The differentiable and causal structures of space-time

An improved version is presented of Ehlers, Schild, and Pirani's axiomatization of the differentiable and causal structures of space-time. It is shown that, under certain physically reasonable axioms, the properties of freely falling particles and light signals define a causal and differentiable structure on space-time. Further, it is shown how the causal structure define a causal and differentiable structure light signals propagate along conformal null geodesics.