Abstract: Two points x,y in a spacetime X are said to be causally related if there is a nonspacelike curve between them, i.e. if one can get from one point to the other moving not faster than the light speed. For globally hyperbolic spacetimes X the light rays through a point x form a Legendrian sphere $S_x$ in the contact manifold N of all light rays in X. We show that if the universal cover of a level set of a timelike function is an open manifold, then x and y are causally related exactly when the Legendrian link $(S_x, S_y)$ is nontrivial in N. In particular this proves the Low conejcture and the Legendrian Low conjecture formulated by Natario and Tod.