According to R. P. Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. This means that Feynman was attempting to combine all of his papers into one paper. It is thus fun to combine some, if not all, into one paper. We may try three of his papers.
Circle and EllipseThey are the same thing! This is what Feynman is talking about. |
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Covariance and Its Historical Background
Unlike classical physics, modern physics depends heavily on observer's state of mind or environment. In special relativity, observers in different Lorentz frames see the same physical system differently. The importance of the observer's subjective viewpoint was emphasized by Immanuel Kant in his book entitled "Kritik der reinen Vernunft" whose first and second editions were published in 1781 and 1787 respectively. However, using his own logic, he ended up with a conclusion that there must be the absolute inertial frame, and that we only see the frames dictated by our subjectivity.Einstein's special relativity was developed along Kant's line of thinking: things depend on the frame from which you make observations. However, there is one big difference. Instead of the absolute frame, Einstein introduced an extra dimension. Let us illustrate this using a CocaCola can. It appears like a circle if you look at it from the top, while it appears as a rectangle from the side. The real thing is a three-dimensional circular cylinder. While Kant was obsessed with the absoluteness of the real thing, Einstein was able to observe the importance of the extra dimension.
I was fortunate enough to be close to Eugene Wigner, and enjoyed the privilege of asking him many questions. I once asked him whether he thinks like Immanuel Kant. He said Yes. I then asked him whether Einstein was a Kantianist in his opinion. Wigner said very firmly Yes. I then asked him whether he studied the philosophy of Kant while he was in college. He said No, and said that he realized he had been a Kantianist after writing so many papers in physics. He added that philosophers do not dictate people how to think, but their job is to describe systematically how people think. Wigner told me that I was the only one who asked him this question, and asked me how I knew the Kantian way of reasoning was working in his mind. I gave him the following answer.
I never had any formal education in oriental philosophy, but I know that my frame of thinking is affected by my Korean background. One important aspect is that Immanuel Kant's name is known to every high-school graduate in Korea, while he is unknown to Americans, particularly to American physicists. The question then is whether there is in Eastern culture a ``natural frequency'' which can resonate with one of the frequencies radiated from Kantianism developed in Europe.
I would like to answer this question in the following way. Koreans absorbed a bulk of Chinese culture during the period of the Tang dynasty (618-907 AD). At that time, China was the center of the world as the United States is today. This dynasty's intellectual life was based on Taoism which tells us, among others, that everything in this universe has to be balanced between its plus (or bright) side and its minus (or dark) side. This way of thinking forces us to look at things from two different or opposite directions. This aspect of Taoism could constitute a ``natural frequency'' which can be tuned to the Kantian view of the world where things depend how they are observed.
I would like to point out that Hideki Yukawa was quite fond of Taoism and studied systematically the books of Laotse and Chuangtse who were the founding fathers of Taoism [1]. Both Laotse and Chuangtse lived before the time of Confucius. It is interesting to note that Kantianism is also popular is Japan, and it is my assumption that Kant's books were translated into Japanese by Japanese philosophers first, and Koreans of my father's age learned about Kant by reading the translated versions. My publication record will indicate that I studied Yukawa's papers before becoming seriously interested in Wignerism. Indeed, I picked up a signal of possible connection between Kantianism and Taoism while reading Yukawa's papers carefully, and this led to my bold venture to ask Wigner whether he was a Kantianist.
Kant wrote his books in German, but he was born and spent his entire life in a Baltic enclave now called Kaliningrad located between Poland and Lithuania. Historically, this place was dominated by several different countries with different ideologies [2]. However, Kant's view was that the people there may appear differently depending on who look at them, but they remain unchanged. At the same time, they had to entertain different ideologies imposed by different rulers. Kant translated this philosophy into physics when he discussed the absolute and relative frames. He was obsessed with the absolute frame, and this is the reason why Kant is not regarded as a physicist in Einstein's world in which we live.
The people of Kant's land stayed in the same place while experiencing different ideological environments. Almost like Kant, I was exposed to two different cultural environments by moving myself from Asia to the United States. Thus, I often had to raise the question of absolute and relative values. Let us discuss this problem using one concrete example.
About 4,500 years ago, there was a king named Yao in China. While he was looking for a man who could serve as the prime minister, he heard from many people that a person named Shiyu was widely respected and had a deep knowledge of the world. The king then sent his messengers to invite Shiyu to come to his palace and to run the country. After hearing the king's message, Shiyu without saying anything went to a creek in front of his house and started washing his ears. He thought he heard the dirtiest story in his life.
Shiyu is still respected in the Eastern world as one of the wisest men in history. We do not know whether this person existed or is a made-up personality. In either case, we are led to look for a similar person in the Western world. In ancient Greece, each city was run by its city council. As we experience even these days, people accomplish very little in committee meetings. Thus, it is safe to assume that the city councils in ancient Greece did not handle matters too efficiently. For this reason, there was a well-respected wiseman like Shiyu who never attended his city council meetings. His name was Idiot. Idiot was a wiseman, but he never contributed his wisdom to his community. His fellow citizens labeled him as a useless person. This was how the word idiot was developed in the Western world.
Idiot and Shiyu had the same personality if they were not the same person. However, Idiot is a useless person in state-centered societies like Sparta. The same person is regarded as the ultimate wiseman in a self-centered society like Korea. I cannot say that I know everything about other Asian countries, but I have a deep knowledge of Korea where I was born and raised. The same person looks quite differently to observers in different cultural frames. While doing research in the United States with my Eastern background, I was frequently forced to find a common ground for two seemingly different views. This cultural background strongly influenced me in producing the further contents of Einstein's E = mc2 tabulated in the following table.
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Let us go back to the question of relative values. For Taoists, those two opposite faces of the same person is like ``yang'' (plus) versus ``ying'' (minus). Finding the harmony between these two opposite points of view is the ideal way to live in this world. We cannot always live like Shiyu, nor like Idiot. The key to happiness is to find a harmony between the individual and the society to which he/she belongs. The key word here seems to be ``harmony.''
To Kantianists, however, it is quite natural for the same character to appear differently in two different environments. The problem is to find the absolute value from these two different faces. Does this absolute value exist? According to Kant, it exists. To most of us, it is very difficult to find it if it exists.
Let us finally visit Einstein. He avoids the question of the existence of the absolute value. Instead, he introduces a new variable. The variable is the ratio between the individual's ability to contribute and the community's need for his service. The best way to live in this world is to adjust this variable to the optimal value. Einstein's approach is to a quantification of Taoism by introducing a new variable.
If Taoism is so close to Einsteinism, why do we have to mention Kant at all? We have to keep in mind that Kant was the first person who formulated the idea that observers can participate in drawing the picture of the world. It is not clear whether Einstein could have formulated his relativity theory without Kant. Indeed, Kant spent many years for studying physics, namely observer-dependent physics. However, because of his obsession toward the absolute thing, he spent all of his time for finding the absolute frame. If one has a Taoist background, he/she is more likely to appreciate the concept of relativistic covariance.
I would like to stress that Taoism is not confined to the ancient Eastern world. It is practiced frequently in the United States. Let us look at American football games. The offensive strategy does not rely on brute force, but is aimed at breaking the harmony of the defense. For instance, when the offensive team is near the end zone, the defense becomes very strong because it covers only a small area. Then, it is not uncommon for the offense to place four wide-receivers instead of two. This will divide the defense into two sides while creating a hole in the middle. Then the quarter-back can carry the ball to the end zone. The key word is to destroy the balance of the defense.
Taoism forms the philosophical base for Sun Tzu's classic book on military arts [5]. When I watch the football games, I watch them as Sun-Tzu games. My maternal grandfather was fluent in the Chinese classic literature, and he was particularly fond of Sun Tzu. He told me many stories from Sun Tzu's books. This presumably was how I inherited some of the Taoist tradition. As I said in this paper, my research life was influenced by my Asian background. Many of my Asian friends complain that they are handicapped to do original research because of the East-West cultural difference. I disagree with them. This difference could be the richest source of originality.
- Y. Tanikawa, "Hideki Yukawa: Scientific Works" (Iwanami Shoten, Tokyo, 1979).
- A. Applebaum, "Between East and West, Across the Borderlands of Europe" (Pantheon Books, New York, 1994)
- Y. S. Kim, "Observable Gauge Transformations in the Parton Picture," Phys. Rev. Lett. {\bf 63}, 348-351 (1989).
- Sun Tzu and Sun Pin (translated by R. D. Sawyer), "The Complete Art of War" (Westview Press, Boulder, CO, 1996).
Click here for a more comprehensive Kant story.
copyright@2000 by Y. S. Kim, unless otherwise specified.
Einstein photo: courtesy of the Niels Bohr Library of the American Institute of Physics.
