I'm an engineer and I'm used to classical mechanics "spatial-vectors" approach, which allows a geometric analysis of rigid bodies motion. In this context, as you know, it is very useful to imagine (and draw) each vector as an arrow.
I am self-studying Einstein's relativity and the abstract "four-vectors". Though I understand the necessity of introducing the time dimension, It is clear that these entities are not intuitive at all: not only they have four dimensions, but their metric is also pseudo-euclidean (in best case). This makes it impossible to draw them or even imagine their shape.
Do you think it would be possible to adopt a more intuitive approach to relativity, which keeps the usual 3d-spatial-vectors but (for example) foresees a "graphical contraction" of vector-arrows depending on the frame? Have you ever heard of a similar approach anywhere? (Clearly the concept of spacetime curvature would decay, but maybe it could be replaced by a less elegant / more practical solution)