Speaker 1: Hey, Daniel, how long does it take you to do
Speaker 1: the research for one of these episodes?
Speaker 2: You know, it used to take me quite a while,
Speaker 2: but I'm getting quicker at it.
Speaker 1: Mmmm. Is that because time passes more quickly as you
Speaker 1: get older, like a special relativity thing?
Speaker 2: Maybe? Or I guess I've just gotten more efficient at
Speaker 2: the preparation.
Speaker 1: Oh, yeah, like you can read faster, or you can
Speaker 1: process information better.
Speaker 2: No, I think I just developed a better mental whorehe
Speaker 2: simulator that can predict what you might be interested in
Speaker 2: or what you might not be interested in.
Speaker 1: Oh, it sounds like you just need like an AI
Speaker 1: version of me. Then I don't even need to be here.
Speaker 2: It's not artificial intelligence. It's natural.
Speaker 1: It's a cartoonist intelligence. Well, I guess you know. It
Speaker 1: kind of depends. You know, what's interesting is kind of relative,
Speaker 1: isn't it.
Speaker 2: Yeah, that's right. What's especially interesting is kind of relative,
Speaker 2: So I guess it kind of it is all special relativity.
Speaker 1: Yeah, I definitely have some special relatives. Did you predict
Speaker 1: I was going to say that.
Speaker 2: I predicted you were going to say something hilarious. Hi.
Speaker 1: I'm Jorge mc cartoonist and the author of Oliver's great,
Speaker 1: big Universe.
Speaker 2: Hi. I'm Daniel. I'm a particle physicist and a professor
Speaker 2: at UC Irvine, and I'm still training my brain to
Speaker 2: understand the universe.
Speaker 1: Wait, don't you need to know how the universe works
Speaker 1: before you can train your brain to understand it.
Speaker 2: We can do two things at once. We can try
Speaker 2: to figure out how the universe works, and we can
Speaker 2: try to wrap our minds around the bits that we
Speaker 2: have figured out and try to gain some intuition for
Speaker 2: all this craziness.
Speaker 1: I feel like this podcast is a little bit of
Speaker 1: training into like how to think about the universe, how
Speaker 1: to explore it, how to ask questions about it. Should
Speaker 1: we be charging tuition?
Speaker 2: We're just sharing the love, you know. But you're right
Speaker 2: because most of our modern theories or physics are expressed
Speaker 2: in a kind of inaccessible language mathematical equations that do
Speaker 2: show us the relationship between bits and pieces and allow
Speaker 2: us to make predictions and stuff. But it's not always
Speaker 2: the way our brains work. So one of the goals
Speaker 2: on this podcast is to break it down and give
Speaker 2: you an intuitive understanding, to try to make it all
Speaker 2: make sense to you.
Speaker 1: Yeah, I guess. We offer free intuition, but not at
Speaker 1: a cost of free tuition.
Speaker 2: No tuition intuition. That should have been the title of
Speaker 2: the podcast.
Speaker 1: Yeah, hopefully it all comes to fruition.
Speaker 2: But I mean, you're welcome to pay tuition if you like,
Speaker 2: send us gold coins or dollars if the inspiration strikes you.
Speaker 1: You take tips. You have a tip jar in your classroom.
Speaker 2: I don't have a tip jar, but I did once
Speaker 2: walk into a classroom and find an envelope with thousands
Speaker 2: of dollars in it.
Speaker 1: Oh, WHOA, where is your university.
Speaker 2: It's a public university, man, So it's not like some
Speaker 2: students just like dropped a pile of cash. I think
Speaker 2: it must have been some club organizing in the room
Speaker 2: before us or something. Hmmmm.
Speaker 1: Sounds like maybe they were trying to bribe you.
Speaker 2: I don't think so. I think somebody must have panicked
Speaker 2: when they realized they left it behind.
Speaker 1: Or could have been a tip. I don't know. You
Speaker 1: could have just assumed it was a tip.
Speaker 2: I'm not so cheaply bought.
Speaker 1: But anyways, welcome to our podcast. Daniel and Jorge Explain
Speaker 1: the Universe, a production of iHeartRadio.
Speaker 2: In which we use our inspiration to improve your intuition
Speaker 2: for absolutely no tuition, whether or not the jokes come
Speaker 2: to any fruition.
Speaker 1: That's right, because it is an amazing universe for us
Speaker 1: to ask questions about and to explore and to learn
Speaker 1: about how it all works.
Speaker 2: And part of the process of doing physics is not
Speaker 2: just writing down on some sheet of paper a bunch
Speaker 2: of math and then gesturing at and saying, trust us,
Speaker 2: this works. It's about understanding. In the end, physics and
Speaker 2: all of science is motivated by our curiosity, our desire
Speaker 2: to understand, and that means translating all of this stuff,
Speaker 2: everything we've learned, back into something that makes sense to us,
Speaker 2: that clicks together in our minds, and we go, oh, well,
Speaker 2: that's kind of weird, but I guess it does make sense. Yeah.
Speaker 1: Plus, I don't know if I trust you anymore. I mean,
Speaker 1: now that I know you're open to bribery.
Speaker 2: I did say I was opening bribery. You said I
Speaker 2: was opening bribery, and I said I.
Speaker 1: Wasn't it sounds like you're open to tips quote unquote tips.
Speaker 2: People are welcome to send us donations to the podcast,
Speaker 2: but it's not going to affect how I grade in
Speaker 2: my class. Now I turned that stack of cash over
Speaker 2: to the campus police.
Speaker 1: Oh wow, are saying you tip the police.
Speaker 2: I don't know what they did with it, but I
Speaker 2: can only assume that they did something responsible.
Speaker 1: But yeah, this university needs to depend on your point
Speaker 1: of view and also how fast you're.
Speaker 2: Going, because something we've learned over the last hundred years
Speaker 2: is that our ancient intuition for how things work doesn't
Speaker 2: always work. It only works in the special cases that
Speaker 2: us and our ancestors got to see things moving pretty slowly.
Speaker 2: And when you take those rules and try to extrapolate
Speaker 2: them up to things moving really, really quickly, you find
Speaker 2: they just don't work anymore. You need a new set
Speaker 2: of rules, and those rules give us weird new insights
Speaker 2: into the actual nature of space and time.
Speaker 1: Yeah, over eight hundred years ago, Einstein discovered something called
Speaker 1: special relativity.
Speaker 2: Einstein developed special and general relativity. That's absolutely true. I
Speaker 2: don't know if he invented it or discovered it, he
Speaker 2: certainly uses it to describe the universe that we see
Speaker 2: around us.
Speaker 1: Yeah. Over a one hundred years hegol Einstein discovered something
Speaker 1: called relativity special in general, in which he discovered that
Speaker 1: things don't always look the same in this universe. Sometimes
Speaker 1: it sort of depends on your relative point of view.
Speaker 2: Yeah, Einstein really shook the foundations of our understanding of reality.
Speaker 2: Newton gave us this idea of space and time as
Speaker 2: being absolute, like the fixed backdrop of the universe, but
Speaker 2: Einstein showed us that space is relative and so is time,
Speaker 2: and it leads to all sorts of bizarre effects. Clock sprunning, slower,
Speaker 2: meter sticks looking shorter, and information disappearing into black holes.
Speaker 1: Yeah, it kind of seems sometimes that the universe has
Speaker 1: these paradoxes and these contradictions, but actually it all sort
Speaker 1: of works if you dig into the math, right, It
Speaker 1: all does actually make sense in the end. It's just
Speaker 1: a different kind of sense. So today on the podcast,
Speaker 1: we'll be tackling the question why do moving objects look shorter?
Speaker 1: I guess moving objects look shorter.
Speaker 2: This is not like how your bank account seems to
Speaker 2: shrink when you're on a trip, you know, or on vacation.
Speaker 2: This is the effect commonly known as length contraction, that
Speaker 2: things going super duper fast relative to you seem to
Speaker 2: look shorter than they do when they're at rest.
Speaker 1: That's one of the consequences of having a speed limit
Speaker 1: in the universe, isn't it.
Speaker 2: Absolutely. It's one of the consequences of special relativity, which
Speaker 2: starts from the postulates if there's a speed limit to
Speaker 2: the universe and that light always moves at the speed
Speaker 2: of life for everybody, regardless of who they are and
Speaker 2: how fast they're going. Out of that comes all sorts
Speaker 2: of weird changes we have to make to space and
Speaker 2: time and velocity in order to make things still make sense.
Speaker 1: And so On the podcast here we've talked about how
Speaker 1: as you're moving at close to the speed of lighter
Speaker 1: moving near really massive objects, time slows down. We've talked
Speaker 1: about that quite a bit, right, Yeah, moving clocks run slow.
Speaker 1: So if you see a clock moving past you at
Speaker 1: half the speed of light, then you will see a
Speaker 1: tick slower than a clock you are holding. That's time dilation,
Speaker 1: a concept we've talked about lots and lots of times, right.
Speaker 1: And then there's the idea that it's not only time
Speaker 1: that can sort of stretch and change, it's also distances
Speaker 1: or the lengths of things.
Speaker 2: Yeah, if you are traveling really really fast, then distances
Speaker 2: in front of you seem shorter, like if you're flying
Speaker 2: between here and Jupiter, and you're moving really really fast,
Speaker 2: then the distance between here and Jupiter seems to shrink.
Speaker 1: So like, if there was a giant meter stick between
Speaker 1: here and Jupiter, and I was moving towards Jupiter really
Speaker 1: really fast, then that meter stick would look shorter than
Speaker 1: it actually is to me.
Speaker 2: It would look shorter to you, but there is no
Speaker 2: what it actually is. There's just a lot of different
Speaker 2: viewpoints on it. It's all relative.
Speaker 1: Well, I guess what it would look like if you
Speaker 1: were not moving relative to the stick exactly.
Speaker 2: Yeah, And that's what we call the proper length.
Speaker 1: In that case, I'm moving really fast, it's not the
Speaker 1: meter stick, or is it the same thing.
Speaker 2: It's exactly the same thing. The meter stick would say
Speaker 2: you look shorter, and you would say the meter stick
Speaker 2: looks shorter. The whole effect is symmetric, same way the
Speaker 2: time valation is symmetric. If I think you're moving fast,
Speaker 2: I see your clock running slow, but you also see
Speaker 2: me moving quickly, so you see my clock running slow.
Speaker 1: But I guess, doesn't it depend on which direction this
Speaker 1: ruler is flying. Like if the ruler is flying let's
Speaker 1: say away for me really fast, it would look shorter.
Speaker 1: But what if it's moving, like from I see, moving
Speaker 1: from my left to my right, would it still look shorter?
Speaker 2: It would look thinner. In that case, the direction it's
Speaker 2: moving relative to you is the direction that gets contracted.
Speaker 2: If it's always moving along its length, then it's going
Speaker 2: to look shorter, even if that length is point. Did
Speaker 2: it along X or along y or along zo or
Speaker 2: in any direction? If it's moving along its length, it's
Speaker 2: going to look shorter.
Speaker 1: I see. So like if someone launched a ruler really
Speaker 1: really fast from my left and my right, it would
Speaker 1: seem shorter than it would if I just held it
Speaker 1: in my hand.
Speaker 2: That's exactly right.
Speaker 1: Yeah, so then the question for today is why does
Speaker 1: that happen? All right? Well, as usual, we were wondering
Speaker 1: how many people out there had thought about this question
Speaker 1: or wonder why things look shorter when they're moving really fast.
Speaker 2: Thanks very much to everybody who answers these questions. We
Speaker 2: love hearing your voices, and we'd love to hear more
Speaker 2: of your voices, So please don't be shy and write
Speaker 2: to us two questions at Danielandhorge dot com.
Speaker 1: So think about it for a second. Why do you
Speaker 1: think moving objects look shorter. Here's what people have to say.
Speaker 1: The Doppler effect is that what it's called the red
Speaker 1: shifting thing.
Speaker 2: So like, basically when the object, the object comes closer
Speaker 2: to you, like I guess, like, it looks like the
Speaker 2: wavelengths wavelengths shorten, right, they get shorter. So like all objects,
Speaker 2: you know, they get a little louder, the colors are a
Speaker 2: little brighter, the wavelengths shorten, and so the object look
Speaker 2: shorter because the wavelengths of the colors of the object
Speaker 2: is shorter.
Speaker 3: Yeah, that's why.
Speaker 4: I think they look shorter, just due to the fact
Speaker 4: that it's more for our brain to process, you know,
Speaker 4: as opposed to if an object was sitting still, and
Speaker 4: then obviously when there's more to interpret, that obviously creates
Speaker 4: more of a margin of error with our perception.
Speaker 5: I would assume that the reason that objects appear shorter,
Speaker 5: especially as they approach light speed, is time and space dilation.
Speaker 5: So as it approaches light speed, it would just appear
Speaker 5: to shrink. Not really sure.
Speaker 3: I think that for a human eye optics, moving objects
Speaker 3: look actually longer because of motion blur, but special relative
Speaker 3: to states that moving objects get shorter, don't exactly remember why.
Speaker 4: Moving objects look shorter because the back has gotten closer
Speaker 4: to where the front was when you saw it by
Speaker 4: the time you see the back.
Speaker 1: All right, Lots of interesting answers.
Speaker 2: Here, very creative answers today, but.
Speaker 1: They also sound very sciensy talking about Doppler effects and
Speaker 1: red shifting and space dilation.
Speaker 2: Yeah, motion blur. Some of these answers are way off
Speaker 2: and some of them are pretty close.
Speaker 1: Pretty cool. These are people that you found in your
Speaker 1: department or people on the internet.
Speaker 2: These are just folks from the internet listeners to this podcast.
Speaker 1: Nice, Well, let's dig into it. Daniel, how what is
Speaker 1: the physicist definition of length dilation?
Speaker 2: So we usually call it length contraction.
Speaker 1: Wait is there a difference? Can you also have that
Speaker 1: length dilation or is it only contract.
Speaker 2: You can only have length contraction. The longest something can
Speaker 2: be is if it's at rest relative to you. So
Speaker 2: you're holding a meter stick, that's the longest you're ever
Speaker 2: going to measure that meter stick to be that meterstick
Speaker 2: is moving past you at a certain speed, then you're
Speaker 2: going to see it shorter. And the way I like
Speaker 2: to phrase it to be very clear to make sure
Speaker 2: it's relative, is that moving objects look shorter.
Speaker 1: And if they're moving like away from you or towards you,
Speaker 1: it still gets shorter.
Speaker 2: They still get shorter. Yeah, that doesn't make any difference.
Speaker 2: In the same way that like moving clocks run slow
Speaker 2: tells you that you are seeing that clock run slow
Speaker 2: because you see it moving and it sees you moving,
Speaker 2: so it sees you running slow. In the same way
Speaker 2: you see a meter stick moving, you see it looking shorter.
Speaker 2: It also sees you looking shorter because it sees you moving.
Speaker 2: It's a symmetric effect.
Speaker 1: All right, I was wrong. Well is the This is
Speaker 1: the definition of the length contraction.
Speaker 2: So it's just that moving objects look shorter. You define
Speaker 2: the proper length of something to be its length when
Speaker 2: it's not moving. So you're holding the meterstick, you call
Speaker 2: that the proper length. Then you zoom that meterstick by
Speaker 2: you at like ten percent of the speed of light,
Speaker 2: which doesn't sound impressive, but it's super duper crazy fast.
Speaker 2: Then you'll see it a little bit shorter. You'll see
Speaker 2: it like a half a percent shorter. You speed it
Speaker 2: up to like half the speed of light, and you'll
Speaker 2: see it be like only eighty five percent of its
Speaker 2: proper length length. And as you get up to like
Speaker 2: ninety nine percent of the speed of light, it'll shrink
Speaker 2: down to like fifteen percent of its proper length. If
Speaker 2: you get to like ninety nine point ninety nine percent
Speaker 2: of the speed of light, it'll be just over one
Speaker 2: percent of its proper length. So you can see things
Speaker 2: getting like super duper short as they get super duper
Speaker 2: fast relative to you.
Speaker 1: I guess I'm wondering what it means to see something
Speaker 1: like that moving that fast. You mean, like if I
Speaker 1: take a picture of it, Like, let's say a ruler
Speaker 1: is zooming by really quickly, buy me from my left
Speaker 1: to my right, and I take a picture of it
Speaker 1: as it's going in front of me. In the picture,
Speaker 1: it's going to seem shorter than it would if I
Speaker 1: held the ruler in my hand.
Speaker 2: It's great that you asked that question, because we have
Speaker 2: to be very specific about what we mean here by
Speaker 2: these measurements, because it makes a difference. And actually, if
Speaker 2: you take a picture, you would see the ruler looking
Speaker 2: weirdly longer because the picture captures all the photons that
Speaker 2: are arriving at you at one moment, and that includes
Speaker 2: another effect, which is that it takes time for the
Speaker 2: infram to get to you, and part of the ruler
Speaker 2: is further from you, and part of the rulers closer
Speaker 2: to you. So that combines two different effects. One is
Speaker 2: that the ruler looks shorter because it's moving faster, and
Speaker 2: the other one at the back of the ruler is
Speaker 2: further from you, so it takes light longer to get
Speaker 2: to you.
Speaker 1: No, now, but if the ruler is moving from my
Speaker 1: left to my right, like it's zooming past me like
Speaker 1: a train would like if I'm standing then next to
Speaker 1: some train tracks and I see the train going from
Speaker 1: my left to my right, and I take a picture
Speaker 1: of the train as it's passing by in front of me.
Speaker 1: Is that draining It seemed shorter in the picture or
Speaker 1: the same length or longer.
Speaker 2: Again, the picture combines two different effects. One is a
Speaker 2: special relativity effect and the other is the very normal
Speaker 2: light takes time to travel effect. And so usually what
Speaker 2: we do is not use the idea of a mental picture,
Speaker 2: but imagine that we have like a bunch of assistants
Speaker 2: all spread out to our left and to our right,
Speaker 2: and they mark like when the train front or when
Speaker 2: the train back passes them, and then we can use
Speaker 2: the distance between the train front and the train back
Speaker 2: to say how long.
Speaker 1: It is h what happens in the picture case, like
Speaker 1: what if I take a picture of the train or
Speaker 1: the ruler moving from my left and my right, Like,
Speaker 1: aren't all those photons leaving the stick at the same time,
Speaker 1: and so then it would arrive at the camera or
Speaker 1: my eye at the same time.
Speaker 2: They're leaving the train or the stick at the same time.
Speaker 2: The stick has length, so it takes longer for the
Speaker 2: back end photons to reach you than the front end photons.
Speaker 2: And I think combining photon travel time and actual length
Speaker 2: combines two different complicated things which are kind of hard
Speaker 2: to hold in your head at the same time. So
Speaker 2: usually when we talk about special relativity, we assume that
Speaker 2: we can take care of the photon travel time and
Speaker 2: say that we have a bunch of assistants all through
Speaker 2: the universe, all making measurements and take local data, and
Speaker 2: then we combine that information later to figure out what happened.
Speaker 2: So we take away this effect of photons take time
Speaker 2: to get somewhere because it adds another confusing layer.
Speaker 1: But I guess I mean we're saying that things look shorter, right,
Speaker 1: and your eye sort of look acts like a camera.
Speaker 1: Are you saying that, like, maybe what you mean by
Speaker 1: looking at something it's not quite the same, but as
Speaker 1: what everyday person might mean by looking at something.
Speaker 2: Yeah, I think that's fair. When we do physics experiments,
Speaker 2: we're very careful about how we make those measurements. So really,
Speaker 2: what we mean here is if we take a very
Speaker 2: careful measurement of the length of the object, we will
Speaker 2: measure it to be shorter than if it was stationary.
Speaker 1: All right, well, I think we just should just be
Speaker 1: kind of clear about what we mean by things looking shorter.
Speaker 2: What we mean is that we make a careful measurement
Speaker 2: of the length of this thing involving us and a
Speaker 2: bunch of assistants all along, like the track of a
Speaker 2: train and noting when it passes by. And then later
Speaker 2: we get together and we compare our measurements and we say,
Speaker 2: you know, Juan measured the back of the train at
Speaker 2: this time, and Sally measured the front of the train
Speaker 2: at that time, and then we can use that to
Speaker 2: figure out how long the train was.
Speaker 1: All right, it sounds like we need to dig into
Speaker 1: this scenario of you and all of your assistance and
Speaker 1: how they're measuring the length of this ruler and or
Speaker 1: this train. Maybe really understand what we mean by things
Speaker 1: looking shorter or not. So let's dig into these details.
Speaker 1: But first let's take a quick break. All right, we're
Speaker 1: talking about length contraction due to special relativity, and that
Speaker 1: doesn't have to do with how long this podcast is,
Speaker 1: right or how much my questions dilate the length of
Speaker 1: the running time of this episode.
Speaker 2: That's exactly what I was going to say. Yeah, no,
Speaker 2: but it's good. It's important we explain exactly what we
Speaker 2: mean and we not use jargon. So let's hash it
Speaker 2: out because there's some really interesting, like apparent paradoxes that
Speaker 2: come up when we try to measure these lengths really carefully.
Speaker 1: Okay, so we're asking the question why the moving objects
Speaker 1: look shorter, and it seems like we're not really asking
Speaker 1: the question why they look shorter. It's more like why
Speaker 1: when a bunch of physicists try to measure something moving fast,
Speaker 1: they measure things to be shorter. Not really because the
Speaker 1: idea of looking at it you're saying, convolutes several things.
Speaker 2: Yeah, I would say, I guess that's how physicists look
Speaker 2: at something. Right, don't just take a picture. We think
Speaker 2: about what that picture is actually measuring and realizing pictures
Speaker 2: are not the best way to measure the length of
Speaker 2: something moving really really fast. And said, we hire a
Speaker 2: bunch of assistants and lay them out in a line
Speaker 2: so we can take measurements and figure out how long
Speaker 2: that thing really is.
Speaker 1: Okay, so then let's maybe paint that scenario. I'm sitting
Speaker 1: by some train tracks, and the train tracks go from
Speaker 1: my left to my right in front of me, and
Speaker 1: now there's going to be a train passing by. I
Speaker 1: want to measure how long the train is. Yeah, and
Speaker 1: you're saying, don't take a picture of it because the
Speaker 1: picture might lie to you. You're saying, hire a bunch
Speaker 1: of people, and then, now what's your scenario.
Speaker 2: What's your setup here with your assistance. So I have
Speaker 2: a bunch of people to my left and a bunch
Speaker 2: of people to my right.
Speaker 1: Like you space them out every ten meters.
Speaker 2: Or something, and we all have a bunch of clocks,
Speaker 2: and we synchronize our clocks. So they all started zero
Speaker 2: at the same moment, and they all read ten seconds
Speaker 2: at the same moment. They all read one hundred seconds
Speaker 2: at the same moment. So we have a bunch of
Speaker 2: people now a different locationations with synchronized clocks.
Speaker 1: How do you synchronize a clock. Wouldn't you run into
Speaker 1: special relativity problems sinking those clocks?
Speaker 2: It's complicated, but you can sink clocks using flashes of light.
Speaker 2: If you assume you know how long it takes light
Speaker 2: to get somewhere, you can synchronize clocks that are distanced.
Speaker 3: Mm.
Speaker 1: Okay, So then each of these systet has a clock
Speaker 1: that's synchronized to yours.
Speaker 2: Right exactly, now the train is passing by us, and
Speaker 2: ask people to write down what time the front or
Speaker 2: the back of the train passed them.
Speaker 1: Which one the front or the back.
Speaker 2: You can have them write down both. And then in
Speaker 2: order to measure the length of the train, what you
Speaker 2: need to do is get a measurement of where the
Speaker 2: back of the train was and where the front of
Speaker 2: the train was at the same time. You combine those
Speaker 2: two numbers and that's your length.
Speaker 1: See it again, You measure where the front and the
Speaker 1: back were at the same time.
Speaker 2: Yeah, you want to know how long something is, Then
Speaker 2: you want to know where's the front and where's the back.
Speaker 2: And you want to take those measurements at the same moment.
Speaker 5: Right.
Speaker 2: If you don't take those measurements at the same moment,
Speaker 2: you're not going to get the length of the train.
Speaker 2: Like if a parade is passing by you, it's moving, right,
Speaker 2: If you measure the front and the back at different moments,
Speaker 2: you're not going to get the actual length of the parade.
Speaker 1: I see, all right, So then you ask your assistance
Speaker 1: to write down when they saw the front of the train,
Speaker 1: when they saw the back of the train. And then
Speaker 1: what do you do. You get together and you have
Speaker 1: a picnic, You.
Speaker 2: Get together, you spend some of that tip money on
Speaker 2: you know, ice sculptures and chocolates for your picnic and whatever.
Speaker 2: And then you look at the numbers and you say,
Speaker 2: all right, one measured the back of the train to
Speaker 2: be negative half a kilometer at the same time Sally
Speaker 2: measured the front of the train to be at a
Speaker 2: location plus half a kilometer, And so, okay, the train
Speaker 2: is one kilometer long because the front and the back
Speaker 2: were one kilometer apart at the same time.
Speaker 1: Oh okay, yeah, yeah, I'm following. I'm following. So now
Speaker 1: like you sort of ask, okay, t equals one minute.
Speaker 1: Where did your assistants measure the front of the train
Speaker 1: and where did they measure the back of the train,
Speaker 1: and then that should tell you the length of the train.
Speaker 2: That should tell you the length of train. And if
Speaker 2: you measure them at different times, like if one's clock
Speaker 2: was out of sync, or one was lazy, or one
Speaker 2: made a mistake or something in a measure of the
Speaker 2: back of the train earlier or later, then we'd get
Speaker 2: the wrong answer for the length of the train. It's
Speaker 2: crucial that you measure the front in the back at
Speaker 2: the same time. It seems sort of obvious to even
Speaker 2: spell that out, sort of dumb, like, duh, that's what
Speaker 2: length really is. But it's going to turn out to
Speaker 2: be really important part of understanding length contraction.
Speaker 1: Okay, So I guess that's one way to measure it,
Speaker 1: or is that the only way to measure the train?
Speaker 2: And that's sort of the standard setup. It allows you
Speaker 2: to avoid things like how longs they take informations, travel
Speaker 2: from here to there, and all that sort of stuff.
Speaker 2: I suppose you could come up with other techniques as well.
Speaker 1: All right, so now you get together and you measure
Speaker 1: the train, and you're saying the number you get from
Speaker 1: this setup is not the same as if the train
Speaker 1: was not moving at all.
Speaker 2: Exactly.
Speaker 1: Well, if the train was not moving at all, you
Speaker 1: were set upon work with.
Speaker 2: Well, if the train is parked in front of you,
Speaker 2: your setup would work.
Speaker 5: Right.
Speaker 2: You have somebody standing at the back of the train
Speaker 2: and somebody standing at the front of the train. They
Speaker 2: know where they are and it doesn't really matter when
Speaker 2: they make the measurement if the train isn't moving.
Speaker 1: I see, Because you know you can measure the road
Speaker 1: in front of you, you can measure the train tracks.
Speaker 2: Yeah, exactly. Like if I line the train up with
Speaker 2: my two assistants and I know how far apart they are,
Speaker 2: then I know how long the train is.
Speaker 1: Okay, So with you're set up on your assistance, which
Speaker 1: hopefully you're tipping generously, you measure the train to be
Speaker 1: one kilometer long, And now you're saying that's not really
Speaker 1: how long the train is.
Speaker 2: Yeah, let's say I measured the train to be one
Speaker 2: kilometer long when it's at rest, when it's not moving,
Speaker 2: and then the train makes a run past me at
Speaker 2: half the speed of light. You know then what I'm
Speaker 2: going to measure this time, is that the train is shorter,
Speaker 2: that it's only eight hundred and fifty meters long instead
Speaker 2: of one kilometer.
Speaker 1: Mmm. Interesting, Now we're going to explain why that happens.
Speaker 1: Where does speasure where tivity come in that makes you
Speaker 1: measure it to be eight hundred and fifty meters. You're
Speaker 1: telling me that the assistance would measure the train to
Speaker 1: be shorter than a kilometer. But I guess my intuition
Speaker 1: is like, what, how can that be? Because like, your
Speaker 1: setup seem perfectly you know, logical and sensical, and it
Speaker 1: should measure my tuition. It should measure the train to
Speaker 1: be a kilometer because you know, Juan measured the front
Speaker 1: of the train moving at this point at this time,
Speaker 1: and Sally measured the back of the train moving a
Speaker 1: kilometer away at the same time. Why would it look
Speaker 1: shorter than a kilometer.
Speaker 2: Let's unpack what that question really means, the why question.
Speaker 2: You're saying that the train was one length at rest,
Speaker 2: and so you expect it to still be that length later.
Speaker 2: That sounds reasonable, but it actually contains a big assumption,
Speaker 2: the assumption that lengths are absolute rather than relative to velocity.
Speaker 2: The lengths are always the same no matter how fast
Speaker 2: you're going. I could ask you, why do you expect
Speaker 2: the train to always have the same length. That's just
Speaker 2: actually an assumption we're making about the world, and it
Speaker 2: turns out it's not how the world actually works. The
Speaker 2: world actually works differently. Lengths are relative. They depend on velocity.
Speaker 2: You just never noticed before because it's a subtle effect.
Speaker 2: So you, like everyone before Einstein, made the wrong assumption
Speaker 2: based on your limited experience, the assumption that length is fixed,
Speaker 2: that it's universal and doesn't depend on velocity. But it
Speaker 2: turns out it's not. It's relative. So that's the experimental observation.
Speaker 2: That's what we see in the world. And on top
Speaker 2: of that, it has to be relative in order to
Speaker 2: make sense, to be consistent with the constant speed of light.
Speaker 2: So A, we can now tell that the world works
Speaker 2: this way. Lengths are relative, not absolute. And B it's
Speaker 2: a natural theoretical consequence of the speed of light being
Speaker 2: the same for everyone, which has important consequences for time
Speaker 2: and then eventually for length. I want to walk you
Speaker 2: through it, but the short version of the story is
Speaker 2: that number one, the speed of light, is constant for everyone,
Speaker 2: which means that number two time is not universal that
Speaker 2: people can disagree about whether things happen at the same time.
Speaker 2: And remember that measuring the front and back of the
Speaker 2: train at the same time was crucial to our measurement.
Speaker 2: So disagreeing about simultaneity when to measure the front and
Speaker 2: back of the train means number three, we're going to
Speaker 2: disagree about the length of the train. Okay, that was
Speaker 2: the short version, so let's back up. Something we know
Speaker 2: is true is that the speed of light is the
Speaker 2: same for everyone. If you're on the train and you
Speaker 2: shine a flashlight from the back of the train towards
Speaker 2: the front, you see it move at the speed of
Speaker 2: light relative to the train and to you on the ground.
Speaker 2: I see it move at the speed of light relative
Speaker 2: to me, which means it's not moving at the speed
Speaker 2: of light relative to the train according to me. That's
Speaker 2: number one, the basic fact from which all special relativity derives.
Speaker 2: That everyone measures the speed of light relative to them
Speaker 2: to be the same. So how does that mess up
Speaker 2: our concept of time? Well, if you stand in the
Speaker 2: middle of the train and shine two flashlights, one forwards
Speaker 2: and one backwards, then you'll see them reach the front
Speaker 2: and the back at the same time. Right makes sense,
Speaker 2: same distance, same speed. But on the ground, I also
Speaker 2: see those beams moving at the speed of light. But
Speaker 2: now I see the back of the train rushing forward
Speaker 2: towards the beam, so it reaches the beam first, compared
Speaker 2: to the front of the train, which is racing away
Speaker 2: from the beam. So you and I disagree about whether
Speaker 2: the beams hit the front and back at the same time.
Speaker 2: That was point number two. It all comes down to
Speaker 2: the end to time. It's because the way Einstein changed
Speaker 2: our understanding of the universe required us to understand that
Speaker 2: time depends on the observer. That's not just location that
Speaker 2: depends on the observer, but also time depends on the observer.
Speaker 2: And because time depends on the observer, whether two things
Speaker 2: happen at the same time depends on the observer. We've
Speaker 2: talked about this a few times, this concept of simultanedy,
Speaker 2: like do two things happen at the same time depends
Speaker 2: on your velocity. And because measurements of length require two
Speaker 2: measurements at the same time, then your measurement of length
Speaker 2: ends on your notion of simultaneity. Do a Juan and
Speaker 2: Sally measure the train front and back at the same time,
Speaker 2: They think so, but the person on the train thinks
Speaker 2: they don't, which is why they have different measurements of
Speaker 2: the length of.
Speaker 1: The train between us and the observers on the train.
Speaker 1: But like, all of your assistants are not moving relative
Speaker 1: to each other, that's right, and they all have synchronized clocks.
Speaker 1: You told me they were synchronized. So what do you
Speaker 1: mean that their measurements are not happening at the same time,
Speaker 1: or like if they measure Jan measures in front of
Speaker 1: the train, Sally measures the back of the train, and
Speaker 1: they write down on a piece of paper what their
Speaker 1: measurements and then they bring the papers to you. Aren't
Speaker 1: those things synchronized. I'm not saying how what you're saying
Speaker 1: about time and how that's changing your assistance measurement.
Speaker 2: Yeah, I think that those measurements are synchronized, and I
Speaker 2: think my measurement of eight hundred and fifty meters is
Speaker 2: totally right. But if you're on the train, then you
Speaker 2: think that those measurements are not synchronized. You're like, No,
Speaker 2: Jan and Sally made those measurements at different times. That's
Speaker 2: why they got a shorter length. From your point of you,
Speaker 2: those two measurements were not made at the same time.
Speaker 1: Why not we synchronized our clocks.
Speaker 2: I'm synchronized with everybody on the ground, but I'm not
Speaker 2: synchronized with people on the train because those people are
Speaker 2: moving relative to me, and moving clocks cannot stay synchronized.
Speaker 1: Okay, so forget the people on the train. Let's just
Speaker 1: focus on Huang and Sally.
Speaker 2: Okay, Huan and Sally on the ground, they.
Speaker 1: Have synchronized clocks to mine. They're synchronized to each other.
Speaker 1: And you're saying they would measure the train to be
Speaker 1: eight hundred and fifty meters.
Speaker 2: Yes, whereas somebody on the train says.
Speaker 1: That, no, forget, forget the person on the train. Now
Speaker 1: the train stops, turns around, comes back, and parts in
Speaker 1: front of me. Mm hmm. Now I would measure the
Speaker 1: train to be a kilometer yes, So what happened there?
Speaker 1: Like did space contract or I guess I'm not seeing
Speaker 1: the connection with time or or at least I feel
Speaker 1: like we're not explaining that.
Speaker 5: Well.
Speaker 2: Velocity and time are very closely related, right, We're not
Speaker 2: talking about a single point. We're talking about two points.
Speaker 2: We're talking about the front of the train and we're
Speaker 2: talking about the back of the train, and we're talking
Speaker 2: about the distances between them, and we're talking about measuring
Speaker 2: them at a certain time, and so of course time
Speaker 2: is going to be involved here, right.
Speaker 1: You say we synchronize our clocks, So isn't it sort
Speaker 1: of like a universal time?
Speaker 2: I mean, you can only synchronize clocks in one frame. Okay,
Speaker 2: So we've established that we can synchronize our clocks on
Speaker 2: the ground, but that doesn't mean they're synchronized for other people,
Speaker 2: like the people on the train.
Speaker 1: I feel like this is maybe confusing more to think
Speaker 1: about the people on the train. Like let's say I
Speaker 1: don't care about the people on the train, Like I
Speaker 1: just care about what Seally and Juan measure now when
Speaker 1: the train is moving, and then later when the train
Speaker 1: stops and comes back and they measure the distance again.
Speaker 1: Why are those two measurements different?
Speaker 2: Okay, your question is if the train is one kilometer
Speaker 2: long when it's sitting in front of me, or equivalently,
Speaker 2: if the people on the train measured to be one
Speaker 2: kilometer because it's not moving relative to them, then why
Speaker 2: do we measure it to be shorter on the ground
Speaker 2: when it's moving past us? How does our disagreement about
Speaker 2: synchronized clocks get translated who is disagreement about the length? Well,
Speaker 2: the most direct way to say it is that to
Speaker 2: measure the length of the train, you have to measure
Speaker 2: the front and back at the same time. But if
Speaker 2: you disagree about what at the same time means, then
Speaker 2: you're going to disagree about the length of the train.
Speaker 2: So what's going on here exactly? How do the UNSYNCD
Speaker 2: clocks make people measure different times. I know you don't
Speaker 2: want to think about the people on the train, but
Speaker 2: you kind of have to, because when we say the
Speaker 2: train is one kilometer in length, what that means is
Speaker 2: that it's one kilometer for people on the train, for
Speaker 2: people not moving relative to the train, by their definition
Speaker 2: of at the same time, the front and back are
Speaker 2: one kilometer apart. That's kind of what it means. But
Speaker 2: for people on the ground, they have a different definition
Speaker 2: of at the same time. They think that the people
Speaker 2: on the train's measurement is wrong. The people on the
Speaker 2: ground think that the people on the train measure in
Speaker 2: the back of the train first and later measure the
Speaker 2: front of the train. The people on the ground think
Speaker 2: that people on the train are not measuring the front
Speaker 2: and back at the same time, which is why they
Speaker 2: get a longer measurement. They get a full kilometer. Like
Speaker 2: imagine if you took a one meter long stick moving
Speaker 2: past you, and you measured the back of it now
Speaker 2: and the front of it later in ten seconds or whatever,
Speaker 2: you get a measurement that was way too long. That's
Speaker 2: what the people on the ground think that people on
Speaker 2: the train are doing to get one kilometer instead of
Speaker 2: eight hundred and fifty meters. The people on the ground
Speaker 2: think that their own measurements are synchronized, and they get
Speaker 2: eight hundred and fifty meters. The people on the train
Speaker 2: think that the measurements on the ground are not at
Speaker 2: the same time. The people on the train think that
Speaker 2: the people on the ground are measuring the front before
Speaker 2: they're measuring the back, and that's why the people on
Speaker 2: the ground are getting a measurement that's too short. So
Speaker 2: there's no like, what is the real length of the train,
Speaker 2: or why does a train look shorter when it's moving faster?
Speaker 2: Its length depends on your velocity. We just never noticed.
Speaker 1: It before, all right, So let's dig into me this
Speaker 1: idea of that. It has to do with time and
Speaker 1: let's talk about how time changes due to special relativity
Speaker 1: and see if that maybe explains why the train. We
Speaker 1: measure the train to meet different lengths here and then
Speaker 1: later when it stops. So we'll dig into that, but
Speaker 1: first let's take another quick break. All right, we're asking
Speaker 1: the question why do moving objects look shorter, and Daniel
Speaker 1: you're saying it really depends on the idea of time
Speaker 1: being variable at this time being variable affect sally and
Speaker 1: why your assistance measurements of the train.
Speaker 2: I think time is crucial to resolving this sort of
Speaker 2: apparent paradox. One of the reasons it's hard to imagine
Speaker 2: a stick getting shorter or a train getting shorter is
Speaker 2: because you think of it as a rigid object which
Speaker 2: throws you off. Instead, just think of three train cars
Speaker 2: moving and sync. One in the back, one in the middle,
Speaker 2: and one in the front. Now, what if the middle
Speaker 2: car tells the other two to speed up? From your
Speaker 2: point of view, the message arrives at the rear car first,
Speaker 2: which speeds up before the lead car can, effectively shrinking
Speaker 2: the distance between them. From their point of view, However,
Speaker 2: the message arrives at the lead and the rear car
Speaker 2: at the same time, and the distance hasn't changed. When
Speaker 2: they decelerate again, the reverse happens and the cars come
Speaker 2: to rest with the same original distance. So you can
Speaker 2: see how different senses of time lead to different measurements
Speaker 2: of distance. But how is it possible for the train
Speaker 2: cars to get closer together and like not? Notice what
Speaker 2: if you exaggerated the effect so they would bump into
Speaker 2: each other. Well, the answer is they also shrink because
Speaker 2: space itself is shrinking. The atoms are like little cars.
Speaker 2: So think of the train as the front of the
Speaker 2: train and the back of the train, not as one object.
Speaker 2: Thinking of it as one long train tricks you into
Speaker 2: using your intuition thinking of it as a rigid object,
Speaker 2: which actually can't exist in our universe. Like when people
Speaker 2: ask what happens if you stick a light year long?
Speaker 2: Does one end move instantly, sending information faster than light
Speaker 2: to the other end. No, there's no rigid stick. You
Speaker 2: push on one end and the pressure wave takes time
Speaker 2: to reach the other end and to move it. It's the
Speaker 2: same with the train. It's linked together, but it's not
Speaker 2: a rigid object of fixed length. So think about the
Speaker 2: front and the back separately. Now, The super confusing thing
Speaker 2: about this whole length contraction thing is that it's relative,
Speaker 2: just the way time dilation is. People on the ground
Speaker 2: think the train has shrunk, but people on the train,
Speaker 2: and I know you don't want to talk about them,
Speaker 2: they think that distances on the ground have shrunk because
Speaker 2: the ground is moving relative to them. Like let's say
Speaker 2: they're about to enter a one kilometer long tunnel. I
Speaker 2: see the trains moving, and so I see it's going
Speaker 2: to be shorter than the tunnel, whereas the train sees
Speaker 2: the tunnel is shorter. So who's right, Like is the
Speaker 2: train actually going to be in the tunnel or not?
Speaker 2: And we construct these situations to like confront the universe
Speaker 2: and say, like, what's really happening because we imagine that
Speaker 2: the concept of length is absolute, that the train has
Speaker 2: an actual length, right, that something has to happen in
Speaker 2: the universe, and only one thing can happen. You can't
Speaker 2: have like two people seeing conflicting events. So understanding how
Speaker 2: time flows and how time is relative is crucial to
Speaker 2: understanding how both of those things can seem true. That
Speaker 2: somebody on the ground can see the train as shorter
Speaker 2: and fitting in the tunnel, and somebody else on the
Speaker 2: train can see the tunnel as shorter, so the train
Speaker 2: always sticks out.
Speaker 1: Okay, here's this inner and we'll go with your tunnel idea. Okay,
Speaker 1: So I have a train that when it's standing still
Speaker 1: in front of me, I measure it to be a kilometer.
Speaker 1: Now I build a tunnel that and the tunnel is
Speaker 1: not moving, and I measure, and I make the tunnel
Speaker 1: to be one kilometer long, exactly the same length as
Speaker 1: the train. Now I put in at one end of
Speaker 1: the tunnel and Sally at the back of the tunnel. Okay,
Speaker 1: and we synchronize our clocks. Okay. Now I move the
Speaker 1: train and I put it inside the tunnel so that
Speaker 1: it's just it fits perfectly inside the tunnel. Sally and
Speaker 1: Juan measure the train to be a kilometer long.
Speaker 2: Yes, everybody with OCD out there is like, oooh, that's
Speaker 2: so satisfying. It fits.
Speaker 1: Yeah. I think by everybody you mean all of our
Speaker 1: listeners if they like the Physics podcast. Now the train
Speaker 1: leaves the tunnel, goes away a few kilometers, and then
Speaker 1: it comes back at half of the speed of light.
Speaker 1: That's say and Sally, Juan and I have our clock synchronized.
Speaker 1: The tunnel is zooming pass and we ask want to
Speaker 1: measure when the front of the train passes his spot,
Speaker 1: And we ask Sally when the back of the train
Speaker 1: passes her spot at the other side of the tunnel.
Speaker 1: Are you saying they're not going to report the same time,
Speaker 1: because if they report the same time, then I have
Speaker 1: to conclude that the train was a kilometer long.
Speaker 2: No, that's right. They will not measure the same time.
Speaker 2: One and at the back of the tunnel will measure
Speaker 2: a time earlier than Sally at the front of the tunnel.
Speaker 2: So quarantine you, Juan and Sally, who are in the
Speaker 2: tunnel's frame of reference. You will see the whole train
Speaker 2: inside the tunnel that when the back end disappears into
Speaker 2: the tunnel, the front nose has not yet emerged from
Speaker 2: the tunnel and still one hundred and fifty meters from
Speaker 2: the exit of the tunnel.
Speaker 1: So Sally at the back is going to write down
Speaker 1: her number, and they're going to both numbers are not
Speaker 1: going to come back the same.
Speaker 2: That's right.
Speaker 1: Can you explain why like nobody is moving like Sally Huang,
Speaker 1: they were both staying the same. They're the same observer
Speaker 1: in the same frame. Their time was synced. The train
Speaker 1: was physically moving past them. Why do they measure a
Speaker 1: different time.
Speaker 2: Yes, and Huan and Sali are synchronized according to themselves
Speaker 2: and people on the ground, so they think their measurement
Speaker 2: makes sense and it does. In their frame. Eight hundred
Speaker 2: and fifty meters is the length of the train, and
Speaker 2: they see the people on the train who are measuring
Speaker 2: the train to be a full kilometer longer than the
Speaker 2: people on the ground are measuring. The people on the
Speaker 2: ground see the people on the train making their measurements
Speaker 2: not at the same time, and the reverse is true.
Speaker 2: On the train, people take measurements at what they think
Speaker 2: is the same time, and they get one kilometer, and
Speaker 2: the people on the train think that people on the
Speaker 2: ground are not syncd. That's why it's all about the
Speaker 2: relativity of simultaneity, whether you think two things happen at
Speaker 2: the same time or not. And that's what sets up
Speaker 2: this fun apparent paradox of whether the train will fit
Speaker 2: into a one kilometer tunnel one in Sally and the
Speaker 2: tunnel when they see it moving through, they see it
Speaker 2: at eight hundred and fifty meters long, and so they say, yes,
Speaker 2: the train fit in the tunnel, but you have people
Speaker 2: on the train. They see the tunnel as shorter. They say, no,
Speaker 2: my train is still a kilometer long because the train
Speaker 2: is not moving for them, and so it's still at
Speaker 2: its same original length. But the tunnel is moving, so
Speaker 2: the tunnel is shorter. So they see the train sticking
Speaker 2: out of the tunnel. And in order for special relativity
Speaker 2: to make sense, you have to somehow reconcile these two things,
Speaker 2: like what really happened. Did the train fit in the
Speaker 2: tunnel or not?
Speaker 1: Okay, So how do you reconcile?
Speaker 2: So it all comes down to time, right, Remember how
Speaker 2: we talked about earlier in the episode. The time is relative,
Speaker 2: not just how time flows, but whether two things happen
Speaker 2: at the same time. That came from the observation that
Speaker 2: the speed of light is the same for everyone, which
Speaker 2: means people have to disagree about whether events happen at
Speaker 2: the same time. The example of the beams of light
Speaker 2: shooting along the train, people see them reaching the front
Speaker 2: and the back of the same time. People off the
Speaker 2: train see the light hitting the back of the train first.
Speaker 2: And the way to reconcile that is to have different
Speaker 2: times for all those people for time to flow differently,
Speaker 2: And that's why it's crucial that we understand the clocks
Speaker 2: and the synchronization, and that the front of the back
Speaker 2: of the train be measured at the same time. And
Speaker 2: the crucial thing is that at the same time is
Speaker 2: different for people on the train and for people on
Speaker 2: the ground because moving clocks flow differently. Right, So on
Speaker 2: the ground, Jan and Sally are synchronized and they measure
Speaker 2: the train to be eight hundred and fifty meters long.
Speaker 2: But to the people on the train, Wan and Sally
Speaker 2: are not synchronized. Wan and Sally are measuring the front
Speaker 2: in the back of the train at different times, which
Speaker 2: is why Wan and Sally think the train is shorter,
Speaker 2: and the people on the train think that it's not shorter.
Speaker 2: Because the people on the train think that One and
Speaker 2: Sally made a mistake. They're like, no, you guys measure
Speaker 2: the front and back at different times, which is why
Speaker 2: you're telling me it's eight hundred and fifty meters long
Speaker 2: when really it's a kilometer. How can it make sense
Speaker 2: for length to be contracted because it seems to violate
Speaker 2: our intuition, like things have a length and they should
Speaker 2: just have a length. And how is it possible for
Speaker 2: things to get shorter as they get faster, because that
Speaker 2: would lead to all sorts of weird paradoxes. It actually
Speaker 2: can kind of make sense, and these paradoxes aren't paradoxes.
Speaker 2: They just show you that the world works differently than
Speaker 2: you imagined. Can it make sense that things moving quickly
Speaker 2: get shorter? Like why doesn't that lead to contradictions?
Speaker 1: Oh? Not like why does it make sense? But like,
Speaker 1: why doesn't it lead to contradictions about the universe? Because
Speaker 1: I think we'd establish it's very hard to make it
Speaker 1: make sense.
Speaker 2: But it is possible to make it make sense, and
Speaker 2: it makes sense to me, And I want to share
Speaker 2: that connection with everybody because it's a wonderful moment when
Speaker 2: it all clicks together in your head and you realize, oh,
Speaker 2: it is possible for both people to think the other
Speaker 2: one is shorter, for the people on the train to
Speaker 2: think the tunnel is shorter, and for the people in
Speaker 2: the tunnel to think the train is shorter. Here's the
Speaker 2: detailed breakdown of what's going on with the train and
Speaker 2: the tunnel. Here's how it's possible for the team on
Speaker 2: the ground to see the train totally inside the tunnel,
Speaker 2: and for the team on the train to see that
Speaker 2: the train is too long to ever all be in
Speaker 2: the tunnel at the same time. From the ground point
Speaker 2: of view, the train is shorter than the tunnel, so
Speaker 2: when the back end is inside the tunnel, the nose
Speaker 2: has not yet left the tunnel. Remember that we are
Speaker 2: comparing two events front and back of the train at
Speaker 2: what we consider to be at the same time. But
Speaker 2: the people on the train think that the ground team
Speaker 2: is making a mistake and that those events are not
Speaker 2: actually at the same time. For the people on the train,
Speaker 2: they think the ground team is comparing the front of
Speaker 2: the train at an earlier moment to the back of
Speaker 2: the train at a later moment, which is how the
Speaker 2: ground team sees the train inside the tunnel. From the
Speaker 2: point of view of the people on the train, the
Speaker 2: train is sticking out both ends of the tunnel at
Speaker 2: the same time because the tunnel is shorter. The people
Speaker 2: on the ground think that's wrong. They think the train
Speaker 2: team came to that conclusion by comparing an earlier back
Speaker 2: end measurement when the train tail was still sticking out
Speaker 2: to a later front end measurement when the train knows
Speaker 2: is now sticking out. And the key is that they're
Speaker 2: measuring the fronts and the backs at different times. And
Speaker 2: it's all because time is relative and simultaneity is different
Speaker 2: and for people moving at different speeds. And you know,
Speaker 2: to me this comes down to like trying to see
Speaker 2: can special relativity makes sense because it fundamentally changes your
Speaker 2: understanding of the world. It tells you the world really
Speaker 2: works in a different way than you imagined, and we
Speaker 2: want the world to make sense. Like I think back
Speaker 2: to the first time I ever heard this example of
Speaker 2: like somebody in a car turning on a flashlight and
Speaker 2: then hearing that those photons move at the same speed
Speaker 2: relative to the car as they do relative to the ground,
Speaker 2: And immediately my brain was like, hold on red flag.
Speaker 2: That can't possibly make sense because then like when do
Speaker 2: those photons hit wall or some obstacle. People in the
Speaker 2: car and people on the ground would disagree about that
Speaker 2: because they all say the photons are moving at the
Speaker 2: same speed, but there's different distances involved and all sorts
Speaker 2: of stuff. And so for me, it's about disentangling these
Speaker 2: feelings of contradiction, these ways that special relativity violates our intuition.
Speaker 2: You know, how can it possibly be that both these
Speaker 2: people make honest measurements which conflict with each other. One
Speaker 2: of the things I love about special relativity is that
Speaker 2: it tells you that, like, people can disagree and'll both
Speaker 2: be correct.
Speaker 5: You know.
Speaker 2: That's like the fundamental conclusion of you know simultaneity, that
Speaker 2: you know, two people can see different orders of events
Speaker 2: and both be honest and both be reporting what they see,
Speaker 2: because the order of events depends on your relative velocity
Speaker 2: and your location, and there is no single absolute clock
Speaker 2: or single sense of space and time in the universe.
Speaker 2: And so people on the ground can see the train
Speaker 2: fitting in the tunnel, and people on the train can
Speaker 2: see the train not fitting in the tunnel, and both
Speaker 2: be correct.
Speaker 1: Like, it's correct that if I measure the train when
Speaker 1: it's standing still, it'll fit in the tunnel, And if
Speaker 1: I measure when it's moving fast, I'm going to measure
Speaker 1: it being shorter than the tunnel.
Speaker 2: Yeah, exactly. And the people can see the train fitting
Speaker 2: in the tunnel because according to them, they're measuring the
Speaker 2: front and the back of the train at the same time.
Speaker 2: The people on the train don't see that happening because
Speaker 2: they think that the people in the tunnel are not
Speaker 2: measuring it at the same time, because their concept of
Speaker 2: what the same time means is different than the people
Speaker 2: on the tunnel. And the end, that's why it all
Speaker 2: comes down to time. Understanding relative time is crucial because
Speaker 2: we're talking about a big extended object. It's a kilometer long,
Speaker 2: so the front in the back are separated by space
Speaker 2: and separated by time, and how time flows then have
Speaker 2: to affect your measurement of the length of it, because
Speaker 2: in the end, measuring length means measuring the front in
Speaker 2: the back at the same time.
Speaker 1: Right, again, you're answering the different question than, maybe than
Speaker 1: the one we started with.
Speaker 2: Yeah, I guess the most direct answer to the question
Speaker 2: of the episode why do things look shorter is that
Speaker 2: they always have. We just never noticed. The fact that
Speaker 2: we ask why is because we've been led astray by
Speaker 2: our intuition, our unfounded assumption that the world has this
Speaker 2: property that lengths are absolute and are always the same
Speaker 2: at any speed. It turns out that's not true, and
Speaker 2: we can see that it's not true by doing experiments
Speaker 2: at various speeds, including very high speeds. Things really do shrink.
Speaker 2: So that explains why we ask the question. Because the
Speaker 2: way the world works is in contrast with the way
Speaker 2: our intuition works. Why does the world work that way
Speaker 2: is the follow up philosophical question. It turns out it
Speaker 2: has to in order to be consistent with this other thing.
Speaker 2: We see that the speed of light is constant for everyone.
Speaker 2: First consequence of the speed of light being constant for
Speaker 2: everyone is that simultaneity is not universal. People at different
Speaker 2: speeds disagree about what at the same time means. I
Speaker 2: think Juan and Sally measure the front and back at
Speaker 2: the same time, but people on the train don't, so
Speaker 2: we measure different lengths. And the beauty part, the really
Speaker 2: gorgeous part, is that this is what makes it all
Speaker 2: click together. You can have some kind of global understanding
Speaker 2: of how everyone is seeing things differently because you can see,
Speaker 2: as we just explained, that people are measuring the train
Speaker 2: at different times and getting different answers. Eight hundred and
Speaker 2: fifty meters or one kilometer, they all get different answers,
Speaker 2: and they're all right because they are measuring different things.
Speaker 2: Length at rest means something different than length in motion
Speaker 2: because it depends on sinking measurements at the front and
Speaker 2: the back of the train. Length is not absolute and
Speaker 2: it can't be from the world too, makes sense at
Speaker 2: high speeds, it has to be relative for everything to
Speaker 2: be coherent.
Speaker 1: Like to us du Juan and Sally, the train really
Speaker 1: did shrink, I think, is what you're saying. Like the
Speaker 1: space that comprises the train, that the space that the
Speaker 1: train sits in that is moving with the train, it contracted,
Speaker 1: It got.
Speaker 2: Smaller, It got smaller for one in Sally, for Juan.
Speaker 1: And Sali, And that's just the way it is. Space
Speaker 1: is contracted, and it's all due to the speed limit
Speaker 1: of the interest because if it didn't, that space didn't contract,
Speaker 1: then things would sort of break down.
Speaker 2: Yeah, if length doesn't contract, then you break all the
Speaker 2: rules of special relativity. Another way to think about it
Speaker 2: is that length contraction is sort of the same thing
Speaker 2: as time dilation. For a completely separate example that helps
Speaker 2: people understand the link between length contraction, which we've been
Speaker 2: talking about today and time dilation. Think about what happens
Speaker 2: if you try to travel to a distant star at
Speaker 2: a really high speed, Say you need to get ten
Speaker 2: light years away, and you travel at ninety eight percent
Speaker 2: of the speed of light. From the point of view
Speaker 2: of people on Earth you left behind, it takes you
Speaker 2: almost ten years to get there. But they also see
Speaker 2: your clock running slowly. They see that for you, it's
Speaker 2: only been two years. That's time dilation, right, But look
Speaker 2: at it from the other point of view, from the ship,
Speaker 2: from the pilot's point of view, the distant star is
Speaker 2: moving towards her at ninety eight percent of the speed
Speaker 2: of light, So the distance to the star is shorter
Speaker 2: than ten light years, and it only takes her about
Speaker 2: two years to get there because it's only about two
Speaker 2: light years for her, So she experiences two years to
Speaker 2: get there because the length was shortened. What's really happening, Well,
Speaker 2: length contraction is just really another way to look at
Speaker 2: time dilation, and in the end, it's all about time.
Speaker 1: I think. Basically you're saying that the train track to Sally.
Speaker 2: And perspective, Yeah, and it's all connected to time. And
Speaker 2: in the end, time dilation and length contraction are really
Speaker 2: just two different ways to see the same effect.
Speaker 1: All right. Well, again, especially relativity is hard.
Speaker 2: Especially in an audio format. For those of you who
Speaker 2: like learning visually. I don't know why you're listening to
Speaker 2: a podcast.
Speaker 1: But we're glad that you are. Let's make that clear.
Speaker 1: We're not saying go watch YouTube.
Speaker 2: But if you do want to learn more about this stuff,
Speaker 2: look up space time diagrams. They're really helpful.
Speaker 1: It's interesting, though, to think about how valuable the universe is, Right,
Speaker 1: like the idea that the train would shrink just because
Speaker 1: it's going fast. It's kind of weird.
Speaker 2: It is very weird. Yeah, And it's weird that it
Speaker 2: makes sense in the end that the universe is just
Speaker 2: so different from the way we imagined it. But you know,
Speaker 2: that's the project of physics is not to just accept
Speaker 2: our intuitions, but to confront them with data and information
Speaker 2: and say, how can we make sense of all this?
Speaker 2: What story can we tell about the universe that ties
Speaker 2: it all together? All?
Speaker 1: Right, the next time I take a train, I'm gonna
Speaker 1: be thinking about this, like, am I thinner or am
Speaker 1: I shorter?
Speaker 2: Depends if you're lying down or standing up?
Speaker 1: Yeah? Exactly right, So I should stand up on the
Speaker 1: train the whole time.
Speaker 2: Don't forget to buy tickets for Juan and Sally.
Speaker 1: Yeah, and don't forget to tip the conductor too, with
Speaker 1: a big, fat envelope of money.
Speaker 2: No tip contractions here please.
Speaker 1: All right, Well, we hope you enjoyed that. Thanks for
Speaker 1: joining us, see you next time.
Speaker 2: Thanks for listening, and remember that Daniel and Jorge Explain
Speaker 2: the Universe is a production of iHeart Radio. For more
Speaker 2: podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or
Speaker 2: wherever you listen to your face. Richells h