Spacetime symplectic extension

Abstract

It is conjectured that in the origin of spacetime there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l, C), l≥1 instead of the pseudoorthogonal one SO(1, d−1), d≥4 is proposed as the spacetime local structure group. A discrete sequence of the metric spacetimes of the fixed dimensionalities d=(2l)² and signatures, with l(2l−1) timelike and l(2l+1) spacelike directions, defined over the set of Hermitian second-rank spin tensors, is considered as an alternative to the pseudo-Euclidean extra dimensional spacetimes. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary spacetime cases with l=1, 2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary spacetime.