This article is from WeChat public account:Back to Park (ID: fanpu2019), author: Thomas Levenson (MIT), Translator: GAO (PhD Astronomy University of Heidelberg), from the title figure: vision China
In order to explain the deviation between the prediction of Mercury’s orbit and Newton’s theory, the French astronomer Levier calculated according to Newton’s law of universal gravitation. In 1859, he made the assumption that there is still an undiscovered planet in the orbit of Mercury. He also named it “Span class=”text-remarks” label=”(Vulcan)” in the name of Vulcan in Roman mythology. Since then, people have been madly looking for this planet, but have never been able to confirm its existence. Until the completion of Einstein’s general theory of relativity in 1915, the first problem solved was to explain the perturbation of Mercury’s orbit. People have since confirmed that Zhu Rongxing does not exist.
The assumption that Zhu Rongxing has disappeared and died, there is absolutely no need to exist. Levier found a planet on his nib, and Einstein’s pen destroyed Zhu Rongxing and re-imagined the universe. Today’s article is excerpted from the book “Hunting Zhu Rongxing”, which tells the story of Einstein’s construction of general theory of relativity under the gloom of the First World War, and finally sees the joy from the unknown darkness. Crazy moments.
For Einstein, this (Editor’s note: the two sides of the war during the war, the continued use of gas as a weapon) is undoubtedly a madman behavior. He wrote:
“All of our proud technological advances and civilizations can be axe in the hands of heartbreaking people.”
This sentence has now become one of his most famous quotes. World War I broke EinsteinSomething in the frankly ruined his faith until the fall of 1914. This belief unites the unselfish elites of all nations: to study “this huge world – it is independent of our human existence, and it is like a great and eternal mystery before us.” When I was young, Einstein quickly noticed that many people whom I respect and admire have found inner freedom and peace while focusing on this cause. He thinks that when he comes to Berlin, he can join the ranks of this group of people. However, now, just a few months after he arrived here, the “elite” left him.
But he is still sticking. He doesn’t have to be like this. He still has Swiss citizenship and can cross the border between Germany and Switzerland during the war, and Zurich has always been his favorite city. In addition, due to the blockade of the British Navy, the wartime Berlin is not only politically grim, but people often have to go hungry. But all of this is not important, Berlin has a unique place. That is, even if all of Einstein’s colleagues were stunned by the enthusiasm of war, at least they did not let him be disturbed. His wife and children have also left, and he lives alone. He is in the Haber (Editor’s note: Einstein’s closest friend in Berlin, Fritz Haber) Institute of Chemistry I keep the office, and I ignore the things around him that make him unhappy at work. He can think without being disturbed.
Therefore, the August shock subsided and Einstein returned to work. On October 19th, he gave a lecture at the Prussian Academy of Sciences, which was the first of two lectures. He is not talking about war, but gravity, and put forward a general theory of relativity that he believes has been basically completed.
In these two lectures, Einstein said that his new theory is not only a solution to a specific problem, but also a new way of thinking. He explained the importance of non-European geometry in this pioneering work. In non-Euclidean geometry systems, parallel lines may intersect in a curved space. He said that these concepts are not just abstract toys in the hands of mathematicians, but should be used as a practical way of describing the real world. The results obtained by these methods make his theory comparable to Newton’s theory of gravity: in Einstein’s theory of gravity, the shape of space and time determines the motion of an object.
The audience heard completely from the lectures. Although logically sufficient, Einstein admits that his theory has not yet been finalized. The most grotesque part of Einstein’s theory is the geometric nature of gravity, which is difficult to understand. Although his German colleague tried his best to hire him, no one really realized the true meaning of the lecture they just listened to. First of all,Newton’s theory of gravity is wrong. Second, to understand gravity properly, physicists must reimagine the basic assumptions about the behavior of the universe. Einstein told them two times in person and published a 55-page paper in the journal of the Prussian Academy of Sciences. After the publication of this article, Einstein received only a few letters from foreign researchers, discussed some minor details with him, and did not discuss the basic assumptions. But in Berlin, no one noticed even the details.
Einstein had expected it. Prior to this, Max Planck, the leader of German physics, had already warned Einstein not to get involved in gravity. This question is too difficult. He said: “Even if you succeed, no one will believe you.” Science will develop because of better ideas, but when these ideas are too novel, scientists will not recognize, at least Will not be recognized immediately every time.
Einstein ignored Planck’s advice and his colleagues’ indifference. The October lecture included the most complete content of the gravitational theory he could complete. There is still an unsolved problem in his equation. In some cases, Einstein’s new theory (1913-1914) violates a key principle in the special theory of relativity: the use of time and space The mathematical language, each observer in the relative movement must make an equivalent description of the same event.
At the time, Einstein believed that the generalization process of relativity necessarily played a role in the movement under the influence of gravity. but it is not the truth. The loss of immutability is indeed worrying. At this moment, Einstein has done his best. He still could not find the errors that might occur in the theory.
At the end of the first year of the war, ordinary soldiers on both sides of the Western Front declared a Christmas truce (Christmas Truce) to celebrate this beautiful and melancholy Christmas. Einstein was somewhat distracted in the first few months of 1915. He tried to get involved in the field of experimental physics but failed. He thought about the war and hated the war. Later that year, he made his first public statement about war and peace, expressing his anger.
After eight months of thinking, he returned to the study of gravity.
David Hilbert (David Hilbert) is the most influential German mathematician of Einstein’s era, and Still learningThe results of the work and “Hilbert’s 23 questions” are well-known in the world – the mathematical problems that Hilbert listed in 1900 that were not solved at the time need to be broken in the 20th century mathematics research. For Einstein, Hilbert, a professor at the University of Göttingen, has a special charm because he is one of the few first-rate mathematicians interested in Einstein’s work. He did what no one in Berlin did – inviting Einstein to give six lectures and an in-depth introduction to his theoretical research. (See “Hilbert and General Relativistic Field Equations”)
At the lectures from the end of June to the beginning of July, Einstein still believed that his previous two years of work were satisfactory. He didn’t care very much that his new results could not be exactly the same as the special theory of relativity, nor did he notice that the equation he proposed in 1914 could not calculate the correct Mercury orbit. He still believes that the essence of gravity is geometric, at least as a whole, just lacking in detail, he said in Göttingen. He felt that his lecture allowed Hilbert to accept these new methods of gravity.
He is right. Hilbert believed in him and began to study the theory of gravity that is consistent with the special theory of relativity. We don’t know when Einstein began to realize that a competitor is studying the problem that has plagued him for eight years; I don’t know when he started to examine the work with a critical eye. . Before September 30, he told his friend, also his supporter, Freundlich, that his theory was in trouble. The opportunity to find trouble was that he suddenly caught the problem that he faced as early as 1912, which was a question raised in the ideal rotating reference frame. When he analyzed the acceleration motion in the rotating reference frame, he found that the result violated the equivalent relationship between acceleration and gravity – and the equivalent principle is the basic principle of the whole theory. He told Freundlich that “there is a clear contradiction” – which is fatal to theory. He added that the same problem also caused the correct Mercury orbit to be obtained according to theory. The worst part is that he can’t find a breakthrough. He wrote, “I can’t believe I found the mistake, because on this issue, I always follow the same line of thought.”
How embarrassed Einstein can get help! However, Freundlich did not respond to (at least the reply letter was not retained), he is not a professional theorist. It doesn’t matter, in the next few weeks, Einstein found a solution. As soon as he formed an answer in his mind, he was almost silent. From October 8th, he only wrote four letters, two of which were written to some machines.A brief introduction to the study; a letter to a friend of Zurich, most of which is related to the family; and a letter to the Dutch physics predecessor Lorenz (Hendrik Lorentz), in the letter discussed his new ideas about gravity. For the rest of the day, Einstein seemed to use all his energy for thinking and calculation.
If you recall, this is the hardest period of Einstein.
In 1914, Einstein was in Berlin
Although there are no detailed records showing the details of Einstein’s work in the next six weeks, the general situation regarding the final inference is clear. In Grossman, who co-authored with Einstein before the war, an Einstein note showed that Einstein studied some problems and added them to the existing theory, eventually getting almost complete. result. He had simply thought about the relevant content in 1913, but he gave up on these ideas. Now, two years have passed and he has a new perspective.
In the next few weeks, he used those methods to solve the big problems in his previous work, proving that acceleration motion and gravity are equivalent in all environments. At the end of October, Einstein knew that his work was almost finished. On November 4th, it was Thursday, when he came to the lower part of Bodhi Tree and showed the first part of his four progress to the Prussian Academy of Sciences. He has not had time to enrich all the new theories, the biggest missing is the final equation of the gravitational field. He has not yet produced specific calculations for any key tests conducted on this idea. But the current work is logically self-consistent. In addition, he proved that the approximate solution of the field equation is Newton’s law of motion, as it is necessary. Because most of the problems in the solar system, Newton’s law is established.
On the next Thursday, he came to the Academy with a new development, but there was a mistake. He corrected this mistake two weeks later.error. He returned home and continued to think and calculate. Another week has passed. This theory is finally reliable enough to accept the test of reality. Although there are still some problems in mathematics, it is not important. Those are the problems of the surface form, not the physical ones. He writes, “I am very satisfied”, and “temporary” does not have to worry about the details.
Instead, he is concerned with the core of the problem: he placed a point quality – the sun at the origin of the coordinate system. Next, he calculated the gravitational field that this point mass can produce. By analyzing this gravitational field, the first novelty can be found almost immediately: the starlight around the sun is bent. This has been predicted in his early theory, but there are some differences in this: the light passing through the solar gravitational field is deflected by 1.7 arc seconds, which is twice the theoretical prediction of 1913.
The result is a prelude, a warm-up match. The important thing is about to happen, it will prove that Einstein’s theory captures some facts that cannot be explained by other methods. Two weeks ago, he showed Newton’s theory of gravity from his first-order approximation of the new mathematical description of gravity (a low-resolution image) It naturally appears. He repeated the analysis and extended it to the next obvious question: What can we find out from the second-order or higher-resolution solution? This is followed by a mathematical proof of a piece of paper, he got a new equation, one of which comes from the approximation of Newton’s gravity.
After deducting seven steps, he gets an equation: this equation can be used to analyze the orbit of a planet orbiting a star. The star is still at the origin of the coordinate. If he knows some parameters obtained through observation, he can predict the perihelion precession of the celestial body moving around the origin.
November 11-18, 1915
Einstein collected some data about Mercury. He wrote the cycle of Mercury, entered the orbital parameters and the minimum distance between Mercury and the Sun, and substituted the speed of light into the equation for calculation. When he completed the calculations for each of these steps, the numbers appeared. He stares at the result…
November 18, 1915
When his work was shown at the Prussian Academy of Sciences, Einstein hided his emotions under the courtesy of scientific communication, showing little trace of excitement. “The calculation of Mercury shows,” he said to the audience. “After a century, its recent point will move 43 degrees.Seconds, while astronomers actually have more observations than the theoretical values calculated by Newtonian mechanics (45±5) angular seconds, and astronomers This cannot be explained by Newton’s theory. “After reviewing this obvious fact, he said, “So this (new) theory is exactly the same as the observations.
This unfeeling tone can’t hide the shock caused by his discovery. The attempt to save Newton’s doctrine for decades has come to an end. In the hypothesis, Zhu Rongxing disappeared and died. There is absolutely no need to exist. There is no longer a large chunk of material in the universe to explain Mercury’s orbit. There are no undiscovered planets, no asteroid belts, no interstellar dust, no spheroidal sun, nothing – except this new concept of “gravitational”. The sun has caused depressions in time and space because of its huge mass. Mercury, surrounded by the gravitational field of our stars, is buried deep in the gravitational pits of the sun. a Like all objects that sail in space and time, Mercury moves along that twisted, four-dimensional curve… until, as Einstein finally captured all of this in mathematical abstraction, the operation of the innermost planet The track is far from Newton’s theory.
It is said that Newton is a lucky person, because only one universe can be found, and he has already discovered it. It is said that Levier found a planet on his nib. However, on November 18, 1915, Einstein’s pen destroyed Zhu Rongxing and re-imagined the universe.
The huge space-time depression around the sun makes the orbit of Mercury elliptical, and its precession at the perihelion coincides with the value of the first observation of the 1859 Levier.
Einstein allowed himself to enjoy victory when he was with friends. Use equations to represent the correct orbit, enter numbers, and then appear Mercury—in Einstein’s own words, it’s like magic. Einstein fully felt that theory and realityA perfect match is a miracle. At some point in the week before he went to the Academy of Sciences, when he was working at the desk and proceeding to the final steps, the correct answer appeared. He told his friend that it was the time when the heart really trembled in the chest – the real heart. He wrote that it felt like something fits with him, and when describing another friend, he said that he was “ecstatic.”
A long time later, Einstein tried to describe his first feelings when he got this major discovery, but he couldn’t do it. “For many years in the dark, I have been looking for the truth that I feel but I can’t express. I am eager to keep on, and my confidence and worries are constantly changing. Until I see the clouds, everything is clear,” he wrote. “Only these have been experienced. People will understand.”
This article is from WeChat public account:Back to Park (ID: fanpu2019), author: Thomas Levenson (MIT), Translator: GAO (PhD Astronomy University of Heidelberg)