A new prediction for the shapiro time delay from a unified description of gravity and motion

A novel theoretical framework for gravity is proposed in which the speed of light is a decreasing function of the cumulative gravitational potential, $\Phi$, generated by the matter content of the universe. In this scenario, the total inertial energy of a particle, $E$, is not conserved when it moves through a non-uniform gravitational field, and the truly conserved quantity is $\mathbb{E}=cE$, where $c$ denotes the effective speed of light, varying with the gravitational potential as $c=c_0/\Phi$. These two fundamental relations, together with $hc=\mathrm{const.}$, allow a mathematical construction that reproduces the solar tests proposed by Einstein, while providing the basis for a theory that is, a priori, compatible with Mach’s principle. A noteworthy finding is that the fourth test of general relativity proposed by Shapiro gives rise, in the present framework, to an additional time delay of approximately $20\,\mu\mathrm{s}$, which may not have been accounted for in previous radio-ranging analyses. For the maximum solar encounter in the Cassini geometry, the additional delay produces a Doppler-tracking signature equivalent to an effective $\Delta\gamma_{\rm eff}\simeq4.3\times10^{-5}$, placing the predicted effect at approximately the sensitivity level of the Cassini experiment.