How does length contraction work in relativity? Do moving objects really get shorter? What about from their perspective? How are we supposed to make sense of any measurement? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO GENERATED)

How can time run at different speeds and reality still be sane? We've learned from Einstein's special theory of relativity that moving clocks run slow. The faster you go in space, the slower you go in time. This is no trick of perception, not just clocks, but all physical processes run slow. If you were to see me blazing by you at nearly the speed of light and you were to look at the watch on my wrist, it will tick slower than the watch on your wrist.

I will age slower than you. It takes forever for me to do literally anything from your perspective. We've done episodes in the past about time dilation, the twin paradox, and all that, the age of the universe, and hopefully, after all those episodes and after a century since Einstein's relativity, while we may not fully understand time dilation, we can at least get used to it, which is common in physics much to the horror of my students. Moving clocks run slow. Okay.

Let's just take that as a bare fact of existence. Einstein said so and he seems like a smart guy, so we'll go with it. But let me illustrate an example to show just how absurd the universe becomes once you allow for time dilation. There's this little subatomic particle called a muon. It's like an electron's more massive cousin.

Because it's massive, it doesn't live all that long, right around 2.2 You make a muon and you blink, and it's gone. Now, we know that muons are created in the upper atmosphere when high energy cosmic rays strike various and sundry air molecules. Muons are a byproduct of this process, which is super fun and deserves its own episodes, so just ask. And we know that we can build muon detectors on the ground and watch as the muons come screaming in from directly above. In fact, you can do this with household equipment to make a cloud chamber, which is yet again another cool topic that you should totally ask about.

And now comes some very basic math. We can record the muons coming into our detectors. We know they're coming in from the upper atmosphere, and we can calculate their speed. And they're pretty fast, nearly the speed of light. But the upper atmosphere is kind of far away.

And even at that speed, the muons simply don't have enough time to make it to the ground in their 2.2 microsecond lifespan. The solution? Moving clocks run slow. The muons are moving close to the speed of light, which means their internal clocks are slower than ours, and so they have a much longer lifespan than they would if they were staying still. Voila, the muons live long enough to reach the surface where they promptly die, but that's another story.

But that's from our perspective. The muons get a perspective too. What's the story from their point of view? According to the muon, it only ever lives for 2.2 microseconds. It knows nothing else.

Remember that for time dilation, that's something that you observe about other moving objects. It's never something that you measure for yourself because you are never moving relative to yourself. You are only ever going to live your life. You will never feel fast or slow. I mean, physically, the psychological perception of time is its own beast that I would love to tackle in a future episode, so you know the drill.

If your lifespan is 70 years, then according to you, you will never live more or less than 70 years. According to other people, it will be different. So according to the muon, it will only live for 2.2 microseconds. So how does the muon have enough time to reach our detectors on the ground? From our perspective, once we fold in time dilation, it makes sense.

It all works. But what about from the muon's perspective? How do we get these 2 radically different viewpoints? Our perspective, where the muon has an extended lifetime, thanks to time dilation and more than enough time to reach the ground, and the muon's own perspective, where it only has its normal lifetime and doesn't have enough time to reach the ground. How do we get these perspectives to agree?

I'll go ahead and spoil the ending here. It's through something called length contraction, which is the other side of the coin from time dilation. But to help us understand length contraction, we need to go back in time and see how the concept developed. From my own perspective, learning physics, I rarely understand something just by being told what the the thing is. I mean, I could grasp the mathematics and solve homework problems and and eventually do physics, but to actually understand these concepts at a deeper level, something I've personally found is that the more I dig into the past to see how a concept was developed, when I learn about the history, the false starts, the almost theres that lead to a new idea, that helps me shape and hold a new concept in my mind.

And that's what I wanna share with you today, so that hopefully, I mean, it's easy. It would take me 30 seconds to just state the fact of length contraction. 1 but one, that's way less fun. And 2, I think this helps me better understand a concept, and I hope the same is true of you. So, hopefully, you walk out of here in about a half hour, not just being able to regurgitate the fact of length contraction, but hold on to a deeper understanding of it.

And don't worry. It's a wild journey. And that journey starts with the myth, the man, the legend, the GOAT of Electricity and Magnetism, James Clerk Maxwell. Now, I have spent way too much time on this podcast gushing about how awesome Maxwell was, and that's not going to stop now. Maxwell was awesome because he unified 3 independent lines of research.

Electricity, magnetism, and light. And that last bit light is what we need to focus on today. Maxwell discovered that what we call light is really waves of electricity and magnetism. He was not the first to guess that light might have a wave like nature or be made of waves that have been going on for decades, if not centuries, before him. But he was able to show for the first time what light it is.

It is waves of electricity and magnetism. But like all waves, these waves needed to, you know, wave something. Sound waves move through air. That's what a sound wave is. It is displacement of air.

Ocean waves move through, well, oceans. It's it's water. You see the waves moving through the water. Waves need a medium, a thing that allows for the wave to pass, something to carry the wave. And so, Maxwell, along with many other people, believed that light waves traveled through a substance, known today as the appropriately old timey phrase of the luminephrous ether.

That's a mouthful, but it's simply the stuff that suffuses all of space and time. It exists in the vacuum. It exists everywhere. It's the thing that allows for light to do its wavy thing. Now, this ether had to have some strange properties.

You couldn't feel it, you couldn't touch it, you couldn't smell it, you couldn't sense it, otherwise, we would have noticed it by now. But it had to allow light to wave through it, so it had to exist even though it was very hard to detect. At the time, in the late 1800, there were many debates about the nature of the ether, most specifically asking whether other stuff like us or the earth that moved through the ether dragged a little bit of it behind us, whether a lot or a little. I will most definitely not be wading into the nature of those debates because, well, it turns out that everybody was wrong, and they were just fighting over nothing, which is like an academic dirty version of holiday dinners with extended family members. So we don't need to go into that debate.

But they didn't know they were wrong until a pair of scientists decided to go and measure our movement through the ether in 18/87. That pair was Albert Michelson of the Case School of Applied Science and Edward Morley of Western Reserve University who devised an experiment that we now call the Michelson Morley experiment at a place that we now call Case Western Reserve University. Of course, other people were going for this too. This wasn't even their first crack at it, but this was the first time there was a successful measurement of what they were aiming for. The basic idea is that if the ether exists, we should be swimming through it right now.

There's this ether, this stuff that's hard to detect, but definitely there That suffuses the entire universe and it allows light to pass from place to place, and, we're we're we're moving through it. We're plowing through it right now. Now, the properties of the ether prevent us from feeling it directly, but we should notice it as a change in the speed of light. Think of all of our motion, especially the rotation of our axis, the orbit around the sun. At different times of day and at different times of the year, we should have different relative motions through the ether.

Sometimes we are going this way through the ether. Sometimes we are going that way through the ether. Sometimes we are just holding steady relative to the ether. This is a rough metaphor. Pretend you are in the middle of the ocean, surrounded by waves, and you start paddling in a circle.

Sometimes you'll go with the current, sometimes you'll go against the current, sometimes you'll go along perpendicular to the current. When you are doing this, the waves that surround you on the ocean will appear to be longer or shorter. So imagine if you're paddling in a circle on the ocean, and the current is going in one direction, there are all these waves going in a direction, you're trying to measure those waves. If you're moving with the waves, then as you're paddling, you go from one crest, and you paddle paddle paddle, and you have to catch up to another crest. It looks like a very long wavelength.

And if you're going in the opposite direction, when you're going against the current, then you reach one crest of a wave and you pat a button, and all of a sudden, the next crest is right there, cause it's coming towards you. So by measuring the speed of light, we can get a sense of our motion through the ether because we'll be moving in different directions relative to the current. This is an incredibly rough metaphor, but I hope it gives you the picture. The M and M experiment. Am I allowed to call it that?

Let's let's roll with it. The m and m experiment did this by being the most precise measurement ever of the speed of light in different directions. They used what's called an interferometer where they took a light source and they split it in 2 different directions that were perpendicular to each other and then allow that light to bounce off mirrors and then interfere with itself. So if the path that the light takes on each of these directions is exactly the same, it will be perfectly interfered, and they won't see anything. But if the speed of light is slowed in one of those directions, it won't be perfectly interfered with each other.

They won't cancel each other out perfectly, and you'll get some sort of signal. That's a very high level overview of the M and M experiment. We'll just we'll just keep going. It was incredibly detailed. They they this was one of the most precise measurements ever made in the 1800.

It was a brilliant experimental design, and so many amazing details went into it that I am unfairly skipping over, but we'll just have to save that for another day, the actual construction of this experiment. The goal was to measure the speed of light in different directions as the earth rotated on its axis and as it orbited around the sun. And the M and M experiment tried to measure these changes in the speed of light as we're moving through the ether, and it totally failed. I mean, hugely failed. Outright bombed.

The M and M experiment didn't see anything. They saw zero changes to the speed of light. Now, earlier experiments had also failed to see a change in the speed of light, but they had large enough uncertainties that you could reasonably claim that we were still moving through the ether, but just not enough to notice it with the crude experiments that we had. But the M and M result was indisputable. The uncertainties, the errors, they were small enough that it ruled out motion through the ether.

The speed of light was the speed of light, No matter where we were moving relative to the ether. And now we've got a problem. Light is a wave, and it must move through something. We call that something the ether. But we can't seem to be able to measure our own motion through the ether.

So what's going on? And it's here where we enter one of my favorite times as a physicist. The part where everybody just starts making things up. You know, whenever theory and experiment collide, or even theory and theory collide, whenever there is a collision, there is this phase, there's this fertile phase where people just start chucking stuff at the wall to see what sticks. It's happened multiple times throughout history, it's going on right now, All sorts of conversations about quantum gravity, cosmological problems.

It's just people making stuff up to see what works and what doesn't work. It's a fun time. It's an exciting time reading about it in history, seeing all these people bubble up with all their outlandish ideas, and then it turns out one of these outlandish ideas is kind of right, but no one expected. It's fun. Amongst all the ideas that were being cooked up in the late 1800 to explain how the ether can exist and yet the speed of light remain constant regardless of our motion through the ether, was devised, started, seeded by a physicist by the name of Oliver Heaviside.

Now, Heaviside, he was self taught. He rewrote Maxwell's equations in the form we use him today. He was a genius. He was a little bit weird, but that he's another story. He noticed something interesting.

He noticed, that we have these things called electric charges, you know, like like an electron. Imagine an electron. All this, by the way, was happening in a time before we knew that electrons existed, which is amazing. We didn't even know that atoms existed yet. But we knew, thanks to the work of people like Michael Faraday and James Clerk Maxwell, that these electric charges like an electron have a field surrounding them.

Now I've talked off and on in this show about fields of various kinds, especially when we talked about quantum field theory. But even in the 1800, we had this concept of a field, or you might be familiar with the magnetic field. You take a bar magnet. You sprinkle some iron filings around it. You get this cool pattern.

What you're mapping out is the magnetic field surrounding the magnet. And electric charges, like an electron, have a field as well. They have an electric field. The electric field measures, you know, how strong its electric force is, basically. Mister Oliver here discovered that when you take an electron and set it in motion, when you start moving it, when you take a charge and you start moving it, its electric field doesn't stay perfectly symmetrical.

It doesn't stay perfectly spherical. It scrunches up. It the field tends to smush along the direction of motion by a certain factor that is related to the speed of light. For the nerds, that factor is the square root of 1 minus the velocity squared divided by the speed of light squared. But we don't need to be nerds right now.

We just need to know that Heaviside discovered that when you set electric charges in motion, natural consequence of equations was that its own electric field tends to squish up a little in the direction of motion. That's weird. Right? Well, he shrugged and moved on with his life, but then someone else picked up the story and that someone else was Heinrich Lorentz. Lorentz had an absolutely wonderful thought.

He's like, look, presumably, you, me, planet earth, the Michelson Morley setup have a bunch of electric charges inside of us. Keep in mind, this is before we knew that atoms existed, but it that's a good guess, like, okay, we discovered these things, electric charges, you've got some inside your body, I've got some inside my body, we're all good. And the fields associated with any of these charges smush up when they are set in motion. So maybe, maybe we physically shrink when we move. Because if I am just like a ball of charges, and the electric field determines how closely connected, how closely packed these charges can be, and if the field starts getting smooshed up, well, that means the electrons themselves can get closer together.

So that when I am set in motion, when I move, I squish a little along the direction of motion. I have a little bit of length contraction physically because my stuff, my guts are getting squeezed together. Voila. This can explain the Michelson Morley experiment. We can't measure changes in the speed of light because, yeah, light is getting squished by our motion through the ether.

We should be seeing changes to the speed of light just like we're paddling around the ocean and trying to measure the speed of the waves going by. We should see different speeds depending on our direction. But our measurement device is also getting squished when it moves. And all the squishes cancel each other out so you never get to see anything different. So, yes, say the Michelson Morley interferometer is going in this direction and it should see a slower speed of light or a faster speed of light, but that part of the device that's moving in that direction is getting squished and it's canceling out.

So you never get to measure changes in the speed of light, because anytime you try to measure changes in the speed of light through motion, your your instrument that you're using to measure gets squished along with the light itself, and they cancel each other out. Length contraction is the answer to this riddle. This was considered a rather successful idea. It worked and explained all the data. The ether existed.

It allowed light to move through it. It allowed light to wave, but we couldn't detect our motion through the ether because any time we try to move through the ether, it does definitely change the speed of light, but it also switches stuff along the direction of motion and this cancels out so we never get to see it. And this worked. Not a bad idea. It's crazy, but we like crazy.

And then Einstein showed up and started being Einstein, and he asked a very important question. He asked, if this lumeniferous ether is always and forever undetectable no matter how clever we are, we're never going to be able to see or sense the ether. We can't even measure a change in the speed of light because our instruments keep squishing every time that we set them in motion. So why do we need it? Why don't we just let things contract on their own?

Not to explain away some experimental result that we don't like, but because it's a bare fact of the universe. And everyone was like, Einstein, dude, what's your Patreon? Patreon.com/pmsutter. He did not have a Patreon subscription channel, but I do. And you can go to patreon.com/pmsutter.

It's how you keep this show going. Yes. You. I believe in you. And if you enjoy the show, please consider going to patreon.com/pmsutter and contributing just a little bit every month to keeping the show going.

I truly do appreciate it. This is Einstein's big result that gave us special relativity. Other people were working in the direction of relativity. Hevyside, Lorenz, other people like Poincare that I haven't mentioned. But nobody made the leap that he did.

Einstein's like, look, you got a problem with your physical theory? Just chuck the entire theory. Can't come up with a satisfactory theory to explain an experimental result? Just to declare the result as a fact of nature and move on. Easy peasy.

Why didn't any of you nerds think of this? You can't measure changes in the speed of light? Speed of light's constant. Objects contract along the direction of motion when they're when they're set in movement? Okay.

Like, they it just is. Like, who cares about trying to explain it physically? It just happens. Einstein declared length contraction to be a feature, not a bug, in the universe. No more ether.

No more attempts to fit a square electromagnetic peg into a round ether hole. Lengths contract when they move. Period. End of discussion. The end.

You're welcome. Here is the key idea though, the key difference. Einstein's length contraction was different than Lorenz's. For Lorenz, it was a physical effect. It was stuff smooshing together because their electric fields got weird.

For Einstein, length contraction was a feature of space itself, independent of the actual objects, and this realization allowed Einstein to take yet another powerful leap. To make it all work, Einstein realized that there has to be some give and take. Length, contraction, and time dilation go hand in hand. No two clocks ever agree, and no two rulers ever agree either. There is always a little bit of give and take.

For every time dilation on one side for one observer, there is a length contraction for the other observer, and this is how it all connects. Einstein was able to get here by taking length contraction away from being a physical effect to effect of space itself, of motion itself. This isn't squishing electric fields. This has nothing to do with our intermolecular forces. It's just a bare fact of reality and it is tied to time dilation.

Folks, I need to take a quick break and mention that this show is sponsored by BetterHelp. Can you believe the year is already halfway over? I swear sometimes you blink, and it's just, what is time? I should do a 10 part series on the nature of time and the human perception of time because it is. It's a little bit challenging to understand.

And with that passage of time comes memory, regret, pride, anticipation, you know, all the human emotions surrounding time. And so now that we're halfway through the year, maybe we should pause to see where we are and if we're we're reaching the goals and achieving the vision that we wanted to achieve this year. And one way to do that is with therapy. I've benefited from years of therapy, and I think you can too. Give it a shot.

If you're thinking of starting it, give BetterHelp a try. It's all online. You just fill out a brief questionnaire, you get matched to a licensed therapist, and you're off to the races. You can switch therapists at any time for no additional charge. Take a moment.

Visit betterhelp.com/spaceman today to get 10% off your 1st month. That's betterhelphelp dotcom/spaceman. Let's come back to the muon and see how this works. From our perspective, the muon's clock runs slow, and it has more than enough time to make it to the ground. From the muon's perspective, rulers shrink.

It only lives for 2.2 microseconds. Its lifetime doesn't change according to its perspective, but from its perspective, the ground is way, way closer. It has more than enough time to cover the very short distance from the upper atmosphere to the ground, and it all works. From our perspective, the muon is able to make it to the ground because it has a longer lifespan, And from the muon's perspective, it's able to make it to the ground because the ground is closer because lengths contract when you're in motion. This is not a physical aspect of the muon itself.

It's not like the muon gets smaller. And from the muon's perspective from the muon's perspective, it's staying still and the ground is rushing up towards it. The Earth is set in motion according to the muon's perspective, and so the air, the ground, the entire globe of the Earth gets squished along its line of sight. From the muon's perspective racing towards the Earth, the Earth looks like a thin pancake. So there you go, flat earthers.

That's your answer. It turns out you're just moving close to the speed of light, and so the Earth appears flat from your perspective. Don't tell them I said that. It all depends. This is how Einstein made it all work.

It all depends on perspective. It all depends on whether you are doing time dilation or length contraction, And it's not a physical manifestation of an object. It is baked into your perspectives of time and space itself. The rulers and clocks you use to measure everything else in the universe. From our perspective, we're staying still.

The muon is in motion. It experiences time dilation and reaches the ground. From the muon's perspective, it's staying still and the earth is rushing towards it. The earth is the one doing the moving, and it measures a length contraction. Its distance to the ground is not a 100 miles or a 100 kilometers.

It's like 2 miles, 2 kilometers, more than enough time to cover in 2.2 microseconds, and it all works, even though it's crazy. We live in a universe where nobody agrees. Everybody's measurements about duration of events, about lengths, they all disagree, but special relativity is exactly the mathematical machinery needed to make the universe make sense again. It's the machinery we need to connect different perspectives. If I say the muon is doing this and the muon is saying it's doing something else, we can all agree.

We're going to agree to disagree. We know we are going to have different perspectives of what goes on, but special relativity is the machinery that allows us to connect from one perspective to another and translate and say, oh, yeah. From our perspective, it's doing this in its time dilation. From the muon's perspective, it's doing that in its length contraction. This doesn't make sense.

It's hard to navigate. But it pains me to say this. The universe doesn't care what we think, what we want, what our intuitions are. This violates everything about common sense. But the universe does what the universe does whether we like it or not.

And while we really like the idea that clocks are synchronized, that links are the same throughout the universe, the universe can do whatever it wants. Here's an example to show how absurd the universe can become once you include length contraction. Because once you have both time dilation and length contraction in the picture, we have to give up something else that seems very, very precious to us. We have to give up the concept of simultaneity. Usually, we assume that everyone will agree when an event starts, when it ends, how long the event takes.

We synchronize our watches, and we go off in our life. And we assume that no matter what we're doing, our our watches will remain synchronized. That when something happens, we all agree that it happened at the same time, at the same location, the same ordering and sequence of events, but special relativity breaks it down. The only way you get length contraction and time dilation to work hand in hand is if we give up our preconceived notions of simultaneity. Let me give you another example to show how this shouldn't work, but it also kinda does.

I can put a 5 meter car into a 2 meter garage. I've got a garage, 2 meters long. It's got doors on both ends, a front side and a back side. And then I've got a car that's 5 meters long, and I can put that car inside of the garage and have both doors closed and not break the car. In order to get it to work, I need the car to be racing towards the garage at roughly 90% the speed of light.

It let's presume it's a very nice car. When the car races through, I will watch watch watch watch watch. And when the car from my perspective from my perspective, the car gets length contracted. If it's traveling 90% of the speed of light towards me, it will appear as if the car is only 2 meters long. That's the effect of length contraction.

The car looks squished along the direction of motion. So this squished car from my perspective comes racing by, it enters into the garage, and at the exact moment when it's bumper to bumper, fits inside the garage, I'm gonna hit a button, and I'm going to close both doors simultaneously, and then I'm going to instantly raise them because the car is moving through. And I don't want my garage to break, and I don't wanna break the car. And I don't want a car traveling at 90% of the speed of light to hit anything. That'll be kind of bad.

So for an instant, I can fit that 5 meter car into a 2 meter garage because it's traveling at 90% of the speed of light, and I see the length contraction. From my perspective, it totally works. Length contraction, check. It appears shorter. For a brief moment in time, it fits inside the 2 meter garage.

But let's say you're the one driving. According to you, the car is still 5 meters long because you're literally inside of it. The car is not moving relative to you. Remember, relativity is all about the perspective of the observer on other objects. It's a property of space and time, not a physical manifestation.

If Lorentz was right, then you would measure a 2 meter car because your car would be literally squished. But Lorentz was wrong and Einstein was right. You can break out a ruler. Anytime you're driving that car, you can brush out your ruler. Bumper to bumper, you're always and forever going to measure 5 meters.

There's no length contraction because it's not moving relative to you. To make it worse from your perspective, the car is staying still and the garage is coming towards you at 90% of the speed of light, so the garage is even smaller than 2 meters. It's less than a meter across. So it makes the problem even worse. How do you fit?

Because we give up simultaneity. In my perspective, hitting the button, the doors of the garage open and close at the same time. They're simultaneous. But from your perspective, because you're in motion, the doors don't close at the same time anymore. Simultaneity isn't a thing.

From your perspective and the machinery, the mathematics of special relativity spells out exactly how this unfolds. You enter the garage and the moment your front bumper goes right up to the edge of that of that back door. You've entered the garage. You've gone through the garage, and now you're right at the edge of the back door. You see the door come down and then the door come up.

That's me hitting the button because that's me thinking you're fitting inside of the garage. But from your perspective, only that back door closes and then opens. Then you move through it, and now your rear bumper is over at the front door over at the entrance, and then you look back and you see that door closed and that door open. According to you and your very nice car, you were never in the garage. You just passed through because the doors opened and closed at different times.

According to me, both doors closed and open. I flipped them closed, flipped them open simultaneously, but simultaneity is broken in special relativity. Different observers will disagree about the ordering of events. You passing through the garage, according to you, you never you passed through the garage, you never fit in it because the doors were open at different times, But according to Mio, it happened. How can both of these statements be true?

Well, the the truth is both of these statements are true. Because statements like this, statements about the length of objects, statements about the duration of events, statements about the ordering of events, depend on the observer, and we have an entire apparatus for translating from one observer to another. What does stay true? What does stay true are the laws of physics. Maxwell's equations say that the speed of light is c, and that's it.

So you'll always ever measure the speed of light to be c, the speed of light, because that's what the laws of physics say. We've tested special relativity in just about every way imaginable because it's more than a theory of physics. It's a metathery. It tells us how we need to construct theories so that all observers are able to account for each other and relate to each other. You take this special relativity toolkit and apply it to other scenarios to get a correct accounting of nature.

Take special relativity plus Newtonian gravity, you get general relativity. You take special relativity plus quantum physics, you get quantum field theory. You take special relativity plus Maxwell's equations, you get Maxwell's equations because he's awesome. Why do we get to apply length contraction to everything? Because length contraction isn't about objects.

It's not about physical manifestations. It's not about compression of objects. It's about space itself. It has to do with the fundamental structure of reality. Moving objects will perceive a different universe, then objects staying still and different observers will disagree.

Some will call things length contraction. Some will call it time dilation. Some will call events simultaneous. Others will call it not simultaneous. It's a big hot mess.

Length contraction is a part of the story. It works because it has to, because it's the only way to explain the evidence. The Michelson Morley experiment tried to find our motion through the ether and failed. So Einstein just said there is no ether. The only way to explain the constancy of the speed of light is to say, well, the speed of light is just constant.

It's just a fact of nature. In order to make that work, Einstein had to take this idea of length contraction that Lorentz created from a physical squishing of the object and elevate it to a property of space itself. And in doing so, he had to connect it to time itself. And in doing so, he had to connect it to the breakdown of simultaneity. No two observers ever agree.

Why does length contract? That's how length contraction works. Because it's tied into our fundamental construction of space and time. You can't have time dilation without length contraction and vice versa, and you can't have either of those without a breakdown of simultaneity. You can't have a universe where everyone agrees about the duration of events, the length of rulers, and the ordering of events.

You can't. Why does length contraction work? Because the universe likes it that way. I hope that by the end of this episode, you've understood a little bit about length contraction. That it's a property of space, not a property of of physical squishing.

And that it depends on the perspective of different observers and it's all a giant mess. But if you don't understand it, that's okay. To be perfectly honest, it it still doesn't quite fit entirely in my head. It's such a weird concept. But like I said, in physics, you don't necessarily understand things.

You just get used to them. And so I guess we just are going to have to get used to length contraction. Thank you to at chewbacco on Twitter, adamh on email, and brandonb on email for the questions that led to today's episode. And thank you to all my Patreon contributors, especially my top ones this month. That's patreon.com/pmsutter.

I'd like to thank Justin g, Chris l, Alberto m, Corey d, Stargazer, Robert b, Tom g, Nyla, Bike Santa, Sam r, John s, Joshua, Scott m, Rob h, Scott m, Lewis m, John w, Alexis Gilbert, m, Rob w, Demetrius j, Jewels r, Mike g, Jim l, Scott j, David s, Scott r, bbjj108, Heather, Mike s, Michelle r, Pete h, Steve s, Wattwatbird, Lisa r Incuzzi. And please keep those questions coming. Askaspaceman@gmail.com or just check out the website, site, askaspaceman.com. Please keep sharing this episode. Word-of-mouth is how more people find out about the show.

I truly do appreciate it. I love all the questions you send me, and I will see you next time for more complete knowledge of time and space.

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