# Children can run on the speed of light train, can't be faster than the speed of light? Junior level can understand, let you doubt life

If you let Einstein answer, it will definitely not exceed the speed of light, and it will be said that this assumption does not exist.

Why did Einstein say definitely not?

First we analyze this problem. The train is in motion and the child is moving on the moving train. The reason for this problem is that the Galileo transformation we have learned tells us that relative speed is the problem of two speed addition or subtraction., So easy. Our first response to this question is the speed of the child plus the speed of the train, which is v = u + c the speed of the child is u and the speed of light is c. The result is more than the speed of light.

Although this is common sense, sometimes you think that common sense is not necessarily right. If you chase me on the ordinary road, or you run on an airplane, you can count this, but when the speed of movement reaches 100%At the speed of light, Einstein would say: "The Galileo transformation in Newton's classical mechanics is no longer applicable, and errors will occur. High-speed motion is the field of special relativity. Besides, the speed of trains is the speed of light."

Einstein's reason

We assume that the child is moving from the back of the train to the front of the train. Because the car is moving at a constant speed and has no acceleration, the child's movement is the movement in the train system and has no relationship with the outside world. Or if the train has no windows, it is closed.We can't observe the scenery outside the window at all, and the passengers can't detect whether the car is in a moving or stationary state. Observing inside is like a child running from front to back on a stationary train.

Then the person in the car observes that the time that the child runs from the back of the car to the front of the car can be calculated according to s = vt is t1

It happened that someone on the ground also observed this process. People on the ground found that the distance the child ran was not the distance from the end of the train to the front of the train, because the train was also running. Similarly, t2 can also be obtained based on s = vt.We don't need to count and know that although s1 is not equal to s2, v1 is not equal to v2, but t1 = t2, but Einstein does not think so. Einstein said that when the train speed is fast enough, t2> t1, the speed is not just the sum.It's that simple.

Take an example to make you doubt life

A spacecraft flies forward at a speed of v. A small round light at the bottom of the spacecraft shoots out at the top of the spacecraft with a speed of light c. When the spacecraft flies from point A to point B, the light just shoots from the bottom to the top.The time for the observation lamp to shoot from the bottom to the top is t ', and the time for the ground observation is t. Ask whether t and t' are equal?

The light observed on the ground is oblique, the distance is ct, the flight distance of the spacecraft is vt, the movement distance of the light from the bottom to the top is observed within the space, ct ', and the three distances are connected to form a triangle.Theorem finds :

It is found that the relative time is not equal to t and t ', and the result depends only on the speed v of the spacecraft. This is the time expansion effect of Einstein's Special Theory of Relativity, which means that the time of moving objects will become slower.

We call the time t 'on a high-speed moving object as the eigen time, and the time t of the observer's frame of reference is called the extrinsic time.

It is called Lorentz factor, it can also be called high-speed correction factor, it is easier to understand. The following is the relationship between speed and Lorentz factor,

When v infinite approaches the speed of light, the correction factor will be infinite. Keeping this in mind, you can understand most problems of special theory of relativity. We can think of it as a correction given to high-speed errors and a mass correction under classical mechanics.Time correction, size correction, speed correction, and macro low-speed conditions in daily life. This correction factor is approximately equal to 1, so no correction will occur, so classic mechanics will not have much error.

Take an example in daily life

In real life, the speed of civil aviation aircraft is about 250m / s and the speed of light is 3x10 ^ 8m / s. If you put it into the above formula, you can find that v ^ 2 / c ^ 2 is too small, and the time change caused by aircraft movementIt can be ignored, that is, t = t ', and it returns to the field of classical mechanics.

Only when very fast speeds are reached will the speed v have an effect on the factor and thus time.

When v infinite approaches the speed of light, t approaches infinity, and the observer observes that the spacecraft approaches stationary.

the speed of light does not change

In fact, one of the conditions missing in the above proof is the principle of constant speed of light. The principle of constant speed is not what Einstein said, but it was confirmed by Michelson Morey experiments. This problem was discovered when Maxwell studied electromagneticsNow, the Lorentz transformation formula is deduced. The above time expansion effect is one of them, that is, the time transformation between two inertial coordinate systems. It can be said that Einstein picked up a ready-made. In addition to time expansion in special relativity, As well as the above-mentioned mass increase effect, scale effect, and speed change. The scale effect, which refers to the size of moving objects will shrink, will not be derived here, formula: ↓

child's speed-speed change

Understanding what Einstein said, we know that Galileo's speed transformation will no longer apply when moving at high speeds. You need to use the speed superposition formula in Lorentz's speed transformation :

Take the child's speed v and train time speed c into it and you will get the result v + c / 1 + v / c.

But in fact, this result is incorrect. In fact, it is impossible for trains to reach the speed of light. More on this below

Let ’s say that when the speed of the train approaches the speed of light, and when the speed of the child also approaches the speed of light C, we can draw the result: the speed of the child observed on the ground approaches the speed of light, but it cannot exceed the speed of light.

More on the mass increase effect

m0 is the static mass of the object, that is, the static mass, and m is the dynamic mass, that is, the mass of the object changes with the rate.

Through the formula we can get the following curve, or take the civil aircraft as an example, the Lorentz factor is approximately equal to 1, the mass change of the aircraft is negligible, m = m0, when the speed infinitely approaches the speed of light, the mass of the object will be infinite.When the speed of the object is the speed of light, the factor is 0, and the special theory of relativity cannot explain it. This does not exist, so when m0 is not 0, the speed of light cannot be reached, that is, a mass object cannot reach the speed of light.

So this assumption is not true, and the speed of the child cannot exceed the speed of light.

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