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Now the question leads to this, the time measured on our ship will be moving relative to the stationary ship, but the equivalence principle tells us that if we accelerate at some magnitude we can't tell it apart from gravity, but gravity bends spacetime...

... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of [the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality