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

Chapter 709 Von Neumann
After winning the Nobel Prize, Wu Youxun was invited to give a lecture tour at several European universities.

Anyway, this is a good thing. It can continue to greatly enhance prestige, and it will also allow us to obtain academician status abroad many years earlier than in history. Reputation is still very useful.

During this period, Li Yuze and Tang Feifan went to Berlin.

Tang Feifan has always been fascinated by the European scientific community, especially Germany, because in the 20s, the language of science was actually German, not English. A large number of scientific and technological documents, especially in the two major pillar disciplines of mathematics and physics, are often first-hand documents in German.

Germany's medicine and biology are also strong. Although Koch has passed away, the German scientific community has always had a tradition. Their scientific association is called the "Union of Natural Sciences and Medicine", and medicine must be included.

Tang Feifan couldn't wait to inspect the Bayer Pharmaceutical Factory first, while Li Yu came to the University of Berlin.

Now the University of Berlin has gathered many great people such as Planck, Einstein, Schrödinger, Meitner and so on.

Einstein was still studying quantum problems with Schrödinger.

"Good morning, professors," Li Yu said with a smile, "What are you talking about?"

"It's still damn probability," Schrödinger said. "I think more and more that the probability explanation is too mathematical, which goes against my original intention."

Einstein was a little hesitant: "There is nothing wrong with mathematization itself. The key is how to find the essence of physics."

Li Yu pointed to the blackboard behind them and said, "There are many things that cannot be explained, such as the solution of the wave function."

Schrödinger said dejectedly: "It's really hard to figure it out."

After careful comparison, it is quite appropriate for the University of Berlin to choose Schrödinger to succeed Planck. The two are very similar in science. Both have made great contributions but are somewhat conservative and dare not take any further steps.

If you look at it from the perspective of the University of Berlin, you might think this is prudent.

The explanation on the small blackboard is nothing special, it's just a solution with an imaginary number i.

A little attention needs to be paid: the square of the wave function Ψ is mentioned in the probability explanation. The calculation is not a simple Ψ×Ψ. The calculation of complex numbers requires the use of complex conjugate and other contents.

In addition to eliminating the probabilistic explanation, there are still many things that are difficult to explain. The most typical one is of course the positron that Dirac later predicted through his own equation.

The combination of mathematics and physics is so magical that many equations can be solved in various ways in mathematics, but it is very difficult to explain what they represent, and it often requires top-notch brains.

Einstein laughed and said, "Fortunately, I didn't come up with this function, otherwise I would go crazy if I heard that little tune every day."

Li Yu asked: "What ditty?"

"Haven't you heard of it?" Einstein asked in surprise, and then hummed a few words:
"Erwin used his

Can do a lot of calculations,
But there is one thing that has not yet been discovered:

What does Ψ mean?”

Li Yu was also amused: "When I left Brussels, I heard Pauli say that Professor Schrödinger didn't even know that his wave function could be explained by probability, so Schrödinger didn't understand the Schrödinger equation."

This is a meme that was popular when Schrödinger was still alive.

Schrödinger was a little embarrassed: "Of course I understand my equation."

Einstein teased: "Why don't you go and listen to von Neumann's recent seminar. He is trying to explain quantum mechanics with mathematics."

Schrödinger shook his head and said, "He is an excellent mathematician, but he is definitely not a good lecturer. It is better to do research on your own than to listen to his lectures."

Li Yu wondered, "Is it so difficult?"

Schrödinger said: "If you don't believe it, try it yourself."

-

Von Neumann is currently a part-time lecturer at the University of Berlin.

He was a Hungarian-American Jewish man. As for the surname "Von", it was given to him by the Emperor of the Austro-Hungarian Empire because his father was a very powerful banker.

Von Neumann was a genius with a photographic memory. His research field was somewhat similar to Dirac's, both were mathematical physics, but Dirac was more inclined towards physics, while von Neumann was more inclined towards mathematics. After all, von Neumann was mainly involved in mathematics.

Li Yu came to his seminar and von Neumann noticed Li Yu.

"Mr. Academician, you are here."

Li Yu smiled slightly: "Sir, just continue talking."

Within ten minutes, Li Yu understood why Schrödinger said he was not a good lecturer.

Von Neumann's thinking, speaking speed and blackboard writing speed were all extremely fast, and he didn't care at all whether the people below could keep up with his pace.

Mathematics, when it reaches a certain level, is incredibly difficult. If you don't give people time to digest it, no one will be able to bear it.

Moreover, von Neumann had no habit of preparing speeches, and no one had any reference materials.

He talked a lot on the stage, and then quickly did mathematical calculations on the blackboard. Once the blackboard was full, he immediately erased a large area of ​​the equations he had written before, and then continued to calculate on his own. Almost no one present had any idea what he was talking about. Many people jokingly called it the "erasing blackboard proof."

Forty minutes later, von Neumann clapped his hands and said, "Okay, I'm done. Is there anything you need to ask?"

The dozen or so people in the audience looked at each other in bewilderment.

"Great!" von Neumann said happily, "I know everyone understands what I said."

Everyone applauded immediately.

After everyone left, von Neumann said to Li Yu: "Most of the people here today are researchers in the field of pure mathematics. Most physicists don't use this kind of calculation, but I know that Mr. Li Yu's calculation ability is also exceptional."

Li Yu smiled and said, "Thank you, thank you."

That's really an exaggeration, because my calculation ability is entirely dependent on a cheating calculator.

Von Neumann, on the other hand, did all the calculations by hand, which was horrifying.

Later he participated in the Manhattan Project and was ranked first in computing ability in the entire research team, with Fermi second.

The first of the two atomic bombs that exploded in Japan was called Little Boy, and the second was called Fat Man. Little Boy was a chain reaction of uranium 235, while Fat Man was replaced with plutonium 239.

Because plutonium 239 is relatively active, precise calculations are required to control its detonation, otherwise it will explode before it hits the ground. This extremely complex calculation was completed by von Neumann, who can be called a humanoid calculator.

In addition, von Neumann used his mathematical ability to analyze the optimal explosion height. He found that the atomic bomb would be much more effective if it was detonated at a certain position in the air than if it exploded after landing. He calculated the height of 550 meters.

A true Showa hero!
Although Fermi's computing ability was inferior to von Neumann's, it cannot be said that he was weaker. During the atomic bomb test, Fermi estimated the magnitude of the explosion energy with just a handful of paper scraps thrown at him.

As for why von Neumann later switched to electronic computers, it was because his computing ability was so outstanding that he accidentally became the father of modern computers (this title is shared by several people, such as Turing).

Li Yu could only change the topic from mathematics and try to lead the discussion to physics: "From your lecture, it seems that you want to explore the essence of the physical world and what quantum mechanics is trying to tell us."

"Mr. Academician has a rare insight in the world. He actually saw my direction in such a short ordinary mathematics seminar," von Neumann was surprised, and then admitted, "Yes, I want to know what is happening under these elegant mathematics."

Li Yu smiled and said, "There must be an undercurrent going on down there."

Von Neumann agreed: "The microscopic field is amazing and much more interesting than any adventure, because it is full of unknowns. I saw that someone had successfully conducted an electron scattering experiment and proved that electrons have wave properties. This is simply terrifying!

“Since it can be a wave, then it is possible for electrons to perform a double-slit experiment, or even a single-electron double-slit experiment. It’s chilling just to think about it!

"A single electron! It wants to interfere with itself?"

This question has troubled physicists for many years, but Li Yu is not one of them...

Li Yu said: "In my opinion, probability is a good thing. What is probability? It is uncertainty and ambiguity. So, I think the electron may not be a solid ball as conventionally believed."

Von Neumann was shocked: "How is this possible!"

Li Yu said: "Only by making such an assumption can many things be explained clearly. Do you still remember Professor Einstein's statement that the universe is finite but unbounded?"

Von Neumann nodded: "Of course I know."

"Similar assumptions can also be used for microscopic particles," Li Yu said. "Electrons may be a kind of fuzzy thing with a radius but no volume..."

"Fuzzy what?" asked von Neumann.

"A fuzzy energy field." Li Yu said.

Von Neumann was not so surprised at this time: "Mr. Academician also wants to use mathematics to deal with physics?"

Li Yu shrugged: "There is no other way. We can only assume that the electron has only radius, but no volume, not even boundaries, and no internal structure."

Von Neumann said, “Wouldn’t that make it a point particle of zero dimension, occupying no space at all, just a point?”

Li Yu said: "Maybe it is like this, at least it can be handled mathematically this way. It won't be long before Mr. Dirac in the UK will write his new paper - that's what he said in Brussels."

"That's interesting!" von Neumann said, "but I still can't accept the idea that electrons have no internal structure."

"It would be boring if we knew everything now." Li Yu said lightly.

Von Neumann said: "It's a pity that I don't know how to do experiments, otherwise I would really like to use the diffraction of electrons to measure the radius of electrons to see if it is as your theoretical deduction suggests."

Li Yu spread his hands and said, "We definitely can't do such a precise experiment under the current conditions."

From an experimental point of view, by bombarding electrons with electrons, we can indeed infer the radius of the electrons through the scattering angle.

Later, physicists used this method to measure the radius of electrons. But the experimental results were shocking and extremely strange:

The radius of the electron being measured will change with the energy of the bombarding electron!
Because the bombarding electron will transfer part of its energy to another electron, causing its energy to increase, the particle nature becomes more obvious and the radius becomes smaller.

If you want to measure a more precise radius, you have to bombard it with electrons with higher energy, which will make the radius smaller and lead to an infinite loop.

Until the wavelength approaches the lower limit of the Compton wavelength.

That is to say, the radius of the electron cannot be measured very accurately. - Well, wave-particle duality and the uncertainty principle are at work again.

That is why physicists speculate that electrons, as elementary particles, most likely have no internal structure, or to put it more rigorously, the internal structure of electrons is unknown to us.

Based on this speculation, the electron may be a vague energy field. So if you say that its volume is infinite, it seems not entirely wrong.

This theory can be used to explain quantum entanglement: because the two split particles use the same energy field, when you measure one of them, you are also measuring the other one at the same time.

Single-electron double-slit interference can also explain it: after all, it is a fuzzy energy field, and it simply passes through two slits at the same time.

Von Neumann was as indifferent as Dirac: "It is still interesting to study theory. There is no need to wait for experimental results. Mathematics can reveal everything."

He sat back in his chair, poured a glass of whiskey and took a sip, then said, "American wine is really boring. With this level of winemaking, why ban wine?"

Li Yu asked curiously, "Will you go to the United States to work?"

"The United States? How could that be! The scientific research capabilities of the United States are too poor!" Von Neumann laughed, and suddenly changed his mind, "But it seems that I can easily become a full professor there."

His family owns a bank, so he is not short of money, but of reputation.

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

Von Neumann's friend Wigner once said in an interview in the late 1980s: "The United States in the 20s was a bit like the Soviet Union: a big country without first-class scientific training or research. At that time, Germany was the greatest scientific country in the world."

Obviously, von Neumann wanted to stay in Germany, especially since he was currently studying the mathematical foundations of quantum theory, and only in Germany could he see the literature in a timely manner.

Although many people don’t know it, von Neumann’s contribution to the quantum field is not small at all. A few years later, he wrote a book called “Mathematical Foundations of Quantum Mechanics”, which is very impressive. In the book, he thoroughly analyzed the so-called “measurement problem” such as how the wave function collapses, when it collapses, and even whether it collapses.

However, his book does not answer another essential question: what causes the collapse of the wave function.

Although von Neumann did not answer, he gave some hints: human consciousness.

Of course, this view is not only rejected by the Copenhagen school, but also by Einstein.

What is more interesting is that as soon as von Neumann's book "Mathematical Foundations of Quantum Mechanics" was published, it had a little fan, this little fan is called Alan Turing. He described the book like this: "It is very interesting to read and not difficult at all."

Li Yu naturally knew that von Neumann would go to Princeton in the United States in two or three years, so he said to him: "Once a country has a strong industry and sufficient funds, it will naturally think about improving its academic level. Maybe universities on the other side will poach people with high salaries."

Von Neumann was honest and acquiesced: "They'd better allow me to drink."