1 00:00:00,060 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,620 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,620 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:20,537 --> 00:00:22,370 NICHOLAS DIBELLA: So this is the fifth week. 9 00:00:22,370 --> 00:00:25,160 I guess it's about halfway over now, the class, 10 00:00:25,160 --> 00:00:27,000 HSSP for the summer. 11 00:00:27,000 --> 00:00:27,500 Thanks. 12 00:00:31,320 --> 00:00:34,754 I know we looked at some-- oh, question? 13 00:00:34,754 --> 00:00:37,172 AUDIENCE: [INAUDIBLE] 14 00:00:37,172 --> 00:00:39,630 NICHOLAS DIBELLA: Yeah, you can get it at the end of class, 15 00:00:39,630 --> 00:00:40,296 or at the break. 16 00:00:43,080 --> 00:00:46,210 OK, so we've looked at some big question 17 00:00:46,210 --> 00:00:49,330 so far in the past four weeks. 18 00:00:49,330 --> 00:00:52,230 Most of these have concerned the whole universe. 19 00:00:52,230 --> 00:00:54,000 Did the universe have a beginning? 20 00:00:54,000 --> 00:00:55,590 Will the universe have an end? 21 00:00:55,590 --> 00:00:57,240 Is the universe infinite? 22 00:00:57,240 --> 00:00:59,610 Are there parallel universes? 23 00:00:59,610 --> 00:01:03,570 Is there other intelligent life in the universe besides us? 24 00:01:03,570 --> 00:01:07,920 And these are some pretty big questions, I think. 25 00:01:07,920 --> 00:01:10,350 Today, I would like to change the subject 26 00:01:10,350 --> 00:01:16,940 and discuss the nature of space and time, particularly time 27 00:01:16,940 --> 00:01:20,670 and whether the possibility of time travel is possible. 28 00:01:20,670 --> 00:01:23,040 So that's what we'll talk about today. 29 00:01:23,040 --> 00:01:24,810 Now, time travel is certainly something 30 00:01:24,810 --> 00:01:27,570 we've all thought about before, probably 31 00:01:27,570 --> 00:01:32,010 somebody we've all wished for at some time. 32 00:01:32,010 --> 00:01:35,130 I mean, how many of us would like to go back to the '60s, 33 00:01:35,130 --> 00:01:37,440 and see the Beatles, or something like that? 34 00:01:37,440 --> 00:01:39,450 Yeah, that would be great, right? 35 00:01:39,450 --> 00:01:41,350 Or maybe go back-- 36 00:01:41,350 --> 00:01:44,794 AUDIENCE: [INAUDIBLE] 37 00:01:47,060 --> 00:01:48,720 NICHOLAS DIBELLA: OK, yeah, I mean, 38 00:01:48,720 --> 00:01:51,629 certainly the past would be fun to see, but the future as well. 39 00:01:51,629 --> 00:01:53,670 Yeah, it would be cool to know what technology is 40 00:01:53,670 --> 00:01:59,750 like in 7,000 years from now. 41 00:01:59,750 --> 00:02:05,040 We've only been really engaged in modern technology 42 00:02:05,040 --> 00:02:07,820 just for the past 200 years or. 43 00:02:07,820 --> 00:02:10,560 Imagine what technology will be like in 7,000 years, or 10,000 44 00:02:10,560 --> 00:02:12,036 years, or a million years. 45 00:02:12,036 --> 00:02:13,410 So there are all sorts of reasons 46 00:02:13,410 --> 00:02:16,470 for wanting to go to the future, all sorts of reasons wanting 47 00:02:16,470 --> 00:02:17,840 to go to the past. 48 00:02:17,840 --> 00:02:21,390 Maybe I said something yesterday that I wish I didn't say. 49 00:02:21,390 --> 00:02:24,600 It would be nice to fix it so I'm not 50 00:02:24,600 --> 00:02:26,160 as distressed as I am today. 51 00:02:26,160 --> 00:02:29,230 So there's all sorts of reasons for wanting time travel. 52 00:02:29,230 --> 00:02:31,410 And just from a scientific perspective, 53 00:02:31,410 --> 00:02:33,720 it's interesting to know if it's possible. 54 00:02:33,720 --> 00:02:37,780 Is it physically possible to travel through time? 55 00:02:37,780 --> 00:02:41,910 So to really get a hold of these questions, 56 00:02:41,910 --> 00:02:43,980 we have to understand what time is. 57 00:02:43,980 --> 00:02:46,650 So what is time? 58 00:02:46,650 --> 00:02:50,006 Can anybody give a definition for what time is? 59 00:02:50,006 --> 00:02:50,902 Yeah? 60 00:02:50,902 --> 00:02:53,150 AUDIENCE: Something that ticks. 61 00:02:53,150 --> 00:02:55,440 NICHOLAS DIBELLA: Something that ticks. 62 00:02:55,440 --> 00:02:57,670 That's a really good definition, actually. 63 00:02:57,670 --> 00:03:00,200 That's a really good definition. 64 00:03:00,200 --> 00:03:03,050 Well, not something that ticks, but the thing that's 65 00:03:03,050 --> 00:03:04,880 responsible for the ticking. 66 00:03:04,880 --> 00:03:06,610 That's probably a better definition. 67 00:03:06,610 --> 00:03:08,600 But, yeah, that's a pretty good definition 68 00:03:08,600 --> 00:03:12,250 to define in terms of things that happen. 69 00:03:12,250 --> 00:03:14,660 Anybody else have a definition for what time is? 70 00:03:17,890 --> 00:03:19,640 Yeah? 71 00:03:19,640 --> 00:03:23,220 AUDIENCE: It's an infinite one way flow of events in history. 72 00:03:23,220 --> 00:03:24,970 NICHOLAS DIBELLA: An infinite one way flow 73 00:03:24,970 --> 00:03:26,890 of events in history. 74 00:03:26,890 --> 00:03:27,546 OK. 75 00:03:27,546 --> 00:03:29,250 AUDIENCE: [INAUDIBLE] 76 00:03:29,250 --> 00:03:30,490 NICHOLAS DIBELLA: Yeah, if it's a one way flow, that would 77 00:03:30,490 --> 00:03:31,760 imply that you can't go back. 78 00:03:31,760 --> 00:03:34,290 But at least it seems to flow in one direction. 79 00:03:34,290 --> 00:03:36,310 There seems to be an arrow in time. 80 00:03:36,310 --> 00:03:38,950 Yeah, it actually turns out to be really 81 00:03:38,950 --> 00:03:40,940 hard to define what time is. 82 00:03:40,940 --> 00:03:44,470 And it's much easier to define how time operates, 83 00:03:44,470 --> 00:03:47,310 like in terms of how it acts on things. 84 00:03:47,310 --> 00:03:50,630 So if I look at a clock, I see a ticking, 85 00:03:50,630 --> 00:03:52,260 then I can say, well, time is acting. 86 00:03:52,260 --> 00:03:54,460 Time is responsible for the ticking. 87 00:03:54,460 --> 00:03:57,310 And that's a much easier way to define time. 88 00:03:57,310 --> 00:03:58,266 Yeah? 89 00:03:58,266 --> 00:04:01,620 AUDIENCE: [INAUDIBLE] 90 00:04:04,397 --> 00:04:05,730 NICHOLAS DIBELLA: Time doesn't-- 91 00:04:05,730 --> 00:04:10,080 AUDIENCE: Time doesn't actually [INAUDIBLE] 92 00:04:12,705 --> 00:04:15,750 We are the ones that are actually aging. 93 00:04:15,750 --> 00:04:18,990 So everything is happening 94 00:04:18,990 --> 00:04:20,388 [INTERPOSING VOICES] 95 00:04:20,388 --> 00:04:23,746 AUDIENCE: Because we can [INAUDIBLE] or change. 96 00:04:23,746 --> 00:04:26,560 It's us [INAUDIBLE] time itself. 97 00:04:26,560 --> 00:04:28,540 NICHOLAS DIBELLA: So time doesn't flow. 98 00:04:28,540 --> 00:04:32,630 We flow through time. 99 00:04:32,630 --> 00:04:39,610 Yeah, I'll talk about time. 100 00:04:39,610 --> 00:04:42,410 Yeah, that's certainly one way of looking at time. 101 00:04:42,410 --> 00:04:42,910 Yes? 102 00:04:42,910 --> 00:04:45,520 AUDIENCE: Doesn't time stop in black holes? 103 00:04:45,520 --> 00:04:48,780 NICHOLAS DIBELLA: Doesn't time stop in black holes? 104 00:04:48,780 --> 00:04:51,460 In a sense. 105 00:04:51,460 --> 00:04:53,730 But it would take me about three minutes 106 00:04:53,730 --> 00:04:56,330 to explain that in a sense. 107 00:04:56,330 --> 00:05:03,180 So I'll get to this later, how gravity actually affects time. 108 00:05:03,180 --> 00:05:08,250 So the theory that we have today that 109 00:05:08,250 --> 00:05:10,770 explains the nature of space and time 110 00:05:10,770 --> 00:05:13,840 is Einstein's theory of relativity. 111 00:05:13,840 --> 00:05:18,762 But before relativity, the way that people thought of time 112 00:05:18,762 --> 00:05:20,220 was the way that Newton essentially 113 00:05:20,220 --> 00:05:21,760 proposed the think of time. 114 00:05:21,760 --> 00:05:24,330 So the way Isaac Newton thought of time 115 00:05:24,330 --> 00:05:29,200 was he thought of space and time as absolutes. 116 00:05:41,650 --> 00:05:44,380 And here's what I mean by absolute. 117 00:05:44,380 --> 00:05:49,720 So space is this thing that all the events of the universe 118 00:05:49,720 --> 00:05:50,650 happen inside of. 119 00:05:50,650 --> 00:05:51,911 It's like a stage. 120 00:05:51,911 --> 00:05:52,660 It's a background. 121 00:05:52,660 --> 00:05:55,660 Space is the background in which things happen. 122 00:05:55,660 --> 00:05:59,140 And time is just this thing that's responsible-- 123 00:05:59,140 --> 00:06:05,470 it's just this thing that continually flows in space. 124 00:06:05,470 --> 00:06:06,850 Things happen in time. 125 00:06:06,850 --> 00:06:09,280 Time is also like a background. 126 00:06:09,280 --> 00:06:11,330 It's always ticking everywhere. 127 00:06:11,330 --> 00:06:13,360 And according to Newton, space and time 128 00:06:13,360 --> 00:06:15,340 are completely separate things. 129 00:06:15,340 --> 00:06:17,980 And they're completely independent of all the objects 130 00:06:17,980 --> 00:06:19,310 in the universe. 131 00:06:19,310 --> 00:06:21,040 So I don't affect time. 132 00:06:21,040 --> 00:06:23,356 You don't affect time. 133 00:06:23,356 --> 00:06:24,230 I don't affect space. 134 00:06:24,230 --> 00:06:25,314 You don't affect space. 135 00:06:25,314 --> 00:06:26,980 They're these completely separate things 136 00:06:26,980 --> 00:06:27,990 that exist out there. 137 00:06:27,990 --> 00:06:32,210 We can't affect it in any kind of way. 138 00:06:32,210 --> 00:06:37,270 And I can ask I can ask questions like, how does 139 00:06:37,270 --> 00:06:38,750 my time compare to your time? 140 00:06:38,750 --> 00:06:40,900 Or how does my space compare to your space? 141 00:06:40,900 --> 00:06:44,740 And when I say space, I'm not just referring to outer space. 142 00:06:44,740 --> 00:06:46,790 I'm referring to just locations. 143 00:06:46,790 --> 00:06:48,140 I mean, we're in space. 144 00:06:48,140 --> 00:06:49,520 This is one point in space. 145 00:06:49,520 --> 00:06:50,470 This is another point in space. 146 00:06:50,470 --> 00:06:51,910 That's just what I mean by space. 147 00:06:51,910 --> 00:06:54,637 I am not necessarily referring to outer space. 148 00:06:54,637 --> 00:06:55,720 But you can ask questions. 149 00:06:55,720 --> 00:06:58,270 Like suppose two events happened. 150 00:06:58,270 --> 00:07:01,480 Suppose lightning strikes, and then a baby cries, 151 00:07:01,480 --> 00:07:03,130 two things happen. 152 00:07:03,130 --> 00:07:08,830 You can ask, what's the duration between the two events? 153 00:07:08,830 --> 00:07:11,710 So suppose I had a clock, or a stopwatch. 154 00:07:11,710 --> 00:07:15,850 And I just timed how long it takes before the baby cries 155 00:07:15,850 --> 00:07:17,320 after the lightning strikes. 156 00:07:17,320 --> 00:07:19,865 And maybe I'll get something like five seconds. 157 00:07:19,865 --> 00:07:21,990 Then I can ask the question, well, what do you get? 158 00:07:21,990 --> 00:07:24,560 Suppose you were to do the same simple experiment. 159 00:07:24,560 --> 00:07:26,909 Suppose you took out a watch, and you also timed it. 160 00:07:26,909 --> 00:07:27,700 What would you get? 161 00:07:30,790 --> 00:07:34,270 What would you get if you were traveling at some speed, 162 00:07:34,270 --> 00:07:37,120 according to me, or if you're flying, or something like that? 163 00:07:37,120 --> 00:07:41,440 Well, according to Newton, according to his absolute time, 164 00:07:41,440 --> 00:07:44,770 everybody would get the same time interval between the two 165 00:07:44,770 --> 00:07:46,659 events. 166 00:07:46,659 --> 00:07:48,700 Also, if you measure the distance between the two 167 00:07:48,700 --> 00:07:51,490 events, maybe I'll measure the lightning 168 00:07:51,490 --> 00:07:55,279 to strike two miles away, and the baby cries right over here. 169 00:07:55,279 --> 00:07:55,945 What do you get? 170 00:07:55,945 --> 00:07:58,750 Do you get two miles? 171 00:07:58,750 --> 00:07:59,959 Do you get some other number? 172 00:07:59,959 --> 00:08:01,291 Does it matter if you're flying? 173 00:08:01,291 --> 00:08:03,100 Or does it matter if you're traveling some 174 00:08:03,100 --> 00:08:06,580 Well, according to Newton, space and time are absolutes. 175 00:08:06,580 --> 00:08:10,491 And that means that we all agree on these time intervals 176 00:08:10,491 --> 00:08:10,990 that we get. 177 00:08:10,990 --> 00:08:12,739 We all agree on these lengths that we get. 178 00:08:15,820 --> 00:08:17,770 It's a very common sense idea. 179 00:08:17,770 --> 00:08:19,240 Why should it be any different? 180 00:08:19,240 --> 00:08:22,690 That would be crazy, right? 181 00:08:22,690 --> 00:08:24,760 Well, it turns out that nature is crazy, 182 00:08:24,760 --> 00:08:28,940 because, in fact, space and time aren't absolute. 183 00:08:28,940 --> 00:08:35,110 So about 100 years ago or so-- 184 00:08:35,110 --> 00:08:35,920 what's that? 185 00:08:35,920 --> 00:08:38,930 AUDIENCE: [INAUDIBLE] 186 00:08:41,496 --> 00:08:42,954 NICHOLAS DIBELLA: It turns out, no. 187 00:08:42,954 --> 00:08:45,340 And I'm going to explain that. 188 00:08:45,340 --> 00:08:47,560 So at the beginning of the last century, 189 00:08:47,560 --> 00:08:50,800 at the beginning of the 1900s, people 190 00:08:50,800 --> 00:08:53,730 started noticing some things, some phenomena 191 00:08:53,730 --> 00:08:56,590 that happened in the world, that Newton's theory just 192 00:08:56,590 --> 00:09:01,330 has a hard time explaining, or else just can't explain at all. 193 00:09:01,330 --> 00:09:03,730 And so Newton's theory was kind of in trouble. 194 00:09:03,730 --> 00:09:05,720 And people had tried to fix the theory, tried 195 00:09:05,720 --> 00:09:07,270 to think of ways of getting around it 196 00:09:07,270 --> 00:09:09,490 to make the theory work. 197 00:09:09,490 --> 00:09:12,466 I won't go into the details of this. 198 00:09:12,466 --> 00:09:16,480 This will have to wait for maybe two weeks from today. 199 00:09:16,480 --> 00:09:19,600 But for now, just know that Newton's theory was in trouble. 200 00:09:19,600 --> 00:09:20,590 It was in trouble. 201 00:09:20,590 --> 00:09:22,540 It had a problem. 202 00:09:22,540 --> 00:09:25,690 And finally, somebody came along, 203 00:09:25,690 --> 00:09:31,560 and fixed these problems, found a way to solve these problems. 204 00:09:31,560 --> 00:09:34,390 And that was Einstein, when he proposed his theory 205 00:09:34,390 --> 00:09:36,140 of special relativity. 206 00:09:36,140 --> 00:09:39,870 So, eventually special relativity came around. 207 00:09:49,640 --> 00:09:51,610 And it fixed all these problems. 208 00:09:51,610 --> 00:09:54,410 It's actually a very simple theory. 209 00:09:54,410 --> 00:09:56,600 It's just based on two fundamental principles, 210 00:09:56,600 --> 00:09:58,670 two fundamental postulates we call them. 211 00:10:01,290 --> 00:10:05,000 A postulate means it's something that it's totally fundamental. 212 00:10:05,000 --> 00:10:06,080 You can't derive it. 213 00:10:06,080 --> 00:10:07,550 You can't justify it. 214 00:10:07,550 --> 00:10:08,780 It just is. 215 00:10:08,780 --> 00:10:10,910 It doesn't make any sense to ask why it is. 216 00:10:10,910 --> 00:10:12,530 It just is. 217 00:10:12,530 --> 00:10:15,320 So the first postulate of special relativity 218 00:10:15,320 --> 00:10:21,525 is that the laws of physics are the same for everybody. 219 00:10:40,197 --> 00:10:42,530 I'll explain in a minute why I have everybody in quotes. 220 00:10:45,910 --> 00:10:48,730 The second postulate is that the speed of light 221 00:10:48,730 --> 00:10:50,223 is the same for everybody. 222 00:11:05,950 --> 00:11:10,250 OK, now, when I say everybody, I don't really mean everybody. 223 00:11:10,250 --> 00:11:12,850 I have some particular type of everybody in mind. 224 00:11:12,850 --> 00:11:15,100 So when I say everybody, I mean everybody 225 00:11:15,100 --> 00:11:17,350 that's moving at some constant velocity, 226 00:11:17,350 --> 00:11:19,340 or some constant speed. 227 00:11:19,340 --> 00:11:23,170 So if I'm walking at two miles per hour, 228 00:11:23,170 --> 00:11:25,570 if my speed is not changing then I'm 229 00:11:25,570 --> 00:11:28,000 moving at a constant velocity. 230 00:11:28,000 --> 00:11:31,060 And I would be the type of everybody 231 00:11:31,060 --> 00:11:32,637 that special relativity refers to. 232 00:11:32,637 --> 00:11:33,970 I'm called an inertial observer. 233 00:11:33,970 --> 00:11:36,610 But that's just a word. 234 00:11:36,610 --> 00:11:39,910 If I'm at rest, if I'm not moving at all to you guys, 235 00:11:39,910 --> 00:11:42,010 then I'm also moving at a constant speed. 236 00:11:42,010 --> 00:11:44,410 So I would also be a valid observer. 237 00:11:44,410 --> 00:11:46,450 But if I start at rest, and then start 238 00:11:46,450 --> 00:11:49,420 walking faster, and faster, and faster, and faster, then 239 00:11:49,420 --> 00:11:50,770 my speed is gradually changed. 240 00:11:50,770 --> 00:11:51,770 And so I've accelerated. 241 00:11:51,770 --> 00:11:53,730 I would be an accelerated observer. 242 00:11:53,730 --> 00:11:55,850 I would be a non-inertial observer. 243 00:11:55,850 --> 00:11:58,210 So then special relativity wouldn't apply to me. 244 00:11:58,210 --> 00:12:00,250 And you actually need general relativity, 245 00:12:00,250 --> 00:12:03,040 which is the extension of special relativity 246 00:12:03,040 --> 00:12:05,050 to take into account accelerated observers. 247 00:12:05,050 --> 00:12:08,670 But I'll talk about general relativity later. 248 00:12:08,670 --> 00:12:13,420 So the first postulate is very simple, very easy to accept. 249 00:12:13,420 --> 00:12:16,220 The laws of physics are the same for everybody. 250 00:12:16,220 --> 00:12:17,890 I mean, that's easy to accept. 251 00:12:17,890 --> 00:12:18,970 Nature is fair. 252 00:12:18,970 --> 00:12:21,860 We all obey the same laws of physics. 253 00:12:21,860 --> 00:12:27,970 So if I drop the chalk, gravity will act in a certain way. 254 00:12:27,970 --> 00:12:30,880 The law of gravity acts in a certain way. 255 00:12:30,880 --> 00:12:35,770 And it shouldn't matter whether I'm dropping the chalk, 256 00:12:35,770 --> 00:12:38,260 or whether you're dropping the chalk. 257 00:12:38,260 --> 00:12:40,120 The same law of gravity will work 258 00:12:40,120 --> 00:12:41,830 for both of us, the same law. 259 00:12:41,830 --> 00:12:44,269 It shouldn't matter if you're standing still, 260 00:12:44,269 --> 00:12:46,060 or if you're moving at some constant speed. 261 00:12:46,060 --> 00:12:47,560 The law of gravity will be the same. 262 00:12:47,560 --> 00:12:49,820 And all the other laws will be the same. 263 00:12:49,820 --> 00:12:52,180 That's just what the first postulate says. 264 00:12:52,180 --> 00:12:56,570 The second postulate is weird. 265 00:12:56,570 --> 00:12:57,820 The second postulate is weird. 266 00:13:00,470 --> 00:13:03,230 And to demonstrate why it's weird, 267 00:13:03,230 --> 00:13:07,040 I need a volunteer, just a very simple experiment. 268 00:13:07,040 --> 00:13:08,240 It will take two minutes. 269 00:13:11,350 --> 00:13:15,410 You're closer, so OK. 270 00:13:15,410 --> 00:13:18,509 OK, so do you know how to walk? 271 00:13:18,509 --> 00:13:19,300 AUDIENCE: Probably. 272 00:13:19,300 --> 00:13:22,870 NICHOLAS DIBELLA: OK, so let's start over here. 273 00:13:22,870 --> 00:13:24,450 We're going to walk across the room. 274 00:13:24,450 --> 00:13:26,710 And I'm going to ask you to walk about half my speed. 275 00:13:26,710 --> 00:13:29,120 Actually, let me walk over here. 276 00:13:29,120 --> 00:13:31,210 I'm going to ask you to walk about half my speed. 277 00:13:39,098 --> 00:13:41,080 You can keep walking. 278 00:13:41,080 --> 00:13:42,080 What's that? 279 00:13:42,080 --> 00:13:43,557 AUDIENCE: [INAUDIBLE] 280 00:13:43,557 --> 00:13:46,140 NICHOLAS DIBELLA: OK, he should have been halfway across here. 281 00:13:46,140 --> 00:13:47,220 Let's assume that he was. 282 00:13:47,220 --> 00:13:51,280 Let's assume he was a competent volunteer. 283 00:13:51,280 --> 00:13:53,490 OK, so how fast would you say I was walking? 284 00:13:56,060 --> 00:13:58,670 Pretty slow, let's say two miles per hour. 285 00:13:58,670 --> 00:14:00,880 And so he was walking one miles per hour. 286 00:14:00,880 --> 00:14:05,010 OK, that's the speed that you guys measured, right? 287 00:14:05,010 --> 00:14:06,030 I was walking two. 288 00:14:06,030 --> 00:14:08,040 He was walking one. 289 00:14:08,040 --> 00:14:11,150 So according to you, relative to you, I was walking two. 290 00:14:11,150 --> 00:14:12,990 And he was walking one. 291 00:14:12,990 --> 00:14:15,277 Now, relative to you, how fast was I walking? 292 00:14:15,277 --> 00:14:15,860 AUDIENCE: One. 293 00:14:15,860 --> 00:14:17,640 NICHOLAS DIBELLA: One, yeah, it's just two minus one. 294 00:14:17,640 --> 00:14:18,890 You just subtract it. 295 00:14:18,890 --> 00:14:19,799 And relative to you-- 296 00:14:19,799 --> 00:14:21,215 AUDIENCE: But relative to me, they 297 00:14:21,215 --> 00:14:22,465 would be walking negative one? 298 00:14:22,465 --> 00:14:24,256 NICHOLAS DIBELLA: Yeah, so relative to you, 299 00:14:24,256 --> 00:14:25,500 they're actually moving. 300 00:14:25,500 --> 00:14:28,830 They're actually moving that way, relative to you. 301 00:14:28,830 --> 00:14:32,580 So the whole notion of motion, that's a fun phrase to say, 302 00:14:32,580 --> 00:14:35,520 the whole notion of motion depends on the observer. 303 00:14:35,520 --> 00:14:37,610 So it doesn't make any sense to say that somebody 304 00:14:37,610 --> 00:14:39,360 is moving with some speed, unless you have 305 00:14:39,360 --> 00:14:41,250 some kind of observer in mind. 306 00:14:41,250 --> 00:14:43,500 So if I'm walking two miles per hour, you have to say, 307 00:14:43,500 --> 00:14:46,640 I'm walking at two miles per hour relative to some observer. 308 00:14:46,640 --> 00:14:49,469 So relative to the people sitting in the classroom, 309 00:14:49,469 --> 00:14:50,760 I'm walking two miles per hour. 310 00:14:50,760 --> 00:14:52,950 Relative to the classroom-- 311 00:14:52,950 --> 00:14:53,730 what's your name? 312 00:14:53,730 --> 00:14:54,270 AUDIENCE: Fred. 313 00:14:54,270 --> 00:14:56,603 NICHOLAS DIBELLA: Fred is walking at one miles per hour. 314 00:14:56,603 --> 00:14:59,550 But relative to Fred, I'm walking at one miles per hour. 315 00:14:59,550 --> 00:15:02,310 And relative to Fred, Fred's not walking at any speed. 316 00:15:02,310 --> 00:15:04,450 He's at rest, relative to himself. 317 00:15:04,450 --> 00:15:05,700 Right? 318 00:15:05,700 --> 00:15:07,940 OK, thanks. 319 00:15:11,030 --> 00:15:14,341 So that's all that relativity is. 320 00:15:14,341 --> 00:15:15,590 Some people measure one thing. 321 00:15:15,590 --> 00:15:17,090 Other people measure something else. 322 00:15:17,090 --> 00:15:18,540 That's just relativity. 323 00:15:18,540 --> 00:15:19,170 It's relative. 324 00:15:19,170 --> 00:15:20,260 It's all relative. 325 00:15:20,260 --> 00:15:22,690 So that's the relativity of speed. 326 00:15:22,690 --> 00:15:26,490 Now, the second postulate says that-- 327 00:15:26,490 --> 00:15:29,300 well, let's suppose that I was light. 328 00:15:34,465 --> 00:15:36,090 Well, actually let's forget about Fred. 329 00:15:36,090 --> 00:15:37,950 Let's just talk about me. 330 00:15:37,950 --> 00:15:41,920 Let's say I shine a flashlight. 331 00:15:41,920 --> 00:15:44,580 Light travels at some speed outside the flashlight, 332 00:15:44,580 --> 00:15:45,240 some speed. 333 00:15:45,240 --> 00:15:50,370 It turns out to be about 186,000 miles per second, very fast. 334 00:15:50,370 --> 00:15:53,370 The second postulate says that I'll measure the same speed, 335 00:15:53,370 --> 00:15:55,682 regardless of whether I'm standing still, 336 00:15:55,682 --> 00:15:56,640 or whether I'm walking. 337 00:16:00,180 --> 00:16:02,130 Remember when we asked, what speed 338 00:16:02,130 --> 00:16:05,250 does Fred get when he measures my speed? 339 00:16:05,250 --> 00:16:07,007 We have to do some kind of subtraction. 340 00:16:07,007 --> 00:16:07,840 It's very intuitive. 341 00:16:07,840 --> 00:16:09,090 You just you just subtract it. 342 00:16:09,090 --> 00:16:12,040 You just subtract, it's called the relative velocity. 343 00:16:12,040 --> 00:16:15,030 But according to the second postulate, 344 00:16:15,030 --> 00:16:17,640 you don't do the subtraction for light. 345 00:16:17,640 --> 00:16:21,240 Light travels at the same speed for everybody. 346 00:16:21,240 --> 00:16:23,640 If you were to chase light, you would never 347 00:16:23,640 --> 00:16:24,990 get any closer to it. 348 00:16:24,990 --> 00:16:26,948 It would always travel the same speed from you. 349 00:16:26,948 --> 00:16:29,190 You'd always be chasing it. 350 00:16:29,190 --> 00:16:30,435 You can't reach it. 351 00:16:30,435 --> 00:16:32,370 It's going so fast. 352 00:16:32,370 --> 00:16:33,510 Sorry, what? 353 00:16:33,510 --> 00:16:34,960 AUDIENCE: [INAUDIBLE]. 354 00:16:34,960 --> 00:16:35,460 Well, 355 00:16:35,460 --> 00:16:36,543 NICHOLAS DIBELLA: I mean-- 356 00:16:36,543 --> 00:16:38,640 AUDIENCE: [INAUDIBLE] 357 00:16:40,696 --> 00:16:41,862 NICHOLAS DIBELLA: Excuse me? 358 00:16:41,862 --> 00:16:45,798 AUDIENCE: [INAUDIBLE] 359 00:16:46,782 --> 00:16:52,686 And you start walking [INAUDIBLE] 360 00:16:55,150 --> 00:16:57,660 NICHOLAS DIBELLA: Well, I mean, in real life 361 00:16:57,660 --> 00:17:00,570 light actually gets absorbed by some materials. 362 00:17:00,570 --> 00:17:04,484 And so it actually gets stopped by some materials. 363 00:17:04,484 --> 00:17:06,150 Let's suppose this isn't the real world. 364 00:17:06,150 --> 00:17:07,650 Let's suppose this is empty space. 365 00:17:07,650 --> 00:17:09,280 There's nothing to absorb the light. 366 00:17:09,280 --> 00:17:11,250 The light would just keep traveling. 367 00:17:11,250 --> 00:17:13,619 Nothing would stop it. 368 00:17:13,619 --> 00:17:16,719 So if I turn on the flashlight, the light 369 00:17:16,719 --> 00:17:18,819 is traveling at some speed relative to me. 370 00:17:18,819 --> 00:17:21,798 And then if I'm walking at some speed relative to you, 371 00:17:21,798 --> 00:17:23,339 light is traveling at the same speed. 372 00:17:23,339 --> 00:17:26,790 And regardless of how fast I'm walking relative to you, 373 00:17:26,790 --> 00:17:30,350 or I'm driving relative to you, or I'm flying relative to you, 374 00:17:30,350 --> 00:17:33,370 light will always be going at that same speed. 375 00:17:33,370 --> 00:17:36,510 It's as though we're trying to chase it, 376 00:17:36,510 --> 00:17:39,210 and we just can't get it. 377 00:17:39,210 --> 00:17:41,500 It's just completely out of our reach. 378 00:17:41,500 --> 00:17:42,244 Yes? 379 00:17:42,244 --> 00:17:45,632 AUDIENCE: [INAUDIBLE] 380 00:17:46,600 --> 00:17:53,376 --miles per hour, and then you turn [INAUDIBLE] 381 00:17:55,485 --> 00:17:56,860 NICHOLAS DIBELLA: So the question 382 00:17:56,860 --> 00:18:01,437 is, is that why when we're in the car and we turn on lights, 383 00:18:01,437 --> 00:18:02,770 light is always in front of you? 384 00:18:09,510 --> 00:18:11,260 Even if the second postulate weren't true, 385 00:18:11,260 --> 00:18:12,820 that would still be the case, because light 386 00:18:12,820 --> 00:18:15,260 is traveling so fast, you're not going to catch up to it. 387 00:18:15,260 --> 00:18:18,460 But even if you made the car go extremely, extremely, extremely 388 00:18:18,460 --> 00:18:21,870 fast, then you still wouldn't catch up to the light. 389 00:18:21,870 --> 00:18:24,410 It actually turns out to be impossible to beat light 390 00:18:24,410 --> 00:18:25,360 in a race. 391 00:18:25,360 --> 00:18:27,640 You can never travel faster than light. 392 00:18:27,640 --> 00:18:29,350 Well, strictly speaking, you can never 393 00:18:29,350 --> 00:18:31,330 start out at a speed less than light, 394 00:18:31,330 --> 00:18:34,229 less than the light speed, and then get faster than it. 395 00:18:34,229 --> 00:18:36,520 So some people have actually considered the possibility 396 00:18:36,520 --> 00:18:39,760 of particles that travel faster than light called tachyons. 397 00:18:39,760 --> 00:18:42,010 But nobody has ever observed a tachyon. 398 00:18:42,010 --> 00:18:44,119 They're completely hypothetical. 399 00:18:44,119 --> 00:18:45,910 And nobody has any idea whether they exist. 400 00:18:45,910 --> 00:18:48,920 So we won't talk about tachyons for the rest of the class. 401 00:18:48,920 --> 00:18:52,720 But they're fun to think about in sci-fi. 402 00:18:52,720 --> 00:18:55,800 And they're just fun to think about. 403 00:18:55,800 --> 00:18:58,180 OK, so these are the two postulates. 404 00:18:58,180 --> 00:19:00,290 The first one is quite simple. 405 00:19:00,290 --> 00:19:02,840 The second one is completely mysterious. 406 00:19:08,730 --> 00:19:12,900 Now, it turns out that these two postulates actually 407 00:19:12,900 --> 00:19:15,240 have a lot of really interesting consequences. 408 00:19:15,240 --> 00:19:20,280 The second postulate itself, I think it's very interesting. 409 00:19:20,280 --> 00:19:23,490 Oh, by the way, it's also been confirmed experimentally. 410 00:19:23,490 --> 00:19:26,010 This isn't just something that people say. 411 00:19:26,010 --> 00:19:28,917 People have tried to see if the speed of light changes, 412 00:19:28,917 --> 00:19:30,000 depending on how you move. 413 00:19:30,000 --> 00:19:33,600 And they found that it doesn't. 414 00:19:33,600 --> 00:19:36,470 They found a null result in these experiments. 415 00:19:36,470 --> 00:19:39,420 The speed of light doesn't change, regardless of how 416 00:19:39,420 --> 00:19:42,900 you move relative to space. 417 00:19:42,900 --> 00:19:48,120 That's just something in the early 20th century 418 00:19:48,120 --> 00:19:51,330 that people were trying to figure out, 419 00:19:51,330 --> 00:19:55,380 whether light propagates inside some kind of mysterious medium. 420 00:19:55,380 --> 00:19:58,369 Anyway, that's another thing. 421 00:19:58,369 --> 00:19:59,910 So these two postulates have a number 422 00:19:59,910 --> 00:20:02,610 of very interesting consequences. 423 00:20:02,610 --> 00:20:05,780 Probably the most interesting is called time dilation. 424 00:20:15,730 --> 00:20:19,496 And this says that moving clocks tick slow. 425 00:20:19,496 --> 00:20:21,370 They tick slower than if they weren't moving. 426 00:20:34,030 --> 00:20:37,900 So let's suppose it's some summer day, some summer 427 00:20:37,900 --> 00:20:42,160 afternoon, like today, a beautiful summer afternoon. 428 00:20:42,160 --> 00:20:44,761 And you have free time. 429 00:20:44,761 --> 00:20:47,260 And so you decide to do your favorite activity on the summer 430 00:20:47,260 --> 00:20:48,230 afternoon. 431 00:20:48,230 --> 00:20:50,440 You go to the train track. 432 00:20:50,440 --> 00:20:52,330 And you like to watch the trains go by. 433 00:20:52,330 --> 00:20:53,200 It's very relaxing. 434 00:20:53,200 --> 00:20:56,550 That's what you like to do in summer afternoons. 435 00:20:56,550 --> 00:21:00,130 So you go to the train track, and sit down on a bench. 436 00:21:00,130 --> 00:21:03,430 And you watch the trains go by. 437 00:21:03,430 --> 00:21:05,830 You also like to measure things with your clock. 438 00:21:05,830 --> 00:21:07,870 So you bring a clock along. 439 00:21:07,870 --> 00:21:11,650 And you like to think about how time passes for you, 440 00:21:11,650 --> 00:21:15,640 and how it passes for observers sitting on the train. 441 00:21:15,640 --> 00:21:20,753 So let's suppose this is you sitting on-- 442 00:21:20,753 --> 00:21:22,330 let's suppose this is you. 443 00:21:25,040 --> 00:21:30,695 No, OK, whatever, let's suppose this 444 00:21:30,695 --> 00:21:35,705 is you sitting on the bench. 445 00:21:35,705 --> 00:21:37,280 A bench is too hard to draw. 446 00:21:37,280 --> 00:21:38,829 So I'm not going to draw the bench. 447 00:21:38,829 --> 00:21:40,370 So you're sitting on the bench, which 448 00:21:40,370 --> 00:21:42,380 I've represented as nothing. 449 00:21:42,380 --> 00:21:48,130 And a train passes by, which I'll 450 00:21:48,130 --> 00:21:51,252 represent with a rectangle. 451 00:21:51,252 --> 00:21:52,230 It's going this way. 452 00:21:57,510 --> 00:21:59,360 Maybe it looks like a bus. 453 00:21:59,360 --> 00:22:01,207 Let's suppose it's a train. 454 00:22:01,207 --> 00:22:03,540 When Einstein was thinking of these thought experiments, 455 00:22:03,540 --> 00:22:05,760 he always used train, because back then that 456 00:22:05,760 --> 00:22:13,110 was the fastest kind of vehicle that people had invented. 457 00:22:13,110 --> 00:22:20,082 Cars, they weren't able to go as fast as trains back then. 458 00:22:20,082 --> 00:22:20,790 Now we have cars. 459 00:22:20,790 --> 00:22:22,950 Now we have planes. 460 00:22:22,950 --> 00:22:24,687 Like in a modern thought experiment, 461 00:22:24,687 --> 00:22:26,520 this is just a thought experiment just think 462 00:22:26,520 --> 00:22:27,769 about we don't actually do it. 463 00:22:27,769 --> 00:22:29,370 In a modern thought experiment, we 464 00:22:29,370 --> 00:22:31,620 might use planes, or maybe spaceships, 465 00:22:31,620 --> 00:22:33,830 or something like that. 466 00:22:33,830 --> 00:22:36,767 Let's think about trains right now, just keep it very simple. 467 00:22:36,767 --> 00:22:38,100 So you're sitting on your bench. 468 00:22:38,100 --> 00:22:40,710 And you watch the trains go by. 469 00:22:40,710 --> 00:22:44,820 Then you wonder to yourself, let's suppose 470 00:22:44,820 --> 00:22:48,300 that some amount of time passes by for me sitting on the bench. 471 00:22:48,300 --> 00:22:50,084 And I look at my clock. 472 00:22:50,084 --> 00:22:50,750 I get something. 473 00:22:50,750 --> 00:22:51,680 I get some number. 474 00:22:51,680 --> 00:22:54,540 What number do people on the train get? 475 00:22:54,540 --> 00:22:57,859 So let's say, for example, it's very relaxing. 476 00:22:57,859 --> 00:23:00,150 It's very relaxing to sit on these benches at the train 477 00:23:00,150 --> 00:23:01,080 track. 478 00:23:01,080 --> 00:23:03,960 And you accidentally doze off. 479 00:23:03,960 --> 00:23:05,820 You fall asleep. 480 00:23:05,820 --> 00:23:07,770 Or maybe it was due to the heat. 481 00:23:07,770 --> 00:23:09,880 The heat got you. 482 00:23:09,880 --> 00:23:13,120 You fell asleep, in any case. 483 00:23:13,120 --> 00:23:15,030 And let's say, somehow, you timed yourself 484 00:23:15,030 --> 00:23:17,480 to see how long you were sleeping for. 485 00:23:17,480 --> 00:23:19,335 And let's say you got three hours. 486 00:23:19,335 --> 00:23:22,540 You determined that you're sleeping for three hours. 487 00:23:22,540 --> 00:23:25,860 How long do the people on the train see you sleeping for? 488 00:23:25,860 --> 00:23:30,480 Well, according to special relativity, 489 00:23:30,480 --> 00:23:32,550 it turns out that if you work out 490 00:23:32,550 --> 00:23:36,530 the mathematical and geometrical consequences of these two 491 00:23:36,530 --> 00:23:37,104 postulates. 492 00:23:37,104 --> 00:23:38,520 You get this time dilation effect, 493 00:23:38,520 --> 00:23:40,720 that moving clocks tick slower. 494 00:23:40,720 --> 00:23:43,110 So if you were to look at a clock on the train, 495 00:23:43,110 --> 00:23:47,150 you'd see them ticking slower than your clock. 496 00:23:47,150 --> 00:23:49,340 So maybe your clock is ticking at this rate. 497 00:23:49,340 --> 00:23:50,260 You just look at it. 498 00:23:50,260 --> 00:23:51,690 It's going something like this. 499 00:23:51,690 --> 00:23:53,520 That's too slow, sorry. 500 00:23:53,520 --> 00:23:57,030 Your clock is maybe ticking at this rate. 501 00:23:57,030 --> 00:23:59,250 It goes around 12 to 12. 502 00:23:59,250 --> 00:24:01,050 And maybe the clock on the train is 503 00:24:01,050 --> 00:24:05,880 going at this rate, relative to that one. 504 00:24:08,840 --> 00:24:11,090 And so you measure three hours sitting on the bench. 505 00:24:11,090 --> 00:24:12,800 What does somebody on the train measure? 506 00:24:12,800 --> 00:24:15,970 Well, since the clock is ticking slower, 507 00:24:15,970 --> 00:24:21,230 as a certain amount passes by on your clock-- 508 00:24:21,230 --> 00:24:23,220 say it's 3:00 o'clock. 509 00:24:23,220 --> 00:24:26,054 And a certain amount of time passes by your clock. 510 00:24:26,054 --> 00:24:27,470 Since this guy was ticking slower, 511 00:24:27,470 --> 00:24:30,260 since this clock was ticking slower, 512 00:24:30,260 --> 00:24:32,480 a smaller amount of time will have passed by. 513 00:24:32,480 --> 00:24:38,150 So maybe for them, only two hours has passed by. 514 00:24:38,150 --> 00:24:39,800 And this is exactly the-- 515 00:24:39,800 --> 00:24:44,300 AUDIENCE: [INAUDIBLE] are always early? 516 00:24:44,300 --> 00:24:45,883 NICHOLAS DIBELLA: No, no they're not-- 517 00:24:45,883 --> 00:24:49,270 AUDIENCE: [INAUDIBLE] 518 00:24:49,270 --> 00:24:52,469 NICHOLAS DIBELLA: No, no, I'm saying something very precise. 519 00:24:52,469 --> 00:24:54,260 I'm saying that if a certain amount of time 520 00:24:54,260 --> 00:24:57,020 passes by for somebody stationary, 521 00:24:57,020 --> 00:24:58,520 then a smaller amount of time passes 522 00:24:58,520 --> 00:25:01,917 by for somebody that's moving. 523 00:25:01,917 --> 00:25:03,750 AUDIENCE: [INAUDIBLE] very, very high speed. 524 00:25:03,750 --> 00:25:06,530 NICHOLAS DIBELLA: OK, so you might wonder, 525 00:25:06,530 --> 00:25:08,764 we never see this happen. 526 00:25:08,764 --> 00:25:10,430 It seems like time is an absolute thing. 527 00:25:10,430 --> 00:25:12,890 It seems like everybody agrees on the same time intervals. 528 00:25:12,890 --> 00:25:14,900 Why don't we actually see this happen? 529 00:25:14,900 --> 00:25:17,840 It turns out for these effects to become noticeable, 530 00:25:17,840 --> 00:25:21,270 the speeds involved have to be near the speed of light. 531 00:25:21,270 --> 00:25:25,140 And the speed of light is really fast. 532 00:25:25,140 --> 00:25:27,700 I mean, how fast does a train move? 533 00:25:27,700 --> 00:25:29,431 50 miles an hour, I don't know. 534 00:25:29,431 --> 00:25:33,359 AUDIENCE: [INAUDIBLE] 535 00:25:38,365 --> 00:25:39,740 NICHOLAS DIBELLA: Would the train 536 00:25:39,740 --> 00:25:42,731 fall apart if you made it move really fast? 537 00:25:42,731 --> 00:25:43,230 Well-- 538 00:25:43,230 --> 00:25:46,750 AUDIENCE: [INAUDIBLE] 539 00:25:46,750 --> 00:25:48,945 NICHOLAS DIBELLA: Well, the thing 540 00:25:48,945 --> 00:25:50,320 that would cause it to fall apart 541 00:25:50,320 --> 00:25:51,690 is when you're accelerating. 542 00:25:51,690 --> 00:25:53,920 You have to push it in some kind of a way. 543 00:25:53,920 --> 00:25:55,420 Once it's going at a constant speed, 544 00:25:55,420 --> 00:25:56,620 it's not feeling any force. 545 00:25:56,620 --> 00:25:59,267 It's not feeling any push or pull. 546 00:25:59,267 --> 00:26:01,600 But the part that might break it is when you're actually 547 00:26:01,600 --> 00:26:02,410 accelerating it. 548 00:26:02,410 --> 00:26:04,286 You have to actually give it a push in order 549 00:26:04,286 --> 00:26:05,410 to get it to go some speed. 550 00:26:05,410 --> 00:26:07,960 And that push might be too much for a train to withstand. 551 00:26:07,960 --> 00:26:10,900 AUDIENCE: So you'd probably want a really long train 552 00:26:10,900 --> 00:26:15,310 to [INAUDIBLE] 553 00:26:15,310 --> 00:26:17,920 NICHOLAS DIBELLA: Well, you don't want to try with a train. 554 00:26:17,920 --> 00:26:19,870 I mean, this is just a thought experiment. 555 00:26:19,870 --> 00:26:22,672 We're not actually going to do this experiment. 556 00:26:22,672 --> 00:26:24,130 It's just an experiment that we can 557 00:26:24,130 --> 00:26:26,635 think of in our minds to help us understand the ideas. 558 00:26:29,156 --> 00:26:30,780 If you like, you can do the experiments 559 00:26:30,780 --> 00:26:33,085 in your thought lab. 560 00:26:33,085 --> 00:26:36,190 The thought lab is a very nice lab, in that it's free. 561 00:26:36,190 --> 00:26:37,455 Everybody has one. 562 00:26:37,455 --> 00:26:39,339 You can always do thought experiments. 563 00:26:39,339 --> 00:26:40,880 But it's also a very dangerous place, 564 00:26:40,880 --> 00:26:43,600 because like you were saying, if you 565 00:26:43,600 --> 00:26:45,870 made a train go too fast, if you tried 566 00:26:45,870 --> 00:26:48,250 to accelerate to make it go so fast, it might explode 567 00:26:48,250 --> 00:26:49,600 or something. 568 00:26:49,600 --> 00:26:53,384 And your thought lab might need serious repairs. 569 00:26:53,384 --> 00:26:54,925 So the thought lab is very dangerous. 570 00:26:54,925 --> 00:26:58,442 AUDIENCE: [INAUDIBLE] 571 00:27:01,240 --> 00:27:03,040 NICHOLAS DIBELLA: So light is very special. 572 00:27:03,040 --> 00:27:03,970 Light is very special. 573 00:27:03,970 --> 00:27:05,740 Light always travels at the speed of light. 574 00:27:05,740 --> 00:27:07,290 It doesn't have to accelerate to get there. 575 00:27:07,290 --> 00:27:08,650 It's just always traveling at the speed of light. 576 00:27:08,650 --> 00:27:09,525 It's very mysterious. 577 00:27:09,525 --> 00:27:12,177 AUDIENCE: But then what if your flashlight's off? 578 00:27:12,177 --> 00:27:14,010 NICHOLAS DIBELLA: If your flashlight is off, 579 00:27:14,010 --> 00:27:17,040 it's no longer producing light. 580 00:27:17,040 --> 00:27:18,440 The flashlight produces light. 581 00:27:18,440 --> 00:27:20,440 And then the light that's produced automatically 582 00:27:20,440 --> 00:27:22,020 travels at some speed. 583 00:27:22,020 --> 00:27:24,564 When you turn off the flashlight, 584 00:27:24,564 --> 00:27:25,980 light is no longer being produced. 585 00:27:25,980 --> 00:27:27,480 So there's just no more light. 586 00:27:27,480 --> 00:27:28,980 But the light that you did produce 587 00:27:28,980 --> 00:27:30,742 is traveling at the speed of light 588 00:27:30,742 --> 00:27:32,950 until it reaches some material that it gets absorbed. 589 00:27:32,950 --> 00:27:34,050 But if you did this in empty space, 590 00:27:34,050 --> 00:27:36,000 if you did it in outer space where there's nothing, 591 00:27:36,000 --> 00:27:36,750 then it wouldn't get absorbed. 592 00:27:36,750 --> 00:27:39,166 It would just keep traveling, and traveling, and traveling 593 00:27:39,166 --> 00:27:40,910 at the same speed. 594 00:27:40,910 --> 00:27:41,617 Question? 595 00:27:41,617 --> 00:27:44,240 AUDIENCE: If you shone a flashlight in space, 596 00:27:44,240 --> 00:27:46,809 could you see the light moving forward? 597 00:27:46,809 --> 00:27:49,350 NICHOLAS DIBELLA: If I shone a flashlight in space then would 598 00:27:49,350 --> 00:27:52,982 I see the light moving forward? 599 00:27:52,982 --> 00:27:54,440 I'm not exactly sure what you mean. 600 00:27:54,440 --> 00:27:58,670 AUDIENCE: If you turned it on, and the light was going, 601 00:27:58,670 --> 00:27:59,620 and you-- 602 00:27:59,620 --> 00:28:06,670 NICHOLAS DIBELLA: Oh, like maybe I've 603 00:28:06,670 --> 00:28:11,170 got a laser right here on the surface of the table. 604 00:28:11,170 --> 00:28:12,430 And it's shining right there. 605 00:28:12,430 --> 00:28:14,020 And I'll suppose that this whole room is outer space. 606 00:28:14,020 --> 00:28:15,850 Would I see something right there? 607 00:28:15,850 --> 00:28:19,730 Would I see a line of light kind of like that? 608 00:28:19,730 --> 00:28:21,940 No I wouldn't, because the light has 609 00:28:21,940 --> 00:28:24,470 to reflect off a something for me to be able to see it. 610 00:28:24,470 --> 00:28:25,150 So if there's nothing there, it's 611 00:28:25,150 --> 00:28:26,691 not going to reflect off of anything. 612 00:28:26,691 --> 00:28:27,986 So I'm not going to see it. 613 00:28:27,986 --> 00:28:31,170 AUDIENCE: How do we see stars? 614 00:28:31,170 --> 00:28:33,310 NICHOLAS DIBELLA: Well, the light eventually, 615 00:28:33,310 --> 00:28:34,180 it hits stuff. 616 00:28:34,180 --> 00:28:36,970 And it reaches us. 617 00:28:36,970 --> 00:28:39,430 Space isn't completely empty. 618 00:28:39,430 --> 00:28:40,570 There's some stuff. 619 00:28:40,570 --> 00:28:43,460 There's some dust that the light hits off. 620 00:28:43,460 --> 00:28:47,200 It hits off of some dust. 621 00:28:47,200 --> 00:28:49,340 So space is almost empty. 622 00:28:49,340 --> 00:28:53,500 But you get about one hydrogen atom per cubic meter. 623 00:28:53,500 --> 00:28:56,260 It's very not dense. 624 00:28:56,260 --> 00:28:57,700 But there is some stuff in space. 625 00:29:01,370 --> 00:29:03,220 So this time dilation effects-- 626 00:29:03,220 --> 00:29:05,500 moving clocks tick slow. 627 00:29:05,500 --> 00:29:07,700 So, as I say, it's important whenever 628 00:29:07,700 --> 00:29:10,400 you're going to mention any speed at all, 629 00:29:10,400 --> 00:29:13,380 it's important to mention the observer that you have in mind. 630 00:29:13,380 --> 00:29:16,090 It's always important to mention what the speed is 631 00:29:16,090 --> 00:29:17,740 relative to somebody. 632 00:29:17,740 --> 00:29:22,730 So as I'm walking, you guys would say that I'm moving. 633 00:29:22,730 --> 00:29:26,800 But I would say that you're moving. 634 00:29:26,800 --> 00:29:29,510 I'm traveling at two miles an hour relative to you. 635 00:29:29,510 --> 00:29:32,650 You're traveling at two miles an hour relative to me. 636 00:29:32,650 --> 00:29:35,620 And, similarly, this time dilation effect 637 00:29:35,620 --> 00:29:37,460 works in the same way. 638 00:29:37,460 --> 00:29:42,250 So this time dilation effects is also symmetrical. 639 00:29:42,250 --> 00:29:44,100 There's a symmetry. 640 00:29:44,100 --> 00:29:47,030 If I observe your clocks ticking slow, 641 00:29:47,030 --> 00:29:50,220 then you'll observe my clock to be ticking slow. 642 00:29:50,220 --> 00:29:52,270 It's symmetrical. 643 00:29:52,270 --> 00:29:53,130 Yes? 644 00:29:53,130 --> 00:29:56,560 AUDIENCE: [INAUDIBLE] 645 00:30:13,040 --> 00:30:15,540 NICHOLAS DIBELLA: So does the discrepancy between cell phone 646 00:30:15,540 --> 00:30:18,060 times have anything to do with time dilation? 647 00:30:18,060 --> 00:30:20,492 That's your question, right? 648 00:30:20,492 --> 00:30:22,950 I don't really know a whole lot about how cell phones work. 649 00:30:22,950 --> 00:30:24,010 But I do know this. 650 00:30:24,010 --> 00:30:25,782 If the cell phone uses GPS at all, 651 00:30:25,782 --> 00:30:27,990 if it uses these satellites, these global positioning 652 00:30:27,990 --> 00:30:31,050 satellites, there are actually time dilation effects 653 00:30:31,050 --> 00:30:34,380 that you have to take into account to get things right, 654 00:30:34,380 --> 00:30:36,660 to pin down this location of a place right, 655 00:30:36,660 --> 00:30:39,012 because you have to communicate with the satellites 656 00:30:39,012 --> 00:30:40,720 that the light bounces back up and forth. 657 00:30:40,720 --> 00:30:42,450 You have to communicate with them. 658 00:30:42,450 --> 00:30:46,692 And you actually have to take into account a different type 659 00:30:46,692 --> 00:30:47,400 of time dilation. 660 00:30:47,400 --> 00:30:49,987 Gravitational time dilation ends up being important. 661 00:30:49,987 --> 00:30:52,320 And that's actually an effect to the general relativity. 662 00:30:52,320 --> 00:30:54,810 I'll get to that later today. 663 00:30:54,810 --> 00:30:56,890 But I have no idea. 664 00:30:56,890 --> 00:30:58,500 I don't know how cell phones work. 665 00:30:58,500 --> 00:31:00,000 I can't really answer that question. 666 00:31:03,050 --> 00:31:04,620 So a moving observer-- 667 00:31:04,620 --> 00:31:06,439 I'll say your clocks are moving slow. 668 00:31:06,439 --> 00:31:07,980 You'll say my clocks are moving slow. 669 00:31:07,980 --> 00:31:10,290 Time relation is reciprocal. 670 00:31:10,290 --> 00:31:13,200 It's symmetric. 671 00:31:13,200 --> 00:31:15,780 Neither of us is wrong. 672 00:31:15,780 --> 00:31:21,270 I'm not wrong to say that a certain amount of time 673 00:31:21,270 --> 00:31:24,392 passes by, and you say another amount of time passes by. 674 00:31:24,392 --> 00:31:25,350 Neither of us is wrong. 675 00:31:25,350 --> 00:31:27,630 We just have different perspectives. 676 00:31:27,630 --> 00:31:30,990 It doesn't make any sense to say, well, 677 00:31:30,990 --> 00:31:32,277 precisely three hours past. 678 00:31:32,277 --> 00:31:33,360 It doesn't make any sense. 679 00:31:33,360 --> 00:31:35,590 You have to specify the observer. 680 00:31:35,590 --> 00:31:38,160 And only then does everything tie together. 681 00:31:38,160 --> 00:31:41,640 Only then does all of this make any sense at all, 682 00:31:41,640 --> 00:31:42,980 is the whole theory consistent. 683 00:31:42,980 --> 00:31:44,700 You have to always mention the observer. 684 00:31:44,700 --> 00:31:46,280 If you don't mention the observer, 685 00:31:46,280 --> 00:31:51,230 then what you're saying is just not meaningful. 686 00:31:51,230 --> 00:31:53,280 It doesn't make any sense at all. 687 00:31:53,280 --> 00:31:54,572 Yes? 688 00:31:54,572 --> 00:31:58,540 AUDIENCE: [INAUDIBLE] If I were to take [INAUDIBLE] to school, 689 00:31:58,540 --> 00:32:02,012 [INAUDIBLE] 690 00:32:03,352 --> 00:32:05,010 My school ends at, like, 3:00. 691 00:32:05,010 --> 00:32:06,880 So if I went to school, and my watch 692 00:32:06,880 --> 00:32:14,245 said 3 o'clock PM, [INAUDIBLE] 3 o'clock when I get [INAUDIBLE] 693 00:32:18,420 --> 00:32:22,500 NICHOLAS DIBELLA: So that's kind of a devious thing to do. 694 00:32:22,500 --> 00:32:26,940 So you're proposing just if I just kind of arbitrarily 695 00:32:26,940 --> 00:32:29,670 set my clock to say 3:00 PM, and I'm 696 00:32:29,670 --> 00:32:32,190 sitting in school, saying, hey, teacher, look, it's 3:00 PM. 697 00:32:32,190 --> 00:32:33,250 Can I go? 698 00:32:33,250 --> 00:32:35,190 Is that a valid thing to do? 699 00:32:35,190 --> 00:32:37,260 That's kind of unfair. that's kind of unfair. 700 00:32:37,260 --> 00:32:40,800 We have to first synchronize our clocks. 701 00:32:40,800 --> 00:32:44,270 We have to make them agree at some point in time. 702 00:32:44,270 --> 00:32:48,870 So let's say that we synchronize them at 7:00 AM. 703 00:32:48,870 --> 00:32:52,350 Then if your clock says 3:00 PM, while your teacher's clock says 704 00:32:52,350 --> 00:32:55,786 1:00 PM, then you might have an argument there. 705 00:32:55,786 --> 00:32:57,660 But what you're proposing is a little unfair. 706 00:32:57,660 --> 00:33:04,900 And I can sense great lack of discipline in you, kidding. 707 00:33:08,760 --> 00:33:11,310 So this time dilation effects is just one 708 00:33:11,310 --> 00:33:16,950 of many interesting features of special relativity. 709 00:33:16,950 --> 00:33:18,710 I'll leave that there. 710 00:33:18,710 --> 00:33:20,920 There are a lot of other interesting features. 711 00:33:20,920 --> 00:33:26,730 For example, sticks like this, sticks actually 712 00:33:26,730 --> 00:33:28,680 get shorter when they move. 713 00:33:28,680 --> 00:33:32,610 So as I walk across the room, it actually 714 00:33:32,610 --> 00:33:35,160 gets a little bit shorter. 715 00:33:35,160 --> 00:33:37,110 Now, obviously, you don't observe 716 00:33:37,110 --> 00:33:38,700 it's at every day speeds. 717 00:33:38,700 --> 00:33:41,570 But if this thing, if this eraser 718 00:33:41,570 --> 00:33:43,750 were moving close to the speed of light, 719 00:33:43,750 --> 00:33:46,290 then you would actually observe it to get smaller. 720 00:33:46,290 --> 00:33:50,460 And the faster you make it go, the smaller it gets, 721 00:33:50,460 --> 00:33:51,810 the shorter it gets. 722 00:33:51,810 --> 00:33:53,280 And, similarly, I forgot to mention 723 00:33:53,280 --> 00:33:59,150 that the faster the train goes, the slower the time ticks. 724 00:33:59,150 --> 00:34:01,820 And so actually, as you approach the speed of light-- 725 00:34:01,820 --> 00:34:05,850 sorry, as the train approaches the speed of light, 726 00:34:05,850 --> 00:34:09,100 the rate of its ticking becomes slower and slower and slower. 727 00:34:09,100 --> 00:34:11,040 And as it approaches the speed of light, 728 00:34:11,040 --> 00:34:13,409 time essentially stops. 729 00:34:13,409 --> 00:34:15,540 The rate of the ticking becomes infinitely slow. 730 00:34:18,170 --> 00:34:19,710 You had a question? 731 00:34:23,100 --> 00:34:27,290 So all these effects, this length shortening time 732 00:34:27,290 --> 00:34:30,800 dilation-- and there are others-- 733 00:34:30,800 --> 00:34:33,170 they only become noticeable, at least to us 734 00:34:33,170 --> 00:34:37,370 because we're used to living in a world where 735 00:34:37,370 --> 00:34:39,980 objects don't move very fast relative to the speed of light. 736 00:34:39,980 --> 00:34:42,860 So we don't have a hardwiring in our brains. 737 00:34:42,860 --> 00:34:44,870 Our brains have a kind of common sense 738 00:34:44,870 --> 00:34:50,947 that things behave in a certain way under certain conditions. 739 00:34:50,947 --> 00:34:53,030 But there are many extreme conditions that we just 740 00:34:53,030 --> 00:34:54,230 haven't experienced. 741 00:34:54,230 --> 00:34:57,560 And our brains just can't really understand them. 742 00:34:57,560 --> 00:34:58,760 So they're not noticeable. 743 00:34:58,760 --> 00:35:00,260 These effects aren't noticeable unless you're traveling 744 00:35:00,260 --> 00:35:02,040 close to the speed of light. 745 00:35:02,040 --> 00:35:02,799 Yes? 746 00:35:02,799 --> 00:35:06,471 AUDIENCE: [INAUDIBLE] 747 00:35:09,650 --> 00:35:12,860 NICHOLAS DIBELLA: It actually shortens its length. 748 00:35:12,860 --> 00:35:16,280 OK, it shortens its length relative to you. 749 00:35:16,280 --> 00:35:20,030 But relative to it, it doesn't get short. 750 00:35:20,030 --> 00:35:22,470 I know it's very weird. 751 00:35:22,470 --> 00:35:25,130 But if you think hard, if you sit down and think 752 00:35:25,130 --> 00:35:30,226 about these two postulates, if you draw everything out, 753 00:35:30,226 --> 00:35:31,850 if you look at how light moves, and you 754 00:35:31,850 --> 00:35:35,100 look at the geometry of sticks and stuff, 755 00:35:35,100 --> 00:35:36,580 then you can actually infer this. 756 00:35:36,580 --> 00:35:38,570 You can actually infer these consequences. 757 00:35:38,570 --> 00:35:40,670 And they're completely strange. 758 00:35:40,670 --> 00:35:43,520 But they're completely logical consequences of these two 759 00:35:43,520 --> 00:35:44,660 very simple postulates. 760 00:35:44,660 --> 00:35:47,840 AUDIENCE: [INAUDIBLE] 761 00:35:49,424 --> 00:35:51,590 NICHOLAS DIBELLA: Yeah, suppose you can't see things 762 00:35:51,590 --> 00:35:52,640 that are very, very thin. 763 00:35:52,640 --> 00:35:58,740 Yeah, it would be so thin that, how are you going to see it? 764 00:35:58,740 --> 00:36:04,010 Now, time dilation has actually been observed many times. 765 00:36:04,010 --> 00:36:07,160 At particle accelerators, we very routinely accelerate 766 00:36:07,160 --> 00:36:11,450 particle to 99.999& the speed of light, things like electrons, 767 00:36:11,450 --> 00:36:13,270 protons, and so forth. 768 00:36:13,270 --> 00:36:16,100 But every day objects like trains, 769 00:36:16,100 --> 00:36:18,800 they require a lot more energy to get them very fast. 770 00:36:18,800 --> 00:36:22,310 So we don't really observe trains getting shorter. 771 00:36:22,310 --> 00:36:27,110 We don't observe the clocks to to tick much slower than ours. 772 00:36:27,110 --> 00:36:29,450 It just takes too much energy to get them to go fast. 773 00:36:29,450 --> 00:36:32,330 But we have definitely observed time dilation 774 00:36:32,330 --> 00:36:35,000 for elementary particles. 775 00:36:35,000 --> 00:36:36,590 So that provides a lot of evidence 776 00:36:36,590 --> 00:36:39,819 for time dilation and special relativity. 777 00:36:39,819 --> 00:36:41,360 But actually for length and traction, 778 00:36:41,360 --> 00:36:45,980 it's just really hard to get big objects going 779 00:36:45,980 --> 00:36:48,110 at a substantial fraction of the speed of light. 780 00:36:48,110 --> 00:36:51,410 So I've never heard of any direct observations 781 00:36:51,410 --> 00:36:54,287 of length contraction. 782 00:36:54,287 --> 00:36:56,370 But special relativity implies it should be there. 783 00:36:56,370 --> 00:37:00,312 And all of our evidence indicates-- 784 00:37:00,312 --> 00:37:02,270 every experiment we've done has been consistent 785 00:37:02,270 --> 00:37:03,720 with special relativity. 786 00:37:03,720 --> 00:37:07,850 So even though we haven't observed length contraction 787 00:37:07,850 --> 00:37:09,802 happen, this shortening, we definitely 788 00:37:09,802 --> 00:37:11,510 have good reason to believe that happens. 789 00:37:15,640 --> 00:37:19,540 Now time dilation in special relativity 790 00:37:19,540 --> 00:37:24,680 actually provides you a way of traveling into the future. 791 00:37:24,680 --> 00:37:25,910 It's very simple. 792 00:37:25,910 --> 00:37:27,770 Here's how to do it. 793 00:37:27,770 --> 00:37:29,350 So let's suppose this is Earth. 794 00:37:32,240 --> 00:37:34,070 That's Earth. 795 00:37:34,070 --> 00:37:37,847 And get yourself a spaceship, just 796 00:37:37,847 --> 00:37:39,430 your average spaceship that can travel 797 00:37:39,430 --> 00:37:44,940 99.99% the speed of light. 798 00:37:44,940 --> 00:37:46,780 Yeah, it doesn't exist, at least today. 799 00:37:46,780 --> 00:37:48,970 It might exist in the future. 800 00:37:48,970 --> 00:37:52,900 Not even close, in fact, I looked it up. 801 00:37:52,900 --> 00:37:57,130 The fastest we've been able to get of any manned spacecraft 802 00:37:57,130 --> 00:38:01,589 to date has been half of a percent of a percent 803 00:38:01,589 --> 00:38:02,380 the speed of light. 804 00:38:04,900 --> 00:38:07,690 But in any case, let's suppose we get a spaceship 805 00:38:07,690 --> 00:38:10,820 that can travel very fast. 806 00:38:10,820 --> 00:38:13,010 So here's a way of theoretically traveling 807 00:38:13,010 --> 00:38:15,540 into the future, a substantial amount into the future. 808 00:38:15,540 --> 00:38:17,090 So you have Earth. 809 00:38:17,090 --> 00:38:21,990 Leave on your spaceship, travel very fast this direction, 810 00:38:21,990 --> 00:38:23,160 and then come back. 811 00:38:26,610 --> 00:38:29,810 You go very fast both of the ways. 812 00:38:29,810 --> 00:38:33,710 Now, because of this time dilation effect, 813 00:38:33,710 --> 00:38:36,410 let's suppose we're sitting on the Earth. 814 00:38:36,410 --> 00:38:38,120 Let's say we're sitting on the Earth. 815 00:38:38,120 --> 00:38:41,600 And we have our clocks. 816 00:38:41,600 --> 00:38:45,110 And if we measure how long it takes for the spaceship 817 00:38:45,110 --> 00:38:47,810 to make its trip, to go all the way to some point 818 00:38:47,810 --> 00:38:49,314 and then come back, let's time. 819 00:38:49,314 --> 00:38:50,480 Let's see how long it takes. 820 00:38:53,480 --> 00:38:56,660 If we're very patient, if we're willing to let this space 821 00:38:56,660 --> 00:38:58,790 ship go very far, we might see that it 822 00:38:58,790 --> 00:39:03,730 takes 100 years for the space ship to make this trip. 823 00:39:03,730 --> 00:39:09,560 But because of time dilation, as 100 years passes by for us, 824 00:39:09,560 --> 00:39:13,340 a smaller amount of time will pass by for the spaceship. 825 00:39:13,340 --> 00:39:14,990 So while 100 years passes by for us, 826 00:39:14,990 --> 00:39:17,810 maybe 10 years passes by for the spaceship 827 00:39:17,810 --> 00:39:20,940 to make this whole journey. 828 00:39:20,940 --> 00:39:21,669 Yes? 829 00:39:21,669 --> 00:39:25,800 AUDIENCE: [INAUDIBLE] 830 00:39:30,580 --> 00:39:32,990 NICHOLAS DIBELLA: Yeah, they'll only age 10 years. 831 00:39:32,990 --> 00:39:36,824 Now, this actually presents a kind of paradox, 832 00:39:36,824 --> 00:39:38,990 because I said before that time dilation is actually 833 00:39:38,990 --> 00:39:44,810 symmetrical, that relative to me you guys are moving. 834 00:39:44,810 --> 00:39:46,940 But relative to you, I'm moving. 835 00:39:46,940 --> 00:39:48,620 I say that your clocks run slow. 836 00:39:48,620 --> 00:39:50,900 You say that my clock runs slow. 837 00:39:50,900 --> 00:39:54,230 But here, I'm claiming that actually, as 100 years passes 838 00:39:54,230 --> 00:39:58,010 by for Earth, only 10 years passes by for the spaceship, 839 00:39:58,010 --> 00:39:59,450 once the whole thing is over. 840 00:40:03,470 --> 00:40:05,630 Couldn't you say that relative to the spaceship, 841 00:40:05,630 --> 00:40:07,080 the Earth is moving? 842 00:40:07,080 --> 00:40:09,080 And so the clocks on the Earth will move slower. 843 00:40:09,080 --> 00:40:11,297 So 100 years passes by the spaceship. 844 00:40:11,297 --> 00:40:12,880 Only 10 years passes by for the Earth. 845 00:40:12,880 --> 00:40:15,449 Couldn't you say that? 846 00:40:15,449 --> 00:40:16,990 But once everything is said and done, 847 00:40:16,990 --> 00:40:20,000 once the spaceship returns back to Earth, 848 00:40:20,000 --> 00:40:22,250 they're either going to be the same age-- 849 00:40:22,250 --> 00:40:23,666 the people on the earth are either 850 00:40:23,666 --> 00:40:27,662 going to have measured some time interval that's 851 00:40:27,662 --> 00:40:29,120 equal to the time interval measured 852 00:40:29,120 --> 00:40:29,930 by the people of the spaceship. 853 00:40:29,930 --> 00:40:31,460 Or they'll measure something else. 854 00:40:31,460 --> 00:40:34,130 Maybe they'll measure a longer interval or a short interval. 855 00:40:34,130 --> 00:40:36,770 At the end of the day, one of those three possibilities 856 00:40:36,770 --> 00:40:38,420 has to happen. 857 00:40:38,420 --> 00:40:41,030 One of them has to be right. 858 00:40:41,030 --> 00:40:44,510 And it turns out that the right one of those possibilities 859 00:40:44,510 --> 00:40:50,450 is actually that the people on the spaceship age less. 860 00:40:50,450 --> 00:40:53,160 And I'll leave that as a mystery for you right now. 861 00:40:53,160 --> 00:40:56,930 I'll let you think about how this paradox actually 862 00:40:56,930 --> 00:40:58,430 gets resolved. 863 00:40:58,430 --> 00:41:01,790 I said before, special relativity, these effects 864 00:41:01,790 --> 00:41:03,320 are symmetrical. 865 00:41:03,320 --> 00:41:06,620 But here, there's some kind of an asymmetry. 866 00:41:06,620 --> 00:41:08,420 There's some kind of a paradox. 867 00:41:08,420 --> 00:41:11,365 But for some reason, which you have to figure out-- 868 00:41:11,365 --> 00:41:12,740 I'm not going to tell you today-- 869 00:41:12,740 --> 00:41:15,848 but for some reason, there's an asymmetry. 870 00:41:15,848 --> 00:41:17,840 AUDIENCE: Do they know why? 871 00:41:17,840 --> 00:41:19,220 NICHOLAS DIBELLA: Excuse me? 872 00:41:19,220 --> 00:41:20,120 Oh yeah, I know why. 873 00:41:20,120 --> 00:41:21,770 Yeah, we know why. 874 00:41:21,770 --> 00:41:24,470 Yeah, there's something very special 875 00:41:24,470 --> 00:41:28,610 about this little method that I mentioned 876 00:41:28,610 --> 00:41:31,790 that's responsible for the asymmetry. 877 00:41:31,790 --> 00:41:32,578 Yes? 878 00:41:32,578 --> 00:41:34,702 AUDIENCE: You said that throughout the whole thing, 879 00:41:34,702 --> 00:41:36,216 [INAUDIBLE] 880 00:41:36,216 --> 00:41:37,132 NICHOLAS DIBELLA: Yes. 881 00:41:37,132 --> 00:41:40,580 AUDIENCE: [INAUDIBLE] 882 00:41:40,580 --> 00:41:42,290 NICHOLAS DIBELLA: Well, I mean over here, 883 00:41:42,290 --> 00:41:43,495 you, in fact, do slow down. 884 00:41:43,495 --> 00:41:44,870 You have to actually turn around. 885 00:41:49,689 --> 00:41:51,605 That's actually the resolution to the paradox. 886 00:41:53,875 --> 00:41:55,250 So when you go in your spaceship, 887 00:41:55,250 --> 00:41:57,710 and you travel very far away and then turn around, 888 00:41:57,710 --> 00:41:59,240 you actually have to decelerate. 889 00:42:02,105 --> 00:42:04,730 Once you get to this point, you have to eventually turn around. 890 00:42:04,730 --> 00:42:06,105 So you have to actually slow down 891 00:42:06,105 --> 00:42:07,460 and turn the other direction. 892 00:42:07,460 --> 00:42:10,310 So you're not actually an observer that's 893 00:42:10,310 --> 00:42:12,380 moving at a constant speed. 894 00:42:12,380 --> 00:42:15,540 You are actually accelerating that little bit over there. 895 00:42:15,540 --> 00:42:18,800 And because of that, special relativity 896 00:42:18,800 --> 00:42:19,990 doesn't apply to you. 897 00:42:19,990 --> 00:42:23,700 It doesn't apply to you, the accelerated observer. 898 00:42:23,700 --> 00:42:26,240 And so that's responsible for the asymmetry. 899 00:42:26,240 --> 00:42:28,610 That's the resolution to the paradox. 900 00:42:28,610 --> 00:42:33,320 Special relativity can deal with accelerated motion. 901 00:42:33,320 --> 00:42:34,940 But you just can't be the observer 902 00:42:34,940 --> 00:42:37,130 that's doing the accelerating. 903 00:42:37,130 --> 00:42:40,760 I can sit here, and then evaluate 904 00:42:40,760 --> 00:42:45,580 how long the accelerated observer will see his clock 905 00:42:45,580 --> 00:42:46,370 tick. 906 00:42:46,370 --> 00:42:47,890 I can evaluate that. 907 00:42:47,890 --> 00:42:50,112 But I just can't be an accelerated observer 908 00:42:50,112 --> 00:42:51,320 when I'm doing that analysis. 909 00:42:51,320 --> 00:42:53,479 Special relativity doesn't apply to me. 910 00:42:53,479 --> 00:42:55,520 But, yeah, that's the asymmetry responsible here. 911 00:42:58,850 --> 00:43:02,480 So this is a very simple method of traveling into the future, 912 00:43:02,480 --> 00:43:04,160 in principle. 913 00:43:04,160 --> 00:43:09,710 You just get a spaceship, go out very far, come back. 914 00:43:09,710 --> 00:43:11,600 And then as some amount of time passes 915 00:43:11,600 --> 00:43:14,000 by for you in the spaceship, a longer amount of time 916 00:43:14,000 --> 00:43:15,833 will have passed by for the people on earth. 917 00:43:15,833 --> 00:43:18,260 So you've effectively traveled into the future. 918 00:43:18,260 --> 00:43:19,730 And depending on how fast you go, 919 00:43:19,730 --> 00:43:21,855 you can travel farther and farther into the future. 920 00:43:26,010 --> 00:43:30,330 So if you travel at 99.99& the speed of light, 921 00:43:30,330 --> 00:43:33,420 I wrote it down. 922 00:43:33,420 --> 00:43:35,610 As 10 years passes by for you in the spaceship, 923 00:43:35,610 --> 00:43:37,920 1,000 years passes by for the earth, 924 00:43:37,920 --> 00:43:40,920 people sitting on the earth. 925 00:43:40,920 --> 00:43:45,100 But if you go even faster, if you go at 99.99999% 926 00:43:45,100 --> 00:43:46,770 the speed of light, then it might 927 00:43:46,770 --> 00:43:50,670 be that as a day passes by for you, 928 00:43:50,670 --> 00:43:52,980 a million years passes by for the people on earth. 929 00:43:52,980 --> 00:43:57,720 That's just what relativity implies, in principle. 930 00:43:57,720 --> 00:44:00,630 So this is all very solid physics. 931 00:44:00,630 --> 00:44:01,950 None of this is controversial. 932 00:44:01,950 --> 00:44:05,063 AUDIENCE: [INAUDIBLE] 933 00:44:05,063 --> 00:44:06,229 NICHOLAS DIBELLA: Excuse me? 934 00:44:06,229 --> 00:44:10,630 AUDIENCE: [INAUDIBLE] 935 00:44:12,585 --> 00:44:14,460 NICHOLAS DIBELLA: Well, I'm not sure how many 936 00:44:14,460 --> 00:44:16,700 nines you have to add for that to be true. 937 00:44:16,700 --> 00:44:18,130 I haven't done the calculation. 938 00:44:18,130 --> 00:44:23,940 But you can arrange for any scenario to happen. 939 00:44:23,940 --> 00:44:28,410 In principle, you can arrange for any kind of future date 940 00:44:28,410 --> 00:44:30,360 to travel to, just by adjusting your speed. 941 00:44:30,360 --> 00:44:33,060 If you travel fast enough, you can get far enough 942 00:44:33,060 --> 00:44:35,397 in the future, if you wanted to. 943 00:44:35,397 --> 00:44:37,730 You would just have to do the calculation to figure out. 944 00:44:37,730 --> 00:44:39,750 But this class is completely non-mathematical. 945 00:44:39,750 --> 00:44:41,260 So I'm not going to the calculation. 946 00:44:41,260 --> 00:44:44,024 But if any of you have questions, 947 00:44:44,024 --> 00:44:45,190 I can show you the formulas. 948 00:44:45,190 --> 00:44:47,148 And you can play around with them, if you want. 949 00:44:47,148 --> 00:44:49,320 I can show you later, if you want. 950 00:44:49,320 --> 00:44:51,680 So in principle, time travel to the future is very easy. 951 00:44:51,680 --> 00:44:52,814 You just do this. 952 00:44:52,814 --> 00:44:54,730 Laws of physics say, time travel to the future 953 00:44:54,730 --> 00:44:56,580 is totally possible. 954 00:44:56,580 --> 00:44:59,190 So it's not really a physics issue 955 00:44:59,190 --> 00:45:02,354 that's responsible for our difficulty in getting 956 00:45:02,354 --> 00:45:03,020 into the future. 957 00:45:03,020 --> 00:45:04,635 It's really an engineering problem. 958 00:45:04,635 --> 00:45:07,710 Time travel into the future is really an engineering problem. 959 00:45:07,710 --> 00:45:10,350 It's just hard to build stuff that 960 00:45:10,350 --> 00:45:15,210 can travel fast enough to get a significant amount of time 961 00:45:15,210 --> 00:45:17,340 dilation to happen. 962 00:45:17,340 --> 00:45:21,080 Last class, when we talked about extraterrestrial intelligence, 963 00:45:21,080 --> 00:45:23,790 extraterrestrial civilizations, I mentioned some methods 964 00:45:23,790 --> 00:45:25,230 that extraterrestrials might want 965 00:45:25,230 --> 00:45:28,630 to use to travel across the galaxy to go very fast. 966 00:45:28,630 --> 00:45:30,990 So they might use something like an anti-matter rocket, 967 00:45:30,990 --> 00:45:34,800 or a nuclear fusion ramjet, or some other stuff. 968 00:45:34,800 --> 00:45:39,930 And people have thought about theoretical ways 969 00:45:39,930 --> 00:45:44,890 of getting to very fast speeds, very high fractions close 970 00:45:44,890 --> 00:45:46,290 to the speed of light. 971 00:45:46,290 --> 00:45:48,540 It's just that we have a hard time building 972 00:45:48,540 --> 00:45:50,720 stuff tend to do that. 973 00:45:50,720 --> 00:45:53,249 Maybe in 1,000 years, this will be feasible. 974 00:45:53,249 --> 00:45:53,790 I don't know. 975 00:45:53,790 --> 00:45:57,240 I'm not going to try to guess at our future technological 976 00:45:57,240 --> 00:45:58,890 evolution. 977 00:45:58,890 --> 00:46:00,190 Yes, in the back? 978 00:46:00,190 --> 00:46:04,190 AUDIENCE: [INAUDIBLE] 979 00:46:06,690 --> 00:46:08,440 NICHOLAS DIBELLA: Warp drive, that 980 00:46:08,440 --> 00:46:11,892 actually has to do with curving space and time. 981 00:46:11,892 --> 00:46:15,159 AUDIENCE: [INAUDIBLE] 982 00:46:15,159 --> 00:46:17,200 NICHOLAS DIBELLA: Yeah, there's kind of a folding 983 00:46:17,200 --> 00:46:18,220 of space and time that goes on. 984 00:46:18,220 --> 00:46:20,261 I'll talk about something similar actually later, 985 00:46:20,261 --> 00:46:21,785 when I talk about wormholes. 986 00:46:21,785 --> 00:46:22,660 It's similar to that. 987 00:46:22,660 --> 00:46:25,360 That has to do with general relativity. 988 00:46:25,360 --> 00:46:26,150 Yes? 989 00:46:26,150 --> 00:46:27,064 AUDIENCE: [INAUDIBLE] 990 00:46:27,064 --> 00:46:28,980 NICHOLAS DIBELLA: How do I travel to the past? 991 00:46:28,980 --> 00:46:30,813 That's what I'll talk about after the break. 992 00:46:33,000 --> 00:46:35,450 AUDIENCE: [INAUDIBLE] 993 00:46:41,100 --> 00:46:42,175 --keep the same speed. 994 00:46:42,175 --> 00:46:43,550 So you wouldn't have to slow down 995 00:46:43,550 --> 00:46:46,980 on [INAUDIBLE] the whole time. 996 00:46:46,980 --> 00:46:50,410 [INAUDIBLE] 997 00:46:52,860 --> 00:46:57,310 NICHOLAS DIBELLA: Oh, so actually when 998 00:46:57,310 --> 00:47:00,260 you're moving in a circle, you're actually accelerating. 999 00:47:00,260 --> 00:47:01,610 OK, your speed isn't changing. 1000 00:47:01,610 --> 00:47:02,920 But your velocity is changing. 1001 00:47:02,920 --> 00:47:06,550 So, actually, to be more precise, when I said everybody, 1002 00:47:06,550 --> 00:47:09,766 you have to be moving at a constant velocity, not just 1003 00:47:09,766 --> 00:47:10,390 constant speed. 1004 00:47:10,390 --> 00:47:12,184 Velocity is speed, plus direction. 1005 00:47:12,184 --> 00:47:13,600 So when you're moving in a circle, 1006 00:47:13,600 --> 00:47:16,030 your direction is constantly changing. 1007 00:47:16,030 --> 00:47:17,610 So you're actually accelerating when 1008 00:47:17,610 --> 00:47:19,720 you're moving in a circle, when you're rotating. 1009 00:47:19,720 --> 00:47:20,457 Yes? 1010 00:47:20,457 --> 00:47:23,936 AUDIENCE: [INAUDIBLE] 1011 00:47:25,427 --> 00:47:29,205 Which one would be faster, and which would be slower? 1012 00:47:29,205 --> 00:47:30,330 NICHOLAS DIBELLA: I forgot. 1013 00:47:33,700 --> 00:47:37,310 So the question is, which one-- 1014 00:47:37,310 --> 00:47:39,540 so in a spaceship, the clock on the front, 1015 00:47:39,540 --> 00:47:43,080 versus the clock in the back, how do the two readings 1016 00:47:43,080 --> 00:47:44,360 compare to each other? 1017 00:47:44,360 --> 00:47:47,220 It turns out that they actually don't show the same time. 1018 00:47:47,220 --> 00:47:50,670 They're actually not synchronized with each other. 1019 00:47:50,670 --> 00:47:53,100 I forgot which one trails which. 1020 00:47:53,100 --> 00:47:55,590 But they're actually not synchronized with each other. 1021 00:47:55,590 --> 00:47:57,680 They're off by a little bit. 1022 00:47:57,680 --> 00:48:00,810 They don't show the same time, which is also unexpected. 1023 00:48:00,810 --> 00:48:02,850 Yeah, there are a lot of unexpected things. 1024 00:48:02,850 --> 00:48:07,100 Time dilation, I mentioned lengths gets shorter. 1025 00:48:07,100 --> 00:48:09,714 Synchronization gets off. 1026 00:48:09,714 --> 00:48:11,880 Things start out synchronized, but they're no longer 1027 00:48:11,880 --> 00:48:13,320 synchronized. 1028 00:48:13,320 --> 00:48:15,840 Simultaneity is also relative. 1029 00:48:15,840 --> 00:48:17,960 The fact that if I observe two things that 1030 00:48:17,960 --> 00:48:19,510 happen at the same time, two things 1031 00:48:19,510 --> 00:48:22,620 happen simultaneously, that you actually won't if you're moving 1032 00:48:22,620 --> 00:48:25,280 at some speed relative to me. 1033 00:48:25,280 --> 00:48:27,540 Relativity is very strange. 1034 00:48:27,540 --> 00:48:29,040 It has lots of strange consequences, 1035 00:48:29,040 --> 00:48:32,890 lots of things that run counter to our common sense. 1036 00:48:32,890 --> 00:48:35,290 But if you work through the details of these two 1037 00:48:35,290 --> 00:48:38,010 postulates, you get all of them. 1038 00:48:38,010 --> 00:48:38,845 Yes? 1039 00:48:38,845 --> 00:48:42,310 AUDIENCE: If you reverse the rotation of the Earth, 1040 00:48:42,310 --> 00:48:44,290 would you go back in time? 1041 00:48:44,290 --> 00:48:46,081 NICHOLAS DIBELLA: If I reverse the rotation 1042 00:48:46,081 --> 00:48:49,330 of the Earth like Superman, would I turn time backwards? 1043 00:48:49,330 --> 00:48:53,270 No, but he was actually-- 1044 00:48:53,270 --> 00:48:55,099 maybe he was traveling faster than light. 1045 00:48:55,099 --> 00:48:56,640 Now, if you travel faster than light, 1046 00:48:56,640 --> 00:49:00,090 then you could actually theoretically 1047 00:49:00,090 --> 00:49:01,646 maybe travel back in time. 1048 00:49:01,646 --> 00:49:05,930 AUDIENCE: [INAUDIBLE] 1049 00:49:10,350 --> 00:49:12,140 NICHOLAS DIBELLA: Yeah, so tachyons, 1050 00:49:12,140 --> 00:49:14,787 these particles that I mentioned earlier, 1051 00:49:14,787 --> 00:49:16,620 they theoretically travel faster than light. 1052 00:49:16,620 --> 00:49:17,994 Special relativity would actually 1053 00:49:17,994 --> 00:49:20,910 imply that they travel back in time. 1054 00:49:20,910 --> 00:49:25,620 So, yeah, they actually travel back in time. 1055 00:49:25,620 --> 00:49:29,240 We have no idea if tachyons exist. 1056 00:49:29,240 --> 00:49:32,600 There's a lot of theoretical problems with them. 1057 00:49:32,600 --> 00:49:35,592 They're purely hypothetical. 1058 00:49:35,592 --> 00:49:36,588 Yeah? 1059 00:49:36,588 --> 00:49:40,572 AUDIENCE: [INAUDIBLE] 1060 00:49:58,145 --> 00:50:00,270 NICHOLAS DIBELLA: So if they're going back in time, 1061 00:50:00,270 --> 00:50:04,790 then do you eventually get back to the beginning of time, 1062 00:50:04,790 --> 00:50:06,910 like to the Big Bang? 1063 00:50:06,910 --> 00:50:08,740 And then what happens after that? 1064 00:50:08,740 --> 00:50:10,630 Yeah, I don't know. 1065 00:50:10,630 --> 00:50:11,480 I don't know. 1066 00:50:11,480 --> 00:50:13,060 I have no idea. 1067 00:50:13,060 --> 00:50:15,370 Tachyons to start off with, they're 1068 00:50:15,370 --> 00:50:17,980 on questionable foundations. 1069 00:50:17,980 --> 00:50:19,480 So any questions you ask about them, 1070 00:50:19,480 --> 00:50:20,646 you might get funny answers. 1071 00:50:20,646 --> 00:50:22,900 And you might not be able to answer them. 1072 00:50:22,900 --> 00:50:24,680 I don't know. 1073 00:50:24,680 --> 00:50:26,790 Yeah, that's a good question, though. 1074 00:50:26,790 --> 00:50:27,549 Question? 1075 00:50:27,549 --> 00:50:32,040 AUDIENCE: [INAUDIBLE] 1076 00:50:33,537 --> 00:50:37,529 --moving at a higher speed at one point in its revolution. 1077 00:50:37,529 --> 00:50:44,520 So that would-- it's moving at light speed so [INAUDIBLE] 1078 00:50:44,520 --> 00:50:48,250 NICHOLAS DIBELLA: OK, so I cheated a little bit. 1079 00:50:48,250 --> 00:50:49,660 Thanks for keeping me honest. 1080 00:50:49,660 --> 00:50:52,270 So I'm assuming the Earth is at rest. 1081 00:50:52,270 --> 00:50:55,810 In fact, Earth is actually rotating. 1082 00:50:55,810 --> 00:50:57,670 It's revolving around the sun. 1083 00:50:57,670 --> 00:51:02,540 It's actually rotating about its axis at a 24 hour period. 1084 00:51:02,540 --> 00:51:04,550 So actually, the Earth is actually 1085 00:51:04,550 --> 00:51:08,570 not the type of non-accelerating inertial observer 1086 00:51:08,570 --> 00:51:09,820 that special relativity needs. 1087 00:51:09,820 --> 00:51:13,210 But it's approximately good. 1088 00:51:16,650 --> 00:51:21,230 For the speeds involved here, it's definitely negligible. 1089 00:51:21,230 --> 00:51:24,220 The rotation and the revolution, it's negligible. 1090 00:51:24,220 --> 00:51:28,154 You can assume that it's essentially at rest, 1091 00:51:28,154 --> 00:51:29,320 or moving at constant speed. 1092 00:51:29,320 --> 00:51:32,560 You can assume that. 1093 00:51:32,560 --> 00:51:35,260 Any more questions about traveling to the future 1094 00:51:35,260 --> 00:51:38,250 by this method? 1095 00:51:38,250 --> 00:51:39,785 OK, we'll take a five minute break. 1096 00:51:39,785 --> 00:51:41,660 Then I'll talk about time travel to the past. 1097 00:51:52,491 --> 00:51:53,990 Yeah, there's a very simple formula. 1098 00:51:59,130 --> 00:52:04,160 So suppose the guy sitting, the guy 1099 00:52:04,160 --> 00:52:07,462 we assume to be at rest, suppose he measures-- 1100 00:52:07,462 --> 00:52:08,670 so he sees two events happen. 1101 00:52:08,670 --> 00:52:11,000 And then he measures on his watch 1102 00:52:11,000 --> 00:52:14,520 how long the time interval between the two events. 1103 00:52:14,520 --> 00:52:16,070 And let's say he gets some number. 1104 00:52:16,070 --> 00:52:18,050 He gets t zero. 1105 00:52:18,050 --> 00:52:20,540 Let's suppose that that's the number that he get. 1106 00:52:20,540 --> 00:52:22,190 And now, let's suppose that the train 1107 00:52:22,190 --> 00:52:25,520 was traveling at some speed v relative to him. 1108 00:52:25,520 --> 00:52:30,090 So the train travels at some speed v. 1109 00:52:30,090 --> 00:52:32,870 And then you ask, what's the time 1110 00:52:32,870 --> 00:52:35,840 interval somebody on the train gets between the two events? 1111 00:52:35,840 --> 00:52:39,890 You ask, what is that time interval called t? 1112 00:52:39,890 --> 00:52:43,130 And call the speed of light c. 1113 00:52:43,130 --> 00:52:45,530 And it turns out, you can prove this, 1114 00:52:45,530 --> 00:52:52,910 that t equals t0, divided by the square root of 1 minus v 1115 00:52:52,910 --> 00:52:55,984 squared, over c squared. 1116 00:52:55,984 --> 00:52:57,900 So you can play around with that, if you want. 1117 00:53:00,570 --> 00:53:09,600 And you can derive it through pure geometry, just based 1118 00:53:09,600 --> 00:53:11,710 on these two postulates. 1119 00:53:16,852 --> 00:53:18,810 I mentioned earlier that the way we define time 1120 00:53:18,810 --> 00:53:20,000 is kind of operationally. 1121 00:53:20,000 --> 00:53:22,290 So one way you can define time is 1122 00:53:22,290 --> 00:53:25,290 just suppose you have some box. 1123 00:53:25,290 --> 00:53:28,100 Just see how long it takes for time to go up and down. 1124 00:53:28,100 --> 00:53:30,490 Maybe have mirrors. 1125 00:53:30,490 --> 00:53:32,850 How long it takes for light to go up and down, 1126 00:53:32,850 --> 00:53:35,340 you have kind of a light clock. 1127 00:53:35,340 --> 00:53:39,300 So we can imagine installing some kind of light clock 1128 00:53:39,300 --> 00:53:41,700 inside of a train. 1129 00:53:41,700 --> 00:53:52,380 And then ask, suppose one bounce up 1130 00:53:52,380 --> 00:53:56,780 and down happens for somebody on the train. 1131 00:53:56,780 --> 00:53:59,610 Then based on the fact that the speed of light 1132 00:53:59,610 --> 00:54:01,830 is the same for everybody, how long 1133 00:54:01,830 --> 00:54:06,930 should it take for somebody sitting on the bench? 1134 00:54:06,930 --> 00:54:10,450 You could just work through the geometry, and you'll get that. 1135 00:54:10,450 --> 00:54:13,960 It doesn't take very long to show it. 1136 00:54:13,960 --> 00:54:18,390 But it takes a while to get used to this kind of thinking. 1137 00:54:18,390 --> 00:54:20,700 But you can basically derive this formula 1138 00:54:20,700 --> 00:54:25,020 in less than five lines, just in a few steps. 1139 00:54:32,580 --> 00:54:34,230 And then there's a similar formula 1140 00:54:34,230 --> 00:54:37,070 for lengths, how short they get, depending 1141 00:54:37,070 --> 00:54:38,620 on how fast you're moving. 1142 00:54:38,620 --> 00:54:43,110 For length, all you do is you move this quantity 1143 00:54:43,110 --> 00:54:45,210 from the denominator to the numerator. 1144 00:54:45,210 --> 00:54:48,150 It turns out that this 1 over the square root 1145 00:54:48,150 --> 00:54:49,310 is always greater than 1. 1146 00:54:51,880 --> 00:54:55,330 So moving clocks ticks low. 1147 00:54:55,330 --> 00:54:56,730 So as some amount of time-- 1148 00:55:02,340 --> 00:55:04,670 yeah, so since they ticks slower-- 1149 00:55:07,620 --> 00:55:12,180 you have to think about it to see why it makes sense. 1150 00:55:12,180 --> 00:55:13,880 It all works out. 1151 00:55:13,880 --> 00:55:15,890 Up to now, I've just talked about time travel 1152 00:55:15,890 --> 00:55:17,287 to the future. 1153 00:55:17,287 --> 00:55:19,370 Special relativity just seems to allow time travel 1154 00:55:19,370 --> 00:55:22,080 to the future, however much we want 1155 00:55:22,080 --> 00:55:25,572 in getting as far into the future as we want. 1156 00:55:25,572 --> 00:55:27,780 I mentioned briefly the possibility of using tachyons 1157 00:55:27,780 --> 00:55:28,571 to get to the past. 1158 00:55:28,571 --> 00:55:30,750 But nobody has any idea if tachyons exist. 1159 00:55:30,750 --> 00:55:33,092 So forget about that. 1160 00:55:33,092 --> 00:55:34,550 So while special relativity doesn't 1161 00:55:34,550 --> 00:55:37,100 seem to offer any possibility of getting to the past, 1162 00:55:37,100 --> 00:55:38,930 general relativity actually seems 1163 00:55:38,930 --> 00:55:43,580 to offer some hope that you might 1164 00:55:43,580 --> 00:55:45,450 be able to get to the past. 1165 00:55:45,450 --> 00:55:49,550 I should mention from the start that nobody in the world 1166 00:55:49,550 --> 00:55:52,730 knows if it's possible to travel back in time. 1167 00:55:52,730 --> 00:55:53,965 Nobody knows. 1168 00:55:53,965 --> 00:55:54,590 Nobody has any. 1169 00:55:54,590 --> 00:55:57,290 Idea everybody agrees that the method I just 1170 00:55:57,290 --> 00:55:59,859 talked about with the spaceship, time dilation 1171 00:55:59,859 --> 00:56:01,400 through special relativity, everybody 1172 00:56:01,400 --> 00:56:02,750 agrees that that works. 1173 00:56:02,750 --> 00:56:04,310 That's completely uncontroversial. 1174 00:56:04,310 --> 00:56:06,440 But nobody has any idea if it's possible to time 1175 00:56:06,440 --> 00:56:08,970 travel to the past. 1176 00:56:08,970 --> 00:56:14,730 But people have come up with ideas that might work. 1177 00:56:14,730 --> 00:56:16,380 It might not work. 1178 00:56:16,380 --> 00:56:19,200 They're just ideas. 1179 00:56:19,200 --> 00:56:24,030 And all these ideas generally rest on general relativity. 1180 00:56:24,030 --> 00:56:26,930 So I mentioned earlier that special relativity just 1181 00:56:26,930 --> 00:56:30,560 applies to observers who are moving a constant speed. 1182 00:56:30,560 --> 00:56:32,780 But general relativity actually applies to observers 1183 00:56:32,780 --> 00:56:34,890 that are accelerating. 1184 00:56:34,890 --> 00:56:36,470 So if I start out and start moving 1185 00:56:36,470 --> 00:56:38,240 at faster and faster speeds, then I'm 1186 00:56:38,240 --> 00:56:39,700 an accelerating observer. 1187 00:56:39,700 --> 00:56:41,930 And then I'd have to use general relativity 1188 00:56:41,930 --> 00:56:43,880 to talk about events, to talk about time 1189 00:56:43,880 --> 00:56:45,870 intervals, and spatial intervals, 1190 00:56:45,870 --> 00:56:48,020 and so forth, and talk about physics. 1191 00:56:50,750 --> 00:56:53,450 Also, if I'm revolving, if I'm rotating, 1192 00:56:53,450 --> 00:56:54,860 then I'm an accelerated observer. 1193 00:56:54,860 --> 00:56:58,530 And I have to use general relativity. 1194 00:56:58,530 --> 00:57:01,220 So according to general relativity, 1195 00:57:01,220 --> 00:57:09,020 space and time are best thought of not as different things, 1196 00:57:09,020 --> 00:57:14,630 but as different elements of an underlying spacetime. 1197 00:57:14,630 --> 00:57:16,970 So this is that space and time are unified 1198 00:57:16,970 --> 00:57:20,840 in an object we call spacetime. 1199 00:57:20,840 --> 00:57:23,330 Now, according to general relativity 1200 00:57:23,330 --> 00:57:25,520 mass curves spacetime. 1201 00:57:37,680 --> 00:57:39,970 So spacetime is just this object that space and time 1202 00:57:39,970 --> 00:57:40,800 are part of. 1203 00:57:40,800 --> 00:57:43,850 They're like different sides of the same coin. 1204 00:57:43,850 --> 00:57:45,310 They're fundamentally different. 1205 00:57:45,310 --> 00:57:47,480 But you can't think of one without the other. 1206 00:57:47,480 --> 00:57:49,670 They're attached to each other. 1207 00:57:49,670 --> 00:57:52,560 So that's what space time is. 1208 00:57:52,560 --> 00:57:55,510 What does it mean that curve space time? 1209 00:57:55,510 --> 00:57:58,630 Well, we say that when there's mass presence, 1210 00:57:58,630 --> 00:57:59,680 space time gets curved. 1211 00:57:59,680 --> 00:58:01,210 The more mass you have somewhere, 1212 00:58:01,210 --> 00:58:03,560 the more space time is curved there. 1213 00:58:03,560 --> 00:58:08,020 So special relativity, not only does 1214 00:58:08,020 --> 00:58:09,850 it not deal with accelerated observers. 1215 00:58:09,850 --> 00:58:11,862 But it also doesn't deal with gravity. 1216 00:58:11,862 --> 00:58:14,320 And there's actually a very deep connection between gravity 1217 00:58:14,320 --> 00:58:15,100 and acceleration. 1218 00:58:15,100 --> 00:58:16,840 It's called the equivalence principle 1219 00:58:16,840 --> 00:58:19,150 that Einstein discovered. 1220 00:58:19,150 --> 00:58:22,930 It actually says that gravity and acceleration are actually 1221 00:58:22,930 --> 00:58:26,560 equivalent to each other, in a certain sense. 1222 00:58:26,560 --> 00:58:30,610 And it was actually-- 1223 00:58:30,610 --> 00:58:34,240 Einstein said it was like the most brilliant insight 1224 00:58:34,240 --> 00:58:35,932 that he ever had. 1225 00:58:35,932 --> 00:58:37,390 It was his happiest moment in life, 1226 00:58:37,390 --> 00:58:39,889 when he had that insight, that acceleration and gravity were 1227 00:58:39,889 --> 00:58:41,350 actually the same. 1228 00:58:41,350 --> 00:58:43,600 But I can't really get into that, because I 1229 00:58:43,600 --> 00:58:46,000 want to explain how this works. 1230 00:58:46,000 --> 00:58:49,780 But so special relativity doesn't deal with acceleration. 1231 00:58:49,780 --> 00:58:51,080 It doesn't deal with gravity. 1232 00:58:51,080 --> 00:58:54,190 But general relativity does. 1233 00:58:54,190 --> 00:58:57,910 So we say that the space time of special relativity is flat. 1234 00:58:57,910 --> 00:58:59,430 It's called a flat space time. 1235 00:58:59,430 --> 00:59:00,970 And everything that I said earlier 1236 00:59:00,970 --> 00:59:03,580 is true just in flat spacetime, the way 1237 00:59:03,580 --> 00:59:05,260 that all that stuff works. 1238 00:59:05,260 --> 00:59:08,940 In curved spacetime, things are very different. 1239 00:59:08,940 --> 00:59:11,380 In curved spacetime, there is another kind 1240 00:59:11,380 --> 00:59:13,120 of time dilation present. 1241 00:59:13,120 --> 00:59:19,270 It turns out that the closer you are to a massive object, 1242 00:59:19,270 --> 00:59:22,090 the slower time goes for you. 1243 00:59:22,090 --> 00:59:26,260 So suppose this is the earth. 1244 00:59:26,260 --> 00:59:28,930 If you're on the surface of the Earth, time goes slower for you 1245 00:59:28,930 --> 00:59:33,470 here that it does for somebody over there. 1246 00:59:33,470 --> 00:59:41,980 So maybe as an hour passes by for somebody over here, 1247 00:59:41,980 --> 00:59:45,440 more than an hour passes by for somebody farther away. 1248 00:59:45,440 --> 00:59:49,360 So the greater the gravity, the more curve the spacetime, 1249 00:59:49,360 --> 00:59:51,616 and then the more time will be stretched, 1250 00:59:51,616 --> 00:59:52,990 the more time we will be dilated. 1251 00:59:52,990 --> 00:59:55,144 So this is called gravitational time dilation. 1252 01:00:09,000 --> 01:00:11,880 Do any of you sleep on bunk beds, maybe a brother 1253 01:00:11,880 --> 01:00:13,990 or sister? 1254 01:00:13,990 --> 01:00:15,280 Once? 1255 01:00:15,280 --> 01:00:15,780 I used to. 1256 01:00:19,440 --> 01:00:21,480 At some point in your life, some region of 1257 01:00:21,480 --> 01:00:25,680 spacetime in your life, me too. 1258 01:00:25,680 --> 01:00:27,840 I shared it with my younger brother. 1259 01:00:27,840 --> 01:00:29,460 So he would sleep on the bottom. 1260 01:00:29,460 --> 01:00:31,770 And I would sleep on the top. 1261 01:00:31,770 --> 01:00:34,635 So gravity is greater-- 1262 01:00:34,635 --> 01:00:36,510 as you get closer to the center of the Earth, 1263 01:00:36,510 --> 01:00:37,280 gravity increases. 1264 01:00:37,280 --> 01:00:39,420 So the gravity is greater on the bottom bunk 1265 01:00:39,420 --> 01:00:42,520 than it is for the top bunk. 1266 01:00:42,520 --> 01:00:46,270 So my brother actually aged less than I did during those years 1267 01:00:46,270 --> 01:00:48,500 that we shared the bunk bed. 1268 01:00:48,500 --> 01:00:51,900 But as I said, here's three years younger than me. 1269 01:00:51,900 --> 01:00:54,940 And so I've had three more years to waste my life to mess up, 1270 01:00:54,940 --> 01:00:56,730 to screw up in life. 1271 01:00:56,730 --> 01:00:58,650 And he's the one gaining the extra time 1272 01:00:58,650 --> 01:01:01,420 over all these years. 1273 01:01:01,420 --> 01:01:03,780 Now that I've thought about it, this is very unfair. 1274 01:01:03,780 --> 01:01:05,939 I should have been the one on the bottom. 1275 01:01:05,939 --> 01:01:07,980 He's been getting this time, all this extra time. 1276 01:01:07,980 --> 01:01:09,570 It's unfair. 1277 01:01:09,570 --> 01:01:12,060 And now studying general relativity, 1278 01:01:12,060 --> 01:01:13,440 I have this outrage. 1279 01:01:13,440 --> 01:01:16,660 AUDIENCE: [INAUDIBLE] 1280 01:01:16,660 --> 01:01:20,430 NICHOLAS DIBELLA: Yeah, so the difference in time 1281 01:01:20,430 --> 01:01:23,390 is completely unmeasurable. 1282 01:01:23,390 --> 01:01:26,010 The difference in gravity is completely unmeasurable. 1283 01:01:26,010 --> 01:01:28,590 So the difference in time is completely unmeasurable. 1284 01:01:28,590 --> 01:01:31,157 But, in principle, it's actually there. 1285 01:01:31,157 --> 01:01:32,240 You just can't measure it. 1286 01:01:32,240 --> 01:01:32,910 It's actually there. 1287 01:01:32,910 --> 01:01:35,160 It's a little element of reality that you can't actually see. 1288 01:01:35,160 --> 01:01:36,030 But it's there. 1289 01:01:36,030 --> 01:01:36,990 It's inside of nature. 1290 01:01:41,400 --> 01:01:45,390 So did you share the bunk bed with a brother? 1291 01:01:45,390 --> 01:01:47,520 You were younger? 1292 01:01:47,520 --> 01:01:55,260 Yeah, we need to educate the next generation of brothers, 1293 01:01:55,260 --> 01:01:56,430 and get things right. 1294 01:01:58,950 --> 01:02:00,240 One day, I shall seek revenge. 1295 01:02:00,240 --> 01:02:03,352 Maybe I'll travel back in time and take care of it. 1296 01:02:03,352 --> 01:02:08,776 AUDIENCE: So the way spacetime occurs [INAUDIBLE] 1297 01:02:13,416 --> 01:02:16,314 Is the universe then longer? 1298 01:02:16,314 --> 01:02:21,983 [INAUDIBLE] 1299 01:02:21,983 --> 01:02:23,066 NICHOLAS DIBELLA: Oh, so-- 1300 01:02:23,066 --> 01:02:29,904 AUDIENCE: [INAUDIBLE] --much, much longer time. 1301 01:02:29,904 --> 01:02:31,320 NICHOLAS DIBELLA: So when I talked 1302 01:02:31,320 --> 01:02:36,880 about the age of the universe in the first couple of lectures, 1303 01:02:36,880 --> 01:02:40,470 I had a particular kind of observer in mind. 1304 01:02:40,470 --> 01:02:45,120 So whenever we make these observations, 1305 01:02:45,120 --> 01:02:46,950 we have to first synchronize our clocks. 1306 01:02:46,950 --> 01:02:49,590 And we have to have some kind of frame in which everything 1307 01:02:49,590 --> 01:02:50,880 is measured in. 1308 01:02:50,880 --> 01:02:54,180 And I mentioned the existence of this microwave background 1309 01:02:54,180 --> 01:02:57,420 that's always out there. 1310 01:02:57,420 --> 01:02:59,700 And the way that-- 1311 01:02:59,700 --> 01:03:01,290 so the time that I was mentioning, 1312 01:03:01,290 --> 01:03:03,450 the way that we synchronize our clocks, 1313 01:03:03,450 --> 01:03:07,020 the way we keep track of time, at least the very natural way 1314 01:03:07,020 --> 01:03:13,140 of doing it, is to just synchronize your clocks 1315 01:03:13,140 --> 01:03:16,830 based on what the temperature of the microwave background is. 1316 01:03:16,830 --> 01:03:19,040 So if it's at a certain temperature, 1317 01:03:19,040 --> 01:03:20,620 you say it's a certain time. 1318 01:03:20,620 --> 01:03:23,259 And so this is one particular type of observer. 1319 01:03:23,259 --> 01:03:24,800 It's a very natural type of observer, 1320 01:03:24,800 --> 01:03:27,000 because the microwave is out there. 1321 01:03:27,000 --> 01:03:30,456 And when it's a certain temperature-- 1322 01:03:34,110 --> 01:03:36,780 you also want it to look uniform, a certain temperature, 1323 01:03:36,780 --> 01:03:39,210 and look reasonably uniform and isotropic, 1324 01:03:39,210 --> 01:03:40,650 the same in all directions. 1325 01:03:40,650 --> 01:03:44,250 When you do this, then you have a kind of natural reference 1326 01:03:44,250 --> 01:03:45,610 frame, we call it. 1327 01:03:45,610 --> 01:03:48,660 And that's the reference frame that I had in mind 1328 01:03:48,660 --> 01:03:51,170 when I was talking about the age of the universe. 1329 01:03:51,170 --> 01:03:54,510 But, yeah, so time will pass by for other kinds of frames, 1330 01:03:54,510 --> 01:03:55,800 for other kinds of observers. 1331 01:03:59,550 --> 01:04:03,530 But they won't be any longer than that, it turns out. 1332 01:04:03,530 --> 01:04:06,162 They won't be no longer than the one that I mentioned. 1333 01:04:06,162 --> 01:04:07,620 It's called the co-moving observer. 1334 01:04:07,620 --> 01:04:09,453 They won't actually be any longer than that. 1335 01:04:09,453 --> 01:04:11,070 They might be shorter. 1336 01:04:11,070 --> 01:04:14,880 But they won't be any longer than that. 1337 01:04:14,880 --> 01:04:19,780 But it's always important to say, who's doing the observing? 1338 01:04:19,780 --> 01:04:22,320 This is the time as measured by who? 1339 01:04:22,320 --> 01:04:24,270 Who measures it? 1340 01:04:24,270 --> 01:04:26,520 Good point. 1341 01:04:26,520 --> 01:04:29,160 So this is called gravitational time dilation. 1342 01:04:29,160 --> 01:04:31,140 And if you think about it, this actually 1343 01:04:31,140 --> 01:04:36,230 provides another way of traveling into the future. 1344 01:04:36,230 --> 01:04:37,880 I'll get to the past in a minute. 1345 01:04:37,880 --> 01:04:38,730 But this actually provides another way 1346 01:04:38,730 --> 01:04:40,150 of traveling into the future. 1347 01:04:40,150 --> 01:04:43,070 So what you can do is you can get a very massive thing, 1348 01:04:43,070 --> 01:04:45,210 like maybe a very massive star, or a black hole. 1349 01:04:47,914 --> 01:04:49,080 I won't go into black holes. 1350 01:04:49,080 --> 01:04:53,250 But black holes can be very massive. 1351 01:04:53,250 --> 01:04:58,060 And if you sit near the edge of where the object ends, 1352 01:04:58,060 --> 01:05:00,390 like if you had a very massive star, you sit over here, 1353 01:05:00,390 --> 01:05:02,790 then time goes slower for you here than it 1354 01:05:02,790 --> 01:05:04,180 does for somebody over here. 1355 01:05:04,180 --> 01:05:07,190 So all you need to do is find a very, very massive thing, 1356 01:05:07,190 --> 01:05:08,700 build it or something, I don't know. 1357 01:05:08,700 --> 01:05:11,595 Get a very, very massive thing, sit at the edge of it, 1358 01:05:11,595 --> 01:05:13,452 and just wait a little bit. 1359 01:05:13,452 --> 01:05:14,260 Just wait a while. 1360 01:05:16,890 --> 01:05:19,860 Depending on the mass of this thing, 1361 01:05:19,860 --> 01:05:23,100 and depending on how far away something else is, then 1362 01:05:23,100 --> 01:05:27,524 as some amount of time passes by for you, more of amount of time 1363 01:05:27,524 --> 01:05:28,440 will pass by for them. 1364 01:05:28,440 --> 01:05:30,940 So you can arrange it so that-- 1365 01:05:30,940 --> 01:05:35,550 if you're an engineer who can do anything, 1366 01:05:35,550 --> 01:05:38,940 if you're a god engineer, then you 1367 01:05:38,940 --> 01:05:42,170 can arrange it so that as a day passes by for you, 1368 01:05:42,170 --> 01:05:43,902 a year passes by for them. 1369 01:05:43,902 --> 01:05:45,860 So you can also use gravitational time relation 1370 01:05:45,860 --> 01:05:48,304 to travel into the future. 1371 01:05:48,304 --> 01:05:51,608 AUDIENCE: [INAUDIBLE] 1372 01:06:00,005 --> 01:06:01,380 NICHOLAS DIBELLA: Well, actually, 1373 01:06:01,380 --> 01:06:03,921 at the center of a black hole, time and space cease to exist. 1374 01:06:06,712 --> 01:06:08,170 If I have time at the end of class, 1375 01:06:08,170 --> 01:06:10,120 I'll talk about black holes for a couple of minutes. 1376 01:06:10,120 --> 01:06:12,536 But now, I want to talk actually about something even more 1377 01:06:12,536 --> 01:06:13,780 interesting than black holes. 1378 01:06:13,780 --> 01:06:15,920 They're called worm holes. 1379 01:06:15,920 --> 01:06:19,450 So over the years, people have proposed a number of ways 1380 01:06:19,450 --> 01:06:20,650 of traveling back in time. 1381 01:06:20,650 --> 01:06:22,937 Nobody knows if any of them can actually happen. 1382 01:06:22,937 --> 01:06:24,520 But today I'll talk about one of them. 1383 01:06:24,520 --> 01:06:27,340 It involves something called a worm hole. 1384 01:06:27,340 --> 01:06:30,980 So let's imagine, just for simplicity, 1385 01:06:30,980 --> 01:06:32,905 let's imagine that space is two dimensional. 1386 01:06:32,905 --> 01:06:36,580 It's like a sheet of paper, just to help us visualize things. 1387 01:06:36,580 --> 01:06:41,140 Just imagine space is two dimensional. 1388 01:06:41,140 --> 01:06:44,500 And we can imagine looking at space from the side. 1389 01:06:44,500 --> 01:06:46,720 So we can imagine-- suppose this is all of space. 1390 01:06:46,720 --> 01:06:48,414 You can imagine looking at it like this. 1391 01:06:48,414 --> 01:06:49,330 So it looks like that. 1392 01:06:52,360 --> 01:06:57,640 General relativity allows for the possibility of these things 1393 01:06:57,640 --> 01:07:02,650 called wormholes, which actually connect two points in space 1394 01:07:02,650 --> 01:07:03,310 like a tunnel. 1395 01:07:17,610 --> 01:07:20,100 It's not just any kind of a tunnel. 1396 01:07:20,100 --> 01:07:24,180 It's actually a shortcut between these two points. 1397 01:07:24,180 --> 01:07:26,760 So this is the space-- 1398 01:07:26,760 --> 01:07:31,082 I mean, you might be wondering why this is curved. 1399 01:07:31,082 --> 01:07:32,790 I've been talking about curved spacetime. 1400 01:07:32,790 --> 01:07:35,730 So maybe you could think, well, maybe that's why it's curved. 1401 01:07:35,730 --> 01:07:39,550 No, don't worry too much about it. 1402 01:07:39,550 --> 01:07:42,210 But general relativity actually allows 1403 01:07:42,210 --> 01:07:45,200 for the possibility of making things, 1404 01:07:45,200 --> 01:07:47,460 we call them warm holes, that can actually connection 1405 01:07:47,460 --> 01:07:49,350 two distant points in space. 1406 01:07:49,350 --> 01:07:51,090 So while it might take-- 1407 01:07:54,360 --> 01:07:58,440 let's get realistic numbers. 1408 01:07:58,440 --> 01:08:02,270 While star Sirius is about 54 trillion miles away. 1409 01:08:02,270 --> 01:08:05,160 It's very far, 54 trillion miles away. 1410 01:08:05,160 --> 01:08:08,045 If you traveled at the speed of light, which is very fast, 1411 01:08:08,045 --> 01:08:09,420 then it would take you nine years 1412 01:08:09,420 --> 01:08:11,462 to reach it if you just traveled in the way 1413 01:08:11,462 --> 01:08:12,420 that we usually travel. 1414 01:08:12,420 --> 01:08:14,711 It would just go from here to there in a straight line. 1415 01:08:14,711 --> 01:08:18,100 It would take you nine years to reach Sirius. 1416 01:08:18,100 --> 01:08:20,130 But if the Earth and the star Sirius-- 1417 01:08:20,130 --> 01:08:27,060 let's say the Earth is right here and Sirius is right here. 1418 01:08:29,939 --> 01:08:33,979 If the Earth and Sirius are connected by a wormhole, 1419 01:08:33,979 --> 01:08:40,729 then you can theoretically create a wormhole of any size. 1420 01:08:40,729 --> 01:08:44,189 And you can make a shortcut between these two points. 1421 01:08:44,189 --> 01:08:47,990 And while this whole thing might be 54 trillion miles 1422 01:08:47,990 --> 01:08:50,720 the usual way, I'm not drawing it to scale, 1423 01:08:50,720 --> 01:08:56,484 this wormhole might only be 10 feet long. 1424 01:08:56,484 --> 01:08:58,359 General relativity allows for the possibility 1425 01:08:58,359 --> 01:09:03,310 of these really weird things, these shortcuts in space. 1426 01:09:03,310 --> 01:09:05,859 They're called wormholes. 1427 01:09:05,859 --> 01:09:10,560 Now, the way that time travel to the past would work 1428 01:09:10,560 --> 01:09:11,260 is like this. 1429 01:09:14,890 --> 01:09:17,856 So the wormhole has a couple of mounds. 1430 01:09:17,856 --> 01:09:19,689 And the way to get from one mouth to another 1431 01:09:19,689 --> 01:09:21,229 is you just go inside of it. 1432 01:09:21,229 --> 01:09:22,270 So you find the wormhole. 1433 01:09:22,270 --> 01:09:23,680 You make it somehow. 1434 01:09:23,680 --> 01:09:26,240 I'm not going to I try to say how to make a. 1435 01:09:26,240 --> 01:09:28,762 Wormhole but general relativity allows for their existence. 1436 01:09:28,762 --> 01:09:30,845 And some people have thought of ways of making it. 1437 01:09:30,845 --> 01:09:34,479 So let's just assume that they can be made. 1438 01:09:34,479 --> 01:09:37,260 You could, in principle, find the mouth of the wormhole, 1439 01:09:37,260 --> 01:09:42,550 go inside of it, then come out, and get to the star, 1440 01:09:42,550 --> 01:09:43,595 make the shortcut. 1441 01:09:43,595 --> 01:09:46,285 AUDIENCE: [INAUDIBLE] 1442 01:09:46,285 --> 01:09:48,160 NICHOLAS DIBELLA: It might be 10 feet across. 1443 01:09:48,160 --> 01:09:49,910 So you can travel whatever speed you want. 1444 01:09:52,819 --> 01:09:56,680 You could walk, or you just hop in it. 1445 01:09:56,680 --> 01:09:59,380 Or maybe it might be in front of you, and you just dive in it. 1446 01:09:59,380 --> 01:10:01,021 It might be something like that. 1447 01:10:01,021 --> 01:10:02,292 AUDIENCE: [INAUDIBLE] 1448 01:10:02,292 --> 01:10:03,750 NICHOLAS DIBELLA: Have I seen what? 1449 01:10:03,750 --> 01:10:06,670 AUDIENCE: [INAUDIBLE] 1450 01:10:07,040 --> 01:10:09,040 NICHOLAS DIBELLA: I only have a few more minutes 1451 01:10:09,040 --> 01:10:10,130 to describe this. 1452 01:10:10,130 --> 01:10:12,520 So here's how time travel to the past would work. 1453 01:10:12,520 --> 01:10:16,120 So you take one of these mounds. 1454 01:10:16,120 --> 01:10:19,420 And you accelerate it. 1455 01:10:19,420 --> 01:10:22,499 You get it to a very fast speed, maybe like 99.99% 1456 01:10:22,499 --> 01:10:23,290 the speed of light. 1457 01:10:23,290 --> 01:10:24,246 Yeah? 1458 01:10:24,246 --> 01:10:27,592 AUDIENCE: [INAUDIBLE] 1459 01:10:33,810 --> 01:10:39,660 NICHOLAS DIBELLA: Maybe, but for now, don't worry about that. 1460 01:10:44,260 --> 01:10:47,966 I only have a couple more minutes to describe this. 1461 01:10:47,966 --> 01:10:49,590 So the way you time travel to the past, 1462 01:10:49,590 --> 01:10:50,798 you take one of these mounds. 1463 01:10:50,798 --> 01:10:54,170 You get it to go very fast, maybe go this way. 1464 01:10:54,170 --> 01:10:58,500 You get it to go very fast, and then bring it back. 1465 01:10:58,500 --> 01:11:01,441 In principle, this kind of thing might be possible, 1466 01:11:01,441 --> 01:11:03,190 similar to what we did with the spaceship. 1467 01:11:03,190 --> 01:11:05,860 Remember, we took the spaceship, made it go out, 1468 01:11:05,860 --> 01:11:07,860 made it come back. 1469 01:11:07,860 --> 01:11:13,890 And if you do this, then general relativity actually 1470 01:11:13,890 --> 01:11:20,220 says than, that outside of the wormhole, if you do this, then 1471 01:11:20,220 --> 01:11:23,785 this mouth will age less than this mouth sitting over here. 1472 01:11:23,785 --> 01:11:25,160 I mean, you only move this mouth. 1473 01:11:25,160 --> 01:11:26,560 This mouth stays at rest. 1474 01:11:26,560 --> 01:11:28,200 It says stationary. 1475 01:11:28,200 --> 01:11:32,760 So while this mouth might age five years when you move it 1476 01:11:32,760 --> 01:11:36,920 very far, very fast that way, then bring it back this way, 1477 01:11:36,920 --> 01:11:40,790 this just ages five years, this mouth might age 10 years. 1478 01:11:40,790 --> 01:11:43,650 And this is what observers outside of the wormhole 1479 01:11:43,650 --> 01:11:44,380 will agree on. 1480 01:11:44,380 --> 01:11:47,310 That's what general relativity says. 1481 01:11:47,310 --> 01:11:50,940 So general relativity says that the two clocks there 1482 01:11:50,940 --> 01:11:54,200 and there will disagree if you're outside of the wormhole. 1483 01:11:54,200 --> 01:11:56,850 But if you're inside the wormhole, 1484 01:11:56,850 --> 01:12:02,350 the general relativity actually says that these two times, 1485 01:12:02,350 --> 01:12:05,990 the times for both mouths, they have to always be synchronized. 1486 01:12:05,990 --> 01:12:07,787 They have to always agree. 1487 01:12:07,787 --> 01:12:09,620 Very peculiar feature of general relativity, 1488 01:12:09,620 --> 01:12:11,460 they have to always agree. 1489 01:12:11,460 --> 01:12:14,790 So here's a possible way that you can travel back in time. 1490 01:12:14,790 --> 01:12:19,975 So you get this mouth to move back and forth very fast 1491 01:12:19,975 --> 01:12:21,600 so that to outside observers, observers 1492 01:12:21,600 --> 01:12:26,310 outside the black hole-- sorry, the wormhole, 1493 01:12:26,310 --> 01:12:29,590 this has only aged five years, while this has aged 10 years. 1494 01:12:29,590 --> 01:12:31,410 So you've done that. 1495 01:12:31,410 --> 01:12:34,230 You move the wormhole back and forth. 1496 01:12:34,230 --> 01:12:36,729 And then you jump inside the wormhole. 1497 01:12:36,729 --> 01:12:37,770 You just go inside of it. 1498 01:12:46,080 --> 01:12:49,170 Or let's say you're accelerating with the mouth, 1499 01:12:49,170 --> 01:12:52,440 so with five years that way, five years that way. 1500 01:12:52,440 --> 01:12:55,590 Then you just hop into the wormhole. 1501 01:12:55,590 --> 01:13:00,040 And what general relativity has to say 1502 01:13:00,040 --> 01:13:02,670 is that these two times have to agree. 1503 01:13:02,670 --> 01:13:06,632 So once you've hopped into the wormhole, 1504 01:13:06,632 --> 01:13:09,750 you're automatically seeing these two times agree. 1505 01:13:09,750 --> 01:13:10,950 So five years has passed. 1506 01:13:10,950 --> 01:13:13,560 Maybe it was the year 30000 when you started this whole thing. 1507 01:13:13,560 --> 01:13:15,410 So it's 3005 when you put it back together. 1508 01:13:15,410 --> 01:13:17,800 It's 3010 here. 1509 01:13:17,800 --> 01:13:20,670 So you can hop into the wormhole. 1510 01:13:20,670 --> 01:13:24,750 And once you're inside of it, it will be 3005 again 1511 01:13:24,750 --> 01:13:26,830 for this mouth. 1512 01:13:26,830 --> 01:13:29,850 And so once you hop out of it, once you jump through it, 1513 01:13:29,850 --> 01:13:33,490 you travel back in time to somebody over here, 1514 01:13:33,490 --> 01:13:36,870 to an observer over here. 1515 01:13:36,870 --> 01:13:39,180 It sounds very strange. 1516 01:13:39,180 --> 01:13:42,930 And I don't know of any way to understand it intuitively. 1517 01:13:42,930 --> 01:13:46,839 But if you work through the math of general relativity, 1518 01:13:46,839 --> 01:13:48,255 it says that this is what happens. 1519 01:13:51,220 --> 01:13:55,020 It just says that that's what happens. 1520 01:13:55,020 --> 01:13:58,350 Now, there are a lot of problems with this method. 1521 01:13:58,350 --> 01:14:00,990 For one, we have no idea if wormholes 1522 01:14:00,990 --> 01:14:02,639 are even possible to create. 1523 01:14:02,639 --> 01:14:03,930 We've certainly never seen one. 1524 01:14:03,930 --> 01:14:05,550 We've never observed one before. 1525 01:14:05,550 --> 01:14:07,800 It might be impossible to create. 1526 01:14:07,800 --> 01:14:10,440 Another problem is that wormholes are actually 1527 01:14:10,440 --> 01:14:11,479 unstable. 1528 01:14:11,479 --> 01:14:13,020 So once you make them, it immediately 1529 01:14:13,020 --> 01:14:16,010 falls apart very quickly, at least 1530 01:14:16,010 --> 01:14:17,910 if you make it using ordinary matter, 1531 01:14:17,910 --> 01:14:20,650 if you create it using ordinary matter. 1532 01:14:20,650 --> 01:14:24,930 But it might be possible to stabilize a wormhole using what 1533 01:14:24,930 --> 01:14:26,940 some people call exotic matter. 1534 01:14:26,940 --> 01:14:29,250 And this is matter that essentially has 1535 01:14:29,250 --> 01:14:32,760 negative mass, which is weird. 1536 01:14:32,760 --> 01:14:35,470 So you need some kind of a weird material to stabilize it, 1537 01:14:35,470 --> 01:14:37,470 or else it's just going to fall apart on you. 1538 01:14:37,470 --> 01:14:42,120 And if it falls apart on you, space and time 1539 01:14:42,120 --> 01:14:43,730 will cease to exist. 1540 01:14:43,730 --> 01:14:46,920 And who knows what happens to you? 1541 01:14:46,920 --> 01:14:50,670 Another problem is that you might actually need a time 1542 01:14:50,670 --> 01:14:52,789 machine to make a wormhole. 1543 01:14:52,789 --> 01:14:54,330 You might need a time machine to make 1544 01:14:54,330 --> 01:14:57,000 this kind of a time machine. 1545 01:14:57,000 --> 01:15:00,540 Nonetheless, if you can get around these difficulties, then 1546 01:15:00,540 --> 01:15:03,090 theoretically it might be possible to travel back 1547 01:15:03,090 --> 01:15:05,490 in time, maybe. 1548 01:15:05,490 --> 01:15:08,580 Nobody really knows if it's possible. 1549 01:15:08,580 --> 01:15:11,070 Most experts, I think they don't think it's 1550 01:15:11,070 --> 01:15:13,500 actually possible to travel back in time with a wormhole. 1551 01:15:13,500 --> 01:15:16,560 But people have proposed other things, like warp drive, 1552 01:15:16,560 --> 01:15:20,550 and other weird things that exploit that curved geometry 1553 01:15:20,550 --> 01:15:23,180 of spacetime. 1554 01:15:23,180 --> 01:15:27,110 But today, nobody knows if time travel to the past as possible. 1555 01:15:27,110 --> 01:15:30,050 Time travel to the future, definitely, everybody 1556 01:15:30,050 --> 01:15:31,460 agrees on that. 1557 01:15:31,460 --> 01:15:32,810 Everybody even agrees on this. 1558 01:15:32,810 --> 01:15:34,059 This is very well established. 1559 01:15:34,059 --> 01:15:37,790 We've actually measured gravitational time dilation. 1560 01:15:37,790 --> 01:15:41,610 Wormholes and more speculative ideas, nobody really knows. 1561 01:15:41,610 --> 01:15:44,910 But if he can conquer these difficulties, 1562 01:15:44,910 --> 01:15:49,250 then the laws of physics say that, well, the past 1563 01:15:49,250 --> 01:15:51,320 might be yours. 1564 01:15:51,320 --> 01:15:54,850 The future definitely is yours. 1565 01:15:54,850 --> 01:15:57,950 In any case, it's good to know at least physics gives us 1566 01:15:57,950 --> 01:15:59,930 some hope that it might be possible. 1567 01:15:59,930 --> 01:16:01,220 Time travel might be possible. 1568 01:16:01,220 --> 01:16:05,840 100 years ago, nobody thought that any of this business 1569 01:16:05,840 --> 01:16:07,680 would be scientific. 1570 01:16:07,680 --> 01:16:11,100 It didn't make any sense to think about it scientifically. 1571 01:16:11,100 --> 01:16:13,869 But today, these are actually topics 1572 01:16:13,869 --> 01:16:16,160 that people actually work on, that researchers actually 1573 01:16:16,160 --> 01:16:18,200 work on. 1574 01:16:18,200 --> 01:16:20,150 So it's really become a real scientific topic, 1575 01:16:20,150 --> 01:16:21,920 this big question of time travel. 1576 01:16:21,920 --> 01:16:24,670 OK, see you next week.