1 00:00:00,500 --> 00:00:02,890 The following content is provided under a Creative 2 00:00:02,890 --> 00:00:04,430 Commons license. 3 00:00:04,430 --> 00:00:06,730 Your support will help MIT OpenCourseWare 4 00:00:06,730 --> 00:00:11,120 continue to offer high quality educational resources for free. 5 00:00:11,120 --> 00:00:13,720 To make a donation or view additional materials 6 00:00:13,720 --> 00:00:17,680 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,680 --> 00:00:20,855 at ocw.mit.edu. 8 00:00:20,855 --> 00:00:21,730 NICHOLAS DIBELLA: Hi. 9 00:00:21,730 --> 00:00:28,390 Welcome to Excitatory Topics in Physics week 3. 10 00:00:28,390 --> 00:00:32,200 And boy do we have an excitatory set of topics for you today. 11 00:00:32,200 --> 00:00:34,600 I'll begin by reviewing special relativity 12 00:00:34,600 --> 00:00:36,390 from the past couple of weeks. 13 00:00:36,390 --> 00:00:39,840 Then I'll tell you a little bit about time travel, 14 00:00:39,840 --> 00:00:42,970 and then I'll talk to you about some general relativity. 15 00:00:42,970 --> 00:00:46,220 Then I'll tell you some more about time travel. 16 00:00:46,220 --> 00:00:52,420 So for the past couple of weeks we saw that special relativity 17 00:00:52,420 --> 00:00:56,590 has some very interesting consequences and among them we 18 00:00:56,590 --> 00:00:59,590 found that some things are relative and something aren't. 19 00:00:59,590 --> 00:01:02,890 And we found a lot of things were relative 20 00:01:02,890 --> 00:01:05,379 that we wouldn't ordinarily expect to be relative. 21 00:01:05,379 --> 00:01:07,670 So I'll just start compiling a list here of things that 22 00:01:07,670 --> 00:01:10,330 are relative that we found. 23 00:01:10,330 --> 00:01:16,769 So some things are relative. 24 00:01:22,520 --> 00:01:24,555 The first example that we saw was speed. 25 00:01:28,350 --> 00:01:29,100 Speed is relative. 26 00:01:29,100 --> 00:01:31,250 I'm going to just underline this. 27 00:01:31,250 --> 00:01:33,680 Speed is relative and that wasn't surprising at all, 28 00:01:33,680 --> 00:01:34,580 right? 29 00:01:34,580 --> 00:01:39,249 I mean we're used to seeing people walking on trains. 30 00:01:39,249 --> 00:01:40,790 Well, maybe not trains but we're used 31 00:01:40,790 --> 00:01:43,580 to seeing people walk by us and moving at relative speeds 32 00:01:43,580 --> 00:01:45,979 to us. 33 00:01:45,979 --> 00:01:48,520 Something that was surprising that we found that was relative 34 00:01:48,520 --> 00:01:49,760 is simultaneity. 35 00:01:57,690 --> 00:02:01,010 If I observed two events happening at the same time-- 36 00:02:01,010 --> 00:02:06,630 event one, event two. 37 00:02:06,630 --> 00:02:09,729 Actually those weren't simultaneous events. 38 00:02:09,729 --> 00:02:12,930 But if I observed two events occurring simultaneously then 39 00:02:12,930 --> 00:02:16,140 that doesn't necessarily mean that somebody moving relative 40 00:02:16,140 --> 00:02:20,220 to me will also observe them to be occurring simultaneously. 41 00:02:20,220 --> 00:02:24,240 And that was very surprising. 42 00:02:24,240 --> 00:02:28,759 Another thing we found that was relative was the time interval. 43 00:02:28,759 --> 00:02:30,300 The time interval between two events. 44 00:02:36,550 --> 00:02:41,380 And this is the phenomenon of time dilation, the fact that 45 00:02:41,380 --> 00:02:44,915 clocks moving relative to you run slow, they tick slower. 46 00:02:48,670 --> 00:02:53,770 Also relative is length. 47 00:02:53,770 --> 00:02:57,480 If an object like this thing, the eraser, 48 00:02:57,480 --> 00:02:59,770 is moving very fast relative to you, 49 00:02:59,770 --> 00:03:02,689 then its length will get shorter. 50 00:03:02,689 --> 00:03:03,730 Its length will decrease. 51 00:03:03,730 --> 00:03:05,165 The length will contract. 52 00:03:07,720 --> 00:03:09,820 I think those are all the relative things 53 00:03:09,820 --> 00:03:11,308 that I talked about. 54 00:03:11,308 --> 00:03:13,391 But there were some more things that are relative. 55 00:03:16,220 --> 00:03:17,532 Energy is relative. 56 00:03:21,150 --> 00:03:23,940 It's easy to see why kinetic energy has to be relative. 57 00:03:23,940 --> 00:03:27,420 If speed is relative then surely the kinetic energy is relative 58 00:03:27,420 --> 00:03:29,947 but also other types of energy are relative as well. 59 00:03:29,947 --> 00:03:31,530 But I won't go into detail about them. 60 00:03:34,500 --> 00:03:36,090 Now, there are other things that are 61 00:03:36,090 --> 00:03:40,998 relative that don't necessarily have to be mathematical. 62 00:03:40,998 --> 00:03:42,885 Hi. 63 00:03:42,885 --> 00:03:45,510 There are other things that are relative they don't necessarily 64 00:03:45,510 --> 00:03:47,190 have to be mathematical. 65 00:03:47,190 --> 00:03:50,390 For example a person's accent. 66 00:03:54,420 --> 00:03:58,190 I mean to an American a British person 67 00:03:58,190 --> 00:04:00,364 would have an accent, right? 68 00:04:00,364 --> 00:04:02,030 But to a British person a British person 69 00:04:02,030 --> 00:04:03,860 doesn't have an accent. 70 00:04:03,860 --> 00:04:06,274 To a British person an American person has an accent. 71 00:04:06,274 --> 00:04:07,940 To an American person an American person 72 00:04:07,940 --> 00:04:09,050 doesn't have an accent. 73 00:04:09,050 --> 00:04:10,438 So accents are relative. 74 00:04:15,590 --> 00:04:18,459 So is humor. 75 00:04:18,459 --> 00:04:22,100 British humor doesn't make any sense to Americans. 76 00:04:22,100 --> 00:04:26,400 Well, in some people's opinions. 77 00:04:26,400 --> 00:04:29,140 Maybe mine, maybe not. 78 00:04:29,140 --> 00:04:31,310 OK. 79 00:04:31,310 --> 00:04:34,970 Einstein actually had a very lovely quote 80 00:04:34,970 --> 00:04:37,670 summarizing the theory of relativity, what it means 81 00:04:37,670 --> 00:04:39,740 for things to be relative. 82 00:04:39,740 --> 00:04:42,650 And it goes like this, "When a man sits 83 00:04:42,650 --> 00:04:46,720 with a pretty girl for an hour it seems like a minute. 84 00:04:46,720 --> 00:04:48,830 But let him sit on a hot stove for a minute 85 00:04:48,830 --> 00:04:50,780 and it's longer than any hour. 86 00:04:50,780 --> 00:04:53,650 That's relativity." 87 00:04:53,650 --> 00:04:54,150 OK. 88 00:04:54,150 --> 00:04:54,810 I thought that was really funny. 89 00:04:54,810 --> 00:04:55,435 AUDIENCE: Yeah. 90 00:04:55,435 --> 00:04:57,839 Our psych teacher has [INAUDIBLE].. 91 00:04:57,839 --> 00:04:58,880 NICHOLAS DIBELLA: Really? 92 00:04:58,880 --> 00:04:59,760 You've heard that? 93 00:04:59,760 --> 00:05:00,260 OK. 94 00:05:00,260 --> 00:05:01,770 But you probably laughed a lot when you first heard it. 95 00:05:01,770 --> 00:05:02,460 AUDIENCE: Yes. 96 00:05:02,460 --> 00:05:03,335 NICHOLAS DIBELLA: OK. 97 00:05:05,810 --> 00:05:08,450 OK. 98 00:05:08,450 --> 00:05:11,749 Not everything is relative. 99 00:05:11,749 --> 00:05:14,040 There are some things that we found not to be relative, 100 00:05:14,040 --> 00:05:15,290 and I'll make a list of those. 101 00:05:19,070 --> 00:05:23,584 Another word for not relative is invariant. 102 00:05:23,584 --> 00:05:25,250 I'm just introducing that word because I 103 00:05:25,250 --> 00:05:26,660 think it sounds really cool. 104 00:05:26,660 --> 00:05:28,620 So I'm going to use the word invariant. 105 00:05:28,620 --> 00:05:35,724 Some things are invariant. 106 00:05:39,440 --> 00:05:41,945 That is not relative. 107 00:05:48,740 --> 00:05:52,260 The most important thing that's definitely not relative 108 00:05:52,260 --> 00:05:54,510 is the laws of physics. 109 00:05:54,510 --> 00:05:57,380 The laws of physics are the same for everybody. 110 00:05:57,380 --> 00:05:59,840 Well so far all we know is the laws of physics 111 00:05:59,840 --> 00:06:02,020 are the same for all inertial observers. 112 00:06:02,020 --> 00:06:06,690 The laws of physics are the same for everybody that's moving, 113 00:06:06,690 --> 00:06:08,029 but not accelerating. 114 00:06:17,490 --> 00:06:20,849 If I drop a chalk here, it will fall down 115 00:06:20,849 --> 00:06:21,890 in a very particular way. 116 00:06:30,090 --> 00:06:33,900 And if I drop a chalk while moving in relative motion 117 00:06:33,900 --> 00:06:40,611 to the floor, then it will also fall-- 118 00:06:40,611 --> 00:06:43,770 well, it broke by accident, but it'll also 119 00:06:43,770 --> 00:06:45,900 fall in a way that's exactly predicted 120 00:06:45,900 --> 00:06:48,280 by certain laws of mechanics. 121 00:06:51,490 --> 00:06:53,620 That was the first postulate of special relativity 122 00:06:53,620 --> 00:06:54,910 that I introduced to you all. 123 00:06:54,910 --> 00:06:57,070 The second postulate was that the speed of light 124 00:06:57,070 --> 00:06:57,760 is invariant. 125 00:07:04,910 --> 00:07:08,600 And that was also very surprising. 126 00:07:08,600 --> 00:07:13,247 It's surprising as any of these surprising relative things 127 00:07:13,247 --> 00:07:13,830 but it's true. 128 00:07:13,830 --> 00:07:18,029 It's been confirmed by a number of experiments. 129 00:07:18,029 --> 00:07:20,320 There are other things that are invariant that I didn't 130 00:07:20,320 --> 00:07:23,370 get to talk about last time. 131 00:07:23,370 --> 00:07:25,860 One of them is the mass of an object. 132 00:07:29,450 --> 00:07:33,380 The mass of an object happens to be something that's invariant. 133 00:07:33,380 --> 00:07:36,410 Another thing that's invariant is the electric charge 134 00:07:36,410 --> 00:07:37,010 of an object. 135 00:07:43,910 --> 00:07:48,010 For those of you who've never heard of this electric charge 136 00:07:48,010 --> 00:07:52,490 it's some number associated to an object that 137 00:07:52,490 --> 00:07:55,494 interacts electrically with another object. 138 00:07:55,494 --> 00:07:57,410 The object is said to have an electric charge. 139 00:07:57,410 --> 00:08:00,500 And it turns out that the electric charge 140 00:08:00,500 --> 00:08:01,910 is an invariant quantity. 141 00:08:05,260 --> 00:08:10,550 Well, finally another very important invariant thing 142 00:08:10,550 --> 00:08:15,530 is love. 143 00:08:15,530 --> 00:08:16,910 Love is invariant. 144 00:08:24,100 --> 00:08:24,600 OK. 145 00:08:27,474 --> 00:08:28,911 AUDIENCE: [INAUDIBLE]. 146 00:08:30,664 --> 00:08:32,330 NICHOLAS DIBELLA: I don't have the proof 147 00:08:32,330 --> 00:08:37,220 for that but if you ask your heart you'll know it's true. 148 00:08:41,150 --> 00:08:42,350 OK. 149 00:08:42,350 --> 00:08:47,400 Now special relativity predicts a lot of interesting things. 150 00:08:47,400 --> 00:08:50,580 It predicts relativity of showing quantities. 151 00:08:50,580 --> 00:08:53,100 And another thing it predicts is the possibility 152 00:08:53,100 --> 00:08:56,040 of time travel into the future. 153 00:08:56,040 --> 00:08:57,600 And I hinted at how this might be 154 00:08:57,600 --> 00:09:00,060 possible at the end of last class. 155 00:09:00,060 --> 00:09:02,640 And I'd like to go over how it's actually 156 00:09:02,640 --> 00:09:06,750 possible through special relativity. 157 00:09:06,750 --> 00:09:13,090 So time travel to the future. 158 00:09:13,090 --> 00:09:14,731 AUDIENCE: Can you come back? 159 00:09:14,731 --> 00:09:16,522 NICHOLAS DIBELLA: The future-- what's that? 160 00:09:16,522 --> 00:09:16,920 AUDIENCE: Can you come back? 161 00:09:16,920 --> 00:09:17,380 NICHOLAS DIBELLA: Can you come-- 162 00:09:17,380 --> 00:09:17,930 AUDIENCE: Can you travel to the past? 163 00:09:17,930 --> 00:09:20,770 Like, if you can go to the future, can you go back? 164 00:09:20,770 --> 00:09:23,061 NICHOLAS DIBELLA: You mean can you travel back in time? 165 00:09:23,061 --> 00:09:23,940 AUDIENCE: Yeah. 166 00:09:23,940 --> 00:09:26,560 NICHOLAS DIBELLA: Well, I'll get to time travel to the past 167 00:09:26,560 --> 00:09:29,050 later on but special relativity actually doesn't provide 168 00:09:29,050 --> 00:09:31,334 any means of getting back. 169 00:09:31,334 --> 00:09:33,070 AUDIENCE: And so [INAUDIBLE]. 170 00:09:36,940 --> 00:09:38,260 NICHOLAS DIBELLA: The future? 171 00:09:38,260 --> 00:09:40,460 Yes, the future. 172 00:09:40,460 --> 00:09:42,040 OK. 173 00:09:42,040 --> 00:09:44,620 And the way it works, as you can guess, 174 00:09:44,620 --> 00:09:50,577 is by using time dilation in some clever way. 175 00:09:50,577 --> 00:09:51,160 Yes, question? 176 00:09:51,160 --> 00:09:53,320 AUDIENCE: [INAUDIBLE]. 177 00:09:53,320 --> 00:09:55,660 NICHOLAS DIBELLA: Oh I'm going explain how it works, OK? 178 00:09:55,660 --> 00:09:57,035 I'm going to explain how it works 179 00:09:57,035 --> 00:09:59,040 because we're limited on time. 180 00:09:59,040 --> 00:09:59,540 OK. 181 00:09:59,540 --> 00:10:02,560 With time travel in the future using special relativity 182 00:10:02,560 --> 00:10:05,140 all that you have to do, all that you have to do 183 00:10:05,140 --> 00:10:11,570 is find a spaceship on Earth, any old spaceship, get on it, 184 00:10:11,570 --> 00:10:19,100 travel at 99.9995% the speed of light, 185 00:10:19,100 --> 00:10:22,040 go about 500 light years away, then come back. 186 00:10:22,040 --> 00:10:25,780 And whereas 1,000 years have passed for Earth people 187 00:10:25,780 --> 00:10:27,856 only 10 years has passed for you. 188 00:10:27,856 --> 00:10:29,215 Simple as that. 189 00:10:29,215 --> 00:10:31,480 AUDIENCE: [INAUDIBLE]. 190 00:10:31,480 --> 00:10:34,820 NICHOLAS DIBELLA: That sound simple? 191 00:10:34,820 --> 00:10:35,710 OK. 192 00:10:35,710 --> 00:10:36,940 And that works. 193 00:10:36,940 --> 00:10:37,630 OK. 194 00:10:37,630 --> 00:10:42,016 That works because of this. 195 00:10:42,016 --> 00:10:43,390 Suppose I'm sitting on the earth, 196 00:10:43,390 --> 00:10:45,010 OK, I'm sitting on the earth-- 197 00:10:45,010 --> 00:10:47,110 well, actually suppose you're sitting on the earth 198 00:10:47,110 --> 00:10:49,120 because I want to be the one in the spaceship. 199 00:10:49,120 --> 00:10:50,800 So as you're sitting on the earth 200 00:10:50,800 --> 00:10:56,440 and you observe me traveling very far, very fast away, 201 00:10:56,440 --> 00:10:59,350 then you observe me coming back, OK? 202 00:10:59,350 --> 00:11:03,670 According to time dilation moving clocks run slow. 203 00:11:03,670 --> 00:11:06,070 They run slow. 204 00:11:06,070 --> 00:11:10,775 And therefore, if say 1,000 years passes by for you 205 00:11:10,775 --> 00:11:13,150 if you happen to live that long and you have the patience 206 00:11:13,150 --> 00:11:15,170 to do these calculations, whatever, 207 00:11:15,170 --> 00:11:17,290 if 1,000 years passes by for you, 208 00:11:17,290 --> 00:11:21,610 then less than 1,000 years will pass by for me. 209 00:11:21,610 --> 00:11:23,110 Now the numbers that I gave you just 210 00:11:23,110 --> 00:11:26,380 before are the numbers that you would 211 00:11:26,380 --> 00:11:28,840 get if you use the time dilation formula that I gave you 212 00:11:28,840 --> 00:11:29,530 last class. 213 00:11:32,560 --> 00:11:35,680 So let me write it down. 214 00:11:35,680 --> 00:11:55,550 99.995% the speed of light-- 215 00:11:55,550 --> 00:11:56,570 of the speed. 216 00:12:01,360 --> 00:12:08,810 We travel at this times the speed of light and 1,000 years 217 00:12:08,810 --> 00:12:21,971 passes by for Earth and only 10 years passed by for me. 218 00:12:21,971 --> 00:12:25,660 So in effect I've traveled into the future. 219 00:12:25,660 --> 00:12:28,700 10 years have passed by for me and 1,000 years 220 00:12:28,700 --> 00:12:30,280 have passed by for you. 221 00:12:30,280 --> 00:12:30,780 Question? 222 00:12:30,780 --> 00:12:33,030 AUDIENCE: Why don't you just go at the speed of light? 223 00:12:33,030 --> 00:12:34,570 Why do you have to go 99%? 224 00:12:34,570 --> 00:12:36,380 NICHOLAS DIBELLA: Oh, you can't actually 225 00:12:36,380 --> 00:12:38,630 reach the speed of light. 226 00:12:38,630 --> 00:12:40,130 There are a lot of reasons you can't 227 00:12:40,130 --> 00:12:42,500 get to the speed of light, but one practical reason 228 00:12:42,500 --> 00:12:46,820 is that the closer you get to the speed of light the more 229 00:12:46,820 --> 00:12:49,960 energy it takes to accelerate. 230 00:12:49,960 --> 00:12:52,250 So from an energy point of view, to actually 231 00:12:52,250 --> 00:12:55,640 reached the speed of light you have to give yourself 232 00:12:55,640 --> 00:12:57,560 an infinite amount of energy. 233 00:12:57,560 --> 00:12:59,900 And where are you going to get that? 234 00:12:59,900 --> 00:13:01,960 I don't know. 235 00:13:01,960 --> 00:13:02,460 Question? 236 00:13:02,460 --> 00:13:04,376 AUDIENCE: But we said moving clocks run slow. 237 00:13:04,376 --> 00:13:06,771 So if somehow you're able to watch, like, 238 00:13:06,771 --> 00:13:09,645 a rocket ship going 99.9 the speed of light, 239 00:13:09,645 --> 00:13:11,082 what would you see? 240 00:13:13,940 --> 00:13:14,930 NICHOLAS DIBELLA: OK. 241 00:13:14,930 --> 00:13:18,079 The question is if I actually watched 242 00:13:18,079 --> 00:13:20,120 a rocket ship traveling at this really fast speed 243 00:13:20,120 --> 00:13:21,460 what would I see? 244 00:13:21,460 --> 00:13:23,620 OK. 245 00:13:23,620 --> 00:13:25,250 This is actually a difficulty I didn't 246 00:13:25,250 --> 00:13:27,680 want to get to but I'm glad you brought it up. 247 00:13:27,680 --> 00:13:30,710 Seeing actually isn't the same as observing. 248 00:13:30,710 --> 00:13:35,510 Because when you see an object you actually 249 00:13:35,510 --> 00:13:37,850 have to wait for the time it takes for light 250 00:13:37,850 --> 00:13:41,160 to travel from the object to reach you. 251 00:13:41,160 --> 00:13:45,950 And so what I'm actually seeing is the past. 252 00:13:45,950 --> 00:13:47,570 I'm actually seeing the past. 253 00:13:47,570 --> 00:13:52,610 I'm seeing approximately nanoseconds in the past 254 00:13:52,610 --> 00:13:58,330 because it takes time for light to travel from you to me. 255 00:13:58,330 --> 00:14:13,390 So well, OK, so I said that traveling objects, 256 00:14:13,390 --> 00:14:15,140 objects in motion will get shorter, right? 257 00:14:15,140 --> 00:14:16,770 I said they'll get shorter. 258 00:14:16,770 --> 00:14:22,140 Well, whether you actually see them to get shorter actually 259 00:14:22,140 --> 00:14:24,560 depends on how it's moving relative to you. 260 00:14:24,560 --> 00:14:27,710 So it could actually happen that you'll 261 00:14:27,710 --> 00:14:30,099 see an object get larger. 262 00:14:30,099 --> 00:14:31,640 You actually see an object get larger 263 00:14:31,640 --> 00:14:33,314 if it's moving at a high speed. 264 00:14:33,314 --> 00:14:34,730 But when you make measurements you 265 00:14:34,730 --> 00:14:38,360 have to take into account these corrections that involve 266 00:14:38,360 --> 00:14:41,470 light traveling from you to me. 267 00:14:41,470 --> 00:14:45,710 And this is similar to the association you make 268 00:14:45,710 --> 00:14:48,710 between thunder and lightning. 269 00:14:48,710 --> 00:14:52,340 You see a bolt of lightning and then you hear it 270 00:14:52,340 --> 00:14:55,520 but you know that the sound was produced right 271 00:14:55,520 --> 00:14:57,110 when the lightning struck. 272 00:14:57,110 --> 00:14:58,640 But since it takes time for sound 273 00:14:58,640 --> 00:15:02,030 to travel from the lightning to you, you as a smart observer 274 00:15:02,030 --> 00:15:03,880 will take that into account and then 275 00:15:03,880 --> 00:15:05,871 say that the sound was simultaneous 276 00:15:05,871 --> 00:15:08,120 with the strike of lightning or at least approximately 277 00:15:08,120 --> 00:15:08,870 simultaneous. 278 00:15:08,870 --> 00:15:14,950 More nearly simultaneous than what you actually hear. 279 00:15:14,950 --> 00:15:16,850 OK? 280 00:15:16,850 --> 00:15:17,360 OK. 281 00:15:17,360 --> 00:15:21,800 So 1,000 years passed by for you, 10 years passed by for me. 282 00:15:21,800 --> 00:15:22,850 So I'm the time traveler. 283 00:15:22,850 --> 00:15:23,750 Another question? 284 00:15:23,750 --> 00:15:25,469 AUDIENCE: How fast is a spaceship? 285 00:15:25,469 --> 00:15:26,510 NICHOLAS DIBELLA: Oh, OK. 286 00:15:26,510 --> 00:15:26,780 Yeah. 287 00:15:26,780 --> 00:15:28,530 You actually asked that question last time 288 00:15:28,530 --> 00:15:29,810 and I wrote down the answer. 289 00:15:29,810 --> 00:15:32,390 The question is, what's the fastest speed 290 00:15:32,390 --> 00:15:36,805 that a human rocket has gone up to, a rocket with humans 291 00:15:36,805 --> 00:15:38,610 inside has gone up to? 292 00:15:38,610 --> 00:15:40,410 And I'll write it here. 293 00:15:40,410 --> 00:15:42,540 Let's see. 294 00:15:42,540 --> 00:15:43,040 OK. 295 00:15:43,040 --> 00:15:46,730 The fastest speed traveled by humans. 296 00:16:01,990 --> 00:16:06,770 It was achieved by Apollo 11 before re-entry. 297 00:16:06,770 --> 00:16:17,030 And it was 24,759 miles per hour, which is approximately 298 00:16:17,030 --> 00:16:30,850 0.0037% the speed of light. 299 00:16:30,850 --> 00:16:36,460 But you want to know how fast we got electrons? 300 00:16:36,460 --> 00:16:40,105 The fastest speed we got any particle to get-- 301 00:16:40,105 --> 00:16:48,390 let's see fastest speed we got any particle, 302 00:16:48,390 --> 00:17:07,737 I'll just write, 99.999946% the speed of light. 303 00:17:07,737 --> 00:17:08,320 AUDIENCE: Wow. 304 00:17:08,320 --> 00:17:09,742 We're so close. 305 00:17:09,742 --> 00:17:10,700 NICHOLAS DIBELLA: Yeah. 306 00:17:10,700 --> 00:17:11,760 We're really close. 307 00:17:11,760 --> 00:17:17,579 I mean, hey, this could have been 0.0000037. 308 00:17:17,579 --> 00:17:23,990 But if we're able to get electrons this fast, 309 00:17:23,990 --> 00:17:27,421 then in principle we should be able to get humans that fast. 310 00:17:27,421 --> 00:17:28,129 Another question? 311 00:17:28,129 --> 00:17:31,050 AUDIENCE: So in theory we could put 312 00:17:31,050 --> 00:17:36,045 particles that could go into the future and have them come back? 313 00:17:36,045 --> 00:17:36,920 NICHOLAS DIBELLA: OK. 314 00:17:36,920 --> 00:17:40,130 You can make particles experience time dilation 315 00:17:40,130 --> 00:17:43,460 but particles don't have brains. 316 00:17:43,460 --> 00:17:47,435 They don't have brains so who cares? 317 00:17:50,640 --> 00:17:51,140 OK. 318 00:17:51,140 --> 00:17:52,869 We do care for experimental reasons 319 00:17:52,869 --> 00:17:54,910 but I mean we want to know what it's like, right? 320 00:17:54,910 --> 00:17:56,576 We want to know what the future is like. 321 00:17:56,576 --> 00:17:57,500 Yeah. 322 00:17:57,500 --> 00:17:59,450 OK. 323 00:17:59,450 --> 00:18:01,940 But if we can get particles this fast, 324 00:18:01,940 --> 00:18:04,640 we should be able to get us this fast in principle. 325 00:18:07,079 --> 00:18:08,495 We just need the right technology. 326 00:18:08,495 --> 00:18:11,505 AUDIENCE: Wouldn't we fall apart if we went that fast? 327 00:18:11,505 --> 00:18:12,380 NICHOLAS DIBELLA: OK. 328 00:18:12,380 --> 00:18:13,640 The question is, wouldn't we fall apart 329 00:18:13,640 --> 00:18:14,800 if we went that fast? 330 00:18:14,800 --> 00:18:20,180 Well we'd crush, we'd break, we'd twist, 331 00:18:20,180 --> 00:18:22,580 we'd get destroyed if we tried to accelerate quickly 332 00:18:22,580 --> 00:18:23,730 to that speed. 333 00:18:23,730 --> 00:18:26,640 But if we accelerate slowly to that speed, 334 00:18:26,640 --> 00:18:30,819 then there's not a problem, and actually I have numbers here. 335 00:18:30,819 --> 00:18:31,610 If you accelerate-- 336 00:18:31,610 --> 00:18:32,120 AUDIENCE: [INAUDIBLE]. 337 00:18:32,120 --> 00:18:33,500 NICHOLAS DIBELLA: I'm glad you asked that. 338 00:18:33,500 --> 00:18:35,000 You guys are asking questions that I 339 00:18:35,000 --> 00:18:36,800 had planned to talk about. 340 00:18:36,800 --> 00:18:39,230 That's good. 341 00:18:39,230 --> 00:18:40,450 OK. 342 00:18:40,450 --> 00:18:47,170 If you accelerated at 1 g which is 343 00:18:47,170 --> 00:18:49,670 the acceleration due to gravity at the surface of the Earth. 344 00:18:49,670 --> 00:18:53,840 If I just dropped the chalk, then it accelerates at 1 g. 345 00:18:53,840 --> 00:18:57,037 And 1 g is an acceleration that we're used to. 346 00:18:57,037 --> 00:18:59,120 So we'd like to travel in a rocket going that fast 347 00:18:59,120 --> 00:18:59,810 because that's comfortable. 348 00:18:59,810 --> 00:19:01,830 We're used to that sort of acceleration. 349 00:19:05,414 --> 00:19:07,080 We're used to that kind of acceleration. 350 00:19:07,080 --> 00:19:10,910 That would be a comfortable acceleration. 351 00:19:10,910 --> 00:19:16,060 It turns out that if we accelerated at 1 g, then 352 00:19:16,060 --> 00:19:16,676 we'd reach-- 353 00:19:16,676 --> 00:19:18,800 I'll write these numbers down for you guys that are 354 00:19:18,800 --> 00:19:20,270 interested in all this stuff. 355 00:19:20,270 --> 00:19:22,071 If you accelerate-- 356 00:19:28,810 --> 00:19:32,751 1 g is the acceleration due to gravity --accelerate at 1 g-- 357 00:19:32,751 --> 00:19:35,820 oh, we don't have all the numbers. 358 00:19:35,820 --> 00:19:45,850 OK, anyway if we accelerate at 1 g reaching 359 00:19:45,850 --> 00:19:52,870 99.9992% the speed of light-- 360 00:19:52,870 --> 00:19:54,837 I'll just write c, then-- 361 00:19:54,837 --> 00:19:56,420 OK, I don't have all the numbers down. 362 00:19:56,420 --> 00:20:03,860 But I think it's something like you'd experience-- 363 00:20:03,860 --> 00:20:07,900 I forgot, but you'd experience I think it's something 364 00:20:07,900 --> 00:20:10,580 like six years instead of-- 365 00:20:10,580 --> 00:20:14,140 if you traveled very far away, traveled very far away 366 00:20:14,140 --> 00:20:16,240 accelerating at 1 g until you reached 367 00:20:16,240 --> 00:20:23,410 99.9992% the speed of light and then turned around 368 00:20:23,410 --> 00:20:26,440 and returned to Earth, 1,000 years would pass by for Earth 369 00:20:26,440 --> 00:20:28,450 and then something that's approximately 10 years 370 00:20:28,450 --> 00:20:29,410 would pass by for you. 371 00:20:29,410 --> 00:20:31,630 But this is a more realistic situation. 372 00:20:31,630 --> 00:20:34,660 So it's important to know how much time actually 373 00:20:34,660 --> 00:20:35,410 passes by for you. 374 00:20:35,410 --> 00:20:37,326 And it's actually a more difficult calculation 375 00:20:37,326 --> 00:20:40,440 to do because it involves accelerations. 376 00:20:40,440 --> 00:20:40,940 Yes? 377 00:20:40,940 --> 00:20:41,434 Question? 378 00:20:41,434 --> 00:20:43,100 AUDIENCE: How long would it take for you 379 00:20:43,100 --> 00:20:44,641 to accelerate to that 99.9%? 380 00:20:44,641 --> 00:20:47,140 NICHOLAS DIBELLA: Oh, yeah, I said it's a harder calculation 381 00:20:47,140 --> 00:20:47,810 to do. 382 00:20:47,810 --> 00:20:49,740 I forgot what the answer is. 383 00:20:49,740 --> 00:20:50,240 Question? 384 00:20:50,240 --> 00:20:50,865 AUDIENCE: Yeah. 385 00:20:50,865 --> 00:20:54,674 What kind of particles would accelerate to that percentage? 386 00:20:54,674 --> 00:20:55,840 NICHOLAS DIBELLA: Oh, it's-- 387 00:20:55,840 --> 00:20:56,350 I forgot. 388 00:20:56,350 --> 00:20:57,558 It might have been electrons. 389 00:20:57,558 --> 00:20:59,925 It might have been muons or positrons. 390 00:20:59,925 --> 00:21:01,860 AUDIENCE: I know electrons have zero mass-- 391 00:21:01,860 --> 00:21:02,950 NICHOLAS DIBELLA: No, no, no, no, no. 392 00:21:02,950 --> 00:21:04,240 Electrons don't have zero mass. 393 00:21:04,240 --> 00:21:06,364 Electrons have a mass of approximately 9.1 times 10 394 00:21:06,364 --> 00:21:08,205 to the negative 31 kilograms. 395 00:21:08,205 --> 00:21:11,920 [LAUGHTER] 396 00:21:11,920 --> 00:21:12,420 Question? 397 00:21:12,420 --> 00:21:14,503 AUDIENCE: Going back to the question [INAUDIBLE].. 398 00:21:17,915 --> 00:21:20,040 NICHOLAS DIBELLA: Are you going to answer something 399 00:21:20,040 --> 00:21:20,998 about the twin paradox? 400 00:21:20,998 --> 00:21:21,850 AUDIENCE: Yeah. 401 00:21:21,850 --> 00:21:24,590 NICHOLAS DIBELLA: Oh, let's talk about that after class. 402 00:21:24,590 --> 00:21:25,391 OK. 403 00:21:25,391 --> 00:21:25,890 Question? 404 00:21:25,890 --> 00:21:30,390 AUDIENCE: 1 g equals how many-- 405 00:21:30,390 --> 00:21:32,770 NICHOLAS DIBELLA: Oh, OK, 1 g no it's not miles. 406 00:21:32,770 --> 00:21:34,360 1 g isn't a unit of speed. 407 00:21:34,360 --> 00:21:36,600 1 g is a unit of acceleration. 408 00:21:36,600 --> 00:21:39,180 And acceleration is measured in well, 409 00:21:39,180 --> 00:21:41,820 I feel like, miles and hours than it's 410 00:21:41,820 --> 00:21:43,560 measured in one-- well, it's measured 411 00:21:43,560 --> 00:21:46,980 in miles per hours squared or in units 412 00:21:46,980 --> 00:21:49,140 that physicists use often. 413 00:21:49,140 --> 00:21:51,250 It would be 9.8 meters per second squared. 414 00:21:51,250 --> 00:21:51,600 AUDIENCE: Per seconds squared. 415 00:21:51,600 --> 00:21:52,558 NICHOLAS DIBELLA: Yeah. 416 00:21:52,558 --> 00:21:57,780 That's the units for g, but it's just 417 00:21:57,780 --> 00:21:59,860 enough to know that 1 g is what we're used to. 418 00:21:59,860 --> 00:22:01,230 It's the acceleration that we're used to when 419 00:22:01,230 --> 00:22:02,460 we're just standing here. 420 00:22:02,460 --> 00:22:03,365 You have a question? 421 00:22:03,365 --> 00:22:03,900 Oh, OK. 422 00:22:03,900 --> 00:22:05,291 Oh, you're saying go on. 423 00:22:05,291 --> 00:22:05,790 OK. 424 00:22:05,790 --> 00:22:06,980 I'm going to. 425 00:22:06,980 --> 00:22:07,650 OK. 426 00:22:07,650 --> 00:22:12,037 Now how can we actually do this and how can we 427 00:22:12,037 --> 00:22:13,245 actually do this in practice? 428 00:22:16,440 --> 00:22:18,990 What kind of ship would we produce? 429 00:22:18,990 --> 00:22:21,780 What kind of fuel would we use? 430 00:22:21,780 --> 00:22:23,480 Why did I do that? 431 00:22:23,480 --> 00:22:24,490 OK. 432 00:22:24,490 --> 00:22:27,390 How do we actually do this? 433 00:22:27,390 --> 00:22:28,390 Here are the steps. 434 00:22:28,390 --> 00:22:29,830 I'm going to write down some steps 435 00:22:29,830 --> 00:22:32,660 for how you can do this if you've 436 00:22:32,660 --> 00:22:34,065 got the right connections. 437 00:22:41,370 --> 00:22:42,120 Step number one. 438 00:22:45,180 --> 00:22:46,530 Get a spaceship. 439 00:22:46,530 --> 00:22:47,790 Any old spaceship will do. 440 00:22:52,060 --> 00:22:53,950 Actually let me just write down the materials 441 00:22:53,950 --> 00:22:54,917 you need first, OK? 442 00:22:58,120 --> 00:23:06,120 Spaceship, very, very powerful lasers. 443 00:23:06,120 --> 00:23:09,480 I'll get to why in a minute. 444 00:23:09,480 --> 00:23:11,760 You need some very, very powerful lasers. 445 00:23:11,760 --> 00:23:14,880 I'll tell you why in a minute. 446 00:23:14,880 --> 00:23:24,210 Very powerful lasers, some very large mirrors. 447 00:23:24,210 --> 00:23:24,960 I'll tell you why. 448 00:23:28,286 --> 00:23:29,910 Not because you're a narcissist and you 449 00:23:29,910 --> 00:23:32,534 get bored on these trips and you just like looking at yourself. 450 00:23:32,534 --> 00:23:34,955 AUDIENCE: You want to have food, water. 451 00:23:34,955 --> 00:23:36,330 NICHOLAS DIBELLA: Food and water? 452 00:23:36,330 --> 00:23:37,690 AUDIENCE: Who needs food and water? 453 00:23:37,690 --> 00:23:39,180 NICHOLAS DIBELLA: Oh, you guys have that disease too 454 00:23:39,180 --> 00:23:40,820 where you need food and water? 455 00:23:40,820 --> 00:23:43,450 Funny. 456 00:23:43,450 --> 00:23:56,275 Some very large mirrors and some matter-anti-matter fuel. 457 00:24:08,675 --> 00:24:09,280 OK, guys. 458 00:24:13,170 --> 00:24:14,580 Careful. 459 00:24:14,580 --> 00:24:15,880 OK. 460 00:24:15,880 --> 00:24:18,520 Now before I tell you how to actually do this, 461 00:24:18,520 --> 00:24:22,600 let me tell you why you need this stuff, OK? 462 00:24:22,600 --> 00:24:24,850 You need lasers and the mirrors-- 463 00:24:24,850 --> 00:24:26,970 the lasers and the mirrors go together. 464 00:24:26,970 --> 00:24:29,990 But you need them because of this very useful effect 465 00:24:29,990 --> 00:24:32,890 called radiation pressure. 466 00:24:32,890 --> 00:24:38,140 It turns out that when you shine lights at an object, 467 00:24:38,140 --> 00:24:40,360 the light actually pushes on it. 468 00:24:40,360 --> 00:24:41,480 It actually pushes on it. 469 00:24:41,480 --> 00:24:42,875 It exerts a force on it. 470 00:24:42,875 --> 00:24:43,750 It exerts a pressure. 471 00:24:43,750 --> 00:24:46,180 It's what we call radiation pressure. 472 00:24:46,180 --> 00:24:49,690 And it turns out that if the object you're 473 00:24:49,690 --> 00:24:51,790 shining a light at is a reflective object, 474 00:24:51,790 --> 00:24:54,820 like a mirror, then you can maximize the force 475 00:24:54,820 --> 00:24:58,210 that you exert on the object with the light. 476 00:24:58,210 --> 00:25:03,910 So if we've got some very powerful lasers stationed 477 00:25:03,910 --> 00:25:06,640 at some places in the solar system 478 00:25:06,640 --> 00:25:11,440 and we've got some very large mirrors on our spaceship 479 00:25:11,440 --> 00:25:17,740 and we shine those lasers at the spaceship mirrors, 480 00:25:17,740 --> 00:25:20,170 then the lasers would actually be powerful enough 481 00:25:20,170 --> 00:25:22,000 to push the ship. 482 00:25:22,000 --> 00:25:24,220 It would be powerful enough to propel it. 483 00:25:24,220 --> 00:25:26,140 And this type of propelling in space 484 00:25:26,140 --> 00:25:29,350 is called using a LightSail. 485 00:25:29,350 --> 00:25:31,572 In the ocean sailors use wind sails. 486 00:25:31,572 --> 00:25:32,155 They use wind. 487 00:25:32,155 --> 00:25:36,460 Well in space you use LightSails. 488 00:25:36,460 --> 00:25:38,620 Oh, by the way, in everyday life you 489 00:25:38,620 --> 00:25:40,780 don't notice light pushing down on you. 490 00:25:40,780 --> 00:25:42,741 Like it's not pushing me down because-- 491 00:25:42,741 --> 00:25:44,740 it's not pushing me down because it's simply not 492 00:25:44,740 --> 00:25:45,630 powerful enough. 493 00:25:45,630 --> 00:25:46,650 It's not intense enough. 494 00:25:46,650 --> 00:25:48,524 The light would have to be enormously intense 495 00:25:48,524 --> 00:25:51,320 for you to even notice it. 496 00:25:51,320 --> 00:25:53,100 Yeah, I don't have any numbers on me. 497 00:25:53,100 --> 00:25:54,378 AUDIENCE: Like the sun? 498 00:25:54,378 --> 00:25:55,660 NICHOLAS DIBELLA: What's that? 499 00:25:55,660 --> 00:25:56,980 AUDIENCE: Like the sun [INAUDIBLE]?? 500 00:25:56,980 --> 00:25:57,490 NICHOLAS DIBELLA: Like the sun? 501 00:25:57,490 --> 00:25:58,390 No, no. 502 00:25:58,390 --> 00:26:00,190 I mean if I go outside, I'm not immediately 503 00:26:00,190 --> 00:26:01,490 pushed down to the floor. 504 00:26:01,490 --> 00:26:01,690 No. 505 00:26:01,690 --> 00:26:03,130 AUDIENCE: What if you're really close? 506 00:26:03,130 --> 00:26:04,740 NICHOLAS DIBELLA: Oh, if you're really close to the sun, then 507 00:26:04,740 --> 00:26:05,620 yes, sure. 508 00:26:05,620 --> 00:26:08,080 Sure you'll be pushed by the sun, and you'll be hurt. 509 00:26:10,370 --> 00:26:10,870 OK. 510 00:26:10,870 --> 00:26:14,860 So this is how we're going to start the ship, the space 511 00:26:14,860 --> 00:26:16,550 ship going off. 512 00:26:16,550 --> 00:26:19,410 Now eventually you're going to have to turn around, right, 513 00:26:19,410 --> 00:26:20,167 to come back. 514 00:26:20,167 --> 00:26:22,000 Now how are you going to slow yourself down? 515 00:26:22,000 --> 00:26:23,380 AUDIENCE: Turn off the lasers. 516 00:26:23,380 --> 00:26:24,700 NICHOLAS DIBELLA: Well, if you turn off the lasers, 517 00:26:24,700 --> 00:26:26,620 you're still going really fast. 518 00:26:26,620 --> 00:26:29,110 You would just stay at that very fast speed. 519 00:26:29,110 --> 00:26:32,110 So you have to have some way of decelerating. 520 00:26:32,110 --> 00:26:35,270 And that's what the matter-anti-matter fuel is for. 521 00:26:35,270 --> 00:26:36,380 OK? 522 00:26:36,380 --> 00:26:40,390 Now you've all heard of matter, what's anti-matter? 523 00:26:40,390 --> 00:26:44,170 Well, so you're all familiar with particles 524 00:26:44,170 --> 00:26:48,070 like protons, neutrons, electrons. 525 00:26:48,070 --> 00:26:50,611 Well it turns out that there exists particles in nature, 526 00:26:50,611 --> 00:26:52,360 which you can find and which you can make. 527 00:26:52,360 --> 00:26:55,660 There exists particles called anti-particles. 528 00:26:55,660 --> 00:26:56,448 And so-- 529 00:26:56,448 --> 00:26:57,759 AUDIENCE: [INAUDIBLE] 530 00:26:57,759 --> 00:26:59,050 NICHOLAS DIBELLA: I'll explain. 531 00:26:59,050 --> 00:26:59,591 I'll explain. 532 00:26:59,591 --> 00:27:00,140 I'll explain. 533 00:27:00,140 --> 00:27:02,110 There exists particles called anti-particles. 534 00:27:02,110 --> 00:27:03,460 There's an anti-proton. 535 00:27:03,460 --> 00:27:04,850 There's an anti-neutron. 536 00:27:04,850 --> 00:27:06,970 There's an anti-electron. 537 00:27:06,970 --> 00:27:11,290 Now whenever a particle meets with its anti-particle, 538 00:27:11,290 --> 00:27:14,980 the two will annihilate each other and produce pure energy. 539 00:27:14,980 --> 00:27:17,500 Something like this will happen. 540 00:27:17,500 --> 00:27:20,080 I'll write it down here. 541 00:27:20,080 --> 00:27:23,260 So you have a particle right here. 542 00:27:23,260 --> 00:27:25,440 I'm not supposed to write on this board but I will. 543 00:27:25,440 --> 00:27:30,180 So a particle here and you have another particle here. 544 00:27:30,180 --> 00:27:31,060 I'll just write it. 545 00:27:34,050 --> 00:27:36,350 They're traveling towards each other. 546 00:27:36,350 --> 00:27:37,679 That's too big. 547 00:27:37,679 --> 00:27:39,220 They're traveling towards each other. 548 00:27:42,850 --> 00:27:44,278 This is the anti-particle. 549 00:27:49,430 --> 00:27:51,260 And this is before. 550 00:27:51,260 --> 00:27:52,640 I'm going to show you an after. 551 00:27:55,470 --> 00:27:55,970 OK. 552 00:28:01,130 --> 00:28:03,050 After the particle and the anti-particle 553 00:28:03,050 --> 00:28:07,865 won't be either anymore but instead there will be photons. 554 00:28:12,090 --> 00:28:14,561 One could go this way and one could go this way. 555 00:28:14,561 --> 00:28:15,310 These are photons. 556 00:28:18,700 --> 00:28:21,010 I might have used a term earlier but a photon 557 00:28:21,010 --> 00:28:23,120 is just a particle of light. 558 00:28:23,120 --> 00:28:25,630 Light happens to come in chunks, and these chunks, 559 00:28:25,630 --> 00:28:28,660 these particles are called photons. 560 00:28:28,660 --> 00:28:29,960 OK? 561 00:28:29,960 --> 00:28:33,910 Now whenever a photon hits an object, 562 00:28:33,910 --> 00:28:36,570 the photon will exert a pressure on it. 563 00:28:36,570 --> 00:28:37,650 It's the same effect. 564 00:28:37,650 --> 00:28:41,500 Radiation pressure applies-- it applies to light 565 00:28:41,500 --> 00:28:43,810 and photons are bits of light. 566 00:28:43,810 --> 00:28:44,500 OK. 567 00:28:44,500 --> 00:28:46,220 So now this deceleration problem. 568 00:28:46,220 --> 00:28:48,580 How are we going to decelerate? 569 00:28:48,580 --> 00:28:52,510 Well initially we're traveling in such a way 570 00:28:52,510 --> 00:28:56,640 that our mirrors are facing-- 571 00:28:56,640 --> 00:28:59,140 they're facing this laser. 572 00:28:59,140 --> 00:29:04,270 Well if we turn the ship around and we 573 00:29:04,270 --> 00:29:06,370 look at our matter-anti-matter fuel 574 00:29:06,370 --> 00:29:09,820 and we let some of the particles annihilate the anti-particles, 575 00:29:09,820 --> 00:29:12,560 if we let that happen, then photons will be produced. 576 00:29:12,560 --> 00:29:15,820 And we can let those photons hit the mirror 577 00:29:15,820 --> 00:29:21,520 and thereby push the ship in the direction opposite 578 00:29:21,520 --> 00:29:24,730 that it was traveling initially so that effectively 579 00:29:24,730 --> 00:29:25,430 decelerates. 580 00:29:25,430 --> 00:29:27,940 It slows down the ship. 581 00:29:27,940 --> 00:29:34,760 And you can let this happen enough times that you 582 00:29:34,760 --> 00:29:35,780 eventually reach rests. 583 00:29:35,780 --> 00:29:37,030 And then you have to get back. 584 00:29:37,030 --> 00:29:43,000 So you're too far away from the lasers and the solar system. 585 00:29:43,000 --> 00:29:45,900 So you turn the ship around again. 586 00:29:45,900 --> 00:29:47,470 No, no, no you have it the right way. 587 00:29:47,470 --> 00:29:48,553 You have it the right way. 588 00:29:48,553 --> 00:29:50,560 You let some particles annihilate 589 00:29:50,560 --> 00:29:52,870 with some more anti-particles, produce more energy, 590 00:29:52,870 --> 00:29:57,820 then you do it enough so that the ship is 591 00:29:57,820 --> 00:29:59,110 moving at a fast speed again. 592 00:29:59,110 --> 00:30:00,550 And then you're going to have to decelerate again. 593 00:30:00,550 --> 00:30:02,133 And after you decelerate again, you're 594 00:30:02,133 --> 00:30:04,360 close enough to the lasers in the solar system 595 00:30:04,360 --> 00:30:05,670 to help you decelerate. 596 00:30:05,670 --> 00:30:07,510 And then eventually you get back. 597 00:30:07,510 --> 00:30:08,970 And that's all there is to it. 598 00:30:08,970 --> 00:30:09,470 Yes? 599 00:30:09,470 --> 00:30:10,895 AUDIENCE: [INAUDIBLE]? 600 00:30:12,994 --> 00:30:14,410 NICHOLAS DIBELLA: If you're smart, 601 00:30:14,410 --> 00:30:16,368 you'd never run out of matter-anti-matter fuel. 602 00:30:16,368 --> 00:30:18,426 You just put enough, right? 603 00:30:18,426 --> 00:30:20,050 Plan beforehand before you time travel. 604 00:30:20,050 --> 00:30:21,760 AUDIENCE: What about [INAUDIBLE]?? 605 00:30:21,760 --> 00:30:23,990 NICHOLAS DIBELLA: Maybe you'll have to bring food. 606 00:30:23,990 --> 00:30:24,490 Question? 607 00:30:24,490 --> 00:30:25,782 AUDIENCE: [INAUDIBLE]? 608 00:30:25,782 --> 00:30:27,240 NICHOLAS DIBELLA: I can't hear you. 609 00:30:27,240 --> 00:30:28,224 AUDIENCE: [INAUDIBLE]? 610 00:30:32,290 --> 00:30:33,540 AUDIENCE: Repeat the question. 611 00:30:33,540 --> 00:30:34,210 NICHOLAS DIBELLA: I can't hear you. 612 00:30:34,210 --> 00:30:34,940 Can you repeat the question. 613 00:30:34,940 --> 00:30:36,428 AUDIENCE: If it has enough energy 614 00:30:36,428 --> 00:30:39,900 to stop [INAUDIBLE] enough energy to accelerate? 615 00:30:39,900 --> 00:30:41,310 NICHOLAS DIBELLA: Oh, yeah. 616 00:30:41,310 --> 00:30:43,401 Once you stop you can accelerate again. 617 00:30:43,401 --> 00:30:43,900 Yeah, sure. 618 00:30:43,900 --> 00:30:46,225 AUDIENCE: But at the same speed? 619 00:30:46,225 --> 00:30:49,024 Why didn't you just do that in the first place? 620 00:30:49,024 --> 00:30:50,940 NICHOLAS DIBELLA: Do you mean why didn't I use 621 00:30:50,940 --> 00:30:52,439 the lasers to decelerate us? 622 00:30:52,439 --> 00:30:52,980 AUDIENCE: No. 623 00:30:52,980 --> 00:30:54,390 Why don't you use the anti-matter? 624 00:30:54,390 --> 00:30:55,560 NICHOLAS DIBELLA: Oh, I could've used that first. 625 00:30:55,560 --> 00:30:58,170 But since we're in the solar system, what the heck. 626 00:31:01,560 --> 00:31:02,060 Question? 627 00:31:02,060 --> 00:31:04,050 AUDIENCE: How is anti-matter created? 628 00:31:04,050 --> 00:31:05,550 NICHOLAS DIBELLA: How is it created? 629 00:31:05,550 --> 00:31:09,360 Well it's created in a lot of different radioactive 630 00:31:09,360 --> 00:31:11,999 decays of particles. 631 00:31:11,999 --> 00:31:13,540 You might have heard of the positron. 632 00:31:13,540 --> 00:31:17,920 The positron is the anti-particle of the electron. 633 00:31:17,920 --> 00:31:21,070 And they're [INAUDIBLE] but they exist. 634 00:31:21,070 --> 00:31:21,600 They exist. 635 00:31:21,600 --> 00:31:22,099 Question? 636 00:31:22,099 --> 00:31:24,340 AUDIENCE: Wouldn't that cost a lot? 637 00:31:24,340 --> 00:31:25,680 NICHOLAS DIBELLA: OK. 638 00:31:25,680 --> 00:31:28,550 Wouldn't it cost a lot? 639 00:31:28,550 --> 00:31:31,140 Are we going to have enough fuel? 640 00:31:31,140 --> 00:31:32,700 These are questions that you have 641 00:31:32,700 --> 00:31:38,100 to prepare for as an aeronautical engineer. 642 00:31:40,710 --> 00:31:41,430 OK. 643 00:31:41,430 --> 00:31:41,930 Sure. 644 00:31:41,930 --> 00:31:44,102 And in today's world, this is completely 645 00:31:44,102 --> 00:31:45,560 impossible because first of all, we 646 00:31:45,560 --> 00:31:47,940 don't have lasers that are nearly powerful enough 647 00:31:47,940 --> 00:31:50,670 to exert enough pressure. 648 00:31:50,670 --> 00:31:53,430 And second of all, we don't have a good way 649 00:31:53,430 --> 00:31:54,630 of making anti-matter. 650 00:31:54,630 --> 00:31:56,504 Right now we're only able to make anti-matter 651 00:31:56,504 --> 00:31:59,350 at a rate of about one atom at a time. 652 00:31:59,350 --> 00:32:03,330 And we're definitely going to need a lot more than 32 atoms 653 00:32:03,330 --> 00:32:05,371 to do this. 654 00:32:05,371 --> 00:32:05,870 Question? 655 00:32:05,870 --> 00:32:07,798 AUDIENCE: How do you contain anti-matter 656 00:32:07,798 --> 00:32:09,884 if it just annihilates itself? 657 00:32:09,884 --> 00:32:11,550 NICHOLAS DIBELLA: How are you going to-- 658 00:32:11,550 --> 00:32:11,850 OK. 659 00:32:11,850 --> 00:32:12,720 You separate them. 660 00:32:12,720 --> 00:32:14,920 You hold them in separate containers, 661 00:32:14,920 --> 00:32:15,890 the matter-anti-matter. 662 00:32:15,890 --> 00:32:17,040 Make sure that they don't-- 663 00:32:17,040 --> 00:32:24,930 AUDIENCE: [INAUDIBLE] 664 00:32:24,930 --> 00:32:26,130 NICHOLAS DIBELLA: OK. 665 00:32:26,130 --> 00:32:28,230 You have to have smart ways of storing this stuff. 666 00:32:28,230 --> 00:32:29,390 These are details. 667 00:32:29,390 --> 00:32:31,380 These are just little details but I'm trying 668 00:32:31,380 --> 00:32:32,801 to emphasize the main points. 669 00:32:32,801 --> 00:32:33,300 Question? 670 00:32:33,300 --> 00:32:37,090 AUDIENCE: How do scientists today contain anti-matter? 671 00:32:37,090 --> 00:32:38,840 NICHOLAS DIBELLA: How did they contain it? 672 00:32:38,840 --> 00:32:42,476 I'm not exactly sure of all these little details. 673 00:32:42,476 --> 00:32:45,020 But of course these are details that have to be worked out. 674 00:32:45,020 --> 00:32:49,130 Anyway this is how you might conceivably reach this speed 675 00:32:49,130 --> 00:32:51,590 and conceivably travel into the future. 676 00:32:51,590 --> 00:32:53,720 Special relativity allows it. 677 00:32:53,720 --> 00:32:57,165 Time travel to the future is certainly possible. 678 00:32:57,165 --> 00:32:58,874 AUDIENCE: Is everybody going to get back? 679 00:32:58,874 --> 00:32:59,748 NICHOLAS DIBELLA: OK. 680 00:32:59,748 --> 00:33:01,700 There's a question of can we get back. 681 00:33:01,700 --> 00:33:04,340 Well I'll talk about time travel to the past in a little bit. 682 00:33:04,340 --> 00:33:07,590 Right now I'm still in the future, OK? 683 00:33:07,590 --> 00:33:08,215 I've got goals. 684 00:33:08,215 --> 00:33:09,839 You know I'm thinking about the future. 685 00:33:09,839 --> 00:33:11,700 I'm not thinking about things that happened. 686 00:33:11,700 --> 00:33:12,200 OK. 687 00:33:12,200 --> 00:33:12,950 Well whatever. 688 00:33:12,950 --> 00:33:14,032 AUDIENCE: [INAUDIBLE]. 689 00:33:14,032 --> 00:33:16,490 NICHOLAS DIBELLA: I'll talk about the past in a little bit, 690 00:33:16,490 --> 00:33:18,730 OK? 691 00:33:18,730 --> 00:33:19,230 OK. 692 00:33:19,230 --> 00:33:23,012 Now somebody was wondering about the speed 693 00:33:23,012 --> 00:33:24,720 that astronauts have reached, the fastest 694 00:33:24,720 --> 00:33:26,100 speed they've reached. 695 00:33:26,100 --> 00:33:28,820 Well even though it's a really, really small fraction 696 00:33:28,820 --> 00:33:32,510 of the speed of light, they have experienced noticeable time 697 00:33:32,510 --> 00:33:33,380 dilation. 698 00:33:33,380 --> 00:33:35,840 And they have traveled into the future more than us. 699 00:33:35,840 --> 00:33:40,590 I mean they've experienced less time than we've experienced. 700 00:33:40,590 --> 00:33:41,690 And I looked this up. 701 00:33:41,690 --> 00:33:45,470 The record for an astronaut traveling 702 00:33:45,470 --> 00:33:49,020 into the future, the record-- 703 00:33:49,020 --> 00:33:52,010 the amount of time that they've gained on us-- 704 00:33:52,010 --> 00:33:54,890 the record amount of time that an astronaut has gained on us 705 00:33:54,890 --> 00:33:57,200 is 1/50 of a second. 706 00:33:57,200 --> 00:34:00,470 And that's 0.02 seconds. 707 00:34:00,470 --> 00:34:04,866 And that's a very large amount of time, right? 708 00:34:04,866 --> 00:34:06,610 You have a question? 709 00:34:06,610 --> 00:34:07,265 Oh yeah. 710 00:34:07,265 --> 00:34:07,765 Yeah. 711 00:34:07,765 --> 00:34:08,265 OK. 712 00:34:08,265 --> 00:34:13,250 So there is time travel to the future for you. 713 00:34:13,250 --> 00:34:15,630 Time travel to the past. 714 00:34:15,630 --> 00:34:18,320 Is time travel to the past possible? 715 00:34:18,320 --> 00:34:19,730 Nobody disagrees about this. 716 00:34:19,730 --> 00:34:22,070 There's nothing controversial. 717 00:34:22,070 --> 00:34:22,580 OK. 718 00:34:22,580 --> 00:34:24,288 There are engineering problems with this. 719 00:34:24,288 --> 00:34:25,969 There are engineering problems with this 720 00:34:25,969 --> 00:34:29,330 but there's certainly nothing scientifically controversial 721 00:34:29,330 --> 00:34:32,671 about time traveling into the future. 722 00:34:32,671 --> 00:34:33,920 There's nothing controversial. 723 00:34:33,920 --> 00:34:37,250 However time travel into the past is more controversial. 724 00:34:37,250 --> 00:34:39,565 And I'll explain why. 725 00:34:42,830 --> 00:34:45,880 Now as far as I know, there are no ways 726 00:34:45,880 --> 00:34:50,480 that special relativity allows for time travel to the past. 727 00:34:50,480 --> 00:34:53,822 The only hopes of traveling to the past-- 728 00:34:53,822 --> 00:34:55,780 I don't have to say time traveling to the past, 729 00:34:55,780 --> 00:34:57,820 I could just say traveling to the past, right? 730 00:34:57,820 --> 00:34:59,780 The only hopes of traveling to the past 731 00:34:59,780 --> 00:35:02,160 are provided by general relativity. 732 00:35:02,160 --> 00:35:04,340 So before I can tell you what these methods are, 733 00:35:04,340 --> 00:35:07,859 I have to tell you a little bit about general relativity. 734 00:35:24,830 --> 00:35:27,920 As I said, special relativity deals only 735 00:35:27,920 --> 00:35:32,930 with observers who are inertial, only observers 736 00:35:32,930 --> 00:35:34,255 who aren't accelerating. 737 00:35:36,886 --> 00:35:38,510 It doesn't say anything about observers 738 00:35:38,510 --> 00:35:39,920 that are accelerating. 739 00:35:39,920 --> 00:35:44,090 And so you might ask, well, can we 740 00:35:44,090 --> 00:35:46,430 say anything about accelerating observers? 741 00:35:46,430 --> 00:35:48,030 I mean they're people too, right? 742 00:35:53,720 --> 00:35:54,380 OK. 743 00:35:54,380 --> 00:35:58,180 Well, Einstein felt the answer is yes. 744 00:35:58,180 --> 00:36:02,630 Yes, well certainly if we're accelerating, 745 00:36:02,630 --> 00:36:04,010 then things happen, right? 746 00:36:04,010 --> 00:36:05,186 Things in universe happen. 747 00:36:05,186 --> 00:36:07,310 But the question is, can we understand those things 748 00:36:07,310 --> 00:36:08,180 that are happening? 749 00:36:08,180 --> 00:36:10,430 Can we understand the laws that govern the things 750 00:36:10,430 --> 00:36:12,620 that we measure? 751 00:36:12,620 --> 00:36:16,820 And it turns out that discovering 752 00:36:16,820 --> 00:36:19,200 the laws of general relativity is really hard. 753 00:36:19,200 --> 00:36:20,960 It's really hard to do. 754 00:36:20,960 --> 00:36:25,100 And it took Einstein about eight years to do it, 755 00:36:25,100 --> 00:36:26,080 and he was Einstein. 756 00:36:26,080 --> 00:36:28,410 It took him eight years to do it. 757 00:36:28,410 --> 00:36:43,340 So in 1905 Einstein published a paper in which he basically 758 00:36:43,340 --> 00:36:46,310 gave you everything about special relativity in one 759 00:36:46,310 --> 00:36:47,750 paper, beautiful paper. 760 00:36:47,750 --> 00:36:50,120 In 1905, you got special relativity, 761 00:36:50,120 --> 00:36:56,030 which I'll abbreviate with SR. And after that he 762 00:36:56,030 --> 00:36:58,835 started thinking about accelerated motions 763 00:36:58,835 --> 00:37:00,460 and accelerated observers. 764 00:37:04,606 --> 00:37:06,230 He felt that the laws of physics should 765 00:37:06,230 --> 00:37:09,700 be the same for non-inertial observers. 766 00:37:09,700 --> 00:37:12,640 He felt it should be the same. 767 00:37:12,640 --> 00:37:15,390 But how might they be the same? 768 00:37:15,390 --> 00:37:23,270 Well, in 1907-- they're not really important, 769 00:37:23,270 --> 00:37:26,660 but since I'm writing them down, it wasn't until 1915-- 770 00:37:26,660 --> 00:37:31,580 that's 1915, 1916 that Einstein finally got down 771 00:37:31,580 --> 00:37:33,920 all the laws of general relativity. 772 00:37:33,920 --> 00:37:39,080 But it was in 1907 that Einstein experienced 773 00:37:39,080 --> 00:37:42,910 what he called the happiest moments of his life. 774 00:37:42,910 --> 00:37:44,647 Yes, aw. 775 00:37:44,647 --> 00:37:45,980 The happiest moment of his life. 776 00:37:49,340 --> 00:37:55,130 And it was a recognition that gravity and acceleration 777 00:37:55,130 --> 00:37:55,940 are the same thing. 778 00:37:59,400 --> 00:38:03,090 Isn't that shocking or have you guys heard that? 779 00:38:03,090 --> 00:38:04,854 Yeah, it's completely shocking. 780 00:38:04,854 --> 00:38:07,020 It's completely shocking the first time you hear it. 781 00:38:07,020 --> 00:38:12,780 And this realization is called the equivalence principle. 782 00:38:12,780 --> 00:38:15,475 And for those of you who don't-- 783 00:38:15,475 --> 00:38:17,100 it's not obvious at all why that's true 784 00:38:17,100 --> 00:38:19,423 but I'll explain in a minute why it's true. 785 00:38:19,423 --> 00:38:21,339 Well this is called the equivalence principle. 786 00:38:31,960 --> 00:38:47,170 Gravity and acceleration are the same. 787 00:38:52,970 --> 00:38:53,860 But why? 788 00:38:53,860 --> 00:38:55,850 But why on earth would this be true? 789 00:38:55,850 --> 00:39:02,090 I mean, when you think about it, why on earth should it be true? 790 00:39:02,090 --> 00:39:06,700 Well, consider the following. 791 00:39:06,700 --> 00:39:09,310 I'll give you two different situations to think about. 792 00:39:09,310 --> 00:39:13,040 And you'll see how this might be true. 793 00:39:13,040 --> 00:39:13,650 OK. 794 00:39:13,650 --> 00:39:18,010 First, say that you're on Earth, you're 795 00:39:18,010 --> 00:39:23,740 on some object that has gravity, that's 796 00:39:23,740 --> 00:39:26,260 exerting a gravitational influence on you. 797 00:39:26,260 --> 00:39:29,500 And suppose also that that object that you're standing on 798 00:39:29,500 --> 00:39:31,024 is not accelerating. 799 00:39:31,024 --> 00:39:32,440 The Earth actually is accelerating 800 00:39:32,440 --> 00:39:34,690 because it's revolving around the sun 801 00:39:34,690 --> 00:39:37,690 and it's also rotating 24 hour period 802 00:39:37,690 --> 00:39:40,030 but it's not doing that stuff very fast. 803 00:39:40,030 --> 00:39:44,170 So the Earth is approximately inertial in the language 804 00:39:44,170 --> 00:39:47,470 that I used before. 805 00:39:47,470 --> 00:39:50,742 The Earth is a pretty good inertial place. 806 00:39:50,742 --> 00:39:52,450 Suppose that we're on a place where there 807 00:39:52,450 --> 00:39:57,951 is gravity but no acceleration. 808 00:40:03,360 --> 00:40:10,097 And suppose I simply drop something. 809 00:40:13,079 --> 00:40:14,690 I drop something. 810 00:40:14,690 --> 00:40:15,770 It goes down, right? 811 00:40:15,770 --> 00:40:16,970 It just goes down. 812 00:40:16,970 --> 00:40:20,230 So that eraser is approximately a sphere 813 00:40:20,230 --> 00:40:24,320 so I'll draw it like this. 814 00:40:24,320 --> 00:40:25,465 And something goes down. 815 00:40:25,465 --> 00:40:26,340 This is what you see. 816 00:40:26,340 --> 00:40:27,673 This is supposed to be an arrow. 817 00:40:30,140 --> 00:40:33,800 Physicists like to make approximations. 818 00:40:33,800 --> 00:40:37,850 Spheres are easy to use. 819 00:40:37,850 --> 00:40:40,310 Rectangular solids are harder to use. 820 00:40:44,060 --> 00:40:48,590 A ball or an eraser would simply move downwards like this. 821 00:40:48,590 --> 00:40:49,130 OK. 822 00:40:49,130 --> 00:40:50,421 Consider another situation now. 823 00:40:53,870 --> 00:40:55,449 So you're on a rocket ship. 824 00:40:55,449 --> 00:40:56,990 You might notice that today I'm using 825 00:40:56,990 --> 00:41:00,859 a lot of rocket ship analogies and not a whole lot of trains. 826 00:41:00,859 --> 00:41:02,150 Trains are so yesterday, right? 827 00:41:07,850 --> 00:41:10,460 OK. 828 00:41:10,460 --> 00:41:15,890 Well let's say that there's a ball inside of a rocket ship. 829 00:41:15,890 --> 00:41:18,730 And the rocket ship is accelerating 830 00:41:18,730 --> 00:41:22,720 but the gravity due to the rocket is negligible. 831 00:41:22,720 --> 00:41:24,030 So it's very small. 832 00:41:24,030 --> 00:41:26,040 It's not even worth considering. 833 00:41:26,040 --> 00:41:32,100 So let's say now that we have an accelerated place, accelerated 834 00:41:32,100 --> 00:41:33,950 but no gravity. 835 00:41:38,260 --> 00:41:42,112 And I'll draw a rocket ship for you guys. 836 00:41:42,112 --> 00:41:43,570 Like I said, this is a rocket ship. 837 00:41:48,299 --> 00:41:49,090 It's a rocket ship. 838 00:41:52,510 --> 00:41:57,030 This is a rocket ship and it's accelerating upwards. 839 00:41:57,030 --> 00:41:59,020 So its speed is changing, it's going upwards 840 00:41:59,020 --> 00:42:01,330 faster and faster. 841 00:42:01,330 --> 00:42:04,950 And suppose there's a ball here that simply gets dropped. 842 00:42:04,950 --> 00:42:08,400 AUDIENCE: It won't go anywhere. 843 00:42:08,400 --> 00:42:10,420 NICHOLAS DIBELLA: Actually it does go somewhere. 844 00:42:10,420 --> 00:42:13,650 But what would you see? 845 00:42:13,650 --> 00:42:17,280 What would you see if you're inside of this rocket ship? 846 00:42:17,280 --> 00:42:19,530 What would you see the ball do? 847 00:42:19,530 --> 00:42:29,760 Well, you'd see the ball go downwards like this 848 00:42:29,760 --> 00:42:33,660 because eventually the floor reaches the ball 849 00:42:33,660 --> 00:42:36,610 and they meet eventually. 850 00:42:36,610 --> 00:42:39,760 And that's what you'd see. 851 00:42:39,760 --> 00:42:43,251 Or if I just forgot about the rocket ship, 852 00:42:43,251 --> 00:42:44,250 it would look like this. 853 00:42:47,200 --> 00:42:49,020 That almost looks like a person now. 854 00:42:49,020 --> 00:42:50,780 But it would look like this. 855 00:42:50,780 --> 00:42:56,970 Now, notice that what you see in these two cases 856 00:42:56,970 --> 00:42:58,970 looks the same, right? 857 00:42:58,970 --> 00:43:02,056 A ball moves downwards at a certain rate. 858 00:43:02,056 --> 00:43:03,680 A ball moves downward at a certain rate 859 00:43:03,680 --> 00:43:05,390 and it looks the same. 860 00:43:05,390 --> 00:43:10,060 Now Einstein's bold move was to say, well, 861 00:43:10,060 --> 00:43:11,940 if it looked the same, then I'm going 862 00:43:11,940 --> 00:43:14,010 to postulate that they actually are the same. 863 00:43:14,010 --> 00:43:16,920 I'm going a postulate that gravity and accelerated motion 864 00:43:16,920 --> 00:43:19,246 are actually the same thing. 865 00:43:19,246 --> 00:43:21,120 And that's what the equivalence principle is. 866 00:43:24,540 --> 00:43:27,660 Take a short break. 867 00:43:27,660 --> 00:43:28,200 OK. 868 00:43:28,200 --> 00:43:34,974 Now this equivalence principle, first of all, it's shocking. 869 00:43:34,974 --> 00:43:36,640 Gravity and acceleration being the same, 870 00:43:36,640 --> 00:43:38,250 wouldn't expect it at all. 871 00:43:38,250 --> 00:43:40,440 But it actually has profound implications 872 00:43:40,440 --> 00:43:42,842 on the nature of space and time. 873 00:43:42,842 --> 00:43:48,245 It implies that spacetime has to be current. 874 00:43:48,245 --> 00:43:49,620 Now what on earth does that mean? 875 00:43:49,620 --> 00:43:52,080 I'll write it down first. 876 00:43:52,080 --> 00:43:54,450 It implies that mass curves spacetime. 877 00:44:05,220 --> 00:44:06,750 OK. 878 00:44:06,750 --> 00:44:07,890 Simple sentence. 879 00:44:07,890 --> 00:44:11,720 Three words period. 880 00:44:11,720 --> 00:44:12,330 Three words. 881 00:44:12,330 --> 00:44:14,696 Do you know what mass is? 882 00:44:14,696 --> 00:44:15,570 What does curve mean? 883 00:44:15,570 --> 00:44:16,640 What does spacetime mean? 884 00:44:16,640 --> 00:44:19,845 Well, spacetime is just the entity of space and time. 885 00:44:19,845 --> 00:44:23,150 And you could think of them as a unified whole. 886 00:44:23,150 --> 00:44:24,660 I didn't actually get to telling you 887 00:44:24,660 --> 00:44:27,720 how they're actually unified but there's 888 00:44:27,720 --> 00:44:30,560 a very nice way in which they're unified, space and time. 889 00:44:30,560 --> 00:44:33,300 And we call this collective object spacetime. 890 00:44:33,300 --> 00:44:38,290 There's actually a very precise mathematical meaning 891 00:44:38,290 --> 00:44:39,609 to spacetime. 892 00:44:39,609 --> 00:44:41,400 And I don't know if any of you have studied 893 00:44:41,400 --> 00:44:43,800 differential geometry but-- 894 00:44:43,800 --> 00:44:46,690 I haven't, but spacetime is actually, 895 00:44:46,690 --> 00:44:50,910 in general relativity, a pseudo-Riemannian manifold. 896 00:44:50,910 --> 00:44:52,410 A pseudo-Riemannian manifold, that's 897 00:44:52,410 --> 00:44:55,450 just a word to impress your friends with. 898 00:44:55,450 --> 00:44:55,950 OK. 899 00:44:58,590 --> 00:44:59,240 OK. 900 00:44:59,240 --> 00:45:03,000 Now what does it mean for spacetime to be curved? 901 00:45:03,000 --> 00:45:06,120 Well before I tell you what it's like for it to be curved, 902 00:45:06,120 --> 00:45:08,910 let me tell you what's like for it not to be curved, 903 00:45:08,910 --> 00:45:10,140 for it to be flat. 904 00:45:10,140 --> 00:45:12,930 Flat spacetime is simply the spacetime 905 00:45:12,930 --> 00:45:14,610 of special relativity. 906 00:45:14,610 --> 00:45:17,820 All of the equations we've got relating length and time 907 00:45:17,820 --> 00:45:21,780 intervals, all those equations are characteristically 908 00:45:21,780 --> 00:45:24,480 called flat spacetime. 909 00:45:24,480 --> 00:45:29,490 Now the more you curve spacetime the more space 910 00:45:29,490 --> 00:45:32,040 and time will deviate from what they 911 00:45:32,040 --> 00:45:33,840 are like in special relativity, the more 912 00:45:33,840 --> 00:45:38,470 they will deviate from those formulas that I wrote down. 913 00:45:38,470 --> 00:45:43,110 Now to curve spacetime you simply need mass. 914 00:45:43,110 --> 00:45:45,780 The more mass you have at a certain place 915 00:45:45,780 --> 00:45:51,060 and a certain time, the more you'll curve spacetime. 916 00:45:51,060 --> 00:45:58,120 And there are very interesting effects 917 00:45:58,120 --> 00:46:01,270 that result from the curvature of spacetime. 918 00:46:01,270 --> 00:46:05,330 One of them is called gravitational time dilation. 919 00:46:20,260 --> 00:46:21,970 Last class I talked about time dilation 920 00:46:21,970 --> 00:46:24,580 that results from simply the relative motion 921 00:46:24,580 --> 00:46:26,140 between objects. 922 00:46:26,140 --> 00:46:30,790 But general relativity predicts another type of time dilation 923 00:46:30,790 --> 00:46:33,467 which is due to gravity or acceleration. 924 00:46:33,467 --> 00:46:35,800 But both of them really because they are the same thing. 925 00:46:39,940 --> 00:46:43,974 It predicts that time-- 926 00:46:43,974 --> 00:46:45,640 let's see, how do I want to phrase this? 927 00:46:49,060 --> 00:46:51,770 The greater the gravity the slower the time passes. 928 00:46:51,770 --> 00:46:52,645 I'll write that down. 929 00:47:16,660 --> 00:47:17,160 OK. 930 00:47:19,137 --> 00:47:20,720 Are you going to ask why this is true? 931 00:47:20,720 --> 00:47:22,230 AUDIENCE: No. 932 00:47:22,230 --> 00:47:23,060 So-- 933 00:47:23,060 --> 00:47:24,185 NICHOLAS DIBELLA: Question? 934 00:47:24,185 --> 00:47:25,800 AUDIENCE: --does that mean like time-- 935 00:47:25,800 --> 00:47:27,060 NICHOLAS DIBELLA: I'm going to describe it. 936 00:47:27,060 --> 00:47:28,185 I'm going to talk about it. 937 00:47:28,185 --> 00:47:31,160 I'm not going to write down a sentence and leave. 938 00:47:31,160 --> 00:47:31,760 OK. 939 00:47:31,760 --> 00:47:39,230 So it means that the closer you are to a massive object, 940 00:47:39,230 --> 00:47:41,210 the slower time will pass for you. 941 00:47:41,210 --> 00:47:46,377 So if I'm very close to the center of the Earth-- well, 942 00:47:46,377 --> 00:47:48,710 I'm not very close to the center of the Earth right now, 943 00:47:48,710 --> 00:47:51,812 but I'm closer to the surface of the Earth than I could be. 944 00:47:51,812 --> 00:47:53,270 So right now I'm a certain distance 945 00:47:53,270 --> 00:47:56,120 from the center of the Earth and I experience 946 00:47:56,120 --> 00:47:57,740 a certain amount of gravity. 947 00:47:57,740 --> 00:48:01,250 If I were to travel 100 miles upwards, 948 00:48:01,250 --> 00:48:02,804 then gravity would be much weaker. 949 00:48:02,804 --> 00:48:04,970 You all know that because you're simply farther away 950 00:48:04,970 --> 00:48:06,740 from the source of gravity. 951 00:48:06,740 --> 00:48:09,590 Well, according to general relativity, 952 00:48:09,590 --> 00:48:14,300 time will pass by slower for the person closer 953 00:48:14,300 --> 00:48:16,280 to the center of the gravity. 954 00:48:16,280 --> 00:48:23,850 Time will pass by slower for clocks in greater gravity. 955 00:48:23,850 --> 00:48:29,322 And this is something I was thinking about. 956 00:48:29,322 --> 00:48:30,780 I don't know about any of you guys, 957 00:48:30,780 --> 00:48:33,950 but I used to share a bunk bed with my brother 958 00:48:33,950 --> 00:48:36,980 for several years. 959 00:48:36,980 --> 00:48:41,030 And I slept on the top, he slept on the bottom. 960 00:48:41,030 --> 00:48:47,620 So he actually aged less than me during those years 961 00:48:47,620 --> 00:48:49,130 and I'm the older brother too. 962 00:48:49,130 --> 00:48:52,235 So I should have been the one aging less. 963 00:48:52,235 --> 00:48:52,930 That's unfair. 964 00:48:52,930 --> 00:48:54,340 And I didn't realize that until I 965 00:48:54,340 --> 00:48:56,090 learned about gravitational time dilation. 966 00:48:59,864 --> 00:49:01,280 Then I kicked him out of the room. 967 00:49:03,960 --> 00:49:07,400 Well, something like that happened. 968 00:49:07,400 --> 00:49:09,540 OK. 969 00:49:09,540 --> 00:49:17,410 And this happens because of this very powerful principle 970 00:49:17,410 --> 00:49:19,300 of general relativity, which is that mass 971 00:49:19,300 --> 00:49:21,400 curves space and time. 972 00:49:21,400 --> 00:49:23,590 Time intervals will be different from what 973 00:49:23,590 --> 00:49:27,370 you would expect in a special relativistic universe, 974 00:49:27,370 --> 00:49:30,436 and spatial intervals will be different. 975 00:49:30,436 --> 00:49:32,560 And that's simply what we mean by curved spacetime. 976 00:49:35,500 --> 00:49:37,410 OK. 977 00:49:37,410 --> 00:49:40,470 You can use the gravitational time dilation 978 00:49:40,470 --> 00:49:42,429 as another means for traveling into the future. 979 00:49:42,429 --> 00:49:44,053 I'll get to the past soon, don't worry. 980 00:49:44,053 --> 00:49:45,930 But you can use gravitational time dilation 981 00:49:45,930 --> 00:49:50,010 as another means for traveling into the future. 982 00:49:50,010 --> 00:49:55,360 All you need to do is find a mass of objects, 983 00:49:55,360 --> 00:49:57,016 stay near it for a while-- 984 00:49:57,016 --> 00:49:59,640 actually this isn't very massive because the earth is much more 985 00:49:59,640 --> 00:50:01,350 massive than this wall. 986 00:50:01,350 --> 00:50:07,440 But find a massive object, stay near it for a long time, 987 00:50:07,440 --> 00:50:12,900 and some amount of time will have passed by for you 988 00:50:12,900 --> 00:50:14,820 and a much longer amount of time will 989 00:50:14,820 --> 00:50:17,980 have passed by for people far away from you. 990 00:50:17,980 --> 00:50:22,650 So for example 10 years passed by for you 991 00:50:22,650 --> 00:50:25,770 whereas 100 years will pass by somebody else. 992 00:50:25,770 --> 00:50:32,310 And I can give you a fun formula to play with but I 993 00:50:32,310 --> 00:50:34,830 might be running low on time. 994 00:50:37,900 --> 00:50:40,690 OK. 995 00:50:40,690 --> 00:50:41,190 Yeah. 996 00:50:41,190 --> 00:50:42,690 I'll give you a cool formula to play 997 00:50:42,690 --> 00:50:44,010 with at the end of the class if there's time, 998 00:50:44,010 --> 00:50:45,620 but there might not be time. 999 00:50:45,620 --> 00:50:50,480 If only we could have a machine for dilating time. 1000 00:50:50,480 --> 00:50:53,620 If only we could have a time machine. 1001 00:50:53,620 --> 00:50:54,461 Question? 1002 00:50:54,461 --> 00:50:56,305 AUDIENCE: So if you live right to Mt. 1003 00:50:56,305 --> 00:50:57,230 Everest-- 1004 00:50:57,230 --> 00:50:57,330 NICHOLAS DIBELLA: I'm sorry. 1005 00:50:57,330 --> 00:50:57,880 Say that again. 1006 00:50:57,880 --> 00:50:59,838 AUDIENCE: So if you live like right next to Mt. 1007 00:50:59,838 --> 00:51:02,590 Everest, you'll have a little more-- 1008 00:51:02,590 --> 00:51:03,540 NICHOLAS DIBELLA: OK. 1009 00:51:03,540 --> 00:51:04,840 If you live next to Mt. 1010 00:51:04,840 --> 00:51:06,660 Everest, will time go slower for you? 1011 00:51:06,660 --> 00:51:08,700 You mean like if you lived next to the base of it which is very 1012 00:51:08,700 --> 00:51:09,690 massive is what you're saying? 1013 00:51:09,690 --> 00:51:10,314 AUDIENCE: Yeah. 1014 00:51:10,314 --> 00:51:11,840 NICHOLAS DIBELLA: OK. 1015 00:51:11,840 --> 00:51:12,710 Well, yeah sure. 1016 00:51:12,710 --> 00:51:14,700 Time will go by slower for you but the Earth is so much more 1017 00:51:14,700 --> 00:51:15,366 massive than Mt. 1018 00:51:15,366 --> 00:51:15,910 Everest. 1019 00:51:15,910 --> 00:51:19,560 I mean as big as Mount Everest is, the Earth is much bigger. 1020 00:51:19,560 --> 00:51:21,600 So, yeah time would go by slower for you 1021 00:51:21,600 --> 00:51:23,980 but not to a very noticeable amount. 1022 00:51:23,980 --> 00:51:26,850 I need to go next to something that's very massive, 1023 00:51:26,850 --> 00:51:29,280 something enormously massive, something 1024 00:51:29,280 --> 00:51:33,180 as massive as a black hole. 1025 00:51:37,190 --> 00:51:39,910 If we could find one or if we could make one. 1026 00:51:39,910 --> 00:51:40,480 OK. 1027 00:51:40,480 --> 00:51:42,022 I was getting to dramatic. 1028 00:51:42,022 --> 00:51:42,730 Is that readable? 1029 00:51:50,200 --> 00:51:50,700 OK. 1030 00:51:50,700 --> 00:51:51,491 It says black hole. 1031 00:51:56,380 --> 00:51:59,080 I'm sure you've all heard of black holes. 1032 00:52:01,946 --> 00:52:03,820 And maybe a lot of you know what a black hole 1033 00:52:03,820 --> 00:52:08,650 is but maybe not in the context of general relativity. 1034 00:52:08,650 --> 00:52:11,080 General relativity predicts the existence of objects 1035 00:52:11,080 --> 00:52:17,179 called black holes but so does Newtonian gravity. 1036 00:52:17,179 --> 00:52:19,720 Newtonian gravity also predicts the existence of black holes. 1037 00:52:19,720 --> 00:52:21,550 Now what is a black hole? 1038 00:52:21,550 --> 00:52:24,880 Well it's simply a region of space 1039 00:52:24,880 --> 00:52:30,010 where there is so much mass that if an object gets 1040 00:52:30,010 --> 00:52:32,470 too close to it, then there is a point 1041 00:52:32,470 --> 00:52:36,370 where if the object passes it, it simply can't return. 1042 00:52:36,370 --> 00:52:38,030 There's a point of no return. 1043 00:52:38,030 --> 00:52:41,660 And that point of no return is called the event horizon 1044 00:52:41,660 --> 00:52:43,410 if any of you have heard that word before. 1045 00:52:43,410 --> 00:52:44,660 It's called the event horizon. 1046 00:52:49,170 --> 00:52:56,680 In language of Newton massive objects 1047 00:52:56,680 --> 00:53:02,950 attract each other because there's a gravitational force. 1048 00:53:02,950 --> 00:53:07,750 And the force is a concept that's 1049 00:53:07,750 --> 00:53:10,320 used a lot in Newtonian physics. 1050 00:53:10,320 --> 00:53:14,290 It's a very useful concept but Einstein actually 1051 00:53:14,290 --> 00:53:16,590 throws that concept away. 1052 00:53:16,590 --> 00:53:20,945 In general relativity there's no need for a notion of force. 1053 00:53:20,945 --> 00:53:23,140 Everything's curvature. 1054 00:53:23,140 --> 00:53:26,030 And here's what I mean. 1055 00:53:26,030 --> 00:53:26,530 OK. 1056 00:53:28,645 --> 00:53:30,520 I'll talk more about black holes in a minute. 1057 00:53:30,520 --> 00:53:32,436 Let me just explain this thing about curvature 1058 00:53:32,436 --> 00:53:35,600 and how objects move in general relativity. 1059 00:53:35,600 --> 00:53:36,100 OK. 1060 00:53:36,100 --> 00:53:42,340 So in the Newtonian way of thinking if I drop an object, 1061 00:53:42,340 --> 00:53:45,100 it will fall down because there is 1062 00:53:45,100 --> 00:53:49,090 a gravitational attraction between the object 1063 00:53:49,090 --> 00:53:50,380 and the center of the Earth. 1064 00:53:50,380 --> 00:53:51,790 That's the direction it's moving. 1065 00:53:51,790 --> 00:53:53,140 So it falls downwards. 1066 00:53:53,140 --> 00:53:55,720 That's the direction of the force. 1067 00:53:55,720 --> 00:53:58,930 Well, general relativity has a different way 1068 00:53:58,930 --> 00:54:00,510 of describing motion. 1069 00:54:00,510 --> 00:54:02,140 It has a way of describing motion 1070 00:54:02,140 --> 00:54:06,420 by what's called geodesics. 1071 00:54:06,420 --> 00:54:09,870 And forget about that word for right now. 1072 00:54:09,870 --> 00:54:11,650 Forget about that word for right now. 1073 00:54:11,650 --> 00:54:12,580 OK. 1074 00:54:12,580 --> 00:54:13,210 OK. 1075 00:54:13,210 --> 00:54:17,350 Here's how general relativity describes motion. 1076 00:54:17,350 --> 00:54:19,720 So I have an object here, right? 1077 00:54:19,720 --> 00:54:21,512 And I'm wondering, how is it going to move? 1078 00:54:21,512 --> 00:54:22,969 You all know how it's going to move 1079 00:54:22,969 --> 00:54:25,360 but suppose you didn't know how it's going to move. 1080 00:54:25,360 --> 00:54:27,840 You can conceive of lots of different ways. 1081 00:54:27,840 --> 00:54:29,590 You can conceive of lots of different ways 1082 00:54:29,590 --> 00:54:32,350 that a given object can move. 1083 00:54:32,350 --> 00:54:34,510 It might go upwards. 1084 00:54:34,510 --> 00:54:35,050 Don't laugh. 1085 00:54:35,050 --> 00:54:37,508 You know the answer but what if you didn't know the answer. 1086 00:54:37,508 --> 00:54:38,950 It can go upwards. 1087 00:54:38,950 --> 00:54:40,300 It can go downwards. 1088 00:54:40,300 --> 00:54:40,990 Maybe? 1089 00:54:40,990 --> 00:54:42,510 It can go sideways. 1090 00:54:45,120 --> 00:54:47,910 It can go some weird curvy path. 1091 00:54:47,910 --> 00:54:50,050 It could go this way. 1092 00:54:50,050 --> 00:54:53,115 It could go this way, go this way, go this way, go this way, 1093 00:54:53,115 --> 00:54:55,240 go this way, go this way, go this way, go this way, 1094 00:54:55,240 --> 00:54:57,430 go this way, go this way, go this way, go this way, 1095 00:54:57,430 --> 00:54:59,920 go this way, go this way and then end up right there 1096 00:54:59,920 --> 00:55:01,330 and stay there. 1097 00:55:01,330 --> 00:55:03,260 That's conceivable, right? 1098 00:55:03,260 --> 00:55:06,070 It's not logically, not philosophically 1099 00:55:06,070 --> 00:55:08,260 impossible to happen. 1100 00:55:08,260 --> 00:55:12,130 You can think of that as a possibility. 1101 00:55:12,130 --> 00:55:17,620 Well, according to general relativity, first of all mass 1102 00:55:17,620 --> 00:55:20,350 tells spacetime how to curve. 1103 00:55:20,350 --> 00:55:22,470 So there's a given amount of mass here 1104 00:55:22,470 --> 00:55:24,350 and there's a given distribution of mass, 1105 00:55:24,350 --> 00:55:28,420 and it tells spacetime how to curve. 1106 00:55:28,420 --> 00:55:30,520 But how does the object move? 1107 00:55:30,520 --> 00:55:34,510 Well, spacetime tells the object how to move. 1108 00:55:34,510 --> 00:55:40,240 So mass grips spacetime, mass grips spacetime and tells it 1109 00:55:40,240 --> 00:55:41,670 how to curve. 1110 00:55:41,670 --> 00:55:47,160 And spacetime grips mass and tells it how to move. 1111 00:55:47,160 --> 00:55:51,160 That's the key idea of how general relativity works. 1112 00:55:51,160 --> 00:55:55,690 Now how exactly does spacetime tell mass how to move? 1113 00:55:55,690 --> 00:55:58,750 Well, let's think about it. 1114 00:55:58,750 --> 00:56:00,440 Well, let me explain it. 1115 00:56:00,440 --> 00:56:01,674 So there's an object here. 1116 00:56:01,674 --> 00:56:03,840 It can go this way, it can go a little bit this way, 1117 00:56:03,840 --> 00:56:05,840 go a little bit this way, a little bit this way, 1118 00:56:05,840 --> 00:56:07,400 a little bit this way. 1119 00:56:07,400 --> 00:56:10,730 But for each infinitesimal step that it makes, 1120 00:56:10,730 --> 00:56:12,880 the laws of general relativity say 1121 00:56:12,880 --> 00:56:15,220 that the object will travel in a path such 1122 00:56:15,220 --> 00:56:18,670 that the time experienced by the object 1123 00:56:18,670 --> 00:56:21,760 will be maximized or minimized. 1124 00:56:21,760 --> 00:56:25,510 One of the two, but not both. 1125 00:56:25,510 --> 00:56:30,880 When you saw for the equations of motion, only one of the two 1126 00:56:30,880 --> 00:56:32,540 will actually be a physical answer. 1127 00:56:32,540 --> 00:56:38,820 So because spacetime is curved in a very specific way 1128 00:56:38,820 --> 00:56:41,302 due to this mass, the object will 1129 00:56:41,302 --> 00:56:43,260 have aged in different ways, depending on which 1130 00:56:43,260 --> 00:56:47,760 way the object could move. 1131 00:56:47,760 --> 00:56:53,130 Well, it turns out that the object will travel downwards 1132 00:56:53,130 --> 00:56:56,730 as you all know because that's the path which gives rise 1133 00:56:56,730 --> 00:57:00,810 to maximal aging of the objects. 1134 00:57:00,810 --> 00:57:06,090 And this is simply a fact that comes out 1135 00:57:06,090 --> 00:57:09,480 of general relativity, simply what happens. 1136 00:57:09,480 --> 00:57:15,990 And objects will move to extremize their time, 1137 00:57:15,990 --> 00:57:17,130 maximize or minimize. 1138 00:57:17,130 --> 00:57:19,620 Only one of the two will actually happen. 1139 00:57:19,620 --> 00:57:20,670 OK. 1140 00:57:20,670 --> 00:57:24,230 Now to get back to black holes. 1141 00:57:24,230 --> 00:57:25,410 OK. 1142 00:57:25,410 --> 00:57:28,320 Now, as I said, in the language of Newton 1143 00:57:28,320 --> 00:57:30,610 we would say that a black hole is 1144 00:57:30,610 --> 00:57:35,370 something that's so massive that there's a point of no return. 1145 00:57:35,370 --> 00:57:36,960 Nothing can escape, not even light. 1146 00:57:39,670 --> 00:57:43,650 In the language of general relativity, 1147 00:57:43,650 --> 00:57:46,050 a black hole is a region of space 1148 00:57:46,050 --> 00:57:52,020 where the spacetime is curved so much that if an object reaches 1149 00:57:52,020 --> 00:57:54,930 this point of no return, the spacetime is simply 1150 00:57:54,930 --> 00:57:59,010 too curved for the object to get out of it. 1151 00:57:59,010 --> 00:58:01,800 It's simply too curved to get back. 1152 00:58:01,800 --> 00:58:07,650 And my shirt actually illustrates this. 1153 00:58:07,650 --> 00:58:08,250 OK. 1154 00:58:08,250 --> 00:58:15,060 So this is supposed to be a representation of a black hole. 1155 00:58:15,060 --> 00:58:16,710 Forget about this formula next to it. 1156 00:58:16,710 --> 00:58:19,209 But this is supposed to be a representation of a black hole. 1157 00:58:21,840 --> 00:58:24,540 As you get closer to the center of a black hole, 1158 00:58:24,540 --> 00:58:27,120 spacetime will get more curved. 1159 00:58:27,120 --> 00:58:31,740 The closer you get, the more curved spacetime becomes. 1160 00:58:31,740 --> 00:58:35,190 And there's a point in the center where 1161 00:58:35,190 --> 00:58:38,790 mathematically space and time actually 1162 00:58:38,790 --> 00:58:41,190 become infinitely curved. 1163 00:58:41,190 --> 00:58:44,130 And one could say, well, spacetime 1164 00:58:44,130 --> 00:58:47,580 ceases to exist at the center of a black hole. 1165 00:58:47,580 --> 00:58:49,740 And that's called the singularity of a black hole. 1166 00:58:57,220 --> 00:59:01,480 And the spacetime approaches infinite curvature 1167 00:59:01,480 --> 00:59:06,110 at the singularity because actually it's just a point 1168 00:59:06,110 --> 00:59:08,860 and there's mass contained in that point. 1169 00:59:08,860 --> 00:59:11,670 So there's actually infinite density 1170 00:59:11,670 --> 00:59:13,420 at the singularity of a black hole. 1171 00:59:22,240 --> 00:59:25,710 And this has mystified physicists for a very long time 1172 00:59:25,710 --> 00:59:27,604 because we're not sure what to make of it. 1173 00:59:27,604 --> 00:59:29,520 Whenever we see infinities crop up in physics, 1174 00:59:29,520 --> 00:59:31,061 we think well maybe there's something 1175 00:59:31,061 --> 00:59:32,340 wrong with the theory. 1176 00:59:32,340 --> 00:59:37,860 But I'll get to this point eventually. 1177 00:59:37,860 --> 00:59:39,916 Most physicists suspect that there actually 1178 00:59:39,916 --> 00:59:42,040 aren't singularities at the center of a black hole. 1179 00:59:42,040 --> 00:59:44,130 They suspect that space and time still 1180 00:59:44,130 --> 00:59:47,414 exists there but quantum effects sort of smooth 1181 00:59:47,414 --> 00:59:49,080 out the space and the time and give rise 1182 00:59:49,080 --> 00:59:52,545 to some finite amount of curvature at the center. 1183 00:59:52,545 --> 00:59:53,045 Question? 1184 00:59:53,045 --> 00:59:55,744 AUDIENCE: On average, how big is an event horizon? 1185 00:59:55,744 --> 00:59:56,910 NICHOLAS DIBELLA: Excuse me? 1186 00:59:56,910 --> 00:59:59,234 AUDIENCE: On average, how big is an event horizon? 1187 00:59:59,234 --> 01:00:01,650 NICHOLAS DIBELLA: On average, how big is an event horizon? 1188 01:00:01,650 --> 01:00:03,858 You mean how far away from the center of a black hole 1189 01:00:03,858 --> 01:00:05,520 might it be on the average? 1190 01:00:05,520 --> 01:00:07,380 AUDIENCE: How big. 1191 01:00:07,380 --> 01:00:09,540 NICHOLAS DIBELLA: Oh, how large? 1192 01:00:09,540 --> 01:00:13,680 Well, you're going to have black holes of various sizes. 1193 01:00:13,680 --> 01:00:15,780 Theoretically you could have a black hole the size 1194 01:00:15,780 --> 01:00:16,790 of a centimeter. 1195 01:00:16,790 --> 01:00:19,810 Actually, since you brought it up, 1196 01:00:19,810 --> 01:00:22,800 I'll talk about this formula on my shirt. 1197 01:00:34,091 --> 01:00:34,590 OK. 1198 01:00:34,590 --> 01:00:39,510 There's a formula that says how large a region of space 1199 01:00:39,510 --> 01:00:43,890 has to be such that a given amount of mass in that space 1200 01:00:43,890 --> 01:00:47,170 is actually enough mass to make a black hole. 1201 01:00:47,170 --> 01:00:55,170 So if I took a lot of mass and compressed it 1202 01:00:55,170 --> 01:00:57,880 so that it had a really high density, 1203 01:00:57,880 --> 01:01:04,110 then it would reach the size necessary to make a black hole. 1204 01:01:04,110 --> 01:01:08,130 At a certain radius from the center of this mass, 1205 01:01:08,130 --> 01:01:10,890 suppose it's spherical, at the center of this mass called 1206 01:01:10,890 --> 01:01:12,570 the Schwarzschild radius. 1207 01:01:12,570 --> 01:01:16,040 And there's a formula for the Schwarzschild radius. 1208 01:01:16,040 --> 01:01:20,490 Rs equals 2MG over C squared. 1209 01:01:20,490 --> 01:01:24,307 M is the mass of the object, C is the speed of light, 1210 01:01:24,307 --> 01:01:25,265 and G is like constant. 1211 01:01:29,956 --> 01:01:32,857 Well, if you're curious about it I'll explain more after class 1212 01:01:32,857 --> 01:01:34,440 but we're kind of running out of time. 1213 01:01:34,440 --> 01:01:36,106 AUDIENCE: Is that the same G Newton had? 1214 01:01:36,106 --> 01:01:37,770 NICHOLAS DIBELLA: Yeah. 1215 01:01:37,770 --> 01:01:41,610 It's the same G that appears in Newtonian gravity. 1216 01:01:41,610 --> 01:01:43,320 And you actually get the right answer 1217 01:01:43,320 --> 01:01:44,275 if you use Newtonian gravity. 1218 01:01:44,275 --> 01:01:46,149 You get the same answer in general relativity 1219 01:01:46,149 --> 01:01:52,480 and Newtonian gravity. 1220 01:01:52,480 --> 01:01:54,201 And it's interesting that that happens. 1221 01:01:54,201 --> 01:01:54,700 OK. 1222 01:02:02,515 --> 01:02:05,530 Well, just a final couple of notes on black holes. 1223 01:02:05,530 --> 01:02:06,750 Do they exist? 1224 01:02:06,750 --> 01:02:09,894 Well I've never seen one because they're black. 1225 01:02:09,894 --> 01:02:11,060 Light can't get out of them. 1226 01:02:11,060 --> 01:02:12,920 We can't actually see them but there 1227 01:02:12,920 --> 01:02:17,900 is a lot of evidence for the existence of black holes. 1228 01:02:17,900 --> 01:02:21,050 One simple piece of evidence is that we 1229 01:02:21,050 --> 01:02:24,530 see a lot of objects in the universe moving in certain ways 1230 01:02:24,530 --> 01:02:28,699 but they're moving in certain ways that indicates 1231 01:02:28,699 --> 01:02:29,990 there should be something here. 1232 01:02:29,990 --> 01:02:31,490 But if we don't see something there, 1233 01:02:31,490 --> 01:02:34,780 then well we can guess maybe it's a black hole. 1234 01:02:34,780 --> 01:02:39,740 That's one simple way of possibly indirectly detecting 1235 01:02:39,740 --> 01:02:40,860 a black hole. 1236 01:02:40,860 --> 01:02:41,590 But there are a lot of other ways too. 1237 01:02:41,590 --> 01:02:42,720 AUDIENCE: [INAUDIBLE]. 1238 01:02:45,520 --> 01:02:47,686 Why don't all the black holes come together and just 1239 01:02:47,686 --> 01:02:48,412 stay there? 1240 01:02:48,412 --> 01:02:50,370 NICHOLAS DIBELLA: Why don't all the black holes 1241 01:02:50,370 --> 01:02:51,950 simply meet up with each other, you're asking? 1242 01:02:51,950 --> 01:02:52,640 AUDIENCE: [INAUDIBLE] 1243 01:02:52,640 --> 01:02:53,360 NICHOLAS DIBELLA: Because they attract each other? 1244 01:02:53,360 --> 01:02:55,035 AUDIENCE: Yes. 1245 01:02:55,035 --> 01:02:56,980 If everything attracts everything else, 1246 01:02:56,980 --> 01:02:59,566 why is it to be [INAUDIBLE]? 1247 01:02:59,566 --> 01:03:00,440 NICHOLAS DIBELLA: OK. 1248 01:03:00,440 --> 01:03:02,270 The question is if everything attracts everything else, then 1249 01:03:02,270 --> 01:03:04,790 why isn't everything moving towards each other? 1250 01:03:04,790 --> 01:03:08,930 And that's because well, because in the early universe 1251 01:03:08,930 --> 01:03:12,180 the universe underwent massive expansion. 1252 01:03:12,180 --> 01:03:16,140 So that's-- this is a cosmology topic, 1253 01:03:16,140 --> 01:03:18,180 which will be talked about in a few weeks. 1254 01:03:18,180 --> 01:03:23,305 But the fact is that they were initially moving very fast 1255 01:03:23,305 --> 01:03:24,680 away from each other so that they 1256 01:03:24,680 --> 01:03:26,030 don't meet up with each other. 1257 01:03:26,030 --> 01:03:27,170 OK. 1258 01:03:27,170 --> 01:03:28,430 The universe is not static. 1259 01:03:28,430 --> 01:03:31,700 If the universe were static, you would eventually 1260 01:03:31,700 --> 01:03:33,847 expect for everything-- 1261 01:03:33,847 --> 01:03:34,430 is that right? 1262 01:03:34,430 --> 01:03:35,360 You can eventually expect for everything 1263 01:03:35,360 --> 01:03:36,485 to meet up with each other? 1264 01:03:36,485 --> 01:03:39,230 Anyway, this will be talked about in a few weeks. 1265 01:03:39,230 --> 01:03:41,690 General relativity also predicts the existence 1266 01:03:41,690 --> 01:03:45,020 of strange objects called wormholes. 1267 01:03:52,970 --> 01:03:54,920 And these are really strange. 1268 01:03:54,920 --> 01:03:56,930 I can't describe them in very much detail 1269 01:03:56,930 --> 01:04:02,120 but they work very simply. 1270 01:04:02,120 --> 01:04:11,150 A wormhole has two mouths, and it has a tunnel 1271 01:04:11,150 --> 01:04:12,800 connecting the two mouths. 1272 01:04:12,800 --> 01:04:21,400 Now a wormhole is a path between two regions in space. 1273 01:04:21,400 --> 01:04:24,140 But it's more than just a path between two regions of space. 1274 01:04:24,140 --> 01:04:27,510 It's a shortcut between those two regions. 1275 01:04:27,510 --> 01:04:29,870 If you find the mouth of a wormhole, 1276 01:04:29,870 --> 01:04:31,790 you go inside the mouth, you travel 1277 01:04:31,790 --> 01:04:35,670 through the throat of the wormhole, and then come out. 1278 01:04:35,670 --> 01:04:37,460 You exit through the other mouth. 1279 01:04:37,460 --> 01:04:42,950 Then you'll have taken a shortcut through space 1280 01:04:42,950 --> 01:04:46,550 to get from one region in space to another time very quickly. 1281 01:04:46,550 --> 01:04:49,591 You could beat out white in a race. 1282 01:04:49,591 --> 01:04:50,090 Question? 1283 01:04:50,090 --> 01:04:52,548 AUDIENCE: If you have a wrinkle in spacetime, [INAUDIBLE]?? 1284 01:04:55,260 --> 01:04:57,620 If you were thinking of spacetime as a flat sheet, 1285 01:04:57,620 --> 01:05:00,410 would a wormhole be-- 1286 01:05:00,410 --> 01:05:02,610 NICHOLAS DIBELLA: OK. 1287 01:05:02,610 --> 01:05:04,440 She's asking about a common way that people 1288 01:05:04,440 --> 01:05:06,984 use to represent wormholes. 1289 01:05:06,984 --> 01:05:08,400 I know what you're thinking about. 1290 01:05:08,400 --> 01:05:10,870 OK. 1291 01:05:10,870 --> 01:05:14,470 We can represent a wormhole quite simply. 1292 01:05:17,070 --> 01:05:19,570 I'll draw the representation first and then I'll explain it. 1293 01:05:22,420 --> 01:05:25,080 OK. 1294 01:05:25,080 --> 01:05:26,710 OK. 1295 01:05:26,710 --> 01:05:30,294 Suppose the universe is two dimensional. 1296 01:05:30,294 --> 01:05:31,710 There are two dimensions of space. 1297 01:05:31,710 --> 01:05:35,459 So suppose it's a flat sheet. 1298 01:05:35,459 --> 01:05:37,250 So let's suppose that this is the universe. 1299 01:05:40,020 --> 01:05:41,490 This is a piece of the universe. 1300 01:05:41,490 --> 01:05:44,493 And this is also a piece of the universe. 1301 01:05:48,152 --> 01:05:49,110 And this is a wormhole. 1302 01:05:53,240 --> 01:06:01,350 A wormhole connects two pieces of the universe in a path that 1303 01:06:01,350 --> 01:06:04,320 can conceivably be a much shorter length than the path 1304 01:06:04,320 --> 01:06:09,730 it would actually take to travel across the universe 1305 01:06:09,730 --> 01:06:12,390 to get to the other mouth of the wormhole. 1306 01:06:12,390 --> 01:06:17,130 Now this kind of diagram can be very confusing. 1307 01:06:17,130 --> 01:06:20,900 Like, what is this space over here? 1308 01:06:20,900 --> 01:06:22,740 It's the one they call hyperspace 1309 01:06:22,740 --> 01:06:25,980 but it actually isn't anything. 1310 01:06:25,980 --> 01:06:28,530 It's a fictitious element in a diagram. 1311 01:06:28,530 --> 01:06:30,210 This isn't anything. 1312 01:06:30,210 --> 01:06:34,016 It's simply a way of representing a wormhole. 1313 01:06:34,016 --> 01:06:35,640 But some people find it useful to think 1314 01:06:35,640 --> 01:06:36,890 about wormholes in this stuff. 1315 01:06:36,890 --> 01:06:38,260 Like, what does this curve mean? 1316 01:06:38,260 --> 01:06:39,730 Don't worry about it? 1317 01:06:39,730 --> 01:06:41,850 It doesn't really mean anything, doesn't really 1318 01:06:41,850 --> 01:06:43,620 mean a whole lot. 1319 01:06:43,620 --> 01:06:44,640 OK. 1320 01:06:44,640 --> 01:06:50,700 Wormholes provide a method of traveling to the past. 1321 01:06:53,480 --> 01:06:56,360 And I'll explain how it might be possible. 1322 01:07:05,950 --> 01:07:08,169 OK. 1323 01:07:08,169 --> 01:07:08,960 Here's what you do. 1324 01:07:12,646 --> 01:07:14,270 I don't actually need to draw anything. 1325 01:07:14,270 --> 01:07:15,186 I could just use that. 1326 01:07:19,430 --> 01:07:22,020 Well, I could just describe it to you. 1327 01:07:22,020 --> 01:07:23,180 OK. 1328 01:07:23,180 --> 01:07:26,180 Suppose you've somehow created a wormhole 1329 01:07:26,180 --> 01:07:28,250 between two regions in space. 1330 01:07:28,250 --> 01:07:30,980 We're not going to say how but suppose you did. 1331 01:07:30,980 --> 01:07:34,029 The actual construction process is very difficult. 1332 01:07:34,029 --> 01:07:36,320 And you might actually need a time machine to make one. 1333 01:07:36,320 --> 01:07:41,150 So some people are highly skeptical of the possibility 1334 01:07:41,150 --> 01:07:43,280 of constructing a wormhole. 1335 01:07:43,280 --> 01:07:44,990 But suppose you have constructed one. 1336 01:07:44,990 --> 01:07:48,080 Suppose you've created something capable of connecting 1337 01:07:48,080 --> 01:07:50,870 two regions in space such that you can get from one point 1338 01:07:50,870 --> 01:07:52,820 to another pretty fast. 1339 01:07:52,820 --> 01:07:55,460 Like you have a [INAUDIBLE] that's only 10 feet long 1340 01:07:55,460 --> 01:07:56,490 for instance. 1341 01:07:56,490 --> 01:07:58,430 Suppose you've created a wormhole. 1342 01:07:58,430 --> 01:08:03,624 Now the wormhole has two mouths. 1343 01:08:03,624 --> 01:08:05,540 One mouth could be next to Earth for instance. 1344 01:08:05,540 --> 01:08:10,670 Another mouth could be next to some galaxy. 1345 01:08:10,670 --> 01:08:16,479 And here's how you could use the wormhole as a time machine. 1346 01:08:16,479 --> 01:08:21,290 You first take one of the mouths and accelerate it 1347 01:08:21,290 --> 01:08:25,760 to a very high fraction of the speed of light 1348 01:08:25,760 --> 01:08:26,809 relative to the Earth. 1349 01:08:26,809 --> 01:08:27,109 OK. 1350 01:08:27,109 --> 01:08:28,025 Relative to the Earth. 1351 01:08:30,930 --> 01:08:31,430 OK. 1352 01:08:31,430 --> 01:08:35,720 So you make it go really fast and very far away 1353 01:08:35,720 --> 01:08:36,800 from the Earth. 1354 01:08:36,800 --> 01:08:40,010 And then you make it go really fast and come back 1355 01:08:40,010 --> 01:08:41,540 to the Earth. 1356 01:08:41,540 --> 01:08:45,830 So according to special relativity-- 1357 01:08:45,830 --> 01:08:48,970 and that first way of traveling through time to the future, 1358 01:08:48,970 --> 01:08:53,709 according to special relativity then the top mouth-- 1359 01:08:53,709 --> 01:08:56,000 let's suppose it was the top mouth that we accelerated, 1360 01:08:56,000 --> 01:08:57,740 the top mouth-- 1361 01:08:57,740 --> 01:09:05,010 sorry let me just bring this down, 1362 01:09:05,010 --> 01:09:11,520 the top mouth will have aged less than the bottom mouth. 1363 01:09:11,520 --> 01:09:15,850 So somebody sitting on the Earth we'll say, 1364 01:09:15,850 --> 01:09:19,200 for instance, five years have passed by for the top mouth 1365 01:09:19,200 --> 01:09:22,290 but 10 years have passed by for the bottom mouth and also 1366 01:09:22,290 --> 01:09:24,990 10 years will have passed by for Earth. 1367 01:09:24,990 --> 01:09:26,620 OK? 1368 01:09:26,620 --> 01:09:38,040 So now, for instance, the top mouth could be at the year 2005 1369 01:09:38,040 --> 01:09:40,580 and the bottom mouth could be at the year 2010, let's say. 1370 01:09:40,580 --> 01:09:41,160 OK. 1371 01:09:41,160 --> 01:09:42,705 Suppose we started at the year 2000, 1372 01:09:42,705 --> 01:09:46,319 and it took us five years to go back and forward, forward 1373 01:09:46,319 --> 01:09:47,149 and back. 1374 01:09:47,149 --> 01:09:49,060 OK. 1375 01:09:49,060 --> 01:09:54,580 Now, so this is a very confusing point what I'm about to say. 1376 01:09:54,580 --> 01:10:04,890 Now it turns out that if you're inside of the wormhole, then 1377 01:10:04,890 --> 01:10:07,860 you'll always observe clocks on the two mouths 1378 01:10:07,860 --> 01:10:09,810 to be synchronized with each other. 1379 01:10:09,810 --> 01:10:12,450 Synchronized just means that they show the same time. 1380 01:10:12,450 --> 01:10:16,320 You'll observe them to always show the same time. 1381 01:10:16,320 --> 01:10:22,710 So time connects differently depending 1382 01:10:22,710 --> 01:10:25,327 on whether you're outside of the wormhole 1383 01:10:25,327 --> 01:10:26,910 or whether you're inside the wormhole. 1384 01:10:26,910 --> 01:10:30,594 If you're outside the wormhole, then the clocks 1385 01:10:30,594 --> 01:10:32,760 at the mouth of the wormhole and the bottom wormhole 1386 01:10:32,760 --> 01:10:33,850 do not have to be synchronized. 1387 01:10:33,850 --> 01:10:35,308 They don't have to be synchronized. 1388 01:10:35,308 --> 01:10:38,550 But it's a consequence of chugging 1389 01:10:38,550 --> 01:10:41,534 through the equations of general relativity 1390 01:10:41,534 --> 01:10:43,200 that if you're inside the wormhole, then 1391 01:10:43,200 --> 01:10:45,690 you'll always observe clocks at the top and the bottom 1392 01:10:45,690 --> 01:10:47,160 to be synchronized. 1393 01:10:47,160 --> 01:10:52,150 So if you've accelerated the top mouth of the wormhole 1394 01:10:52,150 --> 01:10:54,150 to an appreciable fraction of the speed of light 1395 01:10:54,150 --> 01:10:57,000 and then you brought it back, then it 1396 01:10:57,000 --> 01:10:58,760 could be, for instance, the year 2005. 1397 01:10:58,760 --> 01:11:02,190 I'll write this-- could be the year 2005 here 1398 01:11:02,190 --> 01:11:04,020 and the year 2010 here. 1399 01:11:04,020 --> 01:11:06,240 Actually this is probably far off in the future, 1400 01:11:06,240 --> 01:11:12,720 so let's say 3010 and 3005. 1401 01:11:12,720 --> 01:11:13,650 Go ahead. 1402 01:11:13,650 --> 01:11:14,317 OK. 1403 01:11:14,317 --> 01:11:15,150 So you've done this. 1404 01:11:15,150 --> 01:11:15,620 OK. 1405 01:11:15,620 --> 01:11:17,860 You've done the acceleration and you've brought it back. 1406 01:11:17,860 --> 01:11:18,360 OK. 1407 01:11:18,360 --> 01:11:21,890 Now say you go inside the wormhole. 1408 01:11:21,890 --> 01:11:22,494 OK. 1409 01:11:22,494 --> 01:11:23,410 Starting from the top. 1410 01:11:23,410 --> 01:11:28,620 It's 3005 for you, and you go inside the wormhole. 1411 01:11:28,620 --> 01:11:30,570 So your clock initially says 3005. 1412 01:11:30,570 --> 01:11:35,220 Well, if you go inside the wormhole, 1413 01:11:35,220 --> 01:11:39,510 then you have to observe the clocks at both mouths 1414 01:11:39,510 --> 01:11:40,500 to be synchronized. 1415 01:11:40,500 --> 01:11:41,700 You have to. 1416 01:11:41,700 --> 01:11:46,380 I can't really explain why because you 1417 01:11:46,380 --> 01:11:48,150 have to go through the general relativity 1418 01:11:48,150 --> 01:11:50,316 to get at that result. I don't know of an easier way 1419 01:11:50,316 --> 01:11:53,010 to explain how it has to be why, why it has to be true. 1420 01:11:53,010 --> 01:11:55,410 But you go inside the wormhole and the two clocks 1421 01:11:55,410 --> 01:11:56,670 have to be synchronized. 1422 01:11:56,670 --> 01:12:02,050 So if you started at the top, it's 3005 for you. 1423 01:12:02,050 --> 01:12:07,500 Then when you exit out of the bottom, it's 3005 again. 1424 01:12:07,500 --> 01:12:10,080 It's 3005 again. 1425 01:12:10,080 --> 01:12:16,320 So it's now 3005 at the bottom of the wormhole for you. 1426 01:12:16,320 --> 01:12:20,460 And you can travel back to Earth, 1427 01:12:20,460 --> 01:12:24,380 and well, it will be 3005 again on Earth. 1428 01:12:24,380 --> 01:12:29,820 But you'll have traveled back in time via a wormhole 1429 01:12:29,820 --> 01:12:33,210 by this construction, this method which 1430 01:12:33,210 --> 01:12:36,380 is very hard to understand, very hard to prove. 1431 01:12:36,380 --> 01:12:38,130 And I can't really give a good explanation 1432 01:12:38,130 --> 01:12:46,430 for why it works other than very, very smart physicists, 1433 01:12:46,430 --> 01:12:49,800 who know a lot more than I do, have worked it out 1434 01:12:49,800 --> 01:12:52,670 and have come at this results. 1435 01:12:52,670 --> 01:12:55,460 One second, one second. 1436 01:12:55,460 --> 01:12:57,240 So the way I've just described, you 1437 01:12:57,240 --> 01:12:59,430 can use wormholes as time machines. 1438 01:12:59,430 --> 01:12:59,970 OK? 1439 01:12:59,970 --> 01:13:02,820 But you can't actually use a wormhole 1440 01:13:02,820 --> 01:13:05,310 to travel farther in the past than when 1441 01:13:05,310 --> 01:13:06,760 the wormhole was created. 1442 01:13:06,760 --> 01:13:09,920 So if the wormhole was created in the year 3000, 1443 01:13:09,920 --> 01:13:14,940 then you can't travel to the year 2007. 1444 01:13:14,940 --> 01:13:16,900 And why? 1445 01:13:20,070 --> 01:13:25,860 Well simply because you can only get 1446 01:13:25,860 --> 01:13:29,430 to the time of the accelerated mouth of the wormhole. 1447 01:13:29,430 --> 01:13:32,550 And the fact that you can't create this wormhole time 1448 01:13:32,550 --> 01:13:35,790 machine to get you to a farther past 1449 01:13:35,790 --> 01:13:38,370 than when you created the time machine 1450 01:13:38,370 --> 01:13:43,920 is an interesting answer to a very important question 1451 01:13:43,920 --> 01:13:45,510 posed by Stephen Hawking. 1452 01:13:45,510 --> 01:13:48,480 Which is that, if time travel is possible, 1453 01:13:48,480 --> 01:13:51,840 then where are all of the time travel tourists, right? 1454 01:13:51,840 --> 01:13:53,250 Where are they? 1455 01:13:53,250 --> 01:13:55,050 And this provides an explanation. 1456 01:13:55,050 --> 01:13:58,350 It's simply that no time machine has been constructed yet 1457 01:13:58,350 --> 01:14:02,040 so none of the time travelers have been 1458 01:14:02,040 --> 01:14:05,180 able to travel to our time. 1459 01:14:05,180 --> 01:14:05,680 Question? 1460 01:14:05,680 --> 01:14:07,840 AUDIENCE: How would you make a wormhole? 1461 01:14:07,840 --> 01:14:10,521 NICHOLAS DIBELLA: I told you, it's really a complicated. 1462 01:14:10,521 --> 01:14:11,020 Question? 1463 01:14:11,020 --> 01:14:12,936 AUDIENCE: Is it safe to go through a wormhole? 1464 01:14:12,936 --> 01:14:13,840 NICHOLAS DIBELLA: Oh. 1465 01:14:13,840 --> 01:14:15,910 Is it safe to go through a wormhole? 1466 01:14:15,910 --> 01:14:18,940 Well, it turns out that wormholes 1467 01:14:18,940 --> 01:14:21,560 are highly unstable objects. 1468 01:14:21,560 --> 01:14:25,510 And the moment you get inside one, a wormhole 1469 01:14:25,510 --> 01:14:32,235 will very, very quickly form a singularity inside of it. 1470 01:14:32,235 --> 01:14:34,110 So space and time will cease to exist for you 1471 01:14:34,110 --> 01:14:35,568 and you'll be crushed and so forth. 1472 01:14:40,970 --> 01:14:43,300 But a wormhole can be stabilized if you've 1473 01:14:43,300 --> 01:14:46,850 got some exotic matter. 1474 01:14:46,850 --> 01:14:50,230 But any exotic matter is you get matter 1475 01:14:50,230 --> 01:14:53,440 with effectively negative mass. 1476 01:14:59,770 --> 01:15:01,700 It's really crazy to think about, 1477 01:15:01,700 --> 01:15:03,940 but actually some particle physics theories 1478 01:15:03,940 --> 01:15:07,930 predict the existence of some negative mass particles 1479 01:15:07,930 --> 01:15:11,360 that, for example, have to be present in the early universe. 1480 01:15:11,360 --> 01:15:13,240 And so it could be that in the early universe 1481 01:15:13,240 --> 01:15:15,120 there were a lot of time machines 1482 01:15:15,120 --> 01:15:17,470 present, a lot of wormholes, a lot of black holes, 1483 01:15:17,470 --> 01:15:20,770 lots of crazy stuff. 1484 01:15:20,770 --> 01:15:22,990 So is time travel possible? 1485 01:15:22,990 --> 01:15:25,000 Well, to the future, certainly. 1486 01:15:25,000 --> 01:15:26,410 Nobody disagrees about that. 1487 01:15:26,410 --> 01:15:30,800 To the past, maybe. 1488 01:15:30,800 --> 01:15:32,580 We're not so sure about that. 1489 01:15:32,580 --> 01:15:37,640 But to the future certainly we're traveling in the future. 1490 01:15:37,640 --> 01:15:41,590 And it's always fun to think about.