Abstract

Herein we present a whole new approach to the derivation of the Newton's Equation of Motion. This, with the implementation of a metric imposed by quantum mechanics, leads to the findings brought up within the frame of the general theory of relativity (such as the precession of the perihelion of the planets, and the deflection of light nearby a star). To the contrary of what had been generally achieved so far, our basis merely consists in supposing that the gravitational field, through the binding process, alters the ?rest mass? of an object conveyed in it. In fact, the special theory of relativity already imposes such a change. Next to this fundamental theory, we use the classical Newtonian gravitational attraction, reigning between two static masses. We have previously shown however that the 1/r² dependency of the gravitational force is also imposed by the special theory of relativity.

Our metric is (just like the one used by the general theory of relativity) altered by the gravitational field (in fact, by any field the ?measurement unit? in hand interacts with); yet in the present approach, this occurs via quantum mechanics. More specifically, the rest mass of an object in a gravitational field is decreased as much as its binding energy in the field. A mass deficiency conversely, via quantum mechanics yields the stretching of the size of the object in hand, as well as the weakening of its internal energy. Henceforth one does not need the "principle of equivalence" assumed by the general theory of relativity, in order to predict the occurrences dealt with this theory.

Thus we start with the following interesting postulate, in fact nothing else, but the law conservation of energy, though in the broader relativistic sense of the concept of ?energy?.

Postulate: The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-?-vis the gravitational field of concern.

This yields the interesting equation of motion driven by the celestial body of concern, and this already in an integral form.

The differentiation of this relationship leads to the general equation of motion. The resulting differential equation is the classical Newton's Equation of Motion, were the velocity of the object, negligible as compared to the speed of light in empty space.

The stretching of lengths in a gravitational field is equivalent to the slowing down of light, throughout, as referred to a distant observer. Based on this, the above differential equation can be transformed in regards to the distant observer. The mathematical manipulation in question, together with the related solution, will be undertaken in our next article.