1900: A physics genius wandering around Europe

Chapter 307 Two Basic Principles of General Relativity! (Additional chapter by the leader!)

We often encounter the word inertia in our daily lives.

For example, a train is speeding along and even if it has started to brake, it cannot stop immediately.

Because we know that the train has inertia.

And in the common people's cognition, the greater the mass of an object, the greater its inertia.

However, few people have really thought about what the nature of inertia is and why mass can measure the magnitude of inertia?

This is because the education we received did not start from scratch, but rather pre-set a lot of content.

Strictly speaking, physics should have started with Galileo.

The people in ancient Greece paid more attention to ideological debates rather than specific experiments.

For example, about sports.

Ancient Greek philosophers began by studying the nature of motion and discussing why objects move.

But they don't study how objects actually move.

To put it bluntly, they don't study the process and go straight to discussing the results.

But Galileo was different.

He was the first to combine rational thinking and experimentation.

He studied the movement of objects through experiments and discovered the laws of motion.

Among them, the law of inertia is one of his most important discoveries.

Galileo believed that the state of an object at rest and the state of uniform motion in a straight line are completely equivalent.

And he gave this state a name: inertial system.

What does that mean?

For example, if a person is on a high-speed train and all the windows are closed, and the track is very smooth, there will be no bumps on the high-speed train.

In fact, people cannot feel that they are exercising.

Without some other frame 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.

It means that in any inertial system, the laws of mechanics always remain unchanged.

What does that mean?

You do a free fall experiment on a high-speed train and you do a free fall experiment when you are stationary on the ground.

In both cases, the objects seen moving are exactly the same.

The balls all 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 can be easily expressed in mathematical formulas.

Therefore, like the law of inertia, it is an axiom and postulate.

It means you can try to disprove it, but there is no way to prove it.

Newton completely inherited Galileo's two major laws of mechanics.

On this basis, the three laws of Newtonian mechanics were proposed.

So, Newton was right when he said he stood on the shoulders of giants, and Galileo was that giant.

Newton inherited rather than copied blindly.

First, he gave a rigorous definition of the law of inertia.

That is, a particle or object will remain stationary or move in a straight line at a constant speed if there is no external force acting on it.

This is Newton's first law.

Newton is Newton, different from ordinary people.

He did not satisfy the existing laws, but thought one step further.

What will happen if a force is suddenly applied to an object during its inertial motion?

This is Newton's second law.

That is, force will change the state of motion of an object and produce an acceleration.

Expressed in mathematical formula, it is F=ma.

Whether in later generations or now, this is probably the first physical formula that anyone who has just come into contact with physics learns.

It looks very simple, even an elementary school student can do the calculation.

But it will be useless.

In fact, 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 does the same force applied to different objects produce different accelerations?

You are smart and answer immediately: Because the mass m is different.

Congratulations, you got the wrong answer!
Because Newton had not yet derived this formula at that time.

Newton believed that inertia was the cause.

The inertia of an object always causes it to tend 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 ability to resist; conversely, the smaller the inertia, the weaker the ability to resist.

The magnitude of inertia can be expressed by [inertial mass].

That is the m in F=ma derived by Newton.

note!

Here comes the point.

This inertial mass m is not the mass we usually talk about.

What does that mean?

The goddess has a very good figure, she is 170cm tall and weighs only 50kg.

I am now pushing the goddess from behind, which will create an acceleration for her.

When we substitute the formula F=ma, m is the weight of the goddess, which is also 50kg.

but!

These are two completely different masses that 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 reason for the gravitational force between objects.

Their physical meanings are completely different.

The two must never be confused.

As to why the two values ​​are equal, it remains an unsolved mystery.

The relationship between inertial mass and gravitational mass is the core of general relativity.

(Okay, now you can show off.)
After Newton discovered and perfected the second law, he was able to naturally explain a problem.

That is why objects fall back to the ground after being thrown upwards.

Obviously, the object is acted upon by a force.

Otherwise, the object should always be moving upwards.

Therefore, he believed that it was the Earth that exerted a force on objects.

And according to Newton's third law, the forces between objects are mutual.

Therefore, Newton named this force "gravity".

It is the force of gravity that causes an object to produce an acceleration, thereby changing its state of motion.

Newton also directly gave the calculation formula for universal gravitation, namely the law of universal gravitation.

Okay, now comes the problem.

Newton created such a brilliant edifice of physics, but 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 theory of mechanics, have a restriction.

That is, they must exist in an inertial system.

So how do we define the inertial system?

Being smart, you will definitely say: In the absence of external forces, the reference system at rest or in uniform linear motion is the inertial system.

Then I ask: What does it mean to be free from external forces?

Smart answer: When an object is stationary or moving at a constant speed in a straight line, there is no force acting on it.

I asked again: What does it mean when an object is stationary or moving at a uniform speed in a straight line?

The clever one answered: If the object is not subject to force,
You see, this is a circular reasoning problem.

There is no way to define an inertial system itself.

And we can't find any examples of inertial frames in reality.

Because the earth is rotating (rotation is accelerated motion, which does not conform to the definition of an inertial system), and the sun is rotating, there is no inertial system in the world. Newton saw that this was definitely not possible.

My foundation must be impeccable.

So, Newton's genius brain suddenly came up with an idea and defined an absolute space!
He believed that absolute space, its own characteristics have nothing to do with anything, is uniform everywhere and never moves.

Newton is indeed awesome.

He believed that absolute space was the largest and best inertial reference system.

This makes perfect sense.

Space is everywhere, and it is impossible for space to move.

This is the definition of an inertial frame.

Now the problem is solved.

Any reference frame that is at rest or moving at a uniform speed in a straight line relative to absolute space is an inertial reference frame.

Any reference frame that moves at variable speed relative to absolute space is a non-inertial reference frame.

This definition puts Newton's laws of mechanics on a solid foundation.

In an inertial system, his theory is valid.

So what about in non-inertial systems? Newton also has a trick up his sleeve, which is really cool.

He introduced the [force of inertia] to make up for the shortcomings of the theory.

In this way, one's 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 train 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 backwards, with an acceleration also of x.

But according to Newton's theory, the ball is not affected by any force in the forward or backward directions, so why does its state of motion change?

Newton's laws encountered difficulties in non-inertial frames.

But this did not pose a problem for Newton, as he invented the concept of inertia.

The ball moves because it is affected by inertia.

Its 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 inertia is a fictitious force, its effect on objects is real.

At this point, Newton's mechanical system is perfect and can explain all mechanical phenomena in the world.

Until Ridgway and Einstein came out and published the theory of special relativity.

Proved that absolute space does not exist!
(Please refer to the previous content for details. I will write it again in case you say I am writing nonsense.)
Newton's definition of absolute space was wrong.

Time and space are originally one and relative.

Every independently moving object has its own unique space and time.

However, after the special theory of relativity denied absolute space, it also encountered the same problem as Newton.

Without absolute space, how should the inertial system be defined?
You know, the first axiom of the special theory of relativity is that all physical laws are equivalent in all inertial reference frames.

Now that Li Qiwei has denied the existence of absolute space, he cannot explain the problem of inertial systems either.

The special theory of relativity is only valid in an inertial system, just like Newton's laws of mechanics.

But in reality there is no inertial system.

Any object on the earth will be affected by gravity, which will produce an acceleration and become variable speed motion.

Inertial system does not exist!
A theory derived from something that does not exist will of course be questioned.

This is the first core flaw of the special theory of relativity.

In addition, according to the special theory of relativity, the speed of transmission of any information cannot exceed 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 gravity was transmitted instantaneously, far 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 his thinking from the force of inertia.

First he asked himself, is gravity an instantaneous force?

He thought this was impossible because it did 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 the "gravitational field," just like the electric field.

Since there is a gravitational field, the gravitational force on an object is equal to its mass multiplied by the strength of the gravitational field.

Comparing it with F=ma, we will naturally get that the ratio of inertial mass to gravitational mass is a constant.

Later, physicists proved through experiments that this constant is 1.

This means that inertial mass and gravitational mass are equal. (The mass we usually refer to is gravitational mass.)
This is incredible.

All physicists at the time were unclear about the essential principle behind this equality.

They could not provide a theoretical proof.

Einstein didn't understand either.

But it doesn’t matter if you don’t understand, Einstein once again used his super sharp physics intuition.

He made a bold assumption: 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 that mean?

for example.

A man stands on the ground of a spaceship.

If the spacecraft is accelerating upward at an acceleration of g (the acceleration of the earth's gravity) at this time.

Then this person will be affected by an inertial force in the opposite direction at the same time.

The force of inertia pinned him to the ground.

The magnitude of the inertial force is equal to the inertial mass of the person multiplied by the acceleration g.

Because a person's inertial mass and gravitational mass are equal.

At this time, the acceleration a person is subjected to is g, which is the same as the gravitational acceleration of the earth.

Then the person will feel as if he is still on the earth.

In other words, the spacecraft replaces the Earth.

The inertial force field generated by the accelerated motion of the spacecraft replaces the gravitational field of the earth.

This person has no way of telling whether he is on Earth or in a spaceship moving at g acceleration.

The two are completely equivalent.

Acceleration is gravity, and inertia and gravity are equivalent.

This is the connotation of the equivalence principle.

With the equivalence principle, it became very easy for Einstein to deal with the first problem of narrow phase, the problem of inertial system.

Therefore, any non-inertial system with acceleration can be regarded as an inertial system 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 an inertial system that remains unchanged but has a changing gravitational field.

In this way, when dealing with any problem in a non-inertial system, we can just study gravity.

At this point, Einstein could naturally extend the principle of special relativity to all reference frames.

That is the second principle of general relativity: the principle of general relativity. (Also an axiom)

【All laws of physics remain unchanged in any reference frame. 】

The laws of physics are no longer invariant only in inertial frames.

At this point, the two major principles of general relativity have been completed.

Note that these two axioms are not made randomly.

Instead, it was Einstein who made this bold assumption after an in-depth analysis of the laws of physics.

We think it was simple in hindsight, but that was over a hundred years ago.

Next, it was Einstein and Ridgway who used these two principles to pry open the door to general relativity.

Maybe you, a smart person, will ask: Should we start doing experiments to verify it?
Do not!
Doing experiments is too low-level. If you want to do something, just do a thought experiment.

(End of this chapter)