Untying the Knot: how Einstein Found his way Back to Field Equations Discarded in the Zurich Notebook

Abstract

Sometimes the most obvious questions are the most fruitful ones. The Zurich Notebook is a case in point. The notebook shows that Einstein already considered the field equations of general relativity about three years before he published them in November 1915. In the spring of 1913 he settled on different equations, known as the ``Entwurf'' field equations after the title of the paper in which they were first published (Einstein and Grossmann 1913). By Einstein's own lights, this move compromised one of the fundamental principles of his theory, the extension of the principle of relativity from uniform to arbitrary motion. Einstein had sought to implement this principle by constructing field equations out of generally-covariant expressions.1 The Entwurf field equations are not generally covariant. When Einstein published the equations, only their covariance under general linear transformations was assured. This raises two obvious questions. Why did Einstein reject equations of much broader covariance in 1912--1913? And why did he return to them in November 1915? A new answer to the first question has emerged from the analysis of the Zurich Notebook presented in this volume. This calls for a reassessment of Einstein's subsequent elaboration of the Entwurf theory and of the transition to the theory of November 1915. On the basis of a reexamination of Einstein's papers and correspondence of this period, we propose a new answer to the second question.