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

Newton's Second Law, also known as 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 acceleration of a body.

When Newton unified force of earth's gravity –included in his second law or Law of Force– with force of gravity of the planetary orbits in his Law of Universal Gravitation, the principle of equality between inertial 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.

Einstein's Special Theory of Relativity modified Newton's Second Law by including the phenomenon of increasing the mass of a body with velocity –mathematically multiplying the mass at rest by one of the Lorentz transformation constants– and later, by by General Relativity introducing the disturbances in space-time and inertial systems –where the constants of transformation constantly vary.

A constant force is no longer able to accelerate a mass to infinity; however, it maintains a proportional relationship between mass and force to produce acceleration for a particular instant.

The first experiment –by Bücherer in 1908– that confirmed relativistic mass was of the relationship of the charge of the electron and its mass (e/m). It was smaller 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 energy of Classical Mechanics go on to form the more general principle of conservation of relativistic energy-mass.

However, Einstein's Theory of Relativity still does not tell us what presents itself as mass or as energy. Therefore, the idea of countless experiments confirming this theory is a little farfetched. One thing is to achieve mathematically some results, and another one is to clarify the underlying physical reality.

On the contrary, Global Mechanics explains force of gravity as an effect of tension of longitudinal curvature of the reticular structure of matter or Global Aether; do not confuse it with classical aether, or the new luminiferous aether. 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 experimental results coincide with new alternative theory, and with Einstein's Relativistic Mechanics. Furthermore, Global Physics can explain other aspects derived from the non-existent of the typical relativistic singularities and compatibility between theory of the atom of Global Mechanics, Global Dynamics of normal human scale and Global Astrophysics.

As commented earlier, principle of equality of inertial and gravitational mass allows the planets' gravitational force to be consistent with Fundamental Law of Dynamics. Einstein's Relativistic Physics supports this principle but it needs to modify space and time to cohere with small-observed differences in Mercury's orbit and planets' orbits in general. Nevertheless, Paul Gerber explained those differences in 1898 within a classical perspective.

In Global Physics, this principle is no longer necessary, since with definition and characterization of mass, movement of mass follows same rules in the Global Aether, regardless of origin of forces. However, there are peculiarities, besides variation of the mass with velocity; Law of Global Gravity introduces variation of gravitational force per unit of mass with velocity for same spatial localization.

In new model of Global Dynamics, Newton's Second Law, Law of Force, or Fundamental Law of Dynamics continues to be valid as far as relation between force, mass and acceleration, although it is not constant.

When velocity starts to become relevant as regards speed of light, the increase in 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 balance with an increase in gravitational attraction, such as in classical case of the planets' orbits, which is why this effect could not create the anomalous precession in Mercury's perihelion.

Regardless of the increase of mass with speed, gravitational force would increase also due to double gravitational pull of kinetic mass –equivalent mass to kinetic energy.

In other words, there are two components of the atractis causa; the first one is due to longitudinal curvature of the Global Aether, and the second one, which is due to velocity of the bodies with mass with respect to the Global Aether. Only the second is responsible for variation of gravitational force per unit of mass that causes anomalous perihelion precession of planets' orbits, as far as that foreseen by Isaac Newton's Law of Universal Gravitation.

According to Global Mechanics, this conceptual difference is due to the mechanisms of Global Aether as direct supporting medium of mass and kinetic energy, or as indirect support of electromagnetic energy.

Discussion regarding concept of atractis causa takes place in the sections on Newton's Law of Universal Gravitational and the Law of Global Gravity in the book about the latter. Pisa tower Force, mass and acceleration

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

• Principle of equality of inertial and gravitational mass of Newton, and maintained by Einstein, is no longer a principle given the new characteristics of motion of mass.

• An increase in velocity produces an increase in 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. Note that the increase in relativistic mass due to velocity neither affects the proportionality of force and global mass, nor the gravitational force per unit of mass.

• Law of Global Gravity explains the anomalous precession of the planets’ orbits by including an additional force in the Global Aether-mass interaction derived from velocity. In Relativistic Mechanics, this precession is justified by space-time alterations due to energy.

From another point of view, Newton's Second Law has other problems due to the characteristic of Global Aether as a direct material support for mass and gravitational field, and the latter being medium support of electromagnetic energy or luminiferous aether.

According to Global Dynamics, these problems are subsequent from:

• Variation in the spatial position of Global Aether

• Variation in longitudinal tension of the Global Aether for the same spatial point

We could try to resolve 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, strict proportionality with mass would not exist. We could consider displacements derived from two previous points as movement of mass on Global Aether, by supposing a variation in relative velocity, in the sense of Galileo, between Global Aether and mass.

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

Lastly, in relation to Newton’s Second Law, Quantum Mechanics 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 the tunnel effect or the double-slit experiment with photons, where it even resorts to travelling back in time as a possible solution.

Global Mechanics explains, among many other things, the tunnel effect and the double-slit experiment, and it maintains that orbital movement of the electrons come from motion along points of relaxation in the gravito-magnetic tension of the Global Aether. Detailed justification of these statements arises from the new structure of the atom proposed in the book Global Mechanics.