The special relativity theory teaches us that simultaneity is relative to the motion of our reference frame. This seems to contradict the intuitive notion of the present to be instantaneous. Some additional paradoxes from quantum mechanics and general relativity seem to question our intuitive notion of time and present even more so that a static deterministic universe seems to be the only consistent solution compatible with these experimentally well confirmed paradoxes.
However, assume that we are convinced that the universe is dynamic and non-deterministic. Are there any specific properties of the present, like being instantaneous, that are necessarily implied by this? Even if we say that the present is the interface between the past and the future, does it really follow that this interface must be infinitely sharp?
At least for computer simulations of hyperbolic partial differential equations, it can sometimes be convenient to use a multistep scheme, or to use a position dependent time shift (for simulating oblique incidence on a periodic structure). However, this computer simulation is effectively analogous to the static deterministic universe, hence it is unclear what we can really conclude from this for the dynamic non-deterministic case.