When Chen Muwu was an undergraduate student, the two basic mathematics courses of the physics department, "Advanced Mathematics" and "Linear Algebra," were both included in the compulsory course schedule in the first semester of his freshman year.
So in his subconscious mind, the matrix should be something similar to calculus.
But the reality is far from as simple as Chen Muwu thought.
Although people have begun to study determinants as early as ancient times, it is much later to study matrices as a specialized mathematical subject than determinants.
It is generally believed that the British mathematician Arthur Cayley began to establish matrix theory in the 1850s.
It was not until the mid-to-late nineteenth century that the theory of matrices, as a branch of mathematics, was gradually perfected.
In other words, the formation time of the matrix was later than the time when Maxwell proposed the electromagnetic equations named after him.
Compared with the calculus invented by Leibniz and Newton in the mid-to-late seventeenth century, the matrix is more than two hundred years later.
Overall, the mathematical concept of matrices, which has been around for less than fifty years, is considered an emerging subject for physicists.
Even Heisenberg, who is known as the founder of "matrix mechanics", actually didn't know what a matrix was at the beginning.
That's why when he wrote the paper on harmonic oscillators, he spent a lot of time designing a completely "new" algorithm for quantum mechanics.
But Heisenberg had no idea that he had just "invented" a matrix that had long existed in mathematics.
Then Heisenberg's paper was discovered by Born, who was relatively proficient in mathematics. A few months later, the latter suddenly realized that this new algorithm that reminded him of Heisenberg was actually what he had learned. passed matrix.
So Born took his new assistant Jodan and worked on matrix algebra for a while before finally writing a second paper, which standardized this theory.
As for de Broglie, who became a monk and studied physics halfway through ancient European history, it is normal that he could not understand what Chen Muwu wrote in this paper.
"Chen, how did you find this weird mathematical tool? I'm very curious about education in China now. Why do you know so much more than others?"
Chen Muwu did not dare to take what de Broglie said seriously.
In fact, matrices, a branch of mathematics, entered the Chinese literary world even later.
In 1922, when Chen Muwu had just time traveled, the concept of the matrix was translated into Chinese for the first time and introduced into the country. At that time, it was still called "Zonghengzhen".
Therefore, it is absolutely impossible for him to learn the concept of matrix and the corresponding knowledge in the domestic Jiaotong University school.
Of course, this did not stop Chen Muwu from bragging to de Broglie: "Louis, I only had a brief understanding of the concept of matrix mathematics in China. I actually came into contact with and learned it after I went to Cambridge University.
"You may not know that the founder of the matrix theory, Arthur Cayley, was also a graduate of Trinity College and stayed at the school to become a teacher. Therefore, the library of Trinity College has a wealth of books on the matrix. I think it would be easier to understand matrices.
"But France is also a strong country in mathematics, and you are so smart. I think if you want to learn matrices, it should be easy."
De Broglie was doubtful: "Okay Chen, since you have said so, I will go find some books to read tomorrow."
Finally managing to deal with de Broglie, Chen Muwu jumped into the water again and started swimming.
…
However, de Broglie in Paris was not the only one to receive this issue of "Annals of Physics".
In the heart of Bohr in Denmark, Chen Muwu is now a colleague who firmly stands in the same trench as him, and is a strong supporter of the atomic model he proposed.
In particular, Chen Muwu found the fourth quantum number and proposed that electrons have spin, further perfecting Bohr's atomic model.
He also expressed doubts about electron spin, and personally wrote a letter to Chen Muwu, informing him that the electron spin may violate the principle of constant light speed in the theory of relativity.
As a result, Chen Muwu told Bohr in his reply that he did not understand the theory of relativity.
After careful calculation, I found that what Chen Muwu said was true.
This made Bohr very embarrassed. Fortunately, he didn't get mad and write a paper similar to BKS and publish it, otherwise he would have been embarrassed again.
So when Bohr saw Chen Muwu's new paper in the new issue of "Annals of Physics", he quickly called Heisenberg, his new assistant at the Institute of Theoretical Physics in Copenhagen, to help translate the paper. paper.
Bohr had two face-to-face interactions with Einstein and went to Göttingen to give lectures for more than a week, so he knew German.
But the assistant does not need to be used in vain. With help, he can take advantage of this time to smoke a pack of cigarettes.
I have to say that Heisenberg is easier to use than the previous Kramers. If we use the Three Kingdoms figures as an analogy, then the former is Jiang Wei, and the latter is Ma Su.
Listening to Heisenberg translating Chen Muwu's paper word for word in entry-level Danish, which he had just learned for a few months, Bohr lit his pipe and sunk into the sofa comfortably.
But as he listened, Bohr frowned.
“The orbit of electrons in atoms cannot be observed, but if the light emitted from atoms is emitted during the discharge process, we can directly find its frequency and amplitude.
“Knowing the amplitude number and the total amplitude is equivalent to knowing the orbit of the electron in physics so far.
"Since Mach's 'observability principle' only accepts observable quantities, in my opinion, it is natural that only by introducing this whole can it be used as a representative of the electron orbit...
"...
“…the periodic orbit of electrons may not exist at all.
“What people directly observe in experiments is nothing more than discrete stationary energy and spectral line intensity, and perhaps corresponding amplitudes and phases, but it is definitely not the orbit of electrons.
"I think the only way out is to establish a new type of mechanics, in which the concept of discrete stationary states is basic, and the concept of electron orbits seems to be abandoned..."
Okay, Chen Muwu, you are a thick-browed guy, you dare to be sentimental but you are also a traitor to the revolution. Oh no, you are a traitor to the Bohr atomic model?
Two months ago, Chen Muwu just published the exclusion principle. By proposing the existence of spin of electrons, he introduced the fourth quantum number and conclusively confirmed the existence of electron orbits.
Two months later, he started to say that electron orbits did not exist again. Why was he still inconsistent?
Bohr couldn't figure it out for a while.
In this paper, Chen Muwu quoted a philosophical point of view called the "observability principle" proposed by Mach.
Mach originally proposed this idea to deny the existence of atoms.
He believed that reality should not be attributed to entities that have never been observed. People have never observed atoms, so why can they believe that atoms exist?
Einstein was also inspired by Mach's philosophical foundation and believed that the absolute space-time concept in Newtonian mechanics was not valid because it could not be observed.
Therefore, he abandoned absolute space and time and established the theory of relativity.
In this new paper by Chen Muwu, it is the same.
People obviously can't even observe what electrons look like, so why do they insist on imagining an electron orbit? Do electron orbitals really exist?
In Bohr's atomic model, he created an orbit for the electrons outside the nucleus based on the experimentally observed spectrum of hydrogen atoms.
In other words, Bohr's model is "shoot the arrow first, then draw the target."
However, Chen Muwu completely reversed Bohr's atomic model in his paper, that is, the spectral lines cannot be calculated from the imaginary electron orbit, but the movement of electrons should be calculated through the physical variables of the spectrum.
If the hypothetical electron orbit does not exist, the electron's motion can still be inferred from the spectral variables.
"Stop, stop, Werner, don't continue reading here. Bring this paper to me."
The more Bohr listened, the more confused he became, and he simply stopped Heisenberg. He wanted to see with his own eyes what "fallacies" his junior brother Chen Muwu had written in his paper.
Bohr carefully read the first half of the paper "On Quantum Mechanics" from beginning to end. He was dazzled by the weird braces and square brackets, p, q and other messy characters in the second half. .
He felt as if he had been convinced by Chen Muwu.
"Werner, you should also read this paper. After you have read it, we will discuss it with each other."
After a while.
"finish watching?"
"Yes, Director."
"What do you think?"
Heisenberg answered truthfully: "I think...Mr. Chen's paper seems to have convinced me. Indeed, as he said, the orbit of the electron, as well as its position and speed are actually 'physical quantities that cannot be observed in experiments.' . For atoms, the only physical quantities that can be observed in experiments are the frequency and intensity of the spectrum. Other than that, all descriptions of atoms are just 'imaginary concepts'."
Heisenberg's godfather was Mach, the person who proposed the philosophical point of view quoted by Chen Muwu in his paper.
Therefore, he had no difficulty in accepting the new viewpoints proposed by Chen Muwu.
He paused and continued: "Only the mathematical method called 'matrix' introduced in the second half of the paper, I only understood it roughly. I think it may be because I was taking a mathematics class at the University of Göttingen. , because I didn’t listen carefully.”
Bohr smiled and said nothing.
He was thinking in his mind, should he invite a mathematics professor from the University of Copenhagen to come to the Institute of Theoretical Physics to give a lecture to these gangsters and himself?
…
Not only at the University of Copenhagen in Denmark, Pauli at the University of Hamburg also had a new issue of the "Annals of Physics" in front of him.
Being in Germany, he got this journal a few days earlier than Bohr who was far away in Denmark, and also saw Chen Muwu's latest paper a few days earlier.
Pauli rarely criticized the content of the paper, nor did he write any of his three comments in the margins of the journal.
But this does not mean that he completely agrees with Chen Muwu's paper.
Pauli believed that the new theory proposed in the first half of the paper was a wonderful physical picture, and that the quantum field finally had a new mathematical order. This was a gratifying thing, and it made his life regain its luster.
It's a pity that in the second half, Chen Muwu superfluous and used a pure mathematical system to ruin this new theory.
But in the end, the flaws are not concealed. It seems that this Chen Muwu still has some strength, and I, Pauli, cannot always be second to others.
Now that there are new theories and experimental phenomena that have always existed, Pauli plans to use Chen Muwu's method to try to see if he can completely deduce the spectrum of hydrogen atoms.
(End of chapter)
