Energy and equations of motion in a tentative theory of gravity with a privileged reference frame

Abstract

Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as that appearing in special relativity was expressed in terms of these distorted local standards, and it was found to imply geodesic motion. Here, the formulation of motion is reexamined in the most general situation. A consistent Newton law can still be deï¬ned, which accounts for the time variation of the space metric, but it is not compatible with geodesic motion for a time-dependent ï¬eld. The energy of a test particle is deï¬ned: it is constant in the static case. Starting from “dust”, a balance equation is then derived for the energy of matter. If the Newton law is assumed, the ï¬eld equation of the theory allows to rewrite this as a true conservation equation, including the gravitational energy. The latter contains a Newtonian term, plus the square of the relative rate of the local velocity of gravitation waves (or that of light), the velocity being expressed in terms of absolute standards.