Shulou(Shulou.com)11/24 Report--

There are three reasons why the title of this article is not written as "what is the Theory of Relativity":

First, the theory of relativity is too much, how can I dare to write about this topic?

Second, the most important foundation of the theory of relativity is actually the principle of relativity mentioned in this article. If we write it clearly, it will be easy to follow.

Third, this series of articles are carried out around the action in the field of electromagnetism, so we can't rob the host.

All right, you can look down with a relaxed state of mind.

Catalogue 01: a preliminary understanding of the principle of relativity

02 Galileo transformation

03 Maxwell equations of kickfield

04 looking for "etheric wind"

05 Lorentz's last stubbornness

06 re-recognize the principle of relativity

07 find out the time bug

08 Lorentz transformation

09 conclusion

Friendly reminder: when the formula is long, please swipe left and right to see the complete result

When we first understand the principle of relativity, to mention the principle of relativity, we have to move the storyline forward for a long time, because it has something to do with the famous dispute over "earth and sun" in history.

As early as when the ancient Greeks looked at the stars and the moon, people subconsciously thought that the earth in which they lived was the center of the universe, and all the stars revolved around themselves; and after long-term observation, a complex cosmic model established by Ptolemy, the geocentric model, can better explain some astronomical phenomena that can be observed at that time. Presumably high school students have some understanding of these history, but a lot of space has been used to introduce them in the textbook.

This self-centered view of the universe was very much to the taste of the church at that time, so under the official platform, the geocentric theory was able to rule for a long time.

In fact, apart from non-political factors, there were heliocentric ideas before geocentric theory, but heliocentric theory could not answer what seemed to be a thorny problem at that time: since the earth revolves around the sun, then why do we jump up and fall back and not be thrown out?

Up to now, junior high school students will disdain to say four words: because of inertia. But you know, the concept of inertia came into being after Galileo Newton. If you put it in ancient times, it would be embarrassing!

Even if the newcomer Copernicus solemnly put forward the heliocentric theory, not only greatly simplified the model of the movement of celestial bodies, but also the explanation of the retrograde phenomenon of Mars has become an obvious result, but without Galileo's divine assist, Copernicus's point of view will be as shaky as its predecessors.

The core problem Galileo is trying to solve is: if the earth is turning, why can't I feel it? The opinion on this issue has a wonderful account in his masterpiece Dialogue on the two World Systems of Copernicus and Ptolemy.

Galileo envisioned a scenario in which you were thrown in an invisible cabin. Can you tell whether the ship is still or moving in a straight line by observing the situation in the cabin?

Galileo's answer is: no! Whether you are doing a jumping experiment, observing the falling point of water droplets, or observing the surface of the water in a tank, none of these phenomena can help you tell whether the ship is still or moving in a straight line at a uniform speed.

Now you can review the experiment in a closed vertical elevator. As long as the elevator is quiet enough and you don't look at the floor indicator, you certainly can't feel the difference between the two situations when the elevator is at rest and running at a constant speed.

If we raise these facts to a theoretical level, we simply cannot tell whether the ship is at rest or moving in a straight line at a uniform speed through mechanical experiments.

Of course, you can replace the boat with an elevator, a train or even the earth where we live! When they are at rest or moving in a straight line at a uniform speed, there is no difference in the various mechanical phenomena that occur on them. This is the famous Galileo principle of relativity.

Only with such a deep understanding did Copernicus's heliocentric theory gain a firm foothold. Because since you can't prove whether the earth is moving by jumping experiments, isn't the biggest obstacle to heliocentric theory self-defeating?

Now let's jump out of the "earth-sun" debate to examine Galileo's principle of relativity, and there is more to be discovered.

We all know that when describing the motion of an object, we need to choose a reference, the reference can be chosen at will, it can be movable or static.

Although the selection of different reference objects will lead to different results in the description of object motion, when the reference object is in a static state or a uniform linear motion state, even if the motion of the object has different descriptions, but its mechanical characteristics must be the same. This is the essence of Galileo's principle of relativity!

This shows that the reference of static or uniform linear motion is equivalent, and in the words of high forcing lattice, the inertial reference frame is equivalent!

As for what an inertial reference frame is, it can't be explained in a sentence or two. You just need to know that the ground is an approximate inertial reference frame.

In addition, another reference frame that moves in a static or uniform straight line relative to the inertial reference frame is also the inertial reference frame, such as houses standing on the ground, trains running in a straight line on the ground, and so on.

Therefore, we can describe Galileo's principle of relativity as "mechanical experiments are equal to all inertial reference frames."

It seems to be an ugly sentence, but it reveals the universality of the laws of mechanics in the inertial reference frame! Everyone is an inertial reference frame, how can we say who is more special than who? There's no such thing.

Galileo transformation admits that mechanical experiments are equal-weighted for all inertial systems, which means that mechanical laws are equal-weighted for all inertial systems. Because the results of mechanical experiments can be described by mechanical laws, if your mechanical laws are not equal to all inertial systems, how can you ensure that mechanical experiments are equal to all inertial systems?

What does that mean? It shows that the laws of mechanics must have the same mathematical expression in different inertial systems. For example, the well-known expression of Newton's second law, if it is in this form in the ground reference system, and in a train moving uniformly in a straight line relative to the ground, can you get the same mechanical experimental results?

You may think that the above passage is superfluous. This is the only formula. It doesn't matter whether you are on the ground or in a uniform straight-line train.

But if you think about it, who gave you the courage to guarantee it? The more such a conclusion is taken for granted, the easier it is to roll over, sometimes seriously! If you don't believe it, you can see it later.

So now we need a bridge-- a bridge that can change the laws of mechanics in different inertial systems. Only it can answer whether our mechanical laws have the same mathematical expression in different inertial systems.

Because the quantitative description of mechanical experiments requires the establishment of a coordinate system on the reference frame, this bridge is actually a tool to realize the coordinate transformation in different reference frames.

What we use most is the spatial Cartesian coordinate system, with which the position characteristics of objects can be described quantitatively. In addition to the location characteristics of the object need our attention, the time when the object appears in this position must also be recorded.

As for this time, I don't care which inertial reference frame you choose, because in our common sense, what difference can time make? As long as our clocks are good, isn't it the same time you look at on the train and I look at it on the ground? Don't we usually pick up people at the station in this way?

This concept of time, which comes from long-term life experience, is so ingrained that we don't realize what's wrong with it, let alone question its correctness.

Just as water can carry a boat and overturn it, life experience will bring us great benefits, but sometimes it will blind our eyes! You can see it if you continue to look back.

In Galileo's time, there was no doubt that there was nothing wrong with this concept of time. That is to say, in any inertial system, the time is the same! We record the time in two different inertial systems as and, then there are.

After talking about the time, let's talk about the coordinates. Look at the simplest case: the triad axes in the two inertial reference frames correspond to each other in the same direction, the inertial reference frame moves at a uniform speed relative to the inertial reference frame along the coordinate axis, and the origin of the two coordinate systems coincides at the initial moment, as shown in the figure.

Therefore, the position vector of the same object in two different inertial reference frames must satisfy the relationship.

Hey, that's the triangle rule of vectors.

In the two coordinate systems with the simplest correlation, if the position vector relationship is written in the form of coordinate components, we can get the transformation relationship between the two sets of coordinates.

The final time relationship is just to emphasize that the time in the two inertial systems is the same. This is the famous Galileo transformation!

In retrospect, the origin of this set of relationships is that we envision two prerequisites: space is like a solid box that cannot be compressed, and time is the same in all inertial systems. The transformation relationship between coordinates can be obtained only if the former hypothesis is combined with the triangle rule of vectors, while the latter hypothesis directly gives the time relationship.

This absolute concept of time and space, which is in line with the common sense of life, can be said to be natural and well-known. although there are individual doubts, the Newton's law of motion governing heaven and earth and Galileo's transformation match seamlessly, and no one can fight one!

The reason why Galileo and Newton can unite is that they both hold the absolute concept of time and space. Therefore, Newtonian mechanics is a mechanical system under the absolute view of time and space, and Galileo transformation can be obtained smoothly from the absolute view of time and space, so the coordinate transformation in the Newtonian mechanics system which connects the two inertial reference frames is naturally Galileo transformation.

If you don't believe it, use the expression of Newton's second law to verify it. First of all, we can find the velocity and acceleration relations of the object in two different inertial reference frames by slightly dealing with the above position vector relation.

Since the derivative of the position vector of an object to time is the velocity of the object, and the derivative of the velocity of the object to time is the acceleration of the object, there is

The time relationship has come to make a scene, isn't it (because the two inertial reference frames move in a relatively uniform straight line, so there is)?

In the cognition at that time, mass was regarded as a physical quantity that reflected the amount of matter contained in an object, so it did not change with the change of the reference frame. In addition, the force is also a quantity that does not change with the reference frame.

We have just proved that the acceleration of the same object is equal in different inertial reference frames, so in two different inertial reference frames, there are, and.

That is to say, Newton's second law in one inertial reference frame, after Galileo transformation, still exists in another inertial reference frame.

You see, the mathematical form of this formula has not changed at all, so we can use it comfortably in different inertial reference frames.

This feature of keeping the mathematical form unchanged under Galileo transformation is called Galileo covariance-every physical quantity has changed, but everyone has changed together! After the change, we still maintain the relationship before the change! It's like I want to grow old with you in a rocking chair. Although you and I are no longer young, the love between us remains the same!

Not only Newton's second law has Galileo covariance, but all laws of Newtonian mechanical system have Galileo covariance. Keep some homework for you. When you have a thorough understanding of Galileo covariance, you will really understand Galileo's principle of relativity.

After the establishment of Newtonian mechanics of the Maxwell equations of 03 kickfield, it and Galileo transformed like princes and princesses in fairy tales, happily living together without shame for more than 200 years. But how did the emergence of Maxwell's equations disrupt the good life between the two?

Mai Shen finally wrote a set of equations of unified electromagnetism, and we certainly hope that it can satisfy the principle of relativity. Why? Who makes the police who belong to the Pacific Ocean be more lenient? If your system of equations can only be played in a particular frame of reference, do you think Maxwell's equations are still a universally applicable law?

It makes sense, Maxwell's equations should indeed satisfy the principle of relativity! But this will create a contradiction! At the end of the last article, we give a conclusion of Maxwell's equations that the velocity of electromagnetic wave is the speed of light.

Please note that this result is the solution of the system of Maxwell equations. If you admit that the Maxwell equations satisfy the principle of relativity, then the Maxwell equations must have the same mathematical form in different inertial reference frames, which means that its solution is still the same.

In other words, the Maxwell equations + the principle of relativity can boldly say that the speed of light is constant in different inertial reference frames. Please note that we are only having a theoretical discussion and have nothing to do with using experiments to measure the speed of light.

But this conclusion will be immediately hit in the face by Galileo! Because according to Galileo transformation, the propagation speed of light in different inertial reference frames should be satisfied.

Unless the two inertial reference frames are relatively static, that is, how can there be the conclusion that the speed of light is the same in different inertial reference frames?

So now there is such an awkward situation: the Maxwell equations seem to be incompatible with the principle of relativity! Now the choice in front of people seems to be one of two:

1. If the Maxwell equation is wrong, you have to disk it.

2. The principle of relativity is only applicable to the laws of mechanics, and Maxwell's equation is correct, but it can only be applied to a special inertial system. If it were you, which route would you choose?

Although Maxwell's equations are a new melon, the electromagnetic waves and their characteristics predicted by others have been completely tested. If you say it is wrong, what is the evidence?

So Route 2 is favored by most people. after all, this scheme can reconcile the contradictions without too much cost. As for what this special inertial system is, please read on!

Electromagnetic waves are found in the laboratory on the ground, which means that the Maxwell equations are valid in the reference system on the ground. Because of the particularity of this inertial system, it means that the Maxwell equations are not valid in trains running at a uniform speed on the ground. Do you think the fruits of Mai's hard work failed when he got on the train? That's not likely. And heliocentric theory has been recognized for hundreds of years, why does your earth still feel that you occupy a special position?

So one can only imagine such a scenario: the whole universe is full of matter in which electromagnetic waves can propagate; at the same time, it is also a special frame of reference in which the Maxwell equations are established. You have to ask what the name of this substance is, it has a resounding name-ether! The frame of reference made up of it is called the etheric system.

In this way, the principle of relativity does not conflict with the Maxwell equations. My Maxwell equations are only established in the Ethernet system. You Galileo transformation can not control me! Well, I don't offend anyone. This mud is in good harmony. It is just that whether our wishful thinking is tenable or not needs to be verified by experiments.

04 looking for "etheric wind" it takes a little ink to introduce the coming etheric.

The idea of the ether has existed since ancient times. Aristotle, the ancient god, and Descartes, the master of the Mesozoic era, both believed that space was filled with a kind of matter, while Huygens studied waves. Analogy water waves, sound waves are the propagation of vibration in the medium, he believes that light is a kind of elastic pulse in the ether.

Unfortunately, that era was destined to belong only to Niu Yeh, who thought that light was a bunch of particles and explained the propagation of light very well, so the particle theory of light rubbed the etheric theory on the ground.

With the discovery of the typical wave feature of the interference of light by Thomas Young, the view that light is a wave revived and the etheric hypothesis rose.

The experimental results of double-slit interference were later predicted by Maxwell that light was an electromagnetic wave. In order to reconcile the contradiction between the principle of relativity and Maxwell's equations, ethernet and its etheric system officially became the consensus of everyone in that era.

To put it simply, it has been recognized that the earth is "soaked" in the ether and orbits the sun relative to the ether. What needs to be done now is to prove this conjecture through experiments.

In the order of development from easy to difficult, several well-known early experiments support the hypothesis that the etheric is everywhere and still, but that moving objects drive the etheric in it, which is Fresnel's partial pull hypothesis.

This is equivalent to saying that the air is everywhere, and a moving car can drive with the air inside, but the air outside can't move.

So this almost established hypothesis will inevitably come to the conclusion that the moving earth can feel the "etheric wind"! Isn't that nonsense? On a windless day, you are leisurely in your car. Is the wind blowing outside the window?

According to this corollary, if the experiment can measure the speed of the "etheric wind", won't it be possible for the etheric to exist? What are the leaders of the experiment still waiting for? Why don't you risk your life to find "ether wind"?!

But this experiment requires very high precision! Maxwell once suggested that because the various methods of measuring the speed of light on the ground depend on the increased time for light to travel back and forth between two measuring points, which accounts for only 1/100000000 of the total propagation time, so the accuracy of the experiment must reach this level.

Explain a little bit how this accuracy is estimated. If the two measurement points now happen to be in the direction of the "etheric wind", then the light propagating back and forth between the two measurement points is relative to the downwind and then back against the wind. So the total round trip time of light between the two measuring points is

Then move the two measurement points to a place where there is no "etheric wind", then the total round trip time of light between the two measurement points is

So in both cases, the change in propagation time is

Then the proportion of the changing time to the total propagation time is

The speed of the earth's revolution is about, so the wind speed of the "etheric wind" is only so large, while the speed of light is, so the ratio can be 1/100000000.

Wait, didn't you say that Galileo transformation can't control Maxwell's equations? Why is Galileo's velocity superposition formula used here?

Yes, Galileo transformation can not control the result of the solution of Maxwell's equations in Ethernet, that is, the result of the speed of light in Ethernet, but now we are talking about the speed of light on Earth, which is no longer your etheric territory. do you think Galileo's speed transformation formula can control?

No, the KPI has been worked out, so the physicists who are doing the experiment should hurry up for their achievements. As a result, the well-known Morey-Michelson experiment appeared, which well met the precision requirements put forward by Maxwell.

However, after a meal of operation, the results of the experiment poured cold water on people-screw your etheric wind, it doesn't exist! With regard to the above-mentioned experiments and their details, I will hold out an article on waves later, so I won't compete with the topic of this article.

The absence of "etheric wind" means that Fresnel's etheric hypothesis is not self-consistent, which also means that there is still no reasonable description of the etheric theory.

Please note that although the "ether wind" was not found in the experiment, it does not mean that the ether does not exist! Or the example of a moving car listed above, when you sit in a car with closed windows, you can't feel the wind outside the car, but can you say that there is no air in the car?

Moreover, physicists at that time believed in the existence of the ether, but could not reconcile the experimental results of searching for the ether for the time being. Who will give the explanation this time?

05 Lorentz's last stubbornness

Lorentz, please keep in mind this man's name, which will appear frequently in this article. In fact, high school students are no stranger to him. The forces acting on charged particles when they move in a magnetic field are named after him, which shows how much he has contributed.

There is no doubt that its contribution can write a lot of content, readers please look forward to the follow-up update, here a moment of grievance.

In a brief summary, the Maxwell equations are based on the ether, and this is the view of Maxwell himself. Due to the limitations of the times, there are still some conceptual ambiguities after the establishment of Maxwell's theory, which leads to the electronic theory established by Lorentz.

Because the electronic theory is a supplement to Maxwell's theory, the theory is also based on the ether. Naturally, Lorenz would come down to explore the ether himself.

Knowing this background, you will understand the reasons for Lorentz's next attempts. Lorenz was crazy about the results of Morey-Michelson's experiment. He firmly believed in the existence of the ether, so he had to reconcile Fresnel's hypothesis with the results of Morey Michelson's experiment.

The boss is the boss, and he has come up with a brilliant plan-the length of the object will shrink along the direction of motion! If the original length of the object is moving at a speed, the length in the direction of motion will become

Lorentz believes that this is a real phenomenon, caused by the molecular force inside the substance.

According to this clever trick, Lorenz can well explain the results of Morey-Michelson's experiments, predict the effects of "etheric wind" that cannot be observed on Earth, and take into account Fresnel's hypothesis. Don't you think it's cool?

You may have a sense of familiarity when you see it here: isn't this the same way I look at the questions and answers and come up with the process of solving the problem? As long as I can figure out the same result as the answer, how can I care if the teacher will say that he doesn't understand but is shocked?

Ha, there is a joke that goes like this-the life cycle of people who engage in physical theory is: come up with an idea, if it matches the experiment, then go to the Nobel Prize and get to the top; if the idea doesn't match the experiment, start from the beginning. continue on the road to the top.

At the same time, Lorentz also carried out another quantitative work: to keep the form of Maxwell's equations covariant!

He determined that the Maxwell equations were strictly established in the stationary etheric system, so that in another frame of reference relative to the etheric system, the speed of light must be affected by this relative velocity, which is the inevitable conclusion of Galileo transformation.

But this contradicts the Morey-Michelson experiment! If Maxwell's equations remain the same in the frame of reference, the Morey-Michelson experiment can explain it.

Hey, walking around, we finally get back to the question of whether Maxwell's equations satisfy the principle of relativity. Obviously, Lorentz wants to find a "magic" to make the equations covariant!

As "magic", Lorenz himself admitted that he had only done some technical processing in mathematics-in order to achieve covariance, he introduced another hypothetical frame of reference into the frame of reference and gave the coordinate transformation law from the etheric system to the imaginary frame of reference, thus achieving the purpose of making the system of equations covariant.

Speaking of human language, Lorentz believes that Galileo transformation should still be used when changing from the etheric system to the actual reference system.

In this way, the form of Maxwell's equations is bound to change in the frame of reference. In order to achieve the purpose of covariance of the system of equations, he designated that there is a corresponding relationship between the coordinates of the reference frame and the imaginary reference system as follows:

The coefficients in the first two formulas

What's in all the formulas is a proportional coefficient.

Lorentz did not give a reason for this correspondence, but only proved that it would make the Maxwell equations covariant in the Ethernet system and the hypothetical frame of reference.

Strictly speaking, in the process of mathematical proof, Lorentz also put forward a wrong hypothesis, so that only three of Maxwell's equations are identical in form, and the remaining one is slightly different. however, this problem was solved by Poincare of the same period.

We can see that his own hypothesis of length contraction is used in the correspondence. In addition, Lorentz will also be called "local time", which is considered to be unreal time, but the real time is still absolute time used in mathematical transformation.

I have to say, Lorenz has a really strong ability to put together the "problem-solving process". But after all, the pooling process is only reverse thinking, and only when there is a clear understanding from the source, the positive process is correct.

This is true. Subsequent experiments do not confirm Lorentz's view that length contraction is the real contraction of matter, while the above correspondence uses the hypothesis of length contraction, which is a bit embarrassing.

It seems that the nature of the problem has not been grasped, and it is urgent for a pair of eyes with profound insight to appear! Yes, it's time for Einstein to come out.

06 re-understanding the principle of relativity has already pointed out that we have made a big circle, and finally we come back to the question of whether Maxwell's equations and the principle of relativity can coexist.

How important the principle of relativity is, just look at its achievements: the principle of relativity is a great success in the system of Newtonian mechanics. Because of its existence, Newtonian mechanics can be established in any inertial reference frame. The universality of physical laws is reflected incisively and vividly by it.

Therefore, whether from the point of view of fact or from the point of view of the pursuit of beauty, it is difficult to question the principle of relativity.

As for outside the field of mechanics, can the principle of relativity kill all sides? Einstein gave his support! We can write a very detailed process about how Cupid opened the door to the theory of relativity. here we will only look at a few main links.

A question raised at the end of the last article: is there really a clear distinction between dynamic electromotive force and induced electromotive force in electromagnetic induction?

If you look at this example, from the point of view of people on the ground, if the closed coil moves with the train, the electromagnetic induction occurs because the moving closed coil cuts the magnetic induction line, that is, it produces a moving electromotive force.

However, from the point of view of the people on the train, the closed coil does not move, but the electromagnetic induction is caused by the change of the magnetic field, which is caused by the induced electromotive force.

Are the electromagnetic induction phenomena in the two cases essentially the same? If you use Faraday's law of electromagnetic induction, you will find that no matter which point of view you take, you can get the same result. What does that mean? Is it a coincidence or is there a deeper connection?

Einstein said when faced with this problem that he couldn't stand it. It was a coincidence! He firmly believes that there is no essential difference between the above two situations, but only caused by the different frame of reference of the choice. This is an evidence that electromagnetic phenomena satisfy the principle of relativity.

Second, whether it is the experiment that supports the Fresnel hypothesis or the Morey-Michelson experiment, together (the only difference lies in the accuracy of the experiment) shows that optical experiments cannot be used to distinguish whether the earth is stationary or moving at a uniform speed relative to the etheric system. If you see this word for word, you should be familiar with the meaning of this sentence, right? Isn't this the embodiment of the principle of relativity?

Moreover, we cannot ignore Einstein's philosophical thinking. Mach's criticism of Newton's absolute concept of time and space greatly influenced Einstein. After an in-depth study of Mach's thought, Cupid said that Lao Ma you are right, absolute movement does not exist! All we can observe is the relative motion between two objects!

Such being the case, there is no such thing as a privilege for two objects moving in a straight line at a uniform speed. This means that Einstein completely broke with the etheric, because in the mind of the etheric school, the etheric system is a special frame of reference!

These reasons prompted Einstein to rewrite the principle of relativity-all laws of physics are equal to any inertial reference frame.

Galileo only found that the laws of mechanics satisfy the principle of relativity, but now Cupid guarantees all the laws of physics! The courage to be sure is that he has really found the basis for the covariance of all the formulas of the laws of physics!

07 pull out time bug said earlier, the principle of relativity will naturally lead to Galileo transformation, which fits perfectly with Newtonian mechanics. But when it comes to the Maxwell equations, it looks uncomfortable, because if you combine the two, you can naturally get the result that the speed of light has different values in different inertial reference frames; and a number of optical experiments show that the speed of light when propagating in the same medium is the same in different inertial reference frames.

Einstein was convinced of the correctness of Maxwell's equations and knew that some of Lorentz's early research results resolved this contradiction by correcting some of Lorentz's ideas (killing Lorentz's favorite etheric system). But a year later, there was still no progress, causing Cupid to call it a real problem.

In this long process of thinking, Cupid must know something about the "local time" proposed by Lorentz or the corresponding relationship of coordinates. It's just that these skills, which Lorentz sees as pure mathematics, are deeply imprinted in the mind of Cupid, vaguely guiding him to discover the key point of the problem-time!

Moreover, Mach's criticism of the absolute concept of time and space and Poincare's judgment of simultaneity all remind Cupid that the clue is on the concept of time!

What is the time? Presumably each of us can say a thing or two, but we don't seem to have said anything. Time, isn't it the reading shown on the clock? I want to know what time it is and glance at the clock, whether we are standing on the ground or sitting on a train running at a constant speed.

This correct common sense of life leads us to acquiesce in such a practice: anyway, we all look at the clock readings, so there is no need to distinguish between clocks on the ground and clocks on trains running at a uniform speed.

When the TV station strikes the time on the hour, whether you are sitting at home or on a train running at a uniform speed, you will use the time reported by the TV station to set the clock around you. Everybody must have done that, right? Any problems? Isn't it natural? Isn't the time all the same?

This view of time deeply engraved in our minds is the absolute concept of time, it is so in line with our common sense of life! Cupid was no exception when he stumbled here until he completely got through the governor's second pulse after a conversation with his good friend Besso-he realized that time was not absolute, but that there was an inextricable link between time and signal speed.

The boss's original words are a little roundabout, to put it bluntly, that is, the clock readings you see at home and on a train running at a uniform speed only represent the time in their respective inertial reference frame, let's call it the time of the ground system and the time of the train system.

Cupid said that for the occurrence of the same thing, from the point of view of observers in the ground system and the train system, the time of occurrence is different. And we used to have no reason to acquiesce that things must happen at the same time.

To this end, the boss also kindly gave a simple example to illustrate. Of course, the premise is based on another assumption put forward by Cupid: the speed of light in a vacuum is the same for any inertial reference frame in any direction, that is, it has nothing to do with the motion of the light source.

Einstein put forward this hypothesis alone because at that time, most people still believed that light travels at different speeds in different reference systems (an inevitable result of Galileo transformation). Even if the results of optical experiments reveal the constant speed of light, they are just trying to mend the gap between old ideas and new phenomena.

All right, let's talk about the example of Cupid. A train runs at a uniform speed and in a straight line on the ground, assuming that people on the ground find that the front and rear of the train have been struck by lightning at the same time. The projection points at the beginning and end of the train on the ground are and, regardless of the height of the train. Under this premise, do you think the people in the train will see the front and rear of the train struck by lightning at the same time?

The schematic diagram of the lightning strike of the train first asks you a question: standing on the ground, how can you be sure that the front and rear of the car were struck by lightning at the same time?

I think it can only be seen by people on the ground that two things happen at the same time! That is, the flashes of the front and rear of the car are transmitted to the eyes of people on the ground at the same time, which means that the person is standing at the midpoint of the ground.

Now let someone switch to the train, in order for the simultaneity issue we are discussing to be comparable, this person must stand at the midpoint of the train.

Because people will move with the train, the human eye will receive the light from the front of the car, and the light from the rear of the car will chase the human eye. Alas, isn't this what primary school students know about opposing sports and chasing sports and meeting each other?!

Because Cupid put forward the assumption that the speed of light is constant, even if the train is running at a constant speed, the speed of light from the front or rear of the train is still the same! When people stand at the midpoint of the car, do you think it is short time to meet each other in the opposite movement or to meet in pursuit movement?

Obviously, the human eye will first see the light coming from the front of the car, so it will come to the conclusion that the front of the car is struck by lightning first and the rear of the car is struck by lightning! Doesn't this mean that the people on the train think that the lightning strikes in two places don't happen at the same time?

This is what Einstein said that there is an inextricable relationship between time and signal speed. Only when the human eye sees the light signal coming into the eye can you conclude that an event has happened!

Because of the relative motion between the reference frames, even if what happens in the same place, in the view of observers in different reference frames, the time of occurrence will be different. This is the relativity of the same time!

Imagine how Newton would answer this question. In the view of the people on the train, because of the movement of the train, the light from the front of the train travels faster, while the light from the rear of the train travels at a smaller speed, which is to apply the speed formula of Galileo transformation.

But the people on the train will not hesitate to think that the lightning strikes in two places occur at the same time, which is the absoluteness of the same time. So under the default premise that the two beams of light are emitted at the same time, because the speed of the light from the front of the car is faster, the human eye will first see the front of the car being struck by lightning.

While Newton was still smug that his answer was the same as Einstein's, Newton's process of analysis had betrayed himself.

First of all, why do you unthinkingly acquiesce that lightning strikes in two places occur at the same time in the train system?

Second, the conclusion of the speed change you used is not consistent with the constant speed of light reflected in the experiment (although it was not fully recognized at the time).

Finally, you come to the conclusion that the front of the car is struck by lightning first, which means that the lightning strikes in the two places do not occur at the same time in the train system. You see, the logic is not self-consistent and immediately appears.

Looking back at the analysis process of Cupid, the people on the train did not suggest where the lightning strike occurred first, but always adhered to the principle of seeing it first and coming to a conclusion.

In the whole process of analysis, except for the assumption that the speed of light is constant, there is no inconsistency! And the assumption that the speed of light is constant is not unfounded, so if it were you, which way of analysis would you choose?

At this point, the man behind the marriage of the principle of relativity and Maxwell's equations has finally been found out-that is the wrong absolute view of time and space!

There is nothing wrong with the principle of relativity, Maxwell's equations have also stood the test of the experiment, and the guy who created the contradiction is the Galileo transformation based on the absolute concept of time and space.

Ha, now point the finger at Galileo transformation. Wait, Newtonian mechanics is also based on the absolute concept of time and space, do you still have to question the correctness of Newtonian mechanics?

Originally, we just wanted to reconcile the contradiction between Maxwell's equations and the principle of relativity, but now we have to let the two great gods who have long passed away take the blame. Who dares to stand on the horse, but I, Einstein!

At this point, I can't help lamenting that history is always strikingly similar. At the beginning, Galileo easily cracked Aristotle's erroneous view of mechanics with an easy-to-understand counterproof, but now Einstein only used a simple example to point out the relativity of the same time, and then rejected the absolute view of time and space.

I have to admit that the change of ideas can only happen when the historical process reaches an appropriate stage and meets people with profound insight.

08 Lorentz transformation since Einstein rewrote the principle of relativity, then there must be a corresponding coordinate transformation to give mathematical guarantee.

Since Maxwell equations and Galileo transformation formulas have been written in black and white, whether Galileo transformation can make Maxwell equations have covariance is purely a mathematical proving problem. Obviously, the answer is no. It is imperative for us to transform the transformation formula.

After Cupid realized the new concept of time and space, the new coordinate transformation formula was naturally deduced.

It should be emphasized here that the new coordinate transformation formula is the logical result of the new concept of time and space, which is completely different from the reverse approach of Lorentz watching the answer "put together" in the first place.

If you want to understand the original derivation of Cupid, please move on to Cupid's original thesis. Here we will directly throw out the formula of coordinate transformation.

Suppose there is a relative motion relationship between two inertial reference frames as shown in the following figure (that is, there is relative motion only in the axial direction).

The coordinates of the two coordinate systems with relative motion are transformed into:

The coefficients in the first two formulas

The name of this set of coordinate transformations is Lorentz transformation.

Strange, this is the result that Einstein got alone, why is it named Lorentz?

The thing is, as mentioned earlier, Lorentz has given a "two-step transformation method" full of mathematical skills to ensure that the form of Maxwell's equations remains the same in the Ethernet system and the hypothetical frame of reference, but his "two-step transformation method" still has some defects. Poincare pointed out that the flaw is that Lorentz should not set up such an illusory frame of reference as the Ethernet system, but should directly merge the so-called "two-step transformation" into a "one-step transformation".

At the same time, Poincare also proved the undetermined proportional coefficient in the coordinate correspondence given by Lorentz. Now you just need to bring the Galileo transformation into the coordinate correspondence given by Lorentz, and you can get the Lorentz transformation like a fake transformation! Try it if you don't believe it. It's very simple.

I would like to stress again that the same answer does not mean the right way of thinking! Lorentz and Poincare are the result of applying Galileo transformation to an unexplained mathematical technique, which is essentially a repair of Galileo transformation.

On the other hand, Einstein made a new derivation based on the new view of time and space, and its process had nothing to do with Galileo transformation. But Lorenz is very respected by the bosses, and the result of the change is indeed his priority, no matter whether he is accidentally or not, use his name!

When it comes to naming, you will naturally be concerned that the Lorentz transformation can really ensure that the formulas of all physical laws have the same form in different inertial systems. The covariance of Maxwell equations will be written in detail in a later article, where we are only concerned with the relationship between Lorentz transformation and Galileo transformation.

Because Lorentz transformation is the crystallization of relativity principle after rewriting, it can guarantee the covariance of all physical laws, while Galileo transformation can only guarantee the covariance of mechanical laws, so Lorentz transformation should include Galileo transformation. or Galileo transformation is a special case of Lorentz transformation. Is that really the case?

Look at the coefficients in the Lorentz transformation.

When the relative velocity between two inertial reference frames is much less than the speed of light

It's pitifully small, obviously.

So you will see that the second formula of the Lorentz transformation degenerates, which is the result of Galileo's transformation!

In addition, also under the premise that the speed of light is much less than the speed of light, the first formula of the Lorentz transformation will degenerate into (the mathematical proof here is a little troublesome, as you can see in the textbook. This is purely a mathematical problem, which is also the result of Galileo's transformation.

At this point, you will find that Galileo transformation is the approximate result of Lorentz transformation at low speed! Although the absolute concept of time and space has been thrown into the dustbin of history by Cupid, in the field of low speed, the conclusion of the relative concept of time and space is so close to that of the absolute concept of time and space!

Can you estimate for yourself how fast human activities can be encountered before they leave the earth? Even today's space voyage, its speed is only an order of magnitude, you can see how small it should be!

Therefore, in the face of the problem of low speed, Newtonian mechanics and Galileo transformation can undoubtedly be grasped, so there is no need to worry that the coffin boards of the two great gods can not be held down.

09 conclusion, as mentioned earlier, understand the principle of relativity only when you understand Galileo transformation; now you have to understand Lorentz transformation to understand the principle of relativity!

It is the existence of Lorentz transformation that makes all mechanical laws have the same mathematical expression in any inertial reference frame. The field of mechanics shows that there is no pressure to get along with Lorentz transformation.

It is the existence of Lorentz transformation that Maxwell equations have the same mathematical expression in any inertial reference frame, so it can be explained theoretically that the speed of light in vacuum is constant in any inertial reference frame. This coincides with the results of optical experiments, and those maddening contradictions have been eliminated!

From then on, the laws of mechanics, electromagnetism, the constant phenomenon of the speed of light and the principle of relativity lived happily together.

Oh, by the way, you just said that you can ensure the covariance of the Maxwell equations through the Lorentz transformation, but Maxwell's equation has a uniform differential form, and you have to tell me that it obviously has Lorentz covariance. No wonder I'm not in a hurry with you.

This article comes from the official account of Wechat: ID:gh_8bb6a1229347.

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