WEBVTT - What is a space-time interval? 0:00:07.760 --> 0:00:12.080 Special relativity brings space and time together and in the 0:00:12.200 --> 0:00:17.320 darkness binds them into space time. That sounds pretty awesome, 0:00:17.320 --> 0:00:19.840 and it was fun to say, like something that could 0:00:19.880 --> 0:00:23.279 only happen in Mordoor or during the Big Bang. But 0:00:23.600 --> 0:00:27.920 what does it actually mean? What is space time? How 0:00:27.960 --> 0:00:31.960 do you measure distances in four dimensional space time? And 0:00:32.159 --> 0:00:35.920 why would you? Physicists are always saying that space and 0:00:36.000 --> 0:00:39.159 time are like two sides of the same coin making 0:00:39.240 --> 0:00:42.959 more sense together. What are they talking about? In what 0:00:43.040 --> 0:00:46.480 way do they make more sense together? Today We're gonna 0:00:46.479 --> 0:00:48.760 blow up all of those analogies and give you a 0:00:48.840 --> 0:00:54.640 real conceptual understanding of how relativity breaks space and twists time, 0:00:55.120 --> 0:00:58.720 but then clicks them back together into a harmonious hole. 0:00:59.360 --> 0:01:02.120 We'll talk about what that really means and the crucial 0:01:02.480 --> 0:01:05.480 but rarely explain concept at the heart of it all 0:01:05.920 --> 0:01:11.319 the space time interval. Welcome to Daniel and Kelly's spacey 0:01:11.520 --> 0:01:12.839 timey Universe. 0:01:26.120 --> 0:01:26.440 Hello. 0:01:26.560 --> 0:01:29.200 I'm Kelly Wiener Smith. I study parasites and space, and 0:01:29.240 --> 0:01:38.959 I have fun in all spaces and at all times. Hi. 0:01:39.080 --> 0:01:41.200 I'm Daniel. I'm a particle physicist who likes to think 0:01:41.240 --> 0:01:43.920 about aliens, and I was having fun this morning until 0:01:44.000 --> 0:01:46.120 Kelly showed me the crusher. 0:01:46.319 --> 0:01:49.320 Oh was it sure you were going to mention the 0:01:49.360 --> 0:01:50.360 crusher on the show. 0:01:50.480 --> 0:01:52.280 It's the only thing I can think about now, Thank 0:01:52.320 --> 0:02:01.400 you very much. Kelly. Tell everybody what does the crusher crush. 0:01:59.120 --> 0:02:02.080 The tube that goes to the testicle and connects it 0:02:02.080 --> 0:02:04.360 to the rest of the body. I am looking into 0:02:04.520 --> 0:02:10.000 methods for what we'll say, weathering are male goats, and 0:02:10.040 --> 0:02:11.840 I'm trying to figure out what method I would feel 0:02:11.840 --> 0:02:14.079 comfortable doing, or if I need to call the vets 0:02:14.240 --> 0:02:16.440 and Wow, the crusher is a big piece of equipment 0:02:16.520 --> 0:02:18.520 that once I have it in my hands, I am 0:02:18.680 --> 0:02:22.120 not sure that I am up for actually using. 0:02:22.400 --> 0:02:25.320 But you were up for brandishing it on our video 0:02:25.400 --> 0:02:26.360 call this morning. 0:02:28.520 --> 0:02:30.200 Everybody needs to stop it. 0:02:31.280 --> 0:02:34.280 Away the crusher, all right, But today we are not 0:02:34.360 --> 0:02:37.040 crushing goats or any of their bits. We are crushing 0:02:37.040 --> 0:02:41.160 your confusion. We are explaining the way the universe works. 0:02:43.440 --> 0:02:47.839 You always pull us back somehow, Okay, So today we're 0:02:47.840 --> 0:02:50.600 talking about space time, yes, which got me thinking about 0:02:50.840 --> 0:02:53.160 all of space and all of time. And so, Daniel, 0:02:53.160 --> 0:02:56.920 if you could snap your fingers and for five minutes, 0:02:57.240 --> 0:02:59.040 you would be in a protective bubble, and you could 0:02:59.080 --> 0:03:01.800 go anywhere in space, but you couldn't change the time, 0:03:01.919 --> 0:03:05.440 like you had to just pop up right there. Now, 0:03:05.880 --> 0:03:07.040 what would you want to see? 0:03:07.520 --> 0:03:10.480 Kelly? You need this episode because if you had heard 0:03:10.480 --> 0:03:12.720 this episode already, you would know that that question is 0:03:12.720 --> 0:03:16.600 incoherent because there is no universal now. That's right, right, 0:03:16.680 --> 0:03:19.880 there's no sense of time across the whole universe where 0:03:19.919 --> 0:03:22.080 you can say this now is the same as that now. 0:03:22.280 --> 0:03:25.600 It's observer dependent. We're gonna talk about and. 0:03:25.560 --> 0:03:26.919 You know what, I should have known that from our 0:03:26.960 --> 0:03:31.080 What Is Time and What Is Space? Episode series? But okay, 0:03:31.080 --> 0:03:33.120 so is there some way to constrain it so I 0:03:33.160 --> 0:03:34.960 can say, like, you can't go back to the beginning 0:03:35.040 --> 0:03:37.480 of the universe. I was trying to, like, why do. 0:03:37.440 --> 0:03:38.840 You want to stop me from going back to the 0:03:38.840 --> 0:03:39.440 beginning of the. 0:03:39.480 --> 0:03:40.920 Universe, because that's what I thought you'd say. 0:03:41.040 --> 0:03:43.240 You were totally right, that is what I was gonna. 0:03:42.920 --> 0:03:45.880 Say, But you said that on the show before. So 0:03:46.000 --> 0:03:47.440 trying to figure out what you think is the most 0:03:47.440 --> 0:03:50.040 interesting thing happening now. And my guess is that you 0:03:50.080 --> 0:03:52.200 were gonna say black holes. 0:03:52.240 --> 0:03:54.440 I'm gonna go to the factory that makes the crusher 0:03:54.480 --> 0:03:58.960 and I'm gonna burn it down. Okay, No, but if 0:03:59.000 --> 0:04:03.720 I could go somewhere in the modern universe, then for 0:04:03.800 --> 0:04:06.720 sure I would like to see not only what's inside 0:04:06.760 --> 0:04:09.360 a black hole, but the immediate vicinity of a black 0:04:09.360 --> 0:04:13.280 hole would be super fascinating to see frame dragging and 0:04:13.360 --> 0:04:16.440 to see all that time dilation and all the extreme 0:04:16.680 --> 0:04:20.440 events around a black hole. I think my second choice 0:04:20.480 --> 0:04:24.279 would be the heart of a neutron star, because when 0:04:24.600 --> 0:04:28.640 every other defense against gravity has already collapsed and matter 0:04:28.680 --> 0:04:32.760 becomes insanely dense so the protons and electrons eat each 0:04:32.760 --> 0:04:36.400 other and become neutrons, then you have this fascinating environment 0:04:36.520 --> 0:04:40.000 where quantum mechanics and gravity are at about the same strength. 0:04:40.440 --> 0:04:42.080 And we don't know what's going on at the heart 0:04:42.120 --> 0:04:44.760 of neutron stars because we can't calculate that stuff because 0:04:44.760 --> 0:04:47.559 we don't have a theory of quantum gravity. We'll never 0:04:47.720 --> 0:04:49.720 go inside a black hole, so that's sort of just 0:04:49.760 --> 0:04:52.680 like fun to say, but hopeless. But the inside of 0:04:52.720 --> 0:04:55.279 a neutron star is out there and real and on 0:04:55.320 --> 0:04:58.279 the outside of event horizon, so in principle we could 0:04:58.320 --> 0:05:00.680 one day see it, and that be the key to 0:05:00.800 --> 0:05:02.000 unlocking quantum gravity. 0:05:02.080 --> 0:05:04.799 WHOA Okay, So, how could I have worded the question 0:05:05.600 --> 0:05:09.320 to constrain your ability to see the Big Bang? What 0:05:09.360 --> 0:05:10.599 would have been the right way to word that? 0:05:11.400 --> 0:05:12.880 Of Daniel? What would you like to see in the 0:05:12.920 --> 0:05:14.320 universe except for the Big Bang? 0:05:18.000 --> 0:05:20.640 Well, wouldn't you have to go backwards in time to 0:05:20.680 --> 0:05:21.400 see the Big Bang? 0:05:21.520 --> 0:05:23.320 It depends a little bit of what you mean by sea. 0:05:23.520 --> 0:05:26.000 I mean the information from the Big Bang is out 0:05:26.040 --> 0:05:29.839 there in some respects. People often say seeing the CMB 0:05:30.000 --> 0:05:32.080 is like seeing the Big Bang, though it actually comes 0:05:32.120 --> 0:05:35.120 from three hundred and eighty thousand years later. There is 0:05:35.160 --> 0:05:38.040 information from the Big Bang out there and gravitational waves, 0:05:38.080 --> 0:05:42.640 and so like seeing it means detecting those and reconstructing 0:05:42.680 --> 0:05:45.800 what happened. We can do that today without like being 0:05:45.839 --> 0:05:48.840 there during the Big Bang. In that sense, everything you 0:05:48.880 --> 0:05:50.760 see happened in the past already. 0:05:51.080 --> 0:05:54.039 So but I feel like you understand that that's not 0:05:54.120 --> 0:05:58.160 what I mean like that, like, like, yes, you can 0:05:58.160 --> 0:06:02.279 see evidence from it, yes, but like I don't you know, 0:06:02.320 --> 0:06:03.839 So if I go to a civil war site and 0:06:03.880 --> 0:06:07.080 I find a like bullet case, that's like evidence that 0:06:07.120 --> 0:06:10.040 it happened. Yeah, but it's not the same as being 0:06:10.080 --> 0:06:13.440 there and watching both sides run across a field and 0:06:13.520 --> 0:06:14.840 start fighting each other. 0:06:15.279 --> 0:06:18.160 Right, No, but it's sort of like going really really 0:06:18.240 --> 0:06:21.760 far away instantaneously and capturing the light that left that 0:06:21.800 --> 0:06:26.480 Civil War battlefield contemporaneously and using it to watch in 0:06:26.560 --> 0:06:29.880 real time the battle, which is something you could literally. 0:06:29.480 --> 0:06:32.360 Do, right, All right, all right, all right, Well I'm 0:06:32.360 --> 0:06:33.960 gonna have you be more careful next time I ask you 0:06:33.960 --> 0:06:37.560 a question. But we've all learned something from Kelly's bad question, 0:06:38.120 --> 0:06:39.599 which is why Kelly's here. 0:06:40.000 --> 0:06:42.479 So, and these are really fun topics to think about 0:06:42.560 --> 0:06:45.520 because our intuition is broken about how all of this 0:06:45.560 --> 0:06:48.359 stuff works. We tend to think that time flows the 0:06:48.400 --> 0:06:51.400 same way for everyone. We tend to think that distances 0:06:51.520 --> 0:06:54.919 are real and they're universal. When it turns out the 0:06:55.000 --> 0:06:58.479 universe operates in a way that's fundamentally in conflict with 0:06:58.560 --> 0:07:03.200 our intuition but amazingly does make sense. So we have 0:07:03.320 --> 0:07:06.880 this task ahead of us to incorporate this new intuition 0:07:07.040 --> 0:07:10.080 about the universe into our minds. But often this means 0:07:10.120 --> 0:07:11.880 just like, read a bunch of equations and use them 0:07:11.880 --> 0:07:14.440 to predict what happens. But I think it's possible to 0:07:14.480 --> 0:07:18.160 develop a new kind of intuition, a conceptual understanding for 0:07:18.240 --> 0:07:21.000 how the universe really does work. And that's what we're 0:07:21.000 --> 0:07:23.000 going to try to do today by introducing you to 0:07:23.120 --> 0:07:26.320 one of the most important concepts in special relativity that 0:07:26.400 --> 0:07:29.160 almost nobody talks about and that we've never covered on 0:07:29.200 --> 0:07:29.600 this show. 0:07:29.680 --> 0:07:33.320 What. Yes, Well, this is a very exciting day here 0:07:33.320 --> 0:07:38.000 at dk EU, and let's see if our audience heard 0:07:38.040 --> 0:07:40.480 about this thing that pretty much no one talks about. 0:07:40.520 --> 0:07:44.240 And so we asked our audience, what is a space 0:07:44.400 --> 0:07:45.760 time interval? 0:07:46.200 --> 0:07:50.760 Well, I would expect that that would be the reduction 0:07:51.200 --> 0:07:56.920 of Einstein's space time into a quantum type interval, but 0:07:57.000 --> 0:08:02.560 I'm really not too sure. It's the between two objects 0:08:02.600 --> 0:08:03.400 and space. 0:08:03.680 --> 0:08:04.640 Maybe I don't know. 0:08:05.280 --> 0:08:08.320 Could a space time interval be the point where one 0:08:09.040 --> 0:08:12.760 max plank length ends and one begins. 0:08:13.240 --> 0:08:16.320 I'm not sure a space time interval is the required 0:08:16.360 --> 0:08:21.120 time frame between semi convincing scientific mumbo jumbo that you 0:08:21.240 --> 0:08:25.560 hear on sci fi shows and movies. But seriously, maybe 0:08:25.600 --> 0:08:29.800 it's some form of the smallest unit of space time 0:08:30.440 --> 0:08:34.520 length and distance, kind of almost a singularity, but not quite. 0:08:35.000 --> 0:08:38.480 I've never actually heard the term space time interval before, 0:08:38.559 --> 0:08:42.000 but guessing from context, I would imagine a space time 0:08:42.000 --> 0:08:49.480 interval is one like frame of the universe. So you know, 0:08:49.559 --> 0:08:52.960 you move forward one unit of time and look at 0:08:53.080 --> 0:08:56.080 the way everything else changed. That's one interval of space type. 0:08:56.520 --> 0:08:59.920 All right, Daniel, I asked a question that belied my ignorance, 0:09:00.360 --> 0:09:03.880 and so I'm not going to even attempt to say 0:09:03.920 --> 0:09:07.320 if I think the audience was correct or not with 0:09:07.400 --> 0:09:09.160 this question. How close were they? 0:09:09.679 --> 0:09:13.200 Pretty much? Zero points all around? A few points for 0:09:13.360 --> 0:09:16.480 people thinking this is a kind of distance, because that's 0:09:16.520 --> 0:09:19.400 the closest. It has nothing to do with the plank 0:09:19.520 --> 0:09:24.120 length or frames of the universe or minimum distances or 0:09:24.160 --> 0:09:27.480 anything like that. It's really an analog to what we 0:09:27.559 --> 0:09:31.240 think of as distance, but now in four dimensional space 0:09:31.280 --> 0:09:34.320 time with an uncomfortable twist in it. That we're going 0:09:34.360 --> 0:09:34.800 to get. 0:09:34.640 --> 0:09:39.120 To good news everybody. We all need this episode. So 0:09:39.200 --> 0:09:42.040 here we go, and we are going to start from 0:09:42.080 --> 0:09:44.560 the beginning, because clearly Kelly needs to go back to 0:09:44.640 --> 0:09:48.120 first principles. So what I want you to explain to me, Daniel? 0:09:48.160 --> 0:09:51.360 So space time sounds like space and time and distance, 0:09:51.400 --> 0:09:56.000 and there's like, so what is distance? Let's start there. 0:09:56.000 --> 0:09:58.200 Yeah, let's build our intuition with stuff that makes sense 0:09:58.200 --> 0:10:02.280 to us. And let's start easy. Let's start in one dimension, right. 0:10:02.679 --> 0:10:06.160 So imagine, for example, you have a pencil and you 0:10:06.240 --> 0:10:09.000 have a ruler, and you want to know how long 0:10:09.240 --> 0:10:11.760 is my pencil? What do you do? Well, you put 0:10:11.840 --> 0:10:14.240 it along the ruler. You're operating in one dimension, right, 0:10:14.280 --> 0:10:16.760 So the pencil and the ruler are lined up, and 0:10:16.800 --> 0:10:18.840 you say, well, the back of the pencil, you know, 0:10:19.080 --> 0:10:21.160 is that two centimeters on the ruler, and the front 0:10:21.200 --> 0:10:23.520 of the pencil is that eight centimeters on the ruler. 0:10:23.640 --> 0:10:26.240 And then you subtract it's like eight minus two six 0:10:26.320 --> 0:10:27.160 centimeters long. 0:10:27.440 --> 0:10:28.839 I don't know why you wouldn't just put it at 0:10:28.840 --> 0:10:30.679 the beginning of the ruler and then you don't have 0:10:30.720 --> 0:10:31.839 to do any subtraction. 0:10:32.200 --> 0:10:33.880 Exactly. You could put it at the beginning of the 0:10:33.960 --> 0:10:36.920 ruler so that you get zero and six. But what 0:10:37.040 --> 0:10:39.640 happens You get the same answer, right, if you put 0:10:39.640 --> 0:10:41.720 the pencil at the beginning or if you slide it along, 0:10:41.800 --> 0:10:44.800 It doesn't matter. The answer you get does not depend 0:10:44.920 --> 0:10:47.200 on where on the ruler of your pencil is. Right, 0:10:47.240 --> 0:10:50.559 It's invariant. Okay, that's cool. That all makes sense. It's 0:10:50.679 --> 0:10:53.000 makes so much sense. It's kind of blindingly obvious, which 0:10:53.000 --> 0:10:55.400 is where we want to begin, right with, like firmly 0:10:55.480 --> 0:10:56.720 grounded in our intuition. 0:10:56.960 --> 0:10:59.040 This is very comforting, unlike the crusher. 0:11:01.360 --> 0:11:04.920 Okay, so why do you keep bringing that up? Kelly? 0:11:04.920 --> 0:11:06.680 You just like I don't want to throw me off. 0:11:06.840 --> 0:11:09.120 I wasn't going to mention it on this episode, but 0:11:09.280 --> 0:11:12.280 you brought it up because you did the whole crushing 0:11:12.360 --> 0:11:14.840 thing on the video before the episode, And now there's 0:11:14.840 --> 0:11:15.920 nothing else in my mind. 0:11:15.960 --> 0:11:18.360 I'm trying to get space time in my brain, but 0:11:18.400 --> 0:11:19.520 that's all I can see you. 0:11:19.679 --> 0:11:21.440 I'm so sorry. I'm sorry. 0:11:22.000 --> 0:11:26.080 It's fine, all right. So now let's go to two dimensions. 0:11:26.120 --> 0:11:28.280 How do things change? Well, imagine you have like a 0:11:28.320 --> 0:11:30.439 piece of graph paper and the little squares on the 0:11:30.480 --> 0:11:34.240 graph paper are one centimeter by one centimeter, and you 0:11:34.320 --> 0:11:36.920 drop your pencil onto the graph paper and ask you 0:11:36.960 --> 0:11:39.480 how long is your pencil? So how do you figure 0:11:39.520 --> 0:11:41.400 out how far it is from one side of the 0:11:41.440 --> 0:11:42.720 pencil to the other. 0:11:43.120 --> 0:11:44.840 But the Agrean theorem. 0:11:45.040 --> 0:11:49.079 Yes exactly, So you say, well, how many squares does 0:11:49.120 --> 0:11:51.640 it cross in one direction and how many squares in 0:11:51.640 --> 0:11:54.280 the other? Direction, and now you have a right triangle 0:11:54.559 --> 0:11:56.840 where the pencil is the hyphpot news right, it's the 0:11:56.880 --> 0:11:59.520 long part of the right triangle, and we can calculate 0:11:59.600 --> 0:12:02.320 one side because it's just counting squares. We can calculate 0:12:02.360 --> 0:12:05.080 the length may the other side just counting squares, and 0:12:05.120 --> 0:12:07.080 then the diagonal, which is the length of the pencil. 0:12:07.280 --> 0:12:10.480 That's the Pythagorean theorem. Right, So a squared plus b 0:12:10.559 --> 0:12:14.160 squared equal c square. Boom, we have an answer. And 0:12:14.600 --> 0:12:17.200 just like in the one dimensional case, it doesn't matter 0:12:17.400 --> 0:12:20.000 where the pencil was on the graph paper. If you 0:12:20.160 --> 0:12:22.760 dropped it in a different direction, you might have gotten 0:12:23.200 --> 0:12:25.920 more squares on one side and few or on the other, 0:12:26.080 --> 0:12:29.319 but the answer wouldn't change. Or even if by chance 0:12:29.360 --> 0:12:31.520 you happen to drop the pencil so it liigned up 0:12:31.559 --> 0:12:35.680 perfectly in one direction right like along the X axis 0:12:35.760 --> 0:12:38.800 conceptually right, then it's basically back to the one dimensional 0:12:38.800 --> 0:12:42.960 problem or the other axis. The point is in this picture, 0:12:43.240 --> 0:12:46.640 distance is real. It's invariant. It does not depend on 0:12:47.200 --> 0:12:49.800 where you drop the pencil, or like the size of 0:12:49.800 --> 0:12:52.880 these squares, if you made them two centimeters or five centimeters, 0:12:52.960 --> 0:12:55.640 or like a furlong or whatever. All those are just 0:12:55.760 --> 0:13:00.520 arbitrary choices humans have imposed. The pencil distance is the real. 0:13:00.240 --> 0:13:04.320 Thing, right, Yes, this is very comforting. Can we stay 0:13:04.360 --> 0:13:07.640 here for the rest of the episode. No, let's push 0:13:07.679 --> 0:13:08.280 our boundaries. 0:13:08.360 --> 0:13:11.800 Let's keep going, all right, And so now it's easy 0:13:11.800 --> 0:13:14.359 to imagine how we might extend this to three dimensions, 0:13:14.480 --> 0:13:17.840 or really any number of dimensions. Like if you have 0:13:17.920 --> 0:13:20.680 your pencil and it's not on the paper, but it's 0:13:20.720 --> 0:13:23.240 like floating in space. We're on the space station now, right, 0:13:23.280 --> 0:13:25.840 and the pencils floating in space, and you imagine like 0:13:26.240 --> 0:13:29.560 not graph paper, but like laser lines through space, and 0:13:29.600 --> 0:13:31.400 you want to measure how long is it from one 0:13:31.480 --> 0:13:33.760 edge of my pencil to the other. Well, you play 0:13:33.800 --> 0:13:36.200 the same game, but now you have three directions of 0:13:36.280 --> 0:13:39.400 counting squares and you can still do the pythagoranth theorem. 0:13:39.480 --> 0:13:42.240 It's just A squared plus B squared plus C squared 0:13:42.280 --> 0:13:45.560 equals D squared. Right, it's the same game fundamentally that 0:13:45.559 --> 0:13:48.360 the geometry has not changed because the nature of these 0:13:48.360 --> 0:13:50.760 dimensions are all the same, And so we can just 0:13:50.840 --> 0:13:53.040 keep doing this. And if you wanted to work in 0:13:53.120 --> 0:13:56.760 eleven dimensional space or twenty six dimensional space, the concept 0:13:56.800 --> 0:14:01.600 of distance wouldn't change mathematically or in intuitively, because the 0:14:01.679 --> 0:14:05.320 distance is the real thing, right, Everything else is just bookkeeping. 0:14:05.840 --> 0:14:09.120 Okay, So I'm trying to imagine a pencil floating in space, 0:14:09.160 --> 0:14:11.600 and now a squared plus B squared plus b squared 0:14:12.160 --> 0:14:16.520 equals the length of the pencil squared. Yeah, my gut 0:14:16.520 --> 0:14:19.200 feels like the more dimensions you add, the bigger the 0:14:19.240 --> 0:14:21.200 pencil's going to get because you've got all these extra 0:14:21.280 --> 0:14:25.520 squared terms that are gonna keep getting added. But that's 0:14:25.640 --> 0:14:28.680 not true because why. 0:14:28.040 --> 0:14:31.400 Yeah, that's not true because the pencil is a certain length, 0:14:31.800 --> 0:14:35.000 and if you add squares in one of the dimensions, 0:14:35.040 --> 0:14:37.600 the other ones will shrink. Okay, Just like if the 0:14:37.640 --> 0:14:39.800 pencil falls to the floor and it's now on a 0:14:39.840 --> 0:14:42.720 two dimensional surface, you only have two contributions, or the 0:14:42.760 --> 0:14:46.240 third one is just zero, right, and those are longer 0:14:46.280 --> 0:14:49.080 than if it's floating up above the graph and it 0:14:49.160 --> 0:14:51.840 gets a third dimension, the first two dimensions are going 0:14:51.920 --> 0:14:54.280 to shrink a little bit. So they all act in 0:14:54.360 --> 0:14:57.880 harmony to make sure the distance never changes. You like 0:14:57.960 --> 0:15:00.040 flip a pencil from one astronaut to another se so 0:15:00.080 --> 0:15:03.280 it's like rotating through space. You know, your intuition tells 0:15:03.320 --> 0:15:05.920 you the length of the pencil is not changing. The 0:15:06.000 --> 0:15:10.000 difference between its front and its back along some axis 0:15:10.120 --> 0:15:12.520 might change, right, it might go up and down and 0:15:12.560 --> 0:15:14.920 be negative or whatever, But the length of the pencil 0:15:14.920 --> 0:15:18.080 doesn't change because all three dimensions are working in harmony 0:15:18.640 --> 0:15:22.200 to contribute various pieces to the length, and it always 0:15:22.200 --> 0:15:25.160 adds up to the same number. Because that's the physical thing. 0:15:25.440 --> 0:15:28.560 Everything else is just bookkeeping. It wouldn't make sense if 0:15:28.560 --> 0:15:31.240 the length of the pencil depended on like where the 0:15:31.280 --> 0:15:34.680 graph paper was right, or which ruler you used. It's 0:15:34.720 --> 0:15:36.760 a real thing in the universe. 0:15:36.720 --> 0:15:40.200 All right. But I bet that if I were to say, Daniel, 0:15:40.240 --> 0:15:43.960 you can travel a billion, a trillion, a quadrillion miles 0:15:44.000 --> 0:15:46.040 away in any direction in space. What is it that 0:15:46.080 --> 0:15:50.280 you want to see within that area? Everybody should know 0:15:50.320 --> 0:15:52.520 what I'm talking about. Are you going to tell me 0:15:52.600 --> 0:15:56.440 that something about that doesn't work? Like the pencil? 0:15:57.160 --> 0:15:59.320 I see, you're asking me to be the physics sweat 0:15:59.320 --> 0:15:59.920 blanket here. 0:16:00.720 --> 0:16:02.840 I mean we have to take turns there, right. 0:16:04.960 --> 0:16:08.440 Well, if you said I could go at quadrillion miles 0:16:08.480 --> 0:16:11.000 with respect to Earth, then you've given me a frame 0:16:11.040 --> 0:16:14.240 of reference. In which that is well defined. Okay, so yeah, 0:16:14.280 --> 0:16:15.520 I could totally do that, all. 0:16:15.480 --> 0:16:16.800 Right, that's what I should have asked anyway. 0:16:16.800 --> 0:16:20.400 All right, moving on, and so we have three dimensions 0:16:20.440 --> 0:16:24.520 of space. We're comfortable with the idea of distance in space. Cool, 0:16:24.760 --> 0:16:27.240 let's put that aside for now and think about time. 0:16:27.880 --> 0:16:31.280 Time is one dimensional, right, We don't have like two 0:16:31.440 --> 0:16:33.840 clocks going on, we don't think, so it's actually a 0:16:33.880 --> 0:16:36.280 super fun theory we can explore. And we did an 0:16:36.280 --> 0:16:39.040 episode a couple of years ago about two dimensions of time. 0:16:39.120 --> 0:16:42.360 But for now, let's just think about one dimension of time, right, 0:16:42.440 --> 0:16:45.040 And so, for example, you can click your stop watch 0:16:45.120 --> 0:16:47.840 when this episode starts and when the episode ends, and 0:16:47.880 --> 0:16:50.160 you can ask how long is this episode of the 0:16:50.200 --> 0:16:52.880 pod and you can look at the difference, and that's 0:16:52.920 --> 0:16:56.120 the length, right, totally obvious, basic subtraction. 0:16:56.600 --> 0:16:59.080 Perfect. Yes, for our poor audio guy, it probably feels 0:16:59.160 --> 0:17:02.040 like an hour is infinite, but it is still just 0:17:02.080 --> 0:17:03.680 an hour exactly. 0:17:03.720 --> 0:17:06.240 And in the same way, it doesn't actually matter when 0:17:06.320 --> 0:17:08.960 you hit the stopwatch to start, as long as you 0:17:09.080 --> 0:17:11.840 noted when the episode started. If you'd accidentally hit your 0:17:11.880 --> 0:17:14.880 stopwatch like an hour before, as long as you wrote down. Oh, 0:17:14.920 --> 0:17:17.760 the episode started at one hour in you could still 0:17:17.840 --> 0:17:22.040 measure the length of the episode by looking at the difference, right, 0:17:22.119 --> 0:17:25.720 because when you started it is arbitrary. What you're interested 0:17:25.760 --> 0:17:28.200 in is the physical thing, which is the difference between 0:17:28.240 --> 0:17:31.480 the start and the end of the episode. So intervals 0:17:31.480 --> 0:17:34.080 and time are also physical in that sense, right, They're real, 0:17:34.119 --> 0:17:35.439 It's not just bookkeeping. 0:17:35.680 --> 0:17:38.280 What does physical mean in this case? Like physical I 0:17:38.280 --> 0:17:40.960 think of as something I can touch. Oh, I see, 0:17:41.160 --> 0:17:42.720 you mean physics all. 0:17:44.480 --> 0:17:46.439 I mean it's a part of the universe. It's not 0:17:46.480 --> 0:17:50.359 part of our measurement system, and it's invariant in that way. 0:17:50.760 --> 0:17:53.720 And here so far, all these definitions are in a 0:17:53.760 --> 0:17:58.280 classical world, right before relativity. This is Newton's idea about 0:17:58.320 --> 0:18:02.000 how time and distance were worked, Right, that anybody could 0:18:02.000 --> 0:18:04.760 measure the difference between two things that happened in the 0:18:04.840 --> 0:18:08.119 universe and the time difference or the space difference, and 0:18:08.119 --> 0:18:10.640 they would always get the same answer. That's the way 0:18:10.720 --> 0:18:12.840 Newton thoughts the universe worked, and that's the way I 0:18:12.960 --> 0:18:15.720 operate and you operate. And this whole segment of the 0:18:15.720 --> 0:18:18.800 pod has been like, let's confirm our intuition about how 0:18:18.840 --> 0:18:22.400 distances work and that's all very comforting until we learn 0:18:22.680 --> 0:18:23.600 that it's all wrong. 0:18:24.040 --> 0:18:29.720 Oh no, you pulled the soft blanket of Newtonian physics off. Yeah, 0:18:29.760 --> 0:18:33.959 and now it's cold and unwelcoming. Let's take a break 0:18:34.200 --> 0:18:37.520 before we have to sit with our discomfort for too long. 0:18:37.720 --> 0:18:39.840 And when we get back, we'll hear what Einstein had 0:18:39.880 --> 0:19:02.880 to add. And we're back. We had a very comforting 0:19:02.920 --> 0:19:05.919 discussion about distance and time where everything felt like it 0:19:05.960 --> 0:19:07.760 made sense. And now we're at the point of the 0:19:07.800 --> 0:19:10.040 episode where we are going to expand our brains and 0:19:10.119 --> 0:19:13.120 learn something new. So all right, Daniel, make us uncomfortable, 0:19:13.960 --> 0:19:16.440 all right, So not crusher level uncomfortable. 0:19:17.119 --> 0:19:20.399 Well, in nineteen oh five, Einstein pulled out the metaphorical 0:19:20.440 --> 0:19:23.439 crusher and he said to Newton, he said, you know, 0:19:23.520 --> 0:19:26.119 put your theories in this, buddy, because here I come. 0:19:28.920 --> 0:19:31.119 It took me a second. Sorry for the delay. I 0:19:31.160 --> 0:19:34.080 was drinking water. It almost totally destroyed my computer. 0:19:34.119 --> 0:19:36.800 All right, go on, and you know these intuitive notions 0:19:36.840 --> 0:19:39.840 of how the universe works, they do work for us 0:19:39.920 --> 0:19:43.680 at our basic level. But Einstein discovered that when speeds 0:19:43.720 --> 0:19:47.160 get high relative speeds get high, then they don't work. 0:19:47.200 --> 0:19:49.879 The universe is broken. It actually works in a fundamentally 0:19:50.160 --> 0:19:53.440 different way. And it's important to understand where this comes from. 0:19:53.840 --> 0:19:56.359 It all comes from the same source, which is the 0:19:56.400 --> 0:19:59.880 fact that the speed of light is constant for all observed. 0:20:00.520 --> 0:20:03.840 That is at the heart of everything. If you accept 0:20:04.080 --> 0:20:06.439 that the speed of light is the same number no 0:20:06.480 --> 0:20:09.560 matter who measures it, no matter how fast they are 0:20:09.600 --> 0:20:12.440 moving with respect to like the flashlight that gave off 0:20:12.480 --> 0:20:15.639 that beam, then you'll see that everything breaks. And we're 0:20:15.640 --> 0:20:17.960 going to walk you through that and how it crushes 0:20:18.000 --> 0:20:19.280 your intuition, all. 0:20:19.320 --> 0:20:21.640 Right, crush away. 0:20:22.640 --> 0:20:25.760 So imagine here's the setup. Kelly gives two flashlights to 0:20:25.760 --> 0:20:28.320 her goats and puts those goats in a crate and 0:20:28.359 --> 0:20:31.200 puts that crate on a self driving tractor to the 0:20:31.320 --> 0:20:34.840 vet to you know, have their problems taken care of 0:20:34.960 --> 0:20:39.080 with great anesthetic, of course, and very humanely good, all right. 0:20:39.119 --> 0:20:42.080 And so they have two flashlights and one is pointed 0:20:42.119 --> 0:20:44.080 towards the front of the crate and one is pointed 0:20:44.119 --> 0:20:46.960 towards the back of the crate. Okay, and they turn 0:20:47.000 --> 0:20:49.440 the flashlights on at the same moment, so they click 0:20:49.520 --> 0:20:53.000 both buttons. And then we're interested in, like, well, how 0:20:53.040 --> 0:20:55.200 long does it take for that beam of light to 0:20:55.280 --> 0:20:57.679 hit the front of the crate versus the back of 0:20:57.720 --> 0:21:00.440