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

Chapter 675 God’s Prophecy
The overall situation in Munich was not very optimistic, but the level of Munich University at this time was extraordinary. In the classical field, Roentgen was the leader, in the quantum field, there was Sommerfeld, and among the students there were a pair of explosive classmates: Pauli and Heisenberg. .

Therefore, when Einstein and Li Yu hold lectures, they can talk about difficult topics.

Einstein wrote his field equations on the blackboard and preached:

"Three years ago, I first thought about the appearance of the universe and proposed the theory that the universe is finite and boundless. Now that the general theory of relativity has been confirmed through solar eclipse observations, we can conduct further research.

"You see, if there is a spherical shell, that is, a two-dimensional surface of a sphere in a three-dimensional space, it is obviously finite, but two-dimensional creatures living on the spherical shell will definitely not find the boundary.

"Our three-dimensional world is similar. We just need to imagine the two-dimensional spherical shell as a three-dimensional space. In other words, our space is just a three-dimensional hypersphere in four-dimensional space-time."

Pauli immediately raised his hand and asked: "If the universe is finite and boundless, can I drive an aircraft like the spaceship in Mr. Li Yu's book, travel along a certain direction in the universe, and return to the starting point assuming infinite life?" "

Einstein said: "Yes, this also explains Olbers' Paradox by the way. Because the universe is finite, the sky at night cannot be bright.

"At the same time, such an assumption can also solve the field equations of general relativity. The system of partial differential equations requires initial conditions and boundary conditions. The initial conditions are easy to solve and can be solved according to the current universe; and the boundary conditions, since the universe is finite and boundless, there is no need for boundaries. conditions."

Heisenberg said: "The professor seems to be guiding us to solve this extremely difficult partial differential equation?"

"It can be understood this way," Einstein said, "but I have to add something to the field equation, because this equation only reflects gravity. And if there is only gravity in the universe, it should not be static and should collapse under gravity. So I think there is still an unknown exclusion term, but as for what it is, I don’t know, so I will use a capital Λ to represent it for the time being, and let’s call it the cosmic term.”

This is the famous Einstein's cosmological constant.

Pauli liked to play devil's advocate and immediately asked: "Professor Einstein, I admit that after introducing this cosmological term, gravity and repulsion can reach balance, forming what you call a static universe model. But the most critical issue is that the repulsion is Where and what provides it? No matter whether it is experimental observation or theoretical derivation, there is no so-called repulsion. "

"Excellent question," Einstein said, "but I regret to tell you that I really don't know, and even doubt it."

Pauli said: "Then the field equation after adding the cosmological term has unknown defects and is incomplete?"

"Well... you can put it this way," Einstein admitted. "After all, there are still many things we don't know about the universe. But it's okay, this way we have a research direction."

Einstein successfully resolved his embarrassment and saw Pauli's reputation as a "God-defying" - he said whatever he wanted and was not afraid of authority at all.

Pauli had always been like this. Fortunately, he studied with the good-tempered Sommerfeld at the University of Munich. When he transferred to Göttingen to study next year, Born couldn't stand Pauli very much.

After the lecture, he came to the office of the Department of Physics, where Sommerfeld praised Einstein's general theory of relativity.

Li Yuze suddenly took out a small magazine and said to Einstein: "Have you read this article?"

Einstein glanced at it and said, "I saw it. It was a manuscript submitted by a Russian mathematician named Friedman. He actually said that he had solved the new universe model through the field equations of general relativity, and divided it into Euclidean geometry and In the three cases of non-Euclidean geometry, the universe may be contracting or expanding, but no matter which one, he claims that the universe is not static.”

In fact, there are three situations of different spatial curvatures.

The world we usually recognize is a straight space, which is Euclidean geometry, or simply Euclidean geometry. The sum of the interior angles of a triangle is equal to 180°. Such a universe is infinite;

If it is a spherical space, that is, the finite and edgeless model assumed by Einstein, it is a space with positive curvature, and the sum of the interior angles of the triangle is >180°;

There is also a negative curvature space in the shape of a saddle surface. The sum of the interior angles of a triangle is less than 180°, which is also infinite.

Sommerfeld took it over, looked at it, and said, "The mathematical process is quite complete. Why wasn't it published in the Yearbook of Physics?"

"Because I reviewed the manuscript, I thought it was full of loopholes, so I rejected it. There were too many such strange articles." Einstein said.

"It's not necessarily wrong," Li Yu said. "I have observed the red shift phenomenon at the Harvard Observatory before. Although the amount of data is very small, at least it means that the stars are moving away from us."

"Isn't that extragalactic galaxy, called the Andromeda Galaxy, a blue shift?" Einstein said. "On a large scale, the universe should be static, although I don't have much evidence."

Sommerfeld said: "Guess? Professor Einstein really likes thought experiments. You can do the experiments in your mind, which is much faster than us working hard to make experimental instruments."

Li Yuze said: "If this cosmic term really exists and can provide repulsive force, physics will cause another wave. As the student named Pauli said when he asked the question, we have not observed this repulsive force. "If it exists, the universal gravitation we can observe is probably the resultant force."

Einstein said helplessly: "It is indeed a bit unbelievable, but I really don't know what this cosmic term is, it is just a conjecture."

His cosmological term constant will be full of twists and turns in the future.

A few years later, a Belgian priest, Lemaître, obtained the same results as the Russian scientist Friedman, believing that the universe was not static, but dynamic, either shrinking or expanding.

——Lemaître is amazing enough. He had been a professional priest before 1927. In 1927, he suddenly switched to astrophysics and achieved outstanding results.

Seeing more and more people deducing this result, Einstein began to feel that something was not right.

By 1929, Hubble measured a large number of stars and found that they were all redshifted. Almost intuitively, Hubble found that the farther away the stars, the greater the redshift, proving that the universe is expanding.

Only then did Einstein realize that he was wrong and admitted that "the cosmological constant was the biggest mistake of his life."

But Li Yu knew that the matter was not that simple, so he did not directly refute Einstein.

Half a century later, astronomers unexpectedly discovered that the expansion of the universe began to accelerate 60 billion years ago.

This thing is quite strange, because we don’t know where the energy that accelerates the expansion comes from.

Therefore, the scientific community speculates that there is a kind of "dark energy" in the universe, and this dark energy also provides repulsion and is evenly distributed (seriously suspected to be related to vacuum, because evenly distributed is vacuum).

Later, some people predicted that the universe would tear apart in the future through dark energy.

The most important scientists have calculated the cosmological constant, and it is extremely close to the -1 predicted by Einstein. It is really amazing!
Therefore, the cosmological constant that was abandoned by Einstein has magically returned (there are still many doubts to be studied).

Li Yu said: "Friedman's results can be shown to students and professors from major universities. If they can't find faults, it's not necessarily a bad thing."

Einstein said awkwardly: "If he is right, I will really become an ugly authority suppressing other scientists."

Li Yu laughed and said, "Are you living in such a disgusting way? Haha!"

Einstein shrugged: "Then I will send this paper to Göttingen and have a look. They are better at mathematics."——

In the next two days, Li Yu visited Röntgen who was ill in bed, and then set off for Berlin.

Germany is now called the Weimar Republic. Rathenau, the Minister of Reconstruction, invited Li Yu and Einstein to meet him at the mansion where he lived.

Rathenau didn't mention much about the fact that Li Yu had borrowed tens of millions of marks. After all, Germany's economy was in a mess at the moment, and marks were worth less than during the war. How could he dare to mention repaying the money.

He now occupies a high position and is one of the few people at the pinnacle of power in the Weimar Republic, but his personal wealth has not been greatly affected.

Einstein had met Rathenau four years earlier. At the banquet, he said: "I am very surprised and happy to see that our views on life are so consistent."

Rathenau smoked a big cigar and said with a smile: "I have also read popular explanations of the theory of relativity in newspapers and magazines. I can't say that it is easy to understand, but it is relatively easy."

He deliberately emphasized the word "relatively".

Einstein said: "As long as the paper is not published in a scientific magazine, it should not be particularly difficult, at least it will not involve complicated mathematics and mathematics."

"I even specialized in doing thought experiments, and recently I was thinking, how does a gyroscope know that it's spinning? How does it tell the direction in space that it doesn't want to veer," Rathenau said.

Li Yu smiled and said: "It's a good idea, but it's easy to solve. Just treat yourself as a top and spin it a few times."

"That's not a thought experiment, but just using yourself as an experimental instrument." Rathenau also smiled.

Einstein changed the subject: "Mr. Minister, I was entrusted by Weizmann for this visit."

"You know, I am opposed to his Zionism," Rathenau, who is also a Jew, stated his attitude directly, and then said, "I think the best way at the moment is to let Jews assume public roles and become the German power structure. a part of."

Einstein said: "Mr. Weizmann asked me to tell you that it is wrong for a Jew to manage the national affairs of another nation."

"No, no, no!" Rathenau shook his hand, "Jews like me can reduce anti-Semitism by completely assimilating into good Germans. Wouldn't this also help Mr. Weizmann's career?"

"Well, I will convey your message to Mr. Weizmann." Einstein said.

He was just passing on a message and would not take the initiative to persuade Rathenau.

The Minister for the Restoration of the Weimar Republic would also serve as the Minister of Foreign Affairs a year later. Several moves to sign contracts with the Soviet Union put him on the verge of danger. He was assassinated during an outing.

This was a very significant event during the Weimar Republic and was mourned by millions because it was a dangerous sign that more assassinations would follow.

Mustache must have praised the assassin.

At Heidelberg University, Leonard, who had always been opposed to Einstein and Judaism, also decided to hold classes as usual on the day of mourning.

Since then, Einstein's situation in Germany has not been as comfortable as it is now, because it is said that he was also on the assassination list, mainly due to his great fame.

Assassinations usually target big politicians or very representative figures.

Leaving Rathenau's mansion, Einstein casually asked: "Where are you going to give your lecture next?"

Li Yu said: "The lecture is temporarily suspended, I am going to write a paper."

"What paper?" Einstein asked.

Li Yu said: "I saw in a magazine that an associate professor named Stern of the University of Rostock and his assistant Gerlach conducted an interesting experiment."

"Another little magazine?" Einstein asked curiously, "How come you have so much time to read these things?"

Li Yu said with a smile: "I happened to see it, and it was related to quantum theory, so I studied it carefully."

"If you, Academician Li Yu, like it, their experiments may soon be published in the "Annals of Physics."" Einstein said.

Li Yu is concerned about the Stern-Gerlach experiment.

At first, the experiments of Stern and Gerlach did not attract attention, and they were not engaged in theoretical physics. Stern originally just wanted to verify who was right and who was wrong between Sommerfeld and Bohr.

After Bohr proposed the energy level theory, didn't Sommerfeld expand it on him? Sommerfeld felt that Bohr's orbital model was not necessarily a plane, and that the orbits of different electrons might have angles. But this suddenly changes from plane geometry to three-dimensional geometry, and the difficulty increases significantly.

Academic circles call it orbital quantization.

Sommerfeld proposed this theory before the First World War, but it was indeed difficult. In addition, due to the war, there has been little progress.

After the war, Stern, an "outsider", suddenly wanted to verify the theories of Sommerfeld and Bohr.

For quantum theory, Stern is indeed an outsider. He has been studying thermodynamics before and does not understand quantum theory very well.

He started the experiment quite simply, which was to let the heated silver atoms (the movement of the atoms become more chaotic after heating) pass through an uneven magnetic field and then project it on the screen.

According to Bohr's theory, the imaging will be two points, because the quantization of angular momentum can only take two values; according to Sommerfeld, adding the z direction, there will be three points.

Starting the Gerlach check revealed that there was nothing on the screen.

When Stern took it over and looked at it, there were two points. Because Stern smoked low-quality cigars, which contained sulfur, and when they encountered silver, they turned into silver sulfide.

——But it doesn’t actually prove that Bohr was right.

For them, the experiment ended here.

But Li Yu knew that this experiment had nothing to do with space quantization, but discovered an extremely important property - electron spin.