Difference between revisions of "TFNR - Translation - Divergence"

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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 the 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 distributions of the spatial (linear) orientations of the elementary spatial fluctuations in the Elementary Field.

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.

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 temporal distributions of the Elementary Events.

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 Action and Reaction.

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

The causal perspective

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

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

From the causal point of view, Translation can be represented as the Operator Translation, a functional derivation of the Source of Reality that organizes the reactions of the Elementary Field produced by Perturbation into fluxes (reorientation of the elementary spatial fluctuations), directed toward the restoration of homogeneity and isotropy within the Elementary Field.

The variational perspective

Symmetrically, from the variational perspective, Translation manifests as the reaction of the Field to Perturbations, to gradients (Micro-gradients) in the temporal distributions of the minute elementary spatial fluctuations resonating around 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 dynamics of the Field, though extremely small, always represent extended regions in three-dimensional Space, with an evolution in Time, representable within the four-dimensional continuum so central to relativistic physics.

Thus, not grains of Space and Time, but rather a kind of bubbles, "convective cells" in the elementary dynamics of the Field—pulsating regions, so to speak—that tend to exhibit an average extension and a pulsation dynamics in Time comparable to the Planck scale lengths and durations. Expansion and contraction. Force and resistance. Action and constraint. The whole of mechanics concentrated within an infinity of dynamic micro-structures that embody the dynamics of the Field and project it into an initial seed of discreteness (Principle of Individuation) within the fundamental continuity.

An infinity of dynamic micro-structures that, through their incessant activity, sustain and support the Existence and the Essence / Form of the ever-changing structuration of the Elementary Field. This structuration manifests as Structures of Information—interacting, propagating, and conserving within Space-time—both in the medium-dimensional domain (Vortices/Particles, Waves and their Interactions that compose Ordinary Matter) and in the large domain (Vortices/Dark Halos, Dark Waves and their Interactions that compose the Dark Matter/Dark Energy side of the Universe).

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 tiny elementary spatial fluctuations of the Field resonating around the Planck scale. I use the term "spatial" even though Space, the spatial dimensions, technically emerge at an evolutionary stage of Reality that is temporally concurrent but causally subsequent to the expression of the Perturbation Operator. It is precisely this expression that produces the premises—the causal and variational substrate—for the emergence of the spatial dimension, of Space itself. We could say that spatial Dimensionality, inherent in the variational aspect of the Agency of the Source, through the expression of the Perturbation Operator, is the causal seed that enables the subsequent manifestation of Space and of the spatial dimension of Reality (as well as of Time and of the temporal dimension).

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.

We will then see how Translation and Rotation represent, from the causal point of view, the subsequent steps in defining the dimensional framework of Physical Reality, the first being understood as Propagation and Conservation in Space and the second as Propagation and Conservation in Time. Taken together with Perturbation, all three constitute the elementary dynamic basis (the dynamism of the Elementary Field under the incessant Action of the Fundamental Force, the expression/manifestation of the Agency of the Primary Source) upon which the Fundamental Physical Quantities are founded: Metric/Mass, Motion, Charge, Spin, and the related phenomenological domains that combine in different forms within gravity, electromagnetism, and the more complex phenomenologies of the weak and strong nuclear interactions, as well as all the natural phenomena that contribute to the incessant Formation of Reality and to the complex life of the Universe.

Inhomogeneities tend to cause the re-Action of the Field, toward the restoration of homogeneity. The Field’s reaction to these inhomogeneities, which I here call Perturbation, is part of this spontaneous process aimed at restoring homogeneity. These reactions generate oriented flows—flows of orientation—of more or less intense reorientation of the spatial (linear) directions of the elementary spatial fluctuations, of the Elementary Events.

These flows in the distributions of the reorientations of Elementary Events, precisely because they occur on extremely small scales and at the level of individual event-points of the Field, can be called Micro-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 Variation 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

Translation transmutes the basic form of Action, Perturbation, into an incessant Process of Propagation of Action, propagation of inhomogeneities in the Field, in its dynamics at the most elementary level of organization.

The essential question is: what propagates? What propagates are the same inhomogeneities (Perturbation and Rotation) in the distributions of Elementary Events and the correlation schemes, the patterns of Relations among them. Any deviation from homogeneity—any change in stochastic independence or correlation—tends to propagate through the Field and tend to produce propagation flows (Traslation) in the dynamics 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 correlations 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 temporal distribution of elementary 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 spatial orientation of these fluctuations is entirely random. At each event-point the spatial 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 Elementary Events of the Field, radically changes the situation. We must imagine that to the primary inhomogeneity constituted by elementary spatial fluctuations, there is associated an inhomogeneity in the temporal distributions of these fluctuations.

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 Field to its deformation 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 temporal distribution of 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 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 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 elementary 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 elementary spatial fluctuations and their relative temporal 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 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 from Perturbation arises Translation, and how from gradients emerges divergence.

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 the elementary spatial 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 (harmonic) pulsation that we identify as a continuous succession of Elementary Events—elementary 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; 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 temporal duration of these 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.

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 we call Perturbation.

This Process is a manifestation of the 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 that we call Perturbation.

An alteration, a deformation of the distribution of the temporal durations of the spatial pulsations will correspond to an alteration, a deformation of their temporal distribution. This temporal distribution tells us how much of the flowing Time corresponds to each amplitude value of spatial fluctuations (which, 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 temporal prevalence of the extensions of 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: spatial inhomogeneities and those of their 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 in the 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 standpoint of the InfoStructures propagating "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 we 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 where the Field is continuous, and which we 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.

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, and that even the discreteness we observe (InfoStructures, Particles, etc.) arises through nonlinear processes/behaviors and scale resonances from that same continuous Field.

We have seen that Perturbation may be conceived as the temporal distribution of spatial amplitudes (together with their associated durations, interpretable in the same way as "frequencies") of 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.

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. 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 at 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).

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. It is the same Elementary Field, in its aspect of spacetime Metric, each of its infinitesimal volumes that expands and contracts, pulsating at a rhythm that may be equal to, greater than, or less than the average of the universal pulsation rhythms 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 us recall 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 around 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 shows an absolutely flat Space; in this first causal/variational aspect, Translation is identified with the expansion/contraction of the elementary spatial fluctuations, therefore with the spatial dynamics of the Elementary Events;

• a second form of manifestation (temporal dynamics of spatial expansion/contraction) appears when we observe the temporal aspects of these pulsations; this pulsating dynamics occurs over infinitesimal spatial distances and equally minute temporal durations; distances and durations linked by a specific relation, the most elementary expression of the Principle of Uncertainty. When, in Time, the magnitude of the 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 General Equivalence Principle for Perturbation, under these dynamic conditions at the Level of Elementary Action, 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 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 temporal distributions of the elementary spatial fluctuations (let us imagine that turbulence forms in the Field with micro-vortices of minimal spatial extension and ephemeral 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 spatial and 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 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, although in its causal and variational evolution it manifests the existence of Information Structures 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. It is a non-material Field, in the sense we attribute to the adjective "material", even though from its incessant dynamics 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 (elementary 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 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 (resistance to deformation), on the magnitude of the deformation, both in the spatial and in the 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 a volume of varying size, or the entire infinite Field.

Step four: let us try to heat one face of the box by applying a Force associated with Energy in the form of heat. In the gas, a thermal gradient will appear—or more likely, a complex set of interacting thermal gradients, with convective motions tending to diffuse the heat under a tension toward achieving thermal equilibrium (a return to homogeneity). We may imagine analogies between thermal gradients (volumes with distributions of molecular velocities above or below the average) and non-zero Perturbation (volumes with temporal distributions of elementary spatial fluctuations above or below the 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 diffuse 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 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 temporal distributions of elementary 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, 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 an instantiation of the Principle of Propagation.

This principle, in particular, describes how the Elementary Field responds to the manifestation of Perturbation—to the inhomogeneities in the temporal distributions of the minute elementary spatial variations resonating around the Planck scale—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 elementary spatial fluctuations of an event-point (the temporality and 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 temporal and 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 temporal distributions of spatial fluctuations, that is, of Perturbation.

We must think of the Field as a spatially elastic field at the lower scales—at, and slightly (by a few orders of magnitude) above, 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 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 temporal distributions of these 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 spatial fluctuations—and from the complete perspective of the temporal distributions of those same spatial fluctuations, which in the temporal view, as we have seen, can be regarded as pulsations, expansion/contraction processes whose durations are proportional to the 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 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 an elementary spatial fluctuation of the Field itself (an expansion/compression event of the volume of an infinitesimal region of the Field).

An event-point We 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—spatial extension (volume), "point‑like" only in the classical sense; a region that does not exist as an individual entity, but that we choose, case by case, as an object 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.

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We can analyze the energetic aspect of the dynamics of the Elementary Field from the two perspectives mentioned above: that of event‑points, and that of volumes—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.

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In summary, the three points of observation:

• event-points, partial perspective — purely spatial (Elementary Events): can be regarded as a kind of "virtual" Energy
• event-points, complete perspective — temporal distributions of the spatial fluctuations (Elementary Action): Energy of the pulsations -> Elementary Energy, Energy of the Unstructured Field
• larger regions, sets of more that one event-point—spatial correlations between the temporal distributions of the spatial fluctuations (Information / Energy): Energy of Metric/Mass, Motion, Charge and Spin

Let us first consider the event‑point perspective. Imagine an infinitesimal volume that expands and is then pushed to contract and return to the “standard” extension of the 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). Let us therefore imagine a kind of pulsation, a sequence of 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 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).

Let us imagine that this dynamic process is neither spatially homogeneous (not symmetric with respect to spatial directions) nor temporally homogeneous (the temporal distributions of these pulsations may show inhomogeneities, becoming faster or slower in correspondence with larger or smaller spatial fluctuations). In other words, expansions and contractions are not symmetric. 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 we can conceive—indeed stretching the very concept of Energy as hypothesized in this model (linked to the notion of Relation, of correlation between Events, between dynamic manifestations of the Field)—is precisely what we may call “elementary deformation”: the change of shape of event‑points, of the imaginary infinitesimal volumes whose dynamics we wish to analyze ideally, a deformation that changes incessantly throughout the fluctuations, the 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.).

A second form of Energy can be conceived as a deformation of the temporal distribution of the pulsation process described above. If the inhomogeneity of the temporal distribution of the volume’s pulsations corresponds to Elementary Action in the Mode / Component we call Perturbation, ...

The correlation of Translation values in a portion of the Field defines its Elementary Energy in the component Translation, which we call Motion. Motion is the organized manifestation of Translation: inertia as persistence of correlated orientations, acceleration as intensification of those correlations. Translation is therefore the energetic substrate of kinetic phenomena, the bridge between perturbative inhomogeneities and macroscopic motion.

The correlation between the Translation values ​​in a given portion of the Elementary Field (Relationship between Elementary Action of a contiguous set of event-points) defines the Elementary Energy of that portion in the Component Translation, which we call Motion (in both aspects: inertia and acceleration), the root of kinetic phenomena.

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

Formulation in vector calculus

In mathematical terms, Translation is embodied by the divergence operator (DIV). Divergence measures the density of sources or sinks of a vector field, expressing the outward or inward flux from an infinitesimal volume. In the Elementary Field, Translation corresponds to the propagation of perturbative gradients, the directed spreading of inhomogeneities.

In the context of Evolutionary Knowledge, divergence is any propagation of a gradient, intended as any variation of the parameters that describe the Elementary Field along a chosen direction, the most elementary form of inhomogeneity, of anisotropy, of deformation of the Field.

Secondary manifestation of Action. Elementary divergences are produced by the reaction of the Elementary Field to the deformations produced by the action of the Fundamental Force on the Field itself.

At more complex levels, the gradients are divergences by the reaction to the perturbation of the Derived Acted / Fields under the action of Derived Agents / Forces.

The Operator Translation is responsible for the formation of divergence in the Elementary Field, propagation of inhomogeneities, anisotropies, in the Field and their dynamics.

In vector calculus, Translation is embodied by the vector operator called "Divergence" (DIV), which represents a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point (the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point).

The phenomenological perspective

Translation manifests phenomenologically through inertia, acceleration, and gravity.

• Inertia is the presence of Translation within the dynamics of a structure, the persistence of correlated orientations of fluctuations.
• Acceleration is the variation of Translation, the intensification of correlations in the Field.
• Gravity emerges as the combined expression of Perturbation (Mass) and Translation (Motion): gradients of Perturbation produce non‑zero values of Translation in surrounding regions, which we observe as attraction, accelerated motion, and gravitational phenomena.

Thus, Translation is not merely the propagation of perturbations, but the very mechanism through which Motion and gravitational dynamics arise. It is the divergence of Reality’s elementary fluctuations, the directed flux that sustains the dynamism of Space.

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

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.

Inertia is the manifestation of the presence of Translation in the dynamics of the object and not in the region of the Elementary Field where the object is moving. What does "presence of Translation" or a non null value of Translation means? It means that the amount of Elementary Action, in the mode we call Translation is greater that zero. In other word, in more detail, with reference to the Elementary Events, which represent the dynamics of the Elementary Field at its fundamental level, the tiny fluctuations of the Elementary Field at the Planck-scale, it means that we are in presence of some form and quantity of organization of the correlations among the inhomogeneities of the distributions of those fluctuations, the Elementary Events. And in particular, for Translation, and therefore for inertia and acceleration, what matters is not the intensity, but the intensity of the correlations of the (spatial) orientations of that fluctuations. The more intense the correlations of the orientation of the fluctuations, the greater the inertial velocity, the stronger the increase in those correlations, the greater the acceleration.

Acceleration

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

Acceleration is the manifestation of the presence of Translation in the dynamics of the Elementary Field, in the region where the object is at rest (the value of Translation in the object is zero) or in motion (Translation in the object is non null). An object with a given intensity of correlations of the orientation of the fluctuations, a given Translation value, which moves in the Field showing a given intensity of correlations of the orientation of the fluctuations, the object's Translation interacting with the Translation in / of the Field, acquires more Translation, i.e. the fluctuations at the Planck-scale will show increasing correlations in the orientation of the fluctuations. Result: an object accelerating in a Field showing a potential (like a gravitational potential of a gravitational field). The amount of Translation, and therefore of acceleration, is proportional to the spatial distribution of the amounts of Perturbation in the Field (quantities and distances), and therefore to the spatial distribution of mass densities in Space-time, in the Metric field, or, as stated by the Principle of General Equivalence, to the (local) curvature of Space-time, to the (local) speed limit of the propagation of Information, or the local temperature of the Field, etc.

Gravity

Gravity is commonly seen as a natural phenomenon produced by Mass and the dynamics of objects with mass.

Perturbation is causal origination of Gravity, while Translation is its variational effect.

In terms of the Elementary Field and Dynamics of Elementary Action, and its Modes /Components, gravity can be seen as the combined expression of the modes of Elementary Action that we call Perturbation and Translation. Perturbation is the root of Mass, while Translation is the root of Motion. Mass and Motion are two closely related phenomena. Gradients in Perturbation, inhomogeneities in the spatial distribution of Perturbation represent what we commonly call curvature of Space-time and produce reactions from / in the Elementary Field in the form of non-zero values of Translation in the surrounding regions of massive structures, which "cause" the attraction between massive bodies and their accelerated motion in the Field.

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"