[EINSTEIN, ALBERT] | AN EXCEPTIONAL SIGNED PHOTOGRAPH OF EINSTEIN AT CHALKBOARD, 1931, SIGNED BY EINSTEIN

[EINSTEIN, ALBERT]

An exceptional signed photograph of Albert Einstein at Chalkboard, taken 14 January, 1931, SIGNED and dated by him in 1933

Silver gelatin print, 8 x 10 inches. SIGNED and dated to middle right "A. EINSTEIN./ 1933."

ONE OF THE MOST ICONIC IMAGES OF EINSTEIN, taken by a press photographer at Cal Tech’s Mount Wilson Observatory in Pasadena, CA. Einstein had given a lecture in the observatory’s library, and he is here photographed in front of the blackboard he used, on which he has written the equation for a vanishing Ricci Curvature Tensor – R_ik = 0 — an equation intriguingly followed by a question mark.

Edwin Hubble, who worked at the observatory, had only just recently published his first article on the expanding universe, and Hubble himself was in attendance at the lecture. Albert A. Michelson (of Michelson and Morley fame) was also present, as were a small number of other notable astronomers, many of whom were in fact skeptical of the Theory of Relativity (despite having themselves provided empirical evidence proving its validity).

The Ricci Curvature Tensor is a key term in Einstein’s field equations, and it is used both in General Relativity and in Einstein’s Unified Field Theory. (The expression R_ik is now typically written R_μν). An expression of the matter/energy content of the universe, the Ricci tensor measures the deviation of a curved spacetime from a Euclidean framework, and its value determines whether a particularized spacetime (and the matter within it) will converge or diverge over time.  (More technically, the Ricci tensor represents “the amount by which the volume of a narrow conical piece of a small geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.”) A zero value of the Ricci tensor is indicative of a static state of universe, whereas a non-zero value indicates the state is non-static and either expanding or contracting. In context of the Einstein Field Equations, a vanishing Ricci tensor is equivalent to a zero stress-energy tensor, i.e. a vacuum – the which is again to say that it is equivalent to the non-existence (or zero value) of a cosmological constant. 

No transcript exists of Einstein’s lecture at the observatory, and the reason why he wrote the equation on the blackboard remains speculative. Hubble himself was present at the lecture and Einstein was at this point in time considering changes to his General Relativity equations via his work on Unified Field Theory. It is therefore reasonable to conjecture that in writing “R_ik = 0?” on the blackboard, Einstein was asking “can the Ricci curvature tensor for the universe as a whole equal zero?” I.e. is the universe spatially flat or not; or, again, is the actual quantity of matter/energy in the universe (including electro-magnetic forces)  too small – or effectively “zero” – to enable gravity to prevent the indefinite expansion of the universe?

“R_ik = 0” has been called “Einstein’s favorite equation” and it is very certainly the case that Einstein spent the second half of his life and career “fiddling” with this equation.

One of the most famous photographs of the 20th century, this Cal Tech photo captures Einstein at a critical moment for his thought – pondering the implications of Hubble’s expanding universe for his own General Relativity equations. It is the most meaningful scientific photographs of Einstein ever taken. This is the only known signed copy of this world famous photograph.