the Riemann curvature tensor is defined in terms of infinitesimally small closed paths around which one does parallel transport.

in general relativity, a portion any closed path through spacetime must travel against the flow of time. this seems weird.

given the need for backward time travel or superluminal travel in its definition, it's a little bit surprising that Riemann curvature of spacetime can (in principle) be physically measured: watch how two neighboring particles, initially set on parallel trajectories, diverge from parallel due to gravity, or more generally, due to curved spacetime. repeat with many pairs of particles headed in different directions at different speeds. (how many pairs are necessary?) this assumes stationary spacetime: gravity not changing as a function of time. then, do some math.

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