Modern Physics - Part 13

[00:00:00]today is part 13 of our look at modern physics and today we are going to look at how general relativity affects space around a black hole now we've already talked about the fact that one of the earliest predictions of general relativity is that gravity should bend light now remember einstein said that gravity isn't really a force that reaches out and grabs light but is the very bending or warping of the fabric of space-time around a central mass so let's take for example an object that is behind the black hole now because the black hole is by its nature black it is a region of space that light is not emanating from you would if you were close enough see it as sort of a black sphere in space just a blackness a devoid of light now if there were an object behind the black hole you would think that the silhouette of the black hole would block your view of that object but because space-time is so severely distorted around a black hole the light from that object would bend around the black hole and towards our eyes in other words we would essentially be able to see around the back side of the black hole but what's behind the black hole would appear shifted off to the side a little bit from our perspective but the really weird thing is this happens on all sides of the black hole remember a black hole is a three-dimensional object so that very same object whose light is bending around the right side of the black hole in this image well light will also bend around the left side of the black hole and that produces something super weird because i'm getting an image of that same object coming at me from the right side making it appear it's to the right of the black hole but i'm also also getting an image of that very same object bending around the left side of the black hole and i'll see another image of the same object on the left side of the black hole so i will end up seeing multiple distorted images of the exact same object and so as i approach a black hole i will begin to see that light from objects behind the black hole starts to become distorted and stretched out in sort of a ring around the region of space where the black hole is this phenomenon is called gravitational lensing and it's based on the idea that gravity basically acts like a lens so just like a lens that you would have in your glasses your contact lenses or in a telescope or a microscope what a lens does is it takes light coming in and it bends its path so that it bends towards in this case a single point in space which you call the focal point well that's essentially what's happening here light from this distant galaxy is bending through the distorted space time around this foreground galaxy and it's lensing the light towards the earth and as a result i end up seeing light from that galaxy gravitationally lensed so here's an example of a foreground galaxy this is called an elliptical galaxy it's basically a big ball of mostly reddish stars and that's what you see at the center of this image but if you look around it you'll see these little streaks these arcs that seem to be parts of a circle going around that and this is a real image taken by the hubble space telescope and what these streaks are are not some super flat weird bent galaxy but the light from galaxies that are behind this foreground galaxy bending around the gravitational well created by that foreground galaxy and being stretched and distorted out and so we can see that stretching and distortion of light around that galaxy here's some more extreme examples so here's a foreground galaxy and then you see what is almost a complete ring around that galaxy what that actually is is light bending around that foreground galaxy and there's a more distant galaxy behind it which is most likely a blue spiral galaxy and its light is getting bent in all directions around that and coming to our eyes and so we see that distorted image lastly this is an interesting phenomenon that um einstein predicted and therefore it's named after him but if you look at this uh spiral galaxy right here if you zoom in on it you'll see that there are these four yellow dots the top the bottom the left and the right of that galaxy those are not four different objects those are the same object seen from four different perspectives as light from that object that's behind that spiral galaxy bends around the top bends around the bottom bends around the right bends around the left and it creates what's known as an einstein cross and and if you have the right kind of object in the right alignment you'll create this sort of these four different images of the same object okay so this brings us to perhaps the most important image of the last decade and that is in 2019 uh published to the general public was the first direct image of a black hole now prior to 2019 we knew that black holes existed because we had indirect images of black holes what do i mean by that well many black holes are actually what we kind of call feeding black holes they're stuff falling into them and this stuff falls into them for reasons we'll talk about a little bit later the material gets torn to shreds and settles into a rapidly spinning disc around the black hole as it spirals in and this is called an accretion disk and as that material gets torn apart and collides with itself it heats up to tremendous temperatures that release x-rays a very high energy form of light and so we can see these really bright x-ray sources in our galaxy coming from very concentrated regions of space which is exactly what you would expect to see around a black hole so these x-ray images we know are black holes but in those images you can't actually see the black hole directly so in 2019 last year this image was released and this is the very first direct image of a black hole that has ever been seen and what you're basically looking at is this dark region in the middle of this bright region is what we call the shadow of the black hole it's essentially the black hole but for reasons that you can explore further in a video that i will post on schoology it is it is basically you're looking at that region of dark space you're looking at the black hole now the bright region around it is the accretion disk and this is the super cool part so pay attention because this part gets pretty awesome because black holes are so concentrated space and time warp severely when you are close to them and so as material falls into a black hole forming this accretion disk that accretion disk basically settles into a ring not unlike the rings of saturn now when you look at saturn you can see the sides of the ring and you can see the front of the ring but you can't see the back of the ring because of course the back of the ring is behind saturn and you can't see through saturn well with black holes something really weird happens so i want you to imagine that this is like saturn you've got a central object with a flat disc of material around it that goes from the sides to the front to the sides and back around the back but because space-time is so severely distorted around a black hole light from the back side of the ring can actually bend around the top of the black hole and make it to your eyes essentially allowing you to see around the black hole to the other side and so this top portion of the ring that appears to form this sort of rainbow over the top of the black hole is an optical illusion it's not really above the black hole but you are able to see light from that back side of the ring bending around the top and so what you're basically seeing is the top side the top surface of the far side of the ring so you're basically seeing what's behind the black hole by standing in front of the black hole and so it makes it look like the secretion disk comes around and then suddenly bends up and over the black hole and then back around the front it's not a real physical bending of matter but instead of bending of light but here's what's super weird what is this ring below the black hole well that is the underside of that back portion of the ring so just like the top surface of the ring shoots light over the top of the black hole the bottom surface of the ring shoots light under the bottom of the black hole allowing us to see around the bottom of the black hole and up towards the underside of that back surface so it's as though it's basically taking the disc behind it and it's splitting it into two allowing us to be see both the top and the bottom of it simultaneously so what you're basically seeing in this image is the sides the front and then the back top half and the back bottom half all simultaneously from one perspective this is what you would see if you neared a black hole with an accretion disk around it and in fact that's exactly what you're seeing in this image so that ring is basically the light coming from the accretion disk bending around the black hole and creating this ring of light around this dark region of space in between so now you have some idea of how light is severely distorted around a black hole and how that might affect what you would see as you approach a black hole well let's talk about what you would experience as you neared the black hole and even fell into it i want to remind you first of all that the idea of gravity and the warping of space-time is simply that the denser the object that is the more mass compacted in a smaller amount of volume the more distorted or more extreme the curvature or if you want to think of it as the flow of space-time gets near the surface of that object a black hole is infinitely dense and therefore it has no surface it's it's a it's matter concentrated in a volume of zero so without any surface in the way you can go through an infinite amount of space-time curvature before you end up hitting the singularity and so as a result within a black hole space-time is allowed to curve or flow infinitely and that means that as you get closer and closer to the singularity of a black hole things can get super extreme in fact more extreme than any other object in the universe well that extremity of space-time curvature or space-time flow is felt as an extremity of gravity so from the newtonian perspective this gravitational pull we feel as we get into more and more distorted space time so let me give you an example of this imagine that this represents the fabric of space-time around a black hole and let's imagine that up here where this green line is you are farther from the black hole and down here where this red line is you are closer to the black hole now you can see just based on the way the image is drawn that space-time is more stretched or more distorted when you're closer to the center than when you're further so if we take a look at this green line here let's imagine that this green line is your body well far from the black hole you could argue that the force of gravity on your feet is a little bit stronger than the force of gravity on your head because your feet are closer to the black hole than your head is but if you're far from the black hole the difference in those forces might be relatively insignificant so much so that you don't even feel that difference and in fact if you stand up right now it is technically true that earth's gravity is pulling harder on your feet than it is on your head but you don't feel that difference because it's very insignificant but if you got closer to the black hole the difference in gravity between the part of your body that is closest to the black hole and the party of your body that's furthest from the black hole becomes more and more and more significant and it is this difference in the gravitational force or if you want the flow of space time or curvature of space time between part of an object that's closer and part of an object that's further that creates some intense outcomes now let's start with something not particularly intense but that you're most familiar with and that is tides on earth most of you probably know that the tides on earth are caused by the moon's gravity as it pulls on the oceans of the earth but how does it work well works the same way we just described okay the side of earth that is closest to the moon gets pulled more strongly by the moon's gravity than the side of the earth that is farther from the moon and so the difference between gravity pulling stronger on one side and less strong on the other side creates a sort of stretching force and that stretching force is what in physics we call tidal forces and the reason we call them tidal forces is because that stretching force is what creates the tides on earth and so what happens is that this stretching force as a result of the stronger pull on the closer end and the weaker pull on the further end causes the oceans to bulge outward and so as the earth rotates once every 24 hours we will move into a tidal bulge and out and then 12 hours later we will move into another tidal bulge and out again and this is what creates the two high tides and the two low tides every single day it is this stretching of the oceans of the earth due to the moon's gravity due to the tidal force of the moon's gravity now a more intense example of this is the rings of saturn which we referenced earlier why does saturn have rings around it and the answer we think is because at some point in the past an icy moon strayed too close to saturn and because one side of the moon was closer to saturn than the back side there was this stretching or tidal force created by saturn's gravity and if that moon gets close enough to saturn those tidal forces can be strong enough to actually tear the moon apart and as the moon gets torn apart it breaks into pieces and those pieces settle into a disk orbiting around saturn which we today see as saturn's rings we know saturn's rings are basically chunks of ice with some rock in there and for an icy object which is less dense than say a rocky object the tidal forces of saturn are enough to tear that object apart and strip it into a system of rings now just a fun fact and we'll refer to this later at the end of the lesson the distance at which this tearing apart occurs is called the roche limit so just keep in mind the roche limit is the distance at which an object gets torn apart by tidal forces gravity doesn't get any more severe than around a black hole and therefore tidal forces don't get any more severe than around a black hole and because a black hole has no surface and therefore you can just infinitely get closer and closer and closer there will come a point where the title forces between your head and your feet becomes severe enough that you basically cross the roche limit for your body and that means that you will get torn apart and so at some point the difference in the force of gravity between your feet and your head will become so intense that it will actually tear your body in half so if you were to dive feet first into a black hole you would get stretched vertically as you simultaneously get squeezed horizontally and that's because not only is gravity stretching you vertically but space-time itself is being stretched and narrowed down into an ever steeper tube of space-time and so it's kind of like taking your body and squeezing it through a tube and so this is what would happen to your body your body would eventually snap in two and then those pieces would eventually snap into and then as you got closer and the tidal forces become more extreme those pieces would snap into and at some point the tidal forces would be at so extreme that even the difference in gravitational force between one side of an atom and another side of an atom would be so extreme it would tear the atom apart and so the end result would be your body turning into a stream of subatomic particles funneling infinitely towards the singularity at the center of the black hole this is a process that astrophysicists refer to as spaghettification because essentially it's like squeezing pasta through a pasta extruder and on the other side you get spaghetti this is what would happen to the atoms of your body so the question is if you're going to get spaghettified as you fall into a black hole when does that spaghettification happen does it happen before you cross the event horizon or does it happen after you cross the event horizon or put yet another way would you have any time to experience what the inside of a black hole is like before you're torn apart or would you get torn apart before you ever got to experience the inside of a black hole and the answer is it depends okay so the short shield radius which i will remind you is what determines the where the event horizon of the black hole is is directly proportional to the mass of the black hole so if i increase the mass of a black hole by a factor of a thousand then its event horizon will expand outward by a factor of a thousand as well so a black hole that's a thousand times more massive will have an event horizon that's a thousand times further out but what about the roche limit remember the roche limit is the distance at which you start getting torn apart the spaghettification distance well the roche limit depends on the cube root of the mass so what does that mean that means if i have a black hole that's a thousand times more massive the roche limit doesn't increase by a factor of a thousand but only increases by a factor of 10.

[00:18:45]what this means is that as you increase the mass of a black hole the event horizon grows much faster than the roche limit does so what does this mean practically well for black holes that form from the collapse of a single star which we call stellar mass black holes those black holes have low enough mass that the roche limit is outside of the event horizon which basically means that as you approach the black hole you will get spaghettified before you have a chance of crossing the event horizon so if you want to dive into a black hole and have some time to experience what it's like to be inside of a black hole don't dive into a stellar mass black hole you will get spaghettified before you cross the event horizon but for a super massive black hole a black hole that has a mass of millions or even billions of times that of a stellar mass black hole the event horizon is actually far outside the roche limit and what that means is that you could cross the event horizon to the black hole and feel almost nothing until later on falling deeper into the black hole you finally get ripped to shreds so if you're going to dive into a black hole and you want to be able to experience what it's like to be inside you want to dive into a super massive black hole and you will still have some time before you get ripped to shreds but here's the key point you will not be able to avoid getting ripped to shreds because once you cross the event horizon every direction in the black hole is down and no matter which way you turn no matter which way you travel you will go straight towards the singularity space only points in one direction in fact more accurately time only points in one direction inside of a black hole and time only moves forward towards the singularity which means you will get spaghettified but at least you'll have some time to experience what it's like so if you could cross the event horizon of a supermassive black hole without being spaghettified what would you experience inside the black hole and if somebody watched you fall into that black hole what would they see would they see you cross the event horizon and then just suddenly disappear from the universe would they be able to watch you get spaghettified once you got close enough to the center what would we see and in order to answer that we have to account not only for the distortion of space but also the distortion of time and that's what we'll get to next time