  We formulate conjectures generalizing some known results to the category of
virtual Legendrian knots. This includes statements relating virtual Legendrian
knots to ordinary Legendrian knots, non-existence of positive virtual
Legendrian self isotopy for the class of the fiber of $ST^*M$ and the
conjectural relation of virtual Legendrian isotopy to causality in generalized
spacetimes. We prove the conjectures in the case of $2$-dimensional $M$ and
$(2+1)$-dimensional spacetimes. We also formulate and prove the version of the
Arnold's $4$ cusp conjecture for virtual isotopies.
