Albert Einstein
n.p., September 29, 1937
Albert Einstein ALS On Rik = 0 & "It is therefore a generalization of the old gravitational equations through a single differentiation"
ALS

A 1p autograph letter in German signed by physicist Albert Einstein (1879-1955) as "A. Einstein" at lower right. September 29, 1937. N.p. On lightweight onion skin paper, with contemporaneous edits including cross-outs, insertions, and substitutions. The letter features nearly 200 words in Einstein's hand; as well as about half a dozen equations or scientific formulae, including "Rik = 0" located near the bottom. Rik = 0 is perhaps the second most recognized formula associated with Albert Einstein after E = MC2, thanks to a famous press photo snapped of Einstein writing it on a chalkboard. The letter has been professionally matted next to a high-quality photo reproduction of the Einstein chalkboard photo. The letter shows expected wear including flattened transmittal folds and a few extra wrinkles. Isolated minor chips along the right and left edges, with a small area along the lower right edge discretely and professionally repaired. Else near fine. The actual size of the letter is 8.5" x 10.875" while the overall size of the mat is 24.5" x 17" x .75." Ex-Sotheby's. Accompanied by a full German transcript and a full English translation.

Rik = 0 was the "simple formula" that Einstein had famously scrawled on a chalkboard following an astronomy lecture at the California Institute of Technology's Mt. Wilson Observatory in Pasadena, California on January 14, 1931. The lecture was delivered by Dr. Gustaf Stromberg, a staff astronomer at the observatory, who speculated about such crowd-pleasing questions as the "size, shape, [and] age of [the] universe." Einstein, one of several world-renown scientists who attended Dr. Stromberg's lecture, apparently strode up the chalkboard after the lecture concluded, having given up the struggle to properly articulate one of his ideas into words. He wrote "Rik = 0 ?" on the chalkboard, posing it in relation to an attempt to calculate the density formula of the Milky Way. The incident is remarkable, not only because it suggests another example of Einstein's genius, but also because it underscores the important working relationship between theoretical physicists like Einstein and astronomers like Dr. Stromberg. Astronomers could and did prove Einstein's theory of relativity.

Albert Einstein wrote this letter to the brilliant Hungarian-Jewish physicist Cornelius (also Cornel) Lanczos (1893-1974). The letter relates to the two scientists' ongoing quest to more fully understand and articulate the theory of general relativity using elements of tensor calculus.

In Einstein's letter, "Rik" appears in one form or another no fewer than five times, with "Rik = 0" explicitly appearing once. "Rik" was an abbreviation for the Ricci tensor, a concept in differential geometry developed by the Italian mathematician Gregorio Ricci-Curbastro (1853-1925). The Ricci tensor is used to visually represent how the volume of something in curved space changes due to the presence of curves, or arcs; and to quantify and document how the volume of something performs differently in curved space compared to in normal three-dimensional space. In general relativity, the Ricci tensor represents volume changes caused by spacetime volume, or gravitational tides.

Einstein was interested in the Ricci tensor in its relation to general relativity; one of the three "classic tests" of general relativity is trying to calculate the perihelion (closest point of orbit to the sun) of the planet Mercury using the equation Rik = 0, which are essentially vacuum conditions not permitting the presence of an electromagnetic field. The Ricci tensor enabled physicists and astronomers to better conceptualize how bodies and gases behaved in the universe.

Einstein's manuscript also mentions the "Bianchi operation," referring to mathematical concepts established by the prolific Italian mathematician Luigi Bianchi (1856-1928). Bianchi gave his name to Bianchi classification, Bianchi groups, Bianchi identities, and Bianchi transforms, concepts which explored mapping in curved and three-dimensional space.

Einstein wrote, translated in part:

"According to your explanations, your Bik tensor has the property

Riklm = Biklm + L (Rik),

wherein L () means a linear formation by means of the gik.

If you now perform the Bianchi operation on this equation, the left side disappears identically and you obtain the Biklm ; n (the dash means cyclic displacement) used for the field equations in the form

L (Rik;l,R;e)

wherein L again means a linear-homogeneous formation.

From this it is immediately apparent that your equations contain all the solutions of the old gravitational equations as solutions. It is therefore a generalization of the old gravitational equations through a single differentiation.

However, your equations form an over-determined system of equations if they do not possess a sufficient number of (differential) identities. In fact, only 6 equations may be independent of each other. These identities would be easy to find, as they would all have to follow from the identities ([Rik - 1/2gikR]; k20) (as long as they are not purely algebraic).

If there are not enough independent identities, then the system is essentially not more general than the system Rik=0. In my opinion, clarification of this formal point should precede all attempts at interpretation.

I would be delighted if you could write to me about such matters. There must be a reasonable interpretation for the electric field!"

Cornelius Lanczos's career was hugely influenced by Einstein's work, and the two became friends and close work associates. Lanczos had boldly dedicated his 1921 doctoral thesis, "Relation of Maxwell's Aether Equations to Functional Theory" to Einstein, and three years later, in 1924, he provided an exact solution to the Einstein field equation. Lanczos worked as Einstein's assistant in 1928-1929, later splitting up his time between the United States and Europe pursuing other research opportunities. Lanczos took a particular interest in the theory of relativity; about one third of his scientific publications related to the subject. After Einstein's death, Lanczos wrote and lectured extensively about Einstein's work.

This item comes with a Certificate from John Reznikoff, a premier authenticator for both major 3rd party authentication services, PSA and JSA (James Spence Authentications), as well as numerous auction houses.

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matted: 24.5" x 17" x .75"
Ex-Sotheby's, November 26, 1980, lot 159.