High School Relativity Problems, High School Relativity Problems Solved

In physics, this problem is called the twin paradox. Astronauts will find that their peers on Earth have become old men because the spacecraft is a non-inertial frame. The premise of special relativity is "in an inertial frame", we can think of the earth as an inertial frame, but the spacecraft will inevitably accelerate and decelerate during takeoff and landing.

To use the general theory of relativity to answer, the spacecraft must have acceleration from leaving the earth to returning to the earth, and there is inertial force with acceleration, and the inertial force is equivalent to gravity, the stronger the gravitational force, the slower the time, so the time on the spacecraft is slow, the gravitational force on the earth is relatively small and negligible, and the conclusion is that the earthlings are older.

It is true that the two people feel that each other's time is slow, but there is no contradiction. Since the special theory of relativity is only for inertial frames, it is impossible for the two to return to Earth (which requires an acceleration process), and there is no question of who is getting old when they return to Earth. As for if there is acceleration, that's a matter of general relativity.

As answered upstairs, I won't repeat it.

Slowing down just means that the events you see on the other side are slowing down, because it takes time for events to travel to your eyes, and you are getting farther away and taking longer to propagate.

Your problem is going back to Earth, when you go back to Earth, how many years older are you, and how many years older are the people you know.

If you ask that, you know that you are just applying some theories mechanically, without understanding yourself.

It is true that moving objects slow down in time, which is mentioned in the book and is well understood.

As for this topic, the rocket is moving at high speed, but for the people on the rocket, then in fact, the rocket is stationary, and the ground is the high-speed departure arrow, that is, for the people on the rocket, the ground is moving at high speed, so the clock on the ground moves slowly. On the contrary, people on the ground will feel that the clock on the rocket is slow.

This is indeed also a question of the frame of reference, with the person on the rocket as the frame of reference.

Isn't there a movie clip where a guy has been flying on a spaceship, and when he comes back to Earth, his brother finds himself more than ten years old, and he's still very young.

These are a bit winding, but you can understand it when you look at it.

That's right, if you look at the rocket, the ground is moving, so you see that the clock on the ground is moving slowly. It's all about the frame of reference.

The person on the rocket saw the clock on the ground slow down, and the person on the ground saw the clock on the rocket slow down.

It is a problem with the frame of reference, because motion is relative (principle of relativity) When the observer on the rocket observes the ground clock, he uses the rocket as the frame of reference, then the ground frame of reference is in motion at this time.

Albert Einstein, an ancient, didn't understand the theory of relativity, and he didn't understand the problem.

If the spacecraft is flying west and east at infinity, the parallax is negligible, and the velocity is approximately sum; If the spacecraft is facing the observer, the event at a distance of 1 light-second will be seen by the observer after 1 second, when the spacecraft has been flying for 1 second, let the distance x, this event is observed at (1-x) seconds, substitute the observation, the distance x divided by the motion time 1-x, and the solution is x=3 8c.

In the same way, the actual velocity of the comet is calculated, and the addition of the two velocities is the relative velocity in the physical sense.

The ground line-of-sight is calculated using (.

The apparent velocity on the spacecraft is also calculated in this way, note that if the relative velocity is exceeded, you will not see the object flying closer, but will see the object moving away in both directions.

Einstein only deduced the case of distance, and he also miscalculated, and deduced the case of proximity, and I don't see anyone else, they think that they can replace the case of proximity with the case of distance.

In addition, since air is a light medium, if the air moves relative to the ground, it will affect the visual effect. Einstein did not know, and there may still be people who do not know, or do not admit, or perhaps do not think that the discovery of optical media will have a huge impact on the theory of relativity.

If you don't think that absolute time exists, you won't be able to get a recognized result. Because science is an objective law, and it is not science if it is not an objective and recognized result.

Neither infinity nor almost towards the observer, there is a component of the speed of light to consider, which Einstein and his disciples did not take into account.

The teacher who made the question didn't know how to understand it, so I couldn't guess his answer, but it was definitely one-sided. I can make a lot of results with sound experiments. Sound experiments also have relativistic problems, and at the same time they are relative.

(2) The state of the spacecraft at t0 t 0 0 is regarded as one event, and the collision between the spacecraft and the comet is regarded as the second event Both events occur in the same place in the S system (i.e., on the spacecraft), and the observer on the spacecraft measures the time interval between the two events δt s is longer than the inherent time, and δt can be obtained according to the time delay effectThat is, δt s 5 s, and δt s is solved, that is, judging from the clock on the spacecraft, there is still s of time to allow it to leave its original course

If you directly apply the formula of the moving ruler, it will definitely be because you miss the impact of the relativity of the same time, and the first set of formulas will be fine, there is nothing to say.

The second question is to analyze it in the "language of events": remember event a as the event that occurred at the location of the spacecraft at this time, b as the event that occurred at the location of the comet at this time, and event c as the collision between the two.

Obviously, A and C both happen on the spacecraft, so why can't you use the formula of moving the clock to shorten it directly? Because when you switch to the inertial frame where the spaceship is located, a and b do not happen at the same time, and the distance between the positions where these two things occur in the spacecraft system is not obtained by the ruler shrinkage, but this distance is reduced to 5*( in the preset system. You shorten it with a moving ruler at this point, showing that you don't understand the process of measuring the moving scale.

However, I really appreciate the interest of high school students in the theory of relativity.

Let's start with a physical phenomenon: if you are still holding a gun and shooting, the bullet velocity is the same as when you shoot forward and backward. If you are riding a galloping horse and shooting forwards and backwards, the speed of the bullet on the ground is faster than the speed of shooting backwards, the difference is 2 times the speed of the horse's running speed.

This is easy to understand.

However, at the end of the 19th century, scientists discovered an unexplained phenomenon, if a person on the ground shines forward and backward with a lamp, the speed of light is the same, if a horse shines forward and backward, physicists at that time thought that the speed of light on the ground should be faster than the speed of light backward, but the experimental result is that the two speeds of light are the same. Even more curiously, the same is true for measuring the speed of light forward and backward on horseback (with the horse as the rest of the earth as motion). This is unexplainable in classical mechanics.

Einstein's theory of relativity explains this experiment. Because in classical mechanics, we believe that the time on the ground is as fast as the time on the ground, and the length of the ruler seen immediately on the ground is the same length as the length of the ruler seen on the ground. Einstein's theory of relativity cast doubt on this, and on the basis of rejecting the above "self-explanatory" common sense, the theory of relativity was introduced.

In the theory of relativity, the time measured for the same object is not the same in different frames of reference.

If the horse is running at a constant speed, the problem is special relativity, and if the horse is running at an accelerated pace, the problem is general relativity. According to Einstein's theory, there is no such thing as an absolutely stationary frame of reference (such as the earth), and there is no question of who is at rest and who is in motion between the frame of reference on horseback and the frame of reference of the earth, and the motion is relative. Einstein's theory makes inertial forces, gravitational forces, and so on self-consistent in this theory of relativity.

A coordinate system that strictly follows Newton's laws of motion is called an inertial frame. Coordinate systems that move in a uniform linear line with respect to inertial frames are all inertial frames. Albert Einstein's "In any frame of inertia, all the laws of physics are the same."

It means that the mathematical expressions of the laws of motion (fundamental laws) of objects and matter are the same whether it is mechanics, electricity, optics, etc., and this also includes Einstein's bold assumption in the theory of relativity that the speed of light measured in a vacuum is the same in any inertial frame. This is the central idea of special relativity.

For example, if there are two inertial frames A and B with relative velocity v and their relative velocities are v, then the object obeys f=ma (Newton's second law) in the frame of reference A and f=ma in the frame of reference b as well.

As the central idea of the special theory of relativity, the velocity of the same beam of light, measured with A as the reference frame, is C, and the measured velocity with B as the reference frame is also C. This is known as the principle of invariance of the speed of light in a vacuum.

In the special theory of relativity, the time and space coordinates satisfy the Lorentz law of variation, and the law of output transformation can also be analyzed.

In the general theory of relativity, the spatial tension is equivalent to the gravitational force, so there is also a transformation relationship between the laws of mechanics.

However, for non-inertial frames, the coordinate system of arbitrary motion in classical Newtonian mechanics will produce Coriolis force and centrifugal force, which are related to the speed of motion of the object, so the laws of mechanics are different.

Newtonian mechanics is established on the basis of an inertial frame of reference, and the universality of the non-inertial frame of reference is not considered, so the laws of mechanics derived are not applicable to the non-inertial frame of reference. Special relativity, on the other hand, states that "all physical laws are the same in different inertial frames of reference." It is a four-dimensional transformation under different inertial reference frames based on the Lorentz transform, which considers the relativity of time in different reference frames.

On the other hand, general relativity considers the non-inertial reference frame that is not considered by Newtonian mechanics and special relativity, weakens the superior position of the inertial reference frame and generalizes it to the non-inertial reference frame, that is, introduces the gravitational field effect.

You also have to consider the direction in which the object is moving.

1. Suppose there is a reference system S, so that the velocity of A and B relative to S is equal and let S be at the midpoint of AB, and the time is right before SAB starts, then in the table of S, at a certain time, AB stops at the same time and sends an optical signal to S and the other party, and S receives the signal and learns that AB stops at the same time and the pointer is the same. However, in A's opinion, when he stopped and sent the signal, he had not received the signal that B had stopped, so A thought that the two tables did not stop at the same time, so there is the following :

2. If A is used as the reference system, B's clock slows down, so it takes the longest time. The explanation is as follows: B stops and sends light signals to A and S, and A stops immediately after seeing the signal that B stops, but B has stopped for a while at this time, so A has a long time (the same is true with B as a reference frame, B thinks that it will take a long time to stop at the same time).

But in S's view, AB does not stop at the same time, but B stops first (because it receives B's signal first), so it causes A to take a long time.

This is the relativity of simultaneity, and what appears to be simultaneous in S may not be in A. In the same way, what appears to be a simultaneous occurrence in S may not be in the case of S. Therefore, when looking at this kind of problem, it is important to have a clear frame of reference.

If A is used as the frame of reference, it means that the time measured by Table A is long.

If B is used as the frame of reference, it means that B is counted as a long time.

If we use other frames of reference as frames, it means that the table that moves slowly relative to the frame of reference has a long time [relativity], which means that we should look at the problem ...... relativelyIt's not absolute that the watch is long.