Written by | Oak wind
Since the Spring Festival, the physics community has opened a lively "Maxwell's equations" debate [1-14]. We commissioned several teachers to collect some relevant questions, and after listening to Mr. Wang Qing's academic report, we collected a round of questions, and this article will be developed in the form of "questions and answers".
1
Hit the core hotspot directly
Question 1: In order to satisfy everyone's curiosity as soon as possible, we go straight to the core. In this section, try to go into the details and ask the most critical questions about the hot spots that everyone is most concerned about. First of all, for the majority of physics teachers to ask: Is Maxwell's equation system still correct? Should I change it when I teach?
Answer: So far, Maxwell's equations (Figure 1) are certainly right, and they have always been! Teachers don't need to change their classes.
Question 2: Thank you for your clear answer! Is the extended Maxwell equation proposed by Academician Wang in his first article right or wrong? If so, what does it have to do with the original Maxwell equation? If it's wrong, what's wrong with it?
Answer: Yes, the main mistake is to modify the partial derivative of time in Equations (15c) and (15d) of Equations 2 to the full derivative form shown in Equation (15e) for equations with two derivatives of time in Max's equations. This is wrong in the theory of electromagnetism.
Question 3: Since it is wrong, how did Academician Wang get his equations? I read the (Douyin) news of the Institute of NanoEnergy that the conditions for the establishment of Maxwell's equations are based on static media, and not strictly on dynamic media, is that right?
Answer: Academician Wang's extended Maxwell equations are equivalent to Galilean transformations of Maxwell's equations on the medium. The news report said that "the dynamic medium is not strictly established" is actually the meaning of the first sentence of academician Wang's first paper abstract, which is wrong. Even when the medium is in motion , Maxwell 's equations , both in integral and differential form , are still strictly valid and are not allowed to be extended in a real sense. It's just that some terms in the system of equations, such as the electrical displacement vector, the strength of the magnetic field, and so on, need to increase the effect of the dielectric velocity. The equations of matter (also known as constitutive relations) also require some corrections. These corrections should be obtained by the Lorentz transform, not the Galileo transform.
Question 4: Could that be the case? Although Academician Wang's extension equation is wrong, it can still be applied in a similar way?
Answer: Because the extended equation given by Academician Wang is based on the Galilean transformation, the question becomes when can the Lorentz transform be approximated to the Galilean transformation? Maybe we'll discuss this more closely later. Even if the approximation holds, the extended equation is actually only a deformation of Maxwell's equations, that is to say, Maxwell's equations are still correct, but they are changed to a display form, not an extension. For the reason on which the so-called extension depends, namely that Maxwell's equations cannot describe the medium of motion, is wrong.
2
The original source of Maxwell's equations
Question 5: After directly hitting the core hot questions above, let's start a more detailed discussion step by step. Our readers also have many non-physics majors, so I'd like to start with the basic Maxwell equations. Many engineering courses, such as microwave engineering, electromagnetic fields and electromagnetic waves, and optical engineering, will talk about Maxwell's equations in the first chapter of the textbook. What is the difference between what is being learned here and what the physics major is studying?
Answer: All of these lessons will deal with a fundamental set of field equations that electromagnetic sites must satisfy, Maxwell's equations, which determine the behavior of electromagnetic interactions. Because the various applications of electromagnetic phenomena are very extensive, engineering majors often focus on a few specific application directions when learning related content. They will start from the basic Maxwell equations, step by step to derive the basic equations in a particular direction, and then from these equations, discuss and establish a theoretical framework, while our physics major emphasizes a general physical understanding of Maxwell's equations and their applications.
Question 6: Mr. Yang praised Maxwell's equations as one of the ten major equations that have influenced the world. This article may be of interest to many non-physics readers, so please forgive me, some of the questions are more basic. Tell us what part of Maxwell's equations occupy in the theoretical system of physics. Are there other equations with similar status?
Answer: There are two types of basic theories in physics, one is a general theoretical framework, the other is a theory of fundamental interactions, and the two are not very comparable. For the former, the three major mechanics of the four major mechanics of theoretical physics studied by the university physics major: analytical mechanics, statistical mechanics, and quantum mechanics all belong to this category, and there will be quantum field theory and so on. For the latter, because at present only four basic interactions are found in nature, and each basic interaction has a corresponding set of scientific theories, in this sense, the theory of electromagnetic action and the theory of gravity, the theory of strong action, and the theoretical status of weak action should be the same. It is just that electromagnetic action is the closest to the daily life of our ordinary people, and our classical electrodynamics is precisely the theory that describes the electromagnetic action of the macroscopic world in which human beings live every day, and in this sense it occupies a unique position in the theoretical system of physics. One would argue that the theoretical framework for space-time, special relativity, is very important. I completely agree with that. It is important to emphasize here that, because of its incompatibility with Maxwell's equations, Newtonian mechanics was forced to expand and evolve into special relativity. Special relativity is now also a compulsory part of electrodynamics in our physics department.
Question 7: From the point of view of physics, can it be said that Maxwell's equations have included both observed and temporarily unobserved electromagnetic phenomena? I think of Lord Kelvin's remark about two dark clouds, is it now that some physicists think that the problem of studying electromagnetic fields is to "calculate" Maxwell's equations in different systems and assumptions?
Answer: Yes. If the electromagnetic phenomena you say are not included, it means that Maxwell's equations are "wrong", and there is a page in my report that says "not right", at which time, "new phenomena" and "new physics" appear! Unfortunately, Maxwell's equations have so far been correct!
Indeed, many people think that solving Maxwell's equations can solve all electromagnetic phenomena. I used to have a somewhat similar view, at least non-committal. Later, I taught two related courses, one was electrodynamics, the other was the second book of Feynman physics, which was mainly electromagnetics, and after the implementation of Socrates' midwifery teaching model in the class, I felt more and more that it was not so simple in the rounds of mutual discussion and debate with the brightest students in China. In addition to being organically integrated into many of the most cutting-edge research advances in electrodynamics, our understanding of electromagnetic action is not only the mathematical form of the partial differential equations of Maxwell's equations written down, but also involves its interpretation and understanding. They directly determine how we describe the natural world in terms of this system of equations. The real, real problem is the "constitutive equation," i.e., how to relate matter to electromagnetic fields.
Question 8: As a melon eater, I began to dream of the "wrong" scenario of Maxwell's equations, please tell me specifically how it is "wrong"?
Answer: As I said, only when "new phenomena" occur that Maxwell's equations are likely to change, and then "new physics" appears. The first step here is to define the "new phenomenon". By "new phenomena" I mean that in some cases, Maxwell's equations, no matter how deformed, cannot describe the phenomena seen; in other words, in this case, the experiment no longer corresponds to the theoretical predictions of Maxwell's equations. In the macroscopic world, only two possible "new phenomena" are known: the discovery of magnetic monopoles in nature; the masses of photons or coupled to other fields (e.g., dark photons, axions...). ）。
Question 9: Magnetic monopole, photons have mass, very longing, can we see the new phenomenon "dark clouds" now? If photons have mass, should the theory of relativity be modified?
Answer: The true magnetic monopole in the new phenomenon has not yet been found. At its core, special relativity is the confirmation of a finite rate of propagation of a limit signal in flat space-time independent of the selection of an inertial reference frame, which is also the velocity of motion of all zero-mass particles. If a photon really had a tiny mass, relativity would not need to be modified, but the speed of light that would appear in special relativity would no longer be the velocity of a mass photon (because once a photon has a non-zero mass, its velocity will no longer remain constant and can change), but the velocity of other massless elementary particles in nature.
3
On the expansion and deformation of Maxwell's equations
Question 10: So far, I think I have clearly answered the questions that the melon-eating masses are most concerned about. Let's go into some more depth. Obviously, as you said, Maxwell's equations are still correct, but its extension is not correct, and you mentioned earlier that it can be deformed after taking an approximation, so is it possible to have deformation without approximation? Isn't that an extension?
Answer: Deriving deformations is ok, but with special care, with definitions, and more precisely as "equivalent deformations". It means that Maxwell's equations are essentially unchanged. In the sense of common sense, there is no expansion, and it is necessary to take the side of the sword, and the more appropriate one can only be "equivalent deformation", rather than called expansion. Forcing the use of the word extension additionally involves extending the extended understanding, resulting in semantic ambiguity and ambiguity, so in the subsequent statements, in order to avoid misleading, the correct expression is called deformation, and should no longer be called expansion. On another note, the field variables in various deformations are generally redefined. When applied, it is easy to equate these newly introduced field errors with the fields in the original Maxwell equations, which can be a big mistake.
Question 11: Thank you for your answer to Academician Wang's equation, I understand. Either it doesn't expand, or it's a deformation of Maxwell's equations. But I've heard that there are a lot of details in this that people who do physics don't approve of? Did you also classify the deformations of Maxwell's equations? What do you divide it according to? Is it possible to have different divisions?
Answer: You're right! I was passively involved in this discussion of Maxwell's equations. As a physicist and having taught electrodynamics for more than 30 years, I have been questioned by others since the equations of Academician Wang came out, especially the aforementioned questions of "whether Maxwell's equations are correct or not", or "it may not be right in the case of medium motion". This touched my bottom line and had to come out and deal with it head-on. I've sorted through the work in some detail, so I've mentioned understanding in the titles of my previous two articles[7, 8], which may mislead readers into thinking that I recognize and support extension. According to the acceptance of those who do physics research, I divide the deformation classification of Maxwell's equations into three levels: the standard theoretical physics mode, the primary deformation mode, and the secondary deformation mode. (Note: The word variant was not introduced in my report because I wanted to cite as few new words as possible.) I directly wrote the current deformation as an extension when grading, I thought that after talking about it, everyone would know what my extension refers to, and the feedback obtained from the report found that everyone was more confused. So here I emphasize at the beginning that expansion is wrong, and all that can be allowed is deformation. If other alternative interpretations emerge later, they will either be incorporated into the existing divisions or add new hierarchies. The advantage of this division is to draw a clear boundary, strip away the cocoon, and facilitate a detailed discussion of "Is this deformation ok?" "Why doesn't that deform?"
Of course, there can be different divisions. In fact, how to divide itself is not very important, what is important is to let everyone see that people's various understandings of deformation will have different levels, and it is this hierarchical difference that has created today's controversy. The most important, fundamental, and highest of the layers is Maxwell's equations themselves, which are the common basis and starting point for our current discussions. In my division, the lower the level, the more it deviates from the usual habits of doing physics, especially theoretical physics, and the more unacceptable it is.
Question 12: Our questions were collected, and the questioners were "insiders". I feel like the next question is going to be "getting better". Let's start with the basics. What is the Lorentz transform? What is the Galilean transform? Can you elaborate?
Answer: The Lorentz and Galilean transformations refer to the mutual transformation relationship between the space-time coordinates of one reference frame relative to another reference frame and various physical quantities, that is, given the space-time coordinates of a reference frame and certain physical quantities, how to obtain the values of these quantities in another reference frame that does uniform motion relative to it. The Lorentz transform is a linear transformation that keeps the speed of light constant and also keeps Maxwell's equations invariant; the Galileo transform is a linear transformation that keeps the classical Newtonian second law unchanged, and it does not guarantee the speed of light and the maxwell equations.
Question 13: Echo the previously unexplained question about transformation. With Maxwell's equations as a common basis, should the deformed Maxwell equations be transformed by the Galileo transform or the Lorentz transform? Or is it okay to change both?
Answer: Of course, the Lorentz transform should be taken, and the Galilean transform is not allowed in the strictly correct sense, because it violates the covariance of Maxwell's equations, and it is not allowed to do the v/c expansion of the lorentz transform only as a simple Lorentz transform, retained to the first order. Only by adding an additional condition, i.e. that x/t and velocity v are of the same order in the problem under consideration, is a permissible approximation.
Question 14: Starting from the common basis of Maxwell's equations, adding the same term on both sides of the equation seems to be able to add arbitrary terms? So what's the point of adding these same things?
Answer: I don't think it makes sense, it's all about putting together a specific deformation term on one side of the equation. Without this requirement, you can add items at will. Although the deformation of a particular term is added in this way, it seems that there will be a term on the left side of the equation corresponding to the velocity fork multiplying magnetic induction intensity, and there is a correspondence with the Lorentz force density force received by the unit charge, but these do not explain the deeper problem. I subjectively reject and dislike this deformation, and the reason why it is listed is entirely because this expression already exists.
4
The nature of the electrodynamics course and questions from the middle school teacher
Question 15: The next question is related to teaching, but there are also questions from secondary school teachers. The teacher asked you what kind of knowledge is "electrodynamics" taught at Tsinghua University? What are the core questions it studies? What role can it play in students' subsequent learning and research? What impact might the "Maxwell's equations extension" have on the teaching of electrodynamics?
Answer: Electrodynamics is one of the four major mechanics courses in undergraduate theoretical physics majoring in physics, and it is also a basic theoretical course in many engineering disciplines. It introduces the basic laws of electromagnetic interaction in the macroscopic world and describes its theoretical framework and basic calculation methods. The electrodynamics I taught at Tsinghua is a 64-hour course, which mainly discusses the general laws of electromagnetic phenomena, the steady-state and rapid behavior of electromagnetic fields over time, and the embodiment of electromagnetic action in matter.
Since among the four basic interactions that human beings have discovered for the natural world, electromagnetic interaction is the only basic interaction most closely related to human daily life, this science provides learners with an understanding of various physical phenomena in the surrounding macroscopic nature in which they live from the most basic interaction level, laying a scientific foundation for their subsequent further study and research in all directions. In addition, this course also exercises students' ability to apply advanced mathematics to deal with a variety of complex field distributions and the interaction of matter with fields.
This incident first means that the content of electrodynamics is not outdated, it is at least closely related to cutting-edge application developments, otherwise there would be no controversy today; second, it also means that the teaching of electrodynamics in colleges and universities around the world has not been very successful so far, and it has left a lot of ambiguous problems that have caused today's controversy.
Question 16: Curious, is there any difference in depth and breadth between "electrodynamics" studied at Tsinghua University and "electrodynamics" studied in other physics departments of other universities?
Answer: Even at Tsinghua University, there are completely different types of electrodynamics courses, as far as I know, there are at least four of them, and the electrodynamic goals of different teachers are different, and our physics department has opened two courses. This one I taught was for physics majors, and the other was for non-physics majors. My course is characterized by a relatively deep and extensive discussion of physics, and I often joke that it is the most difficult (not one of the most difficult) basic physics theory courses for physics undergraduates, and it is less involved in specific applications. Similar courses offered by different universities and majors will arrange teaching content according to their talent training goals.
Question 17: How did your electrodynamics class discuss the question of a possible "new phenomenon" that has not yet been proven? Why is this teaching in mind? Is there any consideration for connecting with the content of subsequent courses?
Answer: We have discussed in our class what kind of situations photons may have mass, discussed the whimsy of magnetic monopoles at different times, and discussed the performance of topological terms (axis children) ... These questions not only caused heated discussion among our classmates in the classroom discussions, we also specifically tested them in the electrodynamics exam for the spring semester of 2022 this year. The purpose of this is to let students know that in this classic electrodynamics class, which is often criticized as old, there are hidden roots and seeds of cutting-edge new advances. Considering that subsequent courses may be diverse, it is difficult for this course to make a proper special articulation. Our response is that in this course, all the in-depth content involving frontier or successor courses must form a self-consistent framework that is self-justified in classical electrodynamics and does not rely on successors. We introduce and discuss only those elements that can be clearly explained in terms of the concepts and methods used in this course, and pay special attention to the introduction of these contents without using new concepts and mathematical means beyond the scope of this course.
Question 18: In addition to a little understanding of electric and magnetic fields, you also mentioned polarization and magnetization, please explain it briefly.
Answer: Polarization and magnetization refer to the response of matter to external electric fields and magnetic fields, which are embodied in the fact that the atomic and molecular components of the material are affected by the external electromagnetic field, forming some small electric dipoles and magnetic dipoles. These responses are described in electrodynamics with experimental observable measurements such as polarization intensity and magnetization intensity, which are electric dipole moments per unit volume and magnetic dipole moments, respectively.
Question 19: When you talk about the differential and integral forms of Maxwell's equations in the textbook, you say that uncertainty is encountered when calculating some problems, can you give a simple example? Does this mean that Maxwell's equations are not well formed?
Answer: These are two examples given by Feynman in chapter 17, section 2 of his Book of Feynman Physics, in which the loops of the integrals are not well defined, making Maxwell's equations in integral form inconvenient to discuss. This does not mean that Maxwell's equations are imperfect, but that the representation of your chosen Maxwell equations is technically difficult to describe the problem you are dealing with, and you just need to change the form of expression.
Question 20: Feynman's discussion of electromagnetic field theory was mentioned in your report, and I will give you an example of whether you can see if I understand it correctly, such as when I wave a magnet in my hand, and the magnet should also move with the magnetic field around it?
Answer: It is this image, which is the magnetic field of motion that Feynman mentioned in my report.
Question 21: Why does Feynman think that I am not correct in this understanding? Can you explain?
Answer: Feynman believed that the magnetic field of motion was equivalent to the magnetic field seen standing on a moving magnet (let's call it a comorbid system), and this magnetic field would be very different from the magnetic field we see from the laboratory system where we watch the magnet move, because there is only a magnetic field in the combo operating system, and there will be an electric field in the laboratory system. Feynman believes that the phenomenon of electric field will actually emerge from the movement of this magnetic field, which is a negation of the concept of magnetic field motion, because the implication of saying "magnetic field in motion" alone refers to the fact that there is only a magnetic field and no electric field in the entire system.
Question 22: Why is there so much emphasis on the independence of space and time? If time and space are independent, does it contradict the view of relativity?
Answer: Emphasizing the independence of time and space is a requirement in a specific reference frame, and the reference frame transformation only replaces the old space-time independent coordinates with a new set of independent space-time coordinates.
Question 23: In the teaching of physics in secondary schools, we often encounter the concept of electromagnetic fields [14, 15], can you briefly talk about inductive electromotive forces and inductive electric fields, dynamic electromotive forces and dynamic electric fields from the perspective of the knowledge system of middle school physics teachers? Some middle school physics teachers have noticed the discussion of "kinetic electric field" in the relevant discussion, and they have not understood it, can not say that the kinetic electric field?
Answer: Induced electromotive force and induced electric field are generated by a changing magnetic field, which is generally not disputed. The problem is that the dynamic electromotive force generated by the movement of the circuit is the field corresponding to the Lorentz force density per unit charge, and it is exactly the electric field seen in the loop communion system at the first-order expansion level of the Lorentz transformation to v/c. People do not use the term kinetic electric field, because in electromagnetic action, there are only two physical sources of electric fields, one is from the charge, and the other is from the magnetic field changes over time; there is no electric field that is really generated by the circulating circuit, or the circuit movement does not constitute the real physical source of the electric field. It is just an effective electromagnetic force density per unit of electricity in the laboratory system, and in the follower system, you will find that the electric field there is still the corresponding charge source and magnetic field change in the follower system.
Question 24: The more the truth is debated, the more clear the truth, in a sense, the discussion of The Mai's equation has set a good example for us, and some basic theories can be boldly questioned and discussed, and through your articles and lectures, I have a clearer understanding of this matter. The least effect of this event can prompt pedagogical thinking on electrodynamics and the reinterpretation of Maxwell's equations by physicists. Do you think our young talents need this spirit of questioning? Or how should it be questioned?
Answer: I very much encourage young people to question, science cannot progress without questioning. The classes I teach now, including Feynman physics in the first year of undergraduate, electrodynamics in the third year, and quantum field theory in graduate students, have evolved to completely guide or provoke students to question everything they have to learn from beginning to end. In this process, both my classmates and myself have been greatly exercised and improved, and I have a deeper understanding of the content of the course. I feel that being rational and focused on academia is the first principle that needs to be observed in question.
Questioner: Thank you very much for your patient and helpful answer.
Acknowledgements: This article was organized and organized by Chao Shichen (pen name). Thanks to the interviewers Du Gongbu (pen name) and Chao Shuchen for their work. Thanks to Mr. Ren Weidong of Beijing Chaoyang District Institute of Educational Sciences for organizing middle school teachers to provide relevant issues in the teaching and research of secondary school physics (Mr. Liu Qinghua of Chaoyang Branch of Renmin University Affiliated Middle School, Mr. Li Zhaofeng of Affiliated Middle School of University of International Business and Economics, and Teacher Zhang Junke of Chaoyang Branch of Tsinghua University Affiliated Middle School participated in the discussion).
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Special mention
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