Something Strange Happens When You Follow Einstein's Math

- You can never see anything enter a black hole. (Bell Dings) Imagine that you catch your nemesis on a rocket ship and wake it up towards a black hole. He looks at you shaking his fist at a constant pace. As it approaches, gravity is strengthened, so you would expect it to accelerate, but that is not what you see. Instead, the rocket ship seems to be decreasing. Not only that, he also seems to be shaking his slow and slow fist. This is because from his perspective, his time is slowing down at the same moment that he must cross the horizon of the event, the point beyond which not even the light can escape, he and his rocket ship do not disappear, on the other hand, they seem to stop in time.

The spacecraft light becomes more dim and red until it fades completely from the view. This is how any object would be seen crossing the horizon of the event. The light still comes from the point where it crossed, it is too displaced in the red to see, but if you could see that light, then, you would see everything that has fallen into the black hole frozen on its horizon, including the star that formed it, but in practice, the photons are emitted in discrete intervals, so there will be a last photon emitted outside the horizon and, therefore, these images will fade away After some time. - This is only one of the

strange

results that comes out of the general theory of relativity, our best gravity theory.

The first solution of Einstein's equations predicted not only black holes, but also their opposite white holes. It also implied the existence of parallel universes and even possibly a way of traveling between them. This is a video about the true science of black holes, white holes and wormholes. - The general theory of relativity arose at least in part due to a fundamental failure in Newtonian gravity. In the seventeenth century, Isaac Newton contemplated how an apple falls to the ground, how the moon orbit the earth and the earth orbits the sun and concluded that each object with mass must attract everyone else, but Newton was worried about its own theory.

How could the masses separated by such great distances apply a force from each other? He wrote: "That one body can act on another distance through a void without the mediation of anything else is for me, so great and absurd that I think that no man who has a competent faculty of thought could fall into it." A man who definitely had a competent faculty of thinking was Albert Einstein and more than 200 years later, discovered how he is mediated by gravity. The bodies do not exert forces directly. Instead, a dough like the sun curves the space -time in its vicinity.

This, then the spatial time around it is curved and so on to the earth. Then the earth orbits the sun, because the land of space -time is happening is curve. The masses are affected by the local curvature of space -time, so no remote action is required. Mathematically, this is described by Einstein's field equations. Can you write Einstein's field equation? - This was the result of Einstein's hard decade after a special relativity and essentially what we have in the field equations on one side, he says, tell me about the distribution of matter and energy. The other side tells him what is the curvature resulting from the space -time for that distribution of matter and energy and is a single line.

It seems that Oh, this is a simple equation, right? But it is not really an equation. It is a family of equations and to make life more difficult, they are coupled equations, so they depend with each other and are differential equations, so it means that there are integrals that must be done, da, da da. Therefore, there are a lot of steps to solve the field equations. To see how a solution to these equations would be seen, we need a tool to understand the space -time. So imagine they float in the empty space. A flash of light goes out over his head and extends in all directions.

Now all his future, anything that can and

happens

to him will once happen inside this bubble because the only way to get out of it would be to travel faster than the light. In two dimensions, this bubble is just a circle of growth. If we leave time to execute the screen and take snapshots at regular intervals, then this bubble of light draws a cone, its future light cone. By convention, the axes are climbed so that the light rays always travel to 45 degrees. This cone reveals the only region of space -time that can expect to explore and influence.

Now imagine that instead of a flash of light on their head, those photons really traveled from all corners of the universe and found themselves at that moment and then continued traveling in their separate directions. Well, in that case in the past, these photons also reveal a cone of light, their last light cone. Only the events that happened within this cone could have affected you until the present moment. We can simplify this diagram even more drawing only one spatial and unique dimension. This is the empty space space diagram. If you want to measure how separate two events are in spatial time, use

something

called space interval -time.

The square interval is equal to less dt, more dx squared, since the space -time is flat, geometry is the same everywhere and, therefore, this formula is maintained throughout the diagram, which makes it really easy to measure the separation between two events, but around a mass, the space -time is curved and, therefore, it must modify the equation to take into account the geometry. This is how the solutions to Einstein's equations are. They tell you how space curves -time and how to measure separation between two events in that curved geometry. Einstein published his equations in 1915 during World War I could not find an exact solution.

Fortunately, a copy of his article came to the eastern front where Germany was fighting against Russia, parked, there was one of the best astrophysicists of the time, Karl Schwarzschild. Despite being 41 years old, he had volunteered to calculate the artillery trajectories for the German army. At least until a greater challenge will call your attention, how to solve Einstein's field equations. Schwarzschild did the standard physical and imagined the simplest possible stage, an eternal static universe with nothing except a single mass of symmetrical point spherically. This mass was electrically neutral and did not turn. Since this was the only characteristic of his universe, he measured everything using spherical coordinates in relation to this center of this mass.

Then R is the radio and Theta and Phi give the angles. For his coordinate time, he chose time as measured by someone away from the dough, where space -time is essentially flat. Using this approach, Schwarzschild found the first non -trivial solution to Einstein's equations, which today we write like this. This Schwarzschild metric describes how space curves -time outside the dough. It is quite simple and makes intuitive sense, far from space -mass time is almost flat, but as you approach more and more, the space -time becomes increasingly curved, attracts objects in time and time is slower. (shooting shots) Schwarzschild sent his solution to Einstein, concluding with: "War treated me kind enough despite the heavy shots to allow me to get away from everything and give this walk in the land of his ideas." Einstein replied: "I have read his article with the greatest interest, I did not expect one to formulate the exact solution to the problem in such a simple way." But what at first seemed quite simple, soon became more complicated.

Shortly after the Schwarzschild solution was published, people noticed two problematic points. In the center of the dough, in R is equal to zero, this term is divided by zero, so it explodes to infinity and, therefore, this equation is broken and can no longer describe what is happening physically. This is what is called singularity. Maybe that point could be excused, because it is in the middle of the Mass, but there is another problematic place outside it at a special distance from the center known as the Schwarzschild radius, this term explodes. Then there is a second singularity. What is happening here?

Well, on the radius of Schwarzschild, the curvature of space -time becomes so high that the exhaust speed, the speed that anything would need to leave there is the speed of light and that would mean that inside the radius of Schwarzschild, nothing, not even the light could escape. Therefore, you would have this dark object that swallows matter and light, a black hole, so to speak, but most scientists doubted that such an object could exist, because it would require a lot of mass to collapse in a small space. How could that happen that? (Exciting music) Astronomers at that time were studying what

happens

at the end of the life of a star.

During his life, the internal force of gravity is balanced with the external radiation pressure created by the energy released through nuclear fusion, but

when

the fuel is exhausted, the radiation pressure falls. So, gravity carries all the star material inwards, but how far? Most astronomers believed that some physical process would maintain it and in 1926, Ralph Fowler came up with a possible mechanism. Pauli's Exclusion Principles states that, "Ferms Like Electrons Cannot Occupy The Same State, So As Matter Gets Pushed Closer and Closer Together, The Electrons EACHUCUE OCCUPY THES THES Position and momentum of a partle with absolute certainty, so the partners Become More and More Constrained in Space, The Uncertainty in Their Momentum, and hence their velocity must rise. " So, the more a star is compressed, faster electrons will move and that creates external pressure.

This electron degeneration pressure would prevent the star from collapsing completely. Instead, it would form a white dwarf with the density much higher than a normal and significantly enough astronomers had observed stars that fit this description. One of them was Sirius B. But the relief of this discovery was of short duration. Four years later, Subrahmanyan Chandrasekhar, 19, traveled by boat to England to study with Fowler and Arthur Eddington, one of the most venerated scientists of the time. During his trip, Chandrasekhar realized that electron degeneration pressure has its limits. Electrons can move faster and faster, but only to the speed of light.

That means that this effect can only support the stars to a certain dough, Chandrasekhar's limit. Beyond this, Chandrasekhar believed that not even the pressure of electron degeneration could prevent a star from collapsing, but Eddington was not impressed. He publicly criticized Chandrasekhar saying: "There should be a law of nature to prevent a star from behaving in this absurd way" and in fact, scientists discovered a form that is heavier than Chandrasekhaha's limit could keep themselves. When a star collapses beyond a white dwarf, electrons and protons merge to form neutrines and neutrons. These neutrons are also fermions, but with almost 2000 times the dough an electron, its degeneration pressure is even stronger.

So this is what holds neutron stars. There was this conviction among scientists that even if we did not know the mechanism,

something

would prevent a star from collapsing in a single point and forming a black hole, because black holes were too absurd to be real. The great blow to this belief came to the end of the 1930s

when

Jay Robert Oppenheimer and George Volkoff discovered that neutron stars also have a maximum mass. Shortly after Oppenheimer and Hartland Snyder show that for the heaviest stars, there is nothing left to save them when their fuel is exhausted, "this contraction will continue indefinitely," but Einstein could not believe it yet.

Oppenheimer said that the stars can collapse indefinitely, but when Einstein looked at

math

ematics, he discovered that time freezes on the horizon. Therefore, it seemed that nothing could enter, which suggested that or there is something that we do not understand or that black holes cannot exist, (Star explodes) but Oppenheimer offered a solution to the problem. He told an external observer that he could never see anything entered, but if he travels through the event horizon, he would not notice anything unusual and would happen without even knowing it. So how is this possible? We need a space diagram -time for a black hole.

On the left is the uniqueness in R is equal to zero. The line dotted in R is equal to 2m is the event horizon. As the black hole does not move, these lines rise directly on time. Now let's see how incoming and outgoing light rays travel in this curved geometry. When you are very far, future light cones are in the usual 45 degrees, but as you approach the horizon, the light cones become narrower and more narrower, until just on the horizon of theevent, they are so narrow that they point up and inside the horizon, the light cones lean to the left, but something

strange

happens with the rays of Ingoing light. - They fall, but they do not reach R is equal to 2m, actually as well as that value as time goes to infinity, but they do not end in infinity, right?

Mathematically, they are connected and returned and traveling in this direction and this bothered many people, this bothered people like Einstein, because he looked at these equations and it was: "Well, if nothing can cross this type of limit, how could there be black holes? How could black holes be formed?" - So what is happening here? Well, what is important to recognize is that this diagram is a projection. It is basically a 2D map of four -dimensional curved space space. It's like projecting the 3D Earth on a 2D map. When you do that, you always get distortions. There is no perfectly precise way to map the earth on a 2D surface, but different maps can be useful for different purposes.

For example, if you want to keep the angles and shapes in the same way, as if you navigate the ocean and you need to find turstations, you can use the projection of Mercator, that is the one that uses Google Maps. An inconvenience is that sizes. Africa and Greenland seem like the same size, but Africa is actually about 14 times larger. The projection of the crossbows maintains the precise relative sizes, but as a result, the angles and the shapes are distorted. Similarly, we can make different 4D space projections to study different properties of it. Physical reality does not change, but the way the map describes it does. - I had chosen to put a particular coordinate system of a space and have a time coordinate, and outside.

It's the most sensible thing, right? - People realize that if you choose a different coordinate system by making a coordinate replacement, then the singularity in the event horizon disappears. - He leaves. That problem disappears and things can cross the black hole. - What this tells us is that there is no real physical singularity on the event horizon. It simply resulted from a bad choice of the coordinate system. Another way to visualize what is happening is to describe that the space flows to the black hole, like a waterfall. As you approach, the space begins to flow faster.

Photons emitted by the spacecraft have to swim against this flow, and this becomes increasingly difficult the closer. Photons issued on the outskirts of the horizon can barely leave, but it takes more and more time. On the horizon, space falls as fast as photons are swimming. So, if the horizon had a finite wide, then the photons would get stuck here, the photons of everything that once fell, but the horizon is infinitely thin. Then, in reality, photons eventually escape or fall. Within the horizon, the space falls faster than the speed of light, so everything falls into singularity. Then Oppenheimer was right.

Someone outside a black hole can never see anything in because the last photons they can see will always be outside the horizon, but if you go, it will fall right through the horizon of the event and in the singularity. Now you can extend the waterfall model to cover the three spatial dimensions, and that gives this, a true space simulation that flows to a static black hole made by my friend Alessandro in Scienceclic. Later we will use this model to see what it is like to fall into a rotating black hole. Now, I have never been absorbed by a black hole, but sometimes it feels like that when I am trapped on the phone with a spam necklace.

Fortunately, today's sponsor unknown can help. You know, I used to receive several spam calls a day, and they frustrated me so much that I wrote a letter to the No Call record to eliminate my number, but that did not work and, therefore, wanted to go to the offensive. I even contemplated to make a video in which I got with the people who call by unwanted mail to take revenge for all frustration and lost time, but I don't have to do it thanks to Incogni. There are many data runners that absorb information about you, a bit like a black hole.

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So go to incog.com/veritasium to start. I want to thank Incogni for sponsoring this part of the video and now return to Spacetime maps. If you take this map and transform it so that the rays of incoming and outgoing light travel to 45 degrees as we are used to, then something fascinating happens. The uniqueness of the black hole to the left is transformed into a curved line in the upper part and, since the future always points to this map, tells us that the singularity is not really a place in space, on the other hand, it is a moment in time, at the last moment for anything that enters a black hole.

The map we just created is a Kruskal-Szekers diagram, but this only represents a part of the universe, the part within the horizon of black holes events and the part of the closest universe to him, but what we can do is get the entire universe, the infinite past, the infinite distance and the infinite future, and the morfura in a single map. It's like using the best fish -eyed lens in the universe. That gives us this Penrose diagram. Again, light rays are still 45 degrees. Then the future always points out. The infinite past is at the bottom of the diagram.

The infinite future at the top and the sides of the right are infinitely far. The uniqueness of the black hole is now a straight line at the top, a final moment over time. These lines are at the same distance from the black hole. Therefore, the singularity is in R is equal to zero, the horizon is equally 2 m, this line is equally 4 m, and this is infinitely very far. All these lines are at the same time. The good thing about this map is that it is very easy to see where it can go and what could have affected you.

For example, when you are here, you have a lot of freedom. You can enter the black hole or fly to the infinity, and you can see and receive information from this area, but if it goes beyond the horizon, its only possible future is to meet the singularity. However, you can still see and receive information from the universe. You just can't send any setback. Now think about being at this point on the map. This is on the horizon of the event, and now all its future is inside the black hole, but what is the past of this moment?

Well, you can draw the cone of past light and reveal this new region. If it is within this region, you can send signals to the universe, but it does not matter where you are in the universe, nothing can enter this region because it will never be inside your light comb. Then things can leave, but never enter. This is the opposite of a black hole, a white hole. What color is a white hole? (Geraint exhala) (Derek laughs) - I mean, it will be the, it will not have a color, right? It will be whatever it is out of it.

It depends on what is there and throws, that is what you are going to see. So, if he has light there, he has mass there, everything will be expelled. Then, the type of image of the white hole is the reverse image of a black hole, instead of things falling, things are expelled out and, therefore, although a black hole has a membrane, the Schwarzschild horizon, which once you cross, you cannot leave, the white hole has the opposite. If you are inside the event horizon, you must be expelled, so it gives you something like that, right? Relativity does not tell you in which direction time flows.

There is nothing there to say that, that's the future and that's the past. When you are doing your

math

ematics and you are working on the behavior of objects, you choose in which direction the future is, but mathematically, you could have chosen to the other side, right? You could have had a time point in the opposite direction. Any solution that you find in relativity, mathematically, can turn it and obtain an inverse solution solution and that is also a solution to equations. - Now, we have been showing things that are expelled to the right, but they could also be expelled to the left.

So what is there? This line is not in infinity, so there should be something beyond. If we expel things in this direction, you discover that they enter a completely new universe, one parallel to ours. - We can fall into this black hole, and someone in this universe here could fall into this black hole in its universe, and we would find ourselves in the same black hole. (Derek laughs) - The only inconvenience is that both would soon end in singularity. I guess I am only trying to understand where that universe appears in the mathematical part of the solution.

As, can you point out the part of the equation and be like, so that is our universe, and then these terms here, that is the other universe, or do you know what I mean? I like it- - Yes, well, they are coordinates, right? Imagine someone, of course, came up with a coordinate system for Earth, but only the northern hemisphere and looked at that coordinate system, right? And you looked at him and said: "Ah, I can see the coordinate system, it looks good, but mathematically latitudes can be negative, right? You just have positive latitudes in your solution.

What about negatives?" And they told you: (they make fun) "Negative? There is no southern hemisphere, right?" And you have to go: "Well, mathematics says you can have negative latitudes. Maybe we should go and review Ecuador to see if there is something here" and I know it is a kind of extreme example, because we know that we live in a globe, but we do not know the complete geometry of what is happening here in the sense that Schwarzschild established in the coordinates of the solution. It was as if it were only placing coordinates in the northern hemisphere and other people had come and said: "Hey, there is a southern hemisphere" and more than that, there are two lands.

That is why it is called maximum extension. It's like, if I have this mathematical structure, what is the scope of the coordinates that I can consider? And with the Schwarzschild Black Hole, you get a second universe that has its own independent coordinate set of our universe. I want to emphasize well, this is the simplest solution for Einstein's field equations, and already contains a black hole, white hole and two universes. - That is what you get when you take this map to its limits so that each edge ends with a uniqueness or infinity. - And in fact, there is another small feature here, which is that little, that small point where they cross, that is an Einstein Rosen bridge. - To see it, we need to change the coordinates.

Now this line is at the constant moment of the bark and connects the space of both universes. You can see what is the time of space -time

follow

ing this line from right to left. Far from the event horizon, Spacetime is basically flat, but as you approach the event horizon, Spacetime begins to curve more and more. In this cross, you are on the horizon of the event, and if you go beyond it, you end up in the parallel universe that gives you a worm hole that looks like this. - So that is hypothetically how we could use a black hole to travel from one universe to another. - Hypothetically, because these wormholes are not really stable over time. - It is a bit like a bridge, but it is a bridge that is long and then becomes shorter and then turns long again and if you try to cross this bridge, at some point, the bridge is only very short, right?

And you say: "Oh, well, let me cross this bridge." But as you start crossing the bridge and start running, your speed is finite, right? The speed of the light approximately and then the bridge begins, stretches and never leave the other side. - This pinch always happens too fast for anything to travel. You can also see this if you look at the Penrose diagram, because when you are inside a universe, there is no light cone that can take you to the other universe. The only way to do it would be to travel faster than light, but there could be anothershape.

The Schwarzschild solution describes a black hole that does not turn. However, each star revolves and, since the angular momentum must be kept, each black hole must also be rotating. While Schwarzschild found his solution a few weeks after Einstein published his equations, resolving them for a rotating mass turned out to be much more difficult. The physicists tried, but 10 years after the Schwarzschild solution, they had not yet resolved it. 10 years became 20, which became 40 and then in 1963, Roy Kerr found the solution to Einstein's equations for a rotating black hole, which is much more complicated than Schwarzschild's solution and this comes with some dramatic changes.

The first is that the structure is completely different. The black hole now consists of several layers. Nor is it spherical symmetrical. This happens because the rotation makes it abullage around Ecuador. Then it is only symmetrical on its turn axis. Alessandro de Science Click simulated what happens around this rotating black hole. The space is dragged with the black hole that carries it and the particles along with it. When you approach, the space is dragged faster and faster until it says faster than the speed of light, you have now entered the first new region, the Ergosphere. No matter how much you disagree here, it is impossible to remain still in relation to the stars away, but because the space does not flow directly inward, you can still escape the black hole.

When he travels beyond, he passes through the next layer, the outer horizon, the point without return. Here you can only go in, but as they drag you more and more, something crazy happens, you enter another region, one in which you can move freely again, so that you are not condemned to the Singularity. Now you are inside the internal events horizon. Here you can see the singularity: in a normal black hole, it is a point, but in a rotating black hole, it actually expands to be a ring and there are strange things happening with the space space within the center of a black hole, a rotating black hole, but it is believed that you can actually fly through singularity. - We need a Penrose diagram of a rotating black hole, where before the singularity there was a horizontal line at the top here, the singularity rises and moves to the sides, revealing this new region within the internal horizon.

Here we can move freely and avoid uniqueness, but these edges are not in infinity or a uniqueness, so there must be something beyond them. Well, when you venture more, you can find yourself in a white hole, which would push you to an entire universe. - You can have these images for which you are in a universe, fall in a rotating black hole, you fly through the singularity and go to a new universe of a white hole, and then you can continue playing this game. - Extend this diagram infinitely far. But there is still one thing we have not done, brave singularity.

So point directly to the center of the ring and go towards him, but instead of finishing, now you find yourself in the universe, a strange universe, one where gravity pushes instead of pulls. This is known as anti-reverse. If that is too strange, you can always return through singularity and return to a normal universe. - And I know that this is basically science fiction, right? But if you take the relativity solutions, essentially, essentially to the nominal value and add a bit, which is what Penrose does here, says this: "Oh, look, these forms are very similar, I can unite them." So this is the conclusion you get.

Now we have an infinite number of universes connected with black holes, white holes and you, of you, you will explore, but it will be a very brave person who is the first to jump to a rotating black hole to find out if this is correct. (Derek laughs) - Yes, I wouldn't register for that. So, could there be these Schwarzschild and Kerrzschild and Kerr solutions in nature in nature? Well, there are some problems. Both the extended solutions of Schwarzschild and Kerr are solutions of eternal black holes in an empty universe. - As you say, it is an eternal solution.

Therefore, it extends infinitely in the past and infinitely in the future, so there is no formation mechanism there, it is only a static solution and I think that is part of the reason for the reason why black holes are made in our universe and white holes are not, or may not be. - Or it might not be, or I am, personally, I am reasonably sure that they do not exist, right? - For the maximum extended Kerr solution, there is also another problem. If you are an immortal astronaut inside the universe, you can send light to the black hole, but because there is an infinite time compressed in this upper corner, you can accumulate light along this edge, which creates an infinite energy flow along the internal horizon.

This energy concentration creates its own singularity, sealing the uniqueness of the ring and beyond. - My suspicion and suspicion of other people in the field is that this internal horizon will become unique and you will not be able to go through these second copies. - Then all white holes, wormholes, other universes and anti universes disappear. Does that mean that true wormholes are impossible? In 1987, Michael Morris and Kip Thorne looked at the wormholes that an advanced civilization could use for interstellar trips, those who do not have horizons, so they can travel from side to side, are stable in time and have other properties such as being able to build them.

They found several geometries allowed by Einstein's general relativity. In theory, they could connect different parts of the universe, making a kind of interstellar road. They could even connect to different universes. The only problem is that all these geometries require an exotic type of matter with a negative energy density to prevent the worm hole from collapsing. - This type of exotic matter is really against the loss of physics, so it is, I have the prejudice that it will not exist. The fact that we say that science fiction wormholes are mathematically possible bothers me. It is true, it is mathematically possible in the sense that there is some geometry that can exist, but Einstein's theory is not only geometries, they are geometries more field equations.

If you use the types of properties of the subject that you really have, then they are not possible. So I feel that the reason why they are not possible is very strong. - Then, according to our best current understanding, white holes, traversable worm holes and these parallel universes do not exist, but we also used to think that there were no black holes. So, maybe we are surprised again. - I mean, we have a universe, right? Well, why can't we have two? (Capricious music)