A. Einstein. Autograph letter signed ("A.E.") about representing curved space-time in his Unified Field Theory, 
Autograph letter signed (“A.E.”) to Erich Gabor Straus, about representing curved spacetime [in his Unified Field Theory], 
written in German, expressing his appreciation of Straus’s concerns that the various projections (“Koordinatenwahl“) chosen to represent spacetime on a flat surface should be made compatible, seeking to allay his fears and providing an explanation in three parts with several equations; he explains that there are 16 freely-selectable patches (“Schnittfunktionen”) which he can use to make these projections compatible by using the projection Mi=0 (i = 1, 2, 3), which is possible even where the first vector Mi (including M4) is discarded, and that, with any solution of (Ia), M4o is a transition function that is generally different from O; Einstein says that, since the general solution of (Ia) contains sixteen freely-selectable patches, these can be selected so that M4o disappears, and that this specialization means that instead of 16 only 15 patches remain
"...Das schwacherere System (Ia) sei allgemein gelöst. Es treten dann in der Lösung (abgesehen von der durch die freie Koordinatenwahl bedingten Freiheit der Darstellung) 16 frei wählbare Schnitt-Funktionen auf..."
1 page, 4to (c.27.5 x 21.5cm), paper watermarked "Whiting Mutual Bond", no place, June 1950 (the date inscribed in another hand: "15-6-50")
Albert Einstein was the most famous scientist of the twentieth century, most celebrated for his theory of relativity, one of the pillars of modern physics. He subsequently attempted to unify relativity with electromagnetism, and worked for years on seeking to unify concepts of space and time into an entity we now call spacetime. from 1915 on, he developed his theory of Special Relativity into a description of gravity ("General Relativity"), using a field to describe the curved geometry of four-dimensional spacetime.
Einstein here seeks to explain how to project a "map" of spacetime onto a flat surface. The problem he is solving is to coordinate the different projections of spacetime so they represent all four dimensions comprehensively. This is somewhat akin to patching over holes and inaccuracies in cartographic projections of the Globe, but here incorporating the time dimension. Einstein’s correspondent was the German-born mathematician Ernst Gabor Straus (1922-1983), who emigrated to the USA in 1933 and became Einstein’s assistant at the Institute of Advanced Study, Princeton between 1950 and 1953, when he moved to UCLA. Einstein credited him with help in developing his Unified Field Theory.
Sotheby's is happy to acknowledge the help and advice of Professor Gary Gibbons in preparing our description of this lot.
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