The Mass Deficiency Correction to Classical and Quantum Mechanical Descriptions : Alike Metric Change and Quantization Nearby an Electric Charge, and a Celestial Body. Part I : A New General Equation of Motion for Gravitationally, or Electrically Bound Particles

Via Newton's law of gravitation between two static masses exculsively, and the energy conservation law, in the broader sense of the concept of energy embodying the relativistic mass & energy equivalence, on the one side, and quantum mechanics, on the other, one is able to derive the end results aimed by the General Theory of Relativity. The energy conservation law, in the broader sense of the concept of "energy" embodying the relativistic mass & energy equivalence, is anyway a common practice, chiefly nuclear scientists make use of. Yet amazingly, besides it is not applied to gravitational binding, it also seems to be overlooked for atomic and molecular descriptions. Thus herein, next to the reestablishment of celestial mechanics, we propose to reformulate the relativistic quantum mechanics on the basis of Coulomb Force, but assumed to be valid only for "static electric charges"; when bound though, the rest mass of an electric charge, must be decreased as much as the "binding energy" it delineates.

Along the sameline, one can remarkably derive the de Broglie relationship, for both electrically and gravitationally interacting objects. Our results, furthermore, seem capable to clarify the results of an experiment achieved long time ago, at the General Physics Institute of the Russian Academy of Sciences, but left unveiled up to now.

The frame we draw amazingly describes in an extreme simplicity, both the atomic scale, and the celestial scale, on the basis of respectively, Coulomb Force (written for static electric charges, exclusively), and Newton Force (written for static masses, exclusively), in exactly the same manner. Our approach yields precisely the same metric change and quantization, at both scales, in question.

For simplicity, the presentation is made based on just two particles, one very massive, the other one very light, at both scales, without though any loss of generality.

Our predictions, perfectly agree with all available experimental results.