Following the change of the Bohr radius, quantum mechanics predicts a change of quantum levels, due to the change of electron mass, giving also a change of rate of atomic clocks [1]. It is also demonstrated that all matter, including organic matter and even human bodies, function at a different rate when electrons forming them have acquired or released some potential or kinetic energies.
Since Mercury in its orbit has a different gravitational energy and possesses a different kinetic energy, matter on Mercury (i.e. due to its Mercury distance from the Sun) has a different mass. In addition, clocks on Mercury are functioning at a different rate. We consider that Newton's laws are perfectly valid on Mercury (as everywhere else) using the masses and the clock rates that are existing on Mercury. This is the universality of the physical laws. This requires using all proper values on Mercury, taking into account that the standard kilogram and the clock rate on Mercury clocks are slightly different from the standard kilogram and the clock rate on Earth. Furthermore, since the principle of mass-energy conservation has modified the mass of the particles on Mercury, it would not make sense to use the mass of the particles on Earth to calculate the interaction of the particles on Mercury immerged in the solar gravitational field. Consequently, one must always use everywhere (here Mercury) the units of mass, of lengths and the clock rate existing at the location where the interaction takes place. The relationships transforming the units between locations at different gravitational potentials and different velocities have already been calculated [1]. We have seen that the number of units representing the physical length of an object in different frames, can be expressed with respect to any standard reference in any given reference location. This gives us the possibility to calculate the same absolute physical length, either using Mercury or Earth meters. Physical lengths can be expressed either in Earth meters [meterE] or in Mercury meters [meterm]. The physical length of the radius of the orbit of Mercury is a real physical quantity, therefore absolute. It is equal to the number of Mercury-meters times the length of the local standard Mercury-meter. The same orbit of Mercury can also be measured using the shorter standard Earth-meter. Then, the number of Earth-meters to measure the same physical orbit of Mercury is larger when it is measured using the shorter Earth-meter.
We must notice that Newton's laws of physics deals with the numbers that are fed into the equations. Since the number of meters to measure the same physical length (using the longer Mercury meters) is smaller than the number of Earth meters, we must not be surprised to find different physical results when Newton's laws uses the correct local (proper) number.
In physics, there exist several systems of units using meters, feet, kilograms, pounds, coulombs, statcoulombs, abcoulombs etc. that have been devised in a coherent way so that the coherent use of any set of units leads to answers which are compatible, independently of any system of units. In fact, one has a complete choice of systems of units that leads to the same physical answer, although represented by different numbers and using units having different names. However, contrarily to the above, when we apply the principle of mass-energy conservation, the relationship between the units of mass, energy, lengths and clock rates do not vary in the same proportion which previously led to the same physical result, when we switch to locations having different energies. Most importantly, the principle of mass-energy conservation must be satisfied. Consequently, the application of the same Newton's laws at Mercury location (with Mercury units) will give a different physical prediction than using Earth units. Of course, the correct calculation is the one existing at the place where the phenomenon takes place. Doing otherwise would be absurd. Physics does not depend on observer's location. We show here below, that this logical correction explains perfectly the advance of the perihelion of Mercury without any relativity principle.
