 00:57:36,400 dna molecule 1584 00:57:40,950 --> 00:57:38,000 what we're looking for are deviations in 1585 00:57:42,789 --> 00:57:40,960 the inverse square law and this number 2 1586 00:57:44,950 --> 00:57:42,799 here is actually 1587 00:57:46,230 --> 00:57:44,960 can be generalized to higher dimensions 1588 00:57:48,630 --> 00:57:46,240 dim 1589 00:57:50,710 --> 00:57:48,640 minus 2 where i'm including time here to 1590 00:57:52,950 --> 00:57:50,720 make this simple so for us it's 4 minus 1591 00:57:54,470 --> 00:57:52,960 2 which is what gives rise to this 1592 00:57:55,829 --> 00:57:54,480 inverse square law but if we're in 1593 00:57:57,270 --> 00:57:55,839 higher dimensions then we'll see a 1594 00:57:58,870 --> 00:57:57,280 different number here 1595 00:58:00,470 --> 00:57:58,880 this becomes one over the dimension of 1596 00:58:02,390 --> 00:58:00,480 the manifold that you're on minus two 1597 00:58:03,910 --> 00:58:02,400 and in the manifold i'm including time 1598 00:58:05,589 --> 00:58:03,920 just to make it simple 1599 00:58:07,190 --> 00:58:05,599 okay as for how we derive this don't 1600 00:58:09,670 --> 00:58:07,200 worry about that you can just think of 1601 00:58:12,309 --> 00:58:09,680 the flow through a surface if we're in 1602 00:58:14,230 --> 00:58:12,319 r3 then a sphere around us is like a 1603 00:58:16,150 --> 00:58:14,240 shell and that's a two-dimensional 1604 00:58:18,069 --> 00:58:16,160 surface so if you're in r3 you go one 1605 00:58:19,829 --> 00:58:18,079 dimension down if you're an r4 you go 1606 00:58:21,829 --> 00:58:19,839 one dimension down so it's r3 and so on 1607 00:58:23,349 --> 00:58:21,839 and so on technically to be rigorous you 1608 00:58:26,630 --> 00:58:23,359 need to show that the potential of some 1609 00:58:27,750 --> 00:58:26,640 laplacian vanishes but we can leave that 1610 00:58:30,069 --> 00:58:27,760 let's get to looking at some of the 1611 00:58:32,789 --> 00:58:30,079 papers on extra dimensions here we go so 1612 00:58:34,630 --> 00:58:32,799 firstly notice this this is inverse r 1613 00:58:36,390 --> 00:58:34,640 which is related to an energy and so 1614 00:58:38,069 --> 00:58:36,400 this makes sense because you know length 1615 00:58:39,670 --> 00:58:38,079 is inverse energy 1616 00:58:41,190 --> 00:58:39,680 now you're starting to get a handle on 1617 00:58:43,910 --> 00:58:41,200 all of this let's take a look at another 1618 00:58:45,670 --> 00:58:43,920 paper which i'll link in the description 1619 00:58:48,150 --> 00:58:45,680 this is actually a section from a book i 1620 00:58:49,670 --> 00:58:48,160 believe and you can take a look well 1621 00:58:51,829 --> 00:58:49,680 here what this is saying is that if we 1622 00:58:53,589 --> 00:58:51,839 have extra dimension c here is four plus 1623 00:58:55,589 --> 00:58:53,599 the extra spatial dimensions right there 1624 00:58:58,549 --> 00:58:55,599 that's delta you have the einstein 1625 00:59:02,230 --> 00:58:58,559 hilbert action this we know if we remove 1626 00:59:03,430 --> 00:59:02,240 this d delta y this is just the standard 1627 00:59:05,670 --> 00:59:03,440 action that leads to the einstein 1628 00:59:07,349 --> 00:59:05,680 equations and we trivially add some more 1629 00:59:08,549 --> 00:59:07,359 spatial dimensions right here and then 1630 00:59:10,150 --> 00:59:08,559 here's some matter fields you want to 1631 00:59:11,750 --> 00:59:10,160 couple some matter to it and notice that 1632 00:59:14,150 --> 00:59:11,760 it's four dimensional here whereas this 1633 00:59:16,390 --> 00:59:14,160 one is four plus delta and that's saying 1634 00:59:18,470 --> 00:59:16,400 hey let's restrict our standard model 1635 00:59:20,470 --> 00:59:18,480 matter field to this four dimensional 1636 00:59:22,309 --> 00:59:20,480 manifold and that explains why we see 1637 00:59:23,589 --> 00:59:22,319 them as fairly strong but then gravity 1638 00:59:25,829 --> 00:59:23,599 is allowed to 1639 00:59:27,190 --> 00:59:25,839 leak out into the extra delta dimensions 1640 00:59:28,870 --> 00:59:27,200 if we take a look at this this also 1641 00:59:30,549 --> 00:59:28,880 gives us some bounds on the extra 1642 00:59:32,470 --> 00:59:30,559 dimensions now there are large extra 1643 00:59:33,670 --> 00:59:32,480 dimensions as well the add model i 1644 00:59:35,990 --> 00:59:33,680 mentioned before 1645 00:59:37,510 --> 00:59:36,000 isn't a compactification and you can 1646 00:59:39,270 --> 00:59:37,520 similarly find bounds on them which are 1647 00:59:41,750 --> 00:59:39,280 found here now that you're becoming more 1648 00:59:44,069 --> 00:59:41,760 and more familiar with tevs and gevs and 1649 00:59:46,069 --> 00:59:44,079 so on you can at least skim this paper 1650 00:59:47,510 --> 00:59:46,079 and get an idea of what's being said 1651 00:59:49,829 --> 00:59:47,520 notice here another number you should 1652 00:59:52,230 --> 00:59:49,839 recognize is the planck scale which is 1653 00:59:54,150 --> 00:59:52,240 10 to the 16 tev we have it written down 1654 00:59:55,510 --> 00:59:54,160 as 10 to the 19 gev but those are the 1655 00:59:57,430 --> 00:59:55,520 same numbers 1656 00:59:59,750 --> 00:59:57,440 now let's have a quick aside on knots if 1657 01:00:01,750 --> 00:59:59,760 i have enough room here what is a knot a 1658 01:00:06,549 --> 01:00:01,760 knot is an embedding of 1659 01:00:08,309 --> 01:00:06,559 a circle into r3 let's take an example 1660 01:00:09,750 --> 01:00:08,319 right there is a knot and this what 1661 01:00:11,430 --> 01:00:09,760 we're actually seeing this is not a knot 1662 01:00:13,510 --> 01:00:11,440 this is an embedding of a knot 1663 01:00:16,230 --> 01:00:13,520 technically these should be modded out 1664 01:00:18,630 --> 01:00:16,240 by isotopic equivalents i'll include a 1665 01:00:20,789 --> 01:00:18,640 link to a podcast where we go into more 1666 01:00:22,630 --> 01:00:20,799 about knots and quantum field theory 1667 01:00:26,549 --> 01:00:22,640 each one of these guys can directly 1668 01:00:26,559 --> 01:00:30,630 in two plus one dimensions 1669 01:00:33,510 --> 01:00:31,910 now you may ask well why is it that 1670 01:00:36,470 --> 01:00:33,520 we're going from 1671 01:00:40,069 --> 01:00:36,480 a circle to r3 but not to rd well there 1672 01:00:43,750 --> 01:00:40,079 are extensions except you can't have s1 1673 01:00:45,589 --> 01:00:43,760 you cannot have s1 into r4 you can 1674 01:00:48,069 --> 01:00:45,599 except that every single knot can be 1675 01:00:49,990 --> 01:00:48,079 trivially unknotted so it can be morphed 1676 01:00:51,990 --> 01:00:50,000 into a circle 1677 01:00:54,470 --> 01:00:52,000 so that's why you'll have to have s2 if 1678 01:00:57,670 --> 01:00:54,480 you're going into r4 and then 1679 01:00:59,349 --> 01:00:57,680 s3 into r5 etc if you want to have 1680 01:01:01,109 --> 01:00:59,359 higher dimensional generalization of 1681 01:01:03,589 --> 01:01:01,119 knots but then their connection to 1682 01:01:05,190 --> 01:01:03,599 findment diagrams are 1683 01:01:06,549 --> 01:01:05,200 more complicated and i believe it's 1684 01:01:11,270 --> 01:01:06,559 current research 1685 01:01:14,710 --> 01:01:12,630 additionally whenever you hear about the 1686 01:01:17,510 --> 01:01:14,720 plank length that will come up the plank 1687 01:01:19,270 --> 01:01:17,520 length it can't be that space is quote 1688 01:01:21,030 --> 01:01:19,280 unquote trivially 1689 01:01:23,349 --> 01:01:21,040 made up into some lattice of discrete 1690 01:01:24,950 --> 01:01:23,359 lattice of plank lengths plank cubed and 1691 01:01:27,030 --> 01:01:24,960 so on and the reason is that that 1692 01:01:28,390 --> 01:01:27,040 concept is not lawrence and variant 1693 01:01:29,589 --> 01:01:28,400 because what if you're zooming past it 1694 01:01:31,589 --> 01:01:29,599 then do you get smaller than the planck 1695 01:01:32,950 --> 01:01:31,599 length what if you make this room into 1696 01:01:34,870 --> 01:01:32,960 the plank length and should this room 1697 01:01:36,950 --> 01:01:34,880 exist from another perspective you get 1698 01:01:38,309 --> 01:01:36,960 into plenty of paradoxes and that's 1699 01:01:39,910 --> 01:01:38,319 because we don't have 1700 01:01:41,990 --> 01:01:39,920 an understanding as to what happens 1701 01:01:43,670 --> 01:01:42,000 around that scale another way that extra 1702 01:01:45,910 --> 01:01:43,680 dimensions can be tested is if you 1703 01:01:48,549 --> 01:01:45,920 collide particles so let's say they look 1704 01:01:51,670 --> 01:01:49,910 and then 1705 01:01:53,190 --> 01:01:51,680 what who knows what happens here no one 1706 01:01:54,470 --> 01:01:53,200 actually knows their finemen diagrams 1707 01:01:55,990 --> 01:01:54,480 and so on but whether or not that 1708 01:01:58,549 --> 01:01:56,000 corresponds to something physical who 1709 01:02:00,069 --> 01:01:58,559 knows imagine they come out like this 1710 01:02:01,750 --> 01:02:00,079 well 1711 01:02:03,349 --> 01:02:01,760 what happened here 1712 01:02:05,030 --> 01:02:03,359 this is the same as this but then this 1713 01:02:06,710 --> 01:02:05,040 is less than this which means we have a 1714 01:02:08,549 --> 01:02:06,720 if they're the same particles we don't 1715 01:02:09,990 --> 01:02:08,559 have a conservation of momentum and then 1716 01:02:11,750 --> 01:02:10,000 we can say that perhaps what happened 1717 01:02:13,589 --> 01:02:11,760 was some of the momentum leaked into 1718 01:02:14,549 --> 01:02:13,599 another dimension so this is also being 1719 01:02:16,150 --> 01:02:14,559 looked for 1720 01:02:24,630 --> 01:02:16,160 this is called discrepancies and 1721 01:02:28,870 --> 01:02:26,470 now let's take a dive into penrose's 1722 01:02:30,630 --> 01:02:28,880 theory the microtubules of consciousness 1723 01:02:32,470 --> 01:02:30,640 because this is meant to be an overview 1724 01:02:33,910 --> 01:02:32,480 and each one of these is could be its 1725 01:02:36,470 --> 01:02:33,920 own two hour three hour four hour 1726 01:02:38,950 --> 01:02:36,480 podcast on its own at least let's simply 1727 01:02:40,630 --> 01:02:38,960 go to wikipedia and get familiar with 1728 01:02:42,870 --> 01:02:40,640 using these 1729 01:02:44,390 --> 01:02:42,880 conversion equations and natural units 1730 01:02:46,630 --> 01:02:44,400 the whole point of this video the 1731 01:02:48,789 --> 01:02:46,640 founders of this theory are penrose and 1732 01:02:50,230 --> 01:02:48,799 stuart hamerov 1733 01:02:51,829 --> 01:02:50,240 so if we take a look we're just looking 1734 01:02:53,589 --> 01:02:51,839 for equations right now we're scrolling 1735 01:02:56,309 --> 01:02:53,599 through i'm not concerned too much with 1736 01:02:58,150 --> 01:02:56,319 the background notice this this looks 1737 01:02:59,190 --> 01:02:58,160 extremely similar to 1738 01:03:01,349 --> 01:02:59,200 this 1739 01:03:03,270 --> 01:03:01,359 and it is it's called penrose's 1740 01:03:05,510 --> 01:03:03,280 indeterminacy principle much like 1741 01:03:07,589 --> 01:03:05,520 heisenberg's uncertainty principle what 1742 01:03:09,190 --> 01:03:07,599 penrose is saying is that imagine we 1743 01:03:11,270 --> 01:03:09,200 have one particle and then it's in a 1744 01:03:13,190 --> 01:03:11,280 superposition so let's imagine it's 1745 01:03:16,230 --> 01:03:13,200 a superposition of just two states which 1746 01:03:18,549 --> 01:03:16,240 can be left or right let's call this 1747 01:03:20,870 --> 01:03:18,559 option a and let's call this option b 1748 01:03:22,549 --> 01:03:20,880 along with option a and option b they 1749 01:03:24,150 --> 01:03:22,559 have their own warping of space time so 1750 01:03:25,910 --> 01:03:24,160 gravity anytime you hear about a 1751 01:03:28,549 --> 01:03:25,920 gravitational field usually when you 1752 01:03:30,789 --> 01:03:28,559 hear the term gravitational field it's 1753 01:03:33,029 --> 01:03:30,799 the metric the space-time metric in 1754 01:03:34,870 --> 01:03:33,039 general relativity however 1755 01:03:36,710 --> 01:03:34,880 technically speaking the gravitational 1756 01:03:39,190 --> 01:03:36,720 field tensor is the romanian tensor and 1757 01:03:41,109 --> 01:03:39,200 the gravitational potential is the 1758 01:03:42,710 --> 01:03:41,119 metric regardless we take a look here 1759 01:03:44,549 --> 01:03:42,720 and we say that there are different 1760 01:03:46,549 --> 01:03:44,559 warpings of space time associated with 1761 01:03:48,630 --> 01:03:46,559 each of the options so a may have some 1762 01:03:50,950 --> 01:03:48,640 warping that looks like this as you go 1763 01:03:53,190 --> 01:03:50,960 outward and then b may look like let's 1764 01:03:54,870 --> 01:03:53,200 say this and then you wonder well is 1765 01:03:56,950 --> 01:03:54,880 this the superpositions that ordinarily 1766 01:03:58,870 --> 01:03:56,960 be denoted this plus this 1767 01:04:01,029 --> 01:03:58,880 well are we to have a superposition of 1768 01:04:02,789 --> 01:04:01,039 space times what penrose is saying is 1769 01:04:04,870 --> 01:04:02,799 that once the particles are of a 1770 01:04:07,670 --> 01:04:04,880 sufficient distance from one another in 1771 01:04:09,109 --> 01:04:07,680 metric space so over here it says eg is 1772 01:04:10,950 --> 01:04:09,119 the gravitational self energy and the 1773 01:04:12,710 --> 01:04:10,960 degree of space time separation so the 1774 01:04:14,789 --> 01:04:12,720 degree of space-time separation is a bit 1775 01:04:16,390 --> 01:04:14,799 of a misnomer here what's meant is that 1776 01:04:18,549 --> 01:04:16,400 there's a symplectic measure on the 1777 01:04:20,710 --> 01:04:18,559 metric of space times and then from that 1778 01:04:22,150 --> 01:04:20,720 you assign a number to the metric of a 1779 01:04:24,230 --> 01:04:22,160 and then to the metric of b and you see 1780 01:04:26,870 --> 01:04:24,240 the difference once that difference is 1781 01:04:29,589 --> 01:04:26,880 large enough then there's a collapse so 1782 01:04:31,510 --> 01:04:29,599 this is a mechanism that merges gravity 1783 01:04:33,990 --> 01:04:31,520 as well as the quantum collapse as well 1784 01:04:36,309 --> 01:04:34,000 as consciousness so like three 1785 01:04:37,910 --> 01:04:36,319 mysteries in one there's an episode with 1786 01:04:39,430 --> 01:04:37,920 stewart hamrov if you want to see more 1787 01:04:41,829 --> 01:04:39,440 about that over here it says one 1788 01:04:44,230 --> 01:04:41,839 kilogram of an object will reach its 1789 01:04:46,150 --> 01:04:44,240 objective reduction within 10 to the 1790 01:04:47,829 --> 01:04:46,160 minus 37 seconds i believe this is 1791 01:04:49,750 --> 01:04:47,839 incorrect on wikipedia because when you 1792 01:04:51,109 --> 01:04:49,760 take a look at the reference here 1793 01:04:54,230 --> 01:04:51,119 it 1794 01:04:56,150 --> 01:04:54,240 actually doesn't make a 1795 01:04:58,069 --> 01:04:56,160 it only has one reference to kilograms 1796 01:04:59,829 --> 01:04:58,079 and it's 10 kilograms not one and then 1797 01:05:01,510 --> 01:04:59,839 it says 10 to the minus 43. so i'm 1798 01:05:04,150 --> 01:05:01,520 unsure where wikipedia gets their number 1799 01:05:05,910 --> 01:05:04,160 from and here is the better diagram that 1800 01:05:08,390 --> 01:05:05,920 i was trying to draw before of the 1801 01:05:10,150 --> 01:05:08,400 different space times and you can see 1802 01:05:11,589 --> 01:05:10,160 let's see yes that's correct there is 1803 01:05:13,589 --> 01:05:11,599 technically a sympathetic measure on the 1804 01:05:14,950 --> 01:05:13,599 space of four metrics that's right and 1805 01:05:16,789 --> 01:05:14,960 penrose is not going into extra 1806 01:05:18,870 --> 01:05:16,799 dimensions here okay so let's write down 1807 01:05:20,069 --> 01:05:18,880 that equation it's the gravitational 1808 01:05:21,430 --> 01:05:20,079 self energy 1809 01:05:25,190 --> 01:05:21,440 one over 1810 01:05:27,750 --> 01:05:25,200 h bar is one in our context and tau 1811 01:05:30,150 --> 01:05:27,760 which is the time 1812 01:05:32,630 --> 01:05:30,160 so let me as well just write that as t 1813 01:05:36,309 --> 01:05:32,640 what is the gravitational self energy 1814 01:05:38,630 --> 01:05:36,319 one may guess naively that it is m1 m2 1815 01:05:39,670 --> 01:05:38,640 and then g over r and that would be 1816 01:05:41,589 --> 01:05:39,680 correct 1817 01:05:42,950 --> 01:05:41,599 because of this however if you look it 1818 01:05:45,430 --> 01:05:42,960 up online there's about a there's a 1819 01:05:46,870 --> 01:05:45,440 correction of about five thirds or so 1820 01:05:47,829 --> 01:05:46,880 that doesn't matter because we're using 1821 01:05:49,190 --> 01:05:47,839 this 1822 01:05:50,950 --> 01:05:49,200 then what i'm unclear about is that 1823 01:05:53,109 --> 01:05:50,960 there's still an r here so we have an 1824 01:05:54,549 --> 01:05:53,119 extra factor and i'm unsure of how he's 1825 01:05:56,230 --> 01:05:54,559 deriving 1826 01:05:58,309 --> 01:05:56,240 this number when there should be one 1827 01:06:00,309 --> 01:05:58,319 more factor to me this r should be a 1828 01:06:03,029 --> 01:06:00,319 function of t and this should be related 1829 01:06:04,630 --> 01:06:03,039 to the measure that we had here 1830 01:06:07,349 --> 01:06:04,640 i mean the measure that's generated from 1831 01:06:09,589 --> 01:06:07,359 the metrics however i'm unsure of this 1832 01:06:11,589 --> 01:06:09,599 and i'm going to be speaking to stuart 1833 01:06:13,910 --> 01:06:11,599 hameroff at the end of the summer in 1834 01:06:16,549 --> 01:06:13,920 order to verify all of this an essential 1835 01:06:18,789 --> 01:06:16,559 feature of penrose's theory is that when 1836 01:06:21,510 --> 01:06:18,799 there's a wave function collapse where 1837 01:06:24,309 --> 01:06:21,520 it collapses to is chosen neither 1838 01:06:26,309 --> 01:06:24,319 randomly nor algorithmically this is 1839 01:06:28,870 --> 01:06:26,319 outlined in his book called the 1840 01:06:30,710 --> 01:06:28,880 emperor's new mind where penrose makes 1841 01:06:33,990 --> 01:06:30,720 an analogy between something called 1842 01:06:35,829 --> 01:06:34,000 non-recursively innumerable sets and 1843 01:06:38,069 --> 01:06:35,839 truths in mathematics that can't be 1844 01:06:40,789 --> 01:06:38,079 proven yet we as 1845 01:06:42,950 --> 01:06:40,799 people as humans with minds are able to 1846 01:06:44,630 --> 01:06:42,960 see this as being true by the way if you 1847 01:06:46,630 --> 01:06:44,640 have questions about any of this you can 1848 01:06:48,069 --> 01:06:46,640 go to the discord or to the subreddit 1849 01:06:49,510 --> 01:06:48,079 people will help you there and people 1850 01:06:51,349 --> 01:06:49,520 will also be just as confused as 1851 01:06:53,029 --> 01:06:51,359 yourself and as myself and we help one 1852 01:06:54,470 --> 01:06:53,039 another out links to all of those the 1853 01:06:55,670 --> 01:06:54,480 subreddit and the discord will be in the 1854 01:06:57,029 --> 01:06:55,680 description 1855 01:07:01,670 --> 01:06:57,039 you may wonder why is it that we're 1856 01:07:03,750 --> 01:07:01,680 using one gev instead of one mev because 1857 01:07:05,670 --> 01:07:03,760 this one's the proton and this one is 1858 01:07:07,990 --> 01:07:05,680 the electron why are you prioritizing 1859 01:07:09,029 --> 01:07:08,000 the proton over the electron well it 1860 01:07:11,029 --> 01:07:09,039 just makes some of the napkin 1861 01:07:13,270 --> 01:07:11,039 calculations easier so this is all about 1862 01:07:15,109 --> 01:07:13,280 nc's napkin calculations as well as it 1863 01:07:17,109 --> 01:07:15,119 gives you a much more concrete physical 1864 01:07:18,710 --> 01:07:17,119 intuition later we'll derive the radius 1865 01:07:20,710 --> 01:07:18,720 of an atom but for now you can see that 1866 01:07:22,309 --> 01:07:20,720 this is the radius of a proton it's also 1867 01:07:24,150 --> 01:07:22,319 the energy of a proton the mass of a 1868 01:07:26,309 --> 01:07:24,160 proton which as we mentioned earlier 1869 01:07:28,789 --> 01:07:26,319 this means my desk is 10 to the 16 1870 01:07:30,309 --> 01:07:28,799 protons long if you take 10 to the 16 1871 01:07:33,510 --> 01:07:30,319 protons and stack them you get the 1872 01:07:35,829 --> 01:07:33,520 length of my desk and i said 1873 01:07:37,750 --> 01:07:35,839 desk so don't get excited okay now let's 1874 01:07:39,109 --> 01:07:37,760 get to vacuum energy 1875 01:07:41,270 --> 01:07:39,119 okay you've heard the story that the 1876 01:07:43,270 --> 01:07:41,280 universe is expanding and because it's 1877 01:07:46,069 --> 01:07:43,280 expanding it has a positive cosmological 1878 01:07:48,150 --> 01:07:46,079 constant and much fervor is expressed to 1879 01:07:49,750 --> 01:07:48,160 the disdain of the word prediction the 1880 01:07:51,910 --> 01:07:49,760 worst prediction of physics i'm sure 1881 01:07:55,109 --> 01:07:51,920 you've heard worst 1882 01:07:58,309 --> 01:07:56,630 and many people dislike this word 1883 01:08:00,470 --> 01:07:58,319 prediction because it's not as if a 1884 01:08:02,230 --> 01:08:00,480 specific theory was said to be false 1885 01:08:03,829 --> 01:08:02,240 because of this prediction however that 1886 01:08:05,910 --> 01:08:03,839 gives the impression of discounting the 1887 01:08:08,390 --> 01:08:05,920 calculation completely it wasn't a 1888 01:08:12,390 --> 01:08:08,400 prediction per se it was a comportment 1889 01:08:15,109 --> 01:08:12,400 namely if lambda was to 1890 01:08:18,789 --> 01:08:16,229 with 1891 01:08:20,630 --> 01:08:18,799 the standard model 1892 01:08:22,149 --> 01:08:20,640 that is if it was to be a consequence of 1893 01:08:23,829 --> 01:08:22,159 absolute energy from the vacuum 1894 01:08:25,590 --> 01:08:23,839 fluctuations from the planck scale 1895 01:08:27,430 --> 01:08:25,600 upward then it should be of order let's 1896 01:08:29,269 --> 01:08:27,440 say x we're going to calculate that it 1897 01:08:31,189 --> 01:08:29,279 was a comportment test rather than a 1898 01:08:33,910 --> 01:08:31,199 prediction the mechanism could have been 1899 01:08:35,669 --> 01:08:33,920 the vacuum fluctuations of qed i believe 1900 01:08:37,910 --> 01:08:35,679 weinberg calculated this but it turns 1901 01:08:39,829 --> 01:08:37,920 out to be vastly vastly incorrect so 1902 01:08:43,030 --> 01:08:39,839 let's take a look there are three main 1903 01:08:43,040 --> 01:08:46,390 of vacuum energy 1904 01:08:49,829 --> 01:08:47,990 and this is just from the standard model 1905 01:08:52,470 --> 01:08:49,839 forget about general relativity so 1906 01:08:55,430 --> 01:08:52,480 number one qcd and these are these 1907 01:08:58,870 --> 01:08:55,440 little cork bilinears number two 1908 01:09:01,030 --> 01:08:58,880 it's the higgs field 1909 01:09:03,189 --> 01:09:01,040 and number three it would be the zero 1910 01:09:09,510 --> 01:09:03,199 point 1911 01:09:13,590 --> 01:09:12,709 and this one is of order 10 to the minus 1912 01:09:15,910 --> 01:09:13,600 one 1913 01:09:18,149 --> 01:09:15,920 g e v 1914 01:09:20,630 --> 01:09:18,159 and what power goes here 1915 01:09:24,070 --> 01:09:20,640 it's a pressure it's dark energy it's a 1916 01:09:25,510 --> 01:09:24,080 property of space time itself so four 1917 01:09:26,870 --> 01:09:25,520 simple 1918 01:09:30,309 --> 01:09:26,880 then what is the higgs fields 1919 01:09:32,309 --> 01:09:30,319 contribution ten squared gev 1920 01:09:34,630 --> 01:09:32,319 and what power goes here well what else 1921 01:09:36,149 --> 01:09:34,640 could it be number four 1922 01:09:38,309 --> 01:09:36,159 let's get to the calculation of the zero 1923 01:09:40,149 --> 01:09:38,319 point fluctuations what this means is 1924 01:09:41,910 --> 01:09:40,159 that at each space-time volume 1925 01:09:43,990 --> 01:09:41,920 space-time so now we're dealing with 1926 01:09:47,030 --> 01:09:44,000 four not just three volumes but i'll 1927 01:09:48,470 --> 01:09:47,040 draw it as a cube at each space-time 1928 01:09:50,550 --> 01:09:48,480 volume 1929 01:09:52,070 --> 01:09:50,560 of length let's say l 1930 01:09:54,550 --> 01:09:52,080 so l 1931 01:09:57,510 --> 01:09:54,560 cubed in this case but actually it's 1932 01:09:59,110 --> 01:09:57,520 truly l4 so let's just place 1933 01:10:01,350 --> 01:09:59,120 l4 here 1934 01:10:04,470 --> 01:10:01,360 that corresponding to this length is 1935 01:10:06,470 --> 01:10:04,480 some frequency omega the reason why is 1936 01:10:07,910 --> 01:10:06,480 that we have this relation that energy 1937 01:10:09,750 --> 01:10:07,920 is related to 1938 01:10:11,669 --> 01:10:09,760 frequency which means there's a tight 1939 01:10:13,350 --> 01:10:11,679 relationship between frequency and 1940 01:10:14,550 --> 01:10:13,360 energy you can convert between the two 1941 01:10:17,270 --> 01:10:14,560 we're going to do that later once we 1942 01:10:19,430 --> 01:10:17,280 analyze the sun from each space time 1943 01:10:22,390 --> 01:10:19,440 volume of length l there's a 1944 01:10:24,229 --> 01:10:22,400 contribution of a certain mode that 1945 01:10:26,470 --> 01:10:24,239 happens within here so let's call that 1946 01:10:28,470 --> 01:10:26,480 frequency well whatever it's omega in 1947 01:10:31,669 --> 01:10:28,480 this case so we constantly get these 1948 01:10:33,510 --> 01:10:31,679 omegas associated with length one plus 1949 01:10:34,550 --> 01:10:33,520 an omega associated with length length 1950 01:10:36,630 --> 01:10:34,560 two 1951 01:10:39,590 --> 01:10:36,640 so on and so on and because of this 1952 01:10:42,390 --> 01:10:39,600 relation here the shorter the length 1953 01:10:44,390 --> 01:10:42,400 the larger the energy firstly that means 1954 01:10:46,709 --> 01:10:44,400 that it's infinite technically the zero 1955 01:10:48,950 --> 01:10:46,719 point fluctuation yields an infinite 1956 01:10:51,270 --> 01:10:48,960 energy but that doesn't mean that it's 1957 01:10:53,030 --> 01:10:51,280 literally true it means technically it's 1958 01:10:54,070 --> 01:10:53,040 true with our theories which already 1959 01:10:57,110 --> 01:10:54,080 break down 1960 01:10:59,590 --> 01:10:57,120 planck scale this is what you've heard 1961 01:11:01,910 --> 01:10:59,600 so how about we simply cut it off at the 1962 01:11:04,470 --> 01:11:01,920 length scale so we let this be the 1963 01:11:07,830 --> 01:11:04,480 planck length which by the way is what 1964 01:11:09,510 --> 01:11:07,840 well it's the inverse of the planck mass 1965 01:11:11,590 --> 01:11:09,520 because we're taking an inverse of an 1966 01:11:15,990 --> 01:11:11,600 inverse we simply get that the energy 1967 01:11:18,709 --> 01:11:17,750 from 1968 01:11:43,430 --> 01:11:18,719 the 1969 01:11:45,910 --> 01:11:43,440 contributes this is why this nc or this 1970 01:11:48,229 --> 01:11:45,920 napkin calculation which is contingent 1971 01:11:50,709 --> 01:11:48,239 on this on the order of symbol this 1972 01:11:53,030 --> 01:11:50,719 tilde here is so vital this is what 1973 01:11:55,669 --> 01:11:53,040 allows you to do this quickly without 1974 01:11:58,630 --> 01:11:55,679 thinking eventually 1975 01:12:01,910 --> 01:11:58,640 this gives an nc of what a napkin 1976 01:12:03,750 --> 01:12:01,920 calculation of 10 to the 18 1977 01:12:05,030 --> 01:12:03,760 g e v 1978 01:12:07,350 --> 01:12:05,040 to the fourth 1979 01:12:10,470 --> 01:12:07,360 well this should be that and then that 1980 01:12:18,790 --> 01:12:10,480 means that this is 10 to the 72 1981 01:12:22,390 --> 01:12:20,149 what's observed is what you can get 1982 01:12:24,630 --> 01:12:22,400 online because this is what's calculated 1983 01:12:26,390 --> 01:12:24,640 by data 1984 01:12:27,910 --> 01:12:26,400 you'll see these strange units and then 1985 01:12:30,149 --> 01:12:27,920 you'll have to look up on some other 1986 01:12:31,669 --> 01:12:30,159 conversion site so for example let's 1987 01:12:34,229 --> 01:12:31,679 take a look here 1988 01:12:35,590 --> 01:12:34,239 here's some conversion table 1989 01:12:38,310 --> 01:12:35,600 you can find online they've set the 1990 01:12:40,229 --> 01:12:38,320 boltzmann constant to one as well 1991 01:12:41,350 --> 01:12:40,239 and here's another one 1992 01:12:43,030 --> 01:12:41,360 i'll leave these links in the 1993 01:12:45,030 --> 01:12:43,040 description because these can be helpful 1994 01:12:47,510 --> 01:12:45,040 you'll notice that some of them differ 1995 01:12:49,350 --> 01:12:47,520 at the last digits and the reason is 1996 01:12:51,189 --> 01:12:49,360 again i mentioned this some places round 1997 01:12:52,790 --> 01:12:51,199 up some places round down 1998 01:12:58,470 --> 01:12:52,800 this then becomes 1999 01:13:02,709 --> 01:13:00,630 to the 4. you may wonder why am i not 2000 01:13:04,790 --> 01:13:02,719 placing square brackets here well you 2001 01:13:06,950 --> 01:13:04,800 can it doesn't matter because you know 2002 01:13:08,550 --> 01:13:06,960 that this is the only unit anyway 2003 01:13:10,550 --> 01:13:08,560 you may wonder well where does this 2004 01:13:11,990 --> 01:13:10,560 observation come from like i mentioned 2005 01:13:15,030 --> 01:13:12,000 people look at data and then they have 2006 01:13:16,709 --> 01:13:15,040 some assumptions like homogeneity and an 2007 01:13:18,550 --> 01:13:16,719 isotropic universe and then you get the 2008 01:13:20,470 --> 01:13:18,560 friedman equations which you can look up 2009 01:13:22,470 --> 01:13:20,480 which relates the acceleration to the 2010 01:13:25,110 --> 01:13:22,480 cosmological constant and thus the 2011 01:13:28,149 --> 01:13:25,120 pressure and density 2012 01:13:31,350 --> 01:13:28,159 the above then yields slash implies that 2013 01:13:34,070 --> 01:13:31,360 our napkin calculation is the same as 2014 01:13:37,910 --> 01:13:34,080 the observed 2015 01:13:40,149 --> 01:13:37,920 times 10 to the 120 2016 01:13:43,270 --> 01:13:40,159 and now you know about the vacuum energy 2017 01:13:46,709 --> 01:13:44,870 now let's get on to calculating with the 2018 01:13:48,870 --> 01:13:46,719 swinger limit if you watched the 2019 01:13:51,110 --> 01:13:48,880 salvator pius interview you'll notice 2020 01:13:53,350 --> 01:13:51,120 that one coulomb of charge was brought 2021 01:13:55,270 --> 01:13:53,360 up so firstly let's talk about what is 2022 01:13:58,630 --> 01:13:55,280 one coulomb of charge let's get a handle 2023 01:13:59,990 --> 01:13:58,640 on it let's go to wikipedia our friend 2024 01:14:02,229 --> 01:14:00,000 we take a look and we see that the 2025 01:14:04,870 --> 01:14:02,239 elementary charge was assigned to this 2026 01:14:08,390 --> 01:14:04,880 exact value in 2019. so this is the 2027 01:14:10,070 --> 01:14:08,400 exact value of one elementary charge it 2028 01:14:12,470 --> 01:14:10,080 turns out that elementary charge is a 2029 01:14:15,430 --> 01:14:12,480 dimensionless quantity let's write this 2030 01:14:17,350 --> 01:14:15,440 down here 2031 01:14:20,229 --> 01:14:17,360 elementary charge 2032 01:14:24,310 --> 01:14:20,239 is on the order of 10 to the minus 19 2033 01:14:28,470 --> 01:14:26,149 this means that one coulomb which i'm 2034 01:14:32,310 --> 01:14:28,480 going to denote as c 2035 01:14:34,550 --> 01:14:32,320 1 coulomb is the same as 10 to the 19 2036 01:14:38,070 --> 01:14:34,560 charges 2037 01:14:40,070 --> 01:14:38,080 they're the same they're just the 2038 01:14:42,870 --> 01:14:40,080 reverse of one another plus or minus 2039 01:14:47,830 --> 01:14:42,880 let's deal with protons 10 to the 19 2040 01:14:49,750 --> 01:14:47,840 protons that's 10 to the 19 g e v 2041 01:14:52,550 --> 01:14:49,760 let's get a handle on that number if we 2042 01:14:55,189 --> 01:14:52,560 were to stack protons one after the 2043 01:15:02,709 --> 01:14:58,709 10 to the 19 times 2044 01:15:04,149 --> 01:15:02,719 then going up to our conversion chart 2045 01:15:10,630 --> 01:15:04,159 that is 2046 01:15:14,630 --> 01:15:12,870 that's the definition of one kilometer 2047 01:15:16,229 --> 01:15:14,640 that means if you were to take protons 2048 01:15:18,709 --> 01:15:16,239 and stack them stack them stack them 2049 01:15:21,110 --> 01:15:18,719 without any gap in between it would be a 2050 01:15:22,950 --> 01:15:21,120 strip of one proton wide and then one 2051 01:15:25,110 --> 01:15:22,960 kilometer high 2052 01:15:26,550 --> 01:15:25,120 that's an extreme amount of charge great 2053 01:15:28,390 --> 01:15:26,560 now we've gotten out of the way what is 2054 01:15:29,750 --> 01:15:28,400 one coulomb let's get to the schwinger 2055 01:15:33,189 --> 01:15:29,760 limit 2056 01:15:35,590 --> 01:15:33,199 scale above which the electromagnetic 2057 01:15:37,270 --> 01:15:35,600 field is expected to become non-linear 2058 01:15:38,470 --> 01:15:37,280 so we haven't observed this because this 2059 01:15:39,910 --> 01:15:38,480 is an extreme amount we're going to 2060 01:15:42,470 --> 01:15:39,920 actually deal with what the heck does 2061 01:15:44,470 --> 01:15:42,480 this mean in our manageable units 2062 01:15:46,709 --> 01:15:44,480 the limit is typically reported as some 2063 01:15:49,270 --> 01:15:46,719 maximum electric field or magnetic field 2064 01:15:50,630 --> 01:15:49,280 before some non-linear effects kick in 2065 01:15:53,430 --> 01:15:50,640 if we take a look here we see this 2066 01:15:55,030 --> 01:15:53,440 firstly let's just analyze this 2067 01:15:57,430 --> 01:15:55,040 we notice there's a c we notice there's 2068 01:15:59,350 --> 01:15:57,440 an h bar we set those to one that means 2069 01:16:01,030 --> 01:15:59,360 that all that's left over is mass over 2070 01:16:03,270 --> 01:16:01,040 charge charge is dimensionless mass 2071 01:16:05,510 --> 01:16:03,280 squared that means energy squared that 2072 01:16:06,950 --> 01:16:05,520 means that this is energy squared this 2073 01:16:08,790 --> 01:16:06,960 is a force 2074 01:16:11,350 --> 01:16:08,800 and then this has the same units this is 2075 01:16:13,830 --> 01:16:11,360 also a force so tesla has the units of 2076 01:16:15,830 --> 01:16:13,840 force energy squared e has this volts 2077 01:16:17,510 --> 01:16:15,840 over meter has the unit's energy squared 2078 01:16:19,430 --> 01:16:17,520 you can get that right now just by 2079 01:16:23,350 --> 01:16:19,440 looking at this for three seconds 2080 01:16:27,990 --> 01:16:24,709 so e is 2081 01:16:30,950 --> 01:16:28,000 on the order of 10 to the 18 volts per 2082 01:16:32,229 --> 01:16:30,960 meter this is also as defined here m e 2083 01:16:35,510 --> 01:16:32,239 squared c 2084 01:16:39,189 --> 01:16:35,520 to the 3 over h bar the charge of the 2085 01:16:41,270 --> 01:16:39,199 electron that is in our units m e so the 2086 01:16:43,910 --> 01:16:41,280 mass of the electron those become one 2087 01:16:45,669 --> 01:16:43,920 this becomes one and then we get this 2088 01:16:48,149 --> 01:16:45,679 now the charge of the electron is just 2089 01:16:50,149 --> 01:16:48,159 one let's get a handle on this number so 2090 01:16:53,270 --> 01:16:50,159 firstly what is a volt we don't have to 2091 01:16:55,030 --> 01:16:53,280 do much work because a volt 2092 01:16:58,470 --> 01:16:55,040 well a gev 2093 01:17:00,390 --> 01:16:58,480 is 10 to the 9 volts and that means so 2094 01:17:02,550 --> 01:17:00,400 we can just take 9 from inside there and 2095 01:17:06,149 --> 01:17:02,560 it becomes ten to the nine so nine plus 2096 01:17:07,510 --> 01:17:06,159 nine g e v over meters and then we can 2097 01:17:08,470 --> 01:17:07,520 go up 2098 01:17:09,669 --> 01:17:08,480 stairs 2099 01:17:13,189 --> 01:17:09,679 to 2100 01:17:16,310 --> 01:17:13,199 16. 2101 01:17:18,950 --> 01:17:16,320 using our formula from above we get that 2102 01:17:20,870 --> 01:17:18,960 a meter is this and i will just put some 2103 01:17:22,950 --> 01:17:20,880 clouds around this 2104 01:17:25,110 --> 01:17:22,960 as well 2105 01:17:27,430 --> 01:17:25,120 because we have an inverse meter here we 2106 01:17:30,070 --> 01:17:27,440 take the inverses of this so we take one 2107 01:17:31,910 --> 01:17:30,080 here minus and plus that becomes a plus 2108 01:17:34,709 --> 01:17:31,920 one this then implies that we take the 2109 01:17:38,630 --> 01:17:34,719 nine we plus 16 to it so we get 10 to 2110 01:17:40,470 --> 01:17:38,640 the 25 gev 2111 01:17:42,470 --> 01:17:40,480 squared this is by the way a unit of 2112 01:17:44,470 --> 01:17:42,480 force like we mentioned before 2113 01:17:46,790 --> 01:17:44,480 ah and those again who have watched the 2114 01:17:49,110 --> 01:17:46,800 salvator pius interview you know that he 2115 01:17:50,550 --> 01:17:49,120 mentions the super force and what the 2116 01:17:51,270 --> 01:17:50,560 super force is 2117 01:17:55,270 --> 01:17:51,280 is 2118 01:17:57,030 --> 01:17:55,280 it's simply the planck force 2119 01:17:58,870 --> 01:17:57,040 now you should have more of an intuition 2120 01:17:59,510 --> 01:17:58,880 as to what this actually means so this 2121 01:18:04,630 --> 01:17:59,520 is 2122 01:18:08,229 --> 01:18:04,640 we've calculated before the square of 2123 01:18:11,590 --> 01:18:09,669 and you can see that makes sense in 2124 01:18:13,030 --> 01:18:11,600 terms of units because mass squared is 2125 01:18:15,510 --> 01:18:13,040 the same as energy squared is the same 2126 01:18:17,189 --> 01:18:15,520 as force now as i've mentioned before i 2127 01:18:19,510 --> 01:18:17,199 don't think force is a particularly 2128 01:18:21,750 --> 01:18:19,520 useful concept in fundamental physics i 2129 01:18:23,270 --> 01:18:21,760 think pressure is so there should be a 2130 01:18:23,990 --> 01:18:23,280 planck pressure 2131 01:18:27,110 --> 01:18:24,000 and 2132 01:18:28,310 --> 01:18:27,120 plank density i call it the plank 2133 01:18:30,229 --> 01:18:28,320 pressure it doesn't seem like anyone 2134 01:18:32,070 --> 01:18:30,239 else calls it that but anyway how do you 2135 01:18:34,310 --> 01:18:32,080 get the plank pressure well you take 2136 01:18:35,750 --> 01:18:34,320 some energy and you divide it by volume 2137 01:18:37,910 --> 01:18:35,760 what's the energy that we have we have 2138 01:18:40,149 --> 01:18:37,920 the mass the plank mass and we divide it 2139 01:18:42,709 --> 01:18:40,159 by some volume what's the volume that we 2140 01:18:44,550 --> 01:18:42,719 have we have the plank length and we 2141 01:18:45,910 --> 01:18:44,560 just cube that 2142 01:18:47,350 --> 01:18:45,920 and that's how you derive the planck 2143 01:18:48,870 --> 01:18:47,360 pressure at least that's what i think it 2144 01:18:51,189 --> 01:18:48,880 should be called now at first i was 2145 01:18:53,110 --> 01:18:51,199 going to draw some picture to give some 2146 01:18:55,350 --> 01:18:53,120 interesting ideas to what the schwinger 2147 01:18:57,189 --> 01:18:55,360 limit is in some fundamental manner but 2148 01:18:59,270 --> 01:18:57,199 actually force isn't 2149 01:19:01,189 --> 01:18:59,280 a particularly interesting 2150 01:19:03,669 --> 01:19:01,199 concept because it requires extra 2151 01:19:05,510 --> 01:19:03,679 structure so for example we know that we 2152 01:19:07,669 --> 01:19:05,520 have these inverse squared laws that 2153 01:19:10,709 --> 01:19:07,679 characterize the coulomb force and 2154 01:19:12,709 --> 01:19:10,719 gravity which technically means that you 2155 01:19:14,709 --> 01:19:12,719 can get however 2156 01:19:17,350 --> 01:19:14,719 large of a force you'd like depending on 2157 01:19:18,790 --> 01:19:17,360 how close you are to the original source 2158 01:19:22,870 --> 01:19:18,800 to the point source if it's a point 2159 01:19:25,990 --> 01:19:22,880 source this to me demonstrates a flaw 2160 01:19:28,950 --> 01:19:26,000 in newtonian mechanics from the get-go 2161 01:19:31,270 --> 01:19:28,960 and yet it works so well thus if a 2162 01:19:33,270 --> 01:19:31,280 particular theory has a major flaw 2163 01:19:37,189 --> 01:19:33,280 perhaps give it a chance to breathe 2164 01:19:40,550 --> 01:19:37,199 before dismissing it as patently broken 2165 01:19:42,630 --> 01:19:40,560 see all of this is decidedly simple and 2166 01:19:44,790 --> 01:19:42,640 often you'll be confused but not know 2167 01:19:46,790 --> 01:19:44,800 where your confusion is often what will 2168 01:19:48,470 --> 01:19:46,800 happen is you'll ask someone to explain 2169 01:19:50,390 --> 01:19:48,480 or re-explain some phenomenon or some 2170 01:19:51,669 --> 01:19:50,400 mathematical trick and then they'll say 2171 01:19:53,270 --> 01:19:51,679 well what part of it did you not 2172 01:19:55,270 --> 01:19:53,280 understand and you won't be able to give 2173 01:19:57,030 --> 01:19:55,280 an account because your confusion is 2174 01:19:59,189 --> 01:19:57,040 such that you're unable to see where 2175 01:20:00,950 --> 01:19:59,199 your confusion is that is to say you 2176 01:20:02,870 --> 01:20:00,960 don't know the aspects of the technique 2177 01:20:05,430 --> 01:20:02,880 or the mathematical trick or formula or 2178 01:20:06,870 --> 01:20:05,440 structure etc that you don't understand 2179 01:20:08,709 --> 01:20:06,880 so asking someone to explain a 2180 01:20:09,669 --> 01:20:08,719 particular part because you just chose 2181 01:20:11,350 --> 01:20:09,679 in some part and you say i don't 2182 01:20:12,470 --> 01:20:11,360 understand this somewhat fruitless 2183 01:20:14,550 --> 01:20:12,480 because that was 2184 01:20:16,149 --> 01:20:14,560 arbitrarily chosen by you this is one of 2185 01:20:18,310 --> 01:20:16,159 the reasons why it's great to read from 2186 01:20:20,149 --> 01:20:18,320 multiple sources so watch multiple 2187 01:20:22,070 --> 01:20:20,159 videos on the same phenomenon the same 2188 01:20:23,110 --> 01:20:22,080 trick the same formula you'll see 2189 01:20:24,229 --> 01:20:23,120 professors when they're being 2190 01:20:25,990 --> 01:20:24,239 interviewed or when you go to their 2191 01:20:27,830 --> 01:20:26,000 office they'll often have 2192 01:20:29,270 --> 01:20:27,840 a plethora of books and then you think 2193 01:20:30,470 --> 01:20:29,280 well they're extremely bright and they 2194 01:20:32,550 --> 01:20:30,480 are they're extremely extremely 2195 01:20:33,669 --> 01:20:32,560 extremely bright hardworking people but 2196 01:20:35,590 --> 01:20:33,679 then you wonder why do you have five 2197 01:20:37,590 --> 01:20:35,600 books on linear algebra and it's because 2198 01:20:39,350 --> 01:20:37,600 even ed whitson needs to read from 2199 01:20:41,430 --> 01:20:39,360 multiple sources on the same topic in 2200 01:20:43,189 --> 01:20:41,440 order to truly understand it you need to 2201 01:20:44,870 --> 01:20:43,199 see it from multiple perspectives 2202 01:20:46,550 --> 01:20:44,880 actually i spoke to jordan peterson 2203 01:20:48,470 --> 01:20:46,560 about this exact topic i'll leave the 2204 01:20:50,550 --> 01:20:48,480 podcast in the description so if you 2205 01:20:52,149 --> 01:20:50,560 feel like some concept is far beyond you 2206 01:20:53,750 --> 01:20:52,159 perhaps it's not perhaps you need to 2207 01:20:55,750 --> 01:20:53,760 re-watch the video so you can re-watch 2208 01:20:57,669 --> 01:20:55,760 this one if you like or you can watch 2209 01:20:59,430 --> 01:20:57,679 from multiple sources and then it will 2210 01:21:01,830 --> 01:20:59,440 slowly start to make sense you'll start 2211 01:21:03,590 --> 01:21:01,840 to see this baroque intricate complex 2212 01:21:05,510 --> 01:21:03,600 object from multiple perspectives you 2213 01:21:07,350 --> 01:21:05,520 can only see a projection of it and then 2214 01:21:08,790 --> 01:21:07,360 you start to build a shape of it seeing 2215 01:21:10,950 --> 01:21:08,800 it from one source generally doesn't 2216 01:21:12,709 --> 01:21:10,960 help to sum up learn from multiple 2217 01:21:14,550 --> 01:21:12,719 sources read multiple sources watch 2218 01:21:15,990 --> 01:21:14,560 multiple sources sometimes you don't 2219 01:21:17,669 --> 01:21:16,000 need to know where your confusion is 2220 01:21:18,870 --> 01:21:17,679 because at least you don't consciously 2221 01:21:20,870 --> 01:21:18,880 need to know because it will 2222 01:21:23,590 --> 01:21:20,880 unconsciously resolve itself after 2223 01:21:25,990 --> 01:21:23,600 learning from different perspectives 2224 01:21:28,709 --> 01:21:26,000 okay now let's get to number eight which 2225 01:21:30,310 --> 01:21:28,719 is annihilating positron electron pairs 2226 01:21:31,430 --> 01:21:30,320 and quantum gravity we got to get 2227 01:21:33,030 --> 01:21:31,440 through this quick i'm likely going to 2228 01:21:34,790 --> 01:21:33,040 turn this screen off i'm making way too 2229 01:21:36,470 --> 01:21:34,800 many mistakes i'm recording this over 2230 01:21:37,830 --> 01:21:36,480 and over and different parts aren't 2231 01:21:39,750 --> 01:21:37,840 working so 2232 01:21:41,270 --> 01:21:39,760 if there are any errors here obviously 2233 01:21:43,110 --> 01:21:41,280 leave them in the comments it's great if 2234 01:21:45,110 --> 01:21:43,120 you unceremoniously point them out i 2235 01:21:47,030 --> 01:21:45,120 don't mind i'll highlight them 2236 01:21:49,110 --> 01:21:47,040 annihilating pairs of positron electrons 2237 01:21:51,030 --> 01:21:49,120 and quantum gravity so firstly what 2238 01:21:52,390 --> 01:21:51,040 happens when you look at the vacuum 2239 01:21:55,189 --> 01:21:52,400 simply look 2240 01:21:57,430 --> 01:21:55,199 well we know this relation which is e is 2241 01:21:58,870 --> 01:21:57,440 the inverse of time 2242 01:22:01,189 --> 01:21:58,880 and let's imagine that we wanted to 2243 01:22:03,590 --> 01:22:01,199 create particles that were 2244 01:22:05,990 --> 01:22:03,600 on the order of an electron so electron 2245 01:22:08,070 --> 01:22:06,000 positron then we just replace this e 2246 01:22:09,910 --> 01:22:08,080 with the mass of an electron technically 2247 01:22:15,189 --> 01:22:09,920 it's two but it doesn't matter because 2248 01:22:18,950 --> 01:22:17,750 this means that for a small amount of 2249 01:22:21,510 --> 01:22:18,960 time 2250 01:22:23,669 --> 01:22:21,520 an electron positron pair can be created 2251 01:22:25,990 --> 01:22:23,679 and then you can also ask this is a unit 2252 01:22:28,310 --> 01:22:26,000 of length which means that if you were 2253 01:22:30,390 --> 01:22:28,320 to probe the vacuum if you were to look 2254 01:22:32,629 --> 01:22:30,400 close enough and exactly how close 2255 01:22:36,629 --> 01:22:32,639 enough well what is m e m e remember 2256 01:22:39,750 --> 01:22:36,639 it's akin to 1 mev which is the same as 2257 01:22:42,070 --> 01:22:39,760 10 to the minus 3 g e v 2258 01:22:44,550 --> 01:22:42,080 this means looking at empty space itself 2259 01:22:47,350 --> 01:22:44,560 if you look close enough just the act of 2260 01:22:49,430 --> 01:22:47,360 looking close enough will create the 2261 01:22:50,870 --> 01:22:49,440 electron positron pairs now this is 2262 01:22:52,310 --> 01:22:50,880 something you know from quantum field 2263 01:22:54,550 --> 01:22:52,320 theory and by the way when people say 2264 01:22:56,229 --> 01:22:54,560 quantum field theory there's not the 2265 01:22:58,070 --> 01:22:56,239 quantum field theory there are multiple 2266 01:22:59,590 --> 01:22:58,080 it's it's more like a framework so 2267 01:23:01,830 --> 01:22:59,600 there's five four and then there are 2268 01:23:03,590 --> 01:23:01,840 different well string theory itself can 2269 01:23:05,990 --> 01:23:03,600 be thought of as a generalization of 2270 01:23:07,590 --> 01:23:06,000 quantum field theory so when people say 2271 01:23:09,110 --> 01:23:07,600 quantum field theory you should ask them 2272 01:23:10,629 --> 01:23:09,120 well which quantum field theory are you 2273 01:23:12,470 --> 01:23:10,639 referring to now let's talk about 2274 01:23:14,229 --> 01:23:12,480 quantum gravity forget about field 2275 01:23:16,070 --> 01:23:14,239 theory when it comes to quantum gravity 2276 01:23:25,430 --> 01:23:16,080 there are several conceptual infinities 2277 01:23:28,310 --> 01:23:26,790 so firstly if you're going to be 2278 01:23:30,470 --> 01:23:28,320 infinitely accurate about let's say 2279 01:23:32,550 --> 01:23:30,480 where an electron is you have to measure 2280 01:23:33,990 --> 01:23:32,560 it an infinite amount of time or prepare 2281 01:23:35,510 --> 01:23:34,000 something and then measure that in 2282 01:23:37,750 --> 01:23:35,520 infinite amount of time because there's 2283 01:23:39,430 --> 01:23:37,760 an error an uncertainty associated with 2284 01:23:41,110 --> 01:23:39,440 the measurement and then another 2285 01:23:43,430 --> 01:23:41,120 infinity comes in when you're having to 2286 01:23:44,709 --> 01:23:43,440 store all of those bits somewhere and 2287 01:23:47,189 --> 01:23:44,719 then you also need to make your 2288 01:23:48,390 --> 01:23:47,199 apparatus size infinitely large because 2289 01:23:50,790 --> 01:23:48,400 you want to make sure that there's no 2290 01:23:52,550 --> 01:23:50,800 quantum fluctuations that make an error 2291 01:23:54,550 --> 01:23:52,560 in one of your bits as well as well 2292 01:23:56,870 --> 01:23:54,560 decoherence etc so there are many 2293 01:23:59,189 --> 01:23:56,880 antinomies that crop up which imply that 2294 01:24:01,910 --> 01:23:59,199 however we're ordinarily viewing our 2295 01:24:03,669 --> 01:24:01,920 laws or viewing space time it must be 2296 01:24:05,590 --> 01:24:03,679 some approximation 2297 01:24:07,830 --> 01:24:05,600 also interestingly enough when it comes 2298 01:24:09,430 --> 01:24:07,840 to higher energies it doesn't mean lower 2299 01:24:11,590 --> 01:24:09,440 distances when it comes to quantum 2300 01:24:13,750 --> 01:24:11,600 gravity ordinarily we think well you 2301 01:24:15,990 --> 01:24:13,760 just place in plenty of energy to probe 2302 01:24:17,910 --> 01:24:16,000 a smaller and smaller distance well 2303 01:24:25,189 --> 01:24:17,920 that's true except at some point you 2304 01:24:28,470 --> 01:24:26,950 that is to say if you want to measure a 2305 01:24:30,070 --> 01:24:28,480 small distance while you put in more 2306 01:24:31,350 --> 01:24:30,080 energy but if you want to measure an 2307 01:24:33,430 --> 01:24:31,360 even smaller distance you put in more 2308 01:24:34,950 --> 01:24:33,440 energy at some point you just create a 2309 01:24:37,110 --> 01:24:34,960 black hole and then the more energy you 2310 01:24:39,750 --> 01:24:37,120 put in the larger the radius of the 2311 01:24:42,070 --> 01:24:39,760 black hole so at some point larger 2312 01:24:44,149 --> 01:24:42,080 energy actually means larger distance 2313 01:24:46,310 --> 01:24:44,159 and then even more fundamental than that 2314 01:24:48,870 --> 01:24:46,320 the black hole will start to evaporate 2315 01:24:51,030 --> 01:24:48,880 and let out hawking radiation which is 2316 01:24:53,350 --> 01:24:51,040 low energy particles even though what 2317 01:24:55,510 --> 01:24:53,360 you inputted was high energy particles 2318 01:24:57,669 --> 01:24:55,520 so you get a strange intermingling of 2319 01:24:59,430 --> 01:24:57,679 high and low and the reversal of it from 2320 01:25:01,590 --> 01:24:59,440 what you'd expect from our ordinary 2321 01:25:04,229 --> 01:25:01,600 calculations okay now let's talk about 2322 01:25:07,189 --> 01:25:04,239 black holes so how much density is 2323 01:25:08,550 --> 01:25:07,199 required to create a black hole turns 2324 01:25:10,709 --> 01:25:08,560 out that's an ill-defined question 2325 01:25:12,310 --> 01:25:10,719 because we need to pick a test mass much 2326 01:25:14,709 --> 01:25:12,320 like with gravity and the coupling 2327 01:25:16,229 --> 01:25:14,719 constant it's dependent upon mass same 2328 01:25:18,629 --> 01:25:16,239 with black holes you can get whatever 2329 01:25:21,030 --> 01:25:18,639 density you like so let's just choose a 2330 01:25:23,990 --> 01:25:21,040 mass and then ask a different question 2331 01:25:25,830 --> 01:25:24,000 how small of a region what is the radius 2332 01:25:27,830 --> 01:25:25,840 called the schwarzschild radius what is 2333 01:25:29,750 --> 01:25:27,840 the radius that we can take this mass 2334 01:25:31,750 --> 01:25:29,760 and squeeze it into such that it will 2335 01:25:33,990 --> 01:25:31,760 produce a black hole i'm going to call 2336 01:25:35,910 --> 01:25:34,000 this schwarzschild radius capital r 2337 01:25:38,070 --> 01:25:35,920 and first we need to choose a mass so 2338 01:25:40,470 --> 01:25:38,080 let's choose a copacetic one perhaps the 2339 01:25:42,390 --> 01:25:40,480 planck mass and then think well what 2340 01:25:44,470 --> 01:25:42,400 region of space how small do we have to 2341 01:25:46,390 --> 01:25:44,480 squeeze the plank mass to create a black 2342 01:25:48,870 --> 01:25:46,400 hole we'll do this in a variety of ways 2343 01:25:51,350 --> 01:25:48,880 number one naively it's simple the 2344 01:25:53,750 --> 01:25:51,360 standard physics folklore says what we 2345 01:25:55,510 --> 01:25:53,760 do is we take a plank mass and we stuff 2346 01:25:57,750 --> 01:25:55,520 it into a plank length and that creates 2347 01:25:59,750 --> 01:25:57,760 a black hole then we wonder well what is 2348 01:26:03,830 --> 01:25:59,760 a plank length what's a plank length but 2349 01:26:06,470 --> 01:26:05,030 so let's say 2350 01:26:07,430 --> 01:26:06,480 plank length 2351 01:26:09,750 --> 01:26:07,440 is 2352 01:26:11,510 --> 01:26:09,760 inverse planck mass 2353 01:26:14,229 --> 01:26:11,520 we've used this answer many times and 2354 01:26:16,149 --> 01:26:14,239 we're done that's the answer in one line 2355 01:26:18,709 --> 01:26:16,159 we've derived the schwarzschild radius 2356 01:26:20,470 --> 01:26:18,719 of a mass flank of a planck mass another 2357 01:26:22,709 --> 01:26:20,480 way of calculating this again this is 2358 01:26:24,950 --> 01:26:22,719 also naive is to think okay what does it 2359 01:26:27,270 --> 01:26:24,960 involve it involves gravity so newton's 2360 01:26:29,750 --> 01:26:27,280 constant and it involves some mass let's 2361 01:26:32,870 --> 01:26:29,760 give it a variable name for now mu so it 2362 01:26:34,390 --> 01:26:32,880 involves g and it involves mu 2363 01:26:36,629 --> 01:26:34,400 which is a mass 2364 01:26:39,110 --> 01:26:36,639 we then use these quantities to come up 2365 01:26:41,430 --> 01:26:39,120 with a radius which is length now how do 2366 01:26:43,990 --> 01:26:41,440 we combine g and mu so 2367 01:26:48,310 --> 01:26:44,000 newton and a mass to make the units 2368 01:26:50,310 --> 01:26:48,320 match up well it's as simple as 2369 01:26:52,550 --> 01:26:50,320 combining it in this manner because 2370 01:26:54,470 --> 01:26:52,560 recall this is of units inverse mass 2371 01:26:56,790 --> 01:26:54,480 squared and this is of unit's mass and 2372 01:26:58,870 --> 01:26:56,800 so we have an inverse mass in total and 2373 01:27:01,030 --> 01:26:58,880 this is an inverse mass unit as well 2374 01:27:02,550 --> 01:27:01,040 keep in mind that there are no alphas 2375 01:27:05,030 --> 01:27:02,560 here and the reason is that we're not 2376 01:27:06,790 --> 01:27:05,040 referencing electric charge at all 2377 01:27:09,430 --> 01:27:06,800 now we know that g 2378 01:27:14,229 --> 01:27:11,669 mass planck squared inverse 2379 01:27:17,030 --> 01:27:14,239 and we know that we can set mu in this 2380 01:27:20,070 --> 01:27:17,040 case to be mass planck and then we 2381 01:27:22,390 --> 01:27:20,080 recover the same formula let's do 2382 01:27:24,629 --> 01:27:22,400 another naive calculation what would the 2383 01:27:27,110 --> 01:27:24,639 density of such a black hole be we know 2384 01:27:29,270 --> 01:27:27,120 that it only involves the planck mass 2385 01:27:31,189 --> 01:27:29,280 and we know the units of density and so 2386 01:27:33,750 --> 01:27:31,199 we would imagine that the density would 2387 01:27:35,350 --> 01:27:33,760 be mass length to the fourth and that's 2388 01:27:37,189 --> 01:27:35,360 actually correct 2389 01:27:39,430 --> 01:27:37,199 and then for a final way of calculating 2390 01:27:41,430 --> 01:27:39,440 this we go to wikipedia 2391 01:27:43,189 --> 01:27:41,440 what is the schwarzschild radius and we 2392 01:27:44,149 --> 01:27:43,199 see that it is 2393 01:28:00,229 --> 01:27:44,159 r 2394 01:28:02,709 --> 01:28:00,239 which you'll notice is the exact same as 2395 01:28:04,390 --> 01:28:02,719 this formula that we have here except we 2396 01:28:05,830 --> 01:28:04,400 just called it mu and they called it 2397 01:28:08,229 --> 01:28:05,840 capital m 2398 01:28:11,030 --> 01:28:08,239 note one needs to be a bit prudent here 2399 01:28:12,790 --> 01:28:11,040 because the volume inside a horizon is 2400 01:28:14,709 --> 01:28:12,800 dependent on the coordinate system and 2401 01:28:16,310 --> 01:28:14,719 so the densities are also dependent on 2402 01:28:17,990 --> 01:28:16,320 the observer 2403 01:28:20,950 --> 01:28:18,000 if you don't have a lesson on this then 2404 01:28:22,390 --> 01:28:20,960 it will appear as if this is magic or 2405 01:28:24,550 --> 01:28:22,400 that it requires years and years of 2406 01:28:27,189 --> 01:28:24,560 training but it's not either of those 2407 01:28:29,910 --> 01:28:27,199 two the popularizers of science have an 2408 01:28:33,189 --> 01:28:29,920 incentive to mystify these subjects for 2409 01:28:35,350 --> 01:28:33,199 you unless you're in the universities 2410 01:28:36,470 --> 01:28:35,360 however it's fairly effortless if it's 2411 01:28:38,870 --> 01:28:36,480 explained 2412 01:28:41,189 --> 01:28:38,880 by belaboring these technical details 2413 01:28:42,950 --> 01:28:41,199 and being extremely precise now you may 2414 01:28:45,830 --> 01:28:42,960 also say hey kurt well i could have come 2415 01:28:49,030 --> 01:28:45,840 up with any first attempt at a formula g 2416 01:28:51,350 --> 01:28:49,040 to the power of 5 and m to the power of 2417 01:28:53,430 --> 01:28:51,360 2 and so on and so on 2418 01:28:55,430 --> 01:28:53,440 or square root of so on and so on and 2419 01:28:57,270 --> 01:28:55,440 yes that's correct which is why it 2420 01:29:00,149 --> 01:28:57,280 requires a certain amount of physical 2421 01:29:01,990 --> 01:29:00,159 intuition as well however in this case 2422 01:29:04,229 --> 01:29:02,000 the dimensional analysis would make all 2423 01:29:05,910 --> 01:29:04,239 of this trivial because you have to have 2424 01:29:07,669 --> 01:29:05,920 inverse square mass as the left and the 2425 01:29:09,350 --> 01:29:07,679 right side dimension anyway the left 2426 01:29:11,110 --> 01:29:09,360 hand side of the radius the short style 2427 01:29:12,550 --> 01:29:11,120 radius which is a length has to match 2428 01:29:14,470 --> 01:29:12,560 with whatever the units are on the right 2429 01:29:16,550 --> 01:29:14,480 hand side which severely limits the 2430 01:29:18,149 --> 01:29:16,560 amount of formulas you can generate 2431 01:29:20,629 --> 01:29:18,159 also keep in mind that some of these 2432 01:29:23,430 --> 01:29:20,639 formula depend on the fact that we're in 2433 01:29:26,790 --> 01:29:23,440 fairly low dimensions where in 2434 01:29:28,149 --> 01:29:26,800 let's say dim of our manifold is four 2435 01:29:30,390 --> 01:29:28,159 well it's 2436 01:29:32,470 --> 01:29:30,400 three plus one so that's space 2437 01:29:34,790 --> 01:29:32,480 that's when we're calculating the 2438 01:29:36,950 --> 01:29:34,800 density of a neutron star and we said 2439 01:29:38,950 --> 01:29:36,960 hey what we do is we look to our left 2440 01:29:40,950 --> 01:29:38,960 look up look down look look toward and 2441 01:29:42,470 --> 01:29:40,960 backward and all we see are neutrons and 2442 01:29:44,149 --> 01:29:42,480 thus we get 2443 01:29:46,550 --> 01:29:44,159 gev 2444 01:29:49,350 --> 01:29:46,560 to the fourth this actually depends on 2445 01:29:51,030 --> 01:29:49,360 sphere packing because the atoms act 2446 01:29:52,950 --> 01:29:51,040 like spheres and in higher dimensions 2447 01:29:54,629 --> 01:29:52,960 this doesn't work because 2448 01:29:56,149 --> 01:29:54,639 spheres don't act like cubes in higher 2449 01:29:57,910 --> 01:29:56,159 dimensions they become less and less of 2450 01:29:59,830 --> 01:29:57,920 the space and thus over here we're 2451 01:30:02,149 --> 01:29:59,840 drastically overestimating or 2452 01:30:04,310 --> 01:30:02,159 underestimating our quantity and this by 2453 01:30:06,709 --> 01:30:04,320 the way is assuming flat space if we're 2454 01:30:08,470 --> 01:30:06,719 in hyperbolic space well then it becomes 2455 01:30:10,149 --> 01:30:08,480 even different there's no limit to the 2456 01:30:12,790 --> 01:30:10,159 amount of spheres that can surround 2457 01:30:15,030 --> 01:30:12,800 another sphere and the concept of 2458 01:30:17,750 --> 01:30:15,040 average quote-unquote density becomes 2459 01:30:19,750 --> 01:30:17,760 more difficult to define accurately 2460 01:30:21,350 --> 01:30:19,760 now one of the reasons for being this 2461 01:30:23,510 --> 01:30:21,360 captious or 2462 01:30:26,070 --> 01:30:23,520 let's say scrupulous let's say over 2463 01:30:27,590 --> 01:30:26,080 scrupulous is because 2464 01:30:29,669 --> 01:30:27,600 there are enthymemes what are called 2465 01:30:31,430 --> 01:30:29,679 enthemines which are unstated data 2466 01:30:33,430 --> 01:30:31,440 unstated assumptions that go into an 2467 01:30:35,350 --> 01:30:33,440 argument and the reason they're unstated 2468 01:30:37,669 --> 01:30:35,360 is because they're so simple they're so 2469 01:30:39,430 --> 01:30:37,679 familiar many people like even nima 2470 01:30:40,870 --> 01:30:39,440 arkani hamed don't go through each of 2471 01:30:42,629 --> 01:30:40,880 these assumptions one it would just take 2472 01:30:44,790 --> 01:30:42,639 too long but two is that they're so 2473 01:30:46,390 --> 01:30:44,800 familiar they are generally glossed over 2474 01:30:48,950 --> 01:30:46,400 but i like to make as much of what's 2475 01:30:50,790 --> 01:30:48,960 ordinarily below the earth i'd like to 2476 01:30:52,790 --> 01:30:50,800 unearth it because then perhaps you 2477 01:30:54,390 --> 01:30:52,800 won't be as confused as myself when i 2478 01:30:55,669 --> 01:30:54,400 was learning these subjects if you'd 2479 01:30:57,669 --> 01:30:55,679 like to learn a little bit more about 2480 01:30:59,669 --> 01:30:57,679 enthymemes some example of them in 2481 01:31:01,750 --> 01:30:59,679 physics then you can check out this clip 2482 01:31:03,510 --> 01:31:01,760 with luis elisondo linked in the 2483 01:31:05,669 --> 01:31:03,520 description okay so that was a quick 2484 01:31:07,350 --> 01:31:05,679 detour into quantum gravity if you want 2485 01:31:09,430 --> 01:31:07,360 to learn more like i mentioned there's 2486 01:31:11,830 --> 01:31:09,440 an extremely detailed episode on quantum 2487 01:31:13,430 --> 01:31:11,840 gravity with salvator pious and that's 2488 01:31:15,590 --> 01:31:13,440 linked in the description now we should 2489 01:31:17,189 --> 01:31:15,600 get onto the sponsor message just so you 2490 01:31:19,510 --> 01:31:17,199 know anytime there's a sponsor message 2491 01:31:21,110 --> 01:31:19,520 on the toe channel there's usually a 2492 01:31:22,950 --> 01:31:21,120 timestamp here that says click on this 2493 01:31:24,550 --> 01:31:22,960 timestamp which somewhere here as well 2494 01:31:26,149 --> 01:31:24,560 as in the description because i don't 2495 01:31:28,550 --> 01:31:26,159 want to manipulate anyone into watching 2496 01:31:30,390 --> 01:31:28,560 a sponsor message that generally means 2497 01:31:32,390 --> 01:31:30,400 because this channel depends on the 2498 01:31:34,390 --> 01:31:32,400 patrons which we'll talk about and the 2499 01:31:36,149 --> 01:31:34,400 sponsors that's the only reason i'm able 2500 01:31:38,229 --> 01:31:36,159 to do this full time it usually means 2501 01:31:40,390 --> 01:31:38,239 that the sponsors pay less because 2502 01:31:42,709 --> 01:31:40,400 people will just click on the time stamp 2503 01:31:44,709 --> 01:31:42,719 however i'm hoping and i well i hope 2504 01:31:47,189 --> 01:31:44,719 this is the case that in the long run 2505 01:31:48,950 --> 01:31:47,199 the trust that's built between myself 2506 01:31:50,470 --> 01:31:48,960 and you by seeing you're not being 2507 01:31:52,629 --> 01:31:50,480 manipulated into a sponsor message you 2508 01:31:53,750 --> 01:31:52,639 can always click out of them and the 2509 01:31:55,350 --> 01:31:53,760 sponsors hopefully it's better for 2510 01:31:57,669 --> 01:31:55,360 everyone the sponsors myself and the 2511 01:32:00,229 --> 01:31:57,679 audience in the long run now the sponsor 2512 01:32:01,750 --> 01:32:00,239 for today is brilliant brilliant.org 2513 01:32:04,149 --> 01:32:01,760 toe is where you can visit if you want 2514 01:32:06,070 --> 01:32:04,159 to get 20 off an annual subscription 2515 01:32:07,350 --> 01:32:06,080 what brilliant is that it's a website 2516 01:32:09,270 --> 01:32:07,360 where you can go and you can take 2517 01:32:11,030 --> 01:32:09,280 courses and they don't feel like courses 2518 01:32:13,830 --> 01:32:11,040 it makes learning math and science and 2519 01:32:15,910 --> 01:32:13,840 engineering an extremely practical fun 2520 01:32:17,830 --> 01:32:15,920 enterprise where it's interactive rather 2521 01:32:19,910 --> 01:32:17,840 than you being told information you can 2522 01:32:21,990 --> 01:32:19,920 play with the information and speaking 2523 01:32:23,910 --> 01:32:22,000 of information in a little while from 2524 01:32:26,950 --> 01:32:23,920 now i hope to speak to chiara marletto 2525 01:32:29,350 --> 01:32:26,960 or david deutsch on constructor theory 2526 01:32:31,590 --> 01:32:29,360 and that's heavily based in information 2527 01:32:33,590 --> 01:32:31,600 theory so i decided to take a course on 2528 01:32:35,830 --> 01:32:33,600 information theory and 2529 01:32:41,430 --> 01:32:35,840 from that you find that this formula 2530 01:32:45,189 --> 01:32:43,350 this formula is an extremely natural 2531 01:32:47,510 --> 01:32:45,199 formula for entropy and it would be 2532 01:32:50,470 --> 01:32:47,520 strange to define it in any other manner 2533 01:32:52,470 --> 01:32:50,480 again visit brilliant.org tow to get 20 2534 01:32:54,390 --> 01:32:52,480 off your annual subscription the second 2535 01:32:56,149 --> 01:32:54,400 sponsor is algo and algo is an 2536 01:32:57,830 --> 01:32:56,159 end-to-end supply chain optimization 2537 01:32:59,669 --> 01:32:57,840 software company with software that 2538 01:33:01,750 --> 01:32:59,679 helps business users optimize sales and 2539 01:33:03,669 --> 01:33:01,760 operations planning to avoid stockouts 2540 01:33:05,750 --> 01:33:03,679 reduce returns and inventory write downs 2541 01:33:08,470 --> 01:33:05,760 while reducing inventory investment it's 2542 01:33:11,430 --> 01:33:08,480 a supply chain ai that drives smart roi 2543 01:33:12,950 --> 01:33:11,440 headed by amjad hussein you can support 2544 01:33:15,750 --> 01:33:12,960 the tow podcast as well as your own 2545 01:33:18,790 --> 01:33:15,760 learning by visiting brilliant.org toe 2546 01:33:20,629 --> 01:33:18,800 and also by visiting amjad algo.com all 2547 01:33:22,470 --> 01:33:20,639 the links are in the description you 2548 01:33:24,550 --> 01:33:22,480 should also know that it's the patrons 2549 01:33:26,310 --> 01:33:24,560 as well that allow this to happen i was 2550 01:33:28,310 --> 01:33:26,320 supposed to spend about 2551 01:33:29,910 --> 01:33:28,320 two hours on a video like this it's been 2552 01:33:31,910 --> 01:33:29,920 almost two weeks at this point because 2553 01:33:34,149 --> 01:33:31,920 of different errors and so on but i'm 2554 01:33:36,229 --> 01:33:34,159 able to do this because of the patrons 2555 01:33:37,910 --> 01:33:36,239 so if you want to support content like 2556 01:33:40,790 --> 01:33:37,920 this then please do consider going to 2557 01:33:42,950 --> 01:33:40,800 patreon.com 2558 01:33:44,950 --> 01:33:42,960 my wife is also extremely thankful too 2559 01:33:46,470 --> 01:33:44,960 as now she's full time with me 2560 01:33:49,030 --> 01:33:46,480 responding to the community and helping 2561 01:33:50,629 --> 01:33:49,040 me plan the direction of toe and she's 2562 01:33:52,550 --> 01:33:50,639 extremely extremely 2563 01:33:55,510 --> 01:33:52,560 grateful every time we get a new patron 2564 01:33:57,910 --> 01:33:55,520 she's like oh my gosh that's so sweet 2565 01:34:00,550 --> 01:33:57,920 so both my wife and myself thank you so 2566 01:34:02,790 --> 01:34:00,560 much okay let's get back to these nc's 2567 01:34:04,470 --> 01:34:02,800 these napkin calculations with one about 2568 01:34:06,390 --> 01:34:04,480 the length of an atom the radius of an 2569 01:34:07,350 --> 01:34:06,400 atom we'll start to move quick from this 2570 01:34:11,510 --> 01:34:07,360 point 2571 01:34:16,709 --> 01:34:14,870 we have a model here with the electron 2572 01:34:19,110 --> 01:34:16,719 on the outside and then the proton in 2573 01:34:20,950 --> 01:34:19,120 the center so how do we determine the 2574 01:34:26,550 --> 01:34:20,960 radius of an atom 2575 01:34:31,030 --> 01:34:29,110 firstly what do we know the energy 2576 01:34:36,390 --> 01:34:31,040 has a contribution that looks like this 2577 01:34:41,110 --> 01:34:38,790 and we have another contribution 2578 01:34:44,470 --> 01:34:41,120 which comes from the kinetic term 2579 01:34:46,550 --> 01:34:44,480 and this we can use equation number two 2580 01:34:50,310 --> 01:34:46,560 the bolded number tube 2581 01:34:50,320 --> 01:34:56,870 into an r squared 2582 01:35:01,030 --> 01:34:58,629 which mass is this this is the mass of 2583 01:35:03,430 --> 01:35:01,040 an electron 2584 01:35:04,229 --> 01:35:03,440 and for our purposes we can get rid of 2585 01:35:05,510 --> 01:35:04,239 these 2586 01:35:08,629 --> 01:35:05,520 factors here 2587 01:35:13,110 --> 01:35:08,639 and just say well what minimizes this 2588 01:35:16,950 --> 01:35:15,110 this and then there's a minimum point 2589 01:35:19,270 --> 01:35:16,960 and then it starts to look like 2590 01:35:21,270 --> 01:35:19,280 1 over r 2591 01:35:22,629 --> 01:35:21,280 in the long run yes it looks like 1 over 2592 01:35:24,950 --> 01:35:22,639 r and then in the short run it looks 2593 01:35:27,110 --> 01:35:24,960 like this guy over here 2594 01:35:30,390 --> 01:35:27,120 we want to know what is the minimum 2595 01:35:34,229 --> 01:35:31,830 you can differentiate this to get the 2596 01:35:36,149 --> 01:35:34,239 answer or you can guess and then you get 2597 01:35:41,990 --> 01:35:36,159 that 2598 01:35:45,350 --> 01:35:43,669 this is the bohr radius and we were able 2599 01:35:47,669 --> 01:35:45,360 to derive that in maybe two or three 2600 01:35:50,149 --> 01:35:47,679 lines with napkin calculations we can go 2601 01:35:54,550 --> 01:35:50,159 back over here where i should have said 2602 01:36:01,030 --> 01:35:56,709 and now we get that from equation number 2603 01:36:03,590 --> 01:36:02,149 and by the way because this is the 2604 01:36:05,030 --> 01:36:03,600 average speed of the electron of the 2605 01:36:07,030 --> 01:36:05,040 atom this is the reason why 2606 01:36:08,310 --> 01:36:07,040 schrodinger's equation works because 2607 01:36:10,470 --> 01:36:08,320 schrodinger's equation is 2608 01:36:12,390 --> 01:36:10,480 non-relativistic and you can see that 2609 01:36:16,229 --> 01:36:12,400 just from the factor alpha which means 2610 01:36:19,189 --> 01:36:17,830 let's skip forward because we're going 2611 01:36:21,590 --> 01:36:19,199 to need this for our next napkin 2612 01:36:23,750 --> 01:36:21,600 calculation i realized that the size of 2613 01:36:25,270 --> 01:36:23,760 the earth comes first how would we go 2614 01:36:26,950 --> 01:36:25,280 about calculating the size of the earth 2615 01:36:27,990 --> 01:36:26,960 well that occurs when the gravitational 2616 01:36:30,310 --> 01:36:28,000 pressure 2617 01:36:32,229 --> 01:36:30,320 is counterbalanced by the atomic 2618 01:36:34,070 --> 01:36:32,239 pressure so this is unlike the neutron 2619 01:36:36,390 --> 01:36:34,080 star it requires a bit more work so what 2620 01:36:38,790 --> 01:36:36,400 is the gravitational pressure let's call 2621 01:36:41,430 --> 01:36:38,800 it capital p and it's going to be some 2622 01:36:43,590 --> 01:36:41,440 energy over some volume what energy well 2623 01:36:45,510 --> 01:36:43,600 the gravitational energy sum m we don't 2624 01:36:49,030 --> 01:36:45,520 know what m yet we'll figure this out 2625 01:36:50,709 --> 01:36:49,040 over r and then over some volume so 2626 01:36:51,669 --> 01:36:50,719 r cubed 2627 01:36:53,030 --> 01:36:51,679 however 2628 01:36:55,910 --> 01:36:53,040 recall 2629 01:36:57,669 --> 01:36:55,920 that g g newton so the gravitational 2630 01:37:00,310 --> 01:36:57,679 constant 2631 01:37:02,310 --> 01:37:00,320 is the planck mass squared inverse and 2632 01:37:04,629 --> 01:37:02,320 also let's make a density so a density 2633 01:37:07,990 --> 01:37:04,639 is what it's some mass over some volume 2634 01:37:09,669 --> 01:37:08,000 which is let's say mass over r cubed 2635 01:37:11,510 --> 01:37:09,679 then these two 2636 01:37:14,390 --> 01:37:11,520 combine to help make 2637 01:37:19,109 --> 01:37:15,189 and 2638 01:37:20,310 --> 01:37:19,119 this 2639 01:37:22,870 --> 01:37:20,320 now we would like to know what the 2640 01:37:24,950 --> 01:37:22,880 atomic pressure is so this atomic 2641 01:37:26,550 --> 01:37:24,960 pressure which i should denote these 2642 01:37:27,910 --> 01:37:26,560 differently let's say 2643 01:37:30,310 --> 01:37:27,920 the pressure due to gravity and the 2644 01:37:31,590 --> 01:37:30,320 pressure due to the atoms this atomic 2645 01:37:34,149 --> 01:37:31,600 pressure is going to be again some 2646 01:37:35,750 --> 01:37:34,159 energy over some volume so what is the 2647 01:37:37,510 --> 01:37:35,760 energy well it's going to be the energy 2648 01:37:41,189 --> 01:37:37,520 associated with the atom which we have 2649 01:37:44,070 --> 01:37:41,199 over here so let's call this ea 2650 01:37:45,510 --> 01:37:44,080 ea and this is going to be over r a to 2651 01:37:50,229 --> 01:37:45,520 the third 2652 01:37:54,709 --> 01:37:51,990 then we want to know well what is this 2653 01:37:56,310 --> 01:37:54,719 density here this row this row is going 2654 01:37:57,510 --> 01:37:56,320 to be some mass 2655 01:37:59,669 --> 01:37:57,520 over some 2656 01:38:03,669 --> 01:37:59,679 volume because that's what a density is 2657 01:38:06,390 --> 01:38:03,679 and what mass well a proton mass 2658 01:38:09,189 --> 01:38:06,400 over what volume 2659 01:38:12,070 --> 01:38:09,199 making in substitutions we get one over 2660 01:38:13,270 --> 01:38:12,080 the planck mass this is different i 2661 01:38:14,629 --> 01:38:13,280 should have used different notation but 2662 01:38:16,390 --> 01:38:14,639 this is the proton mass this is the 2663 01:38:17,750 --> 01:38:16,400 planck mass 2664 01:38:20,070 --> 01:38:17,760 squared 2665 01:38:23,109 --> 01:38:20,080 alpha sixth 2666 01:38:25,669 --> 01:38:23,119 m proton 2667 01:38:33,430 --> 01:38:27,510 of the electron 2668 01:38:47,750 --> 01:38:36,149 and this implies that the radius of the 2669 01:38:50,790 --> 01:38:49,189 this implies that the radius of the 2670 01:38:53,030 --> 01:38:50,800 earth is this 2671 01:38:55,109 --> 01:38:53,040 so this is in general for rocky planets 2672 01:38:57,189 --> 01:38:55,119 now this means that alpha factors in the 2673 01:38:59,109 --> 01:38:57,199 mass of the electron the planck mass fat 2674 01:39:01,830 --> 01:38:59,119 while g factors in the mass of the 2675 01:39:03,750 --> 01:39:01,840 proton all of this comes into play to 2676 01:39:05,590 --> 01:39:03,760 derive the size of the earth or the size 2677 01:39:07,030 --> 01:39:05,600 of rocky planets in general like mars 2678 01:39:09,030 --> 01:39:07,040 and venus and so on this is what's 2679 01:39:11,109 --> 01:39:09,040 extremely powerful about this napkin 2680 01:39:13,510 --> 01:39:11,119 calculation technique and natural units 2681 01:39:16,149 --> 01:39:13,520 etc this was perhaps six or seven lines 2682 01:39:18,629 --> 01:39:16,159 of derivation that you do in a closet to 2683 01:39:20,390 --> 01:39:18,639 figure out the radius of the earth 2684 01:39:22,310 --> 01:39:20,400 by the way for fun if you want to 2685 01:39:24,629 --> 01:39:22,320 calculate what is the weight of the 2686 01:39:26,870 --> 01:39:24,639 world you can do so in a second so we 2687 01:39:29,669 --> 01:39:26,880 have some guy here 2688 01:39:33,990 --> 01:39:29,679 and he is some angry 2689 01:39:42,950 --> 01:39:37,030 and let's just make the rest of his body 2690 01:39:42,960 --> 01:39:47,430 and he's holding the world 2691 01:39:50,950 --> 01:39:49,590 well what is the weight of the world the 2692 01:39:52,229 --> 01:39:50,960 weight of the world not the mass of the 2693 01:39:53,590 --> 01:39:52,239 world well you can get the mass from 2694 01:39:55,270 --> 01:39:53,600 this but the weight of the world is 2695 01:39:56,629 --> 01:39:55,280 actually zero so when you hear that and 2696 01:39:58,310 --> 01:39:56,639 the reason is because it's all pointing 2697 01:39:59,750 --> 01:39:58,320 toward the center you're experiencing 2698 01:40:01,590 --> 01:39:59,760 the weight of the world actually the 2699 01:40:03,750 --> 01:40:01,600 weight of the world if you want to be 2700 01:40:05,350 --> 01:40:03,760 atlas you just do a handstand because 2701 01:40:06,870 --> 01:40:05,360 the weight of the world is well it's 2702 01:40:08,709 --> 01:40:06,880 technically zero because it's pointing 2703 01:40:10,470 --> 01:40:08,719 from every single direction zero now the 2704 01:40:12,470 --> 01:40:10,480 reason why i say technically zero is 2705 01:40:14,149 --> 01:40:12,480 because then you may say well okay let's 2706 01:40:15,830 --> 01:40:14,159 imagine that we're here on earth so we 2707 01:40:17,910 --> 01:40:15,840 want the gravitational force of the 2708 01:40:19,590 --> 01:40:17,920 earth to hold up another gravitational 2709 01:40:21,189 --> 01:40:19,600 force well let's say you place some mass 2710 01:40:22,629 --> 01:40:21,199 here yes it's heavy let's say you 2711 01:40:24,470 --> 01:40:22,639 increase it you increase it you increase 2712 01:40:25,750 --> 01:40:24,480 it to the size of another earth then 2713 01:40:27,750 --> 01:40:25,760 actually the weight is zero because 2714 01:40:29,830 --> 01:40:27,760 you're in the in between points of the 2715 01:40:31,109 --> 01:40:29,840 same masses so in some sense the weight 2716 01:40:32,629 --> 01:40:31,119 of the world is 2717 01:40:35,189 --> 01:40:32,639 fairly manageable 2718 01:40:37,350 --> 01:40:35,199 all right now let's get to cutting a 2719 01:40:39,030 --> 01:40:37,360 solid now by the way i left out some 2720 01:40:40,470 --> 01:40:39,040 factors here which i've corrected here 2721 01:40:42,149 --> 01:40:40,480 and the reason it's written in this 2722 01:40:43,669 --> 01:40:42,159 manner is because you can then relate 2723 01:40:45,669 --> 01:40:43,679 the size of the earth to the size of an 2724 01:40:47,990 --> 01:40:45,679 atom and the fact that gravity is 2725 01:40:49,590 --> 01:40:48,000 quote-unquote weak is what plays into 2726 01:40:51,910 --> 01:40:49,600 the largeness of a planet or the 2727 01:40:56,229 --> 01:40:51,920 smallness of a planet as for cutting a 2728 01:40:57,590 --> 01:40:56,239 solid what we want is just this equation 2729 01:40:59,750 --> 01:40:57,600 all we have to do 2730 01:41:02,390 --> 01:40:59,760 is exceed the atomic pressure all we 2731 01:41:04,629 --> 01:41:02,400 have to do is just place what is greater 2732 01:41:07,189 --> 01:41:04,639 than this equation there we go extremely 2733 01:41:09,430 --> 01:41:07,199 extremely simple notice this this is the 2734 01:41:11,270 --> 01:41:09,440 most important aspect of this video is 2735 01:41:13,030 --> 01:41:11,280 that there's a perspective shift you can 2736 01:41:14,950 --> 01:41:13,040 now carry this around with you and do 2737 01:41:16,470 --> 01:41:14,960 napkin calculations nc's you can even 2738 01:41:17,669 --> 01:41:16,480 leave them in the comments and derive 2739 01:41:18,470 --> 01:41:17,679 what ordinarily you would think you 2740 01:41:20,790 --> 01:41:18,480 would need 2741 01:41:22,870 --> 01:41:20,800 nuclear physics or special relativity by 2742 01:41:24,629 --> 01:41:22,880 the way about special relativity many 2743 01:41:26,550 --> 01:41:24,639 people talk about time dilation and so 2744 01:41:29,109 --> 01:41:26,560 on but to me what's most interesting 2745 01:41:31,350 --> 01:41:29,119 about special relativity is that it 2746 01:41:33,990 --> 01:41:31,360 messes with what you think existence is 2747 01:41:35,430 --> 01:41:34,000 it places you in an unhinged manner so 2748 01:41:36,310 --> 01:41:35,440 let's take a look over here if there's 2749 01:41:37,830 --> 01:41:36,320 some 2750 01:41:40,790 --> 01:41:37,840 event that occurs outside your light 2751 01:41:42,950 --> 01:41:40,800 cone then what's considered simultaneous 2752 01:41:45,590 --> 01:41:42,960 is a dubious concept the reason being 2753 01:41:47,430 --> 01:41:45,600 that if you were to say for example the 2754 01:41:49,669 --> 01:41:47,440 corner store the store on your corner 2755 01:41:52,310 --> 01:41:49,679 doesn't exist anymore well why are you 2756 01:41:54,550 --> 01:41:52,320 saying that it's because now it is no 2757 01:41:56,070 --> 01:41:54,560 longer there it is now 2758 01:41:57,510 --> 01:41:56,080 bought by someone else or it is now 2759 01:41:59,990 --> 01:41:57,520 demolished 2760 01:42:02,550 --> 01:42:00,000 well there exists another perspective 2761 01:42:04,790 --> 01:42:02,560 where it does exist this is explored in 2762 01:42:06,709 --> 01:42:04,800 the carlo ravelli interview and this is 2763 01:42:09,430 --> 01:42:06,719 because the notion of simultaneity is 2764 01:42:11,350 --> 01:42:09,440 placed on an unassured grounding 2765 01:42:13,669 --> 01:42:11,360 let's get to a laconic derivation of the 2766 01:42:15,669 --> 01:42:13,679 casimir falloff so all you need to know 2767 01:42:17,430 --> 01:42:15,679 about it is what you've heard from 2768 01:42:19,510 --> 01:42:17,440 popular science which is that it's a 2769 01:42:21,030 --> 01:42:19,520 demonstration of the vacuum fluctuations 2770 01:42:23,189 --> 01:42:21,040 because there's certain modes that are 2771 01:42:25,189 --> 01:42:23,199 allowed and not allowed in between the 2772 01:42:27,669 --> 01:42:25,199 plates there are more outside than 2773 01:42:30,229 --> 01:42:27,679 inside and thus they come together 2774 01:42:32,550 --> 01:42:30,239 you know that it's a pressure and we 2775 01:42:34,790 --> 01:42:32,560 have that it falls off as some r to the 2776 01:42:36,870 --> 01:42:34,800 n what is the n what could it be but 2777 01:42:39,590 --> 01:42:36,880 pressure so it's r to the fourth there 2778 01:42:41,669 --> 01:42:39,600 we go we get that the casimir pressure 2779 01:42:43,590 --> 01:42:41,679 falls off and it's a minus because it's 2780 01:42:45,910 --> 01:42:43,600 an attractive force 2781 01:42:47,990 --> 01:42:45,920 as one over r to the fourth ordinarily 2782 01:42:49,750 --> 01:42:48,000 this is an extremely tedious calculation 2783 01:42:50,709 --> 01:42:49,760 we can go to wikipedia right now just to 2784 01:42:52,149 --> 01:42:50,719 check 2785 01:42:54,310 --> 01:42:52,159 you can see from wikipedia that it 2786 01:42:56,390 --> 01:42:54,320 requires quantum field theory and you go 2787 01:42:58,149 --> 01:42:56,400 through plenty and plenty of rigmarole 2788 01:42:59,590 --> 01:42:58,159 just to arrive at this which is the a to 2789 01:43:01,750 --> 01:42:59,600 the fourth minus that we were referring 2790 01:43:03,189 --> 01:43:01,760 to these factors are what we firstly 2791 01:43:04,870 --> 01:43:03,199 these are set to one this is what we 2792 01:43:07,109 --> 01:43:04,880 didn't derive but you were able to get 2793 01:43:09,030 --> 01:43:07,119 an estimate now you may wonder why is it 2794 01:43:11,510 --> 01:43:09,040 that we go through so much pedantic 2795 01:43:12,870 --> 01:43:11,520 palaver just to arrive at a small 2796 01:43:14,950 --> 01:43:12,880 correction when we could have done this 2797 01:43:16,950 --> 01:43:14,960 in one laconic line 2798 01:43:18,870 --> 01:43:16,960 the reason is that sometimes often you 2799 01:43:20,870 --> 01:43:18,880 want to be precise for example you don't 2800 01:43:22,470 --> 01:43:20,880 want a surgeon that approximately 2801 01:43:24,310 --> 01:43:22,480 operates on you 2802 01:43:27,270 --> 01:43:24,320 thus in mathematics one goes through 2803 01:43:28,870 --> 01:43:27,280 great pains to make explicit each axiom 2804 01:43:30,470 --> 01:43:28,880 and line of reasoning now there are 2805 01:43:32,390 --> 01:43:30,480 other reasons for being axiomatic and 2806 01:43:34,870 --> 01:43:32,400 specific for example you may wonder why 2807 01:43:37,109 --> 01:43:34,880 does it take 100 pages to arrive at one 2808 01:43:38,790 --> 01:43:37,119 plus one equals two so there are a 2809 01:43:41,109 --> 01:43:38,800 couple of reasons so one of the reasons 2810 01:43:44,149 --> 01:43:41,119 is that we don't derive that one plus 2811 01:43:46,310 --> 01:43:44,159 one equals two we validate the axiomatic 2812 01:43:48,390 --> 01:43:46,320 system by seeing one plus one equals two 2813 01:43:50,229 --> 01:43:48,400 as a valid target and knowing we need to 2814 01:43:52,310 --> 01:43:50,239 hit it seeing we hit it validates the 2815 01:43:54,709 --> 01:43:52,320 axiomatic system that produced it number 2816 01:43:56,229 --> 01:43:54,719 two is because now that we have axioms 2817 01:43:57,910 --> 01:43:56,239 and then we show that something is 2818 01:44:00,070 --> 01:43:57,920 constructed in this manner because we've 2819 01:44:01,590 --> 01:44:00,080 set it to be then that means that we can 2820 01:44:03,430 --> 01:44:01,600 set it differently we could have 2821 01:44:05,510 --> 01:44:03,440 constructed it differently so for 2822 01:44:07,750 --> 01:44:05,520 example setting the curvature to zero 2823 01:44:09,590 --> 01:44:07,760 gives euclidean geometry and then we 2824 01:44:11,510 --> 01:44:09,600 wonder well what happens if we don't set 2825 01:44:13,910 --> 01:44:11,520 it to zero then we get more general 2826 01:44:15,669 --> 01:44:13,920 spaces like non-euclidean geometry which 2827 01:44:19,510 --> 01:44:15,679 as you know has a crucial role to play 2828 01:44:23,750 --> 01:44:21,030 all right now let's get to analyzing the 2829 01:44:25,030 --> 01:44:23,760 sun this one is a simple one we firstly 2830 01:44:27,189 --> 01:44:25,040 go to 2831 01:44:28,709 --> 01:44:27,199 our friend google and we search for the 2832 01:44:31,109 --> 01:44:28,719 sunlight spectrum and we see it looks 2833 01:44:33,430 --> 01:44:31,119 something like this 2834 01:44:37,750 --> 01:44:33,440 and we see okay this peaks approximately 2835 01:44:41,189 --> 01:44:37,760 at let's say 500 so it's 500 2836 01:44:43,350 --> 01:44:41,199 nanometers is the wavelength we then go 2837 01:44:44,950 --> 01:44:43,360 to our conversion charts 2838 01:44:47,270 --> 01:44:44,960 and we see okay we can use equation 2839 01:44:56,229 --> 01:44:47,280 number three 2840 01:45:06,470 --> 01:44:56,239 use this and we're going to use this 2841 01:45:12,709 --> 01:45:09,669 this gives a temperature on the order of 2842 01:45:14,790 --> 01:45:12,719 5000 or so well let's say on the order 2843 01:45:16,709 --> 01:45:14,800 of 2844 01:45:18,310 --> 01:45:16,719 it's about 5000 kelvin if you want to 2845 01:45:19,430 --> 01:45:18,320 work it out specifically or you can 2846 01:45:21,030 --> 01:45:19,440 simply say it's on the order of 2847 01:45:22,149 --> 01:45:21,040 so-and-so 2848 01:45:23,669 --> 01:45:22,159 and we can search what is the 2849 01:45:25,910 --> 01:45:23,679 temperature of the sun and we see that 2850 01:45:27,350 --> 01:45:25,920 it's approximately correct 2851 01:45:29,350 --> 01:45:27,360 where i just round it up here so it 2852 01:45:30,950 --> 01:45:29,360 could be between 10 to the 3 ten to the 2853 01:45:32,870 --> 01:45:30,960 four that's actually 2854 01:45:35,830 --> 01:45:32,880 halfway in between 2855 01:45:37,669 --> 01:45:35,840 by the way it's from this fact that you 2856 01:45:39,510 --> 01:45:37,679 can look at leds that come from your 2857 01:45:41,430 --> 01:45:39,520 lights or your cell phone screen and 2858 01:45:43,669 --> 01:45:41,440 determine what temperature it would have 2859 01:45:45,270 --> 01:45:43,679 if it were a black body radiator and 2860 01:45:47,030 --> 01:45:45,280 note that your cell phone isn't 2861 01:45:49,270 --> 01:45:47,040 thousands of degrees hot 2862 01:45:52,149 --> 01:45:49,280 thus allowing you to infer just from a 2863 01:45:54,149 --> 01:45:52,159 napkin calculation that leds that 2864 01:45:57,030 --> 01:45:54,159 characterize your phone screen don't 2865 01:45:58,550 --> 01:45:57,040 produce light as black body radiators in 2866 01:46:01,430 --> 01:45:58,560 the same way that for example 2867 01:46:03,430 --> 01:46:01,440 incandescents do 2868 01:46:05,109 --> 01:46:03,440 now let's intuit the radius of the 2869 01:46:07,350 --> 01:46:05,119 electron as you know the radius of the 2870 01:46:09,270 --> 01:46:07,360 electron is well it's a point particle 2871 01:46:10,950 --> 01:46:09,280 however let's think about it classically 2872 01:46:12,709 --> 01:46:10,960 so here's how lorentz and others thought 2873 01:46:14,950 --> 01:46:12,719 about it classically we have this 2874 01:46:16,709 --> 01:46:14,960 electron here let's call it e 2875 01:46:17,590 --> 01:46:16,719 and it's emitting some electric field 2876 01:46:19,830 --> 01:46:17,600 here 2877 01:46:21,590 --> 01:46:19,840 what we want is that the energy of the 2878 01:46:24,629 --> 01:46:21,600 electron so 2879 01:46:26,390 --> 01:46:24,639 alpha over r e which we have before so 2880 01:46:28,629 --> 01:46:26,400 the energy of the electron 2881 01:46:31,750 --> 01:46:28,639 we don't want that to be much greater 2882 01:46:33,910 --> 01:46:31,760 than m c squared of the electron so in 2883 01:46:35,350 --> 01:46:33,920 our units m c squared is just m 2884 01:46:38,629 --> 01:46:35,360 which implies 2885 01:46:43,350 --> 01:46:41,109 is simply this and there we go we have a 2886 01:46:46,070 --> 01:46:43,360 classical derivation of the radius of 2887 01:46:47,510 --> 01:46:46,080 the electron turns out that 2888 01:46:49,750 --> 01:46:47,520 and by the way lawrence and others 2889 01:46:50,950 --> 01:46:49,760 thought that okay the classical laws 2890 01:46:53,030 --> 01:46:50,960 have to break down somewhat here 2891 01:46:54,629 --> 01:46:53,040 something strange has to occur at that 2892 01:46:55,990 --> 01:46:54,639 radius it and they were trying to 2893 01:46:57,270 --> 01:46:56,000 analyze it and they didn't get the right 2894 01:46:58,950 --> 01:46:57,280 answers and that's because quantum 2895 01:47:01,030 --> 01:46:58,960 mechanics comes in and they had no idea 2896 01:47:03,990 --> 01:47:01,040 about quantum mechanics which says 2897 01:47:05,990 --> 01:47:04,000 actually around the electron is positron 2898 01:47:08,870 --> 01:47:06,000 electron pairs and so on and so it's 2899 01:47:11,510 --> 01:47:08,880 cloudy and the radius of this if we go 2900 01:47:13,430 --> 01:47:11,520 in here the radius of one of these what 2901 01:47:15,910 --> 01:47:13,440 is it what do you think it may be well 2902 01:47:17,750 --> 01:47:15,920 it's an electron positron pair so it's 2903 01:47:18,870 --> 01:47:17,760 this much well it's two of that but it 2904 01:47:20,229 --> 01:47:18,880 doesn't matter 2905 01:47:23,109 --> 01:47:20,239 the point is that the law started 2906 01:47:24,709 --> 01:47:23,119 breaking down at a distance 137 times 2907 01:47:26,870 --> 01:47:24,719 greater than where they thought it would 2908 01:47:28,709 --> 01:47:26,880 have broken down if we extrapolate this 2909 01:47:30,870 --> 01:47:28,719 line of reasoning to our current models 2910 01:47:32,790 --> 01:47:30,880 that is the standard model and general 2911 01:47:34,390 --> 01:47:32,800 relativity while they suggest that 2912 01:47:36,629 --> 01:47:34,400 there's some breakdown that occurs at 2913 01:47:39,350 --> 01:47:36,639 the planck scale my money would be that 2914 01:47:42,550 --> 01:47:39,360 new laws would be required far before we 2915 01:47:44,950 --> 01:47:42,560 get to the planck scale maybe not 130 2916 01:47:47,350 --> 01:47:44,960 times before the planck scale but many 2917 01:47:49,590 --> 01:47:47,360 many more orders of magnitude prior to 2918 01:47:51,270 --> 01:47:49,600 that energy 2919 01:47:53,270 --> 01:47:51,280 all right now we're on to solids and 2920 01:47:55,109 --> 01:47:53,280 x-rays if we want to find out the number 2921 01:47:57,430 --> 01:47:55,119 density that is the number of atoms in a 2922 01:48:00,550 --> 01:47:57,440 solid per unit volume what does it look 2923 01:48:02,950 --> 01:48:00,560 like well number 2924 01:48:05,030 --> 01:48:02,960 density 2925 01:48:09,189 --> 01:48:05,040 firstly let's think about the units 2926 01:48:11,590 --> 01:48:09,199 it's gev to sum n what is n is it minus 2927 01:48:13,109 --> 01:48:11,600 three it's plus three 2928 01:48:15,910 --> 01:48:13,119 and what information do we have we have 2929 01:48:17,910 --> 01:48:15,920 the radius of the atom and so it's that 2930 01:48:19,189 --> 01:48:17,920 cubed and we can use this equation from 2931 01:48:21,590 --> 01:48:19,199 before 2932 01:48:28,149 --> 01:48:21,600 alpha times the mass of the electron is 2933 01:48:31,990 --> 01:48:30,629 which is kev to the third and this is 2934 01:48:34,070 --> 01:48:32,000 one of the reasons why it's much better 2935 01:48:35,590 --> 01:48:34,080 to work with gevs and so on because this 2936 01:48:37,189 --> 01:48:35,600 gives you an actual 2937 01:48:40,149 --> 01:48:37,199 tangible amount you understand what a 2938 01:48:41,910 --> 01:48:40,159 kev is and by the way kev what is its 2939 01:48:44,870 --> 01:48:41,920 relationship to light 2940 01:48:46,629 --> 01:48:44,880 that is to say if we're on the order of 2941 01:48:48,950 --> 01:48:46,639 a length that is 2942 01:48:50,390 --> 01:48:48,960 let's say just one kev then we'll need 2943 01:48:53,910 --> 01:48:50,400 to shine a light 2944 01:48:55,669 --> 01:48:53,920 whose wavelength is at least one kev in 2945 01:48:56,870 --> 01:48:55,679 order to resolve this distance i'll 2946 01:48:58,470 --> 01:48:56,880 explain exactly what that means to 2947 01:49:00,870 --> 01:48:58,480 resolve it and then you can wonder well 2948 01:49:02,950 --> 01:49:00,880 what is one kev of light you can look 2949 01:49:05,189 --> 01:49:02,960 that up online let's do that right now 2950 01:49:07,830 --> 01:49:05,199 so you can see from this napkin 2951 01:49:10,229 --> 01:49:07,840 calculation that an x-ray is what allows 2952 01:49:12,629 --> 01:49:10,239 you to probe solids that's why we use 2953 01:49:14,550 --> 01:49:12,639 x-rays because their wavelength is just 2954 01:49:16,470 --> 01:49:14,560 short enough to resolve the distance of 2955 01:49:18,229 --> 01:49:16,480 the atoms within a solid and when we 2956 01:49:19,430 --> 01:49:18,239 talk about a certain wavelength is 2957 01:49:21,189 --> 01:49:19,440 what's needed to resolve a certain 2958 01:49:23,669 --> 01:49:21,199 distance that was never explained at 2959 01:49:25,590 --> 01:49:23,679 least not to me properly i always heard 2960 01:49:27,109 --> 01:49:25,600 of it in terms of balls you take some 2961 01:49:28,870 --> 01:49:27,119 large ball and you try and throw it and 2962 01:49:30,390 --> 01:49:28,880 you try and resolve you need smaller and 2963 01:49:32,229 --> 01:49:30,400 smaller balls in order to get higher 2964 01:49:33,750 --> 01:49:32,239 resolution but i think a better way of 2965 01:49:36,709 --> 01:49:33,760 understanding this understanding why we 2966 01:49:38,709 --> 01:49:36,719 need x-rays or whatever uv rays whatever 2967 01:49:40,229 --> 01:49:38,719 the light is to resolve a certain 2968 01:49:41,590 --> 01:49:40,239 distance i think it's better explained 2969 01:49:44,470 --> 01:49:41,600 like this 2970 01:49:45,270 --> 01:49:44,480 if we zoom in here so let's zoom in this 2971 01:49:47,030 --> 01:49:45,280 is 2972 01:49:49,830 --> 01:49:47,040 let's see how many pixels wide maybe 2973 01:49:54,390 --> 01:49:51,669 one two three maybe this is on the order 2974 01:50:00,790 --> 01:49:54,400 of 50. who knows but then if i say let's 2975 01:50:05,350 --> 01:50:03,189 see if we make this cell size the cell 2976 01:50:07,270 --> 01:50:05,360 size by the way is equivalent to a 2977 01:50:10,149 --> 01:50:07,280 wavelength so we want the wavelength 2978 01:50:12,950 --> 01:50:10,159 small in order to resolve 2979 01:50:15,270 --> 01:50:12,960 shorter and shorter distances 2980 01:50:18,310 --> 01:50:15,280 if we make the cell size fairly large 2981 01:50:20,550 --> 01:50:18,320 like 200 then we can just make out that 2982 01:50:21,830 --> 01:50:20,560 there exists some substructure here we 2983 01:50:24,149 --> 01:50:21,840 cannot make out that there was any 2984 01:50:26,310 --> 01:50:24,159 structure above and as soon as we start 2985 01:50:27,910 --> 01:50:26,320 reducing it we're resolving with higher 2986 01:50:29,910 --> 01:50:27,920 and higher frequencies you can think of 2987 01:50:33,669 --> 01:50:29,920 it like that so if 2988 01:50:35,270 --> 01:50:33,679 this is let's say on the order of a 2989 01:50:37,910 --> 01:50:35,280 cell and then we want to get to the 2990 01:50:40,149 --> 01:50:37,920 order of an atom well we need to shoot 2991 01:50:42,070 --> 01:50:40,159 smaller and smaller wavelengths of light 2992 01:50:43,510 --> 01:50:42,080 this corresponds to the wavelength and 2993 01:50:44,870 --> 01:50:43,520 all of a sudden now you can resolve that 2994 01:50:46,390 --> 01:50:44,880 distance 2995 01:50:47,910 --> 01:50:46,400 i'm placing that as an aside here 2996 01:50:50,870 --> 01:50:47,920 because the way that it's ordinarily 2997 01:50:53,030 --> 01:50:50,880 explained is a bit confusing by the way 2998 01:50:55,510 --> 01:50:53,040 based on this number density you can now 2999 01:50:57,430 --> 01:50:55,520 get a actual density so what do you do 3000 01:50:59,350 --> 01:50:57,440 is you times it by the proton mass 3001 01:51:01,590 --> 01:50:59,360 because the proton slash the neutron are 3002 01:51:03,910 --> 01:51:01,600 what hold the most well the largest 3003 01:51:06,470 --> 01:51:03,920 contribution to the mass 3004 01:51:08,149 --> 01:51:06,480 and then you get the density of solids 3005 01:51:10,390 --> 01:51:08,159 which is the approximate density of the 3006 01:51:13,030 --> 01:51:10,400 earth too see all of this which is 3007 01:51:15,510 --> 01:51:13,040 ordinarily seen as tremendously advanced 3008 01:51:17,350 --> 01:51:15,520 can be calculated extremely easily with 3009 01:51:18,870 --> 01:51:17,360 napkin calculations 3010 01:51:20,870 --> 01:51:18,880 okay now we're on the last one the 3011 01:51:23,830 --> 01:51:20,880 scales of the universe in particular the 3012 01:51:25,189 --> 01:51:23,840 higgs boson which is extremely easy now 3013 01:51:27,109 --> 01:51:25,199 that we've gone through 3014 01:51:29,430 --> 01:51:27,119 plenty of these exercises and you're so 3015 01:51:32,310 --> 01:51:29,440 familiar with natural units and gevs and 3016 01:51:34,390 --> 01:51:32,320 so on what is the scale that you should 3017 01:51:36,470 --> 01:51:34,400 find the higgs boson how far should you 3018 01:51:38,390 --> 01:51:36,480 zoom in to find it well firstly let's go 3019 01:51:40,950 --> 01:51:38,400 on google 3020 01:51:43,830 --> 01:51:40,960 and we see look they give you the mass 3021 01:51:46,830 --> 01:51:43,840 in terms of gev now this c we set to one 3022 01:51:48,550 --> 01:51:46,840 so this gev it's 125 gev 3023 01:51:52,070 --> 01:51:48,560 125 3024 01:51:54,790 --> 01:51:52,080 g e v higgs 3025 01:51:58,229 --> 01:51:56,470 from the above conversion chart or we 3026 01:52:00,310 --> 01:51:58,239 can go to a website and see what does 3027 01:52:02,629 --> 01:52:00,320 that correspond to in terms of length 3028 01:52:05,270 --> 01:52:02,639 now you can see how far do you have to 3029 01:52:07,990 --> 01:52:05,280 zoom in in order for you to find the 3030 01:52:09,109 --> 01:52:08,000 higgs boson you can convert that or you 3031 01:52:11,189 --> 01:52:09,119 can use another chart they're all 3032 01:52:13,189 --> 01:52:11,199 approximately the same remember we only 3033 01:52:14,950 --> 01:52:13,199 care about the order we can also type in 3034 01:52:16,550 --> 01:52:14,960 well what is the lhc 3035 01:52:17,830 --> 01:52:16,560 what is the highest energy of the 3036 01:52:21,189 --> 01:52:17,840 particles that have been collided and 3037 01:52:24,470 --> 01:52:21,199 it's 13 tev we covered this earlier that 3038 01:52:26,790 --> 01:52:24,480 tells you something concrete about how 3039 01:52:28,790 --> 01:52:26,800 small the distances are now these 3040 01:52:30,070 --> 01:52:28,800 numbers are no longer foreign to you 3041 01:52:31,830 --> 01:52:30,080 you're extremely familiar with 3042 01:52:33,910 --> 01:52:31,840 manipulating them you can get a handle 3043 01:52:35,510 --> 01:52:33,920 on them by the way another reason why 3044 01:52:37,189 --> 01:52:35,520 they're afraid that black holes could be 3045 01:52:39,109 --> 01:52:37,199 created well i didn't mention this in 3046 01:52:41,350 --> 01:52:39,119 the extra dimensions part but it's 3047 01:52:43,430 --> 01:52:41,360 because if gravity is leaking in to some 3048 01:52:45,350 --> 01:52:43,440 other dimension then that means that 3049 01:52:47,270 --> 01:52:45,360 gravity is in fact stronger than we 3050 01:52:49,030 --> 01:52:47,280 think somewhere else so it's weaker here 3051 01:52:50,950 --> 01:52:49,040 but it's stronger somewhere else and so 3052 01:52:52,709 --> 01:52:50,960 what we think of what would ordinarily 3053 01:52:54,470 --> 01:52:52,719 create a black hole the conditions may 3054 01:52:55,990 --> 01:52:54,480 be much smaller because gravity is much 3055 01:52:58,070 --> 01:52:56,000 stronger than we think though luckily 3056 01:53:03,910 --> 01:52:58,080 the earth hasn't been enveloped by a 3057 01:53:08,870 --> 01:53:06,310 okay great you should congratulate 3058 01:53:10,310 --> 01:53:08,880 yourself because in about two hours or 3059 01:53:12,790 --> 01:53:10,320 an hour and a half however long this 3060 01:53:15,589 --> 01:53:12,800 video is you've now covered quite a 3061 01:53:17,910 --> 01:53:15,599 significant amount of work we've gone 3062 01:53:19,589 --> 01:53:17,920 through newton's constant and seeing 3063 01:53:22,390 --> 01:53:19,599 that it's actually mass dependent or 3064 01:53:25,189 --> 01:53:22,400 energy it's proportional to the 3065 01:53:27,750 --> 01:53:25,199 mass to the inverse square of a mass and 3066 01:53:29,589 --> 01:53:27,760 pressure and speed is dimensionless 3067 01:53:31,910 --> 01:53:29,599 this pressure in a neutron star the 3068 01:53:33,589 --> 01:53:31,920 proportionate strength of forces knots 3069 01:53:35,270 --> 01:53:33,599 and extra dimensions calculating the 3070 01:53:37,510 --> 01:53:35,280 swinger limit just getting a handle on 3071 01:53:39,830 --> 01:53:37,520 it the size of the earth analyzing the 3072 01:53:41,750 --> 01:53:39,840 sun the casimir effect how it falls off 3073 01:53:43,030 --> 01:53:41,760 a vacuum expectation energy the length 3074 01:53:44,629 --> 01:53:43,040 of an atom 3075 01:53:47,189 --> 01:53:44,639 microtubules 3076 01:53:48,629 --> 01:53:47,199 sk the higgs boson the god particle you 3077 01:53:51,350 --> 01:53:48,639 even learned about deriving the 3078 01:53:53,990 --> 01:53:51,360 schwarzschild radius and black holes and 3079 01:53:57,430 --> 01:53:54,000 by the way for fun these acrostically 3080 01:53:59,350 --> 01:53:57,440 spell out napkin calculations 3081 01:54:01,270 --> 01:53:59,360 all of this becomes 3082 01:54:03,990 --> 01:54:01,280 virtually child's play 3083 01:54:05,990 --> 01:54:04,000 once you use natural units and then 3084 01:54:07,350 --> 01:54:06,000 some physical intuition 3085 01:54:09,510 --> 01:54:07,360 all right now continue watching for the 3086 01:54:11,430 --> 01:54:09,520 next couple minutes because this will 3087 01:54:14,070 --> 01:54:11,440 help you contextualize what came before 3088 01:54:16,229 --> 01:54:14,080 and so it will stick more readily recall 3089 01:54:18,070 --> 01:54:16,239 unlike giving viewer exercises quote 3090 01:54:21,030 --> 01:54:18,080 unquote which is par for the course in 3091 01:54:23,109 --> 01:54:21,040 most courses and lectures and so on 3092 01:54:24,550 --> 01:54:23,119 people almost never do exercises 3093 01:54:26,870 --> 01:54:24,560 including myself and i'm extremely 3094 01:54:28,390 --> 01:54:26,880 motivated to do so the most nourishing 3095 01:54:30,310 --> 01:54:28,400 approach is to provide a point of view 3096 01:54:31,990 --> 01:54:30,320 shift and that's what you now have there 3097 01:54:34,709 --> 01:54:32,000 are a variety of phenomenon that you can 3098 01:54:36,870 --> 01:54:34,719 now do an nc too so a napkin calculation 3099 01:54:38,390 --> 01:54:36,880 and if you find a particularly inventive 3100 01:54:41,030 --> 01:54:38,400 one then share it in the comments 3101 01:54:43,109 --> 01:54:41,040 section but delineate each step don't 3102 01:54:44,470 --> 01:54:43,119 skip when explaining to people now as 3103 01:54:46,070 --> 01:54:44,480 you go through life and you want to 3104 01:54:48,149 --> 01:54:46,080 develop a bit more of a physical 3105 01:54:49,750 --> 01:54:48,159 intuition then constantly think about 3106 01:54:51,510 --> 01:54:49,760 what you're seeing and the numbers that 3107 01:54:53,990 --> 01:54:51,520 you're hearing and the lengths and the 3108 01:54:56,070 --> 01:54:54,000 times and the quantities etc in terms of 3109 01:54:57,669 --> 01:54:56,080 gev and also think about how you can 3110 01:55:00,149 --> 01:54:57,679 derive them from these somewhat 3111 01:55:01,669 --> 01:55:00,159 fundamental principles a last note on 3112 01:55:03,350 --> 01:55:01,679 learning every time that you hear 3113 01:55:04,550 --> 01:55:03,360 someone describe some object in a 3114 01:55:06,629 --> 01:55:04,560 different way 3115 01:55:09,189 --> 01:55:06,639 so for example you may hear me refer to 3116 01:55:11,189 --> 01:55:09,199 fields in some other video as a 3117 01:55:12,790 --> 01:55:11,199 group twice over and what's meant by 3118 01:55:14,950 --> 01:55:12,800 that what do i mean by that it's that 3119 01:55:16,470 --> 01:55:14,960 you have these field axioms so 3120 01:55:18,709 --> 01:55:16,480 commutative associative neutral elements 3121 01:55:21,109 --> 01:55:18,719 so on so on so on and it's it's two of 3122 01:55:23,350 --> 01:55:21,119 them whereas one of these is like 3123 01:55:25,910 --> 01:55:23,360 a group a commutative group and so it's 3124 01:55:27,510 --> 01:55:25,920 somewhat like a twice over group this is 3125 01:55:29,350 --> 01:55:27,520 this is false because there's an 3126 01:55:31,830 --> 01:55:29,360 interplay between these like you need to 3127 01:55:33,990 --> 01:55:31,840 exclude the neutral element here for the 3128 01:55:36,149 --> 01:55:34,000 multiplicative inverse and so on however 3129 01:55:37,669 --> 01:55:36,159 the point is that when you hear someone 3130 01:55:39,510 --> 01:55:37,679 explain something that you think you 3131 01:55:41,189 --> 01:55:39,520 know but explained in a different way 3132 01:55:42,870 --> 01:55:41,199 it's useful to write that down in some 3133 01:55:44,470 --> 01:55:42,880 reference document and then eventually 3134 01:55:47,109 --> 01:55:44,480 go back and think how are all these 3135 01:55:48,470 --> 01:55:47,119 disparate lessons or views the same 3136 01:55:49,990 --> 01:55:48,480 another one may be how are all the 3137 01:55:52,149 --> 01:55:50,000 exponentials the definitions of 3138 01:55:55,109 --> 01:55:52,159 exponentials the same so we know that an 3139 01:55:58,470 --> 01:55:55,119 exponential map goes from t e g so the 3140 01:56:00,470 --> 01:55:58,480 lead algebra to the group itself well 3141 01:56:02,870 --> 01:56:00,480 how is that related to 3142 01:56:04,790 --> 01:56:02,880 what we know as e to the e squared for 3143 01:56:06,709 --> 01:56:04,800 example equals so and so on 3144 01:56:08,790 --> 01:56:06,719 as a number by the way almost no one 3145 01:56:11,589 --> 01:56:08,800 will do this exercise that is you write 3146 01:56:13,350 --> 01:56:11,599 down the disparate lessons and teachings 3147 01:56:15,910 --> 01:56:13,360 and then you try to relate them there's 3148 01:56:17,350 --> 01:56:15,920 about n choose two of them so how is 3149 01:56:18,550 --> 01:56:17,360 this related to that how is this related 3150 01:56:20,709 --> 01:56:18,560 to that how is this related to that how 3151 01:56:22,149 --> 01:56:20,719 is this related to that and so on 3152 01:56:24,310 --> 01:56:22,159 almost no one will do that because it's 3153 01:56:25,910 --> 01:56:24,320 extremely tedious which means if you do 3154 01:56:28,550 --> 01:56:25,920 this then you'll garner far more insight 3155 01:56:29,510 --> 01:56:28,560 than your peers maybe that 3156 01:56:31,189 --> 01:56:29,520 that 3157 01:56:33,430 --> 01:56:31,199 competitive edge will 3158 01:56:35,430 --> 01:56:33,440 tickle your rivalrous nature if it does 3159 01:56:37,189 --> 01:56:35,440 then you can use it as motivation and 3160 01:56:39,430 --> 01:56:37,199 for myself i may be doing a video at 3161 01:56:41,270 --> 01:56:39,440 some point i'm not don't hold me to this 3162 01:56:43,030 --> 01:56:41,280 on how the various definitions of 3163 01:56:45,189 --> 01:56:43,040 entropy are all related so there's 3164 01:56:48,070 --> 01:56:45,199 shannon there's thermal 3165 01:56:49,109 --> 01:56:48,080 there's neg entropy there's residual 3166 01:56:51,750 --> 01:56:49,119 entropy 3167 01:56:53,589 --> 01:56:51,760 and so on so on as i mentioned before 3168 01:56:55,510 --> 01:56:53,599 this video will be akin to an 3169 01:56:57,589 --> 01:56:55,520 introduction to another video that i 3170 01:56:59,830 --> 01:56:57,599 plan on releasing at some point now this 3171 01:57:01,109 --> 01:56:59,840 one has taken way way way too long so 3172 01:57:03,109 --> 01:57:01,119 perhaps i thought i was going to do it 3173 01:57:04,550 --> 01:57:03,119 in a few months this going through a 3174 01:57:06,070 --> 01:57:04,560 theoretical physics paper you don't 3175 01:57:07,750 --> 01:57:06,080 currently understand 3176 01:57:09,350 --> 01:57:07,760 i was going to go through geometric 3177 01:57:10,550 --> 01:57:09,360 unity perhaps i won't do that in a few 3178 01:57:13,109 --> 01:57:10,560 months perhaps it will be the winter 3179 01:57:14,470 --> 01:57:13,119 time now because this was way way way 3180 01:57:16,070 --> 01:57:14,480 more difficult than i thought it would 3181 01:57:17,990 --> 01:57:16,080 be regardless you can expect that at 3182 01:57:19,510 --> 01:57:18,000 some point so the question is is this 3183 01:57:21,350 --> 01:57:19,520 leading anywhere this 3184 01:57:23,189 --> 01:57:21,360 lecture series and i don't plan on 3185 01:57:24,390 --> 01:57:23,199 releasing more content like this as this 3186 01:57:25,750 --> 01:57:24,400 is not my forte 3187 01:57:27,990 --> 01:57:25,760 i'm interested in what i call 3188 01:57:29,990 --> 01:57:28,000 explicating the landscape of theories of 3189 01:57:32,149 --> 01:57:30,000 everything which means to intensely 3190 01:57:33,750 --> 01:57:32,159 investigate each toe geometric unity 3191 01:57:36,070 --> 01:57:33,760 wolf rooms so there's a thumbnail here 3192 01:57:37,510 --> 01:57:36,080 you can click on or in the description 3193 01:57:39,430 --> 01:57:37,520 thomas campbells there's theories on 3194 01:57:41,510 --> 01:57:39,440 consciousness there's veltan xiaowungs 3195 01:57:43,189 --> 01:57:41,520 like ian ian mcgillcrist and john 3196 01:57:45,030 --> 01:57:43,199 verveicky i mentioned before there's 3197 01:57:46,950 --> 01:57:45,040 interpretations of quantum theory like 3198 01:57:48,629 --> 01:57:46,960 carlo rivelli and nicholas jisson 3199 01:57:51,109 --> 01:57:48,639 there's even how to go about learning 3200 01:57:52,790 --> 01:57:51,119 mathematics with norman weilberger and 3201 01:57:54,629 --> 01:57:52,800 richard borchards 3202 01:57:57,030 --> 01:57:54,639 i highly recommend both of their youtube 3203 01:57:58,950 --> 01:57:57,040 channels by the way norman in particular 3204 01:58:01,990 --> 01:57:58,960 is great at making whatever is complex 3205 01:58:03,589 --> 01:58:02,000 seems so elementary that it's criminally 3206 01:58:05,030 --> 01:58:03,599 humiliating 3207 01:58:06,950 --> 01:58:05,040 now most people have a subscriber 3208 01:58:09,270 --> 01:58:06,960 request but i have a request for you to 3209 01:58:11,510 --> 01:58:09,280 not subscribe unless you're interested 3210 01:58:13,270 --> 01:58:11,520 in podcasts about the above 3211 01:58:15,669 --> 01:58:13,280 as this channel's 3212 01:58:17,350 --> 01:58:15,679 bread and butter are those podcasts you 3213 01:58:19,990 --> 01:58:17,360 will be sorely disappointed if you 3214 01:58:21,430 --> 01:58:20,000 expect more videos like this so check 3215 01:58:23,669 --> 01:58:21,440 out some of the other podcasts on this 3216 01:58:25,350 --> 01:58:23,679 channel here's a playlist for you to get 3217 01:58:26,790 --> 01:58:25,360 started also it's linked in the 3218 01:58:29,510 --> 01:58:26,800 description 3219 01:58:32,870 --> 01:58:29,520 again if you have an interesting nc 3220 01:58:35,189 --> 01:58:32,880 about some napkin calculation about some 3221 01:58:37,109 --> 01:58:35,199 observable that ordinarily is a tedious 3222 01:58:39,430 --> 01:58:37,119 calculation that you can arrive at 3223 01:58:41,270 --> 01:58:39,440 simply from this new natural unit point 3224 01:58:43,589 --> 01:58:41,280 of view then make sure to leave it in 3225 01:58:45,750 --> 01:58:43,599 the comments and make it clear what each 3226 01:58:47,910 --> 01:58:45,760 step is don't skip any steps i'll also 3227 01:58:50,870 --> 01:58:47,920 place a thread in the subreddit 3228 01:58:51,990 --> 01:58:50,880 reddit.com r theories of everything and 3229 01:58:54,070 --> 01:58:52,000 i'll try to comment on the most 3230 01:58:56,310 --> 01:58:54,080 interesting ones if you want to share or 3231 01:58:57,750 --> 01:58:56,320 get feedback on your nc or on your 3232 01:59:00,709 --> 01:58:57,760 theory of everything let's imagine you 3233 01:59:02,550 --> 01:59:00,719 have one then or some ideas to one then 3234 01:59:04,550 --> 01:59:02,560 go to the discord that's also linked in 3235 01:59:06,790 --> 01:59:04,560 the subreddit below again like i 3236 01:59:08,470 --> 01:59:06,800 mentioned there's no one source on this 3237 01:59:10,229 --> 01:59:08,480 it's strewn generally across several 3238 01:59:11,750 --> 01:59:10,239 lectures and you start to intuit it as a 3239 01:59:13,910 --> 01:59:11,760 physics student 3240 01:59:16,629 --> 01:59:13,920 however videos that served as 3241 01:59:19,510 --> 01:59:16,639 inspiration to this one are that of nima 3242 01:59:21,109 --> 01:59:19,520 arkani hamed andrew dotson 3243 01:59:22,870 --> 01:59:21,119 pretty much physics and sabine 3244 01:59:24,870 --> 01:59:22,880 hostenfelder i recommend you check out 3245 01:59:26,709 --> 01:59:24,880 all of those channels the links to their 3246 01:59:31,109 --> 01:59:26,719 work are in the description 3247 01:59:34,790 --> 01:59:33,030 the podcast is now finished if you'd 3248 01:59:37,910 --> 01:59:34,800 like to support conversations like this 3249 01:59:42,070 --> 01:59:37,920 then do consider going to patreon.com 3250 01:59:44,709 --> 01:59:42,080 c-u-r-t j-a-i-m-u-n-g-a-l 3251 01:59:46,470 --> 01:59:44,719 that is kurt jaimungle it's support from 3252 01:59:48,310 --> 01:59:46,480 the patrons and from the sponsors that