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Speaker 4: Hey Daniel, how long does it take you to do

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Speaker 4: the research for one of these episodes?

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Speaker 1: You know it used to take me quite a while,

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Speaker 1: but I'm getting quicker at it.

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Speaker 4: Mm Is that because time passes more quickly as you

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Speaker 4: get older, like a special relativity thing?

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Speaker 1: Maybe, Or I guess I've just gotten more efficient at

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Speaker 1: the preparation.

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Speaker 4: Oh, yeah, like you can read faster, or you can

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Speaker 4: process information better.

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Speaker 1: No, I think I just developed a better mental whorehe

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Speaker 1: simulator that can predict what you might be interested in

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Speaker 1: or what you might not be interested in.

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Speaker 4: Oh it sounds like you just need like an AI

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Speaker 4: version of me. Then I don't even need to be here.

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Speaker 1: It's not artificial intelligence. It's natural.

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Speaker 4: It's a cartoonist intelligence. Well, I guess you know it

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Speaker 4: kind of depends. You know, what's interesting is kind of relative,

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Speaker 4: isn't it.

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Speaker 1: Yeah, that's right. What's especially interesting is kind of relative.

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Speaker 1: So I guess it kind of is all special relativity.

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Speaker 4: M Yeah, I definitely have some special relatives. Did you

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Speaker 4: predict I was going to say that.

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Speaker 1: I predicted you were going to say something hilarious. Hi.

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Speaker 4: I'm Jorge mat cartoonist and the author of Oliver's Great

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Speaker 4: Big Universe.

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Speaker 1: Hi. I'm Daniel. I'm a particle physicist and a professor

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Speaker 1: at UC Irvine, and I'm still training my brain to

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Speaker 1: understand the universe.

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Speaker 4: Wait, don't you need to know how the universe works

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Speaker 4: before you can train your brain to understand it.

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Speaker 1: We can do two things at once. We can try

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Speaker 1: to figure out how the universe works, and we can

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Speaker 1: try to wrap our minds around the bits that we

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Speaker 1: have figured out and try to gain some intuition for

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Speaker 1: all this craziness.

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Speaker 4: M I feel like this podcast is a little bit

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Speaker 4: of training into like how to think about the universe,

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Speaker 4: how to explore it, how to ask questions about it.

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Speaker 4: Should we be charging tuition?

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Speaker 1: We're just sharing the love, you know. But you're right

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Speaker 1: because most of our modern theories or physics are expressed

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Speaker 1: in a kind of inaccessible language mathematical equations that do

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Speaker 1: show us the relationship between bits and pieces and allow

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Speaker 1: us to make predictions and stuff. But it's not always

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Speaker 1: the way our brains work. So one of the goals

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Speaker 1: on this podcast is to break it down and give

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Speaker 1: you an intuitive understanding to try to make it all

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Speaker 1: make sense to you.

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Speaker 4: Yeah, I guess we offer free intuition, but not at

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Speaker 4: a cost of free tuition.

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Speaker 1: No tuition intuition. That should have been the title of

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Speaker 1: the podcast.

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Speaker 4: Yeah, hopefully it all comes to fruition.

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Speaker 1: But I mean, you're welcome to pay tuition if you like,

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Speaker 1: send us gold coins or dollars. If the inspiration strikes.

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Speaker 4: You, you take tips. You have a tip jar in

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Speaker 4: your classroom.

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Speaker 1: I don't have a tip jar, but I did once

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Speaker 1: walk into a classroom and find an envelope with thousands

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Speaker 1: of dollars in it.

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Speaker 4: Oh, WHOA, where is your university.

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Speaker 1: It's a public university, man, So it's not like some

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Speaker 1: students just like draw a pile of cash. I think

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Speaker 1: it must have been some club organizing in the room

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Speaker 1: before us or something.

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Speaker 4: Hmmm. Sounds like maybe they were trying to bribe you.

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Speaker 1: I don't think so. I think somebody must have panicked

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Speaker 1: when they realized they left it behind.

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Speaker 4: Or could have been a tip. I don't know. You

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Speaker 4: could have just assumed it was a tip.

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Speaker 1: I'm not so cheaply bought.

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Speaker 4: But anyways, Welcome to our podcast Daniel and Jorge Explain

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Speaker 4: the Universe, a production of iHeartRadio.

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Speaker 1: In which we use our inspiration to improve your intuition

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Speaker 1: for absolutely no tuition, whether or not the jokes come

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Speaker 1: to any fruition.

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Speaker 4: That's right, because it is an amazing universe for us

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Speaker 4: to ask questions about and to explore and to learn

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Speaker 4: about how it all works.

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Speaker 1: And part of the process of doing physics is not

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Speaker 1: just writing down on some sheet of paper a bunch

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Speaker 1: of math and then gesturing at and saying, trust us,

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Speaker 1: this works. It's about understanding. In the end, physics and

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Speaker 1: all of science is motivated by our curiosity, our desire

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Speaker 1: to understand, and that means translating all of this stuff,

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Speaker 1: everything we've learned, back into something that makes sense to us,

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Speaker 1: that clicks together in our minds, and we go, oh, well,

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Speaker 1: that's kind of weird, but I guess it does make sense. Yeah.

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Speaker 4: Plus, I don't know if I trust you anymore. I mean,

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Speaker 4: now that I know you're open to bribery.

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Speaker 1: I did say I was opening bribery. You said I

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Speaker 1: was opening bribery, and I.

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Speaker 4: Said I wasn't it sounds like you're open to tips

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Speaker 4: quote unquote tips.

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Speaker 1: People are welcome to send us donation to the podcast,

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Speaker 1: but it's not going to affect how I grade in

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Speaker 1: my class. Now, I turned that stack of cash over

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Speaker 1: to the campus police.

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Speaker 4: Oh wow, are you saying you tip the police.

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Speaker 1: I don't know what they did with it, but I

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Speaker 1: can only assume that they did something responsible.

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Speaker 4: But yeah, this university needs to depend on your point

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Speaker 4: of view. And also how fast you're.

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Speaker 1: Going, Because something we've learned over the last hundred years

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Speaker 1: is that our ancient intuition for how things work doesn't

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Speaker 1: always work. It only works in the special cases that

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Speaker 1: us and our ancestors got to see things moving pretty slowly.

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Speaker 1: And when you take those rules and try to extrapolate

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Speaker 1: them up to things moving really really quickly, you find

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Speaker 1: they don't work anymore. You need a new set of rules,

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Speaker 1: and those rules give us weird new insights into the

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Speaker 1: actual nature of space and time.

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Speaker 4: Yeah, over eight hundred years ago, Einstein discovered something called

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Speaker 4: special relativity.

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Speaker 1: Einstein developed special and general relativity. That's absolutely true. I

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Speaker 1: don't know if he invented it or discovered it. He

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Speaker 1: certainly uses it to describe the universe that we see

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Speaker 1: around us.

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Speaker 4: Yeah, over all hundred years hegol Einstein discovered something called

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Speaker 4: relativity special in general, in which he discovered that things

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Speaker 4: don't always look the same in this universe. Sometimes it

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Speaker 4: sort of depends on your relative point of view.

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Speaker 1: Yeah, Einstein really shook the foundations of our understanding of reality.

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Speaker 1: Newton gave us this idea of space and time as

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Speaker 1: being absolute, like the fixed backdrop of the universe. But

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Speaker 1: Einstein showed us that space is relative and so is time,

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Speaker 1: and it leads to all sorts of bizarre effects clocks

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Speaker 1: running slower, meter sticks looking shorter, and information disappearing into

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Speaker 1: black holes.

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Speaker 4: Yeah, it kind of seems sometimes that the universe has

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Speaker 4: these paradoxes, these contradictions, but actually it all sort of

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Speaker 4: works if you dig into the math right.

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

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Speaker 1: just a different kind of sense.

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Speaker 4: So today on the podcast, we'll be tackling the question

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Speaker 4: why do moving objects look shorter? I guess moving objects

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Speaker 4: look shorter.

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Speaker 1: This is not like how your bank account seems to

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Speaker 1: shrink when you're on a trip, you know, or on vacation.

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Speaker 1: This is the effect commonly known as length contraction, that

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Speaker 1: things going super duper fast relative to you seem to

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Speaker 1: look shorter than they do when they're at rest.

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Speaker 4: That's one of the consequences of having a speed limit

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Speaker 4: in the universe, isn't it.

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Speaker 1: Absolutely It's one of the consequences of special relativity, which

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Speaker 1: starts from the postulates that there's a speed limit to

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Speaker 1: the universe and that light always moves at the speed

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Speaker 1: of life for everybody, regardless of who they are and

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Speaker 1: how fast they're going. Out of that comes all sorts

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Speaker 1: of weird changes we have to make to space and

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Speaker 1: time and velocity in order to make things still make sense.

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Speaker 4: And so on the podcast here we've talked about how

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Speaker 4: as you're moving at close to the speed of lighter

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Speaker 4: moving near really massive objects, time slows down. We've talked

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Speaker 4: about that quite a bit, right.

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Speaker 1: Yeah, moving clocks run slow. So if you see a

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Speaker 1: clock moving past you at half the speed of light,

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Speaker 1: then you will see a tick slower than a clock

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Speaker 1: you are holding. That's time dilation, a concept we've talked

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Speaker 1: about lots and lots.

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Speaker 4: Of times, right, And then there's the idea that it's

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Speaker 4: not only time that can sort of stretch and change,

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Speaker 4: it's also distances or the lengths of things.

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Speaker 1: Yeah, if you are traveling really really fast, then distances

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Speaker 1: in front of you seem shorter. Like if you're flying

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Speaker 1: between here and Jupiter and you're moving really really fast,

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Speaker 1: then the distance between here and Jupiter seems to shrink.

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Speaker 4: So like if there was a giant meter stick between

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Speaker 4: here and Jupiter, and I was moving towards Jupiter really

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Speaker 4: really fast, then that meter stick would look shorter than

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Speaker 4: it actually is to me.

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Speaker 1: It would look shorter to you, but there is no

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Speaker 1: what it actually is. There's just a lot of different

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Speaker 1: viewpoints on it. It's all relative.

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Speaker 4: Well, I guess what it would look like if you

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Speaker 4: were not moving relative to the stick exactly.

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Speaker 1: Yeah, And that's what we call the proper length.

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Speaker 4: In that case, I'm moving really fast, it's not the

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Speaker 4: meter stick, or is it the same thing.

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Speaker 1: It's exactly the same thing. The meter stick would say

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Speaker 1: you look shorter, and you would say the meter stick

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Speaker 1: looks shorter. The whole effect is symmetric, same way the

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Speaker 1: time valuation is symmetric. If I think you're moving fast,

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Speaker 1: I see your clock running slow, but you also see

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Speaker 1: me moving quickly, so you see my clock running slow.

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Speaker 4: But I guess, doesn't it depend on which direction this

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Speaker 4: ruler is flying. Like if the ruler is flying let's

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Speaker 4: say away, for me really fast, it would look shorter.

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Speaker 4: But what if it's moving like from I see moving

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Speaker 4: from my left to my right, would it still look shorter?

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Speaker 1: It would look thinner. In that case. The direction it's

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Speaker 1: moving relative to you is the direction that gets contracted.

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Speaker 1: If it's always moving along its length, then it's going

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Speaker 1: to look shorter. Even if that length is pointed along

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Speaker 1: X or along Y or along zo or in any direction.

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Speaker 1: If it's moving along its length, it's going to look shorter.

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Speaker 4: I see. So like if someone launched a ruler really

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Speaker 4: really fast from my left and my right, it would

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Speaker 4: seem shorter than it would if I just held it

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Speaker 4: in my hand.

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Speaker 1: That's exactly right.

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Speaker 4: Yeah, So then the question for today is why does

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Speaker 4: that happen? All right? Well, as usual, we were wondering

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Speaker 4: how many people out there had thought about this question

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Speaker 4: or wonder why things look shorter when they're moving really fast.

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Speaker 1: Thanks very much to everybody who answers these questions. We'd

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Speaker 1: love hearing your voices, and we'd love to hear more

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Speaker 1: of your voices, so please don't be shy and write

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Speaker 1: to us two questions at Danielandjorge dot com.

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Speaker 4: So think about it for a second. Why do you

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Speaker 4: think moving objects look shorter? Here's what people have to say.

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Speaker 5: The Doppler effect is that what it's called the red

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Speaker 5: shifting thing. So like, basically when the object, the object

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Speaker 5: comes closer to you, like I guess like it looks

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Speaker 5: like the wavelengths wavelengths shorten, Right, they get shorter, So

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Speaker 5: like all objects, you know, they get a little louder,

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Speaker 5: the colors look little brighter, the wavelengths shorten, and so

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Speaker 5: the object looks shorter because the wavelengths of the colors

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Speaker 5: of the object to shorter.

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Speaker 6: Yeah, that's why I.

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Speaker 7: Think they look shorter, just due to the fact that

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Speaker 7: it's more for our brain to process, you know, as

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Speaker 7: opposed to if an object was sitting still, and then

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Speaker 7: obviously when there's more to interpret, that obviously creates more

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Speaker 7: of a margin of error with our perception.

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Speaker 8: I would assume that the reason that objects appear shorter,

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Speaker 8: especially as they approach light speed, is time and space dilation.

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Speaker 8: So as it approaches light speed, it would just appear

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Speaker 8: to shrink. Not really sure.

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Speaker 9: I think that for a human eye optics, moving objects

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Speaker 9: look actually longer because of motion blur, but special relative

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Speaker 9: to states that moving objects get shorter.

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Speaker 2: Don't exactly remember.

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Speaker 10: Why moving objects look shorter because the back has gotten

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Speaker 10: closer to where the front was when you saw it

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Speaker 10: by the time you see the back.

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Speaker 4: All right, lots of interesting answers here.

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Speaker 1: Very creative answers today, but.

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Speaker 4: They also sound very sciency talking about Doppler effects and

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Speaker 4: red shifting and space dilation.

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Speaker 1: Yeah, motion blur. Some of these answers are a way

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Speaker 1: off and some of them are pretty close.

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Speaker 4: Pretty cool. These are people that you found in your

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Speaker 4: department or people on the internet.

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Speaker 1: These are just folks from the internet listeners to this podcast.

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Speaker 4: Nice. Well, let's dig into it, Daniel, how what is

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Speaker 4: the physicist definition of length dilation?

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Speaker 1: So we usually call it length contraction.

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Speaker 4: Wait, is there a difference? Can you also have the

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Speaker 4: length dilation or is it only contract.

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Speaker 1: You can only have length contraction. The longest something can

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Speaker 1: be is if it's at rest relative to you. So

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Speaker 1: you're holding a meter stick, that's the longest you're ever

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Speaker 1: going to measure that meter stick to be. That meterstick

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Speaker 1: is moving past you at a certain speed, then you're

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Speaker 1: going to see it shorter. And the way I like

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Speaker 1: to phrase it to be very clear to make sure

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Speaker 1: it's relative, is that moving objects look shorter.

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Speaker 4: Even if they're moving like away from you or towards you,

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Speaker 4: it still gets shorter.

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Speaker 1: They still get shorter. Yeah, that doesn't make any difference.

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Speaker 1: In the same way that like moving clocks run slow

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Speaker 1: tells you that you are seeing that clock run slow

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Speaker 1: because you see it moving and it sees you moving,

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Speaker 1: so it sees you running slow. In the same way

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Speaker 1: you see a meter stick moving, you see it looking shorter.

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Speaker 1: It also sees you looking shorter because it sees you moving.

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Speaker 1: It's a symmetric effect.

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Speaker 4: All right, I was wrong? Well, is the is the

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Speaker 4: definition of length contraction.

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Speaker 1: So it's just that moving objects look shorter. You define

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Speaker 1: the proper length of something to be its length when

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Speaker 1: it's not moving. So you're holding the meterstick, you call

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Speaker 1: that the proper length. Then you zoom that meterstick by

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Speaker 1: you at like ten percent of the speed of light,

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Speaker 1: which doesn't sound impressive, but it's super duper crazy fast.

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Speaker 1: Then you'll see it a little bit shorter. You'll see

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Speaker 1: it like a half a percent shorter. You speed it

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Speaker 1: up to like half the speed of light, and you'll

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Speaker 1: see it be like only eighty five percent of its

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Speaker 1: proper length. And as you get up to like ninety

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Speaker 1: nine percent of the speed of light, it will shrink

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Speaker 1: down to like fifteen percent of its proper length. If

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Speaker 1: you get to like ninety nine point ninety nine percent

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Speaker 1: of the speed of light, it'll be just over one

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Speaker 1: percent of its proper length. So you can see things

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Speaker 1: getting like super duper short as they get super duper

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Speaker 1: fast relative to you.

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Speaker 4: I guess I'm wondering what it means to see something

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Speaker 4: like that moving that fast. You mean, like if I

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Speaker 4: take a picture of it, Like let's say a ruler

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Speaker 4: is zooming by really quickly, buy me from my left

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Speaker 4: to my right, and I take a picture of it

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Speaker 4: as it's going in front of me. In the picture,

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Speaker 4: it's going to seem shorter than it would if I

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Speaker 4: held the ruler in my hand.

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Speaker 1: It's great that you asked that question, because we have

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Speaker 1: to be very specific about what we mean here by

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Speaker 1: these measurements, because it makes a difference. And actually, if

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Speaker 1: you take a picture, you would see the ruler looking

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Speaker 1: weirdly longer, because the picture captures all the photons that

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Speaker 1: are arriving at you at one moment. And that includes

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Speaker 1: another effect, which is that it takes time for the

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Speaker 1: information to get to you, and part of the rulers

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Speaker 1: further from you and part of the rulers closer to you.

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Speaker 1: So that combines two different effects. One is that the

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Speaker 1: ruler looks shorter because it's moving faster, and the other

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Speaker 1: one at the back of the ruler is further from you,

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Speaker 1: so it takes light longer to get to you.

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Speaker 4: No, no, But if the ruler is moving from my

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Speaker 4: left to my right, like it's zooming past me like

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Speaker 4: a train would Like if I'm standing then next to

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Speaker 4: some train tracks and I see the train going from

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Speaker 4: my left to my right, and I take a picture

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Speaker 4: of the train as it's passing by in front of me,

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Speaker 4: is that draining It seemed shorter in the picture or

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Speaker 4: the same length or longer?

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Speaker 1: Again, the picture combines two different effects. One is the

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Speaker 1: special relativity effect and the other is the very normal

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Speaker 1: light takes time to travel effect. And so usually what

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Speaker 1: we do is not use the idea of a mental picture,

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Speaker 1: but imagine that we have like a bunch of assistants

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Speaker 1: all spread out to our left and to our right,

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Speaker 1: and they mark like when the train front or when

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Speaker 1: the train back passes them, And then we can use

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Speaker 1: the distance between the train front and the train back

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Speaker 1: to say how long.

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Speaker 4: It is what happens in the picture case, like what

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Speaker 4: if I take a picture of the train or the

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Speaker 4: ruler moving from my left and my right, Like, aren't

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Speaker 4: all those photons leaving the stick at the same time,

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Speaker 4: and so then it would arrive at the camera or

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Speaker 4: my eye at the same time.

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Speaker 1: They're leaving the train or the stick at the same time.

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Speaker 1: The stick has length, so it takes longer for the

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Speaker 1: back end photons to reach you than the front end photons.

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Speaker 1: And I think combining photon travel time and actual length

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Speaker 1: combines two different complicated things which are kind of hard

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Speaker 1: to hold in your head at the same time. So

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Speaker 1: usually when we talk about special relativity, we assume that

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Speaker 1: we can take care of the photon travel time and

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Speaker 1: say that we have a bunch of assistants all through

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Speaker 1: the universe, all making measurements and take local data, and

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Speaker 1: then we combine that information later to figure out what happened.

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Speaker 1: So we take away this effect of photons take time

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Speaker 1: to get somewhere because it adds another confusing layer.

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Speaker 4: But I guess I mean we're saying that things look shorter, right,

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Speaker 4: and your eye sort of look acts like a camera.

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Speaker 4: Are you saying that, like, maybe what you mean by

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Speaker 4: looking at something is not quite the same, but as

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Speaker 4: what everyday person might mean by looking at something.

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Speaker 1: Yeah, I think that's fair. When we do physics experiments,

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Speaker 1: we're very careful about how we make those measurements. So really,

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Speaker 1: what we mean here is if we take a very

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Speaker 1: careful measurement of the length of the object, we will

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Speaker 1: measure it to be shorter than if it was stationary.

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Speaker 4: All right, well, I think we just should just be

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Speaker 4: kind of clear about what we mean by things looking shorter.

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Speaker 1: What we mean is that we make a careful measurement

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Speaker 1: of the length of this thing involving us and a

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Speaker 1: bunch of assistants all along, like the track of a train,

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Speaker 1: and noting when it passes by. And then later we

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Speaker 1: get together and we compare our measurements and we say,

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Speaker 1: you know, Juan measured the back of the train at

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Speaker 1: this time, and Sally measure the front of the train

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Speaker 1: at that time, and then we can use that to

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Speaker 1: figure out how long the train was.

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Speaker 4: All right, it sounds like we need to dig into

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Speaker 4: this scenario of you and all of your assistance and

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Speaker 4: how they're measuring the length of this ruler and or

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Speaker 4: this train. Maybe really understands what we mean by things

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Speaker 4: looking shorter or not. So let's dig into these details.

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Speaker 4: But first let's take a quick break.

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Speaker 4: All Right, we're talking about length contraction due to special relativity,

478
00:22:47,240 --> 00:22:49,800
Speaker 4: and that doesn't have to do with how long this

479
00:22:49,880 --> 00:22:53,800
Speaker 4: podcast is, right or how much by questions that dilate

480
00:22:53,920 --> 00:22:56,560
Speaker 4: the length of the running time of this episode.

481
00:22:56,640 --> 00:22:58,800
Speaker 1: That's exactly what I was going to say. Yeah, no,

482
00:22:58,880 --> 00:23:01,159
Speaker 1: but it's good. It's important explain exactly what we need.

483
00:23:01,280 --> 00:23:04,120
Speaker 1: We not use jargon. So let's hash it out because

484
00:23:04,119 --> 00:23:08,040
Speaker 1: there's some really interesting, like apparent paradoxes that come up

485
00:23:08,080 --> 00:23:10,200
Speaker 1: when we try to measure these lengths really carefully.

486
00:23:10,400 --> 00:23:13,000
Speaker 4: Okay, so we're asking the question why the moving objects

487
00:23:13,000 --> 00:23:15,200
Speaker 4: look shorter, and it seems like we're not really asking

488
00:23:15,200 --> 00:23:18,480
Speaker 4: the question why they look shorter It's more like, why

489
00:23:18,560 --> 00:23:21,560
Speaker 4: when a bunch of physicists try to measure something moving fast,

490
00:23:21,760 --> 00:23:24,240
Speaker 4: they measure things to be shorter. Not really, because the

491
00:23:24,600 --> 00:23:27,920
Speaker 4: idea of looking at it, you're saying, convolutes several things.

492
00:23:28,080 --> 00:23:30,000
Speaker 1: Yeah, I would say, I guess that's how physicists look

493
00:23:30,000 --> 00:23:32,320
Speaker 1: at something, right. Don't just take a picture. We think

494
00:23:32,359 --> 00:23:35,440
Speaker 1: about what that picture is actually measuring and realizing pictures

495
00:23:35,560 --> 00:23:37,800
Speaker 1: are not the best way to measure the length of

496
00:23:37,880 --> 00:23:40,639
Speaker 1: something moving really really fast. And said, we hire a

497
00:23:40,680 --> 00:23:42,960
Speaker 1: bunch of assistants and lay them out in the line

498
00:23:43,240 --> 00:23:45,240
Speaker 1: so we can take measurements and figure out how long

499
00:23:45,280 --> 00:23:46,080
Speaker 1: that thing really is.

500
00:23:46,240 --> 00:23:49,359
Speaker 4: Okay, so then let's maybe paint that scenario. I'm sitting

501
00:23:49,359 --> 00:23:52,080
Speaker 4: by some train tracks, and the train tracks go from

502
00:23:52,080 --> 00:23:54,640
Speaker 4: my left to my right in front of me, and

503
00:23:54,680 --> 00:23:56,600
Speaker 4: now there's going to be a train passing by, and

504
00:23:56,600 --> 00:24:00,240
Speaker 4: I want to measure how long the train is. Yeah, saying,

505
00:24:00,240 --> 00:24:02,480
Speaker 4: don't take a picture of it because the picture might

506
00:24:02,600 --> 00:24:06,000
Speaker 4: lie to you. You're saying, hire a bunch of people

507
00:24:06,080 --> 00:24:08,119
Speaker 4: and then now what's your scenario. What's your setup here

508
00:24:08,160 --> 00:24:08,840
Speaker 4: with your assistance.

509
00:24:09,119 --> 00:24:10,840
Speaker 1: So I have a bunch of people to my left

510
00:24:10,880 --> 00:24:11,800
Speaker 1: and a bunch of people.

511
00:24:11,600 --> 00:24:13,680
Speaker 4: To my right, like you space them out every ten

512
00:24:13,760 --> 00:24:14,520
Speaker 4: meters or something.

513
00:24:15,160 --> 00:24:17,040
Speaker 1: And we all have a bunch of clocks, and we

514
00:24:17,080 --> 00:24:19,879
Speaker 1: synchronize our clocks. So they all started zero at the

515
00:24:19,880 --> 00:24:21,960
Speaker 1: same moment, and they all read ten seconds at the

516
00:24:22,000 --> 00:24:24,320
Speaker 1: same moment. They all read one hundred seconds at the

517
00:24:24,320 --> 00:24:26,520
Speaker 1: same moment. So we have a bunch of people now

518
00:24:26,560 --> 00:24:29,480
Speaker 1: at different locations with synchronized clocks.

519
00:24:29,840 --> 00:24:34,240
Speaker 4: How do you synchronize a clock. Wouldn't you run into

520
00:24:34,280 --> 00:24:36,560
Speaker 4: special relativity problems sinking those clocks.

521
00:24:36,760 --> 00:24:39,600
Speaker 1: It's complicated, but you can sink clocks using flashes of light.

522
00:24:39,680 --> 00:24:41,679
Speaker 1: If you assume you know how long it takes light

523
00:24:41,760 --> 00:24:44,720
Speaker 1: to get somewhere, you can synchronize clocks that are distanced.

524
00:24:44,800 --> 00:24:48,280
Speaker 4: M okay. So then each of these assistants has a

525
00:24:48,280 --> 00:24:49,639
Speaker 4: clock that's synchronized to yours.

526
00:24:49,720 --> 00:24:52,560
Speaker 1: Right exactly now, the train is passing by us, and

527
00:24:52,560 --> 00:24:54,280
Speaker 1: I ask people to write down what time the front

528
00:24:54,400 --> 00:24:56,240
Speaker 1: or the back of the train pass them.

529
00:24:56,280 --> 00:24:57,760
Speaker 4: Which one the front or the back.

530
00:24:57,920 --> 00:24:59,879
Speaker 1: You can have them write down both, and then in

531
00:25:00,000 --> 00:25:02,439
Speaker 1: in order to measure the length of the train, what

532
00:25:02,520 --> 00:25:04,400
Speaker 1: you need to do is get a measurement of where

533
00:25:04,400 --> 00:25:06,439
Speaker 1: the back of the train was and where the front

534
00:25:06,440 --> 00:25:09,560
Speaker 1: of the train was at the same time. You combine

535
00:25:09,600 --> 00:25:11,320
Speaker 1: those two numbers, and that's your length.

536
00:25:11,680 --> 00:25:13,679
Speaker 4: See it again, You measure where the front and the

537
00:25:13,680 --> 00:25:15,000
Speaker 4: back were at the same time.

538
00:25:15,359 --> 00:25:17,600
Speaker 1: Yeah, you want to know how long something is. Then

539
00:25:17,640 --> 00:25:20,040
Speaker 1: you want to know where's the front and where's the back,

540
00:25:20,200 --> 00:25:22,359
Speaker 1: and you want to take those measurements at the same moment.

541
00:25:22,480 --> 00:25:22,640
Speaker 8: Right.

542
00:25:22,640 --> 00:25:24,480
Speaker 1: If you don't take those measurements at the same moment,

543
00:25:24,680 --> 00:25:26,280
Speaker 1: you're not going to get the length of the train.

544
00:25:26,480 --> 00:25:28,960
Speaker 1: Like if a parade is passing by you, it's moving, right.

545
00:25:29,240 --> 00:25:31,600
Speaker 1: If you measure the front and the back at different moments,

546
00:25:31,640 --> 00:25:33,880
Speaker 1: you're not going to get the actual length of the parade.

547
00:25:35,240 --> 00:25:37,880
Speaker 4: I see, all right, So then you ask your assistance

548
00:25:37,920 --> 00:25:39,800
Speaker 4: to write down when they saw the front of the train,

549
00:25:39,880 --> 00:25:41,560
Speaker 4: when they saw the back of the train. And then

550
00:25:41,600 --> 00:25:43,600
Speaker 4: what do you do. You get together and you have

551
00:25:43,720 --> 00:25:46,000
Speaker 4: a picnic, You.

552
00:25:45,960 --> 00:25:48,159
Speaker 1: Get together, you spend some of that tip money on

553
00:25:48,240 --> 00:25:50,919
Speaker 1: you know, ice sculptures and chocolates for your picnic and whatever.

554
00:25:51,240 --> 00:25:52,639
Speaker 1: And then you look at the numbers and you say,

555
00:25:52,640 --> 00:25:55,119
Speaker 1: all right, one measure the back of the train to

556
00:25:55,200 --> 00:25:57,879
Speaker 1: be negative half a kilometer at the same time. Sally

557
00:25:57,960 --> 00:26:00,520
Speaker 1: measured the front of the train to be a location

558
00:26:01,000 --> 00:26:03,840
Speaker 1: plus half a kilometer. So okay, the train is one

559
00:26:03,960 --> 00:26:06,840
Speaker 1: kilometer long because the front and the back were one

560
00:26:06,880 --> 00:26:09,000
Speaker 1: kilometer apart at the same time.

561
00:26:09,920 --> 00:26:13,280
Speaker 4: Oh okay, yeah, yeah, I'm following and following. So now

562
00:26:13,560 --> 00:26:15,720
Speaker 4: like you, you sort of ask, okay, it t equals

563
00:26:15,720 --> 00:26:18,560
Speaker 4: one minute, where did your assistance measure the front of

564
00:26:18,600 --> 00:26:20,240
Speaker 4: the train and where did they measure the back of

565
00:26:20,240 --> 00:26:22,040
Speaker 4: the train, And then that should tell you the length

566
00:26:22,080 --> 00:26:22,520
Speaker 4: of the train.

567
00:26:22,600 --> 00:26:24,480
Speaker 1: That should tell you the length of train. And if

568
00:26:24,480 --> 00:26:27,440
Speaker 1: you measure them at different times, like if one's clock

569
00:26:27,520 --> 00:26:29,440
Speaker 1: was out of sync, or one was lazy, or one

570
00:26:29,480 --> 00:26:31,240
Speaker 1: made a mistake or something in a measure of the

571
00:26:31,240 --> 00:26:33,280
Speaker 1: back of the train earlier or later, then we'd get

572
00:26:33,280 --> 00:26:35,720
Speaker 1: the wrong answer for the length of the train. It's

573
00:26:35,760 --> 00:26:37,760
Speaker 1: crucial that you measure the front in the back at

574
00:26:37,800 --> 00:26:40,480
Speaker 1: the same time. It seems sort of obvious to even

575
00:26:40,520 --> 00:26:42,919
Speaker 1: spell that out, sort of dumb, like, duh, that's what

576
00:26:43,000 --> 00:26:45,080
Speaker 1: length really is. But it's going to turn out to

577
00:26:45,080 --> 00:26:47,560
Speaker 1: be really important part of understanding length contraction.

578
00:26:47,800 --> 00:26:51,200
Speaker 4: Okay, So that's I guess that's one way to measure it,

579
00:26:52,040 --> 00:26:54,040
Speaker 4: or that is that the only way to measure the train.

580
00:26:54,040 --> 00:26:55,840
Speaker 1: And that's sort of the standard setup. It allows you

581
00:26:55,880 --> 00:26:58,399
Speaker 1: to avoid things like how longs they take informations, travel

582
00:26:58,600 --> 00:27:00,800
Speaker 1: from here to there, and all that stuff stuff. I

583
00:27:00,800 --> 00:27:03,120
Speaker 1: suppose you could come up with other techniques as well.

584
00:27:03,160 --> 00:27:06,280
Speaker 4: All right, So now you get together and you measure

585
00:27:06,320 --> 00:27:09,320
Speaker 4: the train, and you're saying the number you get from

586
00:27:09,359 --> 00:27:11,840
Speaker 4: this setup is not the same as if the train

587
00:27:11,960 --> 00:27:14,200
Speaker 4: was not moving at all, exactly. Well, if the train

588
00:27:14,280 --> 00:27:16,240
Speaker 4: was not moving at all, your setup wo work.

589
00:27:17,160 --> 00:27:18,680
Speaker 1: Well, if the train is parked in front of you,

590
00:27:18,680 --> 00:27:21,320
Speaker 1: your setup would work. Right, you have somebody standing at

591
00:27:21,320 --> 00:27:22,800
Speaker 1: the back of the train and somebody standing at the

592
00:27:22,800 --> 00:27:25,399
Speaker 1: front of the train. They know where they are and

593
00:27:25,440 --> 00:27:27,320
Speaker 1: it doesn't really matter when they make the measurements of

594
00:27:27,359 --> 00:27:28,200
Speaker 1: the train isn't moving.

595
00:27:28,280 --> 00:27:32,399
Speaker 4: Mmm, I see. Because you know you can measure the

596
00:27:32,480 --> 00:27:34,639
Speaker 4: road in front of you, you can measure the train tracks.

597
00:27:34,800 --> 00:27:36,919
Speaker 1: Yeah, exactly. Like if I line the train up with

598
00:27:37,000 --> 00:27:39,160
Speaker 1: my two assistants and I know how far apart they are,

599
00:27:39,280 --> 00:27:40,800
Speaker 1: then I know how long the train is.

600
00:27:41,000 --> 00:27:43,720
Speaker 4: Okay, So with your setup and your assistance, which hopefully

601
00:27:43,760 --> 00:27:46,040
Speaker 4: you're tipping generously, you measure the trains will be one

602
00:27:46,080 --> 00:27:48,880
Speaker 4: kilometer long. And now you're saying that's not really how

603
00:27:48,920 --> 00:27:49,600
Speaker 4: long the train is.

604
00:27:49,760 --> 00:27:51,440
Speaker 1: Yeah, let's say I measured the train to be one

605
00:27:51,480 --> 00:27:53,800
Speaker 1: kilometer long when it's at rest, when it's not moving,

606
00:27:53,920 --> 00:27:56,280
Speaker 1: and then the train makes a run past me at

607
00:27:56,280 --> 00:27:59,119
Speaker 1: half the speed of light. You know, then what I'm

608
00:27:59,119 --> 00:28:01,000
Speaker 1: going to measure this time time is that the train

609
00:28:01,160 --> 00:28:04,000
Speaker 1: is shorter, that it's only eight hundred and fifty meters

610
00:28:04,080 --> 00:28:05,800
Speaker 1: long instead of one kilometer.

611
00:28:06,160 --> 00:28:06,480
Speaker 12: Mmm.

612
00:28:07,880 --> 00:28:10,560
Speaker 4: Interesting, Now we're going to explain why that happens. Where

613
00:28:10,600 --> 00:28:13,359
Speaker 4: does special where activity come in that makes you measure

614
00:28:13,359 --> 00:28:15,560
Speaker 4: it to be eight hundred and fifty meters. You're telling

615
00:28:15,600 --> 00:28:18,119
Speaker 4: me that the assistance would measure the train to be

616
00:28:18,160 --> 00:28:21,040
Speaker 4: shorter than a kilometer. But I guess my intuition is, like,

617
00:28:21,080 --> 00:28:23,879
Speaker 4: what how can that be? Because like, your setup seemed

618
00:28:23,880 --> 00:28:27,000
Speaker 4: perfectly you know, logical and sensical, and it should measure

619
00:28:27,160 --> 00:28:29,199
Speaker 4: In my intuition, it should measure the train to be

620
00:28:29,200 --> 00:28:33,000
Speaker 4: a kilometer Because you know, Juan measured the front of

621
00:28:33,040 --> 00:28:35,280
Speaker 4: the train moving at this point at this time, and

622
00:28:35,560 --> 00:28:38,080
Speaker 4: Sally measured the back of the train moving a kilometer

623
00:28:38,120 --> 00:28:40,640
Speaker 4: away at the same time. Why would it look shorter

624
00:28:40,680 --> 00:28:41,320
Speaker 4: than a kilometer.

625
00:28:41,520 --> 00:28:44,600
Speaker 1: Let's unpack what that question really means. The why question.

626
00:28:45,480 --> 00:28:48,440
Speaker 1: You're saying that the train was one length at rest,

627
00:28:48,520 --> 00:28:51,480
Speaker 1: and so you expect it to still be that length later.

628
00:28:51,960 --> 00:28:55,440
Speaker 1: That sounds reasonable, but it actually contains a big assumption,

629
00:28:56,040 --> 00:29:00,320
Speaker 1: the assumption that lengths are absolute rather than real relative

630
00:29:00,360 --> 00:29:03,080
Speaker 1: to velocity, that lengths are always the same no matter

631
00:29:03,080 --> 00:29:06,080
Speaker 1: how fast you're going. I could ask you, why do

632
00:29:06,160 --> 00:29:08,280
Speaker 1: you expect the train to always have the same length.

633
00:29:08,560 --> 00:29:12,120
Speaker 1: That's just actually an assumption we're making about the world,

634
00:29:12,400 --> 00:29:15,400
Speaker 1: and it turns out it's not how the world actually works.

635
00:29:15,520 --> 00:29:19,360
Speaker 1: The world actually works differently. Lengths are relative. They depend

636
00:29:19,560 --> 00:29:23,000
Speaker 1: on velocity. You just never noticed before because it's a

637
00:29:23,000 --> 00:29:26,920
Speaker 1: subtle effect. So you, like everyone before Einstein, made the

638
00:29:26,960 --> 00:29:31,040
Speaker 1: wrong assumption based on your limited experience, the assumption that

639
00:29:31,160 --> 00:29:35,240
Speaker 1: length is fixed, that it's universal and doesn't depend on velocity.

640
00:29:35,640 --> 00:29:38,400
Speaker 1: But it turns out it's not. It's relative. So that's

641
00:29:38,440 --> 00:29:41,120
Speaker 1: the experimental observation. That's what we see in the world.

642
00:29:41,240 --> 00:29:44,200
Speaker 1: And on top of that, it has to be relative

643
00:29:44,280 --> 00:29:47,560
Speaker 1: in order to make sense, to be consistent with a

644
00:29:47,640 --> 00:29:51,600
Speaker 1: constant speed of light. So A, we can now tell

645
00:29:51,640 --> 00:29:55,480
Speaker 1: that the world works this way lengths are relative, not absolute,

646
00:29:55,760 --> 00:30:00,000
Speaker 1: and B it's a natural theoretical consequence of the speed

647
00:30:00,160 --> 00:30:03,160
Speaker 1: of light being the same for everyone, which has important

648
00:30:03,160 --> 00:30:07,800
Speaker 1: consequences for time and then eventually for length. I want

649
00:30:07,800 --> 00:30:09,880
Speaker 1: to walk you through it. But the short version of

650
00:30:09,920 --> 00:30:13,160
Speaker 1: the story is that number one, the speed of light

651
00:30:13,280 --> 00:30:17,600
Speaker 1: is constant for everyone, which means that number two, time

652
00:30:17,840 --> 00:30:22,520
Speaker 1: is not universal. That people can disagree about whether things

653
00:30:22,600 --> 00:30:25,840
Speaker 1: happen at the same time. And remember that measuring the

654
00:30:25,880 --> 00:30:29,000
Speaker 1: front and back of the train at the same time

655
00:30:29,680 --> 00:30:34,160
Speaker 1: was crucial to our measurement. So disagreeing about simultaneity when

656
00:30:34,240 --> 00:30:36,640
Speaker 1: to measure the front and back of the train means

657
00:30:36,880 --> 00:30:40,200
Speaker 1: number three, we're going to disagree about the length of

658
00:30:40,240 --> 00:30:43,200
Speaker 1: the train. Okay, that was the short version, so let's

659
00:30:43,240 --> 00:30:46,320
Speaker 1: back up. Something we know is true is that the

660
00:30:46,360 --> 00:30:49,480
Speaker 1: speed of light is the same for everyone. If you're

661
00:30:49,600 --> 00:30:51,960
Speaker 1: on the train and you shine a flashlight from the

662
00:30:51,960 --> 00:30:54,200
Speaker 1: back of the train towards the front, you see it

663
00:30:54,320 --> 00:30:56,760
Speaker 1: move at the speed of light relative to the train

664
00:30:56,920 --> 00:30:59,840
Speaker 1: and to you on the ground. I see it move

665
00:31:00,160 --> 00:31:03,040
Speaker 1: the speed of light relative to me, which means it's

666
00:31:03,240 --> 00:31:05,560
Speaker 1: not moving at the speed of light relative to the

667
00:31:05,640 --> 00:31:09,600
Speaker 1: train according to me. That's number one, the basic fact

668
00:31:09,640 --> 00:31:13,960
Speaker 1: from which all special relativity derives that everyone measures the

669
00:31:14,000 --> 00:31:16,320
Speaker 1: speed of light relative to them to be the same.

670
00:31:16,560 --> 00:31:19,680
Speaker 1: So how does that mess up our concept of time. Well,

671
00:31:19,920 --> 00:31:21,960
Speaker 1: if you stand in the middle of the train and

672
00:31:22,000 --> 00:31:25,720
Speaker 1: shine two flashlights, one forwards and one backwards, then you'll

673
00:31:25,760 --> 00:31:27,720
Speaker 1: see them reach the front and the back at the

674
00:31:27,760 --> 00:31:31,640
Speaker 1: same time. Right, makes sense, same distance, same speed. But

675
00:31:31,760 --> 00:31:34,200
Speaker 1: on the ground, I also see those beams moving at

676
00:31:34,200 --> 00:31:36,400
Speaker 1: the speed of light. But now I see the back

677
00:31:36,440 --> 00:31:39,280
Speaker 1: of the train rushing forward towards the beam, so it

678
00:31:39,320 --> 00:31:42,160
Speaker 1: reaches the beam first compared to the front of the train,

679
00:31:42,200 --> 00:31:44,560
Speaker 1: which is racing away from the beam. So you and

680
00:31:44,600 --> 00:31:47,200
Speaker 1: I disagree about whether the beams hit the front and

681
00:31:47,280 --> 00:31:49,880
Speaker 1: back at the same time. That was point number two.

682
00:31:50,320 --> 00:31:52,040
Speaker 1: It all comes down to the end to time. It's

683
00:31:52,080 --> 00:31:55,240
Speaker 1: because the way Einstein changed our understanding of the universe

684
00:31:55,640 --> 00:31:59,000
Speaker 1: required us to understand that time depends on the observer,

685
00:32:00,120 --> 00:32:03,680
Speaker 1: not just location that depends on the observer, but also

686
00:32:03,960 --> 00:32:07,400
Speaker 1: time depends on the observer. And because time depends on

687
00:32:07,440 --> 00:32:10,800
Speaker 1: the observer, whether two things happen at the same time

688
00:32:11,280 --> 00:32:14,080
Speaker 1: depends on the observer. We've talked about this a few times,

689
00:32:14,080 --> 00:32:17,120
Speaker 1: this concept of simultaneiti, like do two things happen at

690
00:32:17,120 --> 00:32:21,280
Speaker 1: the same time depends on your velocity. And because measurements

691
00:32:21,280 --> 00:32:25,960
Speaker 1: of length require two measurements at the same time, then

692
00:32:26,000 --> 00:32:29,080
Speaker 1: your measurement of length depends on your notion of simultaneiti

693
00:32:29,840 --> 00:32:32,640
Speaker 1: do a Juan and Sally measure the train front and

694
00:32:32,680 --> 00:32:35,960
Speaker 1: back at the same time. They think so, but the

695
00:32:35,960 --> 00:32:38,680
Speaker 1: person on the train thinks they don't, which is why

696
00:32:38,680 --> 00:32:40,520
Speaker 1: they have different measurements of the length of.

697
00:32:40,440 --> 00:32:43,160
Speaker 4: The train between us and the observers on the train.

698
00:32:43,320 --> 00:32:46,600
Speaker 4: But like, all of your assistants are not moving relative

699
00:32:46,640 --> 00:32:49,320
Speaker 4: to each other, that's right, and they all have synchronized clogs.

700
00:32:49,360 --> 00:32:51,800
Speaker 4: You told me they were synchronized. So what do you

701
00:32:51,840 --> 00:32:54,360
Speaker 4: mean that their measurements are not happening at the same time,

702
00:32:54,480 --> 00:32:57,000
Speaker 4: or like if they measure why measures in front of

703
00:32:57,040 --> 00:32:59,239
Speaker 4: the train, Sally measures the back of the train, and

704
00:32:59,280 --> 00:33:02,960
Speaker 4: they write down than a piece of paper what their

705
00:33:03,080 --> 00:33:06,040
Speaker 4: measurements and then they bring the papers to you. Aren't

706
00:33:06,080 --> 00:33:08,600
Speaker 4: those things synchronized. I'm not saying how what you're saying

707
00:33:08,600 --> 00:33:11,600
Speaker 4: about time and how that's changing your assistance measurement.

708
00:33:11,880 --> 00:33:14,160
Speaker 1: Yeah, I think that those measurements are synchronized. And I

709
00:33:14,160 --> 00:33:16,120
Speaker 1: think my measurement of eight hundred and fifty meters is

710
00:33:16,160 --> 00:33:18,960
Speaker 1: totally right. But if you're on the train, then you

711
00:33:19,000 --> 00:33:21,600
Speaker 1: think that those measurements are not synchronized. You're like, no,

712
00:33:21,680 --> 00:33:25,120
Speaker 1: Wan and Sally made those measurements at different times. That's

713
00:33:25,160 --> 00:33:27,680
Speaker 1: why they got a shorter length. From your point of view,

714
00:33:27,720 --> 00:33:30,120
Speaker 1: those two measurements were not made at the same time.

715
00:33:30,360 --> 00:33:32,400
Speaker 4: Why not we synchronized our clocks.

716
00:33:32,600 --> 00:33:35,160
Speaker 1: I'm synchronized with everybody on the ground, but I'm not

717
00:33:35,200 --> 00:33:37,760
Speaker 1: synchronized with people on the train because those people are

718
00:33:37,800 --> 00:33:41,680
Speaker 1: moving relative to me, and moving clocks cannot stay synchronized.

719
00:33:41,880 --> 00:33:44,400
Speaker 4: Okay, so forget the people on the train. Let's just

720
00:33:44,440 --> 00:33:45,640
Speaker 4: focus on Huang and Sally.

721
00:33:45,800 --> 00:33:47,960
Speaker 1: Okay, Wan and Sally on the ground, they.

722
00:33:47,920 --> 00:33:50,720
Speaker 4: Have synchronized clocks to mine. They're synchronized to each other.

723
00:33:51,560 --> 00:33:53,200
Speaker 4: And you're saying they would measure the thing to be

724
00:33:53,280 --> 00:33:54,480
Speaker 4: eight hundred and fifty.

725
00:33:54,240 --> 00:33:57,000
Speaker 1: Meters yes, whereas somebody on the train says.

726
00:33:56,800 --> 00:33:59,560
Speaker 4: That, no, forget, forget the person on the train. Now

727
00:33:59,600 --> 00:34:03,120
Speaker 4: the train stops, turns around, comes back, and parts in

728
00:34:03,160 --> 00:34:03,560
Speaker 4: front of me.

729
00:34:03,640 --> 00:34:04,000
Speaker 1: Mm hmm.

730
00:34:04,600 --> 00:34:07,080
Speaker 4: Now I would measure the train to be a kilometer yes.

731
00:34:07,440 --> 00:34:10,480
Speaker 4: So what happened there? Like did space contract or? I

732
00:34:10,480 --> 00:34:13,800
Speaker 4: guess I'm not seeing the connection with time, or or

733
00:34:13,800 --> 00:34:15,440
Speaker 4: at least I feel like we're not explaining that.

734
00:34:15,600 --> 00:34:18,680
Speaker 1: Well, velocity and time are very closely related. Right, We're

735
00:34:18,680 --> 00:34:21,200
Speaker 1: not talking about a single point. We're talking about two points.

736
00:34:21,239 --> 00:34:22,920
Speaker 1: We're talking about the front of the train and we're

737
00:34:22,960 --> 00:34:25,160
Speaker 1: talking about the back of the train, and we're talking

738
00:34:25,200 --> 00:34:28,200
Speaker 1: about the distances between them, and we're talking about measuring

739
00:34:28,239 --> 00:34:31,600
Speaker 1: them at a certain time. And so of course time

740
00:34:31,680 --> 00:34:33,080
Speaker 1: is going to be involved here, right.

741
00:34:33,440 --> 00:34:36,560
Speaker 4: You say we synchronize our clocks, So isn't it sort

742
00:34:36,560 --> 00:34:37,759
Speaker 4: of like a universal time?

743
00:34:37,880 --> 00:34:40,800
Speaker 1: I mean, you can only synchronize clocks in one frame. Okay,

744
00:34:40,880 --> 00:34:44,040
Speaker 1: so we've established that we can synchronize our clocks on

745
00:34:44,080 --> 00:34:47,960
Speaker 1: the ground, but that doesn't mean they're synchronized for other people,

746
00:34:48,200 --> 00:34:49,520
Speaker 1: like the people on the train.

747
00:34:49,840 --> 00:34:53,080
Speaker 4: I feel like this is maybe confusing anymore to think

748
00:34:53,080 --> 00:34:54,920
Speaker 4: about the people on the train. Like, let's say I

749
00:34:54,920 --> 00:34:56,920
Speaker 4: don't care about the people on the train, Like I

750
00:34:57,040 --> 00:35:00,000
Speaker 4: just care about what Sally and Juan measure now when

751
00:35:00,040 --> 00:35:02,120
Speaker 4: the train is moving, and then later when the train

752
00:35:02,160 --> 00:35:05,399
Speaker 4: stops and comes back and they measure the distance again,

753
00:35:05,760 --> 00:35:07,240
Speaker 4: Why are those measurements different?

754
00:35:07,320 --> 00:35:10,560
Speaker 1: Okay, your question is if the train is one kilometer

755
00:35:10,680 --> 00:35:13,319
Speaker 1: long when it's sitting in front of me. Or equivalently,

756
00:35:13,680 --> 00:35:15,920
Speaker 1: if the people on the train measured to be one

757
00:35:16,000 --> 00:35:19,080
Speaker 1: kilometer because it's not moving relative to them, then why

758
00:35:19,120 --> 00:35:21,280
Speaker 1: do we measure it to be shorter on the ground

759
00:35:21,360 --> 00:35:24,520
Speaker 1: when it's moving past us. How does our disagreement about

760
00:35:24,520 --> 00:35:29,440
Speaker 1: synchronized clocks get translated to a disagreement about the length. Well,

761
00:35:29,440 --> 00:35:31,279
Speaker 1: the most direct way to say it is that to

762
00:35:31,320 --> 00:35:33,880
Speaker 1: measure the length of the train, you have to measure

763
00:35:33,920 --> 00:35:36,239
Speaker 1: the front and back at the same time. But if

764
00:35:36,280 --> 00:35:40,000
Speaker 1: you disagree about what at the same time means, then

765
00:35:40,040 --> 00:35:42,000
Speaker 1: you're going to disagree about the length of the train.

766
00:35:42,800 --> 00:35:46,839
Speaker 1: So what's going on here exactly? How do the UNSYNCD

767
00:35:46,880 --> 00:35:50,839
Speaker 1: clocks make people measure different times. I know you don't

768
00:35:50,880 --> 00:35:52,319
Speaker 1: want to think about the people on the train, but

769
00:35:52,440 --> 00:35:55,440
Speaker 1: you kind of have to, because when we say the

770
00:35:55,560 --> 00:35:59,520
Speaker 1: train is one kilometer in length, what that means is

771
00:35:59,520 --> 00:36:02,480
Speaker 1: that it's one kilometer for people on the train, For

772
00:36:02,520 --> 00:36:06,960
Speaker 1: people not moving relative to the train, by their definition

773
00:36:07,040 --> 00:36:09,480
Speaker 1: of at the same time, the front and back are

774
00:36:09,560 --> 00:36:13,040
Speaker 1: one kilometer apart, that's kind of what it means. But

775
00:36:13,120 --> 00:36:15,719
Speaker 1: for people on the ground, they have a different definition

776
00:36:15,800 --> 00:36:19,280
Speaker 1: of at the same time, they think that the people

777
00:36:19,280 --> 00:36:22,759
Speaker 1: on the train's measurement is wrong. The people on the

778
00:36:22,800 --> 00:36:25,360
Speaker 1: ground think that the people on the train measured in

779
00:36:25,400 --> 00:36:29,080
Speaker 1: the back of the train first and later measure the

780
00:36:29,080 --> 00:36:31,719
Speaker 1: front of the train. The people on the ground think

781
00:36:31,719 --> 00:36:33,760
Speaker 1: that people on the train are not measuring the front

782
00:36:33,760 --> 00:36:36,239
Speaker 1: and back at the same time, which is why they

783
00:36:36,280 --> 00:36:40,239
Speaker 1: get a longer measurement. They get a full kilometer. Like

784
00:36:40,360 --> 00:36:42,680
Speaker 1: imagine if you took a one meter long stick moving

785
00:36:42,719 --> 00:36:44,840
Speaker 1: past you, and you measured the back of it now

786
00:36:44,960 --> 00:36:48,040
Speaker 1: and the front of it later in ten seconds or whatever,

787
00:36:48,320 --> 00:36:51,000
Speaker 1: you get a measurement that was way too long. That's

788
00:36:51,000 --> 00:36:52,920
Speaker 1: what the people on the ground think that people on

789
00:36:52,960 --> 00:36:55,600
Speaker 1: the train are doing to get one kilometer instead of

790
00:36:55,600 --> 00:36:58,000
Speaker 1: eight hundred and fifty meters. The people on the ground

791
00:36:58,080 --> 00:37:00,560
Speaker 1: think that their own measurements are synchronized, and they get

792
00:37:00,600 --> 00:37:03,160
Speaker 1: eight hundred and fifty meters. The people on the train

793
00:37:03,880 --> 00:37:06,279
Speaker 1: think that the measurements on the ground are not at

794
00:37:06,320 --> 00:37:09,080
Speaker 1: the same time. The people on the train think that

795
00:37:09,120 --> 00:37:11,840
Speaker 1: the people on the ground are measuring the front before

796
00:37:11,880 --> 00:37:14,279
Speaker 1: they're measuring the back, and that's why the people on

797
00:37:14,280 --> 00:37:17,399
Speaker 1: the ground are getting a measurement that's too short. So

798
00:37:17,440 --> 00:37:20,120
Speaker 1: there's no like, what is the real length of the train,

799
00:37:20,360 --> 00:37:23,720
Speaker 1: or why does a train look shorter when it's moving faster?

800
00:37:24,280 --> 00:37:26,680
Speaker 1: Its length depends on your velocity.

801
00:37:26,800 --> 00:37:29,600
Speaker 4: We just never noticed it before, all right, So let's

802
00:37:29,600 --> 00:37:32,360
Speaker 4: dig into me this idea of that. It has to

803
00:37:32,400 --> 00:37:35,080
Speaker 4: do with time, and let's talk about how time changes

804
00:37:35,840 --> 00:37:38,520
Speaker 4: due to special relativity and see if that maybe explains

805
00:37:38,560 --> 00:37:40,880
Speaker 4: why the train we measure the train can be different

806
00:37:40,960 --> 00:37:43,480
Speaker 4: lengths here and then later when it stops. So we'll

807
00:37:43,480 --> 00:37:45,760
Speaker 4: dig into that, but first, let's take another quick break.

808
00:37:49,960 --> 00:37:51,719
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809
00:37:51,840 --> 00:37:55,000
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810
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811
00:37:59,120 --> 00:38:01,720
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812
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815
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Speaker 4: All right, we're asking the question why do moving objects

865
00:40:59,160 --> 00:41:02,680
Speaker 4: look shorter and danny You're saying it really depends on

866
00:41:02,800 --> 00:41:05,839
Speaker 4: the idea of time being variable at this time being

867
00:41:05,880 --> 00:41:10,439
Speaker 4: variable affect sally and why your assistance measurements of the train.

868
00:41:10,640 --> 00:41:12,719
Speaker 1: I think time is crucial to resolving this sort of

869
00:41:12,760 --> 00:41:16,000
Speaker 1: apparent paradox. One of the reasons it's hard to imagine

870
00:41:16,040 --> 00:41:18,719
Speaker 1: a stick getting shorter or a train getting shorter is

871
00:41:18,719 --> 00:41:21,120
Speaker 1: because you think of it as a rigid object, which

872
00:41:21,200 --> 00:41:24,120
Speaker 1: throws you off. Instead, just think of three train cars

873
00:41:24,160 --> 00:41:26,600
Speaker 1: moving and sync. One in the back, one in the middle,

874
00:41:26,600 --> 00:41:28,480
Speaker 1: and one in the front. Now, what if the middle

875
00:41:28,520 --> 00:41:30,879
Speaker 1: car tells the other two to speed up? From your

876
00:41:30,960 --> 00:41:34,000
Speaker 1: point of view, the message arrives at the rear car first,

877
00:41:34,360 --> 00:41:37,560
Speaker 1: which speeds up before the lead car, can effectively shrinking

878
00:41:37,600 --> 00:41:40,480
Speaker 1: the distance between them from their point of view. However,

879
00:41:40,719 --> 00:41:42,879
Speaker 1: the message arrives at the lead and the rear car

880
00:41:42,920 --> 00:41:45,640
Speaker 1: at the same time and the distance hasn't changed. When

881
00:41:45,680 --> 00:41:48,879
Speaker 1: they decelerate again, the reverse happens and the cars come

882
00:41:48,920 --> 00:41:51,680
Speaker 1: to rest with the same original distance. So you can

883
00:41:51,680 --> 00:41:55,600
Speaker 1: see how different senses of time lead to different measurements

884
00:41:55,640 --> 00:41:57,680
Speaker 1: of distance. But how is it possible for the train

885
00:41:57,760 --> 00:42:00,239
Speaker 1: cars to get closer together and like not? Notice what

886
00:42:00,280 --> 00:42:03,040
Speaker 1: if you exaggerated the effect so they would bump into

887
00:42:03,040 --> 00:42:06,160
Speaker 1: each other. Well, the answer is they also shrink because

888
00:42:06,200 --> 00:42:10,280
Speaker 1: space itself is shrinking. The atoms are like little cars.

889
00:42:10,360 --> 00:42:12,600
Speaker 1: So think of the train as the front of the

890
00:42:12,640 --> 00:42:15,239
Speaker 1: train and the back of the train, not as one object.

891
00:42:15,680 --> 00:42:17,839
Speaker 1: Thinking of it as one long train tricks you into

892
00:42:17,960 --> 00:42:20,680
Speaker 1: using your intuition thinking of it as a rigid object,

893
00:42:20,880 --> 00:42:23,880
Speaker 1: which actually can't exist in our universe. Like when people

894
00:42:23,920 --> 00:42:26,200
Speaker 1: ask what happens if you push a stick a light

895
00:42:26,280 --> 00:42:29,640
Speaker 1: year long? Does one end move instantly, sending information faster

896
00:42:29,680 --> 00:42:32,600
Speaker 1: than light to the other end. No, there's no rigid stick.

897
00:42:32,719 --> 00:42:35,200
Speaker 1: You push on one end and the pressure wave takes time.

898
00:42:35,280 --> 00:42:37,359
Speaker 1: To reach the other end and to move it. It's

899
00:42:37,400 --> 00:42:39,879
Speaker 1: the same with the train. It's linked together, but it's

900
00:42:39,920 --> 00:42:42,799
Speaker 1: not a rigid object of fixed length. So think about

901
00:42:42,800 --> 00:42:45,560
Speaker 1: the front and the back separately. Now, the super confusing

902
00:42:45,600 --> 00:42:48,960
Speaker 1: thing about this whole length contraction thing is that it's relative,

903
00:42:49,200 --> 00:42:51,760
Speaker 1: just the way time dilation is. People on the ground

904
00:42:51,800 --> 00:42:54,200
Speaker 1: think the train has shrunk, But people on the train,

905
00:42:54,360 --> 00:42:55,879
Speaker 1: and I know you don't want to talk about them,

906
00:42:56,280 --> 00:42:59,040
Speaker 1: they think that distances on the ground have shrunk because

907
00:42:59,080 --> 00:43:02,239
Speaker 1: the ground is moving relative to them. Like, let's say

908
00:43:02,239 --> 00:43:05,359
Speaker 1: they're about to enter a one kilometer long tunnel. I

909
00:43:05,400 --> 00:43:07,399
Speaker 1: see the train as moving and so I see it's

910
00:43:07,400 --> 00:43:09,600
Speaker 1: going to be shorter than the tunnel, whereas the train

911
00:43:09,640 --> 00:43:12,960
Speaker 1: sees the tunnel as shorter. So who's right, Like is

912
00:43:13,000 --> 00:43:15,319
Speaker 1: the train actually going to be in the tunnel or not?

913
00:43:16,040 --> 00:43:19,000
Speaker 1: And we construct these situations to like confront the universe

914
00:43:19,000 --> 00:43:22,360
Speaker 1: and say, like, what's really happening because we imagine that

915
00:43:22,440 --> 00:43:25,160
Speaker 1: the concept of length is absolute, that the train has

916
00:43:25,239 --> 00:43:28,840
Speaker 1: an actual length, right, that something has to happen in

917
00:43:28,880 --> 00:43:30,799
Speaker 1: the universe, and only one thing can happen. You can't

918
00:43:30,800 --> 00:43:35,239
Speaker 1: have like two people seeing conflicting events. So understanding how

919
00:43:35,280 --> 00:43:37,799
Speaker 1: time flows and how time is relative is crucial to

920
00:43:37,880 --> 00:43:41,400
Speaker 1: understanding how both of those things can seem true. That

921
00:43:41,480 --> 00:43:44,000
Speaker 1: somebody on the ground can see the train as shorter

922
00:43:44,160 --> 00:43:46,400
Speaker 1: and fitting in the tunnel, and somebody else on the

923
00:43:46,440 --> 00:43:49,440
Speaker 1: train can see the tunnel as shorter, so the train

924
00:43:49,520 --> 00:43:50,439
Speaker 1: always sticks out.

925
00:43:51,160 --> 00:43:54,480
Speaker 4: Okay, here's this inner and we'll go with your tunnel idea. Okay,

926
00:43:54,560 --> 00:43:57,839
Speaker 4: So I have a train that when it's standing still

927
00:43:57,840 --> 00:43:59,560
Speaker 4: in front of me, I measured it to be a kilometer.

928
00:44:00,000 --> 00:44:02,920
Speaker 4: I build a tunnel that and the tunnels not moving,

929
00:44:02,960 --> 00:44:05,480
Speaker 4: and I measure, and I make the tunnel to be

930
00:44:05,560 --> 00:44:08,439
Speaker 4: one kilometer long, exactly the same length as the train.

931
00:44:08,760 --> 00:44:12,000
Speaker 4: Now I put Juan in at one end of the

932
00:44:12,040 --> 00:44:14,520
Speaker 4: tunnel and Sally at the back of the tunnel. Okay,

933
00:44:14,560 --> 00:44:17,120
Speaker 4: and we synchronize our clocks. Okay. Now I move the

934
00:44:17,160 --> 00:44:19,719
Speaker 4: train and I put it inside the tunnel so that

935
00:44:19,760 --> 00:44:22,320
Speaker 4: it's just it fits perfectly inside the tunnel. Sally and

936
00:44:22,360 --> 00:44:24,319
Speaker 4: Juan measured the train to be a kilometer long.

937
00:44:24,600 --> 00:44:27,120
Speaker 1: Yes, everybody with OCD out there is like, ooh, that's

938
00:44:27,160 --> 00:44:28,280
Speaker 1: so satisfying. It fits.

939
00:44:29,520 --> 00:44:32,960
Speaker 4: Yeah. I think by everybody, you mean all of our listeners.

940
00:44:33,760 --> 00:44:37,080
Speaker 4: If they like the Physics podcast. Now the train leaves

941
00:44:37,120 --> 00:44:41,279
Speaker 4: the tunnel, goes away a few kilometers and then it

942
00:44:41,320 --> 00:44:43,799
Speaker 4: comes back at half of the speed of light. That's

943
00:44:43,840 --> 00:44:47,359
Speaker 4: say and Sally, Juan and I have our clock synchronized.

944
00:44:47,600 --> 00:44:51,840
Speaker 4: The tunnel is zooming pass and we ask want to

945
00:44:51,880 --> 00:44:53,920
Speaker 4: measure when the front of the train passes his spot,

946
00:44:53,960 --> 00:44:56,279
Speaker 4: And we ask Sally when the back of the train

947
00:44:56,280 --> 00:44:58,720
Speaker 4: passes her spot at the other side of the tunnel.

948
00:44:58,800 --> 00:45:01,359
Speaker 4: Are you saying they're going to report the same time,

949
00:45:01,440 --> 00:45:03,200
Speaker 4: because if they report the same time, then I have

950
00:45:03,280 --> 00:45:05,319
Speaker 4: to conclude that the train was a kilometer long.

951
00:45:05,480 --> 00:45:07,680
Speaker 1: No, that's right, They will not measure the same time.

952
00:45:07,800 --> 00:45:10,160
Speaker 1: One at the back of the tunnel will measure a

953
00:45:10,200 --> 00:45:13,040
Speaker 1: time earlier than Sally at the front of the tunnel.

954
00:45:13,120 --> 00:45:16,040
Speaker 1: So according to you, Juan and Sally, who are in

955
00:45:16,080 --> 00:45:19,040
Speaker 1: the tunnel's frame of reference, you will see the whole

956
00:45:19,080 --> 00:45:22,320
Speaker 1: train inside the tunnel that when the back end disappears

957
00:45:22,320 --> 00:45:25,120
Speaker 1: into the tunnel, the front nose has not yet emerged

958
00:45:25,160 --> 00:45:27,200
Speaker 1: from the tunnel and is still one hundred and fifty

959
00:45:27,239 --> 00:45:29,600
Speaker 1: meters from the exit of the tunnel.

960
00:45:29,840 --> 00:45:32,120
Speaker 4: So Sally at the back is going to write down

961
00:45:32,160 --> 00:45:34,120
Speaker 4: her number and they're going to both numbers are not

962
00:45:34,160 --> 00:45:35,040
Speaker 4: going to come back the same.

963
00:45:35,200 --> 00:45:35,640
Speaker 1: That's right.

964
00:45:35,719 --> 00:45:39,560
Speaker 4: Can you explain why, like nobody is moving like Sally Huang,

965
00:45:39,600 --> 00:45:43,000
Speaker 4: they were both staying the same They're the same observer

966
00:45:43,280 --> 00:45:47,000
Speaker 4: in the same frame. Their time was synced. The train

967
00:45:47,160 --> 00:45:50,600
Speaker 4: was physically moving past them. Why did they measure a

968
00:45:50,600 --> 00:45:51,120
Speaker 4: different time.

969
00:45:51,600 --> 00:45:55,760
Speaker 1: Yes, and Juan and Sally are synchronized according to themselves

970
00:45:56,040 --> 00:45:58,680
Speaker 1: and people on the ground, so they think their measurement

971
00:45:58,800 --> 00:46:02,560
Speaker 1: makes sense. It does in their frame. Eight hundred and

972
00:46:02,560 --> 00:46:05,359
Speaker 1: fifty meters is the length of the train, and they

973
00:46:05,440 --> 00:46:07,879
Speaker 1: see the people on the train or measuring the train

974
00:46:07,920 --> 00:46:10,520
Speaker 1: to be a full kilometer longer than the people on

975
00:46:10,520 --> 00:46:13,759
Speaker 1: the ground are measuring. The people on the ground see

976
00:46:13,760 --> 00:46:16,680
Speaker 1: the people on the train making their measurements not at

977
00:46:16,719 --> 00:46:20,720
Speaker 1: the same time, and the reverse is true. On the train.

978
00:46:21,200 --> 00:46:24,560
Speaker 1: People take measurements at whether they think is the same time,

979
00:46:25,160 --> 00:46:27,360
Speaker 1: and they get one kilometer and the people on the

980
00:46:27,400 --> 00:46:29,920
Speaker 1: train think that people on the ground are not syncd

981
00:46:30,040 --> 00:46:33,600
Speaker 1: That's why it's all about the relativity of simultaneity, whether

982
00:46:33,680 --> 00:46:36,799
Speaker 1: you think two things happen at the same time or not.

983
00:46:37,200 --> 00:46:39,960
Speaker 1: And that's what sets up this fun apparent paradox of

984
00:46:40,440 --> 00:46:43,360
Speaker 1: whether the train will fit into a one kilometer tunnel.

985
00:46:43,440 --> 00:46:45,200
Speaker 1: One in Sally in the tunnel when they see it

986
00:46:45,200 --> 00:46:47,120
Speaker 1: moving through, they see it at eight hundred and fifty

987
00:46:47,120 --> 00:46:49,600
Speaker 1: meters long, and so they say, yes, the train fit

988
00:46:49,680 --> 00:46:52,280
Speaker 1: in the tunnel. But you have people on the train.

989
00:46:52,480 --> 00:46:55,279
Speaker 1: They see the tunnel as shorter. They say, no, my

990
00:46:55,440 --> 00:46:58,000
Speaker 1: train is still a kilometer long because the train is

991
00:46:58,040 --> 00:46:59,759
Speaker 1: not moving for them, and so it's still at its

992
00:46:59,760 --> 00:47:02,719
Speaker 1: same original length. But the tunnel is moving, so the

993
00:47:02,760 --> 00:47:05,959
Speaker 1: tunnel is shorter. So they see the train sticking out

994
00:47:06,000 --> 00:47:08,120
Speaker 1: of the tunnel. And in order for special relativity to

995
00:47:08,120 --> 00:47:10,279
Speaker 1: make sense, you have to somehow reconcile these two things,

996
00:47:10,320 --> 00:47:12,640
Speaker 1: like what really happened? Did the train fit in the

997
00:47:12,640 --> 00:47:13,400
Speaker 1: tunnel or not?

998
00:47:13,719 --> 00:47:15,840
Speaker 4: Okay, so how do you reconcile it?

999
00:47:15,920 --> 00:47:17,520
Speaker 1: So it all comes down to time.

1000
00:47:17,680 --> 00:47:17,839
Speaker 13: Right.

1001
00:47:18,000 --> 00:47:20,200
Speaker 1: Remember how we talked about earlier in the episode that

1002
00:47:20,320 --> 00:47:23,520
Speaker 1: time is relative, not just how time flows, but whether

1003
00:47:23,600 --> 00:47:26,920
Speaker 1: two things happen at the same time. That came from

1004
00:47:26,960 --> 00:47:29,400
Speaker 1: the observation that the speed of light is the same

1005
00:47:29,480 --> 00:47:32,840
Speaker 1: for everyone, which means people have to disagree about whether

1006
00:47:32,880 --> 00:47:35,120
Speaker 1: events happen at the same time. The example of the

1007
00:47:35,160 --> 00:47:37,680
Speaker 1: beams of light shooting along the train people see them

1008
00:47:37,760 --> 00:47:39,560
Speaker 1: reaching the front and the back of the same time.

1009
00:47:39,920 --> 00:47:41,960
Speaker 1: People off the train see the light hitting the back

1010
00:47:41,960 --> 00:47:44,200
Speaker 1: of the train first. And the way to reconcile that

1011
00:47:44,480 --> 00:47:46,920
Speaker 1: is to have different times for all those people, for

1012
00:47:47,040 --> 00:47:49,440
Speaker 1: time to flow differently. And that's why it's crucial that

1013
00:47:49,480 --> 00:47:52,799
Speaker 1: we understand the clocks and the synchronization, and that the

1014
00:47:52,840 --> 00:47:54,680
Speaker 1: front to the back of the train be measured at

1015
00:47:54,719 --> 00:47:57,799
Speaker 1: the same time. And the crucial thing is that at

1016
00:47:57,840 --> 00:48:00,360
Speaker 1: the same time is different for people on the train

1017
00:48:00,560 --> 00:48:04,719
Speaker 1: and for people on the ground because moving clocks flow differently. Right,

1018
00:48:04,800 --> 00:48:07,719
Speaker 1: So on the ground, One and Sally are synchronized and

1019
00:48:07,719 --> 00:48:09,680
Speaker 1: they measure the train to be eight hundred and fifty

1020
00:48:09,760 --> 00:48:12,480
Speaker 1: meters long. But to the people on the train, Wan

1021
00:48:12,560 --> 00:48:15,680
Speaker 1: and Sally are not synchronized. Wan and Sally are measuring

1022
00:48:15,719 --> 00:48:17,840
Speaker 1: the front in the back of the train at different times,

1023
00:48:18,000 --> 00:48:20,480
Speaker 1: which is why Wan and Sally think the train is shorter,

1024
00:48:20,880 --> 00:48:23,280
Speaker 1: and the people on the train think that it's not shorter.

1025
00:48:23,520 --> 00:48:25,279
Speaker 1: Because the people on the train think that One and

1026
00:48:25,320 --> 00:48:27,640
Speaker 1: Sally made a mistake. They're like, no, you guys measure

1027
00:48:27,680 --> 00:48:29,759
Speaker 1: the front and back at different times, which is why

1028
00:48:29,800 --> 00:48:31,799
Speaker 1: you're telling me it's eight hundred and fifty meters long

1029
00:48:32,000 --> 00:48:34,960
Speaker 1: when really it's a kilometer. How can it make sense

1030
00:48:35,400 --> 00:48:37,960
Speaker 1: or length to be contracted, because it seems to violate

1031
00:48:38,040 --> 00:48:40,960
Speaker 1: our intuition, like things have a length and they should

1032
00:48:41,000 --> 00:48:43,200
Speaker 1: just have a length. And how is it possible for

1033
00:48:43,480 --> 00:48:46,600
Speaker 1: things to get shorter as they get faster, because that

1034
00:48:46,600 --> 00:48:48,920
Speaker 1: would lead to all sorts of weird paradoxes. It actually

1035
00:48:48,920 --> 00:48:51,960
Speaker 1: can kind of make sense, and these paradoxes aren't paradoxes.

1036
00:48:52,000 --> 00:48:54,120
Speaker 1: They just show you that the world works differently than

1037
00:48:54,120 --> 00:48:58,560
Speaker 1: you imagined. Can it make sense that things moving quickly

1038
00:48:58,840 --> 00:49:02,240
Speaker 1: get shorter? Why doesn't that lead to contradictions?

1039
00:49:02,440 --> 00:49:02,640
Speaker 5: Oh?

1040
00:49:02,920 --> 00:49:05,880
Speaker 4: Not like why does it make sense? But like, why

1041
00:49:05,920 --> 00:49:09,319
Speaker 4: doesn't it lead to contradictions about the universe? Because I

1042
00:49:09,320 --> 00:49:12,479
Speaker 4: think we'd establish it's very hard to make it make sense,

1043
00:49:13,520 --> 00:49:13,799
Speaker 4: but it.

1044
00:49:13,800 --> 00:49:15,640
Speaker 1: Is possible to make it make sense, and it makes

1045
00:49:15,640 --> 00:49:17,520
Speaker 1: sense to me, And I want to share that connection

1046
00:49:17,640 --> 00:49:20,279
Speaker 1: with everybody because it's a wonderful moment when it all

1047
00:49:20,280 --> 00:49:23,160
Speaker 1: clicks together in your head and you realize, oh, it

1048
00:49:23,239 --> 00:49:25,879
Speaker 1: is possible for both people to think the other one

1049
00:49:25,960 --> 00:49:27,799
Speaker 1: is shorter, for the people on the train to think

1050
00:49:27,800 --> 00:49:29,279
Speaker 1: the tunnel is shorter, and for the people in the

1051
00:49:29,280 --> 00:49:31,880
Speaker 1: tunnel to think the train is shorter. Here's the detailed

1052
00:49:31,920 --> 00:49:34,400
Speaker 1: breakdown of what's going on with the train and the tunnel.

1053
00:49:35,000 --> 00:49:37,680
Speaker 1: Here's how it's possible for the team on the ground

1054
00:49:37,920 --> 00:49:41,400
Speaker 1: to see the train totally inside the tunnel, and for

1055
00:49:41,480 --> 00:49:43,719
Speaker 1: the team on the train to see that the train

1056
00:49:43,840 --> 00:49:46,520
Speaker 1: is too long to ever all be in the tunnel

1057
00:49:46,560 --> 00:49:50,000
Speaker 1: at the same time. From the ground point of view,

1058
00:49:50,320 --> 00:49:53,960
Speaker 1: the train is shorter than the tunnel, so when the

1059
00:49:54,000 --> 00:49:56,520
Speaker 1: back end is inside the tunnel, the nose has not

1060
00:49:56,640 --> 00:49:59,799
Speaker 1: yet left the tunnel. Remember that we are comparing two

1061
00:49:59,840 --> 00:50:02,160
Speaker 1: of events front and back of the train at what

1062
00:50:02,280 --> 00:50:04,759
Speaker 1: we consider to be at the same time. But the

1063
00:50:04,760 --> 00:50:07,200
Speaker 1: people on the train think that the ground team is

1064
00:50:07,200 --> 00:50:10,080
Speaker 1: making a mistake and that those events are not actually

1065
00:50:10,120 --> 00:50:12,040
Speaker 1: at the same time. For the people on the train,

1066
00:50:12,280 --> 00:50:14,640
Speaker 1: they think the ground team is comparing the front of

1067
00:50:14,680 --> 00:50:17,600
Speaker 1: the train at an earlier moment to the back of

1068
00:50:17,600 --> 00:50:20,440
Speaker 1: the train at a later moment, which is how the

1069
00:50:20,480 --> 00:50:23,400
Speaker 1: ground team sees the train inside the tunnel. From the

1070
00:50:23,440 --> 00:50:25,560
Speaker 1: point of view of the people on the train, the

1071
00:50:25,640 --> 00:50:27,880
Speaker 1: train is sticking out both ends of the tunnel at

1072
00:50:27,920 --> 00:50:30,440
Speaker 1: the same time. Because the tunnel is shorter. The people

1073
00:50:30,480 --> 00:50:33,120
Speaker 1: on the ground think that's wrong. They think the train

1074
00:50:33,200 --> 00:50:36,520
Speaker 1: team came to that conclusion by comparing an earlier back

1075
00:50:36,600 --> 00:50:39,479
Speaker 1: end measurement when the train tail was still sticking out

1076
00:50:39,600 --> 00:50:42,800
Speaker 1: to a later front end measurement when the train knows

1077
00:50:42,960 --> 00:50:45,319
Speaker 1: is now sticking out. And the key is that they're

1078
00:50:45,360 --> 00:50:48,000
Speaker 1: measuring the fronts and the backs at different times. And

1079
00:50:48,040 --> 00:50:51,080
Speaker 1: it's all because time is relative and simultaneity is different

1080
00:50:51,120 --> 00:50:53,920
Speaker 1: and for people moving at different speeds. And you know,

1081
00:50:53,960 --> 00:50:56,080
Speaker 1: to me, this comes down to like trying to see

1082
00:50:56,480 --> 00:50:59,480
Speaker 1: can special relativity makes sense because it fundamentally changes your

1083
00:50:59,560 --> 00:51:02,279
Speaker 1: understanding of the world. It tells you the world really

1084
00:51:02,280 --> 00:51:04,759
Speaker 1: works in a different way than you imagined, and we

1085
00:51:04,800 --> 00:51:07,480
Speaker 1: want the world to make sense. Like I think back

1086
00:51:07,520 --> 00:51:09,480
Speaker 1: to the first time I ever heard this example of

1087
00:51:09,560 --> 00:51:12,160
Speaker 1: like somebody in a car turning on a flashlight and

1088
00:51:12,200 --> 00:51:14,520
Speaker 1: then hearing that those photons move at the same speed

1089
00:51:14,880 --> 00:51:17,240
Speaker 1: relative to the car as they do relative to the ground,

1090
00:51:17,480 --> 00:51:20,120
Speaker 1: And immediately my brain was like, hold on, red flag.

1091
00:51:20,280 --> 00:51:23,840
Speaker 1: That can't possibly make sense because then, like when do

1092
00:51:23,920 --> 00:51:27,040
Speaker 1: those photons hit a wall or some obstacle. People in

1093
00:51:27,040 --> 00:51:28,960
Speaker 1: the car and people on the ground would disagree about

1094
00:51:29,000 --> 00:51:30,840
Speaker 1: that because they all say the photons are moving at

1095
00:51:30,840 --> 00:51:33,879
Speaker 1: the same speed, but there's different distances involved and all

1096
00:51:33,920 --> 00:51:36,600
Speaker 1: sorts of stuff. And so for me, it's about disentangling

1097
00:51:36,719 --> 00:51:41,000
Speaker 1: these feelings of contradiction, these ways that special relativity violates

1098
00:51:41,000 --> 00:51:43,759
Speaker 1: our intuition. You know, how can it possibly be that

1099
00:51:44,000 --> 00:51:47,919
Speaker 1: both these people make honest measurements which conflict with each other.

1100
00:51:48,120 --> 00:51:50,600
Speaker 1: One of the things I love about special relativity is

1101
00:51:50,640 --> 00:51:53,360
Speaker 1: that it tells you that, like, people can disagree and'll

1102
00:51:53,360 --> 00:51:54,400
Speaker 1: both be correct.

1103
00:51:54,760 --> 00:51:54,920
Speaker 5: You know.

1104
00:51:54,960 --> 00:51:58,480
Speaker 1: That's like the fundamental conclusion of you know, simultaneity, that

1105
00:51:58,600 --> 00:52:00,680
Speaker 1: you know, two people can see different diferent orders of

1106
00:52:00,719 --> 00:52:03,839
Speaker 1: events and both be honest and both be reporting what

1107
00:52:03,920 --> 00:52:06,960
Speaker 1: they see, because the order of events depends on your

1108
00:52:07,000 --> 00:52:10,000
Speaker 1: relative velocity and your location, and there is no single

1109
00:52:10,080 --> 00:52:13,400
Speaker 1: absolute clock or single sense of space and time in

1110
00:52:13,400 --> 00:52:16,319
Speaker 1: the universe. And so people on the ground can see

1111
00:52:16,360 --> 00:52:18,400
Speaker 1: the train fitting in the tunnel, and people on the

1112
00:52:18,440 --> 00:52:20,840
Speaker 1: train can see the train not fitting in the tunnel,

1113
00:52:21,000 --> 00:52:22,240
Speaker 1: and both be correct.

1114
00:52:22,680 --> 00:52:24,640
Speaker 4: Like, it's correct that if I measure the train when

1115
00:52:24,680 --> 00:52:27,319
Speaker 4: it's standing still, it'll fit in the tunnel, And if

1116
00:52:27,320 --> 00:52:29,520
Speaker 4: I measure when it's moving fast, I'm going to measure

1117
00:52:29,560 --> 00:52:31,080
Speaker 4: it being shorter than the tunnel.

1118
00:52:31,440 --> 00:52:34,400
Speaker 1: Yeah, exactly, and the people can see the train fitting

1119
00:52:34,400 --> 00:52:36,880
Speaker 1: in the tunnel because according to them, they're measuring the

1120
00:52:36,880 --> 00:52:38,920
Speaker 1: front and the back of the train at the same time.

1121
00:52:39,640 --> 00:52:42,600
Speaker 1: The people on the train don't see that happening because

1122
00:52:42,640 --> 00:52:44,319
Speaker 1: they think that the people in the tunnel are not

1123
00:52:44,400 --> 00:52:47,000
Speaker 1: measuring it at the same time, because their concept of

1124
00:52:47,040 --> 00:52:50,800
Speaker 1: what the same time means is different than the people

1125
00:52:50,840 --> 00:52:53,160
Speaker 1: on the tunnel. In the end, that's why it all

1126
00:52:53,160 --> 00:52:57,200
Speaker 1: comes down to time. Understanding relative time is crucial because

1127
00:52:57,239 --> 00:52:59,959
Speaker 1: we're talking about a big extended object. It's a kilometer long,

1128
00:53:00,040 --> 00:53:01,840
Speaker 1: so the front in the back are separated by space

1129
00:53:01,880 --> 00:53:05,160
Speaker 1: and separated by time, and how time flows then has

1130
00:53:05,239 --> 00:53:08,600
Speaker 1: to affect your measurement of the length of it, because

1131
00:53:08,600 --> 00:53:11,080
Speaker 1: in the end, measuring length means measuring the front in

1132
00:53:11,120 --> 00:53:12,720
Speaker 1: the back at the same time.

1133
00:53:13,239 --> 00:53:15,920
Speaker 4: Right again, you're answering the different question than, maybe than

1134
00:53:16,000 --> 00:53:16,920
Speaker 4: the one we started with.

1135
00:53:17,320 --> 00:53:20,040
Speaker 1: Yeah, I guess the most direct answer to the question

1136
00:53:20,239 --> 00:53:23,400
Speaker 1: of the episode why do things look shorter is that

1137
00:53:23,400 --> 00:53:25,799
Speaker 1: they always have. We just never noticed. The fact that

1138
00:53:25,800 --> 00:53:29,279
Speaker 1: we ask why is because we've been led astray by

1139
00:53:29,360 --> 00:53:32,920
Speaker 1: our intuition, our unfounded assumption that the world has this

1140
00:53:33,040 --> 00:53:35,799
Speaker 1: property that lengths are absolute and are always the same

1141
00:53:35,800 --> 00:53:38,960
Speaker 1: at any speed. It turns out that's not true, and

1142
00:53:39,000 --> 00:53:41,680
Speaker 1: we can see that it's not true by doing experiments

1143
00:53:41,680 --> 00:53:46,000
Speaker 1: at various speeds, including very high speeds. Things really do shrink.

1144
00:53:46,239 --> 00:53:49,320
Speaker 1: So that explains why we ask the question. Because the

1145
00:53:49,360 --> 00:53:51,680
Speaker 1: way the world works is in contrast with the way

1146
00:53:51,719 --> 00:53:54,799
Speaker 1: our intuition works. Why does the world work that way

1147
00:53:54,920 --> 00:53:58,040
Speaker 1: is the follow up philosophical question. It turns out it

1148
00:53:58,120 --> 00:54:01,080
Speaker 1: has to in order to be consistent with this other thing.

1149
00:54:01,160 --> 00:54:04,520
Speaker 1: We see that the speed of light is constant for everyone.

1150
00:54:04,640 --> 00:54:07,360
Speaker 1: First consequence of the speed of light being constant for

1151
00:54:07,400 --> 00:54:11,200
Speaker 1: everyone is that simultaneity is not universal. People at different

1152
00:54:11,239 --> 00:54:15,399
Speaker 1: speeds disagree about what at the same time means. I

1153
00:54:15,440 --> 00:54:17,600
Speaker 1: think Juan and Sally measure the front and back at

1154
00:54:17,600 --> 00:54:19,600
Speaker 1: the same time, but people on the train don't, so

1155
00:54:19,680 --> 00:54:22,880
Speaker 1: we measure different lengths. And the beauty part, the really

1156
00:54:22,920 --> 00:54:26,000
Speaker 1: gorgeous part, is that this is what makes it all

1157
00:54:26,000 --> 00:54:29,719
Speaker 1: click together. You can have some kind of global understanding

1158
00:54:29,840 --> 00:54:33,680
Speaker 1: of how everyone is seeing things differently because you can see,

1159
00:54:33,719 --> 00:54:36,399
Speaker 1: as we just explained, that people are measuring the train

1160
00:54:36,480 --> 00:54:39,200
Speaker 1: at different times and getting different answers. Eight hundred and

1161
00:54:39,239 --> 00:54:42,160
Speaker 1: fifty meters or one kilometer. They all get different answers,

1162
00:54:42,200 --> 00:54:46,040
Speaker 1: and they are all right because they are measuring different things.

1163
00:54:46,560 --> 00:54:49,640
Speaker 1: Length at rest means something different than length in motion

1164
00:54:50,000 --> 00:54:52,600
Speaker 1: because it depends on sinking measurements at the front and

1165
00:54:52,640 --> 00:54:55,440
Speaker 1: the back of the train. Length is not absolute, and

1166
00:54:55,480 --> 00:54:58,319
Speaker 1: it can't be from the world who makes sense at

1167
00:54:58,400 --> 00:55:01,600
Speaker 1: high speeds, it has to be relative for everything to

1168
00:55:01,640 --> 00:55:02,400
Speaker 1: be coherent.

1169
00:55:02,960 --> 00:55:05,680
Speaker 4: Like to us du Juan and Sally, the train really

1170
00:55:05,719 --> 00:55:08,040
Speaker 4: did shrink, I think, is what you're saying. Like the

1171
00:55:08,080 --> 00:55:12,239
Speaker 4: space that comprises the train, that the space that the

1172
00:55:12,280 --> 00:55:15,879
Speaker 4: train sits in that is moving with the train, it contracted,

1173
00:55:16,239 --> 00:55:17,600
Speaker 4: It got smaller.

1174
00:55:17,239 --> 00:55:20,000
Speaker 1: It got smaller for want In, Sally, for Juan.

1175
00:55:19,760 --> 00:55:22,160
Speaker 4: And Sali, And that's just the way it is. Space

1176
00:55:22,280 --> 00:55:25,000
Speaker 4: is contracted and it's all due to the speed limit

1177
00:55:25,040 --> 00:55:28,280
Speaker 4: of the universe. Because if it didn't, that space didn't contract,

1178
00:55:28,360 --> 00:55:29,879
Speaker 4: then things would sort of break down.

1179
00:55:29,960 --> 00:55:32,080
Speaker 1: Yeah, if length doesn't contract, then you break all the

1180
00:55:32,160 --> 00:55:34,680
Speaker 1: rules of special relativity. Another way to think about it

1181
00:55:34,719 --> 00:55:37,800
Speaker 1: is that length contraction is sort of the same thing

1182
00:55:38,200 --> 00:55:41,760
Speaker 1: as time dilation. For a completely separate example that helps

1183
00:55:41,760 --> 00:55:45,000
Speaker 1: people understand the link between length contraction, which we've been

1184
00:55:45,040 --> 00:55:47,640
Speaker 1: talking about today and time dilation. Think about what happens

1185
00:55:47,680 --> 00:55:49,960
Speaker 1: if you try to travel to a distant star at

1186
00:55:50,000 --> 00:55:52,439
Speaker 1: a really high speed, Say you need to get ten

1187
00:55:52,560 --> 00:55:55,200
Speaker 1: light years away, and you travel at ninety eight percent

1188
00:55:55,239 --> 00:55:57,319
Speaker 1: of the speed of light. From the point of view

1189
00:55:57,360 --> 00:55:59,560
Speaker 1: of people on Earth you left behind, it takes you

1190
00:55:59,640 --> 00:56:02,640
Speaker 1: almost ten years to get there. But they also see

1191
00:56:02,680 --> 00:56:06,399
Speaker 1: your clock running slowly. They see that for you, it's

1192
00:56:06,440 --> 00:56:09,960
Speaker 1: only been two years. That's time dilation, right, But look

1193
00:56:10,000 --> 00:56:11,960
Speaker 1: at it from the other point of view, from the ship,

1194
00:56:12,280 --> 00:56:14,960
Speaker 1: from the pilot's point of view, the distance star is

1195
00:56:15,000 --> 00:56:17,640
Speaker 1: moving towards her at ninety eight percent of the speed

1196
00:56:17,640 --> 00:56:20,320
Speaker 1: of light, So the distance to the star is shorter

1197
00:56:20,440 --> 00:56:22,480
Speaker 1: than ten light years, and it only takes her about

1198
00:56:22,520 --> 00:56:24,640
Speaker 1: two years to get there because it's only about two

1199
00:56:24,719 --> 00:56:28,120
Speaker 1: light years for her, So she experiences two years to

1200
00:56:28,160 --> 00:56:32,040
Speaker 1: get there because the length was shortened. What's really happening, Well,

1201
00:56:32,160 --> 00:56:35,359
Speaker 1: length contraction is just really another way to look at

1202
00:56:35,520 --> 00:56:39,040
Speaker 1: time dilation, and in the end, it's all about time.

1203
00:56:39,440 --> 00:56:42,839
Speaker 4: I think. Basically, you're saying that the train track to Sally.

1204
00:56:42,600 --> 00:56:46,399
Speaker 1: And perspective, Yeah, and it's all connected to time. And

1205
00:56:46,440 --> 00:56:49,239
Speaker 1: in the end, time dilation and length contraction are really

1206
00:56:49,320 --> 00:56:51,240
Speaker 1: just two different ways to see the same effect.

1207
00:56:51,560 --> 00:56:55,040
Speaker 4: All right, Well again, special relativity is hard.

1208
00:56:54,920 --> 00:56:56,680
Speaker 1: Especially in an audio format. For those of you who

1209
00:56:56,719 --> 00:56:58,640
Speaker 1: like learning visually. I don't know why you're listening to

1210
00:56:58,640 --> 00:56:59,680
Speaker 1: a podcast.

1211
00:56:59,280 --> 00:57:02,080
Speaker 4: But we're glad that you are. Let's make that clear.

1212
00:57:02,400 --> 00:57:04,120
Speaker 4: We're not saying go watch YouTube.

1213
00:57:05,560 --> 00:57:07,160
Speaker 1: But if you do want to learn more about this stuff,

1214
00:57:07,160 --> 00:57:09,560
Speaker 1: look up space time diagrams. They're really helpful.

1215
00:57:09,800 --> 00:57:14,080
Speaker 4: It's interesting, though, to think about how valuable the universe is, right,

1216
00:57:14,239 --> 00:57:17,120
Speaker 4: like the idea that the train would shrink just because

1217
00:57:17,120 --> 00:57:18,760
Speaker 4: it's going fast. It's kind of weird.

1218
00:57:18,920 --> 00:57:21,680
Speaker 1: It is very weird. Yeah, And it's weird that it

1219
00:57:21,720 --> 00:57:24,040
Speaker 1: makes sense in the end that the universe is just

1220
00:57:24,080 --> 00:57:26,120
Speaker 1: so different from the way we imagined it. But you know,

1221
00:57:26,160 --> 00:57:28,560
Speaker 1: that's the project of physics is not to just accept

1222
00:57:28,560 --> 00:57:31,760
Speaker 1: our intuitions, but to confront them with data and information

1223
00:57:31,920 --> 00:57:34,120
Speaker 1: and say, how can we make sense of all this?

1224
00:57:34,200 --> 00:57:37,360
Speaker 1: What story can we tell about the universe that ties

1225
00:57:37,360 --> 00:57:38,000
Speaker 1: it all together?

1226
00:57:38,160 --> 00:57:39,760
Speaker 4: All Right? The next time I take a train and

1227
00:57:39,760 --> 00:57:42,360
Speaker 4: I'm going to be thinking about this, like, am I

1228
00:57:42,440 --> 00:57:43,800
Speaker 4: thinner or am I shorter?

1229
00:57:45,080 --> 00:57:46,800
Speaker 1: Depends if you're lying down or standing up?

1230
00:57:46,880 --> 00:57:49,120
Speaker 4: Yeah, exactly right. So I should stand up on the

1231
00:57:49,160 --> 00:57:50,200
Speaker 4: train the whole time.

1232
00:57:50,720 --> 00:57:52,520
Speaker 1: Don't forget to buy tickets for Juan and Sally.

1233
00:57:52,640 --> 00:57:55,400
Speaker 4: Yeah, and don't forget to tip the conductor too, with

1234
00:57:55,520 --> 00:57:57,280
Speaker 4: a big fat envelope of money.

1235
00:57:58,800 --> 00:58:00,360
Speaker 1: No tip contractions here please.

1236
00:58:00,560 --> 00:58:02,640
Speaker 4: All right, Well, we hope you enjoyed that. Thanks for

1237
00:58:02,720 --> 00:58:04,840
Speaker 4: joining us, see you next time.

1238
00:58:12,600 --> 00:58:15,400
Speaker 1: Thanks for listening, and remember that Daniel and Jorge Explain

1239
00:58:15,480 --> 00:58:19,480
Speaker 1: the Universe is a production of iHeartRadio. For more podcasts

1240
00:58:19,480 --> 00:58:24,120
Speaker 1: from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever

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