A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Chapter 694: Incomprehensible Paper
Göttingen.

Heisenberg, who had just returned from recuperation, wrote a paper to avenge his previous defeat.

Previously, in the doctoral thesis defense at the University of Munich, I only received an ordinary average evaluation, just higher than the lowest "pass".

According to the doctoral grading standards of the University of Munich at that time, a doctoral candidate's score was determined only based on his thesis and performance in the final oral examination, with four passing scores: I (excellent), II (good), III (fair), and IV (pass).

Since physics at the University of Munich was conducted separately by Wien and Sommerfeld, both of them attended the oral examination and had to agree on a single grade.

Wien had some private conflicts with Heisenberg before and did not want to award Heisenberg his doctorate degree. The reason was still the earlier debate about which was more important, experiment or theory.

Wien's score was failing (V), while Sommerfeld's score was excellent (I), so the final score was the average (III).

This made Heisenberg quite unconvinced, so he immediately left Munich and went to Göttingen and Copenhagen to continue his studies under Born. During this period, Heisenberg went to an island to recuperate for several months due to hay fever.

While the big shot was recuperating, he was fishing while enjoying the sea breeze and suddenly had an inspiration. He found a breakthrough in Bohr's energy level theory and then returned to Göttingen with this paper.

Heisenberg handed the paper to his mentor Born: "I have discovered a new way to establish a theoretical foundation for quantum mechanics, and this method is based only on quantities that can be observed in principle."

After all, it was in Göttingen, a place where mathematics was more dominant, and Born immediately thought: "You want to axiomatize quantum mechanics?"

"To be precise, it is mathematization," Heisenberg said. "Previous theories, even Mr. Bohr's atomic energy level orbit theory, are based on some assumptions. Sometimes it is difficult to convince others. This is also the reason why quantum mechanics has been silent for many years. It is too ethereal and not mathematical enough."

Born agreed with Heisenberg: "You are right, but when quantum theory was first developed by Professor Planck 20 years ago, he thought it was just a mathematical trick. That is to say, from the beginning everyone wanted to move closer to mathematics, but it was not easy."

Heisenberg said confidently: "It was indeed not easy and took me a long time. This is because I only conducted theoretical analysis based on observable experimental results, that is, atomic spectra."

"It doesn't sound any different from what Professor Bohr did," Born said.

"Very different!" Heisenberg continued to explain, "I no longer care about Mr. Bohr's energy level orbit, but use a new physical quantity - state."

Born said: "State? It seems easier to understand. It is related to classical thermodynamics. What's next?"

Heisenberg opened the paper and said: "I have arranged the various states of electrons one by one with numbers to form some small squares, which can represent all the possible situations of an electron. If we deal with them well, we can deal with the problem of electrons."

"You got the result?" Born's brows had begun to frown, and the answer was indeed a little complicated.

"Otherwise I wouldn't dare show you the paper," Heisenberg said, fearing that he might not understand it, so he turned directly to the last page. "I have calculated the problem of the one-dimensional resonator."

Born was a little surprised: "Did you really figure it out?!"

To put it simply, Heisenberg first confined the electron to a single dimension, that is, running in a straight line, rather than in three dimensions. If this model works, it can be expanded to produce a more realistic version of the theory for the atomic model.

This method is very common in both mathematics and physics. It is to slowly approximate, such as the Goldbach conjecture, from 9+9 to 1+1; or Professor Zhang Yitang's paper on the twin prime conjecture, which also provides a method.

As for science, we are not afraid of difficulties. What we are afraid of is not being able to find a way to solve the problem.

Heisenberg's ideas are so brilliant because he really found a way.

He also broke through an inherent concept: there is an assumption in Bohr's energy level theory that there are some fixed orbits in atoms and electrons can only move on these orbits.

Heisenberg thought about it and found that this seemingly flawless hypothesis was actually the most likely to have problems, so he started from here.

In addition, in previous quantum theories, there was almost no mention of using numbers to represent electrons. Heisenberg was the first to do so.

That's right, his paper is really too obscure and difficult to understand.

Born, who was an excellent mathematician, read it for several days but still couldn't fully understand what he was talking about. It seemed like a mystery, but at least he had a result, so he signed and published it anyway.

A few days later, Born suddenly realized that Heisenberg's paper was clearly about matrices!
Heisenberg had never studied matrices, and didn’t even know what matrices were. When he represented the different states of electrons with small digital squares and then calculated them, he immediately encountered a problem, a fatal problem: P×Q was not equal to Q×P!

This is commonplace for people who have studied linear algebra, but Heisenberg had never heard of matrices, and he suddenly had to use very complex calculations.

Heisenberg couldn't understand why these small squares didn't even satisfy the most conventional mathematical commutative law of multiplication (also known as commutativity)!

Since he didn't know about the matrix, Heisenberg could only force himself to find another way around it, and he actually managed to get around it.

But the result is that he is basically the only one who can understand the paper.

Born was incredibly good at mathematics, and once he knew it was a matrix, the rest of the problem became easy to solve.

But even in Göttingen, few people had studied matrices, so he immediately called Pauli to his office.

"Can you help revise Heisenberg's paper? Use the correct mathematical language," Born said.

Pauli's reputation as a man who defies God was always reflected. He didn't like the mathematicians in Göttingen. In his eyes, those who had physical thinking were the best. So without even looking at it, he said, "I think Heisenberg's physical thinking is already excellent and does not need to be changed."

Born said: "Just because you can understand it doesn't mean others can understand it, because it is too unmathematical. If you write it in formal mathematics, you may be able to make new discoveries."

Pauli still directly refused: "New discovery? I don't think mathematics has such a great ability."

As one of the few people who understood both relativity and quantum theory, Pauli was also the most arrogant person in the physics world. Because of this personality trait, the extremely intelligent Pauli missed many great discoveries.

After Pauli refused, Born had no choice but to call another student named Jordan, who modified the article using matrix language and solved the core problem of the article: Since P×Q is not equal to Q×P, what is P×QQ×P equal to?
In addition, Born asked Heisenberg to send a paper to Cambridge.

-

After Li Yu and Oppenheimer arrived in Cambridge, they found that it was better than before.

But the Cavendish Laboratory building remains largely unchanged: exposed brick walls, old wooden floors, pedal-brake lathes, manual vacuum pumps, glassblowing equipment, and greasy tools and equipment placed on benches, so rudimentary that no one would want them at a flea market.

Cambridge University has also considered whether such an environment is suitable for British gentlemen, but the laboratory's achievements in recent years have been so remarkable that they feel there is nothing wrong with maintaining the status quo.

"Professor Thomson, this is Oppenheimer," Li Yu introduced.

"Professor Thomson, I have admired you for a long time," Oppenheimer said respectfully.

Thomson nodded and said, "Hello. The laboratory is short of manpower. During this period of time, you can help prepare beryllium foil for electronic research. Go find Kapitsa first. No, go find Blackett. He will tell you how to do it."

Kapitsa is also known as a genius. It is difficult for two unruly people to get along together. Blackett is more stable.

"Okay, professor," Oppenheimer said. He would have to carry out this complicated work for some time. Beryllium foil is not so easy to prepare, especially with simple equipment. First, the vaporized beryllium must be attached to collodion, and then the collodion must be removed with great effort. It is undoubtedly a delicate job, and Oppenheimer is estimated to be unable to cope with it.

The two then went to Rutherford's laboratory, where he was sorting out last year's laboratory funding settlement.

Li Yu specially bought a box of premium Cuban tobacco and placed it on his desk.

"Thank you very much!" said Rutherford.

Thomson asked, “How much did the lab spend last year?”

"That's £9628," said Rutherford.

"So little?" Li Yu was surprised. "Does it include all the employees' salaries and equipment expenses?"

"Including," Rutherford said, and then he put the tobacco into his pipe and lit it with a match. The tobacco instantly sparked like a small volcano.

Thomson said: "It is too economical. Now that I am the president of the Royal Society and the president of Trinity College, you can increase this year's budget significantly."

"It couldn't be better!" Rutherford asked. "How much better?"

"Start with 20% and then increase gradually," said Thomson.

"If we want to expand, 200% won't be enough." Fowler walked in.

Fowler was Rutherford's son-in-law and the only theoretical physicist in the Cavendish Laboratory who had his own office, besides Rutherford and Thomson. If you were a visiting scholar, there was no room in the laboratory and you could only stay in the unheated library or the shabby tea room.

"The expansion project is too big to be feasible at this time," Rutherford said.

Fowler said: "Eddington went to the United States and always said that the buildings in American universities were much better than ours."

"There's nothing to worry about, they can only do what we have left," Rutherford said, and then asked, "Did you go to Eddington's lecture?"

"I heard it," Fowler said. "It was a stellar lecture called 'The Philosophy of Physical Science.' It was incredible that he could memorize such a long number."

"What number?" asked Thompson.

"I can't remember it," Fowler said, pulling out a copy of his speech. "You can read it for yourself."

Li Yu took it and saw that it said "Stars have stable masses, such as the mass of the sun, which is 2×10 to the 27th power tons." This sentence was relatively normal, although it had a few minor flaws. But the next sentence was a bit explosive:
"I believe there are 157477241 36275002577605653961181555468044717914527116709366231425076185631031296 protons and the same number of electrons in the universe."

Li Yu asked: "Can he give the complete number?"

"And not a single number is wrong," Fowler said.

"He must be able to recite at least 300 digits of pi." Li Yu said with a smile.

"It's possible," Fowler said. "Eddington was a mad man for numbers! It is said that when he was six years old he could recite the 24 x 24 multiplication table."

It seems that this is still quite popular in the UK.

Rutherford took another puff of his pipe and stood up. "Maybe I'll meet him in the cafeteria soon. I've seen the menu. Today's food is very good."

Li Yu had no expectations for British cuisine: "I've had enough of potatoes."

"Of course not potatoes. I hate potatoes too. When I mention potatoes, I think of the days when I dug potatoes in New Zealand!" Rutherford said. "The cafeteria serves French food today."

"French food?" Fowler was a little shocked.

Rutherford said: "It's a rare opportunity, so we can't miss it."

Li Yu went to the restaurant with them and found that the menu was also written in French. The first course was roasted cod with cream; then the main course was a choice between braised hare or boiled ox tongue; and finally, a choice between gooseberry pie with cream, watercress, radish and cheese, or sardine toast.

Although it is a very simplified French meal, it is definitely quite presentable for the British.

Eddington sat next to them.

Fowler said to him: "Professor Eddington, your speech today was so successful. Those freshmen who have just entered Cambridge must be delighted to apply for the Department of Mathematics and Physics."

Eddington was dressed very neatly, in a formal three-piece suit, with a black bow tie neatly tied below the first button of his shirt. He said: "I am going to dig out first-class talents from this group of students, just like you, Mr. Fowler."

The Department of Mathematics and Physics is the largest and most famous department in Cambridge, with strong academic standards and competitive graduates.

However, in the past 100 years, geometry, which was the most popular subject in British mathematics, has gradually lost its popularity, and the mathematics community has tended to focus on mathematical analysis. British physics also focuses more on experiments and does not pay much attention to the emerging quantum theory and relativity.

Of course, just as France had a de Broglie, Britain now also has a genius that is rare in history.

Fowler said, "You mean Dirac?"

"Yes," Eddington said, "Although Dirac didn't like to participate in any sports or social activities, he worked hard enough and his academic performance was extremely good. No one in Cambridge dared to say that he was a top student, but Dirac had this ability."

Cambridge attaches great importance to sports and social achievements in addition to academics. Only those who excel in both academics and sports can often receive the highest honors. But Dirac was average in both aspects.

Fowler said: "Hard work does not necessarily lead to success, at least not now."

Eddington said, "Well, I heard that you will be visiting Copenhagen for six weeks. Why don't you put Dirac under my management during this time?"

Fowler spread his hands and said, "What a pity! Just last night, after hearing that Mr. Li Yu was here, Dirac took the initiative to ask for advice from him for those six weeks."

Li Yu was surprised and said, "Cambridge never said they would arrange a teaching job for me. I am just a visiting professor."

Fowler said, "Not only Dirac proposed it, but also Kapitsa and Blackett. It's only six weeks. Don't worry, we will pay you a semester's salary."

Li Yu said awkwardly: "It's fine to give lectures, but I'm really not good at giving lectures and teaching people."

Rutherford had just finished his second serving of celery, radish and cheese and wiped his mouth. "It's a good opportunity to practice. It's just some homework. It's much easier than doing scientific research."

Thomson also tried to keep him, saying, "I calculated that you have only attended less than five annual meetings of the Royal Society in all these years..."

Li Yu quickly surrendered: "Okay, okay! I agree to it."