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Speaker 1: Hey, Daniel, how long does it take you to do

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Speaker 1: the research for one of these episodes?

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Speaker 2: You know, it used to take me quite a while,

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Speaker 2: but I'm getting quicker at it.

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Speaker 1: Mmmm. Is that because time passes more quickly as you

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Speaker 1: get older, like a special relativity thing?

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Speaker 2: Maybe? Or I guess I've just gotten more efficient at

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Speaker 2: the preparation.

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Speaker 1: Oh, yeah, like you can read faster, or you can

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Speaker 1: process information better.

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Speaker 2: No, I think I just developed a better mental whorehe

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Speaker 2: simulator that can predict what you might be interested in

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Speaker 2: or what you might not be interested in.

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Speaker 1: Oh, it sounds like you just need like an AI

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Speaker 1: version of me. Then I don't even need to be here.

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Speaker 2: It's not artificial intelligence. It's natural.

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Speaker 1: It's a cartoonist intelligence. Well, I guess you know. It

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Speaker 1: kind of depends. You know, what's interesting is kind of relative,

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Speaker 1: isn't it.

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Speaker 2: Yeah, that's right. What's especially interesting is kind of relative,

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Speaker 2: So I guess it kind of it is all special relativity.

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Speaker 1: Yeah, I definitely have some special relatives. Did you predict

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Speaker 1: I was going to say that.

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Speaker 2: I predicted you were going to say something hilarious. Hi.

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Speaker 1: I'm Jorge mc cartoonist and the author of Oliver's great,

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Speaker 1: big Universe.

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Speaker 2: Hi. I'm Daniel. I'm a particle physicist and a professor

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Speaker 2: at UC Irvine, and I'm still training my brain to

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Speaker 2: understand the universe.

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Speaker 1: Wait, don't you need to know how the universe works

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Speaker 1: before you can train your brain to understand it.

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Speaker 2: We can do two things at once. We can try

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Speaker 2: to figure out how the universe works, and we can

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Speaker 2: try to wrap our minds around the bits that we

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Speaker 2: have figured out and try to gain some intuition for

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Speaker 2: all this craziness.

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Speaker 1: I feel like this podcast is a little bit of

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Speaker 1: training into like how to think about the universe, how

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Speaker 1: to explore it, how to ask questions about it. Should

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Speaker 1: we be charging tuition?

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Speaker 2: We're just sharing the love, you know. But you're right

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Speaker 2: because most of our modern theories or physics are expressed

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Speaker 2: in a kind of inaccessible language mathematical equations that do

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Speaker 2: show us the relationship between bits and pieces and allow

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Speaker 2: us to make predictions and stuff. But it's not always

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Speaker 2: the way our brains work. So one of the goals

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Speaker 2: on this podcast is to break it down and give

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Speaker 2: you an intuitive understanding, to try to make it all

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Speaker 2: make sense to you.

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Speaker 1: Yeah, I guess. We offer free intuition, but not at

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Speaker 1: a cost of free tuition.

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Speaker 2: No tuition intuition. That should have been the title of

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Speaker 2: the podcast.

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Speaker 1: Yeah, hopefully it all comes to fruition.

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Speaker 2: But I mean, you're welcome to pay tuition if you like,

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Speaker 2: send us gold coins or dollars if the inspiration strikes you.

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Speaker 1: You take tips. You have a tip jar in your classroom.

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Speaker 2: I don't have a tip jar, but I did once

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Speaker 2: walk into a classroom and find an envelope with thousands

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Speaker 2: of dollars in it.

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Speaker 1: Oh, WHOA, where is your university.

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Speaker 2: It's a public university, man, So it's not like some

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Speaker 2: students just like dropped a pile of cash. I think

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Speaker 2: it must have been some club organizing in the room

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Speaker 2: before us or something. Hmmmm.

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Speaker 1: Sounds like maybe they were trying to bribe you.

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Speaker 2: I don't think so. I think somebody must have panicked

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Speaker 2: when they realized they left it behind.

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Speaker 1: Or could have been a tip. I don't know. You

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Speaker 1: could have just assumed it was a tip.

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Speaker 2: I'm not so cheaply bought.

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Speaker 1: But anyways, welcome to our podcast. Daniel and Jorge Explain

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Speaker 1: the Universe, a production of iHeartRadio.

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Speaker 2: In which we use our inspiration to improve your intuition

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Speaker 2: for absolutely no tuition, whether or not the jokes come

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Speaker 2: to any fruition.

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Speaker 1: That's right, because it is an amazing universe for us

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Speaker 1: to ask questions about and to explore and to learn

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Speaker 1: about how it all works.

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Speaker 2: And part of the process of doing physics is not

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Speaker 2: just writing down on some sheet of paper a bunch

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Speaker 2: of math and then gesturing at and saying, trust us,

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Speaker 2: this works. It's about understanding. In the end, physics and

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Speaker 2: all of science is motivated by our curiosity, our desire

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Speaker 2: to understand, and that means translating all of this stuff,

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Speaker 2: everything we've learned, back into something that makes sense to us,

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Speaker 2: that clicks together in our minds, and we go, oh, well,

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Speaker 2: that's kind of weird, but I guess it does make sense. Yeah.

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Speaker 1: Plus, I don't know if I trust you anymore. I mean,

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Speaker 1: now that I know you're open to bribery.

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Speaker 2: I did say I was opening bribery. You said I

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Speaker 2: was opening bribery, and I said I.

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Speaker 1: Wasn't it sounds like you're open to tips quote unquote tips.

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Speaker 2: People are welcome to send us donations to the podcast,

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Speaker 2: but it's not going to affect how I grade in

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Speaker 2: my class. Now I turned that stack of cash over

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Speaker 2: to the campus police.

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Speaker 1: Oh wow, are saying you tip the police.

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Speaker 2: I don't know what they did with it, but I

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Speaker 2: can only assume that they did something responsible.

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Speaker 1: But yeah, this university needs to depend on your point

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Speaker 1: of view and also how fast you're.

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Speaker 2: Going, because something we've learned over the last hundred years

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Speaker 2: is that our ancient intuition for how things work doesn't

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Speaker 2: always work. It only works in the special cases that

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Speaker 2: us and our ancestors got to see things moving pretty slowly.

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Speaker 2: And when you take those rules and try to extrapolate

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Speaker 2: them up to things moving really, really quickly, you find

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Speaker 2: they just don't work anymore. You need a new set

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Speaker 2: of rules, and those rules give us weird new insights

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Speaker 2: into the actual nature of space and time.

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Speaker 1: Yeah, over eight hundred years ago, Einstein discovered something called

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Speaker 1: special relativity.

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Speaker 2: Einstein developed special and general relativity. That's absolutely true. I

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Speaker 2: don't know if he invented it or discovered it, he

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Speaker 2: certainly uses it to describe the universe that we see

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Speaker 2: around us.

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Speaker 1: Yeah. Over a one hundred years hegol Einstein discovered something

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Speaker 1: called relativity special in general, in which he discovered that

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Speaker 1: things don't always look the same in this universe. Sometimes

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Speaker 1: it sort of depends on your relative point of view.

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Speaker 2: Yeah, Einstein really shook the foundations of our understanding of reality.

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Speaker 2: Newton gave us this idea of space and time as

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Speaker 2: being absolute, like the fixed backdrop of the universe, but

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Speaker 2: Einstein showed us that space is relative and so is time,

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Speaker 2: and it leads to all sorts of bizarre effects. Clock sprunning, slower,

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Speaker 2: meter sticks looking shorter, and information disappearing into black holes.

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Speaker 1: Yeah, it kind of seems sometimes that the universe has

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Speaker 1: these paradoxes and these contradictions, but actually it all sort

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Speaker 1: of works if you dig into the math, right, It

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Speaker 1: all does actually make sense in the end. It's just

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Speaker 1: a different kind of sense. So today on the podcast,

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Speaker 1: we'll be tackling the question why do moving objects look shorter?

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Speaker 1: I guess moving objects look shorter.

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Speaker 2: This is not like how your bank account seems to

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Speaker 2: shrink when you're on a trip, you know, or on vacation.

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Speaker 2: This is the effect commonly known as length contraction, that

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Speaker 2: things going super duper fast relative to you seem to

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Speaker 2: look shorter than they do when they're at rest.

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Speaker 1: That's one of the consequences of having a speed limit

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Speaker 1: in the universe, isn't it.

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Speaker 2: Absolutely. It's one of the consequences of special relativity, which

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Speaker 2: starts from the postulates if there's a speed limit to

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Speaker 2: the universe and that light always moves at the speed

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Speaker 2: of life for everybody, regardless of who they are and

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Speaker 2: how fast they're going. Out of that comes all sorts

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Speaker 2: of weird changes we have to make to space and

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Speaker 2: time and velocity in order to make things still make sense.

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Speaker 1: And so On the podcast here we've talked about how

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Speaker 1: as you're moving at close to the speed of lighter

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Speaker 1: moving near really massive objects, time slows down. We've talked

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Speaker 1: about that quite a bit, right, Yeah, moving clocks run slow.

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Speaker 1: So if you see a clock moving past you at

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Speaker 1: half the speed of light, then you will see a

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Speaker 1: tick slower than a clock you are holding. That's time dilation,

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Speaker 1: a concept we've talked about lots and lots of times, right.

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Speaker 1: And then there's the idea that it's not only time

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Speaker 1: that can sort of stretch and change, it's also distances

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Speaker 1: or the lengths of things.

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Speaker 2: Yeah, if you are traveling really really fast, then distances

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Speaker 2: in front of you seem shorter, like if you're flying

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Speaker 2: between here and Jupiter, and you're moving really really fast,

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Speaker 2: then the distance between here and Jupiter seems to shrink.

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Speaker 1: So like, if there was a giant meter stick between

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Speaker 1: here and Jupiter, and I was moving towards Jupiter really

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Speaker 1: really fast, then that meter stick would look shorter than

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Speaker 1: it actually is to me.

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Speaker 2: It would look shorter to you, but there is no

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Speaker 2: what it actually is. There's just a lot of different

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Speaker 2: viewpoints on it. It's all relative.

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Speaker 1: Well, I guess what it would look like if you

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Speaker 1: were not moving relative to the stick exactly.

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Speaker 2: Yeah, And that's what we call the proper length.

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Speaker 1: In that case, I'm moving really fast, it's not the

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Speaker 1: meter stick, or is it the same thing.

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Speaker 2: It's exactly the same thing. The meter stick would say

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Speaker 2: you look shorter, and you would say the meter stick

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Speaker 2: looks shorter. The whole effect is symmetric, same way the

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Speaker 2: time valation is symmetric. If I think you're moving fast,

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Speaker 2: I see your clock running slow, but you also see

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Speaker 2: me moving quickly, so you see my clock running slow.

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Speaker 1: But I guess, doesn't it depend on which direction this

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Speaker 1: ruler is flying. Like if the ruler is flying let's

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Speaker 1: say away for me really fast, it would look shorter.

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Speaker 1: But what if it's moving, like from I see, moving

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Speaker 1: from my left to my right, would it still look shorter?

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Speaker 2: It would look thinner. In that case, the direction it's

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Speaker 2: moving relative to you is the direction that gets contracted.

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Speaker 2: If it's always moving along its length, then it's going

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Speaker 2: to look shorter, even if that length is point. Did

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Speaker 2: it along X or along y or along zo or

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Speaker 2: in any direction? If it's moving along its length, it's

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Speaker 2: going to look shorter.

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Speaker 1: I see. So like if someone launched a ruler really

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Speaker 1: really fast from my left and my right, it would

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Speaker 1: seem shorter than it would if I just held it

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Speaker 1: in my hand.

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Speaker 2: That's exactly right.

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Speaker 1: Yeah, so then the question for today is why does

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Speaker 1: that happen? All right? Well, as usual, we were wondering

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Speaker 1: how many people out there had thought about this question

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Speaker 1: or wonder why things look shorter when they're moving really fast.

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Speaker 2: Thanks very much to everybody who answers these questions. We

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Speaker 2: love hearing your voices, and we'd love to hear more

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Speaker 2: of your voices, So please don't be shy and write

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Speaker 2: to us two questions at Danielandhorge dot com.

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Speaker 1: So think about it for a second. Why do you

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Speaker 1: think moving objects look shorter. Here's what people have to say.

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Speaker 1: The Doppler effect is that what it's called the red

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Speaker 1: shifting thing.

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Speaker 2: So like, basically when the object, the object comes closer

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Speaker 2: to you, like I guess, like, it looks like the

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Speaker 2: wavelengths wavelengths shorten, right, they get shorter. So like all objects,

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Speaker 2: you know, they get a little louder, the colors are a

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Speaker 2: little brighter, the wavelengths shorten, and so the object look

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Speaker 2: shorter because the wavelengths of the colors of the object

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Speaker 2: is shorter.

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Speaker 3: Yeah, that's why.

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Speaker 4: I think they look shorter, just due to the fact

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Speaker 4: that it's more for our brain to process, you know,

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Speaker 4: as opposed to if an object was sitting still, and

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Speaker 4: then obviously when there's more to interpret, that obviously creates

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Speaker 4: more of a margin of error with our perception.

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Speaker 5: I would assume that the reason that objects appear shorter,

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Speaker 5: especially as they approach light speed, is time and space dilation.

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Speaker 5: So as it approaches light speed, it would just appear

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Speaker 5: to shrink. Not really sure.

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Speaker 3: I think that for a human eye optics, moving objects

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Speaker 3: look actually longer because of motion blur, but special relative

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Speaker 3: to states that moving objects get shorter, don't exactly remember why.

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Speaker 4: Moving objects look shorter because the back has gotten closer

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Speaker 4: to where the front was when you saw it by

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Speaker 4: the time you see the back.

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Speaker 1: All right, Lots of interesting answers.

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Speaker 2: Here, very creative answers today, but.

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Speaker 1: They also sound very sciensy talking about Doppler effects and

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Speaker 1: red shifting and space dilation.

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Speaker 2: Yeah, motion blur. Some of these answers are way off

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Speaker 2: and some of them are pretty close.

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Speaker 1: Pretty cool. These are people that you found in your

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Speaker 1: department or people on the internet.

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Speaker 2: These are just folks from the internet listeners to this podcast.

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Speaker 1: Nice, Well, let's dig into it. Daniel, how what is

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Speaker 1: the physicist definition of length dilation?

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Speaker 2: So we usually call it length contraction.

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Speaker 1: Wait is there a difference? Can you also have that

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Speaker 1: length dilation or is it only contract.

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Speaker 2: You can only have length contraction. The longest something can

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Speaker 2: be is if it's at rest relative to you. So

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Speaker 2: you're holding a meter stick, that's the longest you're ever

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Speaker 2: going to measure that meter stick to be that meterstick

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Speaker 2: is moving past you at a certain speed, then you're

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Speaker 2: going to see it shorter. And the way I like

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Speaker 2: to phrase it to be very clear to make sure

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Speaker 2: it's relative, is that moving objects look shorter.

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Speaker 1: And if they're moving like away from you or towards you,

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Speaker 1: it still gets shorter.

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Speaker 2: They still get shorter. Yeah, that doesn't make any difference.

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Speaker 2: In the same way that like moving clocks run slow

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Speaker 2: tells you that you are seeing that clock run slow

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Speaker 2: because you see it moving and it sees you moving,

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Speaker 2: so it sees you running slow. In the same way

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Speaker 2: you see a meter stick moving, you see it looking shorter.

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Speaker 2: It also sees you looking shorter because it sees you moving.

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Speaker 2: It's a symmetric effect.

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Speaker 1: All right, I was wrong. Well is the This is

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Speaker 1: the definition of the length contraction.

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Speaker 2: So it's just that moving objects look shorter. You define

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Speaker 2: the proper length of something to be its length when

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Speaker 2: it's not moving. So you're holding the meterstick, you call

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Speaker 2: that the proper length. Then you zoom that meterstick by

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Speaker 2: you at like ten percent of the speed of light,

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Speaker 2: which doesn't sound impressive, but it's super duper crazy fast.

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Speaker 2: Then you'll see it a little bit shorter. You'll see

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Speaker 2: it like a half a percent shorter. You speed it

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Speaker 2: up to like half the speed of light, and you'll

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Speaker 2: see it be like only eighty five percent of its

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Speaker 2: proper length length. And as you get up to like

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Speaker 2: ninety nine percent of the speed of light, it'll shrink

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Speaker 2: down to like fifteen percent of its proper length. If

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Speaker 2: you get to like ninety nine point ninety nine percent

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Speaker 2: of the speed of light, it'll be just over one

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Speaker 2: percent of its proper length. So you can see things

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Speaker 2: getting like super duper short as they get super duper

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Speaker 2: fast relative to you.

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Speaker 1: I guess I'm wondering what it means to see something

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Speaker 1: like that moving that fast. You mean, like if I

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Speaker 1: take a picture of it, Like, let's say a ruler

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Speaker 1: is zooming by really quickly, buy me from my left

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Speaker 1: to my right, and I take a picture of it

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Speaker 1: as it's going in front of me. In the picture,

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Speaker 1: it's going to seem shorter than it would if I

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Speaker 1: held the ruler in my hand.

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Speaker 2: It's great that you asked that question, because we have

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Speaker 2: to be very specific about what we mean here by

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Speaker 2: these measurements, because it makes a difference. And actually, if

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Speaker 2: you take a picture, you would see the ruler looking

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Speaker 2: weirdly longer because the picture captures all the photons that

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Speaker 2: are arriving at you at one moment, and that includes

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Speaker 2: another effect, which is that it takes time for the

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Speaker 2: infram to get to you, and part of the ruler

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Speaker 2: is further from you, and part of the rulers closer

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Speaker 2: to you. So that combines two different effects. One is

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Speaker 2: that the ruler looks shorter because it's moving faster, and

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Speaker 2: the other one at the back of the ruler is

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Speaker 2: further from you, so it takes light longer to get

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Speaker 2: to you.

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Speaker 1: No, now, but if the ruler is moving from my

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Speaker 1: left to my right, like it's zooming past me like

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Speaker 1: a train would like if I'm standing then next to

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Speaker 1: some train tracks and I see the train going from

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Speaker 1: my left to my right, and I take a picture

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Speaker 1: of the train as it's passing by in front of me.

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Speaker 1: Is that draining It seemed shorter in the picture or

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Speaker 1: the same length or longer.

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Speaker 2: Again, the picture combines two different effects. One is a

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Speaker 2: special relativity effect and the other is the very normal

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Speaker 2: light takes time to travel effect. And so usually what

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Speaker 2: we do is not use the idea of a mental picture,

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Speaker 2: but imagine that we have like a bunch of assistants

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Speaker 2: all spread out to our left and to our right,

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Speaker 2: and they mark like when the train front or when

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Speaker 2: the train back passes them, and then we can use

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Speaker 2: the distance between the train front and the train back

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Speaker 2: to say how long.

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Speaker 1: It is h what happens in the picture case, like

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Speaker 1: what if I take a picture of the train or

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Speaker 1: the ruler moving from my left and my right, Like,

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Speaker 1: aren't all those photons leaving the stick at the same time,

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Speaker 1: and so then it would arrive at the camera or

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Speaker 1: my eye at the same time.

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Speaker 2: They're leaving the train or the stick at the same time.

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Speaker 2: The stick has length, so it takes longer for the

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Speaker 2: back end photons to reach you than the front end photons.

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Speaker 2: And I think combining photon travel time and actual length

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Speaker 2: combines two different complicated things which are kind of hard

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Speaker 2: to hold in your head at the same time. So

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Speaker 2: usually when we talk about special relativity, we assume that

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Speaker 2: we can take care of the photon travel time and

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Speaker 2: say that we have a bunch of assistants all through

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Speaker 2: the universe, all making measurements and take local data, and

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Speaker 2: then we combine that information later to figure out what happened.

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Speaker 2: So we take away this effect of photons take time

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Speaker 2: to get somewhere because it adds another confusing layer.

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Speaker 1: But I guess I mean we're saying that things look shorter, right,

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Speaker 1: and your eye sort of look acts like a camera.

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Speaker 1: Are you saying that, like, maybe what you mean by

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Speaker 1: looking at something it's not quite the same, but as

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Speaker 1: what everyday person might mean by looking at something.

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Speaker 2: Yeah, I think that's fair. When we do physics experiments,

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Speaker 2: we're very careful about how we make those measurements. So really,

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Speaker 2: what we mean here is if we take a very

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Speaker 2: careful measurement of the length of the object, we will

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Speaker 2: measure it to be shorter than if it was stationary.

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Speaker 1: All right, well, I think we just should just be

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Speaker 1: kind of clear about what we mean by things looking shorter.

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Speaker 2: What we mean is that we make a careful measurement

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Speaker 2: of the length of this thing involving us and a

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Speaker 2: bunch of assistants all along, like the track of a

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Speaker 2: train and noting when it passes by. And then later

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Speaker 2: we get together and we compare our measurements and we say,

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Speaker 2: you know, Juan measured the back of the train at

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Speaker 2: this time, and Sally measured the front of the train

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Speaker 2: at that time, and then we can use that to

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Speaker 2: figure out how long the train was.

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Speaker 1: All right, it sounds like we need to dig into

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Speaker 1: this scenario of you and all of your assistance and

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Speaker 1: how they're measuring the length of this ruler and or

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Speaker 1: this train. Maybe really understand what we mean by things

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Speaker 1: looking shorter or not. So let's dig into these details.

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Speaker 1: But first let's take a quick break. All right, we're

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Speaker 1: talking about length contraction due to special relativity, and that

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Speaker 1: doesn't have to do with how long this podcast is,

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Speaker 1: right or how much my questions dilate the length of

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Speaker 1: the running time of this episode.

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Speaker 2: That's exactly what I was going to say. Yeah, no,

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Speaker 2: but it's good. It's important we explain exactly what we

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Speaker 2: mean and we not use jargon. So let's hash it

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Speaker 2: out because there's some really interesting, like apparent paradoxes that

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Speaker 2: come up when we try to measure these lengths really carefully.

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Speaker 1: Okay, so we're asking the question why the moving objects

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Speaker 1: look shorter, and it seems like we're not really asking

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Speaker 1: the question why they look shorter. It's more like why

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Speaker 1: when a bunch of physicists try to measure something moving fast,

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Speaker 1: they measure things to be shorter. Not really because the

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Speaker 1: idea of looking at it you're saying, convolutes several things.

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Speaker 2: Yeah, I would say, I guess that's how physicists look

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Speaker 2: at something. Right, don't just take a picture. We think

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Speaker 2: about what that picture is actually measuring and realizing pictures

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Speaker 2: are not the best way to measure the length of

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Speaker 2: something moving really really fast. And said, we hire a

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Speaker 2: bunch of assistants and lay them out in a line

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Speaker 2: so we can take measurements and figure out how long

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Speaker 2: that thing really is.

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Speaker 1: Okay, so then let's maybe paint that scenario. I'm sitting

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Speaker 1: by some train tracks, and the train tracks go from

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Speaker 1: my left to my right in front of me, and

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Speaker 1: now there's going to be a train passing by. I

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Speaker 1: want to measure how long the train is. Yeah, and

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Speaker 1: you're saying, don't take a picture of it because the

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Speaker 1: picture might lie to you. You're saying, hire a bunch

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Speaker 1: of people, and then, now what's your scenario.

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Speaker 2: What's your setup here with your assistance. So I have

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Speaker 2: a bunch of people to my left and a bunch

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Speaker 2: of people to my right.

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Speaker 1: Like you space them out every ten meters.

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Speaker 2: Or something, and we all have a bunch of clocks,

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Speaker 2: and we synchronize our clocks. So they all started zero

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Speaker 2: at the same moment, and they all read ten seconds

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Speaker 2: at the same moment. They all read one hundred seconds

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Speaker 2: at the same moment. So we have a bunch of

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Speaker 2: people now a different locationations with synchronized clocks.

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Speaker 1: How do you synchronize a clock. Wouldn't you run into

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Speaker 1: special relativity problems sinking those clocks?

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Speaker 2: It's complicated, but you can sink clocks using flashes of light.

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Speaker 2: If you assume you know how long it takes light

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Speaker 2: to get somewhere, you can synchronize clocks that are distanced.

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Speaker 3: Mm.

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Speaker 1: Okay, So then each of these systet has a clock

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Speaker 1: that's synchronized to yours.

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Speaker 2: Right exactly, now the train is passing by us, and

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Speaker 2: ask people to write down what time the front or

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Speaker 2: the back of the train passed them.

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Speaker 1: Which one the front or the back.

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Speaker 2: You can have them write down both. And then in

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Speaker 2: order to measure the length of the train, what you

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Speaker 2: need to do is get a measurement of where the

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Speaker 2: back of the train was and where the front of

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Speaker 2: the train was at the same time. You combine those

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Speaker 2: two numbers and that's your length.

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Speaker 1: See it again, You measure where the front and the

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Speaker 1: back were at the same time.

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Speaker 2: Yeah, you want to know how long something is, Then

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Speaker 2: you want to know where's the front and where's the back.

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Speaker 2: And you want to take those measurements at the same moment.

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Speaker 5: Right.

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Speaker 2: If you don't take those measurements at the same moment,

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Speaker 2: you're not going to get the length of the train.

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Speaker 2: Like if a parade is passing by you, it's moving, right,

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Speaker 2: If you measure the front and the back at different moments,

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Speaker 2: you're not going to get the actual length of the parade.

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Speaker 1: I see, all right, So then you ask your assistance

443
00:20:10,720 --> 00:20:12,600
Speaker 1: to write down when they saw the front of the train,

444
00:20:12,640 --> 00:20:14,360
Speaker 1: when they saw the back of the train. And then

445
00:20:14,359 --> 00:20:16,399
Speaker 1: what do you do. You get together and you have

446
00:20:16,480 --> 00:20:18,840
Speaker 1: a picnic, You.

447
00:20:18,720 --> 00:20:20,959
Speaker 2: Get together, you spend some of that tip money on

448
00:20:21,000 --> 00:20:23,719
Speaker 2: you know, ice sculptures and chocolates for your picnic and whatever.

449
00:20:24,000 --> 00:20:25,399
Speaker 2: And then you look at the numbers and you say,

450
00:20:25,440 --> 00:20:27,879
Speaker 2: all right, one measured the back of the train to

451
00:20:27,960 --> 00:20:30,679
Speaker 2: be negative half a kilometer at the same time Sally

452
00:20:30,720 --> 00:20:32,879
Speaker 2: measured the front of the train to be at a

453
00:20:32,880 --> 00:20:36,240
Speaker 2: location plus half a kilometer, And so, okay, the train

454
00:20:36,359 --> 00:20:39,240
Speaker 2: is one kilometer long because the front and the back

455
00:20:39,280 --> 00:20:41,840
Speaker 2: were one kilometer apart at the same time.

456
00:20:42,720 --> 00:20:46,040
Speaker 1: Oh okay, yeah, yeah, I'm following. I'm following. So now

457
00:20:46,359 --> 00:20:49,080
Speaker 1: like you sort of ask, okay, t equals one minute.

458
00:20:49,240 --> 00:20:51,680
Speaker 1: Where did your assistants measure the front of the train

459
00:20:51,720 --> 00:20:53,359
Speaker 1: and where did they measure the back of the train,

460
00:20:53,520 --> 00:20:55,280
Speaker 1: and then that should tell you the length of the train.

461
00:20:55,359 --> 00:20:57,239
Speaker 2: That should tell you the length of train. And if

462
00:20:57,280 --> 00:21:00,240
Speaker 2: you measure them at different times, like if one's clock

463
00:21:00,359 --> 00:21:02,199
Speaker 2: was out of sync, or one was lazy, or one

464
00:21:02,240 --> 00:21:04,000
Speaker 2: made a mistake or something in a measure of the

465
00:21:04,040 --> 00:21:06,000
Speaker 2: back of the train earlier or later, then we'd get

466
00:21:06,040 --> 00:21:08,480
Speaker 2: the wrong answer for the length of the train. It's

467
00:21:08,520 --> 00:21:10,560
Speaker 2: crucial that you measure the front in the back at

468
00:21:10,560 --> 00:21:13,280
Speaker 2: the same time. It seems sort of obvious to even

469
00:21:13,280 --> 00:21:15,679
Speaker 2: spell that out, sort of dumb, like, duh, that's what

470
00:21:15,800 --> 00:21:17,840
Speaker 2: length really is. But it's going to turn out to

471
00:21:17,840 --> 00:21:20,360
Speaker 2: be really important part of understanding length contraction.

472
00:21:20,600 --> 00:21:24,000
Speaker 1: Okay, So I guess that's one way to measure it,

473
00:21:24,800 --> 00:21:26,640
Speaker 1: or is that the only way to measure the train?

474
00:21:26,840 --> 00:21:28,600
Speaker 2: And that's sort of the standard setup. It allows you

475
00:21:28,640 --> 00:21:31,159
Speaker 2: to avoid things like how longs they take informations, travel

476
00:21:31,400 --> 00:21:33,359
Speaker 2: from here to there, and all that sort of stuff.

477
00:21:33,520 --> 00:21:35,880
Speaker 2: I suppose you could come up with other techniques as well.

478
00:21:35,920 --> 00:21:39,040
Speaker 1: All right, so now you get together and you measure

479
00:21:39,080 --> 00:21:42,080
Speaker 1: the train, and you're saying the number you get from

480
00:21:42,119 --> 00:21:44,600
Speaker 1: this setup is not the same as if the train

481
00:21:44,720 --> 00:21:45,760
Speaker 1: was not moving at all.

482
00:21:45,920 --> 00:21:46,400
Speaker 2: Exactly.

483
00:21:46,480 --> 00:21:47,840
Speaker 1: Well, if the train was not moving at all, you

484
00:21:47,880 --> 00:21:49,240
Speaker 1: were set upon work with.

485
00:21:49,920 --> 00:21:51,480
Speaker 2: Well, if the train is parked in front of you,

486
00:21:51,480 --> 00:21:52,400
Speaker 2: your setup would work.

487
00:21:52,760 --> 00:21:52,920
Speaker 5: Right.

488
00:21:53,040 --> 00:21:54,680
Speaker 2: You have somebody standing at the back of the train

489
00:21:54,720 --> 00:21:56,840
Speaker 2: and somebody standing at the front of the train. They

490
00:21:56,880 --> 00:21:59,200
Speaker 2: know where they are and it doesn't really matter when

491
00:21:59,200 --> 00:22:00,960
Speaker 2: they make the measurement if the train isn't moving.

492
00:22:03,160 --> 00:22:05,440
Speaker 1: I see, Because you know you can measure the road

493
00:22:05,480 --> 00:22:07,399
Speaker 1: in front of you, you can measure the train tracks.

494
00:22:07,600 --> 00:22:09,720
Speaker 2: Yeah, exactly. Like if I line the train up with

495
00:22:09,800 --> 00:22:11,960
Speaker 2: my two assistants and I know how far apart they are,

496
00:22:12,080 --> 00:22:13,560
Speaker 2: then I know how long the train is.

497
00:22:13,760 --> 00:22:16,160
Speaker 1: Okay, So with you're set up on your assistance, which

498
00:22:16,160 --> 00:22:18,600
Speaker 1: hopefully you're tipping generously, you measure the train to be

499
00:22:18,640 --> 00:22:21,359
Speaker 1: one kilometer long, And now you're saying that's not really

500
00:22:21,440 --> 00:22:22,399
Speaker 1: how long the train is.

501
00:22:22,560 --> 00:22:24,199
Speaker 2: Yeah, let's say I measured the train to be one

502
00:22:24,280 --> 00:22:26,560
Speaker 2: kilometer long when it's at rest, when it's not moving,

503
00:22:26,680 --> 00:22:29,040
Speaker 2: and then the train makes a run past me at

504
00:22:29,080 --> 00:22:31,920
Speaker 2: half the speed of light. You know then what I'm

505
00:22:31,920 --> 00:22:34,399
Speaker 2: going to measure this time, is that the train is shorter,

506
00:22:34,640 --> 00:22:37,720
Speaker 2: that it's only eight hundred and fifty meters long instead

507
00:22:37,720 --> 00:22:38,560
Speaker 2: of one kilometer.

508
00:22:38,960 --> 00:22:43,000
Speaker 1: Mmm. Interesting, Now we're going to explain why that happens.

509
00:22:43,160 --> 00:22:45,320
Speaker 1: Where does speasure where tivity come in that makes you

510
00:22:45,840 --> 00:22:48,040
Speaker 1: measure it to be eight hundred and fifty meters. You're

511
00:22:48,080 --> 00:22:50,800
Speaker 1: telling me that the assistance would measure the train to

512
00:22:50,840 --> 00:22:53,440
Speaker 1: be shorter than a kilometer. But I guess my intuition

513
00:22:53,560 --> 00:22:56,000
Speaker 1: is like, what, how can that be? Because like, your

514
00:22:56,000 --> 00:22:59,040
Speaker 1: setup seem perfectly you know, logical and sensical, and it

515
00:22:59,080 --> 00:23:01,879
Speaker 1: should measure my tuition. It should measure the train to

516
00:23:01,920 --> 00:23:05,720
Speaker 1: be a kilometer because you know, Juan measured the front

517
00:23:05,720 --> 00:23:07,880
Speaker 1: of the train moving at this point at this time,

518
00:23:08,000 --> 00:23:10,320
Speaker 1: and Sally measured the back of the train moving a

519
00:23:10,440 --> 00:23:13,080
Speaker 1: kilometer away at the same time. Why would it look

520
00:23:13,119 --> 00:23:14,080
Speaker 1: shorter than a kilometer.

521
00:23:14,280 --> 00:23:17,399
Speaker 2: Let's unpack what that question really means, the why question.

522
00:23:18,280 --> 00:23:21,240
Speaker 2: You're saying that the train was one length at rest,

523
00:23:21,280 --> 00:23:24,240
Speaker 2: and so you expect it to still be that length later.

524
00:23:24,720 --> 00:23:28,240
Speaker 2: That sounds reasonable, but it actually contains a big assumption,

525
00:23:28,800 --> 00:23:33,879
Speaker 2: the assumption that lengths are absolute rather than relative to velocity.

526
00:23:33,920 --> 00:23:36,359
Speaker 2: The lengths are always the same no matter how fast

527
00:23:36,359 --> 00:23:39,359
Speaker 2: you're going. I could ask you, why do you expect

528
00:23:39,400 --> 00:23:41,800
Speaker 2: the train to always have the same length. That's just

529
00:23:42,000 --> 00:23:45,399
Speaker 2: actually an assumption we're making about the world, and it

530
00:23:45,480 --> 00:23:48,359
Speaker 2: turns out it's not how the world actually works. The

531
00:23:48,400 --> 00:23:53,240
Speaker 2: world actually works differently. Lengths are relative. They depend on velocity.

532
00:23:53,800 --> 00:23:56,439
Speaker 2: You just never noticed before because it's a subtle effect.

533
00:23:56,520 --> 00:24:00,640
Speaker 2: So you, like everyone before Einstein, made the wrong assumption

534
00:24:00,800 --> 00:24:05,040
Speaker 2: based on your limited experience, the assumption that length is fixed,

535
00:24:05,359 --> 00:24:08,639
Speaker 2: that it's universal and doesn't depend on velocity. But it

536
00:24:08,680 --> 00:24:12,600
Speaker 2: turns out it's not. It's relative. So that's the experimental observation.

537
00:24:12,640 --> 00:24:14,760
Speaker 2: That's what we see in the world. And on top

538
00:24:14,800 --> 00:24:17,600
Speaker 2: of that, it has to be relative in order to

539
00:24:17,680 --> 00:24:21,680
Speaker 2: make sense, to be consistent with the constant speed of light.

540
00:24:22,400 --> 00:24:25,359
Speaker 2: So A, we can now tell that the world works

541
00:24:25,359 --> 00:24:29,920
Speaker 2: this way. Lengths are relative, not absolute. And B it's

542
00:24:29,920 --> 00:24:33,639
Speaker 2: a natural theoretical consequence of the speed of light being

543
00:24:33,680 --> 00:24:37,080
Speaker 2: the same for everyone, which has important consequences for time

544
00:24:37,280 --> 00:24:41,000
Speaker 2: and then eventually for length. I want to walk you

545
00:24:41,080 --> 00:24:43,760
Speaker 2: through it, but the short version of the story is

546
00:24:43,800 --> 00:24:47,480
Speaker 2: that number one, the speed of light, is constant for everyone,

547
00:24:47,920 --> 00:24:52,520
Speaker 2: which means that number two time is not universal that

548
00:24:52,680 --> 00:24:56,960
Speaker 2: people can disagree about whether things happen at the same time.

549
00:24:57,200 --> 00:24:59,560
Speaker 2: And remember that measuring the front and back of the

550
00:24:59,560 --> 00:25:04,160
Speaker 2: train at the same time was crucial to our measurement.

551
00:25:04,280 --> 00:25:08,119
Speaker 2: So disagreeing about simultaneity when to measure the front and

552
00:25:08,200 --> 00:25:11,119
Speaker 2: back of the train means number three, we're going to

553
00:25:11,280 --> 00:25:14,800
Speaker 2: disagree about the length of the train. Okay, that was

554
00:25:14,840 --> 00:25:17,520
Speaker 2: the short version, so let's back up. Something we know

555
00:25:17,720 --> 00:25:20,240
Speaker 2: is true is that the speed of light is the

556
00:25:20,280 --> 00:25:23,359
Speaker 2: same for everyone. If you're on the train and you

557
00:25:23,440 --> 00:25:25,840
Speaker 2: shine a flashlight from the back of the train towards

558
00:25:25,920 --> 00:25:28,040
Speaker 2: the front, you see it move at the speed of

559
00:25:28,119 --> 00:25:31,400
Speaker 2: light relative to the train and to you on the ground.

560
00:25:31,800 --> 00:25:34,160
Speaker 2: I see it move at the speed of light relative

561
00:25:34,280 --> 00:25:37,359
Speaker 2: to me, which means it's not moving at the speed

562
00:25:37,359 --> 00:25:40,160
Speaker 2: of light relative to the train according to me. That's

563
00:25:40,320 --> 00:25:45,199
Speaker 2: number one, the basic fact from which all special relativity derives.

564
00:25:45,359 --> 00:25:48,199
Speaker 2: That everyone measures the speed of light relative to them

565
00:25:48,320 --> 00:25:50,879
Speaker 2: to be the same. So how does that mess up

566
00:25:50,880 --> 00:25:53,639
Speaker 2: our concept of time? Well, if you stand in the

567
00:25:53,640 --> 00:25:56,960
Speaker 2: middle of the train and shine two flashlights, one forwards

568
00:25:56,960 --> 00:25:59,560
Speaker 2: and one backwards, then you'll see them reach the front

569
00:25:59,560 --> 00:26:02,280
Speaker 2: and the back at the same time. Right makes sense,

570
00:26:02,560 --> 00:26:05,639
Speaker 2: same distance, same speed. But on the ground, I also

571
00:26:05,680 --> 00:26:08,239
Speaker 2: see those beams moving at the speed of light. But

572
00:26:08,320 --> 00:26:10,639
Speaker 2: now I see the back of the train rushing forward

573
00:26:10,720 --> 00:26:14,000
Speaker 2: towards the beam, so it reaches the beam first, compared

574
00:26:14,040 --> 00:26:16,080
Speaker 2: to the front of the train, which is racing away

575
00:26:16,080 --> 00:26:18,840
Speaker 2: from the beam. So you and I disagree about whether

576
00:26:18,880 --> 00:26:21,359
Speaker 2: the beams hit the front and back at the same time.

577
00:26:21,520 --> 00:26:23,800
Speaker 2: That was point number two. It all comes down to

578
00:26:23,840 --> 00:26:26,439
Speaker 2: the end to time. It's because the way Einstein changed

579
00:26:26,480 --> 00:26:29,760
Speaker 2: our understanding of the universe required us to understand that

580
00:26:29,880 --> 00:26:34,280
Speaker 2: time depends on the observer. That's not just location that

581
00:26:34,320 --> 00:26:38,680
Speaker 2: depends on the observer, but also time depends on the observer.

582
00:26:38,920 --> 00:26:42,000
Speaker 2: And because time depends on the observer, whether two things

583
00:26:42,040 --> 00:26:45,720
Speaker 2: happen at the same time depends on the observer. We've

584
00:26:45,720 --> 00:26:48,280
Speaker 2: talked about this a few times, this concept of simultanedy,

585
00:26:48,640 --> 00:26:51,240
Speaker 2: like do two things happen at the same time depends

586
00:26:51,280 --> 00:26:55,440
Speaker 2: on your velocity. And because measurements of length require two

587
00:26:55,560 --> 00:26:59,720
Speaker 2: measurements at the same time, then your measurement of length

588
00:27:00,119 --> 00:27:03,480
Speaker 2: ends on your notion of simultaneity. Do a Juan and

589
00:27:03,560 --> 00:27:06,760
Speaker 2: Sally measure the train front and back at the same time,

590
00:27:07,320 --> 00:27:10,160
Speaker 2: They think so, but the person on the train thinks

591
00:27:10,200 --> 00:27:12,720
Speaker 2: they don't, which is why they have different measurements of

592
00:27:12,760 --> 00:27:13,280
Speaker 2: the length of.

593
00:27:13,240 --> 00:27:15,920
Speaker 1: The train between us and the observers on the train.

594
00:27:16,080 --> 00:27:19,400
Speaker 1: But like, all of your assistants are not moving relative

595
00:27:19,440 --> 00:27:22,119
Speaker 1: to each other, that's right, and they all have synchronized clocks.

596
00:27:22,160 --> 00:27:24,520
Speaker 1: You told me they were synchronized. So what do you

597
00:27:24,600 --> 00:27:27,120
Speaker 1: mean that their measurements are not happening at the same time,

598
00:27:27,240 --> 00:27:29,800
Speaker 1: or like if they measure Jan measures in front of

599
00:27:29,800 --> 00:27:32,000
Speaker 1: the train, Sally measures the back of the train, and

600
00:27:32,080 --> 00:27:35,840
Speaker 1: they write down on a piece of paper what their

601
00:27:35,880 --> 00:27:38,840
Speaker 1: measurements and then they bring the papers to you. Aren't

602
00:27:38,840 --> 00:27:41,360
Speaker 1: those things synchronized. I'm not saying how what you're saying

603
00:27:41,400 --> 00:27:44,360
Speaker 1: about time and how that's changing your assistance measurement.

604
00:27:44,640 --> 00:27:46,919
Speaker 2: Yeah, I think that those measurements are synchronized, and I

605
00:27:46,960 --> 00:27:48,919
Speaker 2: think my measurement of eight hundred and fifty meters is

606
00:27:48,920 --> 00:27:51,720
Speaker 2: totally right. But if you're on the train, then you

607
00:27:51,800 --> 00:27:54,359
Speaker 2: think that those measurements are not synchronized. You're like, No,

608
00:27:54,480 --> 00:27:57,880
Speaker 2: Jan and Sally made those measurements at different times. That's

609
00:27:57,920 --> 00:28:00,359
Speaker 2: why they got a shorter length. From your point of you,

610
00:28:00,480 --> 00:28:02,879
Speaker 2: those two measurements were not made at the same time.

611
00:28:03,160 --> 00:28:05,160
Speaker 1: Why not we synchronized our clocks.

612
00:28:05,400 --> 00:28:07,919
Speaker 2: I'm synchronized with everybody on the ground, but I'm not

613
00:28:07,960 --> 00:28:10,520
Speaker 2: synchronized with people on the train because those people are

614
00:28:10,560 --> 00:28:14,440
Speaker 2: moving relative to me, and moving clocks cannot stay synchronized.

615
00:28:14,680 --> 00:28:17,199
Speaker 1: Okay, so forget the people on the train. Let's just

616
00:28:17,200 --> 00:28:18,399
Speaker 1: focus on Huang and Sally.

617
00:28:18,600 --> 00:28:20,760
Speaker 2: Okay, Huan and Sally on the ground, they.

618
00:28:20,680 --> 00:28:23,520
Speaker 1: Have synchronized clocks to mine. They're synchronized to each other.

619
00:28:24,359 --> 00:28:26,000
Speaker 1: And you're saying they would measure the train to be

620
00:28:26,080 --> 00:28:27,720
Speaker 1: eight hundred and fifty meters.

621
00:28:27,520 --> 00:28:29,840
Speaker 2: Yes, whereas somebody on the train says.

622
00:28:29,600 --> 00:28:32,360
Speaker 1: That, no, forget, forget the person on the train. Now

623
00:28:32,400 --> 00:28:35,919
Speaker 1: the train stops, turns around, comes back, and parts in

624
00:28:35,920 --> 00:28:38,280
Speaker 1: front of me. Mm hmm. Now I would measure the

625
00:28:38,280 --> 00:28:41,160
Speaker 1: train to be a kilometer yes, So what happened there?

626
00:28:41,320 --> 00:28:43,960
Speaker 1: Like did space contract or I guess I'm not seeing

627
00:28:43,960 --> 00:28:47,240
Speaker 1: the connection with time or or at least I feel

628
00:28:47,280 --> 00:28:48,200
Speaker 1: like we're not explaining that.

629
00:28:48,400 --> 00:28:48,520
Speaker 5: Well.

630
00:28:48,600 --> 00:28:51,600
Speaker 2: Velocity and time are very closely related, right, We're not

631
00:28:51,640 --> 00:28:54,000
Speaker 2: talking about a single point. We're talking about two points.

632
00:28:54,000 --> 00:28:55,720
Speaker 2: We're talking about the front of the train and we're

633
00:28:55,720 --> 00:28:57,880
Speaker 2: talking about the back of the train, and we're talking

634
00:28:57,960 --> 00:29:01,000
Speaker 2: about the distances between them, and we're talking about measuring

635
00:29:01,000 --> 00:29:04,360
Speaker 2: them at a certain time, and so of course time

636
00:29:04,440 --> 00:29:05,840
Speaker 2: is going to be involved here, right.

637
00:29:06,200 --> 00:29:09,320
Speaker 1: You say we synchronize our clocks, So isn't it sort

638
00:29:09,360 --> 00:29:10,520
Speaker 1: of like a universal time?

639
00:29:10,680 --> 00:29:13,600
Speaker 2: I mean, you can only synchronize clocks in one frame. Okay,

640
00:29:13,640 --> 00:29:16,840
Speaker 2: So we've established that we can synchronize our clocks on

641
00:29:16,880 --> 00:29:20,719
Speaker 2: the ground, but that doesn't mean they're synchronized for other people,

642
00:29:20,960 --> 00:29:22,280
Speaker 2: like the people on the train.

643
00:29:22,600 --> 00:29:25,840
Speaker 1: I feel like this is maybe confusing more to think

644
00:29:25,880 --> 00:29:27,680
Speaker 1: about the people on the train. Like let's say I

645
00:29:27,720 --> 00:29:29,719
Speaker 1: don't care about the people on the train, Like I

646
00:29:29,800 --> 00:29:32,720
Speaker 1: just care about what Seally and Juan measure now when

647
00:29:32,760 --> 00:29:34,880
Speaker 1: the train is moving, and then later when the train

648
00:29:34,920 --> 00:29:38,200
Speaker 1: stops and comes back and they measure the distance again.

649
00:29:38,520 --> 00:29:40,000
Speaker 1: Why are those two measurements different?

650
00:29:40,080 --> 00:29:43,320
Speaker 2: Okay, your question is if the train is one kilometer

651
00:29:43,440 --> 00:29:46,080
Speaker 2: long when it's sitting in front of me, or equivalently,

652
00:29:46,480 --> 00:29:48,680
Speaker 2: if the people on the train measured to be one

653
00:29:48,760 --> 00:29:51,880
Speaker 2: kilometer because it's not moving relative to them, then why

654
00:29:51,880 --> 00:29:54,040
Speaker 2: do we measure it to be shorter on the ground

655
00:29:54,120 --> 00:29:57,280
Speaker 2: when it's moving past us? How does our disagreement about

656
00:29:57,320 --> 00:30:02,200
Speaker 2: synchronized clocks get translated who is disagreement about the length? Well,

657
00:30:02,240 --> 00:30:04,040
Speaker 2: the most direct way to say it is that to

658
00:30:04,080 --> 00:30:06,680
Speaker 2: measure the length of the train, you have to measure

659
00:30:06,680 --> 00:30:09,000
Speaker 2: the front and back at the same time. But if

660
00:30:09,040 --> 00:30:12,800
Speaker 2: you disagree about what at the same time means, then

661
00:30:12,800 --> 00:30:14,800
Speaker 2: you're going to disagree about the length of the train.

662
00:30:15,560 --> 00:30:19,560
Speaker 2: So what's going on here exactly? How do the UNSYNCD

663
00:30:19,640 --> 00:30:23,640
Speaker 2: clocks make people measure different times. I know you don't

664
00:30:23,640 --> 00:30:25,120
Speaker 2: want to think about the people on the train, but

665
00:30:25,200 --> 00:30:28,200
Speaker 2: you kind of have to, because when we say the

666
00:30:28,320 --> 00:30:32,280
Speaker 2: train is one kilometer in length, what that means is

667
00:30:32,320 --> 00:30:35,240
Speaker 2: that it's one kilometer for people on the train, for

668
00:30:35,280 --> 00:30:39,720
Speaker 2: people not moving relative to the train, by their definition

669
00:30:39,800 --> 00:30:42,240
Speaker 2: of at the same time, the front and back are

670
00:30:42,320 --> 00:30:45,800
Speaker 2: one kilometer apart. That's kind of what it means. But

671
00:30:45,920 --> 00:30:48,480
Speaker 2: for people on the ground, they have a different definition

672
00:30:48,560 --> 00:30:52,040
Speaker 2: of at the same time. They think that the people

673
00:30:52,080 --> 00:30:55,520
Speaker 2: on the train's measurement is wrong. The people on the

674
00:30:55,560 --> 00:30:58,160
Speaker 2: ground think that the people on the train measure in

675
00:30:58,200 --> 00:31:01,840
Speaker 2: the back of the train first and later measure the

676
00:31:01,880 --> 00:31:04,480
Speaker 2: front of the train. The people on the ground think

677
00:31:04,520 --> 00:31:06,520
Speaker 2: that people on the train are not measuring the front

678
00:31:06,560 --> 00:31:09,040
Speaker 2: and back at the same time, which is why they

679
00:31:09,040 --> 00:31:13,040
Speaker 2: get a longer measurement. They get a full kilometer. Like

680
00:31:13,160 --> 00:31:15,440
Speaker 2: imagine if you took a one meter long stick moving

681
00:31:15,480 --> 00:31:17,600
Speaker 2: past you, and you measured the back of it now

682
00:31:17,760 --> 00:31:20,800
Speaker 2: and the front of it later in ten seconds or whatever,

683
00:31:21,120 --> 00:31:23,760
Speaker 2: you get a measurement that was way too long. That's

684
00:31:23,800 --> 00:31:25,720
Speaker 2: what the people on the ground think that people on

685
00:31:25,760 --> 00:31:28,360
Speaker 2: the train are doing to get one kilometer instead of

686
00:31:28,360 --> 00:31:30,760
Speaker 2: eight hundred and fifty meters. The people on the ground

687
00:31:30,840 --> 00:31:33,320
Speaker 2: think that their own measurements are synchronized, and they get

688
00:31:33,360 --> 00:31:35,920
Speaker 2: eight hundred and fifty meters. The people on the train

689
00:31:36,680 --> 00:31:39,080
Speaker 2: think that the measurements on the ground are not at

690
00:31:39,080 --> 00:31:41,880
Speaker 2: the same time. The people on the train think that

691
00:31:41,880 --> 00:31:44,600
Speaker 2: the people on the ground are measuring the front before

692
00:31:44,640 --> 00:31:47,040
Speaker 2: they're measuring the back, and that's why the people on

693
00:31:47,080 --> 00:31:50,160
Speaker 2: the ground are getting a measurement that's too short. So

694
00:31:50,200 --> 00:31:52,880
Speaker 2: there's no like, what is the real length of the train,

695
00:31:53,120 --> 00:31:56,479
Speaker 2: or why does a train look shorter when it's moving faster?

696
00:31:57,080 --> 00:32:01,160
Speaker 2: Its length depends on your velocity. We just never noticed.

697
00:32:00,800 --> 00:32:03,080
Speaker 1: It before, all right, So let's dig into me this

698
00:32:03,280 --> 00:32:06,080
Speaker 1: idea of that. It has to do with time and

699
00:32:06,120 --> 00:32:09,880
Speaker 1: let's talk about how time changes due to special relativity

700
00:32:09,920 --> 00:32:12,600
Speaker 1: and see if that maybe explains why the train. We

701
00:32:12,640 --> 00:32:14,560
Speaker 1: measure the train to meet different lengths here and then

702
00:32:14,640 --> 00:32:16,840
Speaker 1: later when it stops. So we'll dig into that, but

703
00:32:16,880 --> 00:32:32,000
Speaker 1: first let's take another quick break. All right, we're asking

704
00:32:32,000 --> 00:32:35,760
Speaker 1: the question why do moving objects look shorter, and Daniel

705
00:32:35,800 --> 00:32:38,760
Speaker 1: you're saying it really depends on the idea of time

706
00:32:38,920 --> 00:32:43,000
Speaker 1: being variable at this time being variable affect sally and

707
00:32:43,040 --> 00:32:45,160
Speaker 1: why your assistance measurements of the train.

708
00:32:45,400 --> 00:32:47,520
Speaker 2: I think time is crucial to resolving this sort of

709
00:32:47,520 --> 00:32:50,800
Speaker 2: apparent paradox. One of the reasons it's hard to imagine

710
00:32:50,800 --> 00:32:53,440
Speaker 2: a stick getting shorter or a train getting shorter is

711
00:32:53,480 --> 00:32:55,840
Speaker 2: because you think of it as a rigid object which

712
00:32:55,960 --> 00:32:58,880
Speaker 2: throws you off. Instead, just think of three train cars

713
00:32:58,920 --> 00:33:01,360
Speaker 2: moving and sync. One in the back, one in the middle,

714
00:33:01,360 --> 00:33:03,240
Speaker 2: and one in the front. Now, what if the middle

715
00:33:03,240 --> 00:33:05,640
Speaker 2: car tells the other two to speed up? From your

716
00:33:05,720 --> 00:33:08,719
Speaker 2: point of view, the message arrives at the rear car first,

717
00:33:09,120 --> 00:33:12,280
Speaker 2: which speeds up before the lead car can, effectively shrinking

718
00:33:12,360 --> 00:33:15,240
Speaker 2: the distance between them. From their point of view, However,

719
00:33:15,440 --> 00:33:17,600
Speaker 2: the message arrives at the lead and the rear car

720
00:33:17,680 --> 00:33:20,400
Speaker 2: at the same time, and the distance hasn't changed. When

721
00:33:20,400 --> 00:33:23,600
Speaker 2: they decelerate again, the reverse happens and the cars come

722
00:33:23,640 --> 00:33:26,400
Speaker 2: to rest with the same original distance. So you can

723
00:33:26,440 --> 00:33:30,360
Speaker 2: see how different senses of time lead to different measurements

724
00:33:30,360 --> 00:33:32,440
Speaker 2: of distance. But how is it possible for the train

725
00:33:32,520 --> 00:33:34,960
Speaker 2: cars to get closer together and like not? Notice what

726
00:33:35,000 --> 00:33:37,760
Speaker 2: if you exaggerated the effect so they would bump into

727
00:33:37,800 --> 00:33:40,880
Speaker 2: each other. Well, the answer is they also shrink because

728
00:33:40,960 --> 00:33:45,040
Speaker 2: space itself is shrinking. The atoms are like little cars.

729
00:33:45,120 --> 00:33:47,360
Speaker 2: So think of the train as the front of the

730
00:33:47,400 --> 00:33:50,000
Speaker 2: train and the back of the train, not as one object.

731
00:33:50,400 --> 00:33:52,600
Speaker 2: Thinking of it as one long train tricks you into

732
00:33:52,680 --> 00:33:55,440
Speaker 2: using your intuition thinking of it as a rigid object,

733
00:33:55,640 --> 00:33:58,640
Speaker 2: which actually can't exist in our universe. Like when people

734
00:33:58,680 --> 00:34:01,480
Speaker 2: ask what happens if you stick a light year long?

735
00:34:01,640 --> 00:34:04,760
Speaker 2: Does one end move instantly, sending information faster than light

736
00:34:04,800 --> 00:34:07,520
Speaker 2: to the other end. No, there's no rigid stick. You

737
00:34:07,640 --> 00:34:09,960
Speaker 2: push on one end and the pressure wave takes time

738
00:34:10,040 --> 00:34:12,239
Speaker 2: to reach the other end and to move it. It's the

739
00:34:12,280 --> 00:34:14,759
Speaker 2: same with the train. It's linked together, but it's not

740
00:34:14,800 --> 00:34:17,640
Speaker 2: a rigid object of fixed length. So think about the

741
00:34:17,640 --> 00:34:20,520
Speaker 2: front and the back separately. Now, The super confusing thing

742
00:34:20,560 --> 00:34:23,719
Speaker 2: about this whole length contraction thing is that it's relative,

743
00:34:23,920 --> 00:34:26,520
Speaker 2: just the way time dilation is. People on the ground

744
00:34:26,560 --> 00:34:28,920
Speaker 2: think the train has shrunk, but people on the train,

745
00:34:29,120 --> 00:34:30,640
Speaker 2: and I know you don't want to talk about them,

746
00:34:31,040 --> 00:34:33,799
Speaker 2: they think that distances on the ground have shrunk because

747
00:34:33,840 --> 00:34:37,000
Speaker 2: the ground is moving relative to them. Like let's say

748
00:34:37,000 --> 00:34:40,120
Speaker 2: they're about to enter a one kilometer long tunnel. I

749
00:34:40,160 --> 00:34:42,279
Speaker 2: see the trains moving, and so I see it's going

750
00:34:42,320 --> 00:34:44,640
Speaker 2: to be shorter than the tunnel, whereas the train sees

751
00:34:44,680 --> 00:34:47,839
Speaker 2: the tunnel is shorter. So who's right, Like is the

752
00:34:47,880 --> 00:34:50,080
Speaker 2: train actually going to be in the tunnel or not?

753
00:34:50,800 --> 00:34:53,720
Speaker 2: And we construct these situations to like confront the universe

754
00:34:53,760 --> 00:34:57,120
Speaker 2: and say, like, what's really happening because we imagine that

755
00:34:57,200 --> 00:34:59,879
Speaker 2: the concept of length is absolute, that the train has

756
00:35:00,040 --> 00:35:03,600
Speaker 2: an actual length, right, that something has to happen in

757
00:35:03,640 --> 00:35:05,560
Speaker 2: the universe, and only one thing can happen. You can't

758
00:35:05,560 --> 00:35:10,000
Speaker 2: have like two people seeing conflicting events. So understanding how

759
00:35:10,040 --> 00:35:12,520
Speaker 2: time flows and how time is relative is crucial to

760
00:35:12,600 --> 00:35:16,160
Speaker 2: understanding how both of those things can seem true. That

761
00:35:16,239 --> 00:35:18,760
Speaker 2: somebody on the ground can see the train as shorter

762
00:35:18,920 --> 00:35:21,120
Speaker 2: and fitting in the tunnel, and somebody else on the

763
00:35:21,200 --> 00:35:24,160
Speaker 2: train can see the tunnel as shorter, so the train

764
00:35:24,280 --> 00:35:25,200
Speaker 2: always sticks out.

765
00:35:25,920 --> 00:35:29,240
Speaker 1: Okay, here's this inner and we'll go with your tunnel idea. Okay,

766
00:35:29,280 --> 00:35:32,560
Speaker 1: So I have a train that when it's standing still

767
00:35:32,600 --> 00:35:34,320
Speaker 1: in front of me, I measure it to be a kilometer.

768
00:35:34,520 --> 00:35:37,239
Speaker 1: Now I build a tunnel that and the tunnel is

769
00:35:37,280 --> 00:35:40,000
Speaker 1: not moving, and I measure, and I make the tunnel

770
00:35:40,000 --> 00:35:42,839
Speaker 1: to be one kilometer long, exactly the same length as

771
00:35:42,880 --> 00:35:46,560
Speaker 1: the train. Now I put in at one end of

772
00:35:46,600 --> 00:35:49,240
Speaker 1: the tunnel and Sally at the back of the tunnel. Okay,

773
00:35:49,280 --> 00:35:51,880
Speaker 1: and we synchronize our clocks. Okay. Now I move the

774
00:35:51,920 --> 00:35:54,440
Speaker 1: train and I put it inside the tunnel so that

775
00:35:54,520 --> 00:35:57,080
Speaker 1: it's just it fits perfectly inside the tunnel. Sally and

776
00:35:57,120 --> 00:35:59,080
Speaker 1: Juan measure the train to be a kilometer long.

777
00:35:59,320 --> 00:36:01,879
Speaker 2: Yes, everybody with OCD out there is like, oooh, that's

778
00:36:01,920 --> 00:36:03,000
Speaker 2: so satisfying. It fits.

779
00:36:04,239 --> 00:36:07,200
Speaker 1: Yeah. I think by everybody you mean all of our

780
00:36:07,239 --> 00:36:11,400
Speaker 1: listeners if they like the Physics podcast. Now the train

781
00:36:11,520 --> 00:36:15,920
Speaker 1: leaves the tunnel, goes away a few kilometers, and then

782
00:36:15,960 --> 00:36:18,359
Speaker 1: it comes back at half of the speed of light.

783
00:36:18,400 --> 00:36:22,120
Speaker 1: That's say and Sally, Juan and I have our clock synchronized.

784
00:36:22,360 --> 00:36:26,600
Speaker 1: The tunnel is zooming pass and we ask want to

785
00:36:26,640 --> 00:36:28,680
Speaker 1: measure when the front of the train passes his spot,

786
00:36:28,719 --> 00:36:31,000
Speaker 1: And we ask Sally when the back of the train

787
00:36:31,040 --> 00:36:33,440
Speaker 1: passes her spot at the other side of the tunnel.

788
00:36:33,520 --> 00:36:36,120
Speaker 1: Are you saying they're not going to report the same time,

789
00:36:36,200 --> 00:36:37,960
Speaker 1: because if they report the same time, then I have

790
00:36:38,000 --> 00:36:40,080
Speaker 1: to conclude that the train was a kilometer long.

791
00:36:40,239 --> 00:36:42,439
Speaker 2: No, that's right. They will not measure the same time.

792
00:36:42,560 --> 00:36:44,800
Speaker 2: One and at the back of the tunnel will measure

793
00:36:44,800 --> 00:36:47,800
Speaker 2: a time earlier than Sally at the front of the tunnel.

794
00:36:47,880 --> 00:36:50,920
Speaker 2: So quarantine you, Juan and Sally, who are in the

795
00:36:50,960 --> 00:36:54,080
Speaker 2: tunnel's frame of reference. You will see the whole train

796
00:36:54,280 --> 00:36:57,239
Speaker 2: inside the tunnel that when the back end disappears into

797
00:36:57,239 --> 00:36:59,960
Speaker 2: the tunnel, the front nose has not yet emerged from

798
00:37:00,080 --> 00:37:02,960
Speaker 2: the tunnel and still one hundred and fifty meters from

799
00:37:03,200 --> 00:37:04,360
Speaker 2: the exit of the tunnel.

800
00:37:04,560 --> 00:37:06,879
Speaker 1: So Sally at the back is going to write down

801
00:37:06,880 --> 00:37:08,880
Speaker 1: her number, and they're going to both numbers are not

802
00:37:08,920 --> 00:37:09,759
Speaker 1: going to come back the same.

803
00:37:09,960 --> 00:37:10,399
Speaker 2: That's right.

804
00:37:10,480 --> 00:37:14,320
Speaker 1: Can you explain why like nobody is moving like Sally Huang,

805
00:37:14,360 --> 00:37:17,720
Speaker 1: they were both staying the same. They're the same observer

806
00:37:18,040 --> 00:37:21,800
Speaker 1: in the same frame. Their time was synced. The train

807
00:37:21,920 --> 00:37:25,360
Speaker 1: was physically moving past them. Why do they measure a

808
00:37:25,360 --> 00:37:25,879
Speaker 1: different time.

809
00:37:26,360 --> 00:37:30,480
Speaker 2: Yes, and Huan and Sali are synchronized according to themselves

810
00:37:30,800 --> 00:37:33,400
Speaker 2: and people on the ground, so they think their measurement

811
00:37:33,560 --> 00:37:37,239
Speaker 2: makes sense and it does. In their frame. Eight hundred

812
00:37:37,239 --> 00:37:39,480
Speaker 2: and fifty meters is the length of the train, and

813
00:37:39,880 --> 00:37:42,360
Speaker 2: they see the people on the train who are measuring

814
00:37:42,360 --> 00:37:44,880
Speaker 2: the train to be a full kilometer longer than the

815
00:37:44,880 --> 00:37:47,799
Speaker 2: people on the ground are measuring. The people on the

816
00:37:47,880 --> 00:37:50,920
Speaker 2: ground see the people on the train making their measurements

817
00:37:50,960 --> 00:37:54,320
Speaker 2: not at the same time, and the reverse is true.

818
00:37:54,719 --> 00:37:58,000
Speaker 2: On the train, people take measurements at what they think

819
00:37:58,400 --> 00:38:01,480
Speaker 2: is the same time, and they get one kilometer, and

820
00:38:01,520 --> 00:38:03,360
Speaker 2: the people on the train think that people on the

821
00:38:03,400 --> 00:38:05,840
Speaker 2: ground are not syncd. That's why it's all about the

822
00:38:05,920 --> 00:38:10,279
Speaker 2: relativity of simultaneity, whether you think two things happen at

823
00:38:10,280 --> 00:38:12,920
Speaker 2: the same time or not. And that's what sets up

824
00:38:12,960 --> 00:38:16,439
Speaker 2: this fun apparent paradox of whether the train will fit

825
00:38:16,520 --> 00:38:19,120
Speaker 2: into a one kilometer tunnel one in Sally and the

826
00:38:19,120 --> 00:38:20,799
Speaker 2: tunnel when they see it moving through, they see it

827
00:38:20,800 --> 00:38:23,360
Speaker 2: at eight hundred and fifty meters long, and so they say, yes,

828
00:38:23,600 --> 00:38:26,320
Speaker 2: the train fit in the tunnel, but you have people

829
00:38:26,400 --> 00:38:29,600
Speaker 2: on the train. They see the tunnel as shorter. They say, no,

830
00:38:29,960 --> 00:38:32,600
Speaker 2: my train is still a kilometer long because the train

831
00:38:32,680 --> 00:38:34,440
Speaker 2: is not moving for them, and so it's still at

832
00:38:34,440 --> 00:38:37,319
Speaker 2: its same original length. But the tunnel is moving, so

833
00:38:37,360 --> 00:38:40,400
Speaker 2: the tunnel is shorter. So they see the train sticking

834
00:38:40,480 --> 00:38:42,800
Speaker 2: out of the tunnel. And in order for special relativity

835
00:38:42,800 --> 00:38:45,040
Speaker 2: to make sense, you have to somehow reconcile these two things,

836
00:38:45,080 --> 00:38:47,360
Speaker 2: like what really happened. Did the train fit in the

837
00:38:47,360 --> 00:38:48,160
Speaker 2: tunnel or not?

838
00:38:48,480 --> 00:38:50,480
Speaker 1: Okay, So how do you reconcile?

839
00:38:50,680 --> 00:38:53,319
Speaker 2: So it all comes down to time, right, Remember how

840
00:38:53,320 --> 00:38:56,040
Speaker 2: we talked about earlier in the episode. The time is relative,

841
00:38:56,440 --> 00:38:59,320
Speaker 2: not just how time flows, but whether two things happen

842
00:38:59,440 --> 00:39:02,520
Speaker 2: at the same time. That came from the observation that

843
00:39:02,560 --> 00:39:05,600
Speaker 2: the speed of light is the same for everyone, which

844
00:39:05,640 --> 00:39:08,440
Speaker 2: means people have to disagree about whether events happen at

845
00:39:08,440 --> 00:39:10,520
Speaker 2: the same time. The example of the beams of light

846
00:39:10,560 --> 00:39:13,160
Speaker 2: shooting along the train, people see them reaching the front

847
00:39:13,160 --> 00:39:15,319
Speaker 2: and the back of the same time. People off the

848
00:39:15,360 --> 00:39:17,600
Speaker 2: train see the light hitting the back of the train first.

849
00:39:17,719 --> 00:39:20,160
Speaker 2: And the way to reconcile that is to have different

850
00:39:20,200 --> 00:39:23,120
Speaker 2: times for all those people for time to flow differently,

851
00:39:23,200 --> 00:39:25,560
Speaker 2: And that's why it's crucial that we understand the clocks

852
00:39:25,560 --> 00:39:28,200
Speaker 2: and the synchronization, and that the front of the back

853
00:39:28,200 --> 00:39:31,000
Speaker 2: of the train be measured at the same time. And

854
00:39:31,040 --> 00:39:33,480
Speaker 2: the crucial thing is that at the same time is

855
00:39:33,560 --> 00:39:36,120
Speaker 2: different for people on the train and for people on

856
00:39:36,160 --> 00:39:40,080
Speaker 2: the ground because moving clocks flow differently. Right, So on

857
00:39:40,160 --> 00:39:43,040
Speaker 2: the ground, Jan and Sally are synchronized and they measure

858
00:39:43,120 --> 00:39:45,160
Speaker 2: the train to be eight hundred and fifty meters long.

859
00:39:45,320 --> 00:39:47,760
Speaker 2: But to the people on the train, Wan and Sally

860
00:39:47,840 --> 00:39:50,759
Speaker 2: are not synchronized. Wan and Sally are measuring the front

861
00:39:50,760 --> 00:39:52,919
Speaker 2: in the back of the train at different times, which

862
00:39:53,000 --> 00:39:55,200
Speaker 2: is why Wan and Sally think the train is shorter,

863
00:39:55,640 --> 00:39:58,000
Speaker 2: and the people on the train think that it's not shorter.

864
00:39:58,280 --> 00:40:00,080
Speaker 2: Because the people on the train think that One and

865
00:40:00,080 --> 00:40:02,400
Speaker 2: Sally made a mistake. They're like, no, you guys measure

866
00:40:02,400 --> 00:40:04,520
Speaker 2: the front and back at different times, which is why

867
00:40:04,560 --> 00:40:06,600
Speaker 2: you're telling me it's eight hundred and fifty meters long

868
00:40:06,719 --> 00:40:09,720
Speaker 2: when really it's a kilometer. How can it make sense

869
00:40:10,080 --> 00:40:12,760
Speaker 2: for length to be contracted because it seems to violate

870
00:40:12,760 --> 00:40:15,720
Speaker 2: our intuition, like things have a length and they should

871
00:40:15,760 --> 00:40:17,960
Speaker 2: just have a length. And how is it possible for

872
00:40:18,239 --> 00:40:21,320
Speaker 2: things to get shorter as they get faster, because that

873
00:40:21,360 --> 00:40:23,680
Speaker 2: would lead to all sorts of weird paradoxes. It actually

874
00:40:23,680 --> 00:40:26,719
Speaker 2: can kind of make sense, and these paradoxes aren't paradoxes.

875
00:40:26,760 --> 00:40:28,879
Speaker 2: They just show you that the world works differently than

876
00:40:28,880 --> 00:40:33,320
Speaker 2: you imagined. Can it make sense that things moving quickly

877
00:40:33,600 --> 00:40:37,000
Speaker 2: get shorter? Like why doesn't that lead to contradictions?

878
00:40:37,160 --> 00:40:40,120
Speaker 1: Oh? Not like why does it make sense? But like,

879
00:40:40,320 --> 00:40:43,960
Speaker 1: why doesn't it lead to contradictions about the universe? Because

880
00:40:44,000 --> 00:40:46,759
Speaker 1: I think we'd establish it's very hard to make it

881
00:40:46,800 --> 00:40:47,600
Speaker 1: make sense.

882
00:40:48,239 --> 00:40:50,040
Speaker 2: But it is possible to make it make sense, and

883
00:40:50,080 --> 00:40:51,600
Speaker 2: it makes sense to me, And I want to share

884
00:40:51,680 --> 00:40:54,759
Speaker 2: that connection with everybody because it's a wonderful moment when

885
00:40:54,800 --> 00:40:57,719
Speaker 2: it all clicks together in your head and you realize, oh,

886
00:40:57,800 --> 00:41:00,399
Speaker 2: it is possible for both people to think the other

887
00:41:00,440 --> 00:41:02,360
Speaker 2: one is shorter, for the people on the train to

888
00:41:02,360 --> 00:41:03,920
Speaker 2: think the tunnel is shorter, and for the people in

889
00:41:03,960 --> 00:41:06,000
Speaker 2: the tunnel to think the train is shorter. Here's the

890
00:41:06,080 --> 00:41:08,640
Speaker 2: detailed breakdown of what's going on with the train and

891
00:41:08,680 --> 00:41:11,880
Speaker 2: the tunnel. Here's how it's possible for the team on

892
00:41:11,920 --> 00:41:15,160
Speaker 2: the ground to see the train totally inside the tunnel,

893
00:41:15,800 --> 00:41:18,040
Speaker 2: and for the team on the train to see that

894
00:41:18,080 --> 00:41:20,719
Speaker 2: the train is too long to ever all be in

895
00:41:20,760 --> 00:41:24,279
Speaker 2: the tunnel at the same time. From the ground point

896
00:41:24,280 --> 00:41:28,200
Speaker 2: of view, the train is shorter than the tunnel, so

897
00:41:28,440 --> 00:41:30,880
Speaker 2: when the back end is inside the tunnel, the nose

898
00:41:30,960 --> 00:41:33,960
Speaker 2: has not yet left the tunnel. Remember that we are

899
00:41:33,960 --> 00:41:36,759
Speaker 2: comparing two events front and back of the train at

900
00:41:36,760 --> 00:41:39,360
Speaker 2: what we consider to be at the same time. But

901
00:41:39,440 --> 00:41:41,799
Speaker 2: the people on the train think that the ground team

902
00:41:41,880 --> 00:41:44,400
Speaker 2: is making a mistake and that those events are not

903
00:41:44,520 --> 00:41:46,800
Speaker 2: actually at the same time. For the people on the train,

904
00:41:47,040 --> 00:41:49,360
Speaker 2: they think the ground team is comparing the front of

905
00:41:49,400 --> 00:41:52,319
Speaker 2: the train at an earlier moment to the back of

906
00:41:52,360 --> 00:41:55,200
Speaker 2: the train at a later moment, which is how the

907
00:41:55,239 --> 00:41:58,160
Speaker 2: ground team sees the train inside the tunnel. From the

908
00:41:58,200 --> 00:42:00,360
Speaker 2: point of view of the people on the train, the

909
00:42:00,400 --> 00:42:02,640
Speaker 2: train is sticking out both ends of the tunnel at

910
00:42:02,640 --> 00:42:05,200
Speaker 2: the same time because the tunnel is shorter. The people

911
00:42:05,239 --> 00:42:07,879
Speaker 2: on the ground think that's wrong. They think the train

912
00:42:07,960 --> 00:42:11,279
Speaker 2: team came to that conclusion by comparing an earlier back

913
00:42:11,360 --> 00:42:14,239
Speaker 2: end measurement when the train tail was still sticking out

914
00:42:14,360 --> 00:42:17,520
Speaker 2: to a later front end measurement when the train knows

915
00:42:17,719 --> 00:42:20,080
Speaker 2: is now sticking out. And the key is that they're

916
00:42:20,120 --> 00:42:22,760
Speaker 2: measuring the fronts and the backs at different times. And

917
00:42:22,800 --> 00:42:25,800
Speaker 2: it's all because time is relative and simultaneity is different

918
00:42:25,880 --> 00:42:28,680
Speaker 2: and for people moving at different speeds. And you know,

919
00:42:28,680 --> 00:42:30,760
Speaker 2: to me this comes down to like trying to see

920
00:42:31,239 --> 00:42:34,279
Speaker 2: can special relativity makes sense because it fundamentally changes your

921
00:42:34,360 --> 00:42:37,000
Speaker 2: understanding of the world. It tells you the world really

922
00:42:37,040 --> 00:42:39,520
Speaker 2: works in a different way than you imagined, and we

923
00:42:39,560 --> 00:42:42,200
Speaker 2: want the world to make sense. Like I think back

924
00:42:42,280 --> 00:42:44,239
Speaker 2: to the first time I ever heard this example of

925
00:42:44,280 --> 00:42:46,920
Speaker 2: like somebody in a car turning on a flashlight and

926
00:42:46,920 --> 00:42:49,280
Speaker 2: then hearing that those photons move at the same speed

927
00:42:49,640 --> 00:42:52,000
Speaker 2: relative to the car as they do relative to the ground,

928
00:42:52,200 --> 00:42:54,880
Speaker 2: And immediately my brain was like, hold on red flag.

929
00:42:55,040 --> 00:42:58,600
Speaker 2: That can't possibly make sense because then like when do

930
00:42:58,680 --> 00:43:01,880
Speaker 2: those photons hit wall or some obstacle. People in the

931
00:43:01,880 --> 00:43:03,920
Speaker 2: car and people on the ground would disagree about that

932
00:43:04,040 --> 00:43:05,640
Speaker 2: because they all say the photons are moving at the

933
00:43:05,680 --> 00:43:08,919
Speaker 2: same speed, but there's different distances involved and all sorts

934
00:43:08,920 --> 00:43:11,680
Speaker 2: of stuff. And so for me, it's about disentangling these

935
00:43:11,680 --> 00:43:16,360
Speaker 2: feelings of contradiction, these ways that special relativity violates our intuition.

936
00:43:16,640 --> 00:43:19,160
Speaker 2: You know, how can it possibly be that both these

937
00:43:19,200 --> 00:43:23,000
Speaker 2: people make honest measurements which conflict with each other. One

938
00:43:23,000 --> 00:43:25,440
Speaker 2: of the things I love about special relativity is that

939
00:43:25,480 --> 00:43:28,359
Speaker 2: it tells you that, like, people can disagree and'll both

940
00:43:28,440 --> 00:43:29,160
Speaker 2: be correct.

941
00:43:29,480 --> 00:43:29,680
Speaker 5: You know.

942
00:43:29,719 --> 00:43:33,239
Speaker 2: That's like the fundamental conclusion of you know simultaneity, that

943
00:43:33,360 --> 00:43:35,880
Speaker 2: you know, two people can see different orders of events

944
00:43:36,000 --> 00:43:39,160
Speaker 2: and both be honest and both be reporting what they see,

945
00:43:39,239 --> 00:43:42,640
Speaker 2: because the order of events depends on your relative velocity

946
00:43:42,640 --> 00:43:45,840
Speaker 2: and your location, and there is no single absolute clock

947
00:43:46,280 --> 00:43:48,760
Speaker 2: or single sense of space and time in the universe.

948
00:43:49,280 --> 00:43:51,479
Speaker 2: And so people on the ground can see the train

949
00:43:51,560 --> 00:43:53,640
Speaker 2: fitting in the tunnel, and people on the train can

950
00:43:53,680 --> 00:43:56,239
Speaker 2: see the train not fitting in the tunnel, and both

951
00:43:56,320 --> 00:43:56,960
Speaker 2: be correct.

952
00:43:57,440 --> 00:43:59,359
Speaker 1: Like, it's correct that if I measure the train when

953
00:43:59,400 --> 00:44:02,040
Speaker 1: it's standing still, it'll fit in the tunnel, And if

954
00:44:02,080 --> 00:44:04,280
Speaker 1: I measure when it's moving fast, I'm going to measure

955
00:44:04,320 --> 00:44:05,840
Speaker 1: it being shorter than the tunnel.

956
00:44:06,160 --> 00:44:09,120
Speaker 2: Yeah, exactly. And the people can see the train fitting

957
00:44:09,160 --> 00:44:11,640
Speaker 2: in the tunnel because according to them, they're measuring the

958
00:44:11,640 --> 00:44:13,680
Speaker 2: front and the back of the train at the same time.

959
00:44:14,360 --> 00:44:17,360
Speaker 2: The people on the train don't see that happening because

960
00:44:17,400 --> 00:44:19,080
Speaker 2: they think that the people in the tunnel are not

961
00:44:19,160 --> 00:44:21,759
Speaker 2: measuring it at the same time, because their concept of

962
00:44:21,760 --> 00:44:25,560
Speaker 2: what the same time means is different than the people

963
00:44:25,600 --> 00:44:27,879
Speaker 2: on the tunnel. And the end, that's why it all

964
00:44:27,920 --> 00:44:31,960
Speaker 2: comes down to time. Understanding relative time is crucial because

965
00:44:32,000 --> 00:44:34,680
Speaker 2: we're talking about a big extended object. It's a kilometer long,

966
00:44:34,760 --> 00:44:36,560
Speaker 2: so the front in the back are separated by space

967
00:44:36,640 --> 00:44:39,759
Speaker 2: and separated by time, and how time flows then have

968
00:44:39,960 --> 00:44:43,360
Speaker 2: to affect your measurement of the length of it, because

969
00:44:43,360 --> 00:44:45,800
Speaker 2: in the end, measuring length means measuring the front in

970
00:44:45,840 --> 00:44:47,480
Speaker 2: the back at the same time.

971
00:44:48,000 --> 00:44:50,719
Speaker 1: Right, again, you're answering the different question than, maybe than

972
00:44:50,760 --> 00:44:51,640
Speaker 1: the one we started with.

973
00:44:52,040 --> 00:44:54,800
Speaker 2: Yeah, I guess the most direct answer to the question

974
00:44:54,960 --> 00:44:58,120
Speaker 2: of the episode why do things look shorter is that

975
00:44:58,160 --> 00:45:00,520
Speaker 2: they always have. We just never noticed. The fact that

976
00:45:00,560 --> 00:45:04,040
Speaker 2: we ask why is because we've been led astray by

977
00:45:04,080 --> 00:45:07,680
Speaker 2: our intuition, our unfounded assumption that the world has this

978
00:45:07,800 --> 00:45:10,520
Speaker 2: property that lengths are absolute and are always the same

979
00:45:10,560 --> 00:45:13,719
Speaker 2: at any speed. It turns out that's not true, and

980
00:45:13,760 --> 00:45:16,400
Speaker 2: we can see that it's not true by doing experiments

981
00:45:16,440 --> 00:45:20,760
Speaker 2: at various speeds, including very high speeds. Things really do shrink.

982
00:45:20,960 --> 00:45:24,080
Speaker 2: So that explains why we ask the question. Because the

983
00:45:24,120 --> 00:45:26,440
Speaker 2: way the world works is in contrast with the way

984
00:45:26,480 --> 00:45:29,560
Speaker 2: our intuition works. Why does the world work that way

985
00:45:29,680 --> 00:45:32,799
Speaker 2: is the follow up philosophical question. It turns out it

986
00:45:32,880 --> 00:45:35,839
Speaker 2: has to in order to be consistent with this other thing.

987
00:45:35,920 --> 00:45:39,240
Speaker 2: We see that the speed of light is constant for everyone.

988
00:45:39,400 --> 00:45:42,120
Speaker 2: First consequence of the speed of light being constant for

989
00:45:42,160 --> 00:45:45,960
Speaker 2: everyone is that simultaneity is not universal. People at different

990
00:45:45,960 --> 00:45:50,160
Speaker 2: speeds disagree about what at the same time means. I

991
00:45:50,200 --> 00:45:52,319
Speaker 2: think Juan and Sally measure the front and back at

992
00:45:52,360 --> 00:45:54,360
Speaker 2: the same time, but people on the train don't, so

993
00:45:54,440 --> 00:45:57,600
Speaker 2: we measure different lengths. And the beauty part, the really

994
00:45:57,680 --> 00:46:00,719
Speaker 2: gorgeous part, is that this is what makes it all

995
00:46:00,760 --> 00:46:04,480
Speaker 2: click together. You can have some kind of global understanding

996
00:46:04,600 --> 00:46:08,439
Speaker 2: of how everyone is seeing things differently because you can see,

997
00:46:08,480 --> 00:46:11,160
Speaker 2: as we just explained, that people are measuring the train

998
00:46:11,200 --> 00:46:13,960
Speaker 2: at different times and getting different answers. Eight hundred and

999
00:46:14,000 --> 00:46:16,920
Speaker 2: fifty meters or one kilometer, they all get different answers,

1000
00:46:16,960 --> 00:46:20,760
Speaker 2: and they're all right because they are measuring different things.

1001
00:46:21,280 --> 00:46:24,400
Speaker 2: Length at rest means something different than length in motion

1002
00:46:24,760 --> 00:46:27,360
Speaker 2: because it depends on sinking measurements at the front and

1003
00:46:27,400 --> 00:46:30,200
Speaker 2: the back of the train. Length is not absolute and

1004
00:46:30,239 --> 00:46:33,120
Speaker 2: it can't be from the world too, makes sense at

1005
00:46:33,160 --> 00:46:36,319
Speaker 2: high speeds, it has to be relative for everything to

1006
00:46:36,400 --> 00:46:37,120
Speaker 2: be coherent.

1007
00:46:37,719 --> 00:46:40,440
Speaker 1: Like to us du Juan and Sally, the train really

1008
00:46:40,440 --> 00:46:42,799
Speaker 1: did shrink, I think, is what you're saying. Like the

1009
00:46:42,840 --> 00:46:47,000
Speaker 1: space that comprises the train, that the space that the

1010
00:46:47,040 --> 00:46:50,640
Speaker 1: train sits in that is moving with the train, it contracted,

1011
00:46:51,000 --> 00:46:51,560
Speaker 1: It got.

1012
00:46:51,400 --> 00:46:54,680
Speaker 2: Smaller, It got smaller for one in Sally, for Juan.

1013
00:46:54,480 --> 00:46:56,880
Speaker 1: And Sali, And that's just the way it is. Space

1014
00:46:57,040 --> 00:46:59,719
Speaker 1: is contracted, and it's all due to the speed limit

1015
00:46:59,760 --> 00:47:03,040
Speaker 1: of the interest because if it didn't, that space didn't contract,

1016
00:47:03,120 --> 00:47:04,600
Speaker 1: then things would sort of break down.

1017
00:47:04,719 --> 00:47:06,840
Speaker 2: Yeah, if length doesn't contract, then you break all the

1018
00:47:06,920 --> 00:47:09,440
Speaker 2: rules of special relativity. Another way to think about it

1019
00:47:09,480 --> 00:47:12,520
Speaker 2: is that length contraction is sort of the same thing

1020
00:47:12,920 --> 00:47:16,520
Speaker 2: as time dilation. For a completely separate example that helps

1021
00:47:16,520 --> 00:47:19,759
Speaker 2: people understand the link between length contraction, which we've been

1022
00:47:19,760 --> 00:47:22,400
Speaker 2: talking about today and time dilation. Think about what happens

1023
00:47:22,400 --> 00:47:24,719
Speaker 2: if you try to travel to a distant star at

1024
00:47:24,760 --> 00:47:27,200
Speaker 2: a really high speed, Say you need to get ten

1025
00:47:27,320 --> 00:47:29,960
Speaker 2: light years away, and you travel at ninety eight percent

1026
00:47:30,000 --> 00:47:32,080
Speaker 2: of the speed of light. From the point of view

1027
00:47:32,080 --> 00:47:34,319
Speaker 2: of people on Earth you left behind, it takes you

1028
00:47:34,440 --> 00:47:37,399
Speaker 2: almost ten years to get there. But they also see

1029
00:47:37,440 --> 00:47:41,160
Speaker 2: your clock running slowly. They see that for you, it's

1030
00:47:41,160 --> 00:47:44,680
Speaker 2: only been two years. That's time dilation, right, But look

1031
00:47:44,760 --> 00:47:46,720
Speaker 2: at it from the other point of view, from the ship,

1032
00:47:47,040 --> 00:47:49,680
Speaker 2: from the pilot's point of view, the distant star is

1033
00:47:49,719 --> 00:47:52,359
Speaker 2: moving towards her at ninety eight percent of the speed

1034
00:47:52,400 --> 00:47:55,080
Speaker 2: of light, So the distance to the star is shorter

1035
00:47:55,200 --> 00:47:57,200
Speaker 2: than ten light years, and it only takes her about

1036
00:47:57,239 --> 00:47:59,359
Speaker 2: two years to get there because it's only about two

1037
00:47:59,440 --> 00:48:02,880
Speaker 2: light years for her, So she experiences two years to

1038
00:48:02,920 --> 00:48:06,799
Speaker 2: get there because the length was shortened. What's really happening, Well,

1039
00:48:06,920 --> 00:48:10,120
Speaker 2: length contraction is just really another way to look at

1040
00:48:10,280 --> 00:48:13,800
Speaker 2: time dilation, and in the end, it's all about time.

1041
00:48:14,200 --> 00:48:17,640
Speaker 1: I think. Basically you're saying that the train track to Sally.

1042
00:48:17,360 --> 00:48:21,160
Speaker 2: And perspective, Yeah, and it's all connected to time. And

1043
00:48:21,200 --> 00:48:24,000
Speaker 2: in the end, time dilation and length contraction are really

1044
00:48:24,040 --> 00:48:26,040
Speaker 2: just two different ways to see the same effect.

1045
00:48:26,320 --> 00:48:29,800
Speaker 1: All right. Well, again, especially relativity is hard.

1046
00:48:29,680 --> 00:48:31,359
Speaker 2: Especially in an audio format. For those of you who

1047
00:48:31,440 --> 00:48:33,360
Speaker 2: like learning visually. I don't know why you're listening to

1048
00:48:33,400 --> 00:48:33,920
Speaker 2: a podcast.

1049
00:48:34,040 --> 00:48:36,839
Speaker 1: But we're glad that you are. Let's make that clear.

1050
00:48:37,160 --> 00:48:38,840
Speaker 1: We're not saying go watch YouTube.

1051
00:48:40,320 --> 00:48:41,920
Speaker 2: But if you do want to learn more about this stuff,

1052
00:48:41,920 --> 00:48:44,320
Speaker 2: look up space time diagrams. They're really helpful.

1053
00:48:44,560 --> 00:48:48,839
Speaker 1: It's interesting, though, to think about how valuable the universe is, Right,

1054
00:48:48,960 --> 00:48:51,880
Speaker 1: like the idea that the train would shrink just because

1055
00:48:51,880 --> 00:48:53,520
Speaker 1: it's going fast. It's kind of weird.

1056
00:48:53,640 --> 00:48:56,400
Speaker 2: It is very weird. Yeah, And it's weird that it

1057
00:48:56,480 --> 00:48:58,759
Speaker 2: makes sense in the end that the universe is just

1058
00:48:58,840 --> 00:49:00,880
Speaker 2: so different from the way we imagined it. But you know,

1059
00:49:00,920 --> 00:49:03,280
Speaker 2: that's the project of physics is not to just accept

1060
00:49:03,320 --> 00:49:06,520
Speaker 2: our intuitions, but to confront them with data and information

1061
00:49:06,680 --> 00:49:08,880
Speaker 2: and say, how can we make sense of all this?

1062
00:49:08,960 --> 00:49:12,080
Speaker 2: What story can we tell about the universe that ties

1063
00:49:12,120 --> 00:49:13,000
Speaker 2: it all together? All?

1064
00:49:13,120 --> 00:49:14,919
Speaker 1: Right, the next time I take a train, I'm gonna

1065
00:49:14,920 --> 00:49:18,040
Speaker 1: be thinking about this, like, am I thinner or am

1066
00:49:18,040 --> 00:49:18,520
Speaker 1: I shorter?

1067
00:49:19,800 --> 00:49:21,560
Speaker 2: Depends if you're lying down or standing up?

1068
00:49:21,640 --> 00:49:23,880
Speaker 1: Yeah? Exactly right, So I should stand up on the

1069
00:49:23,920 --> 00:49:24,800
Speaker 1: train the whole time.

1070
00:49:25,480 --> 00:49:27,280
Speaker 2: Don't forget to buy tickets for Juan and Sally.

1071
00:49:27,400 --> 00:49:30,160
Speaker 1: Yeah, and don't forget to tip the conductor too, with

1072
00:49:30,239 --> 00:49:32,040
Speaker 1: a big, fat envelope of money.

1073
00:49:33,560 --> 00:49:35,120
Speaker 2: No tip contractions here please.

1074
00:49:35,320 --> 00:49:37,400
Speaker 1: All right, Well, we hope you enjoyed that. Thanks for

1075
00:49:37,480 --> 00:49:39,600
Speaker 1: joining us, see you next time.

1076
00:49:47,360 --> 00:49:50,160
Speaker 2: Thanks for listening, and remember that Daniel and Jorge Explain

1077
00:49:50,239 --> 00:49:53,479
Speaker 2: the Universe is a production of iHeart Radio. For more

1078
00:49:53,560 --> 00:49:58,400
Speaker 2: podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or

1079
00:49:58,440 --> 00:50:06,239
Speaker 2: wherever you listen to your face. Richells h