TFNR - Translation - Divergence
From the point of view of the Elementary Events and the Dynamics of Elementary Action
Let us 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.
An alteration, a deformation of the temporal distribution of the durations of the spatial pulsations will correspond to an alteration, a deformation of their temporal distribution. 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. It 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.
Thus, analogous—though in a different form—is the Field’s reaction to the appearance of an inhomogeneity in the temporal distribution of such pulsations. The more intense the reaction, the greater the deviation of the altered temporal distribution from the "standard". Adjacent event-points will react to the alteration of the pulsation distribution of the considered event-point, the greater the compression or expansion of its spatial volume with the associated alteration of the pulsation "frequency". We are speaking here of the most elementary form of deformation of the Elementary Field, the most elementary form of Existence.
We can imagine the Elementary Field as an infinite volume in which the infinitesimal volumes we call event-points are like tiny elastic spheres pulsating randomly in all directions, compressing and expanding 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 endured. From the dynamic equilibrium of these two interconnected components arises what I here call Elementary Action. The endured 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.
We have seen how Perturbation can be imagined as the distribution of durations associated with the spatial amplitudes of infinitesimal pulsations. Now we can imagine Translation as the Elementary Action produced by the reactions of the dynamics of surrounding event-points, naturally directed toward the imaginary center 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 reaction of the Field to the presence of a Perturbation—an inhomogeneity in the temporal distribution of spatial fluctuations at an event-point—nothing is actually moving. It is the infinitesimal volume 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). Within the domain 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 us 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 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 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 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.
Translation transmutes the basic form of Action, Perturbation, into an incessant Process of Propagation of the inhomogeneities in the Field, in its dynamics at the most elementary level of organization.
The essential question is: what propagates? What propagates are the inhomogeneities (Perturbation and Rotation) in the distributions of Elementary Events and the correlation schemes 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 as a network of stochastic processes whose correlations diffuse through Translation.
