III. Motion equation under gravity (free fall).

As the speed of light decreases from space towards dense objects, we consider that it decreases from C_o= 299792458 m/s in space (my definition in advance of a future BIPM congress), toward c(r)<C₀ at the distance r of the center of a pinpoint mass M.

But to simplifie calculations later, I write c(r)= F(r).C_o where F(r) is a fonction which decreases from 1 towards less near dense objects. The same way we define the energetic mass of the electron (at rest) as to be: m(r)= mo.sqrt[F(r)] to take into account its variations of the whole energy Mo.sq[Co].sqrt[F(r)] by a factor very close to the rest mass factor mo , because F(r) is very closed to 1 (except on quasars).

The factor sqrt[F(r)] is due to the main hypothesis.

Thus, at a distance r from the center of a pinpoint mass M towards r+dr, the infinitesimal change of energy of the electron (not in motion) in gravity is: where the gravity force is considered acting on the energetic mass (light speed dependant).

The integration from r to infinity yields :

We obtain thus the following interesting results for an electron in gravity:

Local speed of light: .

Energy of the electron (at rest):

Energetic mass (electron ar rest): .

But now we go to a revolutionary idea, if the internal energy of the electron at rest changes when the speed of light changes, and if the internal energy changes when the electron is in motion, we have good reasons to believe that when the electron is in motion in gravity (free fall) where the speed of light is not constant, the change of velocity is a necessity in order to maintain the internal energy constant.

Gravity is an internal conversion of the energy of matter (hypersound-wave energy).

We see immediately from the formula of the whole energy:, that what is constant in gravity is the following value:.

Written differently, we have: . Thus the time derivative is:

. In reintroducing H, we obtain:

. And finally, with the obvious hypothesis that the vectorial speed variation is in the direction of the light speed variation:

This formula shows that when the electron goes to a place where the speed of light changes, the vectorial velocity v must change.

And this phenomenon has already been observed by Newton when he received an apple on his head (like me).

The motion equation is very simple and very beautiful when the the velocity v is weak (very common) relatively to the speed of light:

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