  It is shown that if the universal cover of a manifold $M$ is an open
manifold, then two different fibres of the spherical cotangent bundle $ST^*M$
cannot be connected by a non-negative Legendrian isotopy. This result is
applied to the study of causality in globally hyperbolic spacetimes. It is also
used to strengthen a result of Eliashberg, Kim, and Polterovich on the
existence of a partial order on $\widetilde{\mathrm{Cont}}_0 (ST^*M)$.
