What the HECK is Time?! (in Einstein’s Relativity)

hey crazies we all know the difference between space and time right you measure space with rulers and you measure time with clocks then Einstein comes along with his crazy hair and says they're just two parts of the same thing space-time who does he think he is a scientist how dare he just prove our feelings with facts oh wait okay so so let's assume he's right about this what the heck is time then this episode was made possible by generous supporters on patreon a major goal of physics is to make accurate predictions about the behavior of matter and light and for centuries that was done through three dimensional dynamics the study of forces and their effects on motion Newton's laws were of pinnacle importance objects might sit still but they could also move from one place to another over time whether or not the forces were balanced determined exactly what the objects would do forces determined acceleration acceleration determined velocity and velocity determined the path taken it was very methodical a leads to B which leads to C dynamics is all about keeping track of vectors to predict paths the simplest example is a straight path with steady motion that means there are no forces on the object or if there are forces they're perfectly balanced if the object speeds up there's an unbalanced force in the direction of motion if it slows down the unbalanced force is against the motion if it changes direction the unbalanced force is toward the new direction that's the jist of dynamics and it served as well for centuries then Einstein came along and changed everything well not just Einstein but also makovski then Hilbert and Grossman and levy savita all built on the ideas of Gauss Riemann and Christoffel nobody lives in a vacuum what was i right I'm Stein Einstein came along and showed how space and time are just two parts of the same thing space-time but if that's true we can measure time with a ruler or space with a clock which is actually not as weird as it sounds hey map clone how far away is that place again about ten minutes thanks man so it's pretty common to give distance measurements and time units right okay maybe that's just a Midwestern thing the point is we actually go the other way with Einstein's model we measure time as a distance multiplied by the speed of light and fam distance units of course time isn't actually distance there there are some differences which we'll get to later but this new model gives us insights we wouldn't normally see let's say we've got a clone on a spring his position is changing in time why are you using a clone I thought it would look funny and it did kitchen.you something else ok fine I'll use a squirrel this animation is exactly what we'd expect out of dynamics but Einstein and friends imagine time is just another dimension so instead of this we have something that looks more like this as the squirrel bounces back and forth he also moves up through time we call it a spacetime diagram because it has both the space axis and a time axis points on this diagram are called events and this path represents all the events in the squirrels past and future history it's everything that has happened in everything that ever will happen to the squirrel well at least what we predict has happened and predict will happen this is just a mathematical prediction no one actually expects him to do this forever treating time is if it's just another dimension turns three-dimensional dynamics into four-dimensional static geometry yes static geometry I'm only showing motion in this animation so it feels more familiar to you but this is more like an omnipresent and on the temporal viewpoint in this model nothing moves all these events just exist it's a static image again it's not necessarily reality I'm not saying the past and the future are already written this is just a model a powerful model but a model nonetheless so let's see what some of those dynamics examples earlier look like now if a squirrel is sitting still on a table this is its path through space-time it's completely up and down it's only through time a squirrel moving steadily to the right has a spacetime path like this a squirrel moving steadily to the left has the opposite path accelerated paths look a little different if the squirrel is speeding up as it moves across the table its space-time path is curved a similar thing happens if the squirrel slows down its path is also curved straight paths are steady motion curved paths are accelerated motion a spacetime diagram makes telling them apart extremely obvious you don't have to consider the dynamics you can just see it in the geometry so far this is all pretty general stuff to do anything more specific we need some math say we've got two events maybe up high five in Michigan and a rocket launch in Florida each of them happens at a particular place and a particular time maybe they happen 1,200 miles apart and one day apart but how long is this separation line directly between them to figure that out we're gonna need Pythagorean theorem yep the thing you probably had memorized in elementary school a squared plus B squared equals C squared where a B and C are the side lengths of a triangle in space it tells us the straight-line distance between objects or locations given some set of coordinates why is that an S you know I don't actually know okay Google why is s used for position it's short for the German word stricka-- which means roots huh who knew okay so S is for route apparently Delta means change in so this is the change in position otherwise known as displacement we also have a triangle in our space-time diagram but we have a slight problem I've been saying the entire video that space and time aren't exactly the same thing this squirrel can move in either direction in space along the table but it must always move forward in time the forward more time we're just pretending like in space you might say we're imagining it the time axis is more like an imaginary axis than a real one so let's stop dancing around it and just say it's imaginary that means Pythagorean theorem for this triangle looks like this we've picked up a negative sign space-time is non Euclidean that means these diagrams aren't going to obey your intuitions about geometry these axes are perpendicular but so are these seriously these are perpendicular this this and this are right triangles all of them are right triangles any paths along the 45 degree diagonals have a length of zero this picture and this picture are the same picture just from two different perspectives parallelism and causality might be preserved but angles and distances are not the geometry is super-weird to emphasize this difference instead of calling it a four-dimensional space-time we call it a 3d plus 1 D space-time or just a three plus one space-time with this model wall extremely weird makes predictions that match reality this equation keeps the speed of light constant it's just the maximum speed of causality it's the maximum speed of cause and effect with some quick trigonometry it predicts the time and length depend on the observer well as long as you remember to use hyperbolic trig functions instead of the regular ones it predicts a lot of weird things but we've verified them all by experiment they're all real things that happen and things get even weirder when space-time is curved let's consider a path like this hey didn't you agree not to use clothes change my mind I do what I want there are actually two possible reasons it would be curved the first possibility is that there's a force on the clothes we mentioned that one earlier the other possibility is that space-time itself is curved yes this is a real possibility to describe a curved path with Pythagorean theorem we need to be a little more careful this only works on straight paths between events so let's imagine this curved path is just a collection of events if the events are close enough together then the mini path between each pair of events is approximately straight buckle-up crazies it's calculus time each of those little straight pieces is called a line element and since they're straight we can use Pythagorean theorem on them it's just like the one with the deltas except we use a lowercase D instead it lets us know it's a tiny change rather than a big change this notation is really important so you better get used to the D wait that came out wrong you know what I mean a line element tells us how nearby events in space-time are separated from each other this is for what we'd call flat space-time meaning there's no curvature but the space-time around a non rotating spherical object will look different it's curved the line element must be adjusted because different events have different separations even the time component has to be adjusted time can be curved this path might be curved not because of a force but because time itself is curved which is kind of crazy but the concept of curved space-time has made accurate predictions about our universe deviations in the orbit of mercury gravitational lensing gravitational waves the existence of black holes even the appearance of black holes time isn't universal anymore it depends on an observers motion and their proximity to high concentrations of matter and light time is relative and it can be curved but you know what isn't relative causality if one event can influence another then the order of those events is always maintained even in all this relativistic weirdness so what exactly is time time is a representation of causality including a time axis in our diagram turns a dynamics problem into a geometry problem straight paths are steady motion curved paths are accelerated space-time diagrams are powerful tools but they're just tools when it comes down to it time is about causality we may not agree on the space between two events or the time between two events but if they're causally connected everyone agrees on the order of those events without causality we might not even agree on past present and future causality is where our concept of time comes from causality is more fundamental than time so did I set off your Google assistant today please share 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 I don't believe 2d creatures could see each other that way I'm not sure we can imagine one or two dimensional spaces can they really see that 2d surface is a 3d sphere doesn't light need three dimensions to exist it's just a metaphor for us okay I do appreciate you keeping me on my toes though anyway thanks for watching

Channel: The Science Asylum

Views: 400,065

Rating: 4.9320221 out of 5

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Id: 7HBKEDyFTv8

Length: 11min 49sec (709 seconds)

Published: Tue Apr 28 2020