Scalar theory of gravity as a pressure force
Résumé
The construction of this theory starts with Newtonian space-time and a tentative interpretation of gravity as Archimedes' thrust exerted on matter at the scale of elementary particles by an imagined perfect fluid or ether. This leads to express the gravity acceleration by a simple formula in which the "ether pressure" pe plays the role of the Newtonian potential. The instantaneous propagation of Newtonian gravity is obtained with an incompressible ether, giving a field equation for pe. For a compressible ether, this equation holds in the static case and results in a non-linear influence of the mass distribution. The extension of the field equation to non-static situations follows the lines of acoustics and leads to gravitational (pressure) waves. To account for metric effects, first the modern version of the Lorentz-Poincaré interpretation of special relativity is summarized. Then Einstein's equivalence principle (EP) is seen as a correspondence between the metric effects of gravity and those of uniform motion with respect to the ether : a gravitational contraction (dilation) of space (time) standards is assumed, and it implies geodesic motion for test particles in a static field. The same field equation is now expressed in terms of the physical space and time metrics in the frame of ether; since both metrics depend on pe due to the EP, it becomes non-linear in pe. In the spherical static situation, Schwarzschild's exterior metric is predicted, but the interior metric differs from GR, though it agrees with the EP. Since pressure produces gravitation also in the proposed theory, no equilibrium is possible for very massive objects. But the gravitational collapse in free fall does not lead to any singularity. Moreover, gravitational waves, and even shock ones, can exist in vacuo also with spherical symmetry.