Hi guys! I'm Jade, you're watching up and atom, and today we're diving into the weird and wonderful world of relativity with an Einsteinian paradox. Needless to say get ready for your mind to be blown, and then blown again. And make sure you stick around to the end because the solution to this paradox is pretty juicy. So there's a mysterious pole vaulter. Let's call her Alberta. Alberta is running toward a bar which just happens to be on a farm. This farm is pretty small so she needs to run through an open barn on her way. Earlier that day she was curious about the length of her pole so he measured it against the side of the barn and found it was exactly twice its length. Knowing nothing about a strange pole-vaulter running around the farm, you're busy working on a new contraption in there. You've set up a timer where, when it goes off, signals to the front and back doors of the barn to simultaneously close and opened again. You go out to see if your contraption works and just as the timer goes off Alberta runs through the barn! So the question is: can both doors be closed with Alberta inside the barn? Well no, I mean we just said that the pole was twice the length of the barn, so there's no way she could fit inside if she were running at any kind of normal human speed. But let's make things interesting. What if Alberta was running at nearly the speed of light? This is where things start to get a bit crazy. When objects are traveling at nearly the speed of light they actually contract in length. This is known as length contraction. So you might be thinking yeah cool I mean that makes sense if an object is moving by really fast my eyes don't have time to keep up with it so it looks shorter than what it is. But it doesn't just look shorter, it actually is shorter. If you fire a meter long missile at close to the speed of light, and take a snapshot of it in mid- flight, it will actually measure to be less than 1 meter. By how much depends on how fast it's going. So is Alberta is running toward the barn at near lights peed, from your reference frame she contracts in length in the direction of travel. In other words, to you, she looks all squished up. So it's perfectly plausible that both doors can be closed with her inside, even if it's just for a split second. While this is all very bizarre, it still isn't a paradox until we consider things from Alberta's perspective. And why would her perspective be different from yours I hear you ask? Well, because all motion is relative. Imagine you're at the train station watching a train go by. From your reference frame you are standing stationary on the platform and it's the train that's whizzing past. Now imagine you're on that train. Now you are standing stationary on the train and it's the platform that's whizzing past. So you might be thinking: well really it's the train its moving even if it doesn't seem that way. But think about this. Imagine you're floating up in space watching the train drive across the Earth. It's a very high speed train travelling at a thousand miles an hour east to west. The Earth spins on its axis a thousand miles an hour in the exact opposite direction, so to you up in space, it looks like the train is stationary and the earth is moving. All motion is relative, now let's get back to the barn. So far you're an observer watching a squished up Alberta run through the barn. The timer goes off closing both doors with Alberta inside, they open again and she continues on it near light speed. The real paradox begins when we take a look from Alberta's reference frame, because to her, she is stationary and it's the barn that's moving toward her at nearly the speed of light. So then if the barn is what's moving it's also what's getting squished up in length contraction, there's no way that at any point Alberta could fit in the barn with both doors closed. From your reference frame Alberta easily fits in the barn, but from her's it's impossible. So what's actually happening? I mean surely you're not both right? Well actually you are. This is the juicy part. The solution lies in what we mean by the doors closing at the same time. Special relativity tells us that there is no absolute time, there are only reference frames. We experience different things happening at different times depending on where we are and how fast we're moving. The reason why you haven't experienced this and why you might not believe me is because these effects are only obvious at near light-speeds. The fastest you've probably ever traveled was on an airplane which are about a millionth of the speed of light. Relativistic effects are pretty hard to detect when you're moving around so slowly. So if we look back at what's happening with Alberta and her pole, from your reference frame the timer goes off, and the signal reaches does A and B at the exact same time, and so both doors shut simultaneously with Alberta safely inside. Now from Alberta's reference frame the barn and its doors are all moving. Door A is effectively running away from the signal, so it takes a longer time to reach it because it has more distance to cover in the chase. Door B on the other hand is moving to meet the signal, so it takes a shorter time to reach it because it has less distance to cover. So put together, as Alberta enters the squished up barn, door B closes and quickly opens again letting her through, and then once the back of her pole is inside, door A closes and opens again. Told you it was juicy. Thanks so much for watching I hope you enjoyed this video if you did make sure to give it a like and share with a friend if you think that they would enjoy it. If this is your first time here welcome to the channel and don't forget to subscribe because I upload a new physics video every Thursday. Oh! And one more thing, if you know any physics paradoxes please let me know in the comments below I love paradoxes and i would love to do more videos on paradoxes if that's what you guys like so yeah let me know if you know any good if these paradoxes and i got from that i will see you next time Bye!
