Coordinates and covariance: Einstein's view of space-time and the modern view

Where modern formulations of relatively theory use differentiable manifolds to space-time, Einstein simply used open sets of R4, following the then current methods of differential geometry. This fact aids resolution of a number of outstanding puzzles concerning Einstein's use of coordinate systems and covariance principles, including the claimed physical significance of covariance principles, their connection to relativity principles, Einstein's apparent confusion of coordinate systems and frames of reference, and his failure to distinguish active and passive transformations, especially in the context of his hole and point-coincidence arguments

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