Difference between revisions of "TFNR - Rotation - Curl"

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===The variational perspective===
 
===The variational perspective===
  
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Symmetrically, from the variational perspective, Rotation manifests as the '''reaction of the Field to Perturbations''', to gradients (Micro-gradients) in the temporal distributions of the minute elementary '''vortical fluctuations''' resonating around the Planck scale.
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Symmetrically, from the variational perspective, Rotation manifests as the '''reaction of the Field to Translation''', to divergences (Micro-flows) in the pre-temporal distributions of the vortical aspects of the sub-elementary pre-spatial fluctuations, resonating around the Planck scale.
  
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When, in these pages, I speak of [[Micro-gradients]], [[Micro-flows]], [[Micro-torsions]] (or Micro-vorticities), [[Micro-states]], I am referring to gradients, flows (divergence), torsions (rotor, curl), states, '''within the dynamics of the Elementary Field at the level of individual "event points"—infinitesimal portions of the Field''' which, for the sake of treatment and visualization, we may consider as point-like. But '''they are not truly point-like'''. As I have already emphasized on several occasions, in this model there is no place for point-like Entities, Events, Relations, Processes or Structures. Everything possesses a spatial and temporal extension, however infinitely small. We must therefore not forget that these dimensional resonances, like micro-bubbles forming within the dynamics of the Field, though extremely small, '''always represent extended regions in three-dimensional Space, with an evolution in Time, representable within the four-dimensional continuum''' so central to relativistic physics.
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'''I resume here what was stated in the corresponding subsection (The variational perspective) of the previous section dedicated to Translation''' about [[Micro-gradients]], [[Micro-flows]], [[Micro-torsions]] (or Micro-vorticities), [[Micro-states]], about the infinitesimal portions of the Field I call "event-points", and about the fact that inhomogeneities tend to cause the re-Action of the Field, toward the restoration of homogeneity. The Field's reaction to these inhomogeneities, which I here call Perturbation, is '''part of this spontaneous process aimed at restoring homogeneity'''. These reactions '''generate oriented flows—flows of orientation—of more or less intense reorientation of the vortical (axial) directions of the elementary vortical fluctuations, of the Elementary Events'''.
  
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Thus, '''not grains of Space and Time, but rather a kind of bubbles, "convective cells" in the elementary dynamics of the Field—pulsating regions''', so to speak—that tend to exhibit an average extension and a pulsation dynamics in Time comparable to the Planck scale lengths and durations. Expansion and contraction. Force and resistance. Action and constraint. The whole of mechanics concentrated within an infinity of dynamic micro-structures that embody the dynamics of the Field and project it into an initial seed of discreteness (Principle of Individuation) within the fundamental continuity.
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These torsions in the Elementary Events, precisely because they occur on extremely small scales and at the level of individual event points of the Field, can be called [[Micro-torsions]] or [[Micro-vorticities]].
  
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An infinity of dynamic micro-structures that, '''through their incessant activity, sustain and support the Existence and the Essence / Form of the ever-changing structuration of the Elementary Field'''. This structuration manifests as '''Structures of Information—interacting, propagating, and conserving within Space-time'''—both in the medium-dimensional domain (Vortices/Particles, Waves and their Interactions that compose Ordinary Matter) and in the large domain (Vortices/Dark Halos, Dark Waves and their Interactions that compose the Dark Matter/Dark Energy side of the Universe).
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Rotation is therefore the Field's spontaneous way of '''reorganizing divergences (Translation) into curl patterns'''—localized rotational regions—that embody the '''Principle of Conservation''': every propagation of variations tends to generate rotational persistence, every fluctuation tends to induce a torsional memory that affects its own existence and causal permanence.
  
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Here '''we must focus on what happens to the Field under the incessant Action of the Fundamental Force in the form of the Perturbation Operator'''. On the Variations produced by the internal interaction between Force and Field, between Agent and Acted, on what occurs in this interaction'''—on the Events I call Elementary precisely because they represent the most elementary form of Existence''', the simplest occurrences that can manifest within Reality and that lie at the foundation of its very existence. This is the essence of the sub‑Process of Creation, as part of the Process of Formation of Reality.
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In this context, Rotation is '''a form of Conservation produced by the Field in reaction to the Propagation of the most elementary Variations, to translation'''—a Variation that takes the form of rotational dynamics, of axial reorientation of the vortical aspects of sub-elementary fluctuations.
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As already stated countless times in this work, by Elementary Events I mean '''the tiny elementary vortical fluctuations of the Field resonating around the Planck scale'''. I use the term "vortical" even though Space, the spatial dimensions, technically emerge at an evolutionary stage of Reality that is temporally concurrent but causally subsequent to the expression of the Perturbation Operator. It is precisely this expression that produces the premises—the causal and variational substrate—for the emergence of the spatial dimension, of Space itself. We could say that spatial Dimensionality, inherent in the variational aspect of the Agency of the Source, through the expression of the Perturbation Operator, is '''the causal seed that enables the subsequent manifestation of Space and of the spatial dimension of Reality (as well as of Time and of the temporal dimension)'''.
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Everything occurs in parallel from the variational point of view (spatial and temporal), but from the causal point of view '''the order of expression of the Operators at the level of Elementary Action is crucial''' and fundamental for the Creation and Evolution of Physical Reality as we know it, in its causal, spatial, and temporal dimensions.
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'''We will then see how Translation and Rotation represent, from the causal point of view, the subsequent steps in defining the dimensional framework of Physical Reality''', the first being understood as Propagation and Conservation in Space and the second as Propagation and Conservation in Time. Taken together with Perturbation, '''all three constitute the elementary dynamic basis''' (the dynamism of the Elementary Field under the incessant Action of the Fundamental Force, the expression/manifestation of the Agency of the Primary Source) upon which the Fundamental Physical Quantities are founded: Metric/Mass, Motion, Charge, Spin, and the related phenomenological domains that combine in different forms within gravity, electromagnetism, and the more complex phenomenologies of the weak and strong nuclear interactions, as well as all the natural phenomena that contribute to the incessant Formation of Reality and to the complex life of the Universe.
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'''Inhomogeneities tend to cause the re-Action of the Field, toward the restoration of homogeneity'''. The Field's reaction to these inhomogeneities, which I here call Perturbation, is '''part of this spontaneous process aimed at restoring homogeneity'''. These reactions '''generate oriented flows—flows of orientation—of more or less intense reorientation of the vortical (axial) directions of the elementary vortical fluctuations, of the Elementary Events'''.
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These flows in the distributions of the reorientations of Elementary Events, precisely because they occur on extremely small scales and at the level of individual event points of the Field, can be called [[Micro-torsions]] or [[Micro-vorticities]].
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Rotation is therefore the Field's spontaneous way of '''reorganizing gradients (Perturbation, inhomogeneities in temporal distributions) into curl patterns'''—localized rotational regions—that embody the '''Principle of Conservation in Time''': every variation tends to generate rotational persistence, every fluctuation tends to induce a torsional memory that affects its own existence and causal permanence.
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In this context, Rotation is '''a form of Variation produced by the Field in reaction to the most elementary Variations, to Perturbation'''—a Variation that takes the form of rotational modulation, of axial reorientation of the elementary vortical fluctuations.
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Rotation can be seen and understood as '''Propagation and Conservation in Time'''.
 
Rotation can be seen and understood as '''Propagation and Conservation in Time'''.
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===From the point of view of the Elementary Events and the Dynamics of Elementary Action===
 
===From the point of view of the Elementary Events and the Dynamics of Elementary Action===

Revision as of 19:01, 9 March 2026

Rotation, or Rotational Action, is the instantiation through which Conservation manifests at the most elementary level of Physical Reality.

It is the third fundamental Mode of manifestation of the Elementary Action, its third Component. The third of the Modes of Physical Action.

From a causal perspective, we can represent it as the Rotation Operator, the Operational Agent responsible for the formation of vorticity, with its sub-components of chirality and axial orientations, in the elementary spatial fluctuations of the Elementary Field.

From a variational perspective, Rotation manifests as inhomogeneities (torsion / curl) in the distributions of chirality and axis orientation of circulation / vorticity of the minute pre-spatial fluctuations.

Rotation is the way in which the Elementary Field reacts to the interaction of Elementary Action in the Mode that I call here Translation, one of the ways in which the Field responds in order to restore homogeneity in the temporal distributions of Elementary Events.

It is the Field's response which, still driven by the tension to restore homogeneity, but due to micro‑interactions—occurring at the same event‑points—between Translations with different directions, produces the opposite effect: it preserves inhomogeneities, transforming them into dynamic micro‑torsions that tend to maintain anisotropies and more or less coherent structures over Time. Micro-torsions that in turn tend to produce regions of non‑zero Perturbation, which themselves become sources of Translation and centers of Rotation, and so on, in a progressive unfolding of dynamic complexity.

The causal expression and the variational manifestation—two sides of the same coin—of this Mode of Elementary Action are governed by the Principle of Conservation, which, at the Level of Elementary Action, takes the form of the Principle of Least Action.

Rotation is the root of vorticity, in its fundamental aspects of chirality and axis orientation.

Rotation:Chirality

Sub‑Mode of the Rotation Motion of the Elementary Action corresponding to the manifestation of inhomogeneities in the pre‑temporal distributions of the chirality of the vorticity that characterizes the sub‑elementary dynamism of the Field (pre‑spatial fluctuations, Elementary Events).

The Rotation:Chirality correlation within a region of the Field that, moment by moment, supports/sustains an InfoStructure is the root of the Charge of that Structure, whereas the Rotation:Chirality correlation independent of the Field (produced by other Structures with non‑zero Charge present in the Field itself) is the root of the electric potential (or electric potential energy).

Rotation:AxisOrientation

Sub‑Mode of the Rotation Motion of the Elementary Action corresponding to the manifestation of inhomogeneities in the pre‑temporal distributions of the orientation of the vorticity axis that characterizes the sub‑elementary dynamism of the Field (pre‑spatial fluctuations, Elementary Events).

The Rotation:Axis‑Orientation correlation within a region of the Field that, moment by moment, supports/sustains an InfoStructure is the root of the Spin of that Structure, whereas the Rotation:Axis‑Orientation correlation independent of the Field (produced by other Structures with non‑zero Charge present in the Field itself) is the root of the magnetic potential (or magnetic potential energy).

The causal perspective

Let us hold firm to what was stated regarding the causal perspective in the previous sections, dedicated to Perturbation and Translation, namely that:

  • the causal perspective focuses on the active aspect of the Source's Agency,
  • the Operators of Reality are functional / operational derivations of the Primary Agent, of the Fundamental Force acting upon the Elementary Field,
  • the Operators are Entities not in the classical sense, but in their function of producing Existence, a Phenomenon—something that occurs, something that exists in the very act of generating Existence, a product of the dynamics of the inner interaction of the two aspects of the Source of Reality.

From the causal point of view, Rotation, in both its sub-Modes, can be represented as the Operator Rotation, a functional derivation of the active aspect of the Source of Reality that organizes the interacting reactions of the Elementary Field represented by Translation into rotational patterns (vortical reorientation of the pre-spatial fluctuations), directed toward the conservation of the inhomogeneities within the Elementary Field in both the aspects of chirality and axis-orientation.

The variational perspective

Symmetrically, from the variational perspective, Rotation manifests as the reaction of the Field to Translation, to divergences (Micro-flows) in the pre-temporal distributions of the vortical aspects of the sub-elementary pre-spatial fluctuations, resonating around the Planck scale.

I resume here what was stated in the corresponding subsection (The variational perspective) of the previous section dedicated to Translation about Micro-gradients, Micro-flows, Micro-torsions (or Micro-vorticities), Micro-states, about the infinitesimal portions of the Field I call "event-points", and about the fact that inhomogeneities tend to cause the re-Action of the Field, toward the restoration of homogeneity. The Field's reaction to these inhomogeneities, which I here call Perturbation, is part of this spontaneous process aimed at restoring homogeneity. These reactions generate oriented flows—flows of orientation—of more or less intense reorientation of the vortical (axial) directions of the elementary vortical fluctuations, of the Elementary Events.

These torsions in the Elementary Events, precisely because they occur on extremely small scales and at the level of individual event points of the Field, can be called Micro-torsions or Micro-vorticities.

Rotation is therefore the Field's spontaneous way of reorganizing divergences (Translation) into curl patterns—localized rotational regions—that embody the Principle of Conservation: every propagation of variations tends to generate rotational persistence, every fluctuation tends to induce a torsional memory that affects its own existence and causal permanence.

In this context, Rotation is a form of Conservation produced by the Field in reaction to the Propagation of the most elementary Variations, to translation—a Variation that takes the form of rotational dynamics, of axial reorientation of the vortical aspects of sub-elementary fluctuations.

Rotation can be seen and understood as Propagation and Conservation in Time.

From the point of view of the Elementary Events and the Dynamics of Elementary Action

From the point of view of the Fundamental Principles of Evolutionary Dynamics

The Information / Energy perspective

Formulation in vector calculus

The phenomenological perspective

Charge and Electric potential

Electric Fields (E): Generated by electric charges; they exert forces on other charges.

Spin and Magnetic potential

Magnetic Fields (B): Generated by moving charges (currents); they exert forces on other moving charges.

Maxwell's Equations

The foundation of the theory, consisting of four equations that relate electric and magnetic fields to their sources (charge density and current density).

Electromagnetic Waves

Propagating waves of electric and magnetic fields that travel at the speed of light.




Rotation represent the specification of "Conservation" at the most elementary level of Physical Reality.

Rotation is a specification of Conservation. It is the third fundamental mode of expression of the Elementary Action.

In term of Elementary Events, Rotation represents any action that tends to conserve Perturbation in the Elementary Field.

Perturbations, inhomogeneities in the distributions of the intensities of the Elementary Events, the intensities of the deformations of the Elementary Field under the incessant pressure of the Fundamental Force, the products of the Elementary Events, "conserve", persist, showing rotation, chirality, vorticity in the Field.

In the Dynamics of the Elementary Action we call "Rotation ", or Rotational Action, the vorticity of the perturbations, produced by the action tending to conserve inhomogeneity, in the points of expression of the action itself.

Like Perturbation, we cannot say that Rotation is something that exists, an entity. It is a phenomenon, a product of the dynamics of the inner interaction of the two aspects of the Source of Reality.

Rotation is associated with the Operator of Reality that has the same name and is the expression of the Fundamental Principle that we call Principle of Conservation (the mutations described by the Principle of Variation, the incessant variations of the states of the Entities, the Events, always tend to conserve). The Operator Rotation organizes Perturbations, the fluctuations of the Acted / Fields, in vortices of Action directed to maintain homogeneity, isotropy of the Elementary Field. The Operator Translation is responsible for the formation of vortices / curl aimed at conserve gradients (inhomogeneities, anisotropies) in the Acted / Fields.

Perturbation is the way in which the Elementary Field react to the Elementary Action of the Fundamental Force, the way in which the Elementary Field receive the expression of the Fundamental Force, its the product of the expression of Causality at the most elementary level of Reality. Variation is the root of the emergence of the Dimensionalities of Reality that we call Spatiality and Temporality, the fundaments of Space and Time.

Rotation is the way in which the Elementary Field reacts to the appearing of Perturbations produced by the Action of the Fundamental Force, the way in which the Elementary Field receives the expression of the Fundamental Force, it is the product of the expression of Causality. Rotation is the root of the emergence of the Dimensionality of Reality that we call Temporality, the fundament of Time.

The best question with respect to Translation undoubtedly is: what conserve? What conserve is the inhomogeneity in the distributions of the Elementary Events and the patterns of correlations among them. Any departure from an homogeneous distribution of Events as any change in that distribution (and in their stochastic independence / correlation) represents a variation that tend to conserve to maintain inhomogeneity. At any level of complexity, from the most elementary to the Universe as a whole, Reality can be described as a net of more or less independent / correlated stochastic processes that conserve in the Fields.

The Modes of Action are intimately connected with the Dimensionalities of Reality: Physical Causality and Physical Variationality, that produce the Dimensions of Physical Reality: Cause, Space and Time. They represent three fundamental operators in the Formation of Physical Reality. The Operator Perturbation can be seen as the result of expression of Physical Causality, the active side of Physical Agency, while Translation and Rotation can be seen as expressions of the two aspects of its passive side, Physical Variationality: Physical Spatiality and Physical Temporality.

The Operator Rotation is responsible for the formation of curl in the Elementary Field, conservation of inhomogeneities, anisotropies, in the Field and their dynamics.

In vector calculus, Rotation is embodied by the vector operator called "Curl" (CURL or ROT), which represents a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field.

Rotation is:


Rotation Sub-modes / Sub-components

Rotation:Chirality

Rotation:Chirality is the first of the two sub-modes of Rotation. It refers to chirality, the sense of circulation of Elementary Action, the sense of circulation of the Elementary Events in the Elementary Field. It is the root of Charge and electric phenomena.

Rotation:AxisOrientation

Rotation:AxisOrientation is the second of the two sub-modes of Rotation. It refers to the spatial direction of orientation of the axis of vorticity in circulation of Elementary Action, the direction of the orientation of the axis of vorticity in circulation of the Elementary Events in the Elementary Field. It is the root of Spin and magnetic phenomena.


Charge

Rotation:Chirality is the causal origination of Charge, while Translation is the variational effect produced by the presence of different sources of Rotation in the Field, which produces attraction / repulsion of charges and the electric domains.


Spin

Rotation:AxisOrientation is the causal origination of Spin, while Translation is the variational effect produced by the presence of different orientations of the axis of Rotation in the Field, which produces attraction / repulsion of spins and the magnetic domains.



Rotation:Chirality

Parameter that expresses "the chirality of the spatial fluctuations (spatial distances) of the Elementary Field" (spatial chirality of the variational effects on the Elementary Field produced by the causal Action of the Fundamental Force, chirality of the Elementary Action, the most elementary form of Existence, primary manifestation of the Source of Reality).

The correlation between the Rotation:Chirality values ​​in a given portion of the Elemental Field (Relationship between Elementary Action of a contiguous set of event points) defines the Elemental Energy of that portion in the Component Rotation:Chirality, which we call Charge, the root of electric phenomena.


Rotation:AxisOrientation

Parameter that expresses "the orientation of the axis of rotation/chirality (spin axis) of the spatial fluctuations (spatial distances) of the Elementary Field" (orientation of the axis of rotation/chirality - spin axis - of the variational effects on the Elementary Field produced by the causal Action of the Fundamental Force, orientation of the axis of rotation/chirality - spin axis - of the Elementary Action, the most elementary form of Existence, primary manifestation of the Source of Reality).

The correlation between the Rotation:AxisOrientation values ​​in a given portion of the Elementary Field (Relationship between Elementary Action of a contiguous set of event points) defines the Elementary Energy of that portion in the Rotation:AxisOrientation Component, which we call Spin, the root of magnetic phenomena.


Rotation represent the specification of "Conservation" at the most elementary level of Physical Reality.

Rotation is a specification of Conservation. It is the third fundamental mode of expression of the Elementary Action.

In term of Elementary Events, Rotation represents any action that tends to conserve Perturbation in the Elementary Field.

Perturbations, inhomogeneities in the distributions of the intensities of the Elementary Events, the intensities of the deformations of the Elementary Field under the incessant pressure of the Fundamental Force, the products of the Elementary Events, "conserve", persist, showing rotation, chirality, vorticity in the Field.

In the Dynamics of the Elementary Action we call "Rotation ", or Rotational Action, the vorticity of the perturbations, produced by the action tending to conserve inhomogeneity, in the points of expression of the action itself.

Like Perturbation, we cannot say that Rotation is something that exists, an entity. It is a phenomenon, a product of the dynamics of the inner interaction of the two aspects of the Source of Reality.

Rotation is associated with the Operator of Reality that has the same name and is the expression of the Fundamental Principle that we call Principle of Conservation (the mutations described by the Principle of Variation, the incessant variations of the states of the Entities, the Events, always tend to conserve). The Operator Rotation organizes Perturbations, the fluctuations of the Acted / Fields, in vortices of Action directed to maintain homogeneity, isotropy of the Elementary Field. The Operator Translation is responsible for the formation of vortices / curl aimed at conserve gradients (inhomogeneities, anisotropies) in the Acted / Fields.

Perturbation is the way in which the Elementary Field react to the Elementary Action of the Fundamental Force, the way in which the Elementary Field receive the expression of the Fundamental Force, its the product of the expression of Causality at the most elementary level of Reality. Variation is the root of the emergence of the Dimensionalities of Reality that we call Spatiality and Temporality, the fundaments of Space and Time.

Rotation is the way in which the Elementary Field reacts to the appearing of Perturbations produced by the Action of the Fundamental Force, the way in which the Elementary Field receives the expression of the Fundamental Force, it is the product of the expression of Causality. Rotation is the root of the emergence of the Dimensionality of Reality that we call Temporality, the fundament of Time.

The best question with respect to Translation undoubtedly is: what conserve? What conserve is the inhomogeneity in the distributions of the Elementary Events and the patterns of correlations among them. Any departure from an homogeneous distribution of Events as any change in that distribution (and in their stochastic independence / correlation) represents a variation that tend to conserve to maintain inhomogeneity. At any level of complexity, from the most elementary to the Universe as a whole, Reality can be described as a net of more or less independent / correlated stochastic processes that conserve in the Fields.

The Modes of Action are intimately connected with the Dimensionalities of Reality: Physical Causality and Physical Variationality, that produce the Dimensions of Physical Reality: Cause, Space and Time. They represent three fundamental operators in the Formation of Physical Reality. The Operator Perturbation can be seen as the result of expression of Physical Causality, the active side of Physical Agency, while Translation and Rotation can be seen as expressions of the two aspects of its passive side, Physical Variationality: Physical Spatiality and Physical Temporality.

The Operator Rotation is responsible for the formation of curl in the Elementary Field, conservation of inhomogeneities, anisotropies, in the Field and their dynamics.

In vector calculus, Rotation is embodied by the vector operator called "Curl" (CURL or ROT), which represents a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field.

Rotation is:


Rotation Sub-modes / Sub-components

Rotation:Chirality

Rotation:Chirality is the first of the two sub-modes of Rotation. It refers to chirality, the sense of circulation of Elementary Action, the sense of circulation of the Elementary Events in the Elementary Field. It is the root of Charge and electric phenomena.

Rotation:AxisOrientation

Rotation:AxisOrientation is the second of the two sub-modes of Rotation. It refers to the spatial direction of orientation of the axis of vorticity in circulation of Elementary Action, the direction of the orientation of the axis of vorticity in circulation of the Elementary Events in the Elementary Field. It is the root of Spin and magnetic phenomena.


Charge

Rotation:Chirality is the causal origination of Charge, while Translation is the variational effect produced by the presence of different sources of Rotation in the Field, which produces attraction / repulsion of charges and the electric domains.


Spin

Rotation:AxisOrientation is the causal origination of Spin, while Translation is the variational effect produced by the presence of different orientations of the axis of Rotation in the Field, which produces attraction / repulsion of spins and the magnetic domains.

Links to the tables of contents of TFNR Paper


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