The following is a summary and article by AI based on a transcript of the video "Something Strange Happens When You Follow Einstein's Math". Due to the limitations of AI, please be careful to distinguish the correctness of the content.
00:00 | - You can never see anything enter a black hole. |
---|---|
00:03 | (bell dings) |
00:04 | Imagine you trap your nemesis in a rocket ship |
00:07 | and blast him off towards a black hole. |
00:10 | He looks back at you shaking his fist at a constant rate. |
00:14 | As he zooms in, gravity gets stronger, |
00:17 | so you would expect him to speed up, |
00:19 | but that is not what you see. |
00:21 | Instead, the rocket ship appears to be slowing down. |
00:25 | Not only that, he also appears |
00:27 | to be shaking his fist slower and slower. |
00:30 | That's because from your perspective, |
00:32 | his time is slowing down |
00:35 | at the very instant when he should cross the event horizon, |
00:38 | the point beyond which not even light can escape, |
00:41 | he and his rocket ship do not disappear, |
00:45 | instead, they seem to stop frozen in time. |
00:51 | The light from the spaceship gets dimmer and redder |
00:54 | until it completely fades from view. |
00:57 | This is how any object would look |
00:59 | crossing the event horizon. |
01:01 | Light is still coming from the point where he crossed, |
01:04 | it's just too redshifted to see, |
01:08 | but if you could see that light, |
01:10 | then in theory you would see everything |
01:12 | that has ever fallen into the black hole |
01:14 | frozen on its horizon, including the star that formed it, |
01:19 | but in practice, photons are emitted at discreet intervals, |
01:22 | so there will be a last photon emitted outside the horizon, |
01:26 | and therefore these images will fade after some time. |
01:29 | - This is just one of the strange results |
01:32 | that comes outta the general theory of relativity, |
01:34 | our current best theory of gravity. |
01:36 | The first solution of Einstein's equations |
01:38 | predicted not only black holes, |
01:40 | but also their opposite, white holes. |
01:43 | It also implied the existence of parallel universes |
01:46 | and even possibly a way to travel between them. |
01:50 | This is a video about the real science of black holes, |
01:53 | white holes, and wormholes. |
01:56 | - The general theory of relativity |
01:58 | arose at least in part due to a fundamental flaw |
02:00 | in Newtonian gravity. |
02:02 | In the 1600s Isaac Newton |
02:04 | contemplated how an apple falls to the ground, |
02:06 | how the moon orbits the earth and earth orbits the sun |
02:09 | and he concluded that every object with mass |
02:12 | must attract every other, |
02:14 | but Newton was troubled by his own theory. |
02:17 | How could masses separated by such vast distances |
02:20 | apply a force on each other? |
02:22 | He wrote, "That one body may act upon another at a distance |
02:26 | through a vacuum without the mediation of anything else |
02:29 | is to me, so great and absurdity that I believe no man |
02:33 | who has a competent faculty of thinking |
02:34 | could ever fall into it." |
02:38 | One man who definitely had a competent faculty of thinking, |
02:42 | was Albert Einstein and over 200 years later, |
02:45 | he figured out how gravity is mediated. |
02:48 | Bodies do not exert forces on each other directly. |
02:52 | Instead, a mass like the sun curves the spacetime |
02:55 | in its immediate vicinity. |
02:58 | This, then curves the spacetime around it |
03:00 | and so on all the way to the earth. |
03:03 | So the earth orbits the sun, because the spacetime |
03:06 | earth is passing through is curved. |
03:09 | Masses are affected by the local curvature |
03:12 | of spacetime, so no action at a distance is required. |
03:16 | Mathematically, this is described |
03:18 | by Einstein's field equations. |
03:20 | Can you write down the Einstein field equation? |
03:23 | - This was the the result of Einstein's decade of hard work |
03:26 | after special relativity |
03:28 | and essentially what we've got in the field equations |
03:30 | on one side it says, |
03:32 | tell me about the distribution of matter and energy. |
03:34 | The other side tells you what the resultant curvature |
03:37 | of spacetime is from that distribution |
03:40 | of matter and energy and it's a single line. |
03:43 | It looks like, oh, this is a simple equation, right? |
03:46 | But it's not really one equation. |
03:47 | It's a family of equations and to make life more difficult, |
03:51 | they're coupled equations, so they depend upon each other |
03:54 | and they are differential equations, |
03:56 | so it means that there are integrals |
03:58 | that have to be done, da, da da. |
04:00 | So there's a whole bunch of steps that you need to do |
04:02 | to solve the field equations. |
04:04 | To see what a solution to these equations would look like, |
04:07 | we need a tool to understand spacetime. |
04:11 | So imagine your floating around in empty space. |
04:14 | A flash of light goes off above your head |
04:16 | and spreads out in all directions. |
04:19 | Now your entire future, anything that can |
04:22 | and will ever happen to you will occur within this bubble |
04:27 | because the only way to get out of it |
04:29 | would be to travel faster than light. |
04:31 | In two dimensions, this bubble is just a growing circle. |
04:35 | If we allow time to run up the screen |
04:37 | and take snapshots at regular intervals, |
04:39 | then this light bubble traces out a cone, |
04:41 | your future light cone. |
04:43 | By convention, the axes are scaled so that light rays |
04:46 | always travel at 45 degrees. |
04:48 | This cone reveals the only region of spacetime |
04:51 | that you can ever hope to explore and influence. |
04:55 | Now imagine that instead of a flash of light |
04:57 | above your head, those photons were actually traveling in |
05:00 | from all corners of the universe |
05:02 | and they met at that instant |
05:03 | and then continued traveling on |
05:05 | in their separate directions. |
05:08 | Well, in that case then into the past, |
05:10 | these photons also reveal a light cone, |
05:13 | your past light cone. |
05:15 | Only events that happened inside this cone |
05:17 | could have affected you up to the present moment. |
05:21 | We can simplify this diagram even further |
05:23 | by plotting just one spatial and one time dimension. |
05:26 | This is the spacetime diagram of empty space. |
05:29 | If you want to measure how far apart |
05:31 | two events are in spacetime, you use something called |
05:34 | the spacetime interval. |
05:36 | The interval squared is equal to minus dt squared, |
05:39 | plus dx squared, since spacetime is flat, |
05:43 | the geometry is the same everywhere |
05:45 | and so this formula holds throughout the entire diagram, |
05:48 | which makes it really easy to measure the separation |
05:50 | between any two events, but around a mass, |
05:54 | spacetime is curved and therefore you need to modify |
05:57 | the equation to take into account the geometry. |
06:00 | This is what solutions to Einstein's equations are like. |
06:04 | They tell you how spacetime curves |
06:06 | and how to measure the separation between two events |
06:09 | in that curved geometry. |
06:12 | Einstein published his equations in 1915 |
06:15 | during the First World War, |
06:16 | but he couldn't find an exact solution. |
06:19 | Luckily, a copy of his paper made its way |
06:22 | to the eastern front where Germany was fighting Russia, |
06:25 | stationed there was one of the best astrophysicists |
06:27 | of the time, Karl Schwarzschild. |
06:30 | Despite being 41 years old, he had volunteered |
06:33 | to calculate artillery trajectories for the German army. |
06:36 | At least until a greater challenge caught his attention, |
06:40 | how to solve Einstein's field equations. |
06:45 | Schwarzschild did the standard physicist thing |
06:47 | and imagined the simplest possible scenario, |
06:49 | an eternal static universe with nothing in it |
06:52 | except a single spherically symmetric point mass. |
06:55 | This mass was electrically neutral and not rotating. |
06:59 | Since this was the only feature of his universe, |
07:01 | he measured everything using spherical coordinates |
07:04 | relative to this center of this mass. |
07:06 | So r is the radius and theta and phi give the angles. |
07:10 | For his time coordinate, he chose time as being measured |
07:13 | by someone far away from the mass, |
07:15 | where spacetime is essentially flat. |
07:18 | Using this approach, Schwarzschild found the first |
07:20 | non-trivial solution to Einstein's equations, |
07:23 | which nowadays we write like this. |
07:26 | This Schwarzschild metric describes how spacetime curves |
07:30 | outside of the mass. |
07:32 | It's pretty simple and makes intuitive sense, |
07:34 | far away from the mass spacetime is nearly flat, |
07:37 | but as you get closer and closer to it, |
07:39 | spacetime becomes more and more curved, |
07:41 | it attracts objects in and time runs slower. |
07:45 | (gunshots firing) |
07:47 | Schwarzschild sent his solution to Einstein, |
07:49 | concluding with, "The war treated me kindly enough |
07:52 | in spite of the heavy gunfire |
07:54 | to allow me to get away from it all |
07:55 | and take this walk in the land of your ideas." |
08:00 | Einstein replied, "I have read your paper |
08:02 | with the utmost interest, I had not expected |
08:04 | that one could formulate the exact solution to the problem |
08:06 | in such a simple way." |
08:12 | But what seemed at first quite simple, |
08:15 | soon became more complicated. |
08:17 | Shortly after Schwarzschild solution was published, |
08:19 | people noticed two problem spots. |
08:22 | At the center of the mass, at r equals zero, |
08:25 | this term is divided by zero, so it blows up to infinity |
08:30 | and therefore this equation breaks down |
08:32 | and it can no longer describe what's physically happening. |
08:35 | This is what's called a singularity. |
08:38 | Maybe that point could be excused, |
08:40 | because it's in the middle of the mass, |
08:42 | but there's another problem spot outside of it |
08:45 | at a special distance from the center |
08:47 | known as the Schwarzschild radius, this term blows up. |
08:50 | So there is a second singularity. What is going on here? |
08:57 | Well, at the Schwarzschild radius, |
09:00 | the spacetime curvature becomes so steep |
09:02 | that the escape velocity, the speed that anything would need |
09:06 | to leave there is the speed of light |
09:10 | and that would mean that inside the Schwarzschild radius, |
09:13 | nothing, not even light would be able to escape. |
09:17 | So you'd have this dark object |
09:18 | that swallows up matter and light, |
09:22 | a black hole, if you will, |
09:26 | but most scientists doubted that such an object could exist, |
09:29 | because it would require a lot of mass |
09:31 | to collapse down into a tiny space. |
09:35 | How could that possibly ever happen? |
09:39 | (thrilling music) |
09:40 | Astronomers at the time were studying |
09:42 | what happens at the end of a star's life. |
09:44 | During its lifetime the inward force of gravity is balanced |
09:47 | by the outward radiation pressure |
09:49 | created by the energy released through nuclear fusion, |
09:52 | but when the fuel runs out, the radiation pressure drops. |
09:55 | So gravity pulls all the star material inwards, but how far? |
10:01 | Most astronomers believed some physical process |
10:04 | would hold it up and in 1926, |
10:07 | Ralph Fowler came up with a possible mechanism. |
10:10 | Pauli's exclusion principles states that, |
10:11 | "Fermions like electrons cannot occupy the same state, |
10:15 | so as matter gets pushed closer and closer together, |
10:18 | the electrons each occupy their own tiny volumes," |
10:21 | but Heisenberg's uncertainty principle says that, |
10:23 | "You can't know the position and momentum of a particle |
10:26 | with absolute certainty, so as the particles become |
10:29 | more and more constrained in space, |
10:32 | the uncertainty in their momentum, |
10:34 | and hence their velocity must go up." |
10:37 | So the more a star is compressed, |
10:39 | the faster electrons will wiggle around |
10:41 | and that creates an outward pressure. |
10:44 | This electron degeneracy pressure would prevent the star |
10:47 | from collapsing completely. |
10:49 | Instead, it would form a white dwarf |
10:51 | with the density much higher than a normal star |
10:54 | and remarkably enough astronomers had observed stars |
10:57 | that fit this description. |
10:58 | One of them was Sirius B. |
11:04 | But the relief from this discovery was short-lived. |
11:06 | Four years later, 19-year-old Subrahmanyan Chandrasekhar |
11:09 | traveled by boat to England to study with Fowler |
11:12 | and Arthur Eddington, one of the most revered scientists |
11:15 | of the time. |
11:17 | During his voyage, Chandrasekhar realized |
11:19 | that electron degeneracy pressure has its limits. |
11:22 | Electrons can wiggle faster and faster, |
11:24 | but only up to the speed of light. |
11:27 | That means this effect can only support stars |
11:30 | up to a certain mass, the Chandrasekhar limit. |
11:33 | Beyond this, Chandrasekhar believed, |
11:35 | not even electron de degeneracy pressure |
11:37 | could prevent a star from collapsing, |
11:40 | but Eddington was not impressed. |
11:42 | He publicly blasted Chandrasekhar saying, |
11:45 | "There should be a law of nature |
11:47 | to prevent a star from behaving in this absurd way" |
11:51 | and indeed scientists did discover a way |
11:53 | that stars heavier than the Chandrasekhar limit |
11:55 | could support themselves. |
11:58 | When a star collapses beyond a white dwarf, |
12:00 | electrons and protons fuse together |
12:02 | to form neutrinos and neutrons. |
12:05 | These neutrons are also fermions, |
12:07 | but with nearly 2000 times the mass an electron, |
12:10 | their degeneracy pressure is even stronger. |
12:13 | So this is what holds up neutron stars. |
12:16 | There was this conviction among scientists |
12:19 | that even if we didn't know the mechanism, |
12:21 | something would prevent a star from collapsing |
12:23 | into a single point and forming a black hole, |
12:28 | because black holes were just too preposterous to be real. |
12:34 | The big blow to this belief came in the late 1930s |
12:38 | when Jay Robert Oppenheimer and George Volkoff |
12:40 | found that neutron stars also have a maximum mass. |
12:44 | Shortly after Oppenheimer and Hartland Snyder |
12:47 | showed that for the heaviest stars, |
12:49 | there is nothing left to save them when their fuel runs out, |
12:53 | they wrote, "This contraction will continue indefinitely," |
12:58 | but Einstein still couldn't believe it. |
13:00 | Oppenheimer was saying that stars can collapse indefinitely, |
13:03 | but when Einstein looked at the math, |
13:05 | he found that time freezes on the horizon. |
13:08 | So it seemed like nothing could ever enter, |
13:11 | which suggested that either |
13:12 | there's something we don't understand |
13:14 | or that black holes can't exist, |
13:17 | (star explodes) |
13:21 | but Oppenheimer offered a solution to the problem. |
13:23 | He said to an outside observer, |
13:26 | you could never see anything go in, |
13:27 | but if you were traveling across the event horizon, |
13:31 | you wouldn't notice anything unusual |
13:33 | and you'd go right past it without even knowing it. |
13:37 | So how is this possible? |
13:39 | We need a spacetime diagram of a black hole. |
13:43 | On the left is the singularity at r equals zero. |
13:46 | The dotted line at r equals 2M is the event horizon. |
13:49 | Since the black hole doesn't move, |
13:51 | these lines go straight up in time. |
13:55 | Now let's see how ingoing and outgoing light ray travel |
13:58 | in this curved geometry. |
14:01 | When you're really far away, |
14:02 | the future light cones are at the usual 45 degrees, |
14:06 | but as you get closer to the horizon, |
14:07 | the light cones get narrower and narrower, |
14:11 | until right at the event horizon, |
14:13 | they're so narrow that they point straight up |
14:16 | and inside the horizon, the light cones tip to the left, |
14:22 | but something strange happens with ingoing light rays. |
14:26 | - They fall in, but they don't get to r equals 2M, |
14:29 | they actually asymptote to that value |
14:32 | as time goes to infinity, |
14:34 | but they don't end at infinity, right? |
14:36 | Mathematically they are connected and come back in |
14:41 | and they're traveling in this direction |
14:44 | and this bothered a lot of people, |
14:46 | this bothered people like Einstein, |
14:48 | because he looked at these equations and went, |
14:50 | "well, if nothing can cross this sort of boundary, |
14:55 | then how could there be black holes? |
14:57 | How could black holes even form?" |
15:00 | - So what is going on here? |
15:02 | Well, what's important to recognize |
15:04 | is that this diagram is a projection. |
15:06 | It's basically a 2D map |
15:08 | of four dimensional curved spacetime. |
15:12 | It's just like projecting the 3D Earth onto a 2D map. |
15:15 | When you do that, you always get distortions. |
15:18 | There is no perfectly accurate way |
15:20 | to map the earth onto a 2D surface, |
15:22 | but different maps can be useful for different purposes. |
15:25 | For example, if you wanna keep angles and shapes the same, |
15:28 | like if you're sailing across the ocean |
15:30 | and you need to find your bearings, |
15:31 | you can use the Mercator projection, |
15:33 | that's the one Google Maps uses. |
15:35 | A downside is that it misrepresent sizes. |
15:39 | Africa and Greenland look about the same size, |
15:42 | but Africa is actually around 14 times larger. |
15:46 | The Gall-Peters projection keeps relative sizes accurate, |
15:49 | but as a result, angles and shapes are distorted. |
15:53 | In a similar way, we can make different projections |
15:56 | of 4D spacetime to study different properties of it. |
16:00 | Physical reality doesn't change, |
16:01 | but the way the map describes it does. |
16:05 | - He had chosen to put a particular coordinate system |
16:07 | of a space and have a time coordinate, and off you go. |
16:11 | It's the most sensible thing to do, right? |
16:14 | - [Derek] People realize that if you choose |
16:15 | a different coordinate system |
16:17 | by doing a coordinate substitution, then the singularity |
16:20 | at the event horizon disappears. |
16:23 | - It goes away. |
16:24 | That problem goes away and things can actually cross |
16:27 | into the black hole. |
16:30 | - What this tells us is that there is |
16:32 | no real physical singularity at the event horizon. |
16:36 | It just resulted from a poor choice of coordinate system. |
16:41 | Another way to visualize what's going on |
16:44 | is by describing space as flowing in towards the black hole, |
16:48 | like a waterfall. |
16:49 | As you get closer, space starts flowing in |
16:52 | faster and faster. |
16:54 | Photons emitted by the spaceship have to swim |
16:56 | against this flow, and this becomes harder and harder |
17:00 | the closer you get. |
17:02 | Photons emitted just outside the horizon |
17:04 | can barely make it out, but it takes longer and longer. |
17:09 | At the horizon, space falls in |
17:11 | as fast as the photons are swimming. |
17:13 | So if the horizon had a finite width, |
17:16 | then photons would get stuck here, |
17:18 | photons from everything that ever fell in, |
17:21 | but the horizon is infinitely thin. |
17:23 | So in reality, photons either eventually escape or fall in. |
17:29 | Inside the horizon, space falls faster |
17:31 | than the speed of light, |
17:33 | and so everything falls into the singularity. |
17:36 | So Oppenheimer was right. |
17:38 | Someone outside a black hole can never see anything enter |
17:42 | because the last photons they can see |
17:44 | will always be from just outside the horizon, |
17:48 | but if you yourself go, |
17:50 | you will fall right across the event horizon |
17:52 | and into the singularity. |
17:55 | Now you can extend the waterfall model |
17:57 | to cover all three spatial dimensions, |
17:59 | and that gives you this, a real simulation |
18:02 | of space flowing into a static black hole |
18:05 | made by my friend Alessandro from ScienceClic. |
18:08 | Later we'll use this model to see what it's like |
18:10 | falling into a rotating black hole. |
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20:19 | and now back to spacetime maps. |
20:22 | If you take this map and transform it |
20:25 | so that incoming and outgoing light ray |
20:27 | all travel at 45 degrees like we're used to, |
20:30 | then something fascinating happens. |
20:33 | The black hole singularity on the left |
20:35 | transforms into a curved line at the top |
20:40 | and since the future always points up in this map, |
20:44 | it tells us that the singularity is not actually |
20:47 | a place in space, instead, it's a moment in time, |
20:52 | the very last moment in time for anything |
20:55 | that enters a black hole. |
20:58 | The map we've just created is a Kruskal-Szekers diagram, |
21:02 | but this only represents a portion of the universe, |
21:04 | the part inside the black holes event horizon |
21:07 | and the part of the universe closest to it, |
21:10 | but what we can do is contract the whole universe, |
21:13 | the infinite past, infinite distance, and infinite future, |
21:17 | and morph it into a single map. |
21:20 | It's like using the universe's best fish eye lens. |
21:24 | That gives us this penrose diagram. |
21:28 | Again, light rays still always go at 45 degrees. |
21:31 | So the future always points up. |
21:33 | The infinite past is in the bottom of the diagram. |
21:36 | The infinite future at the top |
21:39 | and the sides on the right are infinitely far away. |
21:42 | The black hole singularity is now a straight line |
21:44 | at the top, a final moment in time. |
21:49 | These lines are all at the same distance |
21:51 | from the black hole. |
21:52 | So the singularity is at r equals zero, |
21:55 | the horizon is at r equals 2M, |
21:57 | this line is at r equals 4M, |
21:59 | and this is infinitely far away. |
22:02 | All of these lines are at the same time. |
22:05 | What's great about this map is that it's very easy to see |
22:09 | where you can still go and what could have affected you. |
22:12 | For example, when you're here, you've got a lot of freedom. |
22:15 | You can enter the black hole or fly off to infinity, |
22:19 | and you can see and receive information from this area, |
22:23 | but if you go beyond the horizon, |
22:25 | your only possible future is to meet the singularity. |
22:29 | You can still, however, see and receive information |
22:32 | from the universe. |
22:33 | You just can't send any back out. |
22:36 | Now think about being at this point in the map. |
22:39 | This is at the event horizon, |
22:41 | and now your entire future is within the black hole, |
22:45 | but what is the past of this moment? |
22:48 | Well, you can draw the past light cone |
22:51 | and it reveals this new region. |
22:54 | If you're inside this region, |
22:56 | you can send signals to the universe, |
22:58 | but no matter where you are in the universe, |
23:00 | nothing can ever enter this region |
23:02 | because it will never be inside your light comb. |
23:06 | So things can come out, but never go in. |
23:09 | This is the opposite of a black hole, a white hole. |
23:15 | What color is a white hole? |
23:18 | (Geraint exhales) |
23:19 | (Derek laughs) |
23:20 | - I mean, it's gonna be the, |
23:22 | it's not gonna have a color, right? |
23:24 | It's gonna be whatever's being spat out of it. |
23:27 | It depends what's in there and gets thrown out, |
23:31 | that's what you are going to see. |
23:33 | So if it's got light in there, it's got mass in there, |
23:35 | it's all gonna be ejected. |
23:36 | So the white hole kind of picture |
23:39 | is the time reverse picture of a black hole, |
23:42 | instead of things falling in, things get expelled outwards |
23:46 | and so whilst a black hole has a membrane, |
23:51 | the Schwarzschild horizon, which once you cross, |
23:53 | you can't get back out, the white hole has the opposite. |
23:56 | If you're inside the event horizon, you have to be ejected, |
23:59 | so it kicks you out kind of thing, right? |
24:01 | Relativity doesn't tell you which way time flows. |
24:04 | There's nothing in there that says that, that is the future |
24:08 | and that is the past. |
24:10 | When you are doing your mathematics |
24:12 | and you're working out the behavior of objects, |
24:15 | you make a choice about which direction is the future, |
24:19 | but mathematically, you could have chosen |
24:21 | the other way, right? |
24:22 | You could have had time point in the opposite direction. |
24:25 | Any solution that you find in relativity, |
24:28 | mathematically, you can just flip it |
24:30 | and get a time reverse solution |
24:32 | and that's also a solution to the equations. |
24:36 | - [Derek] Now, we've been showing things |
24:37 | being ejected to the right, but they could just as well |
24:40 | be ejected to the left. |
24:42 | So what's over there? |
24:44 | This line is not at infinity, |
24:46 | so there should be something beyond it. |
24:49 | If we eject things in this direction, |
24:51 | you find that they enter a whole new universe, |
24:55 | one parallel to our own. |
25:01 | - [Geraint] We can fall into this black hole, |
25:03 | and somebody in this universe here |
25:05 | could fall into this black hole in their universe, |
25:08 | and we would find ourselves in the same black hole. |
25:11 | (Derek chuckles) |
25:12 | - The only downside is that |
25:14 | we'd both soon end up in the singularity. |
25:18 | I guess I'm just trying to understand |
25:20 | where that universe appears |
25:22 | in the mathematical part of the solution. |
25:24 | Like, can you point to the part of the equation and be like, |
25:27 | so that's our universe, and then these terms here, |
25:30 | that's the other universe, or do you know what I mean? |
25:32 | Like- - Yeah, |
25:33 | well, it's coordinates, right? |
25:35 | Imagine somebody, right, came up with a coordinate system |
25:40 | for the earth, but only the northern hemisphere |
25:43 | and you looked at that coordinate system, right? |
25:45 | And you looked at it and you said, |
25:47 | "Ah, I can see the coordinate system, it looks fine, |
25:50 | but mathematically latitudes can be negative, right? |
25:55 | You've only got positive latitudes in your solution. |
25:58 | What about the negative ones?" |
25:59 | And they said to you, (scoffs) "Negative ones? |
26:02 | No southern hemisphere, right?" |
26:05 | And you've gotta go, "Well, the mathematics says that |
26:08 | you can have negative latitudes. |
26:09 | Maybe we should go and look over the equator |
26:12 | to see if there is something down there" |
26:13 | and I know that's a kind of extreme example, |
26:16 | because we know we live on a globe, |
26:17 | but we don't know the full geometry |
26:20 | of what's going on here in the sense that |
26:22 | Schwarzschild laid down coordinates |
26:24 | over part of the solution. |
26:26 | It was like him only laying down coordinates |
26:28 | on the northern hemisphere |
26:30 | and other people have come along and said, |
26:32 | "Hey, there's a southern hemisphere" |
26:34 | and more than that, there's two earths. |
26:36 | That's why it's called maximal extension. |
26:39 | It's like, if I have this mathematical structure, |
26:43 | then what is the extent of the coordinates |
26:47 | that I can consider? |
26:49 | And with the Schwarzschild black hole, |
26:51 | you get a second universe |
26:52 | that has its own independent set of coordinates |
26:56 | from our universe. |
26:57 | I want to emphasize right, this is the simplest solution |
27:00 | to the Einstein field equations, |
27:02 | and it already contains a black hole, |
27:03 | white hole and two universes. |
27:05 | - [Derek] That's what you get |
27:07 | when you push this map to its limits |
27:09 | so that every edge ends at a singularity or infinity. |
27:13 | - And in fact, there's another little feature in here, |
27:16 | which is that, that little point there where they cross, |
27:19 | that is an Einstein Rosen Bridge. |
27:24 | - To see it, we need to change coordinates. |
27:27 | Now this line is at constant crustal time |
27:30 | and it connects the space of both universes. |
27:33 | You can see what the spacetime is like |
27:35 | by following this line from right to left. |
27:38 | Far away from the event horizon, |
27:39 | spacetime is basically flat, |
27:41 | but as you get closer to the event horizon, |
27:43 | spacetime starts to curve more and more. |
27:46 | At this cross, you are at the event horizon, |
27:49 | and if you go beyond it, you end up in the parallel universe |
27:53 | that gives you a wormhole that looks like this. |
27:59 | - So that is hypothetically how we could use a black hole |
28:04 | to travel from one universe to another. |
28:06 | - Hypothetically, because these wormholes |
28:08 | aren't actually stable in time. |
28:11 | - It's a bit like a bridge, but it's a bridge that is long |
28:14 | and then becomes shorter and then becomes long again |
28:17 | and if you try to traverse this bridge, |
28:19 | at some point, the bridge is only very short, right? |
28:21 | And you say, "Oh, well, let me just cross this bridge." |
28:23 | But as you start crossing the bridge and start running, |
28:25 | your speed is finite, right? |
28:27 | The speed of light roughly and then the bridge starts, |
28:30 | becoming stretching and you never come out the other side. |
28:35 | - [Derek] This pinching off always happens too fast |
28:38 | for anything to travel through. |
28:40 | You can also see this if you look at the Penrose diagram, |
28:43 | because when you're inside one universe, |
28:45 | there isn't a light cone that can take you |
28:47 | to the other universe. |
28:49 | The only way to do that |
28:50 | would be to travel faster than light, |
28:54 | but there might be another way. |
28:57 | Schwarzschild solution describes a black hole |
28:59 | that doesn't rotate. |
29:00 | Yet, every star does rotate |
29:02 | and since angular momentum must be conserved, |
29:04 | every black hole must also be rotating. |
29:08 | While Schwarzschild found his solution within weeks |
29:10 | after Einstein published his equations, |
29:12 | solving them for a spinning mass |
29:14 | turned out to be much harder. |
29:15 | Physicists tried, but 10 years after Schwarzschild solution, |
29:19 | they still hadn't solved it. |
29:21 | 10 years turned into 20, which turned into 40 |
29:24 | and then in 1963, Roy Kerr found the solution |
29:28 | to Einstein's equations for a spinning black hole, |
29:32 | which is far more complicated than Schwarzschild solution |
29:35 | and this comes with a few dramatic changes. |
29:40 | The first is that the structure is completely different. |
29:43 | The black hole now consists of several layers. |
29:47 | It's also not spherically symmetric anymore. |
29:50 | This happens because the rotation |
29:52 | causes it to bulge around the equator. |
29:54 | So it's only symmetric about its axis of spin. |
29:59 | Alessandro from science click simulated what happens |
30:02 | around this spinning black hole. |
30:07 | Space gets dragged around with the black hole |
30:10 | taking you and the particles along with it. |
30:13 | When you get closer, space gets dragged around |
30:15 | faster and faster until it goes around faster |
30:19 | than the speed of light, |
30:20 | you've now entered into the first new region, |
30:24 | the ergosphere. |
30:26 | No matter how hard you fire your rockets here, |
30:29 | it's impossible to stay still relative to distance stars, |
30:33 | but because space doesn't flow directly inward, |
30:36 | you can still escape the black hole. |
30:39 | When you travel in further, you go through the next layer, |
30:42 | the outer horizon, the point of no return. |
30:46 | Here you can only go inwards, |
30:49 | but as you get dragged in deeper and deeper, |
30:52 | something crazy happens, you enter another region, |
30:57 | one where you can move around freely again, |
31:00 | so you're not doomed to the singularity. |
31:03 | You're now inside the inner event horizon. |
31:07 | Here you can actually see the singularity |
31:12 | - In a normal black hole, it's a point, |
31:13 | but it in a rotating black hole, |
31:14 | it actually expands out to be a ring |
31:17 | and there are weird things happened |
31:19 | with spacetime inside the center of a black hole, |
31:22 | a rotating black hole, |
31:23 | but it's thought that you can actually |
31:24 | fly through the singularity. |
31:29 | - [Derek] We need a Penrose diagram |
31:31 | of a spinning black hole, where before the singularity |
31:35 | was a horizontal line at the top |
31:37 | here, the singularity lifts up and moves to the sides, |
31:40 | revealing this new region inside the inner horizon. |
31:45 | Here we can move around freely and avoid the singularity, |
31:49 | but these edges aren't at infinity or a singularity, |
31:53 | so there must be something beyond them. |
31:55 | Well, when you venture further, |
31:57 | you could find yourself in a white hole, |
32:00 | which would push you out into a whole nother universe. |
32:05 | - You can have these pictures whereby |
32:08 | you're in one universe, you fall into a rotating black hole, |
32:12 | you fly through the singularity, |
32:14 | and you pop out into a new universe from a white hole, |
32:18 | and then you can just continue playing this game. |
32:21 | - Extending this diagram infinitely far. |
32:25 | but there is still one thing we haven't done, |
32:27 | brave the singularity. |
32:30 | So you aim straight towards the center of the ring |
32:33 | and head off towards it, but rather than time ending, |
32:37 | you now find yourself in universe, a strange universe, |
32:40 | one where gravity pushes instead of pulls. |
32:44 | This is known as an anti-verse. |
32:48 | If that's too weird, you can always jump back |
32:50 | across the singularity and return to a universe |
32:53 | with normal gravity. |
32:55 | - And I know this is basically science fiction, right? |
32:57 | But if you take the solutions of relativity at, |
33:02 | you know, essentially at face value and add on a little bit, |
33:05 | which is what Penrose does here, he says this, |
33:07 | "oh look, these shapes are very similar, |
33:10 | I can just stick these together." |
33:12 | Then this is the conclusion that you get. |
33:14 | Now we have effectively an infinite number |
33:17 | of universes all connected with black hole, white holes |
33:20 | all the way through and you, of you go to explore, |
33:25 | but it'll be a very brave person who's the first one |
33:28 | who's gonna leap into a rotating black hole |
33:30 | to find out if this is correct? |
33:31 | (Derek chuckles) |
33:33 | - Yeah, I would not sign up for that. |
33:35 | So could these maximally extended Schwarzschild |
33:38 | and Kerr solutions actually exist in nature? |
33:41 | Well, there are some issues. |
33:43 | Both the extended Schwarzschild and Kerr solutions |
33:46 | are solutions of eternal black holes in an empty universe. |
33:50 | - As you say, it's an eternal solution. |
33:52 | So it stretches infinitely far into the past |
33:55 | and infinitely far into the future |
33:57 | and so there's no formation mechanism in there, |
33:59 | it's just a static solution |
34:02 | and I think that is part of the, |
34:07 | part of the reason why black holes |
34:10 | are realized in our universe and white holes aren't- |
34:15 | - Or might not be. |
34:16 | - Or might not be, |
34:16 | or I'm reasonably I, |
34:18 | personally, I'm reasonably confident |
34:20 | that they don't exist, right? |
34:22 | - [Derek] For the maximally extended Kerr solution, |
34:24 | there's also another problem. |
34:26 | If you're an immortal astronaut inside the universe, |
34:28 | you can send light into the black hole, |
34:31 | but because there's infinite time compressed |
34:34 | in this top corner, you can pile up light along this edge, |
34:37 | which creates an infinite flux of energy |
34:40 | along the inner horizon. |
34:42 | This concentration of energy |
34:43 | then creates its own singularity, |
34:46 | sealing off the ring singularity and beyond. |
34:50 | - My suspicion and the suspicion |
34:51 | of some other people in the field is that |
34:55 | this inner horizon will become singular |
34:56 | and you will not be able to go through these second copies. |
34:59 | - So all the white holes, wormholes, other universes |
35:03 | and anti universes disappear. |
35:06 | Does that mean that real wormholes are impossible? |
35:10 | In 1987, Michael Morris and Kip Thorne looked at wormholes |
35:13 | that an advanced civilization could use |
35:15 | for interstellar travel, ones that have no horizons, |
35:18 | so you can travel back and forth, are stable in time, |
35:20 | and have some other properties like |
35:22 | being able to construct them. |
35:24 | They found several geometries that are allowed |
35:26 | by Einstein's general relativity. |
35:28 | In theory, these could connect different parts |
35:31 | of the universe, making a sort of interstellar highway. |
35:34 | They might even be able to connect to different universes. |
35:39 | The only problem is that all these geometries |
35:42 | require an exotic kind of matter |
35:44 | with a negative energy density |
35:45 | to prevent the wormhole from collapsing. |
35:48 | - This exotic kind of matter, |
35:50 | is really against the loss of physics, so it's, |
35:54 | I have the prejudice that it will not exist. |
35:56 | I'm bothered by the fact that we say that |
35:58 | the science fiction wormholes are mathematically possible. |
36:01 | It's true, it's mathematically possible |
36:03 | in the sense that there's some geometry that can exist, |
36:05 | but Einstein's theory is not just geometries, |
36:09 | it's geometries plus field equations. |
36:12 | If you use the kinds of properties of matter |
36:14 | that matter actually has, then they're not possible. |
36:17 | So I feel that the reason they're not possible |
36:20 | is very strong. |
36:22 | - So according to our current best understanding, |
36:25 | it seems likely that white holes, traversable wormholes, |
36:28 | and these parallel universes don't exist, |
36:32 | but we also used to think that black holes didn't exist. |
36:35 | So maybe we'll be surprised again. |
36:38 | - I mean, we have one universe, right? |
36:41 | Good, why can't we have two. |
36:46 | (whimsical music) |