2.b) Newton's Second Law or Law of Force

Newton's Second Law, also known as the Fundamental Law of Dynamics, establishes a proportional relationship between force and variation of linear momentum of a body. In other words, force is directly proportional to mass and to the acceleration of a body.

When Newton unified the force of earth's gravity, included in his second law or Law of Force, with the force of gravity of the planetary orbits in his Law of Universal Gravitation, the principle of equality between the mentioned inertial mass and gravitational mass made sense since it was evident in all the scientific experiments and natural phenomena.

Force / mass = acceleration
F = m a 

Furthermore, Newton's Classical Physics proposes that a constant force could accelerate a mass to infinity.

Newton's Second Law has been modified by Einstein's Special Theory of Relativity by including the phenomenon of increasing the mass of a body with velocity and, later by General Relativity by introducing the disturbances in space-time. A constant force is no longer able to accelerate a mass to infinity, however, the proportional relationship between mass and force that produces acceleration is maintained for mass in a particular instant.

The first experiment that confirmed relativistic mass was the discover by Bücherer in 1908 of the relationship of the charge of the electron and its mass ( e / m) was less for fast electrons than for the slow ones. Eventually, countless experiments confirm the results and previous physics formulas.

Mass and energy become, therefore, two forms of the same thing. The principles of conserving mass and conserving energy of Classical Mechanics go on to form the more general conservation principle of relativistic energy-mass.

However, Einstein's Theory of Relativity still does not tell us what that thing is that presents itself as mass or as energy. Therefore, the idea of countless experiments that confirm this theory is a little farfetched. One thing is to mathematically correspond with some results, and another is for the underlying physics reality to be supported by Relativistic Mechanics.

On the contrary, Global Mechanics explains the force of gravity as the effect of tension of the longitudinal curvature of the reticular structure of matter, or globine, so as to not confuse it with normal matter. It also explains what electromagnetic energy consists of and how mass forms, that is, it has unified gravity, energy and mass.

Of course, as we will later see, the same experiments and results coincide with the new alternate theory as precisely as those of Einstein's Relativistic Mechanics. Furthermore, other aspects coincide with the Theory of Global Equivalence, which are derived from the non-existent of the typical relativistic singularities and the compatibility between theory of the atom, the dynamics of the normal human scale and Astrophysics corresponding to the physics model of Global Mechanics.

As commented earlier, the principle of equality between inertial mass and gravitational mass allows the planets' gravitational force to be consistent with the Fundamental Law of Dynamics. Einstein's Relativistic Physics supports this principle but it is forced to modify space and time in order to cohere with the small, observed differences in Mercury's orbit and planets' orbits in general.

In the new point of view of the Theory of Global Equivalence, this principle is no longer necessary, since with the definition and characterization of physics mass, the movement of mass follows the same rules in the reticular structure of matter, or globine, regardless of the origin of the forces. Besides the variation of physics mass with velocity, the Law of Global Gravity introduces the variation of gravitational force with velocity in one single point in the globine.

In the new model of Global Dynamics, Newton's Second Law, Law of Force or Fundamental Law of Dynamics continues to be valid as far as the proportionality between force, mass and acceleration.

When velocity starts to become relevant as regards the speed of light, the increase in physics mass is due to the conversion mechanism between applied force, whether it comes out from gravitational energy or not, and stored kinetic energy in form of mass. However, the increase in mass will be compensated by an increase in the gravitational attraction, such as in the case of the planets' orbits, which is why this effect cannot create the anomalous precession in Mercury's perihelion.

In other words, out of the two components of the atractis causa, the first which is due to the longitudinal curvature of globine and the second, which is due to the velocity of the bodies with mass, only the second is responsible for the additional variation of gravitational force that causes the precession anomaly in the planets' orbits as far as that foreseen by Isaac Newton's Law of Universal Gravitation.

According to Global Mechanics, the conceptual difference is due to the mechanisms of globine interacting with the electromagnetic energy and with bodies that have mass, taking into account globine is the material support for both manifestations of energy in general.

The discussion regarding the concept of atractis causa takes place in the sections on Newton's Law of Universal Gravitational and the Law of Global Gravity in the online book about the latter.

Pisa tower
Force, mass and acceleration 

In short, Global Dynamics maintains that physics mass in movement behaves the same with or without forces of gravity as far as proportionality of force, mass and acceleration, thereby making it necessary to carry out the following clarifications:

• The principle of equality between Newton and Einstein's inertial mass and gravitational mass is no longer a principle but rather it becomes a reality in characterizing the motion of physics mass.

• An increase in velocity produces an increase in physics mass. Although there are conceptual differences in regards to the reference system of movement, this effect in Relativistic Mechanics is similar to that in Global Dynamics. Notice that the increase in relativistic mass due to velocity does not affect the proportionality of force and global, or total, mass.

• The Law of Global Gravity explains the anomalous precession of the planets’ orbits by including an additional force in the globine-mass interaction derived from velocity. In Einstein's Relativistic Mechanics and in Quantum Mechanics, this precession is justified by space-time alterations.

From another point of view, in carrying out Newton's Second Law, there are problems due to the mentioned characteristic of globine as a material support for electromagnetic energy and mass.

According to Global Dynamics, the problems are subsequent from the following:

• The variation in the spatial position of globine.

• The variation in the longitudinal tension of globine for the same spatial point.

We could try to resolve the problems in Newton's Fundamental Dynamics or Law of Force with a more general definition of force that would include the respective displacements, but we would have to be cautious since, besides disguising different concepts, the strict proportionality with mass would not exist.   The displacements derived from the two previous points can probably be treated as movement of mass on globine by supposing a variation in the relative velocity in the sense of Galileo between globine and mass.

It is important to remember that while the Theory of Global Equivalence clarifies Newton’s Second Law, it does so within the context in which the motion of bodies does not take place in an abstract vacuum but rather in the three-dimensional reticular structure of matter, or globine, with its characteristic radial symmetry in a Euclidean space.

Lastly, Quantum Mechanics says anything in relation to Newton’s Second Law, except that it proposes a macroscopic approximation of reality due to its uncertainty principle. However, within the subatomic level, Quantum Mechanics does not know very well what an electron is either, and it keeps reaching for explanations for what is known as the tunnel effect or the double slit experiment with photons, where it even resorts to travelling back in time as a solution.

Global Mechanics explains, among many other things, the tunnel effect and the double slit experiment, and maintains that the orbital movement of electrons is the result of the motion in the points of relaxation in the gravito-magnetic tension of globine. The detailed justification of these statements is deduced from the new structure of the atom proposed in the online book, Global Mechanics.