Length Contraction is NOT an Illusion!

thanks to brilliant for helping support this episode hey crazies you've probably heard of length contraction and time dilation before it's the idea that your length shrinks and your time slows the faster you move but it's not just an idea it's real it's measurable we've tested it we'll spend this entire video discussing how and why it happens and we'll do it visually so it's as intuitive as possible no ridiculous hypotheticals no fluid analogies no historical fluff just geometry let's do this [Music] this episode was made possible by generous supporters on patreon sure sure welcome to relativity the show where everything is made up and the measurements don't matter all right stop right there this model is real it's been experimentally tested atomic locks in the iss particle accelerators muons from space muons from space the universe looks different to different observers and actually a looks is an understatement the universe doesn't just look different to different observers it is different to different observers that's why we call it relativity observers disagreeing about measurements doesn't make those measurements fake it just makes them relative say we're looking out the window of my space station at a couple identical rockets one is at rest relative to us the other is being flown by rocket clone they're both identical but the moving one is shorter that's length contraction so are they like physically compressed well not really stress compression is when the atoms get closer together that's not what i mean length contraction is just when two observers disagree about how to measure length it's not an optical illusion though the rocket is shorter for one of the observers but rule number one of relativity says no frame of reference gets priority over any other frame of reference if rocket clone measures the length of their own rocket it would appear normal for them it's my space station that's moving and therefore my space station that's length contracted measurements like length are relative to the observer and so is time it would look to us as the rocket clone's clock is ticking slower we call that kinetic time dilation time dilation caused by motion according to rocket clone it's our clock that ticks slower the ideas in relativity are weird i'll give you that but they're very real and they actually make a lot more sense if you just suck it up and do the geometry doing dynamics in space is fine but you miss a lot of intuition that way adding a time axis changes everything this is a space-time diagram the rocket is still moving directly to the right in space that upward motion you're seeing is only through time if you've seen a lot of my videos you've seen diagrams like this before they're very powerful powerful space-time is what we call a hyperbolic geometry anyone's first exposure to hyperbolas is usually with conic sections it's what you get when you slice a cone parallel to its height on an xy plane the most basic hyperbola would look something like this x squared minus y squared equals one if we include scaling factors for each direction we can tweak it a little but the basic shape is always the same any geometry that has that specific pattern is called a hyperbolic geometry the minkowski space time in special relativity is a hyperbolic geometry the x-axis is space and the y-axis is time this minus sign makes it hyperbolic in fact these hyperbolas would be the paths of something accelerating just remember we've suppressed the other two space dimensions these accelerating rockets are only moving left and right not up and down the up and down direction is time not space you still with me okay let's keep going anything stationary follows a path that lines up with the time axis anything moving steadily follows a straight path anything accelerating follows a hyperbolic path because hyperbolic geometry the axes are not absolute though these belong to our space station but these belong to rocket clone notice how the time axis lines up with his path now different observers can and will disagree about lots of measurements because they take those measurements in their own frame of reference the angle that a path makes with the time axis tells you the speed of that thing in that reference frame i repeat speeds are measured as angles small angles are slow large angles are fast angles close to 45 degrees are near the speed of light fast fast wasn't this video supposed to be about length contraction yes yes we're almost there every individual point on this diagram is called an event grid lines that line up with the space axis are all the events that happen at the same time grid lines that line up with the time axis are all the events that happen at the same place that last bit is going to be very important because before we can understand how length contraction happens we need to define length first length is the space-time separation between two events that occur at the same time what think about any length you've ever measured you put some kind of ruler or tape measure down and you look at the markings the reason that works is because you have two events one on each end of the ruler and you're measuring them simultaneously you do essentially the same thing if you're measuring the length of a rocket it's just that not everyone agrees on which events happen at the same time remember grid lines that line up with the space axis are all the events that happen at the same time if two observers have different space axes they'll disagree on which events are connected since the events that define length have to be simultaneous they'll disagree about length too and space-time diagrams allow us to predict what those lengths will be if we measure the length of the rocket we would use these two events because for us those happen at the same time if rocket clone measures the length he would use these two events because for him those events happen at the same time you can see right away the lengths are different the real question is how different well remember that speeds are measured as angles this angle is the relative speed between us and the rocket do some quick trigonometry and bam you've got yourself a ratio if we see rocket clone moving at 55 the speed of light he might measure a length of 20 meters but we'll measure 16.7 meters we see a contracted length what about time dilation the geometry works for that too a time interval is the space-time separation between two events that occur at the same place grid lines that line up with the time axis are all the events that fit that description if two observers have different time axes they'll disagree on which events are connected based on this definition of time intervals that means they'll disagree about clocks too so let's say my clone's clock is at the center of his rocket we need two events these two occur at the same place for him but not for us we'll need to use these two events again these separations are obviously different the question is how different using the relative speed and some trig bam you've got a ratio if we see rocket clone moving at 55 percent the speed of light he might measure a time interval of one minute but will measure 1.2 minutes that's kinetic time dilation so you can see now that weird relativistic effects are just the result of geometry a hyperbolic geometry where speeds are measured as angles but a geometry nonetheless if two different observers disagree on which events happen at the same place and which events happen at the same time then they're going to disagree on just about everything they'll disagree on how long a rocket is they'll disagree on how much time has passed for that rocket but it all makes sense in the geometry of space-time frankly it couldn't be any other way so did that help you understand length contraction a little better or did i go too deep let us know in the comments thanks for liking and sharing this video don't forget to subscribe if you'd like to keep up with us and until next time remember it's okay to be a little crazy if you want to learn more about special relativity brilliant is a good place to start the first section of their course on special relativity has a quiz on length contraction and time dilation where you'll use lorentz transformations to solve problems later in the course you'll get a chance to see the full power of space-time diagrams in action it's just one of over 60 interactive courses in math science and computer science that brilliant has to offer their thought-provoking content helps guide you to mastery by taking complex concepts and breaking them into bite-sized understandable chunks you'll start by having fun with their interactive explorations and over time you'll be amazed at what you can accomplish if this sounds like a service you'd like to use go to brilliant.org science asylum today the first 200 subscribers will get 20 off an annual subscription [Music] in our last video we talked about the cmb in orbano kiro said wait a minute isn't orange the new black nope technically speaking black is the new orange i'm such a dork anyway thanks for watching you

Channel: The Science Asylum

Views: 135,463

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Id: TxW6_E3uLuo

Length: 10min 19sec (619 seconds)

Published: Wed Jul 29 2020