Daniel and Kelly’s Extraordinary Universe - Why do moving objects look shorter?

Episode Date: September 12, 2023

Daniel and Jorge wrestle with the weird consequences and hard questions of special relativity!See omnystudio.com/listener for privacy information.

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oh yeah like uh you can read faster or you can process information better no i think i just developed a better mental hori simulator that can predict what you might be interested in or what you might not be interested in oh sounds like you just need like an ai version of me then i don't even need to be here it's not artificial intelligence it's natural it's uh cartoonist and intelligence. Well, I guess, you know, it kind of depends. You know, what's interesting is kind of relative, isn't it? Yeah, that's right. What's especially interesting is kind of relative. So I guess it kind of is all special relativity. Yeah, I definitely have some special relatives. Did you predict I was going to say that? I predicted you were going to say

something hilarious. Hi, I'm Jorge McCartunist and the author of Oliver's Great Big Universe. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I'm still training my brain to understand the universe. Wait, don't you need to know how the universe works before you can train your brain to understand it? We can do two things at once. We can try to figure out how the universe works, and we can try to wrap our minds around the bits that we have figured out and try to gain some intuition for all.

this craziness. I feel like this podcast is a little bit of training into like how to think about the universe, how to explore it, how to ask questions about it. Should we be charging tuition? We're just sharing the love, you know? But you're right because most of our modern theories of physics are expressed in a kind of inaccessible language, mathematical equations that do show us the relationship between bits and pieces and allow us to make predictions and stuff, but it's not always the way our brains work.

So one of the goals on this podcast is to break it down and give you an intuitive understanding to try to make it all make sense to you. Yeah, I guess we offer free intuition, but not at a cost of free tuition. No tuition intuition, that should have been the title of the podcast. Yeah. Hopefully it all comes to fruition. But, I mean, you're welcome to pay tuition if you like. Send this gold coins or dollars if the inspiration strikes you.

You take tips. Do you have a tip jar in your classroom? I don't have a tip jar, but I did once walk into a classroom and find an envelope with thousands of dollars in it. Whoa. Where is your university? It's a public university, man. So it's not like some student just like dropped a pile of cash. I think it must have been some club organizing in the room before us or something.

Sounds like maybe they were trying to bribe you. No, I don't think so. I think somebody must have panicked when they realized they left it behind. Or it could have been a tip. I don't know. You could have just assumed it was a tip. I'm not so cheaply bought. But anyways, welcome to our podcast, Daniel and Jorge

Explained the Universe, a production of IHeart Radio. In which we use our inspiration to improve your intuition for absolutely no tuition, whether or not the jokes come to any fruition. That's right, because it is an amazing universe for us to ask questions about and to explore and to learn about how it all works. And part of the process of doing physics is not just writing down on some sheet of paper, a bunch of math, and then gesturing it and saying, trust us this works it's about understanding in the end physics and all of science is motivated by our

curiosity our desire to understand and that means translating all of this stuff everything we've learned back into something that makes sense to us that clicks together in our minds and we go oh well that's kind of weird but I guess it does make sense yeah plus I don't know if I trust you anymore I mean now that I know you're open to bribery I didn't say I was open to bribery you said I was open bribery and I said I wasn't. It sounded like you're open to tips, quote unquote, tips. People are welcome to send us donations to the podcast, but it's not going to affect how I grade in my class.

No, I turned that stack of cash over to the campus police. Oh, wow. Are you saying you tip the police? I don't know what they did with it, but I can only assume that they did something responsible. But yeah, this university seems to depend on your point of view and also how fast you're going. Because something we've learned over the last 100 years is, that our ancient intuition for how things work doesn't always work. It only works in the special

cases that us and our ancestors got to see. Things moving pretty slowly. And when you take those rules and try to extrapolate them up to things moving really, really quickly, you find they just don't work anymore. You need a new set of rules. And those rules give us weird new insights into the actual nature of space and time. Yeah, over a hundred years ago, Einstein discovered something called special relativity. Einstein developed special and general relativity. That's absolutely true. I don't know if he invented it or discovered it.

He certainly uses it to describe the universe that we see around us. Yeah, over 100 years ago, Einstein discovered something called relativity, special and general in which he discovered that things don't always look the same in this universe. Sometimes it sort of depends on your relative point of view. Yeah, Einstein really shook the foundations of our understanding of reality. Newton gave us this idea of space and time as being. being absolute, like the fixed backdrop of the universe. But Einstein showed us that space is relative and so is time.

And it leads to all sorts of bizarre effects, clocks running slower, meter sticks looking shorter and information disappearing into black holes. Yeah, it kind of seems sometimes that the universe has these paradoxes and these contradictions, but actually it all sort of works if you dig into the math, right? It all does actually make sense in the end. It's just a different kind of sense. So today on the podcast, we'll be tackling the question. Why do moving objects look shorter?

I guess moving objects look shorter. This is not like how your bank account seems to shrink when you're on a trip, you know, or on vacation. This is the effect commonly known as length contraction, that things going super duper fast relative to you seem to look shorter than they do when they're at rest. That's one of the consequences of having a speed limit in the universe, isn't it? Absolutely. It's one of the consequences of special relativity, which starts from the postulates that there's a speed limit to the universe and that light always moves at the speed of life for everybody, regardless of who they are and how fast they're going.

Out of that comes all sorts of weird changes we have to make to space and time and velocity in order to make things still make sense. And so on the podcast here, we've talked about how as you're moving at close to this speed of light are moving near really massive objects. Time slows down. We've talked about that quite a bit, right? Yeah, moving clocks run slow. So if you see a clock moving past you at half the speed of light, then you will see a tick slower than a clock you are holding. That's time dilation, a concept we've talked about lots and lots of times. Right. And then there's the idea that it's not only time that can sort of stretch and change, it's also distances or the length of things.

Yeah, if you are traveling really, really fast, then distances in front of you seem shorter. Like if you're flying between here and Jupiter and you're moving really, really fast, then the distance between here and Jupiter seems to shrink. So like if there was a giant meter stick between here and Jupiter and I was moving towards Jupiter really, really fast, then that meter stick would look shorter than it actually is to me. It would look shorter to you, but there is no what it actually is. There's just a lot of different viewpoints on it. It's all relative.

Well, I guess what it would look like if you were not moving relative to the stick. Exactly. Yeah, and that's what we call the proper length. But in that case, I'm moving really fast. It's not the meter stick, or is it the same thing? It's exactly the same thing. The meter stick would say you look shorter and you would say the meter stick looks shorter. The whole effect is symmetric.

Same way the time dilation is symmetric. If I think you're moving fast, I see your clock running slow, but you also see me moving quickly, so you see my clock running slow. But I guess doesn't it depend on like which direction this rule? is flying, like if the ruler is flying, let's say, away for me really fast, it would look shorter, but what if it's moving like from, I see it moving from my left to my right? Would it still look shorter? It would look thinner in that case. The direction it's moving relative to you is the direction that gets contracted. If it's always moving along its length, then it's going to look shorter,

even if that length is pointed along X or along Y or along Z or in any direction. If it's moving along its length, it's going to look shorter. I see. So like if someone long long, launched a ruler really fast from my left to my right, it would seem shorter than it would if I just held it in my hand. That's exactly right, yeah. So then the question for today is, why does that happen? All right? Well, as usual, we were wondering how many people out there had thought about this question

or wondered why things look shorter when they're moving really fast. Thanks very much to everybody who answers these questions. We love hearing your voices and we'd love to hear more of your voices. So please don't be shy and write to us to questions at danielandhorpe.com. So think about it for a second. Why do you think moving objects looked shorter? Here's what people have to say. The Doppler effect, is that what it's called?

The red shifting thing. So like basically when the object, the object comes closer to you, like I guess like it looks like the wavelengths. Wave lengths shorten, right? They get shorter. So like objects, you know, they get a little louder. The colors look a little brighter. The wavelengths shorten and so the object looks shorter

because the wavelengths of the colors of the object is shorter. Yeah. So that's why. I think they look shorter just due to the fact that it's more for our brain to process, you know, as opposed to if an object was sitting still. And then obviously when there's more to interpret, that obviously creates more of a margin of error with our perception. I would assume that the reason that objects appear shorter, especially as they approach

light speed, is time and space dilation. So as it approaches light speed, it would just appear to shrink. I'm not really sure. I think that for a human eye optics, moving objects look actually longer because of motion blur. But special relativity states that moving objects get shorter. I don't exactly remember why. Moving objects look shorter because the back has gotten closer to where the front was when you saw it by the time you see the back. All right. Lots of interesting answers here.

very creative answers today but they all sound very sciencey talking about Doppler effects and red shifting and space dilation yeah motion blur some of these answers are way off and some of them are pretty close pretty cool these are people that you found in your department or are people on the internet these are just folks from the internet listeners to this podcast nice well let's dig into it uh Daniel what what is the physicist definition of Length dilation. So we usually call it length contraction. Wait, is there a difference? Can you also have that length dilation or is it only contract?

You can only have length contraction. The longest something can be is if it's at rest relative to you. So you're holding a meter stick, that's the longest you're ever going to measure that meter stick to be. That meter stick is moving past you at a certain speed, then you're going to see it shorter. And the way I like to phrase it to be very clear to make sure it's relative is that moving objects look shorter. Even if they're moving, like, away from you or towards you, it still gets shorter.

They still get shorter. Yeah, that doesn't make any difference. In the same way that, like, moving clocks run slow, tells you that you are seeing that clock run slow because you see it moving. And it sees you moving, so it sees you running slow. In the same way, you see a meter stick moving, you see it looking shorter. It also sees you looking shorter because it sees you moving. It's a symmetric effect.

All right. I was wrong. What is the definition of length contraction? So it's just that moving objects look shorter. You define the proper length of something to be its length when it's not moving. So you're holding the meter stick. You call that the proper length. Then you zoom that meter stick by you at like 10% of the speed of light, which doesn't sound

impressive, but it's super duper crazy fast. Then you'll see it a little bit shorter. You'll see it like a half a percent shorter. You speed it up to like half the speed of light. and you'll see it be like only 85% of its proper length. And as you get up to like 99% of the speed of light, it'll shrink down to like 15% of its proper length. If you get to like 99.99% of the speed of light,

it'll be just over 1% of its proper length. So you can see things getting like super duper short as they get super duper fast relative to you. I guess I'm wondering what it means to see something like that moving that fast. You mean like if I take a picture of it, like let's say a ruler is zooming by really quickly by me from my left to my right and I take a picture of it as it's going in front of me. In the picture, it's going to seem shorter than it would if I held the ruler in my hand. It's great that you ask that question because we have to be very specific

about what we mean here by these measurements because it makes a difference. And actually, if you take a picture, you would see the ruler looking weirdly longer because a picture captures all the photons that are arriving at you at one moment. And that includes another effect, which is that it takes time for the information to get to you. And part of the ruler is further from you and part of the ruler is closer to you. So that combines two different effects. One is that the ruler looks shorter because it's moving faster. And the other one that the back of the ruler is further from you.

So it takes light longer to get to you. No, no. But if the ruler is moving from my left to my right, like it's zooming past me like a train would. Like if I'm standing next to some train tracks and I see the train going from my left to my right and I take a picture of the train as it's passing by in front of me, is that train going to seem shorter in the picture or the same length or longer? Again, the picture combines two different effects. One is the special relativity effect and the other is the very normal light takes time to travel effect. And so usually what we do is not use the idea of a mental picture, but imagine that we have like a bunch of assistants all spread out to our left and to our.

are right and they mark like when the train front or when the train back passes them. And then we can use the distance between the train front and the train back to say how long it is. What happens in the picture case? Like what if I take a picture of the train or the ruler moving from my left to my right? Like aren't all those photons leaving the stick at the same time? And so then it would arrive at the camera or my eye at the same time? They're leaving the train or the stick at the same time. The stick has length.

So it takes longer for the back end photons to reach you than the front end photons. And I think combining photon travel time and actual length combines two different complicated things, which are kind of hard to hold in your head at the same time. So usually when we talk about special relativity, we assume that we can take care of the photon travel time and say that we have a bunch of assistance all through the universe, all making measurements, and take local data, and then we combine that information later to figure out what happened. So we take away this effect of photons take time. to get somewhere because it adds another confusing layer.

But I guess, I mean, we're saying that things look shorter, right? And your eyes sort of acts like a camera. Are you saying that like maybe what you mean by looking at something is not quite the same but as what everyday person might mean by looking at something? Yeah, I think that's fair. When we do physics experiments, we're very careful about how we make those measurements. So really what we mean here is if we take a very careful measurement of the length of the object, we will measure it to be shorter than if it.

It was stationary. Oh, all right. Well, I think we should just be kind of clear about what we mean by things looking shorter. What we mean is that we make a careful measurement of the length of this thing involving us and a bunch of assistants all along like the track of a train and noting when it passes by. And then later we get together and we compare our measurements. We say, you know, Juan measured the back of the train at this time and Sally measured the front of the train at that time. And then we can use that to figure out how long the train was. All right. It sounds like we need to dig into this scenario of you and all of your assistants

and how they're measuring the length of this ruler and or this train to maybe really understand what we mean by things looking shorter or not. So let's dig into these details. But first, let's take a quick break. Imagine that you're on an airplane and all of a sudden you hear this. Attention passengers. The pilot is having an emergency, and we need someone, anyone, to land this plane. Think you could do it? It turns out that nearly 50% of men think that they could land the plane with the help of air traffic control. And they're saying like, okay, pull this, do this, pull that, turn this. It's just, I can do it in my eyes closed.

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No, but it's good. It's important. We explain exactly what we mean and we not use jargon. so let's hash it out because there's some really interesting like apparent paradoxes that come up when we try to measure these lengths really carefully. Okay, so we're asking the question, why do moving objects look shorter? And it seems like we're not really asking the question why they look shorter. It's more like why when a bunch of physicists try to measure something moving fast,

they measure things to be shorter. Not really because the idea of looking at it, you're saying convolutes several things. Yeah, I would say I guess that's how physicists look at something, right? Don't just take a picture. We think about what that picture is actually measuring and realizing pictures are not the best way to measure the length of something moving really, really fast. And instead, we hire a bunch of assistants

and lay them out in a line so we can take measurements and figure out how long that thing really is. Okay, so then let's maybe paint that scenario. I'm sitting by some train tracks, and the train tracks go from my left to my right in front of me. And now there's going to be a train passing by and want to measure how long the train is.

Yeah. And you're saying, don't take a train. picture of it because the picture might lie to you. You're saying hire a bunch of people and then now what's your scenario? What's your setup here with your assistance? So I have a bunch of people to my left and a bunch of people to my right. Like you space them out every 10 meters or something. And we all have a bunch of clocks and we synchronize our clocks. So they all started zero at the same moment and they all read 10 seconds at the same moment. They all read 100 seconds at the same moment. So we have a bunch of people now at different locations with synchronized clocks. How do you

synchronize the clocks? Wouldn't you run into special relativity problems, sinking those clocks? It's complicated, but you can sink clocks using flashes of light. If you assume you know how long it takes light to get somewhere, you can synchronize clocks that are distant. Okay, so then each of these assistance has a clock that's synchronized to yours, right? Exactly. Now the train is passing by us and I ask people to write down what time the front or the back of the train pass them. Which one? The front or the back? You can have them write down both. And then And in order to measure the length of the train, what you need to do is get a measurement of where the back of the train was and where the front of the train was at the same time.

You combine those two numbers and that's your length. Say it again, you measure where the front and the back were at the same time? Yeah, you want to know how long something is. Then you want to know where's the front and where's the back and you want to take those measurements at the same moment, right? If you don't take those measurements at the same moment, you're not going to get the length of the train. Like if a parade is passing by you, it's moving, right?

If you measure the front and the back at different moments, you're not going to get the actual length of the parade. I see. All right. So then you ask your assistance to write down when they saw the front of the train, when they saw the back of the train, and then what do you do? You get together and you have a picnic. You get together.

You spend some of that tip money on ice sculptures and chocolates for your picnic and whatever. And then you look at the numbers and you say, all right, Juan measured the back of the train to be negative half a kilometer. At the same time, Sally measured the front of the train. train to be at a location plus half a kilometer. And so, okay, the train is one kilometer long because the front and the back were one kilometer apart at the same time. Oh, okay.

Yeah, yeah. I'm following. I'm following. So now, like, you sort of ask, okay, a T equals one minute, where did your assistance measure the front of the train and where did they measure the back of the train? And then that should tell you the length of the train. That should tell you the length of the train. And if you measured them at different times, like if one's clock was out of sync or one

was lazy or Juan made a mistake or something and you measured the back of the train earlier or later then we'd get the wrong answer for the length of the train. It's crucial that you measure the front and the back at the same time. It seems sort of obvious to even spell that out. It's sort of dumb like, duh, that's what length really is, but it's going to turn out to be a really important part

of understanding length contraction. Okay, so I guess that's one way to measure it? Or is that the only way to measure the train? That's sort of the standard setup. It allows you to avoid things like how long does it take information to travel from here to there and all that sort of stuff. I suppose you could come up with other techniques as well. All right.

So now you get together and you measure the train and you're saying the number you get from this setup is not the same as if the train was not moving at all. Exactly. Well, if the train was not moving at all, your setup would work. Well, if the train is parked in front of you, your setup would work, right?

You have somebody standing at the back of the train, somebody standing at the front of the train. They know where they are. And it doesn't really matter when they make the measurements if the train isn't moving. Hmm. I see. Because you know you can measure the road in front of you. You can measure the train tracks. Yeah, exactly. Like if I line the train up with my two assistants and I know how far apart they are, then I know how long the train is. Okay. So with your setup and your assistance, which hopefully you're tipping generously, you measure the trains to be one kilometer long. And now you're saying that's not really how long the train is.

Yeah, let's say I measure the train to be one kilometer long when it's at rest, when it's not moving. And then the train makes a run past me at half the speed of light, you know? then what I'm going to measure this time is that the train is shorter, that it's only 850 meters long instead of one kilometer. Interesting. Now, are we going to explain why that happens? Where does special relativity come in that makes you measure it to be 850 meters? You're telling me that the assistants would measure the train to be shorter than a kilometer. But I guess my intuition is like, what?

How can that be? Because your setup seemed perfectly, you know, logical and sensical. and it should measure, in my intuition, it should measure the train to be a kilometer because, you know, Juan measured the front of the train moving at this point at this time, and Sally measured the back of the train moving a kilometer away at the same time.

Why would it look shorter than a kilometer? Let's unpack what that question really means, the why question. You're saying that the train was one length at rest, and so you expected to still be that length later. That sounds reasonable, but it actually contains a big assumption. The assumption that lengths are absolute rather than relative to velocity, that lengths are always the same, no matter how fast you're going. I could ask you, why do you expect the train to always have the same length?

That's just actually an assumption we're making about the world. And it turns out it's not how the world actually works. The world actually works differently. Lengths are relative. They depend on velocity. You just never noticed before because it's a subtle effect. So you, like everyone before Einstein, made the wrong assumption based on your limited experience, the assumption that length is fixed, that it's universal and doesn't depend on velocity.

But it turns out it's not. It's a relative. So that's the experimental observation. That's what we see in the world. And on top of that, it has to be relative in order to make sense, to be consistent with a constant speed of light. So, A, we can now tell that the world works this way. Lengths are relative, not absolute. And B, it's a natural theoretical consequence of the speed of light being the same for everyone,

which has important consequences for time and then eventually for length. I want to walk you through it, but the short version of the story is that, number one, the speed of light is constant for everyone, which means that number two, time is not universal. that people can disagree about whether things happen at the same time. And remember that measuring the front and back of the train at the same time was crucial to our measurement. So disagreeing about simultaneous when to measure the front and back of the train means, number three, we're going to disagree about the length of the train. Okay, that was the short version, so let's back up.

Something we know is true is that the speed of light is the same for everyone. If you're on the train and you shine a flashlight from the back of the train towards the front, you see it move at the speed of light relative to the train and to you. On the ground, I see it move at the speed of light relative to me, which means it's not moving at the speed of light relative to the train, according to me. That's number one, the basic fact from which all special relativity derives, that everyone measures the speed of light relative to them to be the same. So how does that mess up our concept of time?

Well, if you stand in the middle of the train and shine two flashlights, one forwards and one backwards, then you'll see them reach the front and the back at the same time, right? Makes sense. Same distance, same speed. But on the ground, I also see those beams moving at the speed of light. But now I see the back of the train rushing forwards towards the beam. So it reaches the beam first compared to the front of the train, which is racing away from the beam. So you and I disagree about whether the beams hit the front and back at the same time.

That was point number two. It all comes down to the end to time. It's because the way Einstein changed our understanding of the universe required us to understand that time depends on the observer. That's not just location that depends on the observer, but also time depends on the observer. And because time depends on the observer, whether two things happen at the same time depends on the observer. We've talked about this a few times, this concept of simultaneity.

Like, do two things happen at the same time? Depends on your velocity. And because measurements of length require two measurements at the same time, then your measurement of length depends on your notion of simultaneity. Do Juan and Sally measure the train front and back at the same time? They think so, but the person on the train thinks they don't, which is why they have different measurements of the length of the train. between us and the observers on the train,

but like all of your assistants are not moving relative to each other. That's right. And they all have synchronized clocks. You told me they were synchronized. So what do you mean that their measurements are not happening at the same time? Or like if they measure, Juan measures the front of the train, Sally measures the back of the train, and they write down in a piece of paper what their measurements

and then they bring the papers to you, aren't those things synchronized? I'm not saying what you're saying about time and how that's changing your assistant. distance measurement. Yeah. I think that those measurements are synchronized and I think my measurement of 850 meters is totally right.

But if you're on the train, then you think that those measurements are not synchronized. You're like, no, Juan and Sally made those measurements at different times. That's why they got a shorter length. From your point of view, those two measurements were not made at the same time. Why not? We synchronized our clocks. I'm synchronized with everybody on the ground, but I'm not synchronized with people on the train because those people are moving relative to me and moving clocks cannot stay.

They synchronized. Okay, so forget the people on the train. Let's just focus on Huang and Sally. Okay, Juan and Sally on the ground. They have synchronized clocks to mine. They're synchronized to each other. And you're saying they would measure the train to be 850 meters. Yes.

Whereas somebody on the train says that... No, no, forget the person on the train. Okay. Now the train stops, turns around, comes back, and parks in front of me. Now I would measure the train to be a kilometer. Yes. So what happened there? Like, did space contract?

or I guess I'm not seeing the connection with time or at least I feel like we're not explaining that. Well, velocity and time are very closely related, right? We're not talking about a single point. We're talking about two points. We're talking about the front of the train and we're talking about the back of the train and we're talking about the distances between them

and we're talking about measuring them at a certain time. And so, of course, time is going to be involved here, right? So you say we synchronized our clocks. So isn't it sort of like a universal time? But you can only synchronize clocks in one frame. Okay, so we've established that we can synchronize our clocks on the ground. But that doesn't mean they're synchronized for other people like the people on the train. I feel like this is maybe confusing me more to think about the people on the train.

Like, let's say I don't care about the people on the train. Like I just care about what Sally and Juan measure now when the train is moving. And then later when the train stops and comes back and they measure the distance again. Why are those two measurements different? Okay, your question is, if the train is one kilometer long when it's sitting in front of me, or equivalently, if the people on the train measured to be one kilometer because it's not moving relative to them, then why do we measure it to be shorter on the ground when it's moving past us? How does our disagreement about synchronized clocks get translated to his disagreement about the length?

Well, the most direct way to say it is that to measure the length of the train, you have to measure the front and back at the same time. But if you disagree about what at the same time means, then you're going to disagree about the length of the train. So what's going on here exactly? How do the unsinked clocks make people measure different times? I know you don't want to think about the people on the train, but you kind of have to because when we say the train is one kilometer in length, what that means is that it's one kilometer for people on the train, for people not moving relative to the train. By their definition of at the same time, the front and back are one

kilometer apart. That's kind of what it means. But for people on the ground, they have a different definition of at the same time. They think that the people on the train's measurement is wrong. The people on the ground think that the people on the train measure the back of the train first and later measured the front of the train. The people on the ground think the people on the train are not measuring the front and back at the same time, which is why they get a longer measurement. They get a full kilometer. Like imagine if you took a one meter long stick moving past you and you measured the back of it now and the front of it later in 10 seconds or whatever, you'd get a measurement that was way too long. That's what the people on the ground think the people

on the train are doing to get one kilometer instead of 850 meters. The people on the ground think that their own measurements are synchronized and they get 850 meters. The people on the train think that the measurements on the ground are not at the same time. The people on the train think that the people on the ground are measuring the front before they're measuring the back. And that's why the people on the ground are getting a measurement that's too short. So there's no like what is the real length of the train or why does a train look shorter when it's moving faster. Its length depends on your velocity. We just never noticed it before. All right. So let's dig to me this idea of that it has to do with time and let's talk about how time changes due to

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AXS.com. All right, we're asking the question, why do moving objects look shorter? And Daniel, you're saying it really depends on the idea of time being variable. How does time being variable affect Sally and Huang your assistant's measurements of the train? I think time is crucial to resolving this sort of apparent paradox. One of the reasons it's hard to imagine a stick getting shorter or a train getting shorter is because you think of it as a rigid object, which throws you off. Instead, just think of three train cars moving in sync, one in the back, one in the middle,

and one in the front. Now, what if the middle car tells the other two to speed up? From your point of view, the message arrives at the rear car first, which speeds up before the lead car can, effectively shrinking the distance between them. From their point of view, however, the message arrives at the lead and the rear car at the same time, and the distance hasn't changed. When they decelerate again, the reverse happens and the cars come to rest with the same original distance. So you can see how different senses of time lead to different measurements

of distance. But how is it possible for the train cars to get closer together and like not notice? What if you exaggerated the effect so they would bump into each other? Well, the answer is they also shrink because space itself is shrinking. The atoms are like little cars. So think of the train as the front of the train and the back of the train, not as one object. Thinking of it as one long train tricks you into using your intuition, thinking of it as a rigid object, which actually can't exist in our universe. Like when people ask, what happens if you push a stick a light year long? Does one end move instantly sending information faster than light to the other end? No, there's no rigid stick. You push on one end and the pressure wave takes time to reach the other end and to move

it. It's the same with the train. It's linked together, but it's not a rigid object of fixed length. So think about the front and the back separately. Now the super confusing thing about this whole length contraction thing is that it's relative just the way time dilation is. People on the ground think the train has shrunk, but people on the train, and I know you don't want to talk about them, they think the distances on the ground have shrunk because the ground is moving relative to them. Like, let's say they're about to enter a one kilometer long tunnel. I see the train is moving, and so I see it's going to be shorter than the tunnel, whereas the train sees the tunnel is shorter, so who's right? Like, is the train actually going to be in the tunnel or not? And we can,

construct these situations to like confront the universe to say like what's really happening because we imagine that the concept of length is absolute that the train has an actual length right that something has to happen in the universe and only one thing can happen you can't have like two people seeing conflicting events so understanding how time flows and how time is relative is crucial to understanding how both of those things can seem true that somebody on the ground can see the train as shorter and fitting in the tunnel and somebody else on the train can see the tunnel is shorter, so the train always sticks out. Okay, here's this scenario.

And we'll go with your tunnel idea. Okay, so I have a train that when it's standing still in front of me, I measure it to be a kilometer. Now, I build a tunnel that, and the tunnel's not moving, and I measure it, and I make the tunnel to be one kilometer long exactly the same length as the train. Now, I put Juan in the front, at the one end of the tunnel and sadly at the back of the tunnel, okay, and we synchronize our clocks, okay? Now I move the train and I put it inside the tunnel so that it fits perfectly inside the tunnel.

Sally and Juan measure the train to be a kilometer long. Yes. Everybody with OCD out there is like, oh, that's so satisfying. It fits exactly on the tunnel. Yeah. I think by everybody you mean all of our listeners, if they like a physics podcast. Now the train leaves the tunnel, goes away a few kilometers, and then it comes back at half of the speed of light, let's say. And Sally, Juan and I have our clock synchronized.

The tunnel is zooming pass. And we ask Juan to measure when the front of the train passes his spot. And we asked Sally when the back of the train passes her spot at the other side of the tunnel. Are you saying they're not going to report the same time? Because if they report the same time, they don't have to conclude that the train was a kilometer long. No, that's right. They will not measure the same time. Juan, at the back of the tunnel, we'll measure a time earlier than Sally at the front of the tunnel.

So according to you, Juan and Sally, who are in the tunnel's frame of reference, you will see the whole train inside the tunnel. That when the back end disappears into the tunnel, the front nose has not yet emerged from the tunnel and is still 150 meters from the exit of the tunnel. So Sally at the back is going to write down her number and both numbers are not going to come back the same. That's right. Can you explain why? Like nobody is moving. Like Sally, Huang, they were both staying the same. they're the same observer in the same frame, their time was synced, the train was physically

moving past them. Why do they measure a different time? Yes, and Juan and Sally are synchronized according to themselves and people on the ground. So they think their measurement makes sense. And it does. In their frame, 850 meters is the length of the train. And they see the people on the train who are measuring the train to be a full kilometer longer than the people on the ground of measuring, the people on the ground, see the people on the train making their measurements not at the same time. And the reverse is true. On the train, people take measurements at what they think is the same time, and they get one kilometer. And the people on the train think the people on the ground are not synced. That's why it's all about the relativity of simultaneity,

whether you think two things happen at the same time or not. And that's what sets up this fun apparent paradox of whether the train will fit into a one kilometer tunnel. Juan and Sally in the tunnel, when they see it moving through, they see it at 850 meters long. And so they say, yes, the train fit in the tunnel. But you have people on the train, they see the tunnel as shorter. They say, no, my train is still a kilometer long because the train is not moving for them. And so it's still at its same original length. But the tunnel is moving. So the tunnel is shorter. So they see the train sticking out of the tunnel. And in order for special relativity to make sense, you have to somehow are reconciled these two things like what really happened. Did the train fit in the tunnel or not?

Okay. So how do you reconcile it? So it all comes down to time, right? Remember how we talked about earlier in the episode that time is relative, not just how time flows, but whether two things happen at the same time. That came from the observation that the speed of light is the same for everyone, which means people have to disagree about whether events happen at the same time. The example of the beams of light shooting along the train, people see them reaching the front and the back of the time, people off the train see the light hitting the back of the train first. And the way to reconcile that is to have different times for all those people, for time to flow differently. And that's why it's crucial that we understand the clocks and the synchronization and that the front of the

back of the train be measured at the same time. And the crucial thing is that at the same time is different for people on the train and for people on the ground because moving clocks flow differently. Right. So on the ground, Juan and Sally are synchronized and they measure the train to be 850 meters long, but to the people on the train, Juan and Sally are not synchronized. Juan and Sally are measuring the front and the back of the train at different times, which is why Juan and Sally think the train is shorter, and the people on the train think that it's not shorter because the people on the train think that Juan and Sally made a mistake. They're like, no, you guys measure the front and back at different times, which is why you're

telling me it's 850 meters long when really it's a kilometer. How can it make sense for length to be contracted? because it seems to violate our intuition. Like, things have a length, and they should just have a length, and how is it possible for things to get shorter as they get faster because that would lead to all sorts of weird paradoxes? It actually can kind of make sense, and these paradoxes aren't paradoxes that show you that the world works differently

than you imagine. Can it make sense that things moving quickly get shorter? Like, why doesn't that lead to contradictions? Oh, not like why does it make sense, but like why doesn't it leave? to contradictions about the universe because I think we've established it's very hard to make it make sense but it is possible to make it make sense and it makes sense to me and I want to share that connection with everybody because it's a wonderful moment when it all clicks together in your

head and you realize oh it is possible for both people to think the other one is shorter for the people on the train to think the tunnel is shorter and for the people in the tunnel to think the train is shorter here's the detailed breakdown of what's going on with the train and the tunnel Here's how it's possible for the team on the ground to see the train totally inside the tunnel and for the team on the train to see that the train is too long to ever all be in the tunnel at the same time. From the ground point of view, the train is shorter than the tunnel. So when the back end is inside the tunnel, the nose has not yet left the tunnel. Remember that we are comparing two events front and back of the train at what we consider to be at the same time.

But the people on the train think that the ground team is making a mistake and that those events are not actually at the same time. For the people on the train, they think the ground team is comparing the front of the train at an earlier moment to the back of the train at a later moment, which is how the ground team sees the train inside the tunnel. From the point of view of the people on the train, the train is sticking out in both ends of the tunnel at the same time because the tunnel is shorter. The people on the ground think that's wrong. They think the train team came to that conclusion by comparing an earlier back end measurement when the train tail was still sticking out to a later front end measurement when the train knows is now sticking out. And the key is that they're measuring the fronts and the backs at different times.

And it's all because time is relative and simultaneousity is different for people moving at different speeds. And, you know, to me this comes down to like trying to see can special relativity make sense because it fundamentally changes your understanding of the world. that tells you the world really works in a different way than you imagined. And we want the world to make sense. Like, I think back to the first time I ever heard this example of like somebody in a car turning on a flashlight and then hearing that those photons move at the same speed relative

to the car as they do relative to the ground. And immediately my brain was like, hold on, red flag that can't possibly make sense because then like when do those photons hit a wall or some obstacle? People in the car and people on the ground would disagree about that because they all say the photons are moving at the same speed, but there's different distances involved and all sorts of stuff. And so for me, it's about disentangling these feelings of contradiction, these ways that special relativity violates our intuition. You know, how can it possibly be that both these people make honest measurements which conflict with each other? One of the things I love about special

relativity is that it tells you that like people can disagree and both be correct. You know, that's like the fundamental conclusion of, you know, simultaneous that, you know, two people can see different orders of events and both be honest and both be reporting what they see because the order of events depends on your relative velocity in your location and there is no single absolute clock or single sense of space and time in the universe and so people on the ground can see the train fitting in the tunnel and people on the train can see the train not fitting in the tunnel and both be correct like it's correct that if I measure the train when it's standing still it'll fit in the tunnel. And if I measure when it's moving fast, I'm going to measure it being shorter than the

tunnel. Yeah, exactly. And the people can see the train fitting in the tunnel because according to them, they're measuring the front and the back of the train at the same time. The people on the train don't see that happening because they think that the people in the tunnel are not measuring it at the same time because their concept of what the same time means is different than the people on the tunnel. In the end, that's why it all comes down to time, understanding relative time. is crucial because we're talking about a big extended object. It's a kilometer long. So the front and the back are separated by space and separated by time.

And how time flows then has to affect your measurement of the length of it. Because in the end, measuring length means measuring the front and the back at the same time. Right. But again, you're answering the different question than maybe than the one we started with. Yeah. I guess the most direct answer to the question of the episode, why do things look shorter, is that they always have. We just never noticed.

The fact that we ask why is because we've been led astray by our intuition, our unfounded assumption that the world has this property that links are absolute and are always the same at any speed. It turns out that's not true. And we can see that it's not true by doing experiments in various speeds, including very high speeds. Things really do shrink. So that explains why we ask the question because the way the world works is in contrast with the way our intuition works. Why does the world work that way is the follow-up philosophical question? It turns out it has to, in order to be consistent with this other thing we see, that the speed of light is constant for everyone.

First consequence of the speed of light being constant for everyone is that simultaneously is not universal. People at different speeds disagree about what at the same time means. I think Juan and Sally measure the front and back at the same time, but people on the train don't, so we measure different lengths. And the beauty part, the really gorgeous part, is that this is what makes it all click together. You can have some kind of global understanding of how everyone is seeing things differently because you can see, as we just explained, that people are measuring the train at different times

and getting different answers, 850 meters or one kilometer. They all get different answers and they are all right because they are measuring different things. Length at rest means something different than length in motion because it depends. on sinking measurements at the front and the back of the train. Length is not absolute, and it can't be from the world to make sense at high speeds. It has to be relative for everything to be coherent. Like to us, to Juan and Sally, the train really did shrink, I think is what you're saying. Like the space that comprises the train, the space that the train sits in, that is moving

with the train, it contracted. It got smaller. It got smaller for Juan and Sally. for Juan and Sally. And that's just the way it is. Space is contracted. And it's all due to the speed limit of the universe because if it didn't, if that space didn't contract, then things would sort of break down. Yeah. If length doesn't contract, then you break all the rules of special relativity. Another way to think about it is that length contraction is sort of the same thing as time dilation. For a completely separate example that helps people understand the link between length contraction, which we've been talking about today and time dilation, think about what happens if you try to travel to a a distant star at a really high speed. Say you need to get 10 light years away and you travel at 98% of the speed of light. From the point of view of people on earth you left behind, it takes you almost 10 years to get there. But they also see your clock running slowly. They see that for you it's only been two years. That's time dilation, right? But look at it from the other point of view,

from the ship. From the pilot's point of view, the distant star is moving towards her at 98% of the speed of light. So the distance to the star is shorter than 10 light years. And it only takes for about two years to get there because it's only about two light years for her. So she experiences two years to get there because the length was shortened. What's really happening? Well, length contraction is just really another way to look at time dilation. And in the end, it's all about time. I think basically you're saying that the train track to Sally and to Juan's perspective. Yeah. And it's all connected to time. And in the end, time dilation. and length contraction are really just two different ways to see the same effect.

All right. Well, again, special relativity's heart. Especially in an audio format. For those of you who like learning visually, I don't know why you're listening to a podcast. But we're glad that you are. Let's make that clear. We're not saying go watch YouTube. But if you do want to learn more about this stuff, look up space time diagrams.

They're really helpful. It's interesting, though, to think about how malleable the universe is, right? Like the idea that the train would shrink just because it's global. going fast. That's kind of weird. It is very weird. Yeah. And it's weird that it makes sense in the end. That the universe is just so different from the way we imagined it. But you know, that's the project of physics. It's not to just accept our intuitions, but to confront them with data and information and say, how can we make sense of all this? What story can we tell about the

universe that ties it all together? All right. The next time I take a train, I'm going to be thinking about this. Like, am I thinner or am I shorter? Depends if you're lying down or standing up. Yeah, exactly, right? So I should stand up on the train the whole time. Don't forget to buy tickets for Juan and Sally. Yeah, and don't forget to tip the conductor too with a big, fat envelope of money.

No tip contractions here, please. All right, well, we hope you enjoyed that. Thanks for joining us. See you next time. Thanks for listening. And remember that Daniel and Jorge Explain the Universe is a production. of iHeartRadio. For more podcasts from IHeartRadio,

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