The Einstein Essays

Einstein and Hilbert’s Race to Generalize Relativity

Who got there first?

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Left: Physicist Albert Einstein (1879–1955). Right: Mathematician David Hilbert (1862–1943).

The published version of a talk by mathematician David Hilbert, dated the 20th of November 1915 is entitled Die Grundlagen der Physik, “On the Foundations of Physics”. It was held five days before Einstein’s momentous paper Die Feldgleichungen der Gravitation (“The Field Equations of General Relativity”) establishing the mathematical foundation for general relativity. Hilbert’s talk, eventually published on the 31st of March 1916, presented a theory of gravitation, including field equations describing the fundamental interactions of gravity as a result of spacetime being curved by mass and energy.

Einstein had by November of 1915 been working away at his grand theory since the publication of the first paper on special relativity in 1905. However, it would take him ten years, from 1905 to 1915 to generalize the theory so that it would relate the curvature of spacetime to the energy and momentum of whatever matter and radiation was present. Einstein’s field equations — the system of differential equations that specify general relativity — describe this relationship and were the last missing piece to his epic puzzle.

Left: Einstein (1915). Die Feldgleichungen der Gravitation (“The Field Equations of Gravitation”). Right: Hilbert (1916). Die Grundlagen der Physik (“On the Foundations of Physics”).

David Hilbert, generally acknowledged to be one of the greatest mathematicians of his era, was in the audience when Einstein spoke at Göttingen University about his new theory of gravitation in early 1915. In fact, he had been the one to invite Einstein to speak. In his lecture, Einstein presented his progress and the difficulties he was having with making his field equations generally covariant (independent of their coordinate system).

By fall, Einstein had not made any discernible progress. Hilbert, however, through various channels made it known that he was working on his own theory of gravitation, and making progress. By November, both were furiously working away at providing the correct equations for their theories. By the end of the month, both had.