# Manuscript

Princeton, NJ: before 1945. 8 1/2 x 11 in. 3 pages on 2 leaves. Item #15577

The calculations in the first two pages relate to a generalization of the general theory of relativity that Einstein was working on in connection with his unified field theory. In a paper of June 19, 1945, Einstein had proposed a generalization of the mathematical foundations of general relativity. He proposed to generalize the theory such that distances in space would be invariant (unchanging) not only under changes of the frame of reference (as in the original theory) but also invariant under so-called Hermitian transformations. In a follow-up paper of January 24, 1946 (co-written with E.G. Straus), the authors note that Pauli had shown them that the limitation to Hermitian transformations is not necessary for the theory.

Indeed, in the first two pages of the document Pauli shows that a restriction to Hermitian transformations is problematic, and he suggests an even more general transformation group, and thereby provides a generalization of the alleged structure of space and time that goes further than that proposed by Einstein in his 1945 papers.

The pages were very likely written for Einstein. They are not formally addressed to him, most likely because Einstein and Pauli were both at the same Institute at the time and Pauli could just put his notes in Einstein’s departmental pigeonhole himself. Still, the calculations finish on a personal note: “Best regards, on Monday morning I’ll come to the Institute, Yours, W. Pauli”; likely an invitation for further discussion between two of the greatest minds of the twentieth century.

Einstein was at the Institute for Advanced Studies at Princeton from 1933 to his death in 1955. Pauli was a visiting professor in 1935 and then again from 1940 to 1946. When Pauli received the Nobel Prize in 1945, Einstein gave a speech in which he called Pauli his intellectual heir. Indeed, there are many signs that Einstein and Pauli had regular contact and conversations on physics during their joint time at Princeton, and the first two pages of the manuscript are likely an important testament to their collaboration.

The third page is also in Pauli’s hand, but it is not directly related to the preceding pages, even though it, too, contains differential geometric calculations, related to curvature of spacetime and which paths through spacetime are the straightest ones.

Pauli (1900-1958) was certainly one of the foremost theoretical physicist of modern times. He was one of the co-creators of quantum mechanics, he formulated the Pauli exclusion principle (which allows for a quantum mechanical explanation of the periodic table of chemistry), gave the first theoretical account of electron spin, and successfully predicted the elementary particle we today call the neutrino. Pauli formulated the CPT Theorem, which links the symmetries of space and time to the properties of elementary particles. For decades, he was the nexus of international correspondence on theoretical physics, maybe the last theoretician who overlooked the entire field, and was aptly called “the conscience of physics” by most of his contemporaries due to his relentless criticism of everyone’s work, no matter their stature.

By the age of 21 Pauli had authored a comprehensive textbook on the general theory of relativity that was immediately praised by Einstein as an astounding piece of work. It remained one of the most important textbooks on the topic for at least four decades.

Thanks to Dr. Dennis Lehmkuhl of the Einstein Papers Project at Cal Tech for his help in translation and explanation.

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