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

The perfect explanation of the Stark effect relies on the sudden outbreak of Schrödinger more than ten years later.

The specific solution process is quite complicated. He used very complicated mathematics, such as Laguerre polynomials, hypergeometric functions, and differential equations.

If you really look at the paper Schrödinger published around 1926, it is really scary. In the end, two extremely complicated integrals appeared, and Schrödinger solved them abruptly. The streamlined process has several pages, and the scary thing is that there are almost no numbers in the calculation process.

——Once mathematics reaches the point where there are no numbers and only letters and various strange symbols, it becomes quite scary.

However, except for a few who specialize in theory, most physicists have not mastered mathematics to this level, because they still lack the help of a mathematics master-Courant.

This old man, Courant, has just graduated and is still working as an assistant to Hilbert. A few years later, to be precise, after World War I, he was able to free up his hands to engage in applied mathematics with Hilbert, first of all, applying it to physics.

The two collaborated on a very famous textbook "Methods of Mathematical Physics" to help physicists improve their mathematical abilities.

"Mathematical Physics Methods" should be familiar to some college majors. It is almost a "heavenly book" level. It is not ordinary people who can understand it.

Maybe it was because he felt that physicists were so bad at mathematics that Hilbert wanted to practice physics himself. And because of Hilbert's influence, many famous mathematicians from Göttingen have had a profound impact on theoretical physics.

Talking back to the meeting itself, even if Li Yu can ignore the big pitfalls, it is not easy to point out the problem of Bohr's equation.

It is not easy to simply evaluate whether cutting-edge mathematical theories are right or wrong because there is no standard answer.

——Li Yu could easily see it, all because of the traveler’s forward vision.

To verify whether these cutting-edge mathematical theories are right or wrong, professionals with high level of expertise are required to conduct such things as symmetry checks and multi-method calculation checks. Of course, the simplest way is to compare them with experimental results.

Weyl said: "I am impressed by Mr. Academician's mathematical foundation."

Li Yu said: "It just so happens that I am also studying this topic."

Weyl was a first-rate mathematician and later helped Einstein a lot in mathematics.

In addition to general relativity, Weyl also made great contributions to the mathematical foundations of quantum mechanics, such as the famous gauge field theory.

There are few mathematicians who can influence two major theories at the same time.

After all, since Poincaré, mathematicians have no longer pursued mastery of all branches of mathematics, and Weyl may have been the closest to achieving mastery.

"It was only after working in Göttingen that I realized that physics had developed to this extent, and it caught my attention," Weyl said.

Li Yu said with a smile: "Theoretical physics has now hit the target of real mathematicians."

Weyl said: "I don't know whether my gun can shoot accurately. It is impossible for me to understand physics so thoroughly if I rely on myself."

He is quite humble.

However, gauge field theory cannot be solved by one person. Noether's theorem must be the core idea first.

The legendary female mathematician Amy Noether who proposed Noether's theorem has not yet gone to Göttingen to study.

Li Yu said: "If you think about it carefully, it seems that most of the great mathematicians in history have made outstanding contributions to the foundation of physics, whether it is Newton, Lagrange, Euler, Hamilton, Poincaré, or Hilbert and Mr. Weyl now.”

Weyl laughed and said: "On the other hand, there are no good physicists who are bad at mathematics."

Both of them were very comfortable with each other's business exchanges.

Einstein was familiar with Weyl, and he said with a smile: "Both of them are very discerning, and Mr. Weyl is also a bit like Mr. Li Yu. He has made great achievements in literature."

Einstein also recited a poem by Weyl:

“The gods have imposed shackles on my writing in a language that I never heard sung in my cradle.

"What does that feel like? Anyone who dreams of galloping around without a horse knows it."

The original text is in English and it is quite well written. Many people whose native language is English will be shocked.

Weyl said: "I'm afraid Mr. Li Yu's Star Wars series is more attractive."

Planck had long wanted to ask this question: "Mr. Li Yu, it's been a long time since I saw your new work."

Li Yu could only tell him again about his idea of ​​writing a science fiction thriller.

Planck was indeed very interested: "Science fiction plus thriller? It sounds very interesting. When can I see it?"

Li Yu said: "It probably won't take long, but I don't know when it will be translated into German."

Planck said: "An English or French version is enough, I can read it."

Schrödinger interjected in a low voice (he really didn't dare to speak loudly now) and said: "I also like thriller stories that keep me awake at night to think."

Laue smiled and said: "Watching thriller stories tonight, you really are the one to watch."

Weyl suddenly said: "Thriller really caters to the current situation. Now countries are at war with each other, and there is always a tendency to go to war."

Einstein said: "After arriving in Berlin, I also felt such an atmosphere. If I had not separated from German citizenship, I am afraid I would have been forced to perform military service."

Schrödinger said: "Not only Germany, but also the Austro-Hungarian Empire where I live implements a conscription system, and the atmosphere is not much different from Germany."

Weyl asked: "If there was a war, would you do military service?"

Schrödinger said: "That depends on whether you will be recruited."

During World War I, Schrödinger did join the Austro-Hungarian army and became an artillery officer.

Most of the scientists recruited into the army have entered the technical branches, with the artillery unit being the largest and mainly responsible for ballistic calculations. In World War I, there were no advanced weapons like self-propelled artillery. It all depended on who could destroy enemy targets faster with fixed artillery.

It's just that the Austro-Hungarian army was too weak in World War I and was completely defeated. Many soldiers died in battle, and many scientists unfortunately died on the battlefield.

For example, Schrödinger's mentor Hasenel was killed in October 1915 while leading his troops to charge.

Austria has lost an outstanding physicist at the peak of his creativity. This tragic loss is irreparable and irreparable.

Perhaps because he did not want to lose any more famous scholars, Schrödinger was later incorporated into the rear troops and was mainly responsible for training. He taught basic concepts and theories of meteorology to incoming air defense officers at a military camp near Vienna, such as atmospheric composition, solar radiation, atmospheric distribution and daily and annual changes; air pressure, high and low pressure areas, and special atmospheric circulation. These are oceanic, continental and mountainous winds, climatic boundaries, storms, cloud structures, interpretation of weather charts, etc.

Schrödinger studied meteorology very deeply, and his papers were about meteorology.

In addition, he is also a great talent in biology and is quite knowledgeable.

Bohr did not like the topic of war and interrupted their conversation: "War is so stupid!"

"I completely agree with this point of view! But the politicians are even more stupid!" Einstein said, and then asked, "Mr. Bohr, have you received a professorship?"

"No," Bohr said dejectedly, "I would like to return to China and join the University of Copenhagen as a professor of theoretical physics, but unfortunately this application was rejected by the Danish Ministry of Education." Li Yu asked: "Why was it rejected?"

Bohr said: "I don't know, maybe the Danish Ministry of Education believes that theoretical physics has no practical significance."

Li Yu said: "I wonder if it would be helpful for us to jointly write a letter of recommendation?"

Li Yu is determined to help these big guys earlier when they are young, and there will definitely be many benefits in the future.

Bohr was very happy after hearing this: "Thank you!"

Li Yu immediately wrote a letter of recommendation in handwriting and was the first to sign. Planck, Einstein and others also signed.

After sending the letter, everyone happily had a dinner.

The meeting continued the next day.

The discussion today mainly focused on particles, because yesterday Li Yu raised a lot of questions about particle physics, which caused a lot of shock.

Bohr first said: "I had a telegram with Professor Rutherford in the UK last night, and he told me a very important experimental phenomenon. An assistant named Chadwick in Professor Rutherford's laboratory discovered that, When the nucleus of an element decays, it may become the nucleus of a new element and then add beta particles, which seems to explain one of Mr. Li Yu's questions yesterday, which is why beta rays appear in the nucleus."

Of course Li Yu knew about Chadwick's experiment, but he just conducted the experiment and couldn't explain it at all, so he said, "Are there other discoveries?"

Bohr glanced at Li Yu in surprise, as if he knew something, and continued: "Yes, Chadwick also found that the energy before and after was inconsistent. To be precise, the energy after decay was a little less."

The beta rays emitted from the nucleus are produced by decay, but physicists are not very clear about it at present.

This experiment is indeed important, and Bohr's second sentence is even more incredible.

Planck frowned and said, "The energy before and after is inconsistent?"

Bohr said: "Yes, there is less energy after decay."

Laue was surprised and said: "It can't be that the microscopic particle field cannot even maintain the most basic energy conservation?"

"Impossible!" Planck said resolutely, "Conservation of energy is the most basic principle, and there is nothing wrong with it!"

"But..." Lauer paused and said, "Why are the experimental results not conserved?"

Planck asked Bohr: "Are the results of this experiment reliable?"

"It's reliable," Bohr said. "The experiment was not only done in the laboratory of the University of Manchester with advanced equipment, but the same result was obtained in the Cavendish Laboratory of the University of Cambridge."

These two laboratories are already quite authoritative, and other laboratories can only do so.

Planck adjusted his glasses: "Is the building of physics really going to collapse?"

Bohr asked: "Could it be like the statistical mechanics of Maxwell and Boltzmann, which shows energy conservation on a macro scale, but a single particle may not be conserved?"

This is obviously an outrageous statement, but it is obviously even more unacceptable if energy is not conserved.

Planck shook his head: "First of all, although mathematics is very important to physics, and statistics and probability theory are important branches of mathematics, I still cannot accept the introduction of statistics into physics. Physics is not mathematics, and physics cannot allow Certainty and infinite existence. Secondly, the conservation of energy is unshakable, otherwise the entire physics will have to be rewritten! The microscopic can be different from the macroscopic, but it cannot be different in terms of the basic conservation laws."

Einstein said: "I also believe that the conservation of energy cannot be broken."

Planck said to Li Yu: "Where are you?"

"I also firmly believe that there can be no mistakes in the conservation of energy. The macroscopic is just the manifestation of the microscopic," Li Yu said. "As for why the energy is not conserved in the experiment, perhaps it is because there is a kind of particle and ray that we cannot observe in the decay process. .So part of the energy lost in the experiment is not really less, but it is just not observable by our equipment."

As a time traveler, Li Yu knew that this missing energy was caused by neutrinos, but it was indeed incredibly small and could only be found in experiments in 1956.

Li Yu's statement is already very euphemistic, and this explanation is easier for everyone to accept.

Planck said: "I hope Academician Li Yu's statement is correct, because physics really cannot accept the result that energy is not conserved."

The event of non-conservation of energy after decay is known as the "energy theft case" and will plague the physics community for many years.

I feel that after these two days of meetings, everyone is a little disappointed. It seems that while no problems have been solved, countless problems have been added.

Li Yu was ready to tell some good news: "When I was in the United States, I met Professor Millikan of the University of Chicago. He was doing a very interesting experiment."

Planck said: "Professor Millikan who did the oil drop experiment?"

Li Yu said: "Yes."

Since completing the oil drop experiment and determining the basic electric charge, Millikan has become famous in the physics community, making the American physics community raise its head again after Michelson.

However, in general, American physics still lags behind Europe. The rise of science and technology in the United States many years later was completely caused by Germany.

In 1933, Mustache was elected Chancellor of Germany, and he immediately began large-scale anti-Semitism, leading to the exile of a large number of scientists overseas.

After the end of World War II, the United States once again frantically snatched German scientific research talents, namely the famous "Alsos" operation.

After this group of people arrived in the United States, they directly raised the technological level of the United States to a big level.

Planck said: "What new results did he have?"

Li Yu said: "Professor Millikan is preparing to conduct verification experiments on the photoelectric effect. Once successful, he can immediately test the wave-particle duality of real light."

Li Yu deliberately called it a "verification test". In fact, Millikan did not believe in Einstein's theory and wanted to use experiments to overturn it.

But it sounds better to say it this way.

Einstein liked the news so much: "I hope Professor Millikan will speed up the progress of the experiment!"

Anyway, now that the theory has been verified so well, everyone has basically accepted that the experiment can be done, and they are just waiting for the results.

Planck said: "Wave-particle duality? The name is interesting."

Li Yu said: "The experiment can also confirm the correctness of Planck's constant and obtain a more accurate value, which is a great good thing for the entire quantum theory."

After finally hearing good news, Planck smiled and said: "Perhaps many papers will still have to be rewritten by then."

Millikan's experiment was conducted around 1916. Although this experiment to verify the photoelectric effect is far less famous than his oil drop experiment, its physical significance is equally significant.

In any case, wave-particle duality is something that touches the core of the theory of measurement and force.