Significant archive of a five-page letter to Dr. Albert Einstein by Daniel Lipkin on the subject of space-time, copiously annotated in the margins by Einstein with autograph comments and a 9-line signed autograph statement at the end, signed "A. E."; and a TLS from Einstein to Lipkin, signed "A. Einstein," returning the letter with marginal notes on October 13, 1952.
Einstein responds to a college student’s understanding of his Theory of Generalized Gravitation, Einstein’s final approach to Unified Field Theory.
Lipkin’s statements focus on the metric field and the 4-D spacetime coordinate system within the theory, and Lipkin considers the possibility and implications of extending them to include hypercomplex numbers. Einstein’s comments both confirm Einstein’s own understanding of his theory and indicate that Lipkin has markedly misconceived the relationship of these two mathematical components of Generalized Gravitation Theory.
Responding like a professor reading a term paper, Einstein comments on Lipkin’s statements in the blank margins of the letter and pens his own signed summary statement at the conclusion of the text. Einstein responds with characteristic terseness to Lipkin’s statements—often simply notating “yes” or (more often) “no!” alongside them—but two of his marginal comments are highly significant in and of themselves: Einstein stating in one of them that “space is nothing by itself but only the dimensionality of the field”; and affirming “this is what I hope for” in response to Lipkin’s premising that “the Theory of Generalized Gravitation provides an accurate description of all possible physical facts.”
Einstein’s concluding remarks, signed "A. E.," both address the ultimate thrust of Lipkin’s letter and are of import for the future direction of Einstein’s own research efforts (translated): "I can imagine that the [metric] field could be understood as a hyper-complex number, which appears as a function of another (different) hyper-complex number (which would represent the "coordinate space"). But I wonder whether it would be possible to arrive at a system that could give expression to the general covariance. The theory of complex functions (two-dimensional) does not seem to me to offer any analogy, because [equation] is not a general covariant equation." In overall fine condition.
A very rare form of an Einstein autograph, annotated letters such as the present are a product of Einstein’s late years and evidence his remarkable benevolence and willingness to engage with young people. Though such letters often deal with broader aspects of Einstein’s philosophical world view, this particular letter is unusual for addressing a mathematical topic of central importance to his ongoing research into Unified Field Theory. Einstein in fact spent the final years of his life investigating the implications of introducing different complex metrics into Unified Field Theory, and this letter speaks directly to such a concern.
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