When Einstein died in 1955, a small, brown notebook containing his private calculations was found. Called the Zurich notebook, it gives a chance to look over Einstein’s shoulder as he figures out his theory of general relativity. Albert Einstein’s work in science, one discovery stands above all as his greatest achievement. It is the general theory of relativity. In it, Einstein found a new way to think of the gravity that pulls apples from trees and keeps the moon in orbit around our earth. There are no forces pulling on them, he saw. They are merely responding to a curvature in the geometrical fabric of space and time.
The discovery of this theory is somehow more than mere science. It is not the fitting of a formula into a set of data or succumbing to the weight of evidences without answer. General relativity was an achievement of creative imagination. Through it, Einstein found the boundary of science and art. There he wrote equations linking space, time, matter and gravity every bit as beautiful as Shakespeare’s sonnets, but written in the universal language of mathematics. The evidence that favors general relativity is nowhere near as strong or thorough as that which speaks for quantum theory. Yet we favor general relativity simply because no conception this beautiful should be wrong. And it survives because no theorist in the many decades since 1915 has been imaginative enough to find a theory that does better than general relativity. Every time a new test is devised Einstein’s theory wins.
Einstein’s search for general relativity spanned eight years, 1907-1915. Some periods were quiet and some were more intense. The moments when the great transition occurred, came sometime between the late summer of 1912, when Einstein moved from Prague to Zurich, and early 1913. If we could choose one time at which to look over Einstein’s shoulder and watch him work on general relativity, it would be this time.
And that is just what we can do. For, found among his papers when Einstein died in 1955 was a small, brown notebook containing his private calculations. This is the Zurich notebook.
Prior to his move to Zurich in August 1912, Einstein was grappling with the puzzle of accommodating gravitation into his 1905 special theory of relativity. His reflections had borne some fruit, but they were rudimentary, in comparison to what was to come, and still in the simple mathematics of his work of 1905.
Then he saw it, the connection between gravity and non-Euclidean geometry. On could introduce the most general gravitational fields in the spacetime of special relativity merely by curving its geometry. In a few short months, he sketched the structure of the theory based on this idea and began to home in on its central equations that would describe how source matter would affect the geometry of spacetime.
Everyone who knows general relativity is familiar with those equations. They set two quantities equal. One, the “stress-energy tensor,” is simply a compilation of the properties of matter at each point in spacetime. It is a big table whose entries include energy density, momentum fluxes and stresses. The other is a purely geometric quantity, built out of quantities that measure how spacetime curves in the many dimensions that comprise it. That quantity is now known as the Einstein tensor and it is formed from another quantity discovered by the 19th century geometer and mathematician, Riemann. It is called, as you’d guess, the Riemann tensor.
Einstein circled around these equations. But then he abandoned them and by early 1913, settled on a set of equations with no clear geometric meaning. That this should happen is, to modern relativists, unimaginable. Yet it did. Einstein suffered terribly for nearly three years as he tried to resolve the resulting mess before presenting the famous Einstein equations that complete his theory.
The writer is student of Computer Science, BRAC University.