Second gravity

Abstract

A theory of a new gravitational interaction is described. This theory follows naturally from a new Lagrangian formulation of Maxwell’s theory for photons and electrons (and positrons) whose associated Euler Lagrange equations imply the conventional Maxwell equations, but which possesses new bosonic spinor degrees of freedom that may be associated with a new type of fundamental gravitational interaction. The precise character of this gravitational interaction with a photon vector potential is explicitly defined in terms of a local U(1)-invariant Lagrangian in Eq. (86). However, in Sec. ???, in order to parallel the well known Friedmann model in cosmology, a phenomenological description of the new gravitational interaction coupled to Newton–Einstein gravity that is sourced by an ideal fluid is discussed. To lay the foundation for a description of the new gravitational interaction, our new formulation of Maxwell’s theory must first be described. It is cast on the real, eight-dimensional pseudo-Euclidean vector space defined by the split octonion algebra, regarded as a vector space over R and denoted as R4,4≅M3,1⊕M∗3,1. (Here M3,1 denotes real four-dimensional Minkowski space-time and M∗3,1 denotes its dual; R4,4 resembles the phase space of a single relativistic particle.) The new gravitational interaction is carried by a field that defines an algebraically distinguished element of the split octonion algebra, namely, the multiplicative unit element. We call this interaction the “unit” interaction and more descriptively refer to it as “second gravity.”