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Finite projective (lattice) geometries defined over rings instead of fieldshave recently been recognized to be of great importance for quantum informationtheory. We believe that there is much more potential hidden in these geometriesto be unleashed for physics. There exist specific rings over which theprojective spaces feature two principally distinct kinds of basic constituents(points and/or higher-rank linear subspaces), intricately interwoven with eachother -- unimodular and non-unimodular. We conjecture that these two projective"degrees of freedom" can rudimentary be associated with spatial and temporaldimensions of physics, respectively. Our hypothesis is illustrated on theprojective line over the smallest ring of ternions. Both the fundamentaldifference and intricate connection between time and space are demonstrated,and even the ring geometrical germs of the observed macroscopic dimensionality(3+1) of space-time and the arrow of time are outlined. Some other conceptualimplications of this speculative model (like a hierarchical structure ofphysical systems) are also mentioned.

Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?