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Talking about the Galilean transform in Maxwell's equations is naturally approximate, so this is not suitable for extension.
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This video was released on March 11, 2022 and has reached 63,000 views
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Recently, a big news in the Chinese scientific community is the famous nanoscientist Wang Zhonglin, a foreign academician of the Chinese Academy of Sciences, announced the expansion of Maxwell's equations, published in the materials science journal "Materials Today".
On January 13, 2022, the Beijing Institute of Nanoenergy and Systems of the Chinese Academy of Sciences, of which Wang Zhonglin is the director and chief scientist, held a major original scientific achievement conference and released the results to a number of media, including CCTV, People's Daily, China Daily, China Science News, etc.
Academician Wang Zhonglin
However, the response to this incident in academia has been very wonderful. I hardly see a single theorist agree with this, and there are many who question it. On January 17, the "intellectuals" released several scholars' questions about this, as well as Wang Zhonglin's written reply to this (controversy | Academician Wang Zhonglin "Expanding Maxwell's Equations", what does the academic community think? ）。
In my opinion, first of all, the academic controversy that has come and gone is a good thing. Then, after reading the discussions of both sides, I also had my own preliminary judgment. An excerpt from Wang Zhonglin's reply is as follows:
Experts question one
The electrodynamics of moving media is the problem that Einstein wanted to solve 117 years ago, and thinking and researching on this problem led to one of the greatest discoveries in the history of physics, the birth of special relativity. But this problem has been completely solved by Einstein, and the electrodynamics of moving media has long been written into textbooks.
Wang Zhonglin responded:
The theory of relativity is a great theory. And our proposed extended Maxwell equations do not contradict special relativity. Special relativity describes the different observations brought about by the simultaneous observation of an electromagnetic phenomenon occurring in the A reference frame and two different people in the B reference frame in motion, that is, two observers of one electromagnetic phenomenon. In this case, the expression of Maxwell's equations in both coordinate systems is unchanged. However , the extended Maxwell equations describe the results of two different and possibly related electromagnetic phenomena occurring in the A reference frame and the B reference frame in motion being observed by the same person in the A reference frame , i.e. two associated electromagnetic phenomena by one observer , and assume that the speed of the medium is much smaller than the speed of light. Figure 7 in the original text makes this distinction very clear. Landau and Lifshitz's book discusses the situation under special relativity, while we discuss the latter. On page 4 of our article, the earlier paragraph of Formula (14a), we clarified the boundary conditions and assumptions, and for moving objects far below the speed of light, the Galileo transformation can be processed with the equation system. At this point, it is possible that the processed system of equations does not have covariantity, but does not affect the specific object we are going to study and its application in engineering, because we are not strictly discussing field theory.
I'm far from an expert in this area, but I can understand the basic meaning. Maxwell's equations are the basic equations of electrodynamics, and the results must be approximated by using the Galilean transformation in electrodynamics, so Wang Zhonglin's research should be an approximation of Maxwell's equations in some cases. This may indeed lead to a more convenient form of application, but this should not be called extension, but should be called application.
In general parlance, extension means that a theory could not have covered a situation, and now you add something to the theory so that it can cover that situation. Maxwell's unification of traditional electromagnetism into his system of equations is such an extension. Because he proposed the concept of displacement current, which was not originally there, but was confirmed by later experiments. This is a revolutionary breakthrough. What Wang Zhonglin did was to use the existing universally applicable system of equations to some special cases, and then make some approximations, which should be a normal application, and it is quite misleading to call this extension. The premise of all this is that his derivation is correct, and if there is any mistake in it, it is even more impossible to mention.
For those who have studied electrodynamics, the above discussions should be clear enough. For those who haven't studied it, I'll explain it a little bit.
The Galileo transformation refers to the coordinate transformation in Newtonian mechanics, i.e. if the relative velocity of motion between two frames of reference is u, then the relationship between the velocity of an object in frame of reference 1 and its velocity v' in frame of reference 2 is:
v' = v + u。
For example, if a train is moving at a speed of 100 km/h relative to the ground, and you are moving at a speed of 5 km/h relative to the train in the train, and the two speeds are in the same direction, then your speed relative to the ground is 105 km/h.
That sounds like complete common sense, right? But the real point is that this common sense is wrong! To be precise, this common sense is only approximated in the case of low-speed movement, which means much lower than the speed of light.
What if it's close to the speed of light? Then the Galileo transform would cause serious errors, and the correct velocity relation would be the Lorentz transform:
v' = (v + u) / (1 + uv/c^2),
where c is the speed of light. As you can see, when both u and v are much smaller than c, the Lorentz transform is approximately equal to the Galileo transform. But when u or v is close to c, the difference between the two can be great.
For example, taking u and v are equal to c/2, that is, A moves at half the speed of light with respect to B, and B moves at half the speed of light with respect to C, so what is the speed of A relative to C? The Galileo transform yields the speed of light, but the Lorentz transform yields (1/2 + 1/2) / [1 + (1/2)^2] c = 1 / (5/4) c = (4/5) c! It is often asked that if two people walk in opposite directions, and each person's speed relative to the ground is c/2, is the relative speed between them c? Now you know, the answer is (4/5) c.
Another example is to take v = c, at which point you will find that no matter how much u is equal to, v' is equal to c. Because the numerator is C + u and the denominator is 1 + u/c, they always get c when divided. This means that the speed of light relative to any frame of reference is c.
You'll also find that no matter how u and v are valued, v' will never exceed c. For example, taking u = v = (2/3) c, the Galilean transformation yields v' = (4/3) c, while the Lorentz transform yields v' = (2/3 + 2/3) / [1 + (2/3)^2] c = (4/3) / (13/9) c = (12/13) c. It is often thought that when two people go in opposite directions at a speed of (2/3)c, their relative speed will exceed the speed of light, and now you understand that this is wrong, right?
You might ask, lorentz transform is so counterintuitive, why should you believe it? The answer is that it's backed up by experimentation. In fact, the Lorentz transform is thought of because Maxwell's equations satisfy the Lorentz transform, not the Galileo transform. That is, there is a clear contradiction between electrodynamics and Newtonian mechanics. Which one to believe? This can only rely on experimental judgments. For more than a hundred years, countless experiments have proven that the Lorentz transformation is correct.
In fact, this is the basic idea of special relativity, that the laws of physics should be unchanged under the Lorentz transform, not under the Galilean transform. Maxwell's equations naturally satisfy the theory of relativity, while Newtonian mechanics does not satisfy the theory of relativity. What Einstein did was to transform mechanics with the requirements of relativity.
Now do you understand? Talking about the Galilean transform in Maxwell's equations is naturally approximate, so this is not suitable for extension.
Finally, let me quote a comment by Dai Xi, chair professor of physics at the Hong Kong University of Science and Technology(HKUST), | Academician Wang Zhonglin "Expanding Maxwell's Equations", what does the academic community think? ）：
The road of science is arduous, as long as people are not gods will make mistakes, this is nothing, what really bothers me is that a large Institute of Nanoenergy of the Chinese Academy of Sciences, why can no one remind him? Before such a big publicity was promoted to the public media, why didn't the Academy of Sciences consult the relevant units in the academy, such as the Institute of Theoretical Physics or the experts of the Institute of Physics? Without an effective error correction mechanism, how to ensure that the scientific research funds invested by the state every year are put into good use? These questions deserve the deep consideration of the management of the Academy of Sciences.