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Einstein "According to the general theory of relativity, one must consider that the Foucault pendulum adjusts itself to be rotation-free with respect to the total mass of the universe" Nobel Prize Yea
Einstein "According to the general theory of relativity, one must consider that the Foucault pendulum adjusts itself to be rotation-free with respect to the total mass of the universe" Nobel Prize Yea
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Einstein "According to the general theory of relativity, one must consider that the Foucault pendulum adjusts itself to be rotation-free with respect to the total mass of the universe" Nobel Prize Year

EINSTEIN, ALBERT. Typed Letter Signed, “A. Einstein”, with his handwritten annotation, “gµν-Feld”, 1p, in German, 4to, Berlin, February 10, 1921. To Axel Frey Samsoie. Expected folds with minor creasing, minimal scattered foxing, else Fine.

The total gravitational mass of the Universe determines the curvature of Spacetime and the inertial behavior of Matter -- the core idea of General Relativity used to explain the motion of Foucault’s pendulum and the rotation of the Earth. An important and highly condensed statement – almost enigmatic in its terseness -- answering the question: “when we ascertain a rotation of the Earth by means of Foucault’s pendulum, is the rotation a motion with respect to the Sun, the stars, or to something else?”

In two very succinct sentences, Einstein answers: “According to the general theory of relativity, one must consider that the Foucault pendulum adjusts itself to be rotation-free with respect to the total mass of the universe. This mutual influence should however not be interpreted as action at a distance: the [total] masses define the gμν-Feld [i.e., the gravitational metric field] in space, and this field defines the inertial behaviour of the mass of the Foucault pendulum.”

Samsoie’s question is a very profound one, taking us deep into the principles at work in General Relativity. If we start from the assumption that all frames of reference are valid for describing motion, how can a Foucault pendulum either prove or disprove that the earth rotates or is stationary? (Couldn't it just as easily prove that the earth is stationary and that the whole universe rotates around it?) The economy of Einstein’s response is such that one doesn’t readily see how much General Relativity theory it encompasses: Einstein’s answer draws on Mach’s principle and the interdependence of gravity and motion to re-affirm the relativity of all motion and the absence of privileged reference frames. As is very often the case with letters of this type (responding to questions from lay persons), Einstein only gives his correspondent “two sides of the triangle” – leaving it to the reader to do some homework and achieve the full answer by “filling in the blanks” of Einstein’s argument.

Einstein’s answer is very evocative of John Wheeler’s famous assessment of the essence of General Relativity: “Spacetime tells matter how to move; matter tells spacetime how to curve." In indicating that the total mass of the universe gives definition to the metric tensor – influencing through its mediation “the inertial behaviour of the mass of the Foucault pendulum” -- Einstein is implicitly invoking Mach’s Principle and demonstrating the interdependence of gravity and motion. The statement that the pendulum is “rotation-free with respect to the total mass of the universe” is Einstein’s somewhat oblique way of signaling that in actual fact it is the earth itself that is rotating (and not the universe that is rotating around a still earth). In accordance with Newton’s laws of motion, the pendulum is actually moving in a “straight line” (as defined by the curvature of spacetime), and the apparent nonlinear motion the pendulum appears to sustain (from our perspective) is actually its tracing of the rotation of the earth beneath it.

Samsoie’s question in fact touches upon a fragile aspect of the General Theory of Relativity: whether rotational motion is to be taken as absolute or relative. In the wake of Einstein’s publication of the General Theory of Relativity in 1916, the scientific community actively debated whether the theory truly and properly accounted for rotational motion, and the absoluteness and non-relativity of rotation remains a contested issue even today. Einstein himself appears to have changed his position on the issue more than once over the course of his career, and we have him here on record – some five years after the publication of his epochal Grundlage statement – affirming its relativity. (Einstein similarly waffled on his commitment to Mach’s Principle over the years, and the two instances of prevarication are perhaps connected.) Though some attention was paid in the first decade of General Relativity to the question of whether the theory could account for the rotation of a gyroscope, surprisingly little attention was paid to the question of a Foucault pendulum – hence Samsoie’s question to Einstein.

Einstein himself referenced Foucault’s pendulum in context of an important 1912 thought experiment relating to Mach’s Principle, which led Einstein to posit both the relativity of inertial mass and the Einstein-Lense-Thirring frame-dragging effect. (Cf. Einstein’s historic 1913 letter to Mach.) The present letter appears to be Einstein’s most complete statement of how General Relativity interprets the behavior of a pendulum, and it is further of significance to any General Relativity discussion of the origin of inertia or the “frame dragging” effect due to the earth’s rotation.

Samsoie’s original letter, together with the response Einstein originally penned on it, is still extant at the Einstein archives in Jerusalem. Einstein originally thought to begin his answer to Samsoie in stating: “From the point of view of the Lorentzian Theory [i.e., Special Relativity], the answer to your question was that Foucault's experiment indicated the rotation against the ether. One can keep this statement from the standpoint of General Relativity.” Einstein’s response to Samsoie is almost haiku-like in its compression and meaning.

A highly desirable letter from Einstein’s Nobel Prize year, 1921.

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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