Theory of Relativity

Introduction:

Who doesn't know Einstein's formula E = mc 2 or the paradox of the twins who found their twin was much older after traveling at near the speed of light? But not everyone knows that this "miracle" is only a small part of Einstein's theory of relativity, and how Einstein actually got his theory of relativity.

On December 14, 1922, Albert Einstein delivered a public lecture in front of Kyoto Imperial University students about the ideas behind the birth of the special and general theory of relativity. This lecture was part of Einstein's 43-day trip to Japan at the end of 1922 with his wife Elsa. This visit is quite unique, because this is Eistein's only visit to Asia. During these visits, Einstein had a very strict schedule, he had to give lectures for professionals (physicists) as well as the general public.

The following year, these lecture notes were published by a Japanese monthly magazine called Kaizo. Prof. Masahiro Morikawa from Ochanomizu University translated the article into English in the bulletin of the Association of the Association of the Physicists for the Asia Pacific which was published last April. As Prof. Morikawa, I also agree that this article should be made known to the public. One important thing we can learn from this lecture is the fact that as an ordinary human being Einstein had almost given up because of the difficulty of the problem of relativity. But the combination of perseverance, hard work, genius, good relations with fellow scientists, and the luck he had, were the factors that ultimately determined Einstein's success in giving birth to the two theories of relativity.

Here is a translation of Einstein's speech.

It is not an easy thing to tell in full how I got the theory of relativity. This is due to the various complexities that indirectly motivate human thinking. I also do not want to convey in detail the development of my thoughts based on my scientific papers, but I will simply convey to you the essence of the development of these thoughts.

I first got the idea to build the theory of relativity about 17 years ago (1905). I can't say exactly where this kind of idea came from, but I believe it stems from optical problems in moving objects. Light travels in the ether oceans and the earth travels in the same ether. Therefore the ether movement must be observable from the earth. However, I have never found a single observational evidence of this ether flow in the physics literature. I was very compelled to prove the flow of ether relative to the earth, in other words the motion of the earth within the ether. At that time I had absolutely no doubt about the existence of the ether and the movement of the ether. In fact I was expecting the possibility of observing the difference between the speed of light traveling in the same direction as the earth motion and light traveling in the opposite direction (with the help of mirror reflection). My idea can be realized by using a pair of thermocouples to measure the difference in their heat or energy. This idea was similar to the Albert Michelson interference experiment, but at that time I was not very familiar with the Michelson experiment. I became acquainted with the null-result of the Michelson experiment when I was a student and since then I have been very obsessed with my idea. Intuitively I feel that if we accept the zero result it will lead us to the conclusion that our view of the earth moving in the ether is wrong. This was the first step that pulled me toward the special theory of relativity. From then on I began to believe that if the earth moves around the sun then its motion can never be detected by experiments using light.

In 1895 I read Hendrik Lorentz's paper claiming that he could completely solve the electrodynamic problem through the first approach, an approximation in which the power of two or more of the ratio between the speed of the object and the speed of light is neglected. After that I tried to extend Lorentz's argument to the experimental results of Armand Fizeau by assuming that the equations of motion for electrons, as Lorentz proved, apply in coordinate systems that refer to both a moving object and a vacuum. I am convinced of the validity of the electrodynamic formulations of Maxwell and Lorentz and I firmly believe that they correctly explain true natural phenomena. The more so in the fact that the same equation applies in the mobile coordinate system as well as in the vacuum system, clearly shows the invariance (unchanging) nature of light. However, this conclusion contradicts the law of velocity composition adopted at that time. Why do these two basic laws contradict each other? This big problem made me think hard. I had to spend a whole year in vain exploring the opportunity to modify Lorentz's theory. This problem seems too much to me!

One day, a conversation with a friend of mine in Bern helped me solve this huge problem. I visited him on a sunny day and asked him: "Right now I am faced with a big problem that I thought could never be resolved. Now I want to share this problem with you." I spent various discussions with him. Suddenly I had a very important idea. The next day I said to him: "Thank you very much. I have solved all my problems."

My main idea for solving this problem has to do with the concept of time. Time should not be defined a priori as an absolute reality. Time must depend on signal speed. This great problem can be solved with a new concept of time.

In just five weeks I was able to complete the principles of special relativity after the discovery. Nor do I have any doubts about the validity of this principle from a philosophical point of view. Moreover, this principle agrees with Mach's principle, at least in part when compared to the success of the general theory of relativity. This is how I built the special theory of relativity.

The first steps towards the general theory of relativity appeared two years later (1907) in a different way.

I am not very satisfied with the special theory of relativity because the principle of relativity is limited to relative motion with constant velocity but cannot be applied to motion in general. In 1907 I was asked by Johannes Stark to write a review of the various experimental results of the special theory of relativity in his annual report Jahrbuch der Radioaktivitaet und Elektronik. When asked to write this article I realized that the special theory of relativity can be applied to all natural phenomena except gravity. I really wanted to find a way to apply this theory to the case of gravity. But I can't solve this easily. One thing that frustrates me is the fact that while the special theory of relativity provides a perfect relationship between inertia and energy, while the relation between inertia and weight (inertia and gravity system) is not touched at all. I suspect that this problem is far beyond the scope of the special theory of relativity.

One day I was sitting in a chair at the Swiss Patent Office in Bern. This is when a brilliant idea crossed my mind. "A person who is in free fall will not know his weight." This simple idea gave me deep thought. The wild emotions that swept over me at that time pushed me toward the theory of gravity. I thought again, "A person in free fall has acceleration." The observations made by this person were actually carried out on an accelerated system. I decided to expand on the principle of relativity to include acceleration. I also hope that, by generalizing this theory I will simultaneously solve the problem of gravity. This is due to the fact that people in free fall do not feel their weight due to another gravitational field that removes the Earth's gravitational field. In other words, every object that is accelerating requires a new gravitational field.

However, I could not completely solve this problem. I spent eight years putting down real relationships. Prior to that, I only got the basic bits and pieces of the theory.

Ernst Mach also claims the principle of equivalence between accelerated systems. But it is clear that this does not fit into ordinary geometry. This is because if such systems are permitted, Euclidean geometry does not apply to every system. Explaining the laws of physics without geometry is tantamount to explaining a thought without words. We must prepare these words before we can explain our thinking. So, what should I lay down on the basis of my theory?

This problem remained unsolved until 1912. In that year I realized that Karl Friedrich Gauss's surface theory could provide a good basis for solving the above mystery. For me, the coordinates of the surface of Gauss are very important tools. But I did not know that George Riemann had previously developed such profound fundamentals of geometry. I only remember the Gauss theory that I got in lecture from a mathematics lecturer named Carl Friedrich Geiser when I was a student. So I am increasingly convinced that the basic properties of geometry must have a physical meaning.

On my return to Zurich from Prague I met a close friend of mine, a mathematician, Marcel Grossmann. He helped me find mathematical references that were a little foreign to me when I was at the Swiss patent office in Bern. This was the first time I learned from him the work of Curbastro Ricci and Riemann's papers. I asked him if my problem could be solved by Riemann's theory, namely whether the invariance of the line elements was sufficient to determine all the coefficients I was looking for. Subsequently, I collaborated with him in writing a paper in 1913, even though the actual equation of gravity could not be derived at that time. Further investigations using Riemann's theory, unfortunately, yielded many conclusions that contradicted my expectations.

The next two years passed while I was still racking my brains to solve this problem. In the end I found one mistake in my previous calculations. I went back to trying to derive the correct gravity equation based on the invariance theory. After two weeks of work, the final answer appeared in front of me.

After 1915 I started working on the cosmological problem. The research I have done is concerned with the geometry and timing of the universe. This research is based on a discussion of the boundary conditions of the general theory of relativity and Mach's inertia argument. Although I do not know the extent of the impact of Mach's idea on the substance of general relativity from inertia, I do believe that this grand idea is my basic philosophy.

At first I tried to make the boundary conditions for the gravitational equation invariant. Later I was even able to remove this limitation on the assumption that the universe is closed. I was thus successful in solving the cosmological problem. As a result it was found that inertia appeared as a relative property among matter and would have to disappear if no other object had any interaction with it. I believe that this important quality makes the general theory of relativity satisfying even from an epistemological perspective.

I hereby end my short story of how I constructed the theory of relativity. Thank you very much.