In the space-time view of Galileo and Newton , time is absolute, time and space have nothing to do with it, they are independent of each other. However, the Galilean principle of relativity, that is, the physics laws in inertial reference system are the same, and are still valid to this day, which deduces the conservation of energy of and the conservation of momentum. Furthermore, space is not only uniform, but also the same in all directions, which derives another conservation law, namely the conservation of angular momentum. What is the theory of relativity? It is a theory about time and space, and was mainly founded by Einstein . Relativity theory believes that time is no longer independent of space, and time and space are a whole.
In terms of daily experience, time has nothing to do with space. The environment around us is space, it is always there, without moving, but we use movement to calculate time. For example, we regard the period from rising to setting as a day. In this way, time and space really have nothing to do with it.
This daily experience was applied to his mechanics system by Newton. For Newton, there is an absolute space and an absolute time. Of course, the existence of this absolute space has not been proved by experiments. What does that mean? If you are staying in a still room, then the room you are in is a space; if you are taking the high-speed rail, the carriage you are in is also a space. However, the space of the high-speed rail car is of course different from the space in the room, because they are doing and . Then, what Newton said about absolute space cannot be understood. But Newton believed it existed. Let’s talk about this topic when we talk about general relativity .
's concept of absolute time and relative space was inherited by Newton from Galileo.
Galileo pointed out that all inertial systems have exactly the same mechanical laws. For example, if an athlete keeps running at a constant speed, then, whether for a stationary ground reference system or a train reference system that moves at a constant speed, the athlete is doing a constant speed linear motion (that is, the mechanical laws are the same). This is the "Galilean principle of relativity".
What does the principle of relativity in Galileo mean? Let us give an example. If you are enclosed in the cabin, you are trying to test whether the ship is driving on the water. If the ship is driving at a constant speed on the water, then no matter what experiment you do, you cannot determine whether the ship is driving, and you cannot determine how fast the ship is. This is because the experiment you do is just to see if the mechanical laws have changed. If the mechanical laws of a cabin with a constant speed are exactly the same as the mechanical laws of a static cabin, then you cannot determine whether the ship is traveling. Unless you are standing on the deck at this time and see the water retreating, you can confirm that the ship is moving at this time.
Usually we sit in the car. Unless the car accelerates or slows down, you can't feel whether the car is moving when you close your eyes. This is the principle of Galileo's relativity.
's such a simple principle of relativity requires a big man like Galileo to summarize it. Why is this?
Because, in ancient times, people did not think that the principle of relativity was correct. For example, Aristotle believes that a moving object needs force to maintain its speed. Obviously, according to Aristotle, we were sitting in the moving car, and the car and we were both driven by a force, although we were still relative to the car. But on the ground, we don't need force when we are still. Therefore, the mechanical laws in the two systems are different. What does
inertial system mean? Galileo believes that if the earth is an inertial system, then all systems that move at a constant speed relative to the earth are inertial systems. In these systems, any object that is stationary and uniformly moving has inertia, that is, no force is needed to act on them. This is Galileo's law of inertia , and it is also the first Newtonian law in , the Newtonian mechanics system.
However, we need to emphasize that the law of inertia and Galileo's principle of relativity are not the entire connotation of Newton's principles of time and space. In fact, the Galilean principle of relativity is also valid in Einstein's theory of relativity.
So, in addition to the principle of relativity, what principles does time and space in Newton's mechanical system follow?
Simply put, time is absolute. At the same time, Galileo and Newton both believed that speed could be simply superimposed. What does this mean? For example, the train is moving at a speed of 100 meters per second relative to the ground reference system. If a person walks forward at a speed of 4 meters/s on this train, then from the ground, the person's speed is 104 meters/sec. If the person walks in the opposite direction at a speed of 4 meters/second, then from the ground, the person's speed is 96 meters/second. This
is a simple speed superposition.
Because the speed can be superimposed, if the speed of the clock on the train is exactly the same as the clock on the ground, then a simple inference can be derived: the length of a ruler on the train is the same as the length of a ruler on the ground. Of course, for convenience, we will create an coordinate system on the ground and on the train. Then, the distance change between the ground reference system and the train reference system is equal to the speed of 100 meters/second times their movement time. This means that the difference in positions between two inertial systems that move to each other is equal to their relative velocity multiplied by their time of motion, and their time of motion is completely synchronized. This is the famous "Galileo Transformation".
The premise of Galileo's transformation of is that time is absolute, and it is the same whether it is time on the ground or time on the train. This is the first prerequisite for Galileo transformation.
According to the principle of speed superposition, space is also simply transformed, and it is nothing more than one speed multiplied by time. Therefore, it is easy for us to accept the Galilean transformation because these are all felt in daily experience.
Some people may argue that I can measure whether I am walking at a constant speed. For example, I hold an balloon in my hand. When I don’t move, the balloon hangs down. When I walk, the balloon is dragged behind me. Doesn’t this mean I’m walking?
Yes, your reason is very good, but you forgot that there is still air. This effect is achieved because the air is still relative to the ground. If you walk in a vacuum, this effect will not be achieved.
In fact, Aristotle was also confused by something similar. Indeed, because there is friction on the ground, we need force when pushing an object on the ground. Without ground friction, objects moving at a constant speed on the ground do not need any force to push it.
Although the Galilean transformation was later replaced by the theory of relativity, the principle of relativity is not simple, it has profound physical inferences. Outside absolute time, Galileo and Newton also assume that time passes evenly. That is to say, if we know the laws of today and the laws of physics 100 years ago, we will find that they are exactly the same; similarly, if we know the laws of today and the laws of physics 100 million years ago, we will find that they are exactly the same.
Time passes evenly, a simple assumption that was later used by physicists to deduce conservation of energy. Yes, you heard it right, the invariance of the laws of physics in time is closely related to the conservation of energy.
So, in addition to using mathematical deduction of the relationship between symmetry and conservation law, is there any more intuitive physical explanation to explain the relationship between conservation of energy and invariance of time translation? I have thought about this before and got a possible explanation, but it did not satisfy me. In quantum theory , energy is related to the frequency of an object, which is De Broglie's discovery, which we have talked about in Lesson 14. Time translation invariance means that the frequency does not change, that is, the energy does not change. In Einstein's Special Relativity , energy conservation remains true because of the invariance of time translation.Through quantum theory, we can prove that mass actually corresponds to a frequency, and mass is also energy. This is the deduction of Einstein's mass-energy relationship by quantum theory.
The energy of an isolated physical system with a static center of mass is completely equivalent to its static mass. The famous Einstein mass-energy relationship is that energy is equal to mass multiplied by the square of the speed of light. Therefore, conservation of energy can be said to be conservation of mass. This statement is closest to the intuitive concept of matter immortality.
Similarly, the Galilean principle of relativity also assumes that the space is uniform. It means that the conclusions of physics experiments done in Beijing and physics experiments done in New York are the same, and the laws of physics will not change due to changes in spatial location. The uniformity of space also derives a inference that momentum is conserved.
Let’s briefly review the history of energy conservation. In the 18th century, people discovered that kinetic energy could be converted into heat energy. In the 19th century, German doctor Meier discovered the relationship between kinetic energy and thermal energy, and Joule of his contemporary found that potential energy can also be converted into thermal energy. British physicist Grove and German physicist Helmholtz discovered the law of conservation of energy in the modern sense , that is, kinetic energy, potential energy, thermal energy and electromagnetic energy can be converted to each other but the total amount remains unchanged.
Nowadays, we extend the Newtonian mechanics system to include all physical phenomena. Although Newton's view of space-time has been replaced by the theory of relativity, the Galilean principle of relativity continues to hold. This means that time is uniform and space is uniform, so conservation of energy and momentum are suitable for all physical phenomena.
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