A scale-invariant, Machian theory of gravitation and electrodynamics unified
Abstract
As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal.
The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence, the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless.
Thence emerges a scale-invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation thereof, embodied in “energy-momentum super tensors”, follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the general relativity-based standard paradigm could not address.
