Geometry of free fall and simultaneity

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Abstract
It is shown that the differentiable, affine, and metric structure of Newton–Cartan space‐time is uniquely determined by its projective–conformal–material structure. This means physically, that—similarly as in general relativity—it is also possible in classical gravitation to define operations of parallel transport and measurements of length, time, and mass using only three kinds of world lines: world lines of freely falling test particles, of photons, and of gravitational matter.

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