The Dirac equation in physics was described earlier in a simple form through hyperbolic octonion arithmetic, and a circular octonion counterpart exhibited certain behavior which one might expect from a quantum gravitational primitive. Both relations are expressible with use of conic sedenion arithmetic (M-algebra) as the unifying number concept. A general concern exists when proposing physical forces on the same space–time, but with respect to different underlying geometries. Therefore, a needed concept of relativity will now be suggested in terms of an invariant hypernumber modulus, to warrant universal applicability of physical law in equivalent frames of reference. To support validity of such a concept, conic sedenions will be analyzed with respect to their hyperbolic and circular subalgebras. Representing classical Minkowski and a new Euclidean space–time metric respectively, an alignment program for large body (non-quantum) physics will be proposed. Translated into the language and concepts from General Relativity, its effective equivalence in the description of gravity will be shown. Some approaches to physics on number systems other than traditional complex numbers will briefly be compared to the current investigation in this paper.