Vielbein - Relativity and other

Vielbein

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Some notes on Relativity and other arguments

Abiko - Einstein s Kyoto Address: "How I created the Theory of Relativity"

Nella conferenza di Kyoto del 1922 Einstein espone per la prima volta una ricostruzione del percorso che ha seguito per giungere alla Relativit&agrave; Ristretta e a quella Generale. A differenza delle ricostruzioni successive, quella di Kyoto &egrave; interessante in quanto sono presenti anche alcuni spunti emozionali che Einstein ebbe nei momenti nevralgici e problematici del suo cammino. L'articolo di Abiko presenta anche una nuova versione della trascrizione in Giapponese che fa ammenda di alcune imprecisioni delle versioni precedenti e per questo motivo la riportiamo qui di seguito.
"It is never an easy task to talk about how I reached the theory of relativity, because there are many hidden complexities that stimulate one's thinking. Besides, the complexities affect it with various degrees of strength. I intend neither to talk about each of them, nor to quote each of the papers I have written. I shall only try to pick up simply the gist most directly related to the development of my thought. 
It was about seventeen years ago that I first had the idea to establish the principle of relativity. Where the idea came from cannot be expressed accurately. It is certain, however, that the idea was contained in the problems concerning the optics of moving bodies. Light propagates through the sea of ether. The earth also moves in this same ether. If seen from the earth, ether flows against it. Nevertheless, I could not find the facts verifying this flow of ether in any literature on physics. 
Therefore, I wanted somehow to verify this flow of ether against the earth, namely, the movement of the earth. When I posed this problem to my mind at that time, I never doubted the existence of ether and the movement of the earth. Thus, I wanted, by appropriately reflecting light from one source by mirrors, to send one light beam along the motion of the earth and the other along opposite to it. Anticipating that there should be some difference in the energy of these beams, I wanted to verify this by the difference of heat caused by them on two thermocouples. This idea was of the same sort as that of Michelson's experiment, but I did not know this experiment very well then.
While I had these ideas in mind as a student, I came to know the strange result of Michelson's experiment. Then I came to realize intuitively that, if we admit this as a fact, it must be our mistake to think of the movement of the earth against ether. That was the first route that led me to what we now call the principle of special relativity. Since then I have come to believe that, though the earth moves around the sun, we cannot perceive this movement by way of optical experiments.
It was just then that I had the chance to read Lorentz' monograph of 1895. There, Lorentz dealt with the problems of electrodynamics and was able to solve them completely in the first approximation, namely, in so far as he neglected the quantities higher than the second power of the ratio of the moving body's velocity to that of light. Then I dealt with [Armand] Fizeau's experiment and tried to approach it with the hypothesis that the equations for electrons given by Lorentz held just as well for the system of coordinates fixed in the moving body as for that fixed in the vacuum. Anyway, at that time I firmly believed in the correctness of the Maxwell-Lorentz equations of electrodynamics and that they revealed the true reality. What is more, [the hypothesis] that these equations held also good for the moving systems of coordinates, indicated the relation of the so-called invariance of light velocity.
In spite of that, this invariance of light velocity conflicted with the law of the additivity of velocity well known in mechanics. Why on earth did these two contradict each other? I felt I had come up against a serious difficulty. Expecting to modify Lorentz' way of thought somehow, I spent almost one year in useless thoughts. Then, I could not but think that this mystery would be too hard for me to solve.
Nevertheless, a friend [Michele Besso] of mine in Bern relieved me by chance. It was a beautiful day. I visited him and began to talk to him like this.
"I have a problem that I cannot solve for the life of me. Today, I've brought with me the battle to you."
I discussed various things with him. Thereby, I felt inspired and was able to reach the enlightenment. The next day, I revisited him and said to him, "Thanks a lot. I have completely interpreted my problem now."
My interpretation was really about the concept of time. Namely, time could not be defined absolutely, but is in an inseparable relationship with the signal velocity. Thus the previous extraordinary difficulty was solved completely for the first time. Within five weeks of this realization the principle of special relativity as we know it was established. I did not doubt that it was quite acceptable also from the philosophical point of view. Specifically, I noticed that it should agree with Mach's view. As you can see, nothing in the [special] theory is connected with Mach's view so directly as the later problems solved by the general theory of relativity. Nonetheless, following his analyses of the various concepts of science, we can suppose a connection, although it might be indirect.
It was in this way that the special theory of relativity was constructed.
The first idea leading to the general theory of relativity occurred two years later, namely in 1907. It occurred, besides, in a striking fashion.
From the outset, it was not satisfactory to me that the motions to which the [principle of] relativity applied were restricted to those with uniform mutual velocity, and that its application to arbitrary motions was not allowed. I always hoped that somehow I could manage to get rid of this restriction.
In 1907, I was preparing a summary of the results of the special theory of relativity, for the Jahrbuch der Radioaktivitdt at the request of Stark, the editor of the journal. It was then that I realized that, although all other laws of nature satisfied the special theory of relativity, only the law of universal gravitation did not. I felt deeply that I wanted somehow to find the reason why. But, I could not fulfill this purpose easily. Above all, what was most unsatisfactory to me was that, while the relationship between inertia and energy was given excellently by the special theory of relativity, that between this and weight, namely, between energy and the gravitational field, was left quite uncertain. I imagined that its explanation could not be accomplished in terms of the special theory of relativity.
I was sitting in a chair in the patent office at Bern. Suddenly an idea dawned on me: "If a man falls freely, he should not feel his weight himself."
I felt startled at once. This simple thought left me with a deep impression indeed. It was this deep impression that drove me to the theory of gravitation. I went on thinking and thinking.
When a man falls, he has acceleration. The judgements he makes must be those made in the system of reference with acceleration.
Thus, I determined to extend the principle of relativity so as to be applicable not only to systems of reference moving with uniform velocity, but also to ones moving with acceleration. By doing so, I expected that the problem of gravitation could be solved at the same time. I expected so because we can interpret the reason why a person in free fall does not feel his weight, as that there is, other than the gravitational field caused by the earth, another gravitational field compensating it. In other words, in a system of reference moving with acceleration, it is required that there should appear a new gravitational field.
Yet, I could not solve the problem completely at once. It was after another eight years that I found out the true relationships. Nevertheless, before that time, I came to know a little of the somewhat general basis connected with them.
Mach was the one who also insisted that all the systems of reference moving with accelerations relative to each other are equivalent. But, obviously, this conflicted with our geometry. The reason is that, if we admitted all these systems of reference as valid, Euclidean geometry could not hold for each of them. To describe a law discarding geometry is just the same as to describe an idea without language. In order to express our idea, we must seek the language first. What had we to seek then at that point?
This problem remained unsolved for me until 1912. In that year, it occurred to me by chance that there could be a deep reason for regarding the surface theory of [Karl Friedlich] Gauss as the key to opening this mystery. I visualized Gauss' surface coordinates as really meaningful objects. I did not know at that time, however, that Riemann had discussed the foundations of geometry more deeply. I happened to recall that a lecture on geometry in my student years by [Carl Friedlich] Geiser, our professor of mathematics, contained Gauss' theory, hence that idea [of mine]. In that way, I came to realize that the foundations of geometry indeed could bear a physical meaning.
When I returned from Prague to Zurich [in 1912], I met my friend and mathematician Grossmann there. He was the man who had helped me gain access to mathematical literature when I was in the patent office at Bern. This time, he introduced me to the works of [Curbastro Gregorio] Ricci at first, then to those of Riemann. Thus, I asked him whether my problem could be solved by means of Riemann's theory, in other words, whether the coefficients I wanted to find could be completely determined in terms of the invariance of the line elements. Then, in 1913,&nbsp;Iwrote a paper in collaboration with him. Nevertheless, we could not obtain the correct equations of universal gravitation yet. I further dealt with Riemann's equation in various directions, only to find many reasons why the results I imagined could not be obtained in that way.
Two years of struggle passed after that. It was only then that I finally realized that there was an error in my earlier calculation. I returned once again to the former invariance theory and tried to find out the correct equations of universal gravitation. Then, at last, after two weeks, they appeared before my eyes.
Among the work I did after 1915, I would like to take up only the problem of cosmology. This concerns the geometry and the time of the universe. My work on this problem is based on the treatment of boundary conditions in the general theory of relativity and also on Mach's considerations on inertia. Of course, I did not know concretely to what extent his view on the relativistic nature of inertia was definite. But it is nevertheless certain that I received a great mental stimulation from him.
Anyway, I tried to make invariant the boundary conditions on the equations of universal gravitation. Finally, eliminating the boundary by regarding the universe as a closed space, I could solve the problem of cosmology. As a result, inertia emerged as a property altogether of an inter-body character; and it was shown that the inertia of a body would vanish, if it were not for another body opposing to it. I believe the general theory of relativity thereby became satisfactory from the epistemological point of view.
That is the story, I tried to describe concisely and historically how the gist of the theory of relativity was created."