Daniel and Jorge Explain the UniverseDaniel and Jorge wrestle with the weird consequences and hard questions of special relativity!
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Hey Daniel, how long does it take you to do the research for one of these episodes?
You know it used to take me quite a while, but I'm getting quicker at it.
Mm Is that because time passes more quickly as you get older, like a special relativity thing?
Maybe, Or I guess I've just gotten more efficient at the preparation.
Oh, yeah, like you can read faster, or you can process information better.
No, I think I just developed a better mental whorehe simulator that can predict what you might be interested in or what you might not be interested in.
Oh it 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 a cartoonist 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.
M 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 mat cartoonist 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.
M 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 or 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 us gold coins or dollars. If the inspiration strikes.
You, you take tips. 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.
Oh, WHOA, where is your university.
It's a public university, man, So it's not like some students just like draw a pile of cash. I think it must have been some club organizing in the room before us or something.
Hmmm. Sounds like maybe they were trying to bribe you.
I don't think so. I think somebody must have panicked when they realized they left it behind.
Or 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 Explain the Universe, a production of iHeartRadio.
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 at 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 did say I was opening bribery. You said I was opening bribery, and I.
Said I wasn't it sounds like you're open to tips quote unquote tips.
People are welcome to send us donation to the podcast, but it's not going to affect how I grade in my class. Now, 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 needs to depend on your point of view. And also how fast you're.
Going, Because something we've learned over the last hundred 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 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 eight 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 all hundred years hegol Einstein discovered something called relativity special in 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 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, 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 the speed of lighter 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 lengths 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.
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 valuation 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 which direction this ruler 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 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 zo or in any direction. If it's moving along its length, it's going to look shorter.
I see. So like if someone launched a ruler really really fast from my left and 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 wonder why things look shorter when they're moving really fast.
Thanks very much to everybody who answers these questions. We'd love hearing your voices, and we'd love to hear more of your voices, so please don't be shy and write to us two questions at Danielandjorge dot com.
So think about it for a second. Why do you think moving objects look 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 wavelengths shorten, Right, they get shorter, So like all objects, you know, they get a little louder, the colors look little brighter, the wavelengths shorten, and so the object looks shorter because the wavelengths of the colors of the object to shorter.
Yeah, 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. Not really sure.
I think that for a human eye optics, moving objects look actually longer because of motion blur, but special relative to states that moving objects get shorter.
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 also sound very sciency talking about Doppler effects and red shifting and space dilation.
Yeah, motion blur. Some of these answers are a way off and some of them are pretty close.
Pretty cool. These are people that you found in your department or people on the internet.
These are just folks from the internet listeners to this podcast.
Nice. Well, let's dig into it, Daniel, how what is the physicist definition of length dilation?
So we usually call it length contraction.
Wait, is there a difference? Can you also have the 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 meterstick 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? Well, is the 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 meterstick, you call that the proper length. Then you zoom that meterstick by you at like ten percent 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 eighty five percent of its proper length. And as you get up to like ninety nine percent of the speed of light, it will shrink down to like fifteen percent of its proper length. If you get to like ninety nine point ninety nine percent of the speed of light, it'll be just over one percent 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, buy 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 asked 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 the 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 rulers further from you and part of the rulers 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 at 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 then 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 draining It seemed 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 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 and 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 assistants 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 eye sort of look 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 was stationary.
All right, well, I think we just 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 and we say, you know, Juan measured the back of the train at this time, and Sally measure 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 assistance and how they're measuring the length of this ruler and or this train. Maybe really understands what we mean by things looking shorter or not. So let's dig into these details. But first let's take a quick break.
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All Right, we're talking about length contraction due to special relativity, and that doesn't have to do with how long this podcast is, right or how much by questions that dilate the length of the running time of this episode.
That's exactly what I was going to say. Yeah, no, but it's good. It's important explain exactly what we need. 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 the 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 said, we hire a bunch of assistants and lay them out in the 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 I want to measure how long the train is. Yeah, saying, don't take a 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 ten 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 ten seconds at the same moment. They all read one hundred seconds at the same moment. So we have a bunch of people now at different locations with synchronized clocks.
How do you synchronize a clock. 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 distanced.
M okay. So then each of these assistants 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 in 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.
See 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 you know, ice sculptures and chocolates for your picnic and whatever. And then you look at the numbers and you say, all right, one measure the back of the train to be negative half a kilometer at the same time. Sally measured the front of the train to be a location plus half a kilometer. 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 and following. So now like you, you sort of ask, okay, it 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 train. And if you measure them at different times, like if one's clock was out of sync, or one was lazy, or one made a mistake or something in a measure of 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 in the back at the same time. It seems sort of obvious to even spell that out, sort of dumb, like, duh, that's what length really is. But it's going to turn out to be really important part of understanding length contraction.
Okay, So that's I guess that's one way to measure it, or that is that the only way to measure the train.
And that's sort of the standard setup. It allows you to avoid things like how longs they take informations, travel from here to there, and all that stuff 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 wo 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 and somebody standing at the front of the train. They know where they are and it doesn't really matter when they make the measurements of the train isn't moving.
Mmm, 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 will be one kilometer long. And now you're saying that's not really how long the train is.
Yeah, let's say I measured 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 time is that the train is shorter, that it's only eight hundred and fifty meters long instead of one kilometer.
Mmm.
Interesting, Now we're going to explain why that happens. Where does special where activity come in that makes you measure it to be eight hundred and fifty meters. You're telling me that the assistance would measure the train to be shorter than a kilometer. But I guess my intuition is, like, what how can that be? Because like, 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 expect it to still be that length later. That sounds reasonable, but it actually contains a big assumption, the assumption that lengths are absolute rather than real 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 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 simultaneity 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 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 forward 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, 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 simultaneiti, 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 simultaneiti do a 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 clogs. 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 why measures in front of the train, Sally measures the back of the train, and they write down than a piece of paper what their measurements and then they bring the papers to you. Aren't those things synchronized. I'm not saying how what you're saying about time and how that's changing your assistance measurement.
Yeah, I think that those measurements are synchronized. And I think my measurement of eight hundred and fifty meters is totally right. But if you're on the train, then you think that those measurements are not synchronized. You're like, no, Wan 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 synchronized.
Okay, so forget the people on the train. Let's just focus on Huang and Sally.
Okay, Wan 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 thing to be eight hundred and fifty.
Meters yes, whereas somebody on the train says.
That, no, forget, forget the person on the train. Now the train stops, turns around, comes back, and parts in front of me.
Mm hmm.
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 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.
You say we synchronize our clocks, So isn't it sort of like a universal time?
I mean, 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 anymore 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 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 a 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 UNSYNCD 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 measured in the back of the train first and later measure the front of the train. The people on the ground think that 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 ten seconds or whatever, you get a measurement that was way too long. That's what the people on the ground think that people on the train are doing to get one kilometer instead of eight hundred and fifty meters. The people on the ground think that their own measurements are synchronized, and they get eight hundred and fifty 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 into me this idea of that. It has to do with time, and let's talk about how time changes due to special relativity and see if that maybe explains why the train we measure the train can be different lengths here and then later when it stops. So we'll dig into that, but first, let's take another quick break.
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All right, we're asking the question why do moving objects look shorter and danny You're saying it really depends on the idea of time being variable at this time being variable affect sally and why your assistance 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 and 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 that 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 as moving and so I see it's going to be shorter than the tunnel, whereas the train sees the tunnel as shorter. So who's right, Like is the train actually going to be in the tunnel or not? And we construct these situations to like confront the universe and 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 as shorter, so the train always sticks out.
Okay, here's this inner 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 measured it to be a kilometer. I build a tunnel that and the tunnels not moving, and I measure, and I make the tunnel to be one kilometer long, exactly the same length as the train. Now I put Juan in at one end of the tunnel and Sally 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's just it fits perfectly inside the tunnel. Sally and Juan measured the train to be a kilometer long.
Yes, everybody with OCD out there is like, ooh, that's so satisfying. It fits.
Yeah. I think by everybody, you mean all of our listeners. If they like the 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. That's say and Sally, Juan and I have our clock synchronized. The tunnel is zooming pass and we ask want to measure when the front of the train passes his spot, And we ask Sally when the back of the train passes her spot at the other side of the tunnel. Are you saying they're going to report the same time, because if they report the same time, then I have to conclude that the train was a kilometer long.
No, that's right, They will not measure the same time. One at the back of the tunnel will 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 one hundred and fifty meters from the exit of the tunnel.
So Sally at the back is going to write down her number and they're going to 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 did 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. It does in their frame. Eight hundred and fifty meters is the length of the train, and they see the people on the train or measuring the train to be a full kilometer longer than the people on the ground are 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 whether they think is the same time, and they get one kilometer and the people on the train think that people on the ground are not syncd 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. One in Sally in the tunnel when they see it moving through, they see it at eight hundred and fifty 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 reconcile 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 same 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 to 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, One and Sally are synchronized and they measure the train to be eight hundred and fifty meters long. But to the people on the train, Wan and Sally are not synchronized. Wan and Sally are measuring the front in the back of the train at different times, which is why Wan 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 One 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 eight hundred and fifty meters long when really it's a kilometer. How can it make sense or 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. They just show you that the world works differently than you imagined. Can it make sense that things moving quickly get shorter? Why doesn't that lead to contradictions?
Oh?
Not like why does it make sense? But like, why doesn't it lead to contradictions about the universe? Because I think we'd establish 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 of 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 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 simultaneity is different and for people moving at different speeds. And you know, to me, this comes down to like trying to see can special relativity makes sense because it fundamentally changes your understanding of the world. It 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'll both be correct.
You know.
That's like the fundamental conclusion of you know, simultaneity, that you know, two people can see different diferent orders of events and both be honest and both be reporting what they see, because the order of events depends on your relative velocity and 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 in 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 in the back at the same time.
Right 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 lengths 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 at 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 simultaneity 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. Eight hundred and fifty 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 who makes sense at high speeds, it has to be relative for everything to be coherent.
Like to us du Juan and Sally, the train really did shrink, I think, is what you're saying. Like the space that comprises the train, that the space that the train sits in that is moving with the train, it contracted, It got smaller.
It got smaller for want In, Sally, for Juan.
And Sali, 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, 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 distant star at a really high speed, Say you need to get ten light years away, and you travel at ninety eight percent of the speed of light. From the point of view of people on Earth you left behind, it takes you almost ten 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 distance star is moving towards her at ninety eight percent of the speed of light, So the distance to the star is shorter than ten light years, and it only takes her 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 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 is hard.
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 valuable the universe is, right, like the idea that the train would shrink just because it's going fast. It'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 is 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 and 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, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. House US dairy tackling greenhouse gases. Many farms use anaerobic digestors to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit you as dairy dot COM's Last Sustainability to learn more.
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