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

Chapter 699 Probability Explanation
For physicists in the 20s, especially those studying quantum physics, there were still too many things that could not be explained.

Li Yu said casually: "I just came from the UK, and I know you probably don't think highly of the British in theoretical physics. But the Cavendish Laboratory has taken hundreds of thousands of photos using the cloud chamber, and other laboratories combined probably have millions. This is the only way we can observe electrons, and the trajectory it produces does look like the effect of fast-moving particles."

Bohr and Heisenberg had long been troubled by this problem, because the concept of "trajectory" was incompatible with the idea of ​​matrix mechanics.

Current versions of wave mechanics don't quite explain this either. Although in wave theory one can have a localized bunch of waves moving together as a so-called wave packet, this would require a beam of matter spread out over a width much larger than the diameter of an electron, which is clearly not the case in a cloud chamber.

Li Yu mentioned this issue because he wanted to water both sides and put out the fire.

Bohr said with some resignation: "It is wrong to think that the task of physics is to discover how nature exists. Physics is concerned with what we can say about nature."

Einstein finally reached a certain consensus with Bohr: "And it is quite wrong to try to find a theory that is only about the macroscopic scale. Now it is the theory that determines what we can observe."

Heisenberg still said: "Theory must be based on existing experimental results in order to continue to derive new quantum mechanics. Experiments have proved that the microscopic world is discontinuous and quantized. Professor Schrödinger said that particles are waves, but waves are continuous!"

Schrödinger then said: "My wave function is indeed continuous, but when the vibration mode of the wave changes, it is quantized, so it can also explain quantization."

"So, professor, you want to use the idea of ​​continuity to deal with quantum discontinuity?" Heisenberg certainly disagreed. "But how do you explain that my theory is completely based on quantum phenomena and can also deal with quantum problems? After all, you have proved that the two are equivalent."

It’s really hard to answer his question.

Einstein added: “It is a pity that I have not yet made the effort to study Dr. Heisenberg’s paper, because it is incredible to me to represent quantum behavior with simple numbers. They are like witchcraft multiplication tables. Of course, if you forgive my poor mathematical skills, I have not yet understood the matrix.”

Among this group of god-level bosses, Einstein’s mathematics is definitely not the best.

Schrödinger was good at mathematics and said leisurely, "I don't understand matrices either."

Seeing that Heisenberg was about to be dissatisfied again, Li Yu quickly said: "In fact, there are still many areas that need to be improved in the wave equation."

"That's natural!" said Heisenberg. "He couldn't handle spin very well, and spin had already established itself under Pauli's paper."

Heisenberg hit Schrödinger's soft spot again. Master Schrödinger was not very happy. Li Yu immediately said, "But I suddenly thought of a way to explain the physical meaning of the wave equation."

Everyone was surprised: "How do you explain it?"

At this moment, the biggest difference between wave mechanics and matrix mechanics lies in their attitude towards quantum.

Li Yu wrote on the blackboard and said: "Professor Schrödinger wrote in his paper that the wave equation is very similar to a density function in fluid mechanics, so he guessed that the wave equation should also represent a certain density.

"The wave function has its own particularity, it is a function of time.

"So I think the square of the modulus of the wave function, that is, the square of its size, is the probability density. It represents the probability of finding a particle in the spherical space at a certain moment."

This is called the probabilistic explanation.

For most people, this statement is very shocking.

Einstein immediately stopped smoking his pipe and said, "You mean, although the wave equation describes matter waves, even if you go to great lengths to find a wave function that can describe a physical particle like an electron, your ability to find it still depends on a ghostly probability amplitude?"

Li Yu nodded and said, "That's right."

"Unbelievable!" Bohr said. He was actually a little happy in his heart. Probability was Copenhagen's favorite thing. "When Pauli comes back, I will call him to discuss it in detail."

Heisenberg also generally agreed with probability, but if it was correct, wouldn't wave mechanics be ahead of his own matrix mechanics? So he said: "I will first conduct an in-depth study of the wave equation, and then express my opinion on the probability interpretation."

As for Schrödinger himself, his expression was very complicated. He created the wave function to prove continuity, but it turns out that his equation actually represents probability in physics?

"If it's probabilistic, doesn't that mean that an entity like an electron has no definite path or trajectory through space, but can be found anywhere in a region of space determined by probability?" Schrödinger said. "I would rather believe that the particle is somehow controlled by a field, and that the field obeys a wave equation, so the particle moves like a wave, like a surfer."

Li Yu said: "It depends on the perspective of the observer, which one he wants to see as real, the particle or the field."

Historically, the probabilistic interpretation of the Schrödinger equation was proposed by Born, who won the Nobel Prize for it, but Born himself did not quite agree with it.

Because he thought that Schrödinger had already done everything, and he won the Nobel Prize just for proposing an explanation, which was not appropriate and even a little angry.

Born himself always believed that he should win the Nobel Prize in matrix mechanics together with Heisenberg and Jordan.

Schrödinger, Dirac, Heisenberg and others won the award in a short period of time: Heisenberg in 1932, and then Schrödinger and Dirac in 1933.

The Nobel Prize committee made such an arrangement because it is difficult to judge their contributions. They are all too important, and it is not even appropriate to award them one after the other.

So the Nobel Prize Committee's solution was to hold the 1932 Physics Prize until 1933 and award it together, so that no one could find fault and several people could be honored at the same award ceremony.

There are also photos online of Schrödinger, Dirac and Heisenberg going to Stockholm together.

But this raises two questions:
First, why were Born and Jordan, who were also very important to matrix mechanics, not awarded the prize?

Secondly, if the prize was only intended for Heisenberg, Schrödinger and Dirac, why not let them share the physics prize in the same year? After all, the principle of the Nobel Prize Committee is that no more than three people can be selected at a time.

The most likely explanation is that in early 1933, the Nobel Prize Committee had already decided to award the 1932 prize to Heisenberg, Born and Jordan, and the 1933 prize to Schrödinger and Dirac.

But a few months after the initial decision was made, a far-reaching event occurred in Germany: the mustached Hitler became the chancellor.

The mustache was in power in Germany, and Jordan joined the sodium crisp at this time!

The Nobel Prize Committee did not want to be seen as siding with a man who openly supported Hitler's activities, so it eliminated both Born and Jordan from consideration - since it was impossible to separate their joint work and award the prize to one of them alone.

This incident was very embarrassing for Heisenberg himself, because he knew that without Born and Jordan, matrix mechanics would never have been created. Born, as the leader of the Göttingen team, regarded this as a humiliation to himself.

After Heisenberg received the letter from the Nobel Prize Committee, he immediately wrote a letter to Born.

But Born was still upset about the Nobel Prize Committee's actions for many years. In the 1950s, he wrote a letter to Einstein:

“Heisenberg had no idea what a matrix was until I told him. It was he who received all the honors for our work together, such as the Nobel Prize. … I was deeply hurt that I did not receive the Nobel Prize with Heisenberg in 1932, although Heisenberg wrote a very friendly letter.”

Heisenberg felt some relief when Born finally won the Nobel Prize in 1954 at the age of 72.

But this can be seen as a re-award by the Nobel Prize Committee. Although the reason given is "probabilistic interpretation", Born's greatest contribution is matrix mechanics.

Moreover, probability had already been accepted by Copenhagen in the quantum field in the 20s, and it was Copenhagen that later truly developed this concept.

It can be compared to the Nobel Prize Committee awarding Einstein the prize. The reason was not the theory of relativity - it was just a random excuse because his contribution was already worthy of the Nobel Prize.

So the probability explanation Li Yu proposed at this time was not a big deal, and it couldn't even be regarded as a Nobel Prize-level discovery...

Of course, the probabilistic interpretation itself is very important. The Copenhagen interpretation, which integrates probabilistic interpretation, uncertainty principle, wave-particle duality, incompatibility principle, complementarity principle and other physical ideas that are profound enough to be almost philosophical, has brought about the most profound revolution in quantum mechanics.

In the following days, everyone turned their discussion to the strange probability explanation proposed by Li Yu.

Li Yu also wrote a short and concise paper.

As no consensus was reached, everyone decided to go back and prepare and discuss the issue again at the next meeting.

But overall, Bohr and Heisenberg expressed great enthusiasm for this and were prepared to add some details.

Only Einstein said a meaningful sentence: "Quantum mechanics is now magnificent, but there is a voice in my heart telling me that it is not what it seems. Although this theory describes many things, it does not really bring us closer to the secret of the 'old man'. In any case, I am convinced that the 'old man' is not rolling the dice."

The old man Einstein mentioned is God.

This sentence is the original source of the famous "God does not play dice".

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After this small gathering in Copenhagen, Li Yu planned to go to Berlin to see Planck and travel with Einstein and Schrödinger.

Einstein naturally went back to work; Schrödinger went to the University of Berlin to give a lecture and also took part in the "interview".

Planck is going to retire this year, and his position as professor of theoretical physics at the University of Berlin needs a successor. The University of Berlin attaches great importance to this, because this position is almost the highest position in theoretical physics in continental Europe, and they have set up a special committee for this purpose.

Einstein was certainly not among the committee's considerations; he was already a special professor of physics at the University of Berlin, and a professor without any teaching duties.

Li Yu certainly couldn't do it either, as he couldn't stay in Europe for so long, not to mention he wasn't a German.

Heisenberg was considered by the committee, but he was too young, only 24 years old.

So in the end there were only two people on the list: Schrödinger and Born.

The committee was more inclined to Schrödinger because Born's position in Göttingen was not low and he might not give up the position; secondly, this year was Schrödinger's "miracle year" because wave mechanics was born and shocked the world, so the University of Berlin was very optimistic about him.

Einstein smiled and said, "I should congratulate you in advance. We will be colleagues in the future and can have more academic discussions."

In the subsequent great debate of the century, Einstein was in the same camp as Schrödinger.

Schrödinger said: "Just like you left Zurich, I was a little hesitant. After all, life in Zurich is so comfortable and kind to my lungs. Berlin not only has a tense political atmosphere, but also has industrial polluted air that makes it difficult to breathe."

Li Yu said: "What you said is true, but this position is too attractive, isn't it?"

"It was indeed difficult to refuse," Schrödinger said with some entanglement. "After the University of Zurich learned of the invitation from the University of Berlin, they tried their best to retain me and were willing to offer me a joint professorship between the University of Zurich and the Swiss Federal Institute of Technology, doubling my salary."

"What are the teaching tasks?" Li Yu asked.

"Unfortunately, the teaching workload has to double," Schrödinger said bitterly.

His weekly teaching workload is already 11 hours, and if that were doubled it would be over 20 hours, leaving him with no time to do research.

"What else is there to think about?" Einstein said. "Come to Berlin!"

Schrödinger said: "Before that, I will go to the United States to give a series of lectures."

Einstein applauded and said, "What a job! How much do they pay?"

"The University of Wisconsin itself offered $2500," Schrödinger said. "In addition, Johns Hopkins University wanted me to stay in the United States and become their professor of theoretical physics, which would pay me very well."

Einstein immediately shook his head: "The University of Berlin can give you the same treatment, and the academic atmosphere is much better than that of Johns Hopkins University and even the entire United States."

"Of course I won't agree to this," Schrödinger said decisively. "It's hard for me to imagine that the United States is an uncivilized country that prohibits alcohol!"

"Yes, if we can't drink, what's the difference between this and primitive society?" Einstein agreed.

The two of them were talking back and forth, not taking the American academic community seriously at all...

But for now, the Ivy League schools in the United States can only listen to the criticisms from the bigwigs and then look for the reasons in themselves.