Four-dimensional space-time is the lowest dimension that constitutes the real world, and our world happens to be four-dimensional. As for the high-dimensional real space, at least we can't perceive it yet. I mentioned an example in a post. When a ruler rotates in three-dimensional space (excluding time), its length remains unchanged, but when it rotates, all its coordinate values change and the coordinates are related. The significance of four-dimensional space-time lies in that time is the fourth coordinate, which is related to spatial coordinates, that is to say, space-time is a unified and inseparable whole, and they are a kind of "one change and one change" relationship.
Four-dimensional space-time is not limited to this. According to the relationship between mass and energy, mass and energy are actually the same thing. Mass (or energy) is not independent, but related to the state of motion. For example, the greater the speed, the greater the mass. In four-dimensional space-time, mass (or energy) is actually the fourth component of four-dimensional momentum, and momentum is a quantity that describes the motion of matter, so it is natural that mass is related to the state of motion. In four-dimensional space-time, momentum and energy are unified, which are called four vectors of energy momentum. In addition, four-dimensional velocity, four-dimensional acceleration, four-dimensional force and four-dimensional electromagnetic field equations are all defined in four-dimensional space-time. It is worth mentioning that the four-dimensional electromagnetic field equation is more perfect, which completely unifies electricity and magnetism, and the electric field and magnetic field are described by a unified electromagnetic field tensor. The physical laws of four-dimensional space-time are much more perfect than those of three-dimensional, which shows that our world is indeed four-dimensional. It can be said that at least it is much more perfect than Newtonian mechanics. At least because of its perfection, we can't doubt it.
In the theory of relativity, time and space constitute an inseparable whole-four-dimensional spacetime, and energy and momentum also constitute an inseparable whole-four-dimensional momentum. This shows that there may be a deep connection between some seemingly unrelated quantities in nature. When we talk about general relativity in the future, we will also see that there is also a profound relationship between the four vectors of space-time and energy momentum.
3 Basic principles of special relativity
Matter moves forever in interaction, and there is no matter that does not move and there is no matter that does not move. Because matter moves in interaction, it is necessary to describe motion in the relationship of matter, and it is impossible to describe motion in isolation. In other words, motion must have a reference object, and this reference object is the frame of reference.
Galileo once pointed out that the motion of a moving ship is inseparable from the motion of a stationary ship. That is to say, when you are completely isolated from the outside world in a closed cabin, even if you have the most developed mind and the most advanced instruments, you can't perceive whether your ship is moving at a constant speed or at a standstill. There is no way to perceive speed because there is no reference. For example, we don't know the whole motion state of our whole universe, because the universe is closed. Einstein cited it as the first basic principle of special relativity: the principle of special relativity. Its content is: the inertial system is completely equivalent and indistinguishable.
The famous Michelson-Morey experiment completely negates the ether theory of light and draws the conclusion that light has nothing to do with the frame of reference. In other words, whether you stand on the ground or on a speeding train, the measured speed of light is the same. This is the second basic principle of special relativity, the principle of constant speed of light.
From these two basic principles, we can directly deduce all the contents of special relativity, such as coordinate transformation formula and velocity transformation formula. For example, the speed change is contrary to the traditional law, but it has been proved to be correct in practice. For example, the speed of the train is 10m/s, and the speed of a person on the train is also10m/s. People on the ground see that the speed of people in the car is not 20m/s, but (20- 10 (-65438). In general, this relativistic effect can be completely ignored, but it increases obviously when it is close to the speed of light, such as when the train speed is zero. 99 times the speed of light, people's speed is zero. 99 times the speed of light, then the conclusion of the ground observer is not 1. 98 times the speed of light, but 0. 999949 times the speed of light. The people in the car didn't slow down when they saw the light coming from behind, which was also the speed of light for him. So in this sense, the speed of light cannot be surpassed, because no matter in which reference system, the speed of light is constant. Velocity transformation in particle physics has been proved by countless experiments and is impeccable. It is precisely because of this unique property of light that it is chosen as the only scale of four-dimensional space-time.
4 Special Relativity Effect
According to the principle of relativity in a special sense, the inertial system is completely equivalent. So in the same inertial system, there is a unified time, which is called simultaneity. Relativity proves that there is no unified simultaneity in different inertial systems, that is, two events (time and space points) are simultaneous in one relational system and may be different in another inertial system. This is the relativity of simultaneity. In an inertial system, the same physical process. In the future general relativity, we can know that in a non-inertial system, time and space are not unified, that is, in the same non-inertial system, there is no unified time, so the unified simultaneity cannot be established.
Relativity deduces the time progress relationship between different inertial systems, and finds that the inertial system of motion is slow in time progress, which is the so-called clock slow effect. Generally, it can be understood that a moving clock goes slower than a stationary clock, faster and faster, slower and slower, and almost stops when it approaches the speed of light.
The length of a ruler is the difference between the coordinate values of two endpoints obtained at the same time in an inertial system. Because of the relativity of "simultaneity", the length measured in different inertial systems is also different. Relativity proves that the ruler moving in the length direction of the ruler is shorter than the static ruler, which is called scale effect. When the speed approaches the speed of light, the scale shrinks to a point.
5 Special Relativity Effect 2
As can be seen from the above statement, the principle of slow clock and scale contraction is that the progress of time is relative. In other words, the timetable is related to the reference system. This fundamentally negates Newton's absolute view of time and space. Relativity holds that absolute time does not exist, but time is still an objective quantity. For example, in the ideal twin experiment to be discussed in the next issue, my brother is 15 years old after returning from the spaceship, and my brother may be 45 years old, indicating that time is relative, but my brother did live 15 years old, and my brother really thought that he lived 45 years old, which has nothing to do with the frame of reference, and time is "absolute". This shows that no matter what the motion state of an object is, the time it experiences is an objective quantity and absolute, which is called intrinsic time. That is to say, no matter what form you exercise, you think that your coffee drinking speed is normal, and your lifestyle has not been disrupted, but others may see that you have been drinking coffee for 100 years, and it takes only one second from putting down the cup to dying.
6 clock paradox or twin paradox
After the birth of the theory of relativity, there is a very interesting and difficult problem-twin paradox. A pair of twins, A and B, are on the earth, and B travels in a rocket and returns to the earth after a long time. Einstein asserted from the theory of relativity that the two experienced different times, and B would be younger than A when they met again. Many people have doubts, thinking that A watches B exercise and B watches A exercise. Why can't A be smaller than B? Because the earth can be approximated as an inertial system, and B has to go through the process of acceleration and deceleration, and it is a reference system with variable acceleration, so it is really complicated to discuss. So this problem that Einstein has discussed clearly is mistaken by many people as contradictory relativity. It is much easier to discuss this problem with the concepts of Shi Kongtu and World Line, but it requires a lot of mathematical knowledge and formulas. Here, we just use language to describe the simplest situation. However, it is impossible to explain the details in more detail by language alone. If you are interested, you can refer to some books on relativity. Our conclusion is that B is younger than A in any frame of reference.
In order to simplify the problem, we will only discuss this situation. After a while, the rocket accelerated to sub-light speed. After flying for a period of time, turn around in a very short time, fly for a period of time, and slow down to meet the earth in a very short time. The purpose of this treatment is to ignore the effects of acceleration and deceleration. It is easy to discuss in the earth reference system that the rocket is always a moving clock, and B is younger than A when we meet again. In the rocket reference system, the earth is the moving clock in the process of uniform motion, and the time process is slower than that in the rocket, but the most critical place is the process of rocket rotation. In the process of U-turn, the earth crossed half a circle from the distance behind the rocket in a very short time and reached the distance in front of the rocket. This is a "superluminal" process. It's just that this superluminal and relativity are not contradictory. This superluminal can't transmit any information, and it's not superluminal in the real sense. Without this u-turn process, the rocket and the earth would not meet. Because there is no uniform time in different reference systems, it is impossible to compare their ages. Only when they meet can they be compared. After the rocket turns around, B can't accept the message from A directly, because it takes time to transmit it. The actual process that B saw was that during the U-turn, the earth's time schedule accelerated sharply. In B's view, A is younger than B in reality, and then it ages quickly when it turns around, and when it comes back, A ages slower than itself. When we meet again, we are still younger than A. In other words, there is no logical contradiction in the theory of relativity.
7 Overview of Special Relativity
Relativity requires that the laws of physics remain unchanged under coordinate transformation (Lorentz change). Classical electromagnetic theory can be incorporated into the framework of relativity without modification, while Newtonian mechanics remains unchanged only under galilean transformation, and the original simple form becomes extremely complicated under Lorentz transformation. Therefore, classical mechanics needs to be revised, and the revised mechanical system remains unchanged under Lorentz transformation, which is relativistic mechanics.
After the establishment of special relativity, it has played a great role in promoting physics. And it goes deep into the category of quantum mechanics, becoming an indispensable theory for studying high-speed particles, and has achieved fruitful results. However, behind the success, there are two outstanding principles. The first is the difficulty brought by inertial system. After abandoning absolute space-time, inertial system has become an undefined concept. We can say that the inertial system is the reference system for establishing the law of inertia. The law of inertia is essentially a state in which an object remains stationary or moves in a straight line at a constant speed without external force. However, what does it mean to be "free from external forces"? It can only be said that being free from external force means that an object can move in a stationary or uniform straight line in an inertial system. In this way, the definition of inertial system falls into a logical cycle, and such a definition is useless. We can always find very similar inertial systems, but there is no real inertial system in the universe. The whole theory is like building on the beach. The second is the difficulty caused by gravity. The law of universal gravitation is closely related to absolute space-time and must be revised. However, any attempt to change it into a constant situation under Lorentz transformation has failed, and gravity cannot be brought into the framework of special relativity. At that time, only gravity and electromagnetic force were found in the physical world, and one of them came out to make trouble, and the situation was definitely not satisfactory.
It took Einstein only a few weeks to establish the special theory of relativity, while it took ten years to establish the general theory of relativity to solve these two difficulties. In order to solve the first problem, Einstein simply canceled the special position of inertial system in theory and extended the principle of relativity to non-inertial system. Therefore, the first problem is transformed into the space-time structure problem of non-inertial system. The first obstacle encountered in a non-inertial system is inertial force. Through the in-depth study of inertia force, the famous principle of equality is put forward, and it is found that the problem of reference frame may be solved together with the problem of gravity. After many twists and turns, Einstein finally established a complete general theory of relativity. General relativity surprises all physicists, and gravity is far more complicated than imagined. So far, Einstein's field equation has only got a few definite solutions. Its beautiful mathematical form has amazed physicists so far. While the general theory of relativity has made great achievements, quantum mechanics founded and developed by Copenhagen School has also made a major breakthrough. However, physicists soon found that the two theories were incompatible, and at least one of them needed to be revised. This led to the famous debate: Einstein VS Copenhagen School. The debate has not stopped yet, but more and more physicists are more inclined to quantum theory. Einstein spent the last 30 years of his life trying to solve this problem, but he got nothing. However, his work points out the direction for physicists: to establish a hyperunified theory containing four forces. At present, the most promising candidates recognized by academic circles are superstring theory and ultramembrane theory.
Overview of general relativity
When the theory of relativity came out, people saw the following conclusions: four-dimensional curved space-time, finite boundless universe, gravitational wave, gravitational lens, big bang cosmology, black hole, the main theme of 2 1 century, and so on. All this comes too suddenly, which makes people feel that the theory of relativity is mysterious. Therefore, in the early years of the advent of the theory of relativity, some people threatened that "only twelve people in the world understand the theory of relativity." Some people even say that "only two and a half people in the world understand the theory of relativity". What's more, the theory of relativity is compared with spiritualism and idealism. In fact, the theory of relativity is not mysterious. It is the most down-to-earth theory, a truth that has been tested thousands of times, and not unattainable.
The geometry applied by relativity is not ordinary Euclidean geometry, but Riemann geometry. I believe many people know non-Euclidean geometry, which can be divided into Roche geometry and Riemannian geometry. Riemann unified three kinds of geometry from a higher angle, which is called Riemann geometry. Non-Euclidean geometry has many strange conclusions. The sum of the internal angles of a triangle is not 180 degrees, and pi is not 3. 14 and so on. So when it was first put forward, it was ridiculed as the most useless theory. It was not until its application was found in spherical geometry that it was paid attention to.
If there is no matter in space and space-time is flat, then Euclidean geometry is enough. For example, the application in special relativity is four-dimensional pseudo-Euclidean space. Because there is an imaginary unit I in front of the time coordinate, a pseudo word is added. When matter exists in space, the interaction between matter and space-time bends space-time, which means using non-Euclidean geometry.
Relativity predicted the existence of gravitational waves, and found that both gravitational fields and gravitational waves travel at the speed of light, denying the distance effect of the law of universal gravitation. When light comes from a star and meets a massive celestial body, it will converge again, that is, we can observe the stars blocked by celestial bodies. Generally speaking, what you see is a ring called Einstein ring. When Einstein applied the field equation to the universe, he found that the universe was not stable, and it either expanded or contracted. Cosmology at that time believed that the universe was infinite, static and the stars were infinite. So he did not hesitate to modify the field equation, added the universe term, got the stable solution, and put forward the finite infinite universe model. Soon Hubble discovered the famous Hubble law and put forward the theory of cosmic expansion. Einstein regretted this and gave up the cosmological term, calling it the biggest mistake in his life. In later research, physicists were surprised to find that the universe was not only expanding, but also exploding. The very early universe was distributed in a very small area. Cosmologists need to study the content of particle physics to put forward a more comprehensive model of the evolution of the universe, and particle physicists need cosmologists' observations and theories to enrich and develop particle physics. In this way, the two most active branches of physics-particle physics and cosmology-are combined with each other. As the preface of high school physics says, it's like a strange python biting its tail. It is worth mentioning that although Einstein's static universe has been abandoned, its finite boundless universe model is one of the three possible fates of the future universe and the most promising. In recent years, the cosmological term has been revalued. The problem of black holes will be discussed in a future article. Although black holes and big bang are predictions of relativity, their contents have gone beyond the limitation of relativity and are closely combined with quantum mechanics and thermodynamics. I hope the future theory can find a breakthrough here.
Basic principles of general relativity
Because the inertial system cannot be defined, Einstein extended the principle of relativity to the non-inertial system and put forward the first principle of general relativity: the principle of general relativity. Its content is that all frames of reference are equivalent when describing the laws of nature. This is very different from the principle of relativity in a narrow sense. In different reference systems, all physical laws are completely equivalent, and there is no difference in description. But in all reference frames, this is impossible. It can only be said that different frames of reference can also effectively describe the laws of nature. This requires us to find a better description method to meet this requirement. Through the special theory of relativity, it is easy to prove that the pi of a rotating disk is greater than 3. 14。 So the general frame of reference should be described by Riemann geometry. The second principle is the principle that the speed of light is constant: the speed of light is constant in any reference system. The space-time point equivalent to light is fixed in four-dimensional space-time Space-time is straight, and light moves in a straight line at the speed of light in three-dimensional space. When space-time is curved, light moves along the curved space in three-dimensional space. It can be said that gravity can deflect light, but it cannot accelerate photons. The third principle is the most famous principle of reciprocity. There are two kinds of mass. Inertia mass is used to measure the inertia of an object, which was originally defined by Newton's second law. Gravitational mass is a measure of the gravitational charge of an object, which was originally defined by Newton's law of universal gravitation. These are two unrelated laws. Inertial mass is not equal to charge, and it is not even important so far. Then inertial mass and gravitational mass (gravitational charge) should have nothing to do with Newtonian mechanics. However, the difference between them cannot be discovered through the most sophisticated experiments. Inertia mass is strictly proportional to gravitational mass (it can be strictly equal if appropriate coefficients are selected). General relativity regards inertial mass and gravitational mass as the content of equivalence principle. Inertia mass is related to inertia force, and gravitational mass is related to gravity. In this way, the relationship between non-inertial system and gravity is established. Then a very small free-falling reference frame can be introduced at any point in the gravitational field. Because inertial mass is equal to gravitational mass, it is neither inertia nor gravity in this reference system, and all theories of special relativity can be used. When the initial conditions are the same, the orbits of particles with equal mass and different charges are different in the same electric field, but all particles have only one orbit in the same gravitational field. The principle of equivalence made Einstein realize that the gravitational field is probably not the outfield of space-time, but the geometric field, which is an attribute of space-time itself. Due to the existence of matter, the originally flat space-time has become a curved Riemannian space-time. At the beginning of the establishment of general relativity, there was a fourth principle, the law of inertia: an object that is not subjected to force (except gravity, because gravity is not real force) does inertial motion. In Riemann space-time, it moves along geodesic lines. Geodesic is a generalization of straight lines, the shortest (or longest) straight line between two points, and it is unique. For example, the geodesic of a sphere is an arc of a great circle cut by a plane passing through the center of the sphere and the sphere. But after the field equation of general relativity is established, this law can be deduced from the field equation, so the law of inertia becomes the law of inertia. It is worth mentioning that Galileo once thought that uniform circular motion was inertial motion, and uniform linear motion would always close into a circle. This is proposed to explain planetary motion. Naturally, he was criticized by Newtonian mechanics, but the theory of relativity revived it. Planets do inertial motion, but not the standard uniform circular motion.
10 geometry of ants and bees
Imagine a flat ant living on a two-dimensional plane. Because it is a two-dimensional creature, it has no three-dimensional sense. If ants live on a big plane, they will create Euclidean geometry from practice. If it lives on a sphere, it will create a triangle sum greater than 180 degrees and pi less than 3. Spherical geometry at 14. However, if the ant lives on a big sphere, when its "science" is not developed enough and its range of activities is not large enough, it is not enough to find the curvature of the sphere, and the small sphere it lives in is similar to a plane, so it will create Euclidean geometry first. When its "technology" is developed, it will be found that the sum of triangles is greater than 180 degrees, and the pi is less than 3. 14 and other "experimental facts" If ants are smart enough, they will come to the conclusion that their universe is a curved two-dimensional space. When they measure their "universe" all over, they will come to the conclusion that their universe is closed (turned around and returned to its original place) and limited. And because the curvature of "space" (surface) is the same everywhere, they will compare the universe with the circle in their own universe and think that the universe is the same. Because it has no sense of the third dimension, it is impossible to imagine how their universe bends into a ball, let alone how their "boundless" universe becomes a sphere with limited area in a three-dimensional flat space. It is difficult for them to answer "What is beyond the universe?" . Because their universe is a finite and infinite closed two-dimensional space, it is difficult to form the concept of "outer".
A bee can easily describe abstract facts that ants can discover with the help of "advanced technology". Because bees are creatures in three-dimensional space, it is easy to form the concept of sphere by knowing the two-dimensional surface embedded in three-dimensional space at a glance. Ants have come to the same conclusion with their own "science and technology", but it is not vivid or strictly mathematical.
It can be seen that it is not only the creatures in high-dimensional space that can find the situation in low-dimensional space. Smart ants can also find the curvature of the sphere and finally establish the perfect geometry of the sphere, and its understanding depth is not much worse than that of bees.
Riemannian geometry is a huge system of geometric axioms, which is specially used to study various properties of curved space. Spherical geometry is only a small branch of it. It can be used not only to study two-dimensional surfaces such as sphere, ellipse and hyperboloid, but also to study high-dimensional surface space. It is the most important mathematical tool of general relativity. When establishing Riemann geometry, Riemann predicted that the real universe may be curved, and the existence of matter is the reason for the curvature of space. This is actually the core content of general relativity. It's just that Riemann didn't have as rich physical knowledge as Einstein at that time, so he couldn't establish general relativity.
Experimental verification of 1 1 general relativity
When Einstein established the general theory of relativity, he put forward three experiments, which were quickly verified: (1) gravitational redshift (2) light deflection (3) Mercury perihelion precession. Until recently, the fourth verification was added: (4) the time delay of radar echo.
(1) Gravitational redshift: The general theory of relativity proves that the inherent time passes slowly where the gravitational potential is low. In other words, the closer to the celestial body, the slower the time. In this way, the period of light emitted by atoms on the surface of celestial bodies becomes longer, and the corresponding frequency becomes smaller because of the constant speed of light, and moves in the direction of red light in the spectrum, which is called gravitational redshift. There are many dense celestial bodies in the universe. We can measure the frequency of the light they emit and compare it with the light emitted by the corresponding atoms on the earth. It is found that redshift is consistent with relativistic language. In the early 1960s, people used the recoil-free vibration absorption effect (Mossbauer effect) of gamma rays in the earth's gravitational field to measure the vertical propagation of light. 5M, the result is consistent with the prediction of relativity.
(2) Light deflection: According to the fluctuation of light, light should not be deflected in the gravitational field. According to the mixed product of semi-classical "quantum theory plus Newton's gravity theory", the mass of photons is calculated by Planck formula E=hr and mass-energy formula e = MC 2, and then the deflection angle of light near the sun is obtained by Newton's law of universal gravitation. 87 seconds, the deflection angle calculated by general relativity is 1. 75 seconds, twice the angle above. 19 19, just after the first world war, British scientist Eddington sent two expeditions to take advantage of the solar eclipse to observe, and the observation result was about 1. 7 seconds, just within the error range of the relativistic experiment. The main reason for the error is the deflection of light by the sun's atmosphere. Recently, radio telescopes can be used to observe the deflection of quasar waves in the solar gravitational field, without waiting for the rare opportunity of solar eclipse. Accurate measurement further confirms the conclusion of relativity.
(3) Precession of Mercury Perihelion: Astronomical observation records that Mercury Perihelion moves for 5600 seconds every hundred years. People have considered various factors, and according to Newton's theory, only 5557 seconds can be explained, leaving only 43 seconds. The calculation result of general relativity deviates from the law of universal gravitation (inverse square law), which just makes the perihelion of Mercury move for 43 seconds every 100 years.
(4) Radar echo experiment: transmit radar signals from the earth to the planet, receive the signals reflected by the planet, measure the round-trip time of the signals, and check whether the space is bent (check the sum of the angles in the triangle). In 1960s, American physicists did this experiment despite many difficulties, and the result was consistent with the prediction of relativity.
Only relying on these experiments can not explain the correctness of the theory of relativity, but it can only show that it is more accurate than Newton's theory of gravity, because it contains Newton's theory of gravity and can explain phenomena that Newton's theory can't explain. However, there is no guarantee that this is the best theory, and there is no guarantee that the theory of relativity can be established in areas with extremely curved space-time (such as black holes). So the general theory of relativity is still facing a test.
Brief introduction of conventional black holes in 12 black hole ramble
Boiling black hole, where will you lead physics? Through the strange darkness, it radiates the dawn of the new century.
19 at the end of the 20th century, two dark clouds appeared in physics: blackbody radiation and Michelson experiment. A year later, the first cloud gave birth to quantum theory, and five years later, the second cloud gave birth to relativity. After a century of development, at the turn of this century, two dark clouds were born in physics: singularity difficulty and quantization difficulty in gravitational field. These two difficulties may be solved by studying black holes and big explosions.
Fundamental particles, celestial evolution and the origin of life are the three major themes of contemporary natural science. The study of black holes and cosmology is closely related to the evolution of elementary particles and celestial bodies. In particular, the study of black holes involves some fundamental problems, which helps us to understand nature in depth. So black holes are the most important part of this series.
Newton's theory also predicted black holes, treating light as particles, and when light is pulled back by gravity, it becomes a black hole. Different from the black hole predicted by modern theory. Newton's black hole is a death star and the ultimate destination of celestial evolution. However, modern black holes are only an intermediate stage of celestial evolution. Black holes are also changing, and some changes are even extremely violent. Black holes can emit light, give off heat and even explode. Black holes are not death stars, even full of life. Black hole is the product of relativity, but it is beyond the scope of relativity. Quantum theory is closely related to thermodynamics. Black holes formed by the evolution of celestial bodies are called conventional black holes.
1972, Beckenstein, a young graduate student from Princeton University, put forward the hairless theorem of black holes: after a star collapses into a black hole, only three basic conserved quantities, namely mass, angular momentum and charge, continue to do work. All other factors ("hair") disappear after entering the black hole. This must have been strictly proved by Hawking and other four people.
According to this theorem, black holes can be divided into four categories. (1) An uncharged and non-rotating black hole. Its space-time structure was calculated by Schwarzschild in 19 16, and it is called Schwarzschild black hole. (2) A charged black hole that does not rotate is called an R-N black hole. The spatio-temporal structure was solved by Reissner and Nordstrom in1916-1918. (3) A rotating uncharged black hole is called a kerr black holes. The spatio-temporal structure was solved by Kerr in 1963. (4) General black holes are called Kerr-Newman black holes. The spatio-temporal structure was solved by Newman in 1965.
The most important ones are Schwarzschild Black Hole and kerr black holes. Because black holes generally have no charge, but most of them rotate at high speed, and it takes only a few thousandths of a second or even less to rotate once. Generally speaking, the average density of black holes is large, but the greater the mass of black holes, the smaller the density. The black hole density of solar mass is 1000 billion tons/cubic centimeter, while the black hole density of cosmic mass is only 10 (-23) g/cubic meter, which is not much different from the current density of the universe, so it is not unreasonable for some people to guess that the universe may be a black hole.
Black holes make singularities difficult. Mathematical singularities with zero volume and infinite density should not appear in the physical world, but there is really no other force in nature that can resist strong gravity. Therefore, there may be undiscovered interactions or physical laws near the singularity to prevent the formation of the singularity, which is also one of the significance of studying black holes.
Static neutral black hole rambling about 13 black hole
According to Newton's theory, when the escape speed reaches the speed of light, light cannot be emitted from the surface of the planet, which is Newton's black hole. After the wave theory of light defeated particles, Newton's black hole was forgotten because waves were not affected by gravity. Interestingly, the black hole conditions calculated from general relativity are exactly the same as those calculated from Newton's theory. From a modern point of view, Newton's theory made two mistakes: (1) wrote the photon kinetic energy MC 2 as (1/2) MC 2, and (2) regarded the curvature of space-time as universal gravitation. These two mistakes cancel each other out, but they come to the correct conclusion. Therefore, the horizon radius of a static neutral black hole is exactly the same as that of a Newton black hole. The horizon is (in the classical range, relativity belongs to classical physics) the boundary from which no matter can escape.
When we say the size of a black hole, we mean the size of its horizon. In fact, the inside of a black hole is basically empty, with only one singularity. This point is infinitely small in volume and infinite in density, and all substances are compressed to this point. As we said before, the singularity may not exist, so we can treat it as a very small point. Let's look at the scene where the black hole devours matter: suppose there are two people A and B in two spaceships, A is far away from the black hole, and B is attracted by the black hole. In B's view, it keeps approaching the black hole, accelerating, passing through the horizon at a speed close to the speed of light, crashing into the central singularity in a very short time, breaking into pieces, and even the nucleus is crushed. In A's view, he couldn't see the real process of B. He saw that B first accelerated, then slowed down, and finally stopped on the horizon, gradually darkened and finally disappeared. What A sees is only the behavior of light emitted by B's spaceship shell, and the real part of B has unconsciously hit the central singularity in A ... The reason why there is a deceleration process is because the time expansion near the black hole makes the speed seen by A slow down or even close to zero. The light a sees stops on the horizon, which is not contradictory to the principle of light speed invariance. The principle of light speed invariance refers to the four dimensions of light traveling in four-dimensional space-time.