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Reconstruction of the Derivation of the Einstein Field Equations of General Relativity

Robert J. Heaston
Year: 2007
One hundred years ago Einstein began his nine-year odyssey (1907-1916) toward deriving his field equations of general relativity. The difficulty of replicating this derivation exists not only because of the extreme complexity of the equations but also because Einstein omitted references, skipped steps, failed to state many of his assumptions, and neglected to define all his terms in his technical publications. On the other hand, Einstein left extensive personal correspondence that contains a number of details that trace his progress. An excellent source of this correspondence is the 1997 biography Albert Einstein by Albrecht F?lsing, Penguin Books. The objective of this paper is to match Einstein?s correspondence record with his publication record in order to reconstruct the approach that Einstein used in deriving his field equations. The reconstruction dictates the path that Einstein had to take if he wanted his field equations to converge on the Newton gravitational force. The major lesson learned from this reconstruction is that Einstein probably overlooked, ignored, or bypassed some valid alternative options that radically change the interpretation of the field equations. The most significant option reveals that singularities are theoretically impossible, an observation that negates inflation theory and modifies the explanations of theories of black holes, the big bang, and strings. The Einstein field equations are still valid but obviously need reinterpretation based upon the alternatives described here.