Einstein's Zurich Notebook
A complete facsimile of the notebook is available at the Einstein Archive
Online at
http://www.alberteinstein.info/db/ViewImage.do?DocumentID=34421&Page=1
This webpage points to some of the images on the www.alberteinstein.info
server and remarks on them.
Here is the first page one finds on opening the notebook. The calculations on this page pertain to statistical physics.
Here is the first page that deals with gravitation. Einstein is setting up and deducing the law of conservation of energy and momentum.
But it is not the beginning of his work on gravity in the notebook. Einstein also started from the back from the back of the notebook. There we find pages in which Einstein writes the metric tensor in awkward form, possibly for the first time ever! He then turns immediately to seeking gravitational field equations, apparently on the model of his 1912 theory in which the variable speed of light was his gravitational potential.
One of my favorite pages. Einstein recapitulates a result from Newtonian mechanics in Gauss' theory of curved surfaces. A mass constrained to move in a curved surface (but otherwise unconstrained) moves along a geodesic of the spatial surface.
Back to the fron t of the book. Attempts to build a gravitation tensor for the gravitational field equations from the determinant G of the metric tensor?
Eventually, the Riemann curvature tensor enters, with an acknowledgment to Marcel Grossmann. Its first contraction, the Ricci tensor, is tried as a candidate gravitation tensor. Einstein finds that it does not immediately reduce to the right form in the weak field for Newtonian limit.
Eisntein struggles to deal with the huge expressions that are generated by the Riemann tensor. He doesn't always win.
Finally Einstein gets it. If he adds the harmonic coordinate condition, thereby specializing the coordinate system, he can reduce his gravitation tensor to the appropriate Newtonian form in the case of weak fields.
But all is not well and a few pages later Einstein abandons this most promising candidate for a gravitation tensor.
Now Einstein is getting pretty good at handling the Riemann tensor. He's found a different way of extracting the gravitation tensor from the Riemann tensor and reducing the result to the appropriate Newtonian form. This time he uses a different coordinate condition.
That second attempt doesn't survive the page. Here's a third way Einstein found of recovering a suitable gravitation tensor.
All is lost. Einsteing gives up trying to extract a gravitation tensor from the Riemann tensor. Instead he uses the method later published in his "Entwurf" paper. Here is his sketch of that inner workings of that derivation:
All that is left now is clean up. Einstein begins to sketch out a generally covariant formulation of Maxwell electrodynamics.
John D. Norton
August 2007