I N T R O D U C T I O N T O V O L U M E 1 3 l x x v In all probability, the manuscript that Einstein began to write on 9 January 1923 is the one published in this volume as Doc. 417. It was written in part on the steam- er’s stationery and is dated “Singapore, January 1923.” The stopover in Singapore was on 10 January, the next day, and presented an opportunity to send off mail. In Doc. 417, Einstein engages with Weyl’s and Eddington’s ideas about the foundations of general relativity. It begins with a comment on the basic significance of the metric and its role in the general theory of relativity. Einstein then followed up on and modified Eddington’s approach of basing the theory entirely on the con- cept of the linear affine connection. The Riemann curvature tensor and one of its contractions, the Ricci tensor (called “Riemann tensor of second rank” in Doc. 425), can be expressed only in terms of the connection. In this case, the Ricci tensor is no longer symmetric, even if the connection is, and there is a natural met- ric in the theory obtained by defining a line element, with the Ricci tensor taking the role of the metric tensor. In the manuscript, Einstein accepted Eddington’s ap- proach, but criticized the theory in three respects: Eddington had not formulated enough field equations to determine all components of the affine connection, and had not succeeded in either establishing the link to experience or in casting his the- ory in Hamiltonian form. Accordingly, Einstein took it upon himself to do just that. In contrast to Eddington, Einstein from the outset accepted the existence of both the metric and the connection as independent quantities, and he formulated a vari- ational principle for a Lagrangian that depends on both the metric and the connec- tion and their derivatives. Variation with respect to the metric produces the field equations. Variation with respect to the connection, on the other hand, produces compatibility conditions for the metric and the connection. In standard general rel- ativity, this procedure defines the Levi-Civita connection, and it seems that Einstein here employed for the first time in this way a method that later became known as Palatini’s method. Reference to “an Italian mathematician” is made in the paper, but the focus of Palatini’s 1919 paper (Palatini 1919b), which Einstein appears to have in mind, is very different. Palatini’s aim was to preserve general covariance throughout all steps of the variational calculation, rather than deriving the metric- connection compatibility by independent variation with respect to both the metric and the connection. Einstein showed how the vacuum field equations of general rel- ativity and the compatibility condition for the metric arise from variations of the action integral, taking the Riemann curvature scalar as Lagrangian density and varying the action with respect to the components of the metric and of the connection, respectively. What so far appears only as a contribution to the foundations of general relativ- ity, as the title of Doc. 417 also suggests, turns into an attempt at a unified field the- ory by interpreting, following Eddington, the antisymmetrized Ricci tensor as an expression for the electromagnetic field. Einstein followed Eddington in this
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