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livre 3D The General Theory of Relativity

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The Magna carta of modern physics


by Hanoch Gutfreund

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Texts of canonical documents in the history of mankind and of letters exchanged between famous individuals are mostly available in printed form. Still, the handwritten, original manuscripts have a special charm as well as an emotional and aesthetic appeal. They are displayed as cultural treasures in museums and at public exhibitions, and are purchased by collectors at public auctions. They give us a sense of kinship with the author, a glimpse into his or her creative process and become a virtual presence in the time and space of their origin. It is this magic appeal which has been the driving force behind the mission of SP Books to produce high quality facsimile editions of the manuscripts of classical chef-d’œuvres of world literature. The present publication, of Einstein’s masterpiece, expands the scope of the already published landmarks of human culture to include also seminal contributions to our understanding of the physical world.

The manuscript reproduced here, marks the conclusion of Einstein’s convoluted intellectual odyssey toward the General Theory of Relativity. This was an intensive effort to generalize his Special Theory of Gravity, formulated in 1905. The latter could handle electric and magnetic phenomena, but not gravitation, and it was confined to motions at constant velocity. Einstein’s objective was that the theory should include and be applicable to accelerated motion as well. He began work on it in 1907, when he realized the deep underlying connection between acceleration and gravitation and his research continued through alternating phases of brilliant insights and successes, followed by erroneous sidetracks, misunderstandings and failures, until the triumphant end when all the pieces of the complex puzzle came together. In November, 1915, Einstein presented his theory, at four successive weekly meetings, to the Prussian Royal Academy of Sciences. After each of the first three presentations he realized that an additional improvement was required. Finally, on November 25, he was certain that this time he had the correct formulation. He was in an elated mood and shared the joy of achievement in correspondence with friends and colleagues. To the prominent physicist Hendryk Antoon Lorentz, with whom he corresponded extensively along the road to his General Theory, he wrote: “My series of gravitation papers are a chain of wrong tracks, which nevertheless did gradually lead to the objectives. That is why now finally the basic formulae are good, but the derivation is abominable; this deficiency must still be eliminated.” Without eliminating what appeared to him as a dreadful complexity, he sat down to write a comprehensive summary of the new theory “The Foundation of the General Theory of Relativity” (“Die Grundlage der allgemeinen Relativitätstheorie”), which was published in the leading physics journal of those days – Annalen der Physik, 11 May 1916.

Einstein’s General Theory of Relativity replaced Newton’s theory of gravitation, which brought terrestrial and planetary motions together into a single framework. Newton’s theory explained why things fall and why planets remain in their stable orbits around the sun. It became the basis for an encompassing physical worldview elaborated in the eighteenth and nineteenth centuries. Newton’s theory had one fundamental deficiency – it was not clear how the gravitational attraction between two distant masses acts instantaneously without an intermediate agent transferring that force. Newton was aware of this shortcoming, but he did not know how to eliminate it. This problem does not exist in Einstein’s theory, where gravitation is not a force but a geometrical property of space (actually, space-time) surrounding these masses. In this theory, gravitation is the geometry of space-time. An almost poetic formulation of the essence of Einstein’s General Theory of Relativity is: matter tells space how to curve and curved space tells matter how to move. The theory itself is a sophisticated, highly complex, mathematical formulation of this statement. It is summarized in the deceptively simple, concise mathematical expression on page 33 of the manuscript (equation 53). This expression represents what is known as the gravitational field equation.

Einstein’s 1916 article predicts that light reaching us from distant stars is bent by the gravitational field of the sun. When this prediction was confirmed in astronomical observations in November 1919, Einstein was catapulted overnight into a status of world celebrity, a status he maintained until the end of his life. Another prediction of this article is that time on earth proceeds slower than time in space, where the gravitation is much weaker. Had we not known this effect, and had we not known how to take it into account in measuring the time it takes a light signal to reach us from a satellite, we would not, for example, have such precise GPS technology.

Shortly after the publication of his article, Einstein realized that the theory can be applied to the universe as a whole. This was the beginning of relativistic cosmology. Over the years, Einstein’s General Theory of Relativity evolved into a pillar of modern physics, becoming central to the investigation of problems about the origin, the evolution and the structure of our universe. One such problem concerns the expansion of the universe. According to the General Theory of Relativity it began with a singular event, the “big bang”, after which an accelerated expansion took place. Also, the formation of galaxies in more recent times and the synthesis of the chemical elements and of the fundamental particles of matter very early on, are all studied in the framework of General Relativity. Another problem concerns the nature of black holes, whose very existence and curious properties were predicted by this theory. General Relativity also predicted the existence of gravitational waves propagating at the speed of light, and generated by violent motion of large amounts of matter, such as in the collapse of a massive star to form a black hole or in the collision of two black holes. Such waves cause the space they traverse to shrink and expand alternatively. Gravitational waves have indeed been detected very recently and they provide a new window on the universe.

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The detection and study of these and related phenomena are later developments, but their origin is in the manuscript presented here, specifically in equation 53, mentioned above.

In the initial stages of his career, Einstein was not aware of the appeal and value of his written work and usually disposed of the original manuscript as soon as an article was published. Thus, none of the handwritten manuscripts of his groundbreaking papers from 1905, the “miraculous year”, has survived. However, there exists a handwritten version of his seminal 1905 article on the Special Theory of Relativity, “On the Electrodynamics of Moving Bodies”. In 1944, Einstein reproduced it in his handwriting as a contribution to the American war effort. It was put up for auction and sold for $6.5 million and is now preserved in the Library of Congress. Ten years after the publication of the Special Theory, even if Einstein was still being negligent about keeping the manuscripts of his articles, his wife Elsa understood their value and it was thanks to her the manuscript of the Foundation of the General Theory of Relativity survived. How it survived and how it got to the Hebrew University of Jerusalem in 1925, the year of its official opening, is a complex story in itself, the details of which are not known.

Apparently, Einstein gave the manuscript to his friend the physicist and astronomer Erwin Freundlich, with whom he collaborated on possible observational tests of phenomena predicted by his new theory. This was a gift intended to support the construction of the Einstein Tower in Potsdam, where such tests were to be performed. In 1921, the relationship between the two colleagues deteriorated and, at Einstein’s request, Freundlich returned the manuscript to him in April 1922. Einstein then entrusted the industrialist and philosopher of science Paul Oppenheim with selling the manuscript, giving him the following instructions: “The Jewish University of Jerusalem shall be given half of the proceeds; the remaining half you may dispose of as your conscience tells you.” But Oppenheim was a friend of both adversaries and did not want to be involved in their dispute. In July 1923, Einstein asked Heinrich Löwe, a prominent member of the Preparatory Board of the Hebrew University and the National Jewish Library in Jerusalem, to sell the manuscript, again giving specific instructions about the allocation of proceeds.

Once more, the manuscript was not sold. We know about its fate from the correspondence between Einstein and his wife Elsa, when he was on a two months-long trip to South America in 1925. In one of his letters, Einstein wrote: “Do not give away the manuscript, dear Elsa… The time is not good for selling it. Better after my death.” He did not know that at the time of writing this letter, the manuscript was already on its way to Jerusalem. Elsa gave it to a representative of the Board of Governors of the University of Jerusalem. The document which confirmed this transaction stated that 2000 Marks should be allocated to support the work Prof. Freundlich and 400 Marks should be given to Mrs. Einstein for her charities. When Einstein learned about this, he wrote to Elsa with relief: “I am glad that I got rid of the manuscript and thank you for doing me this favor of love; better than burnt or sold.” At that time, Einstein was deeply involved with the initiative to establish the Hebrew University in Jerusalem and acted as Chairman on the Academic Committee of its Board of Governors.

This manuscript has been in the possession of the Hebrew University since its opening on 1 April 1925. Selected pages have been displayed at numerous exhibitions worldwide, but the original version, in its entirety, was exhibited to the general public only once on the occasion of the 50th anniversary of the Israeli Academy of Sciences and Humanities in 2011. Each one of its 46 pages was enclosed in a display case with specially subdued lighting. It attracted crowds of interested and excited visitors. The Albert Einstein Archives at the Hebrew University contain many such manuscripts. They are being studied and edited by historians of science at the Einstein Papers Project in the California Institute of Technology. All shed light on how science was done in the formative years of modern physics. Among them the manuscript presented here is most cherished. We often refer to it as the Magna Carta of Modern Physics.

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© SP Books / Hanoch Gutfreund, 2019

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