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

After the meeting, Einstein immediately suggested that everyone take advantage of the fact that it is winter to go skiing in Munich and continue scientific research at the University of Munich.

Laue was more enthusiastic and was the first to respond: "I have wanted to go skiing for a long time. If I don't go, I won't have the chance this year."

Bohr said: "Professor Sommerfeld of the University of Munich has corresponded with me several times, and I also want to visit him."

Schrödinger and Weyl also agreed.

These young people must like skiing. Plank is somewhat more mature and prudent, saying that he would not suffer in the mountains with his old arms and legs.

So everyone except Planck happily decided to go to Munich together.

Einstein also invited an astronomer, Friedrich, who would be responsible for going to Crimea a few months later to conduct astronomical observations to verify the general theory of relativity - a somewhat unlucky guy.

It’s fun to ski during the day and brag with top physics and math experts at night.

Laue said: "Mr. Friedrich, as far as I know, you have just been married, why didn't you go on your honeymoon?"

Friedrich said: "Every day my wife and I are together is a honeymoon, but it is not easy to meet such outstanding scholars."

Li Yu laughed loudly: "With your sweet words, a short honeymoon really won't have any impact."

Einstein said: "And we are all a bunch of men, which is reassuring not to be."

Friedrich also smiled: "Of course, don't worry."

There are not many astronomy people here, Li Yu is one of them, so Friedrich asked again: "Mr. Li Yu, I admire you very much. Could you please tell me what you think of Mr. Einstein's gravitational bending of space-time?"

Li Yu said: "Theoretically it is tenable and I believe it will be successful."

With Li Yu's words, Friedrich became even more motivated for his trip to Crimea: "It's incredible to think that astronomy can be connected with the theory of relativity. It's so romantic."

Einstein said casually: "I still think there are more romantic things."

Everyone spent several days at the ski resort before returning to Munich with unfinished business.

For Germany, Munich is a very important city. Especially at the beginning of the 20th century, it was an important cultural center, almost second only to Paris in terms of activity.

Scientific research is not weak either. Since then, the University of Munich has become one of the three major centers of quantum mechanics under Sommerfeld's leadership (along with Bohr's institute and Göttingen).

Of course, the current University of Munich is also quite powerful, after all, Roentgen is here.

Although Sommerfeld has been mentioned many times, it seems that many people still don't know much about him. In fact, you only need to name his two apprentices, and you will be able to better understand his value: Heisenberg and Pauli.

Sommerfeld is currently a professor of theoretical physics and director of the Institute of Theoretical Physics at the University of Munich. He is very happy to see such a group of young scholars visiting. Keyly, several of them have already made their mark.

Schrödinger was a meticulous man and took out a pile of manuscripts to Sommerfeld: "Mr. Professor, this is a brief record of the meeting in Berlin a week ago."

"Thank you very much," Sommerfeld said.

After Bohr proposed the energy level orbit theory, Rutherford was the fastest European physicist to make a positive evaluation, followed by Sommerfeld.

After looking at it in general, Sommerfeld knew what was going on: "I have long said that Bohr's model seems reasonable, but I believe that this model needs to be reinterpreted in a more basic way. Sure enough, it didn't take long for Star Grams discovered the splitting of spectral lines."

Bohr originally proposed the energy level theory to explain the spectrum of hydrogen atoms.

Now Stark suddenly said that the spectral lines that everyone thought before were not one at all. Each line was actually composed of two, but they were too close together. In the past, people always thought they were one.

Bohr said: "Things are moving too fast, but I don't think the energy level theory is completely wrong."

Sommerfeld asked: "Have you figured out anything?"

Bohr said: "Not yet, but Mr. Li Yu has some surprising conjectures."

So Sommerfeld asked: "Mr. Li Yu, what do you think?"

Li Yu still collected his thoughts slightly and said: "In Bohr's atomic model, electrons rotate around the nucleus in a circular orbit. I am wondering, can electrons make other types of motion around the nucleus?"

Sommerfeld raised his eyebrows: "Oval? I was just thinking about this possibility."

Li Yu continued: "Moreover, Mr. Bohr's paper does not seem to consider relativistic effects."

Sommerfeld squinted his eyes and thought for a long time, and then said: "A great idea! But it may require troublesome mathematical derivation."

Li Yu said: "Professor, your mathematical skills are excellent, and we also have mathematicians here who came from Göttingen."

Sommerfeld studied mathematics from the beginning.

Weyl said: "I haven't studied quantum theory in depth to the level you have. If I just help with some mathematical calculations, I should be able to do the job."

"What a pity," Sommerfeld said, "it seems that only Mr. Li Yu can help."

Li Yu said: "Do your best."

In the following days, Li Yu spent most of his time conducting theoretical research and mathematical derivation with Sommerfeld. When certain results were obtained, he would discuss them with everyone at the seminar.

They quickly calculated that if an electron revolves around the nucleus in an elliptical orbit, its speed will be different from that of an electron in a circular orbit.

If we consider the relativistic effect of electron motion, then the energy difference between the elliptical orbit and the circular orbit is very small, and this energy difference seems to correspond exactly to the energy difference of the two spectral lines.

Sommerfeld had been thinking about this problem for a long time and took advantage of the situation to introduce new quantum numbers, three to be precise: orbital direction quantum numbers, orbital shape quantum numbers, and self-selected direction quantum numbers.

A more popular understanding is to quantify the shape of the orbit.

In addition, after a lot of calculation, Sommerfeld figured out something strange. He immediately called Li Yu: "I seem to have discovered something strange, look!"

Li Yu only glanced at "1/136" and knew what it was: "Fine structure constant."

"Fine structure constant?"

Sommerfeld was stunned for a moment, then thought about it. Li Yu had written about the term "fine structure" in "Fractals and Chaos", and there seemed nothing wrong with using it. Moreover, the splitting spectral lines they studied are exactly the fine structure of the spectrum of hydrogen atoms.

"I agree with this name," Sommerfeld said. "The most amazing thing is that it has no dimensions, that is, it is a pure number without units. How to explain this?"

Sommerfeld's question stopped Li Yu.

After more detailed calculations later, the fine structure constant was approximately equal to 1/137.

According to the most basic understanding, the fine structure constant is the speed v of the ground state electron of the hydrogen atom divided by the speed of light.

However, later the academic community discovered that this number is so miraculous that it seems to be an Easter egg in the universe, appearing in many places in quantum theory.

For example, the most typical electromagnetic coupling, people found that the strength of electromagnetic interaction is 1/137 of the strong force.

In other words, the fine structure constant determines the strength of the electromagnetic force, and therefore the properties of atoms and molecules. If this constant is too large or too small, atoms and molecules may not be formed.

For this reason, fine structure constants are used in quantum electrodynamics to indicate the strength of the interaction between electrons and electromagnetic fields.

It's quite magical.

The fine structure constant has puzzled many outstanding physicists and mathematicians for hundreds of years.

Dirac once said: "This number is the most fundamental unsolved mystery in physics."

Pauli said: "When I die, the first question I ask God will be: What is the meaning of the fine structure constant?" The ward number where Pauli was hospitalized on his deathbed happened to be No. 137.

(God: You line up first, over there Hilbert wants to ask if the Riemann Hypothesis has been proven!)

It is a pity that until Li Yu traveled through time, people failed to understand the fine structure constant.

Even physicists have temporarily given up thinking about this problem, and instead think about whether this number will change over time.

But this question is even scarier: If the coupling constant of the electromagnetic force changes with time, will the universal gravitational constant (that is, the coupling constant of gravity) change?

If these things change over time, most physical theories will definitely have to be revised.

Because the building of modern physics is, to put it bluntly, based on the premise that these constants remain unchanged.

It is no longer as simple as two dark clouds, but a world-destroying meteorite.

Think carefully!

By the way, in 2018 Sir Attiyah claimed to have proved the Riemann Hypothesis, using the fine structure constant, and the proof process only took one or two pages...

But the matter is controversial.

In short, Sommerfeld discovered something extraordinary.

Li Yu said: "We can only solve the problem bit by bit now, let others solve this matter."

Sommerfeld said: "That's fine! I will spend a few days sorting out the paper, and I will make my husband the second author."

Li Yu smiled and said, "It's not necessary."

Sommerfeld said: "At least you are the one who named it."

Li Yu shrugged, it was not a big deal.

-

The seminar has come to an end for the time being, and we can finally take a breather.

Einstein suggested: "There is an art exhibition recently held in Munich. It is said that the scale is a bit... haha."

Li Yu understood: "Go and have a look!"

Although Germany is a bit weaker than other European countries in terms of art, the artistic atmosphere in Munich is still very good.

On the way to the art exhibition, Li Yu passed by a man wearing a hat. He couldn't help but stop and was surprised: Lenin?

Li Yu looked back and saw that his figure had gradually disappeared into the crowd.

Einstein patted Li Yu on the shoulder: "What are you looking at?"

"It's nothing," Li Yu turned around and said, "continue on your way."

The content of the exhibition is mainly figure paintings, and the sketch part is quite "flavorful".

Li Yu pretended to understand: "Art! It's really art!"

Einstein asked: "I heard that you bought some paintings, why didn't you buy them today?"

Li Yu said: "I just saw many stalls selling paintings on the road. Their prices are much cheaper."

Einstein said: "I also think the art exhibition is too expensive, so I'd better go to the stalls and have a look."

Li Yu asked: "Do you want to buy a painting?"

"Give it away." Einstein nodded.

Li Yu could roughly guess who he wanted to send as gift. At present, the relationship between Einstein and Elsa was extraordinary, and they were almost going to make their relationship public.

"What style of work do you like?" Li Yu came to the street and asked, "I heard that there are three thousand painters in Munich, enough for you to choose from."

"Three thousand painters?" Einstein was a little surprised. "There are only 600,000 people in Munich."

"Art is like thousands of troops crossing a single-plank bridge. It's really complicated to have so many painters come at once," Li Yu glanced over, "otherwise you wouldn't have seen so many paintings selling on the street, and the prices are so Low."

Einstein said: "Why are so many painters concentrated in Munich?"

"Then I don't know," Li Yu said, "Maybe it's closer to Italy and Austria."

Einstein said: "Elsa liked landscape paintings."

Li Yu glanced forward: "These are all portrait paintings, and the ones in front seem to be landscapes."

The two of them had just walked not far when they heard some shouts:

"This painting costs 600 marks!"

"Mine only costs 500 marks!"

"400 marks! Look at mine!"

The further you go, the lower the prices.

Einstein saw the pattern: "The closer to the exhibition, the higher the price."

After walking a few hundred meters, Li Yu suddenly saw a thin young man selling architectural paintings, who turned out to be Hitler with a mustache!

When Mustache saw Li Yu stop, he said, "That's great. Finally, someone is unwilling to buy portrait paintings."

Mustache now really wants to be a painter who makes a living by selling paintings.

However, he failed to apply for the Vienna Academy of Fine Arts several times.

The most recent time, the examiner said that his painting skills were insufficient and he had no talent. He also told him: "Your talent is in architecture. It is recommended that you apply for the School of Architecture."

The better paintings of Mustache are basically architectural style works, so the examiner said this.

The School of Architecture does require a certain amount of art skills.

But this suggestion was unacceptable to Xiaozhu, because to enter the School of Architecture, one must have completed a six-year middle school and have a diploma, but Xiaozhu only had a four-year middle school certificate.

From a professional point of view, the mustache painting is not very perfect. After all, most of his works were created during his youth, without formal art academy education.

——It looks good, but it lacks artistry.

Architecture is Mustache's favorite subject, and his artistic thinking is quite conservative, which was greatly reflected in his later life. He also has a strong sense of rejection towards trendy art such as body art and contemporary art.

Unable to survive in Vienna, Mustache had no choice but to come to Munich to make a living.

Li Yu said: "Actually we want to buy landscape paintings."

Mustache was slightly disappointed, but someone soon said happily: "I'm good at landscape painting!"

Einstein didn't know the name of Mustache now, and thought he was just an ordinary young painter, so he walked over directly to the landscape painting stall and bought one.

It's really interesting today. This small place actually accommodates both poles of the future world.