• gravitation;
  • celestial mechanics;
  • proper motions;
  • cosmology: theory;
  • large-scale structure of Universe


The principle of least action in its original form á la Maupertuis is used to explain geodetic and frame-dragging precessions which are customarily accounted for a curved space–time in general relativity. The least-time equations of motion agree with observations and are also in concert with general relativity. Yet according to the least-time principle, gravitation does not relate to the mathematical metric of space–time, but to a tangible energy density embodied by photons. The density of free space is in balance with the total mass of the Universein accord with the Planck law. Likewise, a local photon density and its phase distribution are in balance with the mass and charge distribution of a local body. Here gravitational force is understood as an energy density difference that will diminish when the oppositely polarized pairs of photons co-propagate from the energy-dense system of bodies to the energy-sparse system of the surrounding free space. Thus when the body changes its state of motion, the surrounding energy density must accommodate the change. The concurrent resistance in restructuring the surroundings, ultimately involving the entire Universe, is known as inertia. The all-around propagating energy density couples everything with everything else in accord with Mach’s principle.