TFNR - Rotation - Curl

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

Conservation

Conservation is the third fundamental mode of expression of Action. It organizes fluxes of Propagations in Action which tends to maintains, to conserve, Variations (the substrate of Existence in its most elementary form, in the Fields), gradients, inhomogeneities, anisotropies, in the Acted / Fields. Variations, Events, "diffuse", propagate, and "maintain", conserve, in the Fields.

In an incessant dynamical interaction of forces and fields, with actions and reactions, that maintains the Sources not too close, not too far from equilibrium, the Evolution of the product of the incessant Creation, produces the whole Reality, both in the physical and in the cognitive domains of the Nature. Reality fluctuates between equilibrium and disequilibrium, between homogeneity and inhomogeneity, isotropy and anisotropy, a dance that manifests itself in the incessant interaction between the two Operators of Reality that we call Propagation and Conservation.

It is a Mode of Action relative to Reality in its most general aspects. The specifications relative to the two domain of Nature, the physical and the cognitive ones, are Translation (root of motion) and Communication respectively. We can say that propagations don't exists, they happen. This is a phenomenon, a product of the dynamics of the inner interaction of the two aspects of the Source of Reality.

It 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 Variation (everything that exists is in incessant mutation, variation, or better, all that exist "is" incessant variation). Variation, as an Operator of Reality, transmutes the pressure of Agents / Forces on Acted / Fields in an incessant flux of variations, fluctuations, of the parameters that describe the same Acted / Fields.

The Operator Conservation organizes Propagations, the fluctuations of the Acted / Fields, in fluxes of Action directed to the maintaining of homogeneity, of isotropy of the Fields. The Operator Conservation is responsible form the formation of vortices / rotation / curl aimed at conserving gradients (inhomogeneities, anisotropies) in the Acted / Fields.

Propagation is the way in which Acted / Fields react to the appearing of Variation and Propagation produced by the Action of Agents / Forces, the way in which Acted / Fields receive the expression of the Agents / Forces, its the product of the expression of Causality. Conservation 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 Conservation undoubtedly is: what conserves? What conserves is the alteration of the distribution of the Events and the patterns of correlations that link them together. 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 homogeneity. 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.

Modes of Action are intimately connected with the Dimensionalities of Reality: Causality and Variationality, that produce the Dimensions of Reality: Cause, Space and Time. They represent three fundamental operators in the Formation of Reality. The Operator Conservation, together with Propagation, can be seen as expressions of Temporality, the second of the two aspects of the passive side of Agency, Variationality.

Rotation - Curl

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:

expression of the Principle of Least Action: it describes the formation of rotational reactions (Rotation), produced by the interactions among translations and aimed at conserving inhomogeneity, or anisotropy, in the distribution of elementary fluctuations
the root of Charge and electric phenomena and Spin and magnetic phenomena
intimately connected with the temporal duration of Elementary Action.

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

Go to the page: Charge and electric phenomena

Spin

Go to the page: Spin and magnetic phenomena