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

0336549 - ÚFCH JH 2011 RIV US eng J - Journal Article
Saniga, M. - Pracna, Petr
Space Versus Time: Unimodular Versus Non-Unimodular Projective Ring Geometries?
Journal of Cosmology. Roč. 4, - (2010), s. 719-735. ISSN 2159-063X
Institutional research plan: CEZ:AV0Z40400503
Keywords : projective ring lines * smallest ring of ternions * Germas: of space-time
Subject RIV: CF - Physical ; Theoretical Chemistry
http://journalofcosmology.com/Multiverse4.html

Both the fundamental difference 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. Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and/or higher-rank linear subspaces), intricately interwoven with each other — unimodular and nonunimodular. We conjecture that these two projective "degrees of freedom" can rudimentary be associated with spatial and temporal dimensions of physics, respectively. Our hypothesis is illustrated on the projective line over the smallest ring of ternions.
Permanent Link: http://hdl.handle.net/11104/0180758