1 00:00:00,190 --> 00:00:01,838 - [Voiceover] In the last videos, we constructed 2 00:00:01,838 --> 00:00:03,928 a little bit of a conundrum for us. 3 00:00:03,928 --> 00:00:07,132 We had the situation where I'm drifting through space, 4 00:00:07,132 --> 00:00:09,222 and right at time equal zero, 5 00:00:09,222 --> 00:00:13,030 one of my friends, she passes me by 6 00:00:13,030 --> 00:00:15,537 in a spaceship going half the speed of light 7 00:00:15,537 --> 00:00:18,463 in the positive x direction, relative to me. 8 00:00:18,463 --> 00:00:20,692 And at time equal zero, 9 00:00:20,692 --> 00:00:23,656 is exactly where she is at my position. 10 00:00:23,656 --> 00:00:26,233 And then she keeps traveling, and so I draw 11 00:00:26,233 --> 00:00:28,137 the path that she is taking. 12 00:00:28,137 --> 00:00:30,227 So after one second, she would be here, 13 00:00:30,227 --> 00:00:32,293 after two seconds, she would be there, 14 00:00:32,293 --> 00:00:33,593 and we set up our scales 15 00:00:33,593 --> 00:00:36,356 so that on our time axis, 16 00:00:36,356 --> 00:00:39,003 one second is the same length 17 00:00:39,003 --> 00:00:42,138 as on our space axis, or on our path axis, 18 00:00:42,138 --> 00:00:44,576 three times ten to the eighth meters. 19 00:00:44,576 --> 00:00:47,269 And we did that so that at least in my frame of reference, 20 00:00:47,269 --> 00:00:50,381 the speed of light would be at a 45 degree angle, 21 00:00:50,381 --> 00:00:52,029 or would have a slope of one. 22 00:00:52,029 --> 00:00:54,142 But the conundrum we hit was 23 00:00:54,142 --> 00:00:56,209 is that the speed of light would be perceived, 24 00:00:56,209 --> 00:00:57,904 based on this model I set up, 25 00:00:57,904 --> 00:00:59,645 would be perceived differently 26 00:00:59,645 --> 00:01:01,944 based on which frame of reference you're in. 27 00:01:01,944 --> 00:01:04,521 The photon that I emit from my flashlight, 28 00:01:04,521 --> 00:01:05,705 right at time equals zero, 29 00:01:05,705 --> 00:01:08,255 well sure I'm going to see that as moving 30 00:01:08,255 --> 00:01:10,879 at the speed of light in the positive x direction. 31 00:01:10,879 --> 00:01:13,410 But my friend, since she's already moving 32 00:01:13,410 --> 00:01:16,265 in that positive x direction at half of the speed of light, 33 00:01:16,265 --> 00:01:18,351 if we assumed a Newtonian world, 34 00:01:18,351 --> 00:01:21,485 she would see that photon going at half the speed of light. 35 00:01:21,485 --> 00:01:26,222 And likewise, if she emitted a photon from her flashlight, 36 00:01:26,222 --> 00:01:28,771 to her, it would look like it's going at the speed of light, 37 00:01:28,771 --> 00:01:31,789 but to me, it would look like it's going faster 38 00:01:31,789 --> 00:01:33,577 than the speed of light. 39 00:01:33,577 --> 00:01:35,779 And the reason why that is a conundrum 40 00:01:35,779 --> 00:01:39,076 is we know from observation of the universe around us, 41 00:01:39,076 --> 00:01:41,699 and this is profound, this is a little mind-blowing, 42 00:01:41,699 --> 00:01:44,532 this is counterintuitive to our everyday experience, 43 00:01:44,532 --> 00:01:46,506 but we know from observation 44 00:01:46,506 --> 00:01:49,919 that the speed of light is absolute, 45 00:01:49,919 --> 00:01:52,914 that it doesn't matter your inertial frame of reference. 46 00:01:52,914 --> 00:01:54,725 As long as you're in an inertial frame of reference, 47 00:01:54,725 --> 00:01:56,954 it doesn't matter your relative velocity 48 00:01:56,954 --> 00:01:59,276 relative to another inertial frame of reference. 49 00:01:59,276 --> 00:02:01,621 You will always measure the speed of light 50 00:02:01,621 --> 00:02:04,291 at three times ten to the eighth meters per second. 51 00:02:04,291 --> 00:02:06,010 But that's at a direct contradiction 52 00:02:06,010 --> 00:02:08,424 with what our model just set up. 53 00:02:08,424 --> 00:02:12,232 So it really forces us to question all of our assumptions. 54 00:02:12,232 --> 00:02:14,341 So what are the assumptions that we made 55 00:02:14,341 --> 00:02:15,896 in this Newtonian world? 56 00:02:15,896 --> 00:02:19,124 Well, we assumed that time is absolute. 57 00:02:19,124 --> 00:02:21,190 Time is absolute. 58 00:02:21,190 --> 00:02:22,792 And what do I mean by that? 59 00:02:22,792 --> 00:02:25,881 Well, we assumed that one second passing for me 60 00:02:25,881 --> 00:02:28,667 is going to be one second passing for my friend. 61 00:02:28,667 --> 00:02:30,733 That's just our everyday notion. 62 00:02:30,733 --> 00:02:33,403 If I'm in a car and you're not in a car, 63 00:02:33,403 --> 00:02:35,958 and we both have watches, and we synchronize our watches, 64 00:02:35,958 --> 00:02:38,233 they seem to say synchronized. 65 00:02:38,233 --> 00:02:42,668 But maybe we need to loosen this assumption. 66 00:02:42,668 --> 00:02:45,918 We also assumed that space is absolute. 67 00:02:45,918 --> 00:02:49,169 Space is absolute. 68 00:02:49,169 --> 00:02:50,539 And what do I mean by that? 69 00:02:50,539 --> 00:02:52,346 Well in our everyday experience, 70 00:02:52,346 --> 00:02:55,596 regardless of what our relative frames of reference are, 71 00:02:55,596 --> 00:02:59,892 we seem to agree that, well if that meter stick over there, 72 00:02:59,892 --> 00:03:01,508 that's riding on that train, 73 00:03:01,508 --> 00:03:03,598 that is a meter stick, whether I'm sitting on the train 74 00:03:03,598 --> 00:03:04,852 or whether I'm not. 75 00:03:04,852 --> 00:03:07,615 But maybe things start to break down a little bit 76 00:03:07,615 --> 00:03:11,135 as we think about higher velocities. 77 00:03:11,135 --> 00:03:13,109 And maybe they break down even at the slower velocities, 78 00:03:13,109 --> 00:03:14,311 but we just don't notice them 79 00:03:14,311 --> 00:03:15,983 because it's a very small error. 80 00:03:15,983 --> 00:03:18,189 And maybe there's something even more interesting. 81 00:03:18,189 --> 00:03:19,805 In our everyday experience, 82 00:03:19,805 --> 00:03:23,868 we just assume that time is somehow 83 00:03:23,868 --> 00:03:26,534 something very different than space, 84 00:03:26,534 --> 00:03:28,902 that you can move in the time direction 85 00:03:28,902 --> 00:03:30,411 without moving in the space direction, 86 00:03:30,411 --> 00:03:32,032 or you can move in the space direction 87 00:03:32,032 --> 00:03:33,495 without moving in the time direction, 88 00:03:33,495 --> 00:03:35,724 and that they're independent regardless 89 00:03:35,724 --> 00:03:38,765 of which inertial frame of reference you're in. 90 00:03:38,765 --> 00:03:40,809 But maybe they aren't separate things. 91 00:03:40,809 --> 00:03:45,499 In fact, maybe they're all one continuum of spacetime, 92 00:03:45,499 --> 00:03:47,519 and I don't mean space dash time, 93 00:03:47,519 --> 00:03:48,698 I mean spacetime. 94 00:03:48,698 --> 00:03:53,063 I mean the word spacetime, 95 00:03:53,063 --> 00:03:54,823 where space and time really aren't different things. 96 00:03:54,823 --> 00:03:57,702 It's just one continuum, spacetime. 97 00:03:57,702 --> 00:03:59,188 And I keep saying it fast like that, 98 00:03:59,188 --> 00:04:03,623 because it's not space dash time, 99 00:04:03,623 --> 00:04:05,504 like thinking about the different dimensions, 100 00:04:05,504 --> 00:04:07,756 or thinking about two different things. 101 00:04:07,756 --> 00:04:11,518 We're renaming one thing called spacetime. 102 00:04:11,518 --> 00:04:13,538 So these are the things that we're going to start 103 00:04:13,538 --> 00:04:14,652 to hold into question. 104 00:04:14,652 --> 00:04:18,158 So what if we loosen these, and we assume the thing 105 00:04:18,158 --> 00:04:20,154 that we have observed in the universe, 106 00:04:20,154 --> 00:04:22,709 that the speed of light is absolute, 107 00:04:22,709 --> 00:04:26,146 regardless of your inertial frame of reference. 108 00:04:26,146 --> 00:04:28,677 So let's word from there, do a little thought experiment, 109 00:04:28,677 --> 00:04:31,272 and then think about what type of a model we can construct, 110 00:04:31,272 --> 00:04:35,243 in which case the speed of light is absolute. 111 00:04:35,243 --> 00:04:36,882 And to do that, we're still going to use 112 00:04:36,882 --> 00:04:38,275 our little model here, 113 00:04:38,275 --> 00:04:41,154 and we're going to focus on my friend's frame of reference, 114 00:04:41,154 --> 00:04:42,455 my friend who's on a spaceship, 115 00:04:42,455 --> 00:04:45,259 who right at time equal zero, is passing me by 116 00:04:45,259 --> 00:04:47,256 at half the speed of light. 117 00:04:47,256 --> 00:04:50,530 And we assumed that she's in this train of spaceships. 118 00:04:50,530 --> 00:04:52,496 So we assumed already that she's, 119 00:04:52,496 --> 00:04:54,081 there are these spaceships that are all moving 120 00:04:54,081 --> 00:04:56,793 at half the speed of light in the positive x direction, 121 00:04:56,793 --> 00:04:57,954 relative to me, 122 00:04:57,954 --> 00:05:01,228 and they're all three times ten to the eighth meters apart. 123 00:05:01,228 --> 00:05:02,505 So they're like that. 124 00:05:02,505 --> 00:05:05,593 So let's say, and I did these axes in blue, 125 00:05:05,593 --> 00:05:07,242 because we're assuming this is my friend's 126 00:05:07,242 --> 00:05:08,862 frame of reference, so you could say 127 00:05:08,862 --> 00:05:10,552 this is the S prime frame of reference, 128 00:05:10,552 --> 00:05:12,294 this is Sally's frame of reference 129 00:05:12,294 --> 00:05:14,082 from a couple of videos ago. 130 00:05:14,082 --> 00:05:16,287 Let's say a second before she gets to me, 131 00:05:16,287 --> 00:05:18,470 and I'm also assuming, the way I've drawn these axes, 132 00:05:18,470 --> 00:05:20,420 and we're going to modify them in the future 133 00:05:20,420 --> 00:05:22,065 where we're actually going to use the same units 134 00:05:22,065 --> 00:05:22,831 for space and time. 135 00:05:22,831 --> 00:05:25,230 Right now, I'm still sticking to what we've classically done 136 00:05:25,230 --> 00:05:26,669 where we use seconds for time 137 00:05:26,669 --> 00:05:29,595 and meters for our path or our space, 138 00:05:29,595 --> 00:05:31,754 but in the future, we'll actually use meters for both. 139 00:05:31,754 --> 00:05:33,287 But we'll get to that, I don't want to do 140 00:05:33,287 --> 00:05:34,982 too many things at once. 141 00:05:34,982 --> 00:05:37,521 But the way I've drawn it 142 00:05:37,521 --> 00:05:39,672 along my space axis, 143 00:05:39,672 --> 00:05:41,512 three times ten to the eighth meters 144 00:05:41,512 --> 00:05:44,484 is going to be the exact same length as one second, 145 00:05:44,484 --> 00:05:47,735 and I'm doing that so that the path of light 146 00:05:47,735 --> 00:05:49,035 on my diagram 147 00:05:49,035 --> 00:05:51,659 can be a 45 degree angle. 148 00:05:51,659 --> 00:05:55,165 So this is three times ten to the eighth meters 149 00:05:55,165 --> 00:05:56,303 right over there. 150 00:05:56,303 --> 00:05:59,460 So let's say a second before Sally gets to me, 151 00:05:59,460 --> 00:06:03,268 she releases a photon from her spaceship 152 00:06:03,268 --> 00:06:06,264 in the direction of the spaceship that is in front of her. 153 00:06:06,264 --> 00:06:07,494 How far is it in front of her? 154 00:06:07,494 --> 00:06:10,582 It's three times ten to the eighth meters in front of her. 155 00:06:10,582 --> 00:06:12,556 And let's say on the back of that spaceship, 156 00:06:12,556 --> 00:06:14,413 there is a mirror. 157 00:06:14,413 --> 00:06:17,385 So she's pointing her flashlight at that mirror. 158 00:06:17,385 --> 00:06:19,731 So what's going to happen from her frame of reference 159 00:06:19,731 --> 00:06:21,147 after one second? 160 00:06:21,147 --> 00:06:23,747 So for one second, from her frame of reference, 161 00:06:23,747 --> 00:06:26,487 she is stationary, so this is Sally still here. 162 00:06:26,487 --> 00:06:30,481 She is going to be still at x prime equals zero 163 00:06:30,481 --> 00:06:31,967 in her frame of reference, 164 00:06:31,967 --> 00:06:34,289 and that ship is still going to be 165 00:06:34,289 --> 00:06:36,611 three times ten to the eighth meters in front of her. 166 00:06:36,611 --> 00:06:39,296 They're all moving, relative to me, at the same velocity, 167 00:06:39,296 --> 00:06:41,967 but relative to each other, they seem to be stationary. 168 00:06:41,967 --> 00:06:43,963 And so what would be the path of that photon? 169 00:06:43,963 --> 00:06:47,117 Well that photon will have gone from Sally's flashlight 170 00:06:47,117 --> 00:06:49,137 from her headlamp, or whatever it is, 171 00:06:49,137 --> 00:06:50,739 to that spaceship in front of her 172 00:06:50,739 --> 00:06:52,852 would've just reached that mirror 173 00:06:52,852 --> 00:06:54,872 on the back of that spaceship. 174 00:06:54,872 --> 00:06:56,928 And so we can draw the path of light. 175 00:06:56,928 --> 00:06:59,435 It will be, so let me, 176 00:06:59,435 --> 00:07:01,409 so that path of light 177 00:07:01,409 --> 00:07:05,328 will look like that on this diagram. 178 00:07:05,328 --> 00:07:07,070 And then right at this moment, 179 00:07:07,070 --> 00:07:10,599 right at t prime equals zero seconds, 180 00:07:10,599 --> 00:07:13,943 the photon will be reflected back to Sally. 181 00:07:13,943 --> 00:07:16,473 Well how long will it take to get back to Sally? 182 00:07:16,473 --> 00:07:19,232 Well Sally's gonna receive the reflection of that photon 183 00:07:19,232 --> 00:07:20,904 after one second, because that's how long 184 00:07:20,904 --> 00:07:21,856 it's going to take it to go 185 00:07:21,856 --> 00:07:23,545 three times ten to the eighth meters. 186 00:07:23,545 --> 00:07:26,076 So the path of that very first photon, 187 00:07:26,076 --> 00:07:28,445 the path of that very first photon 188 00:07:28,445 --> 00:07:31,417 is going to look like that. 189 00:07:31,417 --> 00:07:33,483 All right, well hopefully this is pretty 190 00:07:33,483 --> 00:07:35,317 straightforward here. 191 00:07:35,317 --> 00:07:37,616 This is what would happen from Sally's frame of reference. 192 00:07:37,616 --> 00:07:39,241 A second before she reaches me, 193 00:07:39,241 --> 00:07:43,096 at t prime equals negative one seconds, 194 00:07:43,096 --> 00:07:45,836 emits a photon at t equals zero seconds, 195 00:07:45,836 --> 00:07:47,368 and gets to the spaceship 196 00:07:47,368 --> 00:07:50,201 that's three times ten to the eighth meters in front of her, 197 00:07:50,201 --> 00:07:53,266 essentially one light-second in front of her, 198 00:07:53,266 --> 00:07:54,961 and then a second later, 199 00:07:54,961 --> 00:07:56,934 it's reflecting back, a second later, 200 00:07:56,934 --> 00:07:58,745 she gets the reflection. 201 00:07:58,745 --> 00:08:01,416 And so that's what this diagram is describing. 202 00:08:01,416 --> 00:08:03,482 But now let's draw it projected on top 203 00:08:03,482 --> 00:08:05,015 of my frame of reference. 204 00:08:05,015 --> 00:08:06,501 And this is when things are going to get 205 00:08:06,501 --> 00:08:09,101 really, really, really, really interesting. 206 00:08:09,101 --> 00:08:10,842 So I've drawn my frame of reference here, 207 00:08:10,842 --> 00:08:13,211 and I've intentionally not marked off the seconds 208 00:08:13,211 --> 00:08:14,836 or the meters on my frame of reference, 209 00:08:14,836 --> 00:08:16,856 because once again, I'm not going to assume 210 00:08:16,856 --> 00:08:18,180 that a second in my frame of reference 211 00:08:18,180 --> 00:08:20,858 is a second in hers, or a meter in my frame of reference 212 00:08:20,858 --> 00:08:22,736 is a meter in hers. 213 00:08:22,736 --> 00:08:25,824 I have drawn her t prime axis at the same angle 214 00:08:25,824 --> 00:08:27,124 as I did before, 215 00:08:27,124 --> 00:08:31,396 because for every second 216 00:08:31,396 --> 00:08:34,135 we move into the future, 217 00:08:34,135 --> 00:08:37,943 she's going to move half a light-second in distance, 218 00:08:37,943 --> 00:08:39,224 in the positive x direction. 219 00:08:39,225 --> 00:08:41,895 So this slope right here, one way to think about it, 220 00:08:41,895 --> 00:08:42,964 the way I've drawn it, 221 00:08:42,965 --> 00:08:45,276 this is a slope of two. 222 00:08:47,506 --> 00:08:50,628 For every unit she moves in the x direction, 223 00:08:50,628 --> 00:08:54,413 she will move two in the time direction. 224 00:08:54,413 --> 00:08:55,713 And what we're going to do again 225 00:08:55,713 --> 00:08:58,030 is assume that on her axis, 226 00:08:58,030 --> 00:08:59,377 I haven't drawn the x prime axis. 227 00:08:59,377 --> 00:09:00,626 In fact, this is an exercise to think about 228 00:09:00,626 --> 00:09:03,064 where should the x prime axis be. 229 00:09:03,064 --> 00:09:04,875 Should it be coincident with the x axis 230 00:09:04,875 --> 00:09:05,757 like we assumed before? 231 00:09:05,757 --> 00:09:07,518 Or is it going to be in a different place? 232 00:09:07,518 --> 00:09:10,258 But we're going to assume that the lengths I draw 233 00:09:10,258 --> 00:09:12,231 for one second on, let's say, 234 00:09:12,231 --> 00:09:15,389 in the S prime frame of reference, 235 00:09:15,389 --> 00:09:17,757 is going to be the same as the length I would draw 236 00:09:17,757 --> 00:09:20,126 for three times ten to the eighth meters. 237 00:09:20,126 --> 00:09:21,240 And we're also going to assume 238 00:09:21,240 --> 00:09:22,564 that the speed of light is absolute, 239 00:09:22,564 --> 00:09:25,443 so it's always going to moving at a 45 degree angle 240 00:09:25,443 --> 00:09:29,297 with respect to either frame of reference. 241 00:09:29,297 --> 00:09:31,015 So that's where things are going to get a little bit whacky, 242 00:09:31,015 --> 00:09:32,989 but let's see what's going to happen. 243 00:09:32,989 --> 00:09:35,288 So at negative one seconds, 244 00:09:35,288 --> 00:09:38,585 we still have Sally turning on her flashlight. 245 00:09:38,585 --> 00:09:41,487 She wants to bounce it off of the spaceship in front of her. 246 00:09:41,487 --> 00:09:44,598 And so that photon's going to move with the speed of light 247 00:09:44,598 --> 00:09:46,688 in either frame of reference. 248 00:09:46,688 --> 00:09:48,453 And so let me draw that. 249 00:09:48,453 --> 00:09:49,747 Let me draw that, 250 00:09:49,747 --> 00:09:53,467 so it's going to look like this. 251 00:09:53,467 --> 00:09:55,960 I'm drawing at a 45 degree angle. 252 00:09:55,960 --> 00:09:57,701 So actually, I don't know where it gets reflected. 253 00:09:57,701 --> 00:09:59,861 It's gonna get reflected where it hits that x prime axis, 254 00:09:59,861 --> 00:10:01,231 but I don't know where that is. 255 00:10:01,231 --> 00:10:03,460 But we do know that it then gets reflected, 256 00:10:03,460 --> 00:10:06,339 and then it gets back to Sally at one second in the future. 257 00:10:06,339 --> 00:10:09,195 So the return path of that photon 258 00:10:09,195 --> 00:10:11,401 is going to look something 259 00:10:11,401 --> 00:10:13,397 is going to look something like this. 260 00:10:13,397 --> 00:10:14,930 And that point that it changes direction, 261 00:10:14,930 --> 00:10:16,068 I could have, 262 00:10:16,068 --> 00:10:16,857 let me, 263 00:10:16,857 --> 00:10:18,357 I could have done it like this, 264 00:10:18,357 --> 00:10:19,332 whoops, 265 00:10:19,332 --> 00:10:20,461 I could've done it like this. 266 00:10:20,461 --> 00:10:22,991 But the interesting point is where it changes direction 267 00:10:22,991 --> 00:10:25,308 because that's where that spaceship in front of her 268 00:10:25,308 --> 00:10:28,513 must be at that point in spacetime. 269 00:10:28,513 --> 00:10:30,393 Because now we're going to start thinking of mixing up 270 00:10:30,393 --> 00:10:31,601 space and time, 271 00:10:31,601 --> 00:10:33,783 but I'm not going to get too much involved in that. 272 00:10:33,783 --> 00:10:35,641 Now why is this interesting? 273 00:10:35,641 --> 00:10:38,102 Because from Sally's point of view, 274 00:10:38,102 --> 00:10:39,704 from Sally's point of view, 275 00:10:39,704 --> 00:10:44,116 this point here where the light changes direction, 276 00:10:44,116 --> 00:10:45,904 from Sally's frame of reference, 277 00:10:45,904 --> 00:10:50,037 is happening simultaneously with when she reaches me. 278 00:10:50,037 --> 00:10:52,928 This is happening at t prime 279 00:10:52,928 --> 00:10:55,528 is equal to zero for Sally. 280 00:10:55,528 --> 00:10:59,476 So anything that is t prime is equal to zero for Sally 281 00:10:59,476 --> 00:11:02,007 must be on the x prime axis. 282 00:11:02,007 --> 00:11:05,118 So this must sit on the x prime axis. 283 00:11:05,118 --> 00:11:06,743 Once again, why do I know that? 284 00:11:06,743 --> 00:11:08,879 Because everything on the x prime axis, 285 00:11:08,879 --> 00:11:11,341 any event on the x prime axis, 286 00:11:11,341 --> 00:11:13,407 let me do it in a different color, 287 00:11:13,407 --> 00:11:15,984 I keep doing black. 288 00:11:15,984 --> 00:11:18,771 Any event on the x prime axis 289 00:11:18,771 --> 00:11:22,184 is going to be at t prime is equal to zero seconds, 290 00:11:22,184 --> 00:11:24,088 and from Sally's frame of reference 291 00:11:24,088 --> 00:11:27,013 is going to be simultaneous with when she passes me up. 292 00:11:27,013 --> 00:11:29,591 So based on that, we know that this is going to be, 293 00:11:32,467 --> 00:11:34,603 we know that this point, 294 00:11:34,603 --> 00:11:36,275 which is where Sally is, 295 00:11:36,275 --> 00:11:38,876 that's going to be the origin from her frame of reference. 296 00:11:38,876 --> 00:11:43,078 And we know that this point sits on the x prime axis, 297 00:11:43,078 --> 00:11:45,934 so based on that, we can draw the x prime axis. 298 00:11:45,934 --> 00:11:47,968 You just need two points to define a line, 299 00:11:47,968 --> 00:11:50,220 and so let me try to do it. 300 00:11:50,220 --> 00:11:52,727 So let me try to draw. 301 00:11:52,727 --> 00:11:54,074 I can do a better job than that. 302 00:11:54,074 --> 00:11:55,792 Let me try to draw 303 00:11:55,792 --> 00:11:57,186 the x prime axis. 304 00:11:57,186 --> 00:12:00,204 It's going to look like, 305 00:12:00,204 --> 00:12:02,108 it's going to look like this. 306 00:12:02,108 --> 00:12:04,708 That right over there is the x prime axis. 307 00:12:04,708 --> 00:12:07,704 Now at this point, you should find this mildly mind-blowing. 308 00:12:07,704 --> 00:12:10,281 Actually, even more than mildly mind-blowing. 309 00:12:10,281 --> 00:12:12,533 'Cause it's saying some pretty, pretty crazy things. 310 00:12:12,533 --> 00:12:15,714 First of all, let's just make sure we know how to read this. 311 00:12:15,714 --> 00:12:17,270 So for any event, 312 00:12:17,270 --> 00:12:18,508 and now we're going to start thinking 313 00:12:18,508 --> 00:12:20,033 in terms of spacetime, 314 00:12:20,033 --> 00:12:23,385 although I'm still using different units for space and time, 315 00:12:23,385 --> 00:12:25,126 but we'll address that in the future. 316 00:12:25,126 --> 00:12:27,727 If I want to read its coordinates in my frame of reference, 317 00:12:27,727 --> 00:12:29,492 well if I want to read its x coordinate, 318 00:12:29,492 --> 00:12:31,558 I go parallel to the t axis, 319 00:12:31,558 --> 00:12:33,648 and if I wanna read its t coordinate, 320 00:12:33,648 --> 00:12:35,645 I go parallel to the x axis. 321 00:12:35,645 --> 00:12:36,945 But for Sally's frame of reference, 322 00:12:36,945 --> 00:12:38,617 well I essentially do the same thing. 323 00:12:38,617 --> 00:12:40,567 If I want its x prime coordinates, 324 00:12:40,567 --> 00:12:43,585 I go parallel to the t prime axis, 325 00:12:43,585 --> 00:12:46,163 and if I want the t prime coordinates, 326 00:12:46,163 --> 00:12:49,971 I go parallel to the x prime axis. 327 00:12:49,971 --> 00:12:51,805 But what's really interesting, 328 00:12:51,805 --> 00:12:55,265 and I'll go even deeper into this into the next videos, 329 00:12:55,265 --> 00:12:56,621 that moment, 330 00:12:56,621 --> 00:12:58,920 that moment right over here, 331 00:12:58,920 --> 00:13:01,312 that from Sally's frame of reference, 332 00:13:01,312 --> 00:13:04,887 it looks like it's simultaneous with her passing me up. 333 00:13:04,887 --> 00:13:07,116 It looks like it's happening at t prime equals zero. 334 00:13:07,116 --> 00:13:08,742 In fact, it is happening at t prime equals zero. 335 00:13:08,742 --> 00:13:09,991 From her frame of reference, 336 00:13:09,991 --> 00:13:12,057 it's happening at t prime equals zero. 337 00:13:12,057 --> 00:13:14,054 From our frame of reference, 338 00:13:14,054 --> 00:13:17,398 it is happening after Sally passes us up. 339 00:13:17,398 --> 00:13:20,671 Notice, it is happening at t equals some positive value. 340 00:13:20,671 --> 00:13:23,239 It's not happening at t equals zero. 341 00:13:23,239 --> 00:13:25,434 So this is starting to get a little bit whacky. 342 00:13:25,434 --> 00:13:30,378 One second, and simultaneous, time, and space, 343 00:13:30,378 --> 00:13:33,391 and things being simultaneous, 344 00:13:33,391 --> 00:13:35,829 we're not going to agree on those, 345 00:13:35,829 --> 00:13:37,895 depending on which frame of reference we're in. 346 00:13:37,895 --> 00:00:00,000 The thing we will agree on is the speed of light.