Relativity (Principle of relativity)
Relativity is the basic theory about space-time and gravity. It was mainly founded by Albert Einstein and is divided into special relativity (special theory of relativity) and General relativity (general theory of relativity). The basic assumptions of the theory of relativity are the principle of constant speed of light, the principle of relativity and the principle of equivalence. Relativity and quantum mechanics are the two basic pillars of modern physics. Classical mechanics, which lays the foundation for 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 the problem under microscopic subatomic conditions. The theory of relativity has greatly changed mankind's "common sense" concepts about the universe and nature, and proposed brand-new concepts such as "simultaneous relativity", "four-dimensional space-time" and "curved space".
The process of proposing the theory of relativity
In addition to quantum theory, in 1905 Einstein, who had just received his doctorate, published an article titled "On the Electrodynamics of Moving Bodies" that triggered Another revolution in physics in the twentieth century. The article studied the impact of the motion of objects on optical phenomena, which was another difficult problem faced by classical physics at the time.
In the mid-19th century, Maxwell established the electromagnetic field theory and predicted the existence of electromagnetic waves propagating at the speed of light c. By the end of the nineteenth century, experiments had fully confirmed Maxwell's theory. What are electromagnetic waves? For whom is its propagation speed c? The popular view at that time was that the entire universe was filled with a special substance called "ether", and electromagnetic waves were the propagation of ether vibrations. But people found that this was a theory full of contradictions. If it is believed that the earth is moving in a stationary ether, then according to the principle of velocity superposition, the speed of light propagating in different directions on the earth must be different, but the experiment refutes this conclusion. If it is believed that the ether is carried away by the earth, it is obviously inconsistent with some observations in astronomy.
In 1887, Michelson and Morley made very precise measurements using the interference phenomenon of light, and still did not find any movement of the earth relative to the ether. In this regard, H.A. Lorentz proposed a hypothesis that all objects moving in the ether must shrink along the direction of motion. From this he proved that even if the earth was moving relative to the ether, Michelson would not be able to detect it. Einstein approached the problem from a completely different line of thinking. He pointed out that as long as the concepts of absolute space and absolute time established by Newton are abandoned, all difficulties can be solved, and no ether is needed at all.
Einstein proposed two basic principles as the basis for discussing the optical phenomena of moving objects. The first is called the principle of relativity. It means: If the coordinate system K' moves at a uniform speed relative to the coordinate system K without rotating, then any physical experiment done with these two coordinate systems will not be able to distinguish which is the coordinate system K and which is the coordinate system. K'. The second principle is called the principle of constant speed of light, which means that the speed c of light (in a vacuum) is constant and does not depend on the speed of the luminous object.
On the surface, the constant speed of light seems to conflict with the principle of relativity. Because according to the synthesis law of classical mechanical speed, the speed of light should be different for the two coordinate systems K' and K that are moving relatively uniformly. Einstein believed that in order to admit that there is no conflict between these two principles, the physical concepts of time and space must be reanalyzed.
The velocity composition law in classical mechanics actually relies on the following two assumptions:
1. The time interval between the occurrence of two events has nothing to do with the motion state of the clock used to measure time;
2. The spatial distance between two points has nothing to do with the motion state of the ruler used to measure the distance.
Einstein discovered that if the principle of the constant speed of light and the principle of relativity are admitted to be compatible, then both assumptions must be abandoned. At this time, events that occur at the same time for one clock are not necessarily simultaneous for another clock, and simultaneity becomes relative. In two coordinate systems with relative motion, the values ??obtained by measuring the distance between two specific points are no longer equal. Distance also becomes relative.
If an event in the K coordinate system can be determined by three spatial coordinates x, y, z and a time coordinate t, and the same event in the K' coordinate system is determined by x', y', To determine z' and t', Einstein discovered that x', y', z' and t' can be obtained from x, y, z and t through a set of equations. The relative motion speed of the two coordinate systems and the speed of light c are the only parameters of the equation. This equation was first obtained by Lorentz, so it is called Lorentz transformation.
Using the Lorentz transformation, it is easy to prove that the clock will slow down due to movement, the ruler will be shorter when moving than when it is at rest, and the addition of speeds satisfies a new law. The principle of relativity is also expressed as a clear mathematical condition, that is, under the Lorentz transformation, the primed space-time variables x', y', z', t' will replace the space-time variables x, y, z, t , and the expression of any natural law still takes exactly the same form as before. What are called universal laws of nature are covariant with respect to Lorentz transformations. This is very important in our exploration of universal laws of nature.
Furthermore, in classical physics, time is absolute. It has always played an independent role from the three spatial coordinates. Einstein's theory of relativity connects time and space. It is believed that the physical real world is composed of various events, and each event is described by four numbers. These four numbers are its space-time coordinates t and x, y, z. They form a four-dimensional continuous space, usually called Minkowski four-dimensional space. In the theory of relativity, it is natural to examine the physical world in four dimensions. Another important consequence of special relativity is the relationship between mass and energy. Before Einstein, physicists had always believed that mass and energy were completely different and that they were separately conserved quantities. Einstein discovered that mass and energy are inseparable in the theory of relativity, and that the two conservation laws are combined into one law. He gave a famous mass-energy formula: E=mc2, where c is the speed of light. Mass can then be viewed as a measure of its energy. Calculations show that tiny mass contains huge energy. This wonderful formula laid the theoretical foundation for humans to obtain huge energy, create atomic bombs and hydrogen bombs, and use atomic energy to generate electricity.
Most physicists, including Lorentz, the founder of the transformation relationship of relativity, find it difficult to accept these brand-new concepts introduced by Einstein. The obstacles of the old way of thinking meant that this new physical theory was not familiar to the majority of physicists until a generation later. Even the Royal Swedish Academy of Sciences, when awarding the Nobel Prize to Einstein in 1922, only said "because of His contribution to theoretical physics was due to his discovery of the law of the photoelectric effect. "There is no mention of the theory of relativity.
Einstein further established the general theory of relativity in 1915. The principle of special relativity is limited to two coordinate systems that move at a uniform speed relative to each other, but in the principle of general relativity, this restriction of uniform motion is cancelled. He introduced an equivalence principle, arguing that it is impossible to distinguish between gravitational effects and non-uniform motion, that is, non-uniform motion and gravity are equivalent. He further analyzed the phenomenon that light will be bent by gravity when passing close to a line, and believed that the concept of gravity itself was completely unnecessary. It can be thought that the mass of the planet causes the space near it to become curved, and the light travels along the shortest path. Based on these discussions, Einstein derived a set of equations that determined the geometry of curved space resulting from the presence of matter. Using this equation, Einstein calculated the displacement of Mercury's perihelion, which was completely consistent with the experimental observations. He solved a difficult problem that had not been explained for a long time. This made Einstein very excited. He wrote in a letter to Ehrenfest: "...the equation gives the correct value of perihelion. You can imagine how happy I am! For several days, I was so happy that I didn't know what to do."
On November 25, 1915, Einstein submitted a paper entitled "The Equation of Universal Gravity" to the Prussian Academy of Sciences in Berlin, which completely discussed the general theory of relativity.
In the four-dimensional space-time, momentum and energy are unified and are called the four vectors of energy and momentum. In addition, four-dimensional velocity, four-dimensional acceleration, four-dimensional force, four-dimensional form of electromagnetic field equations, etc. are also defined in four-dimensional space-time. It is worth mentioning that the four-dimensional form of the electromagnetic field equations is more perfect, completely unifying electricity and magnetism. Electric fields and magnetic fields are described by a unified electromagnetic field tensor. The physical laws of four-dimensional space-time are much more perfect than the three-dimensional laws, 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 due to its perfection, we cannot doubt it.
In the theory of relativity, time and space constitute an indivisible whole - four-dimensional space-time. Energy and momentum also constitute an indivisible whole - four-dimensional momentum. This shows that there may be profound connections between some seemingly unrelated quantities in nature. When we discuss general relativity in the future, we will also see that there is a profound connection between space and time and the four vectors of energy and momentum.
Basic principles of special relativity
Matters are in eternal motion in interactions. There is no matter that does not move, and there is no motion without matter. Since matter is interconnected and interacts with each other, Therefore, the movement must be described in the interrelationship of substances, and it is impossible to describe the movement in isolation. In other words, movement must have a reference object, and this reference object is the reference system.
Galileo once pointed out that the motion of a moving ship is indistinguishable from that of a stationary ship. That is to say, when you are in a closed cabin and completely isolated from the outside world, even if you have the most developed mind, the most Even advanced instruments cannot sense whether your ship is moving at a constant speed or stationary. It is even more difficult to perceive the magnitude of the speed because there is no reference. For example, we don’t know the overall motion state of our entire universe because the universe is closed. Einstein cited it as the first basic principle of special relativity: the special principle of relativity. Its content is: the inertial systems are completely equivalent and indistinguishable.
The famous Michelson-Morley experiment completely denied the ether theory of light and concluded that light has nothing to do with the reference frame. In other words, whether you are standing 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 the constant speed of light.
From these two basic principles, we can directly derive the coordinate transformation formula, velocity transformation formula and other contents of the special theory of relativity. For example, speed changes contradict traditional laws, but practice has proven to be correct. For example, the speed of a train is 10m/s, and the speed of a person on the train relative to the train is also 10m/s. People on the ground see that the speed of the train is 10m/s. The speed of the person is not 20m/s, but about (20-10-15) m/s. Under normal circumstances, this relativistic effect can be completely ignored, but when approaching the speed of light, this effect increases significantly. For example, if the speed of a train is 0.99 times the speed of light, and the speed of a person is also 0.99 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 person in the car saw that the light coming from behind did not slow down, and it was also the speed of light to him. Therefore, in this sense, the speed of light is unsurpassable because it is constant no matter in which reference frame. Velocity transformation has been proved impeccable by numerous experiments in particle physics. Because of this unique property of light, it was chosen as the only ruler of four-dimensional space-time.
Special relativity effect
According to the principle of special relativity, inertial systems are completely equivalent. Therefore, in the same inertial system, there is a unified time, which is called simultaneity. The theory of relativity proves that in different inertial systems, there is no unified simultaneity. That is, two events (space-time points) that are simultaneous in one relational system may not be simultaneous in another inertial system. This is simultaneous Relativity, in the inertial system, the time course of the same physical process is exactly the same. If the same physical process is used to measure time, a unified time can be obtained in the entire inertial system. In the future general theory of relativity, we can know that in non-inertial systems, space-time is non-uniform, that is to say, in the same non-inertial system, there is no unified time, so unified simultaneity cannot be established.
The theory of relativity derives the relationship between time progress between different inertial systems and finds that the time progress of moving inertial systems is slow. This is the so-called clock slowness effect. It can be generally understood that a moving clock runs slower than a stationary clock. Moreover, the faster the movement speed, the slower the clock runs. When it is close to the speed of light, the clock almost stops.
The length of the ruler is the difference between the coordinate values ??of the two endpoints obtained "simultaneously" in an inertial system. Due to the relativity of "simultaneity", the lengths measured in different inertial systems are also different. The theory of relativity proves that a ruler moving in the length direction of the ruler is shorter than a stationary ruler. This is the so-called telescope effect. When the speed approaches the speed of light, the ruler shrinks to a point.
It can be seen from the above statement that the principle of clock slowness and ruler contraction is that the progress of time is relative. That is, the progress of time is related to the frame of reference. This fundamentally denies Newton's view of absolute space and time. The theory of relativity holds that absolute time does not exist, but time is still an objective quantity. For example, in the ideal twin experiment that will be discussed in the next issue, the elder brother was 15 years old when he returned from the spaceship, and the younger brother may have been 45 years old. This shows that time is relative, but the elder brother did live for 15 years, and the younger brother did think that he lived. It has been 45 years, which has nothing to do with the reference system, and time is "absolute". This shows that no matter what the state of motion of an object is, the time it experiences is an objective quantity and is absolute. This is called proper time. In other words, no matter what form of exercise you do, you think that the speed at which you drink coffee is normal and your life routine is not disrupted. However, others may see that it took you 100 years to drink coffee, and from the time you put down the cup to It only took a second to die.
The clock paradox or the twins paradox
After the birth of the theory of relativity, there was a difficult problem that was extremely interesting - the twins paradox. A pair of twins A and B, A is on the earth, and B takes a rocket to travel among the stars, and returns to the earth after a long time. Einstein asserted from the theory of relativity that two people experienced different times, and B will be younger than A when they meet again. Many people have questions, thinking that A sees B exercising, and B sees A exercising. Why can't A be younger than B? Since the earth can be approximated as an inertial frame, B has to go through the process of acceleration and deceleration. It is a variable acceleration motion reference frame. It is very complicated to discuss. Therefore, this issue that Einstein has discussed clearly has been mistakenly thought by many people that the theory of relativity is self-contradictory. theory. It would be much easier to discuss this issue using the concepts of space-time diagrams and world lines, but a lot of mathematical knowledge and formulas would be required. Here we only use language to describe the simplest situation. However, words alone cannot explain the details in more detail. If you are interested, please refer to some relativity books. Our conclusion is that B is younger than A in either frame of reference.
To simplify the problem, we will only discuss this situation. The rocket accelerates to sub-light speed in a very short time, flies for a period of time, turns around in a very short time, flies for another period of time, and decelerates in a very short time. Earth meets. The purpose of this processing is to ignore the effects of acceleration and deceleration. It is easy to discuss in the earth's reference system, the rocket is always moving clock, and B is younger than A at the reunion. In the rocket reference frame, the earth is moving at a constant speed, and the time process is slower than that in the rocket, but the most critical point is the process of the rocket turning around. During the U-turn, the Earth travels across half a circle from far behind the rocket to far in front of the rocket in a very short time. This is a "super-light" process. But this super-light speed does not contradict the theory of relativity. This "super-light speed" cannot transmit any information, and it is not super-light speed in the true sense. Without this U-turn process, the rocket and the Earth cannot meet. Since there is no unified time in different reference systems, their ages cannot be compared. They can only be compared when they meet. After the rocket turns around, B cannot directly receive A's information because the information transmission takes time. The actual process that B saw was that during the U-turn, the earth's time progress suddenly accelerated. From B's perspective, A is actually younger than B, and then ages rapidly when turning around. When returning, A ages slower than himself. When we met again, I was still younger than A. In other words, there are no logical contradictions in the theory of relativity.
Riemann unified three geometries from a higher perspective, called Riemannian geometry. In non-Euclidean geometry, there are many strange results. The sum of the interior angles of a triangle is not 180 degrees, nor is the pi ratio 3.14, etc. Therefore, when it was first introduced, it was ridiculed and considered to be the most useless theory. It was not taken seriously until its application was discovered in spherical geometry.
If there is no matter in space, space-time is flat, and Euclidean geometry is enough. For example, what is used in special relativity is the four-dimensional pseudo-Euclidean space. A dummy word is added because there is an imaginary unit i in front of the time coordinate. When matter exists in space, the matter interacts with space-time, causing space-time to curve, which requires the use of non-Euclidean geometry.
The theory of relativity predicts the existence of gravitational waves, and discovers that both gravitational fields and gravitational waves propagate at the speed of light, denying the action at a distance of the law of universal gravitation. When light is emitted by a star and encounters a massive celestial body, the light will re-converge. In other words, we can observe the star blocked by the celestial body. Normally, what you see is a ring, which is called an Einstein ring. When Einstein applied his field equations to the universe, he discovered that the universe was not stable; it was either expanding or contracting. At that time, cosmology believed that the universe was infinite and stationary, and the stars were also infinite. So he did not hesitate to modify the field equations, added a cosmological term, obtained a stable solution, and proposed a finite and boundless universe model. Soon Hubble discovered the famous Hubble's law and proposed the theory of universe expansion. Einstein regretted this and gave up the cosmic term, calling it the biggest mistake of his life. In subsequent studies, physicists were surprised to find that the universe was not only expanding, but actually exploding. The very early universe was distributed on a very small scale. Cosmologists need to study the content of particle physics to propose a more comprehensive model of the evolution of the universe, and particle physicists need the observation results and theories of cosmologists to enrich and develop it. Particle physics. In this way, the two currently most active branches of physics: particle physics and cosmology, the largest and smallest in research, are combined with each other. Just like what was said in the preface to high school physics, it's like a strange python biting its own tail. It is worth mentioning that although Einstein's static universe has been abandoned, his finite and boundless universe model is one of the three possible future fates of the universe, and it is the most promising. In recent years, the cosmic term has received renewed attention. The issue of black holes will be discussed in a future article. Although black holes and the Big Bang are predictions of the theory of relativity, their contents have exceeded the limitations of the theory of relativity and are quite closely integrated with quantum mechanics and thermodynamics. It is hoped that future theories will find a breakthrough here.
Basic principles of general relativity
Since inertial systems cannot be defined, Einstein extended the principle of relativity to non-inertial systems and proposed the first principle of general relativity: general relativity principle. The content is that all reference frames are equivalent in describing the laws of nature. This is very different from the principle of special relativity. In different reference systems, all physical laws are completely equivalent, without any descriptive differences. But in all reference systems, this is impossible. It can only be said that different reference systems can describe the laws of nature equally effectively. This requires us to find a better description method to adapt to this requirement. Through special relativity, it is easy to prove that the pi of a rotating disk is greater than 3.14. Therefore, ordinary reference systems should be described by Riemannian geometry. The second principle is the principle of constant speed of light: the speed of light is constant in any reference system. It is equivalent to the fact that the space-time point of light is stationary in four-dimensional space-time. When space and time are flat, light moves in a straight line at the speed of light in three-dimensional space; when space and time are 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 of the equivalence principles. There are two types of mass. Inertial mass is used to measure the inertia of an object. It was originally defined by Newton's second law. Gravitational mass measures the size of an object's gravitational charge and was originally defined by Newton's law of universal gravitation. They are two independent laws. Inertial mass is not equal to charge, and it doesn't even matter so far. Then inertial mass and gravitational mass (gravitational charge) should not have any relationship in Newtonian mechanics.
However, the difference between them cannot be discovered through the most sophisticated contemporary experiments. Inertial mass is strictly proportional to gravitational mass (choosing appropriate coefficients can make them strictly equal). The general theory of relativity takes the complete equality of inertial mass and gravitational mass as the content of the equivalence principle. Inertial mass is related to inertial force, and gravitational mass is related to gravity. In this way, a connection is also established between the non-inertial frame and gravity. Then a small free fall reference frame can be introduced at any point in the gravitational field. Since inertial mass and gravitational mass are equal, there is neither inertial force nor gravitational force in this reference system, and all theories of special relativity can be used. When the initial conditions are the same, particles of equal mass and unequal charge have different orbits in the same electric field, but all particles have only one orbit in the same gravitational field. The equivalence principle made Einstein realize that the gravitational field is probably not an external field in space-time, but a geometric field and a property of space-time itself. Due to the existence of matter, the originally straight 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: objects without forces (except gravity, because gravity is not a real force) move inertially. In Riemannian space-time, it is moving along the geodesic. A geodesic is a generalization of a straight line. It is the shortest (or longest) line between two points and is unique. For example, the geodesic of a sphere is the arc of a great circle intercepted by a plane passing through the center of the sphere and the sphere. However, after the field equations of general relativity are established, this law can be derived from the field equations, so the inertia law becomes the inertia theorem. It is worth mentioning that Galileo once believed that uniform circular motion is inertial motion, and uniform linear motion will always close into a circle. This was proposed to explain planetary motion. Naturally, he was completely criticized by Newtonian mechanics, but the theory of relativity resurrected it. The planet is indeed inertial motion, but it is not a standard uniform circle.
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