Relativity is a basic theory about space-time and gravity, which was mainly founded by Einstein. It can be 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.
Theory of relativity
An incredible world.
Gu Rui translated the original: Slaven
Interpretation of basic concepts of general relativity;
Before reading this passage and understanding the key features of general relativity, we must assume one thing: the special relativity is correct. In other words, general relativity is based on special relativity. If the latter is proved wrong, then the whole theoretical building will collapse.
In order to understand general relativity, we must know how mass is defined in classical mechanics.
Two different expressions of quality:
First of all, let's think about what quality stands for in our daily life. "Weight"? In fact, we think that mass is something that can be weighed, just like we measure it: we put the object that needs to be measured on the balance. What kind of quality do we use to do this? It is the fact that the earth and the measured object attract each other. This mass is called "gravitational mass". We call it "gravity" because it determines the motion of all stars in the universe: the gravitational mass between the earth and the sun drives the earth to move around the latter in a nearly circular motion.
Now, try to push your car on a flat ground. You can't deny that your car strongly resists the acceleration you want to give it. This is because your car is of great quality. It is easier to move light objects than heavy ones. Mass can also be defined in another way: "It opposes acceleration". This mass is called "inertial mass".
So we come to the conclusion that we can measure quality in two ways. Either we weigh it (very simply) or we measure its resistance to acceleration (using Newton's law).
Many experiments have been done to measure the inertial mass and gravitational mass of the same object. All experimental results come to the same conclusion: inertial mass is equal to gravitational mass.
Newton himself realized that this kind of mass equivalence was caused by some reason that his theory could not explain. But he thinks this result is a simple coincidence. On the contrary, Einstein found that there is a channel in this equation that can replace Newton's theory.
Everyday experience proves this equivalence: two objects (one light and one heavy) will "fall" at the same speed. However, heavy objects are subject to greater gravity than light objects. So why didn't it "fall" faster? Because it is more resistant to acceleration. The conclusion is that the acceleration of an object in the gravitational field has nothing to do with its mass. Galileo was the first person to notice this phenomenon. It is important for you to understand that all objects in the gravitational field "fall at the same speed" are the result of the equivalence of inertial mass and gravitational mass.
Now let's pay attention to the expression "whereabouts". Objects "fall" because the gravitational mass of the earth produces the gravitational field of the earth. Two objects have the same speed in the same gravitational field. Whether it's the moon or the sun, their acceleration speed is the same. In other words, their speed increases by the same amount every second. (Acceleration is the increment of speed per second)
The third hypothesis in Einstein's argument is that gravitational mass and inertial mass are equal.
Einstein has been looking for the explanation that "gravitational mass equals inertial mass". To this end, he put forward a third hypothesis, called "equivalence principle". It shows that if an inertial system is uniformly accelerated relative to a Galileo system, then we can consider it (inertial system) to be stationary by introducing a uniformly accelerated gravitational field relative to it.
Let's examine an inertial system K', which has a uniform acceleration motion relative to Galileo system. There are many objects around k and k'. This object is stationary with respect to K, so these objects have the same accelerated motion with respect to K'. This acceleration is the same for all objects, contrary to the acceleration direction of K' relative to K. As we have said, the acceleration of all objects in a gravitational field is the same, so the effect is equivalent to that K' is static and has a uniform gravitational field.
So if the equivalence principle is established, it is only a simple inference that the masses of two objects are equal. This is why (quality) equivalence is an important argument to support the principle of equivalence.
Assuming that K' is static and the gravitational field exists, we can understand K' as a Galileo system, in which we can study the laws of mechanics. Therefore, Einstein established his fourth principle.
Einstein's second hypothesis
Gu Rui translated the original: Slaven
time and space
We have come to a contradictory conclusion. The "common sense relativity" that we use to convert speed from one frame of reference to another conflicts with Einstein's assumption that the speed of light is the same in all inertial frames. Einstein's hypothesis is correct only in two cases: either the distance between the two inertial systems is different or the time between the two inertial systems is different.
Actually, both of them are right. The first effect is called "length contraction" and the second effect is called "time expansion".
Length contraction:
Length contraction is sometimes called Lorentz contraction or freese Gerard contraction. Before Einstein, Lorenz and freese Grad developed a mathematical formula to describe shrinkage. But Einstein realized its great significance and implanted it into the complete theory of relativity. This principle is:
The length of a moving object in a frame of reference is shorter than that of a stationary object.
In order to facilitate understanding, the following is illustrated by graphics:
The above picture shows that the ruler is at rest in the reference frame. The length of a stationary object in its frame of reference is called its "correct length". The correct length of the yardstick is one yard. The ruler in the picture below is moving. To put it more accurately, we find it (ruler) moving relative to a reference frame. The principle of length contraction points out that the ruler moving in this frame of reference is shorter.
This contraction is not an illusion. When the ruler passes by us, any accurate test shows that its length is shorter than when it is at rest. The ruler doesn't look short, it is! However, it contracts only in the direction of motion. In the figure below, the ruler moves horizontally, so its horizontal direction becomes shorter. You may have noticed that the vertical length in the two pictures is the same.
Time dilation:
The so-called time expansion effect is very similar to the length contraction, and it is like this:
When two events occur in different places, the time interval between them in a reference frame.
It is always longer than the time interval between the same two events in the same place.
This is even more difficult to understand, we still use legends to illustrate:
Both alarm clocks in the picture can be used to measure the time required for the first alarm clock to move from point A to point B, but the two alarm clocks give different results. We can think of it this way: the two events we mentioned are "the alarm clock leaves point A" and "the alarm clock arrives at point B". In our frame of reference, these two events took place in different places (A and B). However, let's observe this matter from the reference frame of the alarm clock itself in the upper part of the picture. From this point of view, the alarm clock in the upper part is stationary (all objects are stationary relative to themselves), while the lines engraved with points A and B move from right to left. So "leaving point A" and "arriving at point B" all happen in the same place! (The time measured by the upper part of the alarm clock is called "correct time") According to the above points, the time recorded by the lower part of the alarm clock will be longer than that recorded by the upper part of the alarm clock from A to B.
A simpler but less accurate statement of this principle is that a moving clock moves slower than a stationary clock. The most famous hypothesis about time dilation is usually called the twin paradox. Suppose there are twins, Harry and Mary. Mary boarded a spaceship that flew away from the earth quickly (in order to be effective, the spaceship must move at a speed close to the speed of light) and returned soon. We can think of two people's bodies as a clock and calculate the passage of time by age. Because Mary walks very fast, her clock in Bihali is slow. Therefore, when Mary returns to Earth, she will make Bihali young. How young she is depends on how fast and how far she walks.
Time dilation is not a crazy idea, it has been confirmed by experiments. The best example is a subatomic particle called a meson. How long it takes for mesons to decay has been measured very accurately. In any case, it is observed that mesons moving near the speed of light have a longer life than those moving at rest or slowly. This is the relativistic effect. From the point of view of the moving meson itself, it did not exist for longer. This is because from its own point of view, it is static; Only by looking at the meson from the laboratory point of view can we find that its life has been "extended" or "shortened". ?
What needs to be added is that many experiments have confirmed this inference of relativity. Other inferences (of relativity) can only be confirmed later. My point is that although we call the theory of relativity "theory", we should not mistake it for proof, and it is (actually) very complete.
Einstein's first hypothesis
All special relativity theories are mainly based on Einstein's two hypotheses about the nature of the universe.
The first one can be stated like this:
The laws of physics are the same in all inertial systems.
The only thing that is slightly difficult to understand here is the so-called "inertial frame of reference". A few examples can clearly illustrate this point:
Suppose you are on an airplane. The plane flies horizontally at a constant speed of several hundred miles per hour without any bumps. A man came up from the hut and said, "Would you please throw your bag of peanuts?" You grab the peanut bag and suddenly stop and think, "I'm sitting on a plane traveling at hundreds of miles an hour." How hard should I throw this bag of peanuts to that person? "
No, you don't have to think about it at all. You just need to throw it with the same action (and strength) as at the airport. The movement of peanuts is the same as that of a plane on the ground.
You see, if the plane flies in a straight line at a constant speed, the natural laws governing the movement of objects are the same as when the plane is at rest. We call the interior of the aircraft an inertial frame of reference. The word "inertia" originally refers to Newton's first law of motion. Inertia is the inherent property that every object stays still or moves in a straight line at a constant speed when there is no external force. Inertial frame of reference is a series of frames of reference for this law.
Another example. Let's look at the earth itself. The circumference of the earth is about 40000 kilometers. Because the earth rotates once every 24 hours, a point on the equator of the earth actually moves eastward at the speed of 1600 km per hour. However, I bet Steve young is telling Jerry Rice (both are football players). I never worry when I pass the ball to the ground. This is because the earth is moving in an approximately uniform straight line, and the surface of the earth is almost an inertial frame of reference. So its motion has little influence on other objects, and all objects behave like the earth is stationary.
In fact, unless we realize that the earth is turning, some phenomena will be very puzzling. (that is, the earth does not move in a straight line, but moves in a great circle around its axis)
For example, many aspects of weather (change) seem to completely violate the laws of physics unless we consider it (the earth is turning). Another example. Long-range shells do not move in a straight line as in inertial system, but slightly to the right (in the northern hemisphere) or to the left (in the southern hemisphere). Outdoor friends, this can't be used to explain your edge ball. For most research purposes, we can regard the earth as an inertial frame of reference. But occasionally, its non-inertial performance will be very serious (I want to be more accurate).
There is a minimum here: Einstein's first hypothesis keeps all the laws of physics in this kind of system unchanged. Examples of moving planes and the earth's surface are just to show you that this is a reasonable assumption that people can make without thinking on weekdays. Who said Einstein was a genius?
Einstein's second hypothesis
/kloc-In the middle of the 0/9th century, people's understanding of electricity and magnetism made a revolutionary leap, among which james maxwell's achievement was the representative. Before Oster and Ampere proved that electricity produces magnetism, electricity and magnetism were considered irrelevant. Faraday and Henry proved that magnetic energy can generate electricity. Now we know that the relationship between electricity and magnetism is so close that physicists often regard electricity and magnetism as one thing when enumerating natural forces.
Maxwell's achievement was to concentrate all the known electromagnetic knowledge at that time in four equations:
If you haven't taken calculus courses for three or four semesters necessary to understand these equations, sit down and watch for a few minutes and enjoy the beautiful scenery. )
Maxwell's equation is of great significance to us, because it not only describes all known electromagnetic knowledge, but also reveals something that people don't know. For example, the electromagnetic fields that make up these equations can propagate in space in the form of vibration waves. When Maxwell calculated the speed of these waves, he found that they were all equal to the speed of light. It is no coincidence that Maxwell (Equation) revealed that light is electromagnetic wave.
It is important to remember that the speed of light is directly derived from Maxwell's equation describing all electromagnetic fields.
Now let's go back to Einstein.
Einstein's first hypothesis is that all inertial frames of reference have the same physical laws. His second hypothesis is to simply extend this principle to the laws of electricity and magnetism. That is to say, if Maxwell's hypothesis is a natural law, then it (and its inference) must be established in all inertial systems. One of the inferences is Einstein's second hypothesis: in all inertial systems, light travels at the same speed.
Einstein's first hypothesis seems reasonable, and his second hypothesis continues the rationality of the first hypothesis. But why does it seem unreasonable?
Tests on the train
To illustrate the rationality of Einstein's second hypothesis, let's take a look at the picture on the train below. The train is traveling at the speed of100,000,000 m/s, Dave is standing on the train, and Nolan is standing on the ground beside the railway. Dave uses his flashlight to emit photons.
The speed of photon relative to Dave is 300,000,000 m/s, and Dave's speed relative to Nolan is100,000,000 m/s. So we come to the conclusion that the speed of photons relative to Nolan is 400,000,000 m/s.
The problem arises: this is inconsistent with Einstein's second hypothesis! Einstein said that the speed of light relative to Nolan frame of reference must be exactly the same as that in Dave frame of reference, that is, 300,000,000 meters per second. So is our "common sense feeling" wrong or Einstein's hypothesis wrong?
Well, many scientists' experiments (results) support Einstein's hypothesis, so we also assume that Einstein is right and help you find out the mistakes of common sense relativity.
Remember? The decision to add up the speeds is very simple. One second later, the photon has moved to 300,000,000 meters in front of Dave, and Dave moved to100,000,000 meters in front of Nolan. The distance between them is not 400 million meters. There are only two possibilities:
1 300,000,000 meters is not 300,000,000 meters relative to Dave for Nolan.
Dave's second is different from Nolan's.
It sounds strange, but in fact they are both right.
Einstein's second hypothesis
time and space
We have come to a contradictory conclusion. The "common sense relativity" that we use to convert speed from one frame of reference to another conflicts with Einstein's assumption that the speed of light is the same in all inertial frames. Einstein's hypothesis is correct only in two cases: either the distance between the two inertial systems is different or the time between the two inertial systems is different.
Actually, they are both right. The first effect is called "length contraction" and the second effect is called "time expansion".
Length contraction:
Length contraction is sometimes called Lorentz contraction or freese Gerard contraction. Before Einstein, Lorenz and freese Grad developed a mathematical formula to describe shrinkage. But Einstein realized its great significance and implanted it into the complete theory of relativity. The principle is that the length of a moving object in a reference frame is shorter than that of a stationary object. In order to facilitate understanding, the following is illustrated by graphics:
The above picture shows that the ruler is at rest in the reference frame. The length of a stationary object in its frame of reference is called its "correct length". The correct length of the yardstick is one yard. The ruler in the picture below is moving. To put it more accurately, we find it (ruler) moving relative to a reference frame. The principle of length contraction points out that the ruler moving in this frame of reference is shorter.
This contraction is not an illusion. When the ruler passes by us, any accurate test shows that its length is shorter than when it is at rest. The ruler doesn't look short, it is! However, it contracts only in the direction of motion. In the figure below, the ruler moves horizontally, so its horizontal direction becomes shorter. You may have noticed that the vertical length in the two pictures is the same.
Time dilation:
The so-called time expansion effect is very similar to the length contraction, and it is like this:
When two events occur in different places, the time interval between them in a reference frame.
It is always longer than the time interval between the same two events in the same place.
This is even more difficult to understand, we still use legends to illustrate:
Both alarm clocks in the picture can be used to measure the time required for the first alarm clock to move from point A to point B, but the two alarm clocks give different results. We can think of it this way: the two events we mentioned are "the alarm clock leaves point A" and "the alarm clock arrives at point B". In our frame of reference, these two events took place in different places (A and B). However, let's observe this matter from the reference frame of the alarm clock itself in the upper part of the picture. From this point of view, the alarm clock in the upper part is stationary (all objects are stationary relative to themselves), while the lines engraved with points A and B move from right to left. So "leaving point A" and "arriving at point B" all happen in the same place! (The time measured by the upper part of the alarm clock is called "correct time") According to the above points, the time recorded by the lower part of the alarm clock will be longer than that recorded by the upper part of the alarm clock from A to B.
A simpler but less accurate statement of this principle is that a moving clock moves slower than a stationary clock. The most famous hypothesis about time dilation is usually called the twin paradox. Suppose there are twins, Harry and Mary. Mary boarded a spaceship that flew away from the earth quickly (in order to be effective, the spaceship must move at a speed close to the speed of light) and returned soon. We can think of two people's bodies as a clock and calculate the passage of time by age. Because Mary walks very fast, her clock in Bihali is slow. Therefore, when Mary returns to Earth, she will make Bihali young. How young she is depends on how fast and how far she walks.
Time dilation is not a crazy idea, it has been confirmed by experiments. The best example is a subatomic particle called a meson. How long it takes for mesons to decay has been measured very accurately. In any case, it is observed that mesons moving near the speed of light have a longer life than those moving at rest or slowly. This is the relativistic effect. From the point of view of the moving meson itself, it did not exist for longer. This is because from its own point of view, it is static; Only by looking at the meson from the laboratory point of view can we find that its life has been "extended" or "shortened". ?
What needs to be added is that many experiments have confirmed this inference of relativity. Other inferences (of relativity) can only be confirmed later. My point is that although we call the theory of relativity "theory", we should not mistake it for proof, and it is (actually) very complete.
Gamma parameter (γ)
Now you may wonder: Why have you never noticed the effects of length contraction and time expansion in your daily life? For example, according to what I just said, if you drive from Oklahoma City to Kansas City and back, you should reset your watch when you go home. Because when you drive, your watch should go slower than the stationary watch at home. If it is 3 o'clock sharp when you go home, your watch at home should show a later time. Why haven't you found such a situation?
The answer is: whether this effect is significant or not depends on the speed of your exercise. And you move very slowly (you may think your car is driving very fast, but this is extremely slow for relativity). The effects of length contraction and time expansion can only be noticed when you are close to the speed of light. The speed of light is about 186300 miles per second (or 300 million meters per second). In mathematics, the relativistic effect is usually described by a coefficient, and physicists usually use the Greek letter γ. This coefficient depends on the speed at which the object moves. For example, a meter scale (the correct length is 1 m) flies quickly in front of us, and its length relative to our frame of reference is 1/γ m. If it takes three seconds for a clock to move from point A to point B, what about our obstacle load? Hey? On the altar? /γ seconds.
To understand why we don't notice the relativistic effect in reality, let's look at the formula of γ: the key here is v2/c2 in the denominator. V is the speed of motion of an object and c is the speed of light. Because the speed of any object of normal size is much less than the speed of light, v/c is very small; When we square it, it is smaller. So for all objects of normal size in real life, the value of γ is 1. So for ordinary speed, the length and time we get after multiplication and division have not changed. To illustrate this point, here is a table of gamma values corresponding to different speeds. The last column is the length of the meter ruler when it moves at this speed (that is, 1/γ meters).
C in the first column still stands for the speed of light. .9c equals nine tenths of the speed of light. For reference, for example, the speed of Saturn V rocket is about 25,000 miles per hour. You see, for any reasonable speed, γ is almost 1. So the length and time have hardly changed. In life, the relativistic effect only appears in science fiction (in which the spacecraft is much faster than Saturn V) and microphysics (electrons and protons are often accelerated to a speed very close to the speed of light). On the way from Chicago to Denver, this effect will not appear.
The adventures of the law enforcers of the universe
AD, the law enforcer of the universe, was captured by the evil Dr. En on Planet A. Dr. En gave AD a glass of 13 hours later, and told AD that the antidote was on Planet B, 400,000,000 kilometers away. After learning this situation, AD immediately flew to Star B on its starship at 0.95 times the speed of light, so:
Can AD even reach Star B and get the antidote?
We make the following calculations:
The distance between the two planets A and B is 40 billion kilometers. The speed of the spacecraft is 1, 025,000,000 km/h. Divide these two numbers, and we get that it takes 39 hours to get from planet A to planet B.
Then AD died.
Wait a minute! This is only for people standing on planet A, because poison is metabolized in AD, so we must study this problem from the frame of reference of AD. We can do it in two ways, and they will come to the same conclusion.
1. Imagine a big ruler extending evenly from planet A to planet B. This ruler is 40 billion kilometers long. However, from AD's point of view, the ruler flew past him at a speed close to the speed of light. We already know that such an object will shrink in length. In the frame of reference of AD, the distance from planet A to planet B is contracted by the parameter γ. At 95% of the speed of light, the value of γ is about 3.2. So AD thinks that the distance is only12,500,000,000 kilometers (40 billion divided by 3.2). We divide this distance by the speed of AD to get 12.2 hours, and AD will arrive at Planet B nearly 1 hour earlier!
2. Observers on planet A will find that it takes about 39 hours for AD to reach B. However, this is the post-inflation era. We know that the "clock" of AD slows down with the parameter γ(3.2). To calculate the time in the AD frame of reference, we divide 39 hours by 3.2 to get 12.2 hours. There are about 1 hour left for AD (which is good, because AD is given 20 minutes to leave the ship and another 20 minutes to find the antidote).
AD will survive and continue to fight evil.
If you study my above description carefully, you will find many specious and very subtle things. When you think deeply, you usually end up asking such a question: "Wait a minute, in AD's frame of reference, en's clock runs slower, so in AD's frame of reference, space travel should take longer, not shorter." ...
If you are interested in or confused about this issue, you should probably read the following article, Cosmic Law Enforcement Adventure-A Subtle Time. Or you can believe what I said, "If you know all the causes and effects, then all of them are correct" and skip to the chapter on quality and energy.
Adventure of cosmic law enforcement-subtle time
Well, that's what we just saw. We found the time dilation relative to the frame of reference. In the EN frame of reference, AD is moving, so the clock of AD moves very slowly. As a result, in this flight, EN's clock ran for 39 hours, while AD's clock ran for 12 hours. This often leads people to have such problems:
Compared with the AD system, EN is in motion, so the clock of EN goes slower. So when AD reaches Planet B, his clock runs longer than en. Who is right? Long or short?
Good question. When you ask this question, I know you have started to enter the situation. Before I begin to explain, I must declare that everything described in the last article is correct. In the situation I described, AD can get the antidote in time. Now let's explain this paradox. This has something to do with the "simultaneity" I haven't mentioned yet. A corollary of the theory of relativity is that two events that occur at the same time (but in different places) in the same frame of reference are not simultaneous with respect to another frame of reference.
Let's study some simultaneous events.
First, let's assume that when AD leaves planet A, EN and AD press the stopwatch at the same time ... According to EN's table, this trip to planet B will take 39 hours. In other words, when it reached Planet B in A.D., En's watch showed 39 hours ... At the same time, because of the time expansion, AD's electric meter reading was 12.2 hours. In other words, the following three things happen at the same time:
The meter reading of 1 and EN is 39.
2. Arrive at Planet B in A.D..
3. The meter reading number of 3.AD is 12.2.
These events happened at the same time in the European standard frame of reference.
Now in the frame of reference of AD, it is impossible for the above three events to happen at the same time. Furthermore, because we know that the meter of en must be slowed down by the parameter γ (here γ is about 3.2), we can calculate that when the meter reading of AD is 12.2 hours, the meter reading of EN is 12.2/3.2 = 3.8 hours. So in the advertising department, these things happen at the same time:
1, AD reaches planet B.
2. The clock reading of 2.AD is 1.2.
The clock reading of en is 3.2.
The first two terms are the same in the two systems because they occur in the same place-planet B. Two events in the same place happen at the same time or not. The frame of reference doesn't work here.
It may be helpful for you to look at this problem from another angle. The event you are interested in is from AD leaving Planet A to AD arriving at Planet B ... Important: AD exists in both events. That is to say, in the frame of reference of AD, these two events took place in the same place. Therefore, the events in the AD frame of reference are called "correct time", and the time in all other systems will be longer than that in this system (see the principle of time expansion). Anyway, if you are confused about the time dilation in advertising adventure, I hope this will clarify it. If you are not confused, I hope you are not confused now.
Slaven
In addition to length contraction and time expansion, relativity has many inferences. One of the most famous and important is about energy.
Energy has many states. Any moving object has what physicists call "kinetic energy" because of its own motion. The magnitude of kinetic energy is related to the speed and mass of an object. ("mass" and "weight" are similar, but not exactly the same) Everything placed on the shelf has "gravitational potential energy". Because if the shelf is removed, it is possible to gain kinetic energy (due to gravity).
Heat is also a form of energy, which can ultimately be attributed to the kinetic energy of atoms and molecules that make up matter, and there are many other forms of energy.
The above phenomena are all related to energy, that is, the relationship between them, which is the law of conservation of energy. This law means that if we add up all the energy in the universe (we can quantitatively describe energy in joules or kilowatt hours), its total amount will never change. That is to say, although energy can be transformed from one form to another, it will never be produced or destroyed. For example, an automobile is a device that can convert thermal energy (in the cylinder of an engine) into kinetic energy (in the movement of an automobile); Light bulbs can convert electric energy into light energy (light energy is another form of energy).
Einstein discovered another form of energy in his theory of relativity, sometimes called "static energy". I have pointed out that a moving object has energy because of its motion. But Einstein found that the same object has energy when it is at rest. The static energy of an object depends on its mass and is given by the formula e = mc2.