Simple question of relativity, 20 points! That was wrong just now.

Suppose we get on the Einstein train again now and run on an infinite track. There are two stations on this track, and the distance between them is 864,000,000 kilometers. This train runs at a speed of 240,000 kilometers per second, and it takes 1 hour to complete this section. Every station has a clock. When a passenger got on the bus at the first stop, he set his watch according to the station clock. When he reached the second stop, he was surprised to find that his watch was slow. What's going on here?

To find out this problem, let's assume that the passenger lit a torch in the car and put it on the floor of the car. The beam of the flashlight quickly reached the top wall of the carriage. On the top wall of the car perpendicular to the torch, there is a mirror that reflects the light beam back to the torch. At this time, passengers see that the route of the light beam is vertical. However, people on the platform saw a completely different scene. Observers on the platform saw that during the process of the light beam from the torch to the mirror, due to the movement of the train, the propagation route of the light beam tilted backwards. In this process, the path of the light beam is the sum of the two waist lengths of an isosceles triangle.

Through this fact, we find that in this process, people on the platform see that the distance of light beam propagation is the sum of the two waists of an isosceles triangle. People on the train saw that the distance traveled by the light beam was only twice as high as this triangle. Obviously, the former is longer than the latter. On the other hand, we know that the speed of light is an absolute speed. For people on the train and people on the platform, the speed of light is of course the same. So we come to the conclusion that from the platform, it takes longer for light to travel from shooting to returning than from passing through the train.

Contradictory clocks and watches

From the above facts, we can easily calculate the result that it takes 10 seconds to get out of the station, but it takes only 6 seconds to get out of the train. That is to say, according to the station clock, if the train runs for an hour and arrives at another station, then according to the passenger's watch, the train only runs for 36 minutes. In other words, the passenger's watch is 24 minutes slower than the clock on the station every hour.

Obviously, the faster the train, the greater the time delay. If the speed of the train is increased to near the speed of light, the speed on the train can be reduced to a minimum in one hour at the station.

From this, we draw the conclusion that all running clocks are slower than static clocks. Does this contradict the theory of relativity that we ask questions? Does this mean that the fastest clock is at absolute rest?

No, that's not the case. Because the speed of the clock on the train and the clock on the station are compared under completely different conditions. Actually, there are three clocks here, not two. The passenger set his watch according to two different clocks at two different stations. On the contrary, if there is a clock in the front and rear carriages of this train, when the train is speeding, when passengers compare the station clock with the two clocks in the front and rear carriages, they will find that the time indicated by the station clock is always behind. Assuming that the train moves in a straight line at a constant speed relative to the station, it can be considered that the train is stationary and the station is moving. The laws of nature are the same to them.

When an observer is stationary relative to his watch, he will find the following facts: it is always faster than his own watch relative to the watch in motion; In addition, the faster the clocks in these movements go, the faster the time they represent.

This phenomenon is the same as the following example: judging from their respective positions, two observers standing next to two different telephone poles observe the telephone poles at a larger angle than the other.

Let's talk about space. We have found that space is relative, however, we still think that volume is an attribute of objects. This property of an object is not transferred by observing its reference system. However, relativity made us give up this belief. Just as the speed of our contact is always much smaller than the speed of light, the prejudice that time is absolute arises.

Let's imagine that Einstein's train will now pass through a platform with a length of 2400000 kilometers. The train arrives at the other end from one end of the platform according to the station clock 10 second. But according to the watches of the passengers on the train, it only takes 6 seconds for the train to pass the platform. Therefore, passengers have every reason to conclude that the platform is not 2400000 kilometers long, but 240000X6= 1440000 kilometers long.

Here, we can see that the platform is longer from the static reference system relative to the platform; However, the platform is shorter from the point of view of the frame of reference relative to the movement of the platform. Therefore, all objects in motion contract along the direction of motion.

But this contraction cannot prove that motion is absolute at all: once we observe an object from a relatively static frame of reference, it has a real volume. Similarly, passengers on the train will find the platform smaller, and people on the platform will think that Einstein's train is shorter. This phenomenon is not an optical illusion. Any length measuring instrument will get the same result.

Related to this discovery, we must correct the previous conclusion about the opening time of the front and rear doors of Einstein train. In the section "Early" and "Late", when we measure the opening time of the front and rear doors from the perspective of the observer on the platform, it is assumed that the moving train is the same as the stationary train. But actually, for people on the platform, the train is shorter. Similarly, according to the station clock, the time interval between opening and closing is actually equal to 24 seconds. Instead of 10 second. Of course, this amendment has no substantial impact on the conclusions we have made.

In terms of length contraction, by the way, the contraction of ruler.

We have to ask, when the spacecraft flies, is the scale on the spacecraft as long as the scale on the earth?

As we have discussed before, the measurement of space is related to the frame of reference for observing this measurement. So the ruler on the spaceship will not be the same as the ruler on the earth. Through the discussion of the length of the train relative to the platform, we know that the ruler fixed on the high-speed spacecraft along the moving direction is shorter than that observed by people on the earth. As for how much the length has shrunk, it is related to the speed of the spacecraft, that is, the relative speed between the two reference frames.

On the contrary, if the length of the ruler fixed on the earth is observed by the observer on the spacecraft, the length along the direction of motion is not lengthened, but shortened.

From this, we come to the conclusion that when an object is stationary relative to a reference frame, the length of the object is the largest relative to this reference frame. When it is perpendicular to the direction of motion, the length is constant.

Is this phenomenon of length contraction true? There is no doubt about it. Moving objects not only contract along the direction of motion, but also contract according to certain laws. These are all confirmed by practical phenomena. We usually don't see this contraction phenomenon because it is not significant in low speed and slow motion. For example, even if an object moves at a speed of 30,000 kilometers per second, its length will only shrink by five thousandths.

But when the speed of the object is close to the speed of light, the situation is different, and the length contraction is very significant. At rest, a one-meter ruler will shrink to several centimeters in the direction of relative motion. If the speed of an object becomes equal to the speed of light, its length will be reduced to zero. However, this is impossible. This also shows that the speed of light is the highest speed limit. The speed of ordinary objects can never reach the speed of light.

Excerpt from the article: On Relativity

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