My question is about foundations of the special relativity theory. In Minkowski's way of presenting special relativity, with a signature "+ - - -", one associates to every couple of events, a spatio-temporal distance which is null on the light cone, positive if the two events are causally linked, and negative otherwise. Now, in special relativity, the physical actions or physical trajectories must not get out of the null cone. In particular, a velocity vector has always a positive Minkowski length. I know that, when we usually develop special relativity, we use as well negative as positive distances between events, and that it is a convenient mean to present special relativity. Nevertheless, from the point of view of the foundations of special relativity, I ask myself if it is absolutely necessary to attribute a (negative) length between two events that are not causally linked. Wouldn't it be possible to reconstruct all the content of special relativity (at least what is really verifiable) without attributing any distance between non causally linked events? In other words, could we reconstruct the essence of the content of special relativity with only half of the Minkowski world, having only a metric in the interior of the null cone? Thanks for any idea on the subject.