Chapter 307 Two basic principles of general relativity! (Add an update from the leader!)
The word inertia is something we often encounter in our daily life.
For example, if a train is coming at a fast speed, even if it starts to brake, it cannot stop immediately.
Because we know that trains have inertia.
And in ordinary people's perception, the greater the mass of an object, the greater its inertia.
However, few people have really thought about what is the nature of inertia? Why is mass a measure of inertia?
This is because the education we receive does not start from scratch, but presupposes a lot of content.
Strictly speaking, physics should begin with Galileo.
The group of people in ancient Greece paid more attention to ideological debates rather than specific experiments.
For example, about sports.
Ancient Greek philosophers studied the nature of motion and discussed why objects move.
But we don’t study how objects move.
To put it bluntly, they don’t study the process and directly discuss the results.
Galileo was different.
He was the first to combine rational thinking and experimentation.
He used experiments to study the movement of objects and discover patterns.
The law of inertia is one of his most important discoveries.
Galileo believed that the resting state of an object and the state of uniform motion in a straight line are completely equivalent.
And he gave this state a name: inertial system.
What does it mean?
For example, if a person is on a high-speed train and the windows are closed, assuming that the track is very smooth, there will be no bumps in the high-speed train.
In fact, people cannot feel that they are moving.
Without other frames of reference, it is impossible to distinguish between uniform linear motion and rest.
The so-called inertia is the ability of an object to maintain this state.
And based on the concept of inertial system, Galileo discovered another important law.
That is the principle of relativity.
What it means is that in any inertial system, the laws of mechanics always remain unchanged.
What does it mean?
You do free fall experiments on the high-speed train, and you do free fall experiments when the ground is stationary.
In both cases, the movement of the objects seen is exactly the same.
The balls fall straight down, and the measured accelerations are exactly the same.
This is the principle of relativity.
It is very consistent with human intuitive experience and is easy to express using mathematical formulas.
So it is the same as the inertia theorem, both axioms and postulates.
It means you can try to falsify it, but there is no way to prove it.
Newton completely inherited Galileo's two laws of mechanics.
On this basis, Newton's three laws of mechanics were proposed.
So, Newton was right when he said that he stood on the shoulders of giants, and Galileo was that giant.
Newton inherited rather than copied mechanically.
First of all, he gave a strict definition to the law of inertia.
That is, if a particle or object is not subject to external force, it will remain stationary or move in a straight line at a uniform speed.
This is Newton's first law.
Newton is Newton, different from ordinary people.
He did not satisfy the existing laws, but thought further.
What will happen if a force is suddenly applied to an object while it is in inertial motion?
This is Newton's second law.
That is, force will change the motion state of the object and generate an acceleration.
The mathematical formula is F=ma.
Whether it is later generations or now, as long as someone is new to physics, it is probably the first physical formula they learn.
It seems very simple, even elementary school students can do calculations.
But it would be useless.
Actually, you have not thought about the profound truth behind the formula.
When Newton was studying the second law, he was thinking about a problem.
Why do the accelerations produced by the same force exerted on different objects be different?
You are smart and answer immediately: Because the mass m is different.
Congratulations, you got the answer wrong!
Because Newton had not yet derived this formula at that time.
Newton thought it was due to inertia.
The inertia of an object always tends to maintain its original state of motion.
That is, the inertia of an object is an ability and inherent property to resist external forces.
The greater the inertia, the stronger the resistance; conversely, the smaller the inertia, the weaker the resistance.
The size of inertia can be expressed by [inertial mass].
That is, m in F=ma derived by Newton.
Attention!
Here comes the point.
This inertial mass m is not the mass we often talk about.
What does it mean?
The goddess has a very good figure, 170cm tall and weighs only 50kg.
I am now pushing the goddess from behind, which will generate an acceleration for the goddess.
When we substitute the formula F=ma, m uses the weight of the goddess, which is also 50kg.
but!
These are two completely different qualities, they just happen to be equal in value.
The weight of the goddess is gravitational mass, not inertial mass.
Inertial mass is the ability of an object to resist external forces, while gravitational mass is the cause of the gravitational force between objects.
Their physical meanings are completely different.
The two must not be confused.
As for why the two values are equal, it is still an unsolved mystery.
The relationship between inertial mass and gravitational mass is the core of the general theory of relativity.
(Okay, you can use it to show off.)
After Newton discovered and perfected the second law, he was able to explain a problem naturally.
That is why after an object is thrown upward, it falls to the ground again.
Obviously, the object is acted upon by a force.
Otherwise, the object should always move upward.
Therefore, he believed that the earth exerted a force on the object.
And according to Newton's third law, the forces between objects interact.
Therefore, Newton named this force "gravitation".
It is the force of gravity that causes an object to accelerate, thereby changing its state of motion.
And Newton also directly gave the calculation formula of universal gravitation, that is, the law of universal gravitation.
Okay, now comes the problem.
Newton created such a brilliant building of physics. When he looked back, he found that there was still a problem.
That is, the first theorem and the second law, which are the foundation of his mechanical theory, have a restriction.
That is, they must be established in an inertial frame.
So how to define the inertial system?
If you are smart, you will definitely say: Without external force, the reference frame of rest or uniform linear motion is the inertial frame.
Then I ask: How can we be free from external forces?
If you are smart, you will answer: An object is at rest or moving in a straight line at a constant speed, so there is no force on it.
I asked again: How can an object be considered stationary or maintain uniform linear motion?
The clever Qian answered again: As long as the object is not subject to force.
You see, this is a circular argument.
The inertial frame itself cannot be defined at all.
And we can't find examples of inertial systems in reality.
Because the earth is rotating (rotation is an accelerated motion and does not meet the definition of an inertial system) and the sun is rotating, there is no inertial system in the world at all. Newton took a look and realized that this was definitely not possible.
My foundation must be impeccable.
So, Newton’s genius brain suddenly had a sudden idea and defined an absolute space!
He believes that absolute space has its own characteristics that have nothing to do with anything, is uniform everywhere, and never moves.
Newton is really awesome.
He believes that absolute space is the largest and best inertial reference system.
This is very consistent with people's intuition.
Space is everywhere, and space cannot move.
This is the definition of inertial system.
This problem is solved.
Any reference system that is stationary or moving in a straight line at a uniform speed relative to absolute space is an inertial reference system.
Any reference system that moves at variable speeds relative to absolute space is a non-inertial reference system.
This definition gives Newton's laws of mechanics a solid foundation.
In the inertial frame, his theory is established.
So in non-inertial systems, Newton also has a clever trick, and he can't hang it.
He introduced [inertia force] to make up for the flaws of the theory.
In this way, your own theory can also be established and used in non-inertial systems.
Let’s take the example of high-speed rail.
Suppose a person places a small ball on the bracket of a high-speed rail seat.
If the high-speed train suddenly speeds up and accelerates, the acceleration is x.
Then the person will immediately see that the ball is also accelerating backward, and the acceleration is also x.
But according to Newton's theory, the ball does not experience any force in the front and rear directions. Why does it change its state of motion?
Newton's laws encounter difficulties in non-inertial frames.
But this did not trouble Newton. He hypothesized the inertial force.
The ball moves because of the inertial force.
The size is related to the acceleration of the train and the mass of the ball itself.
That’s why it’s called inertial force, the force generated by inertia.
Although the inertial force is a false force, its effect on the object is real.
At this point, Newton's mechanical system is perfect and can explain all mechanical phenomena in the world.
Until Li Qiwei and Einstein came out and published the special theory of relativity.
Proved that absolute space does not exist!
(Please read the previous content for details, and write it again to avoid you calling me hydrological.)
Newton’s definition of absolute space is wrong.
Time and space are inherently one and relative.
Every independently moving object has its own unique time and space.
But after the special theory of relativity denied absolute space, it also encountered the same problem as Newton.
Without absolute space, how to define the inertial system?
You must know that the first axiom of special relativity is: all physical laws are equivalent in all inertial reference systems.
Now that Ridgway denies the existence of absolute space, he cannot explain the problem of inertial systems.
The special theory of relativity can only be established in an inertial system like Newton's laws of mechanics.
In reality, there is no inertial system.
Any object on the earth will be affected by gravity, resulting in an acceleration and variable speed motion.
The inertial frame does not exist!
A theory derived based on something that does not exist will of course be questioned.
This is the first core flaw of special relativity.
In addition, according to the special theory of relativity, any information cannot be transmitted faster than the speed of light.
But if we study the formula of universal gravitation carefully, we will find that it does not limit the speed of gravity propagation.
F=GMm/R. There is no time parameter involved.
Moreover, Newton himself believed that the force of gravity is transmitted instantaneously, which is much greater than the speed of light.
This is obviously inconsistent with the special theory of relativity.
Therefore, the law of gravity needs to be reformed.
This is the second core flaw of special relativity.
How to solve it?
In real history, Einstein started thinking from the inertial force.
First he asked himself, is gravity an instantaneous force?
He thinks this is impossible because it does not conform to the special theory of relativity.
Einstein was very fond of Maxwell's equations.
He believes that the transmission of gravity also requires a medium.
He called this medium a "gravitational field," just like an electric field.
Since there is a gravitational field, the gravitational force exerted by an object is equal to the mass multiplied by the strength of the gravitational field.
Comparing it with F=ma, you will naturally get that the ratio of inertial mass and gravitational mass is a constant.
Later, some physicists proved through experiments that this constant is 1.
Then it means that inertial mass and gravitational mass are equal. (The quality we usually talk about is the quality of guidance.)
This is incredible.
All physicists at the time did not know the essential principle behind this equality.
They can't prove it theoretically.
Einstein didn’t understand either.
But it doesn’t matter if you don’t understand. Einstein once again used his super keen physical intuition.
He made the bold assumption that inertial mass and gravitational mass are equivalent.
That is the first principle of general relativity: the equivalence principle. (It is an axiom)
[The dynamic effects of the inertial force field and the gravitational field are locally indistinguishable. 】
What does it mean?
Give me an example.
A man stands on the ground of a spaceship.
If at this time the spacecraft accelerates upward with acceleration g (the earth’s gravity acceleration).
Then the person will receive an inertial force in the opposite direction at the same time.
The force of inertia pressed him firmly to the ground.
The size of the inertial force is equal to the person's inertial mass multiplied by the acceleration g.
Because the inertial mass of a person and the gravitational mass of a person are equal.
At this time, the acceleration experienced by the person is g again, which is the same as the earth's gravitational acceleration.
Then the person will feel as if he is still on the earth.
In other words, the spaceship replaces the earth.
The inertial force field generated by the accelerated motion of the spacecraft replaces the earth's gravitational field.
This person couldn't tell whether he was on the earth or in a spacecraft moving at g acceleration.
Both are completely equivalent.
Acceleration is gravity, and inertial force and gravity are equivalent.
This is the connotation of the equivalence principle.
After having the equivalence principle, it was very simple for Einstein to deal with the first problem of the narrow phase, the inertial system problem.
Therefore, any non-inertial frame with acceleration can be regarded as an inertial frame in a gravitational field.
It’s easy to understand.
Because acceleration and gravitational field are equivalent.
Therefore, there is no so-called non-inertial system.
Any non-inertial system can be regarded as the inertial system is unchanged and the gravitational field is changing.
In this case, when dealing with any problem in non-inertial systems, you can only study gravity.
At this time, Einstein can logically extend the principle of special relativity to all reference systems.
That is the second principle of general relativity: the general principle of relativity. (Also an axiom)
[All laws of physics remain unchanged in any reference system. 】
The laws of physics are no longer constant only in the inertial frame.
At this point, the construction of the two major principles of general relativity is completed.
Note that these two axioms are not proposed randomly.
It was Einstein’s bold assumption after he conducted an in-depth analysis of the laws of physics.
In hindsight we think it was simple, but that was over a hundred years ago.
Next, it was Einstein and Li Qiwei who used these two principles to pry open the door of general relativity.
Maybe you are smart and ask: Should we start doing experimental verification?
No!
Doing experiments is too low. If you want to do it, do thought experiments.
(End of this chapter)