Difference between revisions of "TFNR - Translation - Divergence"

Latest revision as of 18:51, 21 May 2026

Translation, or Translational Action, is the instantiation through which "Propagation" manifests at the most elementary level of Physical Reality.

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

From a causal perspective, we can represent it as the Operator Translation, the Operational Agent responsible for the emergence of inhomogeneities in the pre-temporal distributions (from now on "tau-distributions", or more briefly "τ-dist") of the sub-elementary pre-spatial (linear and extrinsic rotational) fluctuations ("sigma-fluctuations", or "σ-fluct") of the Elementary Field (resulting from an expansion/contraction of infinitesimal volumes). Inhomogeneities that we can represent as divergences.

At the same time, from the variational point of view, Translation appears as inhomogeneities (divergence) in the distributions of the spatial (linear) orientations of the minute spatial fluctuations of the Elementary Field resonating around the Planck scale.

These divergences 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-flows.

Translation is the way in which the Elementary Field reacts to the formation and presence of inhomogeneities / gradients in the Perturbation Mode of Action, produced by the Action of the Fundamental Force on the Field, the way in which the Field responds to restore homogeneity in the pre-temporal distributions of Elementary Events. Translation is the root of the emergence of the Dimensionality of Reality that I call Spatiality, the fundament of Space.

The causal expression and the variational manifestation—two sides of the same coin—of this Mode of Elementary Action are described by the Principle of Propagation, which, at the Level of Elementary Action, takes the form of the Principle of Action and Reaction, which describes how any deformation of the Field produced by the Action of the Force produces a re-Action of the Field, a counter force that opposes the deforming Action.

Translation is the root of Motion, encompassing both inertia and acceleration, and thus the foundation of kinetic Phenomena, particularly the kinetic aspects of gravity.

In this section, I recall the general considerations that I presented in the previous section dedicated to Perturbation, as well as what was discussed in the section The Dynamics of Elementary Action and its Modes / Components.

The causal perspective

Let us retain what was established in the previous section on Perturbation concerning the causal perspective, 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 perspective, Translation can be represented as the Operator Translation, a functional derivation of the active aspect of the Source of Reality that organizes the re-Action of the Elementary Field produced by Perturbation into reorientation of the sub-elementary pre-spatial fluctuations (micro-flows), directed toward the restoration of homogeneity and isotropy within the Elementary Field.

The variational perspective

Symmetrically, from the variational perspective, Translation manifests as the re-Action of the Field to Perturbation, to gradients (Micro-gradients) in the temporal distributions of the sub-elementary pre-spatial fluctuations, resonating near the Planck scale.

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 dynamism of the Field, though extremely small, always represent extended regions in the sub-elementary pre-spatial and pre-temporal dimensions, the causal and variational precursor of what we, from our perspective, observe as three-dimensional Space, with an evolution in Time, representable within the four-dimensional continuum so central to relativistic physics.

Thus, not grains of Space and Time, but rather a kind of bubbles, "convective cells" in the continuum of the elementary dynamism 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 dynamism of the Field and project it into an initial seed of discreteness (Principle of Individuation) within the fundamental continuity.

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—E.M.W. and their Interactions that compose Ordinary Matter) and in the large domain (Vortices/Dark Halos, Dark Waves—G.W.— and their Interactions that compose the Dark Matter/Dark Energy side of the Universe).

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.

As already stated countless times in this work, by Elementary Events I mean the sub-elementary dynamism of the Field manifesting as pre-temporal distributions of spatial fluctuations resonating near the Planck scale. I use the term "pre-spatial" precisely because 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).

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.

Inhomogeneities I amplitudes of Elementary Events 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 a more or less intense reorientation of the spatial (linear) directions of the elementary spatial fluctuations, of the Elementary Events, flows in the dynamism of Field.

These flows in the sub-elementary dynamics, manifesting as 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-flows.

Translation is therefore the Field's spontaneous way of reorganizing gradients (Perturbation, inhomogeneities in temporal distributions) into divergence patterns—sources and sinks—that embody the Principle of Propagation: every variation tends to propagate and generate propagation all around, every fluctuation tends to extend beyond its origin and produce a causal effect that tends to affect its own Existence and causal permanence.

In this context, Translation is a form of Propagation produced by the Field in reaction to the most elementary Variations, to Perturbation—a Variation that takes the form of Propagation, of spatial (linear) reorientation of the elementary spatial fluctuations.

Translation can be seen and understood as Propagation and Conservation in Space.

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

The Operator Translation, as a derived causal expression of the Force, transmutes the basic Mode / Component of the Elementary Action, Perturbation, into an incessant Process of Propagation in the elementary dynamism of the Field, which manifests as a reorientation of pre-spatial fluctuations. At the same time, Translation, as a variational manifestation, is the result of that Process of Propagation. Causality produces the emergence of Spatiality.

The essential question is: what propagates? What propagates are the pre-temporal distributions of the orientation of the Elementary Events, of the sub-elementary sigma-fluctuations. What propagates is the pre-temporal aspect of the orientations of Elementary Events.

Any deviation from homogeneity—any change in stochastic independence or correlation—tends to propagate through the Field and tend to produce propagation flows through reorientation of the sigma-fluctuations (Traslation) in the dynamism of the Field. At every scale, from the Planck domain to the Universe as a whole, Reality can be described by a network of mixed (stochastic "and" deterministic) processes whose distributions propagate/diffuse through Translation.

Let me resume here what has already been said regarding Perturbation and push a little further.

In the absence of Perturbation, when the pre-temporal distribution of amplitudes of sub-elementary pre-spatial fluctuations is uniform at an event-point of the Field, and likewise at the event-points within its causally connected neighborhood, with no inhomogeneities present (zero Perturbation, precisely), the orientation of these fluctuations is entirely random. At each event-point the orientation of the fluctuations will be completely random and stochastically independent from that of the surrounding event-points.

The presence of Perturbation, an alteration of the homogeneity of the temporal distributions of the amplitudes of Elementary Events of the Field, radically changes the situation. We must imagine that to the primary inhomogeneity constituted by sub-elementary pre-spatial fluctuations, there is associated an inhomogeneity in their pre-temporal distributions.

To the spatial amplitude of the fluctuations corresponds a temporal amplitude, a duration of the fluctuations themselves. Larger spatial fluctuations entail longer durations: larger and slower fluctuations. And symmetrically, less wide but faster fluctuations. For simplicity, and in the absence of a detailed description of the laws linking the intensity of the Fundamental Force and the resistance of the Elementary Field to the amplitude of the deformation produced, in a chaotic regime that requires a stochastic description, let us imagine that the amplitudes of spatial fluctuations are normally distributed around a universal mean value, and that to this spatial distribution corresponds a normal temporal distribution centered on the mean duration of the fluctuations. For each event-point it will therefore be possible/necessary to define a temporal distribution of spatial fluctuations that will tell us how the dynamics of the Elementary Field at that precise event-point tends to evolve over Time.

With great simplification, we could express this distribution as a kind of "frequency" of a "quasi" periodic Phenomenon. Of course, this is a forcing, since the Phenomenon is not really periodic; it is stochastically distributed around a mean value, with a variance that may vary depending on the "rigidity or elasticity" of the Field at the event-point considered, depending on the greater or lesser expansion/contraction, with a clearly non-linear behavior, reflecting the resistance that the Field opposes to (further) deformation.

In less abstract terms, the pre-temporal distribution of pre-spatial fluctuations (whose deviation from the distribution we want to consider "standard"—the mean of the distributions at the universal level or of a significantly broad neighborhood, which I here call Perturbation) should allow us to understand how much of the time of the evolution of the dynamics of an event-point corresponds to the various possible amplitudes of spatial fluctuations. In other words, imagining an event-point as an infinitesimal volume of the Elementary Field, the pre-temporal distribution should provide us with a statistical value of how much that volume is, on average over time, expanded or contracted compared to the volume we intend to consider "standard".

If an event-point is on average pre-spatially more extended for a longer time, its "frequency" of fluctuation will be slower, lower than the "frequency" we consider standard. We will therefore say that it manifests negative Perturbation. And, as stated by the principle of General Equivalence for the Mode of Elementary Action that I call Perturbation, to a negative value will correspond to:

• a curvature of the Metric (in particular a slower rate of temporal flow than the "standard" value), a Metric that locally at the infinitesimal level will show deformation both spatial (distances, volumes, extension of Space) and temporal (intervals, durations, rhythm of the flow of Time), while, at scales already a few orders of magnitude above the Planck scale, only Time will remain curved or curvable (Space will appear absolutely flat, due to the compensation of sub-elementary pre-spatial fluctuations that show symmetric positive and negative contributions),
• a non-zero density of negative Mass (the attractive Mass we normally speak of), while a positive value of Perturbation would correspond to a non-zero density of positive Mass (that which we mean by the concept of repulsive Dark Energy),
• a deviation of the limiting value of the propagation speed of Causality / Action / Information in the Elementary Field (speed of light) from the universal limiting value or from that of a significant neighborhood for the undeformed, unstructured Field,
• a deviation of the "temperature" of the Elementary Field from the universal mean temperature or from that of a significant neighborhood—this opens up the analysis and definition of a sort of "thermodynamics" of the Elementary Field, where InfoStructures, Waves and Particles, as well as Dark Structures, Gravitational Waves and Dark Halos, emerge from the collective behavior of an infinity of event-points within the region of the Field that, from time to time, sustains the Structure—an infinity of event-points in incessant dynamic interaction. We are in the continuum, spanning an extremely extended range of size scales, from the Planck scale to the Particle scale and further up to cosmic scales, in the case of the Dark Structures.

The dynamics of the Elementary Field, of its incessant sigma-fluctuations and their relative tau-distributions—the foundation of the dynamics of Elementary Action in its different Modes / Components—is a fundamental aspect that requires profound investigation, as it is crucial for a correct and exhaustive description and modeling of the most elementary dynamics of the Field, upon which we must base the derivation of the Fundamental Physical Quantities and their dynamic parameters,

• both from the point of view "of" the Elementary Field:
  • Metric and universal gravitational constant,
  • Accelerated Motion and the limiting speed of light in vacuum,
  • Electric field and dielectric constant of vacuum or electric permittivity,
  • Magnetic field and magnetic permeability constant of vacuum,
• and from that of the InfoStructures "in" the Field:
  • Mass, e.g. the Masses of Particles,
  • Inertial Motion,
  • electric Charge and Particle Charges,
  • magnetic Spin and intrinsic magnetic moment or Spin of Particles,
  • Planck's constant.

Now that, as a complement to the previous section devoted to Perturbation, we have revisited and deepened the aspects of the dynamics of the Elementary Field that lead to the emergence of Perturbation, we can see how Translation arises from Perturbation, and how divergence emerges from gradients.

If, due to some Phenomenon, some dynamic peculiarity of the Field—for instance, the appearance of vorticity, the formation of a vortex—Perturbation manifests itself in a region of the Field, taking on for example a value less than zero for a certain duration, then in the surrounding region Translation will manifest: a more or less pronounced reorientation of sigma-fluctuations in the direction and orientation leading toward the center of Perturbation (a concept analogous to the center of Mass) of the region affected by such a dynamic configuration. Translation can be represented as a negative "divergence" (convergence) in the Field, centered on the volume that exhibits a negative value of Perturbation.

But let us proceed step by step. We can imagine an infinitesimal volume of the Field, with an extension comparable to the Planck scale, expanding and contracting in an incessant pulsation (random harmonic oscillator with a mean period or mean frequency) that we identify as a continuous succession of Elementary Events—sub-elementary pre-spatial fluctuations, precisely. The extension and duration of such pulsations can be described by a specific stochastic function, with mean and variance depending on the intensity of the Fundamental Force and on the resistance of the Elementary Field to deformation, etc.. All extension deformations (expansion and contraction of infinitesimal volumes, which we may view as a dynamic spatial curvature), as already mentioned, at scales just above the Planck scale compensate one another, rendering Space effectively absolutely flat.

We are always speaking of extremely high frequencies (a not entirely correct term, since these are not perfectly periodic phenomena, having a stochastic component linked to uncertainty; it would be more accurate to use the term quasi‑frequency or pulsation), which correspond to extremely short periods, just as the spatial distances over which the fluctuations manifest are exceedingly small (comparable to the Planck time and length, respectively).

The pre-temporal duration of these pre-spatial fluctuations will tend to distribute stochastically around a mean value, with a given variance. Here we assume that (although this assumption seems counter‑intuitive and therefore requires important and crucial further examination) the greater the spatial expansion or contraction (the departure from the "standard" extension of the infinitesimal volume considered), the larger the pulsation's duration. The greater the dilation or contraction of the considered Field volume, the greater the resistance to further compression or expansion, and the greater the force the Field will express in reaction to such elementary spatial deformation (non-linear behavior).

An alteration, a deformation of the distribution of the spatial extension of pulsations will correspond to an alteration, a deformation of the distribution of their temporal durations.

Here we encounter a first form of inhomogeneity that generates an initial reaction from the Field—the response to the deformation of spatial extension. It is a manifestation of the Field's elasticity, which stores Energy under the Action of the Force that expands infinitesimal volumes, and then releases it by producing a compression that drives the extension of the volume of that region back toward its original value and beyond, into compression, resisted by the incessant pressure of the Force. A dynamic equilibrium which, as mentioned, in specific phenomena and particular dynamics may manifest gradients that represent Perturbation.

This Process is a manifestation of the dynamical balance between the Action of the Force and the re-Action of the Field (the both contains a certain amount of uncertainty), which stores Energy under the Action of the Force that expands infinitesimal volumes, and then releases it by producing a compression that drives the extension of the volume of that region back toward its original value and beyond, into compression, resisted by the incessant pressure of the Force. A dynamic equilibrium which, as mentioned, in specific Phenomena and particular dynamics may manifest gradients.

An alteration, a deformation of the distribution of the temporal durations of the pre-spatial pulsations will correspond to an alteration, a deformation of their pre-temporal distribution. This pre-temporal distribution tells us how often each amplitude value of pre-spatial fluctuations manifests (fluctuations, I recall, are random with a distribution—assumed to be normal—around a mean value, with a given variance depending on constitutive and dynamic factors). It is a continuous function that allows us to represent the pre-temporal prevalence of the extensions of pre-spatial fluctuations and to assess the greater or lesser persistence of pulsation frequencies above or below the mean, which we take as the standard value corresponding to the absence of temporal deformation—the root of the deformation of the Metric (the rhythm of Time)—if we consider a set of event‑points, a region of the Field, which we can observe as a region of the Derived "Metric" Field, that we call Spacetime.

Here we encounter a second form of inhomogeneity that generates a further reaction of the Field—the response to the deformation of the temporal distribution of the spatial extension fluctuations. An event‑point which, whether by chance or—more probably and stably—through a specific phenomenon, for a time longer than the average manifested in the Field, is animated by spatially more extended fluctuations (which therefore appear with longer temporal durations), will produce a reaction of the Field tending to reduce or cancel such temporal inhomogeneity (precisely in the temporal distribution of elementary spatial fluctuations).

Here we are speaking of the most elementary forms of deformation of the Elementary Field, intimately connected and inseparable: pre-spatial inhomogeneities and those of their pre-temporal distributions, which in their dynamic unity represent the most elementary form of Existence—the Elementary Action in its Mode/Component that I here call Perturbation, and which, as seen, generates Translation.

Moving from the Level of Elementary Action to that of Information/Energy, to the Fundamental Physical Quantities and the associated Phenomena, we can associate Perturbation with the curvature of the Metric (of Spacetime), if observed from the standpoint "of" the Field, and with negative or positive Mass, if observed from the perspective of InfoStructures "within" the Field.

And to Translation we can associate accelerated Motion (gravitational acceleration, gravitational potential, etc.), if observed from the standpoint "of" the Field, and inertial Motion (momentum, kinetic Energy), if observed from the perspective of InfoStructures "within" the Field.

I am conscious that I am lingering extensively, perhaps excessively, on this theme. But, the Dynamics of Elementary Action is a cornerstone of the model I advance in this work. It stands far apart from the proposals of conventional physics, requiring a genuine effort of imagination and a visualization that is anything but trivial. Moreover, it is a theoretical domain only sketched out, which demands intense and profound development, both conceptually and in terms of formalization. It is not easy to provide a clear image of Entities, Phenomena, and Dynamics so distant from the experience of both the common person and the scientist.

Here I will attempt to deepen or reformulate some aspects that I consider most important, also in view of what I will need to present in the chapters to come.

We can imagine the Elementary Field as an infinite volume in which the infinitesimal volumes I call event-points are like tiny elastic quasi-spheres, or quasi-cubes, indefinite and indefinable volumes that occupy all the available Space, hypothetical and abstract, which do not exist in Reality because the Field is continuous, and which I employ to attempt to visualize the dynamics of the Field at such a small scale.

These infinitesimal volumes can be conceived as incessantly pulsating randomly in all directions, expanding and compressing in an incessant chaotic dynamic, each animated by a generated positive or negative pressure independent of the others, yet each embedded in a continuous matrix that influences its shape, extension, and dynamics. We are speaking of deformations of shape and extension within the continuous volume occupied, where in each spatial direction the intensities, directions, and orientations vary incessantly—partly due to the pressure exerted by the Fundamental Force in that volume, and partly due to the pressure exerted by the dynamics of other event-points in the neighborhood.

Thus, a dynamic produced and a dynamic undergone. From the dynamic equilibrium of these two interconnected components arises what I here call Elementary Action. The undergone dynamic constitutes what I identify as the reaction of the Elementary Field to the alteration of homogeneity in the dynamics of an event-point, of an infinitesimal volume, of an imaginary micro-elastic sphere pulsating incessantly, presumably in harmonic motion.

And, in the case where InfoStructures are present within the Field — that is, when the Field is structured — the dynamism of the Field in those micro regions that I call event-points becomes the support, the substrate of Information: that which gives Form to Action, to the inhomogeneities of the dynamism that incessantly animates the Field, to the patterns of Relations and correlations that organize the Elementary Events constituting its dynamic manifestation at the sub-elementary, pre-physical level, so to speak. A level from which, through the organization of such correlations, the elementary, physical level of Reality incessantly emerges.

The Level of Physical Action, which supports the Levels of Information/Energy and of InfoStructures, is the Level of Reality from which Metric and Mass emerge from Perturbation, Translation, and Rotation; from which accelerated and inertial Motion arise; from which the electric Field and Charge, the magnetic Field and Spin emerge — and so on, in an increasing crescendo of Complexity that leads to the Forms, the objects that populate the evolving Universe.

I wish to emphasize that these small volumes are imaginary constructs, hypothesized solely for the purpose of attempting to visualize the dynamics of the Field. In Reality they do not exist; it is the Field itself, at every point, that behaves like an infinitesimal volume expanding and contracting, pulsating incessantly. The image I have proposed of quasi-spheres, or quasi-volumes, helps us form a mental picture, but it might lead us to think of some kind of grains of Space and/or Time. This is a notion I categorically reject, since, as stated repeatedly, I hold that Reality is incessantly created as it emerges from the dynamics of a continuous field, the Elementary Field, of which all Derived Fields — such as the electric, magnetic, gravitational fields, all quantum fields, and so on — are particular, partial “views”, obtained by observing the dynamism of the Elementary Field from different and complementary perspectives. Even the discreteness we observe (InfoStructures, Particles, etc.) arises through nonlinear processes/behaviors and scale resonances from that same continuous Field.

I will try to express it in different words, hoping to make this crucial aspect clearer.

Let us try to imagine a spherical region of the Elementary Field with infinitesimal volume (we are near the Planck scale). Under the incessant Action of the Fundamental Force, its form (a sphere), its extension (the volume just mentioned), and its dynamics (how pre-spatial shape and extension vary, and how these variations/fluctuations distribute themselves within the pre-temporal dimension) exhibit indeterminacy — uncertainty around average values, with variances that are themselves variable within the emerging Dimensions of Space and Time. Dimensions which, taken together, constitute the Metric (metric field, potential Metric, or potential Mass — whatever we want to call it).

Like every other aspect of Physical Reality, these too emerge from the sub-elementary dynamism of the unstructured Field as:

• Processes - organized sets of Events and Relations/correlations,
• Phenomena - organized sets of Processes,
• Structures - organized sets of Processes and Phenomena that manifest Properties and Behaviors.

If we could observe the Field at such infinitesimal scales, we would never see a perfectly spherical form. The region selected as a sphere under a hypothetical condition of Field staticity would never appear as such in the Field as it actually manifests itself, perturbed by the incessant Creation of the dynamism that characterizes its Behavior. We would “see” an almost sphere: a form in incessant fluctuation around the spherical shape, which, over extremely small pre-temporal intervals, could assume bizarre configurations, even very far from the spherical one.

This is the realm described by the Uncertainty Principle. Indeterminacy dominates on multiple levels. If we consider the aforementioned region as absolutely independent from the rest of the Field (infinite and unbounded), its form would be shaken by incessant deformations produced by the sub-Process of Creation (the Force acting upon the Field and perturbing it). But in Reality, no region of the Field can be regarded as independent from the rest of the Field, especially from the nearby regions. Thus, the dynamism of the Field manifests itself as doubly characterized by uncertainty. Here enters the indeterminacy arising from the interaction between the local dynamism of the Field and the dynamism of the surrounding regions — and of the entire Field, for all regions that are causally and variationally connected. We may imagine this interaction as a many body dynamics — in fact, an infinite body one — intrinsically uncertain, indeterminate, and unpredictable.

We have seen that Perturbation may be conceived as inhomogeneities in the pre-temporal distributions (together with their associated durations, interpretable in the same way as "periods" or "frequencies" of quasi-pulsations) of amplitudes of pre-spatial infinitesimal fluctuations, which can be regarded as elementary “pulsations” of event-points.

We can imagine the Action of the Fundamental Force on the Elementary Field as a pressure that causes an infinitesimal volume of the Field—associated with what we call the event-point—to expand. The Field's re-Action appears as a counterforce that generates an Action we may picture as the contraction of that same volume, tending to restore the extension of the event-point to a state of homogeneity.

This ongoing dynamic tension between expansion and contraction results in the pulsation mentioned above, and keeps each infinitesimal region of the Field in a state of continuous disequilibrium, which is precisely the sub-elementary dynamism we are referring to.

Now we can see Translation as the Elementary Action produced by the re-Actions of the dynamics of surrounding event-points, naturally directed toward the imaginary centre of the pulsating volume we identify as an event-point (reorientation of the direction of pre-spatial fluctuations). And so it is for all the event-points of the Field, in a continuous network which, as is easily imaginable, will be characterized by an incredible dynamic Complexity. A Complexity that manifests itself at extremely small dimensional scales with a resonance peak near the Planck scale. A dynamic Complexity that, at larger scales, in the absence of a structural organization of the Field (for example, the formation of a vortical structure), will appear homogeneous and therefore not so complex (the Field in the dynamic condition we may identify as absolute Void).

From a certain point of view, we may imagine Translation as the inhomogeneity in the pre-temporal distribution of the orientation of the pre-spatial fluctuations of the event-points adjacent to the one under consideration that has undergone an expansion—an inhomogeneity which, by exerting a compression, tends to restore the spherical form we mentioned above.

Technically, this would not be propagation in the strict sense, since in the translational reaction of the Field to the presence of Perturbation, nothing is actually moving, propagating. It is the same Elementary Field, in its aspect of spacetime Metric, each of its infinitesimal volumes (ideal pre-spatial regions within the continuous Field) that expands and contracts, pulsating at a rhythm that may be equal to, greater than, or less than the average of the pulsation rhythms universal or of a significant neighborhood (corresponding respectively to a null, positive, or negative Perturbation value). Within the aspect of the structured Field that we call the Metric, for regions sufficiently extended with respect to the Planck scale, we can associate a rhythm of Time flow that is respectively equal to, greater than, or less than the universal average rhythm or that of the neighborhood considered (a deformation, or local curvature of the space-time Metric—effectively only of Time, since for sufficiently extended regions the infinitesimal spatial curvatures compensate, leaving Space absolutely flat).

Let me try to clarify more precisely how Translation manifests itself at the level of the Elementary Events and the Dynamics of Elementary Action.

We can imagine several aspects that contribute to shaping the feature of the Dynamics of Elementary Action that I here call Translation:

• a first form of manifestation (spatial expansion/contraction) produced by the expression of the Action of the Fundamental Force in the form of the Translation Operator consists in the production of the expansion of the spatial volume of the Field ideally at each of its points (event-points); let me recall once again that we are in the continuum, but that for the peculiar values of the intensity of the Force (dynamic actions) and of the resistance of the Field to the various modes of deformation (dynamic constraints), a resonance is spontaneously generated which we may imagine at spatial and temporal scales near the Planck scale. We may therefore imagine the Field as a set of bubbles, of cells, of extension comparable to the Planck scale, deformable, with elasticity proportional to the deformation. Cells that expand and contract in an incessant pulsation; these bubbles do not behave like ideal spheres, but in every direction expansion and contraction manifest themselves differently due to the varying intensity of the Force, and above all due to the greater or lesser resistance opposed by the Field, by the event-points, by the surrounding bubbles (according to a quadratic law in relation to distance), depending on their greater or lesser expansion/contraction. Thus not only does their volume change incessantly, but also their shape in Space (in what, in the causal evolution of Reality, is destined to manifest itself as Space). We may imagine an immense network formed by this dynamic "fabric" which, at the level of the event-points, of the micro-cells, shows micro-curvatures of Space, but which at larger scales (due to the compensations between expansions and contractions) shows an absolutely flat Space; in this first causal/variational aspect, Translation is identified with the reaction of the Field to expansion/contraction of the elementary spatial fluctuations, therefore with the pre-spatial dynamics of Elementary Events;

• a second form of manifestation (pre-temporal dynamics of pre-spatial expansion/contraction) appears when we observe the pre-temporal aspects of these pulsations; this pulsating dynamics occurs over infinitesimal pre-spatial distances and equally minute pre-temporal durations; distances and durations linked by a specific relation, the most elementary expression of the Principle of Uncertainty. When, in the pre-temporal dimension, the magnitude of the pre-spatial fluctuations of an infinitesimal volume, of an event-point, persists at a value greater or lesser than the average, we shall say that that infinitesimal volume has a non-null Perturbation, positive or negative respectively (and, as stated by the Principle of General Equivalence for Perturbation, under these dynamic conditions at the Level of Elementary Action, and moving from the observation of individual event-points to the observation of the correlations that bind them into more or less organized patterns, at the Level of Information/Energy, of the Structures of Information, of the Forms, we would observe a rhythm of Time flow respectively greater or lesser than the universal average or that of a significant neighborhood—thus a deformation of the Metric, the presence of positive Mass density—repulsive Dark Energy—or negative Mass—the attractive Mass of which we commonly speak—and again a limiting velocity of propagation of Causality/Action/Information—the so called speed of light—greater or lesser than the average, if ever we could measure it, and likewise a temperature of the Elementary Field higher or lower than the average). Because of the non-uniform distribution in the Field of these different temporal distributions of pulsations, of the elementary spatial fluctuations, the Field reacts with a spontaneous reorientation of the fluctuations themselves in directions that tend to reduce the inhomogeneities of the distributions themselves;

This dynamics of Translation, of rebalancing flows, of divergence aimed at minimizing gradients (Perturbation), may produce translatory flows in the Field that determine the propagation of the dynamic conditions of the infinitesimal volumes; in other words, it may produce a propagation, a displacement in the Field of the turbulence formed by the pre-temporal distributions of the sub-elementary pre-spatial fluctuations (let us imagine that turbulence forms in the Field with micro-vortices of minimal pre-spatial extension and ephemeral pre-temporal duration; we shall then observe Translation in the form of micro-displacements of such impermanent structures). Turbulence which, with the passing of Time, tends to evolve toward more extended forms both in pre-spatial and pre-temporal sense, and in causal sense (greater Complexity).

Let us resume the concepts expressed above by means of a comparison with thermodynamics, with a crucial clarification. While in thermodynamics macroscopic phenomena are traced back to the properties and collective behavior of a multitude of interacting objects (atoms, molecules), here, in the depths of Physical Reality, where Fundamental Force and Elementary Field incessantly interact to create Existence in its most elementary forms, arises the Elementary Action in its various Modes / Components. Here, we do not encounter objects, structures, particles, atoms, or molecules. We are in the realm of the continuum. At most, within resonances that manifest at particular scales, we can glimpse fleeting hints of a subsequent evolution toward discreteness, toward structuring, yet always “emerging from” and “immersed in” the continuum.

The Field is not a fluid, although in some respects it behaves like a superfluid. It is not composed of structures, waves, particles, although in its causal and variational evolution it manifests the existence of Structures of Information that constitute the Forms we observe in the Universe. When we speak of the Field and of Elementary Action, we are far removed from concepts such as the ether, in its various meanings. The model I am hypothesizing and proposing here is as far as possible from the mechanics of a material ether. To investigate the fundamental nature of Physical Reality, we must go beyond matter—beyond materiality itself as a concept. Unfortunately, the notions of field, which General Relativity and Quantum Field Theory have rightly placed at center stage, replacing earlier material entities such as the ether, are too abstract to allow us to imagine the deep dynamism of Reality. We must move from the super‑abstract level of those theories to a more concrete vision which, while preserving indeterminacy, allows us to recover elements of a mechanics that has long been lost. Here I hypothesize a non-material Field, in the sense we attribute to the adjective "material", even though from its incessant dynamism Matter emerges in its multiple forms, both in the dark/invisible sector and in the ordinary/visible one.

Let us begin with a cubic box bounded by ideal walls, permeable to incoming energy yet impermeable to its release. Let us imagine it filled with an ideal gas, with a given volume, constant pressure, and constant temperature.

Step one: we may imagine an analogy between Elementary Events (sub-elementary pre-spatial fluctuations of the Field) and the vibrating molecules of the gas inside the box.

Step two: we may imagine an analogy between the motion of a single gas molecule in the box (describable in terms of trajectory, velocity, and acceleration vectors) and the dynamics of expansion/contraction of infinitesimal volume regions of the Field that I have associated with event-points, which can be characterized through the pre-temporal distribution of such fluctuations. At each event-point of the Field we may imagine associating a random harmonic oscillator with a normal distribution, whose mean and variance depend on the Properties of the Force (intensity and randomness) and of the Field (resistances to the various kinds of deformation), on the magnitude of the deformation, both in the pre-spatial and in the pre-temporal domains, and so forth.

Step three: from the observation/measurement of the collective behavior of the gas molecules we can obtain statistical quantities such as temperature, which represents the average velocity of the gas molecules. Temperature can be observed locally at each point of the box, or in regions of varying extent, or for the box as a whole. Similarly, in the Elementary Field we can observe the dynamics of individual event-points or of sets of event-points composing regions with volumes of different sizes, or, again, the entire infinite Field.

Step four: Let us try to heat one face of the box by supplying thermal Energy to it. In the gas, a thermal gradient will appear—or more likely, a complex set of interacting thermal gradients—with convective motions tending to redistribute the thermal Energy and drive the system toward thermal equilibrium (a return to homogeneity). We may imagine analogies between thermal gradients (regions in which molecular velocities deviate above or below their local average— and non-zero Perturbation, understood as regions in which the temporal distribution of elementary spatial fluctuations deviates above or below its average.

Step five: we may imagine analogies between convective motions in the gas and Translation in the Field, which reacts to Perturbation by attempting to nullify it or, if not possible, to redistribute and level Perturbation so as to recreate the least possible inhomogeneity.

Step six: and again, we can imagine analogies among gradients, flows, torsions, waves, and vorticity, in the form of turbulence and dynamic structures in the gas moving inside the box, and corresponding Phenomena within the dynamics of the Elementary Field—turbulence and Structures as patterns of organization (Information) in the pre-temporal distributions of sub-elementary pre-spatial fluctuations, within the Elementary Events that animate the Field.

Step seven: expanding our perspective just a little more, we may imagine an analogy between the Elementary Field and the Spacetime that contains the box and its content. Everything can move within the Elementary Field just as the box itself and its content can move within Spacetime. Any perturbation of the Field or structure within the Field will have no way of distinguishing between a condition of rest or of inertial motion with respect to the Field (the Field is absolute, but since the existence of fixed reference points is impossible, in practice it is as if it were relative), just as in Space-time the box and any of its contents, in the absence of reference points, will have no possibility of distinguishing a state of motion from one of rest.

By observing the various steps as a whole—both from the perspective of a thermodynamic system such as the box filled with gas, and from the perspective of the Elementary Field perturbed by the incessant Action of the Fundamental Force—we can obtain a representation of how elementary dynamics operate in two different systems, of how gradients are produced, and how from them divergence arises. In the next section we will discuss the Rotation Mode / Component, with their two sub-Modes, and we will see how the interaction of Translation and divergence produces Curl, Rotor, Rotation itself.

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

Translation is an instantiation of the Operator of Reality Propagation that expresses the Fundamental Principle I call Principle of Propagation: the mutations described by the Principle of Variation—the incessant variations in the dynamic conditions of Entities, Events, and the Relations among them—always tend to propagate.

The way Translation manifests itself in the construction of Reality is described by the Principle of Action and Reaction, which is itself a specification of the more general Principle of Propagation.

This principle, in particular, describes how the Elementary Field responds to the manifestation of Perturbation—to the inhomogeneities in the tau-distributions of the sigma-fluctuations—in a natural tension toward restoring homogeneity in the dynamics of the Field, and how this Process generates propagation, spreading, fluxes, and divergence.

This dynamic is the root of "Spatiality" and the dimension of Space.

The Information / Energy perspective

I reiterate that here we are speaking of Action (Force, Space, and Time). To move from the level of Action (the level of Existence, of that which exists insofar as it occurs) to the level of Information (the level of Essence, the Form of what occurs), it is necessary to ideally stop Time flow, focusing on the dynamics of the Elementary Field from the perspective of Force and Space.

Now, if we observe the stochastic processes that describe the physical Processes of Elementary Action as mentioned above, we may imagine that a persistence in Time (temporal distribution, rhythm) of a certain amplitude of the sub-elementary pre-spatial fluctuations of an event-point (the pre-temporality and pre-spatiality of the pulsations of event-points) provokes, as stated, a reaction of the Field equal and opposite, oriented contrary to the expansion of the event-point itself. These are expansions, pulsations of the surrounding event-points, which—depending on the pre-temporal and pew-spatial measure of the expansion of the first event-point—will tend to expand to a greater or lesser degree relative to the average, producing a kind of propagation of Action expressed in this dynamic, which tends toward the restoration of homogeneity in the tau-distributions of sigma-fluctuations, that is, of Perturbation.

We must think of the Field as a spatially elastic field at the lower scales—near the Planck scale—then becoming rigid and flat at larger scales, all the way to infinity. In other words, in this model the Field is elastic at small scales (below and around the Planck scale) but rigid and flat at larger scales (many orders of magnitude below the scale of Particles, and continuing up to cosmic scales and toward infinity).

This small‑scale elasticity is part of the dynamics of the Elementary Field, which manifests itself as Elementary Events: tiny fluctuations or pulsations of pre-spatial dimensions at infinitesimal scale, forming the substrate of the most elementary forms of Existence—the Elementary Action in its Modes / Components.

As we saw in the previous section and recalled above, the most elementary form—what I have called a Perturbation—consists in the inhomogeneity of the tau-distributions of the amplitudes of these sigma fluctuations / pulsations. Such inhomogeneities can be observed from the point of view of each event-point of the Field (an infinitesimal volume, since in the Field nothing can be point-like, nothing can exist with zero spatial and temporal extension) or from the perspective of a larger region of the Field that includes multiple event‑points. And at the level of individual event-points, it can be observed from a partial perspective—that of pre-spatial fluctuations—and from the complete perspective of the pre-temporal distributions of those same fluctuations, which in the pre-temporal view, as we have seen, can be regarded as pulsations, expansion/contraction processes whose durations are proportional to the pre-spatial amplitude (volume, directions, and shape of the deformations).

We therefore have three levels of observation from which we can attempt to characterize their respective forms of Energy: the first, being a partial perspective—purely (pre-)spatial—can be regarded as a kind of "virtual" Energy, partial by its very nature. The second, and even more so the third level of observation, leads us toward increasingly complete concepts and forms of Energy, progressively closer to the notions of Energy that are familiar to us and that we associate with the Fundamental Physical Quantities: Metric/Mass, Motion, Charge, and Spin.

Some notes on spatial domains (regions of the continuous Elementary Field): "event-points" (domains with infinitesimal yet non‑zero volume—non‑pointlike despite the term event-points) and "regions with a broader extension than event-points or that include more than one event-point" (domains of greater, though still very small, volume, within which it is possible to conceive more than one event-point).

The concept of an event-point is not trivial and not easy to describe. I consider here an event‑point to be a point of the Elementary Field where an Event occurs, or can occur, which in its most elementary form, as we have seen, consists of a sub-elementary pre-spatial fluctuation of the Field itself (an expansion/compression event of the volume of an infinitesimal region of the Field).

I have said that an event-point always has a non-zero volume, however small. But we should not think of an event-point as a discrete structure. We are in the continuum, and we must imagine an event-point as a region of the Field with very small—yet non‑zero—pre-spatial extension (volume), "point‑like" in a general sense, to convey the idea of an extremely small pre-spatial extension; a region that does not exist as an individual entity, but that we choose, case by case, as a region of observation and analysis. The fact that elementary dynamic processes in the Field exhibit resonances helps us describe the dynamics of such event-points, since we can imagine taking an infinitesimal volume—as an example of an arbitrary volume—at any position within the Field itself.

Having made this necessary clarification, we can now address the transition from the dimension of Elementary Action to that of Information, of which Energy represents an elementary form with a more strictly physical meaning and analyze the energetic aspect of the dynamism of the Elementary Field from the two perspectives mentioned above: that of event‑points, and that of larger regions that we may regard as sets of event‑points, or rather, continuous regions that can ideally be represented as sets of event‑points.

In reality, we will use not two but four observation points. For greater clarity, event‑points can be analyzed from a partial, purely spatial point of view (restricting ourselves to Elementary Events, the elementary pre-spatial fluctuations that exhibit dimensional resonances near the Planck scale), from a pre-temporal perspective of Elementary Events, and from an overall pre-spatial/pre-temporal point of view (that is, the pre-temporal distributions of the sub-elementary pre-spatial fluctuations — the Elementary Events precisely).

These three perspectives are focused on the event-points of the Field and allow us to explore an embryonic form of Energy—what I call Proto Energy (pre-spatial Proto Energy, pre-temporal Proto Energy, and Elementary Energy), not relational, or not strictly relational, so to say.

The fourth perspective, instead, concerns the observation of the organization of sub-elementary dynamism from the point of view of large regions of the Field. This is where true Information/Energy emerges, relational in nature: correlations among the discrepancies in the pre-temporal distributions of pre-spatial fluctuations—that is, of the Elementary Events.

In summary:

• Event-points partial perspective: first level of inhomogeneity, purely pre-spatial (Level of Elementary Events – pre-spatial) -> Pre-Spatial Proto-Energy
• Event-points complete perspective: second level of inhomogeneity, pre-temporal of pre-spatial (Level of Elementary Events – pre-temporal) -> Pre-Temporal Proto-Energy
• Event-point perspective compared with the Field: third level of inhomogeneity, discrepancies of pre-temporal of pre-spatial (Level of Elementary Action) -> Elementary Energy of the Unstructured Field (Pre-Spatial Pre-Temporal Proto-Energy)
• Regions of the Field perspective, sets of more than one event-point: fourth level of inhomogeneity, spatial correlations between pre-temporal distributions of pre-spatial fluctuations (Level of Information / Energy) -> Information / Energy -> Fundamental Physical Quantities: Metric (the pre-spatial dimension becomes the physical Space, and the pre-temporal one becomes the physical Time) / Mass, Motion, Charge and Spin, and other more complex physical quantities

In this formative context, I use the concept of Proto-Energy to represent an virtual energetic perspective associated with the elementary dynamism of the Field. A dynamism that is indeed sub-elementary for the first two forms of proto-Energy discussed earlier in this section:

• sub-Elementary pre-spatial unmanifested proto-Energy - SE_PS_PE (which originates from the "first level of inhomogeneity" associated with the "pre-spatial asymmetrical dynamics of elementary pre-spatial fluctuations of the Elementary Field (Elementary Events) in amplitude, orientation, chirality and axis-orientation of vorticity, observed from the point of view of the dynamics of individual event-points"),
• sub-Elementary pre-temporal unmanifested proto-Energy - SE_PT_PE (which originates from the "second level of inhomogeneity" associated with the "pre-temporal asymmetrical distributions of the dynamics of the pre-spatial elementary fluctuations of the individual event-points in the mentioned four aspects that correspond to the Modes / Components of Elementary Action, observed from the point of view of the dynamics of individual event-points"),

and elementary in the case of the third form, Elementary Energy proper:

• Elementary Energy or Elementary Pre-Spatial and pre-Temporal unmanifested proto-Energy - E_PST_PE (which originates from the "third level of inhomogeneity" associated with the "pre-temporal asymmetrical distributions of the dynamics of the pre-spatial elementary fluctuations of the individual event-points relative to the Field's standard behavior, that is, when observed from the point of view of the dynamics of individual event-points relative to the average dynamics of the Field").

Let me first examine the forms of elementary Energy associated with the Mode / Component of the Elementary Action that I call "Perturbation" (inhomogeneities in the temporal distributions of the amplitudes of the elementary spatial fluctuations). I will then carry out the same analysis with respect to the "Translation" Mode / Component.

Perturbation

For all perspectives, some preliminary considerations first, followed by the details.

- Event-points partial perspective: first level of inhomogeneity, purely pre-spatial (Level of Elementary Events – pre-spatial) -> Pre-Spatial Proto-Energy

Event-point perspective (pre-spatial only)

• We consider each event‑point as an infinitesimal volume subject to:
  • non‑uniform expansion
  • non‑uniform contraction
• These deformations return the volume to its “standard” size but not its original shape, due to asymmetries in the expansion–contraction cycle.
• Contraction may even overshoot the standard size because of the Field’s elastic reaction to surrounding expansions driven by the Fundamental Force.

Pre‑spatial pulsation

• The event‑point undergoes a quasi‑periodic pulsation: expansion → contraction → expansion…
• The temporal distribution of these pulsations depends on:
  • parameters of the Force and the Field
  • local dynamics of the event‑point
  • dynamics of surrounding event‑points (unstructured Field)
  • larger‑scale inhomogeneities (structured Field)

Spatial and temporal non‑homogeneity

• The process is:
  • spatially non‑homogeneous (asymmetric in pre‑spatial directions)
  • temporally non‑homogeneous (variable pre‑temporal intervals)
• At such small scales, symmetry is impossible: expansions and contractions cannot preserve the shape of the infinitesimal regions.

Multiform, variable regions

• Instead of stable micro‑spheres, we must imagine ever‑changing, irregular regions.
• These transformations occur under the continuous pressure of the Force on every infinitesimal point of the Field, at scales far below the Planck scale.

Elementary (proto)‑Energy as deformation

• The most elementary form of Energy—more precisely proto‑Energy—is:
  • the elementary deformation of event‑points
  • the incessant change of shape produced by sub‑elementary pulsations
• This proto‑Energy is “virtual” because it precedes any manifest physical Energy and is rooted in Relations among Events.

Elastic Field and energetic balance

• In an elastic Field, each instant reflects a shifting balance between:
  • potential Energy
  • expressed Energy (expansion or contraction)
• This can be modeled as a random harmonic oscillator with a variable attractor, whose mean, variance, and distribution evolve with the Field’s dynamics.

I'll try to clarify some of these concepts in more detail.

When I speak of "deformation", I obviously do not mean the deformation of a material medium, a substance in a classical sense. I mean the deformation—an alteration—of a dynamism that has its own pre-spatial distribution (the sigma fluctuations) and its own temporal distribution (the tau distributions). Thus, not only do the fluctuations and distributions exist, but they themselves vary within the pre-spatial and pre-temporal dimensions. This generates a high level of dynamical complexity, necessary to sustain the extraordinary structural complexity of what exists.

Even a "simple" elementary particle such as an electron is a structure constituted by a physical Process supported by a pre-physical Process within the sub-elementary dynamism that incessantly animates the Elementary Field. Turbulence is everywhere, at all dimensional scales. We observe objects that appear ordered, elementary, point-like, monolithic. Yet their Existence and their Essence/Form emerge from—and are sustained by—an incredible dynamical complexity, a turbulence that, under appropriate conditions (conditions of existence and conditions of form), continually organizes and reorganizes itself into what we observe and measure.

Let us first consider the event‑point perspective, and only from the pre-spatial point of view — or rather, from what will emerge, through the dynamism of the Elementary Field, as the "Perturbation" Component of the Elementary Action, the root of Space‑time (the Metric and Mass) and of metric Phenomena.

Imagine an infinitesimal volume that expands (expansion that is not uniform across all directions) and is then pushed to contract (here too in a non homogeneous way) and return to the "standard" extension of the infinitesimal volume we have placed under observation (same volume, but a slightly different shape — a quasi sphere — due to the non homogeneity in the expansion and the subsequent contraction)—or even to contract below its "normal" extension due to the Field's reaction to expansion (a reaction caused by the expansion of the event‑points in the surrounding regions, under the incessant pressure of the Fundamental Force).

Let us therefore imagine a kind of pulsation, a sequence of pre-spatial fluctuations of the volume—expansion/contraction—almost but not strictly periodic, with a temporal distribution whose mean and variance depend on the parameters of the Force and the Field, on the local dynamics of the observed event‑point, and on the dynamics of the surrounding event‑points (the dynamics "of" the Field, the unstructured Field), as well as on possible alterations/inhomogeneities in the dynamics of even larger regions (Structures "in" the Field, the structured Field).

This dynamic process, besides being, as mentioned, spatially non homogeneous (not symmetric with respect to pre-spatial directions), is also temporally non homogeneous (the pre-temporal distributions of these pulsations may display unevenness, becoming more or less rapid in correspondence with wider or narrower fluctuations).

In other words, within the complexity of the Field's chaotic dynamism at small scales, it is unthinkable that expansions and contractions should be symmetric, or that they should leave unaltered the shape of the infinitesimal regions we associate with event‑points. We therefore cannot imagine micro‑spheres of Field that preserve their shape during pulsation; instead, we must imagine multiform and variable regions, since these transformations occur under the pressure exerted by the Force on every infinitesimal point of the Field in the continuum, at infinitesimally small scales, far beyond the Planck scale, toward minus infinity.

The most elementary form of Energy—indeed, strictly speaking, we should call it "virtual or proto" Energy, given that its nature transcends any true concept of Energy (being essentially non relational)—we can conceive, even while stretching the very notion of Energy as hypothesized in this model (linked to the idea of Relation, of correlation between Events, between dynamic manifestations of the Field),is precisely what we may call "elementary deformation": the change in shape of event‑points, of the imaginary infinitesimal regions whose dynamics we wish to analyze ideally, a deformation that varies incessantly throughout the fluctuations, the hypothesized sub-elementary pulsations.

Since we are dealing with an elastic Field, at every instant we can imagine a different balance between potential Energy and effective or expressed Energy (Energy expressed in expansion or contraction), which we could ideally model as a random harmonic oscillator with a variable attractor (in terms of mean and variance, distribution profile, etc.).

To better represent the form of proto‑Energy that I refer to here as "sub‑elementary pre‑spatial", we must imagine what happens to the Elementary Field under the incessant Action of the Fundamental Force. The various inhomogeneities that arise constitute the different pre-spatial components of this form of proto‑Energy:

• the first sub-type of pre‑spatial inhomogeneity could be called "the existence of pre‑spatial fluctuations": the Force perturbs the homogeneous and static Field, producing sub‑elementary fluctuations;
• the second sub- type of pre‑spatial inhomogeneity could be called "the variation of pre‑spatial fluctuations": the fluctuations exhibit a chaotic, random dynamics in all elementary aspects (pre-spatial prevalence):
  • pre‑spatial "amplitude": distributed around a mean value with a given variance,
  • pre‑spatial "orientation": in all directions,
  • "chirality of vorticity": in both senses,
  • pre‑spatial "orientation of the vorticity axis": in all directions.

The aspect we must consider in relation to the Perturbation Mode is obviously the first on the list: the pre-spatial "amplitude" of fluctuations.

- Event-points complete perspective: second level of inhomogeneity, pre-temporal of pre-spatial (Level of Elementary Events – pre-temporal) -> Pre-Temporal Proto-Energy

Definition of the second form of proto‑Energy

• This form of Energy is inhomogeneity / deformation in the pre‑temporal distribution of the pulsation process.
• It concerns the temporal distribution of expansion–contraction of the volume associated with sub‑elementary fluctuations.
• It corresponds to the Perturbation Mode/Component of the Elementary Action.

First emergence of an embryonic form of relation

• At this level, a primitive form of relation appears for the first time.
• The relation links:
  • the amplitudes of pre‑spatial fluctuations,
  • and the pre‑temporal distributions associated with them.
• This relation is:
  • governed by the Uncertainty Principle,
  • yet stabilized by resonance phenomena around chaotic attractors.

Proto-Energy as asymmetry of pre‑temporal distributions

• Proto-Energy can be identified with the asymmetry / inhomogeneity / polarization of pre‑temporal distributions.
• When pre‑spatial amplitude and pre‑temporal duration are not uniformly distributed, the Field tends to restore homogeneity.
• This manifests as:
  • a re‑Action of the Field,
  • interpretable as a counter‑Force.

Non‑uniform spectral profile

• A non‑homogeneous pre‑temporal distribution implies a (pre-)temporal prevalence of certain pre‑spatial amplitudes.
• The temporal spectrum of amplitudes:
  • is not flat,
  • shows peaks and valleys,
  • may become highly complex.
• This complexity arises from:
  • the internal interaction between Force and the Field as expression of the Force,
  • the Field deformation produced by its non‑linear, non‑uniform resistance (its re‑Action).

Autocorrelation of Perturbation

• This form of Proto-Energy can be interpreted as:
  • an autocorrelation of the event‑point’s dynamics with itself,
  • specifically between:
    • the undeformed sub-elementary pre-spatial fluctuations,
    • and the deformed dynamism.
• It is therefore an internal autocorrelation of Perturbation within the event‑point.

A second form of Energy can be conceived as an inhomogeneity, discrepancy, deformation of the pre-temporal distribution of the pulsation process described above. It is associated with the deformation / inhomogeneity of the temporal distribution of the volume's expansion/contraction, which corresponds to the Elementary Action in the Mode/Component I call Perturbation.

Here too, we are dealing with a sui generis form of Energy (proto-Energy), one that nonetheless represents a bridge to the third form we will encounter shortly. At this stage, a form—albeit still embryonic—of relation appears for the first time. The pre-temporal distribution (from which the temporal dimension, Time, emerges) of the sub-elementary fluctuations, which in its most elementary expression focuses on the amplitudes of those pre-spatial fluctuations to which the corresponding pre-temporal distributions are associated, is a relation dominated by the Uncertainty Principle, yet "stabilized" by resonance phenomena around chaotic attractors that draw their pre-temporal evolution toward distributions sufficiently stable to constitute the foundation of Physical Reality, the substance of which the whole is made: the Elementary Action in its various Modes / Components.

In this context, Energy can be identified with the asymmetry / inhomogeneity / polarization of such pre-temporal distributions. If the pre-spatial amplitude and pre-temporal duration of the fluctuations are not uniformly distributed across the pre-temporal spectrum in terms of duration, the dynamics of the Field will tend to restore homogeneity. This tendency, which manifests itself as a reaction of the Field, can be viewed as a "counter‑Force" in Action (re-Action precisely) — a Force that may be interpreted as the expression of a system possessing Energy ("potential" in the phase in which the deformation, the inhomogeneity, is still present, stored in the deformation of the dynamism of the Field, and "effective or expressed" characterizing the reaction that tends toward the restoration of homogeneity).

Non homogeneity in the pre-temporal distributions means that a certain pre-temporal prevalence appears in the amplitude of pre-spatial fluctuations. That is, a greater number of fluctuations falls within a given amplitude interval—greater than what would occur in the case of a uniform (stable) distribution. The temporal spectrum of the pre-spatial amplitudes of sub-elementary fluctuations does not have a flat profile; instead, it shows peaks and valleys corresponding to specific amplitude intervals. This spectrum may take on highly complex forms due to the complexity of the internal interaction between Force and the Field expression of the Force (Action on the Field), and due to the manifestation of Field deformation caused by the non uniform and non linear resistance (the Field’s re Action).

In other words, let us imagine an oscillator (which has a random component and exhibits a chaotic attractor that draws its dynamics toward a mean value with a given variance, dependent on various internal and external factors) oscillating with an amplitude that falls within a sufficiently narrow range. If this range is most frequently positioned far from the "standard" point in the spectrum of possible oscillation amplitudes (standard for that type of oscillator), we may say that it possesses an Energy linked to the discrepancies between the two pre-temporal distributions. This is the form of Energy that we can identify in the context of the pre-temporal dynamics of event‑points.

This is a concept that can be associated with a kind of autocorrelation of the event‑point's dynamics with itself, between the dynamics of the undeformed elementary spatial fluctuations and the deformed dynamics, whatever their cause may be (which we will examine when discussing the Processes of structuring of the Elementary Field). A kind of autocorrelation of Perturbation within the event-point itself. To better represent the form of proto‑Energy that I call here "sub‑elementary pre‑temporal", we must again imagine what happens to the Elementary Field under the incessant Action of the Fundamental Force. The various inhomogeneities that arise constitute the pre‑temporal components of this form of proto‑Energy (which add to the two pre‑spatial inhomogeneities described in the previous point):

• the first sub-type of pre‑temporal inhomogeneity could be called "the existence of pre‑temporal distributions": the pre‑spatial fluctuations exhibit a variable pre‑temporal duration associated with their different amplitudes; these durations can be represented as pre‑temporal distributions, characterized by a density profile and by a proto‑energy spectrum;
• the second sub-type of pre‑temporal inhomogeneity could be called "the variation of pre‑temporal distributions": within the complex dynamism of the Field, in the incessant interaction of event‑points, the pre‑temporal distributions display chaotic, random variations in all elementary aspects (pre‑temporal prevalence):
  • pre‑spatial "amplitude": with a distribution of pre‑temporal prevalence around a mean value and with a given variance,
  • pre‑spatial "orientation": with pre‑temporal prevalence in certain directions,
  • "chirality of vorticity": with pre‑temporal prevalence in one of the two senses,
  • pre‑spatial "orientation of the vorticity axis": with pre‑temporal prevalence in certain directions.

Again, the aspect we must consider in relation to the Perturbation Mode is obviously the first on the list: pre-spatial "amplitude" of fluctuations.

- Event-point perspective compared with the Field: third level of inhomogeneity, discrepancies of pre-temporal of pre-spatial (Level of Elementary Action) -> Elementary Energy of the Unstructured Field (Pre-Spatial Pre-Temporal Proto-Energy)

Conceptual position of this level

• This level examines the discrepancy between the dynamism of the Field as manifested within an individual event-point and the average dynamism of the Field as a whole—whether understood as the infinite Universe or as a surrounding region vastly larger than the extension of the event-point itself.
• It is the event‑point–centric counterpart of the Field‑level correlations described in the next Level (Level of Information/Energy).
• Here, the focus is not on correlations among many event‑points, but on how a single event‑point performs compared to the average dynamism of the Field.

Discrepancies as pre‑temporal asymmetries

• Each event‑point is part of the fluctuating dynamism of the Elementary Field.
  • When an event-point exhibits non‑uniform pre‑temporal distributions of pre‑spatial, this manifests as:
    • local discrepancy,
    • temporal asymmetry,
    • deviation from its intrinsic fluctuation pattern.
• These discrepancies constitute a localized form of Perturbation, but now seen from within the event‑point, not from the Field's global perspective.

Event‑point response: Elementary Action as re‑balancing

• The surrounding event‑points react to these discrepancies through their intrinsic Elementary Action, which attempts to:
  • restore internal homogeneity,
  • re‑align pre‑temporal distribution in the inhomogeneous event-point,
  • reduce the mismatch between the inhomogeneous fluctuation patterns.
• This re‑balancing process is the event‑points‑level expression of the Field's re‑Action described in the previous levels.
• Thus, the event‑point perspective provides the microscopic foundation for the macroscopic phenomena of the Field.

Oscillator analogy

• Consider an oscillator:
  • with a random component,
  • attracted toward a mean value by a chaotic attractor with a given variance.
• If its amplitude most frequently falls within a range far from the standard amplitude for that oscillator, then:
• it possesses Elementary Energy,
• understood as the discrepancy between two temporal distributions (deformed vs. standard).

Therefore, the Elementary Energy I refer to here is a proto‑energetic bridge between the pre‑physical, conceptual, and abstract sub‑elementary domain—used to describe and visualize how the Field's dynamism is incessantly generated by the expression of Force—and the progressive emergence of more articulated structures capable of sustaining Physical Reality in its full complexity. Elementary Energy is the proto energetic form corresponding to Elementary Action. From its manifestation, and from the organization of the correlations among the inhomogeneities of the dynamism expressed at each event-point, arises the physical Information/Energy that underlies the Fundamental Physical Quantities characterizing the InfoStructures that emerge from such organization.

At this level of Reality—within the causal and variational depths where the complexity of the world we inhabit is incessantly "manufactured", at the level of Elementary Action—the proto energetic perspective I am trying to explore hinges on what I call here discrepancy. Internal discrepancy for the two pre-spatial and pre-temporal sub-levels, and external discrepancy for the sub-Level of Elementary Energy, which is the one I am discussing now.

In this context, I am using the term discrepancy in the sense of the distance between the value taken by a variable and a standard reference value—or, since we are not dealing with a static context, the distance between a dynamic flow of values (scalar, vectorial, spinorial, etc.) and a reference flow taken as the standard. This distance, which may take on highly complex characteristics, can indeed be expressed through a discrepancy index (internal or external).

Consider a homogeneous gas that exhibits a different temperature in one of its regions (a temperature gradient). In terms of the Modes of Elementary Action, we can say that Perturbation is manifesting.

Or think of a landscape swept by the wind, where one area shows a wind direction different from that of the rest of the region under consideration. Here we would have Translation (with respect to the direction we take as the standard reference).

And again, imagine a fluid exhibiting left handed chiral vorticity, within which—due to some phenomenon—a volume displays right handed chiral vorticity. In this case, in terms of the Components of EA, we would have Rotation:Chirality being non zero.

Finally, imagine a Bose–Einstein condensate in which all atoms have their spin aligned along the vertical up down direction. Suppose that in a region of the condensate a vortex forms, forcing the atoms within it to orient their spin along the horizontal right left direction. Here, we would have the manifestation of the Rotation:AxisOrientation Component.

While for the two subtypes of proto energy the reference is internal (the sequence of spatial fluctuations, the evolution of the pre-temporal distributions of those fluctuations, always referred to the same single event-point), here, in the case of Elementary Energy, the reference used to evaluate discrepancy is external. It is the first time this occurs. A first hint of a relational aspect—one that will become central at the Reality level of Information / Energy. Physical energy, whereas here we are still at a level in which all dynamics, Action, and Energy (proto energy, precisely) do not yet represent physical entities, phenomena, or processes. We are still in an abstract, conceptual, pre-physical domain, so to speak, which is necessary for describing unobservable processes that are nevertheless crucial for understanding how Reality forms and what its Fundamental Nature is. Unobservable—or rather, observable only indirectly and with great difficulty—through "exotic" physical phenomena that lie at the frontier of current research.

If for the first two subtypes of proto energy we speak of self referential discrepancies (self correlation?), and if at the level of Information / Energy we will speak of correlations between the dynamics of different sets of event-points of the Field, here, for Elementary Energy, we are in an intermediate zone where, as mentioned, the relational aspect appears for the first time, albeit in embryonic form. This leads us to compare and evaluate discrepancies between the dynamics of a single event-point and a reference dynamics (the "average" or standard dynamics of the entire infinite Elementary Field, or the average dynamics of a region significantly larger than the event-point under consideration).

Thus we may say that that event-point manifests a null, positive, or negative value of Perturbation if the pre-temporal distribution of the Field's pre-spatial fluctuations amplitudes at that point shows a null, positive, or negative discrepancy with respect to the "average" pre-temporal distributions of the entire Field, or of a significantly large region of it that includes the event-point in question. I have placed "average" in quotation marks because the average represents an extremely synthetic and "rudimentary" discrepancy index. I believe it is necessary to construct more sophisticated discrepancy indices capable of capturing and representing the complexity of the Field's sub-elementary dynamism—indices that take into account the dispersion and shape of the distributions, variance, skewness, and so on.

Naturally, here we are speaking of Perturbation, and therefore the aspect of sub-elementary dynamism we take into account is the amplitude of the fluctuations. Of course, the same reasoning also applies to the other aspects (orientation, chirality, and axis orientation of vorticity) that underlie Translation and Rotation in its two sub-Components, as we will see below and in the following section.

- Regions of the Field perspective, sets of more than one event-point: fourth level of inhomogeneity, spatial correlations between pre-temporal distributions of pre-spatial fluctuations (Level of Information / Energy) -> Information / Energy -> Fundamental Physical Quantities: Metric (the pre-spatial dimension becomes the physical Space, and the pre-temporal one becomes the physical Time) / Mass, Motion, Charge and Spin, and other more complex physical quantities

Emergence of the first genuine form of Energy (Information)

• At this level, we encounter the first true form of Energy, understood as an elementary form of Information within the physical domain.
• It appears through the correlations among the pre‑spatial and pre‑temporal dynamism of multiple event‑points within a region of the Elementary Field.
• Conceptually, we can “freeze” the temporal flow and observe a snapshot of correlations among the sub-elementary Processes that constitute the dynamism of event‑points of the Field.

Perturbation correlations and the dual perspective: Metric vs. Mass

• When we analyze the Field in terms of Perturbation correlations (i.e., discrepances in the pre‑temporal distributions of prevailing amplitudes of sub‑elementary pre‑spatial fluctuations), two complementary perspectives emerge:
  • From the perspective of the Field itself:
    • we observe Metric, including its possible deformations — the curvature of Space‑time.
  • From the perspective of InfoStructures within the Field:
    • we observe Mass, specifically mass density.
  • These are different viewpoints on the same underlying Phenomenon, revealing the deep interconnection between Metric curvature and Mass — the very link expressed in General Relativity.

A necessary clarification is in order at this point. Tendentially, if we observe the Field, we may imagine the spatial distribution and temporal evolution of the correlations between the tau distributions of sigma fluctuations. We will hardly see patterns characterized by significant order, by a coherent organization that we could associate with a recognizable form (a wave, a particle, a dark halo, etc.). More likely, we would see patterns marked by pronounced random components, which we may picture as turbulence (in the dynamism) of the Field across a very broad spectrum of dimensional scales.

By contrast, if we observe—or rather, imagine observing—InfoStructures within the Field, we will see recognizable patterns, although incessantly deformed by the random component and, above all, by their mutual interactions, which accentuate their "polydynamism". Patterns that we may associate with Structures belonging to the types Waves, Vortices, Interactions (from which composite Structures emerge, such as hadrons, or—within the dark sector—as the composite halos of the Dark Cosmic Web). And for each type, we may observe variants such as the subtypes single cycle or multiple cycle, which characterize Waves and which, in the ordinary sector, we may associate respectively with photons and electromagnetic waves (objects that share the same nature but exhibit different forms).

Phenomenic identity and phenomenic induction

• The classical statement (not correct in my opinion) "Matter tells Space‑time how to curve, and Space‑time tells Matter how to move" conceals two deeper layers:
  • Phenomenic identity (centered on Perturbation)
    • Metric curvature and Mass are two expressions of the same underlying Perturbation correlations.
  • Phenomenic induction (centered on Translation)
    • Perturbation triggers the Field’s re‑Action, whose dynamics organize themselves into Translation correlations.
    • In terms of Fundamental Physical Quantities, Translation correlations manifest as:
      • Motion “of” the Field (potential Motion) -> observed as gravitational acceleration,
      • Motion of InfoStructures “in” the Field (effective Motion) -> observed as inertia.
• Thus, gravitational and inertial Phenomena arise from the same underlying induction process.

Matter (Mass) and the curvature of the Metric (Space time) are the same thing—or rather, Mass is instantiated as a curvature of the Metric with a specific form. Mass and curvature share the same nature when observed from the standpoint of Elementary Action and of the organizational schemes of the spatial correlations of the tau distributions.

Connection between Perturbation and Translation

• At the level of event‑points, this connection is hypothesized as follows:
  • Inhomogeneities in the pre‑temporal distributions of amplitudes of Elementary Events
    • -> trigger the Field's re‑Action,
    • ->which produces inhomogeneities in the pre‑temporal distributions of orientations of the pre‑spatial fluctuations.
• This marks a transition from amplitude‑based Perturbation to orientation‑based Translation, establishing the bridge between the two Modes/Components of Elementary Action.

A first genuine form of Energy (always understood as an elementary form of Information within the physical domain of Reality) is found at this level, where we can observe the emergence—the presence—of correlations among the pre-spatial and pre-temporal dynamism of a set of event‑points, which we may ideally identify/observe/analyze within a region, however tiny, of the Elementary Field. Here we can ideally interrupt the temporal flow and "take a snapshot" of the pattern of correlations among the Processes that characterize the dynamism of event‑points.

When we look at the Elementary Field from the standpoint of Perturbation correlations (a synthetic term I use to identify the inhomogeneities, or discrepances, in the pre-temporal distributions of the (prevailing) amplitudes of sub-elementary pre-spatial fluctuations at the level of the Field's event‑points), observing from the point of view of the Field itself, we see the Metric, with the possible deformations we can call the curvature of Space‑time. Observing the same phenomenon from the point of view of InfoStructures within the Field, we see Mass, Mass density. Different perspectives on the same Phenomenon, revealing Fundamental Physical Quantities that are deeply interconnected. This is why Metric curvature and Mass are so tightly linked in General Relativity.

Indeed, the statement that Matter tells Space‑time how to curve and Space‑time tells Matter how to move conceals a phenomenic identity centered on the concept of Perturbation (Metric curvature and Mass) and a phenomenic induction centered on the concept of Translation (Perturbation triggering the Field's re‑Action, whose dynamics organize themselves by manifesting Translation correlation, which—in terms of the Fundamental Physical Quantities—means Motion: Motion in the dynamism of the Field, which we observe as gravitational acceleration, and Motion in the dynamics of InfoStructures within the Field, which we observe as inertia).

And thus we encounter one of the points of connection between Perturbation and Translation, which—at the level of event‑points—we hypothesize as the Field's re‑Action to the inhomogeneities in the pre-temporal distributions of the amplitudes of Elementary Events, producing inhomogeneities in the pre-temporal distributions of the orientations of the pre-spatial fluctuations, those same Elementary Events.

Translation

Let us now take up what we have just said regarding Perturbation and try to reformulate it for Translation, focusing not on the amplitude of the spatial fluctuations but on their (prevailing) spatial orientation.

- Event-points partial perspective: first level of inhomogeneity, purely pre-spatial (Level of Elementary Events – pre-spatial) -> Pre-Spatial Proto-Energy

Let us first consider the event-point perspective, and only from the pre-spatial point of view—or rather, from what will emerge, through the dynamics of the Elementary Field, as the "Translation" Component of the Elementary Action, the root of Motion and kinetic Phenomena. Imagine an infinitesimal volume that expands and is then pushed to contract and return to the "standard" extension of the infinitesimal volume we have placed under observation—or even to contract below its "normal" extension due to the Field's reaction to expansion (a reaction caused by the expansion of the event-points in the surrounding regions, under the incessant pressure of the Fundamental Force).

A kind of pulsation produced by the Action of the Force upon the Field and by the Field's reaction, which expresses a counter‑force. In both the phase of expansion and that of the subsequent contraction, Action and re‑Action manifest themselves in the form of Translation: a (re)orientation of the directional pattern of sub-elementary pre-spatial fluctuations, which becomes predominant in the pre-temporal distribution of those fluctuations.

The alteration/inhomogeneity in the pre-temporal distribution of the pre-spatial orientation of fluctuations — a local variation in the dynamics of the Elementary Field — can be understood as Propagation, as Action propagating through the Field, aimed at restoring its homogeneity.

It is not guaranteed that Translation cancels the inhomogeneity, for example that of Perturbation. The event‑point toward which the propagation is directed may, in the meantime, have acquired a different configuration of the pre-temporal distribution, and thus Perturbation may have already vanished. What matters, however, is that the propagation event — which we conceive as an inhomogeneity in the pre-temporal distribution of the orientation of pre-spatial fluctuations, therefore as Translation — has occurred. Its manifestation, if the Field conditions along the trajectory are favorable, may continue to express itself, since the Field is conservative, unless destructive or modifying interactions arise with other dynamics manifesting along the trajectory (in other words, unless forces act upon the Translation as it is being expressed).

Translation, precisely because of its nature as an Action (or a re-Action) that propagates — the root of Motion — generally manifests itself in asymmetric, directional, anisotropic terms. Just as we have seen for Perturbation, the inhomogeneities in the pre-temporal distributions of the amplitudes of pre-spatial fluctuations, due to the chaotic dynamism of the Field, imply that pre-spatial symmetry must be regarded as an exception, and never a perfect one. Thus, the pre-spatial orientation of the fluctuations we refer to in the context of Translation is the result of the composition of many different and virtually infinite components along the various pre-spatial directions (the same principle as the composition of forces, velocities, or vector quantities in general). We must therefore think in terms of the prevailing orientation, and it is in these terms that the pre- temporal distributions are to be understood.

We will later see that Translation does not arise only within the dynamics of Perturbation, but also within that of Rotation. Translation is the root of Motion not only for Mass propagating through the Field, but also for Chirality and for the Orientation of the Chirality Axis — corresponding, respectively, to electric potential and magnetic potential from the point of view of the Field, and respectively Charge and Spin from the point of view of InfoStructures within the Field. But we will address this in the next section, dedicated to Rotation in its two sub‑Modes / sub‑Components.

Even for Translation, if we consider only the orientation of the sub-elementary pre-spatial fluctuations and not their pre-temporal distributions, we may regard the most elementary form of Energy—which, strictly speaking, we should call "virtual or proto" Energy—as an "elementary deformation": the change in pre-spatial orientation of the expansive-contractive dynamics of event‑points, of the imaginary infinitesimal volumes whose dynamics we ideally wish to analyse. A deformation that varies incessantly within the fluctuations, the elementary pulsations.

Here too, we can distinguish between potential proto-Energy (the characteristic proto-Energy of each instant of the expanded and contracted state—altered, inhomogeneous, deformed in any case) and the proto-Energy expressed in the process of expansion and contraction (which we may refer to as effective proto-Energy).

- Event-points complete perspective: second level of inhomogeneity, pre-temporal of pre-spatial (Level of Elementary Events – pre-temporal) -> Pre-Temporal Proto-Energy

Symmetrically to what was stated for the Perturbation Mode, here too we can identify a second form of Energy. It can be conceived as a deformation / inhomogeneity in the pre-temporal distribution of the pre-spatial orientation of pulsation process described above, which corresponds to the Elementary Action in the Mode/Component I call Translation.

Here too, we are dealing with a sui generis form of Energy, one that nonetheless represents a bridge to the third form we will encounter shortly. At this stage, a form—albeit still embryonic—of relation appears for the first time. The pre-temporal distribution (or rather, in what will emerge as the temporal dimension) of the elementary fluctuations, which in this expression focuses on the prevailing pre-spatial orientation of those pre-spatial fluctuations to which the corresponding pre-temporal amplitudes are associated, is a relation dominated by the Principle of Action and Reaction, Action of the Force and re-Action of the Field.

In this context, Energy can be identified with the asymmetry / inhomogeneity / polarization of such pre-temporal distributions. If the pre-spatial amplitude and pre-temporal duration of the fluctuations are not uniformly distributed across the pre-temporal spectrum in terms of duration, the dynamics of the Field will tend to restore homogeneity. This tendency, which manifests itself as a re‑Action of the Field, can be viewed as a "counter‑Force" in Action — a Force that may be interpreted as the expression of a system possessing Energy ("potential" in the phase in which the deformation, the inhomogeneity, is still present, and "effective or expressed" characterizing the reaction that tends toward the restoration of homogeneity).

This dynamic within an event‑point—namely, a pre-temporal prevalence of expansion—will induce in the adjacent event‑points a reactive dynamic aimed at containing and compressing the behavior of the first event‑point. This can be interpreted as a propagation dynamic, a form of translation, which stands in opposition to the Translation expressed in the expansive dynamic. A symmetric situation occurs for event‑points that exhibit a pre-temporal prevalence of contraction phases as a consequence of the expansion of surrounding event‑points.

In other words, let us imagine an oscillator (which has a random component and exhibits a chaotic attractor that draws its dynamic amplitude toward a mean value with a given variance, dependent on various internal and external factors) oscillating in absolutely random directions. If this range, for most of the Time, is positioned far from the "standard" point (perfect randomness) in the spectrum of possible oscillation orientations (standard for that type of oscillator for that event-point), we may say that it possesses an Energy linked to the discrepancies between the two pre-temporal distributions (always relative to a single event-point). This is the form of Energy that we can identify in the context of the pre-temporal dynamics of event‑points.

This applies to Perturbation, as we have seen above and recalled here. But it also applies to Translation. What changes is the object of the pre-temporal distributions. For Perturbation, the relevant quantities are the amplitudes of the elementary pre-spatial fluctuations—that is, of the Elementary Events. For Translation, instead, the relevant quantities are the orientations of those pre- spatial fluctuations.

At the level of each event‑point, when the pre-temporal distribution shows a prevalence of fluctuation amplitudes above what we may regard as a "standard" value, we observe that the event‑point's dynamic process enters an expansive phase, with Translation predominantly oriented toward the surrounding event‑points that, in the same time, exhibit less expansive phases. As mentioned, this is not an expansion with a uniform spherical profile, but rather a generally and plausibly asymmetric expansion, with a pre-spatial profile that varies depending on the dynamics of the surrounding event‑points.

When we speak of the second form of Energy—associated with the phenomenology of event‑points from a complete perspective, namely the pre-temporal distributions of pre-spatial fluctuations—what matters are precisely the pre-temporal distributions, the pre-temporal prevalence of the Elementary Field's dynamics at a given event‑point.

This concept can be associated with a kind of autocorrelation of the event‑point's dynamics with itself—between the dynamics of the undeformed elementary pre-spatial fluctuations and their deformed counterparts—considered from the standpoint of propagation, whatever their origin may be (a topic we will address when discussing the Processes that structure the Elementary Field). It is, in this sense, a kind of autocorrelation of Translation within itself, directed both toward and from the surrounding event‑points.

This is the root of all propagation dynamics, the root of Motion itself, which fully manifests at the level of the correlations between analogous dynamics expressed by sets of event‑points within regions of the Elementary Field (fourth level of inhomogeneity).

- Event-point perspective compared with the Field: third level of inhomogeneity, discrepancies of pre-temporal of pre-spatial (Level of Elementary Action) -> Elementary Energy of the Unstructured Field (Pre-Spatial Pre-Temporal Proto-Energy)

As already mentioned a moment ago with regard to Perturbation, this level examines the discrepancy between the dynamism of the Field as manifested within an individual event-point and the average dynamism of the Field as a whole—the infinite Universe or as a surrounding region vastly larger than the extension of the event-point itself. It is the event‑point–centric counterpart of the Field‑level correlations described in the next Level (Level of Information/Energy). Here, the focus is not on correlations among many event‑points, but on how a single event‑point performs compared to the average dynamism of the Field.

Discrepancies can be considered as pre‑temporal asymmetries. Each event‑point is part of the fluctuating dynamism of the Elementary Field. When an event-point exhibits non‑uniform pre‑temporal distributions of the orientation of pre‑spatial fluctuations, this manifests as local discrepancy, temporal asymmetry, deviation from its intrinsic fluctuation pattern. These discrepancies constitute a localized form of Translation, but now seen from within the event‑point, not from the Field's (global) perspective.

From the point of view of the event‑point response, Elementary Action in its Mode Translation appears as a re‑balancing re-Action of the Field. The surrounding event‑points react to the discrepancies through their intrinsic Elementary Action, which attempts to restore internal homogeneity, re‑align pre‑temporal distribution in the inhomogeneous event-point, reduce the mismatch between the inhomogeneous fluctuation patterns. This re‑balancing process is the event‑points‑level expression of the Field's re‑Action described in the previous levels. Thus, the event‑point perspective provides the microscopic foundation for the macroscopic phenomena of the Field.

Again, returning to the oscillator analogy, consider an oscillator with a random component, attracted toward a mean value by a chaotic attractor with a given variance. If the orientation of its pre-spatial fluctuations most frequently falls within a specific range of directions, then we can say that it possesses Elementary Energy, understood as the discrepancy between two temporal distributions (deformed vs. standard, the latter assumed to be homogeneous in orientation).

Elementary Energy is always intended as a proto energetic bridge between the pre-physical, conceptual and abstract, sub-elementary domain that I use to describe and visualize how the dynamism of the Field is incessantly generated by the expression of the Force, and more articulated forms capable of supporting the emergence of Physical Reality in its full complexity. A proto energetic form corresponding to Elementary Action.

Thus we may say that an event-point manifests a null, positive, or negative value of Translation if the pre-temporal distribution of the orientation of the Field's pre-spatial fluctuations at that point exhibits a null, positive (same direction), or negative (opposite direction) discrepancy:

• with respect to the "homogeneous" pre-temporal distributions of randomly oriented pre-spatial fluctuations -> absolute Motion (with respect of the unstructured Field)
• with respect to the "average" pre-temporal distributions of the entire Field, or of a sufficiently large region of it that includes the event-point in question -> relative Motion (with respect to Structures in the Field)

As already said, the mean provides only an extremely synthetic and "rudimentary" discrepancy index. It may therefore be preferable to construct more sophisticated discrepancy indices.

- Regions of the Field perspective, sets of more than one event-point: fourth level of inhomogeneity, spatial correlations between pre-temporal distributions of pre-spatial fluctuations (Level of Information / Energy) -> Information / Energy -> Fundamental Physical Quantities: Metric (the pre-spatial dimension becomes the physical Space, and the pre-temporal one becomes the physical Time) / Mass, Motion, Charge and Spin, and other more complex physical quantities

A first genuine form of Energy, where we can observe the emergence—the presence—of correlations among the pre-spatial and pre-temporal dynamics of a set of event‑points, which we may ideally identify/observe/analyze within a region, however tiny, of the Elementary Field. Here we can ideally interrupt the pre-temporal flow and "take a snapshot" of the pattern of correlations among the Processes that characterize the dynamics of event‑points.

When we look at the Elementary Field from the standpoint of the correlations of Translation (a synthetic term I use to identify the inhomogeneities in the pre-temporal distributions of the (prevailing) pre-spatial orientation of elementary pre-spatial fluctuations at the level of the Field's event‑points), observing from the point of view of the Field itself, we see "potential" Motion, in the form of potential Motion, a potential for acceleration, which in its most familiar expression can be identified as gravitational potential energy. If we combine Action in the two Modes—Perturbation and Translation (at the level of Information / Energy, the two Fundamental Physical Quantities, Mass and Motion)—we obtain precisely the gravitational potential Energy, a form of potential Energy.

Observing the same phenomenon from the point of view of InfoStructures within the Field, we see "effective" Motion, inertial Motion, inertia. In this case, if we combine Action in the two Modes Perturbation and Translation (at the level of Information / Energy, the two Fundamental Physical Quantities, Mass and Motion), we obtain kinetic Energy, a form of effective Energy. Different perspectives on the same phenomenon, revealing Fundamental Physical Quantities that are deeply interconnected. This is why Metric curvature, Mass and Motion are so tightly linked in General Relativity.

In other words, the correlation of Translation in a portion of the Field defines its Elementary Energy structured in the component Translation, which we call Motion, in its two aspects: potential (acceleration) and effective (inertia).

Motion is the organized manifestation of Translation: inertia as persistence of correlated orientations, acceleration as intensification of those correlations, as an effect of the interaction between the Translation structured within an InfoStructure (effective Energy / Information) and the Translation structured in the Field (potential Energy / Information, generated by other InfoStructures or by other Phenomena) in the region through which the InfoStructure is propagating at each moment in Time. Translation is therefore the energetic substrate of kinetic Phenomena, the bridge between variational perturbative inhomogeneities in the dynamics of the Field and macroscopic Motion.

I will return to these themes in the next chapter, when I discuss Information / Energy, and in particular the Energy “of” the Field and the Energy “in” the Structured Field.

Formulation in vector calculus

As seen, Translation can be understood as an inhomogeneity in tau-distributions of orientations of sigma‑fluctuations. In vector calculus, such inhomogeneities in a vector field are captured by the divergence operator, which quantifies how much a vector field spreads out (positive divergence) or converges (negative divergence) from a point, acting respectively as a source or a sink—the net flow of a vector field out of an infinitesimal volume. Here I am referring specifically to the divergence operator (DIV). In this model, divergence denotes any propagation of gradients (inhomogeneities of amplitude, and/or orientation, and/of vorticity, in the tau-distributions of sub-elementary sigma-fluctuations) in the dynamics of the Elementary Field along a direction.

Resuming the analogy of a scalar field representing temperature, a positive divergence of the heat flux corresponds to a heat source (heat spreading out), while a negative divergence corresponds to a heat sink (heat concentrating). This is tightly linked to the underlying dynamics of molecular motions, as in a gas: a dynamics built upon a deeper dynamics. More precisely, it is the vector dynamics (divergence) of an underlying synthetic scalar representation (temperature gradient) of a vector dynamics (molecular velocities).

Within the Elementary Field, Translation corresponds to the propagation of perturbative gradients (Perturbation) and vorticity/curl (Rotation in its two sub-Modes), the directed spreading of dynamical inhomogeneities.

It is a secondary Mode / Component of the manifestation of the Elementary Action. Elementary divergences arise from the reaction of the Elementary Field to the deformations produced by the Action of the Fundamental Force on the Elementary Field itself.

At more complex levels, divergences emerge from the reaction to the variations/deformations of the Derived Acted / Fields under the Action of Derived Agents / Forces.

The phenomenological perspective

Translation manifests phenomenologically through inertia, acceleration, and gravity.

I will now summarize only what has already been stated above regarding these important topics, and on this occasion I will provide a concise representation of Newton's laws of motion in the terms of the Dynamics of Elementary Action:

• Inertia is the presence of correlations of Translation within the dynamics of an InfoStructure, the persistence (pre-temporal distributions) of correlated orientations of pre-spatial fluctuations -> effective Motion, inertial Motion, kinetic Energy.
• Acceleration is:
  • the presence of correlations of Translation in the organization of the dynamism of the Field -> potential Motion, potential Energy.
  • the variation (increase or change) of correlations of Translation within the dynamics of an InfoStructure, the increase or change (variation of pre-temporal distributions) of correlated orientations of pre-spatial fluctuations, as a result of the interaction of correlations of Translation “of” the Field (potential Motion) with the existing correlations of Translation of an InfoStructure “in” the Field (effective Motion) -> variation of effective Motion, accelerated Motion, variation of kinetic Energy.
• Gravity emerges as the combined expression of Perturbation (Metric/Mass) as causal origin and Translation (Motion: acceleration/inertia) as variational manifestation: gradients of Perturbation produce non‑zero values of Translation in surrounding regions, which we observe as attraction or repulsion (depending on the sign), accelerated Motion, and gravitational Phenomena.

Thus, Translation should not be understood merely as the Propagation of Perturbation, but the very mechanism through which Motion and the gravitational dynamics arise.

It is the divergence orientations of the sub-elementary pre-spatial fluctuations, the directed flow that sustains the dynamism of Space.

Inertia (no acceleration)

Inertia is commonly defined as the resistance of any physical object to any change in its velocity (speed and direction of motion). Inertia can be seen as resistance to acceleration, and acceleration as change of a state of inertia.

In this model, inertia is the manifestation of the presence of Translation within the dynamics of the region of the Elementary Field that includes all the event‑points whose moment by moment dynamics support an InfoStructure, or a Form/object composed of multiple InfoStructures.

If, in the same region of the Elementary Field through which the Structure is propagating, there exists no Translation other than (independent of) the one sustaining the propagation of the Structure itself (its inertial Motion), we observe that objects propagate with uniform rectilinear motion — or, more precisely, with "inertial motion".

If independent Translation is present, the Motion is accelerated, due to the interaction between the Translation “of” the Field (potential Motion, acceleration) and the Translation of the InfoStructure propagating “within” the region of the Field that manifests potential Motion

What does "presence of Translation" or a non null value of Translation means? It means that the correlation of the Elementary Action, in the Mode I call Translation, is greater that zero.

In other word, in more detail, with reference to the Elementary Events (sigma-fluctuations) it means that we are in presence of some form and quantity of organization of the correlations among the inhomogeneities of the tau-distributions of the pre-spatial orientation of the sigma-fluctuations. The more intense the correlations of the orientation of the sigma-fluctuations, the greater the inertial velocity. The stronger the increase in those correlations (due to the continuous interaction with the independent Translation), the greater the acceleration.

Acceleration

Acceleration is commonly defined as the rate of change of velocity (magnitude and direction) with respect to time; inertia can be seen as resistance to acceleration, and acceleration as the modification of a state of inertia.

As already illustrated in the previous point, in the language of this model, acceleration is the manifestation of Translation present in the dynamics of the region of the Elementary Field that interacts with the Translation sustaining an InfoStructure (or a Form/object composed of multiple InfoStructures), in the region of the Field where the Structure/object is at rest (the value of Translation "of" the Structure/object is zero) or in motion (Translation in the Structure/object is non null). When, in the same region of the Field through which a Structure propagates, there exists a Translation independent of the one that sustains the Structure, the interaction between these two Translations produces an increase in the organization of correlations among the orientations of the underlying pre-spatial fluctuations: this increase in correlated orientation at the event‑point level is what we identify as acceleration.

Put operationally, acceleration occurs when the Translation associated with the Structure interact/combines with the Translation of the surrounding Field, thereby raising the amount of Elementary Action in the Mode called Translation within the event‑points that support the Structure.

This means that the orientation of pre‑spatial fluctuations is not entirely random, but that for a non‑uniform amount of time a certain direction becomes prevalent. The intensity of this prevalence (that is, the intensity of the correlation of the inhomogeneities in the pre‑temporal distributions of the fluctuations) determines—if we observe the InfoStructures in Motion—the inertial velocity; or—if we observe the Field—the intensity of the potential Motion, of the acceleration potential (the gravitational potential if we observe the Field from the viewpoint of Perturbation, of the Metric, and therefore of gravitational phenomena) of the Field itself in the region under observation.

At the level of the Elementary Events (sub-Elementary dynamics, or micro-dynamics), this corresponds to a growth in the organization of correlations among the inhomogeneities of the tau‑distributions of orientation of pre-spatial fluctuations; the stronger the correlation of the independent Translation of the Field, the stronger the induced increase in these correlations that produce the propagation of the InfoStructures in the Field and the greater the acceleration.

The magnitude of acquired Translation — and thus of acceleration — is proportional to:

• the spatial distribution of Perturbation in the Field (quantities and distances), and therefore to the spatial distribution of Mass densities in Space‑time,
• to the configuration of the Metric Field, or by the Principle of General Equivalence:
  • to the local curvature of Space‑time,
  • to the local limits on Causality / Action / Information propagation speed (c),
  • to the local field temperature, and analogous local field parameters.

In symmetric terms with inertia: inertia denotes the presence of Translation that sustains propagation and, in the absence of independent Translation, yields inertial (geodesic) Motion; acceleration denotes the presence of an independent Translation whose interaction with the Structure's Translation increases orientational correlations of the distributions of the fluctuations and produces non‑inertial, accelerated motion.

Gravity

Gravity is commonly described as the natural phenomenon produced by Mass (and Energy) and by the dynamics of massive bodies.

In the language of this model, Perturbation is the causal origin of gravity while Translation is its variational expression: gravity is the joint manifestation of the Elementary Action Modes I call Perturbation and Translation.

Perturbation represents the causal and variational root of the Mass of (Vortex type) InfoStructures (local, persistent deformations of the Field expressed as correlations of the inhomogeneities in the tau‑distributions of sigma‑fluctuations), as well as the curvature of the Metric of the Field (in fact, the curvature of Time). The first (that of InfoStructures) can be seen as the "effective" form of Metric (Time) curvature, correlation of (dependent) Perturbation of InfoStructures "in" the Field. The second (deformation of the unstructured Field), its potential form, correlation of independent Perturbation "of" the Field.

Translation represents the causal and variational root of Motion (organized correlations of the inhomogeneities/discrepancies in the tau-distributions of the orientations of sigma-fluctuations), both at the level of the Field (potential Motion: acceleration) and at the level of InfoStructures (effective Motion: inertia).

Spatial gradients, inhomogeneities of Perturbation — what we conventionally read as Space‑time curvature — induce the dynamics of the event-points of the surrounding regions of the Elementary Field to reorganize: surrounding event‑points acquire non‑zero values of Translation as a reactive re‑adjustment of the Field. These induced Translations are the local, point‑by‑point expressions that produce the attraction between massive Structures or bodies, which we see as accelerated motion of those Structures and bodies within the Field.

Ontologically, then, gravity is not an external force acting on passive Matter but the emergent co‑expression of (i) a perturbative deformation that grounds Mass and (ii) the Field's variational response in Translation that grounds Motion; quantitatively, the magnitude and direction of the induced Translation (hence the observed acceleration) correlate with the spatial distribution of Perturbation (Mass density/distribution, metric configuration, local curvature, local limits on Information propagation, field temperature, etc.), so that Newtonian and relativistic gravitational behavior appear as higher‑level manifestations of this sub‑elementary Perturbation–Translation dynamics.

In this context, within the domain of gravitational Phenomena, it is the very concept of force that we must reconsider. Retracing the history of physics, we can make a few observations from an ontological, phenomenological, and dynamical point of view.

In classical Newtonian physics, gravity results from an instantaneous force (onto) that attracts (pheno) material bodies, thereby determining gravitational dynamics (dyna).

With General Relativity, everything changes. There is no force: the curvature of Spacetime becomes the structural framework within which gravitational phenomena arise. Objects are not pulled by a mysterious interaction; they move through spacetime by following its natural geodesic structure.

To the Newtonian and General Relativistic descriptions, additional theoretical approaches can be added, each offering a distinct ontological, phenomenological, and dynamical perspective on gravitational phenomena. Among these:

• Linearized gravity, where gravity is treated as a classical tensor field propagating on a nearly flat background.
• Quantum Field Theory approaches, in which gravity is mediated by a hypothetical spin‑2 quantum, the graviton.
• Semiclassical gravity, where quantum matter interacts with a classical spacetime geometry.
• Quantum gravity programs, proposing a discrete, emergent, or string‑based structure of spacetime at the fundamental level.

In the model proposed here, gravity is a Phenomenon that—if it is to be understood in its ontological, phenomenological, and dynamical dimensions—must be situated within the multilayered structure of Reality.

In addition to examining the macro level (Information / Energy, Fundamental Physical Quantities → correlations among the inhomogeneities of the τ distributions of σ fluctuations), one must progressively descend to the level of Elementary Action, to the Modes / Components through which it manifests—most notably Perturbation and Translation, as previously discussed (the inhomogeneities of the τ distributions).

From there, the analysis must extend further, reaching the sub-elementary, pre-physical, proto energetic domain of pre-temporal distributions and pre-spatial fluctuations. It is at this level—at extremely small, sub‑micro scales, near the Planck scale and beyond—that the incessant interaction between the Fundamental Force and the Elementary Field generates the dynamism from whose organization the Derived Entities emerge: the derived Forces and Fields (including the force that expresses gravity and the gravitational field that manifests it), the gravitational Phenomena (observed as attraction/repulsion between masses), and the resulting gravitational dynamics (the influence of gravitation on the motion of massive and non massive InfoStructures, Vortices, and Waves, and on all the Forms arising from their aggregation and organization).

In this model, from an ontological perspective, the Fundamental Force and all Derived Forces play a central role in the Creation of everything that exists and in the Evolution its Essence / Form, just as the Elementary Field and all Derived Fields do—two complementary aspects of the unitary Derived Sources that arise from the Primary Source. In my view, Forces and Fields are fundamental Entities (in fact, sub-Entities of Sources): everything emerges from their expression and manifestation.

Every derived Source, every Force / Field pair and every product of their interaction, every Action, Information / Energy, Structure of Information, every object, system, and Form—the entire Universe—"borrows" its Existence from the original Existence of the Primary Source of Reality, assuming the infinitely diverse Properties, Behaviors, and Forms that we observe in Nature.

In this model, my intention is not to dispute the validity of established physical theories, but to articulate an alternative ontological and phenomenological framework. From this perspective, I do not consider it sufficient to describe gravitational phenomena solely in terms of fields or field deformations, as done in General Relativity. Rather, I maintain that the concept of Force—understood in the specific sense defined within this system—retains an essential explanatory role.

This position does not rely on the Newtonian notion of force, from which we must distance ourselves completely (instantaneous action at a distance, direct mechanical push–pull, etc.). Instead, the term Force here designates a more fundamental Agent or Cause, one that produces variations and deformations in a Field and participates in the emergence of structures and dynamics. I have previously clarified how this concept of Force differs from its classical formulation and how it functions within the architecture of this model.

Within this ontological framework, Forces and Fields are treated as complementary expressions of deeper Sources, and their interaction is considered foundational for the emergence of Phenomena, including those that physics describes through Spacetime curvature. Thus, while General Relativity provides a powerful geometric description of gravitational behavior, this model interprets such behavior as one manifestation of a more fundamental interplay between Force and Field.

To avoid misunderstandings, I reiterate that here I use the term Force to indicate any Agent, any "Cause" that produces deformations in a Field / Acted (deformation in the sense of any "effect" or "variation)". The expression of Force produces the manifestation of the Field, which takes shape precisely as variations—i.e., deformations—of the Field.

Therefore, to claim that the cause of gravity is the curvature of Spacetime produced by the Mass/Energy tensor is, in my model, absurd. It is equivalent to denying that a Cause is a Cause, or to assigning the name of an effect to its cause. Curvature of Spacetime, the force that produces that curvature, the Action that manifests as Field deformation, the presence of Mass and Energy in the Field, Perturbation and Translation—these are all aspects of a single Phenomenon.

This Phenomenon finds its primary origin (onto) in the Fundamental Force and the Elementary Field, and in their incessant internal interaction. It finds its phenomenal manifestation (pheno) in the production of Elementary Action, in its organization into Information / Energy, and in its structuring into InfoStructures and Forms. Finally, it finds its mechanical expression (dyna) in the spatiotemporal distributions and motions that we observe as gravity.

Newton's laws of motion in the terms of Evolutionary Dynamics

First principle (inertia): a body maintains its state of rest or uniform rectilinear motion unless an external force intervenes.

Inertia is commonly defined as a body's resistance to any change in its velocity (speed and direction); inertia can be seen as resistance to acceleration, and acceleration as the modification of a state of inertia.

In the terms of this model, the inertia of an InfoStructure is the manifestation of the Translation present within the micro‑dynamism of the region of the Elementary Field that includes all the event‑points which, moment by moment, support and sustain the Existence and the Essence/Form of that Structure (or of a Form/object composed of multiple InfoStructures).

When, in the region through which the Structure is propagating, there is no independent Translation (expression of the Existence of other Structures—for example, gravity produced by the presence of Vortex‑type Structures with Mass, or regions of the Field with non‑zero Perturbation, positive or negative) other than the Translation that sustains the Structure itself, the propagation proceeds without any change in velocity, without acceleration—that is, inertial Motion along a geodesic—because the orientational correlations of the inhomogeneities in the tau‑distributions of the underlying sigma‑fluctuations are not influenced or modified.

A specular situation—with the same result—occurs when it is not the presence of non‑zero Perturbation that produces Translation independent of the Structure propagating in the Field, but rather the interactions between the chiralities of vorticity (Elementary Action in the Rotation:Chirality Component) of the test Structure (electric Charge "in" the Field) and the chirality associated with other charged Structures that produce an Electric field (the Electric potential “of” the Field in the region that, moment by moment, "supports" the test Structure).

Or, again, the interactions between the orientations of the vorticity axes (Elementary Action in the Rotation:AxisOrientation Component) of the test Structure (magnetic Spin "in" the Field) and the axis orientations associated with other charged Structures that produce a Magnetic field (the Magnetic potential of the Field in the region that, moment by moment, "supports" the test Structure).

In these cases, it is the interaction between the ‘electric potential’ (induced in the Field by a charged Structure A, or by a set of charged Structures) and the ‘electric charge’ of a Structure B that produces a correlation of Translation, attractive or repulsive depending on the signs of the charges and potentials involved. The same reasoning applies to magnetic potentials and spin.

The greater the intensity of these orientational correlations, the larger the inertial velocity associated with the Structure; conversely, only the presence of an independent Translation in the surrounding Field can perturb that organization and produce a departure from inertial propagation.

Second principle (F = ma): the change in motion is proportional to the applied force and occurs in the direction of that force.

In the language of this model, the Second Principle expresses how a variation imposed on the Elementary Field produces a proportional reorganization of the Field’s Translation: what we call force (F) is a localized and directed perturbation of the network of relations (a change in the local dynamic pattern of Elementary Action); Mass (m) is the Field’s local resistance to such reorganization; and acceleration (a) is the resulting change in the pattern of Translation correlations that sustain an InfoStructure.

When an external Perturbation (a spatially structured inhomogeneity in the tau‑distributions of the sigma‑fluctuations) is applied to the region supporting a Structure, the surrounding event‑points adjust their orientational correlations; the magnitude of this adjustment (the induced correlation of Translation) is proportional to the intensity of the variational input and is oriented along the gradient established by the variation.

Mass therefore quantifies how much Elementary Action in the mode of independent Translation (acceleration) must interact with the Structure's Translation (inertia) to obtain a given change in those patterns of orientational correlations of Elementary Action: a greater Mass (greater Perturbation) means greater resistance and therefore a smaller change in Structure’s Translation for the same amount of applied force.

Directionality follows because the Field's reorganization aligns with the local asymmetry introduced by the Force, so the induced Translation (acceleration of the Test Structure) appears along the same vector orientation as the independent Translation applied.

At the sub‑elementary level, this translates into a transfer of independent Translation (potential Motion) from the Field to the Structure propagating within it, which progressively becomes Translation of the Structure itself (effective Motion). This increase in Translation manifests as acceleration, an increase in speed and/or a change in the direction of the Structure's Motion.

The interaction between independent Translation (of the Field) and the Structure's Translation occurs, for each event‑point in the region of the Field that moment by moment supports/sustains the Existence and the Essence/Form of the Structure, according to the rule of vector addition (the parallelogram rule).

This interaction is influenced by the absolute value of Perturbation at each event‑point. Which, stated in the terms of conventional physics, means precisely that Mass is the proportionality constant between the applied force (Translation of the Field) and the resulting acceleration (variation of the Structure’s Translation).

Third principle (action and reaction): for every action there is an equal and opposite reaction.

In the Dynamics of Elementary Action, Action and re-Action are co‑emergent aspects of the same Process. Elementary Action is a local inhomogeneity in the dynamism of the Elementary Field. Every inhomogeneity is a variation of the sub-elementary and elementary dynamism (in amplitude, orientation, chirality and axis orientation of vorticity) of the Field. It tends to propagate through and conserve in it. Propagation is never one‑way: the Field has an intrinsic drive to restore homogeneity and isotropy (due to its resistance to variation -> constraints).

This restoring drive is the re‑Action, emerging point‑by‑point (point-events) from the reorganization of the pre-temporal distributions of pre‑spatial fluctuations (Elementary Events). The Field does not compute a counter‑force: re‑Action is spontaneous self‑regulation of its micro‑dynamics in each event-point of the path/trajectory. Re‑Action, in its most elementary expression, is the release of the Action accumulated in the deformation experienced by the Field — that is, the inhomogeneity produced in the tau‑distributions of the sigma‑fluctuations. This accumulated sub‑elementary Energy is released with the same intensity and in the opposite direction of the original Action. Obviously, this holds only if the dynamic conditions of the surrounding environment are homogeneous and do not deform the dynamics of the infinitesimal region of the Field in which the re Action is expressed.

The Elementary Field is perturbative, dynamic, conservative, and non‑dissipative. For this reason, any deformation introduced by Action cannot simply vanish: it must be returned through a counter‑adjustment of the Field's sub‑elementary dynamism. Ontologically, phenomenologically and dynamically, the principle expresses: the relational nature of all dynamics, the self‑regulating character of the Field, the co‑construction of Action and re‑Action. This process represents the sub‑elementary counterpart of the dynamics expressed by InfoStructures (Waves, Particles, etc.) and by macroscopic Forms/objects. It constitutes the causal and variational root, both ontological and phenomenological, of the Newtonian principle as it manifests at higher and more complex levels of Reality.

Links to the tables of contents of TFNR Paper

• Go to the contents list of the paper "The Fundamental Nature of Reality"

• Go to Chapter 2 "A first look"