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Why does Einstein's theory of relativity say that when people travel faster than the speed of light, they can travel through time and space?
Relativity is the basic theory about space-time and gravity, which was mainly founded by Einstein and divided into special relativity (special relativity) and general relativity (general relativity). The basic assumptions of relativity are the principle of invariance of light speed, the principle of relativity and the principle of equivalence. Relativity and quantum mechanics are two basic pillars of modern physics. Classical mechanics, which laid the foundation of classical physics, is not suitable for high-speed moving objects and objects under microscopic conditions. Relativity solves the problem of high-speed motion; Quantum mechanics solves problems under microscopic subatomic conditions. Relativity has greatly changed the common sense concepts of the universe and nature, and put forward new concepts such as simultaneous relativity, four-dimensional space-time and curved space.

restricted theory of relativity

The philosophy of Mach and Hume had a great influence on Einstein. Mach believes that the measurement of space-time is related to the movement of matter. The concept of time and space is formed through experience. Absolute time and space, no matter what experience is based on, can't be grasped. More specifically, Hume said: Space and extension are just visible objects that are filled with space and distributed in a certain order. And time is always discovered through the perceptual changes of changeable objects. 1905, Einstein pointed out that Michelson and Morey's experiments actually showed that the whole concept of "ether" was redundant and the speed of light was constant. Newton's concept of absolute space-time is wrong. There is no absolutely static reference object, and the measurement of time varies with different reference frames. He put forward Lorentz transformation based on the principle of invariance of light speed and relativity. Created the special theory of relativity.

Special relativity is based on the theory of four-dimensional space-time view, so to understand the content of relativity, we must first have a general understanding of its space-time view. There are various multidimensional spaces in mathematics, but so far, the physical world we know is only four-dimensional, that is, three-dimensional space plus one-dimensional time. The high-dimensional space mentioned in modern microphysics is another meaning, which is only mathematical, so I won't discuss it here.

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.

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's experiment completely negates the etheric 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.

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.

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.

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. Fly for a while, turn around for a short time, fly for a short time, and slow down for a short time to meet the earth. 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 the rocket turning around. 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 quickly ages when he turns around, and when he comes back, A ages slower than himself. When we meet again, we are still younger than A. In other words, there is no logical contradiction in the theory of relativity.

Theory of 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 Riemann 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.

The 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.