A New Approach to Gravitation and Relativity Based upon Enhanced Newtonian Gravity and Special Relativity (I)

The paper presents a critique of the fundamentals of general relativity theory, generalises special relativity theory to non-inertial reference frames and constructs a theory which, in weak gravitational fields, leads to the same results for redshift, light deflection or runtime and perihel precession as the general theory of relativity, all in Euclidean geometry, with a constant speed of light and without recourse to a principle of equivalence or relativity. In strong gravitational fields, different values result, in particular, a yet to be determined portion of dark energy or mass is shown to be of dynamic origin. The new theory characterises that light and massive bodies gain or lose energy and mass, resp., in exchange with an effective Newtonian gravitational potential. Corresponding Lagrangean and Hamilton-Jacobi equations for bodies with variable mass are derived and a Schr?dinger equation is established in gravity the Hamiltonian of which reflects the 4 key experiments. The theory necessarily implies that the rate of a clock and the speed of light do not depend on their position in the gravitational field. That E?tv?s’ theorem only applies to exactly circular orbits, otherwise requiring a relativistic supplement. Furthermore, the shape of a rotating disc or a body orbiting around the centre of gravity does not violate Euclidean geometry. The fact that the general theory of relativity nevertheless agrees perfectly with the new theory is explained by the greater number of degrees of freedom that non-Euclidean geometry has in comparison with Euclidean geometry.