"A great wise man among mankind discovered that on a rotating stage, its space is curved."
On the third day in E City, they came early Arrive at the fifth district of E City.
This activity area has a particularly eye-catching huge circular building. A sign hangs at the entrance, which reads: This is a building designed based on Einstein’s theory, covering an area of Covering an area of ??about 4 hectares, the main body of the building is a large circular rotating stage with a radius of 100 meters. Supporting the entire stage is a thick, solid rigid shaft. The stage can be equivalent to the effect of a uniform rotation of 380,000 revolutions per second. The linear speed of the edge can reach 0.8C, which constitutes a curved time- Empty area.
After reading the introduction, a staff member came and led them into the interior of this huge building. When you look up, you can't see the stage rotating at all. It's no different from the big stages you usually see.
The staff said to them: "This stage looks stationary, just like a large circular stage with a radius of 100 meters. In fact, it is rotating smoothly and at high speed. This There is a super powerful force on the stage that will push you radially outward. The size of the force is proportional to the product of the distance from your position to the center of the stage and the square of the angular velocity. The angular velocity of the stage rotation is approximately ω=2.4×10^ 6 rad/second, so the radially outward pulling force is zero except at the center of the stage. It increases rapidly as the distance from the center of the stage increases. It will be a very large force at the edge of the stage.
“Since any place on the stage except the center will be affected by this force, this forms a circular area where the force vector is distributed: If there is an object on the stage with a mass of m, it It will experience a radially outward force with a magnitude of m*ω^2*r. Moreover, the mass of this object also changes, increasing as the distance from the center increases.
As soon as you enter the stage, you will rotate at high speed with the stage, so it is stationary relative to the stage. But because it will be affected by a huge inertial force, each of you will be given a pair of magic shoes. If you put on these shoes, you can avoid this strong radial outward force, just like walking on a stationary road. Same on the stage. Therefore, you must never take off your magic shoes on the stage. Without these shoes, you may be immediately thrown to the walls around the stage and smashed into pieces. ”
Then he said: “I will give each of you a clock with the same appearance and structure to measure the changes in the running time of the clocks at different locations on the stage; the changes in time After the measurement, you have to go to the center of the stage to get a 1-meter measuring ruler, so that you can observe the changes in its length at different locations on the stage, and measure the stage perimeter to understand the geometric properties of the stage space. "
"Did you hear clearly? Any questions? ”
Yiru asked: “How can we compare the differences in clock speeds in different places and the changes in the length of measuring sticks in different places? Can you be more specific? "
"This classmate asked a good question. I missed the question just now. Whether it is a measurement of time or length, the end result is compared to the clock and ruler at center stage. There is a smart telescope in the center of the stage, which can clearly see images within a hundred meters, and can also directly read the time displayed on the clock and the length of the measuring tape. So when you are doing an event, someone can be on the edge of the stage or somewhere else, but there is always someone in the center of the stage, observing and comparing through the smart telescope with the clock and ruler in the center of the stage.
"Okay, if there are no problems, you can put on the magic shoes just issued to you and enter the stage to carry out activities. I would like to remind you again, you must not take off your shoes on the stage, otherwise The consequences would be disastrous."
The three of them put on their shoes and entered the stage cautiously.
Chen Yiru first calibrated the three bells in the center of the stage, kept one by his side, gave one to Xiaoyun, and asked her to get it to the edge of the stage; the other one was given to Ziye to let her Standing between her and Xiaoyun.
Yiru saw that the clock beside her had gone for a full hour, and she picked up the multifunctional telescope. I saw a strange sight: Xiaoyun's clock only went 37 minutes and 30 seconds; Ziye's clock showed 54 minutes and 54 seconds.
This shows that the clock in the center of the stage runs the fastest, the clocks placed along the radial direction will run slower and slower as the radial direction extends, and the clocks on the edge of the stage run the slowest.
Xiaoyun compared this clock with her familiar heartbeat frequency and did not feel that this clock was running slowly. However, compared with Yiru's clock, her clock was indeed running slower. She concluded that, My own heartbeat also beats slower here.
The three of them exchanged ideas with each other, using different time intervals to measure, and observing without a telescope. They directly put the clock on the edge of the stage for a period of time, and then took it back and compared it with the clock in the center of the stage. By comparison, the same phenomenon was observed: in comparison, the clock in the center of the stage ran the fastest, while the clocks in other places on the stage ran slower. The farther away from the center of the stage, the slower the clock ran. The clocks on the edge of the stage ran slower. It has to be the slowest.
After running around on the stage all morning, the three of them were tired. They walked off the stage, put on their shoes, and went to the nearest dining spot for lunch.
After the meal, they quickly came back, put on the magic shoes, and returned to the stage. According to the arrangement in the morning, the afternoon was to measure the circumference of the stage.
At the beginning, Chen Yiru was still at the center of the stage. Xiaoyun and Ziye went to the center of the stage and each took a one-meter-long rigid measuring stick. Xiaoyun walked to the edge of the stage, and Ziye was next to them. position in between.
The two of them first placed the measuring tape along the radial direction of the disk. If Yiru used a multi-functional telescope to observe it, the displayed readings were all one meter, and there was no change in the measuring tape. Then, when they placed the ruler along the tangential direction of the arc (perpendicular to the radial direction), something strange happened: Yiru found that Xiaoyun's measuring tape was only about 0.7 meters, while the cotyledon's measuring tape was about 0.92 meters. Moreover, both of their bodies have become narrower. Like the young people riding bicycles seen in the first area, Xiaoyun is even more "narrow" than Cotyledon. That is to say, a measuring stick placed tangentially will shrink, and the farther away from the center of the stage, the more severe the shrinkage, while a measuring stick placed in the center will not shrink.
The two of them used rulers to measure the radius of the stage. They measured directly from the center of the stage to the edge of the stage, exactly 100 times, which proved that the radius of the stage had not changed and was still 100 meters. Xiaoyun and Ziye used the measuring sticks in their hands to move along the edge of the stage. They placed the measuring sticks one after another to measure the circumference of the stage. They used their original knowledge of geometry to know that the circumference measured here should be about 628 meters, but after measuring it several times, the result was unexpectedly close to 900 meters. They immediately guessed that this was the result of the shortening of the measuring tape to the edge of the stage.
Yiru seems to have heard from her grandfather that the surface space of a non-rotating stage is flat and conforms to Euclidean geometric relations. However, with the high-speed rotation of the stage, the space and time here will change. The geometric relationship between radius and circumference is abnormal, and Euclidean geometry is invalid here.
After the measurements on the stage were completed, they were very tired and it was already past 7 p.m. They returned to the hotel.
On the fourth day of their arrival in City E, they came to the Sixth District of City E to visit an exhibition about Einstein’s life.
In Einstein’s exhibition hall, there are a large number of pictures, letters and text descriptions at the entrance, which are a brief introduction to Einstein’s life. The summary is as follows.
Albert Einstein (1879-1955) was the greatest natural scientist of the 20th century. He can be ranked with Newton as the two sages who guided mankind to correctly understand the universe. They are the two greatest so far. A scientist. He ushered in two new generations of technology. In December 1999, he was selected as the "Great Man of the Century" in the 20th century by Time Magazine.
Einstein was born on March 14, 1879, in a Jewish family in Ulm, Baden-Württemberg, Germany. His father was very talented in mathematics, but he had no money to go to school. Never give up studying and doing business. His mother was very talented in music. Einstein learned to play the violin from his mother when he was a child. Classical music became Einstein's lifelong hobby.
Einstein was not a smart child since he was a child. It is said that he could not speak well when he was 4 years old. In middle school, in addition to excellent scores in mathematics, my scores in other memorized courses such as Chinese, history, and geography were poor. In 1896, he was admitted to the Normal Department of the Swiss Federal Institute of Technology in Zurich, majoring in theoretical physics. While in college, he diligently studied subjects outside the curriculum according to his own interests.
In 1900, he obtained his diploma with a graduation thesis on heat conduction under the guidance of Weber. Because he was accustomed to independent thinking and his learning style was inappropriate, he was not qualified as a teaching assistant and remained in school.
After graduation, Einstein could not find a regular job. Poverty and hunger drove him to run for a living all day long. It was at this time that hepatitis, which had not been cured, fell. However, poverty did not shake Einstein's determination to study science. He was always thinking about the physics topics he was interested in and conceiving his academic papers.
Later, with the help of his university classmates and friends, he found a permanent job as a technician at the Bern Patent Office. He worked at the Swiss Patent Office for seven years, from 1902 to 1909.
Starting in 1905, Einstein began to publish theoretical physics papers in the prestigious monthly "Annals of Physics", including a paper on special relativity entitled "On the Electrodynamics of Moving Bodies" . This theory explains that some puzzling phenomena will occur when moving close to the speed of light, such as volume reduction, time slowing down, and mass increasing. It provides a clear and reasonable explanation for some phenomena that people could not explain at the time. .
In 1911, Einstein served as a university professor in Prague and in 1912 as a professor at the University of Zurich. He then worked in Berlin as the director of the Kaiser Wilhelm Institute of Physics (1914--1933) until He left Europe.
In 1916, Einstein published "Foundations of General Relativity", which explained the slow rotational precession of Mercury's elliptical orbit that Newton's gravity could not explain. In 1919, his prediction that light would bend when passing through the gravitational field of the sun was confirmed by photos of a solar eclipse taken by the Royal Society in London. In 1921, Einstein won the Nobel Prize in Physics for his work on the photoelectric effect (introducing the idea of ??light quanta and photons).
In 1922, Einstein visited China and sympathized with and supported the Chinese people's struggle for national independence and liberation. After the September 18th Incident, he repeatedly appealed to the world to use joint economic restraint to stop Japan's military aggression against China. In 1936, the "Seven Gentlemen" such as Shen Junru, Zhang Naiqi, Zou Taofen, and Shi Liang were arrested for advocating anti-Japanese resistance. He enthusiastically participated in the rescue and support.
While in Berlin, Einstein was suspected of certain remarks and his Jewish background. After Hitler came to power, Einstein left Germany. He taught at Princeton University in New Jersey from 1934, later became an American citizen, and became a professor at the school in 1940.
Einstein was also an outstanding liberal and a great old man who called for peace. When a German chemist's research on the possibility of powerful explosions caused by the fission of uranium atoms caught his attention, he conducted a series of experiments at Princeton to confirm this possibility. On the advice of others, he sent a letter to Roosevelt in September 1939, asking the president to be wary of Germany possibly building an atomic bomb. Directly contributed to the launch of the "Manhattan Project". After World War II, he actively advocated peace and opposed the use of nuclear weapons. and signed the Russell-Einstein Declaration.
After Weizmann's death in 1952, Israel invited Einstein to serve as president, but he politely declined. In his later years, Einstein attempted to merge quantum theory with general relativity through unified field theory (1950), so that subatomic phenomena and large-scale physical phenomena could be merged into one theory, that is, he conducted theoretical research on the so-called unified field. His efforts were unsuccessful. Judging from his lifelong research, he was always working alone at the forefront of physics, and he would always only do the most difficult pioneering work.
On April 18, 1955, Einstein died in his sleep at Princeton Hospital. He was 76 years old. German scientist Max Planck hailed Einstein as the Copernicus of the 20th century. French physicist Langevin commented: "Among the physicists of our time, Einstein will be at the forefront. He is now and will still be the most brilliant star in the human universe. It is difficult to say, Is he as great as Newton or greater than Newton? However, it can be said with certainty that his greatness is comparable to Newton. According to my opinion, he may be greater than Newton because of his contribution to science. It has entered more deeply into the structure of basic concepts of human thought."
During his lifetime, Einstein made a will not to publish an obituary, hold a funeral, build a tomb or erect a monument, and scatter his ashes anywhere. A well-known place.
When his body was cremated, it was unknown to anyone but his closest followers. At the cremation ceremony, his executor presented him with a poem written by the famous German poet Goethe in memory of his deceased friend Schiller:
"We have all benefited a lot,
The whole world is grateful for his teachings;
What belongs to him personally,
has already spread to the vast number of people,
He seems to be about to perish. The comet, radiant with brilliance,
combines the infinite light with his light forever. ”
There are also many exhibition halls in the exhibition hall that introduce Einstein’s life in middle school. Some introduced his work and study at the Patent Office in Bern, Switzerland, some introduced the special theory of relativity, some introduced the general theory of relativity, some introduced his work at Princeton, etc. Since it was getting late, Chen Yiru and three others , I visited and browsed the parts that interested me most and made brief notes.
They did not return to the hotel until 7:30 pm.
After dinner, when they returned to the room, the three of them sorted out the pictures and materials that had the most profound impact on them, and based on the records of their visits, wrote short essays, and communicated.
Liu Ziye was deeply moved by the friendship between Einstein and his classmate Grossman.
She wrote the following text.
After Einstein entered the Federal University of Technology, he spent a lot of time reading and studying the scientific and philosophical works of the sages, but he was not enthusiastic about most of the courses, so he often skipped classes. He also disliked exams because they forced students to cram a lot of rote learning into their brains.
In order to pass the exam, Einstein borrowed Grossman's class notes, sharpened his skills in battle, and passed the exam.
After graduating from college, I became unemployed. His father was ill and his business suffered setbacks, making him unable to continue to support him. The 21-year-old Einstein had to find his own way. He was running around and bumping into walls, unable to find a permanent job. He had to do some temporary jobs, help people with calculations, and be a tutor to make ends meet. During Einstein's impoverished days, one of his classmates described it this way: "But Einstein next door, all he had to do was take his violin and play and beg from door to door."
Just then. When Einstein was desperate, Grossman solemnly spoke to his father about Einstein's predicament. For this reason, his father strongly recommended Einstein to his friend Haller, director of the Swiss Federal Patent Office. Haller agreed to arrange a temporary job for him and study it for a period of time. By June 1902, Einstein was officially employed as a third-level technician in the Patent Office. This ended his more than two years of unemployment and poverty.
In 1936, Einstein never forgot this friendship in a letter to Mrs. Grossman. In the letter, he wrote: I recall my student days and he (Grossman) was a There is no blame for being a student; I am a deviant and a dreamer. He had a very good relationship with his teacher and was understanding of everything; I was a tramp and unlovable, but we were good friends.
We would go to the coffee shop every two or three weeks to drink iced coffee and chat. This is my happiest memory. Later, when our studies were over and I was suddenly abandoned, he supported me and, thanks to his and his father's help, I found a position in the Patent Office. This was a salvation for me, otherwise my intellect would have been destroyed, if not necessarily dead.
For a period of time, Einstein was more interested in natural science than mathematics, and mathematics became alienated from him. He also believes that mathematics has many specialized fields, each of which can consume a person's short life, so he is afraid of "falling into" this field and delaying physics.
In physics, however, the path to deeper theories of the material world is closely tied to more profound mathematical forms. It was when he created the general theory of relativity that he fully understood this and felt that he had encountered a mathematical obstacle.
In order to find a suitable mathematical theory to satisfy the mathematical expression of general relativity, Einstein went to his old classmate Grossman in 1912 with such a problem. At that time, Grossmann was already a professor of mathematics at the Technical University of Zurich. Einstein's question immediately aroused the old classmate's strong interest.
It was with Grossman's help that the right mathematical tools were found. This is the surface geometry established more than half a century ago by the German mathematicians Gauss (1777-1855) and Riemann (1826-1866), and later by Ricci (1853-1925) and his student Lévi-Chevi Tensor analysis developed by Tower (1873-1941).
Grossmann found the right mathematical theory for Einstein. The two of them collaborated on the paper "Outline of the Theory of General Relativity and Gravity" in 1913, of which Grossman wrote the mathematical part.
From here we can see how much influence Einstein had on his life with the help of a classmate and friend in his college days. If Einstein does not receive this assistance, there may be obstacles to his success, which may cause losses to the progress of human civilization.
He Xiaoyun was deeply impressed by Einstein's strong curiosity, sense of surprise and active self-learning spirit.
The short essay she wrote is as follows.
When Einstein was 5 years old, his father gave him a compass.
He fiddled with it repeatedly and carefully figured it out. He found that no matter how it swung, the pointer on the compass always pointed north. This surprised him and stimulated his curiosity to explore the roots of things. He guessed that there must be something hidden behind this phenomenon. This incident left a deep impression on him, so much so that when he talked about it more than 60 years later, he could still clearly recall the scene at that time.
At the age of 12, Einstein got a small book on Euclidean plane geometry. He marveled at the reliability and clear arguments of many of the conclusions in the book. For example, it is not obvious that the three heights of a triangle intersect at one point, but it can be proven rigorously, leaving no room for doubt. This small book on geometry had a great influence on him, so much so that the structure and expression of the theories he later established can be seen in the shadow of this book.
On March 14, 1953, at Einstein’s 74th birthday party, someone asked Einstein: “It is said that you learned about Einstein when you were 5 years old because of the compass, and when you were 12 years old because of Euclidean geometry. Have these things really had a decisive influence on your life's work?"
Einstein replied: "That's what I think. I believe that these external influences have had a profound impact on me." Development does have a significant impact." He commented on the role of curiosity and wonder: "The best experience we can have is the experience of mystery. It is the basic emotion that remains at the birthplace of true art and true science. Anyone who cannot experience it, who no longer has curiosity and a sense of surprise, is undoubtedly a zombie, his eyes are blurred. "Einstein was driven by his strong curiosity and surprise. Only with a sense of consciousness can we regard problems that others do not think (time, space, gravity, mass, etc.) as big problems worthy of study, and have achieved significant achievements.
His strong curiosity enabled him to discover problems. However, to solve these problems, he must have a strong knowledge base. Einstein relied on his tenacious self-learning spirit to lay a solid foundation for himself.
Throughout Einstein’s self-study career, there were three important periods: the first period was from the age of 10 to 15, when he consciously studied some scientific and philosophical works under the guidance of others. Especially when he was 12 years old, he learned Euclidean plane geometry, and he was obsessed with thinking about the proof methods of these geometric theorems; secondly, during his four years in college, he studied Maxwell's theory and Mach's theory assiduously. "Mechanics"; the third period was the first three years when he was a technician at the Bern Patent Office, where he and his two friends studied and discussed the works of many masters.
In March 1955, Einstein talked about his self-study life in his memoirs written to commemorate the centenary of the founding of his alma mater: "...arrange myself to learn those things that are suitable for me. Something of intellectual curiosity and interest. I attended certain classes with great interest, but I 'swiped' many classes and studied with great enthusiasm at home from the masters of theoretical physics." "I mostly Time was spent working in the physics laboratory, obsessed with direct contact with experience. The rest of the time was mainly spent at home reading the works of Kirchhoff, Helmholtz, Hertz and others.
"
During his first few years at the Bern Patent Office, he and two friends formed the so-called "Olympian Academy of Sciences" - actually a self-study group of three people. They were very enthusiastic about learning. , and studied and discussed together the works of philosophy, physics, and mathematics by Mach, Mill, Hume, Spinoza, Helmholtz, Riemann, and Dedekind, especially Poincaré's "Science and Hypothesis", which was very important to him. They were so impressed that they read and discussed the book intensely for several weeks.
Their discussions were often very intense, and sometimes a page and a half of text, or even a sentence, would last for a long time. There were fierce debates, and some of the more important issues could last for several days.
By 1904 and 1905, the two friends left Bern respectively, and such study discussions stopped. However, the intense study, heated discussions, and constant discussions during this period made the conception of many of Einstein's papers increasingly mature. During this golden period, Einstein's creation of the special theory of relativity had a profound impact on his life.
It was this spirit of hard self-study that on the one hand acquired more systematic knowledge of physics and philosophy; on the other hand it also developed his habit of independent thinking, which helped him achieve great success. Ready for achievement.
Chen Yiru felt deeply about how Einstein viewed nature.
She wrote about her understanding of several of Einstein's remarks. >
Einstein said that nature is "there is a huge world outside us, which exists independently of us humans. It stands before us like a great and eternal mystery, but at least partly it is us. within the reach of observation and thinking. "Einstein told us that nature, for human beings, is an independent existence that does not depend on human beings. It contains countless unknown things, like a great and eternal mystery. However, through observation and thinking, human beings can Understand and explore the various mysteries contained in this existence, and at least partially uncover the answers to these mysteries.
Einstein regarded this existence as God in his heart, with a kind of reverence and piety. This is because he believes that nature shows an incredible order, harmony, symmetry, and unity, showing a kind of great beauty and the super high power of God in his heart to build this world. Reason. He said: "The world is rich in order and harmony, and we can only imperfectly grasp the beauty of its logical simplicity in a humble way. His life's work was to know God's conception of the world. He often said: "I want to know how God created this world." What interests me is not this phenomenon or that phenomenon. I want to know the mind of God and everything else is trivial. ”
Einstein realized this beauty from his own observation and while exploring the unity of nature. He was intoxicated by the perceptual beauty of nature; he was also amazed. To the rational beauty hidden deep in nature
Einstein said: “The most incomprehensible thing about this world is that it is understandable. "This means that this world is understandable, but why is it understandable? This is incomprehensible.
Through this visit, this is how I understood this sentence.
The reason why this world is understandable is that it is orderly and harmonious, that is, there is an inherent beauty, and the phenomena presented are causally connected and have reasonable logical relationships. This becomes the basis for our understanding of the world. The basis enables us to understand the world. On the contrary, if the world is chaotic, unreasonable, and has no causal and logical connections, then we cannot understand why nature. How can there be such beauty? This is something difficult to understand. This may be the most incomprehensible thing about this world.
"God is cunning, but he has no evil intentions." "This is also telling us that because God has no ill intentions, the material world is understandable, but many problems facing mankind today have not yet found answers because God is cunning.
According to plan, they are on E The four days of activities in the city are over. The next journey is to visit Longmen, Daguanlou and other places in the city for a day, then to the Stone Forest for a day, and finally to Jiuxiang.
This is what they expected. The week's activities came to an end soon.