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Based on the concepts which were introduced so far, such as distribution, object, process, flux, and based on the current public available knowledge, we may note that any material system has a spatial structure with a specific number of elements and invariant attributes, therefore, we are dealing with a complex object, with an inner RS against which the elements’ properties are invariant, that is a structure made-up from other objects as well, and these objects have also an invariant inner structure, so on, aspects which have been also postulated by the systemic organization principle (SOP), presented in chapter 1.
Comment 7.7.1: The spatial structure term has a broader meaning according to the objectual philosophy, being synonym with the spatial distribution of the elements belonging to a MS. If it is clear that the geometrical S-type systems (lines, figures, polyhedra etc.) own a spatial (structure) distribution which is invariant as regards the components’ position (both T and R), this aspect is no longer valid for L and G-type distributed MS. However, even in case of these latter types of MS, there are spatial distributions with an invariant character (besides the distributions of atoms, molecules or “clusters”) which have invariant inner references and are also considered in this paper as objects with a spatial structure, but this time, these objects are closed fluxes (namely, objects which are in motion inside MS) and not objects with an invariant spatial position. These fluxes are closed in a limited space with invariant boundaries (enclosure which contains that particular medium), there is an invariant reference direction (local direction of the gravitational field), a masscenter and a pressure center (with invariant position if the enclosure’s position and shape are invariant as well). As compared to these reference elements, the mean statistical attributes of the inner fluxes are kept invariant (if the external conditions are invariant as well), therefore, these attributes will make-up a state (inner) object of MS. In chapter 5, we have also seen that, spatially speaking, the overall state of a flux at a specific moment is represented by Euler distribution of FDV, that is a distribution which is invariant in case of the stationary fluxes. But an invariant spatial distribution means also a spatial structure, even we are dealing with the configuration of a vector field.
The invariant attributes of the spatial structure of a specific MS are also maintained due to the fact that the structure attributes of the constitutive objects are invariant (in other words, these elements are objects as well), and there are invariant spatial relations against an inner overall RS of MS deployed between the inner reference systems of these components. In chapter 4, we have noticed that the state-type abstract objects are divided in processual classes, that the objects with null processes have states belonging to class S0, and the invariant attributes of the processes make-up objects from the classes S1, S2 so on. We have also noticed that the fluxes are processes, therefore, their invariant attributes make-up processual abstract objects, which are distributions with spatial, temporal or frequency support of these attributes. Based on the aforementioned issues and on the generic MS model proposed by the objectual philosophy, it clearly results that if there are specific amount fluxes inside a MS, this means that we shall have support objects of that particular moving amounts; since their motion occurs only inside a RBS of a MS, this motion also means some closed fluxes deployed in the volume occupied by MS, fluxes which must have some invariant attributes in order to form processual objects.
Comment 7.7.2: For instance, the peripheral medium of an atom, made-up only from electrons, has a rigid structure (but not at the level of the electrons’ position but at the level of the orbitals occupied by these electrons), which means that it is a S-type DS (more exactly, SR-type, in which the constitutive elements are maintained despite of the presumed repulsion deployed between them, by the powerful electric interaction with the core subsystem - the nucleus with its positive charges). The main argument which explains this stiffness is that, if it would not be so, neither the crystals, which are also S-type DS, created by means of covalent or ionic bonds (interactions) between the atoms’ peripheral electrons, would be able to exist (no bonds with preferential, invariant directions would be able to exist). Within this electronic medium, each electronic orbital has (under a non-disturbed state) unique and invariant state attributes (whose existential attributes make-up the so-called set of quantum numbers), although each of these electrons performs plenty of motions (therefore, they are fluxes). This means that the quantum numbers which define the state of a specific electron are quantitative attributes of some invariant processual qualitative attributes, namely, parameters of some invariant fluxes. Since we are referring to fluxes which are objects set in motion, it is clear that the moving object’s position (electron) is non-determined, but instead, we may define the invariant attributes for the object’s velocity (with its equivalent that is the energy or the orbital frequency), for the spatial distribution of the flux lines (plane, radius, and orbital axis, the position of axis and orbital plane against an atomic RS, which coincides with the nuclear one), distance of the orbital plane towards the nucleus (that is invariant in case of a specific electronic layer). Therefore, if we cannot define the position of an electron, we can define instead the position of the orbital on which it may be placed (the orbital means an abstract object which gathers all the invariant attributes of the individual electronic flux, which were above mentioned). The reader is invited to observe that S-type systems can be also made-up from fluxes (naturally, from closed, coherent and invariant fluxes), if the spatial parameters of these fluxes (the invariant ones) are able to meet the conditions of S-type systems, characterized by permanent interaction and the restriction of free translation and rotation of the elements (elements which this time are the above-mentioned invariant fluxes).
We may note that the inner structure of a MS, based on fluxes, is generally made-up from a set of support objects of the conveying or storing properties and from an “agent” which sets in motion these objects in order to produce inner fluxes. The “agent” which generates the motion and which is called energy flux, according to the objectual philosophy, was minutely presented in the previous sections. Now, we are most interested in the support objects found inside a MS.
For the generation of a motion (flux) of a material object, besides the energy which is required for the motion, a space for this motion is also needed, that is a space which will confine the resulted flux. In other words, each flux from the set of inner fluxes with simultaneous existence belonging to a MS needs a spatial resource for its existence. The total amount, the union, either disjoint or partly conjoint, of these spatial resources needed for the inner fluxes (defined against the inner RS of MS) shall make-up the total space occupied by that particular MS, namely, the system’s inner spatial range (domain).
Comment 7.7.3: For example, the case of the specific components of the individual (orbital) fluxes of the electrons from the peripheral electronic medium of the isolated atoms, where, as it was mentioned in the previous comment, the spatial domains of the orbitals must be disjoint because the flux’s state attributes (quantum numbers) are different. It is not the same situation in case of two (or more) atoms linked through covalent bonds, in which case the electrons involved in the bond (the valence or conduction electrons of the two linked atoms) must have a partly conjoint spatial domains of the orbitals (their intersection must be non-void). If do you remember what it was said in the previous sections about RBS with spatio-temporal distribution (such as the case of RBS generated by an electron placed on a specific orbital), and about the synchronism required to a constructive interaction, then, it clearly results the reason why two electrons which are connected in a covalent bond (electrons which in the current papers are denoted as “commonly used” by the bound atoms) must have synchronic and co-phasal orbital frequencies, at least at the harmonics level, fact which determines the necessity of orbital interpenetration (conjunction). This argument is valid for any kind of molecule with covalent bonds, but it is more obvious in case of the metallic bonds, where the “massive” conjunction of the atoms’ outer orbitals makes that the electrons placed on this orbitals to be able to “migrate” from an orbital to another during the process of electric current conduction.
If the MS as a whole shall be moving against an outer reference, we shall have an overall flux (of all the inner elements of MS), that is a flux which also needs a spatial resource, a space in which that motion to be possible. Because the inner space of MS is its minimum spatial resource, which is necessary even if the MS is motionless, we may also call it as the system’s rest space. As we have noticed in the section focused on energy, the inner energy of a MS is stored in the rest space, that is an energy which is even named rest energy, in case of EP considered to be motionless against a RS.
Comment 7.7.4: Attention! When we talk about the rest energy of an EP, by taking into account the energy definition from the section 7.6.1, it is clear that at least one MS flux must exist in the inner domain of EP, flux which contains this inner energy of the particle inside it. The existence of this stored flux is also required by the general MS model (3F model), the stored flux being the source of the emergent fluxes produced by the particle (electric, gravitational flux etc.).
The debate which was made so far on the necessary spatial resources of the inner objects and fluxes of a MS is explained by the justification of the fact that each MS, regardless if it is abiotic, biotic or artificial, has a spatial distribution of its properties (rigid, namely invariant for the S systems and fluid for the others), and that this distribution is possible only due to the simultaneous existence of the spatial distributions of the inner components of MS and due to the spatial distributions of the fluxes which involve this components. At the moment of a MS formation, each component will contribute with its own spatial structure at the future aggregate structure of the new MS, otherwise speaking, the necessity that any MS to have a spatial structure requires the necessity of the external contribution of some spatial structure elements. Obviously, the motion necessity of these structural elements also draws the need of an energy component existence.
After all the aspects mentioned so far in this section, the result is that the total amount of the inner fluxes necessary for a MS consists of two major flux classes:
Fluxes of spatial structure elements, which shall be shortly named structural fluxes (SF);
Fluxes able to convey motion to these elements (to set them in motion or to maintain the motion in order to generate and maintain the vital fluxes), fluxes which are named energy fluxes (EF), as we have seen in a previous section.
It is clear that the fluxes triad model postulates the fact that, if the inner fluxes of a MS belong to these two above-mentioned classes, both the input fluxes (which must cover the inner flux demand) and the output fluxes (which are coming from the inner fluxes) of a MS will also belong to these two basic flux classes.
Comment 7.7.5: For example, in case of the atomic MS, the structural fluxes (made-up from protons, neutrons and electrons) are provided during the system’s formation (synthesis) process, its structure being subsequently invariant (if nuclear disintegration or ionization processes do not occur), so that the further demand for an input flux is valid only for the energy fluxes, which must maintain all the inner motion types, and to compensate the losses (exclusive energetic fluxes) through output fluxes (fields of an atom). However, there is a different situation in case of the bio-systems or artificial MS, where the structural elements of the system may be degraded throughout time (they have a shorter existence as compared to the system’s life span), consequently, the input fluxes must contain, besides the compulsory energy flows, some fluxes of structural elements as well (which shall replace the damaged ones). A non-used part from the input structural fluxes or from the structural fluxes generated as a result of elements degradation shall be discharged through the output structural fluxes (in case of the bio-systems, that is the excretion function). It is obvious that the processes which generate a new system must contain both energy fluxes and massive structural fluxes which are needed during the development (growth or synthesis) stage of the new system.
It is worth noticing that the two basic components of the inner fluxes may be found at the same type of input or output flux. For instance, the food ingested by a human contains both structural elements (e.g.: elements required for the synthesis of proteins or of other elements from the cells’ structure), and a certain part of the energy fluxes contained (confined) in the structure of some organic molecules, fluxes which will be released as a result of the enzyme decay of these molecules inside the cells, by providing in this way the intracellular energy resources.
Copyright © 2006-2011 Aurel Rusu. All rights reserved.
