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

Chapter 698: Huashan Sword Contest

In addition to 8 permanent members, the Copenhagen Institute now has about 10 long-term visiting scholars, which is basically at saturation.

The design and planning of the institute is a typical model of theoretical physics institutes in the first half of the 20th century: the top two floors are dormitories, the basement is for experiments, and only a small half of the space is actually used for theoretical physics research.

After Li Yu arrived at the Copenhagen Institute, Bohr said happily: "Do you see this football? It's the one we played together when you came to the University of Copenhagen, Mr. Li Yu."

Li Yu smiled and said, "It is so memorable."

Bohr said: "Given the level of football in your country, it won't be bad at the Olympics."

Li Yu sighed: "It would be great if it could be maintained."

The level of football during the Republic of China period was quite high, at least dominating Asia.

Li Yu saw that their laboratory had a single-photon experiment device and asked, "Do you want to repeat this experiment too?"

Bohr said: "Times are changing too fast. Two years ago, I didn't believe in the wave-particle duality you and Einstein claimed, but now the Compton effect experiment has been done, and I have to choose to accept it. The dilemma between wave and particle nature put me in a difficult situation for a while, but I have to hold a funeral for the BKS theory."

The BKS theory was originally proposed by Bohr and two other scholars in an attempt to resolve the debate between waves and particles.

According to this theory, there are some virtual vibrations corresponding to classical vibrations near every stable atom. They are considered to be just a statistical average. However, this view abandons the most basic laws of conservation of energy and momentum in physics, so there are many opponents, not only Einstein and others, but also Pauli, a staunch follower of Bohr, who strongly disagrees.

In addition, in the past two years, more and more experiments have proved that energy conservation exists not only in a statistical sense for microscopic particles, but also for individual particles. Bohr had no choice but to abandon the somewhat absurd BKS theory.

Li Yu said: "There is a saying in the East, called Nirvana and rebirth, a funeral is not necessarily a bad thing."

"Sir, you are still full of philosophical thoughts as always," Bohr said modestly. "The several doctoral students in the institute must have a lot to talk about with you."

Heisenberg is definitely involved here.

Li Yu asked: "When will Heisenberg return to Copenhagen?"

"It should be soon. Professor Born has received an invitation from the United States to lecture on matrix mechanics at several American universities, and Heisenberg has nothing to do in Göttingen," said Bohr.

"Why not hold a small academic exchange meeting here and invite them all?" Li Yu suggested.

"I think Mr. Einstein would also be interested." Bohr readily accepted the idea.

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The first thing that comes is love for the great God.

Li Yu shook hands with him and said, "Professor, you have helped quantum mechanics take a big step forward."

“In fact, even I am beginning to be confused,” Einstein said, smoking his pipe.

"I read the article on Bose-Einstein condensation. The professor's performance was selfless," Li Yu praised.

Einstein said indifferently: "It is necessary to add his name."

Einstein had a very good personality and charm.

In fact, at least 99% of the credit for Bose-Einstein condensation can be attributed to Einstein.

Bose made a huge mistake at the time, and all the newspaper editors saw it and rejected the manuscript. Bose had no choice but to send it to Einstein, who praised it highly and took the initiative to translate it into German for publication.

Einstein then made a further expansion, predicting that below a certain temperature, all particles would enter the ground state and a phase transition would occur on a macroscopic scale, the so-called Bose-Einstein condensation.

These were all done by Einstein, and Bose didn't even realize that Einstein was doing his calculations in a different way.

Bose-Einstein condensation is clearly an achievement in the quantum field. Even though Einstein had always opposed quantum mechanics, he had been at the forefront of the quantum field several times.

Li Yu asked again: "Professor, have you read the paper on wave mechanics?"

Einstein said: "I have seen it. He has made a perfect extension of de Broglie's paper, which can touch a new world. I have thought before that if a beam of gas molecules is used to do a double-slit interference experiment, they may interfere with each other like waves."

Li Yu said: "The double slit is a bit difficult, but it won't be long before someone can perform a diffraction experiment."

Einstein at least insisted on the wave-particle duality. "I am looking forward to it. But I am still uneasy about the direction of quantum theory. Although there is nothing wrong with it mathematically, its physical properties have been hidden, which is not a good phenomenon."

"Don't you think Heisenberg planted a big seed?" Li Yu asked.

Einstein said bitterly: "I am changing my mind now. What Heisenberg planted was actually a quantum egg! Everyone in Göttingen believed him, but I still can't believe it."

This is Einstein's complex attitude towards quantum.

He may hope that quantum theory and experiments will complement each other and proceed step by step, rather than taking a sudden leap forward in the past two years.

But the experiments in quantum mechanics are actually much simpler than his general theory of relativity... Einstein's predictions of general relativity were not able to be verified until more than half a century later.

"It's an honor, Professor Einstein. I share the same opinion as you!" Schrödinger said, "I also find it difficult to accept Heisenberg's statement."

Bohr asked casually: "Professor Schrödinger, what do you think should be done?"

Schrödinger said: "Wavelength is the only determining factor in quantum mechanics. Even quantum jumps must conform to continuity."

Quantum jump is one of the core ideas of Bohr's energy level theory. Bohr immediately refuted: "Whether it is the atomic spectral lines in the experiment or the energy level theory, as well as the incompatibility principle of two outstanding doctoral students Pauli and Heisenberg's matrix mechanics, they all prove the correctness of quantum theory. Wave nature is not the determining factor! Especially Heisenberg's matrix mechanics, which perfectly embodies the mathematical non-commutativity."

"Matrix mechanics?" Schrödinger seemed to be waiting for this question. "I just happened to have a result that I would like to show you. I have already sent it to the magazine and you will see it in the Annals of Physics in a day or two." Schrödinger took out a stack of papers from his bag. "Matrix mechanics can be derived from wave mechanics by replacing the variables corresponding to position and momentum in my wave equation with two expressions called operators from Heisenberg's matrix mechanics."

This sentence is a bit hurtful.

"You mean that Heisenberg's matrix mechanics and your wave mechanics are actually mathematically equivalent?" Einstein asked in surprise.

"Yes!" Schrödinger said, "My theory can easily deduce atomic spectral lines. So wave and continuity are the basis of the quantum field! Not discontinuity!"

Several people passed around Schrödinger's paper.

Master Xue's handwriting is much more beautiful than Heisenberg's, and his mathematical knowledge is also deeper.

Schrödinger's approach is called "substitution" in mathematics, and it can be used in another way to transform from matrix mechanics to wave mechanics.

He was not the first person to discover that matrix mechanics and wave mechanics are mathematically equivalent. A month ago, the "God of Argument" Pauli had already discovered this connection.

However, although they both proved that the two are equivalent, they did not understand why this was the case and were unable to comprehend the deeper essence of mathematics.

It would take months for Dirac to explain why. He developed another way of looking at the quantum world, which he called transformation theory, and used some difficult mathematics to prove that all versions of quantum mechanics were contained in this all-encompassing theory.

Dirac was really strong, but like Yang Zhenning, most people outside the industry don’t know much about their work. The main reason is that their work is too basic and very mathematical, which is not easy to understand. It often involves various complex and profound field theories.

But most physicists do not want to get involved in too advanced mathematics because it is too painful. After knowing that matrix mechanics and wave mechanics are equivalent, most theoretical physicists will choose Schrödinger's wave mechanics, even though matrix mechanics has more advantages in dealing with spin, but wave mechanics is the differential equation they have been using, which is much more familiar than matrices and has some connection with classical physics.

This result is obviously not what Heisenberg wanted to see. He worked so hard to come up with matrix mechanics, but less than a year later, you, Schrödinger, came up with wave mechanics?
So when Heisenberg arrived, he immediately expressed his own opinion to fight back: "Wave mechanics cannot find sufficient physical meaning."

Schrödinger replied: "The same is true for matrix mechanics."

The two are simply hurting each other, and neither theory has sufficient physical explanation to support it.

Heisenberg said: "Even if they are mathematically equivalent, wave mechanics is inspired by matrix mechanics, and there is a sequence of events."

"Not really," Schrödinger said. "My theory was inspired by de Broglie and benefited from the brief but far-sighted comments of Mr. Einstein and Mr. Li Yu. It has nothing to do with matrix mechanics. Moreover, matrix mechanics is too complicated for me. I am even a little scared by it."

Heisenberg had another card to play: "You can't replace quantum jumps and quantum states and discontinuities with waves and vibrational modes."

Schrödinger said: "My wave mechanics is a step from classical particle mechanics to a continuous theory. This theory is based on a continuous field, although this field does not exist in the actual space we see in daily life, but in an abstract multi-dimensional space. But in this way, physics can be completely pushed back to the classical picture and atomic model."

Heisenberg quipped, "Professor Schrödinger wants to set physics back?"

"It is definitely not a step backward. You can think of it as a philosophical consideration," Schrödinger had been studying philosophy for a long time before, and was almost the best philosopher among physicists. He continued, "The most beneficial to the future development of quantum physics is the 'intuitive' wave mechanics that I insist on, rather than suppressing 'intuition' and using other theories such as transitions, probabilities, energy levels and other abstract concepts."

The two of them were debating about philosophy, and Li Yu quickly interrupted: "Apart from the mathematical debate, I think the bigger disagreement between you two lies in the interpretation of quantum. Is it that Dr. Heisenberg does not recognize determinism, while Professor Schrödinger at least believes that volatility is deterministic."

The two nodded and said, "Yes."

Well, then there is no way to reconcile.

Although Schrödinger and Heisenberg had many debates on matrix mechanics vs. wave mechanics in history, the debate reached a new height, especially after proving the equivalence of the two.

But in essence, the two have very different ideas about quantum, and neither side is willing to give in.

However, the confrontation between the two at this time could only be considered a preliminary one, and the real debate would have to wait until the Solvay Conference next year.

Einstein put down his pipe and said something for his teammate Schrödinger: "The microcosm constitutes the macrocosm. It would be terrible if there was no determinism in the microcosm."

Although Heisenberg did not have Pauli's quick temper, he was very confident in his theory, so he said: "I think indeterminism, that is, the disappearance of strict causality, is necessary! Otherwise, there is no way to explain why quantum jumps are discontinuous!"

Schrödinger objected: “If there is no law to describe the motion of the electrons in the quantum jump, then the whole concept of a quantum jump is a complete fantasy.”

When it comes to quantum jumps, Bohr can no longer remain silent: "This does not prove that there are no quantum jumps, but only proves that we cannot imagine them. For quantum jumps, the experiments and descriptions in classical physics are not enough."

Schrödinger said: "If the damn quantum jump really exists, I shall be very sorry that I ever took part in quantum theory."

This is a famous statement made by Master Xue, indicating that he had firmly stood on Einstein's side at this time.

——It seems that Einstein and Pauli both said similar things.

"We cannot indeed observe the orbits of electrons inside atoms," Heisenberg said, "so a good theory must be based on quantities that are directly observable."

This was Heisenberg's creed. He firmly believed in quantum theory and chose a path that classical physicists could not find fault with: the theory was entirely based on experiments, and the new results derived from it must be true, thus verifying the correctness of quantum theory.

Einstein spoke again: "But you do not really believe that only observables can enter into a physical theory."

Heisenberg was a little surprised: "Isn't that what your theory of relativity does?"

“Perhaps I did use this kind of reasoning,” Einstein admitted, “but it is still nonsense.”

Heisenberg said: "Neither relativity nor quantum mechanics is nonsense."

“Well,” Einstein complained, “but there seems to be a new fashion in physics now, which is to claim that something cannot be observed and therefore is not real.”

Li Yu smiled and said, "The fashion you are talking about is exactly what you did in 1905."

Einstein was stunned and didn't know how to refute. He could only make a joke: "Good jokes should not be repeated all the time!"