Electro-Gravity via Geometric Chronon Field

Aim: To develop a model of matter that will account for electro-gravity.

Interacting particles with non-gravitational fields can be seen as clocks whose trajectory is not Minkowsky geodesic. A field, in which each such small enough clock is not geodesic, can be described by a scalar field of time, whose gradient has non-zero curvature. This way the scalar field adds information to space-time, which is not anticipated by the metric tensor alone. The scalar field can’t be realized as a coordinate because it can be measured from a reference sub-manifold along different curves. In a “Big Bang” manifold, the field is simply an upper limit on measurable time by interacting clocks, backwards from each event to the big bang singularity as a limit only. In De Sitter / Anti De Sitter space-time, reference sub-manifolds from which such time is measured along integral curves, are described as all events in which the scalar field is zero. The solution need not be unique but the representation of the acceleration field by an anti-symmetric matrix, is unique up to SU(2) x U(1) degrees of freedom. Matter in Einstein Grossmann equation is replaced by the action of the acceleration field, i.e. by a geometric action which is not anticipated by the metric alone. This idea leads to a new formalism of matter that replaces the conventional stress-energy-momentum-tensor. The formalism will be mainly developed for classical but also for quantum physics. The result is that a positive charge manifests small attracting gravity and a stronger but small repelling acceleration field that repels even uncharged particles that measure proper time, i.e. have rest mass. Negative charge, manifests a repelling anti-gravity but also a stronger acceleration field that attracts even uncharged particles that measure proper time, i.e. have rest mass.