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

The original title: "do you understand the reference frame and inertial frame?" "

With regard to the definition of the reference system, it is very simple, that is, an object that is used as a reference for the study of the motion of an object. As for what kind of inertial system, it is also very simple: if an object is not affected by the outside world, if it remains at rest or moves in a straight line at a uniform speed, then its reference frame is the inertial frame.

Purely by definition, it seems a little too simple. Here are two issues that readers are concerned about.

The first question: can you look outside the frame of reference? The simple answer is: no!

But the formulation of the problem itself is easy to be misunderstood.

Some people may ask: the object chosen for the frame of reference is not necessarily an airtight space-for example, the cabin, it can also be a bird flying in the air. How can a bullet fired from a pistol be distinguished from inside and outside?

This rhetorical question shows that the definition of the reference system is not understood.

The frame of reference is an abstraction of an object. Mathematically, it is represented by a coordinate system fixed on the object. The coordinate system is determined, which means that the measurement of space and time is determined, including the starting point and interval between time and space.

Therefore, when people say "don't look outside the frame of reference", what he really means is: you can only use that definite spatio-temporal coordinate frame, not beyond that frame. In other words, all your observations must be relative to the frame of reference.

In fact, the frame of reference does not limit your scope of observation.

On the contrary, you can see anything based on the frame of reference. For example, with a moving car as a frame of reference, you can certainly observe anything inside and outside the car. In fact, since you have chosen an object as a frame of reference, you require that any observation you make must use it as a reference, that's all.

So, when you choose a ship as a reference, you can see anything through the window, but you can't stick your head out and look back at the ship itself from the outside, because in that case, it is no longer a reference, but a moving object being studied. But you can look out of the window at everything, including the flowing, receding banks of the river, the birds still in the air, which is your freedom.

The most straightforward example is yourself, you observe the world, in most cases, is based on your own frame of reference, at this time, your eyes are not looking at the things outside you?

Therefore, after the reference frame has been selected, "cannot look out" means "cannot go beyond the reference frame", or "cannot select multiple reference systems", not "cannot look out into the space".

In fact, there is another reason to misinterpret "you can't look out" as "you can't look out of space". This is related to people's misunderstanding of the inertial system.

I'm sure you all know what an inertial system is, right? Its definition was mentioned earlier. Special relativity holds that all physical laws are equivalent in all inertial systems. If you still don't understand, you can refer to the previous article "what is the inertial system?" .

Suppose you are in a closed inertial reference frame, such as the "Salviadi" ship mentioned by Galileo. Since you can't see outside, you really won't find any information about the speed of the ship. For this reason, in order to ensure that the statement "you can't get any information about the speed of your inertial system from observation" is correct, some people are used to adding: "as long as you don't look out."

But in fact, this is a wrong understanding, according to the principle of relativity: there is no special inertial system! In other words, there is no absolutely motionless frame of reference.

Therefore, you cannot obtain the absolute speed of your inertial system by any means. As for you to observe the outside to get the relative speed of your reference system, of course you can!

Such being the case, there is no need to restrict a person from looking out through the cabin window. When he looked out, he only found that the ship was sailing at sea, but he never knew the absolute speed of the ship in the universe. In fact, this absolute speed does not exist.

However, if the airtight object itself has acceleration, even if you don't look out, you can feel the force, so you can still find clues to the motion of the frame of reference.

Therefore, the so-called "inside and outside of the frame of reference" does not mean "inside and outside the space", but "whether it exceeds the limit of a frame of reference". After choosing the only definite frame of reference, your observation is not limited as long as the reference is not used as the object of study.

The second question: does covariance mean that nothing changes? If there is a change, how to perceive it? The laws of physics are equal to all inertial systems, which is the principle of relativity in physics.

The principle of relativity requires that the form of physical laws remain unchanged, that is, the so-called covariance. It means that all physical quantities involved in physical laws change in coordination to ensure that the relationship between them remains the same.

For example, the kinetic energy theorem

When changing different inertial reference frames, the changes of kinetic energy and the work done by external forces are different, but they must maintain a consistent relationship with the above. This is the covariance of the kinetic energy theorem.

Therefore, the principle of relativity does not require that what you see remain the same! In fact, except for the invariants such as rest mass, charge and speed of light, other physical quantities will change in different inertial reference frames.

So, can this change be seen by people in the frame of reference?

I can't!

For example, if you stick your head out of the smooth cabin and look at the river bank, you can see that the river bank is retreating, the clouds are drifting back, the birds are flying towards you, but it is constantly moving away from you!

However, you can only see this phenomenon now, because you are limited to this frame of reference! Your mental judgments of "still riverbank", "motionless white clouds" and "birds flying towards you" are not based on the current frame of reference, unless you choose another frame of reference. But there can only be one frame of reference. Therefore, you cannot compare the results you see now with other reference systems and find the differences between them.

For example, someone said, "I remember Bolt's fastest speed of 100 meters was 9.58 seconds, and now I see that he ran at a speed of 7.58 seconds, which shows that my frame of reference must be moving relative to the ground."

In this statement, the 9.58 seconds mentioned by the observer is not measured in this frame of reference, but something in his memory, but physics is only concerned with the present. Therefore, his comparison is beyond the scope of physics.

Therefore, the changes caused by different inertial reference frames are seen by the bystander standing outside the reference frame-the person with the sharp weapons of Galileo transformation or Lorentz transformation. For an observer in an inertial frame, those changes relative to other reference frames are transparent-he cannot know.

So the question is, since what is in memory is not physics, why does the principle of relativity emphasize the invariance of physical laws in the inertial reference frame? Because the laws of physics are also things in memory, there is no point in emphasizing them.

Wrong! The laws of physics are not in memory! It is the natural law of all the objects in front of you at the moment. It is always there and does not depend on your memory. In other words, as long as you are smart, observant and methodical, you can derive these physical laws from the physical phenomena in front of you.

In philosophical terms, the laws of physics are objective!

The laws of physics must declare the equivalence of all inertial reference frames in a hypothetical way. And the reason why we can't detect the absolute motion of the inertial system by doing any physical experiment is that when we verify those physical laws, we find that those laws are the same in any case. The laws of physics are the same whether we are on the ground, on the ship, or on the plane!

This article is from the official account of Wechat: University Physics (ID:wuliboke), by Xue Debao.

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