1. Mechanical fundamentals of the structuring orbital of particles

Here it will be stressed that particles mass is not a primordial magnitude but a secondary one, in other words it derives from a primary one. This may surprise many readers, just as we were when coming across with it. We had to modify our own educational legacy on the subject, which considered the gravitational field as the most fundamental and universal one. Instead, the primary magnitude will be considered to be the electric charge, since it is the only magnitude with a unique unitary value (sorry for the quark model!). In contrast, particles mass and magnetic moment are magnitudes that can take many different quantized values. Let us point out that the fact that the mass and similarly the magnetic moment may get a multiplicity of quantized values, contrary to the electric charge, already insinuates that they may not be primordial magnitudes. Let us now argue about the underlying reason that makes these two magnitudes diversely quantized and secondary, and also that they are interlinked.

It is well known that the magnetic and the electric fields are intimately akin, the magnetic field deriving from the electric field. However, the gravitional field has never been conceived as subsidiary of the electric one. It will be now argued that the same as for the magnetic field applies to the gravitational field, which will be considered to derive also from the electric one. Just like the magnetic field, the gravitional field represents another subproduct of the electric field.

Let us reconsider our first presentation of the mass in the axiomatic of the "Orbital Conception of Elementary particles" (See in Part I: II. Fundamentals and in Part II: XII. Orbital Mechanics of Particles Structure). Up to now, the mechanics of the particles structuring orbital has been expressed in a somewhat conventional form, in order to avoid introducing concepts that much certainly would not be accepted by the orthodox scientific pool, often paralysed by dogmatic intellectual blockades, and some times by emotional ones too, as the History of Science reveals. Hence, the orbital mechanics has been schematized by means of two antagonistic forces, centripetal and centrifugal, introduced in a simple but somewhat arbitrary way. We will now progressively deepen our conceptualization of both.

2. The centrifugal force

In introducing the centrifugal force an hypothetical mass was attributed to the orbital corpuscular carrier. However, those who have developed an interest for the orbital conception of elementary particles most surely have not felt much easy with the attribution of a mass to the orbital carrier. In fact it was just a handful provisional joker. Let us now improve the approach by identifying the centrifugal force to a restoring force. However its nature will only be specified progressively, in an attempt to avoid contraversials as much as possible, since it appeals to a physical interpretation of the wave function, and also to a quantized reaction to a quantized action. These points will be therefore postponed and let us just assume for the moment that the orbital is submitted to a restoring force when it goes off equilibrium.

Let us now retake thus the analysis of the orbital structure, this time conferring to the corpuscular carrier solely a unitary electric charge and an intrinsic celerity equal to the speed of light. While the electric charge is an intrinsic magnitude which proceeds from the corpuscular carrier, both the mass and magnetic moment are instead extrinsic magnitudes which derive from the carrier kinetics, being thus orbital dependant. This is why there is a variety of particles masses and magnetic moments, while there is a single value of electric charge.

The magnetic moment derives from the carrier rotatory motion, while the mass derives from the orbital departure from its ground state. Furthermore, mass and magnetic moment are interdependant, according to the relationship: Q = mass * magnetic moment * radius = constant. For a fix size, an increment of the particle mass implies a decrease of its magnetic moment and vice versa.

3. The centripetal force

Let us consider now the centripetal force applied to the particle structuring orbital. It has been defined as a Lorentz-like force, arguing that the orbital motion of the carrier creates a magnetic field which reacts with the carrier electric charge, leading to a self-sustained and quantized Lorentz force. Some may disagree with this point of view, however do not refuge too soon in a conventional standpoint presumably well established. In effect, for the present femometric system a straightforward macroscopic extrapolation cannot be done, due to the fact that the corpuscular carrier has an intrinsic celerity and thus its rotatory motion is self-sustained. As a consequence, the magnetic moment is equally self-sustained and the associated magnetic field influences the charge motion as would do an external field. In a generic form, let us say that the cause creates the effect, and on its turn the effect rebounds on the cause. In this self-sustained orbital system the cause is the charged carrier intrinsic celerity, the effect is the magnetic moment and their mutual repercussion is represented by the centripetal Lorentz-like force.

Within the dimensional range of the wavelength associated to the structural orbital system, the magnetic field created would react upon the electric charge, which has generated it. This feedback effect would be a quantum effect highlighting in systems with size of the same order than the system associated wavelength. Let us also mention that the formulation of the feedback effect should express the fact that any alteration of the carrier kinetics rebounds on the orbital magnetic field and thus on the Lorentz force, which acts back on the carrier kinetics, and so on. Only some quantization effect upon the orbital can put an end to this process.

4. Conclusion

Let us summarize all this by a mechanical simile, represented by a spring bent so to form a ring. When no net force is applied to the spring it is unstressed and hence has no inner energy, and it can be considered to constitute the ground state. However if a centripetal force is applied to the spring this one exerts a restoring force. If both forces are considered to be quantified independently then they may mismatch and the resulting deformation of the spring expresses its net energy content. Translated to the orbital system the mass appears as deriving from the restoring force resulting from any orbital departure from its ground state. The mass expresses thus the degree of departure of the particles structuring orbital from its equilibrium state or equivalently its amount of stress. One outstanding novel point is that the mass and hence the gravitational field are not primordial entities such as the electric charge and field, but are instead subproducts of the particles structuring orbital. So, the gravitational field can be seen, in view of its weakness, as a kinetical residue of the electric field.